Jubaraj and Kristopher need to buy new pencils for school. Their old pencils are less than 2 inches long. They found a bargain on pencils at a local store. Four pencils cost $1.00, including tax. If the boys buy 12 pencils, how much will they pay?​

Answer: x=3

Step-by-step explanation:

-2(7-x) + 4= -4

-14 + 2x + 4= -4

2x - 10= -4

2x = 6

x=3

Equation of line p:

[tex]{\sf{2x - 3y = 4}}[/tex]

[tex]{\sf{y = \frac{2x}{3} - \frac{4}{3}}}[/tex]

Slope of line p (m):

[tex]{\sf{\frac{2}{3}}} [/tex]

Since, l is perpendicular to line p, the product of slopes of line l & p should be -1. We assume slope of line l be m2

Hence,

[tex]{\sf{m \times m2 = - 1}}[/tex]

[tex]{\sf{ \frac{2}{3} \times m2 = - 1}}[/tex]

[tex]{\sf{m2 = \frac{ - 3}{2}}}[/tex]

Since, line l passes through points (6, 0).

We apply,

[tex]{\sf{(y - y1) = m2(x - x1)}}[/tex]

[tex]{\sf{y - 0 = \frac{ - 3}{2}(x - 6)}} [/tex]

[tex]{\sf{2y - 0 = - 3x + 18}}[/tex]

[tex]{\sf{3x + 2y - 18 = 0}}[/tex]

The equation of line l:

[tex]{\sf{\red{\boxed{\sf{3x+2y-18=0}}}}}[/tex]

Let's change the equation,

→ 6x - y = 2

→ y = 6x - 2

Then the value of x will be,

→ -4x + 3y = 1

→ -4x + 3(6x - 2) = 1

→ -4x + 18x - 6 = 1

→ 14x = 1 + 6

→ x = 7/14

→ [ x = 1/2 ]

Hence, the value of x is 1/2 (or) 0.5.

Now the value of y will be,

→ y = 6x - 2

→ y = 6(1/2) - 2

→ y = 3 - 2

→ [ y = 1 ]

Hence, the value of y is 1.

Answer:

x = -2

TU = 4

UB = 2

Step-by-step explanation:

you can add x^2 with 4x+10 and equate it to 6:

x^2 + 4x + 10 = 6

x^2 + 4x + 4

then u can use the roots formula : x = (-b ± √ (b2 - 4ac) )/2a

so it'll be   x = {-4±[√16 - 4(4)]}/2

x= -2

then u can substitute it and find TU and UB

TU= (-2)^2 = 4

UB= 4(-2)+10 = 2

Answer:

15

Step-by-step explanation:

225/15

Answer: 13512

100332

Step-by-step explanation:

The shortest time for her run is approximately 36 minutes and the longest time is approximately 67 minutes.

To represent Kenzie's situation, we can use an absolute value equation. Let x represent the length of her run in miles.

The equation would then be |x - 6| ≤ 1, which means the distance between x and 6 is less than or equal to 1.

To find the shortest or longest amount of time for Kenzie's run, we need to consider the speed.

The time can be found by dividing the distance by the speed, so the minimum time would be (6 - 1)/6.25 hours,

which is approximately 0.6 hours or 36 minutes.

The maximum time would be (6 + 1)/6.25 hours,

which is approximately 1.12 hours or 67 minutes.

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Explanation:

The parabola has its lowest point when either x = -8 or x = 8

Plug either value into the function

f(x) = -x^2 + 4

f(-8) = -(-8)^2 + 4

f(-8) = -60

You should find that f(8) = -60 as well

This is the lowest output possible. Confirmation of such can be done using a graph. Look for the lowest point and only focus on the interval [tex]-8 \le \text{x} \le 8[/tex]

The highest point is at the vertex (0, 4), so the largest output is y = 4

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

We have the lowest output y = -60 and the highest output y = 4

The possible set of outputs is the interval [tex]-60 \le \text{y} \le 4[/tex] which turns into the interval notation [-60, 4]

Check out the graph below.

Answer:

750 students are boys, 250 are girls.

Step-by-step explanation:

1/4 of 1000 is 250.

250 + 250 + 250 = 750 boys.

if 3/4 are boys, then 1/4 (the rest of the school population) are girls.

