Lainey runs a string of lights from the ground straight up a door that is 2.5 m tall. Then he runs the rest of the string in a straight line to a point on the ground which is 6 m from the base of the door frame. There are 10 lights per meter of the string. How many total lights are on the string?

Answer:

108º

Step-by-step explanation:

subtract outer angle from circle

360º - 252º = 108º

I hope this helps you

find DCG

360-252=108°

angle DBG=1/2(252-108)

angle DBG=72°

Answer:

B

Step-by-step explanation:

This rectangle appears to have 7 boxes on the bottom, and 3 box for the side.

Since area is base×height

It would be 7×3

Answer:

When you plot the graph, you may see a line or a curve. This presents the trend of the relationship of the two quantities when the independent variable changes.

Graphs visually depict patterns and trends, while equations provide precise mathematical descriptions, both revealing valuable information about the relationship between two quantities.

Graphs visually represent data and patterns, allowing us to identify the nature of the relationship between two quantities. The slope and intercepts of a graph provide information about the rate of change and the values when one quantity is zero.

Equations, on the other hand, offer precise mathematical descriptions of the relationship. The form of the equation reveals the nature of the relationship, while coefficients and constants provide specific information. Solving equations yields solutions that satisfy the relationship.

Both graphs and equations work together to provide a comprehensive understanding of the relationship between two quantities, with graphs offering visual insights and equations providing precise mathematical information.

Learn more about equations here;

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Answer:

Step-by-step explanation:

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

[tex]\frac{14}{30}[/tex] is not equivalent to [tex]\frac{2}{5}[/tex] in the list of fractions [tex]\frac{18}{45}, \frac{14}{30} , \frac{x}{y} \frac{10}{25}, \frac{8}{20}, \frac{16}{40}[/tex].

Equivalent fractions represent the same value even though they look different.

We know we can find an equivalent fraction of a given fraction by or dividing both the numerator and denominator of the given fraction with the same number (maybe LCM or HCF of the numerator or denominator).

[tex]\frac{18}{45}=\frac{18/9}{45/9}=\frac{2}{5}[/tex] (since [tex]9[/tex] is HCF of [tex]18, 45[/tex])

[tex]\frac{14}{30}=\frac{14/2}{30/2}=\frac{7}{15}[/tex] (since [tex]2[/tex] is HCF of [tex]7, 15[/tex])

[tex]\frac{10}{25} =\frac{10/5}{25/5} =\frac{2}{5}[/tex] (since [tex]5[/tex] is HCF of [tex]10, 25[/tex])

[tex]\frac{8}{20} =\frac{8/4}{20/4} =\frac{2}{5}[/tex] (since [tex]4[/tex] is HCF of [tex]8, 20[/tex])

[tex]\frac{16}{40} =\frac{16/8}{40/8} =\frac{2}{5}[/tex] (since [tex]8[/tex] is HCF of [tex]16, 40[/tex])

Thus, [tex]\frac{14}{30}[/tex] is not equivalent to [tex]\frac{2}{5}[/tex].

Learn more about Equivalent fractions here- https://brainly.com/question/17912

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Answer:

The correct option is;

B. Range

Step-by-step explanation:

In descriptive statistics which analyses the quantitative summary of the statistical data, the range is the region or area or the statistical interval where the data is obtained from and as such the range (in descriptive statistics) gives a guide to the dispersion of the statistical information.

The range is best suited for the representation of the dispersion when the size of the data set is small.

Answer:

D. 769.7 ft^3

Step-by-step explanation:

because area of a solid is area of the base times the height, so to find the area of the base, it is pi*r^2(3.14*7^2), and that equals to 153.94, times that by 5 and you get 769.7 ft^3

Answer:

A

Step-by-step explanation:

x^2/y+x^2/z where x=6, y=-4 and z=-2

x^2(1/y+1/z)=36*(-1/4+(-1/2))=-36*(3/4)=-27

Answer:

9

Step-by-step explanation:

kwowoooaloiwknwjsjsisjsjsjsisjsj

Hello!

