The area of the triangle below is 10/9 square feet. What is the length of the base ?

Express your answer as a fraction in simplest form.

4/3ft

Answer:

exact value is 264π and decimal to the thousandths is 829.381m²

Step-by-step explanation:

It gives you the formula.

(pi times 8 times 25) + (pi times 8 squared)

Answer:

A≈829.38

A= pi x 8 x 25 + (pi x 8^2)

A= 200pi + 64 pi

A= 264pi

Answer is 264

Hope this helps!

Step-by-step explanation:

Let the number be \(\overline{abc}=100a+10b+c\).

\(100a+10b+c=34a+34b+34c \\ \\ 66a-24b-33c=0 \\ \\ 22a-8b-11c=0\)

Taking the equation mod \(11\) yields \(-8b \equiv \pmod{11}\), meaning \(b=0\).

So, \(22a-11c=0 \implies c=2a\).

So, the only possibilites are \((a,c)=(1,2), (2,4),(3,6), (4,8)\).

Therefore, there are \(4\) such numbers.

Answer:

see explanation

Step-by-step explanation:

Plants in ratio 7 : 9 = 7x : 9x ( where x is a multiplier )

Taller plant is 26 cm more than height of smaller, then

(a)

9x = 7x + 26 ( subtract 7x from both sides )

2x = 26 ( divide both sides by 2 )

x = 13

taller plant = 9x = 9 × 13 = 117 cm

(b)

shorter plant = 7x = 7 × 13 = 91 cm

(c)

total length = 117 + 91 = 208 cm

Answer:

a)  117 cm b) 91 cm  c) 208 cm

Step-by-step explanation:

given smaller plant:taller plant = 7 : 9

let the height of smaller plant be x

then the height of taller plant will be x + 26

using this a equation can be formed:

9x = 7 ( x + 26 )

9x = 7x + 182

2x = 182

x = 91 cm ......this is the height of smaller plant

the height of taller plant will be:

x + 26 = 91 + 26 = 117 cm .............this is the height of taller plant

Now total length: 117 + 91 = 208 cm .....this is the total length.

The number of students who schedule calculus as one of their classes is given by A = 371 students

Given data ,

24% of college students take calculus as a class in their freshman year

Now , incoming freshman class for a college is 1,547 students

And , The number of students who will schedule calculus as one of their classes is equal to 24% of the total number of students, which can be found by multiplying the total number of students by 0.24:

Number of students taking calculus = 1547 x 0.24 = 371.28

On simplifying the equation , we get

Number of students taking calculus ≈ 371

Hence , about 371 students will schedule calculus as one of their classes

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Answer:

40 students

Step-by-step explanation:

Answer: The slope of parallel lines are the same

Step-by-step explanation:

There are not triangles in the image, but instead two lines creating a corner, they want you to connect the opposite corners of each of these sets of lines to create a triangle.

The bigger set of lines is up 2 right 8. slope is rise/run so the slope is 2/8 or if we simplify 1/4

The smaller set of lines is 1 up 4 right. slope is rise over run so the slope is 1/4.

The problem tries to confuse you by not connecting those lines and by having the bigger one go up first then right, and then the smaller one go right first and then up.

But as you can see the parallel lines both have a slope of 1/4

the only difference between parallel lines is the 'b' in the equation y=mx+b

The requried, if the loan is paid in full at the end of the 5-year period, the borrower would have to pay back $26,130 (rounded to the nearest dollar).

The formula for the future value of an investment with compound interest is:

\(FV = PV * (1 + r)^n\)

Where PV is the present value (the amount borrowed), r is the annual interest rate (as a decimal), and n is the number of compounding periods. In this case, since the interest is compounded annually for 5 years, n = 5.

Substitute in the values given, we get:

\(FV = 22,000 * (1 + 0.035)^5\)

FV = 22,000 * 1.19416

FV = 26,129.09 = 26,130

Therefore, if the loan is paid in full at the end of the 5-year period, the borrower would have to pay back $26,130 (rounded to the nearest dollar).

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Hey mate!

Question:

5x – 1 = x+ 27

Answer:

x=7

Step-by-step explanation:

Step 1:

5x-x=27+1

Step 2:

4x=28

step 3:

x=28÷4

step 4:

x=7

hope it helped you:)

Answer:

B. 2.7 g

Step-by-step explanation:

The half life of a substance is the time taken for the substance to reduce to half of its original amount. It is given by:

\(A=A_o*(\frac{1}{2})^\frac{t}{t_{1/2}}\\ Where\ A\ is \ the \ amount \ of \ substance\ remaining\ after\ t\ years, \\A_o \ is \ the\ initial\ value\ of \ the\ substance,\ t_{1/2} is\ the\ half\ life\ and\\t\ is\ the\ years\ spent\)

Given that:

Ao = 4 g, t = 3 years, t(1/2) = 5.26 years. Therefore:

\(A=A_o*(\frac{1}{2})^\frac{t}{t_{1/2}}\\A=4*(\frac{1}{2} )^\frac{3}{5.26}=4*0.6735=2.7\\ A=2.7\ g\)

9514 1404 393

Answer:

  6. step 2; terms are improperly combined; it should be -61n-8=-8

  7. no; point (2, 5) is not part of the solution in the left graph

Step-by-step explanation:

6. Step 2 should be ...

  -61n -8 = -8 . . . . . because -5n-56n = -61n, not -51n

__

7. The boundary lines of both graphs go through the point (2, 5). In the left graph, the line is dashed, indicating that points on the line are not part of the solution set. The point (2, 5) on the dashed line is not a solution to that inequality.

The solid boundary line indicates that the points on the line are part of the solution set. The point (2, 5) on the solid line is a solution to that inequality.

The point (2, 5) is not a solution to both inequalities.

the perimeter of the equilateral triangle with a side length of 12√3 is 36√3 units.

In order to find the perimeter of the given triangle, we have to find the side of the triangle. The altitude of the triangle  = 18 inches. Let us assume the side of the triangle as a. The formula for calculating the altitude of an equilateral triangle is : Altitude  =√3/2×a  (side)

18 =√3/2 × a

a = 18 × 2√3

a = 36√3

a = 36 ×√3 / √3×√3

a =36√3/3

a = 12√3 inches.

If the side of an equilateral triangle is 12√3, then all three sides of the triangle are of equal length, since it is an equilateral triangle. Therefore, the perimeter of the triangle is simply the sum of the lengths of its three sides. Since each side of the triangle has a length of 12√3, the perimeter is: Perimeter = 3 x (12√3) = 36√3.

Therefore, the perimeter of the equilateral triangle with a side length of 12√3 is 36√3 units.

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Answer:

x=4

Step-by-step explanation:

135+25+5x=180°

160+5x=180

5x=20

x=4

A function for the described sequence is; f(n) = 6• 3^(n-1) and the sixth term is; 1458.

Since, it follows that the first term of the sequence is; 6 and the common ratio is 3, it follows that the recursive function that represents the sequence is; f(n) = 6• 3^(n-1).

Additionally, by substitution of 6 for n; f(6) = 1,458.

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Answer:

x=12

Step-by-step explanation:

Intersecting Chords Formula:

(segment piece) x (segment piece) =  (segment piece) x (segment piece)

10 * x =  ( 3+x) *8

10x = 24+8x

Subtract 8x

10x-8x = 24+8x-8x

2x= 24

Divide by 2

2x/2 =24/2

x = 12

The probability that at least one of the pets selected is a puppy is approximately 0.7887 or 78.87%.

To calculate the probability that at least one of the pets is a puppy, we can find the probability of the complement event (none of the pets being a puppy) and subtract it from 1.

The total number of pets in the store is 6 puppies + 9 kittens + 4 lizards + 5 snakes = 24.

The probability of selecting a pet that is not a puppy on the first selection is (24 - 6) / 24 = 18 / 24 = 3 / 4.

Similarly, on the second selection, the probability of selecting a pet that is not a puppy is (24 - 6 - 1) / (24 - 1) = 17 / 23.

For the third selection, it is (24 - 6 - 1 - 1) / (24 - 1 - 1) = 16 / 22.

For the fourth selection, it is (24 - 6 - 1 - 1 - 1) / (24 - 1 - 1 - 1) = 15 / 21.

For the fifth selection, it is (24 - 6 - 1 - 1 - 1 - 1) / (24 - 1 - 1 - 1 - 1) = 14 / 20 = 7 / 10.

To find the probability that none of the pets is a puppy, we multiply the probabilities of not selecting a puppy on each selection:

(3/4) * (17/23) * (16/22) * (15/21) * (7/10) = 20460 / 96840 = 0.2113 (approximately).

Finally, to find the probability that at least one of the pets is a puppy, we subtract the probability of the complement event from 1:

1 - 0.2113 = 0.7887 (approximately).

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Answer:

The solution set is (1, 4)
There are a finite number of solutions.

Step-by-step explanation:

We have 2x+y=6 and y=4x.

Let's write the first equation into y=mx+b form.

We get: y=-2x+6

Now, we just set the equations equal to each other.

-2x+6=4x Add 2x to both sides.

6=6x Divide both sides by 6

x=1

Now, plug x back into either of the equations given to us.

y=4(1)

y=4

The solution set is (1, 4)

Answer:

The terms are:

\(-x,-9x^{2},12x^{2} ,7\)

The like terms are:

\(-9x^{2},12x^{2}\)

Answer:

620

Explanation:

When the sample is given, the number of elk are likely to be infected is to be considered as the 620.

Calculation of the number of elk:

Since the population is 7,750.

The random sample is 50.

So here be like

= 620

hence, When the sample is given, the number of elk are likely to be infected is to be considered as the 620.

Answer

0= -5

Step-by-step explanation:

6(n) = 6(n-1)+1

6n = 6n - 6 +1

0= -5

(i don't know if this is correct very sorry!!)

Answer:

here you go sweet heart

Step-by-step explanation:

♡♡♡♡♡♡♡♡♡♡

Answer:

  x = 1/2 or 3

Step-by-step explanation:

Compare the given equation to the standard form equation to identify the values of the variables in the formula. Then put those values in the formula and do the arithmetic.

  \(ax^2+bx+c=0\\\\2x^2-7x+3=0\\\\a=2;\ b=-7;\ c=3\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{-(-7)\pm\sqrt{(-7)^2-4(2)(3)}}{2(2)}=\dfrac{7\pm\sqrt{25}}{4}=\dfrac{7\pm 5}{4}\\\\x=\left\{\dfrac{1}{2},3\right\}\)

Answer:

Step-by-step explanation:

\(2x^2-7x+3=0\\\\x_1 ,2 =\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=2\\\:b=-7\\,\:c=3\\:\quad x_{1,\:2}=\frac{-\left(-7\right)\pm \sqrt{\left(-7\right)^2-4\times\:2\times\:3}}{2\times\:2}\\\\=\frac{7+\sqrt{\left(-7\right)^2-4\times\:2\times\:3}}{2\times\:2}\\\\7+\sqrt{\left(-7\right)^2-4\times\:2\times\:3}=7+\sqrt{25}\\\\=\frac{7+\sqrt{25}}{2\times\:2}\\\\=\frac{7+\sqrt{25}}{4}\\\\\sqrt{25}=5\\\\=\frac{7+5}{4}\\\\=\frac{12}{4}\\\\=3 \\\)

\(x=\frac{-\left(-7\right)-\sqrt{\left(-7\right)^2-4\times\:2\times\:3}}{2\times\:2}\\\\=\frac{7-\sqrt{\left(-7\right)^2-4\times\:2\cdot \:3}}{2\times\:2}\\\\7-\sqrt{\left(-7\right)^2-4\times \:2\times\:3}=7-\sqrt{25}\\\\=\frac{7-\sqrt{25}}{2\times \:2}\\\\=\frac{7-\sqrt{25}}{4}\\\sqrt{25}=5\\\\=\frac{7-5}{4}\\=\frac{2}{4}\\\\=\frac{1}{2}\)

Answer:

\(y = \frac{ - 1}{3} x - 8\)

Step-by-step explanation:

slope intercept form is y=mx+b

m is the slope, so it's -1/3 because it goes down one unit and to the right two units. b is -8 because that is the point that it touches the y-axis

Answer:

B

Step-by-step explanation:

Answer:

No no no no nonononononono nononon non ono no non nononononon

Step-by-step explanation:

uhh its B  MuHmuHmUaaahaha

wth who put the muffins in the freezer?? -_-

Answer:

Sides: 20m

Area: 400m²

Step-by-step explanation:

80/4 = 20 for sides

20x20 = 400 for area

Answer: side= 20m  area=400sqm

Step-by-step explanation:

a square has 4 sides so to find 1 side divide by 4= 20m

area of a square is sidexside = 20mx20m= 400sqm

The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

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Answer:

1. x=70

2. x=70

3. x=60

4. x=40

5. x=10

6. x=6

7. x=12

8. x=9

9. 88

10. 76

Step-by-step explanation:

1. Isosceles triangles have two sides equal to each other. If the unequal side is 40 degrees and there are 180 degrees in a triangle, 180-40=140/2=70 degrees for the other two sides.

2. Same explanation as 1.

3. Equilateral triangles all have the same degrees. If 60 is the degree for one angle, it is the degree for the other two as well.

4. Same explanation as 1.

5. All side length of an equilateral triangle are the same. If the side length of one side is 10, the other two sides are 10 too.

6. Same explanation as 5, but with 6 as the side length.

7. It is an isosceles triangle and two sides are equal. Since one side is 12 and the other side is the second of the equal sides, the side length would be 12

8. Same explanation as 7, but with 9 as the side length.

9. 180-46=134-46(other side length)=88 (remaining side length)

10. 2x+2+2x+2+3x+1=7x+5. 7x+5=180. 180-5=175. 175/7=25. 3(25)+1=76.

Hope this helps!!

Step-by-step explanation:

the text that is formatted in bold and underlined fonts are the answers to the missing (blank) terms in the given problem.

Given that  \(\huge\sf{\overline{AB}}\) is a straight line, and that ∠AOE, ∠EOF, and ∠FOB share a common vertex, at point O, whose sum equals 180°.  

1. Statement:  m∠AOB = 180°

  Reason: Definition of a straight angle.

2. Statement:  m∠AOE + m∠EOF + m∠FOB = m∠AOB

   Reason: Angle Addition Postulate.

3. Statement:  x + (2x + 34) + 20° = 180°

   Reason: Substitution.

4. Statement:  x = 42°

   Reason: Algebra.

1)   Straight angles have a measure of 180°.

2)  The Angle Addition Postulate states that if O is in the interior of ∠AOB, then it means that the measure if ∠AOB is equal to the sum of the measures of ∠AOE, ∠EOF, and ∠FOB. In other words:

           ⇒   \(\huge\bf\sf{m\angle{AOB}\:=m\angle{AOE}\:+m\angle{EOF}\:+m\angle{FOB}}\)

3) and 4) Since the ∠AOB is a straight angle, then it means that the sum of the measures of ∠AOE, ∠EOF, and ∠FOB equal the measure of ∠AOB = 180°. Hence, in order to solve for the value of x, simply add the given values for each angle:

x° + (2x + 34)° + 20° = 180°

x° + 2x° + 34° + 20° = 180°

Combine like terms:

3x° + 54° = 180°

Subtract 54° from both sides:

3x° + 54° - 54° = 180° - 54°

3x° = 126°

Divide both sides by 3 to solve for x:

\(\huge\sf{\frac{3x^\circ}{3}\:=\:\frac{126^\circ}{3}}\)

x = 42°

Answer:

y=49x

Step-by-step explanation:

As you can see from the graph, the distance from home increases by 49 miles per hour driven.

Therefore the distance driven for any given time in hours is 49x

Therefore y = 49x