Tabitha wants to hang a painting in a gallery. The painting and frame must have an area of 58 square feet. The painting is 7 feet wide by 8 feet long. Which quadratic equation can be used to determine the thickness of the frame, x? (5 points)

Answer:

x = -6

Step-by-step explanation:

3(x+4)-1=-7

Add 1 to each side

3(x+4)-1+1=-7+1

3(x+4)=-6  

Divide by 3

3/3(x+4)=-6/3

x+4 = -2

Subtract 4 from each side

x+4-4 = -2-4

x = -6

Answer:

Step-by-step explanation:

[tex]3(x + 4) - 1 = - 7[/tex]

Distribute 3 through the parentheses

[tex]3x + 12 - 1 = - 7[/tex]

Calculate the difference

[tex]3x + 11 = - 7[/tex]

Move constant to R.H.S and change it's sign

[tex]3x = - 7 - 11[/tex]

Calculate

[tex]3x = - 18[/tex]

Divide both sides of the equation by 3

[tex] \frac{3x}{3} = \frac{ - 18}{3} [/tex]

Calculate

[tex]x = - 6[/tex]

hope this helps

Best regards!!

Answer:

x = 8.9 units

Step-by-step explanation:

We will use the theorem of intersecting tangent and secant segments.

"If secant and tangent are drawn to a circle from an external point, the product of lengths of the secant and its external segment will equal the square of the length of tangent."

8(8 + 2) = x²

x² = 80

x = √80

x = 8.944

x ≈ 8.9 units

Therefore, length of the tangent = 8.9 units

Answer:

2 < x < ∞

Step-by-step explanation:

We want where the value of y is less than zero

The value of the graph is  less than zero is from x=2 and continues until x = infinity

2 < x < ∞

Answer:

[tex]\boxed{2 < x < \infty}[/tex]

Step-by-step explanation:

The value of y should be less than 0 for the graph of the function to be negative.

In the graph, when it startes from x is 2 the value becomes less than 0 and it keeps continuing until x is equal to infinity.

[tex]2 < x < \infty[/tex]

Answer:

false

Step-by-step explanation:

When solving the distance formula it is the distance from one point to another. If you had a rectangle and used the distance formula from each point then you would have a perimeter

Answer:

192

Step-by-step explanation:

There are a total of 15 marbles . When the lavender is left out 14 remain.

Using combinations we find that each of the four color marbles can be chosen in the following way.

2C1*4C1*4C1*6C1= 2*4*4*6=  192

We select  one of the two red marbles , one of the four green marbles, one of the four yellow marbles, one of the 6 orange marbles leaving the lavender out.. We apply combinations and then multiply to get the answer.

Answer:

A=82°

a= 67.4

c = 60.1

Step-by-step explanation:

For A

A+B+C =180°

A= 180-(B+C)

A= 180-(36+62)

A= 189-(98)

A= 82°

For a

a/sinA= b/sinB

a/sin82= 40/sin36

a= (40*sin82)/sin36

a=( 40*0.9903)/0.5878

a=67.39

Approximately = 67.4

For c

c/sinC= b/sinB

c= (sinC*b)/sinB

c= (sin62*40)/sin36

c =(0.8829*40)/0.5878

c = 60.08

Approximately = 60.1

Answer:

Reject H0

Age and pressure are related

Step-by-step explanation:

The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value. In the given scenario we reject the null hypothesis because job pressure and age are related to each other.

Answer:

the answer is x = sqrt 48

Step-by-step explanation:

Answer:

C. 0.0009

Step-by-step explanation:

0.09/100

= 0.0009

Answer:A

Step-by-step explanation:0.09=0.9

Answer:

Length of Shortest Side = 12 inches

Step-by-step explanation:

Length of Shortest Side = L = 3x

Length of Longest Side = W = 5x-4

Condition:

2L+2W = Perimeter

2(3x)+2(5x-4) = 56

6x+10x-8 = 56

16x-8 = 56

Adding 8 to both sides

16x = 56+8

16x = 64

Dividing both sides by 14

=> x = 4

Now,

Length of the Shortest Side = L = 3(4) = 12 inches

Length of the Longest Side = W = 5(4)-4 = 16 inches

Answer:

12 inches

Step-by-step explanation:

The length is the longest side.

The width is the shortest side.

Length : [tex]l=5x-4[/tex]

Width : [tex]w=3x[/tex]

Apply formula for the perimeter of a rectangle.

[tex]P=2l+2w[/tex]

[tex]P=perimeter\\l=length\\w=width[/tex]

Plug in the values.

[tex]56=2(5x-4)+2(3x)[/tex]

[tex]56=10x-8+6x[/tex]

[tex]56=16x-8[/tex]

[tex]64=16x[/tex]

[tex]4=x[/tex]

The shortest side is the width.

