Please help 20 points

Answer:

The first choice.

Step-by-step explanation:

The area is multiplied by (1/2)^2 = 1/4.

This is because lengths are one dimensional and areas are 2 dimensional.

Answer:

First option is correct i.e: The surface area is multiplied by 1/4

Step-by-step explanation:

Need to compare the surface area of right rectangular prism when the length, width and height are halved as compared to original length, width and height.

length =4,width =2,height =7

Area of right rectangular prism = 2(wl+hl+hw)

=2(2*4 + 7*4 + 7*2)

=2(8+28+14)

=2(50)

= 100 cm³

Now, if the length, width and height are halved, the surface area will be:

length= 2, width=1, height= 3.5

Area of right rectangular prism= 2(1*2 + 3.5*2 + 3.5*1)

= 2(2+7+3.5)

=2(12.5)

=25 cm³

if the length, width and height are halved the surface area is 25 cm³ while if original length, width and height are used the surface area is 100 cm³.

So, first option is correct i.e: The surface area is multiplied by 1/4.

ANSWER

Left

EXPLANATION

The given function is

g(x)=f(x+1)

This means that the base function is:

f(x).

The translation f(x+k) will shift the graph to left by k units while f(x-k) will shift the graph to right by k units

Therefore if g(x)=f(x+1) translates the function f(x) 1 unit left.

Answer: left

Answer:

g(x) translates the function f(x) 1 unit left.

Step-by-step explanation:

Consider the provided function.

g(x)=f(x+1)

Transformation:

Rule 1:  The graph of parent function f(x) move up b unit for f(x)+b.

Rule 2: The graph of parent function f(x) move down b unit for f(x)-b.

Rule 3: The graph of parent function f(x) move left b unit for f(x+b).

Rule 4: The graph of parent function f(x) move right b unit for f(x-b).

From the rule 3  we can say that the graph of parent function move left 1 unit for g(x)=f(x+1)

g(x) translates the function f(x) 1 unit left.

Answer:

D 776 m.

Step-by-step explanation:

Use trigonometry. The line of flight of the plane, it's height above the ground and the  distance travelled along the ground form a right angled triangle.

So sin 15 = opposite side   / hypotenuse.

sin 15 = h / 3000  where h = its height..

h = 3000 sin 15

=  776 m.

The height of the plane from the ground will be 776 m. Then the correct option is D.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

A plane takes off at an angle of elevation of 15° and travels in a straight line for 3,000 meters.

The height of the plane above the ground at this instant is calculated as,

sin 15° = h / 3,000

h = 3,000 x sin 15°

h = 776 meters

Thus, the correct option is D.

More about the right-angle triangle link is given below.

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The intersection of a cone and a plane parallel to its base is a circle. This is due to the concept of 'conic sections' that determine the shape based on the angle and position of the plane's intersection with the cone.

The cross section formed by the intersection of a cone and a plane parallel to the base of the cone is a circle. This shape is one of the conic sections, which also include the ellipse, parabola, and hyperbola. These shapes are formed depending on the angle and position at which a plane intersects with a cone.

A circle is formed when the cutting plane is parallel to the base of the cone. If the plane was at an angle, other shapes like an ellipse, parabola or hyperbola would be obtained. The word 'conic sections' comes from this geometric principle of intersecting a cone with a plane.

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Answer:

the answer 43.5 units²

Step-by-step explanation:

i took this in school and remember it hope it helped

1. The area of the figure is 42 units².

2. The area of the figure is 38 units²

The area of a figure is the extent of its 2D space, quantifying the region it occupies.

It's calculated using specific formulas based on the figure's geometric properties, such as length, width, and shape.

1. The figure can be splitted into 3

Area1 = 1/2bh

= 1/2 × 7 × 2

= 7units²

Area 2 = l × w

= 7 × 4 = 28 units²

Area 3 = 1/2bh

= 1/2 × 7 × 2

= 7 units²

Area of figure = 28+7+7

= 42 units²

2. The shape can be divided into a trapezoid and two equal triangles

area of Trapezoid = 1/2(a+b)h

= 1/2 ( 3+5)8

= 8 × 4

= 32 units²

area of triangle = 1/2bh

= 1/2 × 3 × 4

= 6 units²

area of the figure = 32 + 6

= 38 units²

Answer:

19,262.5

Step-by-step explanation:

If the car decreases by 4.5% eah year for 5 years-

4.5 x 5 = 22.5%

So after 5 years, the car would be 22.5% cheaper.

