Answer: The inequality that can be used to determine the maximum number of days Alyssa can afford to rent for while staying within her budget is:
43d + 0.1(275) <= 100
Step-by-step explanation: The rental car company charges $43 per day to rent a car and $0.10 for every mile driven.
Alyssa wants to rent a car for d days, and she plans to drive 275 miles.
The cost of renting the car for d days is 43d, and the cost of driving 275 miles is 0.1(275)
To determine the maximum number of days Alyssa can afford to rent for while staying within her budget, we can write the inequality:
43d + 0.1(275) <= 100
This inequality represents the total cost of renting the car and the cost of driving, which should be less than or equal to $100 (Alyssa's budget)
On solving the inequality we can determine the maximum days Alyssa can afford.
You manage an ice cream factory that makes two flavors: Creamy Vanilla and Continental Mocha. Into each quart of Creamy Vanilla go 2 eggs and 3 cups of cream. Into each quart of Continental Mocha go 1 egg and 3 cups of cream. You have in stock 500 eggs and 1,050 cups of cream. How many quarts of each flavor should you make in order to use up all the eggs and cream?
Creamy Vanilla
qt
Continental Mocha
qt
If I manage an ice cream factory that makes two flavors: Creamy Vanilla and Continental Mocha. Into each quart of Creamy Vanilla go 2 eggs and 3 cups of cream. Into each quart of Continental Mocha go 1 egg and 3 cups of cream. Where I have in stock 500 eggs and 1,050 cups of cream. The number of quarts of each flavor that I would make in order to use up all the eggs and cream is: 150 quarts of Vanilla and 200 Quarts of Mocha.
Let x and y be the number of Quarts of Vanilla and Mocha respectively.
The total number of eggs used is given as:
2x+y = 500
And the total cups of cream is:
3x + 3y = 1050
Removing the second equation from three times the first, we get:
3(2x + y) - (3x + 3y) = 3(500) -1050
6x + 3y - 3x - 3y = 1500 - 1050
⇒ 3x = 450
⇒ x = 450/3
x = 150
By substituting x back in tot he first equation we find:
2x+y = 500
2 (150) + y = 500
300 + y = 500
y = 500 - 300
y = 200.
Thus, to use up al the eggs and cream, 150 quarts of Vanilla and 200 quarts of Mocha should be produced.
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-
2 x
3
5
сл
6
The volume of a cuboid is 364cm³.
The length is 7cm and the width is 13cm.
Work out the height of the cuboid.
8
The height of the cuboid is 4 cm
What is a cuboid?
A cuboid is a solid shape or a three-dimensional shape in geometry. A cuboid is a convex polyhedron that has eight vertices, twelve edges, and six rectangular faces. A rectangular prism is another name for a cuboid. A cube is an object with six square faces on a cuboid.
volume of a cuboid = l *w*h
where, l= length, w=width, h= height
=> 364 = 7*13*h
=> h=364/(7*13) = 364/91
=> h= 4 cm
Thus, the height of the cuboid is 4 cm
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What is the correct solution set for the following graph?
{ } or empty set
{point in Quadrant II}
{point in Quadrant IV}
{infinite set of points on the line}
The correct solution set for the given graph include the following: D. {infinite set of points on the line}.
What is a quadrant?In Mathematics, a quadrant can be defined as the area that is occupied by the values on the x-coordinate (x-axis) and y-coordinate (y-axis) of a cartesian coordinate.
This ultimately implies that, there are four (4) major quadrants in any graph and these include the following:
Quadrant IQuadrant IIQuadrant IIIQuadrant IVGenerally speaking, the solution set of a graph simply refers to all of the points that lie on its line. By critically observing the graph of lines a and b, we can reasonably infer and logically deduce that they both have the same slope, solution set, as well as increasing and decreasing infinitely.
In this context, the correct solution set lies in both Quadrant II and Quadrant III because both lines move towards negative and positive infinity i.e [-∞, ∞].
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0.15 | 0.3 | 1 | 2 | 2.7 | 5.4 | 6.4 | ? | ?
A 12.2, 12.9
B 9.5, 13.6
C 7.1, 8.6
D 6.8, 7.5
The next two numbers on the number pattern will be 12.2, 12.9 the correct option is A
How to obtain the next two points on the number pattern?To obtain the next two points on the number pattern, first we must identify what is the meaning of pattern.
The pattern is given as follows;
The double of an amount is calculated.
Now 0.7 is increased to double the amount, and we return to step 1, doubling the value.
The final term is 6.1, which is obtained after the addition of 0.7 to 5.4. Double 6.1 is obtained multiplying the number by 2, as follows;
2 x 6.1 = 12.2.
Then the number obtained after 0.7 is added to 12.2 is given as follows;
0.7 + 12.2 = 12.9.
It implies that the correct answer of the given number pattern is 12.2, 12.9
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When a number is decreased by 10% of itself, the result is 99. What is the number?
Answer:990
Step-by-step explanation:10%=0.1
X*0.1=99
99/0.1=990
x=990
Erica earned a total of 67,160 last year from her two jobs. The amount she earned from her job at the store was 1,550 more than three times the amount she earned from her job at the college. How much did she earn (in dollars) from her job at the college
Answer:
Let's call the amount Erica earned from her job at the college "x". We know that:
Total income = $67,160
Income from store = 3x + 1,550
Total income = Income from store + Income from college
67,160 = 3x + 1,550 + x
67,160 = 4x + 1,550
Now we can solve for x:
67,160 - 1,550 = 4x
65,610 = 4x
x = 16,402.5
Erica earned $16,402.50 from her job at the college.
Simplify the following expression.
4√72
O A. 6√24
B.
144√6
OC. 24√6
D. 24√/2
O D.
The expression 4√72 can be simplified by first taking the square root of both sides, which gives us 2√72. Then, we can factor out a 6 from both sides, which gives us 24√6. Therefore, the simplified expression is 24√6.
What is expression?Expression is the process of conveying one’s thoughts, emotions, ideas, and beliefs through speech, writing, art, or any other form of communication. Expression is a form of communication that allows people to express themselves in a way that is meaningful and personal to them. It is a powerful way for individuals to express their thoughts, feelings, and opinions without fear of judgement or criticism. Expression is an important part of self-expression, and it can be used to connect with others through shared experiences, to create a sense of community, and to grow and learn from one another. Expression is an invaluable tool for self-expression, creativity, and communication.
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Quick Help please
I don’t understand please answer all four.
Answer:
To find f(-3), substitute -3 for x in the equation for f(x):
f(-3) = 2(-3) + 5 = -6 + 5 = -1
Answer:
f(-3) = -1
To find g(x) - h(x), first substitute x into both g(x) and h(x) and then subtract h(x) from g(x):
g(x) - h(x) = -3x^2 + 2x - 6 - (-4 - x) = -3x^2 + 3x - 2
Answer:
g(x) - h(x) = -3x^2 + 3x - 2
To solve for x when f(x) = h(x), first substitute x into both f(x) and h(x), and then solve for x:
2x + 5 = -4 - x
3x = -9
x = -3
Answer:
x = -3
To determine which of the functions are linear, we need to look at the degree of the polynomials in each function. Linear functions have a degree of 1, while non-linear functions have a degree greater than 1.
f(x) = 2x + 5 is linear because it has a degree of 1
g(x) = -3x^2 + 2x - 6 is non-linear because it has a degree of 2
h(x) = -4 - x is linear because it has a degree of 1
Answer:
f(x) and h(x) are linear, while g(x) is non-linear.
3. Line DG is the perpendicular bisector of chord El.
EF = 7, EI = 9.5, and DG = 1.8.
What is the diameter of the circle? Show your work.
The diameter of the circle would be given as = 10
What is a diameter?Diameter is defined as the length of a line through the center that touches two points on the edge of the circle.
The diameter of the circle can be found through finding first the radius of the circle.
The radius of the circle is half of the diameter. it is the line DI which is also the longer line of the triangle DGI.
Using the Pythagorean formula c² = a² + b²
The lines that represents ;
a= DG
b= EI/2 = 4.8
C= DI = ?
C² = DI
a² = 1.8²
b² = (9.5/2)² = 4.8²
c² = 2.24 + 23.04 = 25.28
C =√25.28
C = 5
Therefore the diameter of the circle = 5×2 = 10
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Write and solve an equation.
A drink and 7 pizzas cost $94.25. The cost of the drink was $1.50. What was the cost, c, of one pizza?
Answer:
13.25
Step-by-step explanation:
1. you have to subract the cost of the drink:
94.25-1.50=92.75
2.you have to divide to get the individual cost of pizzas by doing
92.75÷7=13.25
so therefore your answer is 13.25 per pizza
It is estimated that wireless soil monitors could save up to 6 trillion gallons of
water per year by reporting precise information needed to irrigate crops
properly. Using this data, express the number of gallons of water saved in two
years, in scientific notation.
Hint:
1Million=6 zeros
1billion=9 zeros
1trillion=12 zeros
____x10____
Using scientific notation, the number of gallons of water saved in two years by the wireless soil monitors is 1.2 x 10^12.
What is scientific notation?Scientific notation is a shorthand way of writing very large numbers or very small numbers in a simpler form.
The parts of a scientific notation are coefficient, base, and exponent.
We state that a number is written in standard notation when the number is between 1 and 10 and it is multiplied by a power of 10.
The number of gallons of water per year saved by wireless soil monitors = 6 trillion
The number of gallons of water saved by wireless soil monitors in 2 years = 12 trillion
In scientific notation, 12 trillion = 1.2 x 10^12.
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What is the equation of this line? y>1/2x−3 y<1/2x−3 y>2x−3 y<2x−3
Answer:
The equation of this line is y>1/2x-3
Step-by-step explanation:
This is an inequality equation that represents a line that is greater than 1/2x-3. The inequality symbol ">" indicates that all the y-coordinates that are on the same side of the line as the y-axis are greater than 1/2x-3.
In other words, all the points that lie above the line will satisfy the inequality, while all the points that lie below the line will not.
It's worth noting that the line y<1/2x-3 represents the same line but the inequality symbol "<" indicates that all the y-coordinates that are on the same side of the line as the x-axis are less than 1/2x-3.
y>2x-3 and y<2x-3 represent different lines, the first one represents a line with a slope of 2 and the second one represents a line with a slope of -2.
Find the measure of < 6.
Answer:
Angle 6 = 70
Step-by-step explanation: Using vertical angles if you look across from angle 6 you would see the angle of 70 degrees which means they are equal because they're across from each other.
Serena added 10 grams of sugar to 20 grams of water.
She made
grams of
%
sugar syrup.
Serena added 10 grams of sugar to 20 grams of water to make a sugar syrup.
The total amount of sugar syrup made is the sum of the weight of sugar and the weight of water, so:
10 grams (sugar) + 20 grams (water) = 30 grams (sugar syrup)
To find the percentage of sugar in the syrup, we can divide the weight of the sugar by the total weight of the syrup and multiply by 100.
% sugar = (weight of sugar / total weight of syrup) * 100
% sugar = (10 / 30) * 100 = 33.333 %
So the sugar syrup made by Serena contains 33.333% sugar by weight.
It's important to note that the sugar syrup doesn't have only sugar, it also have water, the sugar is just the main ingredient and the percentage of sugar is just the proportion of sugar within the syrup.
Answer and explain please
The coordinates of the triangle before and after dilation is
preimage image
R (6, 9) R' (2, 3)
S (3, -9) S' (1, -3)
T (-6, -3) T' (-2, -1)
The rule that best describes the transformation is
(x, y) → (1/3 x, 1/3 y)How to find the coordinates of the imageDilation is a method of transformation that magnify or shrink the preimage depending on the scale factor
The transformation rule for dilation is as follows
(x, y) for a scale factor of r → (rx, ry)
following similar procedure for the given problem we have
preimage image
R (6, 9) → (1/3 * 6, 1/3 * 9) → R' (2, 3)
S (3, -9) → (1/3 * 3, 1/3 * -9) → S' (1, -3)
T (-6, -3) → (1/3 * -6, 1/3 * -3) → T' (-2, -1)
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The debt-to-assets ratio formula is: Debt-to-assets ratio = total liabilities/total assets. If your total liabilities are $3,228 and your total assets are $5,091. What is your debt-to-assets ratio?
The debts to assets ratio is 0.63
How to calculate the debts to assets ratio ?The formula for calculating debts to assets ratio is
total liabilities/total assets
The total liabilities is $3,228
The total assets is $5,091
Therefore the debts to assets ratio is
3228/5091
= 0.63
Hence the debts to assets ratio is 0.63
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There are 135 people in a sport centre.
73 people use the gym.
73 people use the swimming pool.
67 people use the track.
36 people use the gym and the pool.
35 people use the pool and the track.
32 people use the gym and the track.
14 people use all three facilities.
How many people use exactly one of these facilities?
The number of people that uses exactly one of gym, swimming pool and track is 49people
What is set?A set is the mathematical model for a collection of different things. A set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
The number of people that uses gym= 73- ( 32-14+ 36-14 + 14)
73-(18+22+14)
73 - (54) = 19 people
The number of people that use pool only = 73-(36-14+35-14+14)
= 73-(22+21+14)
= 73-(57)
= 16people
The number of people that use track only = 67-(32-14+35-14+14)
= 67-(18+21+14)
= 67-53
= 14people
therefore the number of people that use one of the facility is 19+16+14 = 49people
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Match the image to the scale factor from FG to F'G'.
Image 1
F
F
Image 2
F'
F
Image 3
F'
F
F
Image 4
F
F
Image 5
F'
12
12
8
6
18
12
12
12
12
24
G'
G
G
G'
G
G'
G
F
The scale factor for each of the dilation is given as -
K₁ = 18/12 = 3/2K₂ = 8/12 = 2/3K₃ = 12/12 = 1K₄ = 6/12 = 1/2What is scale factor?Direct variation of a quantity {y} with respect quantity {x} means that the value of {y} increases as the the value of {x} increases. Mathematically -
y = Kx
K = y/x
where -
{K} is scale factor. It also tells by how many times is {y}, greater than {x}.
Given is a line segment and its dilated image.
The scale factor is given by -
K = y/x
[1] -
K₁ = 18/12 = 3/2
[2] -
K₂ = 8/12 = 2/3
[3] -
K₃ = 12/12 = 1
[4] -
K₄ = 6/12 = 1/2
Therefore, the scale factor for each of the dilation is given as -
K₁ = 18/12 = 3/2K₂ = 8/12 = 2/3K₃ = 12/12 = 1K₄ = 6/12 = 1/2To solve more questions on direct variation, visit the link below -
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Consider parallelogram JKLM below.
Use the information given in the figure to find mLNJK, x, and mLNKJ.
K
N
4x - 3
13
AL
50°
42°
M
Answer:
∠NJK = 50°x = 4∠NKJ = 42°Step-by-step explanation:
You want a couple of interior angles and the value of x given the parallelogram in the figure.
AnglesThe diagonals of a parallelogram bisect each other, and divide the figure into two pairs of congruent triangles. Here, the congruent triangles of interest are ...
∆NKJ≅∆NML
In these triangles, that means ...
∠J ≅ ∠L = 50° = ∠NJK
∠K ≅ ∠M = 42° = ∠NKJ
SegmentsThe halves of diagonal JL are congruent, so we have ...
4x -3 = 13
4x = 16 . . . . . . . . add 3
x = 4 . . . . . . . . . divide by 4
What is AE?
Enter you answer in the box.
Answer:It means almost everywhere
Step-by-step explanation:
The value of AE is, 10 units.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Here, From the given figure we can see that two triangle ABE and DEC are similar.
Therefore, The ratio of corresponding sides are equal.
Hence, From figure we get,
⇒ ED/AE = CD/AB
Substitute all the values, we get;
⇒ (x + 6)/(2x + 6) = 8/10
⇒ 10(x + 6) = 8(2x + 6)
⇒ 10x + 60 = 16x + 48
⇒ 16x - 10x = 60 - 48
⇒ 6x = 12
⇒ x = 2
So, The value of AE is,
AE = 2x + 6
AE = = (2 × 2 ) + 6
AE = 4 + 6
AE = 10
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The range of the function f (x) =√x^2−4
is (−∞, −1) ∪ (1, ∞). To explain
why this is true, you have to do two things:
(a) Show that if f (x) = y for some x, then either y > 1 or y < −1.
(b) Show that if y < −1 or y > 1, then the equation f (x) = y has a solution in x.
The solutions for the given function are (-2, 0) and (2, 0).
What is range of a function?The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
The given function is f(x)=√(x²-4).
Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.
Domain: (−∞,−2]∪[2,∞),{x|x≤−2,x≥2}
Range: [0,∞),{y|y≥0}
Therefore, the solutions for the given function are (-2, 0) and (2, 0).
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Recall that during the 2013-2014 academic year, the school board in Wichita Falls, Texas, began planning for new and renovated high school facilities. A committee of community members was formed to explore various options for a bond proposal to pay for the plan¹. The committee presented three options to the board of trustees
Plan A has the majority of votes.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given this, the school board in Wichita Falls, Texas, began planning for new and renovated high school facilities.
There is a total of 3 + 3 +1 = 7 votesthus we can say the total number of members who voted is 7.
For the majority, more than 50% of votes are required. In this case, 50% of 7 = 3.5Therefore, 4 votes are required for the majority.
Here, no plan received 4 Ist choice votes.Therefore, there is no plan that receives a majority of votes.
In the instant run-off method, the candidate with the lowest 1st choice votes is eliminated and his votes are transferred to the candidate of the next choice. This process continues till a majority winner is found. In the initial table:1st choice votes to A=3
1 choice votes to B=3 1st choice votes to C=1
So, C is to be eliminated and his 1 vote is to be transferred to A (as A is the next choice after C in column 3 of the table)
First choice vote to A = 3 + 1 = 4
First choice vote to B = 3
Since A gets the majority of votes A is the winner
Thus, Plan A has the majority of votes.
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Complete question:
Gershon Smudgenick had 4 pounds of broccoli sprouts. He
went to Joe's Discount Bonanza and got some more. He ended up
with 11 pounds of broccoli sprouts. What is the fractional increase
in Gershon's broccoli sprouts? What is the percent increase in
Gershon's broccoli sprouts?
Answer: The fractional increase in Gershon's broccoli sprouts is 7/4 and the percent increase in Gershon's broccoli sprouts is 175%.
Step-by-step explanation:
The fractional increase in Gershon's broccoli sprouts is the difference between the final amount and the initial amount divided by the initial amount.
So in this case, it would be (11 - 4) / 4 = 7 / 4.
The percent increase in Gershon's broccoli sprouts is the fractional increase multiplied by 100.
So, it would be (7 / 4) * 100 = 175%.
It means Gershon's broccoli sprouts increased by 175% from 4 pounds to 11 pounds.
Please answer:
The fraction 1/7 is equal to the repeating decimal 0.142857 . Which digit occurs in the 2023rd place after the decimal point?
The digit that occurs in the 2023rd place after the decimal point is; 1
How to Interpret Repeating Decimals?A repeating decimal has another name called a recurring decimal, and it is defined as a number whose decimal representation eventually becomes periodic
Now, we are given the fraction as 1/7 which is a repeating decimal because its decimal representation is periodic for every 6 decimal units as shown below; 1/7 = 0.142857142857...
Now, the digits are repeated after every 6 digits and as such to get the digit in the 2023rd place;
2023/7 = 337 remainder 1
Thus, the sequence 142857 would be repeated 337 times after which the next digit which is the 2023rd digit will be 1.
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Is 6 inches in 10 seconds proportional to 12 inches in 60 seconds?
Answer: No
Step-by-step explanation:
to be proportional, both numbers have to increase by the same number
because if u multiply 6 by 2 you get 12, but when you multiply 10 by 2 you get 20, not 60 it would be proportional if you said 6 and 10 in to 12 and 20 in
3) The area and
diagonal of a
Kite are 144cm and 8cm respectively, find the other diagonal
Answer:
Step-by-step explanation:
Let the other diagonal be d.
From the Pythagorean theorem,
d2 = 82 + 1442
d2 = 64 + 20736
d2 = 20800
d = √20800
d = 144 cm
After playing 5 games, you have 33 credits left. You play 4 more games and have 21 credits left. Write an equation that represents the number of credits y on the card after x games
Answer:
5x=33y,4x=21y I hope this is helpful
5. An engineer typically makes 50% more than a school teacher. What is the engineer's income as a percentage of the school teacher's income. How many times as large as the teacher's income is the engineer's?
Answer:
If an engineer typically makes 50% more than a school teacher, then the engineer's income is 150% of the school teacher's income. Because 100% represents the school teacher's income, and 50% represents the engineer's additional income, the sum is 100%+50% = 150%.
The engineer's income is also 1.5 times as large as the school teacher's income. This can be found by dividing the engineer's income percentage (150%) by the school teacher's income percentage (100%), which gives 150% / 100% = 1.5.
So the engineer's income is 150% of the school teacher's income, and it is 1.5 times as large as the school teacher's income.
- C
how do you find the distance formula to find the distance between each of the specified points. (ie pythagorean theorem)?
Answer: The distance formula is a mathematical formula used to find the distance between two points in a plane. One way to find the distance formula is by using the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
The distance formula can be derived from the Pythagorean theorem by considering the two points as the two endpoints of a line segment. The formula is as follows:
Distance = √(x2 - x1)^2 + (y2 - y1)^2
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this formula, the difference in the x-coordinates is squared and the difference in the y-coordinates is also squared. Then, these two values are added and the square root of the result gives the distance between the two points.
For example, if we have two points (x1, y1) = (2, 3) and (x2, y2) = (5, 8), we can use the distance formula to find the distance between these two points:
Distance = √((5 - 2)^2 + (8 - 3)^2)
Distance = √(3^2 + 5^2)
Distance = √(9 + 25)
Distance = √(34)
Distance = 5.83
Therefore, the distance between the two points is 5.83 units.
Step-by-step explanation:
Write the sentence as an equation.
106 more than the quantity 68 times y is the same as 36 decreased by y
Answer: 68y+106=36-y
