Write the solution to the inequality in set - builder notation:
5r + 8 < 63
Factor the polynomial: 8t^2 + 8t - 72
Final answer:
To factor the polynomial [tex]8t^2 + 8t - 72,[/tex] we first extract the common factor of 8, then factor the trinomial [tex]t^2 + t - 9[/tex] using the technique of finding two numbers that multiply to -72 and add up to 1, which are 9 and -8. Finally, we group and factor by grouping to get the factored form, 8(t - 8)(t + 9).
Explanation:
To factor the polynomial [tex]8t^2 + 8t - 72,[/tex], we will first look for the common factors and then apply factoring techniques. First, we can take out the common factor of 8:
8[tex](t^2 + t - 9)[/tex]
Next, we factor the trinomial inside the parentheses. We need two numbers that multiply to 8 * -9 = -72 and add up to 1. These numbers are 9 and -8. So, we can split the middle term based on these numbers:
[tex]t^2 - 8t + 9t - 9[/tex]
We group the terms to factor by grouping:
[tex](t^2 - 8t) + (9t - 9)[/tex]t(t - 8) + 9(t - 1)Now we factor out the common binomial factor:
(t - 8)(t + 9)
Therefore, the factored form of [tex]8t^2 + 8t - 72,[/tex] is 8(t - 8)(t + 9).
Adam says that the number 4 has four factors. Explain why this statement is incorrect.
Answer:
Sample response: The number 4 only has three factors: 1, 2, and 4. Adam probably counted the factor 2 twice.
Step-by-step explanation:
a utility bill shows that a household use 2001 gallons of water in a 5-day period. what was the average amount of water used by the households each day
What is the product in lowest terms?
5/6 x -8/15 ( / means fractions)
1.-8/9
2.-4/9
3. -1/3
4. -1/7
Do not answer if aren’t sure.
In a survey about favorite breakfast foods, 3/8 of those surveyed chose cereal , 0.125 chose yogurt, 0.1875 chose fruit, 5/8 chose toast which got the least number of votes.
The given question is a comparison of fractions and decimals to determine the smallest number. When all values are converted to decimals for easier comparison, we find that the smallest number is 0.125, which represents the people who chose yogurt as a breakfast food, hence, yogurt got the least number of votes.
Explanation:The given values in the problem represent different proportions of people's choices for breakfast. The question wants to find the breakfast food with the least number of votes. To do this, we need to understand the numerical values. All are fractions and decimal numbers that represent parts of 1 whole (or 100 percent). Here, the numbers are 3/8 for cereal, 0.125 for yogurt, 0.1875 for fruit, and 5/8 for toast. Converting all to either decimals or fractions for comparison, we get 0.375 for cereal, 0.125 for yogurt, 0.1875 for fruit, and 0.625 for toast.
Comparing these numbers, 0.125 (yogurt) is the smallest number. Therefore, among the given choices, the least number of people chose yogurt for their breakfast food.
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Joel earns 1,700 per month if he spends 425 on rent what percent of his income dose he spend on rent?
Please help. I don’t understand any of this.
Answer:
If the two triangles are congruent (not just similar), then QS and TV would be equal. Thus, 3v + 2 = 7v - 6.
Solving this equation for v: 4v = 8, and v = 2.
Then QS = 3(2) + 2, or 8, and TV should be the same: 7(2) - 6 = 8.
Step-by-step explanation:
A science fair poster is a rectangle 3 feet long and 2 feet wide. What is the area of the poster in square inches? Be sure to include the correct unit in your answer.
The hot summer fair is coming to town! Admission to the fair costs 12.99 and each ride costs 1.75. You have 35 to spend at the fair including admission.
The correct answer is:
12 rides
Explanation:
You have $35 to spend. Taking away the admission price, $12.99, we have
35-12.99 = $22.01 left.
Each ride costs $1.75. This means you can ride
22.01/1.75 = 12.577 or 12 rides. (This does not round up, as you would not have enough money to ride 13 rides.)
Your cousin is taking the train to Washington to visit her parents. She has at most $15.00 to spend on snacks and reading materials. Granola bars cost $1.15 each, and magazines cost $1.25. If your cousin buys the same number of granola bars and magazines, how many can she buy?
I need help ASAP i'm doing math and we are do Addition with mixed numbers
A freight train is loaded with 12 1/2 tons of corn, 11 1/3 tons of oats, and 6 1/4 tons of wheat.how many tons of grain is it carrying? Note: Corn, oats, and wheat are considered grain
A) 29 1/12
B) 30 1/12
C) 29 11/12
D) 30 1/6
1.What is the elapsed time between 11:50 a.m. and 4:05 p.m.?
a.4 hours and 45 minutes
b.15 hours and 15 minutes
c.5 hours and 15 minutes
d.4 hours and 15 minutes
2.Which pair of times has the longest elapsed time between the two times?
a.1:05 to 6:10
b.10:15 a.m. to 3:25 p.m.
c.2:45 to 7:45
d.9:10 p.m. to 1:55 a.m.
3.If it is 12:50, what will the time be 5 hours and 20 minutes later?
a.5:30
b.5:50
c.6:10
d.6:50
4.What would the temperature be on an autumn day?
a.50°F
b.32°C
c.100°F
d.0°C
5.Convert 122°C to Fahrenheit.
a.139.6°F
b.251.6°F
c.212°F
d.218.4°F
6.Convert 124°F to Celsius.
a.50.6°C
b.85.8°F
c.98.6°C
d.165.6°C
7.What temperature is shown on the thermometer?
200°F
90°F
180°F
80°C
8.mark all that apply Which temperatures are below 108°C?
a.230°F
b.212°F
c.225°F
d.228°F
A photographer uses a light meter to measure the intensity of light from a flash bulb. The intensity for the flash bulb,I, in lux, is a function of the distance from the light, d, in meters, and can be represented by I(d)=10/d^2, d>0 determine the approximate instantaneos rate of change in the intensity of light at exactly 3m from flash bulb. determine the approximate instantaneos rate of change in the intensity of light at exactly 3m from flash bulb.
The approximate instantaneous rate of change in the intensity of light at exactly 3m from the flash bulb is -20/27 lux per meter.
Explanation:The photographer uses a light meter to measure the intensity of light from a flash bulb. The intensity of the flash bulb, I, in lux, can be represented by the function I(d) = 10/d^2, where d is the distance from the light in meters.
To determine the approximate instantaneous rate of change in the intensity of light at exactly 3m from the flash bulb, we need to find the derivative of the intensity function with respect to d. Taking the derivative, we get dI/dd = -20/d^3.
Substituting d = 3 into the derivative, we get dI/dd = -20/3^3 = -20/27.
Therefore, the approximate instantaneous rate of change in the intensity of light is -20/27 lux per meter at exactly 3m from the flash bulb.
The approximate instantaneous rate of change in the intensity of light at exactly 3m from the flash bulb is approximately -0.741 lux/m.
Explanation:To determine the instantaneous rate of change in the intensity of light at exactly 3m from the flash bulb, we need to find the derivative of the intensity function with respect to distance.
The intensity function is given as I(d) = 10/d^2, where d is the distance from the light in meters. To find the derivative, we can use the power rule for differentiation.
Taking the derivative of the intensity function gives us: dI/d(d) = -20/d^3.
At exactly 3 meters, the instantaneous rate of change in the intensity of light can be calculated by substituting d=3 into the derivative equation: dI/d(d) = -20/3^3 = -20/27. Therefore, the approximate instantaneous rate of change in the intensity of light at exactly 3m from the flash bulb is approximately -0.741 lux/m.
A telecommunication company has 7 satellites, two of which are sending a week signal. If two are picked at random without replacement, find the probability that both are sending a week signal
Hence, the probability that both are sending a weak signal is [tex]\frac{1}{21}.[/tex]
What is probability?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
The probability of an event is a number between [tex]0[/tex] and [tex]1[/tex], where, roughly speaking, [tex]0[/tex] indicates the impossibility of the event and [tex]1[/tex] indicates certainty.
Since, [tex]\frac{2}{7}[/tex] is the probability that the first satellite sends a weak signal.
And leaves six, and one is sending a weak signal.
So, the probability that the second also sends a weak signal it has the probability [tex]\frac{1}{6}[/tex].
By Combining these and we get
[tex]\frac{2}{7}[/tex]×[tex]\frac{1}{6}[/tex] = [tex]\frac{1}{21}[/tex] .
Hence, the probability that both are sending a weak signal is [tex]\frac{1}{21}.[/tex]
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What is 160/3 in simplest form
Assessment timer and count Assessment items Factor the expression. 24−18y Enter your answers in the boxes to complete the factored expression.
A car detailing company charges $30 plus $18 per hour. Another company charges $25 plus $20 per hour. How long is a job that costs the same no matter which company is used? (There should be a variable on both sides of the equal sign/equation)
( C = 5b+200 ) this equation is used to find C, the total cost for painting a quantity of books (b) . What equation is equivanlent when solved for B in terms of C
To solve the equation C = 5b + 200 for b in terms of C, subtract 200 from both sides of the equation and then divide both sides by 5.
Explanation:To solve the equation C = 5b + 200 for b in terms of C, we need to isolate the variable b. First, subtract 200 from both sides of the equation:
C - 200 = 5b
Next, divide both sides of the equation by 5:
b = (C - 200)/5
So, the equivalent equation when solved for b in terms of C is b = (C - 200)/5.
What did Ranofer notice about the old mans hands ?
What do you get when you cross a weeping willow with a UFO
Marlon used 3 kilograms of almonds to make 9 batches of snack mix. How many kilograms of almonds, on average, were in each batch
Which algebraic expression represents the phrase “two times the quantity of a number minus 12”?
the answer is 2(y-12)
what is 1/10 of .1 thank you
Solve the equation
A+b - c =180 for C
Identify the corresponding word problem given the equation: x + 12.50 = 55.75 A) For mowing the neighbor's yard, Jessy was paid $12.50. If he now has $55.75, how much money did he have before? B) For mowing the neighbor's yard, Jessy was paid $55.75. If he now has $12.50, how much money did he have before? C) For mowing the neighbor's yard, Jessy was paid $43.25. If he now has $55.75, how much money did he have before? D) For mowing the neighbor's yard, Jessy was paid $12.50. If he now has $68.25, how much money did he have before?
Option A is correct. For mowing the neighbor's yard, Jessy was paid $12.50. If he now has $55.75, how much money did he have before?
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is
x + 12.50 = 55.75
x=55.75-12.5
x=43.25
We need to find among the given options which corresponds the given equation
A) For mowing the neighbor's yard, Jessy was paid $12.50. If he now has $55.75, how much money did he have before?
B) For mowing the neighbor's yard, Jessy was paid $55.75. If he now has $12.50, how much money did he have before?
C) For mowing the neighbor's yard, Jessy was paid $43.25. If he now has $55.75, how much money did he have before?
D) For mowing the neighbor's yard, Jessy was paid $12.50. If he now has $68.25, how much money did he have before?
In these options, option A corresponds the equation x + 12.50 = 55.75
The amount Jessy has now is 55.75, 12.75 is paid, x is the money before jessy have.
Hence, Option A is correct. For mowing the neighbor's yard, Jessy was paid $12.50. If he now has $55.75, how much money did he have before?
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Help,Cause homework is hard :/
Can y’all plz help me ignore the writing part on the side of it plz show me the steps or tell me
A satellite makes 4 revolutions of the earth in one day. How many revolutions would it make in 6 1/2 days?
A satellite makes 26 revolutions of the earth in 6 1/2 days.
What is fraction?"A number expressed as a quotient, in which a numerator is divided by a denominator. "
What is unitary method?"It is a method of finding the value of a single unit, and based on that value we can find the required value."
For given question,
A satellite makes 4 revolutions of the earth in one day.
⇒ 1 day = 4 revolutions
We need to find the number of revolutions in 6 1/2 days.
We can write the fraction [tex]6 \frac{1}{2}[/tex] as,
[tex]6 \frac{1}{2}[/tex] days
= [tex]\frac{13}{2}[/tex] days
= 6.5 days
By unitary method, for 6.5 days the number of revolutions would be,
= 6.5 × 4
= 26
Therefore, a satellite makes 26 revolutions of the earth in 6 1/2 days.
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What is 4/5 - 2/3?
Someone please answer.
I have to write up to 20 characters so yh.