22.5% of 25,000 is multiplication-

.225 x 25,000 = 19,262.5

hope this helps!

Answer:

  B)  BD

Step-by-step explanation:

The number of columns of the first matrix (2nd dimension) must match the number of rows of the second matrix (1st dimension). When you write the dimensions together, the two middle numbers must be the same.

AB ⇒ (3x2) × (3x5) . . . . 2 ≠ 3, so cannot be multiplied

BD ⇒ (3x5) × (5x7) . . . . 5 = 5, so can be multiplied

CD ⇒ (2x3) × (5x7) . . . . 3 ≠ 5, so cannot be multiplied

DD ⇒ (3x5) × (3x5) . . . . 3 ≠ 5, so cannot be multiplied

Answer:

B

Step-by-step explanation:

Triangle ABD and triangle ACE are similar.  So we can write a proportion:

AB / BD = AC / CE

5 / 4 = 12 / CE

CE = 9.6

The measure of side CE will be 9.6. Then the correct option is B.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The triangle ΔABD and triangle ΔACE are similar. Then we have

AB / AC = BD / CE

   5 / 12 = 4 / CE

       CE = 9.6

Then the measure of side CE will be 9.6.

Then the correct option is B.

More about the triangle link is given below.

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Answer:

136.015 yd

Step-by-step explanation:

Length of diagonal is:

√( (80 yd)² + (110 yd)² ) = √( 18500 yd² ) = 136.015 yd

You add/subtract complex numbers simply by adding/subtracting real parts and imaginary parts.

So, the real part of this sum is the sum of the real parts:

[tex]-3+6=3[/tex]

And the imaginary part of this sum is the sum of the imaginary parts:

[tex]5i+2i=7i[/tex]

So, you have

[tex](-3+5i)+(6+2i) = 3+7i[/tex]

Answer:

2

Step-by-step explanation:

The maximum value is the amplitude. Looking at graph, it would be the highest point in the graph.

Each unit of the graph is 2 units, hence the maximum value, clearly looking at the graph, would be y = 2. Also the minimum value is y = -2.

So, the maximum value is 2

Answer:

Option b.

y = 4 sin (3x)

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The period is  

T = 2π/3

This means the frequency in radians is

W = 2π/T = 3

The equation is either:

y = 4 cos(3x)

y = 4 sin (3x)

The correct answer is

Option b.

y = 4 sin (3x)

You would multiply 50x16 being 16 ounces= 1 pound and than divide that by 10

Answer:

10.5 in. ²

Step-by-step explanation:

a = (b × h) ÷ 2

a = (7 × 3) ÷ 2

a = 21 ÷ 2

a = 10.5

Answer:

$550

Step-by-step explanation:

You need the equation E(s) = 350 + 0.15s, where E(s) represent his total weekly earnings.

If he earned $432.50 this means E(s) = 432.50 and you can write it as:

350 + 0.15s = 432.50 and this is the equation we need to solve

You need to substract 350 on both sides of the equation

350 - 350 +0.15 s = 432.50 - 350

And we get

0.15s = 82.5

Then we divide both sides of the equation by 0.15

0.15s/0.15 = 82.5/0.15

And we get s = 550.

The correct answer should be A) f(x)=28^2x. Please comment and let me know if I am wrong, and I hope it helps!

Answer:

The correct option is B) [tex]f(x) = 4(49)^x[/tex].

Step-by-step explanation:

Consider the provided function [tex]f(x) = 4(7)^{2x}[/tex]

The above function can be written as:

[tex]f(x) = 4(7)^{2x}[/tex]

[tex]f(x) = 4(7^2)^x[/tex]

[tex]f(x) = 4(7\times 7)^x[/tex]

[tex]f(x) = 4(49)^x[/tex]

Now consider the provided option.

