A rectangular prism has a volume of 750 cubic millimeters. Its length is 15
millimeters, and its width is 10 millimeters. What is its height? You must show your
work to earn full credit.

M = 3

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there are two pieces, both divided in 10 equal segments.

so each piece is 10/10, or namely 1 whole.

two pieces, 10/10 each, is 20/10 for the whole thing, but there are only 11 shaded, so if we take 20 to be the 100%, what is 11 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 20&100\\ 11&x \end{array}\implies \cfrac{20}{11}=\cfrac{100}{x}\implies 20x=1100\\\\\\ x=\cfrac{1100}{20}\implies x=55[/tex]

Answer:

B.

Step-by-step explanation:

The line gets smaller left to right so that means the line is negative. Since the line is negative x must be negative. The line is also touching the y-axis at 6. We are going to use the formula y=mx+b. So our equation is going to be y=6-x.

Answer:

c 8700

Step-by-step explanation:

Answer:

The answer is (C. 8700

Step-by-step explanation:

I took the test

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=5x+3&(1)\\y=4x+6&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\5x+3=4x+6\qquad\text{subtract 3 from both sides}\\5x=4x+3\qquad\text{subtract 4x from both sides}\\x=3\\\\\text{Put the value of x to (1):}\\\\y=5(3)+3\\y=15+3\\y=18[/tex]

Answer:

[tex]553\ acres[/tex]

Step-by-step explanation:

Let

z------> the crop yield

x----> the number of bushels harvested

y----> the number of acres used for the harvest

[tex]z=\frac{x}{y}[/tex]

we have

[tex]x=94,010\ bushels[/tex]

[tex]z=170\ bushels/acre[/tex]

substitute and solve for y

[tex]170=\frac{94,010}{y}[/tex]

[tex]y=\frac{94,010}{170}=553\ acres[/tex]

Answer:

553

Step-by-step explanation:

Answer:

The ordered pair that satisfies this problem is (1, -6); x = 1 when y = -6.

Step-by-step explanation:

Please, rewrite your question as follows:

"Suppose that y varies directly with x and y = 12 when x = -2. What is x when

y = -6?"  The " = " sign must be included.

The pertinent proportional relationship is y = kx, where k is the constant of proportionality.

We must find k here.  Let y = 12 and x = -2.  Then 12 = k(-2), or k = -6.

Then the relationship is y = -6x.

Now let y = -6 and find x:      -6 = -6x, or x = 1.

The ordered pair that satisfies this problem is (1, -6)

The three methods are graphing, substitution and elimination.

In my opinion they are all easy but if I had to choose one it would be graphing because when I did homework assignments for this I always took the longest graphing than just solving the systems using substitution or elimination

Answer:

Option A is correct that It is a FALSE Statement.

Step-by-step explanation:

Given:

Total number of student = 1

Number of student in Physical Science = 0.3

Number of student in Chemistry = 0.35

Number of student in Biology = 0.35

Number of student who are Sophomores = 0.55

To find: False Statement among given ones.

Percentage of the student in Physical Science = [tex]\frac{0.3}{1}\times100[/tex] = 30%

Percentage of the student in Chemistry = [tex]\frac{0.35}{1}\times100[/tex] = 35%

Percentage of the student in Biology = [tex]\frac{0.35}{1}\times100[/tex] = 35%

Percentage of the student who are Sophomores = [tex]\frac{0.55}{1}\times100[/tex] = 55%

Therefore, Option A is correct that It is a FALSE Statement.

Answer:

A is the answer

Step-by-step explanation:

Answer:

4.8 hr, or 4 hr 48 min

Step-by-step explanation:

Let '1' represent 'the whole house-painting job.'

Then perform a dimensional analysis:

    1 whole house job

 -------------------------------- = 12 hours.   →This restates the obvious:  Jim can

          1 job/ 12 hrs                                     paint a house in 12 hours.

Now if both people work together, the total time required to paint the house is:

              1 house job                         1 house job

-----------------------------------------  =  ------------------------------  =  t for whole job

         1 job               1 job               8 job-hr + 12 job-hr        with both people

      ------------    +    ------------          -----------------------------       working

      12 hours           8 hours                        96 hr

This turns out to be:

              1

--------------------------  =  96/20 hr  = 4.8 hr, or 4 hr 48 min

      20/96

It would take Jim and Alex 4.8 hours to paint the house together if they both work at their individual rates.

Now, Let's start by finding the individual rates of Jim and Alex in terms of the fraction of the house they can paint per hour.

Jim can paint a house in 12 hours, so his rate is 1/12 of the house per hour.

Similarly, Alex can paint the same house in 8 hours, so his rate is 1/8 of the house per hour.

Now, let's suppose they work together for t hours to complete the job.

During this time, Jim will be able to paint t/12 of the house and Alex will be able to paint t/8 of the house.

The sum of their individual rates is equal to the combined rate at which they can paint the house together.

So we can set up the following equation:

t/12 + t/8 = 1

Solving for t, we get:

t = 4.8 hours

Therefore, it would take Jim and Alex 4.8 hours to paint the house together if they both work at their individual rates.

Learn more about the mathematical expression visit:

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Answer:

[tex]\lim_{x \to 0} \frac{x^2}{sinx}=0[/tex]

Step-by-step explanation:

[tex]f(-0.03)=-0.0300\\f(-0.02)=-0.0200\\f(-0.01)=-0.0100\\f(0.01)=0.0100\\f(0.02)=0.0200\\f(0.03)=0.0300[/tex]

As the Left side of the function is approaching 0 as it gets closer to x=0 and the Right side is also approaching 0 as it gets closer to x=0, the limit would be 0.

Among the given options, only ((-196)^(1/4)) is equivalent to a real number, as it involves the fourth root of a negative number, which results in a real value.

The correct answer is option B.

To determine which expression is equivalent to a real number, we need to consider the roots involved and whether they result in a real value.

Let's analyze each option:

A. (-1503)^(1/6): The expression involves the sixth root of a negative number. Odd roots of negative numbers are real, but even roots are not. Therefore, this expression is not guaranteed to be real.

B. (-196)^(1/4): The expression involves the fourth root of a negative number. Similar to option A, the fourth root of a negative number is real, so this expression is valid.

C. (-144)^(1/2): This expression involves the square root of a negative number. Square roots of negative numbers are not real; hence, this expression is not equivalent to a real number.

D. (-1024)^(1/2): The expression involves the square root of a negative number as well. Like option C, this expression is not equivalent to a real number.

In summary, option B ((-196)^(1/4)) is equivalent to a real number because it involves the fourth root of a negative number, and odd roots of negative numbers are real.

A would be your best option. Choice A properly displays the equation, 5x+6=4x+(-3), using words. Let me know if you want an explanation of why the other options are invalid. :)

Answer:

A is correct.

Step-by-step explanation:

Which is the correct way to model the equation 5x+6=4x+(-3) using algebra tiles?  

5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side.

5 positive x-tiles = 5x

6 positive unit tiles = 6

4 positive x-tiles = 4x

3 negative unit tiles = -3

-----------------------------------------------------------------------

B - There are 5 x tiles but its given 6 x tiles.

C  - There is 6 positive unit tile and its given 6 negative,

D - There is 3 negative unit tile but here its given positive.

Answer:

• discriminant: 73

• # of real solutions: 2

Step-by-step explanation:

Comparing the equation ...

2x^2 -9x +1 = 0

to the generic form ...

ax^2 +bx +c = 0

we find the coefficient values to be ...

a = 2; b = -9; c = 1

That makes the value of the discriminant, (b^2 -4ac), be ...

(-9)^2 -4(2)(1) = 81 -8 = 73

Since the discriminant is positive, the number of real solutions is 2.

Answer:

$14

Step-by-step explanation:

Wages earned by daniel in one hour = $8

Number of working hours spend by daniel in each week = 35

Wages earned by daniel in each week without pay increase = [tex]35\times 8 = 280[/tex]

Increase in pay per week = [tex]\frac{5}{100} \times 280= 14[/tex]

Therefore extra wages earned by Daniel will be $14.

$14

Step-by-step explanation:

Wages earned by daniel in one hour = $8

Number of working hours spend by daniel in each week = 35

Wages earned by daniel in each week without pay increase =

Increase in pay per week =

Therefore extra wages earned by Daniel will be $14.

