Answer: 4n + 12 = 3d
Step-by-step explanation:
The equation representing "If the numerator of a fraction is increased by 3, the fraction becomes 3/4" is 4(x + 3) = 3y. This, alongside the second condition of the denominator decreased by 7 leading to the fraction becoming 1, provides two equations that can be solved for the original fraction.
Explanation:To represent the situation "If the numerator of a fraction is increased by 3, the fraction becomes 3/4," we can use the variable x for the numerator and y for the denominator of the original fraction. Therefore, the equation would be (x + 3)/y = 3/4. Applying the cross-product rule, we multiply each side of the fraction by the denominator on the other side, leading to 4(x + 3) = 3y. Simplified, this equation is 4x + 12 = 3y, which helps us solve for the original fraction along with the other given condition that reducing the denominator by 7 makes the fraction equal to 1. So, the second condition can be written as x/(y - 7) = 1. These two equations together can be solved simultaneously to find the values of x and y.
davis donates 4/13 of his paycheck to his favorite charity. if he donated $26.80 what is the amount of his paycheck?
1. The graph shows the miles per gallon of gasoline a car uses on a trip.
What does the rate of change represent in this situation?
Select from the drop-down menu to correctly complete the sentence.
The rate of change represents
OPTIONS:
a. the number of miles traveled for every one gallon of gas used
b. the number of gallons of gas used for every 1 mile
c. the distance a car travels every hour
GRAPH:
7. Which ordered pairs match the table?
x 0 1 2 1 3
y 2 2 3 4 1
(0, 2), (1, 2), (2, 3), (1, 4), (3, 1)
(0, 2), (0, 2), (2, 2), (2, 3), (2, 4)
(1, 2), (1, 1), (2, 0), (0, 4), (2, 1)
(2, 0), (2, 1), (3, 2), (4, 1), (1, 3)
The rate of change in miles per gallon for a car trip represents the number of miles the car can travel per gallon of gasoline used. The ordered pairs (0, 2), (1, 2), (2, 3), (1, 4), (3, 1) accurately correspond with the values provided in the given table.
Explanation:In the given situation, the rate of change of a graph showing the miles per gallon of gasoline a car uses on a trip would represent the number of miles traveled for every one gallon of gas used. This is because the rate of change in this context quantifies how much distance can be covered (in miles) using one unit of gasoline (in gallon). For instance, if the rate of change is 30, it indicates that the car can travel 30 miles using just one gallon of gasoline.
For the second part of your question, matching the ordered pairs with the table, the correct match would be (0, 2), (1, 2), (2, 3), (1, 4), (3, 1). This set of pairs corresponds accurately to the values given in your table for x and y. To understand this, you can match each x value with its corresponding y value in the table. For example, when x is 0, y is 2 - and this gives you the ordered pair (0, 2).
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The table shows the heights in inches of trees after they have been planted. Determine the equation which relates x and y.
Height In Pot, x | Height Without Pot, y
30 | 18
36 | 24
42 | 30
48 | 36
A. y = x - 6
B. y = x - 10
C. y = x - 12
D. y = x + 6
The graph of an absolute value function contains the points (1, 2), (0, 0), and (–1, 2). Shawn thinks the function this graph represents is f(x) = 2|–x|. Brielle thinks the function this graph represents is f(x) = 2|x|. Determine who is correct and explain why.
Answer:
The absolute value parent function is symmetric with respect to the y-axis.
The graphs of f(x) = 2|–x| and f(x) = 2|x| are identical because the absolute value of negative x is a reflection across the y-axis.
If you substitute the three given points into both functions, they produce true statements.
Step-by-step explanation:
When the polynomial in P(x) is divided by (x + a), the remainder equals P(a).
A. True
B. False
According to Remainder Theorem for the polynomials, for every polynomial P(x) there exist such polynomials G(x) and R(x), that [tex] P(x)=(x\pm a)G(x)+R(x) [/tex].
When the polynomial in P(x) is divided by (x + a), then there exist such polynomials G(x) and R(x), that P(x)=(x+a)G(x)+R(x). Note that for x=-a:
Answer:
false
Step-by-step explanation:
Name an angle adjacent to ∠DGE
Choices:
∠FGI
∠EGH
∠HGJ
Answer:
The answer is ∠EGH.
Step-by-step explanation:
In order to determine the correct option, we have to know about adjacent angle.
Two angles are adjacent when they have a common side and vertex (corner point). So in this case, the adjacent angle must have GE or DG common side and the G vertex.
According to the options, the adjacent angle to ∠DGE is:
∠EGH
The other options are not adjacent angles because they do not have a common side.
Finally the correct option is ∠EGH.
12 roses cost 18.96 how much is 5 roses
Which expressions are equivalent to the one below? Check all that apply.
10x
A. 50x/5x
B. 10 • 10x - 1
C. 10 • 10x + 1
D. 50x/5
E. (50/5)x
F. x5
The expressions equivalent to 10x are 50x/5 and (50/5)x as they both simplify to 10x. The other options do not simplify to 10x. Hence option D and E are correct.
To determine which expressions are equivalent to 10x, we need to simplify each option. Let us consider the options one by one:
A. 50x/5xTo solve this a simple division is required.
⇒ (50x/5x)= 10÷(1) = 10
⇒ 10 is not equivalent to 10x.
B. 10 • 10x - 1⇒ 100x - 10
This is not equivalent to 10x.
C. 10 • 10x + 1⇒ 10 • 10x • 10 = 100x+10 (Not equivalent to 10x)
D. 50x/5⇒ (50/5)x = 10x (Equivalent to 10x)
E. (50/5)x = 10x (Equivalent to 10x)F. x⁵ (Not equivalent to 10x)The correct answers are D and E, both of which simplify to 10x.
The regular selling price of the recliner at furniture depot is $289 the markdown room is 33% what is this sale price
Given the table of candy distribution below. find P(Not blue). the probability of selecting anything but an blue candy at random from a large bag.
Red=0.13 Orange=0.20 Yellow=? Green=0.16 Blue=0.24 Brown=0.13
Since, probability of selecting a blue candy and anything but a blue candy are mutually exclusive events, the probability of selecting anything but an blue candy at random from a large bag = P(Not blue) = 0.76
What are mutually exclusive events?In logic and probability theory, two events are mutually exclusive or disjoint if they cannot both occur at the same time.
P(Blue) + P(Not blue) = 1 (mutually exclusive events)
0.24 + P(Not blue) = 1
P(Not blue) = 1 - 0.24 = 0.76
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Heather is collecting beanbag animals. she started her collection with six beanbag animals just eight weeks ago. during each of those 8 weeks, she has been given two additional beanbag animals. how many does she have at the end of the 8th week?
what is 1/4 divided by 5?
1/4 divided by 5 results into '0.05'
Given that we need to find 1/4 divided by 5
Thus let the required answer be denoted as "A"
Thus using basic definitions of divisions and fractions we can find out the resultant value
[tex]A=\frac{\frac{1}{4} }{5} \\A=\frac{1}{4*5} \\A=\frac{1}{20}[/tex]
Thus '1/20' is the required answer
Now the resultant value can also be simplified to get a decimal value
[tex]A=\frac{1}{20} \\A=\frac{1}{2*10} \\A=\frac{1}{2} *\frac{1}{10} \\A=0.5*0.1\\A=0.05[/tex]
Thus '0.05' is the final answer
What is 37/15 as a mixed numbers?
What is half of 1 and 1/4 cups?
The value of the phrase is 5/8.
What are arithmetic operators?A subfield of mathematics known as arithmetic operations deals with the study and application of numbers to all other subfields of mathematics. Operations like addition, subtraction, multiplication, and division make up the bulk of them.
We use these fundamental mathematical operations every day (plus, minus, and). Arithmetic operations are used in every aspect of our lives, whether we need to figure out the annual budget or divide something equally among several people.
Given a phrase half of 1 and 1/4 cups,
1 and 1/4 = 1 + 1/4 = 5/4
and half of 5/4 is
1/2(5/4)
1/2 x 5/4 = 5/8
Hence the value is 5/8.
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let Ax=b be any consistent system of linear equations, and let x1 be a fixed solution. show that every solution to the system can be written in form x=x1+x2, where x0 is a solution to Ax=0. show that every matrix of this form is a solution.
...?
h(x)=(g o f)(x)=1/(x+3)^2 which of the fallowing could be a possible decomposition of h(x)? A. f(x)=1/x^2;g(x)=x+3 B. f(x)=x+3; g(x)=1/x^2 C.f(x)=x^2; g(x)=x+3 D. f(x)=1/x;g(x)=x+3
...?
according to poll for an upcoming school board election is 40% of voters are likely to vote for the incumbent. The polls show a margin of error of +-3 percent points.
Kelly invested $1,500 in the stock market on january 1. she lost 1/3 of it by the end of january and 2/5 of the remaining amount by the end of february. how much did she have left?
The population of a town grows exponentially. After 1 year, the population is 34,560. After 2 years, the population is 37,325. Which equation can be used to predict, y, the number of people living in the town after x years? (Round population values to the nearest whole number.)
2614/7=6(47/6b+11/6)
solve x2+10x+21=0 ...?
The original price is 50. the discount is 15%. what is the new price
Given that t is the median of the numbers 32, 64, 22, t, 41, 22, and 78, what is the lowest possible value of t?
Final answer:
The lowest possible value for t as the median of the numbers 32, 64, 22, t, 41, 22, and 78 is 32. This value maintains the order when the numbers are arranged from lowest to highest for t to be the median.
Explanation:
To find the lowest possible value for t given that it is the median of the numbers 32, 64, 22, t, 41, 22, and 78, we first need to arrange the numbers in ascending order.
Since there are seven numbers, the median would be the fourth number when sorted.
To ensure t is the lowest possible median, we sort the remaining numbers excluding t. Thus, we have:
22, 22, 32, 41, 64, 78
The third value is 32, and the fifth value is 41, so for t to be the median, t must be greater than or equal to 32 but less than or equal to 41.
However, since we are looking for the lowest possible value of t, t would be 32, as this is the lowest it can be while still being the median of the sorted list.
A ball is thrown at a 30 degree angle above the horizontal with a speed of 10 ft/s. After 0.50s the horizontal component of it's velocity will be ____? ...?
The horizontal component of the velocity of a ball thrown at a 30 degree angle above the horizontal with an initial speed of 10 ft/s will remain approximately 8.66 ft/s after 0.50s, assuming no air resistance.
Explanation:A ball is thrown at a 30 degree angle above the horizontal with a speed of 10 ft/s. After 0.50s the horizontal component of its velocity will remain the same, assuming no air resistance, because horizontal velocity in projectile motion is constant if air resistance is ignored. The vertical component will change due to gravity, but that does not affect the horizontal component.
To find the horizontal component of the velocity, we can use the cosine of the launch angle:
Horizontal velocity (v_x) = initial speed * cos(launch angle)
So, v_x = 10 ft/s * cos(30 degrees)
= 10 ft/s * (√3/2)
≈ 8.66 ft/s
As there is no horizontal acceleration in ideal projectile motion, after 0.50s, the horizontal component of the ball's velocity will still be approximately 8.66 ft/s.
Determine which two values the following expression is between.
√37
A. 7 and 8
B. 5 and 6
C. 4 and 5
Answer:
none there would be an answer if it was 3√7
Step-by-step explanation:
what is the quotient when -3^3 +5x+14 is divided by x-2? pleas hurry
The quotient is -3x² + 3x + 8.
To find the quotient when [tex]\(-3x^3 + 5x + 14\)[/tex] is divided by x - 2, we can use polynomial long division.
The dividend is [tex]\(-3x^3 + 0x^2 + 5x + 14\)[/tex] (since there is no [tex]\(x^2\)[/tex] term) and the divisor is x - 2.
1. Divide the first term of the dividend by the first term of the divisor: [tex]\(-3x^3 \div x = -3x^2\)[/tex].
2. Multiply the divisor by the result of step 1: [tex]\((-3x^2)(x - 2) = -3x^3 + 6x^2\).[/tex]
3. Subtract the result of step 2 from the dividend: [tex]\((-3x^3 + 0x^2 + 5x + 14) - (-3x^3 + 6x^2) = -6x^2 + 5x + 14\).[/tex]
4. Repeat the process with the new dividend [tex]\(-6x^2 + 5x + 14\)[/tex].
Continuing the division process, we find the quotient:
[tex]\[ \frac{-3x^3 + 5x + 14}{x - 2} = -3x^2 + 3x + 8 \][/tex]
So, the quotient is -3x² + 3x + 8.
Write the product of 7x7x7x7 in exponential form.
Answer:
7^4
Step-by-step explanation:
Every week (w) Sandra will save $10. Which algebraic expression could Sandra use to calculate how much money she has saved after any number of weeks
Nina bought a sweater for 30% off of the original price. The original price was $56. How much did Nina pay for the sweater? Show your work.
Summer clothes are on sale starting September 1st. A swimsuit is on sale for 40% off the regular selling price of $55.00. What is the markdown to the nearest cent?