If the dilation is given: triangle ABC->Triangle ¨A¨B¨C under do.2 which of the following is the scale factor.

Answer:

[tex]Y = 15x+ 100[/tex]

x = 10 months

Step-by-step explanation:

Given:

Initial deposit = $100

Weakly deposit = $15

Solution:

We need to create an equation where total amount is y is equal to initial deposit plus multiplication of weakly deposit and month x, so the equation is written as.

[tex]Y = 15x+ 100[/tex] ---------(1)

Where:

Y = Total amount

x = Number of months.

Second thing we need to find the month for y = $250

Now, we substitute y = 250 in equation 1.

[tex]250 = 15x+ 100[/tex]

[tex]15x=250-100[/tex]

[tex]15x =150[/tex]

[tex]x=\frac{150}{15}[/tex]

x = 10 months

Therefore, we need to required 10 months for $250.

The value of  [tex]3log_{4}(2)+log_{5}(512)[/tex]  is about 5.376

Step-by-step explanation:

Let us revise some rules of logarithm

∵ The expression is [tex]3log_{4}(2)+log_{5}(512)[/tex]

- By using the 1st rule in the first term

∵ [tex]3log_{4}(2)=log_{4}(2)^{3}[/tex]

∵ 2³ = 8

∴ [tex]log_{4}(2)^{3}=log_{4}(8)[/tex]

- By using the second rule

∵ [tex]log_{4}(8)=\frac{log(8)}{log(4)}=1.5[/tex]

∵ [tex]log_{5}(512)=\frac{log(512)}{log(5)}=3.876[/tex]

- Add the two answers

∴  [tex]3log_{4}(2)+log_{5}(512)[/tex] = 1.5 + 3.876

∴  [tex]3log_{4}(2)+log_{5}(512)[/tex] = 5.376

The value of  [tex]3log_{4}(2)+log_{5}(512)[/tex]  is about 5.376

Learn more:

You can learn more about the logarithmic expressions in brainly.com/question/11921476

#LearnwithBrainly

Answer:

[tex]y = - x-1[/tex]

Step-by-step explanation:

The line a passes through th points (-1,0) and (0,-1)

The equation of line which is passes through the point [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is

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

Therefore the equation of line which passes through the points (-1,0) and (0,-1)

is

[tex]y-0=\frac{-1-0}{0-(-1)} [x-(-1)][/tex]       [ [tex]x_1 = -1, y_1= 0[/tex] [tex]x_2 = 0[/tex]  and [tex]y_2 = -1[/tex]]

[tex]\Leftrightarrow y = -1 (x+1)[/tex]

[tex]\Leftrightarrow y = - x-1[/tex]

Answer:

b

Step-by-step explanation:

48 kilograms of 15 % copper is combined with 72 kilograms of 75 % copper to create 120 kg of a 51​% copper​ alloy

Solution:

Let "x" be the kilograms of 15 % copper

Then, (120 - x) be the kilograms of 75 % copper

Then, according to question,

"x" kilograms of 15 % copper is combined with (120 - x) kilograms of 75 % copper to create 120 kg of a 51​% copper​ alloy

Thus we frame a equation as:

15 % of x + 75 % of (120 - x) = 51 % of 120

Solve the equation for "x"

[tex]15 \% \times x + 75 \% \times (120-x) = 51 \% \times 120\\\\\frac{15}{100} \times x + \frac{75}{100} \times (120-x) = \frac{51}{100} \times 120\\\\0.15x + 0.75(120-x) = 0.51 \times 120\\\\0.15x + 90 - 0.75x = 61.2\\\\0.6x = 90 - 61.2\\\\0.6x = 28.8\\\\Divide\ both\ sides\ by\ 0.6\\\\x = 48[/tex]

Thus 48 kilograms of 15 % copper used

Then, (120 - x) = (120 - 48) = 72

Thus, 72 kilograms of 75 % copper is used

To solve the given system of linear equations, we use the elimination method to find the solution, which is (x, y) = (-1, 1).

The student is asking how to find the solution to a system of linear equations:

x + 5y = 4

3x - 7y = -10

To solve this system, one can use the method of elimination.

Multiply the first equation by 3 and the second equation by 1 to align the coefficients of x.

The resulting equations are:

3x + 15y = 12

3x - 7y = -10

Subtract the second equation from the first to eliminate x:

22y = 22

Divide by 22 to find y:

y = 1

Substitute y = 1 into the original first equation:

x + 5(1) = 4

Solve for x:

x = -1

The solution to the system is (x, y) = (-1, 1).

