Two beetles sit at the top edge of the house roof. The roof has two faces. The first face is such that the horizontal shift by 3 cm along this face means 2 cm shift vertically. Simultaneously the beetles start moving downwards, the first beetle by the first face, the second -- the second face of the roof. The first beetle moves twice as fast as the second beetle. Find the altitude of the second beetle above the first beetle when they will be 72 cm apart horizontally, if the second face of the roof is perpendicular to the first face?

The slope-intercept form of (5,-3) and (4,0) is y = -3x + 12.

The slope intercept form is simply writing an equation of a line so that the slope or steepness and y-intercept i.e. where the line crosses the vertical y-axis are immediately apparent.

The slope-intercept equation is y = mx + c, where x and y are two variables, and m is slope.

Slope m = [tex]\frac{y2-y1}{x2-x1}[/tex]

Let,

(x1, y1) = (5, -3)

(x2, y2) = (4, 0)

Slope (m) = [tex]\frac{0 - (-3) }{4 - 5}[/tex]

                = [tex]\frac{3}{-1}[/tex]

                = -3

By substituting x, y, and m values in the equation we can get the value of c.

Consider x = 4 , y = 0, m = -3

y = mx + c => 0 = (-3)4 + c

                      c = 12

Therefore, the slope-intercept form of (5,-3) and (4,0) is y = -3x + 12.

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hello hope you are having a good day

the answer to your question would be A 6 miles i took the test and got an 100% also asked the teacher.

The graph of the transformation of f(x) to f(b·x), where f(1) in f(b·x) is equal to f(5) in f(x) indicates that the value of b is 5

The transformation of a function is represented by a function that changes one function into another function, such that the size, or position of the graph of the original function is modified

The given transformation of the function f is f(b·x)

A formula for the transformation of a function y = f(x) is the function;

y = a·f(b(x + c)) + d

Where;

The a indicates a vertical translation of the function

b indicates an horizontal dilation of f

c stands for a horizontal translation

d stands for a vertical translation

The translation in the question is f(b·x), which is a horizontal dilation, is expressed as follows;

When b > 1, the graph of f(x) shrinks horizontally

When 0 < b < 1, the graph of f(x) is stretched

At x = 1, f(x) = 1, and f(b·x) = 5

The graph of f(x) shrinks to obtain the graph of f(b·x), such that the value obtained at f(5) in f(x) is obtained at f(1) in f(b·x)

f(5) = f(b·1)

b×1 = 5

b = 5 ÷ 1 = 5

The value of b is 5

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The only equation that represents a piecewise defined function is;

Option A: f(x) = {-2, if x ≥ 4

        {x², if x < 4

A piecewise function is defined as a function that consists of multiple subfunctions, whereby each subfunction defined over a specific subset of the domain of the main function which is called a subdomain.

The equation of a piecewise function is usually written with a curly bracket that indicates the fact of being comprised of more than one subfunction. An example of a piecewise function is;

f(x) = {x, x < 0

        {x + 1, x ≥ 0

Let us look at each of the given functions;

Function in option A is clearly a piecewise function when compared to the definition given above

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[tex]\displaystyle\\Answer:\ \left [ {{\boxed{2.1}} \atop {\boxed{3.45}}} \right][/tex]

Step-by-step explanation:

[tex]\displaystyle\\A=\left [ {0.3\ \ \ \ 0.2} \atop {0.35\ \ \ 0.4}} \right]\ \ \ \ \ D=\left [ {{3} \atop {6}} \right]\\\\A*D=\left [ {{c_{11}} \atop {c_{21}}} \right] \\\\c_{11}=a_{11}*b_{11}+a_{12}*b_{21}\\\\c_{11}=0.3*3+0.2*6\\\\c_{11}=0.9+1.2\\\\c_{11}=2.1\\\\c_{21}=a_{21}*b_{11}+a_{22}*b_{21}\\\\c_{21}=0,35*3+0,4*6\\\\c_{21}=1.05+2.4\\\\c_{21}=3.45\\\\Thus,\ A*D=\left [ {{2.1} \atop {3.45}} \right][/tex]

Answer: (0,-13)

Step-by-step explanation:

The y intercept is x=0

Hence,

y=2(0²)-9*(0)-13

y=2(0)-0-13

y=0-13

y=-13

Thus, (0,-13)

Answer:

Step-by-step explanation:

x=2.3

The values of the variables associated ot translation operations are (w, x, y, z) = (3, 1, 0, 2 / 3).

