Each side of the square would be approximately 9.3 units long.
To predict the side length of the square when the area is 86.6 units, we need to use the model that Sam created. Sam likely developed a mathematical relationship between the area (x) and the length of one side of the square (f(x)). This relationship is typically expressed as a function, such as [tex]\( f(x) = \sqrt{x} \),\\[/tex] where [tex]\( x \)[/tex] represents the area and [tex]\( f(x) \)[/tex]represents the length of one side of the square.
In this model, the side length of the square is equal to the square root of the area. Therefore, to predict the side length when the area is 86.6 units, we substitute this value into the function:
[tex]\[ f(86.6) = \sqrt{86.6} \][/tex]
Now, we can calculate this:
[tex]\[ f(86.6) \approx \sqrt{86.6} \approx 9.3 \][/tex]
So, according to Sam's model, when the area is 86.6 units, the length of one side of the square is approximately 9.3 units. This means that if you were to draw a square with an area of 86.6 units, each side of the square would be approximately 9.3 units long.
With the function [tex](f(x) = \sqrt{x - 5} + 3\),[/tex] the predicted side length for an area of 86 is calculated by evaluating f(86).
This results in a side length of 12 units.
Therefore option b. 12 units is correct.
To find the predicted side length of a square when given the area, let's use the function provided by Sam:
[tex]\[f(x) = \sqrt{x - 5} + 3.\][/tex]
Here, x represents the area, and f(x) represents the predicted side length of the square.
Find f(x) for (x = 86):
1. Plug in[tex]\(x = 86\):[/tex]
[tex]\[f(86) = \sqrt{86 - 5} + 3 = \sqrt{81} + 3 = 9 + 3 = 12.\][/tex]
The predicted side length when the area is 86 is 12.
Given the function[tex]\(f(x) = \sqrt{x - 5} + 3\),[/tex] the predicted side length when [tex]\(x = 86\)[/tex] is option b. 12 units.
Question : After plotting the data where x=area, and f(x)=the length of one side of the square, Sam determined the model to approximate the side of a square was f(x)= *square root sign* x-5+3 Use the model Sam created to predict the side length of the square when the area is 86.
a. 6
b. 12
c. 81
d. 144
Which sequence is modeled by the graph below?
coordinate plane showing the points 2, 9; 3, 3; and 4, 1
A) an = one third(27)n − 1
B) an = 27(one third)n − 1
C) an = 1(−3)n − 1
D) an = 3(one half)n − 1
Answer:
an=27(one third) - 1
thanks
The correct answer is:
Option: B
[tex]B.\ a_n=27(\dfrac{1}{3})^{n-1}[/tex]
Step-by-step explanation:We are given that the graph passes through (2,9) , (3,3) and (4,1)
Now, the function which models the graph is given by:
[tex]a_n=27(\dfrac{1}{3})^{n-1}[/tex]
when n=2 we have:
[tex]a_2=27(\dfrac{1}{3})^{2-1}\\\\i.e.\\\\a_2=27(\dfrac{1}{3})^1\\\\i.e.\\\\a_2=9[/tex]
when n=3 we have:
[tex]a_3=27(\dfrac{1}{3})^{3-1}\\\\i.e.\\\\a_3=27(\dfrac{1}{3})^2\\\\i.e.\\\\a_3=3[/tex]
when n=4 we have:
[tex]a_3=27(\dfrac{1}{3})^{4-1}\\\\i.e.\\\\a_3=27(\dfrac{1}{3})^3\\\\i.e.\\\\a_4=1[/tex]
PLEASE HELP ME!! D:
Use the graph of the line to answer the questions.
What is an equation of the line in point-slope form?
How can the point-slope form be written in function notation?
Answer:
Point-slope form:
[tex]y-0=\frac{1}{3} (x-1)\\f(x)-0=\frac{1}{3}(x-1)[/tex]
Slope-intercept form:
[tex]y=\frac{1}{3}x-\frac{1}{3} \\f(x)=\frac{1}{3} x-\frac{1}{3}[/tex]
Step-by-step explanation:
You have points on that line at (-2, -1) and (1, 0). To find your slope using those points, use the slope formula.
