The ratio of boys to girls is 7:12. If there are 76 children how many are girls?

Ricky jogged 6 miles on tuesday and 6 miles on friday

Solution:

Given that,

Rick jogged the same distance on tuesday and friday

Let "x" be the distance jooged on each tuesday and friday

He also jogged for 8 miles on sunday

Total of 20 miles for the week

Therefore, we frame a equation as,

total distance jogged = miles jogged on tuesday + miles jogged on friday + miles jogged on sunday

20 = x + x + 8

20 = 2x + 8

2x = 20 - 8

2x = 12

x = 6

Thus Ricky jogged 6 miles on tuesday and 6 miles on friday

Final answer:

Rick jogged 6 miles each day on Tuesday and Friday. This was found by solving the equation 2x + 8 = 20, where 2x represents the total distance for Tuesday and Friday, and 8 miles is the distance for Sunday.

Explanation:

Rick jogged the same distance on Tuesday and Friday, and 8 miles on Sunday for a total of 20 miles for the week. Since Rick jogged the same distance on both Tuesday and Friday, we can let the distance he jogged on each of those days be represented by the variable x. The total distance jogged over these three days (Tuesday, Friday, and Sunday) can be represented by the equation 2x + 8 = 20.

To solve for x, first subtract 8 from both sides of the equation to isolate the variable:

2x + 8 - 8 = 20 - 8

2x = 12

Then, divide both sides by 2 to get the value of x:

2x / 2 = 12 / 2

x = 6

The distance Rick jogged on Tuesday and Friday was therefore 6 miles each day.

Answer:

QR = 19

SR = 24

PT = 21

SQ = 20

m∠QRS = 74°

m∠PQS = 49°

m∠RPS = 39°

m∠PSQ = 57°

Step-by-step explanation:

Attached is the complete question:

By definition, a parallelogram is a quadrilateral, which means it has 4 sides where the opposite pairs are parallel to each other. These pair of sides are congruent.

With that we can assume the following:

PQ ≅ SR

PS ≅ QR

m∠PQR ≅ m∠ PSR

m∠QRS ≅ m∠ QPS

The given states that:

PQ ≅ SR

PS ≅ QR

then:

PQ = 24

PS = 19

So we know that:

QR = 19

SR = 24

When it comes to the angles, we have the following theorems:

Opposite angles (Opposite edges) are congruent

Consecutive angles are supplementary, or they sum up to 180°

We are given the following angles:

m∠PQR = 106°

m∠QSR = 49°

m∠PRS = 35°

Based on the theorems we know the following:

m∠PQR ≅ m∠PSR

m∠PQR + m∠QRS = 180°

Then:

m∠PQR + m∠QRS = 180°

106° + m∠QRS = 180°

m∠QRS = 180° - 106°

m∠QRS = 74°

In addition, m∠PSR = 106° and m∠QSR = 49° then when we add it to m∠PSQ it should be equal to m∠PSR

m∠QSR + m∠PSQ = m∠PSR

49° + m∠PSQ = 106°

m∠PSQ = 106° - 49°

m∠PSQ = 57°

Now notice that a parallelogram when you cut them in half, it makes two congruent triangles. All angles in a triangle sum up to 180° so we can assume that:

m∠PSR + m∠PRS + m∠RPS = 180°

So:

106° + 35° + m∠RPS = 180°

141° + m∠RPS = 180°

m∠RPS = 180° - 141°

m∠RPS = 39°

Following the same logic:

m∠QPS ≅ m∠QRS

m∠QPS  = 74°

m∠QPS + m∠PSQ + m∠PQS = 180°

74° + 57° + m∠PQS = 180°

131° + m∠PQS = 180°

m∠PQS = 180° - 131°

m∠PQS = 49°

x + 5y = -9

8x - 10y = 28

Set y equal

-2y - 10y = 18

8x - 10y = 28

Subtract from one another

-10x = -10

Divide

x = 1

Plug x in one of the equations and solve

x + 5y = -9

1 + 5y = -9

5y = -10

y = -2

Answer

(1,-2)

Hope this helps! ;)

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x+5y=-9\\8x-10y=28&\text{divide both sides by 2}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}x+5y=-9\\4x-5y=14\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad5x=5\qquad\text{divide both sides by 5}\\.\qquad\boxed{x=1}\\\\\text{Put it to the first equation}\\\\1+5y=-9\qquad\text{subtract 1 from both sides}\\5y=-10\qquad\text{divide both sides by 5}\\\boxed{y=-2}[/tex]

Answer:

Step-by-step explanation:

Answer:

= 8a/b + 6b/a

look at the phot below for more details.

:)

Answer:

3/8

Step-by-step explanation:

The product of the fraction numbers 5/4 and 3/10 in the simplified form will be 3/8.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The fraction numbers are given below.

5/4 and 3/10

Then the product of the fraction numbers 5/4 and 3/10 is given as,

⇒ 5/4 x 3/10

⇒ 15 / 40

⇒ 3/8

The product of the fraction numbers 5/4 and 3/10 in the simplified form will be 3/8.

More about the value of the expression link is given below.

