Answer:
35
Step-by-step explanation:
y = 35x+23 is in the form
y = mx+b where m is the slope and b is the y intercept
The slope can also be called the rate of change
35 is the slope
What is the range of the function f(x) = 3x2 + 6x – 8?
O {yly > -1}
O {yly < -1}
O {yly > -11}
O {yly < -11}
Answer:
Range → {y| y ≥ -11}
Step-by-step explanation:
Range of a function is the set of of y-values.
Given function is,
f(x) = 2x² + 6x - 8
By converting this equation into vertex form,
f(x) = [tex]3(x^2+2x-\frac{8}{3})[/tex]
= [tex]3(x^2+2x+1-1-\frac{8}{3})[/tex]
= [tex]3[(x+1)^2-\frac{11}{3}][/tex]
= [tex]3(x+1)^2-11[/tex]
Vertex of the parabola → (-1, -11)
Therefore, range of the function will be → y ≥ -11
The range of the function f(x) = 3x² + 6x - 8 is {y|y ≥ -11}
What is the range of a function?The range of a function is the set of output values of the function
Since f(x) = 3x² + 6x - 8, we differentiate f(x) = y with respect to x to find the value of x that makes y minimum.
So, df(x)/dx = d(3x² + 6x - 8)/dx
= d(3x²)/dx + d6x/dx - d8/dx
= 6x + 6 + 0
= 6x + 6
Equating the experssion to zero, we have
df(x)/dx = 0
6x + 6 = 0
6x = -6
x = -6/6
x = -1
From the graph, we see that this is a minimum point.
So, the value of y = f(x) at the minimum point is that is a t x = - 1 is
y = f(x) = 3x² + 6x - 8
y = f(-1) = 3(-1)² + 6(-1) - 8
y = 3 - 6 - 8
y = -3 - 8
y = -11
Since this is a minimum point for the graph, we have that y ≥ -11.
So, the range of the function is {y|y ≥ -11}
So, the range of the function f(x) = 3x² + 6x - 8 is {y|y ≥ -11}
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Complete the square to solve the equation below.
Check all that apply.
x^2-10x-4=10
1. Move terms to the left side
2.Subtract the numbers
3.Use the quadratic formula
4.Simplify
5.Separate the equations
6.Solve
Rearrange and isolate the variable to find each solution.
Solution,
Solution
x=5±√39
If in 1 month you can make 6 carpets, how many days will it take for making 10 carpets?
Si en 1 mes puedes hacer 6 alfombras, ¿cuántos días se necesitarán para hacer 10 alfombras?
Step-by-step explanation:
6 carpets=1month
10 carpets=?
1month=31 days
10 /6*31
51
Step-by-step explanatio
What is the answer to this question in the picture
9514 1404 393
Answer:
[tex]\displaystyle\sqrt{x+7}-\log{(x+2)}[/tex]
Step-by-step explanation:
It's pretty straightforward. You want ...
f(x) - g(x)
Substituting the given function definitions gives ...
[tex]\displaystyle\boxed{\sqrt{x+7}-\log{(x+2)}}[/tex]
Use the t-distribution to find a confidence interval for a mean mu given the relevant sample results. Give the best point estimate for mu, the margin of error, and the confidence interval. Assume the results come from a random sample from a population that is approximately normally distributed. A 95% confidence interval for mu using the sample results x-bar equals 76.4, s = 8.6, and n = 42.
Point estimate = ?
Margin of error = ?
Answer:
Point estimate = 76.4
Margin of Error = 2.680
Step-by-step explanation:
Given that distribution is approximately normal;
The point estimate = sample mean, xbar = 76.4
The margin of error = Zcritical * s/√n
Tcritical at 95%, df = 42 - 1 = 41
Tcritical(0.05, 41) = 2.0195
Margin of Error = 2.0195 * (8.6/√42)
Margin of Error = 2.0195 * 1.327
Margin of Error = 2.67989
Margin of Error = 2.680
The soil samples for the next field indicate that fertilizer coverage needs to be
greater. To achieve this, you need to increase flow rate. How would you achieve
this?
