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denis-greek [22]
3 years ago
14

Which equation is equivalent to the given equation? x^2+16x=22

Mathematics
1 answer:
Harlamova29_29 [7]3 years ago
5 0

Answer:

(x+8)^2 = 86

Step-by-step explanation:

Given

x^2 + 16x = 22

Required

Determine an equivalent equation

x^2 + 16x = 22

Get the coefficient of x

Coefficient = 16

Divide this by 2

Result = \frac{16}{2}

Result = 8

Take its square

Result = 8^2

Result = 64

Add this to both sides of the equation

x^2 + 16x + 64 = 22 + 64

x^2 + 16x + 64 = 86

Expand the expression on the right hand side

x^2 + 8x + 8x + 64 = 86

Factorize

x(x+8)+8(x+8) = 86

(x+8)(x+8) = 86

(x+8)^2 = 86

<em>Hence, the equivalent equation is </em>(x+8)^2 = 86<em></em>

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Jack Matthew bought a new diamond ring for $20,000. Sales tax is 5% with a 10% excise tax. The total price including taxes that
Blizzard [7]

Jack paid $ 23000 for the ring.

<u>Solution:</u>

Given that, Jack Matthew bought a new diamond ring for $20,000

Sales tax is 5% with a 10% excise tax

<em><u>To find: total price including taxes</u></em>

Given that sales tax is 5% of 20,000

\begin{array}{l}{\text { Sales tax }=5 \% \times \text { cost price }} \\\\ {\text { Sales tax }=\frac{5}{100} \times 20000=5 \times 200=1000}\end{array}

Also given that excise tax is 10%

\begin{array}{l}{\text { Excise tax }=10 \% \times \text {cost price }} \\\\ {\text { Excise tax }=\frac{10}{100} \times 20000=10 \times 200=2000}\end{array}

<em>Total price = cost price + sales tax + excise tax</em>

Total price = 20,000 + 1000 + 2000

Total price = 23000

Hence, jack paid $ 23000 for the ring.

5 0
4 years ago
Ingrid walked her dog and washed her car. The time she spent walking her dog was one-half the time it took her to wash her car.
Inessa [10]

Answer:

24m+24m=48m

Ingrid spent 48 minutes washing her car

Step-by-step explanation:

Plssss markkk me blainliest

6 0
3 years ago
Pls help i dont get it NO LINK'S or I'll report also do not steal points ​
aleksley [76]

They travel to school by  picking the amount of conductions associated with the classmates. They travel with their belongings and bring them with them as they transport to their location (school). Once they get to school than they must place their belongings. The population is associated with global and significance. They will then conduct and the math teachers wont be worried.

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6 0
3 years ago
Suppose that several insurance companies conduct a survey. They randomly surveyed 350 drivers and found that 280 claimed to alwa
KATRIN_1 [288]

Answer:

Lower limit = 0.76

Upper limit = 0.84

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 350

Number of drivers that buckle = 280

Formula:

p' = \dfrac{x}{n} = \dfrac{280}{350} = 0.8

q' = 1-p' = 1 - 0.8 = 0.2

The standard deviation for sp =

=\sqrt{\displaystyle\frac{p'q'}{n}}\\\\=\sqrt{\dfrac{0.8\times 0.2}{350}} = 0.02138

95% Confidence Interval:

p' \pm z_{critical}(s_p)

z_{critical}\text{ at}~\alpha_{0.05} = \pm 1.96

Putting the values, we get,

0.8 \pm 1.96(0.02138)\\= 0.8 \pm 0.0419048\\=(0.7580952, 0.8419048)\\\approx (0.76,0.84)

Lower limit = 0.76

Upper limit = 0.84

3 0
3 years ago
How do I solve the question the width of a rectangle is six meters more less than it's length. If the area of the rectangle is 1
True [87]

Answer:

Length of rectangle = 14 meters

width of rectangle = 8 meters

Step-by-step explanation:

Let the length of rectangle be x meters

width of the triangle is (x - 6) meters

Area of the rectangle is Length x width

112m² = x * (x -6)

112 = x² - 6x

x² - 6x - 112 = 0

x² - 14x +  8x - 112 = 0

x (x - 14) + 8 ( x - 14) = 0

(x - 14)(x + 8) = 0

x - 14 = 0                                     x + 8 = 0

x = 14                                           x = -8

width can't be negative value

Therefore,

Length of rectangle = 14 meters

width of rectangle = 14 - 6 meters

                              = 8 meters

3 0
3 years ago
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