Match each fraction on the left with an equivalent fraction on the right. Some options on the right will be used more than once.

The option that depicts a translation is option B. See the attached image and the explanation for this answer below.

Translation in Math refers to the movement of a shape vertically or horizontally along the x or y-axis without altering its original dimensions.

Going by the above definition, it is clear that Option B is the translated image (assuming that the original image is as given in the image attached.

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Answer:

Step-by-step explanation:

Ar of circle

A= 49π

B=100π

C=169π

D=121π

Ar of circle A is less than Ar of circle D

Using the slope concept, considering it's value of 0.3415, it is found that the angle of elevation is of 18.86º.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

Hence, we have that:

[tex]\tan{\alpha} = 0.3415[/tex]

[tex]\alpha = \arctan{0.3415} = 18.86^\circ[/tex]

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Answer:

Step-by-step explanation:

The parabola y=x^2 is shifted up by 7 units and to the left by 1 unit.

Answer:

y=(x+1)^2 +7

When the parabola y=x² is  shifted up by 7 units and to the left by 1 unit then the equation of the new parabola is y = (x-1)² + 7.

When a parabola is shifted vertically or horizontally, its equation changes accordingly.

In this case, the parabola y = x² is shifted up by 7 units and to the left by 1 unit.

Adding a constant value to the function shifts the graph vertically.

In this case, adding 7 to the original function y = x² will shift it up by 7 units:

y = x² + 7

Subtracting a constant value from the input of the function shifts the graph horizontally.

In this case, subtracting 1 from the x-values of the function y = x² + 7 will shift it to the left by 1 unit:

y = (x-1)² + 7

Hence,  the equation of the new parabola after both shifts is y = (x-1)² + 7.

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Answer:

The graph has been moved 7 units to the left and 8 units down.

Step-by-step explanation:

When numbers are added directly to the "x" value, the graph shifts to the left. If negative numbers are added directly to the "x" value, the grap shifts to the right. Therefore, if there is a +7 directly altering the "x" value, the function shifts 7 units to the left.

When a number is added to the overall function, it shifts upwards. If this number is negative, the entire function shifts downwards. Therefore, if there is a -8 outside altering the function, then it has been shifted 8 units down.

Answer: Length of side QR is 16 units.

Step-by-step explanation: Given that dimensions of  PQR

QPR= 90degrees

i dont know either your on your own

Step-by-step explanation:

i just dont know

Answer:

the revenue is 280 by 190

The area of a 2D form is the amount of space within its perimeter. The surface area of the cone is 108.79967 units².

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

Given the diameter of the cone is 6 units, therefore, the radius of the cone is 3 units, and the height of the cone is 8 units. Thus, the surface area of the right cone is,

A=πr [r+√(h²+r²)]

A = 108.79967 units²

Hence, the surface area of the cone is 108.79967 units².

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Answer:

  4 square units

Step-by-step explanation:

The vertices of the figure are on grid points, so it is appropriate to use Pick's theorem to find the area.

__

Pick's theorem tells you the area is ...

  A = i +b/2 -1

where i is the number of grid points interior to the figure (0), and b is the number of grid points on the boundary (10).

Using the counted values in the formula, we find the area to be ...

  A = 0 +10/2 -1 = 4

The area of the polygon is 4 square units.

_____

Additional comment

There are several other ways to find the area. Here are a couple:

decompose the figure

A horizontal line 1 unit up from the bottom will divide the figure into a trapezoid and a triangle. The trapezoid has bases 4 and 1, and height 1, so its area is ...

  A = 1/2(b1 +b2)h = 1/2(4 +1)(1) = 5/2

The triangle has base 1 and height 3, so its area is ...

  A = 1/2bh = 1/2(1)(3) = 3/2

Then the total area is 5/2 +3/2 = 8/2 = 4 square units.

subtract empty space

The figure occupies a 4×4 square with triangles removed from the left side and the top. Each of those triangles has a base of 4 and a height of 3. The remaining (shaded) area is ...

  A = s² -1/2bh -1/2bh

  A = 4² -1/2(4)(3) -1/2(4)(3) = 16 -12 = 4 square units

The value of the probability P(multiple of 3) is 0.3333

The spinner that completes the question is added as an attachment

From the attached spinner, we have:

The probability is then calculated as:

P(multiple of 3) = Multiples of 3/Total

This gives

P(multiple of 3) = 4/12

Evaluate

P(multiple of 3) = 0.3333

Hence, the value of the probability is 0.3333

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Answer:

9.3*10^11

Step-by-step explanation:

4/3πr^3=9.3*10^11

The solution to the equation below to the nearest fourth of a unit is 0.7142

Equations and expressions

Given the equation as shown below;

2-5x=2x-3

Collect the like terms

-5x - 2x = -3 - 2

-7x = -5

Divide both sides by -7

x = -5/-7

x = 5/7

x= 0.7142

Hence the solution to the equation below to the nearest fourth of a unit is 0.7142

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The plot of the graph is attached and points have been determined

The two among them are (5,-2) ,(15,4).

