Name two pairs of congruent angles in the figure. Justify the answer.

Answer:

a.)  x= 11

d.) -7

g.) -5

Step-by-step explanation:

a.) x+1 = 4*3

x=12-1

d.)3x+1=-4*5

3x+1=-20

x=-7

g.)11x-1=-8*7

11x-1=-56

11x=-56+1

x=-5

Answer:

Step-by-step explanation:

[tex]a)\\\dfrac{x+1}{3}=4\\\\\dfrac{x+1}{3}=\dfrac{4}{1}\qquad\text{cross multiply}\\\\(x+1)(1)=(3)(4)\\\\x+1=12\qquad\text{subtract 1 from both sides}\\\\x+1-1=12-1\\\\\boxed{x=11}[/tex]

[tex]d)\\\\\dfrac{3x+1}{4}=-5\\\\\dfrac{3x+1}{4}=\dfrac{-5}{1}\qquad\text{cross multiply}\\\\(3x+1)(1)=(4)(-5)\\\\3x+1=-20\qquad\text{subtract 1 from both sides}\\\\3x+1-1=-20-1\\\\3x=-21\qquad\text{divide both sides by 3}\\\\\dfrac{3x}{3}=\dfrac{-21}{3}\\\\\boxed{x=-7}[/tex]

[tex]g)\\\dfrac{11x-1}{8}=-7\\\\\dfrac{11x-1}{8}=\dfrac{-7}{1}\qquad\text{cross multiply}\\\\(11x-1)(1)=(8)(-7)\\\\11x-1=-56\qquad\text{add 1 to both sides}\\\\11x-1+1=-56+1\\\\11x=-55\qquad\text{divide both sides by 11}\\\\\dfrac{11x}{11}=\dfrac{-55}{11}\\\\\boxed{x=-5}[/tex]

Answer:

Step-by-step explanation:

It could be 42 pencils

Answer:

75/2 (or 37 1/2)

Step-by-step explanation:

Here we're multiplying 4 1/2 by 8 1/3.

Converting both numbers to improper fractions:

9/2 times 25/3, or

9      25

---- * ------

 2       3

Reducing the fractions, we get:

3      25

---- * ------ = 75/2 (answer)

 2       1

The value of the given expression is 36.

Use the concept of fraction defined as:

A fraction is part of a whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p / q.

Given that,

[tex]s = 4\dfrac{1}{2}[/tex]

We have to calculate [tex]8\dfrac{1}{3} \test{s}[/tex]

Now convert both fractions into improper fractions,

[tex]4\dfrac{1}2} = \dfrac{8 + 1}{2}\\\\4\dfrac{1}{2} = \dfrac{9}{2}\\\\[/tex]

And [tex]8\dfrac{1}{3} = \dfrac{24}{3}[/tex]

Now we have,

s = 9/2

Therefore,

[tex]8\dfrac{1}{3}s = \dfrac{24}{3}s\\\\8\dfrac{1}{3}s = \dfrac{24}{3}\times\dfrac{9}{2}\\\\[/tex]

Simplifying we get,

[tex]8\dfrac{1}{3}s = 12 \times 3\\\\ 8\dfrac{1}{3}s = 36[/tex]

Hence the value of the expression is 36.

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Answer: 28 inches

Step-by-step explanation:

Side1 + side 2 + side 3 =

7 inches + 8 inches + 13 inches =

28 inches

Answer:

-2/3

Step-by-step explanation:

m=(6-4)/(-2-1)=2/-3=-2/3

Answer:

[tex]\large\boxed{m=-\dfrac{2}{3}}[/tex]

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (1, 4) and (-2, 6).

Substitute:

[tex]m=\dfrac{6-4}{-2-1}=\dfrac{2}{-3}=-\dfrac{2}{3}}[/tex]

Answer:

1:3

Step-by-step explanation:

Sugar : Flour

2 : 6  (substitute the numbers of cups)

1 : 3    (simplify by reducing. divide both sides by 2)

The ratio is 1:3.

Answer:

1:3

Step-by-step explanation:

2:6[sugar is to flour]

1:3[to simplify divide both sides by two]

Answer:

B

Step-by-step explanation:

4 units is the answer. i got an 100% on the quiz

The triangle missing from the question has attached and the opposite side of angle B is 4 units.

A triangle is a three sides lines geometry in which the sum of all angles is 180°.

Given that a triangle ABC and has sides as

AB = 4

BC = 3

AB = 5

It's clearly visible that the opposite side of angle B is AC which has length as 4 units.

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Answer:

C, the answer is 62.

Step-by-step explanation:

Well, 1 x 62 is 62 so that's the only factor of 62 out of all of them.

Answer:

The answer is b = 1/24.

Step-by-step explanation:

Given:

25+11/12b=47.

Now, to solve the equation to get the value of b:

[tex]25+\frac{11}{12b}=47[/tex]

Subtracting both sides with 25 we get:

[tex]\frac{11}{12b}=22[/tex]

Multiplying both sides by 12b we get:

[tex]11=264b[/tex]

Dividing both sides by 264 we get:

[tex]\frac{1}{24}=b[/tex]

Therefore, the answer is b = 1/24.

Answer:

k = 0.28

Step-by-step explanation:

The price of peaches at Al's supermarket can be determined by the equation P = 0.28n ........... (1)

where P is the price and n is the number of pounds of peaches.

Now, it is clear that the price of peaches is proportional to the number of pounds of peaches.

So, we can write,

P ∝ n

⇒ P = kn ............. (2) where k is the constant which we have to multiply to covert from proportionality to equation form.

Now, comparing equations (1) and (2) we get k = 0.28 which is the value of the constant of proportionality. (Answer)

Final answer:

The constant of proportionality in the equation p = 0.28n is 0.28, representing the price per pound of peaches at Al's supermarket.

Explanation:

The constant of proportionality in the equation p = 0.28n, where P is the price and n is the number of pounds of peaches, is 0.28. This constant represents the price per pound of peaches at Al's supermarket. When you want to compute the amount spent on peaches, you multiply the quantity (in pounds) by this constant of proportionality, which is the price per pound. As an example, if you have 10 pounds of peaches, the total cost would be calculated as 10 pounds × $0.28 per pound, resulting in a total of $2.80 for the peaches.

There should be a typo in the question: the correct formula would be

[tex]X\cap(Y\cup Z)=(X\cap Y)\cup (X\cap Z)[/tex]

Let's compute [tex]X\cap (Y\cup Z)[/tex] first. We have

[tex](Y\cup Z)=\{1, 4, 5, 6, 7, 8, 9\}[/tex]

If we intersect this set with X, we have

[tex]X\cap (Y\cup Z) = \{5, 8, 9\}[/tex]

So, that would be the left hand side. For the right hand side, we have

[tex]X\cap Y = \{8\},\quad X\cap Z = \{5,9\}[/tex]

And their union is again [tex]\{5,8,9\}[/tex]

Final answer:

The intersection of two sets can be proven using a membership table for the given sets X, Y, and Z.

Explanation:

The intersection of two sets, written as AnB, is a set consisting of all elements that are both in A and B. We can use a membership table to prove the following equation: X ∩ (Y ∪ Z) = (X ∩ Y) ∪ (Y ∩ Z).

3 x 3 x 3 x 3 x 23 = 1,863. It can also be written in exponential form as 3 to the power of four times 23.

Answer:

Step-by-step explanation:

[tex]\begin{array}{c|cc}1863&3\\621&3\\207&3\\69&3\\23&23\\1\end{array}[/tex]

Answer:

Unit price = $1.31/roll

Step-by-step explanation:

Divide total cost by number of units:

$10.48 / 8 rolls = $1.31/roll

Answer:

115 yards per minute

Step-by-step explanation:

575/5= 115

Answer:

115 yds per minute

The drawing will help

Answer:

6/12

Step-by-step explanation:

A fourth of 8 is 2, so there would be 6/12 of the tub of frosting left.

