Answer:
A' = (5,7)
Step-by-step explanation:
So, we start with the original point A at (3,1), that means x = 3 and y = 1.
We move it 2 units to the right... so we're moving along the X-axis... and we're moving to the right.. so we're increasing the value of x. That means starting with x = 3, we go 2 more units... we then get to x = 5.
In the same way, we move 6 units up... so we move along the Y-axis. We go up, so we also increase the value of y. Starting with y = 1, we move up by 6 units... so we are now at y = 7.
A' point is then at (5,7).
Percent Increase
Example 1: Ann works in a supermarket for $10.00 per hour. If her pay is increased to $12.00, then what is her percent increase in pay?
Analysis: When finding the percent increase, we take the absolute value of the difference and divide it by the original value. The resulting decimal is then converted to a percent.
Answer:
20% increase
Step-by-step explanation:
Percent increase = (difference) / original *100 percent
= (12-10)/10 * 100percent
= 2/10 *100 percent
= 1/5 * 100 percent
=.2 * 100 percent
= 20%
Find two fractions with a sum of 2/3 but with neither denominator equal to 3.
answer: 2/6 +2/6= 4/6 and 4/6 reduced down is 2/3 :)
The two fractions with a sum of 2/3 but with neither denominator equal to 3 is, 2/6 +2/6= 4/6 and 4/6 reduced down is 2/3.
What is fraction?A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.
here, we have,
2/3
= 4/6
=2/6 +2/6
Hence, The two fractions with a sum of 2/3 but with neither denominator equal to 3 is, 2/6 +2/6= 4/6 and 4/6 reduced down is 2/3.
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Jennifer's bill for 6 cans of grape juice and 4 cans of apple juice was $13.10. When she got home she found out that she should have bought 4 cans of grape juice and 6 cans of apple juice. Although she mixed up the order, she did save 60 cents. What is the cost per can of apple and grape juice
Solve the system using substitution and elimination.
Convert your equations to slope intercept form and identify the variables for your x and y axes. Then graph.
SHOW ALL WORK
Answer:
Part 1) The system is solved using elimination
The cost per can of grape juice is [tex]\$1.19[/tex] and the cost per can of apple juice is [tex]\$1.49[/tex]
Part 2) The system is solved using substitution
The cost per can of grape juice is [tex]\$1.19[/tex] and the cost per can of apple juice is [tex]\$1.49[/tex]
Part 3) The system is solved by graphing
The graph in the attached figure
Step-by-step explanation:
Part 1) Solve the system by elimination
Let
x----> the cost per can of grape juice
y----> the cost per can of apple juice
we know that
[tex]6x+4y=13.10[/tex] -----> equation A
[tex]4x+6y=13.10+0.60[/tex]
[tex]4x+6y=13.70[/tex] -----> equation B
Solve the system by elimination
Multiply the equation A by -6 both sides
[tex]-36x-24y=-78.6[/tex] -------> equation C
Multiply the equation B by 4 both sides
[tex]16x+24y=54.8[/tex] -------> equation D
Adds equation C and equation D
[tex]-36x-24y=-78.6\\16x+24y=54.8\\----------\\-36x+16x=-78.6+54.5\\-20x=-23.8\\x=1.19[/tex]
Substitute the value of x in the equation A
[tex]6(1.19)+4y=13.10[/tex]
[tex]4y=5.96[/tex]
[tex]y=1.49[/tex]
therefore
The cost per can of grape juice is [tex]\$1.19[/tex]
The cost per can of apple juice is [tex]\$1.49[/tex]
Part 2) Solve the system by substitution
Let
x----> the cost per can of grape juice
y----> the cost per can of apple juice
we know that
[tex]6x+4y=13.10[/tex]
[tex]4y=-6x+13.10[/tex]
[tex]y=-1.5x+3.275[/tex] -----> equation A
[tex]4x+6y=13.10+0.60[/tex]
[tex]4x+6y=13.70[/tex]
[tex]6y=-4x+13.70[/tex]
[tex]y=-(4/6)x+13.70/6[/tex]
[tex]y=--0.67x+2.28[/tex] -----> equation B
Substitute equation B in equation A and solve for x
[tex]-0.67x+2.28=-1.5x+3.275[/tex]
[tex]1.5x-0.67x=3.275-2.28[/tex]
[tex]0.83x=0.995[/tex]
[tex]x=1.19[/tex]
Find the value of y
Substitute the value of x in the equation A
[tex]y=-1.5(1.19)+3.275=1.49[/tex]
therefore
The cost per can of grape juice is [tex]\$1.19[/tex]
The cost per can of apple juice is [tex]\$1.49[/tex]
Part 3) Solve the system by graphing
we have
[tex]y=-1.5x+3.275[/tex] -----> equation A
[tex]y=-(4/6)x+13.70/6[/tex] -----> equation B
Remember that
The solution of the system of equations is equal to the intersection point both lines
The solution is the point [tex](1.19,1.49)[/tex]
see the attached figure
therefore
The cost per can of grape juice is [tex]\$1.19[/tex]
The cost per can of apple juice is [tex]\$1.49[/tex]
What is the solution for the following system of linear equations? Give your answer in the form of an ordered pair.
3x + 2y = 5
4x − 9y = −5
Giving brainliest + 30 points!
Answer:
(1,1)
Step-by-step explanation:
3x + 2y = 5
4x − 9y = −5
Multiply the first equation by 4 and the second equation by -3 so we can eliminate x
4(3x + 2y) = 5 *4
Distribute
12x +8y = 20
-3(4x − 9y) = −5*-3
-12x +27y = 15
Add the two new equations together
12x +8y = 20
-12x +27y = 15
------------------------
35y = 35
Divide by 35
35y/35 = 35/35
y=1
Now we can find x
3x+2y =5
3x+2(1) =5
3x +2 =5
Subtract 2 from each side
3x+2-2=5-2
3x=3
Divide by 3
3x/3 = 3/3
x=1
(1,1)
15. Divide the polynomial x^3 + x^2 - 2x + 3 by (x - 1).
Answer:
x² + 2x + [3\x - 1]
Step-by-step explanation:
Since the divisor is in the form of x - c, use what is called Synthetic Division. Remember, in this formula, -c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:
1| 1 1 -2 3
↓ 1 2 0
------------------
1 2 0 3 → x² + 2x + [3\x - 1]
You start by placing the c in the top left corner, then list all the coefficients of your dividend [x² + 5x - 36]. You bring down the original term closest to c then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder, which in this case is a 3, so what you is set the divisor underneath the remainder of 3. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an x², 2 becomes 2x, and the remainder of 3 is set over the divisor, giving you the other factor of x² + 2x + [3\x - 1].
If you are ever in need of assistance, do not hesitate to let me know by subscribing to my channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.
Help needed !!! Use synthetic division to find the quotient and remainder!!!
For this case we must build a quotient that multiplied by the divisor, is eliminating the terms of the dividend until you reach the remainder of the division. It must be fulfilled that:
Dividend = Quotient * Divider + Remainder
Answer:
See attached image
Option D
Convert 67,000 pounds to tons. Choose the words and numbers to complete the statements.
Answer: 33.5 tons
Direct conversion formula: 1 Tons (metric) / 2204.5855379189 = 1 Pounds
Opposite conversion: 67000 Pounds to Tons (metric)
Which comparison is NOT correct?
2 > -3
-7 < -5
-9 < 1
0 < -4
2 > -3 (2 is greater than -3, this is true)
-7 < -5 (-7 is less than -5, this is true because -7 is more negative than -5)
-9 < 1 (-9 is less than 1, this is true)
0 < -4 (0 is less than -4, this is false because 0 is greater than -4)
Among the comparisons given, "0 < -4" is incorrect.
The student is asking which comparison is not correct. After evaluating each comparison, it becomes clear that 0 < -4 is not correct because 0 is not less than -4; in fact, 0 is greater. Other comparisons such as 2 > -3, -7 < -5, and -9 < 1 are all correct, as in each case, the number on the left side of the inequality is indeed larger (or smaller, for negative numbers) than the number on the right side as the symbol indicates.
To understand why 0 < -4 is incorrect, consider the number line where any number to the right is greater than the number to the left. Zero (0) lies to the right of any negative number, including -4, which means it is greater, not less.
NEED HELP ASAP!!
20 POINTS and please explain if you can.
Answer:
x = 12 or A
Step-by-step explanation:
Tangents from an exterior point to the circumference of a circle are equal
Since one of the tangents = 17, the other one must as well
x + 5 = 17 Subtract 5 from both sides.
x + 5-5 = 17-5
x = 12
The answer is A
The lions little league team drinks a gallon of Gatorade each game. Every player gets a cup as a serving. 1 cup =1/16 gallon. The last game, The lions only used 1/2 gallon of Gatorade. How many cups of Gatorade were served to the players during the last game?
Answer:
8 cups
Step-by-step explanation:
8/16 equals 1/2 gallonThe number of cups of Gatorade served to the players during the last game was 8 cups.
To solve the problem, we need to determine how many cups are in half a gallon, given that 1 cup is equal to 1/16 of a gallon.
First, we establish the conversion factor between cups and gallons:
1 cup = 1/16 gallon
Now, we need to find out how many cups are in 1/2 gallon. To do this, we multiply the amount of Gatorade used in the last game by the conversion factor:
Cups served = (1/2 gallon) * (16 cups / 1 gallon)
Performing the multiplication:
Cups served = 1/2 * 16
Cups served = 8 cups
Therefore, 8 cups of Gatorade were served to the players during the last game.
when you save, you earn interest on your savings and even earn interest in the previous years interest what is the name for this type of interest brainly
Answer:
A
Step-by-step explanation:
The type of interest where you earn interest on your savings and even earn interest in the previous years interest is compound interest.
What is compound interest?
Compound interest is when both the amount saved and the interest already accured earn interest at the next date interest is being paid. Simple interest rate is the interest that is paid only on the amount saved.
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Drag the values to order them from least to greatest, with the least at the top.
Answer:
√143 = 11.958
√79+√63 = 16.825
4π = 12.66
Im pretty sure this is correct since I used a calculator. Hope it helps
Find the mean for each set of data. Round to the nearest tenth if necessary.
5, 10, 10, 20, 20, 5, 20, 20, 15, 15
Answer:
14
Step-by-step explanation:
Mean = (5+10+10+20+20+5+20+20+15+15)÷10
= 140÷10
= 14
Please help!!!
Use the equation below to find y, if m=8,x=4, and b=6
Equation: y=mx-b
Answer:
y=26
Step-by-step explanation:
We just subsitiute.
y=8(4)-6
8*4=32
y=32-6
y=26
Is (1, 2) a solution of the system y > 2x and x+y<3?
Select one:
a. Yes, because (1, 2) is a solution to both inequalities.
b. Yes, because (1, 2) is the point of intersection of the two boundary lines of
this system.
c. No, because (1, 2) is a solution to only one of these inequalities.
d. No, because (1, 2) is not a solution to either inequality.
Answer:
d
Step-by-step explanation:
To determine if (1, 2) is a solution to the system
Substitute x = 1, y = 2 into the inequalities and check their validity.
y > 2x → 2 > 2 ← incorrect statement
x + y < 3
1 + 2 < 3 → 3 < 3 ← incorrect statement
(1, 2) is not a solution to either inequality → d
dwight is 3 years older than twice his sisters age . how old is dwight (write the expression)
Answer:
Step-by-step explanation:
let dwight represent x nd his sister represent y
y+3x2=x
Answer:
I did not know that Dwight Schrute has a sisterrrrr
Step-by-step explanation:
Um just the other dude brainliest
An elevator in a hotel moves at 20 feet per second. leaving from the ground floor, its height in feet after t seconds is given by the formula h(t)=20t. A bolt comes loose in the elevator shaft above, and its height in feet after falling for t seconds is given by h(t)=-16t^2+200. At what time and at what height does the bolt hit the elevator?
Answer:
After 7.5 seconds and a height of 0
Step-by-step explanation:
The time taken for the bolt to hit the elevator is 3 seconds, at a height of 60 feet.
Given that the elevator height is h(t)=20t while the bolt height is given by h(t)=-16t² + 200.
At the point when the bolt hit the elevator, they would be at the same height, hence:
-16t² + 200 = 20t
16t² + 20t - 200 = 0
t = -4.2 or t = 3
Therefore the time taken for the bolt to hit the elevator is 3 seconds, the height is:
h(3) = 20(3) = 60 feet
The time taken for the bolt to hit the elevator is 3 seconds, at a height of 60 feet.
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what is the midpoint of the segment shown below? (2,3) (10,3)
Answer:
6,3 hope I helped. :) :)
The coordinates of the midpoint of the line segment that has endpoints (2,3) and (10,3) are (6,3).
What are the coordinates of the midpoint of the line segment AB?Suppose we've two endpoints of a line segment as A(p,q), and B(m,n), then let the midpoint be M(x,y) on that line segment. Then, its coordinates are x =(p+m)/2 and y = (q+n)/2.
Given the endpoints of the line segment are A(-3,4) and B(-6,-1), then the coordinates of the midpoint will be,
x = (2+10)/2 = 12/2 = 6
y = (3+3)/2 = 6/2 = 3
Hence, the coordinates of the midpoint of the line segment that has endpoints (2,3) and (10,3) are (6,3).
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A basketball player makes half of his 3 throws. What are the chances he will make his next free throw?
I think it would be 50%
Simplify the rational expression x^2-4/x^2+5x+6. State any restrictions on the variable.
Answer:
The correct answer is option B.
Step-by-step explanation:
The given rational expression is:
[tex]\frac{x^2-4}{x^2+5x+6}[/tex]
Factor the numerator and the denominator:
[tex]\frac{x^2-2^2}{x^2+2x+3x+6}[/tex]
Factor the numerator using difference of two squares and the denominator using factorization by grouping.
[tex]\frac{(x-2)}{x(x+2)+3(x+2)}[/tex]
[tex]\frac{(x-2)(x+2)}{(x+2)(x+3)}[/tex]
This function is defined if and only if the denominator is not zero.
That is: (x+3)(x+2)≠0.
x≠-2,x≠-3
We simplify now to obtain:
[tex]\frac{x-2}{x+3}[/tex]
The correct choice is the second option.
Option B is correct.
I just took the semester review.
Need help with this question in the image
Answer:
s a
6 3
22 1
30 0
Step-by-step explanation:
Download song .50
Download album = 4
Let s = number of songs
a = number of albums
She can spend 15 dollars
.5s +4a =15
If she downloads 6 songs, let s=6
.5(6) +4a = 15
3+4a = 15
Subtract 3 from each side
3-3+4a = 15-3
4a = 12
Divide by 4
4a/4 =12/4
a=3
She can buy 3 albums
If she downloads 1 album, let a=1
.5(s) +4(1) = 15
.5s +4=15
Subtract 4 from each side
.5s +4-4=15-4
.5s = 11
Divide by .5
.5s/.5 = 11/.5
s = 22
She can download 22 songs
If she downloads 30 songs, let s=30
.5(30) +4a = 15
15+4a= 15
Subtract 15 from each side
15-15 +4a = 15-15
4a=0
a=0
A bag contains an orange tile, a yellow tile, and a purple tile. Two tiles are drawn randomly without replacement. If the first tile is yellow, find the probability of drawing a second tile that is orange.
PLEASE HELP ASAP IM TRYING TO GO TO RECESS LOL
Answer:
It's a 50% chance
Step-by-step explanation:
Answer:
1/3 most likely
Step-by-step explanation:
because you take out one tile and it only has one of each color so there are only three left so 1/3
MARKING BRAINLEST HELP ASAP :))))))) SHOW WORK !!
The rectangle shown has a length of 3x+1 and a width of 2x. Show your work. (3 points)
Find the perimeter.
Find the area.
Find the perimeter and area if x=5.
Answer:
perimeter = 10x + 2
area = 6x^2 + 2x
perimeter = 52
area = 160
Step-by-step explanation:
perimeter = 2 * length + 2 * width
perimeter = 2(3x + 1) + 2(2x)
perimeter = 6x + 2 + 4x
perimeter = 10x + 2
area = length * width
area = (3x + 1)(2x)
area = (2x)(3x + 1)
area = 6x^2 + 2x
For x = 5:
perimeter = 10x + 2 = 10(5) + 2 = 50 + 2 = 52
area = 6x^2 + 2x = 6(5^2) + 2(5) = 6(25) + 10 = 150 + 10 = 160
Ashley use 3 yards of ribbon to wrap these presents how many feet and rub it did actually how many inches did she
Answer:
108 inches
Step-by-step explanation:
one yard = 36 inches
multiply 36 by 3
Answer:1 yd= 3 ft
12 inches= 1 ft
Set up a proportion:
1/3=3/x
1×3=3, so 3×3= 9 ft in 3 yds.
9/3=x/12
9×12= 108
9 ft and 108 inches
At a local company, the ages of all new employees hired during the last 10 years are normally distributed. The mean age is 31 years old, with a standard deviation of 10 years. If you were to take a sampling of 10 employees, what is the probability your mean age will be at least 28? Round to the nearest percent.
Answer:
The probability your mean age will be at least 28 is 83%
Step-by-step explanation:
Let X denote the ages of all new employees hired during the last 10 years , then X is normally distributed with;
a mean of 31
a standard deviation of 10.
The sample size obtained is 10 employees. This implies that the sampling distribution of the sample mean will be normal with;
a mean of 31
a standard deviation of [tex]\sqrt{10}[/tex]
The sample mean is a statistic and thus has its own distribution. Its mean is equal to the population mean, 31 and its standard deviation is equal to [tex]\frac{sigma}{\sqrt{n} }[/tex]
where sigma is the population standard deviation, 10 and n the sample size which in this case is 10. [tex]\frac{10}{\sqrt{10} }=\sqrt{10}[/tex]
We are required to find the probability that this sample mean age will be at least 28;
P(sample mean ≥ 28)
Since we know the distribution of the sample mean we simply standardize it to obtain the z-score associated with it;
P(sample mean ≥ 28)
= [tex]P(Z\geq \frac{28-31}{\sqrt{10} } )=P(Z\geq -0.9487)[/tex]
=0.8286
As a percentage this is equivalent to, 83%
g(r)=−(r+11)(r+14)
1) What are the zeros of the function?
Write the smaller r first, and the larger r second.
smaller r____
larger r_____
2) What is the vertex of the parabola
(___,____)
1) What are the zeros of the function?
smaller r: -11, larger r: -14
2) What is the vertex of the parabola
Vertex: (-12.5, 3)
1. Zeros:
The zeros of the function occur when G(r) = 0. So we need to solve the equation:
-(r + 11)(r + 14) = 0
Since the product of two factors is zero when one or both factors are zero, we can set each factor equal to zero and solve for r:
r + 11 = 0 --> r = -11 (smaller r)
r + 14 = 0 --> r = -14 (larger r)
2. Vertex:
The function is given in factored form, which makes finding the vertex a bit easier. The vertex of a parabola in factored form is exactly between the two zeros.
Therefore, the x-coordinate of the vertex is:
(smaller r + larger r) / 2 = (-11 - 14) / 2 = -12.5
To find the y-coordinate (i.e., the function's value at the vertex), we can plug the x-coordinate of the vertex back into the function (G(r)). However, since the function is multiplied by -1, it might be easier to use one of the original zeros (say, r = -11).
G(-11) = -(-11 + 11)(-11 + 14) = 3 (notice how the negative sign cancels out)
Given: Ray BC bisects angle ABD.
Which pair of angles must be congruent?
A) ∠ABD & ∠EBD
B) ∠ABC & ∠DBE
C) ∠ABC & ∠DBC
D) ∠ABD & ∠CBDill mark brainliest if correct and give 50 pts.
Congruent is the same size and same shape. When a ray bisects an angle, the two newly created angles will be congruent, since the ray went right in the middle of the first angle (so in this case, ABC and DBC will be congruent)
Answer: C) ∠ABC & ∠DBC
Step-by-step explanation:
When a ray bisect an angle , then it divided the original angle into two congruent angles.
We are given that Ray BC bisects angle ABD.
Then, Ray BC divides ∠ABD into two congruent angles.
From the picture, The angle formed by it : ∠ABC & ∠DBC
So ∠ABC & ∠DBC must be congruent.
Hence, the pair of angles must be congruent : ∠ABC & ∠DBC
The length of a rectangular garden is represented by 3X -4 and the width is represented by 2X -5. Which of the following represents the total area of the garden
Answer:
6x^2 - 23x + 20
Step-by-step explanation:
Next time, please share all of the possible answer choices.
Here, A = (3x - 4)(2x - 5) = 6x^2 - 15x - 8x + 20, or
6x^2 - 23x + 20
what is blank - 9 =19
Answer:
28
Step-by-step explanation:
19+9=28 and 28-9=19
Hope This Helps! Have A Nice Day!!
28 I think not positive
Which statements are true about finding the volume of the soup cans? Check all that apply.
A) The diameter is squared to find the area of the base of a cylinder.
B) The volume is the area of the base times the height.
C) Given the radius or the diameter, you can calculate the area of the base of a cylinder.
D) The height of a cylinder is the distance between the 2 parallel bases.
E) The radius is half the distance of the height.
Answer:
the answers are B, C, and D.
The given item soup can is a cylinder.
The volume of the cylinder is given as :
[tex]V=\pi r^{2} h[/tex]
Here 'h' is the height and 'r' is the radius.
So, the true statements are:
B) The volume is the area of the base times the height - The base of the cylinder is circular and the area of the circle is [tex]\pi r^{2}[/tex], so the volume is the area of base multiplied by height.
C) Given the radius or the diameter, you can calculate the area of the base of a cylinder - Yes as the area is [tex]\pi r^{2}[/tex] where 'r' is the radius.
D) The height of a cylinder is the distance between the 2 parallel bases. Yes this is right.