Carlos answered 122 questions correctly on his multiple choice science final and earned a grade of 61%. How many total questions were on the final exam?

Answer:

see explanation

Step-by-step explanation:

you are looking for perfect square factors of the numbers under the radical sign. both numbers and the sum are irrational because they contain √5

125 = 5×25

80 = 5×16

3√125 = 3√(25×5) = 3×5√5 = 15√5

√80 = √(16×5) = 4√5

1)  15√5 + 4√5 = 19√5      the √5 is the same square root so you add the coefficients

perfect square factors are bold

4×√(25×2)×√(9×2) =

4×5×3×√(2×2) =

60×√4 =

2)  60 × 2 = 120

the numbers are both irrational but the answer is rational because √2 ×√2 = √4 = 2

Answer:

x = 0.71; y = 2.43

Step-by-step explanation:

y = 2x + 1

y = 9x - 4

9x - 4 = 2x + 1

7x = 5

x = 5/7

y = 2x + 1

y = 2(5/7) + 7/7

y = 10/7 + 7/7

y = 17/7

x = 0.71; y = 2.43

Answer:

578.5

Step-by-step explanation:

Answer:

i am not sure but i think it is 280

Answer:

The number inside radical is 29

Step-by-step explanation:

Given:

To find:

Distance Formula:

[tex]\displaystyle \large{\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}[/tex]

Determine (x2,y2) = (1,1) and (x1,y1) = (3,-4). Therefore:

[tex]\displaystyle \large{\sqrt{(1-3)^2+(1-(-4))^2}}\\\displaystyle \large{\sqrt{(-2)^2+(1+4)^2}}\\\displaystyle \large{\sqrt{4+5^2}}\\\displaystyle \large{\sqrt{4+25}}\\\displaystyle \large{\therefore \sqrt{29}}[/tex]

Therefore, the number inside the radical is 29

Answer:

[tex]\sqrt{29}[/tex]

Step-by-step explanation:

Hi there!

We are given the points (1, 1) and (3, -4)

We want to find the distance between the points

Distance can be found using the formula [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

We can label the values of the points first, before calculating to help avoid confusion and mistakes.

[tex]x_1 = 1\\y_1 = 1\\x_2 = 3 \\y_2 = -4[/tex]

Now substitute these values into the formula

d = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

d = [tex]\sqrt{(3-1)^2 + (-4-1)^2}[/tex]

Now, using order of operations, first simplify what is in the parentheses:

d = [tex]\sqrt{(2)^2 + (-5)^2}[/tex]

Now raise 2 and -5 to the second power.

d = [tex]\sqrt{4 + 25}[/tex]

Add the numbers together under the radical

d = [tex]\sqrt{29}[/tex]

The distance is [tex]\sqrt{29}[/tex]

Hope this helps!

See more on finding the distance here: https://brainly.com/question/24774555

Answer:

x is 25˚

Step-by-step explanation:

Answer:

25 = x

Step-by-step explanation:

Since both angles are vertical angles, they are eqaul to each other and hence we can conclude that;

132° = (5x + 7)°

132 - 7 = 5x

125 = 5x

125/5 = x

25 = x

Hope this helps!

Answer:

  104 feet

Step-by-step explanation:

The Pythagorean theorem can be used to find the hypotenuse of a right triangle with legs 40 feet and 96 feet. It tells you ...

  h² = 40² +96²

  h² = 1600 +9216 = 10816

  h = √10816 = 104

The distance from one corner to the opposite corner is 104 feet.

______

Additional comment

You may recognize that the ratios of the given lengths are 40:96 = 5:12. These match the legs in the Pythagorean triple (5, 12, 13). This tells you the third side (diagonal) of the triangle is 13 ratio units, or 13×(8 ft) = 104 ft.

The equation that represents the number of T-shirt , number of colours of shirt and total order is 3x + 50xy.

The number of colours and T- shirts are the variable quantity while the cost of order is the fixed quantity.

