John ran the​ 100-m dash with a time of 9.87sec. If this pace could be maintained for an entire 26-mi marathon, what would his time​ be? (Notice that 1 m ≈ 3.281 ft and 1 mi = 5280 ft.)

Hr____

Minutes____

Seconds____

1. B

2. C

3. D

4. A

Hope this helps!

Answer:

1. B

2. C

3. D

4. AStep-by-step explanation:

Using the equation of a line as y -y1 = m(x-x1)

Replace m with the given slope and y1 and x1 with the given point:

y - (-92) = -14(x- (-2))

Simpligy:

y + 92 = -14(x +2)

Simplify the right side:

y +92 = -14x -28

Subtract 92 from each side:

y = -14x-120

The y - intercept is -120

Answer:

(-3, 1), 5

Step-by-step explanation:

x² + y² + 6x - 2y - 15 = 0

Rearrange:

x² + 6x + y² - 2y = 15

Complete the square:

x² + 6x + 9 + y² - 2y + 1 = 15 + 9 + 1

(x + 3)² + (y - 1)² = 25

Therefore, the center is (-3, 1) and the radius is 5.

The center of the circle is (-3, 1), and the radius is 5.

To find the center and radius of the circle described by the equation[tex]x^2 + y^2 + 6x - 2y - 15 = 0,[/tex] we'll first rewrite the equation in standard form, which has the general form:

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

Where (h, k) represents the center of the circle, and r represents the radius.

Let's complete the square to rewrite the given equation in standard form:

[tex]x^2 + 6x + y^2 - 2y = 15[/tex]  

Now, we'll complete the square for both the x and y terms.

To complete the square for the x terms, we add and subtract [tex](6/2)^2 = 9:x^2 + 6x + 9 + y^2 - 2y = 15 + 9[/tex]

Now, complete the square for the y terms by adding and subtracting (-2/2)^2 = 1:

[tex]x^2 + 6x + 9 + y^2 - 2y + 1 = 15 + 9 + 1[/tex]

Now, we have:

[tex](x^2 + 6x + 9) + (y^2 - 2y + 1) = 25[/tex]

Next, we can rewrite this as two perfect square trinomials:

[tex](x + 3)^2 + (y - 1)^2 = 25[/tex]

Now, the equation is in standard form. Comparing it to the standard form, we can see that:

h = -3 (opposite sign in the equation)

k = 1 (opposite sign in the equation)

[tex]r^2 = 25[/tex] (radius squared)

To find the radius (r), take the square root of 25:

r = √25 = 5.

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Answer:

Divide the standard deviation of the sample measures by 8

Step-by-step explanation:

Given

measurements in data set=500

measurements in sample=64

Standard error of sample=?

As per the formula of standard error

Standard error= standard deviation/ square root of the number of measurements

                        = σ/√n

Here as we need to find standard error of the sample hence n=64

therefore √64= 8

The above equation will become:

standard error of the sample= σ/8 i.e. Divide the standard deviation of the sample measures by 8!

Step-by-step explanation:

[tex] \frac{1}{2} log(x) + log(4) = 2[/tex]

then

[tex] log( {x}^{ \frac{1}{2} } ) + log(4) = 2 \\ log(4 \sqrt{x} ) = 2 \\ 4 \sqrt{x} = {10}^{2} = 100 \\ \sqrt{x} = 25 \\ x = {25}^{2} = 625[/tex]

I don't know if your Log is natural logarithm then

[tex]4 \sqrt{x} = {e}^{2} \\ \sqrt{x} = \frac{e ^{2} }{4} \\ x = \frac{ {e}^{4} }{16} [/tex]

Answer:

incorrect; Jason must also prove that all sides are congruent by using the distance formula.

Step-by-step:

By definition, a rhombus has two pair of parallel sides and all sides are congruent. Jason must use the distance formula in a formal algebraic proof to prove that all sides are congruent. Just looking at the graph is not sufficient proof.

Answer:

The two integers you are finding is 21 and 23.

x² + y² = 970

970 / 2 = 485 ( divide it to two because we are finding two integers )

√ 485 = 22.022715546 or when rounded off, 22 ( square root because we are finding squares )

It means, the answers are near the number 22.

I found out 21 and 23

21 and 23 is two consecutive odd integers

Let x = 21

Let y = 23

x² + y² = 970

( 21 )² + ( 23 )² = 970

= 441 + 529

= 970

GIVE ME BRAINLIEST PLEASE !!! :)

Answer:

21, 23 and -21, 23

Step-by-step explanation:

The difference between two consecutive odd numbers is 2.

Let the smaller number be x. Then, the larger number is x + 2.

Now add their squares and set it equal to 970. Then  solve for x.

smaller number: x

larger number: x + 2

sum of the squares of the two numbers: x^2 + (x + 2)^2

equation: x^2 + (x + 2)^2 = 970

Solution of the equation:

x^2 + (x + 2)^2 = 970

Expand the square of the binomial:

x^2 + x^2 + 4x + 4 = 970

Combine like terms on the left side:

2x^2 + 4x + 4 = 970

Subtract 970 from both sides:

2x^2 + 4x - 966 = 0

Divide both sides by 2:

x^2 + 2x - 483 = 0

Now we need to factor the binomial. We need two number whose sum is 2 and whose product is -483. Look at 483. It is not divisible by 2, but it is divisible by 3.

483/3 = 161

161 is divisible by 7.

161/7 = 23

23 is prime, so the prime factorization of 483 is

483 = 3 * 7 * 23

Notice that 3 * 7 = 21, so

483 = 21 * 23

Use -21 and 23:

-21 + 23 = 2

-21 * 23 = -483

x^2 + 2x - 483 factors into (x - 21)(x + 23)

Now we continue solving the equation.

x^2 + 2x - 483 = 0

(x - 21)(x + 23) = 0

x - 21 = 0 or x + 23 = 0

x = 21 or x = -23

We let x equal the smaller of the two integers, so now we add 2 to find the second integer.

x = 21; x + 2 = 23

x = -23; x + 2 = -21

There are two sets of consecutive odd numbers that satisfy this problem.

21, 23

-23, -21

The problem did not state positive or negative consecutive odd numbers, so both solutions are valid.

Answer:

Rectangle

Step-by-step explanation:

In order for a paralleligram to be inscribed in a circle it has to have four 90º angles, this is why the only parallelogram that can be inscribed into a circle is the rectangle, this includes sqaures, since squares are basically rectangles with equal sides.

Final answer:

Dayton has 3 bags of frozen vegetables, with each bag weighing 5/8 pound. He can make 1 pot of soup with 7/8 of another pot using these vegetables.

Explanation:

Dayton has 3 bags of frozen vegetables, and each bag contains 5/8 pound of vegetables. To find the total weight of the vegetables, we multiply the weight of one bag by the number of bags: (5/8) * 3 = 15/8 pounds. Since each pot of soup requires 1 pound of vegetables, we divide the total weight of the vegetables by 1 pound to find the number of pots of soup Dayton can make: (15/8) / 1 = 15/8 pots of soup. However, we can simplify this fraction to a mixed number: 15/8 = 1 and 7/8. So Dayton can make 1 pot of soup with 7/8 of another pot.

Answer:

the answer is b

Step-by-step explanation:

Answer:

Quadrant I

Step-by-step explanation:

To find in which quadrant an angle is, you have to locate it between 0 and 360.

Since your angle is larger than 360 degrees, we subtract 360 degrees from it.... to get 27 degrees.

27 degrees and 387 degrees lie on the same spot, since they are exactly one turn around from each other.

Now, angles between 0 degrees and 90 degrees are in quadrant I

angles between 90 and 180 degrees are in quadrant II

Angles between 180 and 270 degrees are in quadrant III

Angles between 270 and 360 degrees are in quadrant IV

So, an angle of 27 degrees would land in Quadrant I.... so is 27 + 360x, where x is any integer representing a number of turns.

The answer is:

The terminal side of the angle 387° lies at the Quadrant I.

