Answers
Answer:
(-∞, 1] or {x|x<=1}
Step-by-step explanation:
Related Questions
Select the graph that correctly displays the solution of the system of inequalities. y > 2x – 4 y ≤ –x – 7
Answers
The solution to the system of given inequalities is (-7, 0).
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given system of inequalities are y> 2x-4 and y≤ -x-7.
The solution of the system of inequalities is the intersection region of all the solutions in the system.
x<y/2 +2 and x≤-y-7
The solution of the system of inequalities is (-7, 0)
Therefore, the solution to the system of given inequalities is (-7, 0).
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The value of a second-hand car is £8,000.
Each year it loses 20% of its value.
Work out the value of the car after 5 years.
Answers
The value of the car will be £2,621 after 5 years.
What is exponential decay?Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time.
Given that, The value of a second-hand car is £8,000. Each year it loses 20% of its value, we are asked to find its value after 5 years.
This is a situation of exponential decay.
Hence, using the exponential decay formula =
A = P(1-r)ⁿ
Where A is final value, P is principal value, r is rate of decrease and n is the number of years.
Here, we will find A, and we have,
P = £8,000.
r = 20% = 0.20
t = 5
Therefore,
A = 8000(1-0.20)⁵
A = 8000(0.80)⁵
A = 8000(0.32768)
A ≈ 2,621
Hence, the value of the car will be £2,621 after 5 years.
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The Science Club went on a two-day field trip. On the first day, the members paid $60 for transportation plus $15 per ticket to the planetarium. On the second day, they paid $95 for transportation plus $12 per ticket to the geology museum.
Write an expression to represent the total cost for two days for the ₙ members of the club.
Answers
Answer: Let n be the number of members in the Science Club.
On the first day, the total cost for transportation plus the cost of tickets is 60 + (15n) dollars.
On the second day, the total cost for transportation plus the cost of tickets is 95 + (12n) dollars.
So, the total cost for both days is (60 + 15n) + (95 + 12n) = 155 + 27n dollars.
The expression to represent the total cost for two days for the n members of the club is 155 + 27n dollars.
This equation represents the total cost for the transportation, planetarium and geology museum for 2 days for the n members in the club.
It should be noted that this is the monetary representation and it might vary depending on other factors, such as group discounts.
Step-by-step explanation:
Answer:
(n x 27)+155
Step-by-step explanation:
15 +12 = 27
Each member pays $27 for the tickets so we multiply it by the number of members.
95 + 60 = 155
The members pay $155 in total for transportation.
A new business borrows $320,000 at a yearly simple interest rate of 7%.
The total
amount the company repays for the loan and interest is $678,400. How long did it
take to pay off the loan? Pls help Mee!!
Answers
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 678400\\ P=\textit{original amount deposited}\dotfill & \$320000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years \end{cases} \\\\\\ 678400 = 320000[1+(0.07)(t)] \implies \cfrac{678400}{320000}=1+0.07t\implies \cfrac{53}{25}=1+0.07t \\\\\\ \cfrac{53}{25}-1=0.07t\implies \cfrac{28}{25}=0.07t\implies \cfrac{\frac{23}{25}}{0.07}=t\implies \boxed{16=t}[/tex]
A savings account increased by $75 is now more than $500. What is the least amount of money that was originally put in the savings account?
Answers
The least amount of money that was originally put in the savings account is $426.
What is the least amount of money?The amount of money in the savings account is a function of the money that was originally in the account and the amount by which the account was increased by.
The inequality that represents the total amount of money in the savings account is:
amount originally in the account + amount deposited > 500
x + $75 > $500
x > $500 - $75
x > $425
The least amount would be $426 because this is the smallest number that is greater than $425 that would make the total amount more than $500.
To check:
$75 + $426 = $501
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Peter works in the Spring Roll restaurant. He earns $15.50 per hour plus tips of 15% of food sales. If Peter works 35 hours this week and has $4000 of food sales, how much does he earn in total?
Base salary =
Tips =
Total earnings =
Answers
pls help, last question. the one circled in red
Answers
On solving the provided question, we can say that - in the linear equation y = 1/2x + 5, slope, m = 1/2
What is a linear equation?The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
here,
in the linear equation =>
y = +1/2x + 5
on comparing with y = mx +c
slope, m = 1/2
and, c= +5
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find angle D thank you so much need help. geomtry
Answers
The angle m∠D of the triangle is 78 degrees.
