A painting with dimensions 10 inches by 14 inches is placed in a picture frame (of constant width), increasing its area to 221 square inches. How many inches is the width of the picture frame?

Answer:

The length of AE is 39 units.

Step-by-step explanation:

Given:

G is the centroid of a triangle ABC.

Lines are drawn from each point through the centroid to the midpoint of the opposite side to form line segments AE, BF, and CD.

The length of line segment A G is 2 x + 10, the length of line segment F G is 2 x minus 1, and the length of line segment G B is 3 x + 6

To Find: Length of the AE.

The centroid of the triangle is always cut the line in the ratio of 2:1. For clarification, the image is provided.

Hence,

G divides the line BF into a 2:1 ratio.

Thus,

[tex]\begin{aligned}&2FG=BG\\&2(2x-1)=3x+6\\&4x-2=3x+6\\&x=8 \end{aligned}[/tex]

Also,

G divides the line AE into a 2:1 ratio.

Therefore,

[tex]AG=2GE\\GE=AG/2[/tex]

Line segment AE is the sum of AG and GE.

Thus,

[tex]AE=AG+GE\\AE=AG+AG/2\\AE=3AG/2\\AE=3(2x+10)/2\\AE=39[/tex]

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The length of AE is 9 units.

Given that G is the centroid, it divides each median into two segments with the ratio of 2:1, where the longer segment is toward the vertex and the shorter segment is toward the midpoint of the opposite side.

Let's denote the length of AG as a, the length of BG as b, and the length of FG as c. According to the given information:

1. AG = 2x + 10

2. FG = 2x - 1

3. BG = 3x + 6

We know that AG = 2GE and BG = 2GE. Thus:

[tex]\[ AG = 2GE \implies GE = \frac{AG}{2} = \frac{2x + 10}{2} = x + 5 \]\[ BG = 2GE \implies GE = \frac{BG}{2} = \frac{3x + 6}{2} = \frac{3}{2}x + 3 \][/tex]

Since GE is common, we can equate the expressions:

[tex]\[ x + 5 = \frac{3}{2}x + 3 \][/tex]

Solving for x:

[tex]\[ \frac{1}{2}x = 2 \][/tex]

x = 4

Now that we've found the value of x, we can substitute it back into the expressions for AG and FG to find their lengths:

AG = 2x + 10 = 2(4) + 10 = 18

FG = 2x - 1 = 2(4) - 1 = 7

Now, we know that AE = AG - GE:

AE = AG - GE = 18 - (x + 5) = 18 - (4 + 5) = 18 - 9 = 9

So, the length of AE is 9 units.

Answer: 172, 174 and 176

Step-by-step explanation:

Since they are even numbers,

Let x be the number, x + 2 be the second number and x +4 the third number

can think of this as x+(x+2)+(x+4)=522

so you get 3x=522-6

3x= 516

so x=172

If x is 172, second number is 174 and third number is 176

Answer:

Step-by-step explanation:2x=145-15

2x=130

X=130/2

X=65

It's a stretch by coefficient of two.

Hope this helps.

Answer:

A centimeter is 100 times the length of a meter.

A kilometer is 1,000 times the length of a meter.

The statement that asserts a true claim would be:

B). A kilometer is [tex]1,000[/tex] times the length of a meter.

Metric System

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Answer:

D) 262,144

Step-by-step explanation:

The given sequence is given explicitly as:

[tex]A_n = {4}^{n - 1} [/tex]

We want to find the tenth term of this sequence.