We know that there are four quadrants on the plane, those quadrants goes from 0° to 360°, however, since the quadrant is going only from 0° to 360°, if we want to know where an angle greater than 360° is located, we need to take only the excess, so:

We are asked to find where the angle 387° is located, we can write the angle by the following way:

[tex]387\°=360\°+27\°\\[/tex]

So, we have that there are 27° more than 360°, if we want to find where the 367° we only need to locate where the excess (27°) angle is located.

Also, we know that:

Quadrant I: 0° to 90°

Quadrant II: 90° to 180°

Quadrant III: 180° to 270°

Quadrant IV: 270° to 360°

We have that 27° is between 0° and 90°, so, it's located on the first quadrant.

Hence, we have that the angle 367° is located at the Quadrant I.

Have a nice day!

Answer:

A distribution that is skewed to the right is likely to have a mean higher than the median.

The sequence {1, 8, 27, 64} is not an arithmetic sequence.

An arithmetic sequence is defined by having a constant difference between consecutive terms. To check if a sequence is arithmetic, we subtract each term from the one that follows.

The difference between 8 and 1 is 7

(8 - 1 = 7)

The difference between 27 and 8 is 19

(27 - 8 = 19)

The difference between 64 and 27 is 37

(64 - 27 = 37)

Since these differences are not equal, the sequence is not arithmetic.

Answer:

d. distributive property

Option D is correct, distributive property of multiplication over subtraction​ is the property used by Evan in first step.

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

12x²- 7x = 6-2(x² - 1).

The first step written by Evan is 12x²- 7x = 6-2x² +2

We have to find the property which was used for the first step

In the equation splitted 2(x² - 1) using distributive property of multiplication over subtraction​.

The distributive property of multiplication over subtraction is applied when we multiply a value by the difference of two numbers.

Hence, option D is correct,  distributive property of multiplication over subtraction​ is the property used by Evan in first step.

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Answer:

with what you didnt say what you needed help with

Step-by-step explanation:

For this case we have by definition, that the Greatest Common Factor or GFC, of two or more whole numbers is the largest integer that divides them without leaving a residue.

Now, we look for the factors of 72 and 210:

72: 1,2,3,4,6,8,9,12,16,24,36,72

210: 1,2,3, 5,6,7 ...

Thus, the GFC of both is 6.

Then, the GFC of [tex]72x ^ 3y ^ 2[/tex] and [tex]210x ^ 2y ^ 5[/tex] is given by:

[tex]6x ^ 2y ^ 2[/tex]

ANswer:

[tex]6x ^ 2y ^ 2[/tex]

The sum of the series 14+20+26+...+1244 is 129,045.

The question is to find the sum of the sequence 14+20+26+...+1244. This is an arithmetic series where the common difference (d) is 6, since each term is 6 more than the previous term. The first term (a1) is 14.

To find the sum of the series, we need to determine the number of terms (n). The nth term of an arithmetic series is given by an = a1 + (n-1)d. We will set an to 1244, the last term, and solve for n:

1244 = 14 + (n-1) × 6

n = (1244 - 14)/6 + 1

n = 205

Now that we have the number of terms, we can use the sum formula for an arithmetic series which is S = n/2  × (a1 + an). Thus:

S = 205/2 × (14 + 1244)

S = 102.5 × 1258

S = 129,045

So, the sum of the series 14+20+26+...+1244 is 129,045.

Hello There!

85% = 85/100

85/100 = 0.85

0.85/1 * 100/100

85/100

SIMPLIFIED IS 17/20

Percent are always out of 100 so...

[tex]\frac{85}{100}[/tex]

Simplifying:

[tex]\frac{85}{100}/\frac{5}{5}=\frac{17}{20}[/tex]

Hope this helped!

Answer:

x ≈ 6.5

Step-by-step explanation:

We have the epresion [tex]tan(18)=\frac{x}{20}[/tex] and we want to find the value of [tex]x[/tex].

Let's do it step-by-step

Step 1. Multiply both sides of the equation by 20

[tex]tan(18)=\frac{x}{20}[/tex]

[tex]20tan(18)=(\frac{x}{20} )(20)[/tex]

[tex]20tan(18)=x[/tex]

Step 2. use the reflexive property of equality: if [tex]a=b[/tex] then [tex]b=a[/tex]

[tex]20tan(18)=x[/tex]

[tex]x=20tan(18)[/tex]

Step 3. Using a calculator we get that [tex]tan(18)=0.325[/tex].  Replacing that value we get

[tex]x=20(0.325)[/tex]

x ≈ 6.5

We can conclude that the value of x is approximately 6.5

The correct comparison for the expressions 2b and b+g is 2b > b+g.

Let's analyze the expressions:

Comparing 2b and b+g, the correct statement is A. 2b > b+g as having more green balls than blue balls implies the total green balls are more, making the expression 2b greater than b+g.

Based on these cases, the only condition that aligns with g > b is when [tex]\(2b < b + g.[/tex]

Thus, the correct answer is: B. 2b < b + g.

To find which statement is correct, let's consider the relationship between the number of green balls (g) and the number of blue balls (b). Since the bag has more green balls than blue balls, it means that g > b.

To compare the expressions 2b and b + g, let's examine their relationship under the condition g > b

When 2b > b + g

Rearranging 2b > b + g, we get:

b > g.

This contradicts the condition g > b.

So, this case is not possible.

Case 2: When 2b < b + g :

Rearranging 2b < b + g, we get:

b < g,

which aligns with the given condition g > b.

Hence, this condition is possible.

When 2b = b + g

Rearranging 2b = b + g, we get: [tex]\[b = g.\][/tex]

This condition contradicts the original requirement g > b, so this case is also not possible.

The only condition that aligns with g > b is when [tex]\(2b < b + g.[/tex] Thus, the correct answer is: B. 2b < b + g.

Question : A bag has more green balls than blue balls, and there is at least one blue ball. Let b represent the number of blue balls and let g represent the number of green balls. Let's compare the expressions 2b and b+g. Which statement is correct?

A. 2b>b+g

B. 2b C. 2b=b+g

D. There is not enough information to tell.

Answer:

x=9

Step-by-step explanation:

Your number is 9.

Set this up as 10(x^2) = 90x where x > 0 or x< 0.

Factor by 10 on both sides.

10x(x) = 10x(9)

x=9

Hope this helped you!

Answer:

16100

Step-by-step explanation:

n = 100

a1 = 15

a100 = 307

The first thing you have to do is solve for d

a100 = a1 + (n - 1)*d

307 = 15 + (100 - 1)*d

307 = 15 + 99*d

307 - 15 = 99*d

292 = 99 d

d = 292 / 99

d = 2.94949494

That's a real odd result, but it is what you get.

Sum = (a + L)*n/2

sum = (15 + 307)*n/2

Sum = 322 * 100 / 2

Sum = 16100 It looks like I didn't have to solve for d. The person who made this up sure didn't

Answer:

None

Step-by-step explanation:

Follow me To get The Answer

Answer:

123. [tex]A=lw[/tex], [tex]A=72[/tex]

124. B) 20 square feet

125. C) [tex]\frac{1}{6}[/tex]

126. A) 24 + 12, B) (4*6)+(4*3)

127. 30, 36, 44

Step-by-step explanation:

123. Area = length*width

Substitute '9' for [tex]l[/tex] and '8' for [tex]w[/tex].

[tex]A=(9)(8)[/tex] or [tex]A=(9*8)[/tex]

[tex]9*8=72[/tex], so [tex]A=72[/tex].

124. Using the formula [tex]A=lw[/tex], substitute '5' for [tex]l[/tex] and '4' for [tex]w[/tex].

[tex]A=(5)(4)[/tex] or [tex]A=(5*4)[/tex]

[tex]5*4=20[/tex], so [tex]A=20[/tex].

125. The hexagon was divided into 6 triangles, so each of the triangles is one out of six, one sixth ([tex]\frac{1}{6}[/tex].

126. The lighter rectangle's area is 24 and the darker's is 12 because (4*6) = 24 and (4*3) = 12.

127. For these shapes, I am using the 'subtraction' method (find the area of the shape as if it were a larger rectangle, then subtract the 'blank' spaces).

A(larger rectangle) = [tex]6*7=42[/tex]

A('blank' space) = [tex]3*4=12[/tex]

A(larger rectangle - 'blank' space) = [tex]42-12=30[/tex]

A(larger rectangle) = [tex]8*7=56[/tex]

A('blank' space) = [tex]5*4=20[/tex]

A(larger rectangle - 'blank' space) = [tex]56-20=36[/tex]

A(larger rectangle) = [tex]8*6=48[/tex]

A('blank' space) = [tex]2*1=2[/tex]  (there are two of them (both equal), so add them both together) 2 + 2 = 4.

A(larger rectangle - 'blank' space) = [tex]48-4=44[/tex]

Answer:

[tex]3x+5[/tex]

Step-by-step explanation:

we have

[tex](8x-2)-(5x-7)[/tex]

step 1

Eliminate the parenthesis

[tex](8x-2)-(5x-7)=8x-2-5x+7[/tex]

step 2

Groupe terms that contain the same variable

[tex]8x-5x-2+7[/tex]

step 3

Combine like terms

[tex]3x+5[/tex]

The simplified expression  of  (8x-2) -(5x-7) is said to be 3x + 5.

To subtract the expression (8x - 2) - (5x - 7), we can use the distributive property to remove the parentheses. Here's the step-by-step solution:

(8x - 2) - (5x - 7)

Do, Remove the parentheses:

8x - 2 - 5x + 7

Combine like terms:

(8x - 5x) + (-2 + 7)

Hence:

3x + 5

Therefore, the simplified expression is 3x + 5.

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Answer:

172 degrees

Step-by-step explanation:

The complement of an angle, when added to that angle is equal to 90, so do x + 82 = 90

x = 8

The supplement of a an angle when added to that angle is equal to 180 so do

y + 8 = 180

y = 172

Applying the definition of supplementary angles and complementary angles, if angle A is 82 degrees, the supplement of the complement of angle A is: 172 degrees.

Recall:

Given that Angle A equals 82 degrees.

Thus:

The supplement of 8 degrees will be: 180 - 8 = 172 degrees.

Therefore, applying the definition of supplementary angles and complementary angles, if angle A is 82 degrees, the supplement of the complement of angle A is: 172 degrees.

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Answer:

Yes that is true

because the lines on the opposite side will never intersect

Answer:

The correct option is A. FLED is definitely a parallelogram .

Step-by-step explanation:

From the given figure it is clear that the angle F and angle E are same. Angle L and angle D are same.

[tex]\angle F=\angle E[/tex]

[tex]\angle L=\angle D[/tex]

According to the properties of parallelogram, a quadrilateral is called parallelogram if and only if there are two pairs of congruent opposite angles (but not equal to 90°, otherwise it will be a square or rectangle).

Since we have two pairs of congruent opposite angles which are not a right angle, therefore the statement "FLED is definitely a parallelogram" is true.

Hence, option A is correct.

Answer:

[tex]\large\boxed{\{x\ |\ x>2\}}[/tex]

Step-by-step explanation:

[tex]5x+7>17\qquad\text{subtract 7 from both sides}\\\\5x>10\qquad\text{divide both sides by 5}\\\\x>2[/tex]

Answer:

2 is C. , 3 is C. , 4 is D.  

Step-by-step explanation:

2

Square roots are not polynomials

3

The highest degree of one term in the polynomial is 4

4

Terms are separated by (+) or (-) signs. If you count them up there are 4

Answer:

C, D, D, B

Step-by-step explanation:

2. A polynomial has only integer exponents, no square roots.  So C is not a polynomial.

3. The degree of the polynomial is the sum of the exponents of the highest term.  p has an exponent of 1 and q has an exponent 4, so 1+4 = 5. D

4. Count the number of terms being added or subtracted.  p^3, 4pq^2, q^2, and -3q.  So there are 4 terms. D

5. Standard form of a polynomial is written from the highest exponent to the lowest.  So the answer is B.

Answer:

the graph will be vertically compressed i just answered apex

Step-by-step explanation:

Answer:

The graph will be compressed vertically.

Step-by-step explanation:

Not all heroes wear capes. Anyways thank you!

Answer:

thanks for this! <3

Step-by-step explanation: