At 9:00 AM, a person running a race was 2 1/2 miles from the start. By 11:30 AM, he was 13 miles from the start. From 9:00 AM to 11:30 AM, at what rate was he running per hour?

Answer:

[tex]\huge\boxed{(2.5,\ -1)}[/tex]

Step-by-step explanation:

[tex]\underline{+\left\{\begin{array}{ccc}6x+y=14\\-2x-y=-4\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad4x=10\qquad\text{divide both sides by 4}\\.\qquad\dfrac{4x}{4}=\dfrac{10}{4}\\.\qquad\boxed{x=2.5}\\\\\text{put it to the first equation}\\6(2.5)+y=14\\15+y=14\qquad\text{substract 15 from both sides}\\15-15+y=14-15\\\boxed{y=-1}[/tex]

Answer:

x = 5/2, y = -1

Step-by-step explanation:

6x + y = 14

-2x - y = -4

Add the two equations together to eliminate y

6x + y = 14

-2x - y = -4

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

4x = 10

Divide by 4

4x/4 = 10/4

x = 5/2

Now solve for y

-2x -y = -4

-2( 5/2) -y = -4

-5 -y = -4

Add 5 to each side

-5+5 -y =-4+5

-y = 1

Divide by -1

y = 1

Answer:  D

Step-by-step explanation:

The solution of the two equations does not exist since they are parallel.

Slope of a line is the ratio of the change in y coordinates to the change in x coordinates of two points.

Equation of a line in slope intercept form is y = mx + b, where m is the slope and b is y intercept.

Given linear equation of a line in slope intercept form as,

y = 1/2 x + 1

Here slope = 1/2 and y intercept = 1

y intercept is the y value of a point where it touches the y axis.

A second linear equation is to be found by using the values in the table.

Taking two points (2, 7) and (0, 6).

Slope = (6 - 7) / (0 - 2) = (-1) / (-2) = 1/2

Since the point (0, 6) is given, 6 is the y coordinate when the line touches the Y axis.

y intercept = 6

Equation of the second line is,

y = 1/2 x + 6

Since the slopes of two lines are equal, they are parallel.

There is no solution for two parallel lines.

Hence there is no solution for the linear equations given.

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Answer:

The answer is option D.

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

Equation of a line from given a Slope and a point is

y - y1 = m(x - x1)

Where ( x1 , y1) is the point

Equation of the line using point (-6 , -5) and slope 6 is

Hope this helps you

Answer:

60 pieces

Step-by-step explanation:

The rate of pieces to packages is 15/1.

Multiply this rate by 4 to get the answer.

15 * 4 = 60

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▹ Answer

60 pieces of gum

▹ Step-by-Step Explanation

[tex]\left[\begin{array}{cccc}1&2&3&4\\15&30&45&60\\\end{array}\right][/tex]

The pattern is multiply the number of packs by 15 therefore, the answer will be 60 pieces of gum.

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

The angles are

∠A = 90°, ∠B = 26.56°, ∠C = 63.43°

Step-by-step explanation:

We have that the angles of a vector are given as follows;

[tex]cos\left ( \theta \right ) = \dfrac{\mathbf{a\cdot b}}{\left | \mathbf{a} \right |\left | \mathbf{b} \right |}[/tex]

Whereby the vertices are represented as

A= (2, 5, 0), B = (4, 11, 0), C = (-1, 6, 0),

AB =(4, 11, 0) - (2, 5, 0) = (2, 6, 0) ,  BA = (-2, -6, 0)

BC = (-1, 6, 0) - (4, 11, 0) = (-5, -5, 0), CB = (5, 5, 0)

AC = (-1, 6, 0) - (2, 5, 0) = (-3, 1, 0), CA = (3, -1, 0)

θ₁ = AB·AC

a·c = a₁c₁ + a₂c₂ + a₃c₃ = 2×(-3) + 6×1 = 0

Therefore, θ₁ = 90°

BA·BC = (-2)×(-5) + (-6)×(-5) = 40

[tex]{\left | \mathbf{}BA \right |\left | \mathbf{}BC \right |}[/tex] = (√((-2)² + (-6)²)) × (√((-5)² + (-5)²)) = 44.72

cos(θ₂) = 40/44.72 = 0.894

cos⁻¹(0.894) =θ₂= 26.56°

CA·CB = 5×3 + 5×(-1) = 10

[tex]{\left | \mathbf{}CA \right |\left | \mathbf{}CB \right |}[/tex] = (√((3)² + (-1)²)) × (√((5)² + (5)²)) = 22.36

10/22.36 = 0.447

cos(θ₃) = 0.447

θ₃ = cos⁻¹(0.447) = 63.43°.

Answer:

Step-by-step explanation:

According to recipe, Amanda should cook for total of 1/2 hour which is 30 minutes. If she has been cooking for 25 minutes, the remaining time needed for the turkey to cook will be the difference between the total time and the time she has already spent in cooking.

[tex]minutes\ left = 30 minutes - 25 minutes\\\\munites\ left = 5 minutes[/tex]

Hence, the turkey needs to cook for 5 more minutes

Answer:

3x+3y and distributive property

Step-by-step explanation:

It is given that

Gretchen buys three bags of apples = 3X

Hayley buys three bunches of bananas = 3Y

As it is also mentioned that it first it is multiplied and then it is added

So, the expression for determining the total number of fruit pieces is

3X + 3Y

And, this expression denotes the distributive property in which we multiplied the each variable and then added it

Answer:

The formula would be

T(n) = 64 (-3/4)^n, n=0,1,2,...

or sometimes

T(n) = T(n-1)(-3/4),     T(0) =64, n=0,1,2,...

Step-by-step explanation:

The common ratio is -3/4, i.e.

(-3/4) * 64 = -48

(-3/4) * 48 = 36

(-3/4) * 36 = -27

...

The formula would be

T(n) = 64 (-3/4)^n, n=0,1,2,...

or sometimes

T(n) = T(n-1)(-3/4),     T(0) =64, n=0,1,2,...

Note: Would have been easier if the choices were supplied.

Answer:

The logarithmic parent function is the only one with negative numbers in the range

Step-by-step explanation:

Hello,

These functions have been very well known, I remind you their graphs below

The logarithmic parent function is the only one with negative numbers in the range

range for square root is [tex]\mathbb{R^{+}}[/tex]

range for logarithmic is [tex]\mathbb{R}[/tex]

range for exponential is [tex]\mathbb{R^{+}}[/tex]

THAT S TRUE

The square root and logarithmic parent functions have the same domain

domain for square root is [tex]\mathbb{R^{+}}[/tex]

domain for logarithmic is [tex]\mathbb{R}[/tex]

THAT S WRONG

The square root parent function domain is the most restricted

domain for square root is [tex]\mathbb{R^{+}}[/tex]

domain for exponential is [tex]\mathbb{R^{+}}[/tex]

THAT S WRONG

All three parent functions have the same domain

domain for square root is [tex]\mathbb{R^{+}}[/tex]

domain for exponential is [tex]\mathbb{R^{+}}[/tex]

domain for logarithmic is [tex]\mathbb{R}[/tex]

THAT S WRONG

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

$ 5.65

Step-by-step explanation:

let the cost of a pencil and a ruler be $p and $r respectively.

4p +r= 1 -----(1)

6p +3r= 2.10

divide by 3 throughout:

2p +r= 0.70 -----(2)

Q: 3p +13r= ?

(1) -(2):

(4p +r) -(2p +r)= 1 -0.70

4p +r -2p -r= 0.30 (expand)

2p= 0.30 (simplify)

p= 0.30 ÷2 (÷2 on both sides)

p= 0.15

subst. into (1):

4(0.15) +r= 1

r +0.60= 1

r= 1 -0.60

r= 0.40

cost of three pencils and thirteen rulers

= 3p + 13r

= 3(0.15) + 13(0.40)

= 0.45 + 5.20

= $5.65

Answer:

78

Step-by-step explanation:

Let x be the score on the next test

We are averaging 6 tests and want an average of 75

( 82+91+38+78+83+x) /6 = 75

Multiply each side by 6

( 82+91+38+78+83+x) = 75*6

( 82+91+38+78+83+x)  =450

Combine like terms

x+372 = 450

Subtract 372 from each side

x+372-372 = 450-372

x =78

Answer:

5 1/3 or 5.33333333333333333333333333333333333333333333333333333

Step-by-step explanation:

to find the scale factor, you must divide the two equal sides.

