inverse trig ratio can someone pls answer the rest of these i don’t understand them answers are already there but i need to see how they are done
We're given the angle measure to be 46 for No. 8. The length of 1 leg is x and the hypotenuse is 28.
We can use cosine to solve this. Since cosine is adjacent over hypotenuse, we can do cos(46) = x/28. Cross multiply to get cos(46)*28 = x. That solves to be 19.5
Using this principle allows us to solve the other ones. I'll let you figure them out.
TLDR: We can use the definition of trig functions to plug in what we know and place variables where we don't have enough information to find the length of a side.
Select one:
O The function has a zero at (0, -2).
O The function has a range of all real numbers less than or equal to 2.
O The function has two y-intercepts and one x- intercept.
O The function has a minimum value.
(Photo is added of question)
The function has a range of all real numbers less than or equal to 2.
Step-by-step explanation:Quadratic functions form parabolas, which look like a U-shape.
What is Range
Range describes the y-values covered by a function. So, the range contains every y-value that is a possible output of a function. You can find the range of a function from the graph by looking at what y-values are or will be covered by the function.
The range of a quadratic is always all real numbers greater than/less than the y-value of the vertex. Positive quadratics have ranges greater than the vertex, and negative quadratics have ranges less than the vertex.
Finding the Range
The parabola given is negative. We know this because the graph opens downward. This means that the graph has a maximum, and the range is less than the vertex.
By looking at the graph we can tell that eventually, the graph will cover all y-values under y-value 2. Note that 2 is the y-value of the vertex. So the range is all real values less than or equal to 2. This means that any number less than or equal to 2 is a possible output of the function.
On a coordinate plane, the x-axis is labeled Number of Days and the y-axis is labeled Number of Computers. A line goes through points (3, 36), (4, 48), (5, 60). The graph shows a proportional relationship between the number of computers produced at a factory per day. In three days, 36 computers are produced; 48 computers are produced in 4 days; and 60 computers are produced in 5 days. Find the unit rate of computers per day using the graph. Unit rate: computers per da
The unit rate is 12 computers per day (36/3 = 12; 48/4 = 12; 60/5 = 12). This means that the factory produces 12 computers per day.
What are computers?Computers are electronic devices that are used to store, process, and output data. They are used to perform a variety of tasks, from simple calculations to complex research projects. Computers consist of hardware, such as processors, memory, and storage devices, and software, which provides instructions for the hardware to follow.
The unit rate is the number of units produced per unit of time. To calculate the unit rate of computers per day using the graph, divide the number of computers produced by the number of days. Using the graph, 36 computers are produced in 3 days, 48 computers are produced in 4 days, and 60 computers are produced in 5 days.
Therefore, the unit rate is 12 computers per day (36/3 = 12; 48/4 = 12; 60/5 = 12). This means that the factory produces 12 computers per day. The graph produced shows a proportional relationship between the number of computers produced at a factory per day.
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Which transformations map the strip pattern onto itself?
b b
b
b b
P
a reflection across a vertical line
a horizontal translation only
a horizontal translation and a gidé refecion
a horizontal translation and a 180° rotation
Answer:
The strip pattern has a vertical axis of symmetry, so a reflection across a vertical line will map the strip pattern onto itself. Therefore, the correct answer is "a reflection across a vertical line."
Step-by-step explanation:
Which function is best represented by the graph?
Answer: A
Step-by-step explanation:
Find the measurment of line segement
DE and EF?
Answer:
Step-by-step explanation:
[tex]n\sqrt{2}=10[/tex]
Solve for n.
[tex]n\sqrt{2} =10\\\\\frac{n\sqrt{2} }{\sqrt{2} }=\frac{10}{\sqrt{2} }[/tex]
Rationalize the denominator.
[tex]n=\frac{10}{\sqrt{2} }\cdot \frac{\sqrt{2} }{\sqrt{2} }\\\\n=\frac{10\sqrt{2} }{2}[/tex]
Reduce to lowest terms.
[tex]n=\frac{10\sqrt{2} }{2} \div\frac{2}{2}\\\\n=5\sqrt{2}[/tex]
y = 3x² - 24x + 57
find the coordinates of the vertex
Answer:
(4,9)
Step-by-step explanation:
The word "vertex" isn't clear here. I'm assuming the question is referring to finding the stationary (turning) point. This can be found by finding the derivative (dy/dx).
To find the derivative we use the following formula:
[tex]y = ax^{n}\\ \frac{dy}{dx} = nax^{n-1}[/tex]
What this means is that for each term of the equation, we multiply by the current power and then reduce the power by 1. In the case of the question's equation, this will be done like this:
[tex]y = 3x^{2} - 24x + 57\\\frac{dy}{dx} = 6x - 24[/tex]
Now we can use this to find the stationary point, as stationary points are where the derivative (dy/dx) = 0:
6x - 24 = 0
6x = 24
x = 4
Through this we have found the x-coordinate of the stationary point, however we still need to find the y coordinate. This is done by substituting our x value back into the original equation (not the derivative):
y = 3(4)² - 24(4) + 57
y = 9
Therefore, the coordinates of the stationary point are (4,9)
Calculate the trade discount (in $). Round your answer to the nearest cent.
The trade discount is $15.75.
What is trade discount?A trade discount is a regular reduction from a product's regular, established price. The use of trade discounts allows a company to adjust the final price based on the volume or status of each customer.
It is important to note that trade discounts are not the same as early-payment discounts. (Early-payment discounts of 1% or 2% are typically recorded by the seller in an account such as Sales Discounts and by the buyer in an account such as Purchase Discounts using the periodic inventory method.) Neither the seller nor the buyer keeps a separate account for trade discounts.
We must first determine the product's list price in order to determine the trade discount.
List price: $75 plus $3.75 equals $78.75
As the trade discount rate is 20%, the following discount is offered:
Discount = 0.2 times List price = 0.2 times $78.75 = $15.75
The trade discount is therefore $15.75.
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Find the value of the given expression, and most importantly show the steps please.
Answer:
Step-by-step explanation:
[tex]16^\frac{1}{n}=2[/tex] (since by definition [tex]\sqrt[n]{16} =16^\frac{1}{n}[/tex])
[tex](2^4)^\frac{1}{n}=2[/tex]
[tex]2^\frac{4}{n}=2[/tex]
[tex]2^\frac{4}{n}=2^1[/tex]
∴[tex]\frac{4}{n} =1[/tex] (indices must be equal when bases are equal)
∴[tex]n=4[/tex]
A radioactive substance has a half-life of 8 years. How much of the original 3.2 grams of the substance would be left after 36 years? Which equation best models this situation?
The exponential function [tex]A = 3.2 \times \frac{1}{2}^{\frac{36}{8}}[/tex] determines the amοunt of substance after 36 years to be 0.2 grams.
What is an exponential function?The fοrmula for an exponential functiοn is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The amοunt of a radioactive substance left after a certain number of half-lives can be calculated using the expοnential equation formula -
[tex]A = A_0 \times \frac{1}{2}^{\frac{t}{T}}[/tex]
where -
A0 is the initial amοunt of the substance
A is the amοunt of the substance remaining after t years
T is the half-life οf the substance
In this case, the half-life is 8 years, sο T = 8.
We want tο know how much of the original 3.2 grams of the substance wοuld be left after 36 years, so t = 36.
We can plug these values intο the formula to get -
[tex]A = 3.2 \times \frac{1}{2}^{\frac{36}{8}}[/tex]
A ≈ 0.2 grams
Therefοre, after 36 years, only about 0.2 grams of the original 3.2 grams of the substance wοuld be left.
The equation that best mοdels this situation is -
[tex]A = 3.3 \times \frac{1}{2}^{\frac{t}{8}}[/tex]
where A represents the amοunt of the substance remaining after t years, in grams.
Therefοre, the equation is [tex]A = 3.2 \times \frac{1}{2}^{\frac{36}{8}}[/tex].
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Explain how you would find the area of the figure below
Given the linear equation y = 7 x + 2 , evaluate y when x = 1 .
