Mathematics High School

How many solutions are there to the following system of equations? Use any method you like, but be sure to show all work.
4x – 14y = 6
–2x + 7y = –3

Please please help! I'm really bad at this! Please show your work so I can understand

Answers

Answer 1
Normally you would expect one solution for x and y, but in this special case, there are an infinite number of solutions because both equations are the same. If you multiply the bottom one with -2, you get:

-2*-2x + -2*7y = -2*-3 simplifies to
4x - 14y = 6, which is the top equation!

If you have one equation with two variables, it is typically not solvable with one set of solutions. x=5 and y=1 is a solution, but so is x=12 and y=3. Those are just two examples.

Related Questions

A line passes through (2, −1) and (4, 5).

Which answer is the equation of the line?

−3x+5y=−13
−3x+y=−7
−3x+y=17
−3x+5y=13

Answers

The answer to the first problem is the top left corner because it is the only one with a -3 y-intercept and that's in the problem

To find the answer of the second problem you find the slope of the two points with the formula y2-y1 divided by x2-x1 and you just plug it in so 5+1 (the minus signs cancel out and turn into positives) divided by 4-2 and which is 6/2 which is 3 is your slope. then you could plug this information into a point slope form using either point I'm just going to choose the one with no negatives so plugging this in would be y-5=3(x-4) then you distribute the 3 and that gives you y-5=3x-12 then
                               +5       +5 add five to both sides of the equation and get
                             y=3x-7 and then you can put that into standard form which would be -3x+y=-7 and your answer would be the second one.

The points ( - 6, - 2) and ( - 4,6) fall on a particular line. what is its equation in point-slope form?

Answers

The points ( - 6, - 2) and ( - 4,6) fall on a particular line. what is its equation in point-slope form?

determine the equation of the graph and select the correct answer below

Answers

The answer you chose is indeed correct!
Vertex form of a quadratic is y = a(x - h)^2 + k.
( h , k ) is the vertex and in the problem the very is ( 1, -3) so plug that in and:
y = (x - 1 )^2 + (-3) this is equal to:
y = (x -1)^ 2 - 3

hope this helps c:

Answer:

slef

Step-by-step explanation:

The image shows a geometric representation of the function f(x) = x2 – 2x – 6 written in standard form.



What is this function written in vertex form?

A) f(x) = (x –1)2 – 7
B) f(x) = (x +1)2 – 7
C) f(x) = (x –1)2 – 5
D) f(x) = (x +1)2 – 5

It has to be A, B, C, Or D someone has asked this question before but whoever answered it just copied and pasted the question that was asked as the answer so please help the answer has to be one of the above.

Answers

The vertex form of the equation of a parabole is (x - h)^2 + k

So you must complete squares to transform x^2 -2x - 6 in its vertex form.


1) convert x^2 - 2x in a square => (x - 1)^2 - 1

2) Add the constant term - 6 => (x - 1)^2 -1 - 6

3) Add similar terms => (x - 1)^2 - 7

You can verify that (x - 1)^2 - 7 is equal to x^2 - 2x - 6:

x^2 - 2x + 1 - 7 = x^2 - 2x - 6. So, do not doubt it, the vertex form is (x - 1)^2  - 7, where the coordinates of the vertex are (1, - 7)

Answer: option A (x - 1)^2 - 7

What is the scope of government?

Answers

The extent of the area or subject matter that the government deals with or to which it is relevant.

Polly brennan earns $8.32 per hour for playing fuitar at kaldi's coffee shop. she works 12.5 hours a week. what is the musician's stright- time pay?

Answers

8.32 x 12.5= $104
I hope this was helpful
12.5 x $8.32 = $104.00

What is the answer to in a science class the girl to boy ratio is 3 to 7 out of 50 student how many are boys?

Answers

If the ratio of girls to boys is 3:7,
then: 3/10 of the class are girls and 7/10 of the class is boys
Note: 3+7 = 10

If the class has a total of 50 students we can find the number of boys by doing this:

 (total number of kids) x (fraction of the kids that are boys) = # of boys

50 x (7/10) = 35

There are 35 boys in the class.