We substitute n=10 to get:

[tex]A_ {10}= {4}^{10 - 1} [/tex]

Simplify the exponent

[tex]A_ {10}= {4}^{9} [/tex]

Simplify the power

[tex]A_ {10}= 262144[/tex]

Therefore the 10th term is 262,144

Answer:

[tex]x=\frac{1}{4}[/tex]

Step-by-step explanation:

In order to get the answer to this question you will have to subtract 1/2 on both sides:

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

Subtract 1/2 on both sides:

[tex]-\frac{1}{2} -\frac{1}{2}[/tex]

Subtract 1/2 from 3/4:

[tex]\frac{3}{4} -\frac{1}{2}[/tex]

Find the common denominator:

[tex]CD=4[/tex]

[tex]2\times2=4[/tex]

[tex]1\times2=2[/tex]

[tex]=\frac{2}{4}[/tex]

Do the same with the second fraction:

[tex]4\times1=4[/tex]

[tex]3\times1=3[/tex]

[tex]=\frac{3}{4}[/tex]

Subtract the numerators:

[tex]3-2=1[/tex]

Keep the denominator the same:

[tex]=\frac{1}{4}[/tex]

[tex]x=\frac{1}{4}[/tex]

Hope this helps.

Hey there!

12 - 7 - 8 - 9 + 66 = ?

12 - 7 = 5

5 - 7 - 8 - 9 + 66

5 - 8 = -3

-3 - 9 + 66

-3 - 9 = -12

-12 + 66 = 54

Answer: 54

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

Answer:

(8, 2) OR (x + 3, y - 1)

Step-by-step explanation:

Step 1:  Add 3 to 5 and subtract 1 from 3

(5 + 3, 3 - 1)

(8, 2) OR (x + 3, y - 1)

Answer:  (8, 2) OR (x + 3, y - 1)

Answer:

30

Step-by-step explanation:

Answer:$0.27

Step-by-step explanation:

20=$5.49

1=20/5.49

1=$0.2745

Philip ran 3 1/4 miles farther than Michael. We obtained this by subtracting the fraction and whole number of Michael's distance from Philip's and simplified the resultant fraction.

To find out how much farther Philip ran than Michael, you need to subtract the distance run by Michael from Philip's distance. Since we are dealing with fractions with common denominators, this makes the subtraction process easier.

Philip's distance = 4 3/8 miles

Michael's distance = 1 5/8 miles

Subtract Michael's distance from Philip's distance: 4 3/8 - 1 5/8

Since the denominators are the same, you can simply subtract the numerators: 8 (the common denominator) stays the denominator, and subtract 3 from 5 which gives: 2/8

We subtract the whole numbers: 4 - 1 = 3. Therefore, the final difference is 3 2/8 miles. However, you can simplify 2/8 fraction to 1/4. So, the final and simplest difference is 3 1/4 miles.

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To find out how much farther Philip ran than Michael, we need to subtract the fractions representing their respective distances. After converting these to improper fractions, we subtract the numerators, giving us a result of 2 6/8 miles, which is the distance by which Philip ran farther than Michael.

The problem involves subtracting fractions to find the difference between the distances that Philip and Michael ran. First, convert the mixed fractions into improper fractions. Philip ran 4 3/8 miles which equals 35/8 miles and Michael ran 1 5/8 miles which equals 13/8 miles. Subtracting fractions with like denominators is straightforward, so subtract the numerators: 35 - 13 equals 22. Therefore, Philip ran 22/8 or 2 6/8 miles more than Michael.

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Answer:

[tex] \frac{4}{5} [/tex]

Step-by-step explanation:

Total number of marbles

= 3+2+8+4+3

= 20 marbles

P(not red)

=

[tex] \frac{3 + 2 + 8 + 3}{20} \\ = \frac{16}{20} \\ = \frac{4}{5} [/tex]

or P(not red)

=

[tex]1 - \frac{4}{20} \\ = 1 - \frac{1}{5} \\ = \frac{4}{5} [/tex]

There 15 large boxes of popcorn were sold. The option D is correct.

We need to determine the number of large boxes of popcorn sold. Let's denote the number of small boxes as s and the number of large boxes as l. We are given the following information:

The cost of a small box of popcorn is $1.50.

The cost of a large box of popcorn is $4.00.

A total of 25 boxes of popcorn were sold.

The total revenue from popcorn sales was $75.00.

We can set up two equations based on this information:

s + l = 25 (the total number of boxes sold)

1.50s + 4.00l = 75.00 (total revenue from sales)

Let's solve for l using these equations. Multiplying the first equation by 1.50 gives us:

1.50s + 1.50l = 37.50

Subtracting this from the second equation:

(1.50s + 4.00l) - (1.50s + 1.50l) = 75.00 - 37.50

2.50l = 37.50

l = 37.50 / 2.50

l = 15

Answer:

b = 10

Step-by-step explanation:

Divide 20 by 2 to get b by itself:

20/2 = b

10 = b

MARK AS BRAINLIEST!

Answer:

B=10

Step-by-step explanation:

2(b)=20

2(10)=20

Or

2b÷2=20÷2

B=10

Step-by-step explanation:

Diameter of pizza = 12 inch

Therefore, radius r = 6 inch

[tex]Area \: of \: entire \: pizza \\ = \pi {r}^{2} \\ = 3.14 \times {6}^{2} \\ = 3.14 \times 36 \\ = 113.04 \: {inch}^{2} \\ \\ amount \: of \: calories \: in \: entire \: pizza \\ = area \: of \: pizza \\ \times calories \: per \: square \: inch \\ = 113.04 \times 22 \\ = 2,486.88 \\ [/tex]

Answer:

A

Step-by-step explanation:

So that is a 90 degree angle and there is an angle of 30. 30-90 is 60. 60 divided by 4 is 15. So thus the answer is A,15.

Answer:

15

Step-by-step explanation:

90 is right angle

90 - 30 = 60

60 / 4 = 15 <---- theres the answer

hope i helped

Solution:

Given that,

A sequence is defined by the recursive function:

[tex]f(n+1) = \frac{1}{3} \times f(n)[/tex] ------ eqn 1

Given that,

[tex]f(3) = 9[/tex]

Substitute n = 2 in eqn 1

[tex]f(2 + 1) = \frac{1}{3} \times f(2)\\\\f(3) = \frac{1}{3} \times f(2)\\\\Substitute\ f(3) = 9\\\\9 = \frac{1}{3} \times f(2)\\\\f(2) = 27[/tex]

Substitute n = 1 in eqn 1

[tex]f(1 + 1) = \frac{1}{3} \times f(1)\\\\f(2) = \frac{1}{3} \times f(1)\\\\Substitute\ f(2) = 27\\\\27 = \frac{1}{3} \times f(1)\\\\f(1) = 27 \times 3\\\\f(1) = 81[/tex]

Thus f(1) is 81

Answer:

D 81

Step-by-step explanation:

Area of the rectangle is 10.27 cm²

Step-by-step explanation:

Perimeter = 2(length + width)

⇒ 18.4 = 2 (x + 4 + 3x)

⇒ 18.4 = 2(4x + 4)

⇒ 18.4 = 8x + 8

⇒ 8x = 10.4

⇒ x = 10.4/8 = 1.3

∴ 4 + 3x = 4 + 3×1.3 = 7.9

Length = 7.9 cm and width = 1.3 cm

⇒ Area = length × width

             = 7.9 × 1.3 = 10.27 cm²

Time taken by both crew is 48 min and 12 min , when they work together !

Step-by-step explanation:

Here we have , One yard crew works four times faster than the other yard crew. If they work together they can finish a job in 60 minutes. We need to find How fast each yard crew works . Let's find out:

One yard crew works four times faster than the other yard crew

Let speed of one crew be x , So speed of other crew is four times i.e.

⇒ [tex]4x[/tex]

If they work together they can finish a job in 60 minutes.

According to above statement , both can finish work in 60 min i.e.

⇒ [tex]4x+x=60[/tex]

⇒ [tex]5x=60[/tex]

⇒ [tex]x=12[/tex]

So , time taken by other crew is 4x = 4(12) = 48 min . Therefore , Time taken by both crew is 48 min and 12 min , when they work together !

The second yard crew works for 48 minutes.

The first yard crew works for 12 minutes which is four times faster that the second crew.

Step-by-step explanation:

Let us assume,

The second yard crew completes the work in 'x' minutes.

It is given that,

If they work together they can finish a job in 60 minutes.

⇒ x + x/4 = 60 minutes.

⇒ 5x / 4 = 60

⇒ x = 240/5

⇒ x = 48 minutes.

Therefore, the second yard crew works for 48 minutes.

To find the first yard crew :

We already know that, they are 4 times faster that the second yard crew.

Substitute x = 48 in x/4,

⇒ 48 ÷ by 4

⇒ 12 minutes.

Therefore, the first yard crew works for 12 minutes which is four times faster that the second crew.

You have 3 and 3/5 pounds of water.

To find this, simply multiply 3/5 by 6/1 (multiplying straight across). 6 times 3 is 18 and 5 times 1 is 5. Thus meaning you have 18/5 pounds, which simplified is 3 and 3/5 pounds.

I hope this helps!

Answer:

if you multiply 3/5 ×6 that would be 3.6 or in mix number that would be 3⅗

Answer:

15 units

Step-by-step explanation:

The picture of the question in the attached figure

we know that

Triangle XYZ is a right triangle, because segment ZY is tangent to circle X at point Y

so

Applying the Pythagorean Theorem

[tex]XZ^2=XY^2+ZY^2[/tex]

we have

[tex]XZ=8+9=17\ units\\XY=8\ units[/tex]

substitute the given values

[tex]17^2=8^2+ZY^2[/tex]

[tex]ZY^2=289-64\\ZY^2=225\\ZY=15\ units[/tex]

Answer:

15

Step-by-step explanation:

The equation of inequality would be = 2 x + y ≤ 10 for the process of purchase.

Explanation:

Total amount of money tony have , T = $10

Thus the cost of apple, (We can represent as Ca) = $2

Also the cost of banana,(We can represent as  Cb) = $1

Let x be the number of apples bought

Let y be the number of bananas bought

Total expenditure to buy fruits, E = $2 x + $1 y

So,The equation of inequality would be = 2 x + y ≤ 10 for the process of purchase.

Hello!

The answer to your problem is 24 R 14 (R for remainder)

Here is my work show.

Answer: 24.37

Step-by-step explanation:

926/36 = 24.3684

Rounded = 24.37

Answer:

S=21

Step-by-step explanation:

First cross multiply, next divide. I hope this helped!

Answer: S = 12

Step-by-step explanation:

S/84 =3/21

Cross multiply to find the value of S

21 x S= 84 x 3

21S= 252

S= 252/21

S= 12

Answer:

D 180°

Step-by-step explanation:

The measure of a straight angle is 180°.

Answer:

k = 30

Step-by-step explanation:

[tex]\frac{10}{3}=\frac{k}{9}\\\\\frac{k}{9}=\frac{10}{3}\\\\k=\frac{10}{3}*9\\\\k=10*3=30[/tex]

Answer:

k = 30

Step-by-step explanation:

[tex]\frac{10}{3}[/tex] = [tex]\frac{k}{9}[/tex]

We can easily solve this by cross multiplying. Multiply 10 by 9, and multiply the variable (k) by 3.

10 x 9 = 90

3 x k = 3k

These two (90 and 3k) are equal to one another and thus can both be set up into an equation.

3k = 90

Solve for k.

3k/3 = 90/3

k = 30

Answer:

[tex] \frac{8}{3} \div \frac{2}{3} \\ \frac{8}{3} \times \frac{3}{2} = \frac{4}{1} \\ = 4[/tex]

Answer is 4

Answer: 4

Step-by-step explanation:

8/3 ÷ 2/3 = 4

In Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction.

The first step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 2/3 is 3/2.

8/3 × 3/2

Next, multiply the two numerators. Then, multiply the two denominators. In this step, we first cancel by a common factor of 3, which then gives 8/2, then cancel by another common factor of 2, which gives 4.

Thus 8/3 x 3/2 = 4

I hope this helps.

Answer:

784

Step-by-step explanation:

I’m pretty sure I did this right I just multiplied them