What is the gcf of 42 and 56

Answer:

6

Step-by-step explanation:

Jack would need 6 teaspoons of baking powder for 9 cups of flour to maintain the ratio given in the original recipe.

To determine how much baking powder is needed if Jack uses 9 cups of flour instead of 3, you can set up a proportional relationship because the quantity of baking powder required is directly proportional to the amount of flour used.

If the original recipe calls for 2 teaspoons of baking powder for every 3 cups of flour, for 9 cups of flour (which is 3 times as much), you would need 3 times as much baking powder. Hence, the calculation would be as follows:

2 teaspoons baking powder / 3 cups flour = x teaspoons baking powder / 9 cups flour

By cross-multiplication, we can find the value of x:

2/3 * 9 = x

x = 2 * 3 = 6 teaspoons of baking powder

Therefore, Jack would need 6 teaspoons of baking powder for 9 cups of flour to maintain the ratio given in the original recipe.

Answer:

x=6

Step-by-step explanation:

We can find < PMN by using the law of triangles.

The sum of the angles of a triangle adds to 180

<M + <N + < PMN = 180

32 + 64+ < PMN = 180

96 + < PMN = 180

Subtract 96 from each side

96 -96 < PMN = 180-96

< PMN =84

<PMN + <NPQ forms a straight line so it equals 180

<PMN + <NPQ=180

84 + <NPQ=180

Subtract 84 from each side

84-84 + <NPQ=180-84

<NPQ=96

<NPQ = 6x

96 = 6x

Divide each side by 6

96/6 = 6x/6

16 =x

Answer:

additive inverse property

Step-by-step explanation:

which property is used to simplify the expression 5+(6+-6)=5+0

additive inverse property

x+-x = 0

additive identity property

0+8=8

associative property of addition  

a+(b+c) = (a+b)+c

commutative property of addition

a+b=b+a

Answer: additive inverse property

Step-by-step explanation: i looked it up lol

Answer:

The length of each piece of fabric is [tex]L=\frac{3}{5}[/tex]

Step-by-step explanation:

Given : Dai has 3 meters of fabric that he wants to cut into 5 equal sized pieces.

To find : What is true about the length of each piece of fabric ?

Solution :

Dai has 3 meters of fabric.

He cuts the fabric into 5 equal sized pieces.

So, The length of each piece is defined as

[tex]L=\frac{3}{5}[/tex]

Therefore, The length of each piece of fabric is [tex]L=\frac{3}{5}[/tex]

Answer:

[tex]AC=14\sqrt{2}m[/tex]

Step-by-step explanation:

we are given trapezoid ABCD

AC is a diagonal

∠ABC ≅ ∠ACD

we know that

BC and AD are parallel

so, <DAC = <ACB

so, ΔABC ≅ΔACD

Since, both triangles are similar

so, their ratios must be equal

we get

[tex]\frac{BC}{AC} =\frac{AC}{AD}[/tex]

now, we can plug values

[tex]\frac{14}{AC} =\frac{AC}{28}[/tex]

[tex]AC^2=14\times 28[/tex]

[tex]AC^2=14^2\times 2[/tex]

[tex]AC=14\sqrt{2}m[/tex]

To find the length of AC, the diagonal in trapezoid ABCD, we can use the fact that ∠ABC ≅ ∠ACD and the lengths of the bases BC and AD. By setting up a proportion using the corresponding sides of the similar triangles ABC and ACD, we can find that AB/AC = 1/2. Multiplying the length of AB by 2 gives us AC = 28m.

Given that ∠ABC ≅ ∠ACD and the lengths of the bases BC and AD are 14m and 28m respectively, we can find the length of AC, which is a diagonal in trapezoid ABCD.

Answer:

( l + 4) * ( w + 3 ) * ( h + 7)

let l represent the length, w represent the width, and h represent the height of your cub-shaped gift.

Though, if your gift is in the shape of a cube, that would mean all the sides are the same length.

( 2 + 4 ) * ( 2 + 3 ) * ( 2 + 7 )

6 * 5 * 9 = 270

(I haven't done geometry in awhile though, so this may be incorrect unless it actually makes sense.)

Answer:

V = (x+ 4)(x + 3)(x + 7); V = x³ + 14x² + 61x + 84

Step-by-step explanation:

Let x = the side of the cube

Then the dimensions of the gift box are

l   = x + 4

w = x + 3

h = x+ 7

V = lwh

V = (x+ 4)(x + 3)(x + 7)     Multiply the first two terms

V = (x² + 7x + 12)(x+ 7)     Remove parentheses

V = x³ + 14x² + 61x + 84

Answer: 5/8

Step-by-step explanation:

The options are

a.) 5x - 9

b.) 6x + 20

c.) 6x²- 23x + 20

d.) 6x²-14x - 9

Answer:

c.) 6x²- 23x + 20

Step-by-step explanation:

Rectangle area can be computed as length × width . The garden is a rectangle so the area can be computed by multiplying the length and the width.

Area= L × W

Length = 3x - 4

width = 2x - 5

Area = (3x - 4)(2x - 5)

Area = 3x(2x) + 3x(-5) -4(2x) -4(-5)

Note : - × - = +

Area = 6x² -15x - 8x + 20

Area = 6x² - 23x + 20

Answer:

0.1111%

Step-by-step explanation:

2 dice, each with 6 sides. 36 possible outcomes.

Possible sums for 9 are 1,8 2,7 3,6 4,5

That means there is only 4 possible ways to get 9 out of 36 possible outcomes. 4/36 is your probability

Answer:

The length for a rectangle with a perimeter of 34 units and a width of 6.5 units would be 10.5 units.

Step-by-step explanation:

To find the length, you can use the equation [34 - (6.5 x 2) ÷ 2 = the length]. So, 6.5 x 2 = 13, then 34 - 13 = 21, finally, 21 ÷ 2 = 10.5 . So the length of the rectangle is 10.5 . To double check, (6.5 x 2) + (10.5 x 2) (=) 34. So this answer is correct.

Answer:

-2n - 12

Step-by-step explanation:

Combine like terms. Note that each term has one variable (n). Also note  that one negative sign and one positive sign results in a negative sign.

-6n + (-12) + 4n = -6n  + 4n - 12 = -2n - 12

-2n - 12 is your answer

~

Answer:

A

Step-by-step explanation:

4(n-3)-6n

Answer: 169.56

Step-by-step explanation:

A = r²θ

A = (6)²[tex](\frac{3\pi}{2})[/tex]

   = 36[tex](\frac{3\pi}{2})[/tex]

   = 18(3π)

   = 54π

   ≈ 169.56

A negative divided by a positive gives a negative result

So the answer is -3.1

Hope this helps!

this was correct on my test, hope it helps! ;)

(Brainliest would help a lot btw)

Answer:

f is a line through 0 and (2,3)

g is a line through 0 and (3,2)

Step-by-step explanation:

f and g are proportional linear functions. They each have the form y=mx+b where b=0 and m is a fraction. The m or slope tell us the form the function takes on the graph. It is a straight line through 0 with steepness m.

[tex]f(x)=\frac{3}{2} x[/tex] has steepness 3/2. Starting at (0,0) or the origin, move up three grid lines on the y-axis and then over 2 grid lines. Mark your point at (2,3). Then connect and draw arrows on the end.

[tex]g(x)=\frac{2}{3}x[/tex] has steepness 2/3. Starting at (0,0) or the origin, move up two grid lines on the y-axis and over 3 grid lines. Mark your point at (3,2). Then connect and draw he arrows on the end.

Answer:

The graphs are reflections of each other over the y-axis. The graph of g(x) shows exponential decay, while the graph of f(x) shows exponential growth.

Step-by-step explanation:

Answer:

3* ( n+2) = n-4

n=-5

Step-by-step explanation:

Three times the sum of a number and 2 is the same as the number minus 4

3* ( n+2) = n-4

Distribute

3n +6 = n-4

Subtract n from each side.

3n-n +6 =n-n-4

2n +6 = -4

Subtract 6 from each side.

2n +6-6 = -4-6

2n = -10

Divide by 2 on each side.

2n/2 = -10/2

n = -5

Answer:

When Aria had walked 3km along the trail, her vertical distance from the top of the valley was less than 3 km

Step-by-step explanation:

Remember that V(d) denotes Aria's vertical distance from the top of the valley V after she has walked d kilometers along the trail.

This means that V(3) is Aria's vertical distance from the top of the valley after she has walked 3km.

Therefore, V(3)<3 means that Aria's vertical distance from the top of the valley after she has walked 3km, is less than 3km

In other words, the statement means that when Aria had walked 3km along the trail, her vertical distance from the top of the valley was less than 3km

V(3) < 3 means Aria's vertical distance from the top of the valley is less than 3 kilometers after walking 3 kilometers along the trail. It shows her descent into the valley is not more than 3 kilometers vertically at that point.

The inequality V(3) < 3 means that after Aria has walked 3 kilometers along the trail, her vertical distance from the top of the valley is less than 3 kilometers. In other words, Aria has descended into the valley, but her descent after 3 kilometers along the trail is not greater than 3 kilometers vertically. This provides a way to understand her position relative to the top of the valley based on the distance she has walked.

A function is a law that tells you how to associate inputs (x values) and outputs (y values).

In the case of constant functions, it doesn't matter which input you choose, the ouput must always be the same.

So, a constant function has always the same output (y values) for every input (x values) you feed.

Answer:

Step-by-step explanation:

A constant function refers to those functions that only have one variable, which is constant. For example, x=2, y=4, x=-1, are constant function, because they don't variate.

From the given tables, the third and last choices are constant function, because you can observe that one variable doesn't variate. The third function has y=3 as the constant value, and the last table has y=-1 is the constant function.

Therefore, the right choices are third and last table.

Answer:

It will take 6 years

Step-by-step explanation:

Marshall starts at 36,000 dollars and Jim starts at 51,000, multiply the pay raises by 6 and for Jim you get $9,000 and Marshall gets $24,000 pay raise in 6 years.

