John has a monthly net income of $2,376.80. John allots 20% of his income for food, which amounts to
Answer: 20% of 2,7376.80 = 475.36
Step-by-step explanation:
2,376.80(0.2)=475.36
Question 11(Multiple Choice Worth 5 points)
(03.06A LC)
Which statement is true for the equation 2x - 2x - 7 = -7?
O It has infinitely many solutions.
O It has two solutions.
O It has one solution.
It has no solution.
Answer: Option 'a' is correct.
Step-by-step explanation:
Since we have given that
2x-2x-7=-7
We need to solve it first as follows:
[tex]2x-2x-7=-7[/tex]
[tex]2x-2x=-7+7[/tex]
[tex]0=0[/tex]
Since L.H.S. = R.H.S.
So, it satisfies the equation for all x.
So, there will be infinitely many solutions.
Hence, Option 'a' is correct.
someone help with the answer
The answer is
for parallel : y= 4/7-5x/7
for perpendicular: y=10+7x/5
What is slope- intercept equations?The slope-intercept form is written as y = mx+b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis). It's usually easy to graph a line using y=mx+b.
Given line: 5x+7y=9
when our intersection point is (5,-3) the constant
5x+7y
= 5(5)+7(-3)
= 25-21
=4
hence, 5x+7y=4
slope intercept form
7y= 4-5x
y= 4/7-5x/7
Now, for perpendicular lines:
swap the coefficients on x and y with negative sign of x in 5x+7y=9
7x-5y= constant
again, when our intersection point is (5,-3) the constant must be
7x-5y
= 7(5)-5(-3)
=35+15
=50
7x-5y=50
slope intercept form so we solve for y:
y= (50+7x)/5
y=10+7x/5
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he average of 7 consecutive even integers is 10. What is the largest
of the 7 integers?
Answer:
only two brother ok bye
due to inflatation, the cost of harys hot wings grows by 4% every year. this year a dozen hot wings cost 5.99
part a. how much will a dozen hot wings cost next year
part b. how much will a dozen hot wings cost in 2 years
Answer:
Part A : $6.23
Part B : $6.48
Step-by-step explanation:
Let's apply the Simple Interest Formula, which is :
Simple Interest = Principal Amount x Interest rate x Time Period
In one year :
I = 5.99 x 4% x 1I = $0.24Cost = $5.99 + $0.24Cost = $6.23In 2 years :
I = $6.23 x 4% x 1I = $0.25Cost = $6.23 + $0.25Cost = $6.48find the volume of the shape
Answer:
hmmm the mass are the numbers of the up and volume of the bottom
Step-by-step explanation:
Find the value marked b?
Based on the alternate interior angles theorem, the value marked b is calculated as: 190°
What is the Alternate Interior Angles Theorem?The theorem states that two alternate interior angles are always congruent to each other.
The measure of angle b based on the alternate interior angles theorem would be:
m∠b = 50 + (320 - 180)
m∠b = 190°
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Kenny plotted the following pairs of points and said they made a symmetric figure about a line with the rule: y is always 4
If a prism is placed into a basin of water (density: 32.5 lb/ft3) and displaces 3.7 pounds of water, what is the volume of the water that was displaced (in cubic inches)?
The volume of the water that was displaced will be 0.06 cubic feet.
What is density?Density is defined as the mass per unit volume. It is an important parameter in order to understand the fluid and its properties. Its unit is kg/m³.
The mass and density relation is given as
mass = density × volume
If a prism is placed into a basin of water (density: 32.5 lb/ft3) and displaces 3.7 pounds of water.
Then the volume of the water that was displaced will be
We know that the density of the water is 62.4 pounds per cubic foot.
Then we have
3.7 = 62.4 × volume
Volume = 0.059
Volume ≅ 0.06 cubic-foot
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need help with this math
Answer:
h = 5 :)
Step-by-step explanation:
Nick has planted 20 flowers and can plant 7 flowers an hour, Rachel planted 5 flowers and can plant 10 flowers an hour.
f = 7h + 20
f = 10h + 5
f = 7(1) + 20 = 27
f = 10(1) + 5 = 15
(Not this one)
f = 7(2) + 20 = 34
f = 10(2) + 5 = 25
(nope..)
f = 7(3) + 20 = 41
f = 10(3) + 5 = 35
(nope!)
f = 7(4) + 20 = 48
f = 10(4) + 5 = 45
(close, but no)
f = 7(5) + 20 = 55
f = 10(5) + 5 = 55
(Yes!)