150 students are girls.

hmmm from the table, let's just pick one point since we know "y" is inversely proportional, so hmmm let's say hmm the point when x = 4 and y = 9/16

a)

[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" inversely proportional to }x^2}{ {\LARGE \begin{array}{llll} y = \cfrac{k}{x^2} \end{array}}}\qquad \textit{we also know that} \begin{cases} x=4\\ y=\frac{9}{16} \end{cases} \\\\\\ \cfrac{9}{16}=\cfrac{k}{(4)^2}\implies \cfrac{9}{16}=\cfrac{k}{(16)}\implies \cfrac{9(16)}{16}=k\implies 9=k~\hfill \boxed{y=\cfrac{9}{x^2}}[/tex]

b)

when y = 16, what's "x"?  

[tex]16=\cfrac{9}{x^2}\implies x^2=\cfrac{9}{16}\implies x=\pm\sqrt{\cfrac{9}{16}}\implies x=\pm \cfrac{\sqrt{9}}{\sqrt{16}}\implies \stackrel{positive~value}{x=+\cfrac{3}{4}}[/tex]

Answer:

13 1/3

____

         [tex]1\:2/3 = 5/3\\1/8 = 1/8\\\\5/3 \div 1/8\\=\frac{5\cdot8}{3\cdot1}\\= \frac{40}{3}\\= 13\:1/3[/tex]

When working with mixed numbers that are being divided, you know where to start. Start by converting mixed numbers to fractions, then multiply the fractions together to divide them. Simplify your improper fraction by counting how many times it surpasses the denominator.

Scale factor for the drawing from actual park = 1/20

Area of the actual park = 1200 cm²

Area of a Rectangle. A = l × b. The area of any rectangle is calculated, once its length and width are known. By multiplying length and breadth, the rectangle's area will obtain in a square-unit dimension

Length of the rectangular city park = 5 cm

Width of the rectangular park = 6 cm

Using scale factor 1 cm = 20 meters

Scale factor = Length of the park in drawing/ actual length of park

⇒1/20.

5/actual length of park = 1/ 20

Actual length = 5 × 20 = 100 meters

Actual width = 6 × 20 = 120 meters

Area of the rectangular park = length × width

square meters

Therefore, Scale factor from actual length to the length in drawing = 1 : 20

Area of the rectangular park = 1200 square feet

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Beginning with the graph of f(x) = x2, The transformations that are needed to form  [tex]g(x)=\frac{1}{2}(x+4)^2-3[/tex] is

The graph of g(x) is wider than f(x) and is shifted to the left 3 units and down 3 units

This is further explained below.

Generally, A point, a line, or a geometric figure may undergo one of these four distinct transformations in order for the point's, line's, or figure's shape and/or location to be altered.

The shape of the item as it was before the transformation is referred to as the Pre-Image, while the shape and location of the object after the change make up the Image.

In conclusion, The necessary transformations may be found by beginning with the graph of the function f(x) = x2.

[tex]g(x)=\frac{1}{2}(x+4)^2-3[/tex]

The graph of g(x) is bigger than the graph of f(x), and it is displaced 3 units to the left and 3 units down from its original position.

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Answer:

The graph of g(x) is wider than f(x) and is shifted to the left 4 units and down 3 units.

Step-by-step explanation:

I got it right.

Answer:

S' (- 3, 9 ) , V' (- 4, 3 )

Step-by-step explanation:

consider the coordinates of R and R'

R (2, 1 ) , R' (- 4, 8 )

2 → - 4 in the x- direction is - 6

1 → 8 in the y- direction is + 7

then the translation rule is

(x, y ) → (x - 6, y + 7 )

S (3, 2 ) → S' (3 - 6, 2 + 7 ) → S' (- 3, 9 )

V )2, 6 ) → V' (2 - 6, 6 + 7 ) → V' (- 4, 13 )

The amount Jasmin was paid altogether was $210

From the question, we are to determine how much Jasmin was paid altogether

From the given information,

The Smith family pay her $10 an hour.

and

She babysat for the Smith family for 12 hours

Thus,

The amount she was paid by the Smith family is 12 × $10 = $120

Also,

The Johnson family pay her $15 an hour

and

She babysat for the Johnson family for 6 hours

Thus,

The amount she was paid by the Johnson family is 6 × $15 = $90

Therefore,

The amount she was paid altogether = $120 + $90

The amount she was paid altogether = $210

Hence, the amount Jasmin was paid altogether was $210

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The value of the longest of the four side length is 29 inches, if the lengths of the four sides of a quadrilateral (in inches) are consecutive integers.

According to the given question.

The lengths of the four sides of a quadrilateral (in inches) are consecutive integers.

So, let the length of the quadrilateral be x, (x + 1), (x + 2), and (x + 3).

