Write a linear function f with the values f(0)=−5 and f(1)=−3?

Answer:

Answer is D: 9

Step-by-step explanation:

you would do 2x-6=12

Next: add 6 to both sides: 2X=18

Next: divide both sides by 2

Answer: X=9

Given that Benjamin's age is 6 years less than twice Lucas's age and Benjamin is 12 years old.

Let x and y represent Luca's age and Benjamin's age respectively.

Then, according to the given information, we have

y = 2x-6⇒1

y=12      ⇒2

Substituting the value of y from equation (2) in (1), we get

y=2x-6

⇒12=2x-6

⇒2x=12+6

⇒2x=18

⇒x=18/2

∴ x=9

Lucas's age is Option D. 9

Thus, the required age for Luca is 9 years.

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Answer:

y = [tex]\frac{1}{27}[/tex]

Step-by-step explanation:

Given

y = [tex]3^{x}[/tex] and (- 3, y) is a point on the graph, then

y = [tex]3^{-3}[/tex] = [tex]\frac{1}{3^{3} }[/tex] = [tex]\frac{1}{27}[/tex]

Answer:  The required value of y is [tex]\dfrac{1}{27}.[/tex]

Step-by-step explanation:  We are given that the point (-3, y) lies on the graph of the following equation :

[tex]y=3^x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We are to find the value of y.

Since the point (-3, y) lies on the graph of equation (i), so it will satisfy the equation.

Therefore, substituting (-3, y) in equation (i), we get

[tex]y=3^{-3}\\\\\Rightarrow y=\dfrac{1}{3^3}\\\\\\\Rightarrow y=\dfrac{1}{27}.[/tex]

Thus, the required value of y is [tex]\dfrac{1}{27}.[/tex]

The slope of the line shown in the graph is -2.

The slope of a line can be found using the formula slope = (change in y) / (change in x).

Given the points (0, 3) and (1, 1),

we can calculate the slope by finding the difference in y-coordinates and dividing it by the difference in x-coordinates.

Slope = (1 - 3) / (1 - 0) = -2.

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Answer:

minimum = 30,  Q1 = 36, median = 50.5,  Q3 = 80, and maximum = 91.

Step-by-step explanation:

We are given the following data set for the exam scored of 8 students in a math course and we are to find the five number summary:

51, 91, 46, 30, 36, 50, 73, 80

Step 1: For that, we first need to rearrange in an ascending order:

30, 36, 46, 50, 51, 73, 80, 91

Step 2: Now we will spot the smallest and largest number in the data.

Smallest number: 30

Largest number: 91

Step 3: Finding the median (middle number) now:

Median = 50+51/2 = 50.5

Step 4: Placing parenthesis around the number before and after the median values:

(30, 36, 46) 50, 51 (73, 80, 91)

Find Q1 (median in the lower half of the data) and Q3 (median for the upper half of data):

Q1 = 36

Q3 = 80

Five step summary:

minimum = 30,  Q1 = 36, median = 50.5,  Q3 = 80, and maximum = 91.

Answer:

Minimum = 30, Maximum = 91, Median = 50.5, Q₁ = 36, Q₃ = 80

Step-by-step explanation:

We have to find the five-number summary of the given data represents the semester exam scores of 8 students in a math course.

The five-number summary includes 5 items:

1. The minimum

2. Q₁ (First quartile)

3. Median

4. Q₃ (Third quarlile)

5. The maximum

First we put the numbers in ascending order (lowest to highest)

30, 36, 46, 50, 51, 73, 80, 91

Now find the minimum and maximum from your data set.

Minimum = 30 and Maximum = 91

Now find the median, median is the middle number. But we have 50, 51 two middle numbers so we take the median of those numbers =

Median = [tex]\frac{(50+51)}{2}[/tex] = 50.5

Median = 50.5

Now place parenthesis around the numbers before and after the median values

30, 36, 46, 50, 51, 73, 80, 91

Median of lower half of the data Q₁ = 36

Median of upper half of the data Q₃ = 80

Five-number summary found

Minimum = 30, Maximum = 91, Median = 50.5, Q₁ = 36, Q₃ = 80

Answer:

26 mph

Step-by-step explanation:

d/t = r (distance/ time = rate)

104/4 = 26

Answer:

A.

male long sleeves: 3

Male short sleeves: 0

male rolled up sleeves: 2

Female long sleeves: 0

Female short sleeves: 2

Female rolled up sleeves: 1

B. 0/3

C. 2/5

Step-by-step explanation:

Hello There!

Economic utility is the amount of satisfaction a consumer receives from the consumption of a particular product or service.

Answer:

The capacity of a good or service to meet the demand of a consumer. The amount of economic utility of a good or service determines what the demand will be for that good or service, which impacts the price that people will be willing to pay to obtain it

Step-by-step explanation:------------------------------------------)-

Answer:

3.

Step-by-step explanation:

We have a triangle where opposite side = 12 , adjacent side = 5 and hypotenuse =  √(12^2 + 5^2) = 13   (because cot a = adjacent/ opposite side).

So  2sina - 3cosa / 4sina - 9cosa

= (2 * 12/13 - 3 * 5/13) / ( 4 * 12/13 - 9 * 5/13)

= (24/13 - 15/13) / (48/13 - 45/13)

=  9/13 / 3/13

= 9/13 * 13/3

= 3.

Answer:

3

Step-by-step explanation:

To find the lower quartile first locate the median.

The median is the middle value of the data set arranged in ascending order.

The data given is in ascending order

0, 1, 3, 3, 4, 4, 4, 5, 6, 6, 8

                    ↑ ← The median is 4

The lower quartile is then the middle value of the data to the left of the median.

0, 1, 3, 3, 4

       ↑ ← the lower quartile is 3

The lower quartile of the data is given as 3

Lower quartile of the data is the median of all the observations till the median of the given observations.

Median is the middle observations of the set of observations.

The median is the mid value which is 4

So, the values till 4 are 0, 1 , 3, 3, 4,

∴  The median is the mid value which are 3

∴ The lower quartile of the data is given as 3

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Answer:

Step-by-step explanation:

If the line has no x-intercept, then it's a horizontal line with equation

[tex]y=a,\ a\neq0[/tex]

The line passes through the point (0, -4). Therefore the equation of this line is:

[tex]y=-4[/tex]

Answer:

y = 4

Step-by-step explanation:

Since the line has no x-intercept, this means that the line has a slope of 0, meaning it is a horizontal line. So with the equation y = mx + b, mx cancels out to 0 because there is no slope. This leaves y = b, where b = 4. So the answer is y =4

Answer:

135°

Step-by-step explanation:

Draw a line that intersects the endpoint of the angle that is between L and K and is also perpendicular to L and K.

∠a+45°+∠b = 180°

∠a+∠b = 135°

Answer:

Step-by-step explanation:

There are 5 cards we are selecting out of 135 cards so how many ways can we draw 5 cards at a time (w/o replacement)

There are 135 ways to choose the first card.

There are then 134 ways to choose the second card.

There are then 133 ways to choose the third card.

132 to choose the 4th

131 to choose the 5th.

Now multiply those giving 135*134*133*132*131 or you could have just said

135 P 5.

In case you don't know P means permutation.

The mathematics behind determining the number of different ways to get any 5 card hand from a deck of 135 cards involves combinatorics. Specifically, the combinations formula is used, which is C(n, r) = n! / [(n-r)!r!]. In this case, n is 135 (the total number of cards) and r is 5 (the number of cards drawn).

The subject of this question concerns probabilities in the game theory section of mathematics, specifically revolving around understanding the combinatorics of card hands in a uniquely structured card game.

Using combinatorial mathematics, the number of ways to get any 5-card hand from a deck of 135 cards can be calculated by using the combinations formula which is: C(n, r) = n! / [(n-r)!r!]. In this instance, 'n' represents the number of total outcomes (135 cards) and 'r' is the number of outcomes chosen at a time (5 cards).

So to find the number of 5-card hands, you would calculate it as follows:

C(135, 5) = 135! / [(135-5)!5!]

The factorial of a number, denoted as '!', is the product of the number and all the consecutive numbers below it down to 1. So 5! = 5*4*3*2*1. Calculating this large of a number directly can be a bit tricky, but there are online tools that can help!

