Graph the solution to the equations below.
=1/4+2 and =−2−7

The $100 start-up fee and $25 monthly rental gives;

The cost of using the phone for 1 month = $125

The cost of using the phone for 6 months = $250

The cons of using the phone for n months = $(100 + 25·n)

Please find attached the graph of the cellphone plan over a period of two years (24 months)

A graph is a visual representation of the variation of one variable of a function with respect to other variables of the function.

The start-up fee of the cell phone plan = $100

The amount charged each month = $25

First part;

The total cost for the start-up fee and monthly rental for 1 month = $100 + $25

The total cost for 1 month = $125

The total cost for 6 months = $100 + 6 × $25 = $250

The total cost for n months = 100 + n × 25 = $(100 + 25·n)

Please find the graph of the total cost to the number of months created with MS Excel

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Lester's final score from the two Judges is 7.6

The scores of the judges are in percentage and this will be converted to decimal by dividing by 100

impact (worth 40%) = 0.4

composition (worth 30%) = 0.3

lighting (worth 20%) = 0.2

color balance (worth 10%) = 0.1

Average score from the Judges will be used to multiply the percentages

Impact: 8 and 9

= 8.5 * 0.4 = 3.4

Composition: 7 and 7

= 7 * 0.3 = 2.1

Lighting: 8 and 7

= 7.5 * 0.2 = 1.5

Color balance: 5 and 7

= 6 * 0.1 = 0.6

sum of the scores gives Lester's final score as 7.6

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The y-intercept of the graph as shown is 2.

The equation of a line can be represented as follows:

y = mx + b

where

The y-intercept is the point where the graph intersects the y-axis. In other words, it is the value of y when x = 0 .

Therefore, let's trace the value of y when x  = 0 on the graph.

Hence, when x = 0, y = 2

Therefore,

b =  y-intercept = 2

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Answer:b=2b

b=−2b

b=−3b

b=3b

Step-by-step explanation: because I tought myself i know

[tex]{ \huge{ \boxed{ \red{ \sf{x = 7}}}}}[/tex]

Step-by-step explanation:-

[tex]{ \sf{126 = 2 \times 3 \times 3 \times k}}[/tex]

[tex]{ \sf{126 = 6 \times 3 \times k}}[/tex]

[tex]{ \sf{126 = 18 \times k}}[/tex]

[tex]{ \sf{126 = 18k}}[/tex]

Divide both the sides by 18 in order to find the value of k. Then,

[tex]{ \sf{ \frac{126}{18} = \frac{18}{18} k}}[/tex]

[tex]{ \boxed{ \boxed{ \purple{ \sf{x = 7}}}}}[/tex]

The number 5.96 × 10⁴ is 20 times greater than 2.98 × 10³ , the correct option is (a) .

In the question ,

it is given that

the number is 5.96 × 10⁴ ,

we have to find that how many  times greater is 5.96 × 10⁴ then 2.98 × 10³ .

to find that the number is how many times greater ,

we divide 5.96 × 10⁴ by 2.98 × 10³ .

So , on dividing the numbers we get

= ( 5.96 × 10⁴ ) / ( 2.98 × 10³ )

= 5.96/2.98 × 10⁴⁻³

= 2 × 10¹

= 20 times

Therefore , The number 5.96 × 10⁴ is 20 times greater than 2.98 × 10³ .

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Answer:

Raymond

Step-by-step explanation:

1 ) Eve and Patty swam fewer laps than Maureen so...

Eve and Patty < Maureen

2 ) Patty swam more laps than Eve...

Patty > Eve

3 ) Maureen swam fewer laps than Raymond...

Maureen < Raymond

4 ) We can eliminate Eve and Patty since they swam fewer laps than Maureen. The ones who are left are...

Maureen and Raymond

5 ) We know that Maureen swam fewer laps than Raymond so we can eliminate Maureen.

Raymond

6 ) This mean that the one who swam the most laps is...

Raymond

Hope this helps! :)

The length of the straw fitted in the box is 10.67 inches.

A cuboid is a solid three-dimensional object which has six faces that are rectangular with eight vertices, and twelve edges.

