Sam is training for a 5
km run. While training he runs for 6
minutes, then rests for 2
minutes, runs for 6
minutes, rests for 2
minutes, etc., until he finishes the 5
km. It takes him 26
minutes in total (with the rest periods) to finish the 5
km rum. If Sam runs at a constant speed (when he is not resting), what is this speed in kilometers per hour? (Recall there are 60
minutes in 1
hour.)

Answer:

the solution set is { - 7, - 3 }

Step-by-step explanation:

(x + 3)(x + 7) = 0 ← in factored form

equate each factor to zero and solve for x

x + 3 = 0 ( subtract 3 from both sides )

x = - 3

x + 7 = 0 ( subtract 7 from both sides )

x = - 7

solution set is { - 7, - 3 }

The equation is an identity is discussed below.

An identity is a mathematical equation that holds true for all values of the variables involved.

In other words, it is true regardless of the specific values of the variables. When an equation is an identity, it means that both sides of the equation are equivalent and represent the same mathematical relationship.

For example, the equation 2x + 3 = 2(x + 1) is an identity because it holds true for all values of x.

When an equation is an identity, it provides a general statement or rule that is universally applicable and does not depend on specific values or conditions. Identifying an equation as an identity is important because it allows us to make general conclusions and deductions that apply in all cases.

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The measure of angle ACB is half the difference between 180 degrees and the measure of arc AB.

The measure of angle ACB can be determined using the properties of tangents and secants intersecting a circle.

Since side AC is tangent to the circle, angle BAC is a right angle (90 degrees).

According to the tangent-secant theorem, the measure of angle ACB is equal to half the difference between the intercepted arcs AB and AX.

Since angle BAC is a right angle, the intercepted arc AX is a semicircle, which means its measure is 180 degrees. The intercepted arc AB is an arc of the circle and is less than 180 degrees since it is not a full circle.

Therefore, the measure of angle ACB is half the difference between 180 degrees and the measure of arc AB.

To find the exact measure, more information is needed about the length of arc AB or the relationship between the lengths of the sides of the triangle. Without this additional information, we cannot determine the precise measure of angle ACB.

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An equation that is true about segment D prime E prime include the following: A. segment D prime E prime = one half segment DE

In Geometry, a dilation is a type of transformation which typically changes the side lengths of a geometric object, but not its shape.

In this scenario and exercise, we would dilate the coordinates of the vertices of triangle ABC (ΔABC) by applying a scale factor of 1/2 that is centered at point A as follows:

D'E' = 1/2 × DE

In conclusion, line segment D'E' is equal to one half line segment DE.

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1) The three figure bearing of B from A when B is due East of A is 090°

2) Note that Kenzi drives 60km further than Jafar.

A) A bearing is the angle in degrees measured clockwise from north in mathematics. Bearings are often specified in three figures. 30° clockwise from north, for example, is generally represented as 030°.

Hence in the above case of option A,  The three figure bearing of B from A when B is due East of A is 090°

B) To find or compute how much further Kenzi drives than Jafar, we need to convert the distances on the map to their real-world distances using the given scale of 1cm to 200km.

So  A to B for Jafar -

Distance from A to B = 2.4cm x 200km/ cm = 480km

Then for  B to C for Kenzi  -

Distance from B to C = (1.2cm + 1.5cm) x 200km/cm

= 2.7cm x 200km/cm

= 540km

So to  determine how much further Kenzi drives compared to Jafar

Kenzi drives 540km - Distance from A to B

= 540km - 480 km = 60km

Therefore, Kenzi drives 60km further than Jafar.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

Eight fourths is proportional to the value of 2/1

Proportionality of values means the relationship that exists between two variables where their ratios are equivalent to each other.

A ratio that is made up of two variables is said to be proportional to another ratio when after being simplified one arrives at the same ratio.

Using the 8:4 or 8/4. This is equivalent to 2/1 and also equivalent to 16/8 as the simplification leads to 2/1

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The average rate of change for the snowfall amount is given as follows:

2.4 inches per hour.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function.

The change in the output is given as follows:

8.1 - 3.3 = 4.8.

(output is the amount of snow).

The change in the input is given as follows:

2 - 0 = 2.

(input is the time in hours).

Hence the average rate of change of the snowfall over time is given as follows:

4.8/2 = 2.4 inches per hour.

(change in the snowfall divided by the change in time).

The table is given by the image presented at the end of the answer.

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Answer:

2.23

Step-by-step explanation:

You have 3 $5 bills which us 15 dollars. 15 dollars - 5.43 - 3.89 - 3.45 = 2.23 dollars for the bookmark.