Answer:

[tex]x=55[/tex]

Step-by-step explanation:

The given equation is [tex]\sqrt{x-6}+3=10[/tex]

Group similar terms to get:

[tex]\sqrt{x-6}=10-3[/tex]

[tex]\sqrt{x-6}=7[/tex]

Square both sides to obtain:

[tex]x-6=7^2[/tex]

[tex]x-6=49[/tex]

Add 6 to both sides

[tex]x=49+6[/tex]

Simplify the right hand side to obtain;

[tex]x=55[/tex]

The standard form of the equation of the parabola with a focus at (5, 0) and a directrix at x = -5 is (x - 5)^2 = 20y.

The standard form of the equation of a parabola with a focus at (h, k) and a directrix at x = d is given by (x - h)^2 = 4p(y - k), where p is the distance between the vertex and the focus or directrix.

In this case, the focus is at (5, 0) and the directrix is at x = -5. Since the directrix is a vertical line, the parabola opens to the right. The distance between the vertex and the focus or directrix is given by p = |5 - (-5)|/2 = 5 units.

Substituting the values into the standard form equation gives (x - 5)^2 = 4(5)(y - 0), which simplifies to (x - 5)^2 = 20(y - 0). Therefore, the standard form of the equation of the parabola is (x - 5)^2 = 20y.

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Answer:

The entry has an area of __44___ square feet

The total area of the tree house is __345__ square feet

Step-by-step explanation:

Let's first calculate the area of the trapezoid entrance:

The area of a trapezoid is given by:

A =((b1 + b2) * h) / 2

Where b1 and b2 are the bases or parallel sides.  So, we have:

A = ((6 + 16) * 4) / 2 = (22 * 4) / 2 = 44 sq ft

Now, let's look at the other areas... which are all rectangles, so easy to calculate (b * h).

Playroom: 16 x 14 = 224 sq ft

Side Deck: 3 x 14 = 42 sq ft

Back Porch: 6 x6 = 35 sq ft

So, in the total area of the tree house is:

TA = 44 + 224 + 42 + 35 = 345 sq ft

Answer:

The entry terrace has an area of

48

square feet. The total area of the tree house including the entrance, porch, and side deck is

350

square feet.

Step-by-step explanation:

I just took a test with this question and this was the right answer

~Please mark me as brainliest :)

Answer:

- [tex]\frac{2}{729}[/tex]

Step-by-step explanation:

The n th term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

Given a₁ = 6 and r = - [tex]\frac{1}{3}[/tex], then

[tex]a_{8}[/tex] = 6 × [tex](-1/3)^{7}[/tex] = 6 × - [tex]\frac{1}{3^{7} }[/tex] = 6 × - [tex]\frac{1}{2187}[/tex] = - [tex]\frac{2}{729}[/tex]

Answer:

1,-3,-5

Step-by-step explanation:

Given:

f(x)=x^3+7x^2+7x-15

Finding all the possible rational zeros of f(x)

p= ±1,±3,±5,±15 (factors of coefficient of last term)

q=±1(factors of coefficient of leading term)

p/q=±1,±3,±5,±15

Now finding the rational zeros using rational root theorem

f(p/q)

f(1)=1+7+7-15

   =0

f(-1)= -1 +7-7-15

     = -16

f(3)=27+7(9)+21-15

    =96

f(-3)= (-3)^3+7(-3)^2+7(-3)-15

     = 0

f(5)=5^3+7(5)^2+7(5)-15

    =320

f(-5)=(-5)^3+7(-5)^2+7(-5)-15

      =0    

f(15)=(15)^3+7(15)^2+7(15)-15

     =5040

f(-15)=(-15)^3+7(-15)^2+7(-15)-15

      =-1920

Hence the rational roots are 1,-3,-5 !

Answer:

Actual rational zeros of f(x) are x=-5, x=-3, and x=1.

Step-by-step explanation:

Given function is [tex]f(x)=x^3+7x^2+7x-15[/tex].

constant term = p = -15

coefficient of leading term q= 1

then possible rational roots of given function f(x) are the divisors of [tex]\pm \frac{p}{q}=\pm 1, \quad \pm 3, \quad \pm 5, \quad \pm 15[/tex]

Now we can plug those possible roots into given function to see which one of them gives output 0.

test for x=1

[tex]f(x)=x^3+7x^2+7x-15[/tex]

[tex]f(1)=1^3+7(1)^2+7(1)-15[/tex]

[tex]f(1)=1+7+7-15[/tex]

[tex]f(1)=0[/tex]

Hence x=1 is the actual rational zero.

