Proving Vertical Angles Are Congruent

The value of each algebraic expressions are:

1. 16

2. 156

3. 87

4. 3

5. 300

6. 4

7. 68

An algebraic expression is a mathematical statement involving variables and digits. It is evaluated by plugging in the value of the variables.

1. Product of y and 12 is 12y

100 - 12y

Plug in the value of y

100 - 12(7) = 16

2. b(15 + 37) = b(52) = 3(52)

= 156

3. Product of z and 12 is 12z

12z + 27 = 12(5) + 27

= 87

4. 135 ÷ 5c = 135/5(9)

= 3

5. w²(12/4) = 3w²

= 3(10²)

= 300

6. 12d ÷ (25 - 19)

12d/6 = 12(2)/6

= 4

7. 13 + 5x

13 + 5(11)

= 68

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An expression is defined as a set of numbers, variables, and mathematical operations. The correct options are A and C.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given exponential (6⁻¹⁰/6⁻⁴) function can be simplified as shown below,

(6⁻¹⁰/6⁻⁴)

= 6⁻¹⁰ × 6⁴

= 6⁽⁻¹⁰⁺⁴⁾

= 6⁻⁶

= 1/6⁶

Hence, the correct options are A and C.

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Answer:

18

Step-by-step explanation:

substitute x = 5 into g(x) and x = 2 into h(x)

g(5) + h(2)

= 2(5) - 5 + 4(2) + 5

= 10 - 5 + 8 + 5

= 5 + 13

= 18

The average rate of change on the interval (5, 6) is 9. So the correct option is D.

Here we want to find the average rate of change of f(x), the function on the table, on the interval (5, 6).

This is just:

[tex]r = \frac{f(6) - f(5)}{6 - 5}[/tex]

[tex]f(x) = a*x^2 + b*x + c[/tex]

I we look at the table we see that:

[tex]f(1) = 1 = a + b + c[/tex]

[tex]f(2) =2 = 4a + 2b + c[/tex]

[tex]f(3) = 5 = 9a + 3b + c[/tex]

This is a system of equations.

If we subtract the second and first functions, we get:

[tex]2 - 1 = (4a + 2b +c) - (a + b + c)\\1 = 3a + b = a + b + c[/tex]

From that we take two relations:

[tex]1 - 3a = b\\2a = c[/tex]

Now we can replace these two in the last equations so we get:

[tex]5 = 9a + 3b + c\\\\5 = 9a + 3*(1 - 3a) + 2a\\\\5 = 9a + 3 - 9a + 2a\\\\5 = 3 + 2a\\\\5 - 3 = 2a\\\\2 = 2a\\\\a = 1[/tex]

Now that we know the value of a:

[tex]c = 2a = 2*1 = 2\\\\b = 1 - 3a = 1 - 3 = -2[/tex]

The quadratic equation is:

[tex]f(x) = x^2 - 2x + 2[/tex]

Evaluating this in x = 6 we get:

[tex]f(6) = 6^2 - 2*6 + 2 = 26[/tex]

And from the table we know that f(5) = 17, then the average rate of change is:

[tex]r = \frac{f(6) - f(5)}{6 - 5} = \frac{26-17}{1} = 9[/tex]

The correct option is D.

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Answer:

b=5d+5f

solve for b by simplifying both sides and then isolating the variable.

376

Step-by-step explanation:

Answer:

Domain & Range are both all real numbers.

Step-by-step explanation:

i

If this was a traditional parabola, the range would be y<=4. However, the arrow on the left going back up means eventually y will go to both positive & negative infinity.

Using it's concept, it is found that Brandon's net yardage for the game was of 26.

The total net yardage is the sum of all the yardage they gain, that is, the positive gains are added with a plus signal, while the negative gains are added with a negative signal.

Hence, his net yardage, considering that he gained 20 yards on his last 7 carries, is given by:

6 + 20 = 26.

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Answer:

Use the graphing calculator to graph the system of equations and find the solution where x is the total hats sold and y is the total t-shirts sold.

x + y = 152,

8.5x + 12y = 1,656

How many hats were sold?

hats

Step-by-step explanation:

a) 74.857% of adult men are shorter than Michael

b) 84.134% of adult men are taller than Jack

c) 58.991% of adult men are of height between Jack and Michael

Within one standard deviation of the mean is 68% of the population. Within two standard deviations of the mean, 95% of the population is located. The median is within 3 standard deviations for 99.7% of the population.