What is a  Line Function ?

A line function is what can be written in the form of

y =mx +c

where m is the slope and c is the intercept on y axis.

The equation given here is y = (3/5)x -5

m = 3/5

c = -5

The plot of the graph is attached and points have been determined

The two among them are (5,-2) ,(15,4)

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Answer:

4 days

Step-by-step explanation:

first convert 1/4 to eighths

2/8=1/4

to make 2/8 equal 7/8

you have to multiply by 4 for it to be 8/8

it cant be 7/8 because that would be three and a half days and they only read 1/4 each day

so it would take 4 days to finish

Answer:

5/24

Step-by-step explanation:

Probability of selecting a pen :

⇒ Number of pens / Total items in Box 1

⇒ 5 / 7 + 5

⇒ 5/12

=============================================================

Probability of selecting a crayon :

⇒ Number of crayons / Number of items in box 2

⇒ 4 / 4 + 4

⇒ 4/8

⇒ 1/2

===========================================================

Probability (of both events) :

⇒ 5/12 × 1/2

⇒ 5/24

The first step to solving almost any problem is to determine what the question is asking and what is given to us to help solve that problem.  Looking at the problem statement, they are asking for us to determine which option best describes the value of m in the expression provided.  The only thing that we are provided with is an expression which we need to solve for m.

Let's begin to solve the expression for m by first dividing both sides by -5.  However, since we are dividing by a negative, that means that we must flip the sign.

Divide both sides by -5

The next step that we must take is to subtract 1 from both sides but before that let's convert it into an improper fraction with a denominator of 5 so we can easily deal with it with the other fraction.

Subtract both sides by 1

We have finally came up to our final answer which would state that m is greater than or equal to negative 28 over 5.  The options that you have provided seem like the formatting has messed up but I'm sure that on your side you can see the correct answer.

The coordinates of the image of triangle are transformation are X = (1,3), Y = (5,-3) and Z = (-1, -7)

From the figure, the coordinates of the triangle are:

A = (-1, -1)

B = (1, 2)

C = (-2,4)

The transformation rule is given as:

[tex]\triangle XYZ = T_{ < 3,1 > }(R_{x-axis}(D_2(\triangle ABC)))[/tex]

This means that, we start by dilating the triangle by a scale factor of 2.

So, we have:

A' = (-2, -2)

B' = (2, 4)

C' = (-4,8)

Next, we rotate the triangle across the x-axis

So, we have:

A'' = (-2, 2)

B'' = (2, -4)

C'' = (-4,-8)

Lastly, we translate the triangle by (x + 3,y + 1) to get the triangle XYZ

So, we have:

X = (1,3)

Y = (5,-3)

Z = (-1, -7)

See attachment for the image of the transformation

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[tex]\\\\\ \textbf{a)}\\\\~~~\displaystyle \int (6x- \sin 3x) ~ dx\\\\=6\displaystyle \int x ~ dx - \displaystyle \int \sin 3x ~ dx\\\\=6 \cdot \dfrac{x^2}2 - \dfrac 13 (- \cos 3x) +C~~~~~~~~~~~;\left[\displaystyle \int x^n~ dx = \dfrac{x^{n+1}}{n+1}+C,~~~n \neq -1\right]\\\\ =3x^2 +\dfrac{\cos 3x}3 +C~~~~~~~~~~~~~~~~~~~~;\left[\displaystyle \int \sin (mx) ~dx = -\dfrac 1m ~ (\cos mx)+C \right]\\[/tex]

[tex]\textbf{b)}\\\\~~~~\displaystyle \int(3e^{-2x} +\cos (0.5 x)) dx\\\\=3\displaystyle \int e^{-2x} ~dx+ \displaystyle \int \cos(0.5 x) ~dx\\\\\\=-\dfrac 32 e^{-2x} + \dfrac 1{0.5} \sin (0.5 x) +C~~~~~~~~~~~~~~;\left[\displaystyle \int e^{mx}~dx = \dfrac 1m e^{mx} +C \right]\\\\\\=-\dfrac 32 e^{-2x} + 2 \sin(0.5 x) +C~~~~~~~~~~~~~~~~~;\left[\displaystyle \int \cos(mx)~ dx = \dfrac 1m \sin(mx) +C\right]\\\\\\=-1.5e^{-2x} +2\sin(0.5x) +C[/tex]

[tex]\textbf{a)}\\\\y = \displaystyle \int \cos(x+5) ~ dx\\\\\text{Let,}\\\\~~~~~~~u = x+5\\\\\implies \dfrac{du}{dx} = 1+0~~~~~~;[\text{Differentiate both sides.}]\\\\\implies \dfrac{du}{dx} = 1\\\\\implies du = dx\\\\\text{Now,}\\\\y= \displaystyle \int \cos u ~ du\\\\~~~= \sin u +C\\\\~~~=\sin(x+5) + C[/tex]

[tex]\textbf{b)}\\\\y = \displaystyle \int 2(5x-3)^4 dx\\\\\text{Let,}\\~~~~~~~~u = 5x-3\\\\\implies \dfrac{du}{dx} = 5~~~~~~~~~~;[\text{Differentiate both sides}]\\\\\implies dx = \dfrac{du}5\\\\\text{Now,}\\\\y = 2\cdot \dfrac 1 5 \displaystyle \int u^4 ~ du\\\\\\~~=\dfrac 25 \cdot \dfrac{u^{4+1}}{4+1} +C\\\\\\~~=\dfrac 25 \cdot \dfrac{u^5}5+C\\\\\\~~=\dfrac{2u^5}{25}+C\\\\\\~~=\dfrac{2(5x-3)^5}{25}+C[/tex]

[tex]\textbf{a)}\\\\y = \displaystyle \int xe^{3x} dx\\\\\text{We know that,}\\\\ \displaystyle \int (uv) ~dx = u \displaystyle \int v ~ dx - \displaystyle \int \left[ \dfrac{du}{dx} \displaystyle \int ~ v ~ dx \right]~ dx\\\\\text{Let}, u =x~ \text{and}~ v=e^{3x} .\\\\y= \displaystyle \int xe^{3x} ~dx\\\\\\~~= x\displaystyle \int e^{3x} ~ dx - \displaystyle \int \left[\dfrac{d}{dx}(x) \displaystyle \int e^{3x}~ dx \right]~ dx\\\\\\[/tex]

  [tex]=x\displaystyle \int e^{3x}~ dx - \displaystyle \dfrac 13 \int \left(e^{3x} \right)~ dx\\\\\\=\dfrac{xe^{3x}}3 - \dfrac 13 \cdot \dfrac{ e^{3x}}3+C\\\\\\= \dfrac{xe^{3x}}{3}- \dfrac{e^{3x}}{9}+C\\\\\\=\dfrac{3xe^{3x}}{9}- \dfrac{e^{3x}}9 + C\\\\\\= \dfrac 19e^{3x}(3x-1)+C[/tex]

[tex]\bold{\huge{\underline{ Solution }}}[/tex]

• [tex]\sf{ Polynomial :- ax^{2} + bx + c }[/tex]

• The zeroes of the given polynomial are α and β .

Here, we have polynomial

[tex]\sf{ = ax^{2} + bx + c }[/tex]

We know that,

Sum of the zeroes of the quadratic polynomial

[tex]\sf{ {\alpha} + {\beta} = {\dfrac{-b}{a}}}[/tex]

And

Product of zeroes

[tex]\sf{ {\alpha}{\beta} = {\dfrac{c}{a}}}[/tex]

Now, we have to find the polynomials having zeroes :-

[tex]\sf{ {\dfrac{{\alpha} + 1 }{{\beta}}} ,{\dfrac{{\beta} + 1 }{{\alpha}}}}[/tex]

Therefore ,

Sum of the zeroes

[tex]\sf{ ( {\alpha} + {\dfrac{1 }{{\beta}}} )+( {\beta}+{\dfrac{1 }{{\alpha}}})}[/tex]

[tex]\sf{ ( {\alpha} + {\beta}) + ( {\dfrac{1}{{\beta}}} +{\dfrac{1 }{{\alpha}}})}[/tex]

[tex]\sf{( {\dfrac{ -b}{a}} ) + {\dfrac{{\alpha}+{\beta}}{{\alpha}{\beta}}}}[/tex]

[tex]\sf{( {\dfrac{ -b}{a}} ) + {\dfrac{-b/a}{c/a}}}[/tex]

[tex]\sf{ {\dfrac{ -b}{a}} + {\dfrac{-b}{c}}}[/tex]

[tex]\bold{{\dfrac{ -bc - ab}{ac}}}[/tex]

Thus, The sum of the zeroes of the quadratic polynomial are -bc - ab/ac

Product of zeroes

[tex]\sf{ ( {\alpha} + {\dfrac{1 }{{\beta}}} ){\times}( {\beta}+{\dfrac{1 }{{\alpha}}})}[/tex]

[tex]\sf{ {\alpha}{\beta} + 1 + 1 + {\dfrac{1}{{\alpha}{\beta}}}}[/tex]

[tex]\sf{ {\alpha}{\beta} + 2 + {\dfrac{1}{{\alpha}{\beta}}}}[/tex]

[tex]\bold{ {\dfrac{c}{a}} + 2 + {\dfrac{ a}{c}}}[/tex]

Hence, The product of the zeroes are c/a + a/c + 2 .

We know that,

For any quadratic equation

[tex]\sf{ x^{2} + ( sum\: of \:zeroes )x + product\:of\: zeroes }[/tex]

[tex]\bold{ x^{2} + ( {\dfrac{ -bc - ab}{ac}} )x + {\dfrac{c}{a}} + 2 + {\dfrac{ a}{c}}}[/tex]

Hence, The polynomial is x² + (-bc-ab/c)x + c/a + a/c + 2 .

• Polynomial is algebraic expression which contains coffiecients are variables.

• There are different types of polynomial like linear polynomial , quadratic polynomial , cubic polynomial etc.

• Quadratic polynomials are those polynomials which having highest power of degree as 2 .

• The general form of quadratic equation is ax² + bx + c.

• The quadratic equation can be solved by factorization method, quadratic formula or completing square method.

Answer: x = 6

Step-by-step explanation: If you take 88.56 + 5x = 19.76x, an equation, you should first rearrange the variables to the left side of the equation: 5x - 19.76x = -88.56.

Next, you should combine your like terms. So, -14.76 = -88.56.

Then, divide both sides of the equation by the coefficient of variable. So, x = -88.56 / -14.76./

Lastly, calculate. Determine the sign for multiplication or division, so x = 88.56 / 14.76. Multiply both the numerator and denominator with the same integer. So, x = 8856 / 1476. Cross out the common factor, then you get your answer of x = 6

length = 17 units, breadth = 9 units

Step-by-step explaination:-

Let the length and the breadth of the rectangle be x units and y units respectively.

Then the area of rectangle = xy square units

According to given conditions, we have

(x -5)(y + 3) = xy - 9 and (x + 3)(y + 2) = xy + 67

=> xy + 3x - 5y - 15 = xy - 9

and xy + 2x + 3x + 6 = xy + 67

=> 3x - 5y - 6 = 0......eqn(i)

and 2x + 3y - 61 = 0.....eqn(ii)

Multiplying equation (i) by 2 and equation (ii) by 3, we get...

6x - 10y - 12 = 0....eqn(iii) and,

6x + 9y - 183 = 0....eqn(iv)

Subtracting equation (iii) from equation (iv), we get...

19y - 171 = 0 => y = 9.

Substituting this value of y in equation (ii), we get

2x + 3 × 9 - 61. = 0 => 9x - 34 = 0 => x = 17.

Hence, the length of rectangle = 17 units and

breadth = 9 units.

The annual percentage rate for a 35 month loan that charges $22.38 per every $100 financed is seen from the table to be 14%.

From the table, the APR for 35 months loan that charges $22.38 per every $100 financed is seen to be 14%.

Thus, we can conclude that the annual percentage rate for a 35 month loan that charges $22.38 per every $100 financed is seen from the table to be 14%.

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Answer:

a. 13%

Step-by-step explanation:

E2020!

The shaded area expressed as a fraction, a decimal, and a percent of the whole is 23/100, 0.23 and 23% respectively

From the question, we are to express the shaded area as a fraction, a decimal, and a percent of the whole.

In the diagram, there are 100 total squares and 23 of them are shaded

Expressing the shaded area as a fraction, we get

[tex]\frac{23}{100}[/tex]

Expressing the shaded area as a decimal, we get

[tex]\frac{23}{100}[/tex] = 0.23

Expressing the shaded area as a percent , we get

[tex]\frac{23}{100}\times 100\%[/tex] = 23%

Hence, the shaded area as a fraction, a decimal, and a percent of the whole is 23/100, 0.23 and 23% respectively

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Answer:

x<_-5

Step-by-step explanation:

-4(x+3)<_-2-2x

-4x-12<_-2-2x

-4x+2x<_-2+12

-2x<_+10

divide both side by -2

-2x/2<_10/-2

x<_-5

it is D