The radius of a circle is 7 kilometres. What is the length of a 90° arc?

[tex] \sf \blue{True✅}[/tex]

Given,

[tex]f(x) = - x + 8 \: and \: f( - 4)[/tex]

Solution:

[tex] f( x) = - ( - 4) + 8 \\ \\ = 4 + 8 \\ \\ = 12[/tex]

The correct answers are:

1. The equation |-x -4| = 8 will have two solutions. (True)

5. The equation |0.5x – 0.75| + 4.6 = 0.25 will have no solutions. (True)

An equation is a mathematical statement with an 'equal to =' symbol between two expressions that have equal values.

1. The equation |-x -4| = 8 will have two solutions. (True)

|-x - 4| = 8

-x -4 = ±8

-x -4 = 8 and -x -4 = -8

-x = 8 + 4 and -x = -8 + 4

-x = 12 and -x = -4

x = -12 and x = 4

Therefore, it has two solutions x ∈ {-12, 4}

2. The equation 3.4|0.5x - 42.1| = -20.6 will have one solution. (False)

Since the right side of the equation has a negative value therefore, according to rules of absolute value equations, it has no solution.

3. The equation |1/2x - 3/4| = 0 will have no solutions. (False)

|(1/2)x - 3/4| = 0

(1/2)x - 3/4 = ±0

Since ±0 is the same

(1/2)x = 3/4

x = 2X3/4

x = 3/2

Therefore, it has one solution x = 3/2

4. The equation |2x – 10| = –20 will have two solutions. (False)

Since the right side of the equation has a negative value therefore, according to rules of absolute value equations, it has no solution.

5. The equation |0.5x – 0.75| + 4.6 = 0.25 will have no solutions. (True)

|0.5x – 0.75| + 4.6 = 0.25

|0.5x – 0.75| = 0.25 - 4.6

|0.5x – 0.75| = -4.35

Since the right side of the equation has a negative value therefore, according to rules of absolute value equations, it has no solution.

6. The equation |(1/8)x - 1| = 5 will have infinitely many solutions. (False)

|(1/8)x - 1| = 5

(1/8)x - 1 = ±5

(1/8)x - 1 = 5 and (1/8)x - 1 = -5

(1/8)x = 5 + 1 and (1/8)x = -5 + 1

(1/8)x = 6 and (1/8)x = -4

x = 6X8 and x = -4X8

x = 48 and x = -32

Thus, it has two solutions x ∈ {48, -32}

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Answer:

0.32

Step-by-step explanation:

2^3 = 2*2*2 = 8

5^2 = 5*5 = 25

------------------------------

8/25 = 0.32

Answer:

17.1

Step-by-step explanation:

Given we have one side and one degree, we can use the trigonometric function "tangent" to solve this right triangle.

Remember that tangent is opposite side over adjacent side, so lets set up the equation:

[tex]tan(35)=\frac{12}{x}[/tex]

Now solve:

[tex]x(tan(35))=12\\x=\frac{12}{tan(35)}[/tex]

As a result, x is equal to approximately 17.1

Any questions feel free to ask :)

Answer:

2

Step-by-step explanation:

[tex]a+b=-5[/tex]

[tex]-(a+b)=-a-b=5[/tex]

[tex]\frac{|-5| + 5}{|5|}[/tex]

[tex]\frac{5+5}{5}[/tex]

[tex]2[/tex]

Answer:

2

Step-by-step explanation:

Given:

To find -a - b  

Factor out the common term -1:

⇒ -a - b = -(a + b)

Substitute a + b = -5:

⇒ -a - b = -(-5)

Apply rule -(-x) = x:

⇒ -a - b = 5

Therefore:

[tex]\begin{aligned}\implies \sf \dfrac{|a+b|+5}{|-a-b|} & = \sf \dfrac{|-5|+5}{|5|}\\\\& = \sf \dfrac{5+5}{5}\\\\& = \sf \dfrac{10}{5}\\\\& = \sf 2\end{aligned}[/tex]

Note:  |-x| = x

The total pounds of fruits bought if he buys 2 pounds of apples and 3 pounds of blueberries is $16.75.

The total pounds of fruits bought if he buys x pounds of apples and y pounds of blueberries is $3.50x + $3.25y.

The total pounds of fruits bought = (pounds of apples x cost per pound) +  (pounds of blueberries x cost per pound)

($3.50 x 2) + (3.25 x 3)

$ 7 + 9.75 = $16.75

($3.50 x x) + (3.25 x y)

$3.50x + $3.25y

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Answer:

y = - 8

Step-by-step explanation:

y = 3 is a horizontal line that includes all of the x coordinates

   just need to find parallel

           y = - 8

Answer:

See below

Step-by-step explanation:

q = quarters       value   = .25 q

n = nickels =  4q     value = .05 (4q)

    summed = 12.60

.25q   + .05(4q) = 12.60      <====== can be used to solve the problem

.45q = 12.60

q = 28     quarters     then nickels = 4q = 112  

Answer:

81 x 10^6

Step-by-step explanation:

x0000000

11111111x

22222222

33333333

....................

88888888

99999999

---------------------

The first digit and 8th digit column has only 9 numbers and the rest 6 column have 10 possible numbers

9 x 9 x 10^6 = 81 x 10^6

Answer:

24-5=19

Step-by-step explanation:

1. (2b)= 2(12)

2. a=5

3. 24-5

4.9

Answer:

2/7

Step-by-step explanation:

To find the fraction that are cherry, take the number that are cherry and put that over the total number of pieces

2 cherry

----------------

7 total

The fraction that are cherry are 2/7

Step-by-step explanation:

if cospheta =3/5 and pheta is located in the fourth quadrant, then sin2pheta=_____

-8/25

24/5

-24/25

8/25

The correct answer for this question is 8/25

Answer:

[tex]\fbox {DF = 20}[/tex]

Step-by-step explanation:

Given :

Step 1 : Find RT

Step 2 : Find SF

Step 3 : Find RY

Step 4 : Find TY

Step 5 : Find DF

Answer:

DF = 20

Step-by-step explanation:

Triangle SDF has side lengths SD, DF, SF.

Triangle RTY has side lengths

RT = (9/4)SD

RY = (9/4)SF

TY = (9/4)DF

"SF is 2 less than RT" Given

SF = RT - 2

SF = (9/4)SD - 2

"SD = 8" Given

SF = (9/4)(8) - 2

SF = 16

"TY is 9 more than RY" Given

TY = RY + 9

(9/4)DF = (9/4)SF + 9

(9/4)DF = (9/4)(16) + 9

(9/4)DF = 45

DF = 45 × 4/9

DF = 20

Answer:

x = -6

Step-by-step explanation:

5x² + 60x + 180 = 0

5 x 180 = 900

you need 2 numbers that multiplies into 900 and adds into 60. these numbers are 30 and 30. now we can rewrite it

5x² + 30x + 30x + 180 = 0.

split it in half and factorise

5x(x + 6) + 30(x + 6) = 0

this means the brackets are:

(5x + 30)(x + 6) = 0

5x + 30 = 0

5x = -30

x = -6

x + 6 = 0

x = -6

therefore, x = -6.

Answer: No solution

Step-by-step explanation:

The red line is y=3x+7 and the blue line is y=3x+2

The lines do not intersect at any time. Therefore, this set of equations has no solution. I hope this helps! Pls mark brainliest!! :)

Answer:

x = 4    y =  1

Step-by-step explanation:

Opposite sides are equal , so

2x-3y = 5  

x+5y =9                <====== multiply this by -2 and add to first equation

-13y = -13

  then y = 1        and x + 5y = 9    so x = 4

The coordinates for the center and length of the radius of this circle are equal to (½, 1), 2 units.

Mathematically, the standard form of the equation of a circle is given by;

(x - h)² + (y - k)² = r²

Where:

In order to determine the coordinates for the center and the length of the radius of this circle, we would use completing the square method:

x² + y² - x - 2y - 11/4 = 0

x² - x + ¼ + y² - 2y = 11/4 + ¼

(x - ½)² + y² - 2y + 1 = 12/4 + 1

(x - ½)² + (y - 1)² = 4

Comparing with the standard form, we have:

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Complete Question:

A circle is defined by the equation given below.

x^2 + y^2 − x − 2y − 11/4 = 0

What are the coordinates for the center of the circle and the length of the radius?

Step-by-step explanation:

please mark me as brainlest

Answer: the number of seconds after the rocket is released

The plot represent the data A box plot titled Scores of Participants and labeled Scores uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35.

The box extends from 17 to 24 on the number line.

A line in the box is at 23 The whiskers end at 12 and 28.

A box plot is a graphical rendition of statistical data based on the minimum, first quartile, median, third quartile, and maximum.

Given:

12 points

21 points

29 points

17 points

24 points

23 points

28 points

According to the given data,

A box plot titled Scores of Participants and labeled Scores uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35.

The box extends from 17 to 24 on the number line.

A line in the box is at 23 The whiskers end at 12 and 28.

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Answer:

y = 5

Step-by-step explanation:

Since the lines are parallel, same side interior angles are supplementary.

That allows us to solve for x.

7x + 17 + 5x - 5 = 180

12x = 168

x = 14

The angles 23yand 5x - 5 are supplementary, so the sum of the measures equals 180°.

23y + 5x - 5 = 180

We already know that x = 14.

23y + 5(14) - 5 = 180

23y = 115

y = 5

[tex]\large\bold{\underline{\underline{Answer:-}}}[/tex]

There are smooth exponential curves that control price performance, capacity, and bandwidth so it easy to predict the cost of something in the future. He said, "When people think about the future they think about it lineraly.

The functions differ from functions that I have used in algebra in the past as the functions can be combined and are more about rotation rather than where they move.

It should be noted that a function simply means an equation where the x that is plugged into the equation will yield exactly on e y from the equation.

In this case, the functions differ from functions that I have used in algebra in the past as the functions can be combined and are more about rotation rather than where they move.

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The measure of angle CED is y. The correct option is the second option-   y, because Triangle ABC is similar to triangle EDC

From the question, we are to determine the measure of angle CED

In the diagram, we can observe that ΔABC is similar to ΔEDC

This is by the Angle-Angle similarity theorem

The theorem states that

If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other

Thus,

Angle CAB = Angle CED

In the diagram,

Angle CAB = y

∴ Angle CED = y

Hence, the measure of angle CED is y. The correct option is the second option-   y, because Triangle ABC is similar to triangle EDC

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