Solve the equation. 2x + 4 = 3x – 2

Answer:

x = 5.7 units

Step-by-step explanation:

By applying Sine rule is the triangle XYZ,

[tex]\frac{\text{SinX}}{\text{WY}}=\frac{\text{SinY}}{\text{WX}}=\frac{\text{SinW}}{\text{XY}}[/tex]

[tex]\frac{\text{SinX}}{\text{x}}=\frac{\text{SinY}}{\text{y}}=\frac{\text{SinW}}{\text{10}}[/tex]

[tex]\frac{\text{Sin33}}{\text{x}}=\frac{\text{SinY}}{\text{y}}=\frac{\text{Sin107}}{\text{10}}[/tex]

[tex]\frac{\text{Sin33}}{\text{x}}=\frac{\text{Sin107}}{\text{10}}[/tex]

[tex]x=\frac{10\times(\text{Sin33})}{\text{(Sin107)}}[/tex]

x = 5.69

x ≈ 5.7 units

Answer:

Step-by-step explanation:

sin ∅ = opposite / hypotenuse

From the question

the hypotenuse is 37

the opposite is 12

So we have

sin (a) = 12/37

Hope this helps you

Answer:

see below

Step-by-step explanation:

9x−7y=14

To find the x intercept set y = 0 and solve for x

9x = 14

Divide by 9

9x/9 = 14/9

x = 14/9

(14/9 ,0)

To find the y intercept set x = 0 and solve for y

-7y = 14

Divide by -7

-7y/-7 = 14/-7

y = -2

(0,-2)

answer = no it does not measure a rate

Answer:

NO

Step-by-step explanation:

Percent is just a number out of 100

Answer:

a) 20 students

b) 20 students

Step-by-step explanation:

a) From the given frequency table, we have to check the number of students that scored above 73.5 and add them up.

Therefore, the number of students that have grades above 73.5 are:

14 + 4 + 2 = 20 students

b) 75 falls in between 74 - 76 and we do not have the individual frequencies of the grades (74, 75, 76).

However, we can use the data we have from the table to make an assumption.

The number of students that have grades below 75 will be:

13 + 5 + 2 = 20 students

Answer:

(6x + 1)^2.

Step-by-step explanation:

1 + 12x + 36x^2

= 36x^2 + 12x + 1

= (6x + 1)(6x + 1)

= (6x + 1)^2.

Hope this helps!

Answer:

[tex](6x+1)^2[/tex]

Step-by-step explanation:

Answer:

[tex] \boxed{\sf b. \ 8(2a + 9)} [/tex]

Step-by-step explanation:

[tex] \sf Factor \: the \: following: \\ \sf \implies 16a + 72 \\ \\ \sf Factor \: 8 \: out \: of \: 16a + 72: \\ \sf \implies 8 \times 2a + 8 \times 9 \\ \\ \sf \implies 8(2a + 9)[/tex]

After translating the expression I got:

[tex] \frac{3}{4} x < 24[/tex]

Once you cross multiply you should have the following expression:

[tex]x < 32[/tex]

Then when you graph, remember it should be an open circle on the 32 and the direction of the arrow should be towards 0

Answer:

D

Step-by-step explanation:

just took the test

Answer:

452.39

Step-by-step explanation:

A=4πr^2

=4·π·6^2

≈452.38934

Answer:

y = 2b/3

Step-by-step explanation:

The x-coordinate of the intersection point of Line B D and Line C E is at [tex]\frac{2(a+c)}{3}[/tex]. Given that:

[tex]y=\frac{b}{a-2c}x -\frac{2bc}{a-2c} \\\\The\ y\ coordinate\ can\ be \ gotten\ by\ substituting\ the \ value\ of\ x\ and\ simplifying.\\ Substituting\ x:\\\\y=\frac{b}{a-2c}(\frac{2(a+c)}{3} ) -\frac{2bc}{a-2c}[/tex]

[tex]Simplyfing\ the\ parenthesis\\y=\frac{2b(a+c)}{3(a-2c)} -\frac{2bc}{a-2c}\\\\y=\frac{2ab+2bc}{3(a-2c)} -\frac{2bc}{a-2c}\\\\Simplyfying\ using\ LCF\\y=\frac{2ab+2bc-6bc}{3(a-2c)}\\\\y=\frac{2ab-4bc}{3(a-2c)}\\\\Factorizing:\\\\y=\frac{2b(a-2c)}{3(a-2c)}\\\\y=\frac{2b}{3}[/tex]

The y-coordinate of the intersection point of Line B D and Line C E is at [tex]\frac{2b}{3}[/tex].

Answer:

b

Step-by-step explanation:

Answer:

Jordon's brother got $40

Step-by-step explanation:

We can set up a system of equations to solve this.

Let's say that Jordon got x dollars.

His brother got y dollars.

x+y=100 since they are dividing the 100 dollars

1/3x=1/2y (the same indicates that they are equal)

Multiply the entire second equation by 3.

x=1.5y

Now we can substitute 1.5y in for x in the first equation.

x+y=100

1.5y+y=100

2.5y=100

Divide both sides by 2.5

y=40

Jordon's brother got $40.

Plug that in to find how much Jordon got.

x+y=100

x+40=100

Subtract 40 from both sides

x=60

Jordon got 60.

Answer:

Step-by-step explanation:

This problem can be solved by applying the permutation strategy since it has to do with the number of ways of selection

Given

Number of items= 3

Therefore 3!= 3*2*1= 6

Hence the number of ways they can distribute the shirt among themselves is 6 ways

Answer:

Option C. f¯¹(x) = x + 3

Step-by-step explanation:

f(x) = x – 3

To find the inverse, f¯¹(x) of f(x), we simply do the following:

f(x) = x – 3

Replace f(x) with y

y = x – 3

Interchange y and x

x = y – 3

Make y the subject by rearranging

x + 3 = y

y = x + 3

Replace y with f¯¹(x)

f¯¹(x) = x + 3

Therefore, the inverse of f(x) = x – 3 is f¯¹(x) = x + 3

The Answer is A.)

A picture of my answer

Answer:

[tex]\large \boxed{\sf \ \ y=-2 \ \ }[/tex]

Step-by-step explanation:

Hello,

To guess the end behaviours when x tends to [tex]\infty[/tex] you only take into account the highest terms of polynomial expressions.

So the expression will be equivalent to

[tex]\dfrac{-2x^2}{x^2}=-2[/tex]

In other words we can say

[tex]\displaystyle \lim_{x\rightarrow+\infty} \dfrac{-2x^2+3x+6}{x^2+1}=\lim_{x\rightarrow+\infty} \dfrac{-2x^2}{x^2}=-2\\\\\displaystyle \lim_{x\rightarrow-\infty} \dfrac{-2x^2+3x+6}{x^2+1}=\lim_{x\rightarrow-\infty} \dfrac{-2x^2}{x^2}=-2\\\\[/tex]

So, the correct answer is y = -2

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

1. True

2. False.

3. True.

Step-by-step explanation:

1. The total area within any continuous probability distribution is equal to 1.00: it is true because the maximum probability (value) is one (1), therefore, the total (maximum) area is also one (1).

Hence, for continuous probability distribution: probability = area.

2. For any continuous probability distribution, the probability, P(x), of any value of the random variable, X, can be computed: False because it has an infinite number of possible values, which can not be counted or uncountable.

Hence, it cannot be computed.

3. For any discrete probability distribution, the probability, P(x), of any value of the random variable, X, can be computed: True because it has a finite number of possible values, which are countable or can be counted.

Hence, it can be computed.

Answer:

48%

Step-by-step explanation:

The total number of votes casted = 1524 votes = 100%

Let a = votes of first place candidate

b = votes of second place candidate

c = votes of third place candidate

The second place candidate had 140 votes less than the winner

b = a - 140 votes...... Equation 1

Hence,

a = b + 140.......... Equation 2

Second place candidate has 395 votes more than the last place candidate

b = c + 395.......Equation 3

Hence,

c = b - 395......Equation 4

a + b + c = 1524 votes....... Equation 5

If a = b + 140 and c = b - 395

The number of votes by b(second place candidate ) =

b + 140 + b + b - 395 = 1524 votes

3b = 1524 + 395 - 140

3b = 1779

b = 1779/3

b = 593 votes.

Therefore, the second place candidate had 593 votes.

Now we can calculate how many votes, the other candidates had.

The second place candidate had 140 votes less than the winner

Votes for the winner( first place candidate)

b = a - 140 votes...... Equation 1

Hence,

a = b + 140.......... Equation 2

Since b = 593

a = 593 + 140

a = 733 votes

Votes for the last place candidate

Since, Second place candidate has 395 votes more than the last place candidate

b = c + 395.......Equation 3

Hence,

c = b - 395......Equation 4

b = 593

c = 593 - 395

c = 198

From the above calculation,

a = votes of first place (winner) candidate = 733

b = votes of second place candidate = 593

c = votes of third(last) place candidate = 198

In the above question, we were asked to calculate the percentage of all the votes cast were received by the winner.

This is calculated as

= Voted received by winner/ Total number of votes casted × 100

= 733/1524 × 100

= 48.09711286%

Approximately to the nearest percent = 48%

Therefore, the percentage of all the votes cast were received by the winner = 48%

Answer:

Some examples are a cereal box, a CD case, or a coffee table. Measure your prism using appropriate units, such as inches, centimeters, or feet. ... If you are using a ruler with a centimeter (cm) scale, then your units are going to be in cm, and if you ... We have to do the same thing to volume like we did with the surface area.

:)

Answer:

Rectangular prism

I chose a box of cereal.

Part 1)List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).

Length: 20 cm

Width: 8 cm

Height: 32 cm

Part 2).

 Describe the shape of the cross-section when the box is cut parallel to the base.

The shape of the cross-section would be a rectangle in dimensions.

20 cm x 8 cm

Part 3)

What is the surface area of the box? 

surface area=2*area of the base + perimeter of the base*height

area of the base=20*8=160 cm²

perimeter of the base=2*[20+8]-----> 56 cm

height=32 cm

surface area=2*160+56*32------> 2,112 cm²

the answer part 3) is

2,112 cm²

Part 4)

What is the surface area of the box if it is scaled up by a factor of 10?

we know that

surface area of the larger box =[scale factor]²*surface area original box

scale factor=10

surface area original box=2,112 cm²

so

surface area of the larger box=10²*2,112-----> 211,200 cm²

the answer part 4) is

211,200 cm²

Part 5) 

What is the volume of the box?

volume of the box = L*W*H 20*8*32-5,120 cm³

the answer Part 5) is

5,120 cm³

Part 6) 

What is the volume of the box if it is scaled down by a factor of 1/10?

we know that

the volume of the smaller box =[scale factor]³volume original box

scale factor=1/10

volume original box=5,120 cm³

so

volume of the smaller box =[1/10]³*5,120 5.12 cm³

the answer part 6) is

5.12 cm³

The length is 6 in., the width is 2 in., and the height is 16 in.

Answer:

544 + 545 + 546 + 547

explanation: if the numbers are consecutive whole numbers then it would be near the ¼ of the given number

Answer:

y= [tex]\sqrt{x}[/tex]

Step-by-step explanation:

Answer: x ≥  -5

Step-by-step explanation:

First, let's see how the function f(x) = IxI works:

if x ≥ 0, IxI = x

if x ≤ 0, IxI = -x

Notice that for 0, I0I = 0.

Ok, we want that:

|x+5| = x+5

Notice that this is equivalent to:

IxI = x

This means that  |x+5| = x+5 is only true when:

(x + 5) ≥ 0

from this we can find the possible values of x:

we can subtract 5 to both sides and get:

(x + 5) -5 ≥ 0 - 5

x ≥  -5

So the graph in the number line will be a black dot in x = -5, and all the right region shaded.

something like:

-7__-6__-5__-4__-3__-2__-1__0__1__2__3__4__ ...

Answer: She had 60% of the money left

Step-by-step explanation:

240/600=0.4

0.4 = 40%

100%-40%=60%

Answer:

60%

Step-by-step explanation:

LETS MAKE IT INTO A FRACTION

FIRST LETS CALCULATE HOW MUCH SHE SPENT

=240/600

WE CAN SIMPLIFY BY DIVIDING THE EQUATION BY 10

=24/60

LETS DIVIDE BY 6

=4/10

DIVIDE BY 2

=2/5

NOW LETS CALCULATE HOW MUCH SHE HAS LEFT

THE EASIEST WAY IS TO SUBTRACT

5/5-2/5=3/5

3/5 IS ALSO EQUAL TO 60/100

SO KAREN HAS 60% OF HER MONEY LEFT

HOPE I HELPED

PLS MARK BRAINLIST

(DESPERATELY TRYING TO LEVEL UP)

        ✌

Answer:

Step-by-step explanation:

After reflection about y-axis, A'B'C' must be translated down 6 units to create image DEF.

ABC and DEF are congruent due to the following common properties of reflections and translations.

1. does not change the nature of geometric elements, i.e. maps a line to a line,  a segment to a segment, etc.

2. preserve lenths of segments.

3. preserves angles

By the congruent theorem of SSS, the two triangles are congruent.

The sequence of transformations that proves the triangles congruent is explained in the solution below.

The geometric transformation is a bijection of a set that has a geometric structure by itself or another set. If a shape is transformed, its appearance is changed.

After reflection about y-axis, A'B'C' must be translated down 6 units to create image DEF.

ABC and DEF are congruent due to the following common properties of reflections and translations.

It does not change the nature of geometric elements, i.e. maps a line to a line, a segment to a segment, etc., preserve lengths of segments, and preserves angles.

By the congruent theorem of SSS, the two triangles are congruent.

Learn more about transformation, click;

https://brainly.com/question/11709244

#SPJ3

Answer:

Below

Step-by-step explanation:

● cos O = 2/3

We khow that:

● cos^2(O) + sin^2(O) =1

So : sin^2 (O)= 1-cos^2(O)

● sin^2(O) = 1 -(2/3)^2 = 1-4/9 = 9/9-4/9 = 5/9

● sin O = √(5)/3 or sin O = -√(5)/3

So we deduce that tan O will have two values since we don't khow the size of O.

■■■■■■■■■■■■■■■■■■■■■■■■■

●Tan (O) = sin(O)/cos(O)

● tan (O) = (√(5)/3)÷(2/3) or tan(O) = (-√(5)/3)÷(2/3)

● tan (O) = √(5)/2 or tan(O) = -√(5)/2

Answer:

hello your question lacks some information below is the complete question

Suppose you are designing a cardboard box that must have a volume of  27 cubic feet. The cost of the cardboard is ​$0.15 per square foot. What is the most economical design for the box​ (one that minimizes the​ cost), and how much will the material in each box​ cost?

Answer : Box design , $8.1 ( cost of material in each box)

Step-by-step explanation:

Volume of cardboard box = 27 cubic feet

cost of cardboard = $0.15 square feet

i) The most economical design for the box would be Designing a square box because the dimensions of the box would be [tex]\sqrt[3]{27}[/tex] = 3 ft

ii) The cost of the material for each box can be calculated as

= surfaces * surface area * cost per square foot

= 6 * 3^2 * $0.15

= $8.1

Each year, your account is multiplied by 1.05 (5% increase). Thus, after 5 years, your account would have been multiplied by that value 5 times.

[tex](1.05)^5=1.27628...[/tex]

Thus, the total percent increase would have been 27.6% (rounded to the nearest tenths).

Answer:

A. Volume = 462 cm³; Surface Area = 458 cm²

B. Volume

C. Surface area

Step-by-step explanation:

A. Given a rectangular box:

[tex] Width (w) = 3 cm [/tex]

[tex] Height (h) = 14 cm [/tex]

[tex] length (l) = 11 cm [/tex]

=>Volume of the juice box

[tex] Volume (V) = whl [/tex]

[tex] Volume (V) = 3*14*11 [/tex]

[tex] = 3*14*11 = 462 [/tex]

Volume of juice box = 462 cm³

=>Surface area (S.A) of juice box:

[tex] S.A = 2(wl + hl + hw) [/tex]

[tex] S.A = 2(3*11 + 14*11 + 14*3) [/tex]

[tex] S.A = 2(33 + 154 + 42) [/tex]

[tex] S.A = 2(229) [/tex]

[tex] S.A = 458 cm^2 [/tex]

Surface area of juice box = 458 cm²

B. Volume would be used to find the amount of juice the box can hold

C. Surface area would be used to know how much wax to buy to use in coating the box.

Answer:

a

Step-by-step explanation:

The standard form of the equation of a circle is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (0, 0), thus

(x - 0)² + (y - 0)² = r², that is

x² + y² = r² → a