the volume of rectangular prism that measures 7 meters long, 9 meters wide, and 6 meters high is 378m^3
True or False

Starting from the Pythagorean identity, we deduce

[tex]\sin^2(x)+\cos^2(x) = 1 \iff \cos^2(x) = 1-\sin^2(x) \iff \cos(x) = \pm\sqrt{1-\sin^2(x)}[/tex]

If we plug in the value 7/10 for sin(x), we have

[tex]\cos(x) = \pm\sqrt{1-\dfrac{49}{100}} = \pm\sqrt{\dfrac{51}{100}}=\pm\dfrac{\sqrt{51}}{10}[/tex]

Let's call dimes x and the quarters x+3 since we have 3 more of them.

x+x+3=45

2x=42

x=21

we have 21 dimes and 23 quarters

21*0.10=2.1

23*0,25=5.98

if we add those together it equals 8.08

Answer:

$8.10

Step-by-step explanation:

Let d and q represent the # of dimes and quarters, respectively.  Then write equations reflecting this story:

q = d + 3, and d + q = 45.  Substitute d + 3 for q in the second equation, obtaining:

d + d + 3 = 45, or 2d = 42, or d = 21.  Then there are 21 dimes and 24 quarters.  That comes to $2.10 + $6.00, or $8.10.

Answer:

$179.17

Step-by-step explanation:

You already know the formula but you have it typed incorrectly.  The rt is raised as a power to the e.  Just in case you didn't know that.  Filling in our formula with what we have gives us:

[tex]A(t)=125e^{(.18)(2)[/tex]

Simplify that power to .36 and we have

[tex]A(t)=125e^{.36}[/tex]

Now raise e to the power of .36 on your calculator and get

A(t)= 125(1.433329415)  and

A(t) = $179.17

Answer:

C 179 is the answer.

Step-by-step explanation:

Answer:

If you could insert a picture of the graphs that would help! thank you!

Step-by-step explanation:

Let [tex]a_1,\ldots,a_4[/tex] denote the ages of the 4 candidates. Then

[tex]\dfrac{a_1+a_2+a_3+a_4}4=40[/tex]

[tex]a_1+a_2+a_3+a_4=160[/tex]

[tex]\dfrac{a_1+a_2+a_3}3+\dfrac{a_4}3=\dfrac{160}3[/tex]

The average age of the first 3 candidates is 42, so

[tex]\dfrac{a_4}3=\dfrac{160}3-42[/tex]

[tex]\implies\boxed{a_4=160-3\cdot42=34}[/tex]

Answer:

Option B is correct.

Step-by-step explanation:

A city has population = 10000

Population increase each year = 4%

So, Population increase after 1 year = 10000 * 4%

                                                           = 10000*4/100

                                                           = 400

Adding in the current population:

10000+400 = 10,400

Population increase after 2 year = 10,400*4%

                                                     = 10400*4/100

                                                      = 416

Adding in the current population:

10400+416 = 10816

Population increase after 3 year = 10,816*4%

                                                     = 10816*4/100

                                                      = 433

Adding in the current population:

10816+433 = 11,249

Population increase after 4 year = 11,249*4%

                                                     = 11249*4/100

                                                      = 450

Adding in the current population:

11249+450 = 11,699

Population increase after 5 year = 11,699*4%

                                                     = 11699*4/100

                                                      = 468

Adding in the current population:

11699+468 = 12167

So, the population after 5 yeras will be 12167.

Option B is correct.

The population of the city will be approximately 12,167 people after 5 years, calculated by using the formula for exponential growth with a 4% annual increase from the initial population of 10,000.

The question involves calculating the future population of a city that is experiencing exponential growth over a period of time. To find the population of a city 5 years later when the population increases by 4% per year, we use the formula for exponential growth, which is:

P = [tex]P0 * (1 + r)^t[/tex]

Where:

P is the future population

P0 is the initial population (which is 10,000)

r is the annual growth rate (which is 4% or 0.04)

t is the number of years (which is 5)

Using the formula, we calculate:

P = 10,000 × (1 + 0.04)⁵

P = 10,000 × (1.04)⁵

P = 10,000 × 1.2166529

P = 12,166.529

So, the population will be approximately 12,167 people 5 years later.

hope this answer your question :)

ANSWER

[tex]\cos( \angle \: F) = \frac{5}{13}[/tex]

EXPLANATION

The side length adjacent to <F is 5 units.

The length of the hypotenuse is 13 units.

The cosine ratio is

[tex] \cos( \angle \: F) = \frac{adjacent}{hypotenuse} [/tex]

This implies that:

[tex] \cos( \angle \: F) = \frac{5}{13}[/tex]

The fourth choice is correct.

