Answers
5x - 2.5y = 5
Align the variables to make solving this easier.
2.5y + 3x = 27
-2.5y + 5x = 5
You can see that the 2.5y and -2.5y cancel each other out. Then add the 3x and 5x, and 27 + 5.
3x = 27
5x = 5
8x = 32
Divide both sides by 8.
x = 4
Now input that x into one of the equations to get y.
2.5y + 3(4) = 27
2.5y + 12 = 27
2.5y = 15
y = 6
The answer to this system of equations is x = 4, y = 6. (4, 6)
Related Questions
Design an equation for the volume of a box made from a cardboard sheet of length q and width p and square cutouts of side length x.
Answers
From the cardboard sheet of length q and width p, we remove from the corners squares of side length x, then fold the cardboard to form a box.
the height of the box is x, the length is q-2x, since 2 x'es are subtracted from the length of the cardboard, similarly the width of the box is p-2x.
The volume of the box is height*length*width:
so the equation is
V=x(q-2x)(p-2x)
An expression is shown below: 3pf^2 - 21p^2f + 6pf - 42p^2. Rewrite the expression completely factored. Show the steps of your work.
Answers
= 3p(f^2 - 7pf + 2f - 14p)
we can factor the terms in the parentheses by grouping:-
= 3p [f(f - 7p) + 2(f - 7p)]
= 3p(f - 7p)( f + 2) answer
The final expression will be equal to 3p(f - 7p)( f + 2).
What is an expression?
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The given expression will be solved as below:-
First find the GCF - this is 3p which we take out:-
E= 3p(f² - 7pf + 2f - 14p)
Factor the terms in the parentheses by grouping:-
E= 3p [f(f - 7p) + 2(f - 7p)]
E= 3p(f - 7p)( f + 2)
Therefore, the final expression will be equal to 3p(f - 7p)( f + 2).
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What is the arc length when 0=3pi over 5 and the radius is 7?
Answers
l=3π/5×7
l=22×3×7÷7÷5
l=66/5
l=13.2 units
Henry is putting money into a checking account. Let y represent the total amount of money in the account (in dollars). Let x represent the number of weeks Henry has been adding money. Suppose that x and y are related by the equation y=20x+650 . Answer the questions below. Note that a change can be an increase or a decrease.
For an increase, use a positive number. For a decrease, use a negative number.
What was the starting amount of money in the account? $
What is the change per week in the amount of money in the account? $
Update: solved
Answers
charge per week : 20 bucks
How many right triangles have a hypotenuse that measures 2x+5 meters and legs that measure 22xminus−33 meters and x+8 meters? what are the dimensions of the triangle(s)?
Answers
Δhello :
by theorem pytagore :
(2x+5)² = (22x-33)² + (x+8)²
4x² +20x +25 = 484x²+1452x + 1089 +x²+16x+64
put this expression in the form ax² +bx+c=0
calculate Δ = b²-4ac ....cpntibue
The two-way table shows the number of students in a class who help in an animal shelter and/or library.
Help in Animal Shelter
Do Not Help in Animal Shelter
Total
Help in Library
12
?
15
Do Not Help in Library
11
10
21
Total
23
13
36
What is the missing number in the table?
3
5
25
27
Answers
Answer: The number 3 is missing from the table!
Step-by-step explanation:
What is the formula for an eastbound car is going 4 miles per hour faster than a westbound car. the cars are 208 miles apart 2 hours after passing each other on a highway. what is the speed, in miles per hour, of the eastbound car?
Answers
The speed of the eastbound car is 56 miles per hour.
Explanation:Let x be the speed of the westbound car. Since the eastbound car is going 4 miles per hour faster, the speed of the eastbound car is x + 4 .
The combined speed of both cars is x + (x + 4) = 2x + 4 miles per hour. In 2 hours, the cars cover a distance of 2(2x + 4) = 4x + 8 miles. This distance is equal to the sum of the distances covered by each car when moving towards each other.
Given that the cars are 208 miles apart, we can set up the equation:
4x + 8 = 208
Subtracting 8 from both sides:
4x = 200
Dividing both sides by 4:
x = 50
So, the speed of the westbound car is 50 miles per hour, and the speed of the eastbound car is 50 + 4 = 54 miles per hour. Therefore, the eastbound car is moving at 54 miles per hour.
In the end, the eastbound car's speed is 54 miles per hour, which is 4 miles per hour faster than the westbound car's speed of 50 miles per hour.
Full Question:An eastbound car is going 4 miles per hour faster than a westbound car. the cars are 208 miles apart 2 hours after passing each other on a highway. what is the speed, in miles per hour, of the eastbound car?
Given a standard deck of playing cards, what is the probability of randomly selecting a card that is either red or a face card or both
Answers
The types of cards and their colors are:
clubs (black), diamonds(red), hearts(red) and spades(black).
each of these contain 3 face cards: a jack, a queen and a king.
so there are in total 6 black face cards, and 6 red face cards.
P(red or a face card or both)=n(red or a face card or both)/52
n(red or a face card or both)=n{26 red + 6 black faces)=32
so the probability is 32/52=0.615
Answer: 0.615
Final answer:
This detailed answer explains the probability of selecting a heart or a face card from a standard deck of cards and the calculation involved.
Explanation:
Calculate the probability of selecting a heart or a face card from a standard deck of cards:
There are 52 cards in a deck, with 13 hearts and 12 face cards (3 each of Jacks, Queens, Kings).The probability of selecting a heart card is 13/52 = 1/4.The probability of selecting a face card is 12/52 = 3/13.By the principle of inclusion-exclusion, you add the probabilities of selecting a heart and a face card and subtract the probability of both (heart face cards, which are only the face cards that are hearts - 3 cards):
(1/4) + (3/13) - (3/52) = 39/52 = 3/4
The height of a triangle is 6 m more than its base. The area of the triangle is 56 m2. Find the length of the base. 7 m 8 m 14 m 15 m
Answers
height = x+6
[tex] \frac{x(x+6)}{2}=56 \\ x(x+6)=56*2 \\ x^2+6x=112 \\ x^2+6x-112=0 \\ x^2+14x-8x-112=0 \\ x(x+14)-8(x+14)=0 \\ (x-8)(x+14)=0 \\ x-8=0 \ \ \ \ \ \ \ or \ \ \ \ \ \ x+14=0\\x=8 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=-14 \ \ \ \O[/tex]
base = 8 m
I was wondering if anybody had the questions to the module 8 DBA for FLVS. I usually dont do well unless I see the question, I dont need the answers just the question.
Answers
select the TWO binomials that are factors of this
Answers
since the last number -s -20 you need the 2 that when multiplied together would equal -20
so x-5 and x +4 are the correct answers
Describe how the graphs of functions f and g are related: f (x) = 2cos(pi x) g(x) = 2cos(2pi x)
Answers
but the period is half in the second case. Period of the first one is 2, in the second one is 1, so it will oscillate twice as many times than the first one, but it will go from -2 to 2, both of them
Hope it helps
f and g have the same trajectory: cosine function
But, g has half of the frequency of f
Evaluate m – n when m = –2.6 and n = 7.9.
a. –10.5
b. –5.3
c. 5.3
d. 10.5
Answers
Final answer:
The value of m – n when m = –2.6 and n = 7.9 is –10.5, which is an option (a).
Explanation:
To evaluate m – n when m = –2.6 and n = 7.9, we simply substitute the given values into the expression and perform the subtraction:
m – n = –2.6 – 7.9
Since subtracting a positive number is the same as adding its negative, this is equivalent to:
m – n = –2.6 + (–7.9)
Adding these two negative numbers together gives us:
m – n = –10.5
Therefore, the correct answer is a. –10.5.
one pinball games 25 cents to play.how much will it cost to play 10 pinball games?
Answers
It would cost $2.50 to play 10 games of pinball.
It would cost 2.50 dollars to play 10 pinball games
The cost of a daily newspaper varies from city to city. however, the variation among prices remains steady with a standard deviation of 20?. a study was done to test the claim that the mean cost of a daily newspaper is $1.00. ten costs yield a mean cost of 96? with a standard deviation of 18?. do the data support the claim at the 1% level?
