Which of the following equations of y = sin x has been transformed by a vertical shift down 3 units and stretch factor of 2?
A. y = sin 20
B. y = 2 sin +3
C. y = -2sin 8 - 3
D. y = 3 sin 0 - 2
E. y = 2sin 0-3

Answer:

a. Translated down  5 units.

b.  Translated 1 to the left.

c.  Stretched vertically  by a factor 2.

Step-by-step explanation:

a. It is translated down by 2 - (-3) = 5 units.

b. The x in f(x) is replaced by (x + 1) to gives g(x).

It is translated left by 1 unit.

c.  The 2 stretches it vertically by a factor of 2.

Using translation concepts, it is found that the correct options are given by:

a) it is translated down 5 units.

b) it is translated left 1 unit.

c) it is stretched vertically by a factor of 2.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem:

More can be learned about translation concepts at https://brainly.com/question/4521517

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I would use the centimeter to measure the height of a bird.

I’m assuming centimeters because km is like miles and mm is for something else not for height

Answer:

Option A. [tex]b=20.8\ units[/tex]

Step-by-step explanation:

we know that

Applying the law of sines

[tex]\frac{a}{sin(A)}=\frac{b}{sin(B)}[/tex]

substitute the values and solve for b

[tex]\frac{10.73}{sin(25\°)}=\frac{b}{sin(55\°)}\\ \\ b=10.73*sin(55\°)/sin(25\°)\\ \\b=20.8\ units[/tex]

Answer:

    20.8          option A  

Step-by-step explanation:

sine law for triangle states that

sin A / a  = sin B / b = sin C / c   ( equation for sine law )

where m A = 25°

           m B = 55°

a = 10.73

b = unknown

from the equation for sine law

sin m A / a = sin m B / b

sin 25° / 10.73 = sin 55° / b

0.4226 / 10.73 = 0.8191 / b

0.0394 = 0.8191 / b  equation 2

cross multiply equation 2 becomes

0.0394 b = 0.8191

therefore b = 0.8191 / 0.0394 = 20.789 to the nearest tenth will be 20.8

All you have to do is divide 9/50, which equals 0.18 Move the decimal 2 units to the right to get 18% as your answer

Hope this helps you!

The 9 is 18% percent of 50.

Given that,

Based on the above information, the calculation is as follows:

[tex]= 18\div 100\\\\= 9\div 50[/tex]

So here we can conclude that The 9 is 18% percent of 50.

Learn more: brainly.com/question/6201432

Answer:

60°

68°

76°

193°

Step-by-step explanation:

step 1

Calculate the sum of the interior angles in a pentagon

The formula to calculate the sum of the interior angles is equal to

S=(n-2)180°

where

n is the number of sides

In this problem

n=5 sides

substitute

S=(5-2)180°=540°

step 2

Find the value of x

(x-8)+(3x-11)+(x+8)+(x+(2x+7)=540°

(8x-4)=540°

8x=540°+4°

x=544°/8=68°

step 3

Find the measures of the internal angles of the pentagon

(68-8)°=60°

(3*68-11)=193°

(68+8)=76°

68°

(2*68+7)=143°

was the answer they put right?

Answer:

The scale factor is 2/3.

Step-by-step explanation:

Given data,

The given image is (6,9)

The image after dilation is (4,6)

The scale factor is calculated by dividing the resultant image by the initial image.

For example, if the initial dimensions are (x1, y1) and the final dimensions are (x2,y2). The scale factor is calculated using x2/x1 = y2/y1 = Scale Factor  

In our scenario,

x1  = 6

x2 = 4

y1  = 9

y2 = 6

Scale Factor = x2/x1

=> 4/6

=> 2/3

Similarly for y axis,

Scale Factor = y2/y1

=> 6/9

=> 2/3

Therefore, the scale factor is 2/3.

Answer:

The answer is $12,000 I think check to be sure...Sorry in advance I'm not the best at math guys...    

Step-by-step explanation:

4% of 8472 = 338.88

The salesman will have made $338.88, which is 4% of $8,472.

2 teaspoons

21+21=42 so for every 1 teaspoon there is 42 people

42+42=84 so it’s 2 teaspoons

Answer:

Let's imagine that x is the number of teaspoon of salt needed to make at least 84 cupcakes.

