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, can the company build 20 child bikes and 6 adult bikes in a week.

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 + 6a ≤ 120 and 4c + 4a ≤ 100

Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100

Answer/Step-by-step explanation:

1. YES.

Converse: If same side interior angles are supplementary, then l || m. (Same side interior angles)

Since the sum of the two same side interior angles, 65° and 115°, equals 180°, therefore, l || m.

2. YES.

Converse: if two angles angles are a linear pair, they are supplementary, therefore l || m. (Linear pair)

Thus,

128° + 53° = 180°.

3. YES.

Converse: if two angles are corresponding angles and congruent, therefore l || m. (Corresponding angles).

Thus,

The indicated angles which are equal to 90°, are corresponding angles therefore, l || m.

4. YES

Converse: if two alternate exterior angles are congruent, then l || m. (Alternate exterior angles)

Thus, the two exterior angles are congruent, therefore l || m.

The converse which would serve as prove that l is parallel to m are given in the answers below:

Considering the information in the given diagrams:

1. Yes, l is parallel to m.

The converse is: "If corresponding angles are equal, then  l is parallel to m".  One of the corresponding angles plus [tex]115^{o}[/tex] equals [tex]180^{o}[/tex].

Thus, l || m.

2. Yes, l is parallel to m.

The converse is: "if two angles are linear pair, then they sum up to [tex]180^{o}[/tex]".

So then, l || m.

3. Yes, l is parallel to m.

The converse is: "if two corresponding angles are right angles, then they are congruent".

Therefore, l || m.

4. Yes, l is parallel to m.

The converse is: :if two alternate exterior angles are congruent, then l is parallel to m".

Therefore, l || m.

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Answer:

$537.60

Step-by-step explanation:

Xochitl has saved $201.60.

Yamka has saved 2/3 the amount Xochitl saved.

The amount Yamka has saved us calculated as:

2/3 × $201.60

= $134.40

Zack has saved 1.5 times the amount Yamka saved.

The amount Zack has saved is

1.5 × $134.40

= $201.60

How much have they saved all together?

This is calculated as:

$201.60 + $134.40 + $201.60

= $537.60

Answer:

3/8

Step-by-step explanation:

Answer:

3/8 = 9/24

1/3 = 8/24

-1/3 is closer to 0

3/8 is farther from 0

Answer:

50 grams

Step-by-step explanation:

36 grams = 72%

→ Find 1% by dividing both sides by 72

0.5 grams = 1%

→ Times both sides by 100 to find 100%

50 grams = 100%

Step-by-step explanation:

Multiply 32 by 72 to get thw mass.

Answer:

$2.50

Step-by-step explanation:

5 divided by 2 is 2.5

Because it it money, u add a zero at the end making it 50 cents. Don't make the mistake of saying its 5 cents. 2.05 would be 5 cents. The place matters.

Answer:

2

Step-by-step explanation:

-3^3+9/3*-3= 2 ypu have tu substitute the x by -3 always.

Answer:

n = 12

Ava has 12 times as many eggs as Cole

Step-by-step explanation:

May I have brainliest please? :)

Answer: 45 tomatillos

Step-by-step explanation: 30 tomatillos divided by 8 ounces is 3.75 tomatillos per ounce. So, multiply 3.75 by 12 ounces. What do we get? 45 tomatillos!

Answer: x = 108

Step-by-step explanation: In this problem, we're given a diagram and

we're asked to find the value of x that would make m ll n.

We can see that the angles that are marked in the diagram

are same-side interior angles since they lie on the same side

of the transversal and they lie on the interior of lines m and n.

Therefore, in order for line m to be parallel to line n,

these angles must be supplementary.

In other words, they must add to 180 degrees.

So we can setup the equation x + 72 = 180.

Subtracting 72 from both sides gives us x = 108.

So the value of x that would make line m ll n is 108.

Answer:2881

Step-by-step explanation:

Answer:

2881

Step-by-step explanation:

Answer:

3x+y=-9= 0 then y=5x+7=0

Step-by-step explanation:

Slope=−

2.000

6.000

=−3.000

x−intercept=−

3

9

=−3

y−intercept=−

1

9

=−9.00000

=

2.000

10.000

=5.000

x−intercept=

−5

7

=−1.40000

y−intercept=

1

7

=7.00000 i believe

Answer:

ABD = CDB

AB is parallel to DC

Step-by-step explanation:

angle a and c are right angles so they are equal and angle b and d are equal because they have a line that touch both letters

AB and DC are parellel because they are the same looking lines just on oppisite sides

As per the ASA congruence theorem, the triangles ΔABD and ΔCDB are congruent.

When two parallel lines are intersected by a transversal, alternate external angles are created.

Given that, m∠A = m∠C = 90° and AB║DC.

In triangles ΔABD and ΔCDB,

m∠A = m∠C = 90°

m∠ABD = m∠BDC (Alternate interior angles)

BD = DB (Common side)

Hence, as per the ASA congruence theorem, the triangles ΔABD and ΔCDB are congruent.

Learn more about the alternate interior angles:

https://brainly.com/question/28380652

#SPJ2

Answer:

I THINK IT IS C.

Step-by-step explanation:

Answer:

5(2+8)+(12-6/3)2

5(10)+(12/1-6/3)2

50+(36/3-6/3)2

50+(30/3)2

50+60/3

50+20

70

Step-by-step explanation:

Answer: 70

If the equation is  [tex]5(2+8)+(12-\frac{6}{3} )2[/tex]

[tex]5*10+(12-2)*2[/tex]

[tex]5*10+10*2[/tex]

[tex]10(5+2)[/tex]

[tex]10*7[/tex]

Answer: 70

Please mark brainliest if correct :)

Answer:

Slope=M=y2-y1/X2-X1=

-1 -2 /4-0=

-3/4  =

-0.75

Step-by-step explanation:

Hope this helped!!!!

Answer:

y=(-3/4)+2

Step-by-step explanation:

Hello there! In order to solve this problem we will have to find the slope of the line and then use the point slope formula

Firstly, lets solve for the slope by finding the change in y over the change in x:

slope (m)= [tex]\frac{y2-y1}{x2-x1}[/tex]

We will plug in the values of the points given and find that:

slope (m)= [tex]\frac{-1-2}{4-0}[/tex]

this equals (-3/4)

from here we will use the point slope formula to find for the equation that the line passes through. You can use either point for this step, I will be using A(0,2).

Point-slope equation:

[tex]y-y1=m(x-x1)[/tex]

Plugging in values:

[tex]y-2=(\frac{-3}{4})(x-0)[/tex]

after isolating y we find that the equation is:

[tex]y=\frac{-3}{4} x+2[/tex]

Hope this helps!

-HM

Answer:

Each pen costs $3.60 (Each calculator costs $14.20).

Step-by-step explanation:

Let c represent calculator

Let p represent pen

3c + 7p = 67.8

6c + 2p = 92.4

Step 1: Solve 3c + 7p = 67.8 for c:

3c + 7p = 67.8

3c + 7p + −7p = 67.8 + −7p (Add -7p to both sides)

3c = −7p + 67.8

3c/3 = −7p + 67.8/3 (Divide both sides by 3)

c = −7/3p + 22.6

Step 2: Substitute −7/3p + 22.6 for c in 6c + 2p = 92.4:

6c+2p=92.4

6(−7/3p + 22.6) + 2p = 92.4

−12p + 135.6 = 92.4 (Simplify both sides of the equation)

−12p + 135.6 + −135.6 = 92.4 + −135.6 (Add -135.6 to both sides)

−12p = −43.2

−12p/−12 = −43.2/−12 (Divide both sides by -12)

p = 3.6

Step 3: Substitute 3.6 for p in c = −7/3p + 22.6:

c = −7/3p + 22.6

c= −7/3(3.6) + 22.6

c = 14.2 (Simplify both sides of the equation)

Answer:

c = 14.2 and p = 3.6

Hope this helps and have a great day :)

And please mark me brainliest if you can :)

Answer:

ANSWER

GIVEN:

OA= 3x-1 , OC= 5x-3, OD= 6x-5 , BO = 2x+1

AO/OC = BO/OD

[The diagonals of a Trapezium divide each other proportionally]

(3x-1)/(5x-3) =( 2x+1)/(6x-5)

(3x-1) (6x-5) = (5x-3) ( 2x+1)

3x(6x-5) -1 (6x-5) = 2x(5x-3)+1(5x-3)

18x² -15x -6x +5 = 10x² -6x +5x -3

18x² -21x +5 = 10x² - x -3

18x² -10x² -21x + x +5+3 =0

8x² - 20x +8= 0

4(2x² -5x +2) = 0

2x² -5x +2 = 0

2x² -4x -x +2= 0

[By factorization]

2x(x-2) -1(x-2)= 0

(2x-1) (x-2) = 0

(2x-1) = 0 or (x-2) = 0

x = ½ or x = 2

If we put x= ½ in OD , The value of OD is negative.

Hence, the value of is x = 2.

Step-by-step explanation:

1 =29 and 2=44...............

Answer:

B: 8,9,10

Step-by-step explanation:

Answer:

Step-by-step explanation:

54-16=38

38 divided by 1/2 is 19

so your answer is 19

hope that helps

Answer:

D. 3

Step-by-step explanation:

3x−2y=−6

solve for y

-2y=-3x-6

y= 3/2x+3

y=mx+b

b= y intercept --> b = 3

Answer:

x = -16/3

Step-by-step explanation:

Answer:

9c2/a4

Step-by-step explanation:

To Clarify 9c is squared and a is held to the fourth power

Answer:

According to me all the options are correct

Answer:

g=12/7

Step-by-step explanation:

Answer:

i'm sorry

Step-by-step explanation:

what do you mean