Sonya made a resolution to walk 2.5 kilometers a day. On Tuesday she walked 4 times around the running track at the local high school (each lap is 0.4 kilometers.) How many additional kilometers does Sonya need to walk? (HINT: this is a multi-step problem with 2 operations...)

2x - 2y = 14

-2y = 14-2x

y= -7 + x

y = x - 7

Answer:

17,19,21

Step-by-step explanation:

let the first odd number be "x"

formular : (x)+(x+2)+(x+4).

3x+6=57

3x=57-6

3x=51

x=51/3

x=17

apply the formular.

17,(17+2),(17+4)

17,19,21.

Answer:

62.182°

Step-by-step explanation:

Using cos and sin you are able to find the height of the ladder from the bottom of the house to the place the top of the ladder is. You can do this by making a triangle. By using the lengths and angles already present you are able to find all angles of the triangle.

The angle at which the ladder is leaning is 62.18°.

Trigonometry is the branch of mathematics that deals with calculating the angles of triangles or the lengths of their sides. It mainly concerned on the properties of right angled triangle.

For the given situation,

The length of the ladder = 15 feet

The distance between the house and the ladder base = 7 feet

The angle at which the ladder is leaning can be found by using trigonometric ratio, cos θ.

we know that, [tex]cos[/tex] θ = [tex]\frac{Base}{Hypotenuse}[/tex]

The figure below shows the relationship between the sides.

⇒ [tex]cos[/tex] θ = [tex]\frac{7}{15}[/tex]

⇒ θ = [tex]cos^{-1}(\frac{7}{15} )[/tex]

⇒ θ = [tex]62.18[/tex]

Hence we can conclude that the angle at which the ladder is leaning is 62.18°.

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Answer:

hey! You have to use the trigonometric formula because it's a rectangle triangle:

(a^2)+(b^2)=(c^2)

(11^2)+(11^2)=(c^2)

√(242)=√(c^2)

15.56=c

So basically, the answer is D!

The square ABCD has equal sides, and the length of the diagonal AC is 15.6 centimeters

The side length of the square is given as:

l = 11 cm

The length of the diagonal is calculated using:

Diagonal = l * √2

This gives

Diagonal = 11 * √2

Evaluate

Diagonal = 15.6

Hence, the length of the diagonal AC is 15.6 centimeters

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Answer:

y= -3x + 20

Step-by-step explanation:

just graph it out

Step-by-step explanation:

11. f(-4)= 4x-1

11a. f(-4)= 4(-4)-1

11b. f(-4)= -16-1

11c. f(-4)=-17

12. For what value of x is g(x)=-4

12a. 4-? = -4

12b. 4-8= -4

12c. x = 8

13. (f(2)= 4x-1)×(g(2)= 4-x)

13a. (f(2)= 4(2)-1)×(g(2)= 4-(2)

13b. (f(2)= 8-1)×(g(2)= 4-2)

13c. (f(2)= 9)×(g(2)= 2)

13d. 18

14. f(-3)= 4x-1

14a. f(-3)= 4(-3)-1

14b. f(-3)= -12-1

14c. f(-3)= -13

Answer:

6 shirts

Step-by-step explanation:

she spent 56 in total

56-20 for the pants

36 left and she bought 6 shirts

36 divided by 6

6

Answer -10x 2- 11x +1 (2 as a exponent) im not completely sure if its right but i tried

Step-by-step explanation:

Answer:

D would be the answer

Step-by-step explanation:

since you have a positive 12 at the end of your equation(thats your y intercept 0,12) then you can eliminate A, B. Next you would plug in (-3,0) in your equation and see if it would work and it did so thats your answer. ( i know thats not the formal way to do it but its a shortcut i like to use ;)

Answer:

N = 18

Step-by-step explanation:

Answer:

18/4

Step-by-step explanation:

Answer:

nice

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

0.4

hope this is usefull to you

Answer:

its a good thing but the warnings u may get banned

Step-by-step explanation:

12) 42

13) 10.4

14)

a) 0.25

b) 0.39

15) 2.1

16) 35.7

17) 270£

4x=67 is the  equation can be used to determine the number of DVDs in Daniel's collection.

Two or more expressions with an Equal sign is called as Equation.

Given that Together, Matthew and Daniel have 67 DVDs.

M+D=67

Let x represents the number of DVDs

Matthew's collection has 3 times as many DVDs as Daniel's collection.

M=3D

Now M=D=x

As Matthew and Daniel have 67 DVDs.

3x+x=67

4x=67

Hence, 4x=67 is the  equation can be used to determine the number of DVDs in Daniel's collection.

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Answer:

Step-by-step explanation:

Stephen : Gavin : Jim

3 : 1 : 2

We can say that this means the total amount of sweets get split between the 3 of them into 6 equal parts ( 3 + 1 + 2).

If Stephen gets 24 sweets, this means

3 parts = 24

So to find 1 part, divide 24 by 3.

1 part = 8 sweets

Now we can find the total by multiplying this by 6.

6 parts = 8 x 6 = 48 sweets.

Answer:

[tex]a_{n}[/tex] = 4n - 2

Step-by-step explanation:

There is a common difference d between consecutive terms in the sequence, that is

6 - 2 = 10 - 6 = 14 - 10 = 18 - 14 = 4

This indicates the sequence is arithmetic with n th term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 2 and d = 4 , thus

[tex]a_{n}[/tex] = 2 + 4(n - 1) = 2 + 4n - 4 = 4n - 2

Answer:

29.11

Step-by-step explanation:

Answer:

a) The equation of the arch is [tex]y = -10\cdot x^{2}[/tex].

b) The height of the arch from the ground is 810 feet.

Step-by-step explanation:

Statement is incomplete. Complete statement is:

An archway in front of a school is in the shape of a parabola. The top of the arch is the vertex (0,0). The school seal is at the focus, 2.5 feet below the vertex, and the arch is 18 feet wide at the ground.

Write an equation  that represents the arch.

What is the height from the top of the arch to the  ground?

a) Write an equation that represents the arch.

According to the statement, the archway is a vertical downward parabola. From Analytical Geometry we know that parabolas are represented by the following equation in standard form:

[tex]y-k = 4\cdot p\cdot (x-h)^{2}[/tex] (Eq. 1)

Where:

[tex]p[/tex] - Distance between vertex and focus, measured in feet.

[tex]x[/tex] - Independent variable, measured in feet.

[tex]y[/tex] - Dependent variable, measured in feet.

[tex]h[/tex], [tex]k[/tex] - Coordinates of the vertex, measured in feet.

If we know that [tex]p = -2.5\,ft[/tex], [tex]h = 0\,ft[/tex] and [tex]k = 0\,ft[/tex], then the equation that represents the arch:

[tex]y = -10\cdot x^{2}[/tex]

The equation of the arch is [tex]y = -10\cdot x^{2}[/tex].

b) What is the height from the top of the arch to the  ground?

Given that parabola is a symmetrical curve, we determine the vertical position at the base of the arch ([tex]x = 9\,ft[/tex]):

[tex]y_{min} = -10\cdot (9\,ft)^{2}[/tex]

[tex]y_{min} = -810\,ft[/tex]

Then, the height of the arch from the ground is given by this difference:

[tex]h = 0\,ft-(-810\,ft)[/tex]

[tex]h = 810\,ft[/tex]

The height of the arch from the ground is 810 feet.

Answer:

96+t=264

Step-by-step explanation:

Answer:

3 because 3 x 2 + 3 x 8 = 30 and 3(2+8)=30

Answer:

0.666667*​x+​4-​3/​5-​2

HOPE I HELP!!!! :)

Answer:

2 inches of snow was left on the ground

Step-by-step explanation:

To calculate the amount of snow on the ground we can take it one step at a time. Since there was no snow on the ground we can start at a level of 0. Then it snowed until 6 inches of snow had fallen, so we can add that to our total.

0 + 6 = 6 inches

Next, it snowed for 2 more hours at a rate of 2 inches per hour, meaning we multiply this by 2 hours and add to the total amount of snow that was already on the ground.

(2*2) + 6 = 10 inches

Lastly, the sun came out and melted the snow on the ground for 2 hours at a rate of 4 inches per hour. Since it is melting the snow, this means that it is subtracting the snow from the total. So we would have to multiply the rate (4 inches per hour) by the number of hours and then subtract that from the amount of snow on the ground.

10 - (4*2) = 2 inches

Answer:

11.0

Step-by-step explanation:

Circumfrence = 2 x pi x r.

making radius, r the subject of relation, you.get 11.003184713

Answer:

Hey!

Your answer is 11cm!

Step-by-step explanation:

So to get the radius from the Circumference we need both the Circumference and the value of pi...3.14

Radius = [tex]\frac{C}{2\pi }[/tex] ... (that's the formula)

WE SUBSTITUTE IN:

Radius = 69.1/2 x 3.14

69.1/6.28

This equals = 10.99760656765

BUT 11cm when you round it to the next whole number or 2sf

Answer:

58

Step-by-step explanation: