If 50 students were surveyed, how many chose
chocolate?
V 20 students
If 80 students were surveyed, how many chose vanilla?
20 students

Answer:

Step-by-step explanation:

[tex]{ \sf{ factorise \: \: { \underline{ \green { \tt{ {x}^{2} (x + 2) - x(x + 2) - 12(x + 2)}}}}}}[/tex]

[tex]{ \sf{ \blue{ \:taking \: (x + 2) \: common}}} \\ \\{ \dashrightarrow { \sf{ \green{(x + 2)( {x}^{2} - x - 12)}}}}[/tex]

[tex]{ \dashrightarrow{ \sf{ \green{(x + 2)( {x}^{2} - (4x - 3x) - 12)}}}} \\ \\ { \dashrightarrow{ \sf{ \green{(x + 2)( {x}^{2} - 4x + 3x - 12)}}}}[/tex]

[tex]{ \dashrightarrow{ \green{ \sf{(x + 2)(x(x - 4) + 3(x - 4))}}}} \\ \\ { \dashrightarrow{ \underline{ \boxed{ \green{ \sf{(x + 2)(x + 3)(x - 4)}}}}}}[/tex]

Answer:

38.21 in

Step-by-step explanation:

Given data

C= 120meters

We also know that circumference

C=2πr

Substitute

120=2*3.142*r

120= 6.28r

r= 120/6.28

r= 19.10 m

Hence the diamter D

D= r*2

D= 38.21 in

Answer:

1 2 1

Step-by-step explanation:

A B A

Answer: sqrt(61)

Step-by-step explanation:

For parts a) and c1), refer to the attached picture.

For part b), the distance formula is:

d = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

Using x1 = -1, y1 = -4, x2 = -6, y2 = 2:

d = sqrt[(-6 + 1)^2 + (2 + 4)^2] = sqrt[25 + 36] = sqrt(61)

Part c2) Another way to find the length of AB without using the distance formula is by drawing the line and measuring it according to the scale.

Part d) This will only work as long as the graph paper is accurately made, and the scale computation is done correctly. However, this will only give approximations, and will not give an exact answer when radicals are involved.

Answer:

1) b - correct statement: The interquartile range of the number of volunteers is 16

2) c - correct statement: About 50% of the students have between a 75 and a 90

Step-by-step explanation:

1B --> 66 - 50

2C --> About 50% of the students have between a 75 and a 90

Answer:

The tangent ratio is the value received when the length of the side opposite of angle theta is divided by the length of the side adjacent to angle theta. It is very commonly abbreviated as tan.

Answer: 6.6

Step-by-step explanation:

Answer:

the answer is 24

Step-by-step explanation:

i got it correct on my test

Answer:

[tex]\Huge\boxed{x=8}[/tex]

Step-by-step explanation:

Hello There!

Remember the sum of all of the angles in a triangle is 180

so we can use this equation to solve for x

180 = 50 + 60 + 8x + 6

now we solve for x

step 1 combine like terms

50 + 60 + 6 = 116

now we have

180=8x+116

step 2 subtract 116 from each side

116 - 116 cancels out

180 - 116  = 64

now we have

8x = 64

step 3 divide each side by 8

8x/8=x

64/8=8

we're left with x = 8

Answer:

96 cm

Step-by-step explanation:

Multiply 6x4x4=96

Answer: 30

Step-by-step explanation:

Answer:

[tex](5y + 1)^{2} - (2(y - 1))^{2} [/tex]

Step-by-step explanation:

1) Rewrite it in the form a² - b², where a = 5y + 1 and b = 2(y - 1 ).

[tex](5y + 1) ^{2} - (2(y - 1)) ^{2} [/tex]

2) Use multiplication Distributive Property: (xy)^a = x^a y^a.

[tex](5y + 1)^{2} - {2}^{2} (y - 1 {)}^{2} [/tex]

3) Simplify 2² to 4.

[tex](5y + 1 {)}^{2} - 4(y - 1 {)}^{2} [/tex]

4) Rewrite it in the form a² - b², where a = 5y + 1 and b = 2(y-1).

[tex](5y + 1 {)}^{2} - (2(y - 1))^{2} [/tex]

Therefor, the answer is ( 5y + 1 )² - (2( y - 1 ))².

Answer:

Took FLVS test and got it right

A. y=x, x-axis, y=x, y-axis.

Step-by-step explanation:

Took FLVS test and got it right

A. y=x, x-axis, y=x, y-axis.

Answer:

8640

Step-by-step explanation:

I = Prt

I = (48000)(0.03)(6)

I = 8640

Hello, I Am BrotherEye

Answer: The Logical Answer Is X√6y

Step-by-step explanation:

Answer Completed Using an Graphing Calculator

Best Of Luck

~

BrotherEye

Answer:

is 6

Step-by-step explanation:

Answer:

x = −2

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3(4x+6)=x−4

(3)(4x)+(3)(6)=x+−4(Distribute)

12x+18=x+−4

12x+18=x−4

Step 2: Subtract x from both sides.

12x+18−x=x−4−x

11x+18=−4

Step 3: Subtract 18 from both sides.

11x+18−18=−4−18

11x=−22

Step 4: Divide both sides by 11.

[tex]\frac{11x}{11}[/tex] = [tex]\frac{-22}{11}[/tex]

x = −2

Answer:

6+8-2=12, 15-12=3 answer=3

Answer:

40°

Step-by-step explanation:

If your are reffering to a triangle the answer would be 40 since the three angles of a triangle must always add up to 180° so you would add b+d (110+30) resulting in 140 which you would then subtract from 180 getting you 40°

[tex]3x^2-5x=2[/tex]

Answer:

Thee  function  is    linear.

Step-by-step explanation:

Answer:

So it becomes a linear equation.

Step-by-step explanation:

Answer:

0=7

Step-by-step explanation:

Distribute

4−5=2(2+1)

4−5=4+2

Add 5 to both sides of the equation

4 − 5 = 4 + 2

4 − 5 + 5 = 4 + 2 + 5

Simplify Add the numbers

Add the numbers

4 = 4 + 7

Result

0=7

Answer:

x=2, y=4. (2, 4).

Step-by-step explanation:

2x+3y=16

3x+4y=22

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

3(2x+3y)=3(16)

-2(3x+4y)=-2(22)

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

6x+9y=48

-6x-8y=-44

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

y=4

2x+3(4)=16

2x+12=16

2x=16-12

2x=4

x=4/2

x=2

Answer:

Step-by-step explanation:

[tex]\huge\large \fbox \green{Answer :}[/tex]

B. 5sqrt(2)

[tex]\huge\Large \fbox \green{Explanation:}[/tex]

We have

We need to find third side of triangle

( x)² = (√34 )² + (4)² ....( by Pythagoras Theorem)

x ² = 34 + 16

x ² = 50

x = √50

x = 5 √2

Hence, the third side is 5√2

Answer:

10

Step-by-step explanation:

sqrt (8^2+6^2) = 10

hope it helps

Answer:

The area of LQM is [tex]48cm^2[/tex]

Step-by-step explanation:

Given

Area of PNQ = 8

Area of LPQ = 16

See attachment for triangles

The area of PNQ is calculated as:

[tex]Area = \frac{1}{2} * PQ * PN[/tex]

Substitute 8 for Area

[tex]8 = \frac{1}{2} * PQ * PN[/tex]

[tex]PQ * PN = 16[/tex]

The area of LPQ is calculated as:

[tex]Area = \frac{1}{2} * PQ * LP[/tex]

Substitute 16 for Area

[tex]16= \frac{1}{2} * PQ * LP[/tex]

From the attachment:

[tex]PN + LP =LN[/tex]

Make LP the subject

[tex]LP = LN -PN[/tex]

So:

[tex]16= \frac{1}{2} * PQ * (LN -PN)[/tex]

We have:

[tex]16= \frac{1}{2} * PQ * (LN -PN)[/tex] and [tex]PQ * PN = 16[/tex]

Equate both expressions:

[tex]\frac{1}{2} * PQ *(LN - PN) = PQ * PN[/tex]

Divide both sides by PQ

[tex]\frac{1}{2} (LN - PN) = PN[/tex]

Multiply both sides by 2

[tex]LN - PN = 2PN[/tex]

[tex]LN= 3PN[/tex]

Since PNQ is similar to LNM, the following equivalent ratios exist:

[tex]\frac{LM}{PQ} = \frac{LN}{PN}[/tex]

Substitute [tex]LN= 3PN[/tex]

[tex]\frac{LM}{PQ} = \frac{3PN}{PN}[/tex]

[tex]\frac{LM}{PQ} = 3[/tex]

[tex]LM = 3PQ[/tex]

Area of LQM is:

[tex]Area = \frac{1}{2} * LM * LP[/tex]

This gives:

[tex]Area = \frac{1}{2} * 3PQ * LP[/tex]

[tex]Area = 3 *\frac{1}{2} *PQ * LP[/tex]

Recall that:

[tex]16= \frac{1}{2} * PQ * LP[/tex]

So:

[tex]Area = 3 *16[/tex]

[tex]Area = 48cm^2[/tex]

Answer:

x = 9/2 or 4.5

Step-by-step explanation:

In order to solve this problem, you first need to identify whether or not the two triangles formed in the image are similar; you can tell that they are similar by the AAA property because they share a vertex, and the other two angles are congruent because of the Corresponding Angles Theorem. Now that you know the triangles are similar, you need to identify the corresponding sides:

x + 6 corresponds to x

21 corresponds to 9 (21 because 30 - 9 = 21)

You can find the scale factor by dividing 21 by 9:

21 ÷ 9 = 7/3

Now that you know the scale factor, you can write and solve an equation:

7/3x = x + 6 (given)

4/3x = 6 (subtract x from both sides)

x = 9/2 (multiply both sides by 3/4)