Armando likes to watch sports on television. He recorded the following statistics about four games he watched. (Note: The times below include television commercials and commentary.) SportTime WatchedAmount of Game Watched basketball1 hr 27 min1 of 2 halves football48 min1 of 4 quarters soccer50 min1 of 2 halves baseball1 hr 24 min4 of 9 innings Order the sports by their unit rates in hours per game from least to greatest.

Answers

For basketball, the unit rate is given by:

[tex] \frac{1\, hr\ 27\, mins}{1\, of\, 2\, halfs} = \frac{1.45}{0.5} =2.9\, hours\, per\, game[/tex]

For football, the unit rate is given by:

[tex] \frac{48\, mins}{1\, of\, 4\, quarters} = \frac{0.8}{0.25} =3.2\, hours\, per\, game[/tex]

For soccer, the unit rate is given by:

[tex] \frac{50\, mins}{1\, of\, 2\, halfs} = \frac{0.8333}{0.5} =1.67\, hours\, per\, game[/tex]

For baseball, the unit rate is given by:

[tex] \frac{1\, hr\ 24\, mins}{4\, of\, 9\, innings} = \frac{1.4}{0.4444} =3.15\, hours\, per\, game[/tex]

Therefore, the order of the unit rates from the least to the greatest is given by:

Soccer ---> Basketball ---> Baseball ---> Football

The equation y=0.25x+50 models the cost y of renting a car if the car is driven x miles according to the model what is the best estimate of the cost for renting a car if you plan to drive 250 miles

Answers

y = 0.25x + 50....where x is the miles driven

for 250 miles...so we sub in 250 for x

y = 0.25(250) + 50
y = 62.5 + 50
y = 112.50 <== total cost

Answer: $112.5

Step-by-step explanation:

Given : The equation [tex]y=0.25x+50[/tex] models the cost y of renting a car if the car is driven x miles according to the model .

To find the cost for renting a car if you plan to drive 250 miles, we substitute x= 250 in the given equation , we get

[tex]y=0.25(250)+50\\\\\Rightarrow\ y=62.5+50\\\\\Rightarrow\ y=112.5[/tex]

Hence, the cost for renting a car if you plan to drive 250 miles = $112.5

Thus , the best estimate of the cost for renting a car if you plan to drive 250 miles = $112.5

I have a math problem

Answers

for the first one
#1 add 6 to both sides
#2 divide by 4
#3 answer is........12
#1 is 12
#2 is $12
#3 is 1.2

A truck is moving at a rate of 105 kilometers per hour and the diameter of its wheels is 1 meter find the angular speed of the wheels in radians per minute

Answers

Final answer:

The angular speed of the truck's wheels is 3500 radians per minute, calculated by dividing the linear speed in meters per minute by the wheel's radius in meters.

Explanation:

To calculate the angular speed of the truck's wheels in radians per minute, we first need to understand the relationship between linear speed and angular speed. Angular speed (
adians) is given by the formula
adians = linear speed (v) divided by the radius of the wheel (r).

First, we convert the truck's speed from kilometers per hour to meters per minute:
105 km/hr = (105 * 1000 meters) / (60 minutes) = 1750 meters/minute.

Since the diameter of the wheel is 1 meter, the radius (r) is half of that, which is 0.5 meters.

Now we can calculate the angular speed:
adians = v / r = 1750 m/min / 0.5 m which gives us 3500 rad/min.

Therefore, the angular speed of the wheels is 3500 radians per minute.

Where does the function f have a zero? (more than one can apply)

Answers

Answers: 
Choice A(-2,-1)
Choice B(-1,0)
Choice E(2,3)

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

Explanation:

The idea is to look for sign changes in f(x). Recall that y = f(x). If the sign of y changes, then y = 0 must be somewhere in the interval if we are to have a continuous function.

