In order to slove the following system of equations by addition, which of the following could you do before adding the equations so that one variable will be eliminated when you add them?
4x-2y=7
3x-3y=15


​

Answer:

[tex]\huge\boxed{\sf x = 6 \ \ \ OR \ \ \ x = -1/6}[/tex]

Step-by-step explanation:

Let the number be x

[tex]\displaystyle x - \frac{1}{x} =\frac{35}{6} \\\\Subtract \frac{35}{6} \ to \ both \ sides\\\\x - \frac{1}{x} -\frac{35}{6} = 0\\\\Multiply \ 6x \ to \ both \ sides\\\\x \times 6x - \frac{1}{x} \times 6x -\frac{35}{6} \times 6x = 0 \times 6x\\\\6x^2-6-35x=0\\\\6x^2-35x - 6 = 0[/tex]

Applying mid term break formula

[tex]6x^2-36x+x-6=0\\\\Take \ common\\\\6x(x-6)+1(x-6)=0\\\\Take \ (x-6) \ common\\\\(x-6)(6x+1)=0[/tex]

Either:

x - 6 = 0     OR    6x + 1 = 0

x = 6          OR      6x = -1

x = 6          OR       x = -1/6

1) You can find the number of possible methods through a tree diagram or the fundamental counting principles.

2) The total number of combinations is 360

To find the total number of combinations,

A Tree Diagram is a the various possibilities in a pictorial way. The diagram begins with a single point, which represents the initial decision, then branches out to indicate all possible outcomes for each successive option.

The Fundamental Counting Principle tells us that if there are 'n' ways doing a thing and 'm' ways to do another, there are n x m ways to do both. Which means that the total number of outcomes equals the product of the number of ways each job can completd.

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Option A graph represents  S(x).

Function is a statement that relates tow variables.

It is given that

the side length of the larger frame S(x)

S(x) =  [tex]\rm 3 \sqrt{x -1}[/tex]

X is the area of the smaller frame in square inches

A square root function is given by

s(x) = [tex]\rm \sqrt{x}[/tex]

when the graph is shifted towards right and stretched by  3 , due to which the graph is taller as compared to the parent graph and

Therefore Option A graph represents  S(x).

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Answer:

17.32

Step-by-step explanation:

since there is a 5 in the thousandths, we round the 1 in the hundredths up and get 17.32

The values of k (i.e. +3 and -2) in functions b and c change the rational graph by (b) shifts right/left

The functions are given as:

[tex]y = \sqrt x[/tex]

[tex]y = \sqrt {x + 3[/tex]

[tex]y = \sqrt {x - 2[/tex]

See attachment for the graphs of the three functions.

From the attached graph, we can see that [tex]y = \sqrt {x + 3[/tex] and [tex]y = \sqrt {x - 2[/tex] are at the left and right of the function [tex]y = \sqrt x[/tex]

Hence, the values of k in functions b and c change the rational graph by shifting it right/left

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The slope-intercept form is y=mx+b

m=slope=-5

y-int/b = 300

so, y = -5x+300 is the equation of the line

Step-by-step explanation:

formula to get the volume of a cylindrical shape =πr²h

π=3.14 , r=diameter /2=19/2= 9.5, h= 40

: πr²h= 3.14 ×9.5²×40

3.14×90.25×40

=11,335.4

=11,335

Explanation:

Dalvin drives 190 miles in 5 hours. His speed is 190/5 = 38 mph.

From here we would say the following

distance = rate*time

distance = (38 mph)*(8 hrs)

distance = 304 miles

Answer:

32+q=x

Step-by-step explanation:

32(jakes) + q (molly) = x(total)

Answer:

32+Q= total number of quarters.

Step-by-step explanation:

Answer:

3:04

Step-by-step explanation:

see image

They will meet after 4 minutes from 3:00 p.m. So, they will meet at 3:04 p.m.

Let's find the time it takes for Tommy and his Dad to meet.

Let t be the time (in seconds) from 3:00 p.m. when they meet.

Tommy's distance covered (T) after t seconds is given by:

T = Tommy's speed * t

   = 1.35 m/s * t

His Dad's distance covered (D) after t seconds is given by:

D = Dad's speed * t

  = 1.65 m/s * t

Since they meet when the sum of their distances is equal to the total distance between home and school, we can write the equation:

T + D = 720 meters

Substitute the expressions for T and D:

1.35t + 1.65t = 720

t = 240 seconds

Since 1 minute is equal to 60 seconds, let's convert the time to minutes:

t = 240 seconds / 60 seconds/minute

t = 4 minutes

They will meet after 4 minutes from 3:00 p.m. So, they will meet at 3:00 p.m. + 4 minutes = 3:04 p.m.

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The slope m = -6 and y-intercept = ( 0, 5 ).

The graph is a dash line, shaded area above the boundary line since y is greater than -6x + 5.

Given that;

y > -6x + 5

We use the slope intercept form y = mx + b to determine the slope (m) and the y-intercept (b).

y > -6x + 5

y = mx + b

We can see that;

m = -6 and b = 5

Hence, slope = -6 and y-intercept = ( 0, 5 ).

The graph is a dash line, shaded area above the boundary line since y is greater than -6x + 5.

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Slope formula: [tex]\frac{y1-y2}{x1-x2}[/tex]

To find the slope:

[tex]\frac{1-0}{0-(-7)} =\frac{1}{7}[/tex]

Hope it helps!

Answer:

Step-by-step explanation:

Good morning/evening!

The table we have is,

[tex]\Large\boxed{\begin{tabular}{c | 1} x & y \\ \cline {1-2} -7 & 0 \\ 0 & 1 \end{tabular}}}[/tex]

This is enough information. Using this we CAN find the slope of the line.

We will utilise the formula,

[tex]\Large\boldsymbol{\sf{m=\dfrac{\triangle y}{\triangle x}}}[/tex]

The change in y is 1, and the change in x is 7.

∵, the slope is [tex]\boxed{\rm{1/7}}[/tex]

done !!

[tex]\orange\hspace{300pt}\above3[/tex]

Answer:

6 projects

Step-by-step explanation:

Original ribbon length = 24 yards

After 10 yards given to sister, Mia is left with 24-10 = 14 yards of ribbon

Each project requires 2 1/4 yards of ribbon.

2 1/4 is 9/4 yards as an improper fraction (2 * 4 + 1 is the numerator and the denominator is unchanged)

We now have to figure out how many times 9/4 yards goes into 14 yards.

For this,

14 ÷ 9/4.
To do this, flip the numerator and denominator of the fraction and multiply

14 ÷ 9/4 = 14 × 4/9 = 56/9 . We ignore any remainder.

9 goes into 56 6 times with remainder of 2 (ignore remainder)
In other words the greatest number of projects = 6

The probability that a randomly selected PC costs more than 1200 will be 0.006. The least expensive 10% of personal computers cost less than what amount will be 820.8.

The Gaussian distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The z-score is given as

z = (x – μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

The average price of a personal computer (PC) is $949.

If the computer prices are approximately normally distributed and standard deviation is $100.

Then the probability that a randomly selected PC costs more than 1200 will be

z = (1200 – 949) / 100

z = 2.51

Then  the probability will be

P(x > 1200) = P(z > 1200)

P(x > 1200) = 1 – P(z < 1200)

P(x > 1200) = 1 – 0.99396

P(x > 1200) = 0.0060366

The least expensive 10% of personal computers cost less than what amount will be

z-value for 10% will be -1.282.

– 1.282 = (x – 949) / 100

– 128.2 = x – 949

          x = 820.8

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Hello!

The weight is 4,338 pounds and 2.169 tons.

Answer: 2 tons and 338 pounds

Step-by-step explanation:

1 ton is 2000 pounds

4338 has 2 tons and 338 pounds

Answer:

[tex] \frac{35}{33} [/tex]

Step-by-step explanation:

[tex] \frac{8}{11} - ( - \frac{1}{3} ) \\ = \frac{8}{11} + \frac{1}{3} \\ = \frac{8 \times 3}{11 \times 3} + \frac{1 \times 11}{3 \times 11} \\ = \frac{24}{33} + \frac{11}{33} \\ = \frac{35}{33} [/tex]

Things to note :

Subtracting a negative value will be equals to adding.

To add/subtract 2 fractions together, the denominator must be the same.

The solution to the system of inequalities given is: [tex]\frac{4}{3} \leq y \leq 4[/tex]

The solution is the set of values that respect all conditions of the system.

The first condition is:

[tex]3y - 13 \geq -9[/tex]

[tex]3y \geq 4[/tex]

[tex]y \geq \frac{4}{3}[/tex]

The second condition is:

[tex]3y - 13 \leq -1[/tex]

[tex]3y \leq 12[/tex]

[tex]y \leq \frac{12}{3}[/tex]

[tex]y \leq 4[/tex]

The intersection of the conditions, which is the solution to the inequality, is:

[tex]\frac{4}{3} \leq y \leq 4[/tex]

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The whale exists swimming at 30 mph in calm water and the current exists flowing at 10 mph.

Let x be the speed of a whale in calm water

and y be the speed of the current

In 7 hours the whale swims against the current and travels 140 miles:

7(x - y) = 140

x - y = 140/7

x - y = 20 ...........(1)

In 3.5 hours the whale swims the same distance with the current:

3.5(x + y) = 140

x + y = 140/3.5

x + y = 40 ...........(2)

Adding (1) and (2), we get the value of x:

x - y = 20  + ...........(1)

x + y = 40 ...........(2)

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

2x = 60

x = 60/2

x = 30

Using this value for "x" in either (1) or (2) we can solve for "y":

x - y = 20 ...........(1)

substitute for "x"

30 - y = 20

10 = y

Therefore, the whale exists swimming at 30 mph in calm water and the current exists flowing at 10 mph.

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Answer:

the value of x will be

x= (10x15)/25=6

A function assigns the values. For every increase of 1 ounce in frozen yogurt the cost will increase by $49.

A function assigns the value of each element of one set to the other specific element of another set.

Given the frozen yogurt store charges C dollars for w ounces of frozen yogurt, C can be modelled by C = 49w+80/100. Therefore, for every increase of 1 ounce in frozen yogurt the cost will increase by $49.

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The number line first represents the solution to the inequality x/-1 > -6 option first is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

The complete question is:

Which of the following number lines represents the solution set of x/-1 > -6?

For the number lines shown in the attached picture, please refer to the picture.

We have an inequality:

x/-1 > -6

x < 6  

x ∈ (-∞, 6)

Thus, the number line first represents the solution to the inequality x/-1 > -6 option first is correct.

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Since for each trial there are more than two outcomes, the random variable x is not a binomial variable.

Three things are required:

In this problem, for each trial, there are six possible outcomes for the sum, hence the random variable x is not a binomial variable.

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Answer:

a) 9×2=18

b)16×2=32

c)14×9=126

d)20×10=200

e)10×3=30

The linear inequality depicted by the graph is: [tex]y \leq \frac{2}{3}x + \frac{1}{5}[/tex]

A linear function is modeled by:

y = mx + b

In which:

For this line, when x = 0, y = 0.2, hence the y-intercept is of b = 0.2. When x = 3, y = 2.2, hence the slope is given as follows:

[tex]m = \frac{2.2 - 0.2}{3 - 0} = \frac{2}{3}[/tex]

Hence the equation of the line is:

[tex]y = \frac{2}{3}x + 0.2[/tex]

[tex]y = \frac{2}{3}x + \frac{1}{5}[/tex]

The inequality is the values below(less) than the line, also including it, as it is not dashed, hence:

[tex]y \leq \frac{2}{3}x + \frac{1}{5}[/tex]

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The two triangles are similar by the AA Similarity theorem.

The height of the tree can be calculated by figuring out the ratio between the distance between the mirror to her feet and the distance from the mirror to the tree

From Law of Reflection, we know that the angle of incidence and the angle of reflection are equal to each other.

Now, triangles can be proved similar by the AA, SAS, or SSS theorems. However, in this question, the triangles as seen in the attached image can be proved similar by the AA similarity theorem.

This is because both triangles have one congruent angle in common.

Sarah and the tree are standing straight and perpendicular to the ground and as such, the angles formed by Sarah and the tree are right angles.

The above tells us that the two triangles have two angles in common, making them similar triangles by the AA (Angle Angle) similarity theorem.

Since the triangles are similar, it means that the ratios of the sides of the triangles will be the same. Thus,  if Sarah knows the distance from the mirror to her feet and the distance from the mirror to the tree, she can create the ratio between the two triangles.

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The percentage discount allowed by the wholesaler is 1%

25 naira = 25 × 100

= 2500 Kobo

Percentage discount allowed = 25 / 2500 × 100

= 0.01 × 100

= 1%

Therefore, the percentage discount allowed is 1%

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Answer:

y = x/3

Step-by-step explanation:

y = 3x

x = 3y

3y = x

y = x/3

⊱_____________________________________________________⊱

Answer:

Step-by-step explanation:

[tex]\large\displaystyle\begin{gathered} \rm{To \ find \ the \ inverse, \ switch \ the \ places \ of \ x \ and \ y} \\ \sf{ y=3x} \\ \sf{x=3y} \\ \rm{Now \ solve \ for y} \\ \sf{x/3=y} \\ \sf{\dfrac{x}{3}=y \end{gathered}[/tex]

done !!

⊰______________________________________________________⊱

The distance traveled by the driver during her reaction time based on her speed was 44 feet.

find the speed in feet per second to be:

= (40 x 5,280 feet per hour) / Number of seconds in an hour

= 211,200 / 3,600

= 58.67 feet per second

With a reaction speed of 3/4 seconds, the distance traveled is:

= 58.67 x 3/4

= 44 feet

Full question is:

The driver of a car traveling at a speed of 40 miles per hour had to stop the car quickly. Using the driver's speed in feet per second, how far did her car travel during her reaction time of 3/4 of a second?Round your answer to two decimal places

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Answer:

1860 yards

Step-by-step explanation: