Option A and C will be the correct answers based on the provided statement.
What is a triangle's three sides?A right triangle's hypotenuse is its longest side, its "opposing" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question. To define the side of right triangles, we utilize specific terminology.
Congruence of the SAS Triangle According to the theorem, two triangles are said to be congruent to one another if they have a single pair of corresponding sides and an incorporated angle that are equal to one another.
The image shows two triangles that are congruent by the SAS Congruence Theorem.
As a result, the following claims satisfy the requirements for two triangles to be regarded as congruent to one another by the SAS Congruity Theorem:
A. the corresponding two sides and the included angle in both triangles are congruent.
C. A pair of two sides that are congruent with the equivalent two sides and angle in the opposite triangle and are parallel to an angle's ray.
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`g\left(x\right)`represents the cost of a stuffed giraffe. The giraffe costs `\$15` and accessories cost `\$3.75` each. What does `g\left(5\right)=33.75` say about this situation?
The statement g(5) = 33.75 represents total cost of $33.75 when the purchase of a stuffed giraffe added to 5 accessories to it, the total cost
How to interpret the function notationFrom the question, we have the following parameters that can be used in our computation:
g(x) = the cost of a stuffed giraffe.
The giraffe costs $15 and accessories cost $3.75 each.
This means that
g(5) = 33.75
Using the above as a guide, we have the following:
The statement g(5) = 33.75 means that if we purchase a stuffed giraffe and add 5 accessories to it, the total cost will be $33.75.
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Add/subtract the radical expressions and simplify: (a) \( -2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-3 \sqrt{112 x^{3} y^{2}} \) (b) \( 7 \sqrt[3]{8 x^{2} y}+2 \sqrt[3]{27 x^{5} y^{4}} \)
\( 7 \sqrt[3]{8 x^{2} y}+6 \sqrt[3]{x^{5} y^{4}} \) = \( 13 \sqrt[3]{x^{5} y^{4}} \)
Adding/subtracting radical expressions and simplifying can be done as follows:
(a) \( -2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-3 \sqrt{112 x^{3} y^{2}} \)
\(-2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-3 \sqrt{112 x^{3} y^{2}}\) = \( -2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-3 \sqrt{28 x^{3} \cdot 4 y^{2}}\)
\(-2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-3 \sqrt{28 x^{3} \cdot 4 y^{2}}\) = \( -2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-12 y \sqrt{7 x^{3}}\)
\(-2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-12 y \sqrt{7 x^{3}}\) = \( -14 y \sqrt{7 x^{3}}+3 x \sqrt{63 x y^{2}}\)
(b) \( 7 \sqrt[3]{8 x^{2} y}+2 \sqrt[3]{27 x^{5} y^{4}} \)
\( 7 \sqrt[3]{8 x^{2} y}+2 \sqrt[3]{27 x^{5} y^{4}} \) = \( 7 \sqrt[3]{8 x^{2} y}+2 \sqrt[3]{3^3 \cdot x^{5} y^{4}} \)
\( 7 \sqrt[3]{8 x^{2} y}+2 \sqrt[3]{3^3 \cdot x^{5} y^{4}} \) = \( 7 \sqrt[3]{8 x^{2} y}+6 \sqrt[3]{x^{5} y^{4}} \)
\( 7 \sqrt[3]{8 x^{2} y}+6 \sqrt[3]{x^{5} y^{4}} \) = \( 13 \sqrt[3]{x^{5} y^{4}} \)
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Today, the sum of Caroline's age and Cameron's age is 73. 5 years ago Cameron was 2 times older than Caroline.
The answer of Caroline is 19.33 years old and Cameron is 53.67 years old
Let's start by assigning variables to represent Caroline's age and Cameron's age. We'll use C for Caroline's age and M for Cameron's age.
According to the problem, the sum of their ages today is 73, so we can write the equation:
C + M = 73
Five years ago, Cameron was 2 times older than Caroline. so we can write the equation:
M - 5 = 2(C - 5)
Now we can use the first equation to solve for one of the variables. Let's solve for C:
C = 73 - M
Next, we can substitute this value of C into the second equation:
M - 5 = 2(73 - M - 5)
Simplifying the equation gives us:
M - 5 = 146 - 2M - 10
3M = 161
M = 53.67
Now we can use this value of M to find C:
C = 73 - 53.67
C = 19.33
So Caroline is 19.33 years old and Cameron is 53.67 years old.
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find the missing side of the triangle
The missing side of the triangle is 16 mm.
What is Trigonometry?Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common uses for an angle in trigonometry.
As per the given diagram:
The sides and angles of the right-angled triangle is given:
To find v using the trigonometric ratio:
sinθ = (P/H) {P is perpendicular and H is hypotunese}
for θ = 30°
sin30° = (8/v)
1/2 = 8/v
v = 16 mm
Hence, the missing side of the triangle is 16 mm.
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x^2 - 5x + 5 = 0 select the two values of x that are roots of this equation
The two values of x that are roots of the given equation are approximately 3.618 and 1.382.
What is quadratic equation ?
Quadratic equations are used to model a wide range of phenomena in many areas of science and engineering, including physics, biology, economics, and finance. They are also used extensively in mathematics for their elegant properties and applications in algebra, geometry, and calculus.
We start with the quadratic equation:
[tex]$x^2 - 5x + 5 = 0$[/tex]
To find the roots of this equation, we use the quadratic formula:
[tex]$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$[/tex]
where [tex]$a$, $b$,[/tex] and [tex]$c$[/tex] are the coefficients of the quadratic equation.
In this case, we have [tex]a = 1$, $b = -5$, and $c = 5$.[/tex] Substituting these values into the quadratic formula, we get:
[tex]$x = \frac{5 \pm \sqrt{(-5)^2 - 4(1)(5)}}{2(1)}$[/tex]
Simplifying the expression under the square root, we get:
[tex]$x = \frac{5 \pm \sqrt{5}}{2}$[/tex]
Therefore, the two roots of the equation are:
[tex]$x = \frac{5 + \sqrt{5}}{2} \approx 3.618$[/tex]
[tex]$x = \frac{5 - \sqrt{5}}{2} \approx 1.382$[/tex]
Hence, the solutions to the equation [tex]$x^2 - 5x + 5 = 0$[/tex] are approximately 3.618 and 1.382.
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Cornidegretting marching all de What is the probably going to the A Ched Comider gering a randonner including devine What is the probability of generating av in bad to the decimal ? A Ched Assume 20.1). What is the probability z = 1.842 Answer Find the proportion of obsertions from the STANDARD NORMANDSTRIBUTION et les than -0.9900 Armer Check Find the proportion of observations from the STANDARD NORMAL DISTRIBUTION that we than 2.9000 Araw r Check Feel the proportion of brunetices from the SACARD NORMAL ISRAENUD-2-4200 me 2.400 me 20.1) Ung the STANDARDNENDETALLE band the LOWER w
The probability of generating a value between -0.9900 and 2.9000 from a standard normal distribution is 0.4781. The probability of generating a value between -2.4200 and 2.4200 from a standard normal distribution is 0.9804. The probability of generating a value between -0.9900 and 20.1 from a standard normal distribution is 1.0000.
The standard normal distribution, also called the z-distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1. Any normal distribution can be standardized by converting its values into z scores.The standard normal distribution is one of the forms of the normal distribution. It occurs when a normal random variable has a mean equal to zero and a standard deviation equal to one. In other words, a normal distribution with a mean 0 and standard deviation of 1 is called the standard normal distribution.
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Krystal throws a rappelling rope at a speed of 10 m/s down a 50 m cliff.
When will the rope hit the ground?
Use the drop-down to put the correct order to solve for when the rope will hit the ground.
With speed = 10 m/s, the rope will hit ground after 3.36 seconds.
What exactly is speed?Speed is a measure of how fast an object is moving, usually measured in units of distance per unit time, such as meters per second (m/s) or kilometers per hour (km/h). It is a scalar quantity, meaning it only has magnitude and no direction.
Mathematically, speed is defined as the distance an object travels per unit time. The formula for calculating speed is:
Speed = Distance / Time
where Distance is the distance traveled by the object, and Time is the time taken to cover that distance.
Now,
To find when the rope will hit the ground, we can use the kinematic equation:
y = vi * t + (1/2) * a * t²
where:
y = 50 m (the height of the cliff)
vi = 10 m/s (the initial velocity of the rope)
a = 9.8 m/s² (the acceleration due to gravity, acting downward)
t = time it takes for the rope to hit the ground
We can solve for t by setting y=50 and solving for t:
50 = 10t + (1/2) * 9.8 * t²
50 = t(10 + 4.9t)
t = 50/14.9=3.36 s
Therefore, the rope will hit the ground after 3.36 seconds.
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If f(v)=12v^(4)-40v^(3)+4v^(2)+17v+21, use synthetic division to find f(3) Submit
The value of f(3) using synthetic division is 72.
To find f(3) using synthetic division, we need to divide the polynomial f(v) by the factor (v - 3). This will give us the quotient and the remainder, which will help us find the value of f(3).
Write the coefficients of the polynomial in a row: 12 -40 4 17 21
Write the value of the factor we are dividing by to the left of the row: 3 | 12 -40 4 17 21
Bring down the first coefficient: 3 | 12 -40 4 17 21
------------------
12
Multiply the first coefficient by the factor and write the result under the second coefficient: 3 | 12 -40 4 17 21
------------------
12 36
Add the second coefficient and the result from step 4: 3 | 12 -40 4 17 21
------------------
12 -4
Repeat steps 4 and 5 for the remaining coefficients: 3 | 12 -40 4 17 21
------------------
12 -4 0 51
The last number in the bottom row is the remainder. This is the value of f(3): 3 | 12 -40 4 17 21
------------------
12 -4 0 51 72
So, f(3) = 72.
Therefore, the value of f(3) using synthetic division is 72.
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Please answer number 15 and 16 show work
Algebra 2
The exponential function that models the percentage as a function of P is given as follows:
P(t) = 100(0.705)^t.
How to define the exponential function?The standard definition of an exponential function is given as follows:
y = a(b)^x.
In which:
a is the value of y when x = 0.b is the rate of change.The parameters for this problem are given as follows:
a = 100, as when x = 0, y = 100, from the second row of the table.b = 70.5/100 = 0.705, as when x increased by one, y was multiplied by 0.705.Hence the function that models the data in the table is defined as follows:
P(t) = 100(0.705)^t.
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Which is it????????////]//////.
The equation that represents the line of best fit for the scatterplot is given as follows:
B. y = -10x + 100.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.From the graph, we have that:
The slope is negative, as when the input increases, the output decreases.The intercept is a value between 90 and 100, as there are two points on the graph when x = 0, (0, 90) and (0,100).Hence option B is correct.
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Kehlani is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 24 meters from the building. The angle of elevation from her eyes to the roof ((point AA)) is 20^{\circ} ∘ , and the angle of elevation from her eyes to the top of the antenna ((point BB)) is 41^{\circ} ∘ . If her eyes are 1.51 meters from the ground, find the height of the antenna ((the distance from point AA to point BB)). Round your answer to the nearest tenth of a meter if necessary.
The antenna's height is 12.1 meters, as stated throughout the announcement.
What does building type mean?Building type refers to a grouping of buildings according to their purpose, location, and style that serves as the standard for evaluating and categorizing variants. Buildings must be categorized as either support, civic, commercial, industrial, or residential. Any kind of fella construction is a structural. It could be anything: a dam or a bridge, for instance. In contrast, a building is a closed construction with walls and a roof. Once more, the more precise phrase is "building," although "structure" is far more generic.
Based on the graph.
[tex]$$\begin{aligned}& \overline{O H}=\overline{C D}=1.51 \mathrm{~mm} . \\& \overline{O C}=24 \mathrm{~m} . \\& \angle O C A=20^{\circ} . \quad \angle O C B=41^{\circ} .\end{aligned}$$[/tex]
In RT [tex]$\triangle A O C_,$[/tex]
[tex]$$\begin{aligned}& \tan 20^{\circ}=\frac{A_0}{O C}=\frac{A_0}{24} \\& \text { So } A_0=\tan 20^{\circ} \times 24=8.74 \mathrm{~m}\end{aligned}$$[/tex]
In Rt ΔOBC.
[tex]$$\begin{aligned}\tan 41^{\circ} & =\frac{O B}{O C}=\frac{O B}{24} \\O B & =\tan 41^{\circ} \times 24=20.86 \mathrm{~m} .\end{aligned}$$[/tex]
[tex]A B=O B-O A=20.86-8.74=12.12 \mathrm{~m} \approx 12.1 \mathrm{~m} .[/tex]
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Answer:
12.1
Step-by-step explanation:
I got the question right
d=640897752 &questionld =18 flushed = false 8 cld =7245967 ¢erwin = yes Builder Solve the inequality algebraically. (x+2)/(x-7)>0
The inequality (x + 2)/(x - 7)>0 can be solved algebraically by first subtracting 2 from both sides. This results in the inequality (x - 7) > 2. By dividing both sides by (x-7), the inequality can be simplified to 1>2/x-7. This simplifies further to -7>2/x, or x>-7/2. Therefore, the solution to the inequality is x>-7/2.
In plain terms, this means that a value of x must be greater than -7/2 in order for the inequality to be true. This implies that the value of x must be a number greater than -3.5, since -7/2 is the same as -3.5. Thus, if x is any number greater than -3.5, then the inequality (x + 2)/(x - 7) > 0 will be satisfied.
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All students attending a homecoming assembly complete a digital survey as they arrive at their seats. The survey questioned them about what they were most looking forward to for the homecoming events. Assume all students in attendance participated and remained at the assembly for its entirety. Write probabilities as decimals rounded to hundredths Freshmen Sophomores Junfors Seniors Total 200 125 St Football Game Dance Total 98 198 500 498 512 Teachers take turns randomly choosing students to participate in the pep assembly games. Students can get selected for multiele suntes a) What is the probability a teacher chooses a sophomore and then another sophomore for the first assembly game? Round to two decimal places
Answer: The probability of choosing a sophomore on the first draw is 125/512. Since the selection is random and without replacement, the probability of choosing another sophomore on the second draw is 124/511. Therefore, the probability of choosing two sophomores in a row is:
(125/512) x (124/511) = 0.0603 or approximately 0.06 (rounded to two decimal places).
Step-by-step explanation:
According to a random sample taken at 12 A.M., body temperatures of healthy adults have a bell-shaped distribution with a mean of 98.33°F and a standard deviation of 0.67°F. Using Chebyshev's theorem, what do we know about the percentage of healthy adults with body temperatures that are within 2 standard deviations of the mean? What are the minimum and maximum possible body temperatures that are within 2 standard deviations of the mean?
Question content area bottom
Part 1
At least enter your response here% of healthy adults have body temperatures within 2 standard deviations of 98.33°F
At least 75% of healthy adults have body temperatures within the range of 96.99°F to 99.67°F.
What is standard deviations?
The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Chebyshev's theorem states that for any distribution (not just the normal distribution), regardless of shape, at least 1 - 1/k^2 of the data values will be within k standard deviations of the mean, where k is any number greater than 1.
In this case, we want to know the percentage of healthy adults with body temperatures that are within 2 standard deviations of the mean. So we need to use Chebyshev's theorem with k = 2.
At least 1 - 1/2^2 = 1 - 1/4 = 0.75, or 75%, of the healthy adults have body temperatures within 2 standard deviations of the mean.
To find the minimum and maximum possible body temperatures that are within 2 standard deviations of the mean, we can use the formula:
Minimum = Mean - k * Standard deviation
Maximum = Mean + k * Standard deviation
Plugging in the values for this problem, we get:
Minimum = 98.33 - 2 * 0.67 = 96.99°F
Maximum = 98.33 + 2 * 0.67 = 99.67°F
Therefore, we can say that at least 75% of healthy adults have body temperatures within the range of 96.99°F to 99.67°F.
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can someone please translate in whatever language u use and do the math task for me me because i am struggling
Answer:
the paper is too blurry i would help if i could.
Step-by-step explanation:
How do you tell a rational number and an irrational number? whats the difference??
Answer:
Rational numbers are those that can be expressed as a ratio of two integers whereas irrational numbers are those which cannot be expressed as a ratio of two integers.
Rational numbers can be written in the form of a fraction whereas irrational numbers cannot be written in the form of fractions.
Rational numbers comprise of those perfect squares whereas irrational numbers comprise of surds.
write an equation in point slope form for a line that passes through(-2,5) and (-1,1)
The equation of line is y = -4x - 3 and the slope is m = -4
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( -2 , 5 )
Let the second point be Q ( -1 , 1 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 1 - 5 ) / ( -1 - ( -2 ) )
On simplifying , we get
Slope m = ( -4 ) / 1
Slope m = -4
Now , the equation of line is y - y₁ = m ( x - x₁ )
y - 5 = -4 ( x - ( -2 ) )
y - 5 = -4 ( x + 2 )
y - 5 = -4x - 8
Adding 5 on both sides , we get
y = -4x - 3
Hence , the equation of line is y = -4x - 3
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Question 4: You are creating an obstacle for a community event. The area of the rectangular space is represented by the expression 8x² - 12x. The width of the rectangular space is represented by the expression 4x.
Part A: Write an expression to represent the length of the rectangular space. Show all work to find the length
Length of Rectangular Space
Part B: Prove your answer from Part A is correct by multiplying the length and width of the rectangle.
Write the expression in standard form:
Answer:
Part A: To find the expression for the length of the rectangular space, we can use the formula for the area of a rectangle, which is length multiplied by width. We have the expression for the area as 8x² - 12x, and the expression for the width as 4x. So, we can write:
Area = Length × Width
8x² - 12x = Length × 4x
Simplifying the right side by multiplying, we get:
8x² - 12x = 4x × Length
2x² - 3x = Length
Therefore, the expression for the length of the rectangular space is 2x² - 3x.
Part B: To prove that the expression for the length from Part A is correct, we can multiply it by the expression for the width and simplify:
Length × Width = (2x² - 3x) × (4x)
= 8x³ - 12x²
= 4x(2x² - 3x)
= 4x(2x(x - 3))
This is in fact the same as the expression for the area of the rectangular space, 8x² - 12x, in standard form.
A sprinkler can water between 1 and 150 square yards of a lawn. The length L in inches of rotating pipe needed to water A square wards is given by the function L = 111.25√A.
Graph the equation on your calculator.
How much area can be watered if the length of the pipe is 400, 700, or 1,100 inches long?
please help me!!
The area that can be watered if the length of the pipe is 400, 700, or 1,100 inches long are:
Where L = 400, A [tex]\approx[/tex] 12.82
Where L = 700 A [tex]\approx[/tex] 44.43
Where L = 1,100 A [tex]\approx[/tex] 86.13
The length of the pipe is given by the function:
L = 111.25√A.