Also, it is given that the perimeter of the quadrilateral is 110 inches.

⇒ x + x+1 + x + 2 + x + 3 = 110

⇒ 4x + 6= 110

⇒ 4x = 110 -6

⇒ 4x = 104

⇒ x = 104/4

⇒ x = 26 inches

Thereofore, the length of the sides of the quadrilaterals is given by

x = 26 inches

x + 1 = 26 + 1 = 27 inches

x + 2 = 26 + 2 = 28 inches

x + 3 = 26 + 3 = 29 inches

Hence, the value of the longest of the four side length is 29 inches, if the lengths of the four sides of a quadrilateral (in inches) are consecutive integers.

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Answer:

see below

Step-by-step explanation:

The interior angle of the triangle on the right is   180 - ( 9x+12)

  this plus the other two sum to 180 degrees

180 - (9x+12)     +     4x-3      +       6x + 3 = 180

  x   = 12

then the angles are        6(12)  + 3 = 75      4(12) -3 = 45    and    60°      

Answer:

14

Step-by-step explanation:

g(3)=(3)+3

g(3)=6

f(3)=-(3)-5

f(3)=-8

6-(-8)=14

Annually The amount after 10 years = $ 7247.295

quarterly compound after 10 years = $7393.5

Continuously interest =$7,419

Given:

P = the principal amount

r = rate of interest

t = time in years

n = number of times the amount is compounding.

Principal =  $4500

time= 10 year

Rate = 5%

To find: The amount after 10 years.

The principal amount is, P = $4500

The rate of interest is, r = 5% =5/100 = 0.05.

The time in years is, t = 10.

Using the quarterly compound interest formula:

A = P (1 + r / 4)4 t

A= 4500(1+.05/4)40

A= 4500(4.05/4)40

A= 4500(1.643)

Answer: The amount after 10 years = $7393.5

Using the Annually  compound interest formula:

A = P (1 + r / 100) t

A= 4500(1+5/100)10

A= 4500(105/100)10

Answer: The amount after 10 years = $ 7247.295

Using the Continuously  compound interest formula:

e stands for Napier’s number, which is approximately 2.7183

[tex]A=Pex^{rt} \\A=4500(e)^{.5} \\A= 4500(2.71)^{.5}[/tex]

A= $2,919

Answer: The amount after 10 years = $4500+$2,919=$7,419

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Darcy requires 24.14 gallons of paint to cover an area of 2716 feet².

Length of the house = 35 feet

width of the house = 28 feet

Height of the house = 6 feet

Total surface area = 2 l b + 2 b h + 2 h l

A = 2 (35) (28) + 2 (28) (6) + 2 (6) (35)

A = 1960 + 336 + 420

A = 2716 feet²

If he uses 2 coats of stain, the area he need to cover = 2 (2716) = 5432 feet²

Gallon of paint required = 5432 / 225 = 24.14 gallons.

Therefore, Darcy requires 24.14 gallons of paint to cover an area of 2716 feet².

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Answer:

see below

Step-by-step explanation:

1/11=0.0909....

3/11=0.090909...*3 or 0.27272727...

Answer:

25n

Step-by-step explanation:

product of n and 25

Product means multiply

25n

Given:

[tex]\begin{aligned}&x^2+y^2=16 \\&z=x y\end{aligned}[/tex]

Express 16 as [tex]4^{2}[/tex]: [tex]x^2+y^2=16[/tex]

[tex]x^2+y^2=4^2\\x^2+y^2=4^2 \times 1[/tex]

Trignometry,

[tex]\cos ^2(t)+\sin ^2(t)=1[/tex]

Now, substitute [tex]\cos ^2(t)+\sin ^2(t)[/tex] for 1:

[tex]\begin{aligned}&x^2+y^2=4^2 \times 1 \\&x^2+y^2=4^2 \times\left[\cos ^2(t)+\sin ^2(t)\right]\end{aligned}\\x^2+y^2=4^2 \times \cos ^2(t)+4^2 \times \sin ^2(t)[/tex]

Law of indicates:
[tex]\begin{aligned}&x^2+y^2=[4 \times \cos (t)]^2+[4 \times \sin (t)]^2 \\&x^2+y^2=[4 \cos (t)]^2+[4 \sin (t)]^2\end{aligned}\\x^2=[4 \cos (t)]^2 \text { and } y^2=[4 \sin (t)]^2[/tex]

Taking positive square roots as follows:

[tex]x=4 \cos (t), y=4 \sin (t)[/tex]

Recall that, z = xy.