A. Increase speed to approximately 7.1 mph so that you cover the field more
quickly
B. Increase the engine speed to approximately 2,000 rpm
C. Decrease speed to approximately 6.0 mph so that you cover the field more
slowly
D. Shift to second gear so that the engine speed slows
Answer:
A. Increase speed to approximately 7.1 mph so that you cover the field more.
Step-by-step explanation:
The soil samples for the next field require more fertilizer coverage therefore there is need for more field coverage by the equipment. The speed of the tractor will be increase to 7.1 mph so that greater area can be covered in lesser time.
Write out the sample space for the given experiment. Use the following letters to indicate each choice: O for olives, M for mushrooms, S for shrimp, T for turkey, I for Italian, and F for French. When deciding what you want to put into a salad for dinner at a restaurant, you will choose one of the following extra toppings: olives, mushrooms. Also, you will add one of following meats: shrimp, turkey. Lastly, you will decide on one of the following dressings: Italian, French
Answer: He can make 36 different salds
Step-by-step explanation:
Given the similarity statement
AJKL ANOP, what's the
corresponding side of ON ?
Answer:
ON = KJ
Step-by-step explanation:
JKL = NOP
We know the angles match
<J = <N
<K = <O
< L = <P
And we know
JK = NO
KL = OP
JL = NP
We are looking for ON = KJ
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Answer:
(d) KJ
Step-by-step explanation:
The segment of interest is named using the 2nd and 1st letters of the right side of the similarity statement.
The corresponding segment will be named using the 2nd and 1st letters of the left side of the similarity statement: KJ.
Y=2.5x+5.8
When x=0.6
Answer:
7.3
Step-by-step explanation:
y=2.5x+5.8
=2.5×0.6+5.8
= 1.5+.8
=7.3
12,963 rounded to the nearest hundredth
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Answer:
12,963.00 (in the US)12,96 (some other places)Step-by-step explanation:
In the US, a decimal point is represented by a period. This value is interpreted as an integer with no fractional part, so the fractional part is zero:
12,963.00
__
Some other places, a comma is used to identify the beginning of the decimal fraction. In that form, this number has a fractional part that has 3 as its thousandths digit. The value of 3 is less than 5, so the number is simply truncated at the hundredths place.
12,96
If the thousandths digit were 5 or greater, then 1 hundredth would be added to the truncated number.
A machining center is in charge of producing 225 parts per day. The parts width. Any parts produced between 250mm and 260mm are considered gless than 250mm must be reworked at an additional cost of $8 per part. 260mm must be reworked at an additional cost of $2.50 per part. The varquantified as a standard deviation of 5.0mm. Measurements on these parhave the ability to set up the machine to achieve whatever mean width value you wish.
Required:
Setup a data table to determine the mean width setting that will minimize expected rework cost ($8 per small part and $2.50 per large part).
If a number is divisible by 6 and 8 then is it also divisible by 48?
Answer:
No
Step-by-step explanation:
Let's look at an example
24
24 is divisible by 6 24/6 = 4
24 is divisible by 8 24/8 = 3
24 is not divisible by 48 24/48 = 1/2 which is not an integer
I need two examples of rounding to the thousandths place. SHOW ALL WORK!
Answer:
3.418
Step-by-step explanation:
3.4175
3.4178
u round if the number behind it is higher than 5
establish this identity
Answer:
see explanation
Step-by-step explanation:
Using the identities
tan x = [tex]\frac{sinx}{cosx}[/tex] , sin²x = 1 - cos²x
sin2x = 2sinxcosx
Consider left side
cosθ × sin2θ
= [tex]\frac{sin0}{cos0}[/tex] × 2sinθcosθ ( cancel cosθ )
= 2sin²θ
= 2(1 - cos²θ)
= 2 - 2cos²θ
= right side , then established
Find the slope of the line which passes through the points A (-4, 2) and B (1,5).
Answer:
3/5 so A.
Step-by-step explanation:
Answer:
slope = [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, 2) and (x₂, y₂ ) = (1, 5)
m = [tex]\frac{5-2}{1-(-4)}[/tex] = [tex]\frac{3}{1+4}[/tex] = [tex]\frac{3}{5}[/tex]
Zelina scored 10% higher on her second quiz than on her first quiz. On her third quiz, Zelina scored 20% higher than on her second quiz. Her third quiz score is what percent higher than her first quiz score?
Answer:
30%
Step-by-step explanation:
you just add 10% and 20%
Hope it helps c:
Zelina scored 32% higher on the third quiz than on her first quiz.
What is the percentage?The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %.
Given that:-
Zelina scored 10% higher on her second quiz than on her first quiz. On her third quiz, Zelina scored 20% higher than on her second quiz.From the given data we will see that:-
1 ) Zelina scored 10% higher on her second quiz than on her first quiz.
SQ = 1.10 FQ
2 ) On her third quiz, Zelina scored 20% higher than on her second quiz
TQ = 1.20SQ
From the above to expression solve for the first quiz:-
TQ = 1.20 x 1.10 FQ
TQ = 1.32FQ
Therefore Zelina scored 32% higher on the third quiz than on her first quiz.
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Simplify.
Multiply and remove all perfect squares from inside the square roots. Assume z is positive.
√z ∗ √30z^2 ∗ √35z^3
Answer:
Step-by-step explanation:
You need to put parentheses around the radicands.
√z · √(30z²) · √(35z³) = √(z·30z²·35z³)
= √(1050z⁶)
= √(5²·42z⁶)
= √5²√z⁶√42
= 25z³√42
The obtained expression would be 25z³√42 which is determined by the multiplication of the terms of expression.
What is Perfect Square?A perfect Square is defined as an integer multiplied by itself to generate a perfect square, which is a positive integer. Perfect squares are just numbers that are the products of integers multiplied by themselves.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operations is called the arithmetic operator.
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
We have been the expression as:
⇒ √z · √(30z²) · √(35z³)
Multiply and remove all perfect squares from inside the square roots
⇒ √(z·30z²·35z³)
⇒ √(1050z⁶)
⇒ √(5²·42z⁶)
Assume z is positive.
⇒ √5²√z⁶√42
⇒ 25z³√42
Therefore, the obtained expression would be 25z³√42.
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Solve the system using substitution. x+y=-2 and x-y=-8
Answer:
1) x+y=-2
x=-2-y
2) x-y=-8
substitude value of x
(-2-y)-y=-8
-2-2y=-8
-2y=-6
y=3
Substitute value of y in 1
x=-2-3
x=-5
Brainliest please~
If\[\displaystyle\frac{\sqrt{600} + \sqrt{150} + 4\sqrt{54}}{6\sqrt{32} - 3\sqrt{50} - \sqrt{72}} = a\sqrt{b},\]where $a$ and $b$ are integers and $b$ is as small as possible, find $a+b.$
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Answer:
12
Step-by-step explanation:
Apparently, you want the sum a+b when ...
[tex]\[\displaystyle\frac{\sqrt{600} + \sqrt{150} + 4\sqrt{54}}{6\sqrt{32} - 3\sqrt{50} - \sqrt{72}} = a\sqrt{b},\][/tex]
A calculator can show you the expression on the left evaluates to √243. In simplest terms, that is 9√3, so we have a=9, b=3 and ...
a+b = 9+3 = 12
Answer:
12
Step-by-step explanation:
The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of 6 cm/s. When the length is 12 cm and the width is 8 cm, how fast is the area of the rectangle increasing
Answer:
Step-by-step explanation:
This is a super simple problem. I'm going to walk through it as I do when I teach this to my students for the first time.
We are given a rectangle. We are told to find how fast the area is changing under certain conditions. That tells us that the main equation for this problem is the area formula for a rectangle which is
[tex]A=lw[/tex]. If we are looking for the rate at which the rectangle's area is changing, that means that we need to find the derivative of the area implicitly. This derivative is found using the product rule because the length is being multiplied by the width:
[tex]\frac{dA}{dt}=l\frac{dw}{dt}+w\frac{dl}{dt}[/tex] . If our unknown is the rate at which the area is changing, [tex]\frac{dA}{dt}[/tex], that means that everything else has to have a value (because you can only have one unknown in an equation). Here's what we're told:
The length of the rectangle is increasing at a rate of 7 cm/s, so that satisfies our [tex]\frac{dl}{dt}[/tex];
the width is increasing at a rate of 6 cm/s, so that satisfies our [tex]\frac{dw}{dt}[/tex];
and all of this is going on when the length = 12 and the width = 8. It looks like everything will have a value except for our unknown. Filling in:
[tex]\frac{dA}{dt}=12(6)+8(7)[/tex] and
[tex]\frac{dA}{dt}=72+56[/tex] so
[tex]\frac{dA}{dt}=128\frac{cm^2}{s}[/tex]
The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 7 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken.
(a) Show the sampling distribution of the sample mean annual rainfall for California.
(b) Show the sampling distribution of the sample mean annual rainfall for New York.
(c) In which of the preceding two cases, part (a) or part (b), is the standard error of x smaller? Why?
The standard error is [larger, smaller] for New York because the sample size is [larger, smaller] than for California.
Answer:
a) [tex]E(\bar x) = \mu_{1} = 22[/tex] inches
The sampling distribution of the sample means annual rainfall for California is 1.278.
b)
[tex]E(\bar x) = \mu_{2} = 42[/tex] inches
The sampling distribution of the sample means annual rainfall for New York is 1.0435.
c)
Here, The standard error of New York is smaller because the sample size is larger than for California.
Step-by-step explanation:
California:
[tex]\mu_{1} = 22[/tex] inches.
[tex]\sigma_{1}[/tex] = 7 inches.
[tex]n_{1}[/tex] = 30 years.
New York:
[tex]\mu_{2} = 42[/tex] inches.
[tex]\sigma_{2}[/tex] = 7 inches.
[tex]n_{2}[/tex] = 45 years.
a)
[tex]E(\bar x) = \mu_{1} = 22[/tex] inches
[tex]\sigma^{p} _{\bar x} = \frac{\sigma_{1} }{\sqrt n_{1} } \\\\\\\sigma^{p} _{\bar x} = \frac{7}{\sqrt 30} \\\\\sigma^{p} _{\bar x} = 1.278[/tex]
b)
[tex]E(\bar x) = \mu_{2} = 42[/tex] inches
[tex]\sigma _{\bar x} = \frac{\sigma_{2} }{\sqrt n_{2} } \\\\\\\sigma_{\bar x} = \frac{7}{\sqrt45} \\\\\sigma _{\bar x} = 1.0435[/tex]
c)
Here, The standard error of New York is smaller because the sample size is larger than for California.
Solve equation by using the quadratic formula
Answer:
x = -2
Step-by-step explanation:
x^2 + 4x + 4 = 0
quadratic formula:
-b +or- sqrt(b^2-4ac)/2a
-4 +/- sqrt ((-4)^2-4*1*4)/2*1
-4+/- sqrt(16-16) / 2
-4 +/- 0 / 2
-4/2
-2
The product of two numbers is 60 and thei r sum is it, find the Numbers
I need help with this
Answer:
Statement A is correct
Step-by-step explanation:
Statement A is correct: Model A1 (0.25) is more prefered than Model C3 (0.15)
Two containers designed to hold water are side by side, both in the shape of a
cylinder. Container A has a diameter of 10 feet and a height of 8 feet. Container B has
a diameter of 12 feet and a height of 6 feet. Container A is full of water and the water
is pumped into Container B until Container A is empty.
To the nearest tenth, what is the percent of Container B that is empty after the
pumping is complete?
Container A
play
Container B
10
d12
8
h6
O
Answer: Volume of Cylinder A is pi times the area of the base times the height
π r2 h = (3.1416)(4)(4)(15) = 753.98 ft3
Volume of Cylinder B is likewise pi times the area of the base times the height
π r2 h = (3.1416)(6)(6)(7) = 791.68 ft3
After pumping all of Cyl A into Cyl B
there will remain empty space in B 791.68 – 753.98 = 37.7 ft3
The percentage this empty space is
of the entire volume is 37.7 / 791.68 = 0.0476 which is 4.8% when rounded to the nearest tenth
.
Step-by-step explanation: I hope that help you.
Note: you may not need to type in the percent sign.
===========================================================
Explanation:
Let's find the volume of water in container A.
Use the cylinder volume formula to get
V = pi*r^2*h
V = pi*5^2*8
V = 200pi
The full capacity of tank A is 200pi cubic feet, and this is the amount of water in the tank since it's completely full.
We have 200pi cubic feet of water transfer to tank B. We'll keep this value in mind for later.
-----------------------
Now find the volume of cylinder B
V = pi*r^2*h
V = pi*6^2*6
V = 216pi
Despite being shorter, tank B can hold more water (since it's more wider).
-----------------------
Now divide the results of each section
(200pi)/(216pi) = 200/216 = 25/27 = 0.9259 = 92.59%
This shows us that 92.59% of tank B is 200pi cubic feet of water.
In other words, when all of tank A goes into tank B, we'll have tank B roughly 92.59% full.
This means the percentage of empty space (aka air) in tank B at this point is approximately 100% - 92.59% = 7.41%
Then finally, this value rounds to 7.4% when rounding to the nearest tenth of a percent.
A tumor is injected with 0.3 grams of Iodine-125, which has a decay rate of 1.15% per day. To the nearest day, how long will it take for half of the Iodine-125 to decay?
Answer:
The time required is 60.3 days.
Step-by-step explanation:
initial amount, No = 0.3 g
rate, r = 1.15 % per day = 0.0115 per day
final amount, N = 0.15 g
Let the time is t.
[tex]N = No e^{-rt}\\\\0.15 = 0.3 e^{-0.0115 t}\\\\0.5 =e^{-0.0115 t}\\\\- 0.6931 = - 0.0115 t \\\\t = 60.3 days[/tex]
On her summer abroad in France, Jane bought a pair of shoes for 54.82 euros. The store owner only had francs to give her as change. She gave him 55 euros. How much did he give her back in francs
Answer:
0.19
Step-by-step explanation:
Jane bought a shoe for 54.82 euros
She gave the store owner 55 euros
= 55-54.82
= 0.18 euros to franc
= 0.18× 1.08222
= 0.19 franc
There is a rack of 15 billiard balls. Balls numbered 1 through 8 are solid-colored. Balsa numbered 9 through 15 contain stripes. If one ball is selected at random, determine the odds for it being striped.
If one ball is selected at random, the odds for it being striped are 7 out of 15, or 7/15.
What do we know?
We know that there are 15 billiard balls.
We also know that balls numbered 1 through 8 are solid-colored, so we have 8 solid-colored balls.
And the other 7 balls are striped.
Now we want to find the probability for a randomly selected ball to be a striped ball.
Because all the balls have the same probability of being randomly selected, the probability of randomly selecting a striped ball is equal to the quotient between the number of striped balls (7) and the total number of balls (15).
Then we have:
P = 7/15 = 0.467
That quotient is also what is called the "odds"
So if one ball is selected at random, the odds for it being striped are 7 out of 15, or 7/15.
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Polynomial: 3x^4 + 5x - 4; Divisor: x - 1
Answer:
3x³+3x²+3x+8+[tex]\frac{4}{x-1}[/tex]
Step-by-step explanation:
You can use synthetic division for this problem since the divisor is in (x-a) form. The fraction is the remainder over the divisor.
Evaluating functions (pic attached)
f(x) = 2x³ - 3x² + 7
f(-1) = 2(-1)³ - 3(-1)² + 7
=> f(-1) = 2(-1) - 3(1) + 7
=> f(-1) = -2 -3 + 7
=> f(-1) = 2
f(1) = 2(1)³ - 3(1)² + 7
=> f(1) = 2(1) - 3(1) + 7
=> f(1) = 2 -3 + 7
=> f(1) = 6
f(2) = 2(2)³ - 3(2)² + 7
=> f(2) = 2(8) - 3(4) + 7
=> f(2) = 16 - 12 + 7
=> f(2) = 11