By Comparing the provided options we can concluded that the correct option is B) [tex]f(x) = 4(49)^x[/tex].

Since the diameter and height of both shapes are the same, we know that the equation to solve for the semi circle is:

πr = 3.1*8 = 24.8

16 + 20 = 36

36 + 24.8 = 60.8

The perimeter of the shape is 60.8 ft

Answer:

[tex]5P3*6C4=60*15=900[/tex]

Step-by-step explanation:

[tex]5P3[/tex] refers to the permutations of 5 items taken 3 at a time. To evaluate this, we use factorials as follows;

[tex]5P3=\frac{5!}{(5-3)!}[/tex]

The factorial of an integer n is evaluated as;

[tex]n!=n*(n-1)*(n-2)*(n-3).......3*2*1[/tex]

Using this concept, the above expression can now be simplified as follows;

[tex]5P3=\frac{5!}{2!}=\frac{5*4*3*2!}{2!}=5*4*3=60[/tex]

Therefore, the permutations of 5 items taken 3 at a time is 60.

The next expression, [tex]6C4[/tex] refers to the combinations of 6 items taken 4 at a time. The simplification utilizes similar concepts of permutations since we shall be involving factorials;

[tex]6C4=\frac{6!}{4!(6-4)!}=\frac{6!}{4!*2!}=\frac{6*5*4!}{4!*2*1}=\frac{6*5}{2*1}=15[/tex]

Therefore, the combinations of 6 items taken 4 at a time is 15.

The final step is to evaluate the product;

[tex]5P3*6C4=60*15=900[/tex]

Answer:

I think the answer is A sorry if I'm wrong

Answer:

z = -0.4.

Step-by-step explanation:

Here's the formula for finding the z-score (a.k.a. standardized normal variable) of one measurement [tex]x[/tex] of a normal random variable [tex]X \sim N(\mu,\; \sigma^{2})[/tex]:

[tex]\displaystyle z = \frac{x-\mu}{\sigma}[/tex],

where

Let the length of a trout in this lake be [tex]X[/tex] inches.

[tex]X \sim N(30, \; 4.5^{2})[/tex].

For this measurement, [tex]x = 28.2[/tex]. Apply the formula to get the z-score:

[tex]\displaystyle z = \frac{x - \mu}{\sigma} = \frac{28.2 - 30}{4.5} = -0.4[/tex].

Answer:

Store #1 : 2x + 40

Store #2 : 3x + 36

he should buy his aquarium from store #1 because (2 * 5) + 40 = 50 and     (3 * 5) + 36 = 51, therefore it is cheaper at store #2 if he is buying 5 fish

To represent the cost of x fish and an aquarium at each store, we can set up a system of equations and solve them. By substituting the given information into the equations and simplifying, we can find the values of the variables. The solution represents the cost of an aquarium at each store. By comparing the total cost at each store, we can determine from which pet store Ronald should buy his aquarium if he wants 5 fish.

To write a system of equations to represent the cost of x fish and an aquarium at each store, let's assign variables to the cost of fish and the cost of an aquarium at each store.

Let:

x = number of fish

y = cost of an aquarium at the first store

z = cost of an aquarium at the second store

The first equation can be set up as: 2x + y = total cost at the first store

The second equation can be set up as: 3x + z = total cost at the second store

Solve this system to find the values of y and z.

Substitute the given information into the equations:

2x + y = 40 (equation 1)

3x + z = 36 (equation 2)

Multiply equation 1 by 3 and equation 2 by 2 to eliminate the y variable:

6x + 3y = 120

6x + 2z = 72

Subtract equation 2 from equation 1:

6x + 3y - (6x + 2z) = 120 - 72

6x - 6x + 3y - 2z = 48

y - 2z = 48

Now we have a system of equations:

y - 2z = 48

3x + z = 36

Solve this system using any method of your choice, such as substitution or elimination, to find the values of y and z.

Once you have the values of y and z, you can determine the cost of an aquarium at each store.

Compare the total cost at each store to decide from which pet store Ronald should buy his aquarium if he wants 5 fish.

Answer:

(10, 4)

Step-by-step explanation:

The horizontal distance from (-4, -2) to the midpoint (3, 1) is 7, and the vertical distance is 3.  To find the other end point of this line segment, add 7 to the x-coordinate of the midpoint:  3+7 = 10, and add 3 to the y-coordinate of the midpoint:  1 + 3 = 4.  The coordinates of the other end of this segment are thus (10, 4) (the fourth possible answer choice).

Answer:

x = 72 degrees

Step-by-step explanation:

If triangle LMN = triangle QPR, that means:

- angle L (x) equals angle Q

- angle M equals angle P

- angle N equals angle R

We know angle Q equals 72 degrees and we know angle Q equals angle L. Since angle L is the "x" we are looking for, we know that x = 72 degrees.

Answer:

i mean you prolly won’t need this anymore but the correct answers are

a, b, and e

Step-by-step explanation:

i got it right on edge

Ms. Elliot figures out 3 trips to work. The correct answer is Ms. Elliot can make 3 trips to school.

An equation in which one or more additional terms exist and a fraction exists is named a fractional equation. To estimate a fractional equation, first eliminate the fractions by multiplying both sides of the equation by the least common denominator (LCD) of every term.

Given:

Ms. Elliot has 6/8 gallons of gas in her, and the car uses 1/4 of a gallon of gas on the drive to work.

Let the equation be (6/8 / 1/4)

Apply the fraction rule,

(a/b) / (c/d) = (a [tex]*[/tex] d) / (b [tex]*[/tex] c)

= (6 [tex]*[/tex] 4) / (8 [tex]*[/tex] 1)

= 3.

Therefore, the correct answer is option E. Ms. Elliot can make 3 trips to school.

To learn more about fraction rule

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Set up an equation to model this situation and solve:

2x=56

*Divide both sides by 2*

x=38

Hope this helps!!

Answer:

{ x | x  ≥  8 }

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The solution to f(x) = g(x) occurs where the two graphs cross.  That's at the point (-2, -1).

Answer A.

To find where f(x) = g(x), set the two functions equal to each other and solve for 'x'. After some mathematical simplification and operations on both sides of the equation, we find that the solution is x = -1/9.

In mathematics, to find the solution for f(x) = g(x), you need to set the two equations equal to each other and solve for x. Here, we have f(x) = 2x and g(x) = 1/-3-x. Setting these two equations equal gives 2x = 1/-3-x.

To solve this equation, first, let's simplify the right hand side by multiplying both sides by -1 to make it easier to solve. Now the equation is -2x = 1/3+x.

Subtracting 'x' from both sides of the equation gives -3x = 1/3. Divide by -3 to solve for x so, x = -1/9. So, the solution for the equation f(x) = g(x) is x = -1/9.

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Answer:

10

Step-by-step explanation:

because tossed 10 times so it would be 1 out of 10

Answer:

The answer is B

Step-by-step explanation:

Remember to be mindful of the signs when adding and subtracting. The answer is:11w^4-5w^2z^2-4z^4

The kid is around 12 years old that visits the doctor 40 times

Answer:

The correct option is C.

Step-by-step explanation:

The graph below shows a scatter plot and the line of best fit relating the ages of children and the total number of times they have visited the doctor.

If a line passes through two points then the equation of line is

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

From the given graph it is clear that the line of best fit passes through the points (0,0) and (3,10). So, the equation of best fit line is

[tex]y-0=\frac{10-0}{3-0}(x-0)[/tex]

[tex]y=\frac{10}{3}x[/tex]           .... (1)

The equation of best fit line is [tex]y=\frac{10}{3}x[/tex]. Where, x is age in year and y shows the total number of visits to the doctor.

We need to estimate the age of a child who has visited the doctor 40 times.

Substitute y=40 in equation (1), to find the value of x.

[tex]40=\frac{10}{3}x[/tex]

Multiply both sides by 3.

[tex]120=10x[/tex]

Divide both sides by 10.

[tex]12=x[/tex]

The value of x is 12. It means the age of a child who has visited the doctor 40 times is 12.

Therefore the correct option is C.