Answers
For the x terms
(3x) plus (-3x) = 3x-3x = (3-3)x = 0x = 0
The result being zero means the x terms effectively cancel out and go away
For the y terms
(-y) plus (3y) = -1y+3y = (-1+3)y = 2y
And finally the terms on the right hand side
(-1) plus (27) = -1+27 = 26
---------------------------------------------------------------
After adding the two equations, we end up with 0+2y = 26
which simplifies to 2y = 26. So the answer is choice D
3x - y - 3x + 3y = 2y
-1 + 27 = 26
So, 2y = 26 is the answer.
Related Questions
Four more than the product of 18 and a number Use the variable n to represent the unknown number.
Answers
hope it helps
Explain how the distributive property helps us multiply the following polynomials and why and how the final products differ:
● (a + b)^2,
● (a – b)^2, and
(a - b)(a + b).
Answers
The distributive property is used to expand [tex](a + b)^2[/tex] and [tex](a - b)^2[/tex], resulting in [tex]a^2 + 2ab + b^2[/tex]and [tex]a^2 - 2ab + b^2[/tex]respectively. The product (a - b)(a + b) uses the distributive property to result in [tex]a^2 - b^2[/tex], showcasing how signs affect the final expressions.
Explanation:The distributive property of multiplication over addition is essential when multiplying polynomials. Let's explore how this property is applied to the given expressions:
For [tex](a + b)^2[/tex], we have to multiply (a + b) by itself. According to the distributive property, it becomes a² + 2ab + b².
Similarly, for [tex](a -b)^2[/tex], distributing (a - b) with itself yields a² - 2ab + b².
Lastly, (a - b)(a + b) represents a difference of squares. By applying the distributive property, the middle terms cancel out, leaving us with a² - b².
The final products differ because of the signs in the original binomials. The squared terms result in a positive sign whether the original binomial had a plus or minus (per rules of multiplying signs), but the product of the mixed terms determines whether you have a sum or difference in the final expression, affecting the middle term.
The circumference of the circle shown below is 75 inches. Which expression gives the length in inches of ?
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Then, you can apply this proportion, naming the curcumference C:
C / 360° = arc / 72°
=> arc = 72° * C / 360°
Now use C =75 in
=> arc = 72° * 75 in / 360 =.15 in
Answer: the length of the arc is 15 in.
An artifact was found to have an original amount of Carbon-14 of 32 grams. Approximately how many grams of Carbon-14 remain after 4300 years? Carbon 14 decays at a rate of -0.00012 grams per year.
9.6 grams
19.1 grams
22.4 grams
31.2 grams
Answers
[tex]A=Pe^{rt} [/tex] where A is what's left in the end, P is the initial amount of carbon, r is the rate at which it deteriorates (sometimes a k in other formulas, but same thing!) and t is the time in years. For us, that formula, filled in, looks like this:
[tex]A=32e ^{(-.00012)(4300)} [/tex]
First thing to do is to simplify that multiplication involving the exponents. Doing that gives us:
[tex]A=32e ^{-.516} [/tex]
On your calculator, you have a 2nd button and an LN button. If you push 2nd and then LN you get this in your display:
[tex]e ^{(} [/tex]
and it's up to you to add the exponent on the e. Our exponent is the -.516. So do that and then multiply that result by 32 to get that your answer is 19.1 g of carbon remaining.
70/x = 15/21 solve proportion
Answers
How to multiply scientific notation with another scientific notation?
Answers
1. Multiply the coefficients and round to the number of significant figures in the coefficient with the smallest number of significant figures.
2. Add the exponents.
3. Convert the result to scientific notation.
Answer:
Let's say that I have to multiply 2.5 x 10^3 and 6.23 x 10^5.
First, Let's multiply 10^3 and 10^5.
It would be 10^8.
next, let's multiply 2.5 and 6.23.
It is 15.575.
So, my answer is 15.575 x 10^8.
You have 63 coins in your piggy bank, all the quarters and nickles. The total amount is $12.55. Hop many quarters do you have?
A.4
B.47
C.16
D.59
Answers
While crossing the Atlantic, sailors spot two mermaids 120° apart on each end of an island that is 6 miles away. How far apart are the mermaids around the outer edge of the island to the nearest tenth of a mile?
