Answer:
A
Step-by-step explanation:
We have the two functions: [tex]f(x)=1-x^2[/tex] and [tex]g(x)=x^2-1[/tex].
And we want to find the value of b such that [tex]f(3b)+8=g(3b)-8[/tex] is true.
Notice that we can multiply f(x) by -1. This yields:
[tex]-f(x)=x^2-1[/tex]
Notice that this is the same as g(x). Therefore:
[tex]-f(x)=g(x)[/tex]
If we substitute 3b for x:
[tex]-f(3b)=g(3b)[/tex]
So, we can go back to our equation. We have:
[tex]f(3b)+8=g(3b)-8[/tex]
Substitute -f(3b) for g(3b):
[tex]f(3b)+8=-f(3b)-8[/tex]
Solve. Subtract 8 from both sides and add f(3b) to both sides:
[tex]2f(3b)=-16[/tex]
Divide both sides by 2:
[tex]f(3b)=-8[/tex]
Now, we can use the function of f(x). Substitute 3b into f(x). So:
[tex]1-(3b)^2=-8[/tex]
Subtract 1 from both sides:
[tex]-(3b)^2=-9[/tex]
Divide both sides by -1:
[tex](3b)^2=9[/tex]
Take the square root of both sides:
[tex]3b=\pm 3[/tex]
Divide both sides by 3. So, the value of b can be:
[tex]b=-1, 1[/tex]
Therefore, our answer is A.
And we're done!
Answer:
A.1
Step-by-step explanation:
f(x) = 1 - x² ⇒ f(3b) = 1 - (3b)² = 1 - 9b²
g(x) = x² - 1 ⇒ g(3b) = (3b)² - 1 = 9b² - 1
f(3b) + 8 = g(3b) - 8 ⇒ (1 - 9b²) + 8 = (9b² - 1) - 8
⇔ 9 - 9b² = 9b² - 9
⇔ 9 + 9 = 9b² + 9b²
⇔ 18 = 18b²
⇔ b² = 1
⇒ b = 1; - 1
Sam sold a watch at 20% less than the cost price. He receive 212$. What was the cost price of the watch?
Answer:
let cp = x
now ,
sp= x-5%ofx
212= 4x/5
x=265$
Answer: Cost price 265$
Step-by-step explanation: Loss% = 20.
Money Earned After loss =212$.
cost price - loss = 265 - 20% = 212.
Graph the solution of this inequality 3/4(x+8)>1/2(2x+10)
Answer:
I'm terrible at explaining so here's a screenshot
- Ripper
Step-by-step explanation:
The Cedarburg High School softball coach is purchasing equipment for her team. She has a
budget of at most $590 to purchase bats and softballs. A case of softballs has a price of $42,
and a bat has a price of $15.
Select the inequality in standard form that describes this situation. Use the given numbers
and the following variables.
x= the number of cases of softballs
y = the number of bats
42x + 15y > 590
42x + 15y < 590
42x + 15y 3 590
42x + 15y 590
Answer:
B.42x + 15y < 590
Step-by-step explanation:
The dosage of cough medicine for a child 4 to 6 is 1/2 every 4 hours. If a child receives 5 doses of medication over 2 day, how many teaspoons has the child receives
- - - - - - - - - - - - - - - -
There is some unnecessary information in the problem, first, it should be removed.
"The dosage of cough medicine for a child 4 to 6..."
"2 days"
Listing the age and days don't matter here, it's the rest of the problem that matters!
- - - - - - - - - - - - - - - -
"1/2(a teaspoon) every 4 hours," This is one dose. Multiply 1/2 by five to see how many teaspoons are consumed.
1/2 x 5 = 2 1/2 (teaspoons)
- - - - - - - - - - - - - - - -
Good luck! :)
~pinetree
Need help quick!!
WILL GIVE BRAINLIEST
Answer:
3 and 4 x=25, y=29
Step-by-step explanation:
If you need a step by step explanation, I will edit this later.
which equation represents the graphed line??? 20POINTS!!!!!!!
Answer:
B. y-1 = -2(x-3)
I think because the line met there
Solve the inequality and graph its solution.
|n| > 7
How long is the minute hand on a clock whose tip travels 15 cm from 1:15 to 1:30 to the nearest tenth?
10.1 cm
9.6 cm
6.0cm
0.2 cm
We will see that the length of the minute hand is 9.6 cm.
How long is the minute hand?
We know that for a circle of radius R, the length of the arc defined by an angle of θ is:
L = θ*R
In this case, the length of the arc is 15 cm, and the angle is the one between 1:15 and 1:30, which is one-fourth of a complete circle.
If a complete circle has an angle of 2pi, then one-fourth of a circle has an angle θ = (2pi)/4 = pi/2
Then, replacing the length of the arc and the angle we have:
15cm = (pi/2)*R
Now we can solve this for R, remember that pi = 3.14:
(15 cm)*(2/3.14) = R = 9.6cm
So the length of the minute hand is 9.6 cm.
So the correct option is the second one.
If you want to learn more about circles, you can read:
https://brainly.com/question/25938845
Answer:
B: 9.6cm
Step-by-step explanation:
took the test
Many utility companies promote energy conservation by offering discount rates to consumers who keep their energy usage below certain established subsidy standards. A recent report notes that 20% of island residents of a country have reduced their electricity usage sufficiently to qualify for discounted rates. If five residential subscribers are randomly selected from a city on this island find the probability of each of the following events.
a. All five qualify for the favorable rate
b. At least four qualify for the favorable rates
Answer: a. 0.00032 B. 0.00672
Step-by-step explanation:
Given: Proportion of island residents of a country have reduced their electricity usage (p) = 20%= 0.20
Here, residents have two choices either reduced electricity usage or not , hence it follows binomial distribution
Let X be a binomial variable that represents the number of successes .
Binomial distribution formula:
[tex]P(X)=^nC_xp^x(1-p)^{n-x}[/tex], n= sample size.
a.
[tex]P(X=5) = ^5C_5(0.20)^5(1-0.20)^{5-5}=(1)(0.20)^5(1)\\\\=0.00032[/tex]
b. [tex]P(X\geq4)=P(4)+P(5)[/tex]
[tex]^5C_4(0.20)^4(1-0.20)^{5-4}+0.00032\\\\=(5)(0.20)^4(0.80)+0.00032\\\\=0.0064+0.00032\\\\=0.00672[/tex]
What is the area, in square centimeters, of the shape below? Express your answer as a fraction in simplest form.
Answer: (2/5) x (3/2) x .5 = 3/10 or .3
Step-by-step explanation: Area of a triangle is (1/2)bh . You substitute your answers and simplify.
At Jack’s ice cream shop, a customer receives a free ice cream cone for every 5 ice cream cones the customer purchases. Which of the following represents the ratio of the number of ice cream cones a customer purchases to the total number of ice cream cones the customer purchases and receives for free?
Answer:
5:1
The question states that for every 5 ice cream cones a customer purchases that they will get one free ice cream cone.
Example:
This means if a customer purchased 25 ice cream cones then they would get 5 free ice cream cones.
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
Answer:
=> 0:2
step by step :divide the first number by the second number and multiply the result by 100 (if necessary)
> first term is 1
> second term is 2
solution :
1 ÷ 5 = 1/2 (2dp) which is =0,2
final solution:
=0:2
NO LINKS!!
The length of a rectangle is 5 less than twice the width. What values of the width will make the area less than 150 square feet? Define your variable(s). Write inequalities that could be used to solve this problem. Then solve the problem.
Answer: Anything between 0 and 10, excluding both endpoints.
In terms of symbols we can say 0 < w < 10 where w is the width.
===================================================
Explanation:
You could do this with two variables, but I think it's easier to instead use one variable only. This is because the length is dependent on what you pick for the width.
w = width
2w = twice the width
2w-5 = five less than twice the width = length
So,
width = wlength = 2w-5which lead to
area = length*width
area = (2w-5)*w
area = 2w^2-5w
area < 150
2w^2 - 5w < 150
2w^2 - 5w - 150 < 0
To solve this inequality, we will solve the equation 2w^2-5w-150 = 0
Use the quadratic formula. Plug in a = 2, b = -5, c = -150
[tex]w = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\w = \frac{-(-5)\pm\sqrt{(-5)^2-4(2)(-150)}}{2(2)}\\\\w = \frac{5\pm\sqrt{1225}}{4}\\\\w = \frac{5\pm35}{4}\\\\w = \frac{5+35}{4} \ \text{ or } \ w = \frac{5-35}{4}\\\\w = \frac{40}{4} \ \text{ or } \ w = \frac{-30}{4}\\\\w = 10 \ \text{ or } \ w = -7.5\\\\[/tex]
Ignore the negative solution as it makes no sense to have a negative width.
The only practical root is w = 10.
If w = 10 feet, then the area = 2w^2-5w results in 150 square feet.
----------------------
Based on that root, we need to try a sample value that is to the left of it.
Let's say we try w = 5.
2w^2 - 5w < 150
2*5^2 - 5*5 < 150
25 < 150 ... which is true
This shows that if 0 < w < 10, then 2w^2-5w < 150 is true.
Now try something to the right of 10. I'll pick w = 15
2w^2 - 5w < 150
2*15^2 - 5*15 < 150
375 < 150 ... which is false
It means w > 10 leads to 2w^2-5w < 150 being false.
Therefore w > 10 isn't allowed if we want 2w^2-5w < 150 to be true.
The time required to play a new video game is normally distributed. If the mean time to play this game is 23.5 hours with a standard deviation of 1.7 hours, what is the probability that a player will complete this game in between 21.8 and 25.2 hours?
47.72%
99.74%
68.24%
95.44%
Answer:
69.24
Step-by-step explanation:
i did the quiz
Answer:
68.24
Step-by-step explanation:
Help me with this any smart math people or mr brainly or any smart Genius Pro Math HELPER
1. GENERALIZE Think about quadrilaterals and rotational symmetry. Write some generalizations of your own about rotational symmetry and quadrilaterals.
Answer:
Step-by-step explanation:
It is a little vague on what the expected answer is. But for quadrilaterals, any rotational symmetry will be along a line that divides the quadrilaterals in two equal halves. This is due to symmetry.
Also the two equal halves will be mirror image of each other at the axis of symmetry. It is again due to properties of symmetry.
Lastly rotating a quadrilateral along its axis of rotational symmetry will create a 3-D cylindrical shape. A cross-section of that shape along the axis will show the same quadrilateral.
Pavit has a clock with a minute hand that extends to the clock's edge. The minute hand is 5.25 inches long. What is the circumference of the clock?
Answer:
10.5[tex]\pi[/tex] Inches
Step-by-step explanation:
C=2[tex]\pi[/tex]r
C=2[tex]\pi[/tex]5.25
C=10.5[tex]\pi[/tex]
t - 2(3 – 2t) = 2t + 9
Answer:
t=-1
Step-by-step explanation:
t - 2(3 - 2t) = 2t - 9
t - 6 + 4t = 2t - 9
5t - 6 = 2t - 9
5t - 2t = -9 + 6
3t = -3
t= -1
Help help math math ASAP pelsss
Answer:
(6, 1)
Step-by-step explanation:
x + 3y = 9
x + 4y = 10
---------------------
-1 (x + 3y = 9)
---------------------
-x - 3y = -9
x + 4y = 10
1y = 1 or y =1
x + 4y = 10
x + 4(1) = 10
x + 4 = 10
-4 -4
x = 6
I hope this helps!
Staples sells boxes of pens ($25) and rubber bands ($5). Leona ordered a total of 20 cartons for $360. How many boxes of each did
Leona order? Hint. Let P= Pens.
Answer:
Step-by-step explanation:
I dont fully know if i am correct but i think its this:
p + r = 22
9p + 6r = 180
p = 22 - r
9(22 - r) + 6r = 180
198 - 9r + 6r = 180
-3r = -18
r = 6
p = 22 - 6
p = 16
HELP!!! Due in 10 mins help me pls! WILL GIVE BRAINLIEST!!!
You need to find a Number with 10 digits.
The first digit is divisible by 1
The second digit is divisible by 2
The third digit is divisible by 3
The fourth digit is divisible by 4
The fifth digit is divisible by 5
The sixth digit is divisible by 6
The seventh digit is divisible by 7
The eigth digit is divisible by 8
The ninth digit is divisible by 9
The full number is divisible by 10
Answer:
1234567890
Step-by-step explanation:
Each of the digits is divisible by their individual index in the number. Adding a 0 at the ends allows for the number to be divisible by 10 and completes the 10 digit requirement.
The first digit is divisible by 1
The second digit is divisible by 2
The third digit is divisible by 3
The fourth digit is divisible by 4
The fifth digit is divisible by 5
The sixth digit is divisible by 6
The seventh digit is divisible by 7
The eigth digit is divisible by 8
The ninth digit is divisible by 9
The full number is divisible by 10
For what value of x must ABCD be a parallelogram?
Answer:
7
Step-by-step explanation:
add 7 to 3x
Then: 4x-3x=1x which gives:
1x=7
7/1=7
Convert 40 ounces into pounds. Round your answer to the nearest tenth.
Hint. There are 16 ounces in one pound.
A. 2.5 pounds
B. 640 pounds
C. 0.4 pounds
Answer:
Step-by-step explanation:
A bottle contains 125 multivitamin tablets. Each tablet contains 20 milligrams of niacin.
How many grams of niacin in all are contained in the bottle?
Answer:
There are 2.5 grams of niacin contained in the bottle.
First you have to find how many milligrams are in the bottle.
So you multiply 125 by 20 since there are 125 tablets and 20 milligrams in each one.
125*20=2500
So there are 2500 milligrams in the bottle. Then you have to convert it into grams. To do that you divide the mass by 1000.
2500/1000=2.5
So there are 2.5 grams in the bottle.
Step-by-step explanation: hope this helps :)
Answer:
2.5
Step-by-step explanation:
125 vitamins, each vitamin has 20 milligrams. convert 20 milligrams to grams. 0.02 grams of niacin in each vitamin. 125 multiplied by 0.02 is 2.5
The grid represents all of the following decimal numbers except
0.300
0.3
0.30
0.030
Answer:
0.030
Step-by-step explanation:
0.030 is 3/100
what is show above is 3/10 and 0.300, 0.3, 0.30 are all equal to 3/10
You deposit $750 into a bank account. The bank pays a simple interest rate of 3%. How much interest have you earned
after three years?
Answer:
You have earned $67.50
Step-by-step explanation:
Since we are working with simple interest, we will use this formula:
[tex]I=Prt[/tex],
where P represents the principal amount (your deposit), r represents the rate as a decimal, and t represents the time in years. First, we need to rewrite our interest as a decimal by dividing 3% by 100:
[tex]3\div 100 = 0.03[/tex]
Now, we also know the values of P and t from the problem:
[tex]P=750\\r=0.03\\t=3[/tex]
We can substitute those values into the formula:
[tex]I=750(0.03)(3)\\I=67.5[/tex]
In context, that means you earned $67.50 in interest.
Need help please
TEST tomorrow
Answer:
you need to use the midpoint formula
Answer:
MN is [-3,2] sorry but not really sure about this because they are just two points and don't seem as segment.But when it asks for MN I don't know what to say else.
and midpoint of MN is -1/2
because
x=(x1+x2)/2=(-3+2)/2=-1/2
Triangle ABC will be reflected over the x-axis to create triangle ABC. Then, triangle A B C will be reflected over the dashed line to create
triangle A" "C".
Which single transformation will have the same effect on the figure?
O reflection over the x-axis
O rotation of 270° about the point (0,0)
o translation described by (x ) - (x - 6,)
o translation described by (x, ) - (xy-6)
PLEASEEE SOMEONE HELP MEE
If triangle ABC is reflected across the x axis, the new point is A'(-3, -2), B'(0, -1) and C'(-2, 3)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.
Triangle ABC has vertices A(-3,2) B(0,1) and C(-2,-3).
If triangle ABC is reflected across the x axis, the new point is A'(-3, -2), B'(0, -1) and C'(-2, 3)
Find out more on transformation at: https://brainly.com/question/1620969
Can you please help me?
9514 1404 393
Answer:
32
Step-by-step explanation:
Use the formula.
[tex]a_2=a_1\times4=2\times4=8\\\\a_3=a_2\times4=8\times4\\\\\boxed{a_3=32}[/tex]
ch rectangle. Then write an equation and solve it.
and width of each rectangle.
- 4
A=64
*-4
loc- 4
*-4
Question
A sportswear manufacturer is introducing a new line of sneakers. To introduce the new line, the company must pay out a
fixed cost of $1.5 million for advertising and equipment, plus there is a cost of 40 cents per pair of sneakers manufactured.
It plans to sell the sneakers for $75 per pair.
Let x be the number of pairs of sneakers manufactured. If the firm only manages to sell 15, 000 sneakers, what is the total
loss?
Step-by-step explanation:
1.5 mill + 40 cent per
sell for 75 per
change numbers
1, 500, 000 + 4 per
sell for 75 per
x = each sneaker
1, 500, 000 + 4 x
sell for 75 x
we want to sell 15, 000
put 15, 000 where x is
1, 500, 000 + 4 (15, 000)
sell for 75 (15, 000)
1, 500, 000 + 4 × 15, 000 = 1, 560, 000
sell for 75 × 15, 000 = 1125000
minus the amount to make sneakers from amount getting for the sneakers
loss = ?
answer in comments
please mark brainest
solve for X (step by step please)
3 (x - 2) = 4x + 2
[?]x - [ ] = 4x + 2