It takes 5 gardeners 48 hours to landscape a gArden how long w I'll it take 8 gardeners to landscape same garden
The time is taken by the 8 gardeners to landscape the same garden will be 30 hours.
What are ratios and proportions?A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.
It takes 5 gardeners 48 hours to landscape a garden.
Then the time taken by the 8 gardeners to landscape the same garden will be
The relationship between the gardeners and time is inversely proportional. Then we have
Let x be the time taken by the 8 gardeners. Then we have
8x = 5×48
x = 30 hours
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Please answer asap! show work!
11. What is (f.g)(x)?
f(x) = x3 +3
g(x) = 2x2 + x - 1
Answer:
2x⁵ + x⁴ - x³ + 6x² + 3x - 3
Step-by-step explanation:
Given :
f(x) = x³ + 3g(x) = 2x² + x - 1Finding (f × g)(x) :
f(x) × g(x)(x³ + 3)(2x² + x - 1)2x⁵ + 6x² + x⁴ + 3x - x³ - 32x⁵ + x⁴ - x³ + 6x² + 3x - 3Solve the inequality.
Answer:
D. t < -4 or t > 5
Step-by-step explanation:
Inequality 1
5t - 1 < -215t < -20t < -4Inequality 2
4t + 2 > 224t > 20t > 5⇒ t < -4 or t > 5
⇒ Option D
Graph
Answer:
[tex]\sf D. \quad t < -4, t > 5[/tex]
Step-by-step explanation:
Given system of inequalities:
[tex]\begin{cases}5t-1 < -21\\4t+2 > 22\end{cases}[/tex]
Solve the inequalities by isolating t.
Inequality 1
[tex]\sf \implies 5t-1 < -21[/tex]
[tex]\implies \sf 5t-1+1 < -21+1[/tex]
[tex]\sf \implies 5t < -20[/tex]
[tex]\sf \implies 5t \div 5 < -20 \div 5[/tex]
[tex]\sf \implies t < -4[/tex]
Inequality 2
[tex]\sf \implies 4t+2 > 22[/tex]
[tex]\sf \implies 4t+2-2 > 22-2[/tex]
[tex]\sf \implies 4t > 20[/tex]
[tex]\sf \implies 4t \div 4 > 20 \div 4[/tex]
[tex]\sf \implies t > 5[/tex]
Therefore, the solution to the system of inequities is:
[tex]\sf t < -4, t > 5[/tex]
When graphing inequalities:
< or > : dashed lines≤ or ≥ : solid line< or ≤ : shading under the line> or ≥ : shading above the lineTherefore, to graph the given system of inequalities:
Draw a straight dashed line at t = -4 and shade under the line.Draw a straight dashed line at t = 5 and shade above the line.(Refer to attachment for the graph).
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The inverse of the function f(x) = 1/2x+10?
Answer:
f'(x) = 2x - 20
Step-by-step explanation:
f(x) = 1/2 x + 10
Switch x and y.
y = 1/2 x + 10
Solve for y by itself.
x = 1/2 y + 10
x - 10 = 1/2 y
y = 2 * (x - 10)
f'(x) = 2x - 20
A dance CD has 10 songs on it - 8 are slow, and 2 are fast. When the DJ at a dance plays a song it is not played again. All songs from the CD are played at random.
What is the probability that the first two songs played are slow songs?
The probability that the first two songs played are slow songs is approximately 0.622 or 62.2%.
To calculate the probability that the first two songs played are slow songs, we need to consider the total number of ways the first two songs can be selected and the number of ways to choose two slow songs out of the eight available.
Given:
Total number of songs = 10
Number of slow songs = 8
Step 1: Calculate the total number of ways to choose two songs out of ten (without replacement), which is represented by "10C2" (combinations of 10 things taken 2 at a time):
10C2 = (10 * 9) / (2 * 1) = 45
Step 2: Calculate the number of ways to choose two slow songs out of eight:
8C2 = (8 * 7) / (2 * 1) = 28
Step 3: Find the probability that the first two songs played are slow songs by dividing the number of favorable outcomes (choosing two slow songs) by the total number of possible outcomes (choosing any two songs from the CD):
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 28 / 45 ≈ 0.622
So, the probability that the first two songs played are slow songs is approximately 0.622 or 62.2%.
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there are light-bulbs at the factory
nice. are they filament lightbulbs or fluorecent lightbulbs
Pls, look at the picture for the question.
Answer:
B
Step-by-step explanation:
surface area = area of base + area of lateral faces
Area of base:
A = lw
A = 4(4)
A = 16
Area of Lateral faces:
A = 1/2 bh
A = 1/2(5)(4)
A = 1/2(20)
A = 10
There are for lateral faces.
s = 16 + 10 + 10 + 10 + 10
If x=−4 is a solution to the equation x2+11x+K=0 , then K= ?
Answer:
x^2 + 11x + k = 0
(-4) ^2 + 11 (-4) + k = 0
16 - 44 + k = 0
-28 + k = 0
K = 28
Hope Helpful ~
Help and show explanation please
Answer:
This app is very good,it help us do our homework.and we make a good passed.
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y = -3/2x + 8
Step-by-step explanation:
Slope: y2 - y1 / x2 - x1
= 5-2 / 2-4
= -2/3
Y intercept is 8
You work at a restaurant and the head manager has sent you to purchase livestock for an experiment. You want to grow the meat for the food right at the restaurant. You have been given 500 gold coins to spend at the store to purchase the livestock. Each sheep costs 12 gold coins, while each chicken costs seven.
If you purchase 32 sheep, how many chickens can you buy? Show all of your work. Hint: you don’t have to spend every coin.
Write an inequality that represents this situation.
If you want to buy twice as many chickens as sheep, what is the maximum number of sheep you can buy? Show all of your work.
Make a graph of the inequality from #2. Remember to label all parts of the graph. Label the intercept points.
Part 2: The animals you bought for the restaurant are doing quite well. You purchased an initial flock of 30 sheep and 20 chickens. The chickens and sheep have been breeding very successfully, and the flocks are growing. The sheep breed at a rate so that they will double every year. The chickens breed faster than the sheep (it helps when you can lay multiple chicks from one hen at a time!) The population of the chickens multiplies by 2.2 each year. (For all of these problems round to the nearest animal.)
5. How many sheep will there be in five years? Show all of your work.
6. Create an exponential equation to represent this situation.
7. How many chickens will there be in eight years? Show all of your work.
8. Create an exponential equation to represent this situation.
9. During what year will there be more chickens than sheep? Show your work or explain how you know.
10. Plot the two curves on a graph together. Remember to label all parts of the graph.
11. What is the domain of each function?
12. What is the y-intercept for each function? Explain what this number means in the context of this situation.
13. Your field can support a maximum of 3000 animals before you run out of vegetation and space. During what year will you need to purchase more land to house the animals?
The number of chickens is 16 if you purchase 32 sheep and inequality is 12x + 7y ≤ 500.
What is an exponential function?
It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent [tex]\rm y = a^x[/tex]
where 'a' is a constant and a>1
Total coins = 500 gold coin
Each sheep costs 12 gold coins, while each chicken costs 7 gold coins.
If purchased 32 sheep, so the total cost for the 32 sheep:
= 32×12
= 384
Remaining gold coin = 500 - 384 = 116 gold coin
Number of chicken can purchase in 166 gold coin = 116/7 = 16.57 ≈ 16
Inequality for the above scenario:
Let x be the number of sheep and y be the number of chickens.
12x + 7y ≤ 500
If you want to buy twice as many chickens as sheep.
y = 2x
12x + 7y = 500
After solving both the equation:
x = 19.23 ≈ 19 (Number of sheep)
y = 38 (double the number of sheep)
For the part 2:
The exponential equation for the sheep:
[tex]\rm y = 30(2)^x^-^1[/tex]
After 5 years, plug x = 5
[tex]\rm y = 30(2)^4[/tex]
y = 480 sheep
The exponential equation for the chicken:
[tex]\rm y = 20(2.2)^x^-^1[/tex]
After 8 years, plug x = 8
[tex]\rm y = 20(2.2)^7[/tex]
y = 4988.71 ≈ 4988 chickens
Similarly, you can find the rest of the data using the above equation.