The number of members in the school choir = 75

The charge for one shirt = $3

Let the number of T-shirts ordered be x

Cost of ordering x shirts = 3x

Therefore,

Charge for each colour to be printed = $50

Let the number of colours to be printed on each T- shirt be represented by y

Therefore,

Cost of printing y colours on each T- shirt = 50y

Cost of printing y colours on x number of T-shirts = x(50y) = 50xy

Hence, the equation that represents the number of T-shirt , number of colours of shirt and total order is as follows:

Total cost  = 3x + 50xy

Hence, the fixed quantity and variable quantity are as follows:

The number of colours on the shirts is a variable quantity

The number of shirts ordered is a variable quantity

The cost of order is fixed quantity

learn more on equation here: https://brainly.com/question/12289422

#SPJ1

Answer:

Volume = 90in^3

Step-by-step explanation:

V = 3in x 15in x 2in = 90in^3

Answer:

Step-by-step explanation:

The volume of the prism must be found in order to solve this problem.

GIVEN:

[tex]\Longrightarrow: \sf{V=L*W*H}[/tex]

[tex]\Longrightarrow: \text{LENGTH: = 3}\\\\\Longrightarrow: \text{WIDTH: = 15}\\\\\Longrightarrow: \text{HEIGHT: = 2}[/tex]

SOLUTION:

Multiply.

[tex]\sf{3\ in*15\ in*2\ in=\boxed{\sf{90\ in^3}}[/tex]

I hope this helps. Let me know if you have any questions.

Answer:

x = 150

y = 30

Step-by-step explanation:

x° = 5y° (corresponding angles) (1)

x° + y° = 180° (Linear pair angles) (2)

From equations (1) and (2), we find:

5y° + y° = 180°

-> 6y° = 180°

-> y° = 180°/6

-> y° = 30°

-> y= 30

-> x° = 5(30°) = 150° (From equation 1)

-> x = 150

Using a system of equations, it is found that:

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

The theater was full, hence:

x + y + z = 277.

There are half as many adults as there are children, hence:

x = 2z.

The theater charges $5.00 for children, $7.00 for students, and $12.00 for adults. The total ticket sales were of $2002, hence:

5x + 7y + 12z = 2002.

Replacing the second equation into the other two:

y + 3z = 277 -> y = 277 - 3z

7y + 22z = 2002.

Then:

7(277 - 3z) + 22z = 2002

z = 63

y = 277 - 3z = 277 - 3 x 63 = 88

x = 2z = 2 x 63 = 126.

Hence:

More can be learned about a system of equations at https://brainly.com/question/24342899

Answer: 0.125

Step-by-step explanation: 70/560

Answer:

5x +35

Step-by-step explanation:

you woul use the distrubitive property

so multiply  by x and and 7

so it becomes 5x +35

Answer:

Step-by-step explanation:

Answer: hope this helps! :)

t - 4

—————

t - 6

Step-by-step explanation:

          t2 + 2t - 24

Simplify   ————————————

            t2 - 36    

Trying to factor by splitting the middle term

  Factoring  t2 + 2t - 24  

The first term is,  t2  its coefficient is  1 .

The middle term is,  +2t  its coefficient is  2 .

The last term, "the constant", is  -24  

Multiply the coefficient of the first term by the constant   1 • -24 = -24  

Find two factors of  -24  whose sum equals the coefficient of the middle term, which is   2 .

    -24    +    1    =    -23  

    -12    +    2    =    -10  

    -8    +    3    =    -5  

    -6    +    4    =    -2  

    -4    +    6    =    2    That's it

Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  6  

                   t2 - 4t + 6t - 24

 Add up the first 2 terms, pulling out like factors :

                  t • (t-4)

            Add up the last 2 terms, pulling out common factors :

                  6 • (t-4)

Step-5 : Add up the four terms of step 4 :

                  (t+6)  •  (t-4)

           Which is the desired factorization

Trying to factor as a Difference of Squares :

1.2      Factoring:  t2-36  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

       A2 - AB + BA - B2 =

       A2 - AB + AB - B2 =

       A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 36 is the square of 6

Check :  t2  is the square of  t1  

Factorization is :       (t + 6)  •  (t - 6)  

Canceling Out :

  Cancel out  (t + 6)  which appears on both sides of the fraction line.

Answer:

Step-by-step explanation:

Given :

Solving :

Answer: X= 306/19

Step-by-step explanation:

Answer: i need time to work on this but i think its 3,3

Step-by-step explanation:

Answer:

Square Root of 10: (3, 4) and (2,1)

(-4,-2) and (-3, 1)  (-2, 3) and (1,2)

Square Root of 29: (3,7) and (5,2)

(5, -2) and (3,3)  (4,-1) and (-1,1)

Step-by-step explanation:

Permutations:

nP r = n!/(n + r)!

Combinations:

nCr = n!/(n - r)!r!

c - combination

p - permutations

Since in both the problems they are looking for different groups, it is a combination problem. the order in which the people were selected in each group is not important, what is required are different groups.

A.

n = 51

r = 3

51C 3 = 51! / ((51 - 3) ×3!)

51C3 = 20 825 groups

OR:

[tex]c = \frac{51}{3} \times \frac{50}{2} \times 49[/tex]

[tex]c = 20825[/tex]

B.

[tex]c = \frac{14}{4} \times \frac{13}{3} \times \frac{12}{2} \times 11[/tex]

[tex]c = 1001[/tex]

Answer:

Area of a circle

=πr^2

therefore...

radius r =13

but π =22/7

so..

=22/7 × 13^2

=22/7 ×169

=531.14m

Area of circle

Answer:

Step-by-step explanation:

Could you update the question? It is not clear enough

Answer:

Are of a Circle = pie x radius squared

Step-by-step explanation:

A = 3.14*2squared

A = 3.14*4

A = 12.56

Answer:

517

Step-by-step explanation:

We can draw a Venn diagram to represent the data.

First, identify the groups.

Then draw the Venn diagram to represent the groups.

Given 73 students study all subjects:

E ∩ M ∩ S = 73   (add this to the middle section)

Next, add the numbers for the sections where the students study 2 topics.

E ∩ M but not S:  152 - 73 = 79

M ∩ S but not E:  79 - 73 = 6

S ∩ E but not M:  139 - 73 = 66

Now complete each circle by making sure that the values add up to the total value given.

Only E = 254 - S ∩ E - E ∩ M - E ∩ M ∩ S = 254 - 66 - 79 - 73 = 36

Only M = 280 - E ∩ M - M ∩ S - E ∩ M ∩ S = 280 - 79 - 6 - 73 = 122

Only S = 280 - M ∩ S - S ∩ E - E ∩ M ∩ S = 280 - 6 - 66 - 73 = 135

To find the total number of students in the school, add the numbers in each section of the Venn diagram:

73 + 79 + 6 + 66 + 36 + 122 + 135 = 517

Answer: D

Step-by-step explanation: The others dont have A m or an s

Answer:

2^4ab

Step-by-step explanation:

By factorizing 48ab^2 I get 2*2*2*2*3*a*b*b

By factorizing 32a^2b I get 2*2*2*2*2*a*a*b

All the factors that these have in common is 4 2's, one a, and one b, which is 2^4*ab, or 16ab.

Answer:

4s+14t

Step-by-step explanation:

2*[(s+5t)+(s+2t)]

=2*(2s+7t)

=4s+14t

Answer:

Step-by-step explanation:

Remark

The Perimeter of a rectangle is found using

P = 2L + 2w

Givens

L = s+2t

w = s + 5t

Solution

P = 2(s + 2t) + 2(s + t5)                     Remove the brackets

P = 2s + 4t + 2s + 10t                       Combine

P = 4s + 14t

Answer P = 4s + 14t                         This cannot be reduced any further.

Answer:

2184 ways because that's how math works

Step-by-step explanation:

14 × 13 × 12

Answer:

In a pair of similar triangles, the corresponding sides are proportional. Corresponding sides touch the same two angle pairs. When the sides are corresponding it means to go from one triangle to another you can multiply each side by the same number

Answer:

yes

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

a^2+b^2=c^2

The sides are greater than the longest side, so that is right but

81+144 should equal c^2 or 18^2, but it is not equal to it.

Answer:

$17.28

Step-by-step explanation:

20% of $86.40

= [tex]\frac{20}{100}[/tex] × $86.40

= 0.2 × $86.40

= $17.28 ← commission