Lisa has $7.80 to spend on some tomatoes and a loaf of bread. Tomatoes cost $1.20 per pound, and a loaf of bread costs $1.80. The inequality 1.20x + 1.80 ≤ 7.80 models this situation, where x is the number of pounds of tomatoes. Solve the inequality. How many pounds of tomatoes can Lisa buy? A. x ≤ 8; Lisa can buy 8 pounds or less of tomatoes. B. x ≥ 5; Lisa can buy 5 pounds or more of tomatoes. C. x ≤ 5; Lisa can buy 5 pounds or less of tomatoes. D. x ≥ 8; Lisa can buy 8 pounds or more of tomatoes.
Answer:
C. [tex]x\leq 5[/tex]; Lisa can buy 5 pounds or less of tomatoes.
Step-by-step explanation:
We have been given an inequality [tex]1.20x+1.80\leq 7.80[/tex], where x is the number of pounds of tomatoes. The inequality represents amount spend by Lisa on tomatoes and loaf. We are asked to find number of pounds that Lisa can buy.
First of all, we will subtract 1.80 from both sides of our inequality.
[tex]1.20x+1.80-1.80\leq 7.80-1.80[/tex]
[tex]1.20x\leq 6.00[/tex]
Now, we will divide both sides of our inequality by 1.20.
[tex]\frac{1.20x}{1.20}\leq \frac{6.00}{1.20}[/tex]
[tex]x\leq 5[/tex]
Therefore, Lisa can buy 5 pounds or less of tomatoes and option C is the correct choice.
Which pair of equations represents perpendicular lines?
a. y=2x-7, y=-0.5x-7
b. y=2x+7, y=2x-7
c. y=2x+7, y=x+7
d. y=2x+7, y=-2x-2
the answer would be A because if you graph those equations they are perpindicular. They cross eachother like a t
Marcial found a recipe for fruit salad that he wanted to try to make for his birthday party. He decided to triple the recipe. a. What are the new amounts for the oranges, apples, blueberries, and peaches? The amount of rhubarb in the original
recipe is 3 1/2 cups. Using what you know of whole numbers and what you know of fractions, explain how you could triple that mixed number.
Suppose you have 30 CDs. You know that you have 11 more CDs than your friend. Write and solve an equation to find the number of CDs your friend has. Question 3 options: n – 11 = 30; 41 30 + n = 11; –19 30 + 11 = n; 41 n + 11 = 30; 19
Answer:
n+11=30
n = 19
Step-by-step explanation:
You have 30 CDs and you friend had n amount of CDs. We also know that you have 11 more CDs than your friends. Therefore we can write expression as:
[tex]n+11=30[/tex] and simplify
[tex]n =30 -11[/tex]
[tex]n=19[/tex]
Therefore you friend will have 11 CDs which is 11 less than what you have.
Which function represents the number if seats in a theater with n rows?
Coffee with sugar and milk added to it can contain up to calories.
What is the sum of the infinite geometric series? -3-3/2-3/4-3/8-3/16
Answer: -6.
Step-by-step explanation: Given geometric series is-
[tex]-3,~-\dfrac{3}{2}, ~-\dfrac{3}{4}, ~-\dfrac{3}{8},~-\dfrac{3}{16},...[/tex]
Here, the first term of the series, [tex]a=-3[/tex]
and the common ratio, [tex]r=\dfrac{1}{2}.[/tex]
Since it is an infinite series, so sum is given by
[tex]S=\dfrac{a}{1-r}\\\\\\\Rightarrow S=\dfrac{-3}{1-\frac{1}{2}}\\\\\\\Rightarrow S=\dfrac{-6}{2-1}\\\\\\\Rightarrow S=-6.[/tex]
Thus, the sum of the series is -6.
Jackson purchased some power tools totaling $1,543 using a six month deferred payment plan with an interest rate of 23.76%. He did not make any payments during the deferment period. What will the total cost of the power tools set be if he must pay off the power tools within two years after the deferment period?
$1,543.00
$1,735.63
$2,197.44
$2,746.80
The total cost of the power tools set if Jackson must pay off the tools within two years after the deferment period is $2,644.82.
To find the total cost of the power tools set after the deferred payment period, we need to consider both the initial cost of the tools and the interest accrued during the deferment period and the subsequent payment period.
First, let's calculate the interest accrued during the deferment period:
Interest = Principal × Rate × Time
Interest = $1,543 × 23.76% × (6/12) (since the deferment period is 6 months)
Interest = $1,543 × 0.2376 × 0.5
Interest = $183.78
Now, add this interest to the initial cost of the power tools:
Total cost after deferment = Initial cost + Interest
Total cost after deferment = $1,543 + $183.78
Total cost after deferment = $1,726.78
Next, we need to calculate the total amount Jackson must pay off within two years after the deferment period. This includes the principal amount and the interest accrued during the payment period. We'll use the formula for calculating the total payment for a loan with compound interest:
[tex]\[A = P(1 + r/n)^{nt}\][/tex]
Where:
A = Total amount to be paid
P = Principal amount (initial cost after deferment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Time in years
In this case, we'll compound interest annually, so (n = 1), and (t = 2) years.
[tex]\[A = $1,726.78(1 + 0.2376/1)^{1*2}\][/tex]
[tex]\[A = $1,726.78(1 + 0.2376)^2\][/tex]
[tex]\[A = $1,726.78(1.2376)^2\][/tex]
[tex]\[A = $2,644.82\][/tex]
So, the total cost of the power tools set if Jackson must pay off the tools within two years after the deferment period is $2,644.82.
B is between A and C, D is between B And C, and C is between B and E. AE = 28cm, BC =10cm. AB = DB = DC. what is the length of CE ?
Final answer:
By using the given lengths of AE and BC, along with the equality of AB, DB, and DC, we can solve for CE to be 14.67cm.
Explanation:
The lengths of AE, BC, AB, DB, and DC are given or can be determined with the information provided. Since AB = DB = DC and BC is given as 10 cm, we can deduce that AB + BC + CE = AE. Given AE is 28cm and BC is 10cm, we can find the length of AB by realizing that AB + AB + AB (which is AB + DB + DC) is the same as BC or 10cm. This makes each section AB, DB, and DC equal to 10cm / 3.
With AB, DB, and DC all being equal to 10cm / 3, and knowing AE is 28cm, we can then calculate the length of CE:
AE = AB + BE (and BE = BC + CE)
28cm = (10cm/3) + (10cm + CE)
To find CE, rearrange the equation:
CE = 28cm - 10cm - (10cm/3)
CE = 28cm - 10cm - 3.33cm
CE = 18cm - 3.33cm
CE = 14.67cm
To solve for the length of CE in a line segment configuration, we calculate CE = AE - BC - DC after determining the lengths of AB, BC, and DC. The solution reveals that CE is 9cm.
Explanation:The student has a geometry problem, which involves calculating the length of segment CE on a line segment AE. We know that AE = 28cm and BC = 10cm, with AB, DB, and DC being equal in lengths.
Since B is between A and C, and D is between B and C, and C is between B and E, we can write the entire length AE as AB + BC + CE. Because AB = DB = DC, we can substitute DB and DC for AB in the sums to get 2(DB) + BC = 28cm.
We are given that BC = 10cm, so we can set up an equation: 2(DB) + 10cm = 28cm. Solving for DB, we find that DB = 9cm. Since DC is equal to DB, DC is also 9cm. CE can be found by subtracting BC and DC from the total length of AE: CE = AE - BC - DC, so CE = 28cm - 10cm - 9cm, resulting in CE = 9cm.
The interior angles of a regular polygon each measure 165 degrees. how many sides does the polygon have
If a regular polygon has interior angles each measuring 165 degrees, the polygon has 24 sides. This is calculated by using the formula to find the number of sides in a regular polygon, given the angle size.
Explanation:To find out how many sides a regular polygon has, based on the size of its interior angles, you can use the formula to calculate the sum of the interior angles of a polygon:
n
= 180(
n
- 2), where
n
is the number of sides.
However, this formula gives the sum of the interior angles as a whole. Since, in a regular polygon, all angles are equal, you can then divide this sum by the known size of each angle.
So the specific formula to calculate the number of sides of a regular polygon, given the angle size, is:
n
= 360 / (180 -
angle size
).
In this case, you can substitute the angle size of 165 degrees into this formula:
n
= 360 / (180 - 165) = 360 / 15 = 24.
So a regular polygon with interior angles each measuring 165 degrees has 24 sides.
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I will mark the correct answer as brainliest! A piece of fabric 180 inches long is cut in 2 pieces such that 3 times the larger piece is greater than 4 times the smaller piece. How large are the 2 pieces. Also please give details if possible
The length of the larger piece lies in the interval [102.85 , 180) and the length of the smaller piece lies in the interval [0 , 77.15]
What is an interval?In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between.
Given here, that 3 times the larger piece is greater than 4 times the smaller piece. let the length of the larger piece be x and length of the smaller piece be 180-x, then we get the following inequality-
3x > 4(180-x)
3x>720-4x
7x>720
x>102.85
therefore 102.85≤ x <180
Hence, the larger piece lies in the interval [102.85 , 180) and the length of the smaller piece lies in the interval [0 , 77.15]
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Ivan has 6 times as many blue beads as red beads. He has 4 red and blue beads in all. How many blue beads does Ivan have?
*NEED HELP!!!
Trystan accepted a job offer with an annual salary of $33,907, paid on a semimonthly basis. What will be his gross pay on each of his paychecks?
A) $652.06
B) $1304.12
C) $1412.79
D) $2825.58
6) Which salary results is the LEAST ANNUAL income?
A) weekly salary of $781
B) biweekly salary of $1430
C) semimonthly salary of $1550
D) monthly salary of $2995
7) Yusef earned a 25% tip on a meal that cost $75.77. What was the tip amount?
A) $9.42
B) $18.94
C) $15.68
D) $18.23
8)Larry earns $11.25/hour selling televisions. He also earns 4.5% commission on his sales.
What is his gross weekly pay for a week in which he worked 35 hours and sold $4000 worth of televisions?
A) $180.00
B) $393.75
C) $573.75
D) $628.45
9) Brea worked 40 hours one week at a rate of $15.60/h. How much money was deducted from her gr
Answer:
C) $1412.79; D) monthly salary of $2995; B) $18.94; C) $573.75
Step-by-step explanation:
Getting paid semimonthly means there will be two paychecks a month. There are 12 months in the year, so this is 24 checks per year. To find the gross pay on each check, divide the salary by 24:
33907/24 = 1412.79
There are 52 weeks per year. This means a weekly salary of 781 would be an annual income of 781(52) = 40,612.
A biweekly salary means getting paid every two weeks. This means there will be 52/2 = 26 paychecks per year; this gives an annual income of 26(1430) = 37,180.
Semimonthly pay means there will be 24 paychecks per year; this gives us an annual income of 24(1550) = 37,200
There are 12 months in the year; this gives us an annual salary of 12(2995) = 35,940. This is the smallest amount in our given choices.
25% = 25/100 = 0.25; this makes the tip 0.25(75.77) = 18.9425 ≈ 18.94.
11.25 per hour for 35 hours is 11.25(35) = 393.75. 4.5% commission is 4.5/100(4000) = 0.045(4000) = 180. Together this gives us
393.75+180 = 573.75
Which of the following describes the location of the opposite of the number that R represents on this line?
what is the mean? if the answer is a decimal, round to the nearest tenth
96. 94. 95. 89. 79
What is the equation for the line of reflection that maps the trapezoid onto itself?
A. x= -2
B. x=0
C. y=2.5
D. y=4
What is the area of a rectangle with vertices at (−3, −1) , (1, 3) , (3, 1) , and (−1, −3) ?
