Question 36 of 40
The distance of a line bound by two points is defined as
L?
O A. a line segment
B. a ray
O
c. a plane
O D. a vertex
SUBMI​

Answer:

Option (G)

Step-by-step explanation:

Let the length of the race = a miles

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

Time taken to cover 'a' miles with the speed = 12 mph,

Time taken '[tex]t_1[/tex]' = [tex]\frac{a}{12}[/tex]

Time taken to cover 'a' miles with the speed = 11 mph,

Time taken '[tex]t_2[/tex]' = [tex]\frac{a}{11}[/tex]

Since the time taken by David to cover 'a' miles was 10 minutes Or [tex]\frac{1}{6}[/tex] hours more than the time he expected.

So, [tex]t_2=t_1+\frac{1}{6}[/tex]

[tex]\frac{a}{11}=\frac{a}{12}+\frac{1}{6}[/tex]

[tex]\frac{a}{11}-\frac{a}{12}=\frac{1}{6}[/tex]

[tex]\frac{12a-11a}{132}=\frac{1}{6}[/tex]

a = 22 mi

Therefore, distance of the race = 22 mi

Option (G) is the correct option.

Step-by-step explanation:

1965 round to the nearest tenth is 1970

Answer:

1965.0

Step-by-step explanation:

Answer:

Slope= 1/9

Y-Intercept= 5

Answer:

The resultant expression is [tex]2x^{2}+5x^{2}-x-6[/tex].

Step-by-step explanation:

The distributive property of multiplication is:

[tex]a\times (b+c)=(a\times b)+(a\times c)[/tex]

The two polynomials provided are:

[tex](2x+3)\\(x^{2}+x-2)[/tex]

Determine the final expression by multiplying the two polynomials as follows:

[tex](2x+3)\times (x^{2}+x-2)=[2x\times(x^{2}+x-2)]+[3\times(x^{2}+x-2)][/tex]

[tex]=[(2x\times x^{2})+(2x\times x)-(2x\times 2)]+[(3\times x^{2})+(3\times x)-(3\times 2)]\\\\=[2x^{3}+2x^{2}-4x]+[3x^{2}+3x-6]\\\\=2x^{3}+2x^{2}+3x^{2}-4x+3x-6\\\\=2x^{3}+5x^{2}-x-6[/tex]

Thus, the resultant expression is [tex]2x^{2}+5x^{2}-x-6[/tex].

Let [tex]\mu[/tex] be the average number of televisions per household in the United States .

As per given ,

[tex]H_0:\mu =2.3\\\\ H_a:\mu\neq2.3[/tex]

Since [tex]H_a[/tex] is two-tailed and population standard deviation is unknown, so the test is two-tailed t-test.

For sample : Sample size : n= 73, sample mean: [tex]\overline{x}[/tex] = 2.1, sample standard deviation : s= 0.84.

[tex]t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}[/tex]

[tex]t=\dfrac{2.1-2.3}{\dfrac{0.84}{\sqrt{73}}}\\\\ t=-2.034[/tex]

T-critical value for degree of freedom n-1 = 73-1=72 and 0.01 significance level is 2.646 . [By students' t-distribution table]

Since, [tex]|2.034|<2.646[/tex] i.e. [tex]|T_{cal}|<|T_{crit}|[/tex]

This means we cannot reject null hypothesis.

We conclude that the average number of televisions per household in the United States is 2.3 at the 0.01 significance level.

Answer: 30 i think 10x3=30

Step-by-step explanation:

Answer:

Three points are (0,-5.5), (-1,-3), (-2.2,0) and graph is shown below.

Step-by-step explanation:

The given equation is

[tex]-2y=5x+11[/tex]

We need to find three points that solve the equation.

Put x=0,

[tex]-2y=5(0)+11[/tex]

[tex]-2y=11[/tex]

[tex]y=-5.5[/tex]

Put x=-1,

[tex]-2y=5(-1)+11[/tex]

[tex]-2y=6[/tex]

[tex]y=-3[/tex]

Put y=0,

[tex]-2(0)=5x+11[/tex]

[tex]5x=-11[/tex]

[tex]x=-2.2[/tex]

So, three points (0,-5.5), (-1,-3) and (-2.2,0) are the solutions of the given equation.

