The correct representations of the inequality are -6x + 15 < 10 - 5x and x <-5. Options C and D
What are inequalities?Inequalities are described as mathematical relations that makes a non-equal comparison between two elements, variables, numbers or mathematical expressions.
They are often used to compare two numbers on the number line based their sizes.
From the information given, we have the inequality;
–3(2x – 5) < 5(2 – x)
expand the bracket
-6x + 15 < 10 - 5x
collect like terms
-6x + 5x < 10 - 15
add or subtract the like terms
-x < -5
Make 'x' the subject of formula
x < 5
Hence, the value is -6x + 15 < 10 - 5x
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The complete question:
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
2. Andrea made a cranberry punch that used 2 1/2 cups of cranberry juice for every 4 cups of club soda. What is the number of cups of cranberry juice needed when the punch is made with 6 cups of club soda?
5 1/2 cups
4 1/2 cups
3 1/8 cups
3 3/4 cups
The number of cups of cranberry juice needed when the punch is made with 6 cups of club soda is
3 3/4 cupsHow to find the number of cups that will be usedIn general, the term "proportion" refers to a part, share, or amount that is compared to a whole.
Two ratios or fractions are equal when an equation or a declaration to that effect is utilized.
the proportion is solved by = (2 1/2) / 4 = 5/8
Using this proportion, the number of cups of cranberry juice needed when the punch is made with 6 cups of club soda
= 6 * 5/8
= 3.75
= 3 3/4 cups
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Solve the variable: 4(3n+ 3) = 60
Answer:
n = 4
Step-by-step explanation:
4(3n + 3) = 60 ( divide both sides by 4 )
3n + 3 = 15 ( subtract 3 from both sides )
3n = 12 ( divide both sides by 3 )
n = 4
The value of n in 4(3n+ 3) = 60 that satisfies the equation is 4.
To solve for the variable n, we need to get n by itself on one side of the equation. We can do this by isolating n by performing the same operations on both sides of the equation.
First, we can simplify the left side of the equation by performing the operations inside the parentheses:
4(3n+ 3) = 4(3n) + 4(3) = 12n + 12
Then, we can subtract 12 from both sides of the equation to isolate n:
12n + 12 - 12 = 60 - 12
12n = 48
Finally, we can divide both sides of the equation by 12 to solve for n:
12n / 12 = 48 / 12
n = 4
Therefore, the value of n that satisfies the equation is 4.
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Kevin has money in two savings accounts. One rate is 7% and the other is 8%. If he has $150 more in the 8% account and the total interest is $51, how much is invested in each savings account?
The amount invested in the account with 8% interest is $410 and the amount invested in the account with 7% interest is $260.
How much was invested in each account?The first step is to form a system of equations using the information in the question:
x - y = 150 equation 1
0.08x + 0.07y = 51 equation 2
Where:
x = amount invested in the account with 8% interest y = amount invested in the account with 7% interestThe elimination method would be used to determine the required values
Multiply equation 1 by 0.08
0.08x - 0.08y = 12 equation 3
Subtract equation 3 from equation 2:
0.15y = 39
y = 39 / 0.15
y = 260
Substitute for y in equation 1 :
x - 260 = 150
x = 260 + 150
x = 410
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What’s the correct answer answer asap for brainlist
Answer:
A. of the Spring shall blow
Step-by-step explanation:
Personification is when you give objects the same actions or qualities of people. I think it would be option A because Spring cannot literally blow because it is a season
a local bookstore charges $22 for every 4 hours of internet use in the store. Which equation models the relationship between the time the number of hours of internet use, x, and the charges incurred, y?
y = 11/2 x
y = 2/11 x
y = -2/11 x
y = -11/2 x
An equation which models the relationship between the time (the number of hours) of internet use, x, and the charges incurred, y include the following: A. y = 11/2 x.
How to write an equation to model this situation?In order to write this equation, we would assign variables to the time (the number of hours) of internet use and Rick's bus ride to school respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x indicate the time (the number of hours) of internet use.Let the variable y indicate the the charges incurred.Next, we would determine the amount if charges per hour (every hour) by using this mathematical expression;
Rate of change (slope) = Charges/Time
Substituting the given points into the rate of change (slope) formula, we have;
Rate of change (slope) = 22/4
Rate of change (slope) = 11/2
In conclusion, an equation which models the relationship between the number of hours of internet use (time) and the charges incurred is given by y = 11x/2.
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20 points!! ASAP!!! This is a geometry problem I need help with!!
need help!!!!!!!!!!!
Answer:
150
Step-by-step explanation:
10 x 15 is 150,
15 x 1 = 15
15 add a zero 150
volume is full
Answer:
4,710 cm^3
Step-by-step explanation:
we find area of circle on top first using circle formula
pi times r^2
the radius is 10 so 10^2 is 100\
and we use 3.14 for pi and 100x3.14= 314
now we multiply 314 by the height
314x15
4710
hopes this helps
using regula falsi method find the
the real roots of ea. Correct
five decimal points.
x log x=1.2
Complete solve
The solution of the logarithmic equation x log x = 1.2 will be 2.74065.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Exponents can also be written as logarithms. A number base logarithm is similar to some other number. It is the exact inverse of the exponent expression.
The equation is given below.
x log x = 1.2
log xˣ = 1.2
Take anti-log, then we have
[tex]\rm x^x = 10^{1.2}[/tex]
xˣ = 15.8489
[tex]\rm x^x = \left (2.74065 \right)^{2.74065 }[/tex]
The solution of the logarithmic equation x log x = 1.2 will be 2.74065.
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PLEASE HELP the question is in the picture
its due in 1 hour pls help
Looking at the triangle, the side CE is solved to be 45 m
What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions
Examining the figure shows that pair of equivalent sides are
AB and BD, AC and CE,
The solution is worked out using sides AB and BD, AC and CE,
AB / BD = AC / CE
290 / 30 = (145 + 290) / CE
cross multiplying
290 * CE = 30 * (145 + 290)
CE = 13050 / 290
CE = 45
hence CE = 45
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f(x)\sqrt(3x+1) for x=8
Answer:
f(8) = ± 5
Step-by-step explanation:
assuming you mean
f(x) = [tex]\sqrt{3x+1}[/tex]
substitute x = 8 into f(x) , that is
f(8) = [tex]\sqrt{3(8)+1}[/tex] = [tex]\sqrt{24+1}[/tex] = [tex]\sqrt{25}[/tex] = ± 5
Match the graph to the slope of that function.
Answer:
See below
Step-by-step explanation:
You did not include the function, so I not sure how to match. This might help. Here is the equation for each graph:
y = 2x -5
y = -1/5 x - 3
y = -1/2 x + 5
y = -4/3 x - 4
20. DEPRECIATION Depreciation is the decrease in the value of an item resulting from its age or wear. When an item loses about the same percent of its value each year, an exponential function can be used to model its decreasing value over time. The function g(x)=12,000(0.85)^x can be used to model the value of a $12,000 car as it depreciates at an annual rate of 15% over x years. g(x) is a dilation of the parent function f(x)=0.85^x. The graph shows the function g(x).
a. Write the equation of a function h(x) that represents the depreciation of a $20,000 car depreciating at the same rate over x years.
b. Describe h(x) as it relates to the parent function.
c. What is the difference between the values of the $12,000 car and the $20,000 car 5 years?
a) The equation of the function h(x) to represent the depreciation of a $20,000 car is given as h(x) = 20,000 (0.85)ˣ.
b). The function h(x) is a decay or dilation of the parent function f(x) = 0.85ˣ by a scale factor of $20,000.
c). The difference between the values of the $12,000 and the $20,000 cars after 5 years is $3550.
What is the equation of the function h(x)?The equation of the function h(x) is an exponential function.
An exponential function is a mathematical function in the form f(x) = aˣ, where “x” is a variable and “a” is a constant (called the base of the function) and it is usually greater than 0.
Exponential functions may represent exponential growth or exponential decay, as in this situation, signifying depreciation.
Therefore, the exponential function equations show the values of the cars after five years of depreciation at 15%.
The value of the $12,000 car after 5 years of depreciation at 15% is:
g(x) = 12,000 (0.85)ˣ
g(5) = 12,000 (0.85)⁵ = $5,324
The value of the $20,000 car after 5 years of depreciation at 15% is:
h(x) = 20,000 (0.85)ˣ
h(5) = 20,000 (0.85)⁵ = $8,874
Thus, the difference between the two values is $3,550 ($8,874 - $5,324).
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there are 240 connecting cubes in the box. five students each take 9 connecting cubes from the box. how many connecting cubes are left in the box? a. write an equation to represent the situation. use a letter for the unknown quantity. b. solve the problem. explain or show your reasoning
The equation representing the situation is y = 240 - 5x
the amount reaming is 195 connecting cubes
How to write the equation representing the situationThe equation is written from the following information
there are 240 connecting cubes in the box
five students each take 9 connecting cubes from the box
let the number of box be x such that
5x = 5 students each taking from the box
let the number remaining be y
y = 240 - 5x
for x = 9
y = 240 - 5 * 9
y = 240 - 45
y = 195
The connecting cubes remaining after each of the 5 students take 9 is 195 connecting cubes
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EASY PLEASE HELP DUE NOWS TYY!Frances and Muriel are picking peaches. Frances has 17 beaches, which is 2more than 3 times the number of peaches that Muriel has. Write an equation that could be used to find the number of peaches p Muriel has? PLS HElp thank u so much due
Answer: Muriel has 5 peaches
Step-by-step explanation:
17 = 3p+2
15 = 3p
p=5
5 peaches
Which of the following is not an example of how you can reduce the full
cost of higher education?
O Buy used textbooks and rent other needed ones.
Live at home and commute to campus nearby.
Live on campus to reduce transportation costs.
Eat at restaurants and fast food places regularly.
-submit
Cost reduction is the process of lowering a business's expenses in order to increase profits.
What is cost reduction?Every year you are in school, start looking and applying. See if merit-based aid is offered by contacting the financial aid office at your institution. You may need to fulfil specific requirements in order to be eligible for merit-based funding.
Utilize tax-advantaged saving tools like Coverdell Education Savings Plans and 529 plans to start saving for college expenses as early as feasible (ESAs). However, only 529 plans are the sole means of education savings that also provide state tax advantages. Both plans offer federal tax advantages.
In order to increase earnings, a company's costs must be reduced. In addition to process optimization to increase productivity, it entails identifying and eliminating expenses that do not offer value for customers. Short-term savings are often the main goal of cost reduction.
Therefore, the correct answer is option d) Eat at restaurants and fast food places regularly.
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thirty seven city buses fully loaded can carry 4403 passengers how many passengers can a single bus carry?
Answer:
One single bus:
119 passengers
Step-by-step explanation:
37 buses ⇒ 4403 passengers
1 bus ⇒ X passengers
X = 4403 passengers * 1 bus / 37 bus
X = 119
Tisha brought chocolate and vanilla cupcakes to school for her birthday. 50 students decided to take a cupcake, and 27 of them picked vanilla. What percentage of the students picked a vanilla cupcake? write your answer using a percent sign (%)
Answer: Unanswerable
Step-by-step explanation:
First, you need to state how many students are in the school, and how many cupcakes of chocolate and vanilla she brought.
I. Find all the missing angles.
II. Using Algebra - Find the value of x.
Answer:
Step-by-step explanation:
1. ∡T= 72° 2. ∡M= 76°
∡U= 54° ∡N= 76°
3. EF = 18 in 4. ∡P= 60°
∡F = 134° ∡Q= 60°
∡R= 60°
Select the correct answer from the drop down menu
The equation of the function is f(x) =x³ - 2x² -5x + 6. Hence option B is the correct option.
What is a function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Given graph cuts x at three points. Thus the degree of the given function is 3.
The x-intercepts of the function are the zeros of the function.
The x-intercepts of the graph are (-2,0), (1,0), and (3,0).
Thus the zeros of the function are -2, 1, and 3.
The equation of a function whose zeros are a,b, c is f(x) = (x-a)(x-b)(x-c).
Therefore the equation of the graph function is
f(x) = (x-(-2))(x-1)(x-3)
f(x) = (x + 2)(x-1)(x-3)
f(x) = (x² + 2x - x -2)(x-3)
f(x) = (x² + x -2)(x-3)
f(x) = (x³ + x² - 2x -3x² -3x +6)
f(x) =x³ - 2x² -5x + 6
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Add.
(6x³ + 3x² − 2) + (x³ - 5x²-3)
Express the answer in standard form.
Enter your answer in the box.
Answer:
7x^3-2x^2-5
Step-by-step explanation:
thats the answer
Which choice is equivalent to the quotient below?
√14
2√2
OA.
B.
S AS
O C.
OD. T
Answer:
Step-by-step explanation its c
A straight line that is parallel to one of the sides of a given triangle intersects its other two sides (or their extensions) and, with them, forms a triangle. Prove that this triangle is similar to the original triangle.
The proof below shows that the triangle is similar to the original triangle is as shown below.
How to identify similar triangles?Similar triangles are defined as the triangles that have the same shape, but their sizes may vary.
We are told that a straight line that is parallel to one of the sides of a given triangle intersects its other two sides. Let the straight line be DE and let the line it is parallel to be BC as shown in the triangle attached. Thus, DE∥BC
In the two triangles formed △ADE and △ABC, we can say that;
∠DAE = ∠BAC because they are common angles.
We can also say that;
∠ADE = ∠ABC [This is because DE∥BC which means ∠ADE and ∠ABC are corresponding angles and as such we say that they are congruent.
By the same concept, we can also say that ∠AED=∠ACB
∴△ADE ∼ △ABC
In similar triangles, corresponding sides are in the same ratio and as such; AD/AB = AE/AC
Thus, we can also simplify this to;
AD/DB = AE/EC
Thus, It is proved that if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.
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2. Find the dimensions (outside parts) of the Area Model below. Then write the area as a
product and as a sum.
X²
3x
-5x
-15
Product
Sum
The area as a product and as a sum will be (x - 5)(x + 3) and x² - 5x + 3x - 15, respectively.
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The dimensions (outside parts) of the Area Model are below.
x² - 5x
3x - 15
Then the sum is given as,
⇒ x² - 5x + 3x - 15
Factorize the expression, then we have
⇒ x² - 5x + 3x - 15
⇒ x(x - 5) + 3(x - 5)
⇒ (x - 5)(x + 3)
The area as a product and as a sum will be (x - 5)(x + 3) and x² - 5x + 3x - 15, respectively.
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what is 0.75 x 0.6? (ToT)/~~~
Answer:
0.45
Step-by-step explanation:
0.75 x 0.6 = 0.45 or in other words
3/4 x 3/5 = 9 / 20 which is 0.45
Operations
1: decrease 11 by r
2: add 6 times x with 2 times s
3: the product of 7 and 2 divided by 2
4: decrease the product of 7 and 6 by a number
For problems 5-11, transcribe the following expressions: (Write it out.)
Example: z + 4 = z plus 4
5. xy
6. 7/t - 4
7. 22 + t2
8. 51 - x
9. x – y^2
10. 36/12 + 12
11. ab - 16
The solution to the algebraic expressions are;
1) 11 - r
2) 6x + 2s
3) (7 * 2)/2
4) (7 * 6) - x
5) The product of x and y
6) 4 subtracted from the product of 7 divided by t
7) The addition of the square of t and 22
8) Decrease 51 by x
9) Subtract the square of y from x.
10) 12 added to the division of 36 divided by 12.
11) 16 subtracted from the product of a and b.
How to solve basic mathematical operations?In mathematics, we know that a basic operations of arithmetic, are addition, subtraction, multiplication, division.
Now, we can solve the questions;
1) Decrease 11 by r;
This means we have to subtract r from 11 and the expression is;11 - r
2) Add 6 times x with 2 times s is expressed as;
6x + 2s
3) The product of 7 and 2 divided by 2 is expressed as;
(7 * 2)/2
4) Decrease the product of 7 and 6 by a number;
Let the number be x and so we have the expression as; (7 * 6) - x
5) xy in word form is;
The product of x and y
6) 7/t - 4 in word form is expressed as;
4 subtracted from the product of 7 divided by t.
7) 22 + t² in word form is;
The addition of the square of t and 22
8) 51 - x in word form is expressed as; Decrease 51 by x.
9) x - y² in word form is;
Subtract the square of y from x.
10) 36/12 + 12 is expressed as;
12 added to the division of 36 divided by 12.
11) ab - 16 expressed in word form is expressed as;
16 subtracted from the product of a and b.
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Divide.
A. 2
B. 3
C. 2 r1
D. 3 r1
Answer: D
Step-by-step explanation:
A boat travels 62 miles in 4 hours. What is the distance it travelled? 248mph
*Include the number and the unit
The distance the boat travelled is 248 miles.
What is distance?
Distance is defined as the amount of space between two objects or points. It can be measured in a variety of ways, such as kilometers, meters, miles, feet, and inches. Distance is not a static concept, as it can change over time, such as when two objects move closer or farther away from each other. Distance can also be used to measure the amount of time it takes for a person or object to travel from one point to another. In addition, distance can refer to the physical separation between two people or the emotional distance between two individuals.
This can be calculated by multiplying the speed of the boat by the amount of time it was travelling, i.e. 62 miles per hour (mph) multiplied by 4 hours. Therefore, the boat travelled a total of 248 miles.
It is important to note that the speed of the boat was 62 mph. This is the average speed of the boat over the 4-hour period. This can be calculated by dividing the total distance travelled by the amount of time it took to travel that distance, i.e. 248 miles divided by 4 hours. Therefore, the average speed of the boat was 62 mph.
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The distance the boat travelled is 248 miles.
What is distance?Distance is defined as the amount of space between two objects or points. It can be measured in a variety of ways, such as kilometers, meters, miles, feet, and inches. Distance is not a static concept, as it can change over time, such as when two objects move closer or farther away from each other. Distance can also be used to measure the amount of time it takes for a person or object to travel from one point to another. In addition, distance can refer to the physical separation between two people or the emotional distance between two individuals.
This can be calculated by multiplying the speed of the boat by the amount of time it was travelling, i.e. 62 miles per hour (mph) multiplied by 4 hours. Therefore, the boat travelled a total of 248 miles.
It is important to note that the speed of the boat was 62 mph. This is the average speed of the boat over the 4-hour period. This can be calculated by dividing the total distance travelled by the amount of time it took to travel that distance, i.e. 248 miles divided by 4 hours. Therefore, the average speed of the boat was 62 mph.
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What’s the correct answer answer asap for brainlist
Answer:
c
Step-by-step explanation:
This table shows how many t-shirts of each color Marcus has in his closet. If he chooses a t-shirt without looking, what is the probability that it will be white?
If Marcus, who has 15 T-shirts in his closet, chooses a T-shirt without looking, the probability that it will be white is 20%.
What is the probability?Probability refers to the likelihood or chance that a defined or expected outcome will occur where there are many possible outcomes.
Probability lies between zero and one in most cases, except where the certainty is 100%.
Colors of Number Probabilities
T-shirts of T-Shirts
White 3 0.2 (3/15)
Gray 8 0.533 (8/15)
Blue 2 0.133 (2/15)
Green 2 0.133 (2/15)
Total 15
Thus, the probability of choosing a white T-shirt from 15 T-shirts depends on the number of white T-shirts to all T-shirts in the closet, which in this situation, is 20%.
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Determine the value of b.
b3 = 125
A: b = 41.7
B: b = ±41.7
C; b = 5
D: b = ±5
Answer:
C
Step-by-step explanation:
The given is b^3 = 125
Can be written as √b^3 = √125
√b^3 = √ (5)^3
Therefore, b = 5
Answer:
Option C; 5
Step-by-step explanation:
This is a problem regarding logarithms. In logarithms, we mainly focus on exponentiation and determining the values of certain values in the logarithm.
[tex]b^{3}[/tex] = 125 (We have to find the value of "b" and we know that it is being cubed)[tex]\sqrt{b^3}[/tex] = [tex]\sqrt{125}[/tex] (To find the value, we have to get rid of the cube and we can do that by using cube root on each side to isolate the variable)b = 5 (When you cube root 125, you get the solution of 5, which is indeed the value for "b" because when you cube it, you get 125)Answer = C; 5Hope this helped! :D
