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Answer:

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Answer:

(x-9)(x-6)

x= 9, x= 6

Step-by-step explanation:

Factored, and roots are:

Answer:

Step-by-step explanation: to answer this question I need to know what 1 inch to a mile is. like    every one inch= 12 miles

Answer:

The new shape will be cone with a radius of 17 units, tilt height 24 and units of height k.

Step-by-step explanation:

The image related to the exercise is necessary, to be able to solve therefore the attached one.

We have the following information:

Perimeter of the triangle = 58 units

Hypotenuse = 24 units

We have that the other two sides are equal and have x units, therefore we have the following:

x + x + 24 = 58

2 * x = 58-24

2 * x = 34

x = 34/2

x = 17

Now the triangle rotates around line k , and then it will result in a cone, which is a three-dimensional shape.

Therefore, the new shape will be cone with a radius of 17 units, tilt height 24 and units of height k.

Answer:

Cone with a radius of 17 units

Answer:

The fraction of Jerry's take-home pay that is left after paying for these two items is 7/12.

Step-by-step explanation:

Consider that the total take-home pay each month Jerry receives is, $x.

It is provided that:

The remaining amount can be computed by subtracting the amount spent from the total amount.

Compute the amount Jerry has spent so far:

Amount Spent = Car Payment + Food

                         [tex]=\frac{1}{6}x+\frac{1}{4}x\\\\=[\frac{1}{6}+\frac{1}{4}]x\\\\=[\frac{2+3}{12}]x\\\\=\frac{5}{12}x[/tex]

Compute the remaining amount as follows:

Remaining Amount = Total Amount - Amount Spent

                                [tex]=x-\frac{5}{12}x\\\\=[1-\frac{5}{12}]x\\\\=[\frac{12-5}{12}]x\\\\=\frac{7}{12}x[/tex]

Thus, the fraction of Jerry's take-home pay that is left after paying for these two items is 7/12.

Answer:

A. AB

Step-by-step explanation:

Given that the musical instrument has a shape of ∆ABC, we can determine the shortest side that would be parallel to the ground by comparison of the 3 angles of the triangle corresponding to each side that is opposite each of them.

What this means is that, the larger angle would have the largest side opposite it. The medium angle will have medium length side opposite it, while the smallest angle will have the smallest side opposite it.

m < A = 59°

m < C = 57°

m < C = 180 - (59+57) (sum of angles in a triangle)

m < C = 64°

The smallest angle out of the three angles is angle C = 57°.

The side opposite it, is side AB.

Side AB is the shortest side of ∆ABC.

Therefore, AB should be parallel to the ground.

The

side

of the musical instrument that should be parallel to the ground if the

dimensions

are as given is side AB, which is option A.

Given that:

Jordon will play a

triangle

in his school’s music program.

When playing, the shortest side

is hanging down,

parallel

to the ground.

From the figure:

m∠A = 59°

m∠C = 57°

By the

angle sum

property,

m∠A + m∠B + m∠C = 180°

59° + m∠B + 57° = 180°

m∠B + 116° = 180°

m∠B = 180° - 116°

        = 64°

The

shortest side

will be the side that is opposite to the smallest angle.

So, the smallest side is the side opposite to C.

So, the side is AB.

Hence, the side is AB, which is option A.

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Triangles

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Answer:

C. 126

Step-by-step explanation:

We can use ratios to solve for corresponding side lengths.

[tex]\frac{140-x}{81} =\frac{x}{9}[/tex]

Cross multiply.

[tex]9(140-x)=81x[/tex]

[tex]140-x=9x[/tex]

[tex]140=10x[/tex]

[tex]14=x[/tex]

Plug x as 14.

[tex]140-14=126[/tex]

Answer:

2

Step-by-step explanation:

Five and above, round up. Four and below, round down.

Answer:

2

Step-by-step explanation:

anything less then five is rounded down anything above 5 is rounded to the higher number

Answer:

Volume of prism = 240 ft²

Step-by-step explanation:

Given:

Base of prism (B) = 10 ft

Length of prism (L) = 8 ft

Height of prism (H) = 6 ft

Find:

Volume of prism

Computation:

Volume of prism = [BHL] / 2

Volume of prism = [(10)(8)(6)] / 2

Volume of prism = [480] / 2

Volume of prism = 240 ft²

Answer:

Choice C :  [tex]6.3*10^{6}[/tex]

Step-by-step explanation:

Choice A won't be it because it's only 3 million.

Choice B won't work because it's 83 million.

Choice C WILL WORK because it's 98 million.

Choice D won't work because it's only 11 million.

Answer:

4√mn/m^2

Step-by-step explanation:

√16n/m^3

= √16n/√m^3

= √4x4xn/√mxmxm

= 4√n/m√m

Rationalize by multiplying the numerator and the denominator by the denominator, which is a surd:

= (4√n x √m)/(m√m x √m)

= 4√mxn/m√mxm

= 4√mn/mxm

= 4√mn/m^2

Answer:

2 and 1/6 feet

Step-by-step explanation:

To do this you would just put aside 17 and 14 and you would subtract 5/12 by 5/8. To subtract these you would just find the lcm which is 48 and that would be denominator and to make the top the same as the bottom you would just multiply how much it took the denominator and multiply the numerator. So to subtract them you would get 20/48 for 5/12 and 30/48 for 5/8. When you subtract them you get -10/12 so then you will subtract 17 and 14 which is 3 then you will subtract 3 - 10/12 and you would get 2 and 2/12 which can simplify to 2 1/6 feet

The difference in the lengths of alligators in zoos and Florida is 2.79 feet.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

Given that

The length of an alligator in a Zoo = 14 5/8 feet.

The length of an alligator in Florida =  17 5/12 feet.

Convert fractions into decimals, and we get

The length of an alligator in a Zoo = 14.625 feet.

The length of an alligator in Florida =  17.416 feet.

So the difference in their lengths = 17.416 - 14.625

So the difference in their lengths = 2.79 feet

Therefore, the difference in the lengths of alligators in zoos and Florida is 2.79 feet.

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Note how the triangles here have the angles between the marked sides. The tickmarks indicate which pair of sides are the same length. The SAS sequence has "A" in the middle of the two "S" letters to mean that the angles are between the sides.

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

Extra info:

The first pair of triangles can be proven congruent by SAS.

SAS postulate says that if two sides and the included angle of a triangle are equal to two sides and the included angle of another triangle, then the two triangles are said to be congruent.

Here, we have,

In the first pair of triangles the included angle of a triangle are equal to two sides and the included angle of another triangle, therefore by SAS postulate the two triangles are said to be congruent.

In the second figure, the pair of triangles are congruent by ASA postulate not SAS.

In the third figure, the pair of triangles are not congruent by any postulate or theorem [Because there is no SSA rule].

In the fourth figure, the pair of triangles are congruent by SSS postulate not SAS.

Hence, The first pair of triangles can be proven congruent by SAS.

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Answer:

The distance between two cities is 60 miles.

Step-by-step explanation:

Time taken to travel from B to A = 2 hours

Time taken to travel from A to B = 1.5 hours

Current speed = 5 mph

Let the speed of ferry in still water = u mph

When the ferry moves with the current, it will taken lesser time (i.e. A to B) and when it moves against the current it will take more time (i.e. B to A).

Let the distance between the two cities A and B = D miles

While moving with the current, speed = [tex](u+5)\ mph[/tex]

While moving against the current, speed = [tex](u-5)\ mph[/tex]

Formula for Distance = Speed [tex]\times[/tex] Time

Distance traveled in each case is same i.e. D.

So,

[tex]D = (u+5) \times 1.5 = (u-5) \times 2\\\Rightarrow 1.5u+7.5=2u-10\\\Rightarrow 0.5u =17.5\\\Rightarrow u = \dfrac{175}{5}\\\Rightarrow u = 35 \ mph[/tex]

Now,

[tex]D = (u+5) \times 1.5\\\Rightarrow D =(35+5) \times 1.5\\\Rightarrow D =(40) \times 1.5\\\Rightarrow \bold{D =60\ miles}[/tex]

So, the distance between two cities is 60 miles.

Answer:

I believe that the answer is 60 miles

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

Again, to find the equation of the line, we need to find the slope and y-intercept. First, let's find the slope. Let (-1,5) be x₁ and y₁ respectively and (1,3) be x₂ and y₂, respectively. So:

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-5}{1--1}=\frac{-2}{2}=-1[/tex]

So the slope is -1.

Now, to find the y-intercept, we can use the point-slope form. I'm going to keep using (-1,5) as the coordinate. Thus:

[tex]y-y_1=m(x-x_1)\\y-5=-1(x-(-1))\\y-5=-(x+1)\\y-5=-x-1\\y=-x+4[/tex]

This is slope-intercept form. We want the answer to be in standard form, where:

[tex]Ax+By=C[/tex]

A, B, and C are integers (and, conventionally, A is positive).

Thus, we need to rearrange the terms:

[tex]y=-x+4\\y+x=4\\x+y=4[/tex]

The answer is B.

