Find the length of the third side. If necessary, write in simplest radical form. 6 and 6

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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Answer:5

Step-by-step explanation:

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 )

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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False, Tossing a coin and then tossing another coin is an example of dependent events .

In statistics, what does a probability mean?

If false, replace the underlined term to make a true sentence. Tossing a coin and then tossing another coin is an example of dependent events .

The outcome of tossing a coin does not affect the out come of rolling a number cube.

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The algebraic expression is the expression that contains numbers and variables and the numerical expression is the expression that contains numbers and operations

Given,

The algebraic expression is the expression that contains numbers and variables

Example : x+3
The numerical expression is the expression that contains numbers and operations

Example : 2+6

Hence, the algebraic expression is the expression that contains numbers and variables and the numerical expression is the expression that contains numbers and operations

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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 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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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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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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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 first five terms of an arithmetic sequence with first term 19 and common difference -4 are 19, 15, 11, 7, 3

The given parameters:

a₁ = 19, d = -4

d is the common difference, hence, the given sequence is an arithmetic sequence.

In an arithmetic sequence, the formula for the nth term is given by:

      a(n) = a(1) + (n - 1) . d

We can also find the terms using recursive formula. The nth term of an arithmetic sequence is equal to the (n-1)th term plus the common difference, d. Mathematically,

      a(n) = a(n -1) + d

Let us start from n = 1

a(1) = 19  (given)

a(2) = a(1) + d = 19 + (-4) = 15

a(3) = a(2) + d = 15 + (-4) = 11

a(4) = a(3) + d = 11 + (-4) = 7

a(5) = a(4) + d = 7 + (-4) = 3

Thus, the first five terms are 19, 15, 11, 7, 3

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

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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I think it's trying to get you to find the side length of the square by using a square root on the area.

Assuming that's the case;

Remember that a square has equal side lengths all around, otherwise it would just be a rectangle. You can actually take the square root of a square to get the side length (hence the name square root). A square root is what number you must multiply by itself to get the root, so for example the square root of 25 is 5 because you can multiply 5 by 5 to get 25. The square root of 100 is 10, because you can multiply 10 by itself to get 100. So you would write this as [tex]\sqrt{100}[/tex], which simplifies down to 10.

Answer: x=4

Step-by-step explanation:

it is impossible to solve x

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:

$144

Step-by-step explanation:

$800 × .60 = $480 spent on media

$480 × .30 = $144 media discount

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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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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Answer:

a) two parallel lines

Step-by-step explanation:

Two parallel lines have the same slope

Let's take a concrete example:
y = 2x + 4        (slope =2, y-intercept = 4)
y = 2x + 10      (slope = 2, y-intercept = 10)

Lines are parallel to each other

If you try to solve this equation you get

2x + 4 = 2x + 10

Subtracting 2x on both sides gives you  the identity 4 = 10 (a contradiction)

This means the 2 line equations are inconsistent

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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A mode can be defined as a statistical term that is used to denote the value that appears most frequently (often) or occurs repeatedly in a given data set. This ultimately implies that, the mode of a data set simply refers to the data point with the highest frequency.

By critically observing the frequencies for the number of TVs shown in the table above, we can logically deduce that the mode is equal to 1.

A mean can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

Mathematically, the mean for this data can be calculated by using the following formula:

Mean = [F(x)]/n

Frequency, n = 3 + 15 + 9 + 11 + 1

Frequency, n = 39.

Total number of TVs = 0(3) + 1(15) + 2(9) + 3(11) + 4(1)

Total number of TVs = 0 + 15 + 18 + 33 + 4

Total number of TVs = 70

Substituting the parameters into the formula, we have;

Mean = 70/39

Mean = 1.80.

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Answer:

A and E (top left and bottom middle)

Step-by-step explanation:

Unit rates are found when a ratio has a denominator of 1.  For the sake of simplicity, I will give the options in the image letter designations. A, B, and C are the top three from left to right, and D, E, and F are the bottom 3 from left to right.

A

[tex]\frac{9}{5} miles:\frac{5}{6}hour[/tex]
Because ratios can be written as fractions, this ratio can be written:

[tex]\frac{\frac{9}{5}}{\frac{5}{6}}[/tex]
That's a mess! Another way to divide fractions is to multiply by the reciprocal of the denominator:

[tex]\frac{9}{5}*\frac{6}{5}[/tex]

Since none of the terms can be cross-cancelled, multiply!

[tex]=\frac{54}{25}[/tex]
Since the numerator is greater than the denominator, the unit rate is greater than one!

B

[tex]4miles:3\frac{1}{3}hours[/tex]

Start by turning the mixed number into an improper fraction:

[tex]3\frac{1}{3}=\frac{10}{3}[/tex]

Now compare by multiplying 4 over 1 by the reciprocal of 10 thirds:

[tex]\frac{4}{1}*\frac{3}{10}[/tex]

Cross-cancel and multiply:

[tex]=\frac{2}{5}[/tex]

Since the numerator is less than the denominator, the unit rate is less than one!

C

[tex]2\frac{1}{2} miles:3hours[/tex]
Convert the mixed number into an improper fraction:

[tex]2\frac{1}{2} =\frac{5}{2}[/tex]
Multiply by the reciprocal of 3:

[tex]\frac{5}{2}*\frac{1}{3}[/tex]
Multiply!

[tex]\frac{5}{6}[/tex]
Since the numerator is less than the denominator, the unit rate is less than one!

D

[tex]\frac{9}{5} miles :3hours[/tex]

Multiply by the reciprocal of 3:

[tex]\frac{9}{5}*\frac{1}{3}[/tex]

Cross cancel and multiply!

[tex]=\frac{3}{5}[/tex]

Since the numerator is less than the denominator, the unit rate is less than one!

E

[tex]7 miles :\frac{3}{4}hour[/tex]

Multiply by the reciprocal of 3 fourths:

[tex]\frac{7}{1}*\frac{4}{3}[/tex]

Multiply:

[tex]=\frac{28}{3}[/tex]

Since the numerator is greater than the denominator, the unit rate is greater than one!

F

[tex]\frac{1}{3}mile:2\frac{3}{8}hours[/tex]

Convert the mixed number into an improper fraction:

[tex]2\frac{3}{8}=\frac{19}{8}[/tex]

Multiply one third by the reciprocal of 19 eighths:

[tex]\frac{1}{3}*\frac{8}{19}[/tex]
Multiply!

[tex]=\frac{8}{57}[/tex]

Since the numerator is less than the denominator, the unit rate is less than one!

The expand each binomial. (x - 2)⁵ is:

x⁴ - 8x³ + 24x² - 32x  + 16

  A polynomial is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms.

Depending on the number of terms it can be :

We solve first by perfect square trinomial, then we apply the distributive property.

(x - 2)⁴ = (x-  2)²(x - 2)²

(x - 2)⁴ = (x² - 4x + 4)(x² - 4x + 4)

(x - 2)⁴ = (x⁴ - 4x³ + 4x²) + (-4x³ + 16x² - 16x) + (4x² - 16x + 16)

(x - 2)⁴ = x⁴ - 4x³ + 4x² -4x³ + 16x² - 16x + 4x² - 16x + 16

(x - 2)⁴ = x⁴ - 8x³ + 24x² - 32x  + 16

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The equation of the line parallel to the first line is y = 3 · x - 9. (Correct choice: B)

In this question we must derive the equation of the line for a given street and look for another equation of the line parallel to the previous one. Lines are first order polynomials of the form y = m · x + b, where m and b are the slope and the y-intercept, respectively.

Now we present the procedure in detail. First, find the equation of the first line:

5 = 4 · m₁ + b₁           (1)

2 = 3 · m₁ + b₁          (2)

(m₁, b₁) = (3, - 7)

Second, determine the equation of the line parallel to the line found in the previous step: (Please notice that two lines are parallel to each other when they share the same slope but have different y-intercepts)

- 3 = 3 · 2 + b₂

b₂ = -3 - 6

b₂ = - 9

The equation of the line parallel to the first line is y = 3 · x - 9. (Correct choice: B)

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Answer: The correct answer is B

The solution of the equation (3x -2)/12 -1/6 = 1/6 is at x = 2.

According to the given question.

We have an equation (3x -2)/12 -1/6 = 1/6 .

As we know that, an equation is a condition on a variable such that two expressions in the variable should have equal value.

Therefore, the solution of the equation (3x -2)/12 -1/6 = 1/6 is given by

(3x -2)/12 -1/6 = 1/6

⇒ (3x -2)/12 = 1/6 + 1/6 (adding 1/6 both the sides)

⇒ (3x -12)/12   = 2/6

⇒ (3x -2)/12 = 1/3

⇒ (3x -2)    = (1/3)12

⇒ 3x -2 = 4

⇒ 3x = 4 + 2

⇒ 3x = 6

⇒ x = 6/3

⇒ x = 2

Hence, the solution of the equation (3x -2)/12 -1/6 = 1/6 is at x = 2.

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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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