Answer:

the third one.

Answer: C) V = 562.5π [tex]in^{3}[/tex] ; S = 225π [tex]in^{2}[/tex]

Step-by-step explanation: Please see the image below!

Answer:

3 1/4

Step-by-step explanation:

I'll assume you meant 3/4 + (1/3 / 1/6) - (- 1/2) and not 3/4 + (1/3 \ 1/6) - (- 1/2)

So we start with 3/4 + (1/3 / 1/6) - (- 1/2)

The toughest part is (1/3 / 1/6) , but remember that when dividing with a fraction, it's like multiplying by the inverse of that fraction, so...

[tex]\frac{1/3}{1/6} = \frac{1}{3} * \frac{6}{1} = \frac{6}{3} = 2[/tex]

Then we return to the original problem with the new value for the parenthesis:

3/4 + 2 + 1/2 = 3/4 + 8/4 + 2/4 = 13/4 or 3 1/4

Answer:

The correct answer is 3 1/4

Step-by-step explanation:

It is given that,

3/4 + (1/3 \ 1/6) - (- 1/2)

To find the value of given expression

3/4 + (1/3 \ 1/6) - (- 1/2) for finding the answer we have to find the value of

(1/3 / 1/6) = 1/3 * 6/1 = 2

3/4 + (1/3 \ 1/6) - (- 1/2 = 3/4 + 2 + 1/2

 = 3/4 + 8/4 + 2/4 = (3 + 8 + 2)/4 = 13/4 = 3 1/4

The correct answer is 3 1/4

see picture attached.

i hope this helped !!

ANSWER

Point-slope form:

[tex]y + 5 = -3(x - 1)[/tex]

Slope-intercept form;

[tex]y = - 3x - 2[/tex]

EXPLANATION

The point-slope form of a line is given by:

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

We need to find the slope using the formula:

[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]

Let us substitute the point (1, –5) and (–3, 7).

This implies that,

[tex]m = \frac{7 - - 5}{ - 3 - 1} [/tex]

[tex]m = \frac{12}{ - 4} = - 3[/tex]

The point slope form now becomes,

[tex]y - - 5 = - 3(x - 1)[/tex]

[tex]y + 5 = -3(x - 1)[/tex]

To find the slope intercept form, we expand to obtain;

[tex]y = - 3x + 3 - 5[/tex]

[tex]y = - 3x - 2[/tex]

Answer:

You take the repeating group of digits and divide it by the same number of digits but formed only by 9s.

Step-by-step explanation:

Let's say you have 0.111111111111...., your repeating pattern is 1, that consists of one digit (1).  You take that digit and you divide it by 9:

1/9 is the fraction equivalent to 0.111111111111111...

Let's say you have 0.12121212121212...., the repeating pattern is 12, that consists of 2 digits (12).  You take those 2 digits and divide them by 99:

12/99 is the fraction equivalent to 0.12121212121212...

which can be reduced to 4/33

If you have 0.363363363363..., your repeating pattern is 363, which is 3 digits, so you divide 363by 999:

363/999 is the fraction equivalent to  0.363363363363...

which can be simplified to 121/333

To write a repeating decimal as a fraction, multiply the decimal by a suitable power of 10 to eliminate the repeating part, subtract the original equation from the new equation, solve for the variable, and simplify the fraction if possible.

To write a repeating decimal as a fraction, you can use a trick that involves using a variable to represent the repeating part of the decimal. Let's take an example of the repeating decimal 0.3333...

Therefore, the repeating decimal 0.3333... can be written as the fraction 1/3. This method can be applied to any repeating decimal to convert it into a fraction.

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Answer:

20√2 meters (approximately 28.28 m)

Step-by-step explanation:

It may help to make a diagram. Because this is a 45 45 90 triangle, you can use those rules to help solve.

Final answer:

The distance from the top of a totem pole to the end of its shadow, when the angle of elevation of the sun is 45 degrees, is approximately 28.28 meters.

Explanation:

The student has presented a problem that involves using trigonometry to calculate the distance from the top of a totem pole to the end of its shadow when the angle of elevation of the sun is 45 degrees. To solve this, we can use the concept of right-angled triangles and the properties of special triangles, specifically a 45-45-90 triangle where the two legs are congruent. Since the angle of elevation is 45 degrees and the length of the shadow is given as 20 meters, we know that in this special right triangle, the lengths of the two legs are equal. Therefore, the distance from the top of the totem pole to the end of the shadow (the hypotenuse of the triangle) is the length of the shadow times the square root of 2, based on the Pythagorean theorem.

Using the formula hypotenuse = leg × √2, we substitute the leg length of 20 meters to get hypotenuse = 20 m × √2, which equals approximately 28.28 meters.

Answer:

https://socratic.org/questions/how-do-you-write-the-equation-of-the-quadratic-function-with-roots-6-and-10-and-

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Given the roots are x = 6 and x = 10, then

the factors are (x - 6) and (x - 10)

The quadratic is then the product of the roots

y = a(x - 6)(x - 10) ← a is a multiplier

To find a substitute (8, 2) into the equation

2 = a(2)(- 2) = - 4a ( divide both sides by - 4 )

a = - [tex]\frac{1}{2}[/tex]

Hence

y = - [tex]\frac{1}{2}[/tex](x - 6)(x - 10) ← expand factors

y = - [tex]\frac{1}{2}[/tex](x² - 16x + 60) ← distribute

y = - [tex]\frac{1}{2}[/tex] x² + 8x - 30

Answer: 45°

Step-by-step explanation:

There are 180 degrees in a triangle so

180-80=100-55=45°

Answer:

The Answer is likely 60.

Step-by-step explanation:

Two standard deviations from 70 is 60, because the actual deviation is 5, so 2 of those equals 10. 10 - 70 = 60.

Answer:

60

Step-by-step explanation:

Two standard deviations below the mean is:

70 - 2(5) = 60

Answer:

x=6

Step-by-step explanation:

15 = 5x + 45

     /5     /5

15 = x + 9

-9        -9

6 = x

The value of x = 6

Answer:

A

Step-by-step explanation:

(x−2) means the graph is shifted 2 units to the right.

+3 means the graph is shifted 3 units up.

So the graph of g(x) is shifted 2 units right and 3 units up.

Answer:

E = (3b+28)/2

T=3b+28

E= t/2

Step-by-step explanation:

The coat of the 4 pizzas would be $28, and an unknown amount of breadsticks that cost 3 dollars each.

Im going to use B as the amount of breadsticks bc i dont know what its supposed to be but that should be the correct answer.

T=3b+28

E= t/2

Answer:

Option a) x = −1, 5.4

Step-by-step explanation:

we have

[tex]f(x)=x^{2} -x-12[/tex]

[tex]g(x)=3.4x-6.6[/tex]

equate f(x) and g(x)

[tex]x^{2} -x-12=3.4x-6.6[/tex]

Solve the quadratic equation by graphing

The solutions are x=-1 and x=5.4

see the attached figure

Answer:

x= -1, 5.4

Step-by-step explanation:

[tex]f(x)= x^2-x-12[/tex]

[tex]g(x)= 3.4x -6.6[/tex]

f(x) is a quadratic equation and g(x) is a linear equation

To find f(x)= g(x) we need to find the point where the graph  of f(x) and g(x) intersects.

The quadratic equation f(x) and linear equation g(X) intersects at two points

from the graph f(x)= g(x) at x= -1 and x=5.4

Fluid ounces, 47 more

I hope it’s correct

Answer:

65 men

91 women

Step-by-step explanation:

the ratio is 5 to 7 and there are 156 total

5+7 is 12

so this gives us

5/12*156=65 men

7/12*156=91 women

65 + 91 = 156

Answer:

[tex]t=7.4years[/tex]

Step-by-step explanation:

Let's clear t from the equation [tex]N=16.10^{0.15t}[/tex]. In order to clear t, we have to apply [tex]log_{10} (x)[/tex] in both side of the equations.

[tex]log_{10}N=log_{10}(16.10)^{0.15t}[/tex]

By using properties of the logarithm

[tex]log_{10} (a.b)}= log_{10}a+log_{10}b[/tex]

We obtain:

[tex]log_{10}N=log_{10}(16)+log_{10} (10^{0.15t})[/tex]

Ordering using the logarithm property  [tex]log_{10}a^{n} =nlog_{10}a[/tex] and [tex]log_{10} 10=1[/tex]

[tex]log_{10}N=log_{10}(16)+0.15tlog_{10}10[/tex]  

[tex]log_{10}N=log_{10}(16)+0.15t[/tex]

Clearing t

[tex]t=\frac{log_{10}N-log_{10}(16)}{0.15}[/tex] using the logarith property [tex]log_{10}a-log_{10}b=log_{10}\frac{a}{b}[/tex]

we obtain:

[tex]t=\frac{log_{10}\frac{N}{16} }{0.15}[/tex]

The number of Elm trees is N = 204

Solving

[tex]t=\frac{log_{10}\frac{204}{16} }{0.15}\\t=\frac{log_{10}12.75}{0.15}=7.370[/tex]

Round to the nearest tenths place [tex]t=7.4years[/tex]

Answer:

To eliminate x multiply the first equation by 3 and the second equation by 4

To eliminate y multiply the first equation by 3 and the second equation by 2

Step-by-step explanation:

We are given a system of linear equations;

4x-2y=7

3x-3y=15

solving by elimination means that we shall be getting rid of one of the variables in order to determine the other. In this case we can either eliminate x or y. In order to eliminate any of these variables, we first must make their coefficients equal in both equations. To eliminate x;

Multiply the first equation by 3 and the second equation by 4.

