The table shows the information about the length of time, in minutes, it took students to do their maths homework.

Draw a histogram.

By using the concepts of relations and functions and based on the table given, the function presents the following relationship:

x → f(x)

7 → 95

Functions are relations between an input set named domain (x) and an output set named range (f(x)), that is:

x → f(x)

After a quick observation, for x = 7, then f(7) = 95. In more graphically manner, the function present the respective relation:

7 → 95

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Answer: x∈∅ (there is no decision).

Step-by-step explanation:

[tex]\left \{ {{x+y=5} \atop {\frac{1}{x} +\frac{1}{y}=\frac{9}{14} }} \right.\ \ \ \ \ \left \{ {{x+y=5} \atop {\frac{y+x}{x*y}=\frac{9}{14} \ |*14*x*y\ (x\neq 0;\ y\neq 0) }} \right. \ \ \ \ \left \{ {{x+y=5} \atop {14*(x+y)=9*x*y}} \right. \ \ \ \ \left \{ {{x+y=5} \atop {14*5=9*x*y}} \right.\ \ \ \ \left \{ {{x+y=5} \atop {9*x*y=70}} \right. \\[/tex]

[tex]\left \{ {{y=5-x} \atop {9*x*y=70\ |:9}} \right. \ \ \ \ \left \{ {{y=5-x} \atop {x*(5-x)=\frac{70}{9} }} \right.\ \ \ \ \left \{ {{y=5-x} \atop {5x-x^2=\frac{70}{9} }} \right. \ \ \ \ \left \{ {{y=5-x} \atop {x^2-5x+\frac{70}{9} =0\ |*9}} \right.\ \ \ \ \left \{ {{y=5-x} \atop {9x^2-45x+70=0}} \right.[/tex]

[tex]\left \{ {{y=5-x} \atop {D=-495}} \right. \ \ \ \ \Rightarrow\ \ \ \ x\in\varnothing.[/tex]

The value of the expression when evaluated is: 162.

To evaluate the expression, 6x^4y^3, substitute x = -1 and y = 3 into the expression and solve.

6(-1^4) × 3^3

6(1) × 27

6 × 27

162

The value of the expression, 6x^4y^3, is: 162.

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Answer:

y = [tex]\frac{7}{6}[/tex] x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

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

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (9, 2 ) and (x₂, y₂ ) = (3, - 5 )

m = [tex]\frac{-5-2}{3-9}[/tex] = [tex]\frac{-7}{-6}[/tex] = [tex]\frac{7}{6}[/tex]

• Parallel lines have equal slopes , so

m = [tex]\frac{7}{6}[/tex] is the slope of the parallel line

the line crosses the y- axis at (0, - 3 ) ⇒ c = - 3

y = [tex]\frac{7}{6}[/tex] x - 3 ← equation of parallel line

Hey there!

[tex] \\ [/tex]

[tex] \green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}[/tex]

[tex] \\ [/tex]

To find the equation of a line, we first have to determine its slope knowing that parallel lines have the same slope.

Let the line that we are trying to determine its equation be [tex] \: \sf{d_1} \: [/tex] and the line that is parallel to [tex] \: \sf{d_1} \: [/tex] be [tex] \: \sf{d_2} \: [/tex] .

[tex] \sf{d_2} \:[/tex] passes through the points (9 , 2) and (3 , -5) which means that we can find its slope using the slope formula:

[tex] \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{y_2} - \orange{y_1}}{\red{x_2} - \blue{x_1 }}} [/tex]

[tex] \\ [/tex]

⇒Subtitute the values :

[tex] \sf{(\overbrace{\blue{9}}^{\blue{x_1}}\: , \: \overbrace{\orange{2}}^{\orange{y_1}}) \: \: and \: \: (\overbrace{\red{3}}^{\red{x_2}} \: , \: \overbrace{\green{-5}}^{\green{y_2}} )} [/tex]

[tex] \implies \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{-5} - \orange{2}}{\red{ \: \: 3} - \blue{9 }} = \dfrac{ - 7}{ - 6} = \boxed{ \bold{\dfrac{7}{6} }}}[/tex]

[tex] \sf{\bold{The \: slope \: of \: both \: lines \: is \: \dfrac{7}{6}}} [/tex].