Now, we have:

[tex]\begin{aligned}&z=4 \cos (t) \times 4 \sin (t) \\&z=16 \cos (t) \cdot \sin (t)\end{aligned}[/tex]

Now, substitute the values:
[tex]r(t)=x_t i+y_t j+z_t k[/tex]

So, the vector r(t) is: [tex]r(t)=(4 \cos (t)) i+(4 \sin (t)) i+(16 \cos (t) \cdot \sin (t)) i[/tex]

Therefore, the vector function r(t) is written as: [tex]r(t)=x_t i+y_t j+z_t k[/tex]

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Answer:

Coordinates of D are (-1, 4)

Step-by-step explanation:

I have assumed that what you wrote as 1n is actually 1/n otherwise the question does not make sense

1/n with n = 5 ==> that D is 1/5th of the distance from C on the CD line segment

Point D is 1/5th of the way from C to D

I will represent the (x, y) coordinates of points C, D and E as
[tex](x_C, y_C), (x_D, y_D) , (x_E, y_E)[/tex] respectively

Then the x-distance from C to E = [tex]x_E - x_C[/tex] and the y-distance from C to E will be [tex]y_E - y_C[/tex]

[tex]\text{1/5th of }[/tex] [tex]x_E - x_C = \dfrac{x_E - x_C}{5}[/tex] but this is relative to the location of [tex]x_C[/tex].
So we have to add this to [tex]x_C[/tex] to get the absolute x-coordinate of D

So
[tex]\displaystyle \large x_{D}=x_{C}+\dfrac{x_{E}-x_{C}}{5}[/tex]

and similarly

[tex]{\displaystyle y_{D}=y_{C}+\dfrac{y_{E}-y_{C}}{5}}[/tex]

Putting in the values for these coordinates we get

[tex]x_{D}=-2.5+\dfrac{5-(-2.5)}{5} \\\\= -2.5 + \dfrac{5 + 2.5}{5}\\\\\= -2.5 + \dfrac{7.5}{5}\\\\= - 2.5 + 1.5\\\\= -1.0[/tex]

[tex]y_{D}=1.25+\dfrac{15-1.25)}{5} \\\\= 1.25+ \dfrac{15 - 1.25}{5}\\\\\ = 1.25+ \dfrac{13.75}{5}\\\\= 1.25+ 2.75\\\\= 4.0[/tex]

So the coordinates of D are:

[tex]\boxed{D(-1, 4)}[/tex]

The graph shows the point D is indeed 1/5th of the distance from C to D

The consecutive even integers are 8, 10 and 12.

Let the integers be x, x + 2, and x + 4.

Therefore, the equation will be:

6(x) = x + 2 + x + 4 + 26

6x = 2x + 32

Collect like term

6x - 2x = 32

4x = 32

Divide

x = 32/4.

x = 8

The numbers are 8, 10 and 12.

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Answer:

E would be 6 spaces or the middle of points C and D.

Step-by-step explanation:

Please see picture.

The function that models the given situation is; f(x) = 109(0.935)^(t) + 72

We are given that;

Temperature of hot tea = 181°F

Room temperature = 72°F

Rate of the hot tea cooling on a desk in the room = 6.5% every minute

We know that an exponential function is of the form of;

y = A(r)^(x)

where;

A is the initial value.

r is the rate of increase/decrease in decimals.

Thus, our initial value is;

A = 181 - 72 = 109

The rate of increase/decrease in decimals = 1 - (6.5%) = 0.935

Since the room temperature is 72 degrees Fahrenheit, then the function is;

f(x) = 109(0.935)^(t) + 72

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Answer:

3.4, 1/4, 12%, -0.01, -26.1

Step-by-step explanation:

The simplest way to do these type of problems is to convert all of the numbers into either a fraction, decimal, or a percentage. In my opinion, it is easier to use a percentage here.

12% is already a percentage

-0.01 = -1%

1/4 = 25%

3.4 = 340%

-26.1 = -2610%

Now that the rational numbers are all in the same unit, it is easier to sort them. In the end, we get this list (from greatest to least):

3.4, 1/4, 12%, -0.01, -26.1

FINAL ANSWER: 3.4, 1/4, 12%, -0.01, -26.1

Answer:

y = [tex]\frac{x+1}{2}[/tex]

Step-by-step explanation:

y = 2x - 1

switch the x and y variables

x = 2y - 1

solve for y

x + 1 = 2y

[tex]\frac{x+1}{2}[/tex] = y