Given:

µ = 70in,  σ = 3in.

We know Z = (x-µ)/σ

a) Actor Michael B. Jordan is 6’0” (72”) tall.

Z = (72-70)/3 = 0.67

So, the probability of an adult man having a height of 0-72 inches, and no greater is 74.857%

b. Comedian Jack Black is 5’7’ (67”) tall.

Z = (67-70)/3 = -1

The corresponding value is .15866 which can be the probability of an adult man having a height of 0-67 inches, and no greater.

But  the percentage of those taller than jack is = 1 – .15866 = 0.84134

c) P(X < 72) – P(x < 67)

= 0.74857 – 0.15866

= 0.58991

= 58.991%

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The Question attached here is incomplete, the complete question is

a. Actor Michael B. Jordan is 6’0” (72”) tall.  What percentage of adult men are shorter than Michael?

b. Comedian Jack Black is 5’7’ (67”) tall. What percentage of adult men are taller than Jack?

c. What percentage of adult men are of height between Jack and Michael?

The Gershwin Theatre collected the money from ticket sales of the Saturday performance would be $89180.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

At the Saturday matinee, 350 people attended the show.

The total number of people who watched the show on Saturday = 350

For the Saturday evening performance, 40% more people attended the performance.

350 x 40%

= 350 x 0.4

= 140

Total people will be = 350 + 140 = 490

If the average cost of tickets was $182

For 490 people = 490 x 182 = $89180

Hence, the Gershwin Theatre collected the money from ticket sales of the Saturday performance would be $89180.

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Answer:

3 days, 27

Step-by-step explanation:

After 3 days :

After 3 days, the number of belts and wallets sold will be the same, equal to 27.

After 3 days, the number of belts and wallets sold will be the same, equal to 27.

It is given that the number of belt sold s, x days after its online lunch  s=3^x

and s=4x+15.

To find correct answer in each box.

The branch of mathematics dealing with the properties and manipulation of numbers.

After 3 days :

3³ = 27 belts

4(3) + 15 = 12 + 15 = 27 belts

So, after 3 days, the number of belts and wallets sold will be the same, equal to 27.

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Answer:

45

Step-by-step explanation:

The coordinates of the image of point B after the triangle is rotated 270° about the origin is (4, 2)

The complete question is added as an attachment

From the attached image, we have the following coordinate

B = (-2, 4)

When the triangle is rotated by 270 degrees, the rule of rotation is:

(x, y) ⇒ (y, -x)

For point B, we have:

B' = (4, 2)

Hence, the coordinates of the image of point B after the triangle is rotated 270° about the origin is (4, 2)

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Answer:

I'll do it the answer to x is 5 0 the answer to y will be 0 10

Answer:

see the attachment photo!

The value of the x will be 25. The force involved vertically to the surface of an object per unit area is pressure.

The force applied perpendicular to the surface of an item per unit area across which that force is spread is known as pressure.

The given data in the problem is;

The base of the block of metal is a rectangle of 20 cm by x cm.

The block exerts a force of 1500 newtons on the ground. The pressure on the ground is 3 newtons/cm²

The area of the rectangle;

A = L × B

A=20 × x

[tex]\rm P = \frac{F}{A}\\\\ 3 N / cm^2 = \frac{1500 N}{20 \times x } \\\\ x= 25[/tex]

Hence the value of the x will be 25.

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A percentage is a way to describe a part of a whole. The amount Emily shared is $30.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Emily works at a local restaurant. She made $200 in tips last night. She shared 15% of her tips with the crew that cleans the tables. The amount Emily shared is,

15% of $200

= 0.15 × $200

= $30

The amount Emily shared is $30.

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Subtraction is a mathematical operation that reflects the removal of things from a collection. The ribbon that Millie already had is 7.1 feet.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

Given Millie needs a total of 7.8 feet of ribbon for a school project. Also, She needs 0.7 more feet of ribbon. Therefore, the ribbon that Millie needs is,

Ribbon Millie had = Total Ribbon - ribbon that is needed

                              = 7.8 feet - 0.7feet

                              = 7.1 feet

Hence, the ribbon that Millie already had is 7.1 feet.

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The quotient of the synthetic division problem is "f(x) = -2x² + 9x + 5" (Option C).

When a polynomial division is executed using the shorthand method, using a linear factor, one is  said to have executed a Synthetic Division.

The synthetic division translates to

- 2 15 -22 -15

3 | -6 27 15

-2 9 5 0

Citing the coefficient of the quotient of the first three numbers:

- 2, 9, 5. The last number is given as the remainder.

Hence the remainder is zero.

Given that the coefficient of the quotient are three, the interpretation is that the polynomial greatest degree is 2.

Thus,

f(x) = -2x² + 9x + 5

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The amount of zippy's gross profit (otherwise know as gross margin) is: $25,337.

Sales revenue $43,189.84

(7,796 units × $5.54)

Less Cost of goods sold $17,852.84

[($22,900/10,000)×7,796]

Gross profit $25,337

( $43,189.84-$17,852.84)

Therefore the amount of zippy's gross profit (otherwise know as gross margin) is: $25,337.

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Answer:

1 - [tex]1^{2}[/tex]

12 - ?

4 - square root of 16

64 - [tex]8^{2}[/tex]

16 - [tex]4^{2}[/tex]

2.828 - square root of 8

Step-by-step explanation:

I need more terms to match

Square root of 16 is 4, square root of 8 is 2, but for an answer it would be , 4² is 16, 1² is 2, number 5 would be 64 and number 6 would be 12.

A mathematical value can generally be any specific mathematical object. This is most frequently a number in elementary mathematics, such as a real number like or an integer like 42. Every integer or even other mathematical object set to a variable or constant is that object's value.

A mathematical expression's value is the outcome of a computation it describes when its variables and constants are given values. The amount that the function assumes for these argument numbers is the result of a function, assuming the value(s) provided to its argument(s).

Square root of 16 is 4, square root of 8 is 2, but for an answer it would be , 4² is 16, 1² is 2, number 5 would be 64 and number 6 would be 12.

Therefore, Square root of 16 is 4, square root of 8 is 2, but for an answer it would be , 4² is 16, 1² is 2, number 5 would be 64 and number 6 would be 12.

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Considering that 160,000 is the y-intercept of the function, it's significance is given by:

the initial population at the time of the estimation.

The y-intercept is f(0), that is, the value of y when x = 0, which is interpreted as the initial value of the function.

Researching this problem on the internet, it is found that f(0) = 160,000, hence the significance of 160,000 in the function is given by:

the initial population at the time of the estimation.

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To use the additive inverse to evaluate an expression that uses subtraction, change the sign of the number to positive

Additive inverse is simply changing the sign of a number and then adding it to the original number to get an answer that is equal to 0.

The additive inverse of a  number is another number

The additive inverse of number 3 is - 3

For an expression that uses subtraction, to use the additive inverse, change the sign of the number to positive

Thus, to use the additive inverse to evaluate an expression that uses subtraction, change the sign of the number to positive

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Answer:

the angle that has the same measure as /2 is A

Answer:

all angles of the triangles is 60

Step-by-step explanation:

the perimeter = 2*side of an isosceles triangle + bottom edge

----> bottom edge = the perimeter - 2*side of an isosceles triangle  =25

----> This is an equilateral triangle ----> all angles of the triangles is 60

The results of the arithmetic evaluations as given in the task content are; 40,42 and 62.

The arithmetic operations above can be evaluated and simplified as follows;

(11-8)x3+7+27-3 = (3×3)+7+27-3 = 40.

(18÷3)+6+(14-8)x5 = (6)+6+(6)x5 = 42.

(11-7)x6+4+32-4 = (5×6) +4 +32-4 = 62.

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Answer:

g = 24 - 1/25m

Step-by-step explanation:

Since the Cadillac Escalade can travel 25 miles per gallon, each mile the Escalade travels is 1/25th of a gallon of gas.

This means that every mile the Escalade travels, 1/25th of a gallon is subtracted from the gas tank. Since the gas tank has a capacity of 24 gallons, the value of the gas tank is 24.

This leads us to the equation:

g = 24 - 1/25m

where g is the amount of gas left, and m is the number of miles driven.