2x^2=3x+10 completing the square

Answer:

Step-by-step explanation:

1.68/6=0.28 per pencil in pack 1

2.34/9 =0.26 per pencil in pack 2

So pack 2 is better in terms of Maths

But in business, people prefer pack 1

Answer:

The required sum is 392

Step-by-step explanation:

Given the sum as shown;

[tex]\sum \left \77} \atop {a=1}} \right. (3a^2-4)[/tex]

When n = 1

f(1) = 3(1)²-4

f(1) = 3 - 4

f(1) = - 1

When n = 2

f(2) = 3(2)²-4

f(2) = 12 - 4

f(2) = 8

When n = 3

f(3) = 3(3)²-4

f(3) = 27 - 4

f(3) = 23

When n = 4

f(4) = 3(4)²-4

f(4) = 48 - 4

f(4) = 44

When n = 5

f(5) = 3(5)²-4

f(5) = 75 - 4

f(5) = 71

When n = 6

f(6) = 3(6)²-4

f(6) = 108 - 4

f(6) = 104

When n = 7

f(7) = 3(7)²-4

f(7) = 147 - 4

f(7) = 143

Taking their sum

Sum = f(1)+f(2)+(3)+f(4)+f(5)+f(6)+f(7)

Sum = -1 + 8 + 23 + 44 + 71 + 104 + 143

Sum = 392

Hence the required sum is 392

Answer:

k=8

Step-by-step explanation:

We can solve using the slope formula

m= (y2-y1)/(x2-x1)

3/5 = (k-2)/(4- -6)

3/5 = (k-2)/(4+6)

3/5 = (k-2)/10

Multiply each side by 10

10*3/5 = (k-2)/10 *10

6 = k-2

Add 2 to each side

6+2 = k-2+2

8 = k

Answer:

y = -1/5x - 3

Step-by-step explanation:

Answer/Step-by-step explanation:

Given:

86.32947

Let's find the place value of each digit

8 => tens which is 80

6 => unit which is 6

3 => tenth which is 0.3

2 => hundredth which is 0.02

9 => thousandth which is 0.009

4 => ten-thousandths which is 0.0004

7 => hundred-thousandth which is 0.00007

If you add all of the it will give you 86.32947

Thus:

1. 6 => b

2. 8 => g

3. 4 => e

4. 7 => d (there's a mistake in the number of zeros written.)

5. 9 => c

Answer:

6 inches by 6 inches

Step-by-step explanation:

Area of the square = 256 inches ²

Given equation:

(x + 10)² = 256

Where,

x = side measure of the original square

(x + 10)² = 256

(x + 10)(x + 10) = 256

x² + 10x + 10x + 100 = 256

x² + 20x + 100 = 256

x² + 20x + 100 - 256 = 0

x² + 20x - 156 = 0

Solve the quadratic equation by factorization

Find two numbers whose product is -156 and sum is 20

The numbers are -26 and 6

x² + 26x - 6x - 156 = 0

x(x + 26) - 6(x + 26) = 0

(x + 26) (x - 6) = 0

x + 26 = 0 or x - 6 = 0

x = -26 or x = 6

Side length of a square can not be negative

Therefore,

x = 6 inches

6 inches by 6 inches

Answer:

7 quarters

26 nickels

Step-by-step explanation:

x = number of quarters

y = number of nickels

x + y = 33

y = 3x + 5

x + 3x + 5 = 33

4x = 28

x = 7

y = 3×7 + 5 = 26

Answer:

24

Step-by-step explanation:

2*1+1+2*2+1+2*3+1+2*4+1=24

Answer:

1.54

Step-by-step explanation:

88° = 88° × π ÷ 180

= 88° × 3.142 ÷ 180

= 88° × 0.0175

= 1.54

Answer:

D. All three chose a valid first step toward solving the equation.

Step-by-step explanation:

Aaron, Blaine, and Cruz are solving the equation 4/7 (7 − n) = −1. Aaron started his solution by multiplying both sides of the equation by 7/4 . Blaine started by using the distributive property to multiply 4/7 by both 7 and −n. Cruz started by dividing both sides of the equation by 4/7 .

Which of the following is true?

A. Blaine and Cruz made an error in picking their first steps.

B. Cruz made an error in picking his first step.

C. All three made an error because the right side equals -1.

D. All three chose a valid first step toward solving the equation.

Given:

4/7(7 - n) = -1

Aaron:

4/7(7 - n) = -1

Multiple both sides by 7/4

4/7(7 - n) * 7/4 = -1 * 7/4

7 - n = -7/4

- n = -7/4 - 7

- n = (-7-28)/4

- n = -35/4

n = 35/4

Blaine:

4/7(7 - n) = -1

4/7(7 - n) × 7 = -1 × 7

4(7 - n) = -7

28 - 4n = -7

-4n = -7 - 28

- 4n = - 35

n = -35/-4

n = 35/4

Cruz:

4/7(7 - n) = -1

Divide both sides by 4/7

4/7(7 - n) ÷ 4/7 = -1 ÷ 4/7

4/7(7 - n) × 7/4 = -1 × 7/4

7 - n = -7/4

- n = (-7-28)/4

- n = -35/4

n = 35/4

D. All three chose a valid first step toward solving the equation.

Answer:

D-All three chose a valid first step toward solving the equation.