Similarly testing other roots, we get final answer as:

Actual rational zeros of f(x) are x=-5, x=-3, and x=1.

Answer:

300cm

Step-by-step explanation:

First you get the length, width, and height. The length is 15, the width is 12, and the height is 10.

15*12=180

Since their is 2 you multiply by 2

180*2=360

12*10=120

Since their is 2 you multiply by 2

120*2=240

Then you divide by 2 since it is a triangle but before that you add the products up

360+240=600

600/2=300

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x^2+y^2=16&(1)\\y+4=x^2&(2)\end{array}\right\qquad\text{substitute (2) to (1)}\\\\(y+4)+y^2=16\\y^2+y+4=16\qquad\text{subtract 16 from both sides}\\y^2+y-12=0\\y^2+4y-3y-12=0\\y(y+4)-3(y+4)=0\\(y+4)(y-3)=0\iff y+4=0\ \vee\ y-3=0\\\\y+4=0\qquad\text{subtract 4 from both sides}\\\boxed{y=-4}\\\\y-3=0\qquad\text{add 3 to both sides}\\\boxed{y=3}[/tex]

[tex]\text{Put the values of y to (2)}:\\\\\text{for}\ y=-4\\x^2=-4+4\\x^2=0\to x=\sqrt0\to\boxed{x=0}\\\\\text{for}\ y=3\\x^2=3+4\\x^2=7\to x=\pm\sqrt{7}\\\boxed{x=-\sqrt7\approx-2.65}\ \vee\ \boxed{x=\sqrt7\approx2.65}[/tex]

Answer:

Perimeter of triangle JKL: [tex]2 \sqrt{17} + 2\sqrt{34}[/tex].

Area of triangle JKL: 17.

Step-by-step explanation:

None of the three sides of triangle JKL is parallel to either the x-axis or the y-axis. Apply the Pythagorean Theorem to find the length of each side.

[tex]\rm JK = \sqrt{(3 - (-5))^{2} + (4- 6)^{2}} = \sqrt{8^{2} + (-2)^{2}} = \sqrt{68} = 2\sqrt{17}[/tex].

[tex]\rm JL = \sqrt{(-2 - (-5))^{2} + (1- 6)^{2}} = \sqrt{3^{2} + (-5)^{2}} = \sqrt{34}[/tex].

[tex]\rm KL = \sqrt{(-2 - 3)^{2} + (1-4)^{2}} = \sqrt{(-5)^{2} + (-3)^{2}} = \sqrt{34}[/tex].

The perimeter of triangle JKL will be:

[tex]\rm JK + JL + KL = 2\sqrt{17} + \sqrt{34} + \sqrt{34} = 2 \sqrt{17} + 2\sqrt{34}[/tex].

In case you realized that [tex]\rm JK : JL : KL = \sqrt{2} : 1 : 1[/tex], which makes JKL an isosceles right triangle:

Area of a right triangle:

[tex]\begin{aligned}\displaystyle \rm Area &= \frac{1}{2} \times \text{First Leg} \times \text{Second Leg}\\ &=\frac{1}{2} \times \sqrt{34}\times\sqrt{34}\\&= 17\end{aligned}[/tex].

Alternatively, apply the Law of Cosines to find the cosine of any of the three internal angles. This method works even if the triangle does not contain a right angle.

Taking the cosine of angle K as an example:

[tex]\displaystyle\begin{aligned}\rm \cos{K}&=\frac{(\text{First Adjacent Side})^{2} + (\text{Second Adjacent Side})^{2}-(\text{Opposite Side})^{2}}{2\times (\text{First Adjacent Side})\times(\text{Second Adjacent Side})}\\&\rm =\frac{(JK)^{2} + (JL)^{2} -(KL)^{2}}{2\times JK \times JL}\\&=\frac{(2\sqrt{17})^{2}+(\sqrt{34})^{2}-(\sqrt{34})^{2}}{2\times\sqrt{34} \times(2\sqrt{17})}\\ &=\frac{2^{2}\times 17}{2\times \sqrt{2}\times\sqrt{17}\times 2\times \sqrt{17}}\\&=\frac{1}{\sqrt{2}}\end{aligned}[/tex].

Apply the Pythagorean Theorem to find the sine of angle K:

[tex]\displaystyle \rm \sin{K} = \sqrt{1 - (\cos{K})^{2}} = \sqrt{1 - \left(\frac{1}{\sqrt{2}}\right)^{2} } = \sqrt{\frac{1}{2}} = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}[/tex].

The height of JKL on the side JK will be:

[tex]\displaystyle \rm KL \cdot \sin{K} = \sqrt{34} \times \frac{\sqrt{2}}{2} = \frac{\sqrt{68}}{2} = \frac{2\sqrt{17}}{2} = \sqrt{17}[/tex].

What will be the area of JKL given its height [tex]\sqrt{17}[/tex] on a base of length [tex]2\sqrt{17}[/tex]?

[tex]\displaystyle \rm Area = \frac{1}{2} \times Base\times Height = \frac{1}{2}\times (2\sqrt{17})\times \sqrt{17} = 17[/tex].

This ones a bit tricky but the answer is A

Answer:

D

Step-by-step explanation:

The n th term ( explicit formula ) of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

The recursive formula allows us to find the next term from the previous term by adding d to it

Given

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 3 ⇒ d = - 3

Hence

[tex]a_{n}[/tex] = 9 + (n - 1)(- 3) ← explicit formula → D

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. The general formula is a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, and d is the common difference.

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. The general formula for an arithmetic sequence is an = a1 + (n-1)d, where an is the nth term, a1 is the first term, and d is the common difference.

For example, in the given sequence 1, 3, 5, 7, 9, the first term a1 is 1, and the common difference d is 2. Using the formula, we can find the nth term by replacing n with the position of the term we want to find. For instance, to find the 5th term, we substitute n = 5:

a5 = 1 + (5-1)2 = 1 + 8 = 9

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Answer: 32

Step-by-step explanation:

A

Step-by-step explanation:

A is a midpoint and so is O, giving reason to why the distances are the same

Answer:

The bird is approximately 9 ft high up in the tree

Explanation:

The required diagram is shown in the attached image

Note that the tree, the cat and the ground form a right-angled triangle

Therefore, we can apply special trigonometric functions

These functions are as follows:

[tex]sin(\alpha)=\frac{opposite}{hypotenuse} \\ \\ cos(\alpha)=\frac{adjacent}{hypotenuse} \\ \\tan(\alpha)=\frac{opposite}{adjacent}[/tex]

Now, taking a look at our diagram, we can note the following:

α = 25°

The opposite side is the required height (x)

The adjacent side is the distance between the cat and the tree = 20 ft

Therefore, we can use the tan function

This is done as follows:

[tex]tan(\alpha)=\frac{opposite}{adjacent}\\ \\ tan(25)=\frac{x}{20}\\ \\x=20tan(25) = 9. 32 ft[/tex] which is 9 ft approximated to the nearest ft

Hope this helps :)

Step-by-step explanation:

The center of the circle is moved 3 units to the left and 4 units down.  So a = -3 and b = -4.

Answer:

[tex]x^{2}+y^{2} +4x-2y+1=0[/tex]

Step-by-step explanation:

we know that

The general form of the equation of a circle is

[tex]x^{2} +y^{2}+ Dx + Ey + F=0[/tex]

where D, E, F are constants

step 1

Find the radius of the circle

Remember that the distance from the center to any point on the circle is equal to the radius

so

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

[tex](-2,1)\\(-4,1)[/tex]  

substitute the values

[tex]r=\sqrt{(1-1)^{2}+(-4+2)^{2}}[/tex]

[tex]r=\sqrt{(0)^{2}+(-2)^{2}}[/tex]

[tex]r=2\ units[/tex]

step 2

Find the equation of the circle in standard form

[tex](x-h)^{2} +(y-k)^{2}=r^{2}[/tex]

In this problem we have

center ( -2,1)

radius r=2 units

substitute

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

[tex](x+2)^{2} +(y-1)^{2}=4[/tex]

Step 3

Convert to general form

[tex](x+2)^{2} +(y-1)^{2}=4\\ \\x^{2}+4x+4+y^{2}-2y+1=4\\ \\x^{2}+y^{2} +4x-2y+1=0[/tex]