The height of a rectangular prism is found by dividing volume, V, by the base area, B.





If the volume of the rectangular prism is represented by 6x2 – 2x + 8 and the base area is 2x – 4, which expression represents the height?

Answer:

x=2

Step-by-step explanation:

(5x–7)–5(7x–12)+7=0

5x-7-35x+60+7=0

-30x=-60

x=2

Answer:

The answer I got was x=2

Answer: third answer

Step-by-step explanation:

Answer:

a = 10√3, b = 5√3, c = 15; d = 5

Step-by-step explanation:

d = 10/2 = 5

b = 5√3

a = 2 * 5√3 = 10√3

c = 5√3 * √3 = 15

Answer is the second option

a = 10√3, b = 5√3, c = 15; d = 5

Step-by-step explanation:

The point-slope of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

We have the slope m = 71 and the point (-2, 4).

Substitute:

[tex]y-4=71(x-(-2))\\\\\bold{y-4=71(x+2)}[/tex]

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

Convert:

[tex]y-4=71(x+2)[/tex]         use the distributive property

[tex]y-4=71x+142[/tex]         add 4 to both sides

[tex]\bold{y=71x+146}[/tex]

The standard form of an equation of a line:

[tex]Ax+By=C[/tex]

Convert:

[tex]y=71x+146[/tex]            subtract 71x from both sides

[tex]-71x+y=146[/tex]        change the signs

[tex]\bold{71x-y=-146}[/tex]

The general form of an equation of a line:

[tex]Ax+By+C=0[/tex]

Convert:

[tex]71x-y=-146[/tex]           add 146 to both sides

[tex]\bold{71x-y+146=0}[/tex]

Formula for area is:

A = pi*r^2

r = 28

so...

A = 3.14 * 28^2

A = 3.14 * 784

A = 2461.76 cm^2

Formula for circumference is:

C = 2*pi*r

r = 28

so...

C = 2*3.14* 28

C = 6.28*28

C = 175.84 cm

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

11/15.

Step-by-step explanation:

If we consider a right angled triangle we see that

in this case  cos θ = sin (90 - θ)  so the answer is 11/15.

My dog died but answer is 0

Answer:

One effect of higher food prices in a given country is higher consumer price index (CPI) inflation.However, higher food prices affect people in different economies differently.

The impact of rapidly rising food prices on CPI inflation is substantially larger in emerging market economies than advanced economies

This effect tends to be much greater for countries that are 1) large net importers of food, and 2) where households spend a greater percentage of their income on food (meaning that they have a much larger weighting of food in their CPI basket).

In short, higher food prices don't hurt everyone equally. Poorer, developing economies feel it much worse.

Step-by-step explanation:

Answer:

Here's some you can use below!:

Step-by-step explanation:

Oil is used in the processing of many food products. In additional, oil is used in the transportation of food. As a result, with oil price increases, the price of food increases as well.

The world population continues to grow, and with that comes increased demand of various food products. As a result, this rising demand directly leads to higher prices.

The increases in food prices have already taken effect and are not likely to improve in the near future. As of February 2011, the price of wheat has increased 83% and the price of corn has doubled since one year earlier. As feed becomes more expensive, the cost of beef products is expected to increase by almost 40%, leading to much higher prices for any meat eaters out there. With unemployment remaining at very high levels, these prices will serve to further put a dent in our wallets.

The situation is even more dire in poorer countries as many of their citizens spend about 80% of their income on basic food products. As a result, food price increases can be devastating to people in these countries, with an additional 44 million people already having been pushed into poverty. The food crisis has inspired riots in countries such as Egypt, Haiti, Tunisia, and Algeria.

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (-3,2)~~ \begin{cases} x=-3\\ y=2 \end{cases}\implies 2=k(-3)\implies -\cfrac{2}{3}=k[/tex]

To find the constant of variation k in the direct variation y = kx for the point (–3, 2), we substitute the point into the equation.

We get k = 2 / (–3), resulting in k = –rac{2}{3}.