Thus, the number of chickens is 16 if you purchase 32 sheep and inequality is 12x + 7y ≤ 500.
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How to simplify question below ?
Answer:
[tex]3x^2y[/tex]
Step-by-step explanation:
The cube root of 27 is 3.
With indices, cube rooting them is the equivalent of multiplying by 1/3 so:
[tex]x^2y[/tex].
Put these 2 things together and you get:
[tex]3x^2y[/tex]
Solve Algebraically
y=x2−4x+3
y=x−5
Answer:
then
x2-4x+3=x-5
or,x2-4x-x= -5-3
or,x2-5x+8=0
Kieran enters four events in an athletics
competition. The probability of him winning each
of the events is shown below.
Order the probabilities from least likely to most
likely.
100 m
Long jump
Discus
Hurdles
2
0.46
²3
23%
3
10
5
Answer:
Discus, Hurdles, Long jump, and 100m
Step-by-step explanation:
7. In which step does a mistake first occur? 8÷2+ (3 x 3-2) Step 1: 8÷2 + (3 x 1) Step 2: 8÷2+3 Step 3: 4+3 Step 4: 7
Answer: Step 1
A mistake first happens in Step #1. PEMDAS is not followed correctly.
(PEMDAS = parentheses, exponents, multiplication, division, addition, subtraction)
When solving 8÷2+(3x3-2), you first move left to write and solve the problems working through the correct order of operations.
Correct Steps:
1) 8÷2 + (3x3-2)
2) 4 + (9-2)
3) 4 + 7
4) 4+7 = 11
What is the equation of the following line? Be sure to scroll down first to see
all answer options.
(0,0) (4,-2)
Answer:
y = -2x
Step-by-step explanation:
From the figure, the given line passes through the points (0, 0) and (-4, 8).
Recall that the equation of a straight line is given by
Thus, the equation of the given figure is given by
-4y = 8x
Therefore, the answer is y = -2x.
Why can’t you Factor x^2+9
Answer:
You can't answer this because there isn't a regular x value, there is only a x squared
Step-by-step explanation:
[tex]~~~~~~x^2 +9 = 0\\\\\implies x^2 = -9\\\\\implies x = \pm\sqrt{-9}\\\\\implies x=\pm 3i\\\\\text{Which is not real, so the given expression can't be factored for} ~x \in \mathbb{R}.[/tex]
A rectangular park has a perimeter of 374 feet and a length of 65 feet.
What is the width of the park?
Answer: 122
Step-by-step explanation:
▪︎ Perimeter = (width + length) * 2
374 = (width + 65) * 2
width + 65 = 374 / 2
width + 65 = 187
width = 187 - 65
width = 122
Prove algebraically that the straight line with equation x =2y+5 is a tangent to the circle with equation x ² +y ²
The intersection point is only one. Then the equation of the line is tangent to the circle at point (1, -2).
What is a circle?It is a locus of a point drawn an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
Prove algebraically that the straight line with equation x = 2y + 5 is a tangent to the circle with equation x² + y² = 5.
x = 2y + 5 ...1
x² + y² = 5 ...2
If the intersection of the point of the circle and line is one. Then the line is tangent to the circle.
Then from equations 1 and 2, we have
(2y + 5)² + y² = 5
4y² + 25 + 20y + y² - 5 = 0
5y² + 20y + 20 = 0
5y² + 10y + 10y + 20 = 0
5y (y + 2) + 10(y + 2) = 0
(5y + 10)(y + 2) = 0
y = -2, -2
Then the value of y is unique then the value of x will be unique.
The value of x will be
x = 2(-2) + 5
x = -4 + 5
x = 1
The intersection point is only one. Then the equation of the line is tangent to the circle at point (1, -2).
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[tex] \sqrt[3]{800} [/tex]
between 2 and 3
between 4 and 5
between 9 and 10