How to find the angles of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
The ΔKDT and ΔKPQ are isosceles triangle.
Isosceles triangle is a triangle that has two sides and angles equal to each other.
Therefore,
∠D + ∠T + ∠k = 180
∠D = 6x + 6
∠T = 6x + 6
∠K = 2x
Therefore,
6x + 6 + 6x + 6 + 2x = 180
14x + 12 = 180
14x = 180 - 12
14x = 168
divide both side by 14
x = 168 / 14
x = 12
Therefore,
m∠D = 6x + 6 = 6(12) + 6 = 72 + 6 = 78 degrees.
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I just need help with question A
Suppose your cousin missed class and asks you, “Why do we plug in 0 for x to find y-intercepts and 0 for y to find x-intercepts? That doesn’t make sense to me.” Explain to your cousin WHY this process works. Use the line
5x+4y=14 as an example.
A) A description in words why this works
Answers
The reason why the cousin's procedure for getting the x and y intercepts work is because they represent the definition of those points on a graph.
How to find the x and y intercepts?The x-intercept of a graph or function simply refers to the point at which the graph crosses the graph crosses the x-axis or the point at which y = 0. In a similar manner, the y-intercept simply refers to the point at which the graph crosses the y-axis or simply the point at which x = 0.
Now, we are given the equation of the line as;
5x + 4y = 14
The general form of equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Rewriting the equation of the line in slope intercept form is;
y = -⁵/₄x + ⁷/₂
Now, the reason why we plug in 0 for x to get the y-intercept is because when x = 0, that is only where we can get the y-intercept as the corresponding value of x will be traced to 0.
Similarly, the reason why we plug in 0 for y to get the x-intercept is because when y = 0, that is only where we can get the x-intercept as the corresponding value of y will be traced to 0.
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32 is 32% of what?????
Answers
Answer:
32 is 32% of 100
Step-by-step explanation:
Answer: 100
Step-by-step explanation: 32 is 32% of 100
Which expression is equivalent to 3/2?
Answers
On solving the provided question we can say that expression which is equivalent form to 3/2 is (5/2-1).
What is Equivalent form ?Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
Equivalent systems refer to sets of equations with the same solution. We can create an analogous system from a system of two equations by replacing one equation with the total of the two equations or by replacing an equation with a multiple of itself.
When two expressions can be reduced to a single third expression or when one of the expressions can be expressed in the same way as the other, they are said to be equivalent. When values are replaced for the variable and both expressions yield the same result, you may also tell if two expressions are equal.
The number is 3/2
The expression which is equivalent to 3/2 is (5/2-1)
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A cone consitst of these measure but need to find the volume and surface area. The diameter is 16m, height is 8m, and the slant height is 11.31m.
A.) V=769.17m³ SA=535.89m²
B.) V= 535.89m SA=769.17m
C.) V=535.89m³ SA= 769.17m²
D.) V=1607.68m³ SA=769.56m²
Answers
Volume = (1/3) * pi * radius^2 * height
Surface area = pi * radius * (radius + slant height)
In this case, the diameter is 16m, so the radius is 8m. The height is 8m and the slant height is 11.31m. Substituting these values into the formulas gives:
Volume = (1/3) * pi * 8m^2 * 8m = (1/3) * pi * 64m^3 = 21.333m^3 * 64m^3 = 1,365.33m^3
Surface area = pi * 8m * (8m + 11.31m) = pi * 8m * 19.31m = pi * 153.48m^2 = 483.04m^2
So, the volume of the cone is 1,365.33m^3 and the surface area is 483.04m^2. The correct answer is therefore C) V=535.89m³ SA= 769.17m².
Find the slope of the line shown on each graph below
Answers
The slope of the lines that passes trough the points (-2,-1) and (-4,-7) is m = 3 , (2,-3) and (6,-13) is m = -2.5 , (-3,4) and (-3,-8) is m = undefined , (-5,7) and (3,-1) is m = -1 .
What is slope ?
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.
The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b).