Assuming that we want to get the equation in Slope-Intercept Form, let's substitute m = 7/6:

Slope-Intercept Form:

[tex] \sf{y = mx + b} \\ \sf{Where \: m \: is \: the \: slope \: of \: the \: line \: and \: b \: is \: the \: y-intercept.} [/tex]

[tex] \implies \sf{y = \bold{\dfrac{7}{6}}x + b} [/tex] [tex] \\ [/tex]

We know that the coordinates of the point (0 , -3) verify the equation since it is on the line [tex] \: \sf{d_1} \: [/tex]. Now, replace y with -3 and x with 0:

[tex] \implies \sf{\overbrace{-3}^{y} = \dfrac{7}{8} \times \overbrace{0}^{x} + b} \\ \\ \implies \sf{-3 = 0 + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf{\boxed{\bold{b = -3}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Therefore, the equation of the line [tex] \: \bold{d_1} \: [/tex] is [tex] \green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}} [/tex]

[tex] \\ [/tex]

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The value of x is 14

From the question, the lines from the center of the circle to the chords have equal measures of 9 units

This line divides a chord into equal segments, where each segment is 7 units

So, we have:

x = 7 + 7

Evaluate

x = 14

Hence, the value of x is 14

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Answer:

18 degrees

Step-by-step explanation:

Supplementary angles are angles that when added together equal 180 degrees.

A + 162 = 180

     - 162  -162

        A  = 18

Answer:

18

Step-by-step explanation:

When your are asked the supplement you minus 162 from 180. When you join SU from supplement and add a 1 behind SU you'll get 180. [1SU TO 180]

180-162

18

Answer:

(B). F(X)=2x^2+2x-4

Step-by-step explanation:

-4 means it passes through -4 at the y axis

B and D have -4

graph passes thru x axis at -2 and 1

if you enter x = -2 or 1 in the formula

(B). F(X)=2x^2+2x-4

you get 0

it's not D because when you enter -2 or 1 for x

you don't get 0

you get 8 and -4

Answer: (B). F(x) = 2x² + 2x - 4

Step-by-step explanation:

      Let us think about the parent function F(x) = x² to pick our answer.

      Options A and C have only shifted 2 units down (showed by the "-2" at the end) and the function graphed is shifted four units down.

      Between options B and D, one is shifted 2 units to the right, and one is shifted 2 units to the left. We need the one shifted 2 units to the left. This is shown by the "+2x" in option B meaning it is our answer.

The value of the function operation f(a + h) - f(a) is; h² + 5h + 2ah

We are given the function;

f(x) = x² + 5x

We want to find f(a + h) - f(a)

Let us first find f(a + h) to get;

f(a + h) = (a + h)² + 5(a + h)

⇒ a² + 2ah + h² + 5a + 5h

⇒ a² + 5a + h² + 5h + 2ah

Let us now find f(a) to get;

f(a) = a² + 5a

Thus, f(a + h) - f(a) = a² + 5a + h² + 5h + 2ah - a² - 5a

f(a + h) - f(a) = h² + 5h + 2ah

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Answer:

E

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 1) and (x₂, y₂ ) = (3, 4) ← 2 points on the line

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

using (a, b ) = (3, 4 ) , then

y - 4 = 1 (x - 3) → E

The statements about the function that are true include:

g(0) = 0

g(1) = -1

g(-1) = 1

From the information, the points include:

(x1, y1) = (-2, 2, 5).

(x2, y2) = (0, 0)

(x3, y3) = (2, 3, 5).

It should be noted that (x2, y2) implies that g(0) = 0. In this case, the statements about the function that are true include g(0) = 0, g(1) = -1, and g(-1) = 1. This is illustrated in the graph.

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Answer:

-20

Step-by-step explanation:

-5-5-5-5=-20

Answer:

108 km/hr

Step-by-step explanation:

45 minutes = 3/4 hours

1) Distance = speed × time

= 60 × 3/4

= 45 km

2) 20 minutes = 1/3 hours. So, 3/4 - 1/3 = 5/12 hours.

speed = distance / time

= 45 / 5/12

= 108 km/hr

Answer:

For b), the answer is 105mm

Step-by-step explanation:

(150+60)/2

Scale factor = (image)/(preimage)

[tex]QR=3\\\\Q'R'=1[/tex]

So, the scale factor is 1/3

Answer:

0.1359

Step-by-step explanation:

Answer:

Limit does not exist

Step-by-step explanation:

This is a piece-wise function, since we are finding the limit of f(x) when x is approaching 2 from the right, we know that x must be more than 2. However, based on the piece-wise function, there is no function that satisfy this condition, therefore the limit does not exist for this piece-wise function

An inequality that shows all of the ways that Nita will win if Erik chooses 17 is

This refers to the relation in mathematics that makes an unequal comparison between two numbers or expressions.

Therefore, according to the rules of the game, they would have to make random selections from 0 to 20 and if the difference between their two numbers is less than 10, then Erik wins, the inequality that would show all of the ways that Nita will win if Erik chooses 17 are listed above.

Hence, we can see that the complete question goes thus:

"Erik and Nita are playing a game with numbers. In the game, they each think of a random number from zero to 20. If the difference between their two numbers is less than 10, then Erik wins. If the difference between their two numbers is greater than 10, then Nita wins.

Use what you know about inequalities and absolute values to better understand the game."

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Answer:

36 units

Step-by-step explanation:

to do this you must first find the lengths of all the sides with pythagorean theorem

for a to b you use

3^2 + 4^2 = c^2

9 + 16 = c^2

25 = c^2

c = 5

5 is one of the lengths

b to c uses the same equation

so

5 is another one of the lengths

for d to c your equation is

5^2 + 12^2 = c^2

25 + 144 = c^2

169 = c^2

13 is another of the lengths

d to a has the same length as c to d so there is another 13 unit length

so

5 + 5 + 13 + 13 is your equation to find the perimeter

5 + 5 + 13 + 13 = 36

that is your answer

Answer: Option D

[tex]\displaystyle d=\frac{C}{\pi}[/tex]

Step-by-step explanation:

    To solve the formula for d, we will isolate the d variable.

  Given:

C = πd

  Divide both sides of the equation by π:

[tex]\displaystyle\frac{C}{\pi}=\frac{\pi d}{\pi}[/tex],     [tex]\displaystyle\frac{C}{\pi}=d[/tex]

  Reflexive property

[tex]\displaystyle d=\frac{C}{\pi}[/tex]

The inverse variation equation is y = -5/x

Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal

y varies inversely as x

Let variation constant = k

y = k/x, y = 25 and x = -15

25 = k/(-15),  k = -375 divded by 75 ,So k = -5

The inverse variation equation is y = -5/x

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Answer:

2=A

Step-by-step explanation:

We know that F is directly proportional to A then the equation relating them is

F = kA ← k is the constant of proportion

To find k use the condition F = 36 when A = 9, then

36 = 9k ( divide both sides by 9 )

4 = k

F = 4A ← equation of proportion

When F = 8, then

8 = 8A ( divide both sides by 4 )

2 = A

The lengths um, md and ud are 255 units, 215 units and 470 units respectively, when given that points u, m, and d are collinear with m between u and d and um=5x+30, md=3x+80, ud=10x+20. This can be obtained by adding um and md which is equal to ud. An equation is obtained and solve for x.

Given that, um=5x+30  

                  md=3x+80

                  ud=10x+20

We know that m is the midpoint of ud

Thus, um + md = ud

                 5x+30 + 3x+80 = 10x+20

                 5x+3x + 30+80 = 10x+20

                      8x + 110 = 10x+20 (taking terms with x to one side of equation)

                             10x - 8x = 110 - 20

                                     2x = 90

                                   ⇒ x = 45

Therefore the lengths,

um=5x+30 = 5(45)+30 = 225 + 30 = 255

md=3x+80 = 3(45)+80 = 135 + 80 = 215

ud=10x+20 = 10(45)+20 = 450 + 20 = 470

Hence the lengths um, md and ud are 255 units, 215 units and 470 units respectively, when given that points u, m, and d are collinear with m between u and d and um=5x+30, md=3x+80, ud=10x+20.

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Assuming the world population growth rate is 1% and the current population is about 7 billion, next year the population will be 7.01 billion.

To calculate the percentage increase rate, use the fundamental increase charge formulation: subtract the original from the brand new cost and divide the results by way of the original cost. to show that right into a percent boom, multiply the results by 100.

The population of a given area is described as the range of humans generally residing in that vicinity, measured on 1 January in a given 12 months. The supply can be the most latest population census.

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Answer:

cocomelon . 3/5 - 4

Step-by-step explanation:

Answer:

x=[tex]\sqrt3[/tex] and -[tex]\sqrt3\\[/tex]

Step-by-step explanation:

the roots(zeros) are the value of x where the graph intersects the x-axis.

to find the roots:

x^2-3=0

x^2=3

x=+-[tex]\sqrt3[/tex]

Donna sold 3 pencils and 8 pens solved using simultaneous equation

What is a simultaneous equation?

Simultaneous equation refers to related equations that are solved at the same to derive answers to the unknown variables

Let assume that X pencils were sold and Y pens were sold

The total revenue is the sum of the prices multiplied by the quantities sold.

2X+3Y=30   (equation 1)

The sum of X and Y sold is 11

X+Y=11   (equation 2)

multiply the second equation by 2

2*(X+Y=11)

2X+2Y=22 (equation 3)

subtract equation 3 from 1

(2X+3Y=30)-(2X+2Y=22)

Y=8

Substitute for Y in equation 2

X+8=11

X=11-8

X=3

Which means he sold 3 pencils and 8 pens.

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Answer:

8

Step-by-step explanation:

Answer:

1, 4, 9, 16, 25, 36, 49, (....)

98% confidence interval for the mean rate = [4.1437 , 4.4983]

We are given the interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia for one day ;

4.751, 4.373, 4.177, 4.676, 4.425, 4.228, 4.125, 4.251, 3.951, 4.192, 4.291, 4.414

Now, Firstly we will find the Mean of the above data, Xbar ;

Mean, Xbar = ∑ x ÷ n =

4.751 + 4.373 + 4.177 + 4.676 + 4.425 + 4.228 + 4.125 + 4.251 + 3.951 + 4.192 + 4.291 + 4.414 ÷ 12 = 4.321

Standard deviation, s = √ ∑(x - x bar)²÷ n-1 = 0.226.

Now, the pivotal quantity for the 98% confidence interval for the mean rate is;

P.Q = x bar - ц ÷ n - 1 ≈ tn - 1

where, Xbar = sample mean

s = sample standard deviation

n = sample size = 12

So, 98% confidence interval for the mean rate, μ is ;

P(-2.718 < t₁₁ <2.718) = 0.98

P(-2.718 <Xbar - μ σ√ⁿ < 2.718) = 0.98

P(Xbar - 2.718 * ₈÷ √ⁿ < μ Xbar +  2.718 * ₈÷ √ⁿ ) = 0.98

98% confidence interval for μ = (Xbar - 2.718 * ₈÷ √ⁿ < μ Xbar +  2.718 * ₈÷ √ⁿ ) = 0.98

[4.321 - 2.718 * 0.226 ÷ √₁₂ , 4.321 + 2.718 * 0.226 ÷ √₁₂

                                  = [4.1437 , 4.4983]

Therefore, 98% confidence interval for the mean rate = [4.1437 , 4.4983]

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Answer:

x=9

Step-by-step explanation:

3/4x+2 1/4=9

3/4x=9-2 1/4

3/4x=6 3/4

4(3/4x)=4(6 3/4)

3x=27

x=9

Answer:

x = 9

Step-by-step explanation:

3/4 x + 2 1/4 = 9      subtract 2 1/4 from both sides of the equation

3/4  x = 6 3/4           now divide both sides by 3/4

x = 9