If m ∠ F D E = ( 3 x − 15 ) ° and m ∠ F D B = ( 5 x + 59 ) ° , find the value of x such that ∠ F D E and ∠ F D B are supplementary.

The value of the inequality is x > 6

Inequalities are defined as mathematical relations that makes a non-equal comparison between two numbers , elements or expressions.

They are also used to compare two numbers on the number line by their size.

It is an order relationship showing —greater than, greater than or equal to, less than, or less than or equal to

Given the expression;

|1.3x + 7.8| > 0

collect like terms

1. 3x > 0 + 7. 8

1.3x > 7. 8

Make 'x' the subject

Divide both sides by 1. 3

1. x/ 1. 3 > 7. 8/ 1. 3

x > 6

Thus, the value of the inequality is x > 6

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By SSS (Side, side, side) congruency;

⇒ Δ T J D ≅ ΔS E K

Given that;

The vertices of ΔT J D  are;

T (-4, -2) , J (0, 5),  and D (1, -1),

The vertices of  ΔS E K  are;

S (-1, 3), E (3, 10) , and K (4, 4)

We have to prove that  Δ T J D ≅ΔS E K.

What is congruency in triangle?

If all three corresponding sides are equal and all the three corresponding angles are equal in measure, then Two triangles are said to be congruent.

Now,

The vertices of ΔT J D  are;

T (-4, -2) , J (0, 5),  and D (1, -1),

The vertices of  ΔS E K  are;

S (-1, 3), E (3, 10) , and K (4, 4)

To prove Δ T J D ≅ΔS E K we use distance formula and prove all sides are equal.

In ΔT J D;

Distance between T and J;

[tex]D_{TJ} = \sqrt{(0-(-4))^2 + (5 -(-2))^2} = \sqrt{65}[/tex]

Distance between J and D;

[tex]D_{JD} = \sqrt{(1-0)^2 + (-1 -5)^2} = \sqrt{37}[/tex]

Distance between D and T;

[tex]D_{DT} = \sqrt{(1-(-4))^2 + (-1 -(-2))^2} = \sqrt{26}[/tex]

In ΔS E K;

Distance between S and E;

[tex]D_{SE} = \sqrt{(3-(-1))^2 + (10-3)^2} = \sqrt{65}[/tex]

Distance between E and K;

[tex]D_{EK} = \sqrt{(4-3)^2 + (4 -10)^2} = \sqrt{37}[/tex]

Distance between K and S;

Clearly, Distance between sides of  Δ T J D and ΔS E K are equal as;

[tex]D_{SE} = D_{TJ} \\\\D_{EK} = D_{JD}\\\\D_{KS} = D_{DT}[/tex]

Hence, By SSS congruency;

⇒ Δ T J D ≅ ΔS E K

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The product of (1 3/4-2.4).[0.5.(2/5 plus 2.6) is 2.75.

It should be noted that we are to find the product of (1 3/4-2.4).[0.5.(2/5 plus 2.6).

This will be:

= (1 3/4-2.4).[0.5.(2/5 plus 2.6)

= (1.75 - 0.5) × [0.5(0.4 + 2.6)]

= 1.25 × 0.5(3)

= 1.25 + 1.5

= 2.75

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Answer:

$0.05

Step-by-step explanation:

First, find the total amount of crackers and the total cost.

Crackers: 6*18=108 crackers

$5.40/108=0.05

$0.05

2 packages of bacon would have to buy for both stores to cost the same.

Given that,
At a store, a carton of eggs costs $2.25 and a package of bacon costs $4.25. At another store, eggs cost $2.75, and bacon costs $4.00. If you were to buy one carton of eggs, how many packages of bacon would you have to buy for both stores to cost the same is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
According to question
WIth the help of arithmetic operators
2.25 + 4.25y = 2.75 + 4.00y
0.25y = 0.50
y = 2

Thus, 2 packages of bacon would have to buy for both stores to cost the same.

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Measure of angle 3 i.e. m∠3 = 130°

The measurement of angle is the degree of that angle or we can also say that the angles are always measured in degree. In geometry, the complete one revolution of four quadrants is of 360 degrees (360°) and divided into total of 360 parts where each part of this represents a degree.

As stated above there are total 360 parts in one revolution thus thus we can find value of particular angle by subtracting the angle from 360 or 180 for a straight line.

In the question,

Let given angle is ∠8.

Given, ∠8 = 50°

Now, according to supplementary angle property

∠8 + ∠6 = 180

50° + ∠6 = 180

∠6 = 130°

As, ∠6 and ∠2 are corresponding angles,

therefore, ∠6 = ∠2 = 130°

Also, ∠2 and ∠3 are vertical opposite angles,

thus, ∠2 = ∠3 = 130°

therefore, ∠3 = 130°

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The complete question is :

Find measures of numbered angle.

a. ∠2

b. ∠3

c. ∠4

Answer: The inverse is b.

Step-by-step explanation:

Answer:

44 °

Step-by-step explanation:

In a right triangle such as this

  sin B = opposite leg / hypotenuse

  sin B =   20 / 29

   B = arcsin (20/29) = 44 degrees

The product of  -2.1. (-3.5) is  7.35

The product of  (-2.1 ) and (-3.5) =  [tex]-2.1\times-3.5[/tex]

                                                    =  7.35

So, the product of (-2.1) and (-3.5) is 7.35.

The quotient is the number which is produced when we perform division operations on two numbers. Fundamentally, it is the result of the division method. There are four primary wordings utilized within the arithmetic division such as divisor, dividend, quotient and remainder.

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Answer:

x= 6

Step-by-step explanation:

10-20x+8x = -19x + 52

10 -12x= -19x +52

10 - 12x +19x =-19x +19x +52

10 + 7x= +52

10 -10 +7x= 52-10

+7x=42

7x= 42/7

x= 6

2(5- 10(6))+8(6)=-19(6)+52

2(5-60)+48=-114+52

10-120+48=-114+52

-110+48=-114+52

-62=-62✅

Answer:

1st convert mixed numbers

19/18 x 23/4

2nd multiply fractions

437/32

Answer: 437/32

The system of equations, -x + y = -2 and 2x - 2y = 0, has no solution.

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

Given two equations in x and y,

-x + y = -2     (equation 1)

2x - 2y = 0     (equation 2)

Rewrite equation 1 as an equation of y and substitute to equation 2.

(equation 1) -x + y = -2     ⇒     y = x - 2

2x - 2y = 0     (equation 2)

2x - 2(x - 2) = 0

2x - 2x + 4 = 0

4 = 0

Since we do not have a definite value for x, and neither will be for y, the system of equation has no solution.

Checking the slope,

(equation 1) -x + y = -2     ⇒     y = x - 2

m = 1

(equation 2) 2x - 2y = 0     ⇒     y = x

m = 1

Since the two equations has the same slopes but different y-intercepts, then these two equations must be parallel with each other.

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The function g(x)  whose graph is the horizontal shrink of the given graph of  f(x) =5x-6 by a factor (horizontal shrink factor) of 1/4 is  g(x)=5/4 x-6.

As per the question statement, we are supposed to find a function g(x) whose graph is a horizontal shrink of the given graph of f(x) =5x-6 by a factor of 1/4.

Before solving it lets assume f(x)=y

so y =5x-6

Comparing with y= mx+c  where m is the slope

so in y =5x-6  slope is m=5

For applying horizontal shrink by a factor of 1/4 we need to multiply the slope by a factor of 1/4

so new slope [tex]m_{1} =5*\frac{1}{4} =\frac{5}{4}[/tex]

Therefore [tex]g(x) = \frac{5}{4} x -6[/tex]

Therefore the function [tex]g(x)[/tex] whose graph is a horizontal shrink of the given graph of  [tex]f(x) = 5x-6[/tex]  by a horizontal shrink factor of  1/4  is [tex]g(x) = \frac{5}{4} x -6[/tex]

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The range of the quadratic function represented with the given parameters is {y | −7 < y ≤ 2}

The range of a function is the set of output values of the graph. This in other words mean the range of a function is the set of y values of the graph.

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

From the question, we have the following parameters:

Write out the vertex

So, we have

Vertex = (0, 2)

Remove the x value

y = 2

From the question, we have

The parabola opens downward

This means that the vertex is a maximum

So, the range is

y ≤ 2

Rewrite properly as

{y | −7 < y ≤ 2}

Hence, the range of the quadratic function is {y | −7 < y ≤ 2}

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Answer:

Answer is A :)

Step-by-step explanation:

The formula for calculating the Hight of the cone as follows h = 3(V/(πr²))

Thus, the volume of a cone is one-third that of a cylinder with the same base radius and height.

Cone and cylinder volumes are related in exactly the same manner as pyramid and prism volumes are related. If the heights of a cone and then a cylinder are the same, the volume of the cylinder equals three times that of the cone.

The volume, V, formula of a cone with radius, r, and height, h.

The volume of the cone  using the formula:

V = 1/2πr²h

h = 3(V/(πr²))

The formula for calculating the Hight of the cone as follows h = 3(V/(πr²)).

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Answer:

The y-value is 1 less than the square of the x-value,

Step-by-step explanation:

if we follow the letters and convert them into numbers we will get:

y-value=y

1 less than=-1

square of x value=x^2

so

we put the number in order according to the words:

y value=1 less than the square of x

so

y=x^2-1

hope this helps!

The speed written in standard form is 0.000008056  miles per second.

Here we know that the average speed of a garden snail is:

8.056 x 10⁻⁶ miles per second.

Notice that it is written in scientific notation and we want to write this in standard form, so we just need to expand the product.

Notice that the exponent is -6, this means that we need to "move" the decimal point 6 times to the left, so we will get:

S = 8.056 x 10⁻⁶ miles per second.

S = 0.000008056  miles per second.

That is the speed written in standard form.

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The nearest tenth value of the given expression is a 18.3. the option D is  a correct option.

According to the statement

We have to find that the value of the tenth digit.

So, For this purpose, we know that the

Tenth digit  is the first digit to the right of the decimal point; one out of 10 equal parts of a whole.

From the given information:

14 plus cube root of 81 to the nearest tenth.

Then

the statement become is

[tex]14+(81)^\frac{1}{3}[/tex]

Firstly we have to find the cube root of the number 8 and then have to add 14 number in the out coming answer.

Then

14+ Cube root of 81

Then

14+ 4.32

Then after adding it

18.32

In the nearest tenth value it will become 18.3.

So, The nearest tenth value of the given expression is a 18.3. the option D is  a correct option.

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1) The line of symmetry is; Vertical Line x = 0

2) The line of symmetry is; Vertical line x = 4 and horizontal line y = -4

3) The line of symmetry is; Vertical Line x = 3

1) A line of symmetry is a line that divides a figure into two parts such that each part is the mirror image of the other.

From the given image, we can see that the line of symmetry here is a vertical line at x = 0. This is because that is the half way point of the object such that when mirrored, it produces the exact same image.

2) The line of symmetry here for the given object is;

x = 4 and y = -4

3) The line of symmetry here for the given parabola curve is;

x = 3

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Show your work given the rule of (x, y)—->(x-7.5,y+6.8)

Original coordinate (5,3)

The output coordinate is if the input coordinate is (5,3) is (-2.5,9.8).

Given that,

(x, y)—->(x-7.5,y+6.8)

Given original coordinate are (5,3).

We substitute the original coordinate in the given point (x, y).

A location on a grid, also known as a coordinate plane, is identified by coordinates, a pair of numbers (also known as Cartesian coordinates), or sometimes a letter and a number. The two axes that make up a coordinate plane are the horizontal x axis and the vertical y axis (vertical).

Put x=5 and y=3 in (x, y)

We get

[tex]=(5-7.5, 3+6.8)\\=(-2.5, 9.8)\\[/tex]

Therefore, The output coordinate is if the input coordinate (5,3) is (-2.5,9.8).

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Bounce 2 is 2

Bounce 4 is 1/2

Bounce 5 is 1/4

Bounce 6 is 1/8

all of your equivalent heights are correct.

8 × 10⁻⁷   is 0.00000008 in scientific notation .

What does a scientific symbol mean?

A frequently used floating-point system where values are expressed as the product of a number between 1 and 10 with the appropriate power of 10 (for example, 1.591 1020).

Example: 700. Why is 700 written as 7 × 102 in Scientific Notation

Example: 4,900,000,000. 1,000,000,000 = 109

Example: 0.0055 is written 5.5 × 10-3

Example: 3.2 is written 3.2 × 100

Why is it employed in scientific notation?

 scientific notation of 0.00000008 = 8 × 10⁻⁷

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Answer: 7

Step-by-step explanation: You can find the mean, or average, of a data set in two simple steps: Find the sum of the values by adding them all up. Divide the sum by the number of values in the data set.

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

In statistics, what does a probability mean?

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

Also, genuineness of the second statement does not give any information whether the first statement is true or not.

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The acceleration when he gets to the top is -0.0325 m/s²

From the question, we are to determine the acceleration when Jacob gets to the top

Using one of the equations of motion, we have that

v = u + at

Where v is the final velocity

u is the initial velocity

a is the acceleration

and t is the time

From the given information,

u = 15 mph = 6.7 m/s

v = 3 mph = 1.34 m/s

t = 2.75 minutes = 165 seconds

Then,

1.34 = 6.7 + a×165

1.34 - 6.7 = 165a

-5.36 = 165a

a = -5.36/165

a = -0.0325 m/s²

NOTE: Negative sign indicates deceleration

Hence, the acceleration when he gets to the top is -0.0325 m/s².

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Step-by-step explanation:

u simply add 307 and 206 to 2,040 giving u 2553

Answer:

(-5, 4)

(-4, 5)

(-2, 5)

(-10, 4)

Step-by-step explanation:

Given points:

To translate a point 3 units down, subtract 3 from its y-coordinate.

To reflect a point across the x-axis, the y-coordinate becomes its additive inverse.

Therefore, the mapping rule is:

[tex](x,y) \rightarrow (x, -(y-3))[/tex]

Translated points:

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