Given that, a straw is placed inside a rectangular box that is 5 inches by 5 inches by 8 inches, the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner,

Diagonal of a cuboid  = √ l² + w² + h²

Therefore, diagonal of the box = √ 5² + 5² + 8² = 10.67 in

Hence, The length of the straw fitted in the box is 10.67 inches.

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[tex]\framebox{w=$\dfrac{25}{3}$}[/tex]

Flip the equation:

[tex]\frac{6}{5} w=10[/tex]

Multiply both sides by [tex]\frac{5}{6}[/tex]:

[tex](\frac{5}{6} )\times(\frac{6}{5} w)=(\frac{5}{6} )\times(10)[/tex]

[tex]w=\frac{25}{3}[/tex]

The equation of the line is y = x -3. The graph of the line is attached below.

What is a line?

A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things. The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends.

Given that the slope of the line is 1.

Assume that the equation of the line is y = mx +c, where m is the slope of the line and c is y-intercepts.

Putting m = 1 in y = mx +c:

y = 1 × x +c

y = x +c

Since the line passes through the point (-2, -5), thus the point satisfies  the given equation of line.

Putting x = -2 and y = -5 in y = x +c

-5 = -2 + c

c = -3

The equation of line is y = x - 3.

The points on the line are

(-2, -5), (0, -3), (3, 0).

Plot the points and join them:

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The probability that exactly two of the four live in elderly care facilities is; 0.244

The binomial probability is defined as the probability of exactly x successes on n repeated trials, with p probability.

The general formula of binomial probability distribution is;

P(X = x) = nCx * p^(x) * (1 - p)^(n - x)

where;

Px = the probability of exactly x events occurring.

x = the number of expected successful outcomes.

p is probability of success

n is sample size

We are given;

p = 72% = 0.72

n = 4

Thus;

P(X = 2) = 4C2 * (0.72)^(2) * (1 - 0.72)^(4 - 2)

P(X = 2) = 0.244

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Number of camels are there at the safari park are 6 unit.

The animals at a safari park include camels, kangaroos and meerkats.

Let kangaroos are represented as K and Camels are represented as C and Meerkats are represented as M.

There are 12 more kangaroos than there are camels which means

K = C + 12.

There are 3 times as many meerkats as there are camels which means

M = 3C.

There are the same number of kangaroos as there are meerkats which means

K = M

If K = M

therefore,

3C = C + 12

2C = 12 ,

C = 6 unit.

So, K = 6 + 12 = 18

Or M = 18

Therefore  number of camels, kangaroos and meerkats at the safari park are 6 , 18 and 18 respectively.

Number of camels are there at the safari park are 6 unit.

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The size of angle QPR is 45° and the length of sides PQ and QR are both 27.20cm

An isosceles triangle is a triangle that has at least two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal angle,

since ∆PQR is a right angle isosceles triangle then, if angle Q is 90^°, QPR = PRQ=x( angles of an isosceles triangle).

Therefore 90+x+x= 180°

2x= 90

x= 45°

To find line PQ and QR, we use trigonometry ratio

cos 45°= adj/hyp

I/√2= QR/38.47

QR= 38.47/√2

= 27.20cm

QR= PQ= 27.20

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Answer:

x+5

Step-by-step explanation:

there are no like terms

The value of WV is 9x - 10

A line segment can be defined as the part of a straight line which is bound by two distinct end points, and is known to be made up of every point on the line that between its endpoints.

From the information given, we can say that WY is a line with V as its midpoint with segments WV and VY.

We have;

This is represented as;

WV + VY = WY

Then;

WV = WY - VY

substitute the values

WV = 5x + 19 - (29 - 4x)

expand the bracket

WV = 5x + 19 - 29 + 4x

collect like terms

WV = 9x - 10

Hence, the value is  9x - 10

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When the the light's angle is 20° from perpendicular to the wall, and the light is rotating at an angular speed of one rotation in 2 seconds the rate the light projected onto the wall is moving is approximately 60.48 feet/s

Angular speed, ω, is the angle, θ, in radians rotated by a rotating object per second. The unit of angular speed is radians per second, rad/s.