Answer:

[tex]\huge\boxed{x = 4.5}[/tex]

Starting with:

5x + 4(-x - 2) = -5x + 2(x - 1) + 12

Distribute terms outside of the parenthesis:

5x + 4(-x) + 4(-2) = -5x + 2(x) + 2(-1) + 12

5x - 4x - 8 = -5x + 2x - 2 + 12

Combine like terms:

x - 8 = -3x + 10

Isolate for the "x" variable by adding 3x for both sides:

4x - 8 = 10

Add 8 to both sides:

4x = 18

Divide both sides by 4:

x = 18/4

x = 4.5

Hope this helped! :)

Answer:

[tex] \boxed{x = 4.5}[/tex]

Step-by-step explanation:

[tex] \mathrm{5x + 4( - x - 2) = - 5x + 2(x - 1) + 12}[/tex]

Distribute 4 through the parentheses

Similarly, Distribute 2 through the parentheses

[tex] \mathsf{ 5x - 4x - 8 = - 5x + 2x - 2 + 12}[/tex]

Collect like terms

[tex] \mathsf{ x - 8 = - 3x - 2 + 12}[/tex]

Calculate the sum

[tex] \mathsf{x - 8 = - 3x + 10}[/tex]

Move variable to L.H.S and change its sign

Similarly, Move constant to R.H.S and change its sign

[tex] \mathsf{ x + 3x = 10 + 8}[/tex]

Collect like terms

[tex] \mathsf{4x = 10 + 8}[/tex]

Calculate the sum

[tex] \mathsf{4x = 18}[/tex]

Divide both sides of the equation by 4

[tex] \mathsf{ \frac{4x}{4} = \frac{18}{4}} [/tex]

Calculate

[tex] \mathsf{x = 4.5}[/tex]

Hope I helped!

Best regards!

7. √9

√9 is a rational number because √9 = 3 = 3/1.

8. No, there is no integer between -6 and -7.

9. π

π is an irrational number

Answer:

[tex]D = 170\º[/tex]

Step-by-step explanation:

Given

Shape: Pentagon

[tex]A = 87\º[/tex]

[tex]B = 125\º[/tex]

[tex]C = 63\º[/tex]

[tex]E = 95\º[/tex]

Required

Find D

From the sum of angles in a Pentagon; we have that

[tex]A + B + C + D + E = 540[/tex]

Substitute values for A, B, C and E

[tex]87\º + 125\º + 63\º + D + 95\º = 540\º[/tex]

Collect Like Terms

[tex]87\º + 125\º + 63\º + 95\º + D = 540\º[/tex]

[tex]370\º + D = 540\º[/tex]

Collect Like Terms

[tex]D = 540\º - 370\º[/tex]

[tex]D = 170\º[/tex]

Hence, from the list of given options, the correct answer is 170

Answer:

12

Step-by-step explanation:

1 inch = 20 miles

240 miles ÷ 20 miles =

12 inches

Answer:

12 inches

Step-by-step explanation:

Hey there!

Well to solve the given question we need to use fractions,

if 1 inch is 20 milles, we can set up the following.

[tex]\frac{1}{20} = \frac{x}{240}[/tex]

Cross multiply

240 = 20x

Divide both sides by 20

x = 12

So it is 12 inches in the map.

Hope this helps :)

Answer:

2039/1000×315/10

642285/10000

=64.2285

Answer:

Here's what I get  

Step-by-step explanation:

Part A

The graph shows a polynomial of odd degree. It is probably a third-degree polynomial — a cubic equation.

Part B

The standard form of a cubic equation is

y = ax³ + bx² + cx + d

The factored form of a cubic equation is

y = a(x - b₁)(x² + b₂x + b₃)

If you can factor the quadratic, the factored form becomes

y = a(x - c₁)(x - c₂)(x - c₃)

Part C

The zeros of the function are at x = -25, x = - 15, and x = 15.

Part D

The linear factors of the function are x + 25, x + 15, and x - 15.

Part E

y = a(x + 25)(x + 15)(x - 15) = a(x + 25)(x² - 225)  

y = a(x³ + 25x² - 225x - 5625)

Part F

When x = 0, y = 1.

1 = a[0³ +25(0)² - 225(0) - 5625] = a(0 + 0 - 0 -5625) = -5625a

a = -1/5625

Part G

[tex]y = -\dfrac{1}{5625}( x^{3} + 25x^{2} - 225x - 5625)\\\\y = \mathbf{ -\dfrac{1}{5625} x^{3} - \dfrac{1}{225}x^{2} + \dfrac{1}{25} x + 1}[/tex]

Answer

Actually, the answer should be -0.0007(x+20)(x+5)(x-15)

Step-by-step explanation:

This is continuing off of the previous answer

PART C

The zeros should be (15,0), (-5,0), and (-20,0)

PART D

x - 15, x + 5, and x + 20

PART E

a(x - 15)(x + 5)(x + 20)

Standard: [tex]a(x^{3} + 10x^{2} -275x-1500)[/tex]

PART F

The y-intercept is at (0,1), so we replace the x's with 0:

1 =[tex][(0)x^{3} +10(0)x^{2} -275(0)-1500][/tex] and this gives us (0+0-0-1500) which also equals -1500

Then we do [tex]\frac{1}{-1500}[/tex] which gives us -0.0006 repeating which rounds to -0.0007

a= -0.0007

PART G

Just place the numbers where they should go and your answer is

y =-0.0007(x + 20)(x + 5)(x - 15)  

the placement for (x + 20) (x + 5) and (x - 15) doesn't matter as long as they are behind -0.0007

Answer:

C. 35

Step-by-step explanation:

x^2 + 12^2 = (x + 2)^2

x^2 + 144 = x^2 + 4x + 4

144 = 4x + 4

4x = 140

x = 35

Answer:

C

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean Theorem (a² + b² = c², in this case a = x, b = 12 and c = x + 2) to solve for x.

x² + 12² = (x + 2)²

x² + 144 = x² + 4x + 4

144 = 4x + 4

140 = 4x

x = 35

Answer:

  y = (x -1)² -3

Step-by-step explanation:

A quadratic with a vertex at (h, k) will have an equation of the form ...

 y = a(x -h)² +k

You have (h, k) = (1, -3), and a vertical scale factor* of 1. So, the equation of the graphed curve is ...

  y = (x -1)² -3

_____

* One way to determine the value of "a" in the form shown is to look at the vertical difference between the vertex and the points 1 unit right or left of the vertex. Here, those points are 1 unit above the vertex, so the vertical scale factor "a" is 1.

Answer:

[tex]a \: and \: b = \frac{5}{ \sqrt{2} } [/tex]

Step-by-step explanation:

[tex] \sin(45) = \frac{a}{5} \\ \frac{1}{ \sqrt{2} } = \frac{a}{5} \\ a = \frac{5}{ \sqrt{2} } \\ \\ \\ \\ \sin(45) = \frac{b}{5} \\ b = \frac{5}{ \sqrt{2} } [/tex]

I hope I helped you^_^

Answer:

A = 36 cm^2

Step-by-step explanation:

The perimeter of a square is given by

P =4s

24 = 4s

Divide by 4

24/4 = 4s/4

6 =s

The area of a square is

A =s^2

A = 6^2

A = 36 cm^2

Answer:

absolute value

Step-by-step explanation:

Answer:

This shows the absolute value of an integer.

Step-by-step explanation:

When you see the lines | | around a number, it should always give you the answer of that number's positive integer. So lets say I out | -2 | the answer for this equation should be 2.

Answer:

10.5

Step-by-step explanation:

2/3=7/x

2x=21

x=21/2=10.5

Hello!

Answer:

[tex]\huge\boxed{59.04 units}[/tex]

To solve, we will need to use Right-Triangle Trigonometry:

Begin by solving for angles ∠S and ∠R using tangent (tan = opp/adj)

tan ∠S = a / (1/2b)

tan ∠S = 3√5 / 14

tan ∠S ≈ 0.479

arctan 0.479  = m∠S (inverse)

m∠S and m∠R ≈ 25.6°

Use cosine to solve for the hypotenuse, or the missing side-length:

cos ∠S = 14 / x

x · cos (25.6) = 14

x  = 14 / cos(25.6)

x ≈ 15.52

Both triangles are congruent, so we can go ahead and find the perimeter of the figure:

RS + RQ + QS = 28 + 15.52 + 15.52 = 59.04 units.

Hope this helped you! :)

Answer:

[tex]\large \boxed{\mathrm{59.05 \ units}}[/tex]

Step-by-step explanation:

Take one small triangle, solve for hypotenuse.

[tex]\frac{b}{2} =\frac{28}{2} =14[/tex]

Use Pythagorean theorem.

[tex]c=\sqrt{(3\sqrt{5})^2 +14^2 }[/tex]

[tex]c= 15.524175...[/tex]

Add the hypotenuse twice because there are two triangles, then add to the length of b to find the perimeter.