Answer:

5/12

Step-by-step explanation:

8/12=2/3

2/3-1/4=8/12-3/12=5/12

Answer:

The slope of the given line 1 is  -4/5.

The slope of the given line 2 is  0.

The line 2 has a greater slope then line 1.

Step-by-step explanation:

The slope of a line with points (x1,y1) and (x2,y2) is given as:

[tex]m = \frac{y_2- y_1}{x_2-x_1}[/tex]

Now, Here the, points of the line 1 are A (-2,7) and B (3,3)

So, here, the slope of line AB  is [tex]m = \frac{3 -7}{3-(-2)}  = \frac{-4}{3 +2} =   \frac{-4}{5}[/tex]

Hence, the slope of the given line 1 is  -4/5.

Now, Here the, points of the line 2 are P (5,1) and Q (9,1)

So, here, the slope of line PQ  is [tex]m = \frac{1-1}{9-5}  = \frac{0}{4} =   0[/tex]

Hence, the slope of the given line 2 is  0.

Now, as we can see  0    >  ( -4 / 5)

So, the line 2 has a greater slope then line 1.

Answer: C

Step-by-step explanation:

The answer is C because it says 360 and 300. If you do a problem solve for that one on a peace of paper I think it would be 16.7%

Answer:

Step-by-step explanation:

Change in number = number visited in 1st week - number visited in 2nd week

= 360-300 = 60

So percentage change in number= 60/360×100=16.67

Answer:

3(x - 3)²

Step-by-step explanation:

Given

3x² - 18x + 27 ← factor out 3 from each term

= 3(x² - 6x + 9)

= 3(x - 3)² ← in factored form

Answer:2

Step-by-step explanation:if she deposits 10 dollars every week she would be adding 10 dollars which means we have to multiply 10 by however many weeks she saves

Sarah's weekly deposits after h weeks can be calculated using the linear equation D = 200 + 10h. This equation includes her starting balance of $200 and adds $10 for each week.

The subject of this question is Mathematics, specifically focusing on the concept of linear equations.

The correct formula to show Sarah's deposits at the end of h weeks would be (3) D = 200 + 10h. This formula works by establishing 200 as her starting amount (her current bank balance), and adding $10 for each week (h).

For instance, if h was 5 weeks, Sarah would have D = 200 + 10 * 5 = 200 + 50 = $250 in her bank account. This demonstrates how the formula allows you to calculate her weekly deposits effectively.

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The greatest possible length of each  piece is 16 inches

Latisha has two pieces of ribbon. One piece of ribbon is 48 inches and  the other is 80 inches

Ribbon is to be cut into pieces of equal length

To find the greatest possible length of each piece, we have to find greatest common divisor of 48 and 80

The greatest common factor, or GCF, is the greatest factor that divides two numbers

Steps to find G.C.F of 48 and 80

1) Find the prime factorization of 48

[tex]48 = 2 \times 2 \times 2 \times 2 \times 3[/tex]

2) Find the prime factorization of 80

[tex]80 = 2 \times 2 \times 2 \times 2 \times 5[/tex]

3) To find the GCF, multiply all the prime factors common to both numbers:

Therefore, [tex]GCF = 2 \times 2 \times 2 \times 2 = 16[/tex]

So, 16 inches is the greatest possible length to cut so that every piece is of equal length.

Answer:

a doesn't equal 0

Step-by-step explanation:

State under which condition the original and the simplified expressions are equivalent

249 children and 394 adults swam at the public pool.

Step-by-step explanation:

Number of people swam at pool = 643

Receipts = $1161.50

Cost for one child = $1.50

Cost for one adult = $2.00

Let,

x be the number of children

y be the number of adults

According to given statement;

x+y=643    Eqn 1

1.50x+2.00y = 1161.50   Eqn 2

Multiplying Eqn 1 by 2

[tex]2(x+y=643)\\2x+2y=1286\ \ \ Eqn\ 3\\[/tex]

Subtracting Eqn 2 from Eqn 3

[tex](2x+2y)-(1.50x+2.00y)=1286-1161.50\\2x+2y-1.50x-2.00y=124.50\\0.5x=124.50[/tex]

Dividing both sides by 0.5

[tex]\frac{0.5x}{0.5}=\frac{124.50}{0.5}\\x=249[/tex]

Putting x=249 in Eqn 1

[tex]249+y=643\\y=643-249\\y=394[/tex]

249 children and 394 adults swam at the public pool.

Keywords: linear equation, subtraction

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If there is a 30% chance of it raining, then that means there is a 70% chance of it not raining.

100%-30%=70%

Answer: 70%

Step-by-step explanation: In terms of probability, 100% is the maximum which means something is certain. There are some occasions where it can be higher than 100% like dealing with percent increase or decrease, but in this case, we're talking about 100%.

In this problem, we're given that the probability of rain for tomorrow is 30% and we're asked to find the probability that it will not rain.

Since 100% will be the maximum when dealing with probability, we will subtract the chance it will rain tomorrow which is 30% from 100%.

100% - 30% = 70%.

Therefore, the probability/chance it will not rain is 70% which means it's likely it will not rain.

I copy the complete questions again to make them clearer:

Priya and Han are biking in the same direction on the same path.

a. Han is riding at a constant speed of 16 miles per hour. Write an expression that shows how many miles Han has gone after    [tex]t[/tex]     hours.

b. Priya started riding a half hour before Han. If Han has been riding for     [tex]t[/tex]     hours, how long has Priya been riding?

c. Priya is riding at a constant speed of 12 miles per hour. Write an expression that shows how many miles Priya has gone after Han has been riding for     [tex]t[/tex]     hours.

d. Use your expressions to find when Han and Priya meet.

Answer:

Explanation:

a. Since Han is riding at a constant speed of 16 miles per hour, the number of miles that he has gone is proportional to the number of hours, t, that he has been riding, the constant of variation is 16, and the expression for the number of miles he has gone is:

Where, H is the number of miles Han has gone, and t is the number of hours.

b. Since Priya started riding a half hour before Han, you have to add 1/2 or 0.5 to the time of Han, which is t, to express how long Priya has been riding:

c. Since, Priya is riding at a constant speed of 12 miles per hour, the number of miles that she has gone is proportional to the number of hours, t + 0.5, that she has been riding, the constant of variation is 12, and the expression for the number of miles she has gone is:

Where P is the number of miles Priya has gone, and t is the number of hours since Han is riding.

d. To find when Han and Priya meet, you just need to solve the sytem of equations, making H = P, which means that the number of miles that both Han and Priya rides is equal:

[tex]H=P\\ \\ 16t=12(t+0.5)\\ \\ 16t=12t+6\\ \\ 4t=6\\ \\ t=6/4=3/2=1.5[/tex]

Which means that they meet when it has passed 1.5  hours since Han started riding.

Answer: There are 16 cups in every gallon so we could divide 152 by 16 and get our number of gallons which would give us 9.63 or a little over 9 and a half gallons.

Step-by-step explanation:

Answer:

x=-117/4

Step-by-step explanation:

5x-15+130=x-2

5x-x+115=-2

4x+115=-2

4x=-2-115

4x=-117

x=-117/4

Answer:

Step-by-step explanation:

it is 145/25 which is reduced to 29/5

Answer:

5 19/25

Step-by-step explanation:

To determine the number of seats left in the basketball arena, the number of tickets sold (5,134) is subtracted from the total arena capacity (7,000), resulting in 1,866 seats remaining available.

A basketball arena can hold approximately 7,000 people.

Fans bought 5,134 tickets before the game.

The number of seats left to fill before the game can be calculated by subtracting the tickets bought from the total arena capacity: 7,000 - 5,134 = 1,866 seats left to fill.

Answer:

0.41

Step-by-step explanation:

formula;  y = kx (where k is the constant variation)

the standard equation representing direct variation

y = 0.41 x is the equation to find the constant of proportionality

so, K = 0.41