To see if you are correct, you can add 3.45, 2.23, 3.89, and 5.43 to get your answer.

To solve the equation |7x - 20| = |2x + 20|, we need to consider two cases based on the absolute values.

Case 1: (7x - 20) = (2x + 20)

Simplifying this equation, we get:

7x - 20 = 2x + 20

Subtracting 2x from both sides:

5x - 20 = 20

Adding 20 to both sides:

5x = 40

Dividing both sides by 5:

x = 8

Case 2: (7x - 20) = -(2x + 20)

Simplifying this equation, we get:

7x - 20 = -2x - 20

Adding 2x to both sides:

9x - 20 = -20

Adding 20 to both sides:

9x = 0

Dividing both sides by 9:

x = 0

Therefore, the solutions to the equation |7x - 20| = |2x + 20| are x = 8 and x = 0.

Answer:

Step-by-step explanation:

easy its A tell me if u got it correct good job (:

Answer:

12 feet

Step-by-step explanation:

1 inch= 8 feet

1/2 inch= 4 feet

1/4 inch= 2 feet

(2x2)/2= 2  (one triangle)

2x4=8 (rectangle)

2+2=4 +8=12

^2 was added 2 times cause there are 2 triangles

(you did not need a 3rd measurement cause the triangle measurements were equal)

The length x in the triangle below is 16 m.

Length is the distance between two points.

To calculate the length of the triangle, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for x

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Para resolver este problema, podemos utilizar el Teorema de los Cosenos para calcular los ángulos interiores del triángulo.

Sea A, B y C los vértices del triángulo correspondientes a los centros de los engranajes. Sea a, b y c las longitudes de los lados opuestos a los ángulos A, B y C respectivamente.

Dado que los radios de los engranajes miden 15 cm, 16 cm y 17 cm, podemos considerar que los lados del triángulo son a = 15 cm, b = 16 cm y c = 17 cm.

El Teorema de los Cosenos establece que en un triángulo con lados a, b y c, y ángulos opuestos A, B y C respectivamente, se cumple la siguiente fórmula:

c^2 = a^2 + b^2 - 2ab * cos(C)

Podemos aplicar esta fórmula para cada uno de los ángulos del triángulo.

Para el ángulo A, tenemos:

c^2 = b^2 + a^2 - 2ab * cos(A)

17^2 = 16^2 + 15^2 - 2 * 16 * 15 * cos(A)

Resolviendo la ecuación, encontramos que cos(A) = -1/8. Tomando el coseno inverso (arcocoseno), encontramos que el ángulo A es aproximadamente 135.2 grados en el sistema de medición radial.

Para el ángulo B, tenemos:

a^2 = c^2 + b^2 - 2cb * cos(B)

15^2 = 17^2 + 16^2 - 2 * 17 * 16 * cos(B)

Resolviendo la ecuación, encontramos que cos(B) = -7/17. Tomando el coseno inverso, encontramos que el ángulo B es aproximadamente 120.6 grados en el sistema de medición radial.

Para el ángulo C, tenemos:

b^2 = a^2 + c^2 - 2ac * cos(C)

16^2 = 15^2 + 17^2 - 2 * 15 * 17 * cos(C)

Resolviendo la ecuación, encontramos que cos(C) = -1/2. Tomando el coseno inverso, encontramos que el ángulo C es aproximadamente 120 grados en el sistema de medición radial.

Entonces, los ángulos interiores del triángulo son:

A ≈ 135.2 grados

B ≈ 120.6 grados

C ≈ 120 grados

Estos valores están expresados en el sistema de medición radial.

Answer:

(d) 18 in.

Step-by-step explanation:

When we're given the three sides of a triangle, one formula we can use for perimeter of a triangle is:

P = s1 + s2 + s3, where

P = 2 + 6 + 10

P = 8 + 10

P = 18

Thus, the perimeter of the triangle is 18 in.

Answer:

[tex]d < 20[/tex]

Step-by-step explanation:

The key words in this question are fewer than, which signifies the less than sign. So, the number of days that Byron worked is less than 20.

The measure of the arc of the circle is mST = 122°

Given data ,

Let the circle be represented as C

where the two chords of the circle are RT and PS

And the chords RT and PS intersect at the point U

Now , when two chords intersect inside a circle, four angles are formed. At the point of intersection, two sets of congruent vertical angles are formed in the corners of the X that appears.

On simplifying , we get

m∠SUT = ( 1/2 ) ( mPR + mST )

123° = ( 1/2 ) ( 124° + mST )

On solving for mST , we get

( 124° + mST ) = 246°

Subtracting 124° on both sides , we get

mST = 122°

Hence , the measure of arc mST = 122°

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If you flip two coins 68 times, the best prediction for the number of times both coins will land on heads is 17.

If you flip two coins 68 times, the best prediction for the number of times both coins will land on tails is 17.

The possible outcomes when two coins are flipped are;

head - head = HH

tail - tail = TT

Head and tail = HT

Tail and head = TH

The probability of getting two heads = 1/4

If you flip two coins 68 times, the best prediction for the number of times both coins will land on heads is calculated as;

Expected value = (68 flips) x (1/4 probability of getting HH) = 17

The probability of getting two tails = 1/4

Expected value = 68 x 1/4 = 17

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Answer:

The answer is 64°

Step-by-step explanation:

opposite angles are equal

x=64°

Answer:

X is 64 degrees.

Step-by-step explanation:

X is directly across from 64 degrees. These angles are equal. So are angle y and 18, and angle z and the blank angle at the bottom.

The requried solution of the given derivative has been given below.

If F(t) is an antiderivative of t⁵, then we have:

F'(t) = d/dt(F(t)) = t⁵

According to the Second Fundamental Theorem of Calculus, we have:

[tex]\int_1^x t^5 dt = F(x) - F(1)[/tex]

Using this formula, we can find [tex]d/dx(\int_1^x t^5 dt)[/tex] as follows:

[tex]d/dx(\int_1^x t^5 dt) = d/dx(F(x) - F(1)) = F'(x) - 0 = t^5[/tex]

Therefore, [tex]d/dx(\int_1^x t^5 dt) = t^5.[/tex]

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The miles you drive must be greater than or equal to 183 miles in order for Plan B to save you money.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

For the mileages, we have that:

Hence the functions are given as follows:

Cost B is the better plan when:

A(x) > B(x)

Hence:

30 + 0.14x > 50

0.14x > 20

x > 20/0.14

x > 142.9 miles -> rounded to 143.

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Answer:

Step-by-step explanation:

A brokerage account is an investment account that allows you to buy and sell a variety of investments, such as stocks, bonds, mutual funds, and ETFs.

Therefore the answer is D

Answer:

147

Step-by-step explanation:

V = h * S = h * Pi R^2 = h * Pi * d^2/4 = 7.5 * 3.14 * 25 / 4 = 147.188

Step-by-step explanation:

Using rules of logs :

9 loga x =  loga x^9

Then using another rule:

loga x^9 + loga y =   loga (x^9 * y )

Answer: 14,5,15 is correct

Step-by-step explanation:

When a person places $12,500 in an investment account earning an annual rate of 8.3%, compounded continuously, based on the formula V = Pe^rt, the amount of money (future value), to the nearest cent, in the account after 12 years, is $33,842.88.

Using the formula A = Pe^rt where V is the future value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest.

In this situation, we can use an online finance calculator to determine the future value compounded continuously as follows:

Principal (P): $12,500.00

Annual Rate (R): 8.3%

Compound (n): Compounding Continuously

Time (t in years): 12 years

Result:

A (Future Value) = $33,842.88

A = P + I where

P (principal) = $12,500.00

I (interest) = $21,342.88

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The weight of a pitaya seed in standard form is [tex]1 \times 10^-^6[/tex]ounce.

In standard form, the weight of a pitaya seed is expressed in scientific notation, where the number is a decimal between 1 and 10, and the exponent is a power of 10. The weight of a pitaya seed is given as [tex]1 x 10^-^3[/tex] ounce, which means that the seed weighs one-thousandth of an ounce.

To write this in standard form, we first convert the number to a decimal between 1 and 10 by moving the decimal point three places to the left. This gives us a decimal of 0.001. The exponent is already in the form of a power of 10, so we can leave it as [tex]10^-^3[/tex]. Thus, the weight of a pitaya seed in standard form is:

[tex]0.001 \times 10^-^3[/tex]

To simplify this expression, we can multiply the decimal and the exponent. This gives us:

[tex]1 x 10^-^6[/tex]

This means that the weight of a single pitaya seed is very small, and it takes many seeds to make up the weight of a whole pitaya fruit.

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The statement that best describes the solution to the inequality in this problem is given as follows:

all real numbers except x = 1.

The inequality in the context of this problem is defined as follows:

2(x + 7) – 1 > 15 or 3(x + 2) < 2x + 7

The solution to the first inequality is given as follows:

2(x + 7) – 1 > 15

2x + 14 > 16

2x > 2

x > 1.

The solution to the second inequality is given as follows:

3(x + 2) < 2x + 7

3x + 6 < 2x + 7

x < 1.

The or operation includes the elements that belong to the solution set of at least one of the inequalities, hence the solution is given as follows:

all real numbers except x = 1.

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