From the situation described, we have that:
a) Tunnel A is a circle with center (-14, 0) and radius 12, meaning that both the width and the height are of 12.
b) Tunnel B is a parabola that has a width of 32 feet and a height of 16 feet.
c) The maximum height of Tunnel A is of 12 feet and of Tunnel B is of 16 feet, hence, since the height of the truck is of 13.5 feet, it can pass through Tunnel B without damage, as it's height is greater than 13.5 feet.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
For Tunnel A, the equation is given by:
x² + y² + 28x + 52 = 0
Completing the squares:
(x + 14)² + y² = -52 + 14²
(x + 14)² + y² = 144.
Hence:
Tunnel A is a circle with center (-14, 0) and radius 12, meaning that both the width and the height are of 12.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
y = ax^2 + bx + c
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]For Tunnel B, the equation is given as follows:
x² - 36x + 16y + 68 = 0.
16y = -x² + 36x - 68.
Simplifying by 16:
y = -0.0625x² + 2.25x - 4.25.
Hence the coefficients are a = -0.0625, b = 2.25, c = -4.25, and the maximum height is:
[tex]y_v = -\frac{(2.25)^2 - 4(-0.0625)(-4.25)}{4(-0.0625)} = 16[/tex]
The width is the difference between the roots, which, using a calculator, are:
2 and 34, hence the width is of 32 feet.
Then:
Tunnel B is a parabola that has a width of 32 feet and a height of 16 feet.
For item c, we have that:
The maximum height of Tunnel A is of 12 feet and of Tunnel B is of 16 feet, hence, since the height of the truck is of 13.5 feet, it can pass through Tunnel B without damage, as it's height is greater than 13.5 feet.
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Given a line with slope of 5 and y-intercept of -1, which of the ordered pairs given below would NOT be on the line?
O (4.18)
(3, 14)
O (0-1)
O (2.9)
Answer:
(4, 18)
Step-by-step explanation:
We can just pluck the x values into the equation: y = 5x -1 to see if the y values fit.
1. y = 5(4) - 1
= 20 - 1
= 19 (Nope, 18 is not 19)
2. y = 5(3) - 1
= 15 - 1
= 14 (Yep, same as option)
3. y = 5(0) - 1
= 0-1
= -1 (Yep, same as option)
4. y = 5(2) - 1
= 10 - 1
= 9 (Yep, same as option)
The point (4, 18) is not lies on the given line.
First option is correct.
The equation of line in slope intercept form is,
[tex]y=mx+c[/tex]
Where m is slope and c is y intercept.
Given that, m = 5 and c = -1
Substitute above values
Equation of line is,
[tex]y=5x-1[/tex]
Substitute first option (4, 18) in equation of line.
[tex]18=5(4)-1\\\\18=20-1\\\\18=19[/tex], which is invalid equation.
Hence, point (4, 18) is not lies on the given line.
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If your claim is in the alternative hypothesis and you fail to reject the null hypothesis, then your conclusion would be:
Answer:
There is not sufficient proof to support the claim.This is a type II error.
Step-by-step explanation:
This is the type II error where the null hypothesis is wrong. But as you have failed to reject the null hypothesis and would not accept the alternate hypothesis it is type II error.
It means that there is not enough statistical evidence to prove your alternative claim.Your claim cannot be accepted or supported through given statistical data.
There is not sufficient proof to support the claim.
When null hypothesis is false then the wrong decision gives a type II error.
Write (p^2)^3 without exponents
Answer:
p^6
Step-by-step explanation:
We are using rule power to a power. x^2^3 = x^(2*3)
p^6
Hope this helps plz hit the crown :D
HELP!! I know how to find the answer but I don't know how to use the number line to find the answer.
Answer: 3.4
Step-by-step explanation:
[tex]\sqrt{9}[/tex]=3
[tex]\sqrt{16}[/tex]=4
16-9=7
12-9=3
3/7 ==> 0.4
[tex]\sqrt{12}[/tex]=
[tex]\sqrt{9+3}[/tex]=
[tex]\sqrt{9}+0.4[/tex]=
3+0.4=3.4
Can anyone help me out with these before 10:00 I’d greatly appreciate it ty!! :)
Answer:
The question and many
I will give you a tip
Use the formulary they use for calculating angle on a straight line that is 180 and angle at a point
Answer:
Please see the picture below
Step-by-step explanation:
Each of there pictures either equal 90 or 18o degrees.
Enter the coefficient in the expression -2x+9
Answer:
there is no
Step-by-step explanation:
-8m+(-15)+4m-2r-10 ?
Answer:
- 4m - 2r - 25
Step-by-step explanation:
-8m + (-15) + 4m - 2r - 10
- 8m - 15 + 4m - 2r - 10
collect the like terms beginning with the positives
4m - 8m - 2r - 10 - 15
- 4m - 2r - 25
The average of 100, M, and 500 is 400. What is M?
Answer:
600
Step-by-step explanation:
(100+M+500)÷3=400
600+M=400×3
600+M=1200
M=1200-600
M=600
help meeeeeeeeeeeeee
Answer:
18
Step-by-step explanation:
basic math .... hopefully it helped
Answer:
18
Step-by-step explanation:
Can someone help please
Answer:
<
Step-by-step explanation:
Answer:
> should be the correct answer as the one on the left is a larger decimal.
On a standard xy-graph, what is the midpoint between (-2, 4) and (1, -2)?
Answer: m=(-1/2. 1)
Step-by-step explanation:
m=midpoint
m=((-2+1)/2, (4+(-2))/2)
m=(-1/2, (4-2)/2)
m=(-1/2, 2/2)
m=(-1/2. 1)
10 POINTS Solve for x:
2x/7 - 18 = -6
x = -43
x = 56/3
x = 42
Answer:
Answer is "X=42"
Step-by-step explanation:
this question is driving me crazy (and no its not <1 ≈ <3)
Of the storage space available on a new tablet computer, 1/8 is used by the operating system. What