David wants to hang a mirror in his room. The mirror and frame must have an area of 8 square feet. The mirror is 2 feet wide and 3 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?

Square with an inner frame with height of 2 ft on the left frame and width of 3 ft on the top. Arrow on the bottom frame with an x and an arrow on the right frame with an x.

2x2 + 14x − 2 = 0
3x2 + 10x − 8 = 0
4x2 + 10x − 2 = 0
x2 + 7x − 8 = 0

Answer:

  (B)  38.4 m³

Step-by-step explanation:

The volume of a prism is given by the formula ...

  V = Bh

where B is the area of the base, and h is the height.

__

The picture tells you the area of the pool is 24 m² and its height is 1.6 m. The volume formula tells you its volume is ...

  V = Bh = (24 m²)(1.6 m) = 38.4 m³

The volume of the prism is 38.4 cubic meters.

Answer:

y = 1/5x + 3

Step-by-step explanation:

y = mx + b

m: slope = 1/5

b: y - intercept

(x, y): (-5, 2)

2 = 1/5(-5) + b

2 = -1 + b

add 1 to both sides to get b alone

2 + 1 = -1 + b + 1

3 = b

If the function is h(t) = - 4.9t² + 39.2t + 5. Then the maximum height will be 83.4 meters.

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

The function is given as

h(t) = - 4.9t² + 39.2t + 5

Then the differentiation of the function will be

h'(t) = - 9.8t + 39.2

For the maximum height, put h'(t) equals zero. Then we have

              h'(t) = 0

- 9.8t + 39.2 = 0

                  t = 4

Then the maximum height will be

h(t) = - 4.9(4)² + 39.2 x 4 + 5

h(t) = - 4.9 x 16 + 39.2 x 4 + 5

h(t) = - 78.4 + 156.8 + 5

h(t) = 83.4 meters

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Answer:

21 cats!

Step-by-step explanation:

the ratio is 3:4

4 being dogs    -     28/4 = 7      -      7 * 3 = 21

hope this helps!!! <3

Answer:

A) 2¹²

Step-by-step explanation:

Given :

Equate the equation to y :

Substituting in the expression :

Answer: Heyaa! ~

Your Answer is... 26.8

Step-by-step explanation:

The estimated answer is D. 27!

Hopefully this helps you! ^^

Answer:

27

Step-by-step explanation:

12.18 + 14.62= 26.80

if the number after the point is greater than 5 or equal to 5, we will add 1 to the number before the point, so now the number is 8 we will add 1 to the number before the point

26+1=27

therefore the sum of 12.18+14.62 = 27

Answer:

[tex]12k^3 -k^2-36k-20[/tex]

Step-by-step explanation:

Step 1:  Distribute

[tex](4k + 5)(3k^2 - 4k - 4)[/tex]

[tex](4k * 3k^2)+(4k*-4k)+(4k*-4)+(5*3k^2)+(5*-4k)+(5*-4)[/tex]

[tex]12k^3-16k^2-16k+15k^2-20k-20[/tex]

Step 2:  Combine like terms

[tex]12k^3+(-16k^2+15k^2)+(-16k-20k)-20[/tex]

[tex]12k^3 -k^2-36k-20[/tex]

Answer: [tex]12k^3 -k^2-36k-20[/tex]

Answer:

Mostly millimeter

Step-by-step explanation:

Length has several unit like m,cm, mm, feet, miles, inches, km etc

we measure the length in units which is more understandable or readable. like thickness of mobile is around 3mm to 1cm or we can even measure in inches like .5inch but if we measure it in meter or feet it will be difficult to understand, read and write similarly the unit of length most suitable for measuring the height of a backyard tree is meter or feet because the length of tree is around 10 feet to 25 feet or 2meter to 6meter if we measure the length in cm or mm or in inches then it will be difficult to understand, read and write.

Answer:

C. x = -1

Step-by-step explanation:

Here :

log 4 (x² + 1) = log 4 (-2x)

Then :

x² + 1 = -2x

x² + 2x + 1 = 0

(x + 1)² = 0

x + 1 = 0

x = -1

Using an exponential function, it is found that it will take 3,252 years for the sample to degrade to 4.5kg.

It is given by:

[tex]A(t) = Pe^{-kt}[/tex]

In which:

The half-life is of 21,400 years, hence, A(21400) = 0.5P, and this is used to find k.

[tex]A(t) = Pe^{-kt}[/tex]

[tex]0.5P = Pe^{-21400k}[/tex]

[tex]e^{-21400k} = 0.5[/tex]

[tex]\ln{e^{-21400k}} = \ln{0.5}[/tex]

[tex]-21400k = \ln{0.5}[/tex]

[tex]k = -\frac{\ln{0.5}}{21400}}[/tex]

k = -0.00003239005

Hence, considering the initial mass is of P = 5 kg, the amount after t years is given by:

[tex]A(t) = 5e^{-0.00003239005t}[/tex]

The amount will be of 4.5 kg at t for which A(t) = 4.5, hence:

[tex]4.5 = 5e^{-0.00003239005t}[/tex]

[tex]e^{-0.00003239005t} = 0.9[/tex]

[tex]\ln{e^{-0.00003239005t}} = \ln{0.9}[/tex]

[tex]-0.00003239005t = \ln{0.9}[/tex]

[tex]t = -\frac{\ln{0.9}}{0.00003239005}[/tex]

t = 3252.

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Answer:

potential to kinetic energy

Answer:

8 then 2 and reflection on y axes

Answer:

The answer is attached.

Answer:

10.5 baskets

Step-by-step explanation:

The median is the middle value, but for this one just add the two in the middle and divide by 2.

4+3 = 7

Each ball is 3 baskets

7×3 = 21

21/2 = 10.5

The correlation coefficient is 0.92

A correlation coefficient is a number between -1 and 1 that tells you the strength and direction of a relationship between variables.

In other words, it reflects how similar the measurements of two or more variables are across a dataset.

When one variable changes, the other variables change in the same direction or opposite direction.

Perfect positive correlation :When one variable changes, the other variables change in the same direction.

Perfect negative correlation :When one variable changes, the other variables change in the opposite direction.

[tex]\rm r = \dfrac{\sum (x_{i}-x')(y_{i}-y')}{\sqrt {\sum (x_{i}-x')^{2} \sum (y_{i}-y')^{2}}}[/tex]

After calculation we get

r = 0.92

Therefore it is a Perfect positive correlation

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The probability the sample mean is more than 10 words for a random sample of 39 messages is 2.12%

An equation is an expression that shows the relationship between two or more numbers and variables.

The z score is given by:

z = (raw score - mean) / (standard deviation / √sample size)

Given mean of 8.6 words and a standard deviation of 4.3 words. If a random sample of 39 messages, hence, for x > 10:

z = (10 - 8.6) / (4.3 / √39) = 2.03

P(x > 10) = P(z > 2.03) = 1 - P(z < 2.03) = 1 - 0.9788 = 0.0212

The probability the sample mean is more than 10 words for a random sample of 39 messages is 2.12%

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Answer:

A. .0210

Step-by-step explanation:

I'm taking the test... could be wrong though...

Answer:

To the nearest 100 miles, Jessica drove about 300 miles since we haven't reached 350 miles.  If we have a number that is greater than 350 miles than we would've rounded it up to 400 but since ours is less than that we round down to the nearest hundred which is 300 miles.

Answer:

B

Step-by-step explanation:

Answer: A

Step-by-step explanation:

Because.....

  -11 - 10 = -21

-32 - (-11) = -21

This tells us that the sequence is adding by -21, which is why the next 2 terms will be -53 and - 74 since....

-32 + -21 = -53

-53 + -21 = - 74

Hence, the answer is A.

Answer:

Your first step in solving the system would be to substitute the value of a variable into one of the equations

Step-by-step explanation:

We know that x = 2y + 2 and y = -1/3x + 4, so we could insert one of these values as the variable in one of the equations

If we were to insert -1/3x + 4 for y, our new equation would be:

x = 2(-1/3x + 4) + 2 (as you can see, the value of y was inserted into the equation)

Find the perimeters of all the figures. = ADD all four sides of shape.

(Length + Width + Height + Base)

Answer:

The area of triangle ABC is 60 mm^2

Step-by-step explanation:

x = the area of triangle ABC

15/6 * x/24

x=60

Answer:

  (d)  150 mm²

Step-by-step explanation:

The scale factor between the triangles is the ratio of the lengths of corresponding sides. The area ratio is the square of the scale factor.

__

ΔABC is larger than ΔPRT by the factor ...

  AC/PT = 15/6 = 5/2

The area of ΔABC is the square of this factor times the area of ΔPRT:

  area ABC = (5/2)²×area PRT

  area ABC = (25/4)×(24 mm²)

  area ABC = 150 mm²

Part A

The yard is a quadrilateral with the following corner points

I'll label those points A through D in the order presented above.

From A to B is 40 feet since 40-0 = 40. We can subtract the y coordinates because the x coordinates are the same.

In short: side AB is 40 feet long.

The length of side BC is not as simple. We'll need the distance formula.

[tex]B = (x_1,y_1) = (0,40) \text{ and } C = (x_2, y_2) = (40,50)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-40)^2 + (40-50)^2}\\\\d = \sqrt{(-40)^2 + (-10)^2}\\\\d = \sqrt{1600 + 100}\\\\d = \sqrt{1700}\\\\d = \sqrt{100*17}\\\\d = \sqrt{100}*\sqrt{17}\\\\d = 10\sqrt{17}\\\\d \approx 41.2311\\\\[/tex]

Segment BC is exactly [tex]10\sqrt{17}[/tex] feet long, which is about 41.2311 feet.

Use the distance formula again to find the distance from point C(40,50) to D(50,0)

[tex]C = (x_1,y_1) = (40,50) \text{ and } D = (x_2, y_2) = (50,0)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(40-50)^2 + (50-0)^2}\\\\d = \sqrt{(-10)^2 + (50)^2}\\\\d = \sqrt{100 + 2500}\\\\d = \sqrt{2600}\\\\d = \sqrt{100*26}\\\\d = \sqrt{100}*\sqrt{26}\\\\d = 10\sqrt{26}\\\\d \approx 50.9902\\\\[/tex]

Lastly, the side AD is exactly 50 feet because 50-0 = 50. We can subtract x coordinates because the y coordinates are the same. Use of the distance formula from A to D should show a result of 50 exactly.

We have these side lengths:

AB = 40

BC = 41.2311 (approximate)

CD = 50.9902 (approximate)

AD = 50

Add up those four sides and we'll get the perimeter of the quadrilateral.

AB+BC+CD+AD = 40+41.2311+50.9902+50 = 182.2213

===================================================

Part B

The garden is a rectangle that is 15 feet across horizontally (since subtracting x coordinates gives us 25-10 = 15) and 20 feet vertically (since subtracting y coordinates gives us 35-15 = 20).

This 15 by 20 rectangle has an area of 15*20 = 300 square feet.

The deck is a trapezoid with the parallel bases of 20 feet up top and 35 feet down below. Like before, we subtract x coordinates to find the horizontal distance (since the y coordinates are the same). The height of this trapezoid is 15 feet. Subtract the y coordinates to find the height.

The area of the trapezoid is

A = h*(b1+b2)/2

A = 15*(20+35)/2

A = 412.5

That decimal value is exact.

Add it onto the area of the rectangle

412.5+300 = 712.5

The surface area of solid Y given the ratio of volume to surface area of solid X is 2,369.25cm²

Volume:

Surface area:

Ratio of volume to surface area of solid X and Y respectively

64 : 208 = 729 : x

64/208 = 729/x

64 × x = 208 × 729

64x = 151,632

x = 151,632 / 64

x = 2,369.25cm²

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Answer:

A. OEO, EOE, EEE, EEO, OOE, OEE

A (probability). [tex]\frac{3}{4}[/tex]

B. OEO, EOE

B (probability). [tex]\frac{1}{4}[/tex]

C. EOE, EEE, OOE, OEE

C (probability). [tex]\frac{1}{2}[/tex]

hope this helps:)

Answer:

A. OEO, EOE, EEE, EEO,  ------- (probability).  3/4

B. OEO, EOE ------(probability). 1/4

C- EOE   --------------(probability). 1/4 aswell

Step-by-step explanation:

Sorry it took so long

I hope this helps C:

Step-by-step explanation:

[tex]\huge{\color{black}{\fbox{\color{pink}{\colorbox{pink}{\color{red}{Answer ✨☑️}}}}}}[/tex]

The number of terms are 8. Step-by-step explanation: Given : The sum n terms of an A.P is 136 the common difference is 4 and last term is 31.

Answer:

Sn=2n{2a+(n−1)d}

a+(n−1)d=31⇒a=31−4(n−1)

∴136=2n{2[31−4(n−1)]+(n−1)d}

n[70−8n+4n−4]=272

n(66−4n)=272

4n2−66n+272=0

2n2−33n+136=0

2n(n−8)−17(n−8)=0

(2n−17)(n−8)=0

∴n=8

Answer:

IT IS 43./45455/.34 LIKE WHEN U ADD 10 TIMES 10 AND DIVIDED 2,000 FROM 20 U THAT ANSWER

Step-by-step explanation:

Triangle MŇO is congruent to Triangle UŤS

NO=4

MN=4

MO=5.6( Which is 140% bigger than 4)

UT=10

TS=10(Therefore this also should be 10)

US=14(Which is 140% bigger than 10)

I think this is the solution but I am not 100% sure

Answer:

x=14

Step-by-step explanation:

Answer:

[tex]\boxed{\bf \sf number : \ \frac{4}{5} }[/tex]

Explanation:

Let the number be n

According to students Condition:

[tex]\rightarrow \sf \dfrac{3}{2} \ x \ n \quad = \quad \dfrac{3n}{2}[/tex]

What He actually Did:

[tex]\rightarrow \sf n \div \dfrac{3}{2} \quad = \quad n \ x \ \dfrac{2}{3} \quad = \quad \dfrac{2n}{3}[/tex]

He got a smaller number by 2/3, so:

[tex]\rightarrow \sf \dfrac{3n}{2} - \dfrac{2n}{3} = \dfrac{2}{3}[/tex]

make the denominator's same

[tex]\rightarrow \sf \dfrac{3(3n)}{6} - \dfrac{2(2n)}{6} = \dfrac{2}{3}[/tex]

multiply the integers

[tex]\rightarrow \sf \dfrac{9n}{6} - \dfrac{4n}{6} = \dfrac{2}{3}[/tex]

Join the fractions

[tex]\rightarrow \sf \dfrac{9n-4n}{6} = \dfrac{2}{3}[/tex]

Subtract integers

[tex]\rightarrow \sf \dfrac{5n}{6} = \dfrac{2}{3}[/tex]

Cross multiply

[tex]\rightarrow \sf n = \dfrac{6 \ * \ 2}{5 \ * \ 3} \quad = \quad \dfrac{4}{5}[/tex]

Lets see

the number be x

The expression is

Answer:

[tex]\boxed{\bf 7 \times 10 {}^{ - 3}} [/tex]

Step-by-step explanation:

Write 0.7 *10^-2 into scientific notation:

Hope this helps! ^^"

Answer:

[tex]7 \times 10^{-3}[/tex]

Step-by-step explanation:

[tex]\begin{aligned}\dfrac{6.3 \times 10^{-5}}{9 \times 10^{-3}} & =\dfrac{6.3}{9} \times \dfrac{10^{-5}}{10^{-3}}\\\\& = 0.7 \times \dfrac{10^{-5}}{10^{-3}}\end{aligned}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\begin{aligned}\implies 0.7 \times \dfrac{10^{-5}}{10^{-3}} &=0.7 \times 10^{-5-(-3)}\\& = 0.7 \times 10^{-2}\end{aligned}[/tex]

[tex]\textsf{Rewrite}\:0.7\:\textsf{as}\: 7 \times 10^{-1}:[/tex]

[tex]\implies 0.7 \times 10^{-2}=7 \times 10^{-1} \times 10^{-2}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \times a^c=a^{bc}:[/tex]

[tex]\implies 7 \times 10^{-1} \times 10^{-2}=7 \times 10^{-3}[/tex]