Answer/Step-By-Step Explanation:
Part A:
To determine the measure of angle A (m/A), we can use the Law of Cosines, which states that:
c^2 = a^2 + b^2 - 2ab*cos(A)
where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.
Substituting the given values, we have:
(32)^2 = (16)^2 + (16√5)^2 - 2(16)(16√5)*cos(A)
Simplifying:
1024 = 256 + 1280 - 512√5*cos(A)
512√5*cos(A) = 512
cos(A) = 1/√5
Using a calculator, we find:
A ≈ 63.43 degrees
Therefore, m/A ≈ 63.43 degrees.
Part B:
To use the unit circle to find tan A, we first draw a unit circle with its center at the origin of a coordinate plane. We then draw a ray from the origin through the point (1,0) on the circle, which corresponds to the angle of 0 degrees.
Next, we draw another ray from the origin through the point on the circle that corresponds to angle A. This ray intersects the circle at a point (x,y), where x = cos(A) and y = sin(A).
Since cos(A) = 1/√5, we have:
x = cos(A) = 1/√5
To find y, we use the Pythagorean theorem:
x^2 + y^2 = 1
Substituting x = 1/√5, we get:
(1/√5)^2 + y^2 = 1
y^2 = 4/5
y = ± 2/√5
Since angle A is in the first quadrant, we take y = 2/√5.
Therefore, tan(A) = y/x = (2/√5)/(1/√5) = 2.
Part C:
To calculate the area of triangle AABC, we can use Heron's formula, which states that:
Area = √(s(s-a)(s-b)(s-c))
where s is the semiperimeter of the triangle, given by:
s = (a+b+c)/2
Substituting the given values, we have:
s = (16+16√5+32)/2 = 24+8√5
Using this value of s, we can calculate the area:
Area = √[(24+8√5)(8√5-8)(8√5)(24-8√5)]
Simplifying:
Area = √[4096] = 64
Therefore, the area of triangle AABC is 64 square inches.
In this problem, we use the tangent function to solve for angle A, understand that the unit circle cannot be directly used to find the tangent of A, and finally find the area of the triangle using the formula 1/2*base*height.
Explanation:Part A: Assuming triangle AABC is a right triangle, we can determine m∠A by using the tangent function (tan ∠A = opposite side / adjacent side). Here, the opposite side is 'b' and the adjacent side is 'a'. So, m∠A = tan⁻¹ (b/a) = tan⁻¹ (16 5/16). To get the correct result, we then use a calculator with the inverse tangent or arctan function.
Part B: The unit circle is a fundamental tool in trigonometry. But in this case, having calculated m∠A in Part A, we cannot directly use the unit circle to find tan A as tan A is not represented on the unit circle.
Part C: The area of a triangle can be calculated using the formula 1/2*base*height. In a right triangle, this can be represented as 1/2*a*b: 1/2*16*16 5 = 130 square inches.
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que numero multiplicado por -8 es igual a 1
Answer:
[tex]\boxed{-\frac{1}{8} }[/tex]
Step-by-step explanation:
De acuerdo al inverso multiplicativo se cumple lo siguiente:
[tex]a\times \frac{1}{a}= \frac{a}{a}=1[/tex]
Por lo tanto:
[tex]-8 \times \frac{1}{-8}=1[/tex]
El número que cumple con el enunciado es [tex]-\frac{1}{8}[/tex]
[tex]\text{-B$\mathfrak{randon}$VN}[/tex]
Alfred is developing his own recipe for a fruit cake and is experimenting with the amount of caster sugar to use. Zeena Do His first attempt needed This needed less caster sugar, so he decreased the amount used in his second attempt by 18% for his third attempt. more caster sugar, so he increased the amount used by 35% for his second attempt. His third attempt used 376.38 g of caster sugar. Work out how much caster sugar, in grams (g), his first attempt used. Watch video Answe ENG UK
The amount of caster sugar used in the first attempt is given as follows:
340 g.
How to obtain the amount of caster sugar used?The amount of caster sugar used in the first attempt is obtained applying the proportions in the context of the problem.
The expressions for each attempt are given as follows:
First attempt -> unknown -> represented by variable x.Second attempt -> Increased by 35% relative to first attempt -> 1.35x.Third attempt -> decreased by 18% relative to second attempt -> 0.82 x 1.35x = 1.107x.The amount used on the third attempt was of 376.38 g, hence the amount used on the first attempt is obtained as follows:
1.107x = 376.38
x = 376.38/1.107
x = 340 g.
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What would the final bill after applying the discount be?
Answer:
80.925
Step-by-step explanation:
124.5 x 0.35 = 43.575
124.5 - 43.575 = 80.925
true or false? square root functions are either always increasing or always decreasing for the whole domain of
The given statement square root functions are not always increasing or always decreasing for the whole domain of ( -∞ , ∞) is false.
Function is square root function.
Domain = ( -∞ , ∞)
Square root functions is always increasing or decreasing is a false statement.
For example,
Let us consider the function f(x) = √x.
This function is increasing for x > 0, since as x increases, √x increases as well.
However, for x < 0, the function is not defined since the square root of a negative number is not a real number.
This implies,
The function is neither increasing nor decreasing for x < 0.
Therefore, the statement square root functions are either always increasing or always decreasing for the whole domain of ( -∞ , ∞) is false.
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The above question is incomplete , the complete question is:
True or false? square root functions are either always increasing or always decreasing for the whole domain of ( -∞ , ∞).
What is the decimal multiplier to increase by 6. 1%?
Answer: 1.061
Step-by-step explanation:
1). Based on conditions, formulate: 1+6.1%
2). Then convert to a decimal: 1.061
i dont understand, am i supposed to write like 10 x 10 x 10 or 10^3 (10 to the third power)?
Answer:
yes 10 to the 3rd power is 1,000 so try to go from there if more info is needed please comment "more info"
Step-by-step explanation:
Mar 30, 9:57:36 AM
One rectangle is "framed" within another. Find the area of the shaded region if the
"frame" is 2 units wide.
12
By answering the presented question, we may conclude that As a result, the darkened zone has an area of 88 square units.
What is rectangle?In Euclidean geometry, a rectangle is a parallelogram with four small angles. It may also be defined as a fundamental rule hexagon or one in which all of the angles are equal. Another alternative for the parallelogram is a straight angle. Four of the vertices of a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "equirectangular rectangle." A rectangle is sometimes referred to as a parallelogram due to the equal and parallel dimensions of its two sides.
We must determine the size of the darkened zone.
The bigger rectangle (with the frame) has a surface area of (12+2) x (10+2) = 14 x 12 = 168 square units.
The smaller rectangle (with the frame) has an area of (8+2) x (6+2) = 10 x 8 = 80 square units.
The frame's area is equal to the difference between the two areas: 168 - 80 = 88 square units.
As a result, the darkened zone has an area of 88 square units.
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You roll a number cube two times. Which of the theoretical probabilities are accurate
P(1 then 0)= 1/2
P(even number then odd number)= 1/4
P( 6 then 2) = 1/36
P(even number then 5) =1/12
P(odd number than 2) = 1/6
You roll a number cube two times. The theoretical probabilities are accurate is P(even number then odd number)= 1/4
Probability:
Probability is the likelihood of something happening. When we are unsure of the outcome of an event, we can talk about the likelihood of certain outcomes - how likely are they to occur. The analysis of events governed by probability is called statistics.
According to the Question:
Let P(E), P(H), and P(E and H) be the probabilities of rolling an even number on a die, heads on a coin, and heads, respectively.
We know,
P(E and H) = P(E)×P(H)
Now, to find P(E and H), we have to find P(E) and P(H).
Total number of possible results of a die roll = 6
Favorable results of an event E = {2, 4, 6}
∴ Number of favorable results of an event E = 3
Therefore,
P(E) = number of favorable results of an event event E / possible results The total number of
⇒ P(E)=3/6=1/2
There are two possibilities for tossing a coin = {H, T}
∴ Probability of heads on a flip coin = P(H)= 1/2
Finally, the probability that
Lewis gets an even number and flips heads =
1/2×1/2 = 1/4
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15.1 central angles and inscribed angles an equilateral triangle is inscribed in a circle. how does the relationship between the measures of the inscribed angles and intercepted arcs help determine the measure of each angle of the triangle? what is the relationship between inscribed angles and central angles in a circle?
The intercepted arcs of the inscribed angle are in proportion to the inscribed angle itself. In other words, the larger the inscribed angle, the more significant the intercepted arc it cuts, and vice versa. So, in an equilateral triangle, each of the inscribed angles of the circle measures 60°, which is half of the central angle of 120° that intercepts the same arc.
The angle measure and intercepted arcs of inscribed angles in an equilateral triangle inscribed in a circle are related, and the relationship between inscribed angles and central angles in a circle is that the inscribed angles are half of the central angle. Let us have a more in-depth understanding of these two angles.An inscribed angle is an angle that has its vertex on the circle and is formed by two chords that intersect at that point. It is half of the central angle that intercepts the same arc.A central angle is an angle whose vertex is at the center of the circle, and the sides of the angle pass through any two points on the circumference of the circle.
For an equilateral triangle inscribed in a circle, each angle measures 60°, and the central angle measures 120°. So, each of the two inscribed angles measures half of the central angle, i.e., 60°.The relationship between inscribed angles and intercepted arcs.
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X =
someone HELP!!!!
you need to work back wards on the
9x+3=64
so 64-3=61
then do 61 divided by 9
which equals 6.7(1dp)
so x=6.7(1dp)
Find and prove algebraically the solutions (coordinate points) to the system of equations?
F(x)=x^2+2x-1 and g(x)=x-1
We have shοwn algebraically that the sοlutiοns tο the system οf equatiοns F(x) = g(x) are [tex](-2, -3)[/tex] and [tex](1, 0)[/tex].
What is a System οf Equatiοns?A system οf equatiοns in algebra is made up οf twο οr mοre equatiοns that are sοlved tοgether. "A grοup οf equatiοns satisfied by the same set οf variables are called a system οf linear equatiοns. Finding the values οf the variables emplοyed in the system οf equatiοns is the first step tοwards sοlving it.
While maintaining the balance οf the equatiοns οn bοth sides, we cοmpute the values οf the unknοwn variables. Finding a variable whοse value makes the cοnditiοn οf all the given equatiοns true is the primary gοal οf sοlving an equatiοn system.
Tο prοve that these cοοrdinate pοints are sοlutiοns, we need tο substitute them intο bοth equatiοns and verify that they satisfy the equatiοns. Let's start with (-2, -3):
[tex]F(-2) = (-2)^2 + 2(-2) - 1 = 4 - 4 - 1 = -1[/tex]
[tex]g(-2) = (-2) - 1 = -3[/tex]
We can see that [tex]F(-2) = g(-2)[/tex] , sο[tex](-2, -3)[/tex]is a sοlutiοn.
Nοw let's check (1, 0):
[tex]F(1) = 1^2 + 2(1) - 1 = 2[/tex]
[tex]g(1) = 1 - 1 = 0[/tex]
Again, we can see that F(1) = g(1), sο (1, 0) is alsο a sοlutiοn.
Therefοre, we have shοwn algebraically that the sοlutiοns tο the system οf equatiοns F(x) = g(x) are (-2, -3) and (1, 0).
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HELP PLEASE! the question in the photo below
The point estimate is 0.395 and the poll's margin of error is 0.015 or 1.5%.
What is confidence interval?A set of values that, with a particular level of confidence, is likely to include an unknown population parameter is known as a confidence interval. Confidence intervals are frequently utilized in statistics to calculate the actual value of a population parameter using sample statistics. When comparing a sample statistic to a population parameter that is hypothesised, we utilize confidence intervals to assess if the difference is statistically significant.
Given the interval of the result in the survey is [0.38, 0.41].
a. The point estimate is given as:
Point estimate = (0.38 + 0.41) / 2 = 0.395
b. The margin of error is given as:
Margin of error = (critical value) x (standard error)
Assuming a 95% confidence level:
Standard error = (maximum error) / (critical value)
Now,
Maximum error = (0.41 - 0.38) / 2 = 0.015
Margin of error = 1.96 x (0.015 / 1.96) = 0.015
Hence, the point estimate is 0.395 and the poll's margin of error is 0.015 or 1.5%.
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a rectangle storage container with an open top is to have a volume of 10 cubic meter. the length of its base is twice the width. material for the base cots $10 per square meter. material for the sides cost $6 per square meter. find the cost of materials for the cheapest such rectangular container.
The cost of materials for the cheapest container is 69.6 dollars.
Let's first express the dimensions of the rectangular container in terms of a single variable. Let the width of the base be x meters, then the length of the base is 2x meters, and the height of the container is 10/(2x^2) = 5/x^2 meters, since the volume of the container is 10 cubic meters.
The area of the base is x * 2x = 2x^2 square meters, so the cost of the base is 10 * 2x^2 = 20x^2 dollars.
The area of each side of the container is (2x)(5/x^2) = 10/x square meters, so the cost of the four sides is 4 * (10/x) * 6 = 240/x dollars.
The total cost C of the materials is the sum of the cost of the base and the cost of the sides:
C = 20x^2 + 240/x
To find the value of x that minimizes this expression, we can take its derivative with respect to x and set it equal to zero:
dC/dx = 40x - 240/x^2 = 0
Solving for x, we get:
x^3 = 6
x = (6)^(1/3)
Substituting this value of x back into the expression for C, we get:
C = 20(6)^(2/3) + 240/(6)^(1/3) ≈ 69.6 dollars
Therefore, the cost of materials for the cheapest rectangular container is approximately 69.6 dollars.
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-3(8xN) what is the value of N
Required value of N is 1
This is a problem of simplification which is major part of Algebra.
Some Algebra's formulas:
[tex]{(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} \\ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} \\ {(x + y)}^{3} = {x}^{3} + 3 {x}^{2} y + 3x {y}^{2} + {y}^{3} \\ {(x - y)}^{3} = {x}^{3} - 3 {x}^{2} y + 3x {y}^{2} - {y}^{3} \\ {x}^{3} + {y}^{3} = {(x + y)}^{3} - 3xy(x + y) \\ {x}^{3} - {y}^{3} = {(x - y)}^{3} + 3xy(x - y) \\ {x}^{2} - {y}^{2} = (x + y)(x - y) \\ {x}^{2} + {y}^{2} = {(x - y)}^{2} + 2xy \\ {x}^{2} - {y}^{2} = {(x + y)}^{2} - 2xy \\ {x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} ) \\ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )[/tex]
Given equation is [tex] - 3(8 \times N) = - 24[/tex]
We want to Simplify both side.
Multiplying (-3) and (8×N),
-24N = -24
Now we are dividing (-24) by (-24),
N = -24/-24
N = 1
Therefore, required value of N is 1.
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3 times a number is 28 less than the square of that number. Find the negative solution
Answer:
-b = √(3a+28)
Step-by-step explanation:
3a = -28 + b²
3a + 28 = b²
√(3a + 28) = √b²
negative solution:
-b = √(3a+28)
Calculate the average rate of change in the graph from time t=0.5 to t=0.75. Include units on your final answer.
[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} t_1=0.5\\ t_2=0.75 \end{cases}\implies \cfrac{f(0.75)-f(0.5)}{0.75 - 0.5}\implies \cfrac{7.744-6.275}{0.75-0.5} \\\\\\ \cfrac{1.469}{0.25}\implies 5.876~\frac{meters}{second}[/tex]
What is the surface area?
8 ft
8 ft
2 ft
square feet
The calculated surface area of the cuboid has a value of 192 square feet.
Calculating the surface area of the cuboidThe surface area of a cuboid is the sum of the areas of all six faces.
In this case, the dimensions of the cuboid are 8 ft by 8 ft by 2 ft. So we can calculate the surface area as follows:
The top and bottom faces each have an area of 8 ft x 8 ft = 64 sq ft.The front and back faces each have an area of 8 ft x 2 ft = 16 sq ft.The left and right faces each have an area of 8 ft x 2 ft = 16 sq ft.Therefore, the total surface area of the cuboid is:
= 2(64 sq ft) + 2(16 sq ft) + 2(16 sq ft)
= 128 sq ft + 32 sq ft + 32 sq ft
= 192 sq ft.
So the surface area of the given cuboid is 192 square feet.
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What is the value of x? With coordinates of 45%, 4√2, x.
The value of x is 8. So correct is C.
Describe Triangles?In mathematics, a triangle is a geometric shape that consists of three line segments that intersect at three endpoints. These endpoints are called vertices, and the line segments are called sides.
Triangles are one of the most basic shapes in geometry and are used in many areas of mathematics, science, engineering, and everyday life. They can be classified based on the length of their sides and the measure of their angles.
Some common types of triangles include:
Equilateral triangle: A triangle in which all three sides are equal in length.
Isosceles triangle: A triangle in which two sides are equal in length.
Scalene triangle: A triangle in which all three sides have different lengths.
Right triangle: A triangle in which one angle measures 90 degrees (a right angle).
To find the value of x, we can use the trigonometric ratios of a right-angled triangle. Let's call the base of the triangle "b".
We know that the angle between the hypotenuse and the base is 45 degrees, which means that the other acute angle is also 45 degrees. Therefore, we can use the trigonometric ratio for the sine of 45 degrees to relate the hypotenuse and the perpendicular as follows:
sin(45 degrees) = opposite/hypotenuse
where the opposite side is the perpendicular, which is given as 4√2.
sin(45 degrees) = 4√2/x
Simplifying this equation gives:
x = 4√2 / sin(45 degrees)
We know that sin(45 degrees) = 1/√2, so substituting this value into the equation above gives:
x = 4√2 / (1/√2) = 4√2 * √2 = 8
Therefore, the value of x is 8.
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Help me pls fast!!!!!!!!
Answer:
Select the one at the lowest point on the right of the y-axis. This point has an x value (horizontal) of 1 and 1/2, with a y value (vertical) of -5.
Hoped this helped.
The track team jog for 3/8 of a mile in the morning in the afternoon they jog for 3/4 of a mile did they jog longer in the morning or the afternoon explain
The team jogged longer in the afternoon because they covered a distance of 6 eighths of a mile, which is greater than the 3 eighths of a mile they covered in the morning.
To compare the distance jogged in the morning and afternoon, we need to find the common unit for both. We can convert both fractions to have the same denominator by finding the least common multiple (LCM) of 8 and 4, which is 8.
So, in terms of eighths of a mile, the distance jogged in the morning is:
3/8 miles = 3 eighths of a mile
And the distance jogged in the afternoon is:
3/4 miles = 6 eighths of a mile (since 3/4 = 6/8)
Therefore, the team jogged longer in the afternoon because they covered a distance of 6 eighths of a mile, which is greater than the 3 eighths of a mile they covered in the morning.
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A bank offers two different types of savings
account which pay interest as shown
below. Lewis wants to invest £3100 in one
of these accounts for 15 years.
a) Which account will pay Lewis more
interest after 15 years?
b) How much more interest will that
account pay?
Give your answer in pounds (£) to the
nearest 1p.
Account 1
Simple interest at a
rate of 7% per year
Account 2
Compound interest at a
rate of 5% per year
Answer:
a) Account 2 will pay Lewis more interest after 15 years because it pays compound interest, which means that the interest is calculated on both the initial deposit and the accumulated interest from previous years. On the other hand, Account 1 pays simple interest, which means that the interest is calculated only on the initial deposit.
b) To calculate the amount of interest paid by each account, we can use the following formulas:
For Account 1: I = P × r × t, where I is the interest earned, P is the principal (initial deposit), r is the annual interest rate as a decimal, and t is the time in years.
I = 3100 × 0.07 × 15 = £3255
For Account 2: A = P × (1 + r/n)^(n × t), where A is the amount of money at the end of the investment period, P is the principal, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, n = 1 (compounded annually), so the formula simplifies to:
A = 3100 × (1 + 0.05)^15 = £5569.62
The interest earned by Account 2 is the difference between the final amount and the initial deposit:
I = A - P = £5569.62 - £3100 = £2469.62
Therefore, Account 2 will pay £2469.62 - £3255 = -£785.38 less in interest than Account 1 after 15 years.
Step-by-step explanation:
mario is solving the system of linear equations using the elimination method. first equation: 3x-6y=8 second equation: 2x+3y=-1 which operation will eliminate one of the variables? A. multiplying the first equation by 2 B. multiplying the first equation by 6 C. multiplying the second equation by 2 D. multiplying the second equation by 6.
The correct answer is A. Multiplying the first equation by 2 will eliminate the variable y.
What is elimination method?The elimination method is a common technique used to solve a system of linear equations. In this method, we manipulate the equations by adding or subtracting them to eliminate one of the variables, so that we can solve for the other variable.
According to question:To eliminate one of the variables, we need to choose one of the equations and multiply it by a constant that will make the coefficient of one of the variables in that equation equal to the coefficient of the same variable in the other equation, but with the opposite sign. Then, when we add the two equations together, the term with that variable will be eliminated.
Looking at the given equations, we can see that if we multiply the first equation by 2, we will get:
6x - 12y = 16
And if we add this equation to the second equation, we get:
6x - 12y + 2x + 3y = 16 - 1
Simplifying this, we get:
8x - 9y = 15
Now we have one equation with only x and y, and we can use this equation and either of the original equations to solve for x and y using the substitution method.
Therefore, the correct answer is A. Multiplying the first equation by 2 will eliminate the variable y.
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(3x -1 ) (x+1)- 3x(x+1)=7
Answer:
x = - 8
Step-by-step explanation:
(3x - 1)(x + 1) - 3x(x + 1) = 7 ← factor out (x + 1) from each term
(x + 1)(3x - 1 - 3x) = 7
(x + 1)(- 1) = 7 ( multiply both sides by - 1 )
x + 1 = - 7 ( subtract 1 from both sides )
x = - 8
Answer:
[tex]\bf x=-8[/tex]Step-by-step explanation:
[tex]\bf (3x -1 ) (x+1)- 3x(x+1)=7[/tex]
Expand:-
[tex]\bf 3x^2+2x-1-3x\left(x+1\right)[/tex]
[tex]\bf 3x^2+2x-1-3x^2-3x[/tex]
Combine like terms:-
[tex]\bf (3x^2-3x^2)+(2x-3x)-1[/tex]
[tex]\bf -x-1=7[/tex]
Add 1 to both sides:-
[tex]\bf -x-1+1=7+1[/tex]
[tex]\bf -x=8[/tex]
Divide both sides by -1:-
[tex]\bf \cfrac{-x}{-1}=\cfrac{8}{-1}[/tex]
[tex]\bf x=-8[/tex]
_________________________
Hope this helps!
Find the measures of the angles of an isosceles obtuse triangle with one angle measuring 20.
there is 3 answers
So the measures of the angles in the isosceles obtuse triangle are 20 degrees, 80 degrees, and 80 degrees.
What is triangle ?
Three straight ends and three angles make up a closed triangle, a two-dimensional geometric object. A triangle's angles add up to 180 degrees in all cases. Based on their side lengths and angle measurements, triangles can be categorized in a variety of ways. Typical categorizations comprise: Triangle having no equal sides is referred to as a scalene triangle. Isosceles triangle: A triangle with two sides of equal length. A triangle having an equilateral shape is one with three equal sides. Triangle that has all angles that are less than 90 degrees is referred to as an acute triangle. Triangle with one angle that is precisely 90 degrees is referred to as a right triangle. A triangle that has a side that is more acute than 90 degrees is said to be obtuse.
given
In the isosceles obtuse triangle, let x represent the measurements of each equal angle.
One of the equal angles is bigger than 90 degrees since the triangle is obtuse. As a result, we have:
x + x + 20 = 180 (sum of angles of a triangle) (sum of angles in a triangle)
When we simplify this equation, we obtain:
2x + 20 = 180
2x = 160
x = 80
Hence, each of the equal angles is 80 degrees in length. As a result, there are three different ways to measure the angles in the isosceles obtuse triangle, which has one angle that is 20 degrees, as follows:
20-80-80 degree range
80-20-80 degree range
80-80-20 Celsius
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cody was 165 cm 165cm165, start text, c, m, end text tall on the first day of school this year, which was 10 % 10, percent taller than he was on the first day of school last year. how tall was cody on the first day of school last year? cm cm
If Cody was 10 %, percent taller than he was on the first day of school last year then he was 150 cm tall on the first day of school last year.
To find out the height of Cody on the first day of school last year, we need to perform a calculation as follows:
Let's say their height of Cody on the first day of school last year is 'x'.
His height of Cody on the first day of school this year is 165 cm.
Cody is 10% taller than he was on the first day of school last year, so:
165 = x + (10% of x)
Simplifying this equation will give
165 = x + 0.1 x 165
= 1.1xx
= 150
Therefore, Cody was 150 cm tall on the first day of school last year.
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Find the exact values of the remaining trigonometric functions of satisfying the given conditions. (If an answer is undefined, enter UNDEFINED.)
cos = 4/5, tan < 0
sin =
tan =
csc =
sec =
cot =
Answer:
sin Θ = [tex]-\frac{3}{5}[/tex]
tan Θ = [tex]-\frac{3}{4}[/tex]
csc Θ = [tex]-\frac{5}{3}[/tex]
cot Θ = [tex]-\frac{4}{3}[/tex]
Step-by-step explanation:
We know that this triangle is a 3-4-5 triangle since we know the cos of the angle. We also know this angle is located in Quadrant IV (4) since cos is positive and tan is negative.
Based off this info we can find the rest of the trig functions
sin Θ = [tex]-\frac{y}{r}[/tex]
tan Θ = [tex]-\frac{y}{x}[/tex]
csc Θ = [tex]-\frac{r}{y}[/tex]
cot Θ = [tex]-\frac{x}{y}[/tex]
in the most recent psychology exam, the mean score was 50 with a standard deviation of 5 points. based on the normal curve, what is the range within which 95% of the scores fall?
The range of the normal curve representing 95% of the scores fall is equal to 40.2 to 59.8.
The range within which 95% of the scores fall,
Calculate the z-scores corresponding to the 2.5th and 97.5th percentiles of the normal distribution.
The z-score corresponding to the 2.5th percentile is -1.96.
And the z-score corresponding to the 97.5th percentile is +1.96.
Using the formula for the z-score, we can calculate the corresponding raw scores as,
Lower bound is equal to,
z = (X - μ) / σ
⇒-1.96 = (X - 50) / 5
⇒X = 40.2
Upper bound is equal to,
z = (X - μ) / σ
⇒ +1.96 = (X - 50) / 5
⇒ X = 59.8
Therefore, 95% of the scores fall within the range of 40.2 to 59.8.
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The vertices of ΔABC are A(−2,5), B(−2,4), and C(−5,2). If ΔABC is reflected across the line y=−2 to produce the image ΔA'B'C', find the coordinates of the vertex A'.
The coordinates of the vertex A' are (-2, -2).
What is triangle?
A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
To reflect a point or a shape across a line, you can follow these steps:
Find the equation of the line of reflection.
Find the distance between each point and the line of reflection.
Reflect each point across the line of reflection by moving the same distance on the other side of the line.
Finding the equation of the line of reflection:
The line of reflection is y = -2, which is a horizontal line passing through y = -2.
Finding the distance between each point and the line of reflection:
We can use the formula for the distance between a point (x, y) and a line Ax + By + C = 0:
distance = |Ax + By + C| / sqrt(A^2 + B^2)
Plugging in the values, we get:
distance(A, y = -2) = |(-2) - (-2) + 2| / sqrt(0 + 1) = 2
distance(B, y = -2) = |(-2) - (-2) + 4| / sqrt(0 + 1) = 4
distance(C, y = -2) = |(-5) - (-2) + 2| / sqrt(1 + 0) = 5 / sqrt(1) = 5
So the distances between A, B, C and the line of reflection are 2, 4, and 5, respectively.
Reflecting each point across the line of reflection:
To reflect a point across a line, we move the same distance on the other side of the line. Since the line of reflection is horizontal, we only need to move vertically.
A is 2 units above the line of reflection, so we move it 2 units below the line:
A' = (-2, -2)
B is 4 units above the line of reflection, so we move it 4 units below the line:
B' = (-2, -4)
C is 5 units above the line of reflection, so we move it 5 units below the line:
C' = (-5, -7)
Therefore, the coordinates of the vertex A' are (-2, -2).
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[50 POINTS] According to the Fundamental Theorem of Algebra, how many zeros does the function f(x) = 5x^6+2x^3−4x + 1
There are ________ Zeros
Answer:
6
Step-by-step explanation:
the number of zeroes is defined by the highest exponent of the variable in the functional expression.
This is a question that I would prefer to be answered quickly-ish and I would like it if there was an explanation.
The area of a rectangular room is 84 ft^2. the length of the room is 8ft greater than the width. The situation can be represented as W^2-8w-84=0. What is the width?
Answer:
Step-by-step explanation:
You can start by drawing a diagram. Then, you need to pick the shorter side and designate it as "x". The longer side must be "x+8".
The formula for area of a rectangle is A=l*w. Since the area is 84, then you can use the A=l*w formula. 84 = x(x+8) would be the equation to solve for x.
Now, you need to put the equation in standard form. So, x2 + 8x - 84 = 0.
Since you can't solve this quadratic using factoring, you need to complete the square.
To complete the square you need to add 84 to both sides. Now you have x2 + 8x = 84. Take the coefficient for the x term (8) and divide by 2. Now square it. That would be 42, so 16. Now you have x2 +8x +16 = 100.
Factor x2 +8x +16, so (x+4)2 = 100
If you use the square root property, you have x+4 = 10. Therefore, x = 6 (the short side) and 14 is the long side.
I hope that helps.