(-2,-1) and (-4,-7)
m=Δy/Δx
m=(y2−y1)/(x2−x1)
m=(−7−−1)/(−4−−2)
m=−6/−2
m = 3
(2,-3) and (6,-13)m=Δy/Δx
m=(y2−y1)/(x2−x1)
m=(−13−−3)/(6−2)
m=−10/4
m=−5/2
m = -2.5
(-3,4) and (-3,-8)m=Δy/Δx
m=(y2−y1)/(x2−x1)
m=(−8−4)/(−3−−3)
m=−12/0
m is undefined
(-5,7) and (3,-1)m=Δy/Δx
m=(y2−y1)/(x2−x1)
m=(−1−7)/(3−−5)
m=−8/8
m = -1
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A new homeowner is purchasing a living room set for $2,975 and must decide between two financing offers.
Offer 1: $250 down payment, 24.90% interest rate, compounded monthly, for 3 years, with no payments due for 6 months and then fixed payments of $139.05 for the remainder of the loan term
Offer 2: $400 down payment, 22.90% interest rate, compounded monthly, for 3 years, with no payments due for 12 months and then fixed payments of $165.76 for the remainder of the loan term
Part A: What is the total cost of offer 1? Explain which technology you used to solve and each step of your process. (3 points)
Part B: What is the total cost of offer 2? Explain which technology you used to solve and each step of your process. (3 points)
Part C: Which financing offer should the new homeowner choose? Explain your reasoning. (4 points)
Answers
Answer:
To compare the two financing offers, we need to calculate the total cost of each offer.
Part A: What is the total cost of offer 1?
To calculate the total cost of offer 1, we need to first calculate the total amount of interest that will be paid over the course of the loan. We can do this using the following formula:
Total interest = (interest rate/12) * loan amount * number of payments
In this case, the loan amount is $2,975, the interest rate is 24.90%, and the number of payments is 36 (3 years * 12 months/year). Plugging these values into the formula, we have:
Total interest = (0.2490/12) * $2,975 * 36
Calculating, we find that the total interest is approximately $1,534.89.
To calculate the total cost of the loan, we need to add the total interest to the original loan amount. In this case, the total cost is $2,975 + $1,534.89 = $4,509.89.
Therefore, the total cost of offer 1 is $4,509.89.
Part B: What is the total cost of offer 2?
To calculate the total cost of offer 2, we need to first calculate the total amount of interest that will be paid over the course of the loan. We can do this using the following formula:
Total interest = (interest rate/12) * loan amount * number of payments
In this case, the loan amount is $2,975, the interest rate is 22.90%, and the number of payments is 36 (3 years * 12 months/year). Plugging these values into the formula, we have:
Total interest = (0.2290/12) * $2,
To continue the calculation of the total cost of offer 2, we need to calculate the total interest using the formula:
Total interest = (interest rate/12) * loan amount * number of payments
In this case, the loan amount is $2,975, the interest rate is 22.90%, and the number of payments is 36 (3 years * 12 months/year). Plugging these values into the formula, we have:
Total interest = (0.2290/12) * $2,975 * 36
Calculating, we find that the total interest is approximately $1,405.70.
To calculate the total cost of the loan, we need to add the total interest to the original loan amount. In this case, the total cost is $2,975 + $1,405.70 = $4,381.70.
Therefore, the total cost of offer 2 is $4,381.70.
Part C: Which financing offer should the new homeowner choose?
Based on the total cost of the two financing offers, it is more cost-effective for the new homeowner to choose offer 2. Offer 2 has a lower total cost ($4,381.70) compared to offer 1 ($4,509.89), so it would be the better choice for the new homeowner.
Step-by-step explanation:
PV = PMT * (1 - (1 + r)^-n) / r
Where PV is the present value (in this case, the total cost of the loan), PMT is the fixed payment amount, r is the monthly interest rate (in decimal form), and n is the number of payments.
Plugging in the values from Offer 1, we get:
PV = $139.05 * (1 - (1 + 0.2490)^-36) / 0.2490
Using a calculator or spreadsheet to compute the exponent and division, we find that the total cost of Offer 1 is $4,941.51.
To calculate the total cost of Offer 2, we can use the same formula:
PV = $165.76 * (1 - (1 + 0.2290)^-36) / 0.2290
Using a calculator or spreadsheet to compute the exponent and division, we find that the total cost of Offer 2 is $4,847.93.
Based on these calculations, the new homeowner should choose Offer 2, as it has a lower total cost. This decision is based on the fact that Offer 2 has a lower interest rate and a longer period of time with no payments due, which results in a lower present value (total cost) of the loan.
To solve these problems, I used the present value of an ordinary annuity formula and a calculator or spreadsheet to compute the exponent and division.
13.A rectangle and a square have the same perimeter 120 cm. Find the side of the square. If the rectangle has a breadth 5cm less than that of the square. Find the breadth, length and area of the rectangle.
Answers
Answer:
Step-by-step explanation:
f(x)=3^x+1 and g(x) = 2x-4, find f(2) - g(-1)
Answers
Answer:
16
Step-by-step explanation:
3^x +1 = f(X)
2x-4 = g(x)
find f(2)-g(-1)
we substitute in function f(X) by value (2), and in function g(X) by value (-1)
1. 3^x +1 becomes 3^2+1 =9+1=10
2. 2(-1)-4= -2-4=-6
then f(2)-g(-1)
= 10-(-6) =10+6=16
Solve: S=2(lw+lw+wh) for w
Answers
Answer:
[tex]w=\frac{s-2lh}{2(h+l)}[/tex]
Step-by-step explanation:
Given the equation, [tex]S=2(lw+lh+wh)[/tex], solve for w.
[tex]S=2(lw+lh+wh)[/tex], distribute the 2.
=> [tex]S=2lw+2lh+2wh[/tex], subtract [tex]2lh[/tex] from both sides.
=> [tex]S-2lh=2lw+2wh[/tex], factor out a [tex]w[/tex] from the right-hand-side.
=> [tex]S-2lh=w(2l+2h)[/tex], now divide [tex](2l+2h)[/tex] from each side.
=>[tex]\frac{S-2lh}{2l+2h}=w[/tex]
Final answer: [tex]w=\frac{s-2lh}{2(h+l)}[/tex]
How can you use this pattern to find 3°
Answers
Number pattern, sequence, finding the algebraic rule and using a ... To illustrate this, consider the following sequence of numbers {1, 3, 5, 7, 9, …}.
What is Number pattern?Number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers.Here, we get the numbers in the pattern by skip counting by 5. Given are the steps to identify a number pattern.To solve the problems of number pattern, we need first to find the rule being followed in the pattern.
To find out the rule, we need to see the first few numbers in the series.Try to see the difference between consecutive numbers, it will help us understand the relationship between the numbers.Number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers. For example: 0, 5, 10, 15, 20, 25, … Here, we get the numbers in the pattern by skip counting by 5.
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The complete question is -
How can you use this pattern to find 3° of the number in Series ?
1. Jason made 3 quarts of corn chowder. He divided it into serving sizes of 1 12 cups each. How many 1 12 -cup servings can be made from 3 quarts of chowder? A. 4 12 servings B. 8 servings C. 12 servings D. 18 servings
Answers
Answer:
B. 8 servings
Step-by-step explanation:
1 quart = 4 cups
3x4=12
3 quarts of clam chowder = 12 cups of chowder
1 1/2 cups each
12 divided by 1 1/2 = 12 divided by 3/2 = 12 divided by 2/3 = 8 servings
y to the -3 power
pls help!!!!!!!!!
Answers
Answer:
any number goes down 3 places
Step-by-step explanation:
EX:10 to the power of -3 = 0.001
What is an equation of the line that passes through the points (4,7) and (-3,7)
Answers
Answer:y=
Step-by-step explanation:Firstly let's find the slope which is (7-7)/(4-(-3))=0. Using the point slope formula y-y1=m(x-x1) we plug in one of the points and simplify y-7=0(x-4). Simplifying and solving for y gives us y=
The equation below represents the amount of work required to complete a project, where x represents the number of hours each group member must contribute to the project. How many hours does each group member work on the project? x+45/4=4x 2 hours 4 hours 16 hours 3 hours
Answers
The number of hours does each group member work on the project is 4 hours. Therefore, the correct answer is option B.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is x+45/4=4x.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
4x-x=45/4
3x=45/4
x=15/4
x=3.75
x≈4 hours
Therefore, option B is the correct answer.
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Solve the following quadratic equation for all values of xx in simplest form.
4(x^2-5)-1=
4(x
2
−5)−1=
\,\,3
3
Answers
The quadratic equation 4(x² − 5) − 1 = 3 has its solutions to be are √6 and -√6
How to determine the solutions to the equation?From the question, we have the following parameters that can be used in our computation:
4(x 2−5)−1=3
Express properly
This gives
4(x² − 5) − 1 = 3
Subtract -1 from both sides of the equation
So, we have the following representation
4(x² − 5) = 4
Divide both sides by 4
This gives
x² − 5 = 1
Subtract -5 from both sides of the equation
So, we have the following representation
x² = 6
Take the square root of both sides
x = ±√6
Hence, the solution is ±√6
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please help me with this thank you.
Answers
B) 1:55 PM
The smallest size of a hybrid bike, a bike that can be ridden both on and off dirt, is 16.9 inches . Bikes are fitted using a person's inseam with the smallest inseam for a hybrid bike being 25 in. For inseams 25 inches ( in .) or longer, each 0.68 of an inch increase in bike size, a person's inseam is 1 inch longer. A medium size bike has a range of 20.9 in. to 22 in. Write an inequality, where x is the length of an inseam, in inches, that can be used to determine the inseam sizes that best fit a medium size bike.
Answers
The inequality that can be used to determine the inseam sizes that best fit a medium size bike is 25 < x < 28.32.
Please help I don’t understand this
Answers
On solving the provided question, we can say that - the area of the following rectangle is 200 cm sq.
What is rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.
here,
we have
L = 20 cm
and B = 10 cm
Area of rectangle, A =L X B = 20 X 10 = 200 cm sq.
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(20 points)which of these equations doesn’t fit with each other with what we’ve been learning about perpendicular lines explain why for full credit, equations in photo
Answers
Answer:
Line D
Step-by-step explanation:
You want to know which line is not parallel or perpendicular to the other given lines:
A: 2y -x = 2
B: 4y = -8x -4
C: y = -2x +4
D: 5y = 10x +15
Standard formWe can write each of these equations in standard form to make it easier to compare them. That form is ...
ax +by = c
where a > 0 and a, b, c are mutually prime.
The equations are ...
A: x -2y = -2
B: 2x +y = -1
C: 2x +y = 4
D: 2x -y = -3
Parallel linesEquations with the same coefficients of x and y will be parallel:
2x +y = -1 and 2x +y = 4 . . . . lines B and C
Perpendicular linesEquations with coefficients that have been swapped, with one negated, will be perpendicular:
x -2y = -2 and 2x +y = -1 . . . . lines A and B
Line A is perpendicular to parallel lines B and C, so line D is the odd one out.
Line D doesn't fit.
7. {MCC.7.G.2} *
Which set of numbers cannot
represent the lengths of the sides
of a triangle?
A) 7, 9, 12
B) 8, 6, 7
C) 8, 20, 12
D) 10, 13, 20
O A
B
O D
Answers
If
f
(
x
)
=
2
x
4
−
9999999kwwkqkkaosos
Which of the following are examples of voluntary exchange ? SELECT ALL THAT APPLY .
Elena swaps her cookies for a
friend's doughnut.
Jesse spends $12 to see a movie.
Jan buys herself a jacket that she really can't afford.
Miguel pays $250,000 for a new house.
Answers
Elena swaps her cookies for a friend's doughnut is the examples of voluntary exchange. Hence,
What is voluntary exchange?A voluntary exchange occurs when two parties freely exchange products or services without the use of coercion or other restrictive measures. Both parties will gain from the deal and both parties want to make the exchanged items. The idea of voluntary exchange is crucial to a free market economy.
Customers also willingly swap money to buy his strawberries. They can choose to buy strawberries somewhere else if they see that some of his strawberries have flaws. This is a voluntary exchange because both sides gain from it.
One of the most crucial principles of economics is voluntary exchange. In a market economy, where producers and consumers freely exchange products and services, this transaction is taking place. In the end, both sides benefit from the process.
Thus, option A is correct.
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(5x3)+(nx4)=5(3+4) write each missing number.
Answers
Answer:
5
Step-by-step explanation:
5 x 3 = 15
n x 4 = 4n
3 + 4 = 7
(5 x 3) + (n x 4) = 5(3 + 4)
15 + 4n = 5*7
15 + 4n = 35
4n = 35 - 15
4n = 20
n = 20/4
n = 5
Hence, the value of missing number (n) is 5.