Answers
First, we establish our hypothesis:
Null hypothesis H0: μ = $1.00
Alternative hypothesis Ha: μ ≠ $1.00
Let’s say X = the sample average cost of a daily newspaper = 0.96
u = population mean cost = 1.00
S = sample standard deviation = 0.18
Calculating for z value:
z = (X – u) / S
z = (0.96 – 1) / 0.18
z = – 0.222
From the standard distribution table at this z value, p-value = 0.4129
Since alpha = 0.01, the decision therefore is:
Do not reject the null hypothesis because the p-value is greater than 0.01. There is enough evidence to support the claim that the mean cost of newspapers is $1.
Medical researchers have determined that for exercise to be beneficial, a person’s desirable heart rate, R, in beats per minute, can be approximated by the formulas
for women
for men,
where a represents the person’s age. If the desirable heart rate for a man is 135 beats per minute, how old is he?
a.
22.5 years old
b.
40 years old
c.
45 years old
d.
42.5 years old
Please select the best answer from the choices provided
Answers
Nevertheless, I searched for them and here they are:
For women, R = 143 - 0.65a
For men, R = 165 - 0.75a
You are asked for the age of a man whose desirable R is 135, so you must use the equation for men, R = 165 - 0.75a, replace 135 for R and solve for a.
=> 135 = 165 - 0.75a
=> 0.75 a = 165 - 135
=> 0.75 a = 30
=> a = 30 / 0.75
=> a = 40.
Answer: option b. 40 years old.
Which graph shows the axis of symmetry for the function f(x) = (x – 2)2 + 1?
Answers
x^2 -4x + 5 = 0
The 'x' value of the axis of symmetry = 'x' value of the vertex.
To get this value, take the derivative of x^2 -4x + 5 = 0 which equals
2x -4 =0
x = 2 which equals the axis of symmetry
Step-by-step explanation:
Please find the attachment of graph representing the axis of symmetry.
We are asked to choose the graph from our given choices, which shows the axis of symmetry for the function:
[tex]f(x)=(x-2)^2+1[/tex]
We can see that our function represents a parabola.
Since we know that axis of symmetry is a vertical line that divides parabola into two congruent parts. The axis of symmetry intersects parabola at its vertex.
Let us find the vertex of our given parabola using formula: [tex]x=\frac{-b}{2a}[/tex], where,
a = Coefficient of [tex]x^{2}.[/tex]
b = Coefficient of x.
To apply this formula we will represent our parabola as a quadratic equation [tex](ax^2+bx+c)[/tex] as:
[tex]f(x)=x^2-4x+4+1[/tex]
[tex]f(x)=x^2-4x+5[/tex]
Upon substituting a= 1 and b= -4 in the formula we will get,
[tex]x=\frac{-(-4)}{2*1}[/tex]
[tex]x=\frac{4}{2}[/tex]
[tex]x=2[/tex]
Therefore, the vertical line passing through point x = 2 will be the axis of symmetry for our given function and graph B is the correct choice.
Divide 40x/ 64y by 5x/ 8y
A. 1
B. 3/4
C. 25x^2/ 64y^2
D. 25/64
Answers
(40x/64y)(8y/5x)
320xy/(320xy)
1
The division to the expression Divide 40x/ 64y by 5x/ 8y is (a) 1
How to evaluate the quotient expression
From the question, we have the following parameters that can be used in our computation:
Divide 40x/ 64y by 5x/ 8y
As an expression we have
40x/ 64y ÷ 5x/ 8y
So, we have
40x/ 64y ÷ 5x/ 8y = 40x/ 64y * 8y/5x
Divide the variables
This gives
40x/ 64y ÷ 5x/ 8y = 40/64 * 8/5
Lastly, we have
40x/ 64y ÷ 5x/ 8y = 1
Hence, the solution to the expression is (a) 1
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Below are two different functions, f(x) and g(x). What can be determined about their y-intercepts? F(x)=-2x-1
Answers
The correct statement is:
The function f(x) has a higher y-intercept.Step-by-step explanation:We know that the general form of a slope intercept form of a line is given by:
[tex]y=mx+c[/tex]
where m is the slope of the line and c is the y-intercept of a line.
The function f(x) is given by:
[tex]f(x)=-2x-1[/tex]
Hence, on comparing the function to the slope-intercept form of a line we get
The y-intercept of function f(x) is: -1
Also, the table for the function g(x) is given by:
x g(x)
2 2
4 6
6 10
The function g(x) satisfies the equation:
[tex]g(x)=2x-2[/tex]
The y-intercept of the function g(x) is: -2
Since we know that:
-1 > -2
This means that the y-intercept of the function f(x) is higher than the y-intercept of the function g(x).
