What is the solution to this system of equations?


4x + 5y = 7


3x – 2y = –12

The coordinates of the point A before dilation is (-12,-12)

Answer:

x = 6

Step-by-step explanation:

Given the 2 equations

x - y = 4 → (1)

x + y = 8 → (2)

Adding the 2 equations term by term eliminates the y- term

(x + x) + (- y + y) = (4 + 8), that is

2x = 12 ( divide both sides by 2 )

x = 6

Answer:

[tex]\large\boxed{y=\dfrac{1}{4}x-1}[/tex]

Step-by-step explanation:

[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\to(0,\ b)\\\\\text{We have the slope}\ m=\dfrac{1}{4}\ \text{and the y-intercept}\ (0,\ -1)\to b=-1.\\\\\text{Substitute:}\\\\y=\dfrac{1}{4}x-1[/tex]

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\\\ ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \left( \cfrac{4^{\frac{5}{4}}\cdot 4^{\frac{1}{4}}}{4^{\frac{1}{2}}} \right)^{\frac{1}{2}}\implies \left( \cfrac{4^{\frac{5}{4}\cdot \frac{1}{2}}\cdot 4^{\frac{1}{4}\cdot \frac{1}{2}}}{4^{\frac{1}{2}\cdot \frac{1}{2}}} \right)\implies \cfrac{4^{\frac{5}{8}}\cdot 4^{\frac{1}{8}}}{4^{\frac{1}{4}}}\implies \cfrac{4^{\frac{5}{8}+\frac{1}{8}}}{4^{\frac{1}{4}}}[/tex]

[tex]\bf \cfrac{4^{\frac{6}{8}}}{4^{\frac{1}{4}}}\implies \cfrac{4^{\frac{3}{4}}}{4^{\frac{1}{4}}}\implies 4^{\frac{3}{4}}\cdot 4^{-\frac{1}{4}}\implies 4^{\frac{3}{4}-\frac{1}{4}}\implies 4^{\frac{2}{4}}\implies 4^{\frac{1}{2}}\implies \sqrt{4}\implies 2[/tex]

Final answer:

The equivalent expression for  [tex](4^5/4 \times 4^1/4 \div 4^1/2)^1/2[/tex] is 2, found by applying properties of exponents such as multiplication, division, and power of a power.

Explanation:

The expression given is  [tex](4^5/4 \times 4^1/4) \div 4^1/2)^1/2.[/tex] To find the equivalent expression, we use the properties of exponents, which include multiplication, division, and taking a power of a power. When you multiply with the same base, you add the exponents, and when you divide, you subtract the exponents. Also, taking a power of a power means you multiply the exponents.

Following these rules:

Combine the exponents for the terms that multiply: 5/4 + 1/4 = 3/2, hence the expression simplifies to [tex]4^{(3/2)}.[/tex]

Subtract the exponent of the denominator: (3/2) - (1/2) = 1, so now we have [tex]4^1.[/tex]

Finally, apply the outer exponent of  [tex]1/2: (4^1)^{(1/2)}[/tex]which means we take the square root of 4, giving us 2 as the final answer.

Answer:

25 m

Step-by-step explanation:

Use the Pythagorean Theorem.

a^2+b^2=c^2

Or just know you are finding the hypotenuse and use c=sqrt(a^2+b^2)

If you were finding a leg use a=sqrt(c^2-b^2).

So sqrt(15^2+20^2)

=sqrt(225+400)

=sqrt(625)

=25

Total Weight = Weight of the book + Weight of the CD + Weight of the box

Total Weight = 1 1/4 pound + 1/5 pound + 3/10 pound

Total Weight = 5/4 + 1/5 + 3/10

To add these fractions, you need to put them over a common denominator.  To do that, find the least common multiple of 4, 5, and 10.  Below is a table of the multiples.  The least multiple they have in common is 20, shown in orange.  So use 20 as your least common denominator.

          1      2      3      4     5      6     7

4 x      4     8     12    16   20    24   ...

5 x      5    10    15    20   25    30   ...

10 x   10   20   30    40    50    60   ...

Can you finish it from here?

Answer: 23 = x

Step-by-step explanation: The first, and in this case, only step, is the simplify the equation. We do not have to get the variable on one side since it already is. 27-4 = 23, so our answer will be 23.

Answer:

-21.79.

Step-by-step explanation:

(-10.5 + m) / 11.57 = -2.748

(-10.5 + m) = -2.748 (11.57)

-10.5 + m = -31.794

m = -31.794 + 10.5 = -21.79.

Answer:

-21.29

Step-by-step explanation:

-10.5+m/11.57=-2.748

-10.5+m=-2.748*11.57

-10.5+m=-31.79436

m=-31.79436+10.5

m=-21.29

Answer:

0

Step-by-step explanation:

To find the slope of a line given two points I just like to line up the points and subtract and then finally put 2nd difference/1st difference like this:

(-3    ,2)

(6    ,2)

----------

-9    0

2nd/1st=0/-9=0

So the slope is 0

P.S. You can also see if you plot the points you get a horizontal line after connection... Slopes of horizontal lines are 0 since slope=rise/run and there is no rise (there is zero rise)

Answer:

0

Step-by-step explanation:

Answer:

(-7, 6).

Step-by-step explanation:

All sides are equal since it is a square.

The length of the side joining the first 2 points is  |-7 - 6| = 13 units and it is horizontal.

The adjacent side is vertical and also has length 13  and moves up from the last line.

So the missing coordinate has a y coordinate of  6 and an x coordinate of -7.

Answer:the answer is y is less than or equal to 17

Step-by-step explanation: if y + 8 is less than or equal to 25, all you have to do is subtract 8 to 25 and the answer has to be less than or equal to the number

Answer:

2 whole 1/4

Step-by-step explanation:

When forming a perfect square trinomial you need to "complete the square".

All of the steps to completing the square when solving an equation:

1.  The leading coefficient must be 1.  

2.  Divide b by 2.

3.  Square (b/2)

4.  Add (b/2)^2 to both sides to keep the polynomial balanced.

5.  You can now write the perfect square trinomial and solve.

x^2 - 3x  

-3/2

(-3/2)^2 = 9/4 = 2 1/4

Answer:

The answer is 2 1/4

Step-by-step explanation:

You are welcome.

Answer:

[tex]36\ m[/tex]

Step-by-step explanation:

Let

x -----> the distance of Ana from the kite

we know that

Applying the law of sines

[tex]\frac{46}{sin(109\°)}=\frac{x}{sin(47\°)}\\ \\x=(46)sin(47\°)/sin(109\°)\\ \\x=35.58\ m[/tex]

round to the nearest meter

[tex]35.58=36\ m[/tex]

Answer:

length=1.05m

perimeter=2.7m

Step-by-step explanation:

18900 in m^2=1.89 m^2

area=length*width

1.89=length*1.8 m

length=1.89÷1.8

length=1.05 m

perimeter=(l+w) 2

perimeter=(1.05+1.8)2

perimeter=2.85×2

perimeter=2.7 m

a. The rectangular backboard’s length in meters is 1.05 meters.

b. The perimeter of the total area in meters is 5.7 meters.

Given the following data:

Conversion:

10,000 [tex]cm^{2}[/tex] = 1 [tex]m^2[/tex]

18,900 [tex]cm^{2}[/tex] = X [tex]m^2[/tex]

Cross-multiplying, we have:

[tex]X = \frac{18900}{10000}[/tex]

X = 1.89 [tex]m^2[/tex]

a. To find the backboard’s length in meters:

Mathematically, the area of a rectangle is given by the formula;

[tex]A = LW\\\\1.89 = L(1.8)\\\\L = \frac{1.89}{1.8}[/tex]

Length, L = 1.05 meters.

b. To find the perimeter of the total area in meters:

Mathematically, the perimeter of a rectangle is given by the formula;

[tex]Perimeter = 2(L+W)[/tex]

Substituting the values into the formula, we have;

[tex]Perimeter = 2(1.05+1.8)\\\\Perimeter = 2(2.85)[/tex]

Perimeter = 5.7 meters

Find more information: brainly.com/question/897975

ANSWER

[tex]p = - 3[/tex]

The completely factored form is

[tex](x + 1)(x - 1)( 3x - 1)[/tex]

EXPLANATION

The given polynomial expression is

[tex]3 {x}^{3} - {x}^{2} + px + 1[/tex]

Let

[tex]f(x) = 3 {x}^{3} - {x}^{2} + px + 1[/tex]

According to the Remainder Theorem, if f(x) is exactly divisible by x-1, then the remainder is zero.

This implies that:

[tex]f(1) = 0[/tex]

[tex]3 {(1)}^{3} - {(1)}^{2} + p(1)+ 1 = 0[/tex]

[tex]3 - 1 + p + 1 = 0[/tex]

[tex]3 + p = 0[/tex]

[tex]p = - 3[/tex]

When we substitute the value of p back into the function, f(x) we get:

[tex]f(x) = 3 {x}^{3} - {x}^{2} - 3x + 1[/tex]

We now perform long division as shown in the attachment.

We can factor the function to get:

[tex]f(x) =(x - 1)( 3 {x}^{2} + 2x - 1)[/tex]

We now split the middle term of the quadratic term and factor it completely to obtain:

[tex]f(x) =(x - 1)( 3 {x}^{2} + 3x - x - 1)[/tex]

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

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

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

Answer:

d.no change

Step-by-step explanation:

There will be no change in the quantity of products sold.

Option D will be the correct answer.

Given that the turnover is increased by 10 % when the price increases by 10 %.

Let us consider that the price of the product is x and the quantity sold is n numbers. Then the turnover t will be given as,

[tex]t = x\times n[/tex]

An increase in the price of the product is 10 % results in an increase in turnover by 10%. Hence the increased price is,

[tex]x' = x+\dfrac{10}{100}\times x[/tex]

[tex]x' = 1.1 x[/tex]

Hence new turnover will be,

[tex]t'= x\times n + \dfrac {10}{100} \times x\times n[/tex]

[tex]t'= 1.1\times x\times n[/tex]

The quantity sold can be calculated by dividing the new turnover by the increased price of the product. Thus, the new quantity of the product will be,

[tex]n' = \dfrac {t'}{x'}[/tex]

[tex]n' = \dfrac {1.1\times x\times n}{1.1\times x}[/tex]

[tex]n' =n[/tex]

We can see that the quantity of the product sold remains unchanged.

Hence option D will be the correct answer, there will be no change in the quantity of product sold.

To know more about the price and quantity, follow the link given below.

https://brainly.com/question/13953486.

Answer:

20

Step-by-step explanation:

5+5+5+5=20

[tex]y=2^{\left(x-2\right)}+3[/tex]

To solve this problem, we need to start with the parent function of the exponential function, which is [tex]f(x)=a^x[/tex], where [tex]a[/tex] is the base. In our problem, [tex]a=2[/tex], so our parent function here is [tex]y=2^x[/tex]. Then, we need to perform some transformations to our parent function. Thus:

1. Vertical shrink:

A vertical shrink is a nonrigid transformation because the graph of the function get a distortion in the shape, so this transformation is as follows:

[tex]g(x)=cf(x)[/tex]

where [tex]c[/tex] in this problem equals 0.25 because:

[tex]y=0.25(2^x) \\ \\ y=\frac{1}{4}(2^x) \\ \\ y=\frac{2^x}{2^2} \\ \\ y=2^{(x-2)}[/tex]

2. Vertical shift:

The graph of the function [tex]y=2^{(x-2)}[/tex] get a vertical shift given by:

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

So the graph is shifted 3 units up. So the result is the graph shown above.

Answer:

The answer is C

Step-by-step explanation:

Answer:

r = 3

Step-by-step explanation:

The common ratio r of a geometric sequence is the ratio between consecutive terms, that is

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

r = 12 ÷ 4 = 3

r = 36 ÷ 12 = 3

Answer: the answer is 40 because 20 plus 20 equals 40

20 + 20 = 40

If you add 2 + 2 = 4 (the number values in the tens place) and 0 + 0 = 0 (the number values in the ones place). Put the 4 in tens place and 0 in the ones place which is 40

Hope this helped!

~Just a girl in love with Shawn Mendes

its 4.8*4.1*15=295.2 cm3

Answer:

295.2 cm^3.

Step-by-step explanation:

The volume of a rectangular prism is

V = w*l*h, where w is the width, l is the long and h is the height. Then,

[tex]V = 4.1 cm * 15 cm * 4.8 cm = 295.2 cm^3[/tex].

Answer: I make 15 dollars every week at my job

Step-by-step explanation: your x is likely representing a time like weeks and your y is most likely going to be the amount of something like money. so if x increases by one every time and y increases by 15 every time your scenario could be i make 15 dollars every week at my job.

Answer:

Step-by-step explanation:

X²=12x-40

X²-12x+40=0

a=1  and b= -12 and c = 40

delta = b² - 4ac

delta = (-12)² - 4(1)(40) = 144 - 160 = - 16 = (4i)² ....i² = -1

x1= (12-4i)/2 =6-2i

x1= (12+4i)/2 =6+2i

Answer:

Step-by-step explanation:

x^2 = 12 x-40

x² - 12x + 40 = 0

a = 1;  b = -12; c = 40

4ac - b² = 4*1*40 - (-12)² = 160 - 144 = 16

x = -b ± √4ac-b² i / 2a

 = -(-12) ± √ 16 i

          2 * 1

= (12 ± 4 i )/ 2

= 2( 6 ±  2i)

        2

=   6 ±  2i

Answer:

C = 58.88 degrees

Step-by-step explanation:

We can use the law of cosines to find the missing angle measurement

c^2 = a^2 +b^2 -2ab cosC

Rearranging and solving for cos C

2ab Cos C = a^2 +b^2 - c^2

Divide by 2ab

cos(C) =  a^2 + b^2 − c^2

             ------------------------

                         2ab

Substituting what we know  a = 31 b = 21   c = 27

                            31^2 + 21^2 - 27^2

     cos C        =  -----------------------------

                             2(31)(21)

      cos C = .516897081

Take the inverse cos on each side

cos^-1 cos C = cos ^-1 (.516897081)

C = 58.88 degrees

Answer:

843.67

Step-by-step explanation:

896 is the original price

A 12% discount will be applied so what is 12% of 896 =.12(896)=107.52

So we started with 896 and we are taking off 107.52=896-107.52=788.48

So the price after the discount is 788.48.

Now to apply the tax which is 7%=.07  so we need to find 7% of 788.48=.07(788.48)=55.19 (This is the tax dollar amount to be added to the price before tax).

So Sara is paying 788.48+55.19=843.67

Answer:

843.67

Step-by-step explanation:

Take the original price and find the discount

896 * 12 %

896 * .12

107.52

The new price is the original price minus the discount

896-107.52

788.48

Now we need to find the tax on the sale price

788.48 * 7%

788.48 *(.07)

55.19

Add the sale price and the tax to find the total price

788.48 +55.19

843.67

Answer:

(2,5)

Step-by-step explanation:

6x+4y=32

-6x+4y=8

We will add the two equations together to eliminate x

6x+4y=32

-6x+4y=8

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

      8y = 40

Divide each side by 8

8y/8 = 40/8

y = 5

Multiply the first equation by -1

-6x-4y = -32

-6x+4y=8

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

-12x = -24

Divide by -12

-12x/-12 = -24/-12

x = 2

Answer:

5[tex]\sqrt{2}[/tex]

Step-by-step explanation:

The geometric mean of 2 numbers a and b is

[tex]\sqrt{ab}[/tex]

Hence

The geometric mean of 5 and 10 is

[tex]\sqrt{5(10)}[/tex]

= [tex]\sqrt{50}[/tex]

= [tex]\sqrt{25(2)}[/tex] = [tex]\sqrt{25}[/tex] × [tex]\sqrt{2}[/tex] = 5[tex]\sqrt{2}[/tex]

Answer:

7.071

Step-by-step explanation:

To find geometric mean of two numbers given , you multiply numbers then find the square root of the result.

For this question we have  the numbers given as 5 and 10. So multiply 5 by 10 then get the square root of the answer.

[tex]=5*10=50\\\\\\\\\sqrt{50} =7.071[/tex]

Answer:

Step-by-step explanation:

You have that [tex]i^2=-1[/tex], so we must have

[tex]i^4=(i^2 )(i^2)=(-1)(-1)=1[/tex].

This says that we must make groups of four [tex]i[/tex]'s for simplify because they becomes 1, and the last group that is not of four [tex]i[/tex]'s is the result.

This is equivalent to divide 256 by 4 and use the remainder of that division, that is 0, as the new power of [tex]i[/tex], and the result is 1 because [tex]i^0 =1.[/tex]. You can see the operation:

[tex]i^{256} = (i^4)^{64}\times i^0 =1[/tex]

Answer:

0.009 units in the positive y direction.

Step-by-step explanation:

Vertical shift is simply the value of the constant.

In this case, if you expand the formula by multiplying 0.9 into the parentheses,

y = 0.9 sin [(π/3) - x] + (0.9)(0.01)

y = 0.9 sin [(π/3) - x] + 0.009

Here the value of the constant is 0.009 and it is positive, hence the vertical shift is 0.009 units in the positive y direction.