Mathematically;

[tex]\omega = \dfrac{\Delta \theta}{\Delta t}[/tex]

Where;

Δt = The time the object rotates through an angle of Δθ

The distance of the light from the wall, x = 17 feet

Time it takes the light to complete one rotation = 2 seconds

Angle the light makes with the perpendicular wall = 20°

[tex]tan(\theta) = \dfrac{y}{x}[/tex]

The distance the light has moved along the wall, y = x × tan(θ)

Therefore;

The y = 17 × tan(θ)

The angular velocity of the light, ω = θ/t

Therefore, θ = ω × t = ω·t

Which gives; y = 17 × tan(ω·t)

[tex]\omega = \dfrac{2\cdot \pi}{2}\ rad/s = \pi \ rad/s[/tex]

Therefore; x = 17 × tan(·t)

[tex]\dfrac{dy}{dt} = \dfrac{d}{dt} \left(17\times tan(\omega\cdot t)\right) = 17\cdot \omega\cdot sec^2(\omega \cdot t)[/tex]

ω = π rad/s (constant)

ω·t = θ

Therefore;

[tex]\dfrac{dy}{dt}= 17\cdot \omega\cdot sec^2(\theta)[/tex]

Rate the light is moving along the wall, dy/dt when θ = 20°, is therefore;

[tex]\dfrac{dy}{dt}= 17\times \pi\cdot sec^2(20^{\circ}) \approx 60.48[/tex]

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Step-by-step explanation:

=6a^3+7a^2-5a^3-9a^2-a

=a^3-2a^2-a this is the final answer.

if we take 25 to be the 100%, what is 100 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 25 & 100\\ 100& x \end{array} \implies \cfrac{25}{100}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{1}{4}=\cfrac{100}{x}\implies x=400[/tex]

Answer:

25

Step-by-step explanation:

25/100=.25x100=25

We got x = 16.54 by using Pythagorean theorem .

What is the Pythagorean theorem in plain English?

angle of semicircle is always be 90° .

   18² = 7.1² + x²

    324 = 50.41 + x²

     x² = 324 - 50.41

          = 273.59

    x = √ 273.59

    x = 16.54

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The time taken is obtained as 3 years.

We know that radioactivity has to do with the fact that a substances does disintegrate gradually over a period of time.

Let us recall the formula;

N/No = (1/2)^t/t1/2

N = The mass of radioactive atoms at time t

No = The mass of radioactive atoms initially present

t = time taken

t/12 = half life of the radioactive nucleus

Then;

32/50 = (1/2)^t/28

0.64 =  (1/2)^t/28

log 0.64 = t/28 log0.5

t/28 = log(0.64/0.5)

t = 28 * log(0.64/0.5)

t = 3 years

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In both triangle one angle is larger than 90 degree . so these triangles are obtuse triangles.

What is  Obtuse triangle?

Triangle B = Obtuse triangle

Triangle C = Obtuse triangle

in both triangle one angle is larger than 90 degree . so these triangles are obtuse triangles.

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Answer:

9.8 * 100 = 980

0.040 * 1000 = 40

61 / 10 = 6.1

8.909 * 100 = 890.9

Step-by-step explanation:

Answer: 10 rows of rose plants

Step-by-step explanation:

The number of rose plants in first, second third,..., and last row are respectively.

23,21,19,....,5.

number of rose plants: n

The sequence 23,21,19,....,5 is an A.P. with first term a(=23), common difference d(=−2) and n

=a+(n−1)d

⟹5=23+(n−1)×−2

⟹5=23−2n+2⟹20=2n⟹n=10

23.45 inches fabric was used on a headband and 9.64 inches fabric was used on a wristband for each player.

No. of players = 29

No. of coaches = 4

Total fabric used for headbands = 773.85 inches

Total no. of people for headbands = 29 + 4

                                                          = 33

Fabric used for headband for 1 person = 773.85/33

                                                                 = 23.45 inches

Total fabric used for wristbands = 279.56 inches

Total no. of people for wristbands = 29

Fabric used for headband for 1 person = 279.56/29

                                                                 = 9.64 inches

Hence, fabric for headband is 23.45 inches and for wristband is 9.64 inches.