Plot these points on a coordinate plane and connect them by a straight line as shown below.

Answer:

its b and e

Step-by-step explanation:

The statements given in options B and E are   true so options B and E are right options.  

Given some statements we have to determine that which of the following statements are true

The given statements are as follows

A. In Euclidean geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is less than 180 degrees.

B. In Euclidean geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is greater than 180 degrees.

C. In Euclidean geometry the sum of the interior angle measures of a triangle is less than 180 degrees, but in hyperbolic geometry the sum is equal to 180 degrees.

D. In Euclidean geometry the sum of the interior angle measures of a triangle is greater than 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.

E. In Euclidean geometry the sum of the interior angle measures of a triangle is 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.

We know some facts about each type of geometry

In Euclidean geometry  plane is used to plot the points and line.

In spherical geometry uses the sphere to plot the points and circles

Elliptical geometry is such a geometry where no parallel lines exists.

The sum of interior angles of a triangle is dependent on the type of geometry we are dealing with   and they can be written down in the following points

So from the above observations we can conclude that statements given in options B and E are   true so options B and E are right options.  

For more information please refer to the link given below

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Answer:

[tex]\sum_{a=1}^{7}(500-a)=3472[/tex]

Step-by-step explanation:

[tex]\sum_{a=1}^{7}(500-a)[/tex] will form a sequence as,

499, 498, 497.......7 terms

Since there is a common difference between successive and previous term,

d = 498 - 499 = -1

This sequence is an arithmetic sequence.

Sum of n terms of an arithmetic sequence is,

[tex]S_{n}=\frac{n}{2}[2a+(n-1)d][/tex]

where a = first term of the sequence

n = number of term

d = common difference

For the given given sequence,

[tex]S_{7}=\frac{7}{2}[2(499)+(7-1)(-1)][/tex]

    = [tex]\frac{7}{2}[998-6][/tex]

    = [tex]\frac{7}{2}(992)[/tex]

    = 3472

Therefore, sum of seven terms of the given sequence will be 3472.

Answer:

  one car at a time

Step-by-step explanation:

For each car in the shorter train* (A) ...

When there are no more train A cars in front of train B, both trains can continue on their journey.

We assume cars can be decoupled at any point in the train, so that any required order of cars can be preserved. We further assume that train B can move any one of train A's cars in addition to all of its own.

_____

* The total number of car lengths that must pass the offshoot is (at least) the product of the number of cars in both trains, so it doesn't seem to matter which train makes use of the offshoot. We choose to decouple the cars of train A so that the minimum number of cycles is required--even though each cycle is longer.

Answer:

[tex]3n + 3[/tex]

[tex]3(n+1)[/tex]

Step-by-step explanation:

Given

[tex]7n - (4n - 3)[/tex]

Required

Simplify

To simplify the given expression, you start by opening  the bracket

[tex]7n - (4n - 3)[/tex]

[tex]7n - 4n + 3[/tex]

Next, you perform arithmetic operations on like terms

[tex]3n + 3[/tex]

The answer can be further simplified;

Factorize [tex]3n + 3[/tex]

[tex]3(n+1)[/tex]

Hence;

[tex]7n - (4n - 3)[/tex] when simplified is equivalent to [tex]3n + 3[/tex] or [tex]3(n+1)[/tex]

Answer:

3n+n

Step-by-step explanation:

Answer:

Linear, Quadratic, Radical, Absolute Value, Cubic, Cube Root

Step-by-step explanation:

To find:

Which functions have an intercept at (0, 0).

That means, when we put a value [tex]x=0[/tex] in the [tex]y =f(x)[/tex], value of [tex]y=0[/tex].

Let us discuss each parent function one by one:

1. Linear:

[tex]y = x[/tex]

When we put x = 0, y = 0

Therefore, it has intercept at (0, 0).

2. Quadratic:

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

When we put x = 0, y = 0

Therefore, it has intercept at (0, 0).

3. Radical:

[tex]y = \sqrt x[/tex]

When we put x = 0, y = 0

Therefore, it has intercept at (0, 0).

4. Absolute Value:

[tex]y = |x|[/tex]

When we put x = 0, y = 0

Therefore, it has intercept at (0, 0).

5. Rational:

[tex]y = \dfrac{1}{x}[/tex]

When we put [tex]x = 0\Rightarrow y \rightarrow \infty[/tex]

Therefore, it does not have intercept at (0, 0).

6. Exponential:

[tex]y = b^x[/tex]

b is any base

When we put [tex]x = 0\Rightarrow y =1[/tex]

Therefore, it does not have intercept at (0, 0).

7. Logarithmic:

[tex]y = logx[/tex]

When we put [tex]x = 0 \Rightarrow y\rightarrow[/tex] Not defined

Therefore, it does not have intercept at (0, 0).

8. Cubic:

[tex]y = x^3[/tex]

When we put [tex]x = 0\Rightarrow y =0[/tex]

Therefore, it has intercept at (0, 0).

9. Cube Root:

[tex]y = \sqrt[3]x[/tex]

When we put [tex]x = 0\Rightarrow y =0[/tex]

Therefore, it has intercept at (0, 0).

X/5 -1/2 = x/6

Find the least common denominator of the 3 denominators:5,2,6

The limited is 30

Multiply all 3 fractions by 30:

6x -15 = 5x

Subtract 6x from both sides:

-15 = -x

Multiply both sides by -1:

X = 15

Answer:

3:50 pm

Step-by-step explanation:

Count backwards with the 25 min.

4:15 - 15 min >

25 - 15 = 10 >

4:00 - 10 = 3:50

Answer:

3:50 pm

Step-by-step explanation:

Starting Time + Time Interval = Ending Time

=> Ending Time - Time Interval = Starting Time

Ending Time = 4:15 pm

Time Interval = 25 minutes

Starting Time = x

=> 4:15 - 25 = x

=> 4:15 - 15 - 10 = x

=> (4:15 - 15) - 10 = x

=> 4:00 - 10 = x

=> 3:50 pm = x

So, she needs to leave the house at 3:50 pm to get to the movie theater on time.

Answer:

135.06 feet

Step-by-step explanation:

Since the side of the building makes a right triangle with the ground and you know one side length and the degree angle between you and the top of the building we can use trigonometric function to find the height of the building. So since we know one side other than the hypotenuse we can use tangent to solve. Tangent is the opposite side over the adjacent side of the known angle.

opposite side = x

adjacent side = 150 feet

angle = 42°

tan(42°) = x/150 feet

150 feet * tan(42°) = x

x = 135.06 feet

Answer: Hi!

We can simplify this by combining like terms:

-12w + 7w - 3 - 6

-12w + 7w = -5w

-3 - 6 = -9

Out equation now looks like this:

-5w - 9

There's nothing left to simplify, so we're done!

Hope this helps!

Answer:

Below

Step-by-step explanation:

First triangle)

This triangle is a right one so we will apply the pythagorian theorem.

● 25 is the hypotenus

● 25^2 = b^2 + 24^2

■■■■■■■■■■■■■■■■■■■■■■■■■■

Seconde triangle)

Again it's a right triangle

x is the hypotenus.

● x^2 = 12^2 +5^2

● 12^2 = x^2-5^2

■■■■■■■■■■■■■■■■■■■■■■■■■■

This is a right triangle

AC is the hypotenus.

● AC^2 = BC^2 + BA^2

Notice that: BC = BE+EC and BA=BD+DA

● AC^2 = (BE+EC)^2 + (BD+DA)^2

Answer:  2) b = 7       3) x = [tex]\sqrt{119}[/tex]

Step-by-step explanation:

Use Pythagorean Theorem: (leg₁)² + (leg₂)² = hypotenuse²

2) b² + 24² = 25²

   b² + 576 = 625

            b² = 49

         [tex]\sqrt{b^2}=\sqrt{49}[/tex]

            b = 7

3) 5² + x² = 12²

   25 + x² = 144

            x² = 119

        [tex]\sqrt{x^2}=\sqrt{119}[/tex]

           [tex]x=\sqrt{119}[/tex]

Answer:

The numbers that are at a distance of 2 from the number 8 can be expressed using absolute value notation as:

|x - 8| = 2

Step-by-step explanation:

The numbers that are at a distance of 2 from the number 8 are the numbers that are satisfied by the equation:

|x - 8| = 2

The equation is written in the notation of absolute value as required.

The question is not clear, but it is possible to obtain distance, s, from the given function. This, I would show.

Answer:

s = 17 units

Step-by-step explanation:

Given f(t) = t³ - 8t² + 27t

Differentiating f(t), we have

f'(t) = 3t² - 16 t + 27

At t = 0

f'(t) = 27

This is the required obtainaible distance, s.

Answer:

the interest is 195dollars

Answer:

The average score of 6 tests is 19.

Step-by-step explanation:

Given that the average score of 5 tests is 18. So first, we have to find the total number of scores for 5 tests :

[tex]let \: x = total \: no. \: of \: scores[/tex]

[tex] \frac{x}{5} = 18[/tex]

[tex]x = 18 \times 5[/tex]

[tex]x = 90[/tex]

We have found out that the total scores for 5 tests is 90. So we have to find the average of 6 scores :

[tex] \frac{x + 24}{5 + 1} = \frac{90 + 24}{6} = \frac{114}{6} = 19[/tex]

[tex] \LARGE{ \boxed{ \rm{ \pink{Solution : )}}}}[/tex]

We need to know how to find the average

☄ For this case, We are gonna find average score...!

[tex] \large{ \boxed{ \sf{Avg. \: score = \frac{Total \: score}{No. \: of \: tests} }}}[/tex]

So, Let's proceed further towards solution....

We have,

Finding total score in 5 tests,

⇛ Total score = Avg. score × No. of tests

⇛ Total score = 18 × 5

⇛ Total score = 90

According to question,

⇛ Total score now = 90 + 24 = 114

Finding the average score of 6 tests,

⇛ Avg. score = 114 / 6

⇛ Avg. score = 19 points

☄ Avg. score of lynette in 6 tests = 19

━━━━━━━━━━━━━━━━━━━━

We have

[tex]2+\dfrac54+\dfrac{11}{16}+\dfrac{23}{64}+\cdots=\displaystyle\sum_{n=0}^\infty\frac{3\cdot2^n-1}{4^n}[/tex]

(notice that each denominator is a power of 4, and each numerator is one less than some multiple of 3, in particular 3 times some power of 2)

Recall for [tex]|x|<1[/tex], we have

[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]

So we have

[tex]\displaystyle\sum_{n=0}^\infty\frac{3\cdot2^n-1}4=3\sum_{n=0}^\infty\left(\frac12\right)^n-\sum_{n=0}^\infty\left(\frac14\right)^n=\frac3{1-\frac12}-\frac1{1-\frac14}=\boxed{\frac{14}3}[/tex]

Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the line perpendicular to

y = -5x + 5 we must first find the slope of

Comparing with the general equation above

Slope = - 5

The slope of the perpendicular line is the negative inverse of the slope of the original line

Slope of perpendicular line = 1/5

Equation of the line using point (5,5) and slope 1/5 is

We have the final answer as

Hope this helps you

Answer:

y=0.2x+4 or y=1/5 x+4.

Step-by-step explanation:

When one line is perpendicular to another, you have to find the opposite reciprocal for the slope of the given equation.

For instance, if you have the number 5, the reciprocal of 5 is 1/5 or 0.2. The opposite of positive is negative. Therefore, it is -0.2.

Therefore, if the slope of the first equation is -5, the slope for the next equation is 1/5. Reciprocal of -5 is -1/5. The opposite of -1/5 is positive 1/5. Or, the opposite of negative is positive. Therefore, it would be 1/5x.

However, we are not done.

Since we are given that the line passes through the point (5,5), we need to find the y-intercept of this equation.

The formula for slope-intercept is y=mx+b.

M is your slope

B is your y-intercept.

We can find the y-intercept by actually plugging in the point (5,5) into the new equation.

5=0.2(5)+b.

5 is x and 5 is also y.

(x,y).

Simplify the equation by multiplying 0.2 times 5. That is equal to 1.

We now have 5=1+b.

Isolate for the letter "b" by subtracting 1 from both sides.

1-1 is 0.

5-1 is 4.

Therefore, b=4.

Finally, we can plug in the y-intercept into the new equation.

y=0.2 or 1/5x+4.

I hope this helps! I also hope you have a great rest of your day!

Answer:

2:3

Step-by-step explanation:

It’s easy

Answer:

2.5

Step-by-step explanation:

i think

Answer:

2 -7  6   7

1 3    -4  5

1 6  -15  -6

Step-by-step explanation:

An augmented matrix is the coefficients of the variables and then the solution in rows

Rewriting the equations

2x -7y +6x = 7

x +3y -4z = 5

x +6y -15z = -6

The matrix is

2 -7  6   7

1 3    -4  5

1 6  -15  -6

Answer:

  146/45

Step-by-step explanation:

Let x represent the value of the number of interest. Then we can do the following math to find its representation as a fraction.

  [tex]x=3.2\overline{4}\\10x=32.4\overline{4}\\10x-x=9x=32.4\overline{4}-3.2\overline{4}=29.2\\\\x=\dfrac{29.2}{9}=\boxed{\dfrac{146}{45}}[/tex]

__

Comment on procedure

The power of 10 that we multiply by (10x) is the number of repeated digits. Here, there is a 1-digit repeat, so we multiply by 10^1. If there were a 2-digit repeat, we would compute 10^2x -x = 99x to rationalize the number.

Answer:

x+12=78

Step-by-step explanation:

like that? x because its an unknown number but if you actually want to know the number just subtract 78-12 equals 66.

Answer:

n + 12 = 78

Step-by-step explanation:

Let n = number.

n + 12 = 78

Answer:

8

Step-by-step explanation:

f(x)=x²+4 ( find quadratic equation: given vertex)

g(x)=x+2  ( find linear equation : given 2 points)

(f-g)(-2)

(x²+4-x-2)of (-2)

x²-x+2  now find (f-g)(-2)

-2²-(-2)+2=4+2+2=8

Answer:

5.17

Step-by-step explanation:

The surface area of a sphere is 4[tex]\pi[/tex]r².

83.96=4[tex]\pi[/tex]r²

Divide by 4

20.99=3.14r²

divide by 3.14

6.6847=r²

take the square root

2.585=r

mulitply by 2 (diameter is twice the radius)

5.17

The diameter of the sphere is 5.17 inches.

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any object is called as the surface area.

The surface area of a sphere is 4πr².

83.96=4πr²

Divide by 4

20.99=3.14r²

Divide by 3.14

6.6847=r²

Take the square root.

2.585=r

Multiply by 2 (diameter is twice the radius).

r= 2 x 2.585

r = 5.17 inches

Therefore, the diameter of the sphere is 5.17 inches.

To know more about a surface area follow

https://brainly.com/question/1293273

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Answer:

Step-by-step explanation:

The money Alonso has is $21 which he wants to use to buy eggs and Avocados. The eggs he bought costs $2.50. Therefore the money remaining after the egg is bought is $18.50 (21 - 2.50)

Each bag of avocado cost $5, therefore the number of bags that can be bought with $18.50 is:

Bags of Avocado = $18.50 / $5 = 3.7 = 3 (to the previous whole number).

This means that the maximum number of bags of Avocado that can be bought is 3 bags. It can be represented by the inequality:

Bags ≤ 3  

Answer:

2.50 + 5B ≤ 21;

Step-by-step explanation:

Cost of eggs = $2.50

Cost of avocado = $5 (bag of 3)

Total budgeted amount = $21

Bags of avocado = B

Therefore :

(Cost of eggs + cost of avocado) ≤ total budgeted amount

($2.50 + $5(B)) ≤ 21

2.50 + 5B ≤ 21

5B ≤ 21 - 2.50

5B ≤ 18.50

B ≤ 18.50 / 5

B ≤ 3.7

Therefore the maximum number of bags can purchase is 3(whole number without exceeding $21)