So we know that, 1 batch makes 21 cupcakes, and we need at least 84 cupcakes, so the number of cupcakes batch needed here should be:

84 ÷ 21 = 4 (batches)

Since we knew the number of batches that we need to make the cupcakes, we now calculate the amount of sugar needed. We have:

1/2 teaspoon of salt for every 1 batch.

x teaspoon of salt for every 4 batches.

x = (4 . 1/2) . 1 = 2 (teaspoons)

Answer:

(x,7) or (x,10)

Step-by-step explanation:

It is given that two vertices of a right triangle have coordinates (3, 7) and (3, 10), we can see that the x-coordinate is same for both vertices, therefore it is a vertical line and thus base of the right angle triangle.

We need to find the height of this triangle which will be perpendicular to this line, so the value of y-coordinate of third point must be either 7 or 10.

Example

(8,7)

Answer:

6pi; 27pi

Step-by-step explanation:

Since 4:00 is 120 degrees on a clock, then it is 120/360 or 1/3 of the clock. Now let’s find the arch length! Since the radius of the clock is 9, then the circumference will be 18pi. Since 1/3 of the clock is 4:00, then the arc length is 1/3 of the circumference. SO the arc length is 6pi.

Now let’s find the area of the sector. Since the radius is 9, then the area is 81pi. So 1/3 of that is 27pi.

Answer:

40

Step-by-step explanation:

The given geometric series is:

[tex]\sum_{n=1}^4(-2)(-3)^{n-1}[/tex].

When n=1, [tex]a_1=(-2)(-3)^{1-1}[/tex], [tex]\implies a_1=(-2)(-3)^{0}=-2[/tex]

When n=2, [tex]a_2=(-2)(-3)^{2-1}[/tex], [tex]\implies a_2=(-2)(-3)^{1}=6[/tex]

When n=3, [tex]a_3=(-2)(-3)^{3-1}[/tex], [tex]\implies a_3=(-2)(-3)^{2}=-18[/tex]

When n=4, [tex]a_4=(-2)(-3)^{4-1}[/tex], [tex]\implies a_4=(-2)(-3)^{3}=54[/tex]

The sum of the given series is:

-2+6-18+54=40

72 square inches.

Start by finding the dimensions of the scale drawing. If 36 divided by a number equals 9, then that number is 4. 36 / 4 = 9

So, you need to divide 32 by 4 as well to get 8.

This means the scale drawing is 9 inches long and 8 inches wide.

Finally, to find the area, multiply the length and width together. 9 * 8 = 72

The area of the scale drawing is 72 square inches.

Answer:

5. LA = 301.6 sq. cm.,  SA = 402.1 sq. cm.

6. LA = 377.0 sq. in.,  SA = 603.2 sq. in.

7.  LA = 113.1 sq. cm.,  SA = 169.6 sq. cm.

8. LA = 502.7 sq. cm.,  SA = 603.2 sq. cm.

9. 396 sq. in.

Step-by-step explanation:

The lateral area is the area of all the faces, except the base(s). The surface area is the area of ALL the faces of the shape.

5.

The lateral area of a cylinder is given by the formula:

LA = 2πrh

where r is the radius and h is the height of the cylinder

So, lateral area would be 2π(4)(12) = 301.6 sq. cm.

The surface are would be the lateral area (301.6) PLUS the area of 2 of the circular bases. Circle has an area of πr^2.

So 2 bases would have area of (π(4)^2)*2=100.5

Thus, the surface area = 301.6 + 100.5 = 402.1

6.

The lateral area would be LA = 2πrh

The radius is given as 6 and height as 10. Plugging it would give us:

LA = 2πrh = 2π(6)(10) = 377.0 sq. in.

For the surface area, we would need to add the top and bottom (which are 2 identical circles with area πr^2 each) with the lateral area. So we have:

2 * (π(6)^2)

=226.2

Surface area = 377.0 + 226.2 = 603.2 sq. in.

7.

The radius of the cylinder is 3 and height is 6. We will plug them into the respective formulas.

lateral area:

LA = 2πrh = 2π(3)(6) = 113.1

surface area:

area of 2 circles (top and bottom) = (πr^2)*2 = (π(3)^2)*2 = 56.5

Surface area = 113.1 + 56.5 = 169.6

8.

diameter is given as 8, so radius is half of it. Hence, radius is 4 and height given as 20.

Plugging these values into the respective formula we will get the answer.

lateral area:

LA = 2πrh = 2π(4)(20) = 502.7

surface area:

area of both the circles (top and bottom) PLUS the lateral area of 502.7.

So, surface area = 502.7 + (πr^2)*2 = 502.7 + (π(4)^2)*2 = 603.2  

9.

The frosting area of area of two rectangles (left and right) + area of two rectangles (back and front) + area of rectangle (top).

So, surface area of the frosting part = 2 (4*15) + 2(4*12) + (12)(15) = 396

The answer is x equals 1/2.

Answer:

X = - 1/2

Step-by-step explanation:

3x+9-7x=2(x+6)

9-4x=2x+12

6x=-3

x=-1/2

All sides of a square/cube are the same. Since this is a cube, you'll find the volume by "cubing" (get it?) 4.4m.

4.4³ or 4.4 * 4.4 * 4.4 = 85.184m³ but you can round that to 85m³

I hope that helps!

4/3πr^3 is the equation to solve for volume.

Since the radius is 5 cm (10/2), we know the equation is 4/3π125

166 2/3π cm^3

or

523 1/3 cm^3

Final answer:

The volume of a sphere with a 10 cm diameter is approximately 523.6 cubic centimeters when rounded to the nearest tenth.

Explanation:

The student is asking for the volume of a sphere with a given diameter of 10 cm. To calculate the volume, you use the formula for the volume of a sphere, which is V = (4/3)πr³.

First, we need to find the radius of the sphere, which is half of the diameter, so the radius (r) is 5 cm. Plugging this into the formula gives us V = (4/3)π(5 cm)³. Now we calculate the volume: V = (4/3)π(125 cm³) ≈ 523.6 cm³ when rounded to the nearest tenth. So, the volume of the sphere is approximately 523.6 cubic centimeters.

Ok I got it.

Question 1 - Demetrius, Jackson, Tyler, and Amelia

Question 2 - Winslow

Question 3 - Joe

Question 4 - Harley and Jasmine

Question 5 - No one recieves fifteen minutes of free time

I hurried this one because Imma go see avengers endgame.

I hope this helps you very much.

I would appreciate making me the brainliest.

Thanks in advance

Answer:

[tex]^{\to}_{PQ}+4^{\to}_{RS}=<\:-14,-21\:>\:[/tex]

[tex]|^{\to}_{PQ}+4^{\to}_{RS}|=7\sqrt{13}[/tex]

Step-by-step explanation:

The given points have coordinates; P=(5,4), Q=(7,3), R=(8,6), and S=(4,1).

[tex]^{\to}_{PQ}=^{\to}_{OQ}-^{\to}_{OP}[/tex]

[tex]^{\to}_{PQ}=<\:7,3\:>\:-\:<\:5,4\:>[/tex]

[tex]^{\to}_{PQ}=<\:7-5,3-4\:>\:[/tex]

[tex]^{\to}_{PQ}=<\:2,-1\:>\:[/tex]

[tex]^{\to}_{RS}=^{\to}_{OS}-^{\to}_{OR}[/tex]

[tex]^{\to}_{RS}=<\:4,1\:>\:-\:<\:8,6\:>[/tex]

[tex]^{\to}_{RS}=<\:4-8,1-6\:>\:[/tex]

[tex]^{\to}_{RS}=<\:-4,-5\:>\:[/tex]

[tex]^{\to}_{PQ}+4^{\to}_{RS}=<\:2,-1\:>\:+4\:<\:-4,-5\:>\:[/tex]

[tex]^{\to}_{PQ}+4^{\to}_{RS}=<\:2,-1\:>\:+\:<\:-16,-20\:>\:[/tex]

[tex]^{\to}_{PQ}+4^{\to}_{RS}=<\:2-16,-1-20\:>\:[/tex]

[tex]^{\to}_{PQ}+4^{\to}_{RS}=<\:-14,-21\:>\:[/tex]

The correct answer is C

The magnitude is given by:

[tex]|^{\to}_{PQ}+4^{\to}_{RS}|=\sqrt{x^2+y^2}[/tex]

[tex]|^{\to}_{PQ}+4^{\to}_{RS}|=\sqrt{(-14)^2+(-21)^2}[/tex]

[tex]|^{\to}_{PQ}+4^{\to}_{RS}|=\sqrt{196+441}[/tex]

[tex]|^{\to}_{PQ}+4^{\to}_{RS}|=\sqrt{637}[/tex]

[tex]|^{\to}_{PQ}+4^{\to}_{RS}|=7\sqrt{13}[/tex]

The correct answer is B

Answer:

300+4x < (9+5)*x

Step-by-step explanation:

x is number of times Robert goes to the gym

Answer:

5d+ 9d=300+4d

Step-by-step explanation:

Answer on EDGE

The pentagon was reflected across the x-axis. By looking at Point A, you can see x was increased 8, x+8. Also, y was increased by 2, y+2.

Answer:

The correct option is c.

Step-by-step explanation:

From the given figure it is clear that the vertices of preimage are A(-5,-2), B(-7,-3), C(-6,-6), D(-3,-5) and E(-3,-3).

The vertices of image are A'(3,6), B'(5,5), C'(4,2), D'(1,3) and E'(1,5).

If figure translated 2 units right and 8 units up then

[tex](x,y)\rightarrow (x+2,y+8)[/tex]

The vertices of pentagon after translation.

[tex]A(-5,-2)\rightarrow A_1(-3,6)[/tex]

[tex]B(-7,-3)\rightarrow B_1(-5,5)[/tex]

[tex]C(-6,-6)\rightarrow C_1(-4,2)[/tex]

[tex]D(-3,-5)\rightarrow D_1(-1,3)[/tex]

[tex]E(-3,-3)\rightarrow E_1(-1,5)[/tex]

If the figure reflected across y-axis, then

[tex](x,y)\rightarrow (-x,y)[/tex]

The vertices of pentagon after translation by rule [tex](x,y)\rightarrow (x+2,y+8)[/tex] followed by reflection across y-axis are

[tex]A_1(-3,6)\rightarrow A'(3,6)[/tex]

[tex]B_1(-5,5)\rightarrow B'(5,5)[/tex]

[tex]C_1(-4,2)\rightarrow C'(4,2)[/tex]

[tex]D_1(-1,3)\rightarrow D'(1,3)[/tex]

[tex]E_1(-1,5)\rightarrow E'(1,5)[/tex]

The pentagon ABCDE translated according to the rule [tex](x,y)\rightarrow (x+2,y+8)[/tex] and reflected across the y-axis to create A'B'C'D'E'.

Therefore, the correct option is c.

data:

2 scored 100

9 scored 95

10 scored 90

3 scored 80

1 scored 70

set of data:

70, 80, 80, 80, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 95, 95, 95, 95, 95, 95, 95, 95, 95, 100, 100

to find the average score of the spelling test, we have to add all of the numbers up and then divide by 2

all of those numbers added up would be 2,265

next, divide 2,265 by 2

2,265 / 2 = 1,132.5

finally, round 1,132.5

= 1,133 (average score of spelling test)

A class of 25 students took a spelling test. The average score of the students on the spelling test is 90.6.

The average data is calculated as follows:

Given that,

A class of 25 students took a spelling test.

The data of scores of those students:

2 students - 100

9 students - 95

10 students - 90

3 students - 80

1 student - 70

Adding all the scores of each student:

2×100 + 9×95 + 10×90 + 3×80 + 1×70 = 2265

Dividing the sum by the number of students (25):

⇒ 2265/25

⇒ 90.6

Therefore, the average of the given data is 90.6.

Learn more about the average of the data here:

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Answer:

y=lxl-1

Step-by-step explanation:

It goes down one.

The formula is:

y=nlx-kl+t

k translates it horizontally.

t translates it vertically.

Answer:

There is more wood in a 60​-foot-high tree trunk with a radius of 2.4 ​feet

Step-by-step explanation:

* Lets talk about the right circular cylinder

- It has two circular bases

- The volume of it = Area of the base × its height

- The area of the base = πr²

- The quantity of wood in the tree is the volume of the cylinder

* Lets calculate the volumes the two trees and compare

 between them

- Volume of the first tree:

∵ Its radius = 2.1 feet

∴ The area of its base = π(2.1)² = 4.41π feet²

∵ Its height = 70 feet

∴ Its volume = 4.41π × 70 = 308.7π = 969.8 feet³

- Volume of the second tree:

∵ Its radius = 2.4 feet

∴ The area of its base = π(2.4)² = 5.76π feet²

∵ Its height = 60 feet

∴ Its volume = 5.76π × 60 = 345.6π = 1085.7 feet³

∵ 1085.7 > 969.8

∴ The volume of wood in 2nd tree > the volume of wood in 1st tree

* There is more wood in a 60​-foot-high tree trunk with a radius of 2.4 ​feet

ANSWER

[tex]( f \circ \: g)( - 5)= -53[/tex]

EXPLANATION

The given functions are:

f(x) = -­2x ­- 7 and g(x) = ­-4x + 3

[tex]( f \circ \: g)(x) = f(g(x))[/tex]

[tex]( f \circ \: g)(x) = f( - 4x + 3)[/tex]

[tex]( f \circ \: g)(x) = - 2( - 4x + 3) - 7[/tex]

Expand:

[tex]( f \circ \: g)(x) = 8x - 6 - 7[/tex]

[tex]( f \circ \: g)(x) = 8x - 13[/tex]

We substitute x=-5

[tex]( f \circ \: g)( - 5) = 8( - 5) - 13 = -53[/tex]

Answer:

Step-by-step explanation:

The correct zero(s) where the lens material starts and ends are at x = 4 and x = 8.

To find the zero(s) of the quadratic equation [tex]-0.5x^2 + 6x - 16 = 0[/tex]  , we can use the quadratic formula, which is given by:

[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

where a, b, and c are the coefficients of the quadratic equation [tex]ax^2 + bx + c = 0.[/tex]

For the given equation, a = -0.5, b = 6, and c = -16. Plugging these values into the quadratic formula, we get:

[tex]\[ x = \frac{-6 \pm \sqrt{6^2 - 4(-0.5)(-16)}}{2(-0.5)} \][/tex]

[tex]\[ x = \frac{-6 \pm \sqrt{36 - 32}}{-1} \][/tex]

[tex]\[ x = \frac{-6 \pm \sqrt{4}}{-1} \][/tex]

[tex]\[ x = \frac{-6 \pm 2}{-1} \][/tex]

Now, we have two possible solutions for x:

[tex]\[ x = \frac{-6 + 2}{-1} = \frac{-4}{-1} = 4 \][/tex]

[tex]\[ x = \frac{-6 - 2}{-1} = \frac{-8}{-1} = 8 \][/tex]

Therefore, the zero(s) where the lens material starts and ends are at x = 4 and x = 8. These are the points where the lens maker cuts the lens material along the x-axis for fitting.

Answer:

C) 160 cm3

Step-by-step explanation:

Since each cube represents 2 centimeters you need to multiply by 2 three times, since there are three dimensions. The volume of the figure is 160 cm3

Answer:

C (160)

Step-by-step explanation:

hope it helps brainliest pls

Answer:

The substitution is

[tex]u = x ^ 4[/tex]

[tex]u ^ 2 -3u +2 = 0[/tex]

Step-by-step explanation:

We have the 8th degree polynomial equation

[tex]x ^ 8 - 3x^4 -+2 = 0[/tex]

To rewrite the equation as a quadratic function, take the common factor of the term x with the smallest exponent, in this case it is [tex]x ^ 4[/tex].

Now make a change of variable

[tex]u = x ^ 4[/tex].

So rewriting the equation in terms of u, we have:

[tex]u ^ 2 -3u +2 = 0[/tex]

Now the initial equation became a quadratic equation

Factoring is left:

[tex](u-2) (u-1) = 0[/tex]

[tex]u = 2[/tex] and [tex]u = 1[/tex]

[tex]x ^ 4 = 2[/tex] and [tex]x ^ 4 = 1[/tex]

Answer:

substitution should be p =  x⁴

Step-by-step explanation:

It is given that,

x⁸ -  3x⁴ + 2 = 0

we can rewrite the equation,

(x⁴)² - 3x⁴ + 2 =0

To find the substitution

Here we can see that x⁴ is common in two terms of the given equation

we can substitute p instead of x⁴, the equation becomes,

p² - 3p +2 = 0

Therefore substitution should be used to rewrite x8 – 3x4 + 2 = 0 as a quadratic equation is p =  x⁴

-7x/7 > 56/7

x < -8

Diagram with a hollow dot on 8.

Answer:

width = 2ft and length = 9ft

Step-by-step explanation:

width W = x

length L = x +7

area of a rectangle A = L * W

18 = (x + 7) * x

18 = x² + 7x

x² + 7x -18 =0

solve the equation by factorisation

x² -2x + 9x - 18 =0

x(x - 2) + 9(x - 2) =0

(x - 2)(x + 9) = 0

x = 2 and -9

therefore the width is 2ft because it is positive and the negative value is ignored

the length = 2 + 7 = 9ft

Answer:

width = 2ft and length = 9ft

Step-by-step explanation:

C is the correct answer