If the area of the triangle is 36 square inches, what is the height of the triangle?

A) 6 inches
B) 12 inches
C) 18 inches
D) 24 inches

Final answer:

The zeros of f(x) = x^3 - 4x^2 - 5x + 20 are 4 and (-1 +/- sqrt(21)) / 2.

Explanation:

The given function is f(x) = x^3 - 4x^2 - 5x + 20. To find the zeros of the function, we need to solve the equation f(x) = 0. One way to find the zeros is by using synthetic division or polynomial long division. However, in this case, we can use factoring by grouping to simplify the equation:

f(x) = (x^3 - 5x) + (-4x^2 + 20)

f(x) = x(x^2 - 5) + (-4)(x^2 - 5)

f(x) = (x - 4)(x^2 + x - 5)

Setting each factor equal to zero, we have:

x - 4 = 0  ---> x = 4

x^2 + x - 5 = 0

Using the quadratic formula, we can find the solutions of the quadratic equation:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

Plugging in the values a = 1, b = 1, and c = -5, we get:

x = (-1 +/- sqrt(1^2 - 4(1)(-5))) / (2(1))

x = (-1 +/- sqrt(1 + 20)) / 2

x = (-1 +/- sqrt(21)) / 2

So, the zeros of f(x) = x^3 - 4x^2 - 5x + 20 are x = 4 and x = (-1 +/- sqrt(21)) / 2.

Answer:

x=-5/3

Step-by-step explanation:

ABD + DBC = ABC

Substitute the values

6x+9  + x+1 = 10x+15

Combine like terms

7x+10 = 10x+15

Subtract 7x from each side

7x-7x+10 = 10x-7x+15

10 = 3x+15

Subtract 15 from each side

10-15 = 3x+15-15

-5 =3x

Divide each side by 3

-5/3 =x

This will give us a negative value for DBC

DBC = -5/3 +3/3 = -2/3

We cannot have a negative value for an angle

Check the values given.

Answer:

2 fluid ounces

Step-by-step explanation:

Answer:

6,30

Step-by-step explanation:

The product of two whole numbers is 180

xy = 180

and their sum is 36

x+y = 36

x = 36-y

Substitute this into the first equation

(36-y) (y) = 180

36y - y^2 = 180

Add y^2 to each side

36y = 180 +y^2

Subtract 36y from each side

0 = y^2 -36y +180

Factor

0=(y-6) (y-30)

Using the zero product property

y-6 =0   y-30 =0

y = 6    y= 30

Now we need to find x

If y =6

x = 36-6=30

If y = 30

x = 36-30=6

The two numbers are 30 and 6

Answer:

Prime: 9/25    Not Prime: 16/25

Step-by-step explanation:

In 1 - 25 there are 9 prime numbers, or numbers that cannot be divided by anything other than 1 or itself. They are  2 3 5 7 11 13 17 19 and 23,

Selecting a NON Prime: 25-9= 16 so we would put 16 over 25.

16/25 since it can not be reduced that is the fraction

Selecting a Prime: We know there is 9 prime numbers so we would put it over 25. 9/25 also cannot be reduced any further,

Answer:

Average speed = 30.2 miles / .4 hours =

75.5 mph

Step-by-step explanation:

Answer:

Average speed of the car is [tex]75.5\text{ miles per hour}[/tex].      

Step-by-step explanation:

We are given the following information:

Distance traveled by the car =

[tex]30\displaystyle\frac{1}{5}\text{ miles}[/tex]

Time taken by the car =

[tex]\displaystyle\frac{2}{5}\text{ hours}[/tex]

Formula:

Speed = [tex]\displaystyle\frac{\text{Distance covered}}{\text{Time taken}}[/tex]

Putting all the values,

[tex]\text{Speed} = \displaystyle\frac{30\frac{1}{5}}{\frac{2}{5}} = \frac{\frac{151}{5}}{\frac{2}{5}} = \frac{151}{2} = 75.5\text{ miles per hour}[/tex]

Average speed of the car is [tex]75.5\text{ miles per hour}[/tex].

[tex]

6(x+xy)-5(y+2xy)=6x+6xy-(5y+10xy) \\

6x+6xy-5y-10xy \\

\boxed{6x-5y-4xy}

[/tex]

Answer:

To solve this problem you would have to distribute the 5 and the 6. Once that is completed you would find the matching pairs and add or subtract them.

The answer is: 6x-4xy-5y

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Substitute the given values for a, b and c into the expression, that is

5 + 6 + (7 × [tex]\frac{1}{7}[/tex])

= 11 + 1

= 12

37 over 8 or 37/8. I plugged it in on my calculator and it was correct.

Answer:

37 over 8 or 37/8 or 37:8 or[tex]\frac{37}{8}[/tex]

Step-by-step explanation:

[tex]A=\frac{14\times8}{2}=\boxed{56cm^2}[/tex]

Answer:

56 cm^2

Step-by-step explanation:

Area of triangle is base times the height and divided by 2.

A = [tex]\frac{1}{2}[/tex] * 14 * 8

A = [tex]\frac{1}{2}[/tex] * 112

A = 56 cm^2

7.8889 I think so so I divided 2.84%39=7.8889

Final answer:

To find the 2010 cost of filling a gas tank based on 1970 prices, divide the 1970 total cost by the price per gallon to find the number of gallons, then multiply that by the 2010 price per gallon. The cost to fill the same tank in 2010 would be $47.34.

Explanation:

The question is asking to calculate the cost of a full tank of gas in 2010 based on the cost from 1970. To find out how much it would cost in 2010, we need to first determine the number of gallons that could be bought for $6 in 1970 at $0.36 per gallon. This can be calculated by dividing $6 by $0.36, which equals 16.67 gallons (approximately). Now, assuming the tank size has not changed, to find out the cost in 2010, we multiply the number of gallons by the 2010 price per gallon. Thus, 16.67 gallons multiplied by $2.84 per gallon equals $47.34.

Adding the student with eight siblings will increase the class average amount of siblings because this student has more siblings than the average.

The new class average for number of siblings is 3.19

Therefore, the average number of siblings that each student has is larger than the original average.

Answer:

The average will go up.

Step-by-step explanation:

The answer is:

The function that can be used to determine the total number of pages that she will read after "x" days is:

[tex]t(x)=11x+27[/tex]

From the statement, we know that Lisa's already read 15 plus 12 additional pages, that it's a fact that will not change over time. Also, we know that she is reading 5 plus 6 additional pages per day, so, the number of pages that she will read after "x" days.

So, determining the number of pages that she will read after "x" days, we have:

We are given that:

[tex]AlreadyReadPages=15+12=27\\PagesToReadPerDay=5+6=11[/tex]

Then, writing the equation, we have:

[tex]t(x)=11x+27[/tex]

Where,

[tex]t=TotalPages\\x=days\\11=PagesToReadPerDay\\27=AlreadyReadPages[/tex]

Hence, the function that can be used to determine the total number of pages that she will read after "x" days is:

[tex]t(x)=11x+27[/tex]

Have a nice day!

Answer:

The diameter of a circle with an area of 804.25 cm is 32 cm

Step-by-step explanation:

We know that formula for area of circle is:

Area of Circle = πr^2

804.25 =  3.14 * r^2

=> r^2 = 804.25 / 3.14

r^2 = 256.13

Taking square root on both sides

√r^2 = √256.13

r = 16.0

and r is half of diameter i.e

r = diameter / 2

=> diameter = 2r

so, diameter = 2 * 16

diameter = 32 cm

So, the diameter of a circle with an area of 804.25 cm is 32 cm.

The diameter is approximately [tex]\(32.02\)[/tex] cm, calculated from [tex]\(d = 2 \times 16.01\)[/tex], where [tex]\(r \approx 16.01\)[/tex] cm.

To find the diameter of a circle with an area of 804.25 cm², follow these steps:

Step 1:

Recall the formula for the area [tex](\(A\))[/tex] of a circle: [tex]\(A = \pi r^2\)[/tex], where r is the radius of the circle.

Step 2:

We're given the area [tex]\(A = 804.25\)[/tex] cm². Rearrange the formula to solve for [tex]\(r\)[/tex]: [tex]\(r = \sqrt{\frac{A}{\pi}}\)[/tex].

Step 3:

Substitute the given area into the equation: [tex]\(r = \sqrt{\frac{804.25}{\pi}}\).[/tex]

Step 4:

Calculate the radius: [tex]\(r[/tex] ≈ [tex]\sqrt{\frac{804.25}{\pi}}[/tex] ≈ [tex]\sqrt{256.25}[/tex] ≈ 16.01 cm.

Step 5:

Recall that the diameter [tex](\(d\))[/tex] of a circle is twice the radius: [tex]\(d = 2r\)[/tex].

Step 6:

Substitute the calculated radius into the equation: [tex]\(d = 2 \times 16.01\)[/tex].

Step 7:

Calculate the diameter: [tex]\(d[/tex] ≈ [tex]2 \times 16.01[/tex] ≈ [tex]32.02\)[/tex] cm.

Therefore, the diameter of the circle with an area of 804.25 cm² is approximately 32.02 cm.

Answer:

80

Step-by-step explanation:

area of trapezoid is given by formula

Area = [tex]\frac{a+b}{2}[/tex]h

where a is one base, b is another base and h is height

In given case, we have

a= 7+7+3 = 17

b= 3

h= 8

Substituting the values

Area= [tex]\frac{17+3}{2}[/tex] x 8

       = [tex]\frac{20}{2}[/tex] x 8

       =  10 x 8

       = 80

!

Answer:

[tex]\large\boxed{256\pi\ sq.in.}[/tex]

Step-by-step explanation:

The formula of a surface area of a sphere:

[tex]S.A.=4\pi R^2[/tex]

R - radius

We have R = 8 in. Substitute:

[tex]S.A.=4\pi(8^2)=4\pi(64)=256\pi\ in^2[/tex]

Answer:

yes,its one way to simplify equations.

Step-by-step explanation:

Answer: The number is 86.

Step-by-step explanation:

Hi, to answer this question we have to write an equation with the information given:

"Six subtracted from a number ", a number means the variable (x), and six subtracted from a number is "x -6".

"The result is divided by 4", so (x-6) /4.

This result is added to then, so: 10+ (x-6) /4.

And finally, to give 30 means that all the expression equals to 30.

10+ (x-6) /4 = 30

Solving:

(X-6) /4 = 30 -10

(X-6) /4 = 20

X-6 = 20x4

X-6 = 80

x =80+6

x= 86

The number is 86.

Answer:

Do pemdas, (parentheses, exponents, multiplication, division, addition and subtraction). But do whatever is first, which in this case is multiplication.

Step-by-step explanation:

Write the equation out.

    105 x 2 + 66x -72 = ?

    105 x 2 = 210

     210 + 66x - 72

    210 + 66x = 276x

     276x - 72 = 204

      ? = 204

Answer:

1. X = 23.8 cm

2. Z = 12.5 Inches

3. x = 14.03 Degrees

Step-by-step explanation:

1. Given

Hypotenuse=25 cm  

Angle=18 Degrees

We will use the trigonometric ratios for right angled triangles for finding the value of X.

In the given triangle, as X is the base, we will use the ration which involves base and hypotenuse.

So,

cos⁡θ=  Base/Hypotenuse

cos⁡18=X/25

0.9510=X/25

0.9510*25=X

X=23.775

X=23.8 cm

2.The ratio of cos will be used for this one too.

Here,

Base=10 inches

Angle=37 Degrees

cos⁡θ=  Base/Hypotenuse

cos⁡37=10/Z

0.7986=10/Z

Z=10/0.7986

Z=12.521  

Z=12.5 inches

3. As we know the values of perpendicular and base ,  

So the ration which involves these both will be used.

The desired ratio is  

tan⁡ x=Perpendicular/Base

tan ⁡x=5/20

tan⁡ x=0.25

x =  tan^(-1)⁡0.25

x = 14.03 Degrees  ..

The value of X and Z in a triangle should be determined by performing mathematical operations and rounding according to the specific rules of significant figures for addition, subtraction, multiplication, and division, following proper rounding at the final calculation to ensure precision.

To answer the question regarding the value of X and Z in a triangle, it's important to note that the rounding of numbers should be done according to certain rules based on the operations involved.

In addition and subtraction, the result should have the same number of decimal places as the measurement with the least number of decimal places. For instance, adding 135.621, 97.33, and 21.2163 we get 254.1673, which is then rounded to 254.17 since the hundredth's place is the last common decimal place.

With multiplication and division, the answer should have the same number of significant figures as the original measurement with the least significant figures. Thus, multiplying 1.35 by 2.1 we get 2.835 and round it off to 2.8.

When dealing with whole numbers or in a series of steps, pay close attention to significant figures and round off only after the final calculation to prevent inaccuracies.

As an example, the complex calculation (13.2 + 12.252) x (1.35 x 2.1) should be rounded only once, after the entire expression is evaluated, leading to a result of 72.

Answer:11%

Step-by-step explanation:

The percentage of followers are actually real = 11%

"It is a number or ratio that can be expressed as a fraction of 100."

For given example,

the number of real followers = 120

the number of fake followers purchased = 1000

So, the total number of followers are

= 1000 + 120

= 1120

Now, we find the percentage of followers that are actually real.

= (120/1120) × 100

= 0.1071 × 100

= 10.71%

≈ 11%

Therefore, the percentage of followers are actually real = 11%

Learn more about percentage here:

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ANSWER

The correct answer is C

EXPLANATION

The conditional probability, P(A|B) means,, probability of A given that B has occurred.

It is given by the formula:[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]

From the Venn diagram, [tex]A\cap =[/tex]{Ian,Ella} and B={Lan,Ella,Micky,Mai, Marcus}

[tex]P(A\cap B)=\frac{2}{10}[/tex] and [tex]P(B)=\frac{5}{10}[/tex]

This implies that:

[tex]P(A|B)=\frac{\frac{2}{10} }{\frac{5}{10} } =\frac{2}{10}\times\frac{10}{5}=\frac{2}{5}[/tex]

The correct answer is C

Answer:

answer is C

Step-by-step explanation:

Answer:

7pm

Step-by-step explanation:

Noon means 12:00pm

Just add 3 hours to their originally 4 hour trip

(1 hour from lunch and 2 from the amusement park)

Answer:

7

Step-by-step explanation:

Answer:im stuck on the same one

Step-by-step explanation:

The center of the circle is (-7,13)

Answer:

x=10

Step-by-step explanation:

110 and 8x + 30 are vertical angles, which means they are equal

110 = 8x+30

Subtract 30 from each side

110-30 = 8x+30 -30

80 = 8x

Divide each side by 8

80/8 = 8x/8

10 =x

Answer:

56.52

Step-by-step explanation:

i did the iready lol

sin x = 32/58

We need to find the angle x.

Take the sine inverse on both sides.

Let arcsin = sine inverse

arcsin(sin x) = arcsin(32/58)

x = 33.485376623

Rounding off to the nearest hundredth, we get x = 33.49°.

Done!

Answer:

33.49

Step-by-step explanation:

I took the test

Answer:

x = 4

Step-by-step explanation:

Evaluate f(2) and equate to g(x)

f(2) = (3 × 2) - 1 = 6 - 1 = 5, then

2x - 3 = 5 ( add 3 to both sides )

2x = 8 ( divide both sides by 2 )

x = 4

Answer:

20 bicycles and 10 tricycles.

Step-by-step explanation:

Let the number of bicycles and tricycles be x and y respectively.

Each vehicle has 1 seat.  Each bicycle 2 wheels and each tricycle 3 wheels.

Then we have the system of equations:

x + y = 30 ............ (1)

2x + 3y = 70.........(2)

Multiply the first equation by -2:

-2x - 2y = -60......(3)

Adding (2) + (3):

y = 10

Substituting for y in equation (1):

x + 10 = 30

x = 20.    

By simultaneous equation, there are a total of 20 bicycles and 10 tricycles.

Let the number of bicycles and tricycles be x and y respectively.

It is given that there is a total of 30 seats and 70 wheels.

Each vehicle has 1 seat.  Each bicycle 2 wheels and each tricycle 3 wheels.

Then we have the system of simultaneous equations:-

x + y = 30 ............ (1)

2x + 3y = 70.........(2)

Multiply the first equation by -2:

-2x - 2y = -60......(3)

Adding (2) + (3):

y = 10

Substituting for y in equation (1):

x + 10 = 30

x = 20.    

Therefore, by simultaneous equation, there are a total of 20 bicycles and 10 tricycles.

To learn more about simultaneous equation, refer -

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Answer:

[tex]\large\boxed{A.\ \dfrac{x+2}{x+5}}[/tex]

Step-by-step explanation:

[tex]x^2+3x+2=x^2+x+2x+2=x(x+1)+2(x+1)=(x+1)(x+2)\\\\x^2+6x+5=x^2+x+5x+5=x(x+1)+5(x+1)=(x+1)(x+5)\\\\\dfrac{x^2+3x+2}{x^2+6x+5}=\dfrac{(x+1)(x+2)}{(x+1)(x+5)}\qquad\text{cancel}\ (x+1)\\\\=\dfrac{x+2}{x+5}[/tex]