[tex]w=3x[/tex]

Plug in the value for x.

[tex]w=3(4)[/tex]

[tex]w=12[/tex]

Answer:

It will take 18,569.2 years for carbon–14 to decay to 10 percent of its original amount

Step-by-step explanation:

The amount of Carbon-14 after t years is given by the following equation:

[tex]A(t) = A(0)e^{-rt}[/tex]

In which A(0) is the initial amount and r is the decay rate, as a decimal.

Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year.

This means that [tex]r = \frac{0.0124}{100} = 0.000124[/tex]

How many years will it take for carbon–14 to decay to 10 percent of its original amount?

This is t for which:

[tex]A(t) = 0.1A(0)[/tex]

So

[tex]A(t) = A(0)e^{-rt}[/tex]

[tex]0.1A(0) = A(0)e^{-0.000124t}[/tex]

[tex]e^{-0.000124t} = 0.1[/tex]

[tex]\ln{e^{-0.000124t}} = \ln{0.1}[/tex]

[tex]-0.000124t = \ln{0.1}[/tex]

[tex]t = -\frac{\ln{0.1}}{0.000124}[/tex]

[tex]t = 18569.2[/tex]

It will take 18,569.2 years for carbon–14 to decay to 10 percent of its original amount

Answer:

1800

Step-by-step explanation:

Hello,

First of all we need to find the prime factorisation of the numbers.

18 = 2 * 3 * 3

40 = 2 * 2 * 2 * 5

75 = 3 * 5 * 5

It means that the LCM should have 5 * 5 , 2 * 2 * 2 and 3 * 3

Then LCM = 3 * 3 * 2 * 2 * 2 * 5 * 5 = 1800

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

1800

Step-by-step explanation:

→ First of all we need to find the prime factorisation of the numbers.

18 = 2 × 3 × 3 or 2 × 3²

40 = 2 × 2 × 2 × 5 or 2³ × 5

75 = 3 × 5 × 5 or 5² × 3

→ Now find the number that appear twice or more and write them down

3 and 3 from 18

2, 2 and 2 from 40

5 and 5 from 75

→ Now multiply all of these numbers together

3 × 3 × 2 × 2 × 2 × 5 × 5 = 3² × 2³ × 5² = 1800

Answer:

second option

Step-by-step explanation:

x / x - 1 + 3x / x + 2

= x(x + 2) / (x - 1)(x + 2) + 3x(x - 1) / (x - 1)(x + 2)

= (x² + 2x) / (x² + x - 2) + (3x² - 3x) / (x² + x - 2)

= (4x² - x) / (x² + x - 2)

Answer:

B. 5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

You know that the empty barrel is 1/4 of the full barrel. Find 1/4 of 20 to get 0.25 x 20 = 5

Answer:

25

Step-by-step explanation:

We can use the Pythagorean theorem to solve

a^2 + b^2 = c^2

We know the two legs and want to find the hypotenuse

15^2+ 20 ^2 = c^2

225 + 400 = c^2

625 = c^2

Taking the square root of each side

sqrt(625) = c^2

25 = c

Answer:

x should equal 1

Step-by-step explanation:

(1*129)-3=126

129-3=126

126=126

Answer:

x=1

Step-by-step explanation:

We can start by adding 3 to both sides to get rid of the -3

That leaves us with 129x=129

It ends up working out really evenly because by dividing both sides by 129, we are left with x=1

Answer:

14π or 43.96

Step-by-step explanation:

C = 2πr and we know that r = 7 so C = 14π or 43.96.

Answer:

At 95% confidence limits for the true difference between the  average Miles per Gallon for the two models is -1.8210  to  4.1789

Yes 95 % confidence means  that there's conclusive evidence to indicate that one model gets a higher MPG than the other.

Step-by-step explanation:

                              Model A              Model B

Sample Size              50                          55

Sample Mean  x`         32                           35

Sample Variance  s²    9                            10

At 95 % confidence limits are given by

x1`-x2` ± 1.96 [tex]\sqrt{\frac{s^{2} }{n1} +\frac{s^{2}}{n2} }[/tex]

Putting the values

32-35  ± 1.96  [tex]\sqrt\frac{9}{50}+\frac{10}{55}[/tex]        ( the variance is the square of  standard deviation)

-3 ± 1.96 [tex]\sqrt{ \frac{495+500}{2750}[/tex]

-3 ± 1.96( 0.6015)

-3 ± 1.17896

-1.8210; 4.1789

Thus the 95% confidence limits for the true difference between the  average Miles per Gallon for the two models is -1.8210  to  4.1789.

Yes 95 % confidence means  that there's conclusive evidence to indicate that one model gets a higher MPG than the other.

Answer:

The volume of sphere is 267.95 units³.

