Can you use the lengths of the hypotenuse and a leg to show right triangles are congruent?

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 equation that defines the parabola with vertex at the point (0, 0) and focus at (0, 7) is:

y = x²/28

  A parabola is a quadratic function that can move on any axis, it is composed of:

   The equation that defines a parabola can be given by:

  This will depend on its aperture

  In this case we have the vertex of the parabola at the point (0, 0) and the focus at the point (0, 7) this is displaced on the y-axis upward, so the parabola is of the form y = x²

(x - 0)² = 4p(y - 0)

Focus

f = (0, 0  + p)

(x- 0)² = 4*7(y - 0)

(x - 0)² = 28(y - 0)

y = x²/28

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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

Answer:

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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 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

Answer: x has no solutions, y has no solutions

Step-by-step explanation:

y = x² - 3

x - y = 1

x - x² - 3 = 1

- x² - x - 3 = 1

- x² - x - 4 = 0

- x² - x - 16/4 = 0

- x² - x - 1/4 - 15/4 = 0

- (x² + x + 1/4) - 15/4 = 0

- (x+1/2)^2 - 15/4 = 0

- (x+1/2)^2 = 15/4

(x+1/2)^2 = -15/4 ==> x has no solutions, y has no solutions

any number to an even power, in this case to the power of 2, has to be positive, but -15/4 is negative.

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 distance from the center to any point on the circle exists comprehended as the radius. The radius is 10cm.

The radius of a circle is the separation between any two points on the circle and its center. The radius of a circle is the separation between any two points on its circumference. R or r is typically used to indicate it.

The distance along a line connecting a circle's center to a point on its perimeter is known as a circle's radius. Therefore, the radius is equal to half the diameter's length. Therefore, the radius is equal to half the diameter's length.

The radius of a circle is the separation between any two points on the circle and its center.

In this instance (using the Pythagorean Theorem)

r = [tex]\sqrt{(7-1)^{2}+(5-(-3))^{2} }[/tex]

= √(36 + 64)

r = 10

If a circle whose center is at (1, -3) passes through the point (7, 5) then the radius of the circle exists 10.

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Answer:

x = 8

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = [tex]\frac{1}{2}[/tex] absinC

where a and b are 2 sides of the triangle and C the angle between them

here a = 13 , b = x , C = 30° and A = 26 , then

[tex]\frac{1}{2}[/tex] × 13 × x × sin30° = 26 ( multiply both sides by 2 to clear the fraction )

13x × sin30° = 52 ( using the exact value of sin30° = [tex]\frac{1}{2}[/tex] )

13x × [tex]\frac{1}{2}[/tex] = 52 ( multiply both sides by 2 to clear the fraction )

13x = 104 ( divide both sides by 13 )

x = 8

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

The explicit relation between x and y in the form is (x2)2+(y2)2=sin2+cos2.

Given that x=2sin, y=2cos, and 0 are constants,

Simplify the parametric functions that are presented. Add their squares after taking them. The following trigonometric identity can be used:

sin2θ+cos2θ=1sin2⁡θ+cos2⁡θ=1

x=2sinθ,

y=2cosθ,0≤θ≤2πsinθ

=x2cosθ,

=y2x

Y=2sin⁡θ,

y=2cos⁡θ,0≤θ≤2πsin⁡θ=x2cos⁡θ=y2

Square them now and add them:

(Using the trigonometric identity sin2+cos2=1)x24+y24=1, where (x2)2+(y2)2=sin2+cos2)

(Using the trigonometric identity sin2+cos2=1)x24+y24=1, where (x2)2+(y2)2=sin2+cos2)

A parameter in a parametric equation can stand in for anything, including an angle. When a parameter is an angle—as opposed to a non-angle parameter—the plane curve can be graphed by choosing values for the angle and computing the x- and y-values.

Hence, the explicit relation between x and y in the form is (x2)2+(y2)2=sin2+cos2.

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Write the first five numbers of two different patterns in which 12 is the third number.

Pattern 1= 4, 8, 12, 16, 20

Pattern 2= 2,4,12,48,240

How to calculate the patterns?

Pattern 1=multiples of 4

4*1=4

4*2=8

4*3=12

4*4=16

4*5=20

Pattern 2= tn=(tn-1)*n

t1=2

t2=2*2=4

t3=4*3=12

t4=12*4=48

t5=48*5=240

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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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The result of true and false is-

a) True: J and J' are opposite of y axis.

b) False: Location of L' is (-3, -4).

c) True: N and N' are at same distance.

d) False: L' is at 3 unit above x axis.

As per the given graph;

Part a: True: J and J' are opposite of y axis.

It is clear from the graph that J and J' lies on the opposite side of Y-axis.

The coordinate of J = (2, -6) and J' = (2, 6).

Part b: False: The location of L' is not (-3, -4)

The correct Location of L' is (3, 4) as seen from the graph.

Part c: True: N and N' are at same distance.

The coordinates of N and N' are (5, -5) and (5, 5).

Thus, they are at the same distance from the both axis.

Part d: False: L' is at 3 unit above x axis.

Point L' lies at the distance of 4 units from the x axis.

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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.

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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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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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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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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Answer:

$144

Step-by-step explanation:

$800 × .60 = $480 spent on media

$480 × .30 = $144 media discount

Answer:

628=10^h

Step-by-step explanation:

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

Answer:5

Step-by-step explanation:

Angle is mistaken because triangles of two pairs of congruent sides and one pair of congruent angles do not always satisfy the SAS criterion.

In the given situation:

Therefore, the angle is mistaken because triangles of two pairs of congruent sides and one pair of congruent angles do not always satisfy the SAS criterion.

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Answer: x=4

Step-by-step explanation:

it is impossible to solve x

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 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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