Herein we find two translation cases of points set on Cartesian plane. Translations are rigid operations of the form:

P'(x, y) = P(x, y) + T(x, y)

Where:

Now we proceed to determine the values of the variables w, x, y, z behind each translation operation, substitute on each component and solve the resulting formula:

T(x, y) = A'(x, y) - A(x, y)

(2 · x + 1, 4) - (- 1, w) = (4, 1)

(2 · x + 2, 4 - w) = (4, 1)

(x, w) = (1, 3)

T(x, y) = B'(x, y) - B(x, y)

(3, 3 · z) - (8 · y - 1, 1) = (4, 1)

(4 - 8 · y, 3 · z - 1) = (4, 1)

(y, z) = (0, 2 / 3)

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The equation of the given values of x and y will be; y = 2x - 2

An equation represents equality of two or more mathematical expression.

Solutions to an equation are those values of the variables involved in that equation for which the equation is true.

We have been given the values of x and y. then we need to find the equations;

First slope

m = (4 +2)/(3 - 0)

m = 6/3 = 2

Now the standard form of the equation is;

y-y₁ = m(x-x₁)

y+ 2 = 2(x- 0)

y = 2x - 2

The graph of the given equation of line is attached below.

Hence, the equation of the given values of x and y will be; y = 2x - 2

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Answer:

Subtract 6 from both sides

3 (2q - s)(p + r) is the factor form of expression 6pq-3rs-3ps+6qr.

A factor is a number that divides another number, leaving no remainder

The given expression is 6pq-3rs-3ps+6qr

We need to factorize the expression.

6pq-3rs-3ps+6qr

= 3 (2pq - rs - ps + 2qr)

= 3 (2pq + 2qr -ps - rs)

= 3 (2q(p + r) -s(p + r))

= 3 (2q - s)(p + r)

Hence, 3 (2q - s)(p + r) is the factor form of expression 6pq-3rs-3ps+6qr.

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The equation of the line with a slope of one third and passes through (-2, 1) is y = one-third x + five-thirds.

The equation of a line can be represented in a slope intercept form as follows:

y = mx + b

where

Therefore, the equation of the line has a slope of 1 / 3. Let's find the y-intercept using the coordinates (-2, 1)

y = 1 / 3 x + b

1 = 1 / 3 (-2) + b

1 + 2 / 3 = b

b = 3 + 2 / 3

b = 5 / 3

Therefore, the equation is y = 1 / 3 x + 5 / 3

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8. -a+b-7

9. m=(y-b)/x

Answer:

first one: C

second one: A

Step-by-step explanation:

4a - 5 + 3b - 2 - 2b - 5a

combine a terms:

-a - 5 + 3b - 2 - 2b

combine b terms:

-a - 5 + b - 2

combine numbers:

-a  + b - 7 (this is option c)

_____________________

y = mx + b, solve for m

subtract b from both sides:

y - b = mx + b - b

y - b = mx

divide both sides by x:

(y - b)/x = mx/x

m = (y - b)/x (this is option a)

Reflecting over the y-axis and then translating to the right 10 units

Step-by-step explanation:

Reflection over the line x=5 gives you the transformation ...

 (x, y) ⇒ (2·5 -x, y) = (-x +10, y)

This is precisely the same transformation you get by reflection over the y-axis:

 (x, y) ⇒ (-x, y)

followed by translation to the right 10 units:

 (-x, y) ⇒ (-x +10, y)

__

Reflection over x=5 is the same as reflection over y and translation right 10.

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Answer:

C

Step-by-step explanation:

C is the input.  The input is the independent variable.  The output would be the dependent variable.

[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{a})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{a}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{10}}} ~~ = ~~\stackrel{\textit{\LARGE m}}{\cfrac{1}{4}} \\\\\\ \cfrac{8-a}{-12}=\cfrac{1}{4}\implies 32-4a=-12\implies 44-4a=0 \\\\\\ 44=4a\implies \cfrac{44}{4}=a\implies \boxed{11=a}[/tex]

The total number of water glasses on the shelf may be 39, 63 or 87.

Given, that there were more than 24 glasses, but less than 100 glasses.

If the glasses were in rows of 6, there would be 3 left over.

If the glasses were in rows of 8, there would be 7 left over.

Let the number of glasses be x,

So, x = 6k1 + 3

=> (x - 3) is a multiple of 6

x = 8k2 + 7

=> (x - 7) is a multiple of 8

Now, the numbers that can satisfy the given conditions are,

39 , 63 & 87.

So, the total number of glasses may be 39, 63 or 87.

Hence, the total number of water glasses on the shelf may be 39, 63 or 87.

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Answer:

The answer is displayed in the attached image.

Step-by-step explanation:

To find the radical form of an expression, first determine what is in the denominator of the fractional exponent. That number will determine the order of the root you will take. The numerator will be the power of your original number

EXAMPLE:

[tex]5^{\frac{3}{4} }[/tex] = [tex]\sqrt[4]{5^3}[/tex]

Answer:

Rs 171.40

Step-by-step explanation:

For 1 apple we have to divide 120 by 14 which is 8.57 to 2d.p.

So 20 * 8.57 = 171.4

to 2d.p. = Rs 171.40

Pls could you give me brainliest

pls:(

The first option Focus(2,-0.5); directrix x=0 of the parabola is the correct answer.

What is a parabola?

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.

The general equation of a parabola is as follows:

[tex](y-k)^2=4a(x-h)[/tex]

Now, consider the given equation.

[tex](y+0.5)^2=4(x-1)[/tex]

Now, compare with the standered equation.

a=1, k=-0.5 and h=1

Here, a is positive hence, the parbola opens right side.

Focus is given by the following coordinate:

[tex](h+a,k)=(1+1,-0.5)\\=(2,-0.5)[/tex]

Now, equation of diretrix is given by the following expression:

[tex]x=h-a\\x=1-1\\x=0[/tex]

Hence, the first option Focus(2,-0.5); directrix x=0 is the correct answer.

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Answer:

$13

Step-by-step explanation:

$65 x 0.20 = 13

Answer: 20% off 65 is $52.00 so it was $13 saved

The population estimated minimum sample size will be 11 , and the critical value will be 1.28.

The average gorilla weight is being calculated as a range estimate by a researcher (in pounds).

She wants to be within 7.1 pounds of the actual average with 80% accuracy.

Previous research has shown that the standard deviation of the weights of gorillas is 18.2 pounds.

a)  Since the confidence is 0.80 or 80% then the value of α is 0.20 and  and we can calculate the critical value. Then the value of the z-score will be  z = 1.28.

b)  The margin of error is given as

M.E.= z*(standard deviation/√n)

We have,

Margin of error = 7.1

From the above formula we get;

n =  ((z* standard deviation )/marginal error)²

n =  ((1.28*18.2)/7.1)²

  =   10.76 ≈ 11

Therefore, the researcher should take 11 samples.

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Answer:

Step-by-step explanation:

Given functions,

→ f(x) = 4x + 5

Now the value of f(-3) will be,

→ f(x) = 4x + 5

→ f(-3) = 4(-3) + 5

→ f(-3) = -12 + 5

→ [ f(-3) = -7 ]

Then the value of f(3) will be,

→ f(x) = 4x + 5

→ f(3) = 4(3) + 5

→ f(3) = 12 + 5

→ [ f(3) = 17 ]

Hence, the answer of f(3) is 17.

Substitute [tex]x=-3[/tex] into [tex]f(x)=4x+5[/tex] :

[tex]f(-3)=4(-3)+5[/tex]

          [tex]=-12+5[/tex]

          [tex]=-7[/tex]

Substitute [tex]x=3[/tex] into[tex]f(x)=4x+5[/tex] :

[tex]f(3)=4(3)+5[/tex]

       [tex]=12+5[/tex]

       [tex]=17[/tex]

[tex]\text{Hence, } f(-3)=-7 \text{ and } f(x)=17.[/tex]

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Answer:

Step-by-step explanation:

You want the radius and water depth in a spherical bowl in which the water level is 10 cm above the center of the sphere, and the circular surface has a diameter of 30 cm.

The geometry of the diameter of the water surface can be modeled as shown in the attachment. The radius of that surface forms one leg of a right triangle with the other leg being 10 cm. The hypotenuse of the triangle is the radius of the sphere, so we have ...

  r² = 15² +10² = 325

  r = √325 = 5√13 ≈ 18.03 . . . . . cm

The water depth is 10 cm more than the radius, so is ...

  d = 10 +r = 10 +5√13 ≈ 28.03 . . . . . cm

The radius of the bowl is about 18.03 cm; the depth of water is about 28.03 cm.

Answer:

23 boxes of pasta