Step-by-step explanation:

Given that the formula of volume of sphere is V = 4/3×π×r³ where r represents radius. Then, you have to substitute the values into the formula :

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

[tex]let \: r = 4[/tex]

[tex]v = \frac{4}{3} \times \pi \times {4}^{3} [/tex]

[tex]v = \frac{4}{3} \times \pi \times 64[/tex]

[tex]v = \frac{256}{3} \times 3.14[/tex]

[tex]v = 267.95 \: {units}^{ 3} [/tex]

Answer:

RA

Step-by-step explanation:

Answer:

[tex] \sqrt{392 {x}^{7} } [/tex]

Simplify

that's

[tex] \sqrt{392} \times \sqrt{ {x}^{7} } \\ \\ = \sqrt{196 \times 2} \: \times \sqrt{ {x}^{7} } \\ \\ = 14 \sqrt{2} \times \sqrt{ {x}^{7} } \\ \\ = 14 \sqrt{2x ^{7} } [/tex]

Hope this helps you

Answer:

Step-by-step explanation:

Let

T = number of trees

A = number of acorns

Given:

A =  18T + 4 ...........................(1)

A = 20T -4 .........................(2)

Equate A from (1) and (2)

20T-4 = 18T+4

simplify and solve for T

20T - 18T = 4+4

2T = 8

T = 4 trees

A = 18T + 4 = 72+4 = 76 acorns, or

A = 20T - 4 = 80 - 4 = 76 acorns.

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The statement for [tex]6x - 3 = 9[/tex] is :

[tex]\boxed{Six (x) .minus. Three .equals. Nine.}[/tex]

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

for labor. Joni paid $85 less per hour for labor. explanation:

The correct comparison of the cost of labor between Shannon and Joni is that Shannon paid $7 more per hour for labor.

It refers to the total amount of the expenditure done on a product in manufacturing or procuring.

It refers to the expenditure done on procuring labor for the work.

In our situation Shannon paid total $339.50 in which the cost of the parts is $112 and 3.5 hours of labor. So,

labor cost Shannon Paid=339.50-112

=$227.50

labor cost per hour=227.50/3.5

=$6.5 per hour

Joni paid total $455 in which the cost of spare parts is $310 and rest is labor

labor cost paid by Joni=455-310

=$145

labor cost per hour=145/2.5

=$58 per hour

So by doing comparing we found that Shannon had paid $6 per hour extra for labor.

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Answer:

120

Step-by-step explanation:

Answer: 120

Hope that helped!(:

Answer:

Inventory turnover ratio is 3.74

explanation:

Inventory turnover is a ratio of the number of times a company's inventory is sold and replaced in a given period.

Inventory turn over ratio is calculated as ; Cost of goods sold ÷ Average stock of goods sold

= $35,500 / $9500

= 3.74

Answer:

I think D

Step-by-step explanation:

Verticle or horizontal line test, it would be a function either way

Answer:

Angle 2= 45

Angle 3= 45

Angle 4= 135

Angle 5= 135

Angle 6= 45

Angle 7= 45

Angle 8= 135

Answer:

[tex]\Large \boxed{\sf \ \ 7 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

The polynomial function is

[tex]x^3-5x^2-12x+14[/tex]

The rational root theorem states that each rational solution

   [tex]x=\dfrac{p}{q}[/tex]    

, written in irreducible fraction, satisfies the two following:

   p is a factor of the constant term

   q is a factor of the leading coefficient

In this example, the constant term is 14 and the leading coefficient is 1. It means that p is a factor of 14 and q a factor of 1.

Let's proceed with the prime factorisation of 14:

14 = 2 * 7

Finally, the possible rational roots of this expression are :

   1

   2

   7

   14

and we need to test for negative ones too

   -1

   -2

   -7

   -14

From your list, the correct answer is 7.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

the answer is C.) 7

Answer:

0.8413

Step-by-step explanation:

Find the z score.

z = (x − μ) / σ

z = (992 − 999) / 7

z = -1

Use a chart or calculator to find the probability.

P(Z > -1)

= 1 − P(Z < -1)

= 1 − 0.1587

= 0.8413

The required probability that a bottle has a volume greater than 992 mL is 0.84134. Option C is correct

Given that,
A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (ml) and a standard deviation of 7 ml. The fill volumes are normally distributed. What is the probability that a bottle has a volume greater than 992 mL, is to be determined

Probability can be defined as the ratio of favorable outcomes to the total number of events.

We use Z-statistic to find out the probability,

z = (x − μ) / σ

x = raw score = 992 mL
μ = population mean = 999 mL
σ = standard deviation
z = [992 − 999]/7
z = -1

P-value from Z-Table:

P(x<992) = 0.15866

P(x>992) = 1 - P(x<992) = 0.84134

Thus, the required probability that a bottle has a volume greater than 992 mL is 0.84134

Learn more about probability here:

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