State whether the sentence is true or false. If false, replace the underlined term to make a true sentence.

Geometric probability involves a geometric measure such as length or area.

The equation of the line r is y = ₋(10/9)x ₊ 7.

Given, parallel lines have the same slope. Solve for the slope in the first line by converting the equation to slope intercept form

equation of line q is y = ₋10/9x ₊ 2

it's already in slope intercept form.

hence slope is:

m = (₋10/9) from the above the equation.

we know that the second line will also have a slope of ₋10/9 and we are given the point (9 , ₋3). We can setup an equation in slope intercept form and use these values to solve for the y inetrcept.

y = mx ₊ b

₋3 = ₋10/9 (9) ₊ b

₋3 = ₋10 ₊ b

b = 7

plug the y intercept back into the equation to get our final answer.

y = ₋(10/9)x ₊ 7

hence  we get the equation of the line r as y = ₋(10/9)x ₊ 7.

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Using z-scores, it is found that:

The value is 0.79 standard deviations below the mean.

The z-score of a measure X of a variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, the parameters are given as follows:

[tex]X = 86, \mu = 101, \sigma = 19[/tex]

Hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (86 - 101)/19

Z = -0.79.

The value is 0.79 standard deviations below the mean.

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So, the statement we are provided with is that,

A classmate says that the systems consisting of

x = 0, y = 0 and, z = 0 has no solution.

This statement is clearly wrong, and we look at the points/ conditions that make this statement completely invalid.

Firstly, a system cannot have only zeros like here. In this case, we have zeros for all three terms (x, y, and z).

Secondly, there will be only one answer for this system, which will be a non-zero value or no answer.

Hence one variable is at least not equal to zero for a proper system.

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Answer:

628=10^h

Step-by-step explanation:

Solve for h in the equation above and you will get your answer. Hope this helps!

The total number of possible solutions for both the inequalities to be true at the same time are 3.

Inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.

Given in the question is the solution of two inequalities as a function of x.

Since, both the inequalities must be true at the same time, this means that only those solutions will be taken into consideration which are common to both. In order to do so, we have to find the intersection of the sets representing their solutions. Now,

Solution set for inequality 1 → S[1] ∈ [-3, 2)

Solution set for inequality 2 → S[2] ∈ (-1, 4]

The set representing the solution for the existence of both the inequalities at the same time is -

S = S[1] ∩ S[2] = [-3, 2) ∩ (-1, 4] = [0, 1, 2]

n(S) = 3

Therefore, the total number of possible solutions for both the inequalities to be true at the same time are 3.

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Answer:

M' (- 1, 2 )

Step-by-step explanation:

under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

M (1, 2 ) → M' (- 1, 2 )

Answer:

0.029

Step-by-step explanation:

The answer

Answer:

Step-by-step explanation:

Perimeter of rectangle = 2(Length+Breadth)

Length= (2+x)ft

Breadth= 3ft

Perimeter= 28ft

P=2(L+B)

[tex]28 = 2((2 + x) + 3) \\ 28 = 2(2 + x + 3) \\ 28 = 2(5 + x) \\ 28 = (2 \times 5) + (2 \times x) \\ 28 = 10 + 2x \\ [/tex]

Collect like terms

[tex]28 - 10 = 2x \\ 18 = 2x \\ \\ \frac{18}{2} = \frac{2x}{2 } \\ \\ 9 = x \\ x = 9[/tex]

Checking

P= 2(L+B)

[tex]28 = 2((x + 2) + 3) \\ 28 = 2((9 + 2) + 3) \\ 28 = 2(9 + 2 + 3) \\ 28 = 2(14) \\ 28 = 2 \times 14 \\ 28 = 28[/tex]

Confirmed

Answer:

3 1/6

Step-by-step explanation:

Hope this helps you :)

Answer:

3 1/6.

Step-by-step explanation:

4 1/2 - 1 1/3

= 9/2 - 4/3

= 27/6 - 8/6

= 19/6

= 3 1/6.

First, he convert the terms into a positive sign, then he replaces the terms, then he used additive and division property for equality.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Ilya was rewriting expressions using the parameters. His work is flawless this time around.

The steps of the solution are given below.

1) 3x - 12 + 7 - 5x = 91

2) 3x + -(12) + 7 + (-5x) = 91

In the 2nd step, he converts all the terms with a positive sign.

3) 3x + (-5x) + (-12) + 7 = 91

In the 3rd step, he places the like terms closer.

4) (3+-5)x + (-12) + 7 = 91

In the 4th step, he took common from the first two terms.

5) -2x + (-5) = 91

6) -2x + 5 + (-5) = 91 +5

In the 6th step, he used the additive property for equality.

7) -2x = 96

8) (-1/2) × (-2x) = 96 × (-1/2)

And in the 8th step, he used division property for equality.

9) x = - 96/2

10) x = - 48

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The equation of the line in slope-intercept form with a slope of 4/5 and y-intercept of (0 , 7) is y = (4/5)x + 7.

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

The slope-intercept form of the equation of a line is given by the formula:

y = mx + b

where m is the slope of the line

b is the y- intercept

Given that the slope of the line is 4/5 and the y-intercept is (0 , 7), write the equation of the line by simply plugging in its values.

y = mx + b

y = (4/5)x + 7

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The product of the irrational numbers 4√21 and 9√6 in simplest radical form is 108√14.

In this problem we must find the product of two radical numbers, whose procedure has to be done by radical properties and other properties:

4√21 × 9√6                           Given

4√(3 × 7) × 9√(2 × 3)             Definition of multiplication

(4√7 × √3) × (9√2 × √3)       Root square of a product

(4√7 × 9√2) × (√3 × √3)       Associative property

36√14 × 3                              Definition of power / Root square of a product

108√14                                  Associative property / Definition of multiplication / Result

The statement is poorly formatted. The correct form is shown below:

What is the product of 4√21 and 9√6 in simplest radical form?

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The coordinates of line segment are (2,2)

The section formula is the method used to get the coordinates of a point on a line segment that divides it into two segments.Lets’s imagine that the line segment marked with the coordinates A ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and B has a point P(x,y) that splits it ([tex]x_{2}[/tex],[tex]y_{2}[/tex]). To find the coordinates, we use the section formula, which is described mathematically as.

P(x, y) =([tex]\frac{m.x_{2}+n.x_{1} }{m+n}[/tex],[tex]\frac{m.y_{2}.n.y_{1} }{m+n}[/tex])

Given that : the point on the directed line segment from (-6,-10) to (6,8) that partitions the segment into a ratio of 2 to 1

Consider two points P([tex]x_{1} ,y_{1}[/tex]) and Q([tex]x_{2},y_{2}[/tex]).Finding the coordinates of the point R that divides PQ in the ratio m: n is necessary because [tex]\frac{PR}{RQ}[/tex] = [tex]\frac{m}{n}[/tex].

Here , p = (-6, -10)

Q= (6, 8)

m :n = (2,1)

x = [tex]\frac{m.x{2} +n.x_{1} }{m+n}[/tex]

y = [tex]\frac{m.y_{2}+n.y_{1} }{m+n}[/tex]

by putting value we get,

x= 2 , y= 2

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Step-by-step explanation:

12c-4c-9d+d

8c-8d..........

Answer:

8c - 8d

Step-by-step explanation:

Combine like terms..

12c-9d-4c+d

8c - 9d + d

then combine the other like terms then you will get

8c - 8d

Answer:

idududydysehwghsysysgsbebeywyehe

Answer:

S₇ = 127

Step-by-step explanation:

the sum to n terms of a geometric series is

[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^n-1) }{r-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 1 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{2}{1}[/tex] = 2 , then

S₇ = [tex]\frac{1(2^7-1)}{2-1}[/tex] = [tex]\frac{2^7-1}{1}[/tex] = [tex]2^{7}[/tex] - 1 = 128 - 1 = 127

The value of the unknown variable x in the equation x² + 5² = 13² is 12.

The use of numbers and words in the same mathematical equation is considered as an algebraic expression.

We can calculate the square of a number by multiplying the number by itself.

Therefore, the square of 5 is equal to 5 multiplied by 5 which is equal to 25.

While the square of 13 is equal to 13 multiplied by 13 which is equal to 169.

So to find the value of x, we can rearrange the given equation as:

x² = 13² - 5 ²

x² = 169 - 25

x² = 144

As x² is equal to 144, we can calculate the value of x by taking the square root of the value of 144.

Therefore,

x= √144

x= 12

Hence, the value of the unknown variable x in this equation is 12.

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The function rule for g(x) is g(x) = -6x

The equation of the function f(x) is given as

f(x) = 6x

From the question, we understand that:

The function g(x) is the reflection of the function f(x) over the x-axis

This means that

g(x) = -f(x)

So, we have

g(x) = -6x

Hence, the function rule for g(x) is g(x) = -6x

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Based on the ratio and the measurement on the scale drawing, Elena's bed's actual measurements are 200 cm by 150cm.

The scale is given as 1 is to 50.

This means that every centimeter on the drawing is 50 actual centimeters for the bed.

The dimensions are:

= 4 x 50 = 200 cm

= 3 x 50 = 150 cm

Remaining part of the question:

The ratio is 1 to 50

In conclusion, the actual measurements are 200 cm by 150 cm.

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The sum of the arithmetic series 4+9+14+19+24+ . . . . . . . +99 is S(20) = 1030

The given series:

4+9+14+19+24+ . . . . . . . +99

We can conclude:

a(1) = 4

a(n) = 99

d = 9 - 4 = 5

Find n using the formula of nth term.

a(n) = a(1) + (n-1) . d

99 = 4 + (n -1). 5

99 = 5n - 1

5n = 100

n = 20

Find the sum for the n terms using the sum formula of an arithmetic series:

S(n) = n/2 (a(1) + a(n))

Substitute n = 20, a(1) = 4, and a(20) = 99

S(20) = 20/2 . (4 + 99)

         = 10 . 103 = 1030

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Answer:5

Step-by-step explanation:

Comparing the unit price of each bag of fries, the large bag of fries, which costs $0.014825 per gram, has the lower cost per gram than the other bag.

Unit price is defined as the price or the cost per unit of the item. The importance of the unit price is that it allows the buyer to understand how the total price has been calculated. Unit price can be solved by dividing the total cost to the total amount of the item.

unit price = total cost/total amount

Solving for the unit price of each bag of fries:

small bag : unit price = $1.39/80 grams = $0.017375/gram

large bag : unit price = $1.69/114 grams = $0.014825/gram

$0.014825 < $0.017375

large bag < small bag

Hence, the large bag which costs $0.014825 per gram has the lower cost per gram.

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Answer: c=110.25

Step-by-step explanation:

[tex]r^2+21r+c\\r^2+(2)(r)(10.5)+(10.5)^2=\\(r+10,5)^2\\Hence,\\c=(10.5)^2\\c=(10.5)(10.5)\\c=110.25[/tex]

The area in square inches of triangle is 36.75.

Given,

∠A ≅ ∠P

Tan A = tan P

6/8 = x/14

X= 21/2

Area = 1/2 * 7*21/2

= 36.75 square

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base. Heron's formula, formula credited to Heron of Alexandria (c. 62 ce) for finding the area of a triangle in terms of the lengths of its sides. In symbols, if a, b, and c are the lengths of the sides.

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h.

Hence, the area in square inches of triangle will be 36.75

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(3/5)^4 and 27/125 which equals 0.216m^3

The equation of the line in standard form of (2/3)x + 3 = 6y - 15 is 2x - 18y = -54.

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.

Given the equation (2/3)x + 3 = 6y - 15, to write the equation in standard form, arrange the variable(s) in one side and the constant(s) in the other.

(2/3)x + 3 = 6y - 15

(2/3)x - 6y = -15 - 3

(2/3)x - 6y = -18

Multiplying both sides by 3 to have integer coefficients.

3[(2/3)x - 6y] = 3(-18)

2x - 18y = -54

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3. Both triangles are congruent by ASA congruence theorem.

4. There is no enough information to prove that the triangles are congruent by neither ASA nor AAS.

If two triangles have two pairs of corresponding congruent angles and a pair of corresponding included congruent sides, then both triangles are congruent by ASA congruence theorem.

If two triangles have two pairs of corresponding congruent angles and a pair of corresponding non-included congruent sides, then both triangles are congruent by AAS congruence theorem.

3. Both triangles are congruent by ASA congruence theorem.

4. There is no enough information to prove that the triangles are congruent by neither ASA nor AAS.

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According to the given question,

A square tile has a side length of X squared Y units , the number of tiles required is 49x^6y^{10}.

a generalization of arithmetic where letters representing numbers are combined according to the rules of arithmetic any of various systems or branches of mathematics or logic concerned with the properties and relationships of abstract entities (such as complex numbers, matrices, sets, vectors, groups, rings, or fields) manipulated in symbolic form under operations frequently analogous to those of arithmetic

According to the given value;

side of square floor 5.6

a = 7x³y⁰

Side of suare tiles s=x²y

Area of square floor is

A = a

A = (7x³y6) ²

A = 49x1012

Area of square tiles,

A₁ = s

A₁ = (x²y)²

A=x⁴y²

Now the number of tiles required,

n=\frac{A}{A_t}

Substitute the data,

n =49x¹ y 12

x¹ y²

2

n=49x^6y^{10}

Thus, the number of tiles required is 49x^6y^{10}.

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After simplifying the expression - 8 ( 10 r + 10 r - 6 ) - 3 r, we get the result as 48 - 163 r.

We are provided with an expression:

- 8 ( 10 r + 10 r - 6 ) - 3 r

We need to write the given expression in the simplest terms that is we need to simplify the expression.

So, we will use the property of BODMAS here.

Solving the bracket first , the expression will become:

= - 8 ( 10 r + 10 r - 6 ) - 3 r

= -8 ( 20 r - 6 ) - 3 r

Now, opening the bracket, we get that:

= - 160 r + 48 - 3 r

Now, combining the like terms, we get the result as:

= - 163 r + 48

= 48 - 163 r

Therefore, after simplifying the expression - 8 ( 10 r + 10 r - 6 ) - 3 r, we get the result as 48 - 163 r.

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The hypotenuse of the larger triangle is 30 inches

The ratio is given as

Ratio = 4 : 5

The smaller triangle has a length of 24 inches

So, we have

24 : Larger triangle = 4 : 5

Multiply 4 : 5 by 6

So, we have:

24 : Larger triangle = 24 : 30

By comparison, we have

Larger triangle = 30

Hence, the hypotenuse of the larger triangle is 30 inches

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