Figure A is the preimage. Which figure is the image of figure A after a dilation with a scale factor of 3 and a center of (0, 0)?
A. Figure R
B. Figure S
C. Figure T
D. Figure U

Answer:  The required co-ordinates of the point are (9, 0).

Step-by-step explanation:  We are given to find the co-ordinates of the point that is [tex]\dfrac{3}{5}[/tex] of the way from A(-9,3) to B(21, -2).

Let K be the required point. Then, we mus have

[tex]AK:AB=3:5\\\\\Rightarrow \dfrac{AK}{AK+BK}=\dfrac{3}{5}\\\\\\\Rightarrow 5AK=3AK+3BK\\\\\Rightarrow 2AK=3BK\\\\\Rightarrow AK:BK=3:2.[/tex]

We know that

the co-ordinates of a point that divides the line joining the points (a, b) and (c, d) in the ratio m : n are given by

[tex]\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{2}\right).[/tex]

For the given division, m : n = 3 : 2.

Therefore, the co-ordinates of the point K are

[tex]\left(\dfrac{3\times21+2\times(-9)}{3+2},\dfrac{3\times(-2)+2\times3}{3+2}\right)\\\\\\=\left(\dfrac{63-18}{5},\dfrac{-6+6}{5}\right)\\\\=\left(\dfrac{45}{5},\dfrac{0}{5}\right)\\\\=(9,0).[/tex]

Thus, the required co-ordinates of the point are (9, 0).

Building and solving an equation, it is found that the coordinates are: (9,0).

C is 3/5 of the way from A to B, thus:

[tex]C - A = \frac{3}{5}(B - A)[/tex]

This is used to find both the x-coordinate and the y-coordinate of C.

First, the x-coordinate, considering [tex]C = x, A = -9, B = 21[/tex].

[tex]C - A = \frac{3}{5}(B - A)[/tex]

[tex]x + 9 = \frac{3}{5}(21 + 9)[/tex]

[tex]x = 18 - 9[/tex]

[tex]x = 9[/tex]

Then, the y-coordinate, considering [tex]C = y, A = 3, B = -2[/tex].

[tex]C - A = \frac{3}{5}(B - A)[/tex]

[tex]y - 3 = \frac{3}{5}(-2 - 3)[/tex]

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

[tex]y = 0[/tex]

Thus, the coordinates are (9,0).

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Answer:

[tex]\boxed{\text{1. y + 5 = -4(x - 3); \qquad 2. y - 8 = x + 1}}[/tex]

Step-by-step explanation:

Question 1

The point-slope formula for a straight line is

y – y₁ = m(x – x₁)

x₁ = 3; y₁ = -5; m = -4  

Substitute the values

[tex]\boxed{\textbf{y + 5 = -4(x - 3)}}[/tex]

The diagram shows the graph of equation 1 (red) with slope -4 passing through (3,-5).

Question 2

x₁ = -1; y₁ = 8; m = 1  

Substitute the values

[tex]\boxed{\textbf{y - 8 = x + 1}}[/tex]

The diagram shows the graph of equation 2 (green) with slope 1 passing through (-1,8).

Answer:

D. 21.

Step-by-step explanation:

The general form of the equation of a circle is:

(x - a)^2 + (y - b)^2 = r^2  where r is the radius.

Comparing:

(x + 5)^2 + (y + 7)^2 = 21^2

So r^2 = 21^2

making r = √21^2

= 21.

The length of the radius of the circle is 21.

Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.

Standard form of a circle is given by the equation,

(x - h)² + (y - k)² = r²

where, (h, k) is the center of the circle and r is the radius of the circle.

Here, given equation is,

(x + 5)² + (y + 7)² = 21²

Comparing this with the standard form,

(-5, -7) is the center and 21 is the radius.

Hence the correct option is D. 21.

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Answer:

[tex]\large\boxed{3^\frac{2}{3}}[/tex]

Step-by-step explanation:

[tex]Use\\\\\sqrt[n]{a^m}=a^\frac{m}{n}\\\\(a^n)^m=a^{nm}\\\\a^n\cdot a^m=a^{n+m}\\\\\bigg(\sqrt[4]{9^{15}}\cdot\sqrt{3^3}\bigg)^\frac{2}{27}=\bigg(\sqrt[4]{(3^2)^{15}}\cdot3^\frac{3}{2}\bigg)^\frac{2}{27}=\bigg(\sqrt[4]{3^{2\cdot15}}\cdot3^{\frac{3}{2}}\bigg)^\frac{2}{27}\\\\=\bigg(3^{\frac{30}{4}}\cdot3^\frac{3}{2}\bigg)^\frac{2}{27}=\bigg(3^{\frac{15}{2}}\cdot3^\frac{3}{2}\bigg)^\frac{2}{27}=\bigg(3^{\frac{15}{2}+\frac{3}{2}}\bigg)^\frac{2}{27}[/tex]

[tex]=\bigg(3^{\frac{18}{2}}\bigg)^\frac{2}{27}=\bigg(3^9\bigg)^\frac{2}{27}=3^{9\cdot\frac{2}{27}}=3^\frac{2}{3}[/tex]

Answer:

See below in bold.

Step-by-step explanation:

(x²-2xy+y²)+(x²+2xy+y²)

= x²-2xy+y²+ x²+2xy+y²

= 2x² + 4xy + 2y².

(x²-2xy+y²)-(x²+2xy+y²)

= x²- 2xy + y²- x² - 2xy - y²

= -4xy.

Answer:

2

Step-by-step explanation:

If the constant of proportionality is k then,

y=kx

What number do we multiply by x to get y?

The constant of proportionality is 2.

Answer:

[tex]6\leq W\leq 8[/tex]

[tex]8\leq L\leq 10[/tex]

Step-by-step explanation:

Let the length of the rug be = L

Let the width of the rug be = W

Area =[tex]L\times W[/tex]

The length is 2 feet more than the width, so [tex]L=W+2[/tex]

Area = [tex](W+2)\times W[/tex]

= [tex]W^{2} +2W[/tex]

Now given is that the area of rug to be no smaller that 48 square feet and no bigger than 80 square feet.

This can be modeled as:

[tex]48\leq W^{2} +2W\leq 80[/tex]

Solving it separately:

[tex]48\leq W^{2} +2W[/tex]

=> [tex]0\leq W^{2}+2W \leq -48[/tex]

=> [tex]6\leq W[/tex]

[tex]W^{2} +2W-80\leq 0[/tex]

=> [tex]W\leq 8[/tex]

We have the following result:

[tex]6\leq W\leq 8[/tex]

And length will be :

[tex]6+2\leq L\leq 8+2[/tex]

[tex]8\leq L\leq 10[/tex]

Answer:

x = 2

Step-by-step explanation:

Collinear means that the points A, B and C all lie in a straight line, hence

AB + BC = AC, substitute values

5x - 1 + 14 = 25 - x

5x + 13 = 25 - x ( add x to both sides )

6x + 13 = 25 ( subtract 13 from both sides )

6x = 12 ( divide both sides by 6 )

x = 2

The value of x is:

                     [tex]x=2[/tex]

Three points are said to be collinear if they lie along a straight line.

Also, it is given that:

Here A, B, and C are collinear points and B is between A and C.

This means that:

           [tex]AB+BC=AC-----------(1)[/tex]

Also we are given:

[tex]AB=5x-1,\ BC=14,\ AC=25-x[/tex]

Using property (1) we have:

[tex]5x-1+14=25-x\\\\i.e.\\\\5x+13=25-x[/tex]

Now on adding x on both the side of the equation we have:

[tex]5x+13+x=25\\\\i.e.\\\\5x+x+13=25\\\\i.e.\\\\6x+13=25[/tex]

Now on subtracting 13 on both the sides of the equation we have:

[tex]6x=25-13\\\\i.e.\\\\6x=12\\\\i.e.\\\\x=\dfrac{12}{6}\\\\i.e.\\\\x=2[/tex]

Answer:

34 bottles per person per week

Step-by-step explanation:

1) identify info: The cycling tour has 340 bottles of water for each week.there are 10 people on the tour.

2) compile info: 340 bottles for 10 people per week

3) calculate: bottles per person = 340/10 = 34 bottles per person each week

The question asks to figure out how many bottles of water each person on a cycling tour gets per week. By dividing the total bottles of water (340) by the number of people (10), we find that each person receives 34 bottles of water per week.

The question is asking us to determine how many bottles of water each person on the cycling tour gets per week. This involves division in mathematics as we are dividing the total number of water bottles by the number of people.

To solve such problems, we start with the total amount given, which is 340 bottles of water here. Then, we divide this total by the number of individuals, which is 10 people in this case. So, the calculation becomes 340 bottles ÷ 10 people.

This calculation gives us 34 bottles. Hence, each person on the cycling tour gets 34 bottles of water per week.

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Answer:3 hours

Step-by-step explanation:

i did it one edg

Step-by-step explanation:

The sum of the product of a and b and the number c:i

[tex]a\cdot b+c=ab+c[/tex]

The sum of the product of a and b and the number c, written as a mathematical expression, is ab + c.

The question is asking for the sum of the product of a and b and the number c. In mathematical terms, this can be written as an expression: ab + c. This expression first calculates the product of a and b (represented by 'ab') then adds the number c to this product.

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Answer:

V=100.63 cubic feet

Step-by-step explanation:

The formula for the volume of the cube is given as

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

Where r=4.3 ft

And h is height = 5.2 ft

Now we put the value of h and r in the formula for volume

[tex]V=\frac{1}{3}\times \pi \times 4.3^{2} \times 5.2[/tex]

[tex]V=\frac{1}{3}\times \pi \times 96.148[/tex]

[tex]V=\frac{1}{3}\times 3.14 \times 96.148[/tex]

[tex]V=\frac{1}{3}\times 301.904[/tex]

V=100.63 cubic feet

To compute the volume of a cone, one needs to use the formula 1/3πr²h, where 'r' represents the radius of the base and 'h' represents the height of the cone. The specific dimensions of the cone are needed to provide a concrete answer. The given options can't be validated without these details.

Without specific parameters such as the radius and height of the cone, we cannot directly calculate the volume of the cone. However, the general formula for finding the volume of a cone is 1/3πr²h, where r represents the radius of the base and h represents the height of the cone. This formula is derived from the geometric principles of a cone's structure. Once the values of r and h are known, they can be substituted into this formula to compute the volume. The answer would then be rounded to the nearest hundredth if necessary. Unfortunately, the choices provided A.32.05 cubic feet, B.38.39 cubic feet, C.56.54 cubic feet, D.100.69 cubic feet aren't helpful without knowledge of the specific cone dimensions.

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if the circle has a diameter of 25.2, its radius is half that or 12.6.

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} r=12.6\\ \theta =168 \end{cases}\implies s=\cfrac{\pi (168)(12.6)}{180} \\\\\\ s=11.76\pi \implies \implies \stackrel{\pi =3.14~\hfill }{s=36.9264}\implies \stackrel{\textit{rounded up}}{s=36.93}[/tex]

the simple fact that 94 is 49 backwards means nothing, anymore than say 001 and 100 are equal quantities or related other than in the digits.

so, 0.49 or 49/100 and 0.94 or 94/100, are two values, both are at the one hundredth level, so to see who is larger, we can nevermind the 100 and look at the numerator, 94 is clearly much larger than 49.

Answer:

19 is the next number

Step-by-step explanation:

5+2=7

7+3=10

10+4=14

14+5=19

The next number in the pattern is 19.

To complete the number pattern 5, 7, 10, 14, we observe that the differences between the numbers increase by 1. Continuing this pattern, we add 5 to the last number, which results in 19. Thus, the next number in the pattern is 19

To complete the given number pattern: 5, 7, 10, 14, we need to find the rule that governs the pattern. Let's look at the differences between the numbers:

We can see that the differences are increasing by 1 each time. If this pattern continues, the next difference should be 5. So we add 5 to the last number in the pattern:

14 + 5 = 19

Therefore, the next number in the pattern is 19.

Answer:Maybe if you studded you would have the answer young man

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that A tank holds 17 3/5 gallons after losing 36 2/3 gallons, 4 5/6 gallons,and 27 1/12 gallons in 3

Consecutive days. If at the beginning the tank was 20 3/4 gallons short of capacity.

Tank full capacity = loss for 3 days + holding of tank after losing + shortage of capacity

To add these first let us convert these into improper fractions, then take lcd to add

Full capacity = [tex]\frac{88}{5} +\frac{110}{3} +\frac{29}{6} +\frac{325}{12} \\=\frac{88}{5} +\frac{440+58+325}{12} \\=\frac{1056+4115}{60} =[/tex][tex]=86.183[/tex] gallons

Answer: 28 km

Step-by-step explanation: For the first 25 minutes, he drove 60 km/h. Since there is 60 minutes in an hour, we know that he drove 25 km. The rest of the journey is 15 minutes. 15 minutes is 1/4 of an hour, so get 1/4 of 12 km/h. This would be 3 km. Add 25 km and 3 km. The distance between the 2 malls is 28 km.

Answer:

A: radius of the sphere

Step-by-step explanation:

The formula for surface area is A = 4πr^2

With r being the radius and A the surface area.

For volume it is

V= (4/3)πr^3

to determine the surface area and volume of sphere A: the radius of the sphere is required.

The formula for surface area is A = 4πr^2

With r being the radius and A the surface area.

For volume it is

V= (4/3)πr^3

The radius is half the diameter, so we use the equation r = D / 2. This is the same method used to calculate the radius from the diameter of a circle. If you have a sphere with a diameter of 16 cm, divide 16/2 to find the radius to make it 8 cm. If the diameter is 42, the radius is 21.

A sphere is defined as a set of all points in distant 3D Euclidean space. ("Radius") From a specific point ("center"). Twice the radius is called the diameter, and the pair of points on the sphere on the opposite side of the diameter is called the antipodes.

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Answer:

3x³ - 13x² + 7x - 12

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor, that is

x(3x² - x + 3) - 4(3x² - x + 3) ← distribute both parenthesis

= 3x³ - x² + 3x - 12x² + 4x - 12 ← collect like terms

= 3x³ - 13x² + 7x - 12

Answer:

[tex]f(x)=2(x-2)^{3}(x+2)^{2}[/tex]

Step-by-step explanation:

we know that

2 is a zero of multiplicity 3 of the polynomial

so

we have that

x=2  is a solution of the polynomial

A factor of the polynomial is

[tex](x-2)^{3}[/tex] ----> is elevated to the cube because is a multiplicity 3

and the other solution is x=-2

since the polynomial  is fifth degree, x=-2 must have a multiplicity 2

so

the other factor of the polynomial is  

[tex](x+2)^{2}[/tex] ----> is squared because is a multiplicity 2

therefore

The polynomial is equal to multiply the factors by the leading coefficient

so

[tex]f(x)=2(x-2)^{3}(x+2)^{2}[/tex]

The polynomial function based on the given properties: zeros at 2 (with multiplicity 3) and -2 (with multiplicity 1), leading coefficient of 2, is f(x) = 2(x - 2)³(x + 2).

To construct a polynomial with given zeros and multiplicities, we need to set up a product of binomial factors based on the zeros, with each binomial factor raised to the power of its respective multiplicity. The resulting polynomial is the given function f(x).

For the given properties, the roots are 2 and -2. The root 2 has multiplicity 3 and the root -2 has multiplicity 1. Also, the leading coefficient is 2. So, we can set up the polynomial function as follows:

f(x) = 2(x - 2)3(x + 2)

This represents a fifth degree polynomial function that has the zeros and multiplicities listed, with the leading coefficient of 2.

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Answer:

I think the answer is d

Step-by-step explanation:

since the graph is a lot bigger than the females, but the box thing is in about the same spot as the females ( you know what i mean), but i'm not 100% sure, but i think its the safest answer

Answer:

The 12 ( after 28) should be 14.

This 12 does not belong to the series.

Step-by-step explanation:

After every 2 numbers,  2 is added to the last number, so we have 100-50 + 2 = 52 - 26, and the second of the paired numbers is 1/2 of the first.

So after  28 the numbers should be 14 - 16 - 8 - 10.  The 12 does not belong.

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Answer:

8 x + 38 higher it is not available

Answer:

[tex]\large\boxed{D.\ -x^2+2x+8}[/tex]

Step-by-step explanation:

[tex](f-g)(x)=f(x)-g(x)\\\\f(x)=2x+1,\ g(x)=x^2-7\\\\\text{substitute:}\\\\(f-g)(x)=(2x+1)-(x^2-7)=2x+1-x^2-(-7)=2x+1-x^2+7\\\\=-x^2+2x+(1+7)=-x^2+2x+8[/tex]

D) two parabolas one facing down with a vertex at 0, 3 and one facing up with a vertex at 0, negative 3

First of all, let's rewrite the equations in a mathematical language:

[tex]y=\frac{3}{4}x^2-3[/tex]

Since the leading coefficient, the number that accompanies [tex]x^2[/tex] is positive, that is, its value is 3/4, then the parabola opens upward. On the other hand, the vertex can be found as:

[tex](h,k)=\left(-\frac{b}{2a},f\left(-\frac{b}{2a}\right)\right) \\ \\ a=3/4 \\ b=0 \\ c=-3 \\ \\ h=-\frac{0}{2(3/4)}=0 \\ \\ k=f(0)=\frac{3}{4}(0)^2-3=-3 \\ \\ \\ \boxed{Vertex \rightarrow (h,k)=0,-3}[/tex]

[tex]y=-\frac{3}{4}x^2+3[/tex]

Since the leading coefficient is negative, that is, its value is -3/4, then the parabola opens downward. Similarly the vertex can be found as:

[tex](h,k)=\left(-\frac{b}{2a},f\left(-\frac{b}{2a}\right)\right) \\ \\ a=-3/4 \\ b=0 \\ c=3 \\ \\ h=-\frac{0}{2(-3/4)}=0 \\ \\ k=f(0)=-\frac{3}{4}(0)^2+3=3 \\ \\ \\ \boxed{Vertex \rightarrow (h,k)=0,3}[/tex]

Both graph are shown below and you can see that the conclusion of our problem is correct.

Answer:

6

Step-by-step explanation:

You can see how f(x) is now f(8), this implies you have to replace any x's you see with an 8.

So f(8) = 2(8-5) = 2(3) = 6

AnswerB. because x is in denominator

Step-by-step explanation:

Answer:

Option A. [tex]f(x)=86[1.04]^{x}[/tex] ; grows approximately at a rate of 0.4% daily

Step-by-step explanation:

we have

[tex]f(x)=86(1.29)^{x}[/tex]

where

f(x) the number of weeds in the garden

x ----> the number of weeks

Calculate how quickly the weeds grow each day

Remember that a week is equal to seven days

so

[tex]f(x)=86(1.29)^{\frac{x}{7}}[/tex]

Using the law of exponents

b^(x/a) = b^(x*(1/a)) = (b^(1/a))^x

so

[tex]f(x)=86[(1.29)^{\frac{1}{7}}]^{x}[/tex]

[tex]f(x)=86[1.04]^{x}[/tex]

therefore

The rate is approximately

1.04=1+r

r=1.04-1=0.04=4% daily

not sorry, but guy above is w.r.o.n.g

0.4 ain't right

yw for saving you an attempt

ANSWER