Write an equation of a line wit the given slope and y intercept

Answer:

2(x^2 + 4x - 28) = 0.

The length of the missing sides are:

4√2 units.

or 5.66 units ( to the nearest hundredth).

Step-by-step explanation:

Applying the Pythagoras Theorem:

8^2 = (x + 2)^2 + (x + 2)^2

2(x^2 + 4x + 4) = 64

2x^2 + 8x + 8 - 64 = 0

2x^2 + 8x - 56 = 0

2(x^2 + 4x - 28) = 0  models the situation.

Solving:

x = [- 4 +/- √(4^2-4*1*-28)]  / 2

= (-4 +/- √128) / 2

= (-4 + 8√2) / 2 ,   (-4 - 8√2) / 2  (we ignore this negative root).

= -2 + 4√2.

This is 3.66 to the nearest hundredth.

So the  length of the 2 equal sides is 2 + (- 2 + 4√2) = 4√2.

or  5.66 to the nearest hundredth.

Answer:

[tex](x-7)^2+(y-4)^2=25[/tex]

Step-by-step explanation:

The circle has diameter endpoints of ( 4, 8 ) and (10, 16 ).

The midpoint of the diameter is the center

[tex](\frac{4+10}{2},\frac{8+16}{2})[/tex]

[tex](\frac{14}{2},\frac{24}{2})[/tex]

[tex](7,12)[/tex]

The radius is the distance from the center to any point on the circumference.

[tex]r=\sqrt{(7-4)^2+(12-8)^2}[/tex]

[tex]r=\sqrt{(3)^2+(4)^2}[/tex]

[tex]r=\sqrt{9+16}[/tex]

[tex]r=\sqrt{25}=5[/tex]

The equation of the circle with center (h,k) and radius r is given by:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

We plug in the values to get:

[tex](x-7)^2+(y-4)^2=5^2[/tex]

[tex](x-7)^2+(y-4)^2=25[/tex]

Answer:

The equation of the circle is (x - 7)² + (y - 12)² = 25

Step-by-step explanation:

* Lets revise the equation of the circle

- The equation of the circle which has center (h , k) is:

 (x - h)² + (y - k)² = r²

- The endpoints of a diameter re (4 , 8) and (10 , 16)

- The center of the circle is the mid-point of the diameter

* Lets revise the rule of the mid point to get the center of the circle

 and revise the rule of the distance to get the length of the diameter

- The mid point (x , y) of segment has endpoints (x1 , y1) and (x2 , y2) is

 x = (x1 + x2)/2  and y = (y1 + y2)/2

- The distance between the two point (x1 , y1) and (x2 , y2) is:

  d = √[(x2 - x1)² + (y2 - y1)²]

* Now lets find the center of the circle

∵ (h , k) is the mid-point of the diameter

∵ (4 , 8) is (x1 , y1) and (10 , 16) is (x2 , y2)

∴ h = (4 + 10)/2 = 14/2 = 7

∴ k = (8 + 16)/2 = 24/2 = 12

∴ The center of the circle is (7 , 12)

∵ The length of the diameter = √[(10 - 4)² + (16 - 8)²

∴ d = √[6² + 8²] = √[36 + 64] = √100 = 10

∵ The radius = 1/2 the diameter

∴ r = 1/2 (10) = 5

* Lets write the equation of the circle

∵ The equation of the circle is (x - h)² + (y - k)² = r²

∵ h = 7 , k = 12 , r = 5

∴ The equation of the circle is (x - 7)² + (y - 12)² = 5²

∴ The equation of the circle is (x - 7)² + (y - 12)² = 25

Answer:

The third one or the first one

Step-by-step explanation:

Can't be +4 or -4

Answer:

The equation of the line on the graph is y - 4 = -3(x+1)

Answer:

All real numbers greater than or equal to -2.

Step-by-step explanation:

The range is the set of values of the y-coordinates of the points on the graph.

The smallest y-coordinate is -2. All real numbers greater than equal to -2 are the range.

Answer: All real numbers greater than or equal to -2.

Answer:

36c^3m^3x^2

Step-by-step explanation:

Answer:

(-1/2,-1.25)

Step-by-step explanation:

Once you plot the points, you should be able to find the midpoint formula.

The midpoint between the points (-2, -3) and (1, 0.5) is (-0.5, -1.25).

To find the midpoint between two points, you average the x-values and the y-values of the given points separately. The formula for the midpoint M between two points P1(x1, y1) and P2(x2, y2) is

M = ((x1 + x2) / 2, (y1 + y2) / 2)

Applying this to the given points (-2, -3) and (1, 0.5), we calculate the midpoint as follows:

Average the x-values:

(-2 + 1) / 2 = -0.5

Average the y-values:

(-3 + 0.5) / 2 = -1.25

X = -3 or X = 7

Step 1: Simplify both sides of the equation.

Step 2: Subtract x^2+15 from both sides.

Step 3: Factor left side of equation.

Step 4: Set factors equal to 0.

Answer:

x=7 or x=-3

Step-by-step explanation:

36+4x=x^2+15

36-15+4x=x^2

21+4x=x^2

0=x^2-4x-21

0=x^2-(7-3)x-21

0= x^2-7x+3x-21

0= x(x-7)+3(x-7)

0= (x-7)(x+3)

so either

x-7=0

x=7

or x+3=0

x=-3

A dilation producing a smaller figure requires a scale factor less than 1. If the scale factor is 1/2, the model size is half the actual size. By setting up and solving a proportion, actual dimensions can be calculated.

When a dilation results in a smaller figure, the scale factor used is less than 1. Think of the scale factor as a fraction where the actual size is the denominator and the model size is the numerator. For instance, a scale factor of 1/2 would mean that the model is half the size of the actual figure.

For a practical example: if we have a scale factor of 1:4 and the scale measurement is 4, the actual dimension can be found by setting up a proportion as 1/4=4/x, solving for x would give us the actual dimension, which in this case would be 16.

Answer:

[tex]\frac{q}{360}[/tex] × π10 = 7

Explanation:

The formula to find arc length is [tex]\frac{x}{360}[/tex] × [tex]\pi r^{2}[/tex]

Simply plug in radius and arc length to get your equation.

Answer:

Central angle = 80.21°

Step-by-step explanation:

The arc length in circle is the product of radius and central angle made by the arc in radians.

That is

              l = rθ

Here given the values r = 5 ft and l = 7 ft

Substituting

             7 = 5 x θ

             θ = 1.4 radians

             [tex]\theta =1.4\times \frac{180}{\pi }=80.21^0[/tex]

Central angle = 80.21°

Answer:

The first one is not a function

The second is a function

Third not a function

Fourth is a function

Step-by-step explanation:

Answer:

Step-by-step explanation:

squirrel speed (r) x seconds (3)  has to be more than 34 feet

3r is greater than 34

r is greater than 11.3

34 / 3 = 11.333

11.3 (squirrels speed) x 3 (seconds) = 33.9 feet

the squirrel can run faster than 11.3

Answer:

A). Option A

B). Option B

C). Option B

Step-by-step explanation:

A). A squirrel runs across a road in 3 seconds.

Width of the road is more than 34 feet.

We have to calculate the squirrel speed.

Speed = [tex]\frac{\text{Distance}}{\text{Time}}[/tex]

           = [tex]\frac{34}{3}[/tex]

Since distance is more that 34 so the speed will be more than [tex]\frac{34}{3}[/tex]

This is because Speed ∝ Distance.

Let r is the speed of squirrel.

r > [tex]\frac{34}{3}[/tex]

3r > 34

Option A is the correct option.

B). Inequality is 3r > 34

r > [tex]\frac{34}{3}[/tex]

r > 11.3

Option B is the answer.

C). The squirrel can run at faster than 11.3 feet per second.

Option B.

Answer:

Third choice.

The right correspondence is [tex]\angle CDB \cong \angle ECD[/tex]

Step-by-step explanation:

The third choice is not true, that is

[tex]\angle CDB[/tex] NOT corresponds to [tex]\angle ECD[/tex]

If [tex]\triangle CBD \sim \triangle CDE[/tex], then corresponding sides are proportional, and corresponding angles are congruent. The corresponding angle of [tex]\angle CDB[/tex] is

[tex]\angle CDB \cong \angle ECD[/tex]

Therefore, the third option shows a wrong correspondence, that's the right choice in this case, because it doesn't express a valid correspondence.

Answer:

x^2 +6x +8

Step-by-step explanation:

The zeros of the graphed function appear to be (-4, 0) and (-2, 0). It appears the vertex is (-3, -1).

The standard form of the function with zeros p and q is ...

