State whether each sentence is true or false. If false, replace the underlined word or phrase to make a true sentence.
The vertex angles of an isosceles triangle are congruent.

If Tamika receives 20 rewards points just for signing up and she earns 10.5 points for each visit to the movie theater and she needs 167 points for a free movie ticket, then an equation to determine x, the number of visits Tamika must make to earn a free movie ticket is 10.5x + 20 = 167 and the value of x is calculated to be 14.

The number of visits Tamika must make can be determined by using a linear equation with one variable.

As,

reward points for signing up = 20

points for each visit = 10.5

points needed for free movie ticket = 167

If we consider x to be the number of visits required, then the linear equation can be given as,

10.5x + 20 = 167

Solving for x,

10.5x = 167 - 20

10.5x = 147

x = 147/10.5 = 14

Hence, the number of visits Tamika must make to earn a free movie ticket is equal to 14.

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The integer value of the mathematical statement  is -2

The mathematical statement is given as:

- 2 Feet taller

- 2 Feet taller implies that we have a negative integer -2

i.e.

Value = -2

Hence, the integer value of the mathematical statement  is -2

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There are 10 people in the 16-18 group , 22 people in the 19-24 group and 18 people who are 25+ in the stratified sample.

A method of sampling from a population that can be divided into subpopulations is known as stratified sampling in statistics. When subpopulations within a larger population differ in statistical surveys, it may be desirable to sample each subpopulation separately.

From the given table we can calculate the total of population:

population = 120 + 250 + 200 = 570 people

Now since it is a stratified sample, the ratio of each age group is equal in the sample as in the population.

∴Number of people in the 16-18 group :

[tex]=\frac{120}{570} \times 50\\\\=10.52[/tex]

∴Number of people in the 19-24 group :

[tex]=\frac{250}{570} \times 50\\\\=21.929[/tex]

∴Number of people in the 19-24 group :

[tex]=\frac{200}{570} \times 50\\\\=17.543[/tex]

Now as 10.52 is closer to 10 than 17.54 is closer to 17 , we will round off 10.52 to 10.

Hence there are 10 people in the 16-18 group , 22 people in the 19-24 group and 18 people who are 25+  in the stratified sample.

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The midpoint is at (0,0,0,)

In the given statement is

To find the midpoint of the line segment joining the pair of points

K(2,2,0) and L(-2,-2,0)

Midpoint:

The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.

m = (A +B)/2

If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =([tex]\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} , \frac{z_{1}+z_{2} }{2}[/tex])

where:

(x1 , y1 ,z1) are the coordinates of the first point:

(x2 , y2 , z2) are the coordinates of the second point:

Now, We are given the three points K(2,2,0) and L(-2,-2,0)

Solving for the midpoint , we have,

m = ([tex]\frac{2+(-2) }{2} ,\frac{2+(-2)_{} }{2} ,\frac{0+0}{2}[/tex])

m = (0 , 0 , 0)

Therefore, the midpoint is at (0, 0, 0,)

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Simplification of the each sum or difference of the given equation [tex]\frac{d-3}{2d+1}+\frac{d-1}{2d+1}[/tex] is equal to 2(d-2)/(2d+1). Restriction on the variables is given by d≠ (-1/2).

As given in the question,

Given equation is [tex]\frac{d-3}{2d+1}+\frac{d-1}{2d+1}[/tex]

Simplify it by taking least common multiple of the denominator,

[tex]\frac{d-3}{2d+1}+\frac{d-1}{2d+1}\\\\\\=\frac{d-3+d-1}{2d+1}\\ \\=\frac{2d-4}{2d+1}\\ \\=\frac{2(d-2)}{2d+1}[/tex]

Restriction on the variables is given by d≠ (-1/2).

Therefore, simplification of the each sum or difference of the given equation [tex]\frac{d-3}{2d+1}+\frac{d-1}{2d+1}[/tex] is equal to 2(d-2)/(2d+1).Restriction on the variables is given by d≠ (-1/2).

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The numerical coefficient in -7yz²  from the expression 5x⁶+3xy-7yz²+2y/z   is  -7 .

A Numerical Coefficient in an Algebraic Expression is defined as the integer value which is written along with the variable .

For Example : the numerical coefficient in 7xy is 7 , and in -5x is -5 as 7 and 5 are the only numerical value along with the variable y and x respectively.

In the question ;

the given Algebraic Expression is 5x⁶+3xy-7yz²+2y/z  

the numerical coefficient in -7yz² is -7 , as -7 is the only  numerical value in -7yz² .

Therefore , the numerical coefficient in -7yz²  from the expression 5x⁶+3xy-7yz²+2y/z   is  -7 . the correct option is (d) -7 .

The given question is incomplete , the complete question is

In the expression 5x⁶+3xy-7yz²+2y/z  , which of the following choices is the numerical coefficient in -7yz²  ?

(a) 2

(b) 3

(c) 5

(d) -7

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Answer:

184

Step-by-step explanation:

My mom is a teacher lol

Answer:

∠9 and ∠11

Step-by-step explanation:

Vertical angles are congruent, and angles 9 and 11 are vertical.

According to the question, to calculate the probability of the event which states that to draw a card from the standard deck but the condition is not getting the diamond.

The total number of the playing cards are [tex]52[/tex]

And total number of diamond cards are [tex]13[/tex]

Therefore, the total number of favorable outcomes in which diamond is not there is [tex]52-13 = 39[/tex]

As per question, the probability can be written as:

P(no diamond card) = [tex]\frac{39}{52} = \frac{3}{4}[/tex]

Hence, the probability of not getting a diamond card is [tex]\frac{3}{4}[/tex].

What is Probability?

The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.

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By using the fact that the internal angles of a triangle always add up to 180°, we will see that x = 100°.

Remember that the sum of all the internal angles of a triangle is always equal to 180°.

On the image we can see two triangles, let's define the angle at the right as A. and the angle at the left as B

We can write:

A + B + x = 180°

And for the inner triangle the angles give:

A/2 + B/2 + 140° = 180°

So we have a little system of equations:

A + B + x = 180°

A/2 + B/2 + 140° = 180°

If we multiply the second equation by 2 we get:

A + B + 280° = 360°

With the first equation we can write:

A + B = 180° - x

And replace that in the above equation

(A + B) + 280° = 360°

180° - x + 280°  = 360°

Now we can solve this to get the value of x:

180° + 280° - 360° = x = 100°

We conclude that the measure of angle x is 100°

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Answer:

Y=7x+1

Step-by-step explain

formula is y=mx+b

your slope is your M and the y-intercept is your B

Answer: 52x^200 + 4x+4x^4

Step-by-step explanation:

Answer: a) 4

Step-by-step explanation:

sides should be equal according to the shape.

7x-2=12x-22

The height of this painting is 4 2/5 cm.

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

It is given that Nisha likes to make small rectangular paintings of cats. Also One of her paintings has an area of 33 cm² and a width of 7/1/2 cm.

The area of the rectangle = length × Width

Now substitute the values;

Area= L x W

33 cm² = L x 7/1/2 cm

33 divided by 7 1/2

L = 4 2/5

Therefore, the height of this painting is 4 2/5 cm.

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Answer:

[tex]\{x \in \mathbb{R}|-4 \le x \le -8\}[/tex]

Step-by-step explanation:

The equation of the line in point-slope form, which passes through the pair of points located at A(-3 , 12) and B(9 , -4), is y - 12 = -4/3(x + 3).

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Getting the slope of the two points: A(-3 , 12) and B(9 , -4).

m = (y2 - y1)/(x2 - x1)

m = (-4 - 12)/(9 - -3)

m = -16/12

m = -4/3

Using the point slope form, plug in the values of the slope and Point A to set up the equation.

(y - y1) = m(x - x1)

where m = -4/3 and (x1 , y1) = A(-3 , 12)

(y - 12) = -4/3(x - -3)

y - 12 = -4/3(x + 3)

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answer:

it would be negative.

explanation:

when you subtract a value from a value, the result will be left to the larger number. if you subtract a larger number from a smaller number, the value will move left but since the value subtracted is more than the number minus itself, you would be subtracting from 0, therefore resulting in a negative number.

Answer:

13 inches

Step-by-step explanation:

Convert to improper fraction and multiply

13/4 x 4/1 (4's cancel out)

13

Answer:

37777777777999999999999999

The volume of the original block and the volume of the wood removed as polynomials in factored form will be 2x³ + 15x² + 31x + 12 and (x + 2)(x + 1)(2x + 1).

Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as

V = L x W x H

A carpenter hollowed out the interior of a block of wood as shown on the right.

The volume of the original block will be

V = (2x + 1)(x + 3)(x + 4)

V = (2x + 1)(x² + 7x + 12)

V = 2x³ + 14x² + 24x + x² + 7x + 12

V = 2x³ + 15x² + 31x + 12

The volume of the wood removed as polynomials in the factored form will be

V = (x + 2)(x + 1)(2x + 1)

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The first differences for each data set is 120 120 120 120 120 120, and the equation to represent the data pattern is y = 120

The table of values represents the given parameters

On the table of values, we have the following function range

60 180 300 420 540 660 780

Calculate the first differences for each data set

i.e. Difference = Tn - T(n-1) Where n > 1

So, we have

120 120 120 120 120 120

The numbers in the above pattern are the same

So, the equation can be represented as

y = 120

Hence, the first differences for each data set is 120 120 120 120 120 120, and the equation to represent the data pattern is y = 120

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Answer: it is 14526.72

what is finite sequence

According to the question, the probability of the event in which rolling a pair of dice and not getting a 3 is as follows:

What is Probability?

The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.

Probability of not getting 3=  1 - P(getting three)/Total number of events

Probability of not getting 3=1-2/36 = 1-1.18 =17/18

Hence, the probability of not getting three while rolling a pair of dice is 17/18 .

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If you want to buy as many bread rolls as possible from one shop, you should use Paul the baker's shop.

Peter:

Unit rate = $2.30 / 6

= $0.383 per pack of bread rolls

Paul:

Unit rate = $3.50 / 10

= $0.35 per pack of bread rolls

So,

Paul the baker bread rolls is cheaper than Peter the baker bread rolls.

Therefore, If you want to buy as many bread rolls as possible from one shop, you should use Paul the baker's shop.

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Answer:

Step-by-step explanation:

A prime number has only two factors (1 and itself). Hence, two prime numbers cannot have any common factor other than 1. Therefore, the greatest common factor of two prime numbers is always 1. For example, the greatest common factor of 5 and 7 is 1.

When we divide [tex]\frac{pq}{p^{2} -q^{2} } +\frac{q}{q-p}[/tex]  by [tex](p-q) +\frac{4q^{2} -p^{2} }{q+p}[/tex] , we get simplified answer [tex]\frac{1}{3(q-p)}[/tex]

What are algebraic identities?

Algebraic identities are set of rules that are derived from binomial theorem and are used to solve algebraic expressions .

One such identity is [tex]a^{2} -b^{2} =(a+b)(a-b)[/tex]    ....(1)

We have to divide [tex]\frac{pq}{p^{2} -q^{2} } +\frac{q}{q-p}[/tex] by [tex](p-q) +\frac{4q^{2} -p^{2} }{q+p}[/tex], we get

=[tex]\frac{\frac{pq}{p^{2} -q^{2} } +\frac{q}{q-p}}{(p-q) +\frac{4q^{2} -p^{2} }{q-p}}[/tex]

=[tex]\frac{\frac{pq}{(p-q)(p+q) } +\frac{q}{q-p}}{\frac{(p-q)(p+q)+4q^{2} -p^{2} }{q+p}}[/tex]

=[tex]\frac{\frac{pq+q(-1)(p+q)}{(p-q)(p+q) } }{\frac{(p-q)(p+q)+4q^{2} -p^{2} }{q+p}}[/tex]

=[tex]\frac{\frac{pq-q^{2}-pq }{(p-q)(p+q) } }{\frac{p^{2} -q^{2} +4q^{2} -p^{2} }{q+p}}[/tex]

=[tex]\frac{\frac{-q^{2} }{(p-q)(p+q) } }{\frac{3q^{2} }{q+p}}[/tex]

[tex]\frac{-q^{2}(q+p) }{3q^{2} (p-q)(p+q) }=\frac{-1}{3(p-q)}\\ =\frac{1}{3(q-p)}[/tex]

On dividing [tex]\frac{pq}{p^{2} -q^{2} } +\frac{q}{q-p}[/tex] by [tex](p-q) +\frac{4q^{2} -p^{2} }{q+p}[/tex] and simplifying the answer we get [tex]\frac{1}{3(q-p)}[/tex].

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