Multiply 8 times the square root of 3 by 9 times the square root of 27.
Answers
8 · 9 ·√3 · √27
72 · √81
72 · 9
648
The answer is 648. :)
8 times the square root of 3 multiplied by 9 times the square root of 27 is equal to 1944.
To multiply 8 times the square root of 3 by 9 times the square root of 27, we can simplify the expression using the properties of square roots and perform the multiplication.
First, let's simplify the square roots:
Square root of 3 can be written as √3.
Square root of 27 can be written as √(9 * 3), which further simplifies to √9 * √3 = 3 * √3.
Now, we have:
8 * √3 * 9 * √27 = 8 * √3 * 9 * (3 * √3) = 8 * 9 * 3 * √3 * √3 = 216 * 3 * √3 * √3.
Since the square root of 3 multiplied by itself (√3 * √3) simplifies to 3, we have:
216 * 3 * 3 = 1944.
Therefore, 8 times the square root of 3 multiplied by 9 times the square root of 27 is equal to 1944.
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Which logarithmic equation is equivalent to the exponential equation below 4c=256
Answers
To convert the exponential equation 4c = 256 into a logarithmic form, one can apply the logarithm to both sides, simplifying using the property that the logarithm of a power is the exponent times the logarithm of the base, yielding the equivalent equation c = 4.
The question requires us to convert the exponential equation 4c = 256 into a logarithmic form. To achieve this, we need to recognize that a logarithm function is the inverse of an exponential function. Therefore, applying a logarithm to both sides of the equation will allow us to solve for the variable c.
It's important to note that any logarithmic base can be used, but common practice is to use either base 10 (common logarithm) or the natural base e (natural logarithm).
Since 256 is 4 raised to the 4th power (4⁴), we can write the equation as 4c = 4⁴. By applying the logarithm, we then get the equivalent logarithmic equation log(4c) = log(4⁴).
Using the property of logarithms that states the logarithm of a number raised to an exponent will be the product of the exponent and the logarithm of the number, we can simplify this to c*log(4) = 4*log(4). Since log(4) is a common factor on both sides, dividing by log(4) gives us c = 4.
Is the centroid of a triangle equidistant from the three vertices?
Answers
Yes, the centroid of a triangle is equidistant from the three vertices.
Explanation:Yes, the centroid of a triangle is indeed equidistant from the three vertices.
The centroid of a triangle is the point where the three medians of the triangle intersect. A median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side.
Since the medians of a triangle intersect at the centroid, the distances from the centroid to each vertex along the medians are equal. This property can be proven using properties of similar triangles.
Factor the following.
Answers
Hope this helps :)
Please give brainliest
I'm just going to simplify all of our answer choices, and see which one is correct.
a) 2(3h+ 5)(h + 12)
Simplify.
(6h + 10)(h + 12)
Simplify.
(6h · h) + (6h · 12) + (10 · h) + (10 · 12)
Simplify.
6h² + 72h + 10h + 120
Add like terms.
6h² + 82h + 120
So, A IS CORRECT.
However, let's just go through the rest just to make sure.
b) (6h + 12)(h - 10)
Simplify. Because we have already showed you the steps on how to multiply this way, I will just simplify it the faster way, without showing all of the work :)
6h² - 60h + 12h - 120
Add like terms.
6h² - 48h - 120
Therefore, B is incorrect.
c) (6h - 12)(h - 10)
Simplify.
6h² - 60h - 12h + 120
Add like terms.
6h² - 72h + 120
Therefore, C is incorrect as well.
d) (6h - 60)²
Simplify.
(6h - 60)(6h - 60)
Simplify.
36h² - 360 - 360h + 3600
Add like terms.
-324h + 3240
Therefore, D is also incorrect.
Because A is the only one that is equal to 6h² + 82h + 120, it is correct.
~Hope I helped!~
The vertex of the functions graph is given. Find c. y=2x^2-6x+c;(3/2, 0.5)
Answers
[tex]2(x- \frac{3}{2})^{2} = \frac{18}{4}-c [/tex]
Since the y coordinate of the vertex is 1/2 and we need to solve for c, set the [tex] \frac{18}{4}-c [/tex] equal to 1/2 and solve for c, which is the whole point of what we are doing, right?
[tex] \frac{18}{4}-c= \frac{1}{2} [/tex] and [tex] \frac{18}{4}- \frac{2}{4}=c [/tex]
[tex] \frac{16}{4}=c [/tex] and c = 4. So that's our answer!
Elisa needs to make a scale drawing of his school building for art class. If the building is 256.25 meters long, and Elisa scales it down using a ratio of 25 meters to 1 inch, how long will the building be in the sketch? (in inches)
Answers
We have to divide the length of a building to 25:
256.25 : 25 = 10.25
Answer: The building will be 10.25 inches long in the sketch.
I won tickets to a trip for four to the Super Bowl. I have eight friends but I can only bring three of them. In how many ways can I form my Super Bowl party?
Answers
[tex] \frac{8!}{(8-5)!5!} = \frac{8!}{3!5!} = 56 [/tex] ways of choosing three friends from eight total friends
Rip the 4 tickets in half lol
Suppose there is a strong positive correlation between v and w which of the following must be true
?
A.)when V increases, w tends to increase
B.)An increase in a V causes W to decrease
C.)An increase in V causes W to increase
D.)When V increases, W tends to decrease
Answers
The truth is when V increases, W tends to increase. Positive correlation between two variables in which both variables move in tandem. Positive correlation exists when one variable decreases as the other also decreases or one variable increases while others increase too.
Answer: A.) when V increases, w tends to increase
Step-by-step explanation:
Positive correlation is a relationship between two variables in which both variables move with the same ratio. A positive correlation exists when one variable increases as the other variable increases, or vice-versa.
A perfect positive correlation means that both variables move by the exact same percentage.
Therefore, if there is a strong positive correlation between v and w then when V increases, w tends to increase .
The football team has 30 more members than the basketball teams. If each group had 10 more members, the ratio of their membership would be 3.2. How many members are in each group? Write your answer as football x basketball y
****PLEASE HELP********
Answers
Determine two pairs of polar coordinates for the point (3, -3) with 0° ≤ θ < 360°
Answers
The two pairs of polar coordinates are : [tex]( 3\sqrt{2}, 315^{0} ) , ( -3\sqrt{2}, 135^{0} )[/tex]
Polar coordinates are coordinates labeled as ( r, θ ) , where r = radial coordinate while θ is known as the angular coordinate. Polar coordinates are also plotted on a polar grid.
Using the given data
Point ( 3 , - 3 )
[tex]r = \sqrt{3^2 + (-3)^2} = 3\sqrt{2}[/tex]
θ =
[tex]tan^{-1} (\frac{-3}{3}) = \pi - \frac{\pi }{4} , 2\pi - \frac{\pi }{4} \\\\= 3\pi , \frac{7\pi }{4} , -\frac{\pi }{4}[/tex]
In degrees = 135° , 315° , -45° ( neglecting -45° )
Hence the two pairs of polar coordinates for the point ( 3 , -3 ) can be taken as ; [tex]( 3\sqrt{2}, 315^{0} ) , ( -3\sqrt{2}, 135^{0} )[/tex]
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Answer:
c on edge
Step-by-step explanation:
The arithmetic mean (i.e., average) of a set of 7 numbers is 20. the mean of a second set of 13 numbers is 40. what is the mean of all 20 numbers?
Answers
Therefore the sum of the 7 numbers is
S₁ = 7*20 = 140
The mean of the second set of 13 numbers is 40.
Therefore the sum of the 13 numbers is
S₂ = 13*40 = 520
The sum of the two sets of numbers is
S = S₁ + S₂ = 140 + 520 = 660
Altogether, there are 7+13 = 20 numbers.
The overall mean of the 20 numbers is
660/20 = 33
Answer: The mean of all 20 numbers is 33.
Using the weighed mean, it is found that the mean of all 20 numbers is of 33.
What is the weighed mean?The weighed mean is given by the sum of all elements in a data-set multiplied by it's weight, divided by the sum of the weights.
In this problem, the means are divided as follows.
Mean of 20 with a weight of 7.Mean of 40 with a weight of 13.Hence:
[tex]M = \frac{20(7) + 40(13)}{20} = 33[/tex]
The mean of all 20 numbers is of 33.
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