To eliminate y;

Multiply the first equation by 3 and the second equation by 2.

Answer:

y=6x-2

Step-by-step explanation:

to find the 6 you have to see the difference in the y values and the y values are going up by 6 each time. the -2 comes from the y intercept. to find the y intercept you have to see when x=0 which in this table is -2

hope i helped

y = 6x - 2. The equation that describes how x and y are related is given by y = 6x - 2.

If we look the table of the image, we can see that the graph that describes the relation between x and y is a straight line.

The set of infinite points aligned in the same direction is known as straight line and its main equation has the form y = mx + b, where m is the slope, and b the y-intercept.

In order to solve this problem, we need to find the slope which is [tex]m = \frac{y_{2}-y_{1} }{x_{2}- x_{1}}[/tex]

Solving m for two points of the straight line, Let's take (0, -2) and (1, 4):

[tex]m = \frac{4-(-2)}{1 - (0)}=\frac{6}{1} \\m = 6[/tex]

We can see if we take two points in order from the table always obtain the value m = 6, which means for each unit of x, y increase 6 units.

To find the y- intercept (0, y), from the table of the image we can see when x = 0, y = -2.

Writing the equation y = mx + b, with m = 6 and b = -2:

y = 6x -2

The polynomial f(x)=x^4+3x^2+7 has four roots over the complex numbers according to the fundamental theorem of algebra, counting roots with multiplicity greater than one as distinct. This is consistent with the theorem's stipulation that a polynomial of degree n has exactly n roots.

The subject of this question is the fundamental theorem of algebra which belongs to the domain of Mathematics, specifically the study of polynomials. As indicated in the question, we have a function, f(x), which represents a polynomial of degree 4 as shown by the highest exponent. According to the fundamental theorem of algebra, a polynomial of degree n has exactly n roots, counting multiplicity. This means a function f(x)=x4+3x2+7, which is a fourth degree polynomial, will have four roots over the complex numbers.

This is also true per the theorem when roots with multiplicity greater than one are considered distinct. For example, f(x)=x2 is a polynomial of degree 2; it has two roots, both are zero, hence the two roots are counted as two distinct roots.

While the quadratic formula is used for finding roots of second degree polynomials, it is not directly applicable here since we are dealing with a fourth degree polynomial.

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Answer:

7x

Step-by-step explanation:

Sorry this is the best way I could show the work as the equation maker on this site does not support doing something in this format

To divide the expression (14x^2 - 21x) by (2x - 3), you can use long division to get the answer 7x.

To divide the expression (14x^2 - 21x) by (2x - 3), we can use long division. Here are the steps:

Therefore, the answer is 7x.

Answer:

you mulitple the two bottomz by the other number

example 3/4 and 2/8

8 is a common mulitple so 3/4 becomes 6/8 and now they have common denominators

Step-by-step explanation:

example 3/4 and 2/8

8 is a common mulitple so 3/4 becomes 6/8 and now they have common denominators

and the numerator gets multipled with the same number as the denominator

Answer:

Step-by-step explanation:

x² + 5x – 104 = 0

Factor using the AC method.  Here, a = 1 and c = -104.  Multiplied together, ac = -104.  Factors of -104 that add up to +5 are +13 and -8.

(x + 13) (x - 8) = 0

x = -13, 8

A negative width doesn't make sense, so x = 8.  Therefore, the width is 8 inches and the length is 5 more than that, or 13 inches.

Answer:

width = 8

length = 13

Step-by-step explanation:

All that is left to do is factor the results that you have

x^2 + 5x - 104 = 0

You need two numbers that are fairly close together (ignore the sign differ by 5) and multiply to 104.

The two numbers are 8 and 13

More formally stated, the quadratic can be factored to

(x + 13)(x - 8) = 0

x - 8 =0

x - 8 + 8 = 8 + 0

x = 8

x + 13 = 0 has no meaning.

That means that the width ( a positive number ) = 8

The length is 5 more = 13

Answer:

The smallest box dimensions are 4 x 4 cm.

Find the diagonal and this would be the diameter of the smallest circle.

Using the Pythagorean theorem:

4^2 + 4^2 = c^2

16 + 16 = c^2

c^2 = 32

c = √32

c = 5.658 cm ( Round answer as needed.)