Mathematics College

I don't understand if this equation is a linear equation or not. Can you please help me?

Answers

Answer 1

we have the equation

[tex]\frac{x}{4}-\frac{y}{3}=1[/tex]

To remove the fractions, multiply both sides by (4*3=12)

[tex]\begin{gathered} \frac{12x}{4}-\frac{12y}{3}=12 \\ 3x-4y=12 \\ 4y=3x-12 \\ y=\frac{3}{4}x-3 \end{gathered}[/tex]

this is the equation of a line

that means

is a linear equation

Related Questions

Jason pays a $100 installation fee and a $40 monthly service charge for his telephone . Which equation shows the amount that Jason pays for x months of telephone service ? A. y= 40 + 100x B. y = 100 + 40xC . y = 100 - 40x

Answers

Given

x: months of telephone service

$100 installation fee (one time)

$40 monthly fee

Equation

[tex]y=100+40x[/tex]

Where 100 is the initial cost and 40 is the monthly cost

Given:• VU is tangent to Circle Q• UV = 20• UT = 8U2000TSFind the length of the radius of the circle.6O 1202142

Answers

To solve this question and find the radius of the circle, we will use the s

I need help please I can’t figure this out and it’s my last question

Answers

QUAD magnified 4 times gives Q'U'A'D'

D(7,0)

Q(0,0)

Then center of rectangle is at (D -Q)/2= 3.5

Area of rectangle QUAD= (7-0)•(5-0) = 35

4times area QUAD = 4x35= 140

Then

Q'= (0,0)

Q'U'= 4xQU = 4x5 = 20

The circumference of a big circle is 36 pi. The area of a smaller circle located inside the bigger circle is 16 pi. If you randomly pick a point inside the big circle, what is the probability the point lands in the smaller one?

Answers

Given:

a.) The circumference of a big circle is 36 pi.

b.) The area of a smaller circle located inside the bigger circle is 16 pi.

The probability that the point lands in the smaller one is,

[tex]\text{ Probability = }\frac{Area_{Small\text{ Circle}}}{Area_{Big\text{ Circle}}}[/tex]

However, only the circumference of the big circle is given. To be able to get the probability, we must first determine the area of the circle.

a.) Area of the big circle.

[tex]\begin{gathered} \text{ Circumference = }2\pi r \\ 36\pi\text{ = 2}\pi r \\ \frac{36\pi}{2\pi}\text{ = r} \\ 18\text{ = r} \end{gathered}[/tex][tex]\begin{gathered} \text{ Area = }\pi r^2 \\ \end{gathered}[/tex][tex]\begin{gathered} \text{ = }\pi(18)^2 \\ \text{ = }\pi(324) \\ \text{ Area = 324}\pi \end{gathered}[/tex]

b.) Let's now determine the probability.

[tex]\text{ Probability = }\frac{Area_{Small\text{ Circle}}}{Area_{Big\text{ Circle}}}[/tex][tex]\text{ = }\frac{16\pi}{324\pi}[/tex][tex]\text{ = }\frac{16}{324}\text{ = }\frac{\frac{16}{4}}{\frac{324}{4}}\text{ = }\frac{4}{81}[/tex][tex]\text{ Probability = }\frac{4}{81}[/tex]

Therefore, the probability that the point lands in the smaller one is 4/81.

PLEASE HELP. FUNCTIONS AND RELATIONS. The height of a model rocket, h(t), is a function of the time since it was launched, t. What is the domain of h(t)?

Answers

Recall that the domain is all the values of the graph from left to right.

From the given graph we get that its domain consists of all values greater than or equal to 0 and less than or equal to 42.

Then the domain of the given function in algebraic notation is:

[tex]0\leq t\leq42.[/tex]

Answer: Option D.

Cecil wrote the fraction 6/4. Susie wants to write anequivalent fraction. Whichof the following could be herfraction? A. 2/3 B. 6/9 C. 8/12 D. All of the above.

Answers

ANSWER

8/12. Option C

EXPLANATION

In a simple term: Equivalent fraction can be determined by simply multiplying the numerator and the denominator by the SAME NUMBER.

That is,

if you have 2/3 the equivalent fraction will be 4/6 (when multiplied by 2) or 6/9 (when multiplied by 3) or 8/12 (when multiplied by 4) etc.

So, from the question above:

The equivalent fraction of 4/6 (when multiplied by 2) is 8/12

A local grocer cut his marketing budget by 54% last year. He spent only $650 on marketing this year and is happy with his decision. How much did the grocer spend on marketing last year? Round your answer to the nearest cent. Do not include units with your answer.

Answers

Given that the grocer spent only $650 on marketing this year, you know that this is 54% of his marketing budget last year.

You can rewrite a percent as a Decimal Number by dividing it by 100:

[tex]\frac{54}{100}=0.54[/tex]

Let be "x" the amount of money (in dollars) the grocer spent on marketing last year.

Knowing all the data, you can set up the following equation:

[tex]x-0.54x=650[/tex]

When you solve for "x", you get:

[tex]0.46x=650[/tex][tex]\begin{gathered} x=\frac{650}{0.46} \\ \\ x\approx1413.04 \end{gathered}[/tex]

Hence, the answer is: He spent $1,413.04 .

what is the surface area for a m rectangular prism. with the measurements as: height = 9 length = 3width = 7

Answers

Answer:

Surface area = 222 square cm

Explanation:

Given the following data

Length = 3 cm

Height = 9 cm

Width = 7 cm

Surface area = 2(wl + hl + hw)

Surface area = 2(7 * 3 + 9 * 3 + 9 * 7)

Surface area = 2( 21 + 27 + 63)

Surface area = 2( 111)

Surface area = 222 square cm

Therefore, the surface area is 222 square cm

disconnect me pls c bc

Answers

tutor loses connection for 30+

-3|2x+1|<4 how is this solved

Answers

Answer:

True for all x

Step-by-step explanation:

Multiply by -1. This reverses the inequality.

[tex]-3\left|2x+1\right| < 4\\\left(-3\left|2x+1\right|\right)\left(-1\right) > 4\left(-1\right)[/tex]

Remember: Negative * Positive = NegativeRemember: Negative * Negative = Positive

[tex]3\left|2x+1\right| > -4:\:Solve\\4\times -1 = -4\\\left(-3|2x+1|\right)\left(-1\right)\\\left(-3\times -1\right)\\\left(-3|2x+1|)[/tex]

Divide by 3

[tex]=\frac{3\left|2x+1\right|}{3} > \frac{-4}{3}[/tex]

___________

[tex]\frac{3\left|2x+1\right|}{3}\\\frac{3}{3}\\= \frac{1}{1}[/tex]

___________

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

___________

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

Because absolute values are greater than or equal to 0, the problem will be classified as "True" for any value of x no matter what.

Hope this helps.

Find the volume of a cone with a slant height of 15 inches and a radius of 9 inches. Leave your answers in terms of π

Answers

Given:

height(h)=15 inches

radius(r)=9 inches

Volume of cone:

[tex]V=\pi\times r^2\times\frac{h}{3}[/tex][tex]V=\pi\times9^2\times\frac{15}{3}=\pi\times81\times5[/tex][tex]V=\pi\times405[/tex][tex]V=405\pi\text{ cubic inches}[/tex]

at a baseball game a vender sold combined total of 103 sodas and hotdogs . The numbers of sodas was sold was 57 more than the number of hot dogs sold . Find the number sodas sold and the number of hot dog sold

Answers

Answer:

Number of sodas sold = 80

Number of hot dogs sold = 23

Explanation:

Let th number of sodas be xs

Let the number of hot dogs be h

The vendor sold a combined total of 103 sodas and hot dogs

s + h = 103............(1)

The nmber of soda sold was 57 more tha n the number of hot dogs sold

s = h + 57........()

Subtitute equation (2) into equation (1)

h + 57 + h = 103

2h = 103 - 57

2h = 46

h = 46/2

h = 23

Substitute h = 23 into equation (2)

s = 23 + 57

s = 80

Number of sodas sold = 80

Number of hot dogs sold = 23

Simplify 5(3p - 2) + 2(p +4)

Answers

[tex]5\mleft(3p-2\mright)+2\mleft(p+4\mright)\text{ = 17p-2}[/tex]

Here, we want to simplify the expression

To do this, we shall use the term outside the bracket to multiply the terms inside the brackets before we proceed to add them together

We have this as follows;

[tex]\begin{gathered} (5\times3p)-(5\times2)\text{ + (2}\times p_{})\text{ + (2}\times4) \\ =\text{ 15p - 10 + 2p + 8} \\ =\text{ 15p}+2p-10+8 \\ =\text{ 17p -2} \end{gathered}[/tex]

Simplify 5(3p-2) +2(p+4)
15p - 10 +2p+8
17p-2

11) Tell whether (3, 20) is a solution of y = 4x +8 A) Yes B) No

Answers

y = 4x + 8

To tell if (3, 20) is a solution, we will substitute the value of x = 3 and y= 20

into the equation to see if the left-hand side equals the right-hand side of the equation

So, upon substituting

20 = 4 x 3 + 8

20 = 12 + 8

20 = 20

Since the left-hand side of the equa

I need help with math

Answers

We have the following problem:

Using the kinematic equation, we know that for movements with constant acceleration the position is

[tex]h(t)=h_0+v_0t-\frac{gt^2}{2}[/tex]

I already wrote the variables convenient for our problem, where

t = time (s)

h₀= initial height (m)

v₀ = initial velocity (m/s)

g = gravity acceleration (m/s²)

h = height after t seconds

We also know that

t = independent variable

h₀= 10m

v₀ = 56 m/s

g ≅ 10 m/s²

h = dependent variable

Therefore our quadratic will be

[tex]\begin{gathered} h(t)=10+56t-\frac{10t^2}{2} \\ \\ h(t)=10+56t-5t^2 \end{gathered}[/tex]

Now we can answer the question in fact.

The rocket will hit the ground when the height is equal to zero, hence, h(t) = 0. In fact, we are looking for the zeros of the quadratic

[tex]\begin{gathered} 10+56t-5t^2=0 \\ \\ t=\frac{-56\pm\sqrt{56^2-4\cdot(-5)\cdot(10)}}{2\cdot(-5)} \\ \\ t=\frac{-56\pm\sqrt{3136+200}}{-10} \\ \\ t=\frac{56\pm\sqrt{3336}}{10} \\ \\ t=11.38\text{ s or }-0.18\text{ s} \end{gathered}[/tex]

See that we have one negative zero, but we will ignore that because it's physically impossible, therefore the rocker will reach the ground after 11.38 seconds

To find the maximum height we must find the max value of the quadratic, we know that the vertex of a quadratic is its max/min, also, we can write it as

[tex]\begin{gathered} y_V=-\frac{\Delta}{4a} \\ \\ x_V=-\frac{b}{2a} \end{gathered}[/tex]

Where

[tex](x_V,y_V)[/tex]

Is the vertex. Here, we want to find the y coordinate, because y here is the height, therefore

[tex]\begin{gathered} \max h=-\frac{\Delta}{4a} \\ \\ \operatorname{\max}h=-\frac{3336}{4\cdot(-5)} \\ \\ \operatorname{\max}h=\frac{3336}{20} \\ \\ \operatorname{\max}h=166.8\text{ m} \end{gathered}[/tex]

The max height of the rocket is 166.8m

Now we have a similar problem, it's also the vertex but now the coordinate x, that here, represents the time, then

[tex]\begin{gathered} t_{\max}=\frac{-b}{2a} \\ \\ t_{\operatorname{\max}}=\frac{-56}{2\cdot(-5)} \\ \\ t_{\operatorname{\max}}=\frac{56}{10} \\ \\ t_{\operatorname{\max}}=5.6\text{ s} \end{gathered}[/tex]

The rocket will reach the maximum height after 5.6 seconds.

Please help me on the question I don’t get it c) For architects, by what percent did the median earnings increase for those who held a graduate degree compared to those who were recent college graduates? (round to the nearest integer)d) For nurses, by what percent did the median earnings increase for those who held a graduate degree compared to those who were recent college graduates? (round to the nearest integer)

Answers

(a) From the graph, the average recent college graduate engineer makes $65000, and the average recent college graduate accountant makes $40000. Therefore, an engineer makes $65000 - $40000 = $25000 more than the accountant.

(b) In marketing, the average graduate degree holder makes approximately $80000 (rounded down to the nearest thousand), and the average recent college graduate makes approximately $35000 (rounded down to the nearest thousand). Therefore, the average graduate degree holder makes $80000 - $35000 = $45000 more than the average recent college graduate

(c) graduate degree holder architect average earning: $75000 (rounded down to the nearest thousand)

average recent college graduate architect average earning: $35000 (rounded down to the nearest thousand)

The percent increase is computed as follows:

[tex]\begin{gathered} \text{percent increase = }\frac{\text{ degr}ee\text{ holder - college graduate}}{\text{college graduate}}\cdot100 \\ \text{percent increase = }\frac{75000-35000}{35000}\cdot100 \\ \text{percent increase }\approx114\text{ \%} \end{gathered}[/tex]

(d) graduate degree holder nurse average earning: $ 80000 (rounded down to the nearest thousand)

average recent college graduate nurse average earning: $45000 (rounded down to the nearest thousand)

The percent increase is computed as follows:

[tex]\begin{gathered} \text{percent increase = }\frac{\text{ degr}ee\text{ holder - college graduate}}{\text{college graduate}}\cdot100 \\ \text{percent increase = }\frac{80000-45000}{45000}\cdot100 \\ \text{percent increase = 78 \%} \end{gathered}[/tex]

(e) Comparison between average earning of a degree holder and of a college graduate for each area:

Engineers