The constant of variation, k, in the direct variation equation y = kx can be found using the coordinates of a given point that lies on the line represented by this equation.

Given a point (–3, 2), we can substitute these values into the equation to find k:

y = kx

2 = k(–3)

To isolate k, we divide both sides of the equation by (–3):

k = 2 / (–3)
k = –rac{2}{3}

Answer:

2824

Step-by-step explanation:

Take the number of pounds and divide by the number of people:

3.474×10⁹ / 1.23×10⁶

Divide the coefficients and subtract the exponents:

(3.474 / 1.23) × 10⁹⁻⁶

2.824×10³

So the country produced about 2,824 pounds of garbage per person in 2005.

The correct option is C.

Probability of selecting all boys from 8 boys and 6 girls for a 4-person committee is 10/143.

To find the probability that the committee consists of all boys, we need to calculate the probability of selecting 4 boys out of 8 boys and no girls out of 6 girls.

The total number of ways to choose a 4-person committee from 14 students (8 boys and 6 girls) is given by the combination formula:

[tex]\[ \text{Total number of ways} = \binom{14}{4} \][/tex]

The number of ways to choose 4 boys out of 8 is given by:

[tex]\[ \binom{8}{4} \][/tex]

And since we don't choose any gi-rls, the number of ways to choose 0 girls out of 6 is simply 1.

So, the probability of selecting all boys is:

[tex]\[ \text{Probability} = \frac{\binom{8}{4} \times \binom{6}{0}}{\binom{14}{4}} \][/tex]

Let's calculate this:

[tex]\[ \text{Probability} = \frac{\binom{8}{4} \times \binom{6}{0}}{\binom{14}{4}} = \frac{\frac{8!}{4!(8-4)!} \times \frac{6!}{0!(6-0)!}}{\frac{14!}{4!(14-4)!}} \][/tex]

[tex]\[ = \frac{\frac{8!}{4!4!} \times 1}{\frac{14!}{4!10!}} \][/tex]

[tex]\[ = \frac{\frac{8 \times 7 \times 6 \times 5}{4 \times 3 \times 2 \times 1}}{\frac{14 \times 13 \times 12 \times 11}{4 \times 3 \times 2 \times 1}} \][/tex]

[tex]\[ = \frac{70}{1001} \][/tex]

[tex]\[ = \frac{10}{143} \][/tex]

So, the correct answer is option C: [tex]\( \frac{10}{143} \)[/tex].

The complete question is here:

A four-person committee is chosen from a group of eight boys and six girls.. If students are chosen at random, what is the probability that the committee consists of all boys?

A. 4/1001

B. 15/1001

C. 10/143

D. 133/143

Answer:The decimal 4.39 equals 439%

To convert from decimal to percent, just multiply the decimal value by 100. In this example we have: 4.39 × 100 = 439% (answer).

The ease way:

1) Move the decimal point two places to the right: 4.39 → 43.9 → 439.

2) Add a % sign: 439%

Answer: 439%

The equivalent value of the percentage is A = ( 4.39/100 ) = 4.39 %

Given data ,

Let the percentage be represented as A

Now , the value of A is

Let the numerator of the fraction be p

where the value of p = 4.39

Let the denominator of the fraction be q

where q = 100

Now , the fraction is A = p/q

On simplifying the expression , we get

So , the left hand side of the equation is equated to the right hand side by the value of p/q

A = 4.39/100

A = 0.0439

On further simplification , we get

A = 0.0439 = 4.39 %

So , the percentage is 4.39 %

Therefore , the value of A = 4.39 %

Hence , the expression is A = 4.39 %

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Around 175 dollars with that because that’s 20 hours

Answer:

$170

Step-by-step explanation:

add the hours first

2+3+4+5+6= 20 hours

multiply that by how much she makes per hour

20*8.75= 175

Answer: 25

Assuming the dotted line touches the middle of the base of the triangle,

Using Pythagoras Theorem,

(30/2)^2 + (20)^2 = x^2

x^2 = (15)^2 + 400

x^2 = 625

x = √625 or -(√625)

x = 25 or -25

But since x needs to be a positive value,

x = 25

Answer:

x = 25 cm

Step-by-step explanation:

Given the triangle is isosceles ( 2 equal sides )

Then the line from the vertex is a perpendicular bisector of the base

We can use Pythagoras' identity on the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

where x is the hypotenuse and the legs are 15 and 20, so

x² = 15² + 20² = 225 + 400 = 625

Take the square root of both sides

x = [tex]\sqrt{625}[/tex] = 25

Answer:

Option A

Step-by-step explanation:

Positive trend will start from bottom to going upwards and negative trend will start from the top to bottom.

Weight and height is also logical because as height goes up, weight will follow up.

Answer:

...

Step-by-step explanation:

can you show us the options of the drop-down menus?

Answer:

Step-by-step explanation:

[tex]3x-3<9\qquad\text{add 3 to both sides}\\3x-3+3<9+3\\3x<12\qquad\text{divide both sides by 3}\\\dfrac{3x}{3}<\dfrac{12}{3}\\\boxed{x<4}\\\\============================\\\\5x+2<32\qquad\text{subtract 2 from both sides}\\5x+2-2<32-2\\5x<30\qquad\text{divide both sides by 5}\\\dfrac{5x}{5}<\dfrac{30}{5}\\\boxed{x<6}[/tex]

Answer:

Amount invested at 8% = $2800

Amount invested at 5.5% = $2200.

Step-by-step explanation:

Let the amount invested at 8% = x

Then the amount invested at 5.5% = 5000-x

Then we get equation:

[8% of x] + [5.5% of (5000-x)] = [6.9% of 5000]

8(x) + 5.5(5000-x) = 6.9(5000)

8x + 27500 - 5.5x = 34500

8x - 5.5x = 34500-27500

2.5x = 34500-27500

2.5x = 7000

x = 7000/2.5

x = 2800

then  the amount invested at 5.5% = 5000-x = 5000-2800 = 2200

Hence final answer is given by:

Amount invested at 8% = $2800

Amount invested at 5.5% = $2200.

-9b + 6

Multiply the -3 by each term in the first parentheses.

(-3 * 3b) + (-3 * -2)

Now just simplify.

-9b + 6

Answer:

Tbh I have no clue..

Answer:

Second point (-5/2, -7/2)

First point (3/2, 17/2)

Step-by-step explanation:

We have two equations, and we want to know at wich poin are equal. Hence, we have a system of equations and the solution is nothing more that the point (x,y) where those functions intercepts.

4x2+ 7x -11=y

3x+4=y

Lets use substitute method

4x2+7x-11=3x+4

This can be re arrange as the following eq:

4x2+4x-15=0

A quadratic equation, its solution can be obtained using the below eq.

[tex]x=\frac{-b+/- \sqrt{x^{2}-4ac } }{2a}[/tex]

where a=4, b=4, c=-15.

Remember, the quadratic equation as a +/- sign, meaning that you will obtain one answer using the + operator and other using the - operator.

By doing the above, we have x=-5/2 and x=3/2

By using x=3/2 in equation of line (3x+4=y)  we have y=17/2

First point (3/2, 17/2)

By using x=-5/2 in equation of line (3x+4=y) we have y= -7/2

Second point (-5/2, -7/2)

Those points are the ones where the line and the parabola intercept.

since TU is the midsegment in the triangle, then T and U are both midpoints.

