Answer:
X = 9,X= -5, a = 2, b = -13
Step-by-step explanation:
For (1),
Using Cross-factorization,
it can be reduced to (X - 9)(X + 5) = 0
Equate each factor to 0:
we have X = 9 and X = -5
For (2),
It is the case of completing the Square,
add 4 so we get the completed square ( we want the form X^2 + 2a + a^2)
(X^2 + 4X + 4) - 9
can be simplified to (X+2)^2 -9
However since we added 4 it means we have to subtract 4
So it becomes (X+2)^2 -9 -4
= (X+2)^2 -13
Charlie does a weekly exercise program consisting of cardiovascular work and weight training. Each week, he exercises for at least 9 hours. He spends at most 12 hours on weight training. He spends at most 6 hours doing cardiovascular work. Let x denote the time (in hours) that Charlie spends doing cardiovascular work. Let y denote the time (in hours) that he spends on weight training. Shade the region corresponding to all values of x and y that satisfy these requirements.
Answer:
[tex](x_1,y_1) = (0,9)[/tex]
[tex](x_2,y_2) = (6,3)[/tex]
[tex](x_3,y_3) = (6,12)[/tex]
Step-by-step explanation:
Given
x = hours spent on cardiovascular work
y = hours spent on weight training
From the first statement,
Each week: he spends at least 9 hours
This is represented as:
[tex]Total \ge 9[/tex]
[tex]x + y \ge 9[/tex]
From the second statement,
Each week: he spends a max of 12 hours on weights
This is represented as:
[tex]Weight \le 12[/tex]
[tex]y \le 12[/tex]
From the third statement,
Each week: he spends a max of 6 hours on cardio works
This is represented as:
[tex]Cardio \le 6[/tex]
[tex]x \le 6[/tex]
So, the inequalities are:
[tex]x + y \ge 9[/tex]
[tex]y \le 12[/tex]
[tex]x \le 6[/tex]
See attachment for the graph where the solution are also highlighted
From the attachment, the solutions are:
[tex](x_1,y_1) = (0,9)[/tex]
[tex](x_2,y_2) = (6,3)[/tex]
[tex](x_3,y_3) = (6,12)[/tex]
Michael has $1,076.98 in his checking account. He is going to spend $536.32 on a new television, and he will spend the rest on
speakers that cost $47.00 each. Which of the following inequalities would determine the maximum number of speakers, x, Michael
can buy without spending more money than he has in his account?
Answer:
11
Step-by-step explanation:
The difference between x and 8 is equal to 15
Answer:
x = 23
Step-by-step explanation:
15 + 8 is 23 so x = 23
Manny's muffins sells 50 muffins each day. 12 of these are blueberry. If they sell a 150 muffins tomorrow, how many blueberry muffins can they expect to sell?
Answer:
36
Step-by-step explanation:
12 times 3
Answer:
probably 36
Step-by-step explanation:
Amira sells balloon animals. She uses the same number of balloons for each animal she makes. The table compares the number of balloon animals sold and the remaining number of balloons on a certain day.
Animals Balloons
20 180
29 144
38 108
How many balloons does Amira use for each balloon animal?
Answer:
36/9=4
Step-by-step explanation:
i tried it on khan it worked
4. Write an equation of a line that passes
through the points (-5, -11) and (-2,1).
Answer:
y=4x+9
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(1-(-11))/(-2-(-5))
m=(1+11)/(-2+5)
m=12/3
m=4
y-y1=m(x-x1)
y-(-11)=4(x-(-5))
y+11=4(x+5)
y=4x+20-11
y=4x+9
LOTS OF POINTS IF U ANSWER
A 30-ounce jar of peanut butter costs $6.00. A 40-
ounce jar costs $7.20. Which jar of peanut butter is
cheaper per ounce? Be sure to justify your reasoning
and SHOW your WORK.
Answer:
The 40 ounce jar is cheaper
Step-by-step explanation:
how i did this was divide 6.00 by 30 to get 0.2 cents per ounce then 7.20 divided by 40 to get 0.18 cents per ounce so the 40 ounce jar would be cheaper, hope this helps.
What is the product?
Select the statement that describes this expression: 32 ÷ 4 + ( fraction 1 over 2 x 16) − 2. (2 points)
Group of answer choices
32 times 4 plus fraction 1 over 2 times 16, then subtract 2
32 divided by 16 added to fraction 1 over 2 plus 4, then subtract 2
Half of 16 divided by 4 plus 32, then subtract 2
The quotient of 32 and 4 added to the product of fraction 1 over 2 and 16, then subtract 2
Answer:
D
Step-by-step explanation:
hope it helps u
The statement is the quotient of 32 and 4 added to the product of fraction 1 over 2 and 16, then subtract 2 describes the expression 32 ÷ 4 + (1/2 x 16) - 2.
The given expression is "32 ÷ 4 + (1/2 x 16) - 2".
"32 ÷ 4" is the division of 32 by 4, which results in the quotient of 8. So, the first part of the expression simplifies to 8.
"(1/2 x 16)" is the product of the fraction 1/2 and 16.
Multiplying these values gives us 8.
Now, we have "8 + 8 - 2". Adding 8 and 8 gives us 16.
Subtracting 2 from 16 results in a final value of 14.
Therefore, the expression "32 ÷ 4 + (1/2 x 16) - 2" simplifies to 14.
To learn more on Expressions click:
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What is the prime factorization of 84?
A. 2•3•7
B. 3•4•7
C. 2•2•21
D. 2•2•3•7
Answer:
D. 2•2•3•7
Step-by-step explanation:
Coach Henderson had 16 gallons of paint. He used an equal amount of the paint each of 5 days. How many gallons of paint did he use each day?
A.
5
16
B.
1
6
5
C.
3
1
5
D.
3
1
16
Answer:
C
Step-by-step explanation:
I just did the test
Answer:
its c
Step-by-step explanation:
a botanist estimated that a maple tree grows 0.24 ft per month. Write a reduced fraction that is equivalent to this amount
Answer:
[tex]\frac{6\\}{25}[/tex]
Which number line shows the solution to the inequality?
Answer:
C
Step-by-step explanation:
I was taking the test and finished an hour ago
Solve the inequality:
8+4x≥12
Select one:
x≤1
x≥5
x≥1
x≤5
Answer:
x >_ 1
Step-by-step explanation:
Solving an inequality is a lot like solving an equation. Just pretend the inequality symbol is an equal sign!
(also i wont be using the _ or equal to symbol because I'm too lazy, so you'll get >_ or <_ for those, sorry)
8 + 4x >_ 12
-8 -8
4x >_ 4
/4 /4
x >_ 1
What is 0.9 divide by 2.647
Answer:
0.340007556
Step-by-step explanation:
its correct
IXL 6th grade FF.1
Im having truoble need some hellllllpppp!!?!!!
Pleas..
Answer:
p=5
Step-by-step explanation:
if 5+3 = 8
13-8=5
and both sides of the triangle need to be the same
Answer:
its 5
Step-by-step explanation:
5 + 3 + p = 13
p=5
Raul wants to buy a new bike from a store having a 10% off sale on
all bikes. The bike he wants has a sale price of $135. Write and solve
an equation to find the original price, b, of the bike.
by
Answer:
p = $150
Step-by-step explanation:
Let p represent the original price. Then 10% of that is the discount: 0.10p.
The price after discount is 90% of the original price, or (1.00-0.10)p = 0.90p = $135. We next solve this equation for p: 0.90p = $135, or p = $150.
25% of ⅛ in percent
Answer:
0.0003125%
Step-by-step explanation:
I need help quick !!!!!!!!!!!!!!!!!!!!!!
Answer:
192ft squared. But remember it says don't put the square feet so just type in: 192.
Step-by-step explanation:
The top triangle is 42 ft squared.
The rectangle below it is 150 feet squared.
You add them together and get 192 ft squared hope this helps!
I need some quick help
Answer:
Answer #2
Y = 1/4x
Step-by-step explanation:
math is so hard :’) and I need help:
Which equation matches this table?
X 0 3 9 11 13
Y 6 9 15 17 19
1. y = x + 5
2. y = x + 6
3. y = x + 3
4. y = x - 6
Answer:
The answer would be
2. y= x + 6
Answer: The answer would be
2. y= x + 6
Step-by-step explanation:
if 4x=60 what is the value of x?
Step-by-step explanation:
if 4x = 60
Then
x = 60 / 4
x = 15
Hope it will help :)❤
ann and bill share an amount of money in ratio 7:n. Ann gets 28%of the money. workout value of n
Please help meeeeee
A carnival game has 150 rubber ducks floating in a pool. The person playing
the game takes out one duck and looks at it.
• If there's a red mark on the bottom of the duck, the person wins a small
prize.
Many ducks do not have a mark.
After 50 people have played the game, only 3 of them have won a small
prize.
Estimate the number of the 150 ducks that you think have red marks on
the bottom.
Answer:
Pretty sure it's 17 ducks.
The correct answer is based on the information given, we can estimate by probability that there are approximately 9 ducks with red marks on the bottom out of the 150 ducks in the pool.
To estimate the number of ducks with red marks on the bottom, we can use the information given: out of 50 people playing the game, only 3 have won a small prize.
We can assume that the probability of winning a small prize is the same for each player, and that each duck is equally likely to have a red mark.
If only 3 out of 50 people have won a small prize, we can estimate that the probability of winning is approximately 3/50.
Let's denote the number of ducks with red marks as "x." The probability of winning a small prize can be represented as x/150 (since there are 150 ducks in total).
Setting up the equation:
x/150 = 3/50
To solve for x, we can cross-multiply:
50x = 3 * 150
50x = 450
Dividing both sides by 50:
x = 9
Therefore, based on the information given, we can estimate by probability that there are approximately 9 ducks with red marks on the bottom out of the 150 ducks in the pool.
Learn more about probability here:
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2. The amount of sap that is collected from
six sugar maples from a 12-acre forest of
sugar maples that are being tapped.
Population:
Sample:
Complete the table. Then
identify the y-intercept
and the coordinate
where x = 1.
Consider the following
exponential equation.
Sketch the graph of the
exponential function.
y = 16(4x+1)
у
х
-2
-1
o
1
2
3
As x increases (x ).
у
As x decreases (x-co),
у
Answer:
y x
-2 1/4
-1 1/2
0 1
1 2
2 4
Step-by-step explanation:
its easy algbra
doing it rn to
A farmer had two different sized rectangular gardens the smaller garden has. Alr the of 24 feet and width of 9 feet what is the area in square feet of the smaller garden
An experiment consists of spinning the spinner once. a: Find the probability of landing on a 2. b: find the probability of landing on a 1. c: Is landing in each section of the spinner equally likely to occur? Explain.
Answer:
points
Step-by-step explanation:
Find the value of x in the triangle shown below
X=?
Answer:
you can use :
cos(X) = ( 5^2 + 6.9^2-5^2) / (2*5*6.9)
use caculator shift cos of this
The probability of spinning an odd number on a spinner is 62 percent. If you spin 100 times, how many times would you expect it to land on an odd number?
Answer:
The spinner will land 1 three times out of every Eight
Step-by-step explanation:
Answer:
62 times
Step-by-step explanation:
if the probability is 62/100 then u get an odd num 62 times out of every 100