A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week. (2 points) No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100

She would use 9/7 of a bottle of conditioner for a full year.

A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.

We have been given that Martina used 3/4 of a bottle of conditioner in 7/12 of a year.

Let the amount of conditioner would be x she uses in a full year

As per the given condition, we can write a proportion as

3/4 of a bottle : 7/12 of a year = x : 1

⇒ (3/4) / (7/12) = x / 1

Reciprocal the terms of the denominators,

⇒ (3/4) × (12/7) = x

⇒ 36 / 28 = x

⇒ x = 9/7

Therefore, she would use 9/7 of a bottle of conditioner for a full year.

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The matter will be looked into by him.

Thankyou

Answer:

7cm

Step-by-step explanation:

Answer:

i think the answer u need is -2-4x

Answer:

-7(x+2)

Step-by-step explanation:

-3(2x+5)-(x-1)

↦ -6x+(-15)-x+1

↦-6x-x-15+1

↦7x-14

↦2(x-7)

Answer:

v = 0.834 m/s or 3 km/h

Step-by-step explanation:

Given that,

Distance between house and playground is 300 meters

If you went 300  metres away in 10 minutes and ran back and  reached in 2 minutes, it means total distance covered by you during whole journey is 300 m + 300 m = 600 m

Total time, t = 10 min + 2 min = 12 min = 720 seconds

Total distance covered divided by total time gives average speed. So,

[tex]v=\dfrac{600\ m}{720\ s}\\\\v=0.834\ m/s[/tex]

or

v = 3 km/h

So, the average speed is 0.834 m/s or 3 km/h.

Answer:

C. The statement is an equation because there is an equality symbol.

Step-by-step explanation:

Equation:

Combination of terms joined by the sign minus, plus, multiplication, and division and has equality sign.

Example

5x+45=-5

Term:

A Numbers. (Only)

Example:

9

Combination of a number and a variable joined by multiplication or division.

Example:

9x, 6ab, 10n

Variable:

a symbol that is written with a number or a term.

6ab

Expression:

Terms joined by the sign plus or minus

Hope this helps ;)❤❤❤

Answer:

x = 21

Step-by-step explanation:

1. Write the equation

(18 + 2x) ÷ 5 = 12

2. Multiply both sides by 5

18 + 2x = 60

3. Subtract 18 from both sides

2x = 42

4. Solve for x by dividing both sides by 2

x = 21

Answer:

the equation is 18+2x/5 =12

Step-by-step explanation:

now

18+2x= 60

or 2x= 60-18

or 2x= 42

or x=21

so the no is 21 (ans)

thank u

Answer:

2000

Step-by-step explanation:

Salim will need to get 2000 clicks in order to get $50 per month or more.

First: 5 cents goes into one dollar 20 times.

Second: You multiply 20 times 50. This is how you get 2000. There is your answer.

Salim needs at least 700 clicks per month  in order to earn $50 per month or more

A linear equation is in the form:

y = mx + b;

where y, x is variable, m is the rate of change and b is the y intercept.

Let y represent the total pay Salim earns and x represent the number of clicks.

Salim's Website earns $15 per month plus $0.05 every time a visitor clicks, hence:

y = 0.05x + 15

To earn for than $50 per month:

0.05x + 15 > 50

0.05x > 35

x > 700

Salim needs at least 700 clicks per month  in order to earn $50 per month or more

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Answer:

The height of the pole is 167 m

Step-by-step explanation:

The given parameters are;

Increase  in the length of the shadow = 90 m

Initial angle of elevation of the Sun = 58°

Final angle of elevation of the Sun = 36°

We have a triangle formed by the change in the length of the shadow and the rays from the two angle of elevation to the top of the pole giving an angle 22° opposite to the increase  in the length of the shadow  

We have by sin rule;

90/(sin (22°)  = (Initial ray from the top of the pole to the end of the shadow's length)/(sin(122°)

Let the initial ray from the top of the pole to the end of the shadow's length = l₁

90/(sin (22°)  = l₁/(sin(122°)

l₁ = 90/(sin (22°) ×(sin(122°) = 283.3 m

Therefore;

The height of the pole = 283.3 m × sin(36°) = 166.52 m

The height of the pole= 167 m to three significant figures.

Answer:

height of pole = 121 m (to 3 significant figures

Step-by-step explanation:

From the diagram attached to this solution:

Let the length of the shadow = b

Let the height of the triangle = h

[tex]Triangle\ 1\\\\Tan\ (58)\ =\ \frac{h}{b}\\1.60\ =\ \frac{h}{b} - - - - - -(1)\\\\[/tex]

[tex]Tan\ (36) = \frac{h}{b+90} \\0.73\ =\ \frac{h}{b+90} - - - - (2)[/tex]

[tex]From\ equation\ (1)\\1.60 = \frac{h}{b}\\ cross-multiplying\\1.60b = h - - - - - (3)\\\\\\from\ equation\ (2)\\0.73\ =\ \frac{h}{b+90}\\ corss-multiplying\\0.73b\ +\ 65.7 = h\\h\ =\ 0.73b\ +\ 65.7- - - - - -(4)\\[/tex]