A. 12.6 miles
B. 3.1 miles
C. 7.2 miles
D. 20.2 miles
Answers
what key features can be identified from graphs of polynomials with higher degrees and explain how the key features can be used to sketch the graph of the polynomial function.
Answers
The key features of graphs of polynomials with higher degrees include the leading coefficient, end behavior, and turning points. These features can be used to sketch the graph of the polynomial function.
Explanation:The key features that can be identified from graphs of polynomials with higher degrees include the leading coefficient, the end behavior, and the number and behavior of the turning points. The leading coefficient determines the orientation of the graph, whether it opens upwards or downwards. The end behavior of the graph shows how the function behaves as x approaches positive or negative infinity. The number and behavior of the turning points indicate the shape and direction of the graph.
These key features can be used to sketch the graph of the polynomial function by following these steps:
Identify the degree of the polynomial and determine the leading coefficient.Use the end behavior to determine the general direction in which the graph will go as x approaches positive or negative infinity.Find the x-intercepts by solving the equation f(x) = 0.Determine the behavior of the turning points by analyzing the sign of the second derivative.Plot the key points on the graph, including the x-intercepts and any turning points.Use the information from steps 2 and 4 to sketch the graph, connecting the key points with a smooth curve.Learn more about Polynomial Graphs here:https://brainly.com/question/4159808
#SPJ11
A normal population has a mean of 75 and a standard deviation of 5. you select a sample of 40. compute the probability the sample mean is
Answers
Error = 5/√40 = 0.791
If score is less than 74, then
z-score = actual score minus the population score divided by standard error.
z-score = 74-75/0.791 = -1.26
Find this value in the area under the distribution curve to the left of the z score of -1.26 and you will find that it is 0.1038. It means that the probability of getting a z-score of less than or equal to -1.26 is equal to 10.38%.
The probability that the sample mean is less than 74 is about 10.38%.
To solve the problem step-by-step, let's go through each calculation in detail:
1. Compute the Standard Error (SE):
Given:
- Population mean [tex](\(\mu\))[/tex] = 75
- Population standard deviation [tex](\(\sigma\))[/tex] = 5
- Sample size (n) = 40
The standard error of the mean is calculated using the formula:
[tex]\[ \text{SE} = \frac{\sigma}{\sqrt{n}} \][/tex]
Substituting the given values:
[tex]\[ \text{SE} = \frac{5}{\sqrt{40}} = \frac{5}{6.3246} \approx 0.791 \][/tex]
2. Compute the Z-score for a sample mean of 74:
The Z-score is calculated using the formula:
[tex]\[ Z = \frac{X - \mu}{\text{SE}} \][/tex]
Where:
- (X) is the sample mean.
Given (X = 74):
[tex]\[ Z = \frac{74 - 75}{0.791} = \frac{-1}{0.791} \approx -1.26 \][/tex]
3. Find the probability corresponding to the Z-score:
The Z-score of -1.26 corresponds to the cumulative probability from the standard normal distribution table.
A Z-score of -1.26 gives a cumulative probability (area under the curve to the left of the Z-score) of approximately 0.1038.
Therefore, the probability that the sample mean is less than 74 is about 10.38%.
Find the z score so that 25% of the standard normal curve lies to the left of z. remember that this means you are looking for the area (which means you need to find the 4 digit number in the area portion of table 3 that is closet to 25% ).
Answers
P(x)=25=0.25
thus checking the z-score that gives us the probability of 0.25 we get:
-0.67
the answer is z=-0.67
To locate the z-score where 25% of the standard normal distribution is to the left, one checks a z-table for the area closest to 0.25, which approximately corresponds to a z-score of -0.675.
Explanation:To find the z-score so that 25% of the standard normal curve lies to the left, we need to look up the corresponding area in a z-table. Since most z-tables represent the cumulative area to the left of a z-score, we must find the value closest to 0.25, the decimal equivalent of 25%. Upon checking a standard z-table, we find that the area closest to 0.25 corresponds to a z-score of approximately -0.675. Therefore, the z-score that has 25% of the area under the normal curve to its left is -0.675.
How far away can a boy ride on a bicycle if he rides away at 10 kilometers per hour and returns at 9 kilometers per hour? The entire trip takes 9.5 hours.
Answers
hmm
d=st
d/s=t
total time is 9.5hr
alright
so distance there=distance back we will call both of them d
so
speed there is 10
speed back is 9
total time is 9.5
so
d/sthere+d/sback=totaltime
d/10+d/9=9.5
times both sides by 90
9d+10d=855
19d=855
divide both sides by 19
d=45
he can ride 45mi away
The vertical distance from a fixture outlet to the trap weir should not be more than _______ inches.
Answers
The maximum allowable vertical distance from a fixture outlet to the trap weir in plumbing is 24 inches. This standard ensures proper drainage and the maintenance of a water seal, preventing sewer gases from entering a building.
The vertical distance from a fixture outlet to the trap weir, which is a critical aspect of plumbing design, should not be more than 24 inches. The fixture outlet is the point where water exits the fixture, and the trap weir is the peak point inside a P-trap, which maintains a water seal to prevent sewer gases from entering the building.
It's important to adhere to this standard to ensure proper drainage and maintain the water seal. If the distance is too great, it could lead to poor drainage and a loss of the trap seal due to siphoning, which would allow sewer gases to enter the home or building.
The original value of a car is 18000 and it depreciates by 15% each year. what is the value of the car after three years?
Answers
What is the length of the third side of the window frame below? (Figure is not drawn to scale.) A picture of a right triangular window frame is shown. The longest side has length labeled as 87 inches. The height of the frame is labeled as 63 inches.
Answers
h^2=x^2+y^2, where h=hypontenuse, and x and y are the side lengths...
87^2=w^2+63^2
w^2=87^2-63^2
w^2=3600
w=√3600
w=60 in
So the base of the frame is 60 inches wide.
Answer: 60 inches
Step-by-step explanation:
Given: A frame in the shape of right triangle with the longest side = 87 inches
The height of the frame is labeled as 63 inches.
Let 'x' be the third side of the frame then by Pythagoras theorem of right triangle , we have
[tex]87^2=x^2+63^2\\\\\Righatrrow\ x^2=87^2-63^2\\\\\Rightarrow\ x^2=3600\\\\\Rightarrow\ x=\sqrt{3600}=60[/tex]
Hence, the length of the third side of the window frame = 60 inches.
Geometry help please.
Answers
trace the line to where the middle of the point looks to be and then find the point. in this instance the segment is 12 points long so the middle would be at six but because it is shifted over to the left 2 points the x coordinate would be 4. Since the line is parallel with the x axis you know that the y coordinate has to be 3. So the answer is (4,3)
Roger is renting a tuxedo for prom. Once he has chosen his jacket, he must choose from three types of pants, four colors of vests, and two different styles of shoes. How many different ways can he select his attire for the prom?
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3 pants x 4 vests x 2 shoes = 24 different ways
if your unsure of your answer, you can always draw a tree diagram.
The number of ways he can select his attire for the prom to look differently will be twenty-four (24).
What are permutation and combination?A permutation is an act of arranging the objects or elements in order. Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.
Roger is renting a tuxedo for prom.
Once he has chosen his jacket, he must choose from three types of pants, four colors of vests, and two different styles of shoes.
Then the number of the ways he can select his attire for the prom will be
[tex]\rm Number \ of \ ways = ^3C_1 \times ^4C_1 \times ^2C_1 \\\\ Number \ of \ ways = 3 \times 4 \times 2\\\\Number \ of \ ways = 24[/tex]
More about the permutation and the combination link is given below.
https://brainly.com/question/11732255
Find the 6th term of the expansion of (2p - 3q)11. a. -7,185,024p4q7 c. -7,185p4q7 b. -7,185,024p6q5 d. -7,185p6q5
Answers
the coefficient for the first term is 1, the next is 11 and so on... now, notice, the elements of the binomial, the 1st element starts off with 11, and every term it goes down by 1, the 2nd element starts off at 0, and goes up by 1 in each term.
now, to get the next coefficient, you simply, "get the product of the current coefficient and the exponent of the 1st element, and divide that by the exponent of the 2nd element in the next term".
for example, how did we get 165 for the 4th term.... well (55*9)/3
how did we get 462 for the 6th term? well (330*7)/5.
and then you can just expand it from there.
Answer: B. [tex]-7185024p^6q^5[/tex]
Step-by-step explanation:
The (r+1)th term in [tex](a+b)^n[/tex] is given by :
[tex]^nC_r(a)^{n-r}(b)^r[/tex]
The given binomial : [tex](2p - 3q)^{11}[/tex]
For the 6th term, we put r=6-1=5 , we get
[tex]^{11}C_5(2p)^{11-5}(-3q)^5\\\\=\dfrac{11!}{5!(11-5)!}(2p)^6(-243q^5)\\\\=-dfrac{11\times10\times9\times8\times7\times6!}{6!5!}(64p^6)(243q^5)\\\\=-462\times(64p^6)(243q^5)\\\\=-7185024p^6q^5[/tex]
Hence, the 6th term of the expansion of [tex](2p - 3q)^{11}[/tex] = [tex]-7185024p^6q^5[/tex]
The money collected from selling bacon at a butcher store is given by the function f(x) = 3.55x – 4, where f(x) is the sales revenue in dollars and x is the number of customers visiting the store each day. If {17, 21, 24, 34} customers visited over four days, what is the income from bacon sales each day?
{50.55, 63.45, 80.34, 99.8}
{43.45, 58.75, 73.4, 93.5}
{56.35, 70.55, 81.2, 116.7}
{45.74, 65.7, 83.8, 105.7}
{63.25, 68.35, 79.7, 97.6}
Answers
The answer is C, hope it helped
Answer:
Hi!
The correct answer is {56.35, 70.55, 81.2, 116.7} .
Step-by-step explanation:
The set {17, 21, 24, 34} represents the values of x.
If you replace each value in the equation:
f(17) = 3.55 * 17 – 4 = 60.35 - 4 = 56.35f(21) = 3.55 * 17 – 4 = 74.55 - 4 = 70.55f(24) = 3.55 * 17 – 4 = 85.2 - 4 = 81.2f(34) = 3.55 * 17 – 4 = 120.7 - 4 = 116.7Then you have the values {56.35, 70.55, 81.2, 116.7} .
What is the location of point F, which partitions the directed line segment from D to E into a 5:6 ratio?
-1/11
1/11
2/15
15/2
Answers
The correct answer is b
F is a point which is greater than zero and F must be in the location of 1/11 and it can be determine by using arithmetic operations.
Given :
F partitions the directed line segment from D to E into a 5:6 ratio.
Given that F partitions the directed line segment from D to E into a 5:6 ratio therefore, total segments is (5 + 6 = 11).
From point D to E in the given line segment there are 9 units. To divide the line segment of 9 unit into 11 unit, first find the distance between two units, that is:
[tex]\dfrac{9}{11}=0.82[/tex]
[tex]0.82\times 5 = 4.1[/tex]
Now, it can be say that F is a point which is greater than zero and F must be in the location of 1/11.
For more information, refer the link given below:
https://brainly.com/question/12431044
What is the slope of the graph of 2y – 5x = 14?
Answers
y=2.5x+7. The slope is the coefficient of x, which is 2.5
The library has at least 5,000 books. Which inequality represents the situation an has an infinite number of solutions?
Answers
what is the solution to the equation 4(3x - 11) + 23 = 5x - 14 ?
Answers
4(3x - 11) + 23 = 5x - 14
Apply the distributive property to 4(3x - 11)
4(3x) + 4(-11)
12x - 44
We now have:
12x - 44 + 23 = 5x - 14
Combine like-terms on the left-hand side of the equation.
-44 + 23 = -21
12x - 21 = 5x - 14
Get x on one side by subtracting 5x from both sides..
12x - 5x = 7x
5x - 5x = 0
7x - 21 = -14
Add 21 to both sides to isolate 7x.
-21 + 21 = 0
-14 + 21 = 7
7x = 7
Divide both sides by 7 to solve for x.
7x / 7 = x
7 / 7 = 1
We are now left with the following solution:
x = 1
I hope this helps!
When x is 2, y is 4, p is 0.5, and m is 2. If x varies directly with the product of p and m and inversely with y, which equation models the situation?
Answers
x=2,y=4,p=0.5, m=2 so:-
2 = k*0.5*2 / 4
2 = 0.25k
k = 2/0.25 = 8
required equation is x = 8pm/y
b. StartFraction x y Over p m EndFraction = 8
What number must be added to the expression below to complete the square? x2 - 11x
Answers
Since we are to complete the square, therefore I believe the correct given should be:
x ^ 2 – 11 x
Take note of the symbol ^ which denotes that 2 is an exponent of x.
The general form of a binomial equation is in the form of:
a x^2 + b x + c
Where in this case:
a = 1
b = -11
c = unknown
To complete the square, we have to find for the value of c. This is calculated using the formula:
c = (b / 2) ^ 2
c = (-11 / 2) ^ 2
c = 30.25
Therefore the complete equation is:
x ^ 2 – 11 x + 30.25
30.25 is correct but apex asks for a fraction so 121/4
Identify the x-intercept and y-intercept of the line 2x−5y=20.
Select one:
a. The x-intercept is (2, 0) and the y-intercept is (0, -5).
b. The x-intercept is (10, 0) and the y-intercept is (0, -4).
c. The x-intercept is (0, -4) and the y-intercept is (10, 0).
d. The x-intercept is (0, 10) and the y-intercept is (-4, 0).
Answers
y intercept x = 0; −5y=20 then y = -4
x intercept (10,0), y intercept (0,-4)
answer
b. The x-intercept is (10, 0) and the y-intercept is (0, -4).
the fraction 6/9 produces a repeating decimal 0.6 ?
true or false
Answers
Which statement is correct with respect to f(x) = -3|x − 1| + 12?
The V-shaped graph opens upward, and its vertex lies at (-3, 1).
The V-shaped graph opens downward, and its vertex lies at (-1, 3).
The V-shaped graph opens upward, and its vertex lies at (1, -12).
The V-shaped graph opens downward, and its vertex lies at (1, 12).
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Replace ? with a whole number to make the statements true.
a. 20 ÷ 4 ? means ? × 4 = 20
b. 2,725 ÷ 5 ? means ? × 5 = 2,725
c. ? ÷ 5 = 0
Answers
Answer:
a. 5
b. 545
c. 0
Step-by-step explanation:
These are straightforward division problems, easily solved using your own memorized multiplication facts, or using a calculator.
a. 20 ÷ 4 = 5 means 5 × 4 = 20
b. 2725 ÷ 5 = 545 means 545 × 5 = 2725
c. 0 ÷ 5 = 0 means 0 × 5 = 0
_____
When using the Google calculator and standard keyboard symbols, you can use the slash (/) for "divided by" and the asterisk (*) for "times."
The sum of the roots of the equation x 2 + x = 2 is:
Answers
x²+x - 2 =0
a=1 b=1 c = -2
The sum of the roots is : S = -b/a
S = - 1/1 = -1
Answer:
The sum of the roots of the equation [tex]x^{2} + x = 2[/tex] is -1
Step-by-step explanation:
You have two options to find the sum of the roots,
The first option is to use the Quadratic Formula to find the two roots:[tex]x_{1,2} = \frac{-b\±\sqrt{b^{2}-4ac}}{2a} [/tex]
[tex]x^{2} + x - 2= [/tex] where:
a = 1
b = 1
c = -2
[tex]x_{1} = \frac{-1-\sqrt{1^{2}-4*1*-2}}{2*1}[/tex] = -2
[tex]x_{2} = \frac{-1+\sqrt{1^{2}-4*1*-2}}{2*1}[/tex] = 1
The sum of the roots is -2 + 1 = -1
2. The second option is use the fact that a general quadratic equation is in the form of:
[tex]ax^{2}+bx+c=0[/tex]
if you divided by [tex]a[/tex] you get:
[tex]x^{2}+\frac{b}{a} x+\frac{c}{a} =0[/tex]
and always the sum of roots will be given for this expression [tex]x_{1} + x_{2} = \frac{-b}{a}[/tex]
Why this is true?
Because if we use the Quadratic Formula as follows:
[tex]x_{1} + x_{2} = \frac{-b+\sqrt{b^{2}-4ac}}{2*a} + \frac{-b-\sqrt{b^{2}-4ac}}{2a}[/tex]
[tex]x_{1} + x_{2} = \frac{-2b+0}{2a}}[/tex]
[tex]x_{1} + x_{2} = \frac{-b}{a}[/tex]
In the case of this equation:
[tex]x_{1} + x_{2} = \frac{-1}{1} = -1[/tex]