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ R(\stackrel{x_1}{0}~,~\stackrel{y_1}{2b})\qquad Q(\stackrel{x_2}{-2a}~,~\stackrel{y_2}{0}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \stackrel{midpoint}{T}=\left( \cfrac{-2a+0}{2}~~,~~\cfrac{0+2b}{2} \right)\implies T=\left( \cfrac{-2a}{2}~,~\cfrac{2b}{2} \right) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill T=(-a,b)~\hfill[/tex]

Answer:

The surface area of the prism is [tex](18\sqrt{3}+180)\ in^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of the triangular prism is equal to

[tex]SA=2B+PH[/tex]

where

B is the area of the triangular base

P is the perimeter of the triangular base

H is the height of the prism

Find the area of the base B

Applying the law of sines to find the area of a equilateral triangle

[tex]B=\frac{1}{2}b^{2} sin(60\°)[/tex]

we have

[tex]b=6\ in[/tex]

[tex]sin(60\°)=\sqrt{3}/2[/tex]

substitute

[tex]B=\frac{1}{2}6^{2}(\sqrt{3}/2)[/tex]

[tex]B=9\sqrt{3}\ in^{2}[/tex]

Find the perimeter P

[tex]P=3*6=18\ in[/tex]

we have

[tex]H=10\ in[/tex]

substitute the values

[tex]SA=2(9\sqrt{3})+(18)(10)=(18\sqrt{3}+180)\ in^{2}[/tex]

It’s > because when you square root 18 it’s 4.24264069

Answer:

The answer would be C, Greater Than, >.

Step-by-step explanation:

In this question, it is asked if 5 is equal to, less than or greater than the square root of 18. So we first need to find out the value of square root 18. We can do it manually or with a scientific calculator. If we do it with a calculator, we would come to know that the answer of square root 18 is 4. 24264068. Now we would compare it with 5. We will have to see if 5 is equal to, less than or greater than this value of square root of 18. So it is clear from the above answer of square root 18, that it is less than 5.

So the answer is C, that shows that 5 is greater than square root of 18, i-e 4.24264068.

Answer:

11x-6y

Step-by-step explanation:

we ignore the parenthesis so we add 8x and 3x since they are both positive which adds up to 11x

for -2y and -4y we add, a negative and a negative equals negative therefor -2y+(-4y)= -6y

11x-6y

For this case we must add the following expressions:

[tex](8x-2y) + (3x-4y) =[/tex]

We eliminate the parentheses, taking into account that:[tex]+ * + = +\\+ * - = -\\8x-2y + 3x-4y =[/tex]

We add similar terms:

[tex]8x + 3x-2y-4y =[/tex]

Equal signs are added and the same sign is placed:

[tex]11x-6y[/tex]

Answer:

[tex]11x-6y[/tex]

Option C

ANSWER

The domain is an empty set

EXPLANATION

The given functions are:

[tex]f(x) = \sqrt{x - 3} [/tex]

and

[tex]g(x) =1 - {x}^{2}[/tex]

[tex](f \circ \: g)(x) = f(g(x))[/tex]

[tex](f \circ \: g)(x) = f(1 - {x}^{2} )[/tex]

[tex](f \circ \: g)(x) = \sqrt{(1 - {x}^{2} ) - 3} [/tex]

[tex](f \circ \: g)(x) = \sqrt{ - {x}^{2} - 2} [/tex]

This function is defined if and only if

[tex] - {x}^{2} - 2 \geqslant 0[/tex]

[tex] {x}^{2} + 2 \leqslant 0[/tex]

There is no real values that satisfies this inequality, because

[tex] {x}^{2} + 2[/tex]

is always positive.

The domain of this composite function is a null set.

Answer:

The domain of f, and thus the range of g, is restricted to values greater than or equal to 3.

If 1 minus x squared is greater than or equal to 3, then x squared must be less than –2.

Since x squared cannot be less than a negative number, the function is undefined for all values of x.

Step-by-step explanation:

Step-by-step explanation:

[tex]f(x)=4-x^2,\ g(x)=2-x\\\\(f+g)(x)=f(x)+g(x)\\\\\text{therefore}\\\\(f+g)(x)=(4-x^2)+(2-x)=-x^2-x+(4+2)=-x^2-x+6\\\\\text{It's the quadratic function. The domain is the set of all real numbers}\ x\in\mathbb{R}[/tex]

Answer with Step-by-step explanation:

A candle is 4 inches tall and burns at the rate of 0.6 inch per hour.

i.e. after 1 hour height of candle=4-0.6 inches

After 2 hours height of candle=4-0.6-0.6 inches

after x hours height of candle=4-0.6x

Also,

If the height of the candle after x hours is 1.5 inches

⇒  4-0.6x=1.5

⇒ 0.6x=4-1.5

⇒ 0.6x=2.5

⇒ x=2.5/0.6

⇒ x=4.166

Hence, equation to represent the situation. is:

4-0.6x=1.5

and the expected number of hours in which the candle  melted to 1.5 inches is:

4.166 hours

After defining and solving the linear equation representing the candle's height over time, it is determined that it will take approximately 4.17 hours for the candle to burn down to 1.5 inches.

This is a problem about rates and linear equations in the subject of mathematics. The candle starts at 4 inches and burns at a rate of 0.6 inch per hour, which decreases the height of the candle. So, the equation would be: height = starting height - (burn rate)x(time), or H = 4 - 0.6x.

From the problem we know, that the height of the candle after x hours is 1.5 inches. So, we substitute H with 1.5: 1.5 = 4 - 0.6x.

To solve for x, first we can subtract 4 from both sides: -2.5 = -0.6x. Then, divide both sides by -0.6 to isolate x. So, x = -2.5/-0.6 which simplifies to approximately 4.17 hours. So, it will take around 4.17 hours for the candle to burn down to 1.5 inches.

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Answer:

30

Step-by-step explanation:

Answer:

30% is greater than 0.03

Step-by-step explanation:

30% = 0.3, which is greater than 0.03

Answer:

The y-intercept would be 12.

Step-by-step explanation:

In the problem:

4x=slope

12=y-intercept

AnswBetty correctly determined that the ordered pair (–3, 5) is a solution to the system of linear equations 6 x + 5 y = 7 and x + 4y = 17. Based on this information, which statement is correct?

(–3, 5) satisfies neither the equation 6x + 5y = 7 nor the equation x + 4y = 17.

(–3, 5) satisfies the equation 6x + 5y = 7 but not the equation x + 4y = 17.

(–3, 5) satisfies the equation x + 4y = 17 but not the equation 6x + 5y = 7.

(–3, 5) satisfies both the equation 6x + 5y = 7 and the equation x + 4y = 17.

Answer:

The center is the point [tex](-1,2)[/tex]

Step-by-step explanation:

we know that

The center of the circle is equal to the midpoint of the endpoints of the diameter

so

The formula to calculate the midpoint between two points is equal to

[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

substitute the values

[tex]M(\frac{-7+5}{2},\frac{3+1}{2})[/tex]

[tex]M(\frac{-2}{2},\frac{4}{2})[/tex]

[tex]M(-1,2)[/tex]

therefore

The center is the point [tex](-1,2)[/tex]

Answer:

3 more trays

Step-by-step explanation:

At 35 cookies per tray, x trays is sufficient for an output of 840 cookies.  Dividing 840 cookies by 35 cookies/tray, we get  24  trays.

But Ms. Sharp already has 21 trays.

Thus, she needs 3 more to be able to bake 840 cookies.

Ms Sharp will need to bake 3 more trays of cookies to meet the requirement of 840 cookies.

To determine how many more trays of cookies Ms. Sharp needs to bake, we first calculate the total number of cookies she has already baked. She baked 21 trays with 35 cookies on each tray:

[tex]\[21 \text{ trays} \times 35 \text{ cookies per tray} = 735 \text{ cookies}\][/tex]

Ms. Sharp needs a total of 840 cookies. Therefore, we need to find out how many more cookies are required:

[tex]\[840 \text{ cookies} - 735 \text{ cookies} = 105 \text{ cookies}\][/tex]

Each tray contains 35 cookies, so we need to determine how many more trays are required to bake 105 cookies:

[tex]\[\frac{105 \text{ cookies}}{35 \text{ cookies per tray}} = 3 \text{ trays}\][/tex]

Therefore, Ms. Sharp will need to bake an additional:

[tex]\[\boxed{3}\][/tex] trays of cookies.