The sign changes happen when we go from...
y = -9 to y = +8 (row 2 to row 3)
y = +8 to y = -5 (row 3 to row 4)
y = -1 to y = +196 (bottom two rows)

Those three sign changes correspond to the following interval notations for x
(-2,-1)
(0,1)
(2,3)
in that exact order

Meaning for instance, that a root must be somewhere in the interval -2 < x < -1 since we have a sign change when we transition from f(-2) to f(-1)

So that's why the answers are choices A, B, & E

Something like the interval notation (1,2) will not work because y = -18 does not change sign to y = -1, which is why D is not an answer. Choice C is similar. 

A class has 17 boys and 8 girls. one student is selected. f is the event of selecting a girl, and k is the event of selecting kate, one of the girls in the class. determine p(k | f) and p(f | k

Answers

B.
The Probability of choosing a girl is 17/30.
The probability of choosing an A student is 5/30
The P(girl) + the P(A student) = 17/30 + 5/30 = 22/30 = 11/15.

Use volume and meniscus in the same sentence

Answers

Here is your answer:                                                                                                                                Man, because of meniscus I have to find the volume of the tube.

Term insurance covers the insured for the stated term of the policy.

True
False

Answers

The Answer is True . . . . 

Answer:

it's true

Step-by-step explanation:


Alexia and Haley start out together to bike from Apple Valley to Hesperia, a distance of 15 miles.

Alexia bikes at 5 miles per hour.
Haley bikes at 7.5 miles per hour.

Which statement is true?

They arrive at the same time.


Alexia arrives 1 hour later than Haley.


Alexia arrives 2.5 hours later than Haley.


Haley arrives 37.5 hours earlier than Alexia.

Answers

It is Alexia arrives 1 hour later than Haley.
Letter B is right, Alexia would arrive 1 hour later than Haley. (7.5:1 for Haley and 5:1 for Alexia, in three hours Alexia would arrive and Haley would take two).

Factor this expression completely 9a4 - b2

Answers

First write out all of the factors you have for each term (I am also making the assumption that the expression is 9a^4 - b^2, where ^ is signifying an exponent)
(3*3*a*a*a*a) - (b*b*1)
Seeing as how there is nothing to factor out of either term, your answer is:
(3a^2 + b)(3a^2 - b) you can check that this is correct by distributing this:
(3a^2)(3a^2 - b) and (b)(3a^2 - b). Let me know if this doesn't make sense!

How much money will be in a bank account after 4 years if $8 is deposited at an interest rate of 5%?

Answers

4 dollars will be left in the account
all you have to do is find 5% of 8 times that by 4 and then add that to 8 and that is how much will be in the acount

1. Link took out a $160,000, 10-year term policy at age 45. The premium per $1,000 is $4.18. He will be 55 years old next year when the premium per $1,000 will be $6.47. What is the amount of the increase?

Answers

Hi there! To find the percent of change, you do change/original = x/100, because we are looking for the percent of change. The change is the amount between the two numbers and the original is the previous amount. 6.47 - 4.18 is 2.29. Plug in the values to get 2.29/4.18 = x/100. Cross multiply the values in order to get 229 = 4.18x. Now, divide each side by 4.18 to isolate the variable. When you do, you get 54.784689 or 54.8% when rounded to the nearest tenth. The amount of decrease is approx. 54.8%.

what is the slope intercept form of 2x+y=8

Answers

The slope-intercept form of 2x+y=8 is y=2x-8 
Slope intercept form is usually in the form y=mx+c 

2x+y=8 
y=-2x+8 

Hope I helped :) 

A new car dealer offered to sell his demonstrator model for 80% of the retail price. If the retail price is $30,863, how much did the customer save?

Answers

multiply original price by 80% retail
$30,863 x 80% = $24,690.40
You'd then subtract the original price and the price of 80% retail
$30,863 - $24690.40 = $6172.80
He saved $6172.80

Answer:

The customer saved $6,167.20

Step-by-step explanation:

Hello, great question. These types are questions are the beginning steps for learning more advanced Algebraic Equations.

To begin solving this problem we need to change the percent into decimal form. We can do this by moving the decimal point 2 digits to the left like so...

80.0%   ⇔   0.80

Now that we have the percent in decimal form we can find how much the customer paid by multiplying the percent by the retail price.

[tex]30,836 * 0.80 = 24,668.80[/tex]

Now that we have the amount the customer paid, we can subtract that value by the retail price of the model to calculate how much the customer saved.

[tex]30,836-24668.80 = 6,167.20[/tex]

Finally, we can see that the customer saved $6,167.20

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

If it took 2.5 gallons of paint to cover 282 square feet of wall, how much paint is needed to paint an additional 423 square feet

Answers

its 3.75 gallons because half of 282 is 141 and 141+282=423. So add half of 2.5 to the amount of gallons you have and you should get 3.75. Half of 2.5 is 1.25 and 1.25+2.50=1.75      (2.50 is the same thing as 2.5)

What is the product of 1/2 times 2/3 times 3/4 .... times 1999/2000?

Answers

1/2 * 2/3 *3/4 * ... * 1999/2000
Observe, every numerator cancels with denominator
that leaves 1/2000

The outdoor furniture buys wooden benches for $50 each. The furniture store owner adds 200% markup to the cost of the bench. After hearing from the costumers the selling cost of the bench is too high, the owner changes the markup to 120%. How much less per bench does the store owner make with the lower markup

Answers

50 x 200% is $100 and 50 x 120% is $60. 100-60= $40 so $40 less per bench

George traveled 300 miles in 8 hours. How far could he travel in 4 hours if he traveled at the same rate?

Answers

Divide 300 by 8 to find the unit rate
300/8= 37.5

He travels 37.5 miles per hour

If he travels 37.5 miles per hour, to find the amount in 4 hours we would do 37.5 times 4


37.5×4=150


In 4 hours he travels 150 miles
In 4 hours George would travel 150 miles . 300/8=37.5×4= 150 miles

What is the number of x intercepts of the parabola with equation y=6x^2-4x-3?

Answers

There will be two x-intercepts at approximately 1.12 and -0.45 on the x-axis. I found those using the quadratic formula.
Final answer:

The parabola y=6x^2-4x-3 has 2 x-intercepts. This is determined by solving the equation for when y equals zero, using the quadratic formula. Because the discriminant is positive, there are two distinct real solutions, indicating the two x-intercepts.

Explanation:

To find the number of x-intercepts of the parabola with equation y=6x^2-4x-3, you need to set y to 0 and solve the equation for x. The solutions for x will be the x-coordinates of the intercepts.

The x-intercept(s) occur where y=0. The quadratic formula, x = [-b ± sqrt(b^2 - 4ac)]/2a is used to find these points.

Substituting the coefficients a=6, b=-4, and c=-3 into the formula, we get:

x = [4 ± sqrt((-4)^2 - 4*6*(-3))]/(2*6)

This simplifies to x = [4 ± sqrt(16+72)]/12 = [4 ± sqrt(88)]/12

Since the value under the square root (the discriminant) is positive, we have two distinct real solutions for x. This means that the parabola crosses the x-axis at two points, so there are 2 x-intercepts.

Learn more about x-intercepts here:

https://brainly.com/question/14180189

#SPJ2

A club treasurer has $28.45 consisting of nickels, dimes, and quarters. she has 9 more nickels than dimes and three times as many dimes as quarters. how many does she have of each coin?

Answers

She has $2.78 of quarters，$8.34 of dimes and $17.34 of nickels.

What is the value of x?
What Theorem of postulate did you apply to determine your answer?

Show your work and explain.

Answers

check the picture below.

notice, both angles are lying on a flat-line, surely you'd know what "x" is then.

In a proportional relationship, how can you determine the unit rate while looking at the graph?

Answers

it depends which Graph it is. so which graph is it?
when you have it comment on this and ill tell you!
The unit rate is the slope of the line.
To find the slope from a graph, do this.
Find the x- and y-coordinates of two points.
Subtract the y-coordinates.
Subtract the x coordinates in the same order.
Divide the first difference by the second difference.
That is the slope and the unit rate.

Patrick has seen 10 movies this year.what is the ratio of comedies to the toatal. 4 actions,1 animated,3 comedys,and 2 dramas

Answers

10 movies total and three comedies is 3:10
The ratio is 3:10 for comedy movies.
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