A picture frame can hold a photograph that is 16 inches long and 12 inches wide.
What is the area of the photo that fits the frame?

Answer:

c

Step-by-step explanation:

y = 5x² - 17x - 12

to find the roots let y = 0 , that is

5x² - 17x - 12 = 0

Factorising the quadratic

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 5 × - 12 = - 60 and sum = - 17

the factors are - 20 and + 3

use these factors to split the x- term

5x² - 20x + 3x - 12 = 0 ( factor first/second and third/fourth terms )

5x(x - 4) + 3(x - 4) = 0 ← factor out (x - 4) from each term

(x - 4)(5x + 3) = 0

equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

5x + 3 = 0 ⇒ 5x = - 3 ⇒ x = - [tex]\frac{3}{5}[/tex] = - 0.6

roots are (4, 0 ) and (- 0.6, 0 )

Answer:

32π

Step-by-step explanation:

The equation for the circumference of a circle is as follows:

C = 2 π r

Since r = 16:

C = 2 π (16) = 32π

Answer:

See below ~

Step-by-step explanation:

Finding the common difference :

Formula :

Answer:

[tex]\large \boxed{\sf 7n + 6}[/tex]

Explanation:

Sequence: 13, 20, 27,...

Find common difference: second term - first term = 20 - 13 = 7

As it is an explicit arithmetic term:

⇒ a + (n - 1)d             (a is the first term, d is common difference)

⇒ 13 + (n -1)(7)

⇒ 7n - 7 + 13

⇒ 7n + 6

Answer:

23 m

Step-by-step explanation:

the median is calculated as

half the sum of the parallel bases , then

median = [tex]\frac{19+27}{2}[/tex] = [tex]\frac{46}{2}[/tex] = 23

Answer:

$ 142100

Step-by-step explanation:

Profit is the difference between the revenue and the cost

        P(x) = R(x) - C(x)

                = 820x - x² - (2300 + 60x)

                = 820x - x² - 2300 - 60x

                = -x² + 820x - 60x - 2300

         P(x) = -x² + 760x - 2300

a =  -1   ; b = 760  and c = -2300

       [tex]\sf \boxed{P_{max} = c - \dfrac{b^2}{4a}}[/tex]

                  [tex]\sf = -2300 - \dfrac{760^{2}}{4*(-1)}[/tex]

                  [tex]\sf = -2300 +\dfrac{577600}{4}\\\\ = -2300 + 144400\\= 142100[/tex]

[tex]\sf \boxed{P_{max}= \$ 142100}[/tex]

The density of an object is the ratio of the mass of the object to its volume. The height of the block of sugar maple is 6cm

The density of an object is the ratio of the mass of the object to its volume. Mathematically;

Density = mass/volume

Given the following

Mass of block = 82.8grams

Density = 0.69g/cm^3

volume = lwh
Volume = 20h

Substitute

0.69 = 82.8/20h
20h = 82.8/0.69
20h = 120

h = 6cm

Hence the height of the block of sugar maple is 6cm

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6cm

Step-by-step explanation i can confirm that the answer is 6 ;}

Answer: yes it is

Step-by-step explanation:

Using the z-distribution, it is found that the 99% confidence interval to estimate Q is (74.4, 96.6). The interpretation is that we are 99% sure that the true mean for all cars rented in the city is between these two values.

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

In this problem, we have a 99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

The other parameters of the interval are given as follows:

[tex]\overline{x} = 85.5, \sigma = 19.3, n = 20[/tex].

Hence the bounds of the interval are given as follows:

[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 85.5 - 2.575\frac{19.3}{\sqrt{20}} = 74.4[/tex]

[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 85.5 + 2.575\frac{19.3}{\sqrt{20}} = 96.6[/tex]

The interpretation is that we are 99% sure that the true mean for all cars rented in the city is between these two values.

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Answer:

Thhe simplified form of the expression is 9

Indices are expressed as power or exponent which is raised to a number or a variable.

According to the law of indices

\begin{gathered}a^n \times a^m = a^{n+m}\\a^n \div a^m = a^{n-m}\end{gathered}

a

n

×a

m

=a

n+m

a

n

÷a

m

=a

n−m

Given the expression

3^{-6} \times (\dfrac{3^4}{3^0} )^23

−6

×(

3

0

3

4

)

2

This can also be expressed as:

\begin{gathered}=\dfrac{1}{3^6} \times (\frac{3^4}{1})^2 \ (3^0 =1)\\= \dfrac{1}{3^6} \times 3^8\\=\dfrac{3^8}{3^6}\\=3^{8-6}\\=3^2\\=9\\\end{gathered}

=

3

6

1

×(

1

3

4

)

2

(3

0

=1)

=

3

6

1

×3

8

=

3

6

3

8

=3

8−6

=3

2

=9

This shows that the simplified form of the expression is 9

Answer:

Represent the thickness of the frame by x.

Framing the mirror will increase both its length and width by 2x. The area of the mirror with the frame is the product of the length and width which can mathematically be expressed as,

A = (3+2x)(2+2x) = 8

The equation above can be simplified into 4x^2 + 10x -2=0.

This equation can still be further simplified by dividing it by 2. However, it will give an answer which is not found on the choices. Thus, the answer is the third choice.

Answer:

The correct option would be C

Step-by-step explanation:

I hope this helps, if it doesn't then just message me and ill be more than happy to help :)

Answer:

The answer is 19.8cm to the nearest tenth

[tex]f(x)=x+10\\\\f(7)=(7)+10\\\\f(7)=17[/tex]

the answer is 17.

Answer:

The answer is 17, x±10 =10+7= 17

Answer:

-x^4-5x^3+2x²+ 10x = (x+5)(2x-x³)

Step by Step explanation

Naming the coefficient of x² as "a" and the independent temine of the first parenthesis as "b", we got:

-x^4-5x^3+ ax^2 +10x=(x+b)(2x-x^3)

- x⁴-5x^3+ ax^2 +10x = 2x²- x⁴+2bx-bx³

-5x^3+ ax^2 +10x = -bx³+2x²+2bx

( Matching the exponents)

For x: 2b= 10; b=10/2. 

            b=5

For x²: a=2

For x³: -b=-5

             b=5

Answer:

see the attachment!

i hope this can help you!

Answer:

268.08 cm

Step-by-step explanation:

we all know that the FORMULA for a sphere is v=4/3 x π x r^3, so we just SUBSTITUTE.

V=4/3 x π x 4^3

which leaves us with 268.08 cm ^2 maybe??

(hope this helps)

Answer: I don't know

Step-by-step explanation:

There are no choices. The question stated choose the polynomial which means it should have choices.

Correct me if I'm wrong though. Hope you won't be offended.

Answer:

Please read explanation... it always helps... trust me...

Step-by-step explanation:

alrighty sooo....

when a polynomial is written in standard form that means that the exponents are in order from greatest to least.... (i hope that isn't confusing....)

here is an example:

x^6  +  x^5  + x^2 + 23     --> this polynomial is in standard form because the exponents are in order from least to greatest..... 6 then 5 then 2 then 1

(remember that a number like 23 have an invisible 1 as the exponent....

(btw, this symbol ^ means "to the power of")

I really hope this helps!!!!

Answer:

B)  2.19 %

Step-by-step explanation:

The rule of 70 is used to estimate the time (in years) it takes for an investment to double.

Rule of 70 Formula

[tex]\textsf{Number of Years to Double}=\sf \dfrac{70}{\textsf{Annual Growth Rate}}[/tex]

Given:

Substituting this into the formula and solving

[tex]\implies \sf 32=\sf \dfrac{70}{\textsf{Annual Growth Rate}}[/tex]

[tex]\implies \textsf{Annual Growth Rate}=\sf \dfrac{70}{32}[/tex]

[tex]\implies \textsf{Annual Growth Rate}=\sf 2.1875[/tex]

[tex]\implies \textsf{Annual Growth Rate}=\sf 2.19 \% \: (nearest\:hundredth)[/tex]

Answer:

I think it is B

Step-by-step explanation:

hope it will help you

The equation for the function g(x) = log₃(x+4) after applying the transformation x → (x+4).

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have equation of the graph:

[tex]\rm f(x) = log_3x[/tex]

Apply transformation in the parent function:

Replace x → (x+4)

The parent function will shift 4 units to the left.

And function becomes:

[tex]\rm g(x) = log_3(x+4)[/tex]

Thus, the equation for the function g(x) = log₃(x+4) after applying the transformation x → (x+4).

Learn more about the function here:

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The ratio of the length of candle A to the length of candle B at first will be 3 / 5.

A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.

Candle A and candle B were lit at the same time. candle a could last 3 hours and candle b could last 5 hours. after 1 hour, both candles were equal in length.

Then the ratio of the length of the candle A to the length of candle B at first will be

Let the length of candle A is x and the length of candle B be y.

The common speed will be S.

Then we have

Time = length / speed

For candle A, we have

Candle A = x / S = 3 ...1

For candle B, we have

Candle B = y / S = 5 ...2

From equations 1 and 2, we have

x / 3 = y / 5

x / y = 3 / 5

More about the ratio and the proportion link is given below.

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Step-by-step explanation:

282.8cm³

Since the volume of each chocolate candy is in the shape of a sphere, it's volume is the volume of a sphere.

Answer:

[tex]20000 \times 0.15 \times 5 = 15000 \\ 20000+15000=35000

Step-by-step explanation:

20000 times (0.15 is rate) times years (5)

Answer you get is 15000 , then you have to take 20000+15000=35000

Answer:

6 donuts are left in the box

Step-by-step explanation:

12 divided by 4 is 3. take those three out of the 12. you are left with nine. 9 divided by 3 is 3. subtract three from the nine. you are left with 6.

Answer:

1407.43

Step-by-step explanation:

The eqaution for surface area of a cylinder is 2πr+2π[tex]r^{2}[/tex]'

but you already got the circumference so you work backwards

16pi/pi=16

16/2=8

r=8

h=20

So you plug it into the eqaution

2π8*20+2π8^2=1407.43

Answer:

(5,2)

Step-by-step explanation:

if it’s (x,y) and 4 to the y to get 2

Find Determinant value

[tex]\\ \rm\Rrightarrow \left|\begin{array}{cc}\rm 3&\rm -6\\ \rm 1&\rm -2\end{array}\right|[/tex]

[tex]\\ \rm\Rrightarrow -6+6[/tex]

[tex]\\ \rm\Rrightarrow 0[/tex]