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Answer:

y = 3x + 1

Step-by-step explanation:

The equation is in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 1) and (x₂, y₂ ) = (1, 4) ← 2 ordered pairs from table

m = [tex]\frac{4-1}{1-0}[/tex] = 3

Note the line crosses the y- axis at (0, 1) ⇒ c = 1

y = 3x + 1

Answer:

b

Step-by-step explanation:

25 minutes

Answer:

B.25

Step-by-step explanation:

To find the amount of minutes, divide the total amount of feet from the feet per minute:

60000/2400 = 25

B. 25 is the amount needed to climb to 60,000 feet.

~

Answer:

5/9 cubic yards

Step-by-step explanation:

Just so L*W*H=24(36)(30)= 25920 cubic inches=25920 (1 in*1 in* 1 in)

36 in=1 yd

so

1 in =1/36 yd

do divide 25920 by (36*36*36)

The answer in cubic yards is 5/9 cubic yards

2/3 hour =2/3×60 min=40 min

2/3 hour=2/3×3600 seconds=2400seconds

x + 16 > 51

x>35

Thus, A and D would be the answers.

Please mark brainliest and have a great day!

That would be 32, 16 and 34.

The formula for perimeter is length + length + width + width

You know that all the sides of a square are equal to each other. That means that all the values in the perimeter formula should be the same. Therefore you can divide 72 by 4 (perimeter divided by the number of sides)

72 / 4 = 18

^^^Each side is 18 in

The formula for are is...

A = length x width

so...

18 * 18 = 324

324 in^2

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

5 nickels

Step-by-step explanation:

You can setup and solve a system of equations, or you can solve by trial and error until you get the correct answer.

Here is the solution by trial and error.

If all 20 coins are quarters, the value is 20 * $0.25 = $5

That is too much value.

Let's try 16 quarters. 16 quarters are worth 16 * $0.25 = $4.

That is the correct value, but it is only with quarters, and only 16 of them.

We need fewer quarters than 16.

Try 12 quarters: 12 * $0.25 = $3.00

The number of nickels is: 20 - 12 = 8

8 nickels are worth 8 * $0.05 = $0.40

12 quarters and 8 nickels are worth $3.00 + $0.40 = $3.40

There are 20 coins, but the value is too low.

The number of quarters is between 12 and 16.

Try 14 quarters and 6 nickels:

14 * $0.25 + 6 * $0.05 = $3.50 + $0.30 = $3.80

We are closer to $4 but not there yet.

Try 15 quarters and 5 nickels.

15 * $0.25 + 5 * $0.05 = $3.75 + $0.25 = $4

The total value is $4 and there are 20 coins. This is the answer.

15 quarters and 5 nickels works.

Answer: 5 nickels

Answer:

The other x-intercept is (-2,0)

Step-by-step explanation:

-x^2-5x-6

-(x^2+5x+6)

We know x=-3 is a x-intercept so x+3 is a factor

-(x+3)(        )

The other factor has to be x+2 since 3(2)=6 and 2+3=5

So -x^2-5x-6 is the same as -(x+3)(x+2)

Which means the other x-intercept is (-2,0)

Answer:

y = (1/3)x

Step-by-step explanation:

If the y-intercept is (0, 0), then y = mx + b becomes y = mx.

Seeing that y increases by 1, going from (-3, 1) to (0, 0), and that x increases by 3, we determine that the slope, m, is 1/3.

The equation of this line is therefore y = (1/3)x.

Answer:it’s Y = - 1/3

Step-by-step explanation:

Answer:

m angle BOC 120

m angle AOB 205

Step-by-step explanation:

So you are given mangle AOC+mangle BOC=mangle AOB.

mangle means measure of angle.

Let's do some substituting into our equation.

85+2x+10=4x-15

Solve for x... First I'm going to combine the like terms on the left hand side:

95+2x=4x-15

Add 15 on both sides

110+2x=4x

Subtract 2x on both sides

110     =2x

Divide both sides by 2

110/2   =x

x         =110/2

x          =55

So Recall mangle BOC=2x+10   =2(55)+10=110+10=120

And you also have mangle AOB=4x-15=4(55)-15=220-15=205

bearing in mind that the squared variable is the "x", and thus this is a vertical parabola, therefore its axis of symmetry will come from the x-coordinate of its vertex.

[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{-2}x^2\stackrel{\stackrel{b}{\downarrow }}{+8}x\stackrel{\stackrel{c}{\downarrow }}{-7} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{8}{2(-2)}~,~-7-\cfrac{8^2}{4(-2)} \right)\implies \left( \cfrac{8}{4}~,~-7+8 \right)\implies (2,1) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{axis of symmetry}}{x=2}~\hfill[/tex]

Answer:

Since AB = BE and DB =CE

Step-by-step explanation:

The ratio and of these two give the concept of slope

The last sentence explains why the slope of AB is equal to slope of BC.

It is the measure of steepness of a line.

In the given figure, AD = BE and DB = EC

So, the ratio AD to BE is equal to the ratio BE to EC.

The slope of a line is given by,

slope = rise / run

Which is same as the above mentioned ratio.

Since AD = BE and DB = EC, their proportions are also equal. Therefore the slope of AB is equal to the slope of BC.

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Answer:

The correct answers are:

(1) The vertical asymptote is x = 0

(2) The horizontal asymptote is y = 0

Step-by-step explanation:

(1) To find the vertical asymptote, put the denominator of the rational function equals to zero.

Rational Function = g(x) = 

Denominator = x = 0

Hence the vertical asymptote is x = 0.

(2) To find the horizontal asymptote, check the power of x in numerator against the power of x in denominator as follows:

Given function = g(x) = 

We can write it as:

g(x) = 

If power of x in numerator is less than the power of x in denominator, then the horizontal asymptote will be y=0.

If power of x in numerator is equal to the power of x in denominator, then the horizontal asymptote will be y=(co-efficient in numerator)/(co-efficient in denominator).

If power of x in numerator is greater than the power of x in denominator, then there will be no horizontal asymptote.

In above case, 0 < 1, therefore, the horizontal asymptote is y =

Answer:

6x^6y^8z^6

Step-by-step explanation:

(3x^3y^4z^4)(2x^3y^4z^2)

= 6x^(3+3) y^(4+4) z^(4+2)

= 6x^6y^8z^6

Answer:

(6x⁶y⁸z⁶)

Step-by-step explanation:

The given expression is (3x³y⁴z⁴) (2x³y⁴z²) and we have to simplify it.

= 6 (x)³⁺³ (y)⁴⁺⁴ (z)⁴⁺²    [Since xᵃ · xᵇ = xᵃ⁺ᵇ]

Therefore, simplified form of the expression is

(6x⁶y⁸z⁶)

Answer:

the slope of jk is -6/5

the slope of pq is 4/5

the lines are (I don't know what options are given)

Step-by-step explanation:

you can use the x1 y1 formula

[tex]\frac{y2-y1}{x2-x1}[/tex]=[tex]\frac{-7-5}{10-0}[/tex]=[tex]\frac{-12}{10}[/tex]=[tex]\frac{-6}{5}[/tex]

therefore, the slope is -6/5

using the same formula;

tex]\frac{y2-y1}{x2-x1}[/tex]= [tex]\frac{4-(-8)}{0-(-5)}[/tex]=[tex]\frac{12}{15}[/tex]=[tex]\frac{4}{5}[/tex]

therefore, the slope is 4/5

and I would glady re-edit this answer if you can comment what the options for the last one are :)

Answer:

The slope of Jk is -6/5

The slope of PQ is 4/5

The lines are neither parallel or perpendicular

Step-by-step explanation:

Step-by-step explanation:

The point-slope of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

We have

[tex]m=1\\\\\left(\dfrac{3}{2},\ -\dfrac{1}{2}\right)\to x_1=\dfrac{3}{2},\ y_1=-\dfrac{1}{2}[/tex]

Substitute:

[tex]y-\left(-\dfrac{1}{2}\right)=1\left(x-\dfrac{3}{2}\right)[/tex]

[tex]y+\dfrac{1}{2}=1\left(x-\dfrac{3}{2}\right)[/tex] → the point-slope form

Convert to the slope-intercept form:

[tex]y+\dfrac{1}{2}=x-\dfrac{3}{2}[/tex]         subtract 1/2 from both sides

[tex]y=x-\dfrac{4}{2}[/tex]

[tex]y=x-2[/tex] → the slope-intercept form

Answer:

Diameter of tank = 19.5 ft

Step-by-step explanation:

Volume of cylinder = Base area x Height.

Base area = Area of circle

[tex]\texttt{ Area of circle}=\frac{\pi d^2}{4}[/tex]

Height = 20 ft.

Volume of tank = 6000 cubic feet .

[tex]\texttt{ Volume of cylinder = Base area x Height.}\\\\6000=\frac{\pi d^2}{4}\times 20\\\\d^2=381.97\\\\d=19.5ft[/tex]

Diameter of tank = 19.5 ft

Answer:

-2/3x = 1/4

x = (1/4)(-3/2)

x = -3/8