[tex]15.524175...+15.524175...+28[/tex]

[tex]59.048349...[/tex]

Answer:

Step-by-step explanation:

3x² + 7x - 6 = 3x² + 9x - 2x - 2*3

                  = 3x (x + 3) - 2(x +3)

                  = (3x - 2)(x + 3)

Area of the rectangle = 3x² + 7x - 6

length * width = 3x² + 7x - 6

length * (x + 3) = (3x -2)(x +3)

          length = [tex]\frac{(3x-2)(x+3)}{(x+3)}[/tex]

          length = (3x - 2)

Answer:

28km to cm = 2,800,000cm

Step-by-step explanation:

In order to convert km to cm you have to times it by 100,000

So... 28 x 100,000 = 2,800,000

Hope this helps

Answer:2,800,000cm

Step-by-step explanation:

To convert a larger unit into a smaller unit, you must first check how much does the smaller unit need to make the larger unit. Then multiply the given larger unit to the amount of smaller unit that is equal to 1 of the larger unit.

Because: 100,000cm = 1km

So = 28km×100,000 =2,800,000cm

Answer:

If it is a straight line then ;

RT= RS+ST

90=(7y+4) + (3y+6)

90 = 10y + 10

10y= 90 – 10

10y = 80

y= 80 / 10

y =8

ST = 3y+6= 3(8)+6= 24 +6 = 30

RS = 7y +4 = 7(8) + 4 = 56 +4 = 60

I hope I helped you^_^

Answer:

15,10

Step-by-step explanation:

let the numbers be 3x and 2x

3x-2x=5

x=5

∴ numbers are 3×5,2×5

or 15,10

Answer:

[tex] 3\sqrt{5} [/tex]

Step-by-step explanation:

Find the largest factor of 45 that is a perfect square.

The factors of 45 are 1, 3, 5, 9, 15, 45.

The largest perfect square is 9.

Now breakup 45 into a product which has 9 as a factor.

45 = 9 * 5

[tex] \sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5} [/tex]

Three million three hundred eighty-eight thousand one hundred ninety-eight - 3388198

Angles ECD  and CEF add to 180

40+140 = 180

So that means we have EF parallel to CD (due to the same side interior angle theorem)

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

Angles BCE and ECD combine to 30+40 = 70, which is congruent to angle ABC = 70 as well.

In other words, this shows angle ABC = angle BCD. Both of these angles are alternate interior angles. Since they're congruent, they lead to AB being parallel to CD.

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

So far we have

AB || CD

CD || EF

Using the transitive property, we can then link the two statements to say AB || EF. Think of a chain where CD is the common link. We go from AB to CD, then from CD to EF. So we can just take a single path from AB to EF.

It's like saying "P --> Q and Q --> R, therefore P --> R"

The coldest time of day in Mumbai is 5 hours after midnight.

Since the average temperature t hours after midnight in Mumbai, India, is given by:

T(t)=24.5-5.5sin((2pi(t+1))/24)

We have that

T(t) = 24.5 - 5.5sin((2π(t+1))/24)

The coldest time of day is when T(t) is minimum.

T(t)  is minimum when 5.5sin((2π(t+1))/24) is minimum where t is the coldest time of day at minimum temperature, T(t).

Since for a sine function, -1 ≤ sinФ ≤ 1, the minimum value of sinФ = -1.

So, T(t) = 24.5 - 5.5sin((2π(t+1))/24) is minimum when

5.5sin((2π(t+1))/24) is minimum.

Also, -5.5sin((2π(t+1))/24) = 5.5 × -1 at minimum temperature T(t)

So, 5.5 × -1 = 5.5 × -sin((2π(t+1))/24)

So, -sin((2π(t+1))/24) = -1

sin((2π(t+1))/24) = 1

Taking inverse sine of both sides, we have

sin⁻¹sin((2π(t+1))/24) = sin⁻¹(1)

((2π(t+1))/24) = π/2

Multiplying both sides by 24, we have

(2π(t+1))/24 × 24 = π/2 × 24

(2π(t+1)) = 12π

Dividing both sides by 2π, we have

2π(t+1)/2π = 12π/2π

t + 1 = 6

t = 6 - 1

t = 5 hours

So, the coldest time of day in Mumbai is 5 hours after midnight.

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Answer:

The quotient to this equation is 4x² + 13x + 1

Step-by-step explanation:

When we divide exponents, we subtract the exponential numbers.

4x³ + 13x² + 5x - 4 / x + 1

Now, we divide. For this problem, we are only dividing the like terms of x because anything divided by 1 will equal to itself.

4x² + 13x + 5 - 4

Now, we combine like terms.

4x² + 13x + 1