Sorry If It Is a bit confusing, I'm not really good with words. :/

Both of them will get the same salary after 6 year.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, Marshall Earns a salary of $36,000, and each year he receives a $4,000 raise. Jim earns a salary of $51,000, and each year he receives a $1,500 raise.

Let x be the year in which they will get the same salary

Establishing the equation, we get

36000+4000x = 51000+1500x

Simplifying the equation,

36+4x = 51+1.5x

2.5x = 15

x = 6

Hence, Both of them will get the same salary after 6 year.

For more references on equations, click;

https://brainly.com/question/29657983

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Answer:

if there are 8 7th graders there are 32 6th graders. 4*8=32

Step-by-step explanation:

Answer:

[tex]m\angle EFG=52^{o}[/tex]

Step-by-step explanation:

We have been given that line m is parallel to line p, [tex]m\angle HEF=39^{o}[/tex] and [tex]m\angle IGF=13^{o}[/tex].

Since line m is parallel to line p and EJ is a transversal, so measure of angle EJG will be 39 degrees as angle EJG is alternate interior angle of angle HEF. Both angles are inside parallel lines m and p and on opposite side of transversal EJ.

We can see that angle EFG is exterior angle of triangle GFJ. Since the measure of an exterior angle of a triangle equals to the sum of the opposite interior angles.

We can see that angle IGF and angle EJG are opposite interior angles of angle EFG.

[tex]m\angle EFG=m\angle IGF+m\angle EJG[/tex]

Upon substituting our given values we will get,

[tex]m\angle EFG=13^{o}+39^{o}[/tex]

[tex]m\angle EFG=52^{o}[/tex]

Therefore, measure of angle EFG is 52 degrees.

Answer: Yes

Step-by-step explanation: 4x5 is 20 + 2 is 22 then when you multiply that by 9 you get 198

36x5 is 180 + 18 is 198

Both answers equal each other

Answer:

The answer is B

Step-by-step explanation:

3 and 6 are alternate exterior angles which make lines l and m parallel.

Answer: c

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

[tex]\frac{3!6!}{5!2!}[/tex]

n! = n * (n-1)!

For example 7!  can be written as 7 * 6!

3! is 3* 2!

6! is 6 * 5!

[tex]\frac{3!6!}{5!2!}[/tex]

[tex]\frac{3*2!6*5!}{5!2!}[/tex]

Cancel out 5!  from the top and bottom . Also cancel out 2! from top and bottom.

[tex]\frac{3*2!6*5!}{5!2!}[/tex]

3*6= 18

Answer:Yes

Step-by-step explanation:

When the negative is on the outside of the bracket you distribute the negative to each term inside the parentheses.

Answer:

yes you would change the signs that are inside the parenthesis

Step-by-step explanation:

you do so because the negative outside the parenthesis mean you are distributing the negative to the terms.

X1 = -6

Y1= 1

X2= 4

Y2 = 8

8 - 1

____

4 + 6

7

_ is your answer

10

Answer:

A. 3

Step-by-step explanation:

To find the midpoint  between two numbers, we add the two numbers and divide by 2

midpoint = (x1+x2)/2

midpoint = (-9+15)/2

midpoint = (6)/2

midpoint =3

Answer:

<1 = 30

<2= 41

<3 = 96

Step-by-step explanation:

 Angle 1  ,66 and 84 form a triangle and triangles add to 180 degrees

<1 + 66 + 84 = 180

Combine like terms

<1 +150 = 180

Subtract 150 from each side

<1 + 150 -150 = 180-150

<1 = 30

Angle 3 and 84 form a straight line.  A straight line is 180 degrees.

<3 + 84  =180

Subtract 84 from each side

<3 +84-84 = 180 - 84

<3 = 96

<2 , <3 and 43 form a triangle which adds to 180 degrees,

<2 + <3 + 43 = 180

We have already found <3 to equal 96 degrees

<2 + 96+43 = 180

Combine like terms

<2 +139=180

Subtract 139 from each side.

<2 +130-139 = 180-139

<2 = 41

Answer:

150

Step-by-step explanation:

The ratio of boys to girls is 3 to 7.

We don't know the number of boys or girls. The number of boys and the number of girls are multiples of 3 and 7, respectively. Since they are in the ratio of 3 to 7, then by multiplying both 3 and 7 by the same number, you will get the number of boys and the number of girls. We need to find that number. Call that number x.

The ratio of boys to girls is:

3x to 7x

There are 3x boys and 7x girls.

The number of girls is 200 more than the number of boys.

7x = 3x + 200

Subtract 3x from both sides.

4x = 200

Divide both sides by 4.

x = 50

The number of boys is 3x, so

3x = 3(50) = 150

150 boys and 350 girls were enrolled that year.

Since a college was previously an all girls college, and then it began to allow boys to enroll, and by 2012 the ratio of boys to girls was 3 to 7, to determine, if there were 200 more girls than boys in 2012, how many boys were enrolled that year, the following cross multiplication calculation must be performed:

Therefore, 150 boys and 350 girls were enrolled that year.

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