[tex]\frac{6}{8}[/tex]

which equals

[tex]\frac{3}{4}[/tex] or 0.75

Now, the way to get the value of x is to divide 4 by 3/4 0r 0.75

[tex]\frac{4}{0.75}[/tex]

Which equals

5.333 repeating or 5 1/3

Hope this helps. If you have any follow-up questions, feel free to ask.

Have a great day! :)

Answer:

The answer is option C.

[tex]g(x) = \frac{1}{2} |x| [/tex]

Hope this helps you

Answer:

O g(x) is shifted 4 units left and 6 units down from f(x).

Step-by-step explanation:

O g(x) is shifted 4 units left and 6 units down from f(x).

The graph of g(x) is shifted 4 units to the left and 6 units down from f(x).

Translation of functions is defined as the when each point in the original graph is moved by a fixed units in the same direction.

There are horizontal translation and vertical translation of functions.

Given functions are,

g(x) = 1/(x + 4) - 6

f(x) = 1/x

Here when a function f(x) changes to f(x + k) when it is translated k units left.

Here 1/x changes to 1/(x + 4).

So g(x) is shifted 4 units left.

Similarly a function f(x) changes to f(x) - k, if it is translated k units down.

So g(x) also shifted 6 units down.

Hence the correct option is D.

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Answer:

Step-by-step explanation:

[tex]area=\frac{\pi r^2 \times\theta}{360} =\frac{\pi 6^2 \times 60}{360} =6 \pi \approx 18.85~ cm^2[/tex]

Answer:

The resistance decreases.

Step-by-step explanation:

The resistance decreases as the conductor is made thicker.

First of all, resistance is like some sort of an obstacle right?

So if the conductor is made thicker it will be easy for the electrons to pass through.

And if the conductor is made thinner it won't be easy for the electrons to pass through. Which makes the resistance increase as there will be collision between the electrons.

Hope this helped ;) ❤❤❤

Answer:

Step-by-step explanation:

The length of this triangle is 10 squares

and the width is 4 squares

The diagonals divide the rectangle into four triangles

These traingles are isoceles

Each two triangles facing each others are identical

<B = 90 degree

B = alpha + Beta

Let Beta be the angle next alpha

The segment that is crossing Beta is its bisector since it perpendicular to the diagonals wich means that:

Beta = 2x

Then B = alpha + 2x

90 = alpha +2x

90-alpha = 2x

x = (90-alpha)/2

Answer:

x = 90 - 2α

Step-by-step explanation:

Solution:-

- Consider the right angled triangle " ABD ". The sum of angles of an triangle is always "180°".

                       < BAD > + < ADB > + < ABD > = 180°

                       < ABD > = 180 - 90° - α

                        < ABD > = 90° - α

- Then we look at the figure for the triangle "ABE". Where " E " is the midpoint and intersection point of two diagonals " AC and BD ".

- We name the foot of the perpendicular bisector as " F ":  " BF " would be the perpendicular bisector. The angle < BAE > is equal to < ABD >.

                    < ABD > = < BAE >  = 90° - α   ... ( Isosceles triangle " BEA " )

Where, sides ( BE = AE ).

- Use the law of sum of angles in a triangle and consider the triangle " BFA " as follows:

                     < ABF> + < BFA > + < BAF > = 180°

                     < ABF > = 180 - (90° - α) - 90°

                    < ABF > = α  

Where,       < BAF > = < BAE >

- The angle < ABD > = < ABE > is comprised of two angles namely, < ABF > and < FBE >  = x.

                        < ABD > = < ABE > = < ABF > + x

                         90° - α = α + x

                        x = 90 - 2α   ... Answer

Answer:

this question is not clear please send clear question

Answer:

The new points after dilation are

(3/2, -3) and (9/2,-3)

Step-by-step explanation:

Here in this question, we want to give the new points of the line segment after it is dilated by a particular scale factor.

What is needed to be done here is to multiply the coordinates of the given line segment by the given scale factor.

Let’s call the positions on the line segment A and B.

Thus we have;

A = (1,-2) and B = (3,-2)

So by dilation, we multiply each of the specific data points by the scale factor and so we have;

A’ = (3/2, -3) and B’= (9/2,-3)

Answer:

P(61≤ X≤94) = 49.85%

Step-by-step explanation:

From the given information:

The mean of the bell shaped fluorescent light bulb μ = 61

The standard deviation σ = 11

The objective of this question is to determine the approximate percentage of light bulb replacement requests numbering between 61 and 94 i.e P(61≤ X≤94)

Using the empirical (68-95-99.7)rule ;

At 68% , the data lies between  μ - σ and μ + σ

i.e

61 - 11 and 61 + 11

50 and 72

At  95%, the data lies between  μ - 2σ and μ + 2σ

i.e

61 - 2(11) and 61 + 2(11)

61 - 22 and 61 +22

39   and   83

At 99.7%, the data lies between  μ - 3σ and μ + 3σ

i.e

61 - 3(11) and 61 + 3(11)

61 - 33 and 61 + 33

28   and   94

the probability equivalent to 94 is when  P(28≤ X≤94) =99.7%

This implies that ,

P(28≤ X≤94) + P(61≤ X≤94) = 99.7%

P(28≤ X≤94) = P(61≤ X≤94) = 99.7 %    

This is so because the distribution is symmetric about the mean

P(61≤ X≤94) = 99.7 %/2

P(61≤ X≤94) = 49.85%

Answer:

2) 30, 70, 80

Step-by-step explanation:

Well there has to be 3 angles that all add up to 180°.

1)

100+130+130

=360

2)

30+70+80

= 180

3)

25+3+35

=63

4)

45 + 105 + 120

=150

150+120

270

Answer:

C. . II and III only

Step-by-step explanation:

Given:

I. V=s^3

II.V=πr^2h

III. V=Bh

From the above

I. V varies directly as cube of s

II. V varies jointly as square of r and h where π is the constant of proportionality.

III. V varies jointly as B and h

Therefore, the volume formula which shows a joint variation are

II.V=πr^2h and III. V=Bh

Answer is C. II and III only

Answer:

Step-by-step explanation:

To find Angle X we use sine

sin∅ = opposite/ hypotenuse

From the question

WY is the opposite

WX is the hypotenuse

So we have

sin X = WY/ WX

sin X = 6/7

X = sin-¹ 6/7

X = 58.99

X = 59° to the nearest tenth

Hope this helps you

Answer:

x=arcsine (6/7) = 58.98 degrees

Step-by-step explanation:

Performing a trigonometrical function. We can find the value of the angle:

1) sin x =6/7

x=arcsine (6/7)

x= 58.98º

Answer: It represents that 2 will be divided into 3 equal parts.

Step-by-step explanation:

The given fraction : [tex]\dfrac{2}{3}[/tex]

here, Numerator = 2

Denominator = 3

It represents that 2 will be divided into 3 equal parts.

as the exterior angle is known

sum of that angle and f angle = 180

142 + f = 180

f = 180 - 142

f = 38

Answer:

38

Step-by-step explanation:

Hope this helps you :)

Answer: B

Step-by-step explanation:

Option A simplifies to 7/15

Option B simplifies to 11/21

If 1/2 is equal to .50, then when subtracted 7/15 would be equal to 0.46666667 and 11/21 would be equal to 0.52380952... meaning that 11/21 would be closer to 1/2 (or .50).

Hope this helps!

Answer:

Theresa is 58.82 in tall

Step-by-step explanation:

Steve: x=1.33y-6

x=72.24

Answer:

The number of students that would have a test score between 61 and 71 are 154 students

Step-by-step explanation:

The given information are;

The mean test score, μ = 61

The standard deviation, σ = 10

The sample size, n = 450

The z score is given as follows;

[tex]Z=\dfrac{x-\mu }{\sigma }[/tex]

We therefore have at x = 61,

[tex]Z=\dfrac{61-61 }{10 } = 0[/tex]

P(x > 61) = P(Z > 0) = 1 - 0.5 = 0.5

For x = 71, we  have;

[tex]Z=\dfrac{71-61 }{10 } = 1[/tex]

P(x < 71) = P(Z < 1) = 0.84134

The probability that the score will be between 61 and 71 is the difference between the two probabilities, which is 0.84134 - 0.5 = 0.34134

Given that the probability is equivalent to  the proportion of the students that would have a test score between 61 and 71, we have;

The number of students that would have a test score between 61 and 71 = 0.34134 × 450 = 153.6 ≈ 154 to the nearest whole number.