[tex]\frac{y2-y1}{x2-x1} \\\\\frac{0-(-1)}{1-(-2)} \\\\\frac{0+1}{1+2} \\\\\frac{1}{3}[/tex]
Now that we have your slope, you can use your slope and one of your points to write an equation in point-slope form.
[tex]y-y1=m(x-x1)\\y-0=\frac{1}{3} (x-1)\\y=\frac{1}{3} x-\frac{1}{3}[/tex]
To put it in function notation, substitute y for f(x).
[tex]f(x)-0=\frac{1}{3} (x-1)\\f(x)=\frac{1}{3} x-\frac{1}{3}[/tex]
First answer is y+1=(1/3) (x+2)
Second answer is f(x) =(1/3) x-(1/3)
Which type of transformation of the parent function is shown by the graph
Answer:
horizontal stretch
Step-by-step explanation:
yeye
Parent functions are the simplest form of a given function. Parent function have x as the term with the highest degree and a general form,
[tex]Y=ax+b[/tex]
Transformation of the function takes basic and changes it slightly with predetermined methods. This change will cause the graph of the function to be shifted or moved from the original position.
Given-
We have given the graphs and we have to identify the transformation of the parent function which is shown in the graph. For this we have an idea about the parent function and transformation of the function.
What is parent function?Parent functions are the simplest form of a given function. Parent function have x as the term with the highest degree and a general form,
[tex]Y=ax+b[/tex]
TransformationTransformation of the function takes basic and changes it slightly with predetermined methods. This change will cause the graph of the function to be shifted or moved from the original position.
Transformation of function is of different types.
Horizontal stretch, when graph is shifted towards right or left it is called the horizontal stretch transformation of the function. Vertical stretch, when graph is shifted towards up or down it is called the horizontal stretch transformation of the function.In the given graph the graph is shifted right and hence the transformation of the parent function is horizontal stretch.
Learn more about the transformation of the function here;
https://brainly.com/question/4135838
What is the slope of the line passing through the points (2,-5) and(4,1)
[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-5)}{4-2}\implies \cfrac{1+5}{2}\implies \cfrac{6}{2}\implies 3[/tex]
The area of rectangle ABCD is 72 square inches. A diagonal of rectangle ABCD is 12 inches and the diagonal of rectangle EFGH is 22 inches. Find the area of rectangle EFGH. Round to the nearest square inch if necessary.
Answer:
The area of rectangle EFGH is [tex]242\ in^{2}[/tex]
Step-by-step explanation:
For this problem I assume that rectangle ABCD and rectangle EFGH are similar
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor
Let
z ------> the scale factor
The scale factor is the ratio between the diagonals of rectangles
so
[tex]z=\frac{22}{12}=\frac{11}{6}[/tex]
step 2
Find the area of rectangle EFGH
we know that
If two figures are similar, then the ratio of its areas is the scale factor squared
Let
z------> the scale factor
x -----> area of rectangle EFGH
y ----> area of rectangle ABCD
so
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]z=\frac{11}{6}[/tex]
[tex]y=72\ in^{2}[/tex]
substitute and solve for x
[tex](\frac{11}{6})^{2}=\frac{x}{72}[/tex]
[tex]\frac{121}{36}=\frac{x}{72}[/tex]
[tex]x=\frac{121}{36}(72)[/tex]
[tex]x=242\ in^{2}[/tex]
The area of rectangle EFGH is approximately 242 square inches.
To find the area of rectangle EFGH given the diagonal lengths of both rectangles and the area of rectangle ABCD, we need to use the properties of rectangles and their diagonals.
Step 1: Analyze Rectangle ABCD
For rectangle ABCD:
- Area [tex]\(A_{ABCD} = 72\)[/tex] square inches
- Diagonal [tex]\(d_{ABCD} = 12\)[/tex] inches
We know the area of a rectangle is given by:
[tex]\[ \text{Area} = \text{length} \times \text{width} \][/tex]
Let the length be l and the width be w. So,
[tex]\[ l \times w = 72 \][/tex]
Also, for the diagonal of a rectangle, we use the Pythagorean theorem:
[tex]\[ d = \sqrt{l^2 + w^2} \]\\Given \(d_{ABCD} = 12\),\[ 12 = \sqrt{l^2 + w^2} \]\[ 144 = l^2 + w^2 \][/tex]
Step 2: Solve for l and w
We have two equations:
[tex]1. \( l \times w = 72 \)\\2. \( l^2 + w^2 = 144 \)[/tex]
We can solve these equations simultaneously. First, express \(w\) in terms of \(l\):
[tex]\[ w = \frac{72}{l} \]\\Substitute this into the second equation:\[ l^2 + \left(\frac{72}{l}\right)^2 = 144 \]\[ l^2 + \frac{5184}{l^2} = 144 \][/tex]
Multiply every term by [tex]\(l^2\)[/tex] to clear the fraction:
[tex]\[ l^4 + 5184 = 144l^2 \]\[ l^4 - 144l^2 + 5184 = 0 \]Let \(x = l^2\). Then the equation becomes:\[ x^2 - 144x + 5184 = 0 \][/tex]
Solve this quadratic equation using the quadratic formula:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]\[ x = \frac{144 \pm \sqrt{144^2 - 4 \cdot 1 \cdot 5184}}{2 \cdot 1} \]\[ x = \frac{144 \pm \sqrt{20736 - 20736}}{2} \]\[ x = \frac{144 \pm 0}{2} \]\[ x = 72 \][/tex]
So, [tex]\( l^2 = 72 \) and \( w^2 = 72 \)[/tex]. Therefore:
[tex]\[ l = \sqrt{72} = 6\sqrt{2} \]\[ w = \sqrt{72} = 6\sqrt{2} \][/tex]
Step 3: Analyze Rectangle EFGH
For rectangle EFGH:
- Diagonal [tex]\(d_{EFGH} = 22\)[/tex] inches
Let the length be L and the width be W. The relationship for the diagonal is:
[tex]\[ d_{EFGH} = \sqrt{L^2 + W^2} \]Given \(d_{EFGH} = 22\),\[ 22 = \sqrt{L^2 + W^2} \]\[ 484 = L^2 + W^2 \][/tex]
Step 4: Determine Area of Rectangle EFGH
Since the diagonals scale, we assume the rectangles are similar. Thus, the ratios of the corresponding sides (lengths and widths) are the same, and their areas scale with the square of the ratio of the diagonals:
[tex]\[ \text{Area ratio} = \left(\frac{d_{EFGH}}{d_{ABCD}}\right)^2 = \left(\frac{22}{12}\right)^2 = \left(\frac{11}{6}\right)^2 = \frac{121}{36} \][/tex]
So, the area of EFGH is:
[tex]\[ A_{EFGH} = A_{ABCD} \times \frac{121}{36} = 72 \times \frac{121}{36} = 72 \times 3.3611 \approx 242 \text{ square inches} \][/tex]
Thus, the area of rectangle EFGH is approximately 242 square inches.
Select the correct answer from each drop-down menu.
Point A is the center of this circle.
The ratio of the lengths of ____ and ____ is 2:1
First Choices : ( EF, BC )
Second Choice ( AD, IH )
The ratio of the lengths of EF and BC is 2:1. The correct answer is (EF, BC), where the length of EF is twice the length of BC.
The ratio of the lengths of two segments is given as 2:1. We can set up a proportion and find that the length of one segment is twice the length of the other.
In this question, the ratio of the lengths of two segments is given as 2:1. We are asked to find the lengths of the two segments, which are represented by two choices: (EF, BC) and (AD, IH). To solve this problem, we can set up a proportion. Let's assume that EF and BC represent the lengths of the segments, and we can write the proportion as:
[tex]\frac {EF}{BC} =\frac {2}{1}[/tex]
To solve for the lengths, we can cross multiply:
[tex]EF \times 1 = BC \times 2[/tex]
[tex]EF = 2 \times BC[/tex]
So, the length of EF is twice the length of BC. Therefore, the correct answer is (EF, BC), where the length of EF is twice the length of BC.
Final answer:
The student's question deals with the concept of ratios and similar triangles in High School level Mathematics. Without additional context to the specific figures and points mentioned, a precise answer cannot be given. Typically, in similar triangles, corresponding side lengths are proportional, allowing calculation of unknown lengths when a ratio is provided.
Explanation:
The question refers to finding a ratio of lengths related to geometrical figures. Since ratios and proportions frequently deal with lengths and geometry, and the provided examples reference triangles, circles, and other geometric shapes, this question is most closely related to the subject of Mathematics. The use of similar triangles to find unknown lengths is a typical high school-level geometry problem.
Based on the information given in the question, it seems we are required to use the property that states the ratios of corresponding sides of similar triangles are equal. To answer the student's question specifically, we'd need more context to the figures in question, such as circle C with center F and point F', or the configuration of the triangles abc and a'b'c'.
For instance, if we have two similar triangles, with corresponding side lengths in a ratio of 2:1, this means that if one triangle has a side length of 'x', the similar triangle's corresponding side length would be '2x'. To answer the student's query correctly, however, additional information on which particular sides of the named points are being inquired about is necessary.
Chris will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $65 and costs an additional $0.80 per mile driven. The second plan has no initial fee but costs $0.90per mile driven. How many miles would Chris need to drive for the two plans to cost the same?
Chris would need to drive 650 miles for the two plans to cost the same.
Further Explanation:
Let d = distance traveled in miles
Plan 1 will have an initial fee of $65 and a cost of $0.80 per mile driven. Therefore, the total cost to drive a distance of d will be:
total cost = $65 + ($ 0.80 × d)
Plan 2 will have no initial fee but has a cost of $0.90 per mile drive. The total cost, then, to drive a distance of d will be:
total cost = $0.90 × d
If the two costs are the same, then:
$65 + ($ 0.80 × d) = $0.90 × d
The distance driven, d, can then be solved algebraically.
Combining like terms:
$65 = $0.90d - $0.80d
$65 = $0.10d
Solving for d:
d = $65/$0.10
d = 650 miles
To check the answer, solve for the total cost of Plan 1 and Plan 2 and see if they are equal.
Plan 1:
total cost = $65 + ($0.80 x 650)
total cost = $65 + $520
total cost = $585
Plan 2:
total cost = $0.90 x 650
total cost = $585
Since both plans cost the same, then the distance 650 mi is correct.
Learn More
Learn more about word problems https://brainly.com/question/12980258Learn more about distance https://brainly.com/question/12971902Learn more about speed https://brainly.com/question/2720926Keywords: word problem, total cost
A special variety of wallpaper covers only 60 square feet per roll. How many single rolls are needed to paper a room measuring 19' by 12' by 8'6"? Show all work.
Answer:
9 rolls
Step-by-step explanation:
The perimeter of the room measures 2(19' +12') = 62', so the area of the walls is ...
(62 ft)(8.5 ft) = 527 ft²
We know that 8 rolls will cover 8×60 ft² = 480 ft², and 9 rolls will cover 540 ft², so we will need 9 rolls to cover the walls.
If f(x) = -7x + 1 and g(x) = Square root of x-5,
what is (fºg)(41)?
This is similar to the other question you posted. Follow the same steps as before.
First find g(41).
g(41) = sqrt{x - 5}
g(41) = sqrt{41 - 5}
g(41) = sqrt{36}
g(41) = 6
We now find f(6).
f(6) = -7(6) + 1
f(6) = -42 + 1
f(6) = -41
Answer:
(fºg)(41) = -41
Did you follow?
There are 527 pencils,646 erasers and 748 sharpeners. These are to be put in separate packets containing the same number of items.find the maximum number of items possible in each packet.
Answer:
31 pencils38 erasers44 sharpenersStep-by-step explanation:
The number of packets is the greatest common divisor of the given numbers of pencils, erasers, and sharpeners.
It can be helpful to look at the differences between these numbers:
748 -646 = 102
646 -527 = 119
The difference of these differences is 17, suggesting that will be the number of packets possible.
527 = 17 × 31
646 = 17 × 38
748 = 17 × 44
The numbers 31, 38, and 44 are relatively prime (31 is actually prime), so there can be no greater number of packets than 17.
There will be 31 pencils, 38 erasers, and 44 sharpeners in each of the 17 packets.
_____
We may have worked the wrong problem. The way it is worded, the maximum number of items in each packet will be 527 pencils, 646 erasers, and 748 sharpeners in one (1) packet. The minimum number of items in each packet will be the number that corresponds to the maximum number of packets. Since 17 is the maximum number of packets, each packet's contents are as described above.
17 is the only common factor of the given numbers, so will be the number of groups (plural) into which the items can be arranged.
Which statements about the diagram are true? Select three options.
x = 63
y = 47
z = 117
x + y = 180
x + z = 180
Answer:
x = 63z = 117x + z = 180Step-by-step explanation:
x is a "corresponding" angle for the one marked 63°. Here, corresponding angles are congruent, so x = 63°.
__
x and z are "same-side interior angles," so are supplementary. Their sum is 180°. x + z = 180°.
__
Because x and z are supplementary and z and 63° are supplementary, you know that ...
z = 180° -63°
z = 117°
_____
Comments on the other answer choices
The value of y can be computed using the fact that the sum of angles interior to the triangle is 180°. The unmarked triangle interior angle is a vertical angle to the one labeled 63°, so it is 63°. Then the value of y is ...
y° = 180° -47° -63° = 70° . . . . . . . not 47°
__
We already know that 63° + y + 47° = 180° and x = 63°. That means ...
x + y + 47° = 180°
so it cannot be true that x+y = 180.
Answers are 1,3, and 5
Please help with this question
Answer:
15/17
Step-by-step explanation:
You can use what is called the Pythagorean identity:
sin(θ)² + cos(θ)² = 1
(-8/17)² + cos(θ)² = 1
cos(θ)² = 1 - 64/289 = 225/289
cos(θ) = √(225/289)
cos(θ) = 15/17 . . . . . . . cosine is positive in the 4th quadrant
A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of each should he use?
Answer:
3lbs of Cashews
Step-by-step explanation:
lbs of Cashews, and 7 lbs of Peanuts
$4.00P + 6.50C = ($4.75/lbs)(10lbs)
$4.00(7) + $6.50(3) = $47.50
$28.00 + $19.50 = $47.50
$47.50 = $47.50
Therefore it's 3lbs of Cashews
Answer:
3lbs of Cashews
hope it helps! x
Find the dimensions and the perimeter of side AEHD.Select all the correct answers. A rectangular prism is 7 centimeters long, 5 centimeters wide, and 4 centimeters tall. Which values are the areas of cross sections that are parallel to a face (or base) of the prism?
Answer:
Step-by-step explanation:
2 x w x l + 2 x l x h + 2 x h x w
* is times 2*5*7+2*7*4+2*4*5 =
= 70+56+40=166 cm
Hope it helps
An employee who earned $550 a week working 35 hours had her pay increased by 5 percent. Later, her hours were reduced to 30 per week, but the new hourly rate of pay was retained. What was her new amount of weekly pay?
Answer:
$495
Step-by-step explanation:
After the 5% raise, her weekly pay was ...
$550 × 1.05 = $577.50
If she works 35 hours for that pay, her hourly rate is
$577.50/35 = $16.50
Then, working 30 hours, her weekly pay will be ...
30 × $16.50 = $495.00
To find the new amount of weekly pay, multiply the increase in pay by the new number of hours. The new amount is $577.50.
Explanation:To find the new amount of weekly pay, we need to calculate the increase in pay and then multiply it by the new number of hours.
The employee's pay increased by 5 percent. This means the pay increased by 5% of $550, which is equal to 0.05 imes 550 = $27.50.
Her new hourly rate of pay is the same, so it remains at $550 + $27.50 = $577.50.
Finally, we need to calculate the new amount of weekly pay, taking into account the reduced number of hours. The new pay per hour is $577.50 / 30 = $19.25. Multiply this by the new number of hours to get the new amount of weekly pay: $19.25 imes 30 = $577.50.
i rlly h8 math so pwease help me asap!!!! i'll give u brainliest if ur correct!
Answer:
see below
Step-by-step explanation:
sqrt(2) * sqrt(2) = sqrt(4) = 2
sqrt(5) * sqrt(7) = sqrt(35)
sqrt(2) * sqrt(18) = sqrt(36) = 6
sqrt(2)*sqrt (6) = sqrt(12) = sqrt(4 *3) = sqrt(4) sqrt(3) = 2 sqrt(3)
4/3 * 12/3 = 48/9 This is rational because it is written as a fraction with no square roots
32/4 * 15/4 = 480/16 =30 This can be rewritten as 30/1. This is rational because it is written as a fraction with no square roots
sqrt(3)/2 * 22/7 = 11 sqrt(3)/7 This is not rational because there is a square root in the numerator
sqrt(11) *2/3 = 2sqrt(11)/3 This is not rational because there is a square root in the numerator
Find the equation of the line passing through 2,11
Answer:
Step-by-step explanation:
There is an infinite number of lines that pass through the point (2, 11). Therefore, there is an infinite number of equations. To define a single line, you must have at least two points. One point is not enough.
Find the value of Y [Inscribed Angle]
Check the picture below.
Answer:
x = 60°
Step-by-step explanation:
From ΔOPQ,
∠OPQ = 120° [ angle at the center inscribed by arc PQ ]
PQ ≅ OQ
so opposite angles to PQ and OQ will be equal
∠OPQ ≅ ∠OQP
∠OPQ + ∠OQP + ∠POQ = 180°
∠OPQ + ∠OPQ + 120 = 180°
2∠OPQ = 180 - 120 = 60°
∠OPQ = 30°
Since radius OP is perpendicular to tangent.
so ∠OPQ + Y = 90°
y + 30° = 90°
y = 90 - 30 = 60°
Answer x = 60°
Select the correct answers in the table.
Answer:
see below
Step-by-step explanation:
To find miles per hour, divide miles by hours:
(5 2/3 mi)/(2 2/3 h) = (17/3 mi)/(8/3 h) = (17/8) mi/h = 2 1/8 mi/h
Hours per mile is the reciprocal of that:
1/(17/8 mi/h) = 8/17 h/mi
Washing his dad's car alone, eight-year-old Levi takes 2.5 hours. If his dad helps him, then it takes 1 hour. How long does it take Levi's dad to wash the car by himself
Answer:
1 hour and 40 minutes
Step-by-step explanation:
Levi's dad takes time to wash the car by himself is 1.667 hours which is 1 hour and 40 minutes.
What are ratio and proportion?A ratio is an ordered couple of numbers a and b, written as a/b where b can not equal 0. A proportion is an equation in which two ratios are set equal to each other.
Washing his dad's car alone, eight-year-old Levi takes 2.5 hours. If his dad helps him, then it takes 1 hour.
Levi's dad take time to wash the car by himself will be
We know that the time is inversely proportional to the work.
Let t₁ is the time taken by Levi and t₂ is the time taken by Levi's dad.
We know that the formula
[tex]\begin{aligned} \dfrac{1}{t_1} + \dfrac{1}{t_2} &= 1\\\\\dfrac{1}{2.5} +\dfrac{1}{t_2} &= 1\\\\\dfrac{1}{t_2} &= 1 - \dfrac{1}{2.5}\\\\\dfrac{1}{t_2} &= \dfrac{3}{5}\\\\t_2 &= \dfrac{5}{3}\\\\t_2 &= 1.667 \end{aligned}[/tex]
Levi's dad takes time to wash the car by himself is 1.667 hours which is 1 hour and 40 minutes.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
Rewrite the equation for x, and express its value in terms of a.
3/a x-4=20
Answer:
x=8a
Step-by-step explanation:
3/a x-4=20
We need to solve for x
Add 4 to each side
3/a x-4+4=20+4
3/a x = 24
Multiply each side by a/3 so we can get x alone
a/3 *3/a x = 24 * a/3
x = 8a
Answer:
x=8a
Step-by-step explanation:
We have to solve for x.
Steps:Add 4 to each side
Multiply each side by a/3 so we can get x
CAN SOMEONE HELP ME WITH THIS MATH QUESTION
Answer:
see explanation
Step-by-step explanation:
Consider the reflection in the y- axis
A point (x, y ) → (- x, y )
Consider the reflection of point A
A(- 5, 2 ) → A'(5, 2 )
Now A → E after the transformations
E = (4, 3 ), thus
A'(5, 2 ) → E(4, 3 )
(x, y ) → (x + (- 1), y + 1 ) = (x - 1, y + 1 )
I would like some help with this question plz
Answer:
Step-by-step explanation:
As the value of a increases, the radical function sweeps out higher, increasing the range of the function. The k value moves it up or down. A "+k" moves up (for example, +3 moves the function up 3 from the origin). The h value moves it side to side. A positive h value moves to the right and a negative h value moves to the left. For example, √x-3 moves 3 to the right and √x+3 moves 3 to the left.
In summary, a and k affect the range of the function, k being the "starting point" and a being the "ending point"; h affects the domain of the function.
Jason considered two similar televisions at a local electronics store. The generic version was based on the brand name and was 35 the size of the brand name. If the generic television set is 16 inches by 40 inches, what are the dimensions of the brand name television?
List the dimensions of the brand name television.
Show your work.
Answer:
The dimensions of the brand name television are [tex]26\frac{2}{3}\ in[/tex] by [tex]66\frac{2}{3}\ in[/tex]
Step-by-step explanation:
we know that
The generic version was based on the brand name and was 3/5 the size of the brand name
Let
x----> the length of the size of the brand name
y----> the width of the size of the brand name
Find the length of the size of the brand name
we know that
[tex]40=\frac{3}{5}x[/tex] -----> equation A
Solve for x
Multiply by 5 both sides
[tex]5*40=3x[/tex]
Rewrite and divide by 3 both sides
[tex]x=200/3\ in[/tex]
Convert to mixed number
[tex]200/3=(198/3)+(2/3)=66\frac{2}{3}\ in[/tex]
Find the width of the size of the brand name
we know that
[tex]16=\frac{3}{5}y[/tex] -----> equation B
Solve for y
Multiply by 5 both sides
[tex]5*16=3y[/tex]
Rewrite and divide by 3 both sides
[tex]x=80/3\ in[/tex]
Convert to mixed number
[tex]80/3=(78/3)+(2/3)=26\frac{2}{3}\ in[/tex]
(WILL MARK BRAINIEST PLEASE ASSIST) Define the inverse secant function by restricting the domain of the secant function to the intervals: 0,π2 and π2,π and sketch the inverse function’s graph.
Answer:
see the attachment
Step-by-step explanation:
The graph attached shows the secant function in red. The restriction to the interval [0, π/2] is highlighted by green dots, and the corresponding inverse function is shown by a green curve.
The restriction to the interval [π/2, π] is highlighted by purple dots, and the corresponding inverse function is shown in purple.
The dashed orange line at y=x is the line over which a function and its inverse are mirror images of each other.
In the circle , mBC =38 and mAD =146
What is m
Answer:
m<AED = 92°
Step-by-step explanation:
It is given that,
measure of arc BC = 38° therefore m<BDC = 38/2 = 19°
measure of arc AD = 146° therefore m<ACD = 146/2 = 73°
To find the measure of <CED
Consider the ΔCDE
m<D = m<BDC = 19° and
m<C = m<ACD = 73°
By using angle sum property m<CED can be written as,
m<CED = 180 -( m<D + m<C )
= 180 - (19 + 73)
= 180 - 92
= 88°
To find the measure of <AED
<AED and <CED are linear pair
m<AED + m<CED = 180
m<AED = 180 - m<CED
= 180 - 88
= 92°
Therefore m<AED = 92°
Scott had an average of 83 on his first three exams. He later scored an average of 92 on the next six exams. What is his average for all nine exams. Round to the nearest tenth if necessary.
Answer:89
Step-by-step explanation:
Given scott had an average of 83 on his first three exams
i.e. the sum of first three exams [tex]\sum S_1=83\times 3[/tex]
later he scored an average on the next six exams
i.e. the sum of later 6 exams is [tex]\sum S_2=92\times 6[/tex]
[tex]\sum S_1+\sum S_2=83\times 3+92\times 6=801[/tex]
therefore his average score is =[tex]\frac{801}{9}=89[/tex]
Thus his average score is 89
To find Scott's average for all nine exams, add up the scores from the first three and next six exams, then divide by the total number of exams.
Explanation:To find Scott's average for all nine exams, we need to calculate the overall average using the given averages for the first three and next six exams.
The average of the first three exams is 83, and the average of the next six exams is 92. To find the average for all nine exams, we can use the formula:Total sum of scores / Number of exams
So, Scott's average for all nine exams is:(83*3 + 92*6) / 9 = 89.1111...
Rounding to the nearest tenth, Scott's average for all nine exams is 89.1.
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In the system below, use equation (1) with equation (2) to eliminate x. Then use equation (1) with equation (3) to eliminate x. x-y-2z=4 (1) -x+3y-z=8 (2) -2x-y-4z=-1 (3) What is the new 2 × 2 system?
Answer:
2y -3z = 12-3y -8z = 7Step-by-step explanation:
(1) +(2) ⇒ (x -y -2z) +(-x +3y -z) = (4) +(8)
2y -3z = 12
__
2(1) +(3) ⇒ 2(x -y -2z) +(-2x -y -4z) = 2(4) +(-1)
-3y -8z = 7
___
The reduced system of equations is ...
2y -3z = 12-3y -8z = 7Answer:
2y - 3z = 12.
-3y - 8z = 7.
Step-by-step explanation:
x - y - 2z = 4 (1)
-x + 3y - z = 8 (2)
-2x - y - 4z = -1 (3)
Adding (1) + (2):
2y - 3z = 12.
2 * (1) + (3) gives:
-3y - 8z = 7.
NEED HELP WITH MATH QUESTION ITS ABOUT FINDING AREA OF A TRIANGLE !! I WOULD BE REALLY GRATEFUL IS SOMEONE HELPED ME WITH A FEW QUESTIONS AFTER THIS
Answer:
65.8 in²
Step-by-step explanation:
Given a triangle with 2 sides and the included angle then the area (A) is
A = 0.5 × a × b × sinΘ
where a, b are the 2 sides and Θ the included angle
here a = 18, b = 12 and Θ = 147°, hence
A = 0. 5 × 18 × 12 × sin147°
= 108 × sin147° ≈ 65.8 ( to the nearest tenth )
Answer:
The area of triangle is 59.2 in².
Step-by-step explanation:
If a, b and c are three sides of a triangle then the area of triangle by heron's formula is
[tex]A=\sqrt{s(s-a)(s-b)(s-c)[/tex] .... (1)
where,
[tex]s=\frac{a+b+c}{2}[/tex]
From the given figure it is clear that the length of sides are 12 in, 18 in and 28.8 in. The value of s is
[tex]s=\frac{12+18+28.8}{2}=29.4[/tex]
Substitute s=29.4, a=12, b=18 and c=28.8 in equation (1).
[tex]A=\sqrt{29.4(29.4-12)(29.4-18)(29.4-28.8)}[/tex]
[tex]A=\sqrt{3499.0704}[/tex]
[tex]A=59.15294[/tex]
[tex]A\approx 59.2[/tex]
Therefore the area of triangle is 59.2 in².
HELLPPPPP!!!!
Which two of the functions shown here have identical graphs and why?
Answer:
Answer C
Step-by-step explanation:
Logs work that way. When you subtract one log from another, you can rewrite it as a fraction.
f and h, because the log of a quotient is the difference of the log.
The answer is option C.
Logs work that way. When you subtract one log from another, you can rewrite it as a fraction.
What do logs mean?A logarithm is a power to which a range of should be raised for you to get a few different wide varieties (see segment 3 of this Math evaluate for extra approximately exponents). As an example, the bottom ten logarithms of a hundred is two because ten raised to the electricity of is one hundred: log a hundred = 2.
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