Notice that equation (3) = equation (4) = h

[tex]1.60b = 0.73b\ + 65.7\\1.60b\ -\ 0.73b\ = 65.7\\0.87b\ =\ 65.7\\b\ =\ \frac{65.7}{0.87} = 75.52\ m\\[/tex]

Now let us find the height of pole from equation (3)

1.60b = h - - - - - - (3)

where b = 75.52

h = 1.60 × 75.52

h = 120.83 m

= 121 m (to three significant figure

Answer:

(A) 70°

(B) 67°, because they are alternate interior angles

Step-by-step explanation:

For a:

The angles of a triangle will all add up to 180°. Using the "feathers" (lines that signify congruence), we can tell that the angle connecting the two congruent lines will be different than the other two, which will be equivalent to each other.

This means that the angle measure of x will be [tex]180-55-55[/tex], or just [tex]180-110[/tex].

This is equal to 70°.

For b:

We know that the 67° angle and y are formed by the same line intersecting two parallel lines. This means that the angle measures of each intersection point will be the same as the other intersection point, however they will be flipped. This makes the concept of alternate interior angles. We know that the 67° angle and y are formed by the same line, this means that their angle lengths are the same - therefore y is 67°.

Hope this helped!

Answer:

C is facing North

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

replace -2 for every in the equation:

-(-2)x2-9x-2=22

Answer:

f(-2)=14

Step-by-step explanation:

[tex]f(x) = -x^2 - 9x\\\\f(-2) = -(-2)^2-9(-2)\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:exponents}\:\left(-2\right)^2\::\quad 4\\=-4-9\left(-2\right)\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:9\left(-2\right)\::\quad -18\\\\=-4-\left(-18\right)\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:-4-\left(-18\right)\:\\f(-2):\quad 14[/tex]

Answer:

Step-by-step explanation:

a.

[tex]AC=\sqrt{AB^2-BC^2} =\sqrt{13^2-5^2} =\sqrt{169-25} =\sqrt{144} =12\\[/tex]

applying sine formula

AB=c

AC=b

BC=a

[tex]\frac{a}{sin A} =\frac{b}{sin B} =\frac{c}{sin C} \\\\\frac{5}{sin A} =\frac{12}{sin B} =\frac{13}{sin 90} \\using~last~two\\\frac{12}{sin B}= \frac{13}{1} \\sin B=\frac{12}{13}\\ B=sin^{-1}(\frac{12}{13}) \approx 67.38 ^\circ[/tex]

b.

third angle ∠Y=180-(30+90)=180-120=60

using sine formula

[tex]\frac{xz}{sin Y} =\frac{xy}{sin Z} = \frac{yz}{sin X} \\\frac{30}{sin 60} =\frac{xy}{sin 90} =\frac{h}{sin 30} \\using ~first~and~last\\\frac{30}{\frac{\sqrt{3} }{2} } =\frac{h}{\frac{1}{2} } \\2h=\frac{60}{\sqrt{3} } \\h=\frac{30}{\sqrt{3} } \times \frac{\sqrt{3} }{\sqrt{3} } =10\sqrt{3}[/tex]

Answer:

The correct options are;

A. 1·2 = 2

B. 1·1 = 1

E. 1 + 1 = 2

Step-by-step explanation:

Given that the equations 1.2 = 2 and 1.1 = 1 are correctly written as 1·2 = 2 and 1·1 = 2, we have;

The product of any number and one is equal the same number, that is a × 1 = a

Whereby we have the expression 1·2 which is 1 × 2,  we therefore have;

1 × 2 = 1 · 2= 2

B. Similarly we have;

1 · 1 = 1 × 1 = 1

Also, 1 + 1 = 2 is correct as the sum of two numbers is equal to the sum of the count of the numbers, therefore;

E. 1 + 1 = 2 is correct.

the answer is 1 because when x is a variable by it self it is 1

Answer: 1

Step-by-step explanation: f(x)=1

Answer:

23 mpg

Step-by-step explanation:

We simply need to evaluate the given function at the speed requested (60 mph):

[tex]f(x)=32-0.15\,x\\f(60)=32-0.15\,(60)\\f(60)=23\,\,mpg[/tex]

Answer:

1/2, 3/6 and 2/4 are equivalent fractions.

Step-by-step explanation:

To know if the fractions are equivalent, their simplest form should be the same.

So we must simplify all the fractions to their simplest form.

To find the simplest form of a fraction, we must divide the numerator and denominator with their GCF (Greatest Common Factor)

So:

1/2 = 1/2

1/3 = 1/3

3/4 = 3/4

3/6 = 1/2 ( The GCF for 3 and 6 is 3)

2/4 = 1/2 ( The GCF for 2 and 4 is 2)

4/10 = 2/5 ( The GCF for 4 and 10 is 2)

Because 1/2, 3/6 and 2/4 has the same simplest form, they are equivalent fractions.