Enter your answer in the box. Do not round any side lengths.
Solve the equation.
–3x + 1 + 10x = x + 4
x = 1/2
x = 5/6
x = 12
x = 18
Answer:
x = 1/2
Step-by-step explanation:
-3x +1 +10x = x + 4
7x + 1 = x + 4
6x + 1 =4
6x = 3
x = 3/6
x = 1/2
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The value of x in the equation -3x + 1 + 10x = x + 4 is 1/2.
x = 1/2
Option A is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 6 is an equation.
3x + 4 = 6 is an equation.
x + 5 is an equation.
3x + 4x + 5 is an equation.
We have,
The equation:
-3x + 1 + 10x = x + 4
We will solve for x.
Add 3x on both sides.
1 + 10x = x + 4 + 3x
1 + 10x = 4x + 4
Subtract 4x on both sides.
1 + 10x - 4x = 4
1 + 6x = 4
Subtract 1 on both sides.
6x = 4 - 1
6x = 3
Divide 6 on both sides.
x = 3/6
x = 1/2
Thus,
The value of x in the equation -3x + 1 + 10x = x + 4 is 1/2.
x = 1/2
Option A is the correct answer.
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The temperature at 5:00 a.m. was –6 °F. By 3:00 p.m., the temperature had risen to a high of 36 °F. If the temperature at 8:00 p.m. decreased from the high by of the change in temperature in Fahrenheit degrees from 5:00 a.m. to 3:00 p.m., what was the temperature at 8:00 p.m.?
EDMENTUM QUESTION:
Kayla set up an outdoor digital thermometer to record the temperature overnight as part of her science fair project. She began recording the temperature, in degrees Fahrenheit, at 10:00 p.m. Kayla modeled the overnight temperature with function t, where h represents the number of hours since 10:00 p.m. t(h) = 0.5h2 − 5h + 27.5
Answer: 15°F at 3:00 a.m.
Step-by-step explanation:
Solve the equation for y
-x+y=0
solve for x...........
If a=2b, then a-c=2b-c
The 26-oz jar of chocolate fudge costs $3.12. The 16-oz jar costs $2.40. How much can you save on each ounce by choosing the better buy?
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test? The test contains 4 three-point questions and 20 five-point questions. The test contains 10 three-point questions and 14 five-point questions. The test contains 14 three-point questions and 10 five-point questions. The test contains 20 three-point questions and 8 five-point questions.
An equation is shown
Y=1/2x+3/4
Select all the points that are contained in the graph of the equation
What are not irrational out of square root of 15,16,17, and 18?
What is the area of rhombus ABCD?
Do not round at any steps
People enjoyed attending the concert in the park. Twice as many men as women attended the concert. If the total attendance was 714, how many women attended the concert?
Almonds cost $15.50 for 6 pounds. Find the unit rate. Round to the nearest cent if necessary.
The unit rate for almonds is approximately $2.58 per pound.
To find the unit rate, we divide the total cost by the total quantity.
In this case, the total cost is $15.50 and the total quantity is 6 pounds.
So, the unit rate is:
[tex]\[ \text{Unit rate} = \frac{\text{Total cost}}{\text{Total quantity}} \][/tex]
[tex]\[ \text{Unit rate} = \frac{15.50}{6} \][/tex]
[tex]\[ \text{Unit rate} \approx \$2.58 \][/tex]
Rounding to the nearest cent, the unit rate is approximately $2.58 per pound.
Which graph represents f(x)=−2x4 ?
abcdefghijklmnopqrstuvwxyz
The graph of y = x⁴ is also a parabola that opens upward and it is an even function.
The blue graph represents a quadratic function and the red graph represents a biquadratic function.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
We also know that graph of a quadratic function y = x² is a parabola,
Now, the graph of y = x⁴ will also be a parabola,
and it is more steeper or has a greater slope than the graph y = x² as the independent variable has a larger exponent value it is also an even function that is symmetric about the y-axis.
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