Where a = (L/111.25)²
Thus, for L = 400inches
A = (400/111.24)²
(400/111.24)² = (400²)/(111.24)²
(400²)/(111.24)² = (160000)/(12369.5776)
Divide 160000 by 12369.5776 to get:
(160000)/(12369.5776) = 12.820128200735
Therefore, A = 12.820128200735,
A [tex]\approx[/tex] 12.82
Thus:
Where L = 700;
A = 44.434243
A [tex]\approx[/tex] 44.43
Where L = 1,100
A = 86.129479
A [tex]\approx[/tex] 86.13
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factor by grouping
5u³+15u²-u-3
Answer:
The answer is [tex](u + 3)(5u^{2} - 1)[/tex]
Write an equation in slope-Intercept form for the line with slope -3 and y-Intercept 5. Then graph the line.
Answer: Y=-3X+5
Step-by-step explanation:
Slope intercept form is Y=mx+b where m is slope and b is slope intercept to graph you can use desmos which is a free graphing calculator just punch in the equation exactly as I gave it. since m is slope it is -3 and b is y intercept so 5 so Y=-3x+5
Answer:
y = -3x + 5
Step-by-step explanation:
y = mx + b The m is the slope and the b is the y intercept. Substitute in the slope and the y-intercept
y = -3x + 5
First, graph the y-intercept. That will be at the point (0, 5). From that point, go down 3 units and then go one unit right. You will be back on the line. That is the slope.
Helping in the name of Jesus.
MY LOAN INFORMATION ?
My Annual Borrowing $1,740
Federal Loans
Private Loans
$
$
Totals $
Annual
Borrowing
0
630
Total
Principal
$ 630
$ 0 2.8%
$630
Annual Federal Borrowing Limit
Annual Private Borrowing Limit
My Years of Borrowing
hp
Interest
Rate
6.5%
Loan
Term
10 years $
10 years $
$
$5,500
Limit Varies
1 Years
Payment
Amount
0 per month
5 per month
5 per month
Mar 1
12:27 US
Answer:
I'm sorry, but it is not clear what you are asking for. Can you please provide more information or a specific question?
An art teacher has 8 gallons of paint. Her class uses 3/4 of the paint. The teacher divided the rest of the paint into 4 bottles. How much paint is in each bottle?
In response to the given query, the result we have is Hence, each expressions container contains 1/2 gallon of paint.
what is expression ?Multiplying, dividing, adding, and subtracting are all mathematical operations. As an example, consider the following expression: Expression, mathematics, and a numeric value Numbers, parameters, and functions are the components of an expression in mathematics. Using opposing words and phrases is possible. An expression, sometimes referred to as an algebraic expression, is any mathematical statement that includes variables, numbers, and a mathematical action between them. For instance, the expression 4m + 5 is made up of the expressions 4m and 5, as well as the variable m from the previous equation, all of which are separated by the mathematical symbol +.
The remaining paint would be as follows if the art teacher had 8 gallons and the students had used 3/4 of it:
8 x 1 - 3/4 = 8 x 1/4 = 2 gallons.
The 4 bottles of the remaining 2 gallons of paint each contain the following amounts of paint:
1/2 gallon is equal to 2/4.
Hence, each container contains 1/2 gallon of paint.
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If \( y \) varies directly as \( x \) and inversely as \( z \) and \( y=24 \) when \( x=120 \) and \( z=16 \), then what is the value of \( y \) when \( x=4 \) and \( z=15 \) ?
Y= 3.2
When \( y \) varies directly as \( x \) and inversely as \( z \), the equation is given by:
\( y = \frac{kx}{z} \)
Where \( k \) is a constant.
Substituting the given values of \( x \), \( y \) and \( z \), we get:
\( 24 = \frac{k(120)}{16} \)
Solving for \( k \):
\( k = \frac{24*16}{120} = 4.8 \)
Substituting the values of \( k \), \( x \) and \( z \) into the equation, we get:
\( y = \frac{(4.8)*4}{15} \)
Therefore, the value of \( y \) when \( x=4 \) and \( z=15 \) is \( 3.2 \).
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I need this by friday
The value of x for the given pentagon will be 125 degrees.
What is a polygon?In Mathematics, a polygon can be defined as a two-dimensional geometric figure that consists of straight line segments and a finite number of sides. Additionally, some examples of a polygon include the following:
• Triangle
• Quadrilateral
• Pentagon
• Hexagon
• Heptagon
• Octagon
• Nonagon
Given the values exterior angles of the pentagon such that, 70°, 60°, 65°, 40°, x°.
To calculate the value of x.
Since the Sum of all exterior angles of a pentagon is 360°,
Thus,
70 + 60 + 65 + 40 +x = 360
x + 235 = 360
x = 360 - 235
x = 125°
Therefore, the value of x for the given pentagon will be 125 degrees.
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The two legs of a right triangle are 11 inches and 24 inches.
Find the hypotenuse of the triangle
To find the hypotenuse of a right triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. The formula for the Pythagorean theorem is:
c^2 = a^2 + b^2
Where c is the hypotenuse, and a and b are the other two sides of the triangle.
In this case, we are given the lengths of the two legs of the triangle, 11 inches and 24 inches.
We can plug these values into the formula and solve for the hypotenuse:
c^2 = 11^2 + 24^2
c^2 = 121 + 576
c^2 = 697
c = √697
c ≈ 26.4 inches
Therefore, the hypotenuse of the triangle is approximately 26.4 inches.
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Mrs. Beck buys 48 pieces of house siding. Each piece is 3.7 meters long.
Part A
Which equation represents the best estimate for the total length of siding Mrs. Beck buys?
The equation which represents the total length of the siding is given by A , where A = 50 x 4 = 200 meters
What do you mean by an Equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.
It displays the similarity of the connections between the phrases on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.
Given data ,
Let the total length of the siding be represented as A
Now , the value of A is
Let the number of pieces be n = 48 pieces
Let the length of each piece be l = 3.7 meters
Now , total length of the siding A = number of pieces x length of each piece
On simplifying the equations , we get
The total length of siding A = 48 x 3.7 = 177.6 meters
Now , n ≈ 50 pieces
l ≈ 4 meters
So , total length of siding A = 50 x 4 = 200 meters
Hence , the equation is A = 50 x 4 = 200 meters
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5.24. Exercise. Make a ruler-and-compass construction of the lines tan- gent to a given circle that pass thru a given point.
Precise and accurate in your construction, using the ruler and compass correctly to create the desired lines.
To make a ruler-and-compass construction of the lines tangent to a given circle that pass through a given point, follow these steps:
1. Draw the given circle using a compass.
2. Mark the given point on the paper with a pencil.
3. Place the point of the compass at the given point and extend the compass until it touches the edge of the circle.
4. Draw a circle with the compass. This circle will intersect the given circle at two points.
5. Use a ruler to draw a line from the given point to each of the intersection points. These lines are the tangent lines to the given circle that pass through the given point.
6. Label the tangent lines and the given point for clarity.
By following these steps, you can create a ruler-and-compass construction of the lines tangent to a given circle that pass through a given point. Remember to be precise and accurate in your construction, using the ruler and compass correctly to create the desired lines.
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Find m∠RTS. PLS HELP IN THE MIDDLE OF A TEST
REVIEW
At a grocery store, Ethan buys 4 bananas and 5 oranges for $5.60. The total cost of one banana and one orange is $1.20.
How much does each orange cost?
Answer:
The answer to your problem is, $0.60
Step-by-step explanation:
1 banana and 1 orange = 1.20.
We divide next:
1.20 / 2 = 0.60.
We know that because in the question it says one banana and one orange is 1.20. Next we divide because two items are sharing the same number.
1.20 / 2 = ? ( ? = 0.60 or 0.6 )
Thus the answer to our problem is, $0.60