I hope this helps! I'm sorry if it's wrong or too complicated.

Answer:

(D) [tex]x>-10[/tex]

Step-by-step explanation:

If we have the inequality [tex]-7x + 4 > -8x - 6[/tex], we can simplify it down and get [tex]x[/tex] isolated on one side of the equation.

Add 6 to both sides:

[tex]-7x + 4 + 6 > -8x - 6 + 6\\\\-7x + 10 > -8x[/tex]

Add [tex]8x[/tex] to both sides of the inequality:

[tex]-7x + 10 + 8x > -8x+8x\\\\x + 10 > 0[/tex]

Subtract 10 from both sides of the inequality:

[tex]x + 10 - 10 > 0 - 10\\\\x > -10[/tex]

So (D) [tex]x>-10[/tex] is the correct simplification.

Hope this helped!

Answer:

a=[tex]\frac{vf - vi }{t}[/tex]

Step-by-step explanation:

vf=vi + at

vf-vi= at

divide  both sides by t

[tex]\frac{vf - vi }{t}[/tex] =[tex]\frac{at}{t}[/tex]

a=[tex]\frac{vf - vi }{t}[/tex]

Answer:

The possible values are less than 4 but greater than –4

Step-by-step explanation:

If the absolute value of integer number is less than 4 then it is 0, 1, 2 or 3.

so the possible integer numbers are: -3, -2, -1, 0, 1, 2 or 3.

All of them are greater than -4 and less than 4

Answer:

Answer is C.

Step-by-step explanation:

Answer: -2b-4

Ok, so I assume you meant b-4-3b. If not, then B-4-3b is the best you can get, since B and b are different in math.

Anyways, we can rearrange b-4-3b into b-3b-4. Calculating b-3b = -2b. That means -2b-4 is the answer.

Hope that helped,

-sirswagger21

Answer:

B - 4 - 3B

=> -2B - 4

Answer:

definition of plagiarism

Step-by-step explanation:

Plagiarism is presenting someone else's work or ideas as your own, with or without their consent, by incorporating it into your work without full acknowledgement. All published and unpublished material, whether in manuscript, printed or electronic form, is covered under this definition.

Answer:

[tex]4n-n^2[/tex]

Step-by-step explanation:

I use 'n' as the unknown value, but you can use any letter you want as the variable.

The product of four and a number would be represented by '4 * n'. The ideal way to write this would be '4n', even though '4 * n' is also correct in value.

The square of the number would be n². Squaring a number is multiplying a number by itself.

The phrase 'difference between...' means subtraction.

Putting it together:

"The difference between the product of 4 and a number and the square of the number" would be:

[tex]4n-n^2[/tex]

Hope this helps.

The value of the angle x will be 40°. Then the correct option is B.

The circle is at equidistant of points drawn from the center. The radius of a circle is the distance between the center and the circumference.

The minor arc  is 75°. And the another arc is 130°.

We know that the complete circle subtends 360 degrees.

Then the measure of the major arc will be

Major arc + 130° + 75° = 360°

       Major arc + 205° = 360°

                   Major arc = 155°

Then the value of the angle x will be given by the half of the difference of the major arc to minor arc.

x = (Major arc – minor arc) / 2

x = (155 – 75)/2

x = 80 / 2

x = 40°

Thus, the value of the angle x will be 40°.

Then the correct option is B.

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Answer:

Hey there!

We can let x be that number.

2x+9=31

2x=22

x=11

The number is 11.

Let me know if this helps :)

Answer:

The whole number is 11.

Step-by-step explanation:

Let's call the whole number x. We can write the following equation:

2x + 9 = 31

Subtracting 9 from both sides of the equation gives us:

2x + 9 - 9 = 31 - 9

2x = 22

Dividing both sides of the equation by 2 gives us:

2x / 2 = 22 / 2

x = 11

Answer:

is this for a test?

Step-by-step explanation:

Answer:

90i

Step-by-step explanation:

18 * sqrt(-25) = 90i

Answer:

Option A must be true.

Step-by-step explanation:

Answer:

[tex] \overline{TQ} \cong \overline {TR} [/tex]

Step-by-step explanation:

Since, endpoints of a segment are equidistant from any point situated on the perpendicular bisector of that segment.

T is a Point on the perpendicular bisector of segment AB.

[tex] \therefore \overline{TQ} \cong \overline {TR} [/tex]

Step-by-step explanation:

[tex] \frac{ log_{5}(25) + log_{5}(125) - log_{5}(625)}{ log_{5}(100) } [/tex]

[tex] \frac{ log_{5}( \frac{25 \times 125}{625} ) }{ log_{5}(25 \times 4) } [/tex]

[tex] \frac{ log_{5}(5) }{ log_{5}(25) + log_{5}(4) } [/tex]

[tex] \frac{1}{2 + 2 log_{5}(2) } [/tex]

[tex]0.3495 = 0.35[/tex]