Step-by-step explanation:

Hope I Helped

Answer:

H0 : μ = 99

H1 : μ > 99

Z statistic = 0.5

Result is not significant at 5% level ;

Step-by-step explanation:

Given that :

σ = 10

μ = 99

Sample size, n = 25

H0 : μ = 99

H1 : μ > 99

The test statistic :

(xbar - μ) ÷ (σ/√(n))

Since the population standard deviation is known, we use the Z statistics.

Z = (100 - 99) ÷ (10/√(25))

Z = 1 / 2

Z = 0.5

The Z critical value at α = 0.05

Zcritical = 1.645

Zstatistic < Zcritical ; Hence, we fail to reject the H0.

Answer:

4. 12√3

5. -35√2

6. 5√2/2

Step-by-step explanation:

4. 3√12+2√27

= 3√(4×3) + 2√(9×3)

= 6√3+6√3

= 12√3

5. 5√8-9√50

= 5×2√2-9×5√2

= 10√2-45√2

= -35√2

6. 5/√2

= 5×√2/(√2×√2)

= 5√2/2

Answered by GAUTHMATH

Answer:

1394

Step-by-step explanation:

Set up equation to find the number:

Variable n = number

65/100 = 1105/n

Cross multiply:

65 × n = 100 × 1105

65n = 110,500

n = 1700

Check your work:

1700 × 65%

Convert percentage into decimal:

1700 × 0.65

1105

Correct!

Find 82% of 1700:

Variable x = 82% of 1700

82/100 = x/1700

82 × 1700 = 100 × x

139,400 = 100x

1394 = x

Check your work:

1700 × 82%

1700 × 0.82

1394

Correct!

The 82% of the original number (1700) is approximately 1394.

Let's denote the original number as N. We know that 65% of N is equal to 1105. We can write this as:

65% of N = 0.65 * N = 1105

Now, to find the value of N, we can rearrange the equation to solve for N:

N = 1105 / 0.65

Now, calculate the value of N:

N ≈ 1700

So, the original number N is approximately 1700.

Next, we need to find 82% of this number. We can express this as:

82% of N = 0.82 * N

Now, substitute the value of N:

82% of 1700 = 0.82 * 1700

                     ≈ 1394

Thus, 82% of the original number (1700) is approximately 1394.

To summarize, first, we found the value of the original number (N) using the given information that 65% of N is equal to 1105. Then, we calculated 82% of N, which turned out to be approximately 1394.

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Answer:

x=7.15

y=0.87

Step-by-step explanation:

First of all u need to let watermelon nd apples x&y. so after that what u have to do is substract the equations.

Answer:

99

Step-by-step explanation:

66 ÷ [tex]\frac{2}{3}[/tex]   = 66 * [tex]\frac{3}{2}[/tex] = 33* 3 = 99

The calculated measure of the angle QSR is 68 degrees

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

Angle b = 136 degrees

The measure of angle QSR can be calculated using

QSR = 1/2 * Angle b

substitute the known values in the above equation, so, we have the following representation

QSR = 1/2 * 136 degrees

Evaluate

QSR = 68 degrees

Hence, the measure of angle QSR is 68 degrees

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A. [tex]6x^2[/tex]+-5x+14x+-35

           [tex]6x^2[/tex]+9x-35

B. [tex]5x^4+-3x^3+10x^3+-6x^2[/tex]

           [tex]5x^4+7x^3-6x^2[/tex]

C. [tex]25x^2+-20x+20x+-16[/tex]

             [tex]25x^2-16[/tex]

D. [tex]x^4+-4x^2+-7x^2+28[/tex]

           [tex]x^4-11x^2+28[/tex]

[tex]====================================[/tex]

Step-by-step explanation:

A. (3x*2x)+(3x*-5)+(7*2x)+(7*-5)

        Multiply and simplify.

                [tex]6x^2[/tex]+9x-35

B. ([tex]x^2*5x^2[/tex])+([tex]x^2*[/tex]-3x)+(2x[tex]*5x^2[/tex])+(2x[tex]*-3x[/tex])

         Multiply and simplify.

              [tex]5x^4+7x^3-6x^2[/tex]

C. [tex](5x*5x)+(5x*-4)+(4*5x)+(4*-4)[/tex]

         Multiply and simplify.

                  [tex]25x^2-16[/tex]

D. [tex](x^2*x^2)+(x^2*-4)+(-7*x^2)+(-7*-4)[/tex]

         Multiply and simplify.

                [tex]x^4-11x^2+28[/tex]

I hope this helps!

But you should really do this yourself.

Answer:

A 5 sided figure

Step-by-step explanation:

To find the sum of interior angles we use the formula

S = (n - 2) *180

540 = 180n - 360

180n = 540 + 360

180n = 900

n = 900/180

n = 5

The number of sides of a polygon with the given sum of interior angles is 5.

Option A)5-sided figure is the correct answer.

A polygon is simply a two-dimensional a plane shape enclosed by line segments called sides.

The formula for calculating the sum of interior angles of a polygon is;

S =  ( n − 2 ) × 180°

Where S is the sum and n is the number of sides.

Given that the sum of the interior angles equal to 540°.

From the above expression;

S =  ( n − 2 ) × 180°

540° =  ( n − 2 ) × 180°

540° =  180°n − 360°

180°n = 540° + 360°

180°n = 900°

n = 900° / 180°

n = 5

The number of sides of a polygon with the given sum of interior angles is 5.

Option A)5-sided figure is the correct answer.

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Answer:

[tex] = { \tt{ \frac{125}{5} }} \\ = { \bf{25 \: frames \: per \: second}}[/tex]

Answer:

B. 25 frames per second

Step-by-step explanation:

To find the rate in frames per second, divide the total frames in 5 seconds by 5. This is because 5/5=1 and that way we're finding the frames per (one) second.

Therefore, we have:

[tex]\frac{125}{5}=\boxed{25\text{ frames per second}}[/tex]

Answer:

Step-by-step explanation:

Use the Pythagorean Theorem

diagonal² = 16² + 12² = 400

diagonal = √400 = 20 cm

Answer:

x=55

Step-by-step explanation:

Since 2 sides are the same length, their base angles much be the same.  The unmarked angle muse also be x

x+x+70 = 180  since the sum of the angles of a triangle must be 180

2x+70 = 180

2x = 180-70

2x = 110

Divide by 2

2x/2 =110/2

x=55

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{x + x + 70 = 180}^\circ[/tex]

[tex]\underline{\large\text{COMBINE the LIKE TERMS}}[/tex]

[tex]\large\textsf{(x + x) + 70 = 180}^\circ[/tex]

[tex]\large\textsf{x + x = \bf 2x}[/tex]

[tex]\large\textsf{2x + 70 = 180}^\circ[/tex]

[tex]\underline{\large\text{SUBTRACT 70 to BOTH SIDES}}[/tex]

[tex]\large\textsf{2x + 70 - 70 = 180 - 70}[/tex]

[tex]\large\text{CANCEL out: 70 - 70 because that gives you 0}[/tex]

[tex]\large\text{KEEP: 180 - 70 because helps solve for the x-value}[/tex]

[tex]\large\textsf{180 - 70 = \bf 110}[/tex]

[tex]\underline{\underline{\large\text{New equation: 2x = 110}}}[/tex]

[tex]\underline{\large\text{DIVIDE 2 to BOTH SIDES}}[/tex]

[tex]\large{\mathsf{\dfrac{2x}{2}=\dfrac{110}{2}}[/tex]

[tex]\large\text{CANCEL out: } \mathsf{\dfrac{2}{2}} \large\text{ because that gives you 1}[/tex]

[tex]\large\text{KEEP: }\mathsf{\dfrac{110}{2}}\large\text{ because that gives you the answer of the x-value}[/tex]

[tex]\mathsf{x = \dfrac{110}{2}}\\\\\large\textsf{x = 110}\div\large\textsf{2}\\\\\large\textsf{x = \bf 55}^\circ[/tex]

[tex]\boxed{\boxed{\huge\text{Therefore, your answer is: \textsf{x = \bf 55}}^\circ}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer: 33

Work Shown:

Apply the pythagorean theorem to get

[tex]a^2 + b^2 = c^2\\\\x^2 + 44^2 = 55^2\\\\x^2 + 1936 = 3025\\\\x^2 = 3025 - 1936\\\\x^2 = 1089\\\\x = 33[/tex]

Answer:

Step-by-step explanation:

17.

The expression 4(x-7) is the product of 4 and the difference of x and 7.

18.

The expression 2+8/c is the sum of 2 and the quotient of 8 and c.

Answer:

x = t/4 and y = (t+17)/3

Step-by-step explanation:

4x-3y+17=0

or, 4x=3y-17

let, 4x = t

so, x = t/4

and 3y-17 = t

or, 3y = t+17

or, y = (t+17)/3

Answered by GAUTHMATH

Answer:

320 shirts

Step-by-step explanation:

Answer:

320 shirts

Step-by-step explanation:

If the shirts were around 400 in January, then you would assume that near June, the number of shirts sold would be 320 shirts.

Answer:

The stock in last three days has a net gain of 3.

Step-by-step explanation:

The net change of the stock is the sum of daily changes in last three days. Please notice that positive sign means means for gain, whereas negative one is for loss. Based on information given on statement, we determine the net change in the stock:

[tex]x = -\left(8 + \frac{3}{8} \right)-\left(1+\frac{5}{8} \right) + 13[/tex]

[tex]x = 3[/tex]

The stock in last three days has a net gain of 3.

Answer:

Cannot be determined.

Step-by-step explanation:

The triangle has three different angles which are not congruent. The sides of the two triangle are not equal therefore these triangle are not determined to be congruent. These triangles share their three angles but not the three sides.