(x -p)(x -q) = x^2 -(p+q)x +pq

So, for zeros p=-4, q=-2, the standard form is ...

x^2 -(-4-2)x +(-4)(-2) = x^2 +6x +8

We can check to make sure the above vertex point satisfies this function:

(-3)^2 +6(-3) +8 = 9 -18 +8 = -1

The vertex satisfies the function we wrote, so there are no additional vertical scale factors required.

The function is ...

y = x^2 +6x +8

Answer:

The missing exponent is 5^7

Step-by-step explanation:

5^11/5^?=5^4

1. Subtract the exponents from each other.

11-4=7

2. Plug 7 in as the exponent.

5^11/5^7

3. 11-7=4 therefore, 5^11/5^7 equals 5^4.

Answer:

Step-by-step explanation:

[tex]\text{We know:}\ \dfrac{a^n}{a^m}=a^{n-m}.\\\\\dfrac{5^{11}}{5^{?}}=5^4\\\\5^{11-?}=5^4\to?=7\ \text{because}\ 11-7=4[/tex]

P: Parentheses

E: Exponents

M: Multiplication

D: Division

A: Addition

S: Subtraction

What PEMDAS stands for is that in a mathematical equation, parentheses has the priority of being solved. The second priority goes to exponents, then Multiplication and Division, and then finally Addition and Subtraction.

[tex]\text{Hey there!}[/tex]

[tex]\text{The P stands for parentheses}[/tex]

[tex]\text{The E stands for exponents}[/tex]

[tex]\text{The M stands for multiplication/multiply}[/tex]

[tex]\text{The D stands for division/divide}[/tex]

[tex]\text{The A stands for Addition/Add}[/tex]

[tex]\text{The S stands for Subtraction/Subtract}[/tex]

[tex]\text{Some people refer to it as: (P)lease (E)xcuse (M)y (D)ear (A)unt (S)ally}[/tex]  [tex]\text{method for the abbreviations}[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

13/20, 65%

Step-by-step explanation:

So he has worked 26 hours out of 40 so that becomes 26/40 that is equal to 13/20 so that is your fraction and to convert to a percentage times 100 go that equals 65 so 65%

Answer:

$67 = $29 + $ x

Step-by-step explanation:

Given that on Saturday morning Owen earned= $29

End of afternoon amount total earned was= $67

Let's find the amount earned in the afternoon=?

Let's take the amount earned in the afternoon to be =$ x

Equation for total amount earned by the end of afternoon= $29 + $x

But we know total amount earned by end of afternoon was=$67 hence

the equation to determine afternoon amount will be;

$67 = $29 + $ x ----------------------------go ahead and solve for x

$67-$29 = $ x

$ 38 = x

Answer:

18.25

Step-by-step explanation:

365 ÷ 20 = 18.25

Jon drove 365 miles on 20 gallons of gas, so to find out how many miles he got per gallon, you divide 365 miles by 20 gallons. The result is 18.25 miles per gallon.

To solve this problem, you need to divide the total number of miles that Jon drove by the number of gallons of gas he used. This is because the miles per gallon is calculated by dividing the total miles driven by the amount of gas used.

So, in this case, you would do the following calculation: 365 miles ÷ 20 gallons = 18.25 miles per gallon

This means that Jon got 18.25 miles per gallon of gas.

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Answer:

$29000 with a margin of error of $5000

Step-by-step explanation:

We have that the midpoint between the given values ​​is

(X1+X2) / 2 = ($34000+$24000)/2 = $29000

We have that the midpoint between the given values ​​would be

(X2-X1)/2=($34000-$24000)/2=$10000/2=$5000

So I can write that approach as $29000 with a margin of error of $5000

Done

Answer:

the answer is A) ( radical 10 , 2 - radical 10 ) and ( radical 10 , 2 + radical 10 )

Step-by-step explanation:

Answer:

Height of tree = 39.2 ft

Step-by-step explanation:

The relationship between the height of an object and the length of it's shadow is directly proportional.

So:

[tex]\frac{4}{2.8} =\frac{h}{27.44}[/tex]

h = Height of tree in feet

Cross multiply

2.8h = 4 · 27.44

Simplify

2.8h = 109.76

÷2.8 both sides

h = 39.2

Height of tree = 39.2 ft

The height  of a tree that cast a shadow of 27.44 ft is 39.2 ft

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that  a 4 ft stick cast a shadow of 2.8 ft.

We have to find the height of a tree that cast a shadow of 27.44 ft

Let us consider x as the  height of a tree that cast a shadow of 27.44 ft.

Let us form a proportional equation

4/2.8=x/27.44

Apply cross multiplication.

4×27.44=2.8x

109.76=2.8x

Divide both sides by 2.8

x=109.76/2.8

x=39.2

Hence, the height  of a tree that cast a shadow of 27.44 ft is 39.2 ft.

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Answer:

it is 20

Step-by-step explanation:

5 * 20 = 100

100 - 10 = 90 which equals a angle in a right angle triangle

Answer:

The value of x is 11 ⇒ answer B

Step-by-step explanation:

* lets check the properties of the square

- Its four aides are equal

- Its four angles are equal and the measure of each one is 90°

- Its diagonals bisect its vertices

∵ BD is a diagonal of the square

∴ BD bisects angle B

∴ m∠ABD = m∠CBD

∵ B is a vertex of the square

∴ m∠B = 90°

∴ m∠ABD = m∠CBD = 90 ÷ 2 = 45°

∵ m∠ABD = (5x - 10)°

∴ (5x - 10)° = 45° ⇒ add 10 to each side

∴ 5x = 55 ⇒ divide both sides by 5

∴ x = 11

* The value of x is 11

To find the zeros set the equation equal to zero:

x^2 - 5x +4 = 0

Factor:

(x-4) (x-1) = 0

Now solve each set of parenthesis so that they equal zero:

(x-4) = 0, x =4

(x-1) = 0, x = 1

The zeros are 1,4

Answer:

[tex]\frac{3}{9}=\frac{4}{x}[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

In this problem

Triangle XVW is similar to triangle XZY

therefore

[tex]\frac{YZ}{VW}=\frac{XZ}{XV}[/tex]

substitute the given values

[tex]\frac{x}{4}=\frac{9}{3}[/tex]

[tex]x=3*4=12\ miles[/tex]

Answer:

A

Step-by-step explanation:

Answer:

The required inequality is [tex]6+4p>17[/tex].

Step-by-step explanation:

Let p represent the number of runs per inning.

It is given that the team scores the same number of runs per inning and the other team did not score any more points. So, the total score of other team after last four inning is 17.

Kim's team total score in last four inning is 4p. So, the total score of Kim's team after last four inning is

[tex]6+4p[/tex]

Kim's team win if the total score of other team after last four inning is less than the Kim's team.

[tex]6+4p>17[/tex]

Therefore the required inequality is [tex]6+4p>17[/tex].

Answer:

6+4p>17

Step-by-step explanation:

3 per inning

Answer:

It depends on which side of the cylinder. If she puts it on the curved side, it will roll off. If she puts it on the flat side and stabalizes it, it will stay in place if no further force is acted on it.

The range of (g * f)(x) is all real numbers (ℝ).

Composing functions: We first need to understand that (g * f)(x) refers to the composition of g and f, where f is evaluated first and then its output is used as the input for g. So, (g * f)(x) = g(f(x)) = g(e^x).

Analyzing g(e^x): The function g(x) simply subtracts 2 from its input. Since e^x is a real number for all real values of x, g(e^x) will also be a real number for all real values of x.

Range of the composed function: Therefore, as g(e^x) can take any real value, the range of (g * f)(x) will be all possible outputs of g(e^x), which is all real numbers (ℝ).

In simpler terms, no matter what real number you input into f(x), the final output after applying g(x) will always be a real number. This is because the subtraction in g(x) doesn't restrict the output in any way.

Replace the x in the equation with the x value in tha table for the missing f(x) and calculate:

f(x) = 2x +1 = 2(2) +1 = 4 +1 = 5

The answer is B) 5

The table represents the function f(x) = 2x +1. The value goes in the empty cell is 5. The answer is B) 5.

A function is a type of relation, or rule, that maps one input to specific single output.

The table represents the function

f(x) = 2x +1

Replace the x in the equation with the x value in the table for the missing f(x)

F( 2) = 2(2) +1

F( 2) = 4 +1

F( 2) = 5

The answer is B) 5

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Answer: Probability theory would be my best guess, but I would need more information to be able to fully answer this question.

Step-by-step explanation:

Answer:

x=178

Step-by-step explanation:

Since 53 is being added to x, you will subtract 53 from both sides. 231-53 equals 178, therefore x=178