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She drinks 1/12 gallons of milk each day

From the question, we have the following parameters that can be used in our computation:

Size of milk = 1/2 gallons

Number of days = 6 days

These parameters can be represented as

(x, y) = (6, 1/2)

The number of gallons a day she drinks can then be represented as the slope/unit rate and the unit rate is then calculated as

unit rate = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (0, 0) and (6, 1/2)

Substitute the known values in the above equation

So, we have the following equation

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

Evaluate the quotient

Slope = 1/12

Hence, the number of gallons she drinks a day is 1/12

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The image of point (2,0) after the transformation involving the dilation and the rotation is given as follows:

(0, -1).

The first transformation applied to the point is a dilation, which multiplies the coordinates of the point by the scale factor.

The point has these following coordinates:

(2,0).

The scale factor of the dilation is:

k = 1/2 = 0.5.

Then each coordinate of the point is multiplied by 0.5, hence:

Hence the coordinates are:

(1,0).

The rule for a rotation of 270º clockwise around the origin is:

(x,y) -> (y,-x).

Then:

Thus the coordinates of the image are given as follows:

(0, -1).

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Answer: The answer is A

Step-by-step explanation:

-5/8 is literally equal to -0.625 meaning this asnwer is equal not less

-0.5 is Greater than -0.625 because -0.6 is much larger

-8/5 is -1.6 which is Less than -0.625

The elevation at the lower end of a drain is 119.8 feet. For the second drain difference in feet will be 10.55 feet and in inches will be 126.6 inch.

The height above or below a fixed reference point, most frequently a reference geoid, which is a mathematical representation of the Earth's sea level as an equipotential gravitational surface, determines a location's elevation. A vertical surface is depicted in an elevation when viewed from a point perpendicular to the viewer's picture plane. You are looking at the front elevation, for instance, if you are standing directly in front of a building and viewing its front. The height between a point and a horizontal surface is known as HEIGHT. The height of a point above (or below) sea level is known as its ELEVATION.

Here,

a. The length of drain= 52 feet

the gradual decrease=0.125 ft

elevation at high end=126.30 feet

elevation at low end,

=126.3-(52*0.125)

=126.3-6.5

=119.8 feet

b. The elevation at one end=94.67 feet

The elevation at other end=84.12 feet

The difference in elevation,

=94.67-84.12

=10.55 feet

=10.55*12

=126.6 inches

The elevation of a drain's lower end is 119.8 feet. The second drain will differ by 10.55 feet in feet and 126.6 inches in inches.

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Answer:

I'm not sure if its right but I got

6/9

Step-by-step explanation:

What I did was:

I took the 2 points:

(-4,4) and (5,-2)

Then did rise over run

Which left me with 6/9

Considering the angle of elevations, the distance from point AA to point BB which is the height of the antenna is 5.34 meters

information given in the question

Mia stands at a horizontal distance of 15 meters from the building

The angle of elevation from her eyes to the roof ((point AA)) is 18

the angle of elevation from her eyes to the top of the antenna ((point BB)) is 53^

her eyes are 1.75 meters from the ground

The direction of movements describes a right angle triangle of

opposite = height of antenna + height of the building

adjacent = 15 meters

The  distance from point AA to point BB and the height of the antenna is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The  the height of the antenna is calculated using tan, TOA let the angle be x

tan x = Opposite / Adjacent

using 53 gives the height of the antenna + height of the building, while using 18 gives height of the building only

tan 53  = opposite / 15

opposite = 15 * tan 53 = 19.906 meters

opposite = 15 * tan 18 = 14.266 meters

Height of the antenna

= 19.606 - 14.266

= 5.34 meters

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Using the geometric mean theorem,

[tex]\frac{y}{14.4}=\frac{14.4}{19.2} \\ \\ y=10.8[/tex]

Using Pythagoras on triangle [tex]ABD[/tex],

[tex]x=\sqrt{14.4^2+10.8^2}=18[/tex]

Triangles [tex]ABD[/tex] and [ted]CBD[/tex] are similar because corresponding angles are congruent and pairs of corresponding sides have proportional lengths.

To determine this, use the complementary angles.