Answer:

  [tex]0.\overline{1}[/tex]

Step-by-step explanation:

The fraction reduces to 1/9. Since you're familiar with the decimal equivalents of fractions with denominators less than 10, you know this has the decimal equivalent:

  1/9 = 0.11111111...(repeating)

_____

Even if you're not familiar with the equivalent of 1/9, you probably know that ...

  1/3 = 0.33333...(repeating)

and

  2/3 = 0.66666...(repeating)

Of course, 1/3 = 3/9, so dividing 0.333... by 3, we get 1/9 = 0.111....

_____

The attachment shows the long division. It gets boring quickly.

Final answer:

The equivalent decimal of the fraction 5/45 is approximately 0.1111

Explanation:

To find the equivalent decimal of the fraction 5/45, we can start by simplifying the fraction. Since both the numerator (5) and the denominator (45) are divisible by 5, we can reduce the fraction to 1/9.

To convert this simplified fraction into a decimal, we divide 1 by 9.

1 ÷ 9 = 0.111...

The decimal 0.111... means that the 1 repeats indefinitely, which is known as a repeating decimal.

If we want to convert this repeating decimal into an approximation with a specific number of decimal places, we could round it. For example, we could say 0.111... is approximately 0.111 when rounded to three decimal places.

Answer:

7 units  

Step-by-step explanation:

I plotted your points to form the polygon in the diagram below.

The vertical side joins the points (0 ,3) and (0, -4).

The vertical distance between them is

3 - (-4) = 3 + 4 = 7

The length of the vertical side is 7 units.

Answer:

7 units

Step-by-step explanation:

Answer:

A, B, and C are true

Step-by-step explanation:

Using the Factor Theorem to find the function, the correct statement is:

The function is positive on (0,∞).

The Factor Theorem states that a polynomial function with roots

x1, x2,...xn  is given by:

f(x) = a(x-x1)(x-x2).....(x-xn)

In which a is the leading coefficient.

here, we have,

The described roots means that:

x1 = 0, x2 = x3= x4 =x5 = 2

Hence the function is:

f(x) = x(x - 2)^4

(x - 2)^4 is always positive, hence the sign depends on the sign of x, which means that the correct statement is:

The function is positive on (0,∞).

More can be learned about the Factor Theorem at brainly.com/question/24380382

#SPJ7

Answer:A ($139.26)

Step-by-step explanation:

Answer:

39 degrees

Step-by-step explanation:

The angle of a straight line is 180 degrees. This is constant and will never change. You will add 57 and 84 to get 141 degrees for <LMP.  Take 180-141 to get 39 degrees for <PMN

Answer:

125%

Step-by-step explanation:

this is because the difference is 25% so b is 125% more than a

Answer:

The function is [tex]f(x) = 4(\sqrt[3]{16} )^{2x}[/tex].

Step-by-step explanation:

We have to choose from options the exponential function which has a simplified base of 4∛4 i.e. ∛(256).

Now, the exponential function in the option III will be the answer.

The function is [tex]f(x) = 4(\sqrt[3]{16} )^{2x}[/tex].

So, the base is [tex](\sqrt[3]{16} )^{2}[/tex] = [tex]\sqrt[3]{16^{2}} = \sqrt[3]{256} = 4\sqrt[3]{4}[/tex]. (Answer)

The general formula of an exponential function is [tex]f(x) = a(b)^{x}[/tex] , where b is called the base of the function.  

The function that has a simplified base of (4∛4) is;

Option C; 4(∛16)^(2x)

From the general formula of an exponential function, we know that;

f(x) = a(b)^(x)

Now, we have;

f(x) = (4∛4)^(x)

Thus, looking at the options, option C is correct because;

In 4(∛16)^(2x), the base is (∛16)² and when we simplify it, we will get 4³(√4) because;

(∛16)² = √(16^(⅔))

>> 256^(⅓)

>> 4∛4

This is the same as our initial value.

Read more about exponential functions at; https://brainly.com/question/13917934

Answer:

4(x-1)units

Step-by-step explanation:

In a given rectangle, the length of the rectangle is the shorter side while its breadth is the longer side.

Since we have 2 lengths and 2 breadths in a rectangle, the perimeter of the rectangle will be 2L+2x where

L is the length(shorter side) and x is the breadth (longer side).

According to the question, the shorter side(L) is 2 units less than the longer side(x). Mathematically,

L = x-2

Substituting L = x-2 into the formula of perimeter of a rectangle we have,

P = 2(x-2) + 2x

P = 2x-4+2x

P = 4x-4

P = 4(x-1)

The perimeter of the rectangle will be 4(x-1)units

Answer:

Adults: $8

Children: $5

Step-by-step explanation:

First Step:

Let's represent The leas by: 2A + 3C = 31

Let's represent The Smiths Station by: 2A+2C=26

Second step:

Solve The leas expression for A → 2A + 3C = 31

[tex]A =\frac{31-3C}{2}[/tex]

Third step:

Replace A on The Smiths Station and solve for C:

2([tex]\frac{31-3c}{2}[/tex]) + 2C = 26

31-3C+2C = 26

31-C=26

31-26 = C

C= 5

Fourth step:

Replace C=5 in expression [tex]A =\frac{31-3C}{2}[/tex]

A = [tex]\frac{31-3*5}{2}[/tex] →→ A=[tex]\frac{31-15}{2}[/tex]  →→ A=[tex]\frac{16}{2}[/tex]  →→ A= 8

Answer:

------------------------------------------------------------------------------------------

Answer:

ç

Step-by-step explanation:

fufujphgfhjunkksbkbbdkdbkdldbdjdbdkdjjdkdmdljdbdivdjbdkd

Answer: A. M, the number of movies. 

Step-by-step explanation: I put A, and it was the right answer.

Answer:

The slope of y=4-2x is -2.

Therefore I earn $50 interest

Therefore I earn $30.88 interest.

I would do the first one.

Step-by-step explanation:

A.

Given , I invested $500 at 5% simple interest for 2 years.

P=$500,  r =5% and t = 2 years

[tex]Interest (I) =\frac{P \times r \times t}{100}[/tex]

                  [tex]=\$\frac{500 \times 5 \times 2}{100}[/tex]

                   =$50

Therefore I earn $50 interest.

B.

Given , I invested $500 at 3% compounded monthly for 2 years.

P=$500,  r =3% = 0.03 and t = 2 years

[tex]Amount (A) =P(1+\frac{r}{n})^{nt}[/tex]  

                   [tex]=\$500(1+\frac{0.03}{12})^{ 2\times 12}[/tex]

                   =$530.88

Interest = $(530.88-530) = $30.88

I would do the first one.

Answer:

C)

Step-by-step explanation:

Step-by-step explanation:

[tex] \because \triangle \: RSU \sim \: \triangle VST \\ \\ \therefore \: \frac{RS}{VS} = \frac{7}{14} = \frac{1}{2} ....(1) \\ \\ \angle RSU \cong \: \angle VST ....(2) \\ (vertically \: opposite \: angles) \\ \\ \frac{US}{TS} = \frac{4}{8} = \frac{1}{2} ....(3) \\ \\ from \: equations \: (1) \: (2) \: and \: (3) \\ it \: is \: clear \: that: \\ \triangle \: RSU \sim \: \triangle VST\\ ..(by \:SAS\:similarity\:postulate) [/tex]

Thus, given triangles are similar by SAS similarity postulate.

When the triangles RSU and VST are said to be similar, it means the corresponding sides and angles are proportional and equal respectively, which is known as the Angle-Angle criterion for similarity.

If the triangles RSU and VST are similar (RSU ~ VST), it means the corresponding sides and angles of the two triangles are proportional, and the corresponding angles are equal. This is also known as the Angle-Angle (AA) criterion for similarity. The order of the letters signifies the corresponding parts of the triangles. R corresponds to V, S to S, and U to T. So, the angles R and V are congruent, as are the angles U and T. Because we have two pairs of congruent angles, we can say that the triangles are similar by the AA criterion.

https://brainly.com/question/31404653

#SPJ11

The radius of grape is 1 cm

Solution:

Given that,

The volume of an object is equal to the ratio of its mass to density

[tex]Volume = \frac{mass}{density}[/tex]

From given,

Mass = 8.4 grams

Density = 2 grams per cubic centimeter

Substituting in above formula,

[tex]Volume = \frac{8.4}{2} = 4.2\ cm^3[/tex]

Given is a spherical grape

The formula for volume of sphere is given as:

[tex]Volume = \frac{4}{3} \pi r^3[/tex]

Where, "r" is the radius of sphere

[tex]4.2 = \frac{4}{3} \times 3.14 \times r^3\\\\4.2 = 4.187 \times r^3\\\\r^3 = \frac{4.2}{4.187}\\\\r^3 = 1.003\\\\\text{Take cube root on both sides}\\\\r = 1.000999 \approx 1[/tex]

Thus the radius of grape is 1 cm

Answer:

1.0 cm

Step-by-step explanation:

y=a.(X-x1)(X-x2)

x1 and x2 are x-intercepts

x1=-3

x2=1

other points: (-1,8) and (0,5)

y=a.(x+3).(x-1)

a=-2

f(x)= -2.(x+3)(x-1)

The equation is [tex]\[f(x) = -2 \cdot (x + 3)(x - 1)\][/tex]

Given the quadratic equation in the form \(y =[tex]a \cdot (X - x_1)(X - x_2)\), where \(x_1\) and \(x_2\)[/tex]represent the x-intercepts, and the given x-intercepts are[tex]\(x_1 = -3\) and \(x_2 = 1\).[/tex]

Using the given x-intercepts [tex]\(x_1 = -3\) and \(x_2 = 1\)[/tex], the equation becomes [tex]\(y = a \cdot (x + 3)(x - 1)\).[/tex]

We are also provided with two other points: (-1, 8) and (0, 5).

We can substitute the point (-1, 8) into the equation to solve for \(a\):

[tex]When \(x = -1\) and \(y = 8\):\[8 = a \cdot ((-1) + 3)((-1) - 1)\]\[8 = a \cdot (2)(-2)\]\[8 = -4a\]\[a = -2\][/tex]

Therefore, the value of \(a\) is -2.

Substituting [tex]\(a = -2\) into the equation \(y = a \cdot (x + 3)(x - 1)\), we get:\[y = -2 \cdot (x + 3)(x - 1)\][/tex]

[tex]\[f(x) = -2 \cdot (x + 3)(x - 1)\][/tex]

Read more on quadratic function https://brainly.com/question/1214333

#SPJ2

Answer:

B. of the AAS congruence theorem.

Step-by-step explanation:

Triangles TSR and QRS share side SR

SR=RS

Angle TSR and Angle QRS are right angles, so

∠S= ∠R

Angle T Is-congruent-to Angle Q, so

∠T= ∠Q

From these data, we have one congruent side and two congruent angles. The possible congruence theorem that we can apply will be either ASA or AAS. In the ASA theorem, the congruence side must be between the two congruent angles.

The congruence side required for the ASA theorem for this triangle is ST = RQ. It is wrong because the congruent side we have is SR=RS. The correct option is the AAS theorem.

Answer:

Harry's solution is incorrect.

Harry can first substitute (30) for t. He can the multiply 1/3 by (30) to get a product of (10). Since 15 (≠) equal to (10), Harry's solution is (not) correct.

Step-by-step explanation:

Given:

Equation = [tex]\frac{1}{3}(t) =15[/tex]

Solution of the equation = [tex]30[/tex]

Lets check the equation whether both sides of the equation gives same result by plugging the values of t = 30.

⇒ [tex]\frac{1}{3}(t) = 15[/tex]

⇒ [tex]\frac{1}{3}(30) = 15[/tex]

⇒ [tex]\frac{30}{3} =15[/tex]

⇒ [tex]10=15[/tex]

We know that 10 ≠ 15 so the solution is incorrect.

According to the question :

Harry can first substitute (30) for t. He can the multiply 1/3 by (30) to get a product of (10). Since 15 (≠) equal to (10), Harry's solution is (not) correct.

Harry's solution is incorrect.

Answer:

[tex]\frac{5x^{2} }{6}[/tex]

Step-by-step explanation:

Given: Base of triangle= [tex]\frac{5x}{3}[/tex]

           Height of triangle= x

Now, finding the area of triangle.

We know area of triangle= [tex]\frac{1}{2} \times base\times height[/tex]

Subtituting the value of base and height in the formula.

⇒[tex]Area\ of\ triangle= \frac{1}{2} \times \frac{5x}{3} \times x[/tex]

Solving it to find area of triangle

∴ [tex]Area\ of\ triangle= \frac{5x^{2} }{6}[/tex]

Hence, area of triangle is [tex]\frac{5x^{2} }{6}[/tex]

Answer:

A=5x^2/6

Step-by-step explanation: