Answer:
With a number line with two points opposite from each other on a number line, the middle of it is always going to be 0. Therefore, both points are the same distance away from 0 just in opposite directions. That means point Q is always going to equal the negative of point P. An example of this is if point p equals 5, point p equals -5.
This method only works when it is specifically stated that the two points are opposite from each other.
Hope this helps!
xx,
myara
The location of Point Q on the number line is the opposite of the location of Point P. If Point P is at +a, then Point Q is at -a, and vice versa.
Explanation:In order to determine the location of Point Q, we first need to know the location of Point P on the number line. If we assume that point P is positive and located at +a, then Point Q, being the opposite of Point P, would be located at -a on the number line. Conversely, if Point P was negative and located at -a, the opposite, Point Q, would be on the +a location on the number line. The important thing to remember here is that opposite points on a number line are simply reflection of each other with respect to the origin (0).
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Eva makes and sells her own cranberry apple fruit punch for the holidays.
In jug A, she mixes 4 cranberry flavored cubes and 3 apple flavored cubes with some water.
In jug B, she mixes 3 cranberry flavored cubes and 2 apple flavored cubes with some water.
If you ask her for a drink that has a stronger cranberry taste, from which jug should Eva pour you drink?
Eva should pour you a drink from jug B for a stronger cranberry taste, as it has a higher ratio of cranberry to apple cubes compared to jug A, demonstrating the use of ratios in mathematics.
To decide which jug of fruit punch has a stronger cranberry taste, we should look at the ratio of cranberry flavored cubes to apple flavored cubes in both jugs. For jug A, the ratio is 4 cranberry cubes to 3 apple cubes, which simplifies to approximately 1.33 cranberry cubes for every apple cube. For jug B, the ratio is 3 cranberry cubes to 2 apple cubes, which simplifies to 1.5 cranberry cubes for every apple cube.
Since jug B has a higher ratio of cranberry to apple, it has a stronger cranberry taste compared to jug A. So, Eva should pour you a drink from jug B if you want a drink with a stronger cranberry flavor. This involves a practical application of ratios and proportions, which are key concepts in mathematics used to compare quantities.
Solve x^2 + 6x + 7 = 0.
A) x = −1 and x = −5
B) 3 plus or minus square root of 2
C) negative 3 plus or minus square root of 2
D) quantity of negative 3 plus or minus square root of 2 all over 2
Answer:
Option C. negative 3 plus or minus square root of 2
Step-by-step explanation:
Please see attachment.
C. negative 3 plus or minus square root of 2
So, the correct answer is indeed option C.
Suppose f(x) =x2. What is the graph of g(x) = f(2x)
The function g(x) is [tex]\rm4x^2[/tex] and the graph is attached in the question the correct option is B.
What is the linear graph?Linear Graph Linear means straight and a graph is a diagram that shows a connection or relation between two or more quantities.
The given graph is;
[tex]\rm f(x)=x^2[/tex]
The graph of g(x) = f(2x) is given by;
[tex]\rm g(x) = f(2x)\\\\g(x) = f(2x)^2\\\\g(x)=4x^2[/tex]
Hence, the function g(x) is [tex]\rm4x^2[/tex] and the graph is attached in the question the correct option is B.
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Rachel paints 5 1 2 512 square meters of wall space in 1 3 13 hour. What area of wall space can she paint in 1 hour? One 200-gram bag of rice costs $8.12. How much does 1 kilogram of rice cost? (Note that 1000 g = 1 kg.) John ran 1 2 12 mile in 5 minutes, and Al ran 1 3 13 mile in 4 minutes. Which runner ran at a faster rate? At a certain store, a half-gallon jug of milk costs $2.95, and a gallon jug of milk costs $5.95. Which milk has a cheaper price: the half-gallon or gallon jug? A package of nine 12-ounce cans of cola costs $7.50. A half-gallon bottle of the same cola is sold for $2.90. Which cola has a cheaper price, the cans or the bottle?
Rachel can paint 16.5 square meters in 1 hour. 1 kilogram of rice costs $40.60. John ran at a faster rate. The half-gallon jug of milk and the half-gallon bottle of cola are cheaper.
Explanation:Rachel paints 5 1/2 square meters of wall space in 1/3 hour, so we have to calculate how much she could paint in a whole hour. We multiply the speed (5.5/1/3) by the desired timeframe (1) to get 16.5 square meters. Therefore, Rachel can paint 16.5 square meters in 1 hour.
One 200-gram bag of rice costs $8.12. To find out how much 1 kilogram of rice costs, we divide 1000 by 200 to get 5 and then multiply this by $8.12 to find that 1 kilogram of rice costs $40.60.
John ran 1/2 mile in 5 minutes, while Al ran 1/3 mile in 4 minutes. To find out who ran faster, we need to calculate each runner's speed in miles per minute. John's speed is 1/2 / 5 = 0.1 mile per minute, while Al's is 1/3 / 4 = 0.083 mile per minute. Therefore, John ran at a faster rate.
A half-gallon jug of milk costs $2.95, and a gallon jug of milk costs $5.95. To compare, we should double the price of the half-gallon to reflect the same quantity as the gallon. $2.95 x 2 = $5.90, which is less than $5.95. Therefore, the half-gallon jug of milk is cheaper.
A package of nine 12-ounce cans of cola costs $7.50, whereas a half-gallon of the same cola costs $2.90. A half-gallon is 64 ounces, which is roughly equivalent to 5.33 cans of cola (64/12). Therefore, a half-gallon of cola costs the equivalent of $4.00 in cans (5.33 x $1.40 [the pricing per single can]). Therefore, the half-gallon bottle of cola is cheaper.
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(a^(2)-4ac+3bc)/(a^(2)-ab+bc-ac)+(a+3b)/(b-a)+(a+2c)/(a-c)
3(bc - ac - ab)/(a²-ab+bc-ac) is the simplified form of the given equation.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given an expression:
(a²-4ac+3bc)/(a²-ab+bc-ac) + (a+3b)/(b-a) + (a+2c)/(a-c)
Simplifying Using PEMDAS starts from the right:
(a²-4ac+3bc)/(a²-ab+bc-ac) + [tex]\frac{a^{2} + 3ab - ac - 3bc }{-a^{2} + ab -bc +ac }[/tex]
Taking negative common from the last term
(a²-4ac+3bc)/(a²-ab+bc-ac) - (a² + 3ab - ac -3bc)/(a²-ab+bc-ac)
Since the base is the same,
(-4ac + 3bc - 3ab +ac +3bc)/(a²-ab+bc-ac)
3(bc - ac - ab)/(a²-ab+bc-ac)
therefore, the simplified form of the given equation is 3(bc - ac - ab)/(a²-ab+bc-ac).
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The solution involves evaluating a complex algebraic expression step by step after substituting given values for variables.
Given the expression, (a2-4ac+3bc)/(a2-ab+bc-ac)+(a+3b)/(b-a)+(a+2c)/(a-c), substitute a = 1, b = 0.0211, and c = -0.0211 to simplify.
After substitution, perform the necessary calculations to evaluate the expression step by step.
Slope of (15,130) and (1,160)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (15, 130) amd (1, 160). Substitute:
[tex]m=\dfrac{160-130}{1-15}=\dfrac{30}{-14}=-\dfrac{15}{7}[/tex]
Hi there! :)
Step-by-step explanation:
[tex]Slope=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]
[tex]\frac{160-130}{1-15}=\frac{30}{-14}=\frac{30/2}{-14/2}=\frac{15}{-7}=-\frac{15}{7}[/tex]
Therefore, the slope is -15/7.
Final answer is -15/7.
Hope this helps!
Have a nice day! :)
:D
-Charlie
Thank you so much! :)
:D
Joshua receive a $70 gift card to use at a clothing store. He buys a pair of jeans for $36 and 8 pair of socks. He does not use the entire amount of the gift card. Write and solve an inequality to find s , the price of each pair of socks?
what equation describes a line passing through (-6,-5) that is perpendicular to a line described by y=-2/3x?
The equation of the line passing through (-6,-5) and perpendicular to y=-2/3x is y=(3/2)x+4.
Explanation:To find an equation of a line passing through the point (-6,-5) that is perpendicular to the line described by y=-2/3x, we first need to determine the slope of the perpendicular line. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of our line will be the negative reciprocal of -2/3, which is 3/2.
Now, using the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we can substitute our point (-6, -5) and slope 3/2 into the formula:
y - (-5) = (3/2)(x - (-6))
Simplifying this, we get:
y + 5 = (3/2)(x + 6)
y + 5 = (3/2)x + 9
Subtracting 5 from both sides, we get the final equation of the line:
y = (3/2)x + 4
A painting, square in shape, is placed in a wooden frame with width of 10% of the length of the side of the paining. The painting was enlarged by 10%. By what percent is the new frame bigger than the original frame if the width of the frame remains the same?
Final answer:
To find out by what percent the new frame is bigger than the original, the percentage increase is calculated as 8.33%. This is done by comparing the change in the total outer dimension of the framed painting after enlargement with the width of the frame unchanged.
Explanation:
If the original side length of the square painting is 's', the width of the frame is 10% of this length, so w = 0.10s. Now, if the painting was enlarged by 10%, the new side length of the painting is 1.10s. The width of the frame remains unchanged, so we only need to consider the change in the total outer dimension of the framed painting.
To find out by what percent the new frame is bigger than the original frame, we compare the change in the outer dimension of the frame to the original dimension. The total outer dimension of the original framed painting is s + 2w, while the total outer dimension of the enlarged framed painting is 1.10s + 2w.
Original frame outer dimension = s + 2(0.10s) = s + 0.20s = 1.20s
Enlarged frame outer dimension = 1.10s + 2(0.10s) = 1.10s + 0.20s = 1.30s
Percentage increase = ((1.30s - 1.20s) / 1.20s) × 100% = (0.10s / 1.20s) × 100% = 8.33%
Therefore, the new frame is 8.33% larger than the original frame.
Please help
What is a function? Can the following set of ordered pairs represent functions? Why or why not? A =(-4,-4), (2,0), (6,4) ,(10,2) B=(9,3), (9,-3), (4,2), (5,-2) C=(-3,7), (-2,7), (1,7),(0,7)
Answer:
A and C represent a function and B doesn't represent.
Step-by-step explanation:
A function is a relation that maps one output value of y for each input value of x.
A. Ordered pairs can be written as relation
-4→-4;2→0;6→4;10→2.Here each input value of x determines one output value of y and this set of ordered pairs represents function.
B. Ordered pairs can be written as relation
9→3;9→-3;4→2;5→-2.Here for input value x=9 there are 2 output values of y (y=3 or y=-3). This set of ordered pairs doesn't represent function.
C. Ordered pairs can be written as relation
-3→7;-2→7;1→7;0→7.There is exactly one y for each x, then this set of ordered pairs represents function.
Georgia spends $39 on gas each week. Approximately how much money does she spend on gas each week?
$30
$40
$50
$78
The correct answer should be B. $40
I'm guessing the question is asking for a precise amount..
Hope we thought this through correctly and you get it right!,
Davinia.
Using the triangle below, answer the following questions.
1. Would you use Law of Sines or Law of Cosines to find the missing measures.
2. Write out the formula for the Law used.
3. Explain in detail why you would use the chosen Law.
Step-by-step explanation:
Answer(1):
Law of Cosines.
Answer(2):
since side "c" is missing so we will write formula used for side "c"
[tex]c^2=a^2+b^2-2ab\cdot\cos\left(C\right)[/tex]
Answer(3):
First lets write both sine and cosine formulas:
Check the attached picture for the list of formulas:
From given picture we see that two angles A and B are missing. Also 1 side "c" is missing.
Sine formula uses two angles while cosine formula uses only one angles.
Hence cosine formula will be best choice to find the missing values.
What does it equal to and how
Answer:
The answer would me 15m
Step-by-step explanation:
1. you multiply both of them together in order to get the area
L x W = A
SOLVE FOR y
8x-12y=24
Answer:
y = 2/3 x -2
Step-by-step explanation:
8x-12y=24
The first step is to subtract 8x from each side
8x-8x-12y=-8x+24
-12y = -8x+24
Now we will divide each side by -12 to isolate y.
-12y/-12 = -8x/-12 +24/-12
y = 2/3 x -2
To solve for y in the equation 8x - 12y = 24, isolate the variable y by following several steps: move the constant term to the other side, move the term with the variable to one side, and divide both sides by the coefficient of y. The solution is y = (8x - 24) / 12.
To solve for y in the equation 8x - 12y = 24, we need to isolate the variable y. First, let's move the constant term to the other side of the equation by adding 12y to both sides:
8x - 12y + 12y = 24 + 12y
Simplifying the equation gives us:
8x = 24 + 12y
Next, let's move the term with the variable to one side and the constant term to the other side. We can do this by subtracting 24 from both sides:
8x - 24 = 24 + 12y - 24
Simplifying the equation further gives us:
8x - 24 = 12y
Finally, to solve for y, divide both sides of the equation by 12:
(8x - 24) / 12 = (12y) / 12
This simplifies to:
(8x - 24) / 12 = y
Therefore, y = (8x - 24) / 12.
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Larry uses his credit card to purchase a new video game system for $445.07 he can pay off off up to $200 per month the card has an annual rate of 13.6% compounded monthly how much total interest will he pay
Larry will pay a total interest of $45.07 when using his credit card to purchase the video game system.
To calculate the total interest Larry will pay when using his credit card to purchase a video game system for $445.07, with a monthly payment limit of $200 and an annual rate of 13.6% compounded monthly, we can follow these steps:
1. Calculate the total amount to be paid off by subtracting the monthly payment from the total purchase amount:
Total amount to be paid off = $445.07 - $200 = $245.07
2. Determine the number of months it will take to pay off the balance by dividing the total amount to be paid off by the monthly payment:
Number of months = $245.07 / $200 = approximately 1.22535 months (round up to the nearest whole month, which is 2 months)
3. Calculate the monthly interest rate by dividing the annual rate by 12 (since it's compounded monthly):
Monthly interest rate = 13.6% / 12 = 1.1333%
4. Use the formula for compound interest to find the total interest paid:
Total interest = Total amount paid - Total principal amount
Total principal amount = $445.07
Total amount paid = $200 * 2 = $400
Total interest = $400 - $445.07 = $45.07
Therefore, Larry will pay a total interest of $45.07 when using his credit card to purchase the video game system.
The multiplication of two or more quantities may be expressed as the ? of the same quantities.
The multiplication of two or more quantities is expressed as the "product" of those quantities. In dimensional analysis, multiplying a quantity by unit conversion factors that are equal to 1 does not change that quantity's value. This is a fundamental principle used in various fields to ensure unit consistency.
The multiplication of two or more quantities may be expressed as the product of the same quantities. When we multiply numbers and units, we apply the mathematical operation to both, resulting in a new number and a combined unit of measurement. For example, if we multiply 86 inches by some quantity in centimeters (cm), the number part gets multiplied to yield the numerical product, and the units inch (in) and centimeter (cm) are multiplied to give a unit product in inches times centimeters (in×cm).
Moreover, in dimensional analysis, we use conversion factors that equate to 1 to change from one unit to another without changing the quantity's value. For example, since 100 centimeters (cm) is equivalent to 1 meter (m), we can create a conversion factor of 1 by writing 100 cm over 1 m or vice versa. This concept is vital for ensuring the consistency of units when performing multiplications or divisions in various fields, including economics, engineering, and physics.
When dealing with expressions, multiplication can also be viewed as a reversal of the distributive law, transforming addition or subtraction statements into a set of multiples or factors that produce an equivalent value.
evaluate the expression for z=3 , 45z + 4,565 + 9,078 ÷ 89
Answer:
4802
Step-by-step explanation:
z=3 , 45z + 4,565 + 9,078 ÷ 89 = 45 * 3 + 4,565 + 9,078 ÷ 89 = 135 + 4,565 + 102 = 4802
10. You have two jobs. You earn $8 for each hour x that you work as a restaurant host and $6 for each hour y that you work as a hair washer. Your earnings for the pay period are $144.
a. Write an equation in standard form that models your earnings.
b. Find the x- and y-intercepts.
c. You worked 10 hours as a hair washer. How many hours did you work as a host?
Answer:
Step-by-step explanation:
The equation in standard form is:
8x + 6y = 144
To find the y-intercept, isolate y.
8x + 6y = 144
Subtract 8x from both sides.
6y = -8x + 144
Divide both sides by 6.
y = -4/3x + 24
From this, we know (0, 24) is the y-intercept because b, which in this case, is the y value for the y-intercept.
To find the x-intercept, input y as 0.
0 = -4/3x + 24
Subtract 24 from both sides.
-24 = -4/3x
Multiply both sides by 3/-4.
18 = x
The x -intercept is (18, 0).
Input 10 for y because that's how many hours you worked as a hair washer.
8x + 6(10) = 144
Simplify.
8x + 60 = 144
Subtract both sides by 60.
8x = 84
Divide both sides by 8.
x = 10.5
You worked 10.5 hours as a host.
Use a shortcut method of your choice to complete the multiplication problems.
a. 973 × 80
b. 56 × 2,000
c. 5.7 × 300
d. 0.46 × 50
Answer:
See below.
Step-by-step explanation:
a. 973 * 80
= 973 * 8 * 10
= 7784 * 10
= 77,840.
b. 56 * 2000
= 2*56 * 1000
= 112,000.
c. 5.7 * 300
= 5.7 * 3 * 100
= 17.1 * 100
= 1710.
d. 0.46 * 50
= (0.46 * 100) / 2
= 46 / 2
= 23.
Answer with Step-by-step explanation:
a. 973 × 80
= 973 × 8 × 10
= 7784 × 10
=77840
b. 56 × 2,000
=56 × 2 × 1000
=112 × 1000
=112000
c. 5.7 × 300
=5.7 × 3 × 100
=17.1 × 100
=1710
d. 0.46 × 50
=0.46 × 5 × 10
=2.3 × 10
=23
Please help simplify!!
Answer:
a) -5n9
Step-by-step explanation:
CAN U PLZZZZ MARK ME BRAINIEST!!!! I REALLY NEED IT
During the first year, ABC's stock starts at $100 and increases 100%. During the second year, its stock prices goes down 25% from its price at the end of the year. What is the price of the stock, in dollars, at the end of the second year?
Answer:
$150
Step-by-step explanation:
$100 + 100% = $200 in the first year
$200 - 25% = $150 in the second year
What is the ratio of 4 shirts for 32.00what is the ratio and percent of 4 shirts for 32.00
Answer:
the answer is $8 for every skirt
A line with a slope of -2 passes through the points (0,d) and (-8,9). What is the value of d?
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have m = -2 and the points (0, d) and (-8, 9). Substitute:
[tex]\dfrac{9-d}{-8-0}=-2\\\\\dfrac{9-d}{-8}=-2\qquad\text{multiply both sides by (-8)}\\\\9-d=16\qquad\text{subtract 9 from both sides}\\\\-d=7\qquad\text{change the signs}\\\\\boxed{d=-7}[/tex]
A construction worker took 1over8
of the bags of cement in a load and separated them into 4 equal piles.
What fraction of the entire load of bags was in each pile?
1over32
8over4
32over1
1over2
Answer:
1/32
Step-by-step explanation:
1/8 divided by 4 = .03125
.03125= 1/32
In triangle FGH, FH=10 units and GH=26 units. Which is the length of FG?
Final answer:
To find the length of FG in triangle FGH, we can use the Pythagorean Theorem. By substituting the given values into the formula and solving for FG, we find that FG is approximately 27.9 units.
Explanation:
To find the length of FG, we can use the Pythagorean Theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
In this case, FH and GH are the two sides of the right triangle FGH, and FG is the hypotenuse. So we have FH² + GH²= FG².
Substituting the given values, we have 10² + 26² = FG². Simplifying this equation, we get 100 + 676 = FG². Adding the numbers gives us 776 = FG². And taking the square root on both sides, we find that FG ≈ 27.9 units.
Find the product and simplify.
5/16 of 24/15
Answer:
1/2
Step-by-step explanation:
First, write out the product. Then, reduce as far as possible:
5 24 5(1)(4)(6)
----- * ------- = --------------- Here, the 5s cancel, and so we get:
16 15 5(3)(4)(4)
4(6)
----------
3(4)(4)
Here, the 4 in the numerator cancels out one of the 4s in the denominator:
6
------
12
and this last result reduces to 1/2.
[tex]Solution, \frac{5}{16}\cdot \frac{24}{15}=\frac{1}{2}\quad \left(\mathrm{Decimal:\quad }\:0.5\right)[/tex]
[tex]Steps:[/tex]
[tex]\frac{5}{16}\cdot \frac{24}{15}[/tex]
[tex]\frac{24}{15}=\frac{8}{5},\\\frac{8}{5}\cdot \frac{5}{16}[/tex]
[tex]\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d},\\\frac{5\cdot \:8}{16\cdot \:5}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:5,\\}\\\frac{8}{16}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:8,\\\frac{1}{2}[/tex]
[tex]\mathrm{The\:Correct\:Answer\:is\:\frac{1}{2}}[/tex]
[tex]\mathrm{Hope\:This\:Helps!!!}[/tex]
[tex]\mathrm{Please\:Mark\:Brainliest!!!}[/tex]
[tex]\mathrm{-Austint1414}[/tex]
if f(1) = -5 and f(n) = f(n-1) +7, find the first four terms and the common difference of the sequence
Answer:
- 5, 2, 9, 16 and d = + 7
Step-by-step explanation:
to obtain the first four terms substitute n = 2, 3, 4 into the recursive formula
f(1) = - 5 ← given
f(2) = f(1) + 7 = - 5 + 7 = 2
f(3) = f(2) + 7 = 2 + 7 = 9
f(4) = f(3) + 7 = 9 + 7 = 16
common difference d = 16 - 9 = 9 - 2 = 2 - (- 5) = 7
problem 1: the longest book toshi had read was 304 pages. she just finished kira-kira by cynthia kadohata, which is 256 pages. how much longer was the longest book toshi read than kira-kira?
Answer:
48
Step-by-step explanation:
304 - 256 equals 48
Which option is is an example of expository writing?
Answer: Your answer would be "B" Hope this helps you!
Please HELP!
How do I factorise 2x^2 - 11x -6x
please include working
Thanks!
Answer:
x(2x-17)
Step-by-step explanation:
2x^2 -11x-6x
2x^2-17x
x is common
x(2x-17)
Answer:
x(2x-17)
Step-by-step explanation:
[tex]2x^2-11x-6x\\2x^2-17x\\x(2x-17)[/tex]
Steps:
Combine Like Terms (-11x and -6x)
Factor out the common term (x)