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Answer:

DC = 4.5

Step-by-step explanation:

Since DC is on AC it is a segment bisector.

This divides AC exactly in half.

AC = 9 / 2  = 4.5

DC = 4.5

Answer:

the ratio of part time workers to total workers are 12/30

Answer:

X + 12x +35+3x + 15=16x+50

Step-by-step explanation:

Answer:

9.01 maybe my math might be wrong

Step-by-step explanation:

Answer:

In total it would be $10.71

Step-by-step explanation:

Turn the percent into a decimal, 6% into 0.06. Then multiply that with 8.50.

8.50×0.06= 0.51

Now, turn 20% into a decimal and multiply that with 8.50.

8.50×0.20= 1.70

Then, add 0.51 and 1.70 to 8.50.

0.51+1.70+8.50= 10.71

6.9

323.6/4=6.885

Round to the nearest tenth=6.9

Answer:

$500

Step-by-step explanation:

We are given;

We are supposed to determine the amount spent on food;

Therefore;

Amount on gas and hotel room = 3/5 × $2500

                                                     = $ 1500

Thus;

Remaining amount = $2500 - $1500

                                = $1000

But;

1/2 of the remainder was spent for the food

Thus;

Amount on food = 1/2 × $1000

                           = $500

Hence, the family spent $500 on food

Answer:

Elephant

Bengal tiger

Lion

Giraffe

Giant panda

Step-by-step explanation:

The expression (4r+6)÷2 can be used to represent the number of females on a team if r is used to represent the number of female team members. Otherwise, it represents what the variable r represents.

The expression (4r+6)÷2 represents an algebraic equation where r is a variable. If r is representing the number of female team members in a sport, then the value for r can be inserted into the equation to find the total. For instance if r=5, representing 5 female team members, the equation would then be (4*5+6) ÷2 = (20+6) ÷ 2 = 26 ÷ 2 = 13.

However, it's important to note that this equation does not inherently represent the number of females on a team. The value it represents is dependent on what the variable r is representing. If r represents something different, then the result would represent that different thing. Thus, the equation can only represent the number of females on a team if r is used to represent that.

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Answer:

2 3

4 5

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

Step-by-step explanation:

Ur welcome

You can construct more than one triangle with Option 1) the measurement of two angles and option 2) the length of the included side, and Option 4) the lengths of the two sides and the measurement of the included angle.

Constructing triangles depends on the given information. According to the rules of geometry, 1) the measurement of two angles alone is not enough to construct a unique triangle. 2) With the measurement of two angles and the length of the included side (also known as Angle-Side-Angle or ASA), you can construct a unique triangle. 3) The measurements of all right angles is irrelevant as a triangle can have only one right angle. 4) With the lengths of two sides and the measurement of the included angle (also known as Side-Angle-Side or SAS), you can also construct a unique triangle.

Therefore, with the measurement of two angles and the length of the included side and the lengths of the two sides and the measurement of the included angle, you can construct more than one triangle.

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Answer:

Simplified: 10x-55

Step-by-step explanation:

Distribute the five into the parenthesis..

(5)2x- (5)11

Then, multiply.

10x-55

10x-55 is the simplified version by the distributive property.

Answer:

10x - 55

Step-by-step explanation:

5(2x-11)

5*2x=10x

5*11

10x-55

Answer:

c=45

Step-by-step explanation:

In triangle ABC, if a=12, b=10 and the measure of angle C=45 ..

Answer:

20.4

Step-by-step explanation:

Answer: -1

Step-by-step explanation:

i^42

(i^2)^21 ( NOTE i^2 = -1 )

(-1)^21

-1 ( -1^odd number is -1 )

Answer:

B. 2 x 40 x pi

Step-by-step explanation:

the other answer lead me to the correct answer. I just chose this option on TTM and it was correct.

An expression that can be used to find the circumference of the skating rink, in feet is: (B) 2 ⋅ 40 ⋅ π

The formula to find the Circumference of a Circle is:

C = 2πr

Where:

C is Circumference

r is radius

We are given that the radius is: r = 40 ft

Thus the circumference is:

C = 2 * 40 * π

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Answer:

0

Step-by-step explanation:

Answer:

[tex]5s^2 +13s-10[/tex]

Step-by-step explanation:

Given the expression

[tex]5s(3+s)-(2s+10)[/tex]

First, use distributive property:

[tex]5s(3+s)=5s\cdot 3+5s\cdot s=15s+5s^2\\ \\-(2s+10)=(-1)\cdot (2s+10)=(-1)\cdot 2s+(-1)\cdot 10=-2s-10[/tex]

Now, the given expression is equivalent to the following expression:

[tex]15s+5s^2-2s-10[/tex]

Rewrite this expression using commutative property:

[tex]5s^2+15s-2s-10\\ \\=5s^2 +13s-10 \ [\text{Add the like terms}][/tex]

Answer:

6.93 in

Step-by-step explanation:

[tex]A = s^{2}[/tex]

[tex]48 = s^{2}[/tex]

[tex]\sqrt{48} = \sqrt{s^{2} }[/tex]

[tex]s = 6.92820323028 in[/tex]

Answer:

Step-by-step explanation:

side = √48 = √4*4*3 = 4*√3 = 4 * 1.732 =6.928 in

Final answer:

The answer is 64 green marbles.