Answer:

20

Step-by-step explanation:

use the cos or sin function to solve

Step-by-step explanation:

using 30°

we use cos

using 60

we use Sin

Answer:

(x+6) / 6

Step-by-step explanation:

(3x+18) /18

Factor out 3 from the numerator

3(x+6) /18

Cancel a 3 from the numerator and denominator

(x+6) / 6

Answer:

D. 48 in.^2

Step-by-step explanation:

Sides DE and AB are corresponding, and the triangles are similar.

linear scale factor = k = AB/DE = 12/60 = 1/5

area square factor = k^2 = (1/5)^2 = 1/25

area of ABC = area of DEF * area scale factor = 1200 sq in * 1/25

area of ABC = 48 sq in

Answer: D. 48 in.^2

Answer:

2 should be distributed as 2y + 8; y = 4

Step-by-step explanation:

Step 2 is wrong.

2(y + 4) = 4y

The step to solve is to expand brackets or distribute 2, not divide both sides by 2.

2y + 8 = 4y

Subtract both sides by 2y.

8 = 2y

Divide both sides by 2.

4 = y

Answer:

$20 i think

Step-by-step explanation: have a good day bye bye yup yup

Answer:

D

Step-by-step explanation:

From the graph, the y-intercept of f(x) is 2 and since the y-intercept is when x = 0, it would fall into the x ≤ 1 category so the y-intercept of g(x) is 0 - 4 = -4. Since 2 > -4, the answer is D.

Answer:

4a) 110 square centimetres

4b) 127 square centimetres

6) 292 square centimetres

8) 800 tiles

Step-by-step explanation:

4. We need to find the area of the large rectangle and then deduct the area of the unshaded part:

a) The large rectangle has dimensions 12 cm by 15 cm. Its area is:

A = 12 * 15 = 180 square centimetres

The unshaded part has a length of 15 - (3 + 2) cm i.e. 10 cm and a width of 7 cm. Its area is:

a = 10 * 7 = 70 square centimetres

Therefore, the area of the shaded part is:

A - a = 180  - 70 = 110 square centimetres

b) The large rectangle has dimensions 13 cm by 11 cm. Its area is:

A = 13 * 11 = 143 square centimetres

The unshaded part has dimensions 8 cm by 2 cm. Its area is:

a = 8 * 2 = 16 square centimetres

Therefore, the area of the shaded part is:

A - a = 143 - 16 = 127 square centimetres

6. The background area of the space not covered by the photograph is the area of the frame minus the area of the photograph.

The frame has dimensions 24 cm by 18 cm. Therefore, its area is:

A = 24 * 18 = 432 square centimetres

The photograph has dimensions 14 cm by 10 cm. Therefore, its area is:

a = 14 * 10 = 140 square centimetres

Therefore, the background area of the space not covered by the photograph is:

A - a = 432 - 140 = 292 square centimetres

8) The floor has dimensions 8 m by 4 m. The area of the floor is:

A = 8 * 4 = 32 square centimetres

Each square tile has dimensions 20 cm by 20 cm. In metres, that is 0.2 m by 0.2 m. The area of each tile is:

a = 0.2 * 0.2 = 0.04 square metres

The number of tiles that are needed is the area of the floor divided by the area of each tile:

A / a = 32 / 0.04 = 800 tiles

Answer:

3.

A. Y = 2x + 30  (red line)

B. Y=5x  (blue line)

C. Y=70  (green line)

From 0 to 10 days, choose option B (shown on graph)

From 10 to 20 days, choose option A (first option)

From 20 days and more, choose option C.

4.

surface area of label = 471.2 cm^2

Step-by-step explanation:

Q1718436 Math Camp

2. At Math Camp, students can either pack their own lunch every day or buy lunch at camp. If they want to buy lunch there are 3 options:  

Option A: they pay an initial fee of $30 and lunches cost $2 each  

Option B: shown on the graph  

Option C: they pay a flat fee of $70 which includes all lunches  

Write an equation for each option. (3 marks) Option A: Option B: Option C:  

A. Y = 2x + 30  (red line)

B. Y=5x  (blue line)

C. Y=70  (green line)

b) Describe under what conditions, a student should choose each option. (Hint: you may want to graph all 3 lines on the same axes) (4 marks)  

Choose Option A if: Choose Option B if: Choose Option C if:  

Least cost is what is below the lowest possible line for the number of days stayed.

From 0 to 10 days, choose option B (shown on graph)

From 10 to 20 days, choose option A (first option)

From 20 days and more, choose option C.

Note that for days 10 and 20, there are two choices each.

3.  

4. A Campbell’s Soup can is 15cm tall and has a radius of 5 cm. How much paper is needed to make the label (think about what the label covers)? (3 marks) How much soup can this hold? (1 cm3 = 1 mL) (3 marks)

The label only covers the curved surface.

Curved surface area  

= 2 pi * r * h

= 2 pi (5) * 15

= 150 pi

= 471.2 cm^2

Answer: about 13u

Step-by-step explanation:

Distance can be calculated as [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\sqrt{(6-(-7))^2+(4-8)^2}\\\\\\\sqrt{(13)^2+(-4)^2}\\\\\\\sqrt{185}\\\\13[/tex]

Hope it helps <3

Answer:

-7/2

Step-by-step explanation:

We can find the slope by using the slope formula

m = (y2-y1)/(x2-x1)

  = ( -3 -11)/( 2- -2)

  = ( -14)/ ( 2+2)

  = -14/4

  = -7/2

Answer:

y=2

Step-by-step explanation:

SEND + MORE = MONEY

notice that send and more have 4 digit ( means the number in thousands ,but the answer is 5 digit  means it is in 10000)

first word : 1000S+100E+10N+1 D

second word: 1000 M +100 O+10 R+1 E

the answer: 10000M+1000O+100N+10E+Y

if the answer is the sum of first word+second word:

(S E N D M O R E Y)

M in word Money can not be zero the range is [1,9]

S also can not be zero

  S   E    N    D    s=9 since E can not equal N it has to be 1+E=N

  9   5     6     7

+

  M   O   R     E     m=1 , then o =0

   1    0    8    5  

M   O    N    E  Y

1     0    6    5   2      

Answer:

Max = (6,0); min = (-2, 4)  

Step-by-step explanation:

1. Summarize the constraints

[tex]\text{Constraints} = \begin{cases}(a)\qquad 2x - y & \leq 12\\(b)\qquad 4x+ 2y & \geq 0\\(c) \qquad x + 2y & \leq 6\\ \end{cases}[/tex]

2. Optimization equation

z = 5x + 2y

3. Graph the constraints to identify the feasible region

See the figure below.

The "TRUE" regions for each graph are the shaded areas to the side of the line indicated by the arrows.

The "feasibility region" is the dark green area where all three areas overlap and all three conditions are satisfied.

5. Determine the points of intersection among the constraints  

(i) Constraints (a) and (b)

[tex]\begin{array}{rcr}2x - y & = & 12\\4x + 2y & = & 0\\4x - 2y & = & 24\\8x&=&24\\x & = & \mathbf{3}\\6 - y & = & 12\\-y & = &6\\y & = & \mathbf{-6}\\\end{array}\\[/tex]

The lines intersect at (3,-6).

(ii) Constraints (a) and (c)

[tex]\begin{array}{rcr}2x - y & = & 12\\x + 2y & = & 6\\4x - 2y & = &24\\5x & = & 30\\x & = & \mathbf{6}\\6 + 2y & = & 6\\2y & = &0\\y & = & \mathbf{0}\\\end{array}[/tex]

The lines intersect at (6,0).

(iii) Constraints (b) and (c)

[tex]\begin{array}{rcr}4x+ 2y &= & 0\\x + 2y &=& 6\\3x & = & -6\\x & = & \mathbf{-2}\\-2 +2y & = & 6\\2y & = &8\\y & = & \mathbf{4}\\\end{array}[/tex]

The lines intersect at (-2,4).

6. Determine the x- and y-intercepts of the feasible region

The five black dots at (3,-6), (6,0), and (-2,4) are the vertices of the polygon that represents the feasible region.

Each vertex is a possible maximum or minimum of z.  

7. Calculate the maxima and minima

Calculate z at each of the vertices.

(i) At (-2,4)

z = 5x + 2y = 5(-2) + 2(4) = -10 + 8 = 2

(ii) At (3,-6)

z =  5(3) + 2(-6) = 15 - 12 = 3

(iii) At (6,0)

z = 5(6)+ 2(0) = 30 + 0 = 30

The maximum of z occurs at (6,0).

The minimum of z occurs at (-2, 4).

2 bcoz vertically opp

the one in front of 3, I can't see that number maybe 4

because corresponding angles

yea that's all

Answer:

17.7 percent

Step-by-step explanation

You find the area of the trapezoid and rectangle. You divide the area of the trapezoid by the rectangle. then move the decimal 2 places to the right.

Answer:

2x2x7

Step-by-step explanation: