Can someone please help me? And it says “Solve each equation. Then, prove that your answer solves the original equation?

let's take a peek at the picture above, hmmm let's notice the vertex is at (-1 , 2), now let's get a point besides the vertex hmmm let's see it passes through (-2 , -1).

So we can reword that as what's the equation of a quadratic whose vertex is at (-1 , 2) and it passes through (-2 , -1)?

\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\begin{cases} h=-1\\ k=2\\ \end{cases}\implies y=a(~~x-(-1)~~)^2 + 2\hspace{4em}\textit{we also know that} \begin{cases} x=-2\\ y=-1 \end{cases} \\\\\\ -1=a( ~~-2-(-1) ~~ )^2 + 2\implies -3=a(-2+1)^2\implies -3=a \\\\\\ ~\hfill~ {\Large \begin{array}{llll} y=-3(x+1)^2 + 2 \end{array}} ~\hfill~\)

Answer:

y = -3(x + 1)^2 + 2

Step-by-step explanation:

y = a(x - h)^2 + k is the vertex form of a quadratic, where

Finding (h, k):

We see from the graph that the vertex is a maximum and its coordinates are (-1, 2).  Thus h is -1 and k is 2.  Since h becomes negative, it will be 1 in the parentheses: (x - (-1) = (x + 1).

Finding a:

In order to find a, we will need to plug in a point on the parabola for (x, y) and (-1, 2) for h and k.  We see that (0, -1) lies on the parabola so we can use this point for (x, y).

-1 = a(0 - (-1))^2 + 2

-1 = a(0 + 1)^2 + 2

-3 = a(1)^2

-3 = a

Thus, a = -3.

Thus, the exact equation in vertex form of the parabola is:

y = -3(x + 1)^2 + 2

I attached a picture from Desmos Graphing Calculator that shows how the equation I provided works and contains the two points you marked on the parabola, including (-1, 2) aka the maximum, and (0, -1) aka the y-intercept.

The solution to the system of equations is x = 4 and y = 0. In summary, the correct substitution step for the system is: -4x - 6(x - 4) = -16 .C answer is correct

To solve the given system of equations:

1) y = x - 4

2) -4x - 6y = -16

We can use the substitution method to eliminate one variable and solve for the other.

Step 1: Solve the first equation (1) for y in terms of x.

  y = x - 4

Step 2: Substitute the expression for y from equation (1) into equation (2).

  -4x - 6(x - 4) = -16

Step 3: Simplify and solve for x.

  -4x - 6x + 24 = -16

  -10x + 24 = -16

  -10x = -16 - 24

  -10x = -40

  x = -40 / -10

  x = 4

Step 4: Substitute the value of x back into equation (1) to solve for y.

  y = 4 - 4

  y = 0

Therefore, the solution to the system of equations is x = 4 and y = 0.

In summary, the correct substitution step for the system is:

-4x - 6(x - 4) = -16

By substituting the expression for y from equation (1) into equation (2) and simplifying, we obtain the equation -4x - 6y = -16, which can be further solved to find the values of x and y. C answer is correct

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Answer: \(14\sqrt 2\)

Step-by-step explanation:

Therefore, the equation of the line passing through the point (1,5) with a slope of 7 is y = 7x - 2.

The equation of a line in the point-slope form is given by the following equation:

y-y_1 = m(x-x_1)

where m is the slope of the line and (x1, y1) is any point on the line.

Therefore, we can write the equation of the line passing through the point (1,5) with a slope of 7 as follows:

y-5 = 7(x-1)

Expanding the right-hand side of the equation gives:

y-5 = 7x-7

Adding 5 to both sides of the equation gives:

y = 7x-2

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Answer:

7.14cm

Step-by-step explanation:

Each person used the computer for \(\frac{3}{2}\) hours.

A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated. For instance, the symbol for half of a complete number or item is 12. The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line. A fractional equation is one in which one or more of its terms have the unknown as their denominator.

Given Data

They worked on their homework for 3 hours, and agreed to share the computer equally for that time.

They share computer equally, so

\(\frac{time}{2}\)

Fraction - \(\frac{3}{2}\)

Each person used the computer for \(\frac{3}{2}\) hours.

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Answer:

The measure of CD is 46

Step-by-step explanation:

From the midpoint theorem, we have,

FG = (1/2)CD

so,

\(13+5x=(1/2)(-3x+52)\\So,\\2(13+5x)=-3x+52\\26+10x=-3x+52\\13x=52-26\\13x=26\\x=26/13\\x=2\)

Now,

\(CD = -3x+52\\since \ x=2\\we \ get\\CD=-3(2) +52\\CD=-6+52\\CD=46\)

The amount received from loans as a number in millions is 242,700 million rand.

Deducing value A requires computation of collective income sources, for which the following summation suffices:

Total Income = Tax + Loans + ASC + QP + Other income + Non-tax income = 1370 + 242.7 + 180.3 + 31.5 + A + 0 = 1825.5 + A

In this context, it follows that A amounts to (1825.5 - 1370 - 242.7 - 180.3 - 31.5) = 0 million rand.

Conversely determining missing value B necessitates subtraction of total expenditure from accumulated revenue, giving rise to the subsequent formula:

Total Income - Total Expenditure = B

(1825.5 - 112.7 - 278.4 - 262.4 - 222.6 - 211.0 - 209.2 - 208.5 - 202.2 - 0) = B

Following calculation, B equates to -77.1 million rand, indicating an overage in expenses during fiscal year 2019/20.

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Answer:

37.5

Step-by-step explanation:

the therom of a parallelogram is width*height

so 7.5*5

=37.5

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Answer:

A = 37.5

Step-by-step explanation:

The area of a parallelogram is:

Area = base × height

In your picture the base is 7.5 and the height is 5.

So multiply 7.5×5 and you get 37.5.

The area is 37.5cm^2

Answer:

Kindly check explanation

Step-by-step explanation:

Company A:

Number of people = 239

Number of sample (n) = 16

Standard deviation (s1) = 589 million

Company B:

Number of people = 121

Number of sample(n) = 10

Standard deviation (s2) = 488 million

We can find the F - statistic:

Fstat = variance 1 / variance 2

Variance = (standard deviation)²

Fstat = 589² / 488²

Fstat = 346921 / 238144

Fstat = 1.4567698 = 1.46

Degree of freedom:

Sample A : (n - 1) = (16 - 1) = 15

Sample B: (n - 1) = (10 - 1) = 9

USing the P-value from F statistic calculator at df(15,9) ; Fstat= 1.46

P value = 0.287797.

Since the p value is > 0.10, then result is not significant, hence we fail to reject the null hypothesis.

Given that the polynomials p(x) = 5x²-x+ 4 and q(x) = 3x² + 7x-1,

a. The polynomial  p(x) + q(x) =  8x² + 6x + 3.

b. The polynomial  2p(x) - q(x) =  7x² - 9x + 9.

c. The polynomial p(x)q(x) = 15x⁴ - 3x³ + 35x² + 27x - 4

A polynomial is a mathematical function in which the power of the unknown is greater than or equal to 2.

1. Given the polynomials p(x) = 5x²-x+ 4 and q(x) = 3x² + 7x-1, we desire to find p(x) + q(x), we proceed as follows.

To find  p(x) + q(x), we add both polynomials. so, we have that

p(x) = 5x²- x + 4 and g(x) = 3x² + 7x - 1.

So,   p(x) + q(x) = 5x²- x + 4 + 3x² + 7x - 1.

Collecting like terms, we have that the equation

p(x) + q(x) = 5x² + 3x² + 7x - x + 4 - 1.

= 8x² + 6x + 3.

So, p(x) + q(x) =  8x² + 6x + 3.

b. To find  2p(x) + q(x), we add both polynomials. so, we have that

p(x) = 5x²- x + 4 and g(x) = 3x² + 7x - 1.

We multiply p(x) by 2 to obtain 2p(x). so,

2p(x) = 2(5x²- x + 4)

= 10x²- 2x + 8

So,   2p(x) + q(x) = 10x²- 2x + 8 - (3x² + 7x - 1)

= 10x²- 2x + 8 - 3x² - 7x + 1)

Collecting like terms, we have that the equation

2p(x) + q(x) = 10x² - 3x² - 7x - 2x + 8 + 1.

= 7x² - 9x + 9.

So, 2p(x) - q(x) =  7x² - 9x + 9.

c. To find  p(x)q(x), we multiply both polynomials. so, we have that p(x) = 5x²- x + 4 and g(x) = 3x² + 7x - 1.

p(x)q(x) = (5x²- x + 4)(3x² + 7x - 1)

= 5x²×3x² + 5x² × 7x + 5x²(-1) - x × 3x² - x × 7x - x × ×(-1) + 4 × 3x² + 4 × 7x  + 4 × (-1)

= 15x⁴ + 35x² - 5x² - 3x³ - 7x² - x + 12x² + 28x - 4

Colecting like terms, we have that

= 15x⁴ - 3x³ + 35x² - 5x²  - 7x² + 12x² - x + 28x - 4

= 15x⁴ - 3x³ + 35x² + 27x - 4

So, p(x)q(x) = 15x⁴ - 3x³ + 35x² + 27x - 4

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For the given percenatge of total cost, the total value of Gabe's health care coverage for the year is $9,984.

What is percentage?

Percentage is a way of expressing a fraction or a part of a whole as a portion out of 100. It is represented by the symbol "%".

We can start by using the information given to determine the total cost of the health care coverage. Let's call this cost "C". Since Gabe contributes 15% of this cost and pays $28.80 per week, we can write:

0.15C = 28.80

To solve for C, we can divide both sides by 0.15:

C = 28.80 / 0.15

= 192

So the total cost of the health care coverage is $192 per week. To find the total value of Gabe's health care coverage for the year, we need to multiply this weekly cost by the number of weeks in a year.

Assuming there are 52 weeks in a year, we have:

Total value of Gabe's health care coverage = 192 x 52

= 9984

Therefore, the total value of Gabe's health care coverage for the year is $9,984.

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Answer:

18

Step-by-step explanation:

(5/6)x – 4 = 11

(5/6)x = 11 + 4

(5/6)x = 15

5x = 15×6 = 90

x = 90/5 = 18

Answer:

x = 18

Step-by-step explanation:

5/6x - 4 = 11

Add 4 to each side

5/6x - 4+4 = 11+4

5/6x = 15

Multiply by 6/5 to isolate x

6/5 * 5/6x = 15 * 6/5

x = 18

Answer:

[g+2/3g-1] ÷ [g^2+2g/6g+2]

g+2/3g-1 × 6g+2/g^2+2g

g+2/3g-1 × 2(3g +1)/g(g+2)

1/ 3g-1 × 2(3g+1)/g

2(3g +1)÷ g(3g-1)

6g+2 ÷[3g^2-g]

Answer:

d

y

d

x

=

−

4

3

x

3

Explanation:

y

=

2

3

x

2

=

2

3

x

−

2

Applying the power rule:

d

y

d

x

=

2

3

⋅

(

−

2

)

x

−

3

=

−

4

3

x

3

Step-by-step explanation:

x and y have the values 7 and 7√2, respectively.

The sides of a right triangle with 45-degree acute angles have a unique ratio of 1:1:2.

We can use this information to determine the values of x and y because the base is specified as being 7.

Let's give the perpendicular side the value of x, and the hypotenuse the value of y.

The perpendicular side (x) and the base (7) have the same length because the acute angles are both 45 degrees.

Consequently, x = 7.

We can determine that x:y:2x using the ratio of 1:1:2.

When we enter the value of x, we may calculate y:

7:y:√2(7)

Simplifying even more

7:y:7√2

Given that the hypotenuse (y) equals 72, we can write:

y = 7√2

Thus, x and y have the values 7 and 7√2, respectively.

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Answer:

You will have saved $69,612 after five years.

Step-by-step explanation:

This can be calculated using the for formula for calculating the future value of a growing annuity as follows:

FV = C * (((1 + r)^n - (1 + g)^n) / (r - g)) ……………………………………… (1)

Where;

FW = future value or amount you will have saved after five years = ?

C = first deposit = $1,000

r = periodic monthly interest rate of = 0.4%, or 0.004

g = growth rate of contribution = 0.1%, or 0.001

n = number of months = 5 years * 12 = 60

Substituting all the values into equation (1), we have:

FV = $1,000 * (((1 + 0.004)^60 - (1 + 0.001)^60) / (0.004 - 0.001))

FV = $1,000 * 69.612001854052

FV = $69,612.00

Therefore, you will have saved $69,612 after five years.

From the problem, we have :

Using long method :

Divide the first digit by 3 and take the whole number. That will be 7/3 = 2.33..

So it is 2.

Write 2 above the first digit.

Then multiply 2 by 3 and subtract it from the first digit.

2 x 3 = 6

Then 7 - 6 = 1

Next is to bring dotn the next digit which is 8.

So it will become 18.

Repeat the steps we did above, divide 18 by 3 and that will be 18/3 = 6

Write down 6 above the digit 8.

Multiply 6 by 3 then subtract it from the number below which is 18.

6 x 3 = 18

Then 18 - 18 = 0

Then bring down again the last digit which is 7

Then divide 7 by 3. 7/3 = 2.333 and take the whole number which is 2.

Write 2 above the digit 7.

Lastly, multiply again 2 by 3 and subtract from 7.

That will be :

2 x 3 = 6

Then 7 - 6 = 1

So the quotient is 262 remainder 1

The power expression "w^5" can be entered as "w^5".

To represent a power using the caret symbol, follow these steps:

Start with the base variable or term, in this case, "w".

Type the caret symbol (^), which can be accessed by pressing SHIFT-6 on your keyboard.

Immediately after the caret symbol, enter the exponent or power value, in this case, "5".

The resulting power expression "w^5" represents the variable "w" raised to the power of 5.

Regarding the use of the fraction tool, it is not required to represent the power "w^5" as it does not involve any fraction. The fraction tool is typically used to enter fractions or rational expressions in the form of numerator/denominator.

Therefore, to represent the power "w^5", simply write it as "w^5" without using the fraction tool.

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The blanks that are missing in the sequence are -3 and 11

from the question, we have the following parameters that can be used in our computation:

The blanks in the sequence

When listed out, we have

_, _, 25, 39

Assuming that the sequence, is an arithmetic sequence, then we have

Common difference = 39 - 25

Common difference = 14

This means that

Previous term = 25 - 14 = 11

Firs term = 11 - 14 = -3

So, the missing terms are -3 and 11

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Answer:

57785/_6÷=6=×÷6776==677/÷567

cancel by 3

Answer:

\(\sf \dfrac{8}{21}\)

Step-by-step explanation:

Given expression:

\(\sf \dfrac{6x}{-7} \cdot \dfrac{4}{-9x}\)

When multiplying fractions, simply multiply the numerators and multiply the denominators:

\(\implies \sf \dfrac{6x}{-7} \cdot \dfrac{4}{-9x} = \dfrac{6x \cdot 4}{-7 \cdot -9x} =\dfrac{24x}{63x}\)

Cancel the common factor x:

\(\implies \sf \dfrac{24 \diagup\!\!\!\!x}{63 \diagup\!\!\!\!x}=\dfrac{24}{63}\)

Rewrite 24 as 3 · 8 and rewrite 63 as 3 · 21:

\(\implies \sf \dfrac{24}{63}=\dfrac{3 \cdot 8}{3 \cdot 21}\)

Cancel the common factor 3:

\(\implies \sf \dfrac{\diagup\!\!\!\!\!3 \cdot 8}{\diagup\!\!\!\!\!3 \cdot 21}=\dfrac{8}{21}\)

Answer:

\(3x^{2} - 20xy + 33y^{2}\)

Step-by-step explanation:

\((x-3y)(3x-11y)\\3x^{2} - 9xy - 11xy + 33y^{2} \\3x^{2} - 20xy + 33y^{2}\)

So there are two angles given in equation I.e :-

And we have to find :-

Solution:-

↬ 2x + 2 = 3x - 52

Reason:-

VOA (Vertically opposite angles)

How to recognize when angles are in voa aka Vertically opposite angles?

it's really easy by the way. when ever there a multiplication sign ( × ) either parallely or horizontally , then the opposite angles formed by them are always equal.

↬2x = 3x - 52 - 2

↬2x = 3x - 54

↬2x - 3x = - 54

↬ - x = - 54

↬ x = 54°

Now Let's Verify:

⇢ 2x + 2 = 3x - 52

put the value of x in the equation

⇢ 2(54) + 2 = 3(54) - 52

⇢ 2 × 54 + 2 = 3(54) - 52

⇢ 108 + 2 = 3(54) - 52

⇢ 110 = 3(54) - 52

⇢ 110 = 3 × 54 - 52

⇢ 110 = 162 - 52

⇢ 110 = 110

LHS = RHS

Hence verified!

______________________♡~

Required Answer:-

x = 54°

The value of x from the figure is 54

The given angles are vertical angles showing that they are equal. Hence;

2x + 2 = 3x - 52

Collect the like terms

2x - 3x =  -52-2

-x = -54

x = 54

HEnce the value of x from the figure is 54

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Answer:

thats not enough info

Step-by-step explanation:

thats not enough information

Answer: 24

Step-by-step explanation: 69-27-18=24. You just subtract the 6th and 8th graders that are in band, from the total.

Let's assume that the corresponding side of the second triangle is \(\displaystyle\sf x\).

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, we can set up the following proportion:

\(\displaystyle\sf \left( \dfrac{x}{6.3} \right)^{2} =\dfrac{49}{81}\)

To find \(\displaystyle\sf x\), we can solve the proportion above:

\(\displaystyle\sf \left( \dfrac{x}{6.3} \right)^{2} =\dfrac{49}{81}\)

Taking the square root of both sides:

\(\displaystyle\sf \dfrac{x}{6.3} =\sqrt{\dfrac{49}{81}}\)

Simplifying the square root:

\(\displaystyle\sf \dfrac{x}{6.3} =\dfrac{7}{9}\)

Cross-multiplying:

\(\displaystyle\sf 9x = 6.3 \times 7\)

Dividing both sides by 9:

\(\displaystyle\sf x = \dfrac{6.3 \times 7}{9}\)

Calculating the value:

\(\displaystyle\sf x = 4.9\)

Therefore, the corresponding side of the second triangle is \(\displaystyle\sf 4.9 \, cm\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

Step-by-step explanation:

let's assume that the corresponding side of the second triangle is .

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, we can set up the following proportion:

To find , we can solve the proportion above:

Taking the square root of both sides:

Simplifying the square root:

Cross-multiplying:

Dividing both sides by 9:

Calculating the value:

Therefore, the corresponding side of the second triangle is 4.9cm


hope it helped u dear...........

Answer:

b=69(alternate angle)

b=37(alternate angle)

Answer:

Hope its help u

Step-by-step explanation:

solve

50 x + 56 y = 690

65 x + 48 y = 711

The solution is find out by Cramer's rule as you have not mentioned any specific method,

Its in image