Explanation:

To find out how many green marbles are there, we can set up an equation based on the given information. Let G represent the number of green marbles and R represent the number of red marbles. We know that the total number of marbles is 77, so we have the equation G + R = 77. We are also given that the number of green marbles is 1 less than 5 times the number of red marbles, which can be written as G = 5R - 1.

We can solve this system of equations by substituting the second equation into the first equation:

5R - 1 + R = 77

6R = 78

R = 13

Substituting the value of R back into the second equation, we can find the number of green marbles:

G = 5(13) - 1 = 64

Therefore, there are 64 green marbles in the bag.

Answer:

(x/2)*4=3

= x*4/2=3

2x=3

x=1.5

Check:

4*(1.5)/2

=6/2

=3

The given equation is y + 2 = 4(x - 1)

The equation of the parallel line in the slope-intercept form is y = 4x - 7

Step-by-step explanation:

Parallel lines have

The slope-intercept form of the equation of a line is y = mx + b, where m is the slope of the line and b is the y-intercept

∵ The equation of the given line is y + 2 = 4(x - 1)

- Change its form to slope-intercept form to find its slope

∵ y + 2 = 4(x) - 4(1)

∴ y + 2 = 4x - 4

- Subtract 2 from both sides

∴ y = 4x - 6

- Compare it with the slope-intercept form to find m

∵ the slope-intercept form is y = mx + b

∴ m = 4

∵ The parallel lines have same slopes

∴ The slope of the parallel line is 4

- Substitute it in the form of the equation

∴ The equation of the parallel line is y = 4x + b

- To find b substitute x and y in the equation by the

   coordinates of a point on the line

∵ The parallel line passes through point (1 , -3)

∴ x = 1 and y = -3

∵ -3 = 4(1) + b

∴ -3 = 4 + b

- Subtract 4 from both sides

∴ -7 = b

∴ The equation of the parallel line is y = 4x + (-7)

∴ The equation of the parallel line is y = 4x - 7

The equation of the parallel line in the slope-intercept form is y = 4x - 7

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Answer:

[tex]r=4\\ \\s=3\\ \\t=-1[/tex]

Step-by-step explanation:

Given the system of three linear equations:

[tex]\left\{\begin{array}{l}-6r+5s+2t=-11\\ \\-2r+s+4t=-9\\ \\4r-5s+5t=-4\end{array}\right.[/tex]

Cheange the positions of the first and the second equations:

[tex]\left\{\begin{array}{l}-2r+s+4t=-9\\ \\-6r+5s+2t=-11\\ \\4r-5s+5t=-4\end{array}\right.[/tex]

Multiply the first equation by -3 and add it to the second equation and then multiply the first equation by 2 and add it to the third equation:

[tex]\left\{\begin{array}{r}-2r+s+4t=-9\\ \\2s-10t=16\\ \\-3s+13t=-22\end{array}\right.[/tex]

Multiply the second equation by 3, the third equation by 2 and add them:

[tex]\left\{\begin{array}{r}-2r+s+4t=-9\\ \\2s-10t=16\\ \\-4t=4\end{array}\right.[/tex]

From the third equation,

[tex]t=-1[/tex]

Substitute it into the second equation:

[tex]2s-10\cdot (-1)=16\\ \\2s+10=16\\ \\2s=6\\ \\s=3[/tex]

Substitute [tex]t=-1[/tex] and [tex]s=3[/tex] into the first equation:

[tex]-2r+3+4\cdot (-1)=-9\\ \\-2r+3-4=-9\\ \\-2r-1=-9\\ \\-2r=-9+1\\ \\-2r=-8\\ \\2r=8\\ \\r=4[/tex]

Hence,

[tex]r=4\\ \\s=3\\ \\t=-1[/tex]

Answer:

A Factor can be explained as combination of the numerator and denominator by which the demo is decided by the numerator

Answer:

factor a number means to break it up into numbers that can be multiplied together to get the original number. EXAMPLES: 6 = 3 x 2 so, factors of 6 are 3 and 2 9 = 3 x 3 so, factors of 9 are 3 and 3 Sometimes, numbers can be factored into different combinations.

Step-by-step explanation:

Answer:

It has 2 solutions

Step-by-step explanation:

Solution 1

-17(y - 2) = -17y + 64 - 17(y - 2)

Solution 2

-17y + 64 - 17(y - 2) = -17y + 64

-17(y - 2) = -17y + 64

-17y  + 34 = -17y + 64

-17y + 17y = 64 - 34

0 = 30 (incorrect)

this system has NO SOLUTIONS

For this case we must simplify the following expression:

[tex]\frac {3- \frac {2} {a}} {5+ \frac {3} {a}}[/tex]

So, we have:

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

We apply double C:

[tex]\frac {a (3a-2)} {a (5a + 3)} =[/tex]

We simplify:

[tex]\frac {3a-2} {5a + 3}[/tex]

Answer:

The simplified expression is:

[tex]\frac {3a-2} {5a + 3}[/tex]