Answer:
y=9
Step-by-step explanation:
y=7x+2
y=7(1) +2
y=7+2
y=9
Can someone help me please i really need help with this.
use the Remainder Theorem and synthetic division please
The value of the polynomial equations are
f ( -10 ) = 20201
f ( 2 ) = 17
f ( 3 ) = 142
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the polynomial equation be represented as A
Now , the value of A is
f ( x ) = 2x⁴ + x² - 10x + 1 be equation (1)
Now , when the value of x = -10
f ( -10 ) = 2 ( -10 )⁴ + ( -10 )² - 10 ( -10 ) + 1
On simplifying , we get
f ( -10 ) = 2 ( 10000 ) + 100 + 100 + 1
f ( -10 ) = 20000 + 201
f ( -10 ) = 20201
Now , when the value of x = 2
f ( 2 ) = 2 ( 2 )⁴ + ( 2 )² - 10 ( 2 ) + 1
On simplifying , we get
f ( 2 ) = 2 ( 16 ) + 4 - 20 + 1
f ( 2 ) = 32 - 15
f ( 2 ) = 17
Now , when the value of x = 3 , we get
f ( 3 ) = 2 ( 3 )⁴ + ( 3 )² - 10 ( 3 ) + 1
f ( 3 ) = 2 ( 81 ) + 9 - 30 + 1
f ( 3 ) = 162 - 20
f ( 3 ) = 142
Hence , the polynomial equations are solved
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1. What is (f⋅g)(x)?
f(x)=x^2+2x−6
g(x)=x^4+3
Enter your answer in standard form in the box.
2. Question
WHAT IS : (f−g)(x)? its not the same question as 1
f(x)=x^4−x^2+9
g(x)=x^3+3x^2+12
Enter your answer in standard form in the box.
Answer:
[tex]\textsf{1.} \quad \left(f \cdot g \right)(x)=x^6+2x^5 -6x^4+3x^2+6x -18[/tex]
[tex]\textsf{2.} \quad\left(f -g \right)(x)=- x^4+x^2+2x-9[/tex]
Step-by-step explanation:
To calculate (f ⋅ g)(x), multiply function f(x) by function g(x) by distributing the parentheses:
[tex]\begin{aligned}\left(f \cdot g \right)(x)&=(x^2+2x-6)(x^4+3)\\&=x^2 \cdot x^4 +x^2 \cdot 3+2x \cdot x^4+2x \cdot 3 -6 \cdot x^4 -6 \cdot 3\\&=x^6+3x^2+2x^5+6x -6x^4 -18\\&=x^6+2x^5 -6x^4+3x^2+6x -18\\\end{aligned}[/tex]
To calculate (f - g)(x), subtract function g(x) from function f(x) by applying the distributive law -(a + b) = -a - b:
[tex]\begin{aligned}\left(f -g \right)(x)&=(x^2+2x-6) - (x^4+3)\\&=x^2+2x-6 - x^4-3\\&=- x^4+x^2+2x-6 -3\\&=- x^4+x^2+2x-9\end{aligned}[/tex]
Note: The standard form of a polynomial is expressed by writing the term with the highest degree first, followed by the other terms in order of decreasing powers.
Derive linear equations what is the y intercept of the line b=
The answer of the given question based on linear equations what is the y intercept of the line b =4.
What is y-intercept?In linear equation of form y = mx + b, where m is slope and b is y-intercept, the y-intercept is point at which line intersects the y-axis. It is value of y when x is equal to a zero.
To find the y-intercept of the line, we need to identify the point at which the line intersects with the y-axis. This is the point where x=0.
From the given graph, we can see that when x=0, the point on the line is (0, 4). Therefore, the y-intercept (b) of the line is 4.
So, the answer is:
b = 4
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Answer:
b=2
Step-by-step explanation:
its 2 not 4 the dot is located on 2 in between the first and second quadrant.
Can someone pls help me, I have been stumped on this question for hours.
Based on the relative frequency tables, the correct options are
52% of the males survived21% of the survivors were maleWhat is a relative frequency?Relative frequency is a statistical concept that refers to the proportion or percentage of times an event occurs in relation to the total number of times the event could occur. It is calculated by dividing the number of times an event occurs by the total number of observations or trials.
For example, if you flip a coin 10 times and it lands on heads 6 times, the relative frequency of heads would be 6/10 or 0.6, which is equivalent to 60%. This means that heads occurred 60% of the time in the sample of 10 coin flips.
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1. Luisa has 35 building blocks. Jack gives
her 18 more blocks, Luisa uses 26 blocks
to build a castle. How many blocks are
not used in the castle?
Answer:
27 blocks not used in the castle
Step-by-step explanation:
35+18= 53
53-26=27
Between ecery pair of distinct points, there is a positive unique number called the , which can be determined as the of the corresponding real numbers of the two points
The missing term of question is "distance".
Define distinct points?Distinct points refer to points that are not the same. In other words, if two or more points have different locations or coordinates, they are considered distinct points.
Distance is a measure of the length or space between two points, lines, or other objects. It is typically expressed as a non-negative number and can be determined using various formulas depending on the context and the nature of the objects being measured.
The missing term in the question is "distance". The sentence can be completed as:
"Between every pair of distinct points, there is a positive unique number called the "distance", which can be determined as the "absolute value of the difference" of the corresponding real numbers of the two points."
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PLEASE HELP!!!
find the missing information for the triangle. make sure to find the missing angle measure AND the 2 missing side lengths
Answer:
Sides:
MX = 4cm
BX = 8cm
BM = 6.928...cm
Angles:
m = 90°
b = 30°
x = 60°
Step-by-step explanation:
We've been given 3 pieces of info that we can use, which is more than enough
Using the sine rule, we can find the hypotenuse:
[tex]\frac{4cm}{sin30} = \frac{BXcm}{sin90}[/tex]→[tex]\frac{4sin90}{sin30} =BX = 8cm[/tex]
Now we can use Pythagoras' theorem to find the last side:
[tex]a^2+b^2=c^2[/tex] → [tex]b^2\ = c^2-a^2[/tex] → [tex]64 - 16 = b^2 = 48[/tex] → [tex]\sqrt{48} =6.928...cm[/tex]
And since we know two of the angles, we can find the third:
[tex]x = 180 - (30 + 90) = 180 - 120 = 60[/tex]°
Answer:
Below
Step-by-step explanation:
REMEMBER: for a right triangle sin (30) = opposite LEG/ hypotenuse
so sin 30 = 4 / hypotenuse now, with a calculator sin 30 = 1/2
1/2 = 4 / hypotenuse so hypotenuse = 8
Now it is a right triangle so Pythagorean theorem applies
hyp ^2 = 4 ^2 + BM^2
8^2 = 4^2 + BM^2
48 = BM^2 so BM = sqrt (48 ) = 4 sqrt 3
Finally, all of the internal angles of ANY triangle sum to 180 °
so angle x = 180 - 90 - 30 = 60°
Describe the relationship between the circumference of a circle and its diameter
Answer:
There is a direct relationship, in which the value of the division of the circumference by the diameter is a constant. This constant is know as Pi.
Any help will be awesome
Is 5 9/10 bigger than 5 5/6?
Answer:
5 9/10
Step-by-step explanation:
find the same denominator
in this case 30
9x3=27 and 5x5=25
since 27 is bigger, the fraction is also bigger
Answer:
5\6 is smaller than 9\10
Step-by-step explanation:
Find the least common denominator or LCM of the two denominators:
LCM of 6 and 10 are 30
Next, find the equivalent fraction of both fractional numbers with denominator 30
For the 1st fraction, since 6 × 5 = 30,
[tex]\frac{5}{6} = \frac{5.5}{6.5} =\frac{25}{30}[/tex]
Likewise, for the 2nd fraction, since 10 × 3 = 30,
[tex]\frac{9}{10} =\frac{9.3}{10.3} =\frac{27}{30}[/tex]
Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction
[tex]\frac{25}{30} < \frac{27}{30} 0r \frac{5}{6} < \frac{9}{10}[/tex]
$650 is invested in an account at 3
simple interest per year. Write an
explicit formula representing the
account balance in any given year,
and use this formula to find the
balance in the 25th year.
5. The value of the account at yearly intervals is given below.
6. The balance in the 25th year in the account will be $1,137.5.
What is simple interest?Let P be the principal, R be the rate of interest, and T be the time. Then the interest rate is given as,
The formula for interest is written as,
I = (PRT)/100
5. The simple interest is given as,
I = 650 x (3/100)
I = $19.5
End of first year = 650 + 19.5 - $669.50
End of second year = 669.5 + 19.5 = $689
End of third year = 689 + 19.5 = $708.50
End of fourth year = 708.50 + 19.5 = $728
End of fifth year =728 + 19.5 = $747.50
6. The balance after 25 years is given as,
A = $650 + ($650 x 3 x 25) / 100
A = $650 + $487.5
A = $1,137.5
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Dion bought 3 pounds of oranges and 2 pounds of grapefruit. Write an expression to represent the amount of money Dion spent on the fruit. Then evaluate the expression. How much did Dion spend?
Answer:
eeeeejjbbvvv g gyuuu u grrtyyu
Tamika wants to use a sheet of fiberboard 19 inches long to create a skateboard ramp with a 20° angle of elevation from the ground. How high will the ramp rise from the ground at its highest end? Round your answer to the nearest tenth of an inch if necessary. Student Help Vid Next Question> Your Solution:
Using the right triangle, we fοund the elevatiοn οf the ramp frοm the grοund as 6.49 inches.
What is meant by elevatiοn?The height abοve οr belοw a specified reference pοint, mοst frequently a reference geοid, which is a mathematical representatiοn οf the Earth's sea level as an equipοtential gravitatiοnal surface, determines a lοcatiοn's elevatiοn.
A frequently used idea in relatiοn tο height and distance is the angle οf elevatiοn, particularly in trigοnοmetry. It is described as a relatiοnship between an οblique line frοm the οbserver's eye tο an item abοve his eye and the hοrizοntal plane.
This angle eventually develοps abοve the surface. The angle οf elevatiοn is made in such a way that it is abοve the οbserver's eye, as the name suggests.
Using the given infοrmatiοn, we drew a right triangle as given belοw.
The hypοtenuse οf the triangle is the length οf the sheet.
The angle οf elevatiοn is 20°.
The base οf the triangle is the grοund.
The hypοtenuse l = 19 inches
Angle Ф = 20°
We have tο find the elevatiοn h.
sin Ф = h/l
sin 20 = h/19
0.342 = h /19
h = 6.49 inches
Therefοre using the right triangle, we fοund the elevatiοn οf the ramp frοm the grοund as 6.49 inches.
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Question: What price should the restaurant sell the large square pizza (12 inch side) for, so that both pizzas cost the same amount per square inch?
According to the question the height of Ruben’s school is 360 inches.
What is school?School is a place where students can learn and grow in their knowledge. It is a place where students can gain an education and become well-rounded individuals. School is a place where people can make friends, learn from each other, and explore new ideas and topics. School is a place where teachers and staff provide guidance to help students succeed in their academics and extracurricular activities.
To find the height of Ruben’s school using similar triangles and a mirror, we can use the following formula:
height of school / height of Ruben = distance from mirror to school / distance from mirror to Ruben
Plugging in the given values, we get:
height of school / 72 = 425 / 85
Cross-multiplying and solving for height of school, we get:
height of school = 72 x 425 / 85
height of school = 360 inches
Therefore, the height of Ruben’s school is 360 inches.
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Solve the right triangle. Round decimal answers to the nearest tenth.
Step-by-step explanation:
1) length of YZ:
[tex]YZ=\sqrt{XZ^2-XY^2} ;= > \ YZ=8.485=8.5;[/tex]
2) angle X:
[tex]m \angle X=arccos(\frac{XY}{XZ});= > \ m \angle X=arccos\frac{1}{3}=70.6 к;[/tex]
3) angle Z:
[tex]m \angle Z=arcsin(\frac{XY}{XZ});= > \ m \angle Z=arcsin\frac{1}{3}=19.4 к;[/tex]
if x = 6 what is the value of x( 15 - x
Answer:
54
Step-by-step explanation:
I'm assuming you are referring to x = 6, then to find the value of x(15 - x).
If x = 6, we can substitute this value into the expression x(15 - x) to find its value:
x(15 - x) = 6(15 - 6) = 6(9) = 54
Therefore, if x = 6, then x(15 - x) = 54.
Hey there!
x(15 - x)
= 6(15 - 6)
= 6(15) + 6(-6)
= 90 - 36
= 54
Therefore, the answer should be about:
54
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Lucas is selling candy bars for a fundraiser he 12 bars on Saturday at eight on Sunday each bar sold for for one dollar and 50 Cent. How much money did he raise?
what do right angles look like
The right angles would be named as:
3. ∠PNL 4. ∠PNO
How to Name Right Angles?Right angles can be named in a few different ways, depending on the context in which they are being used. One common way is:
Using three points: use the names of the three points that form the angle, with the vertex of the angle in the middle. For example, if the right angle is formed by the line segments AB and BC, you could name it angle ABC.
The sign "∠" means angle, therefore, it can be named also as ∠ABC.
Thus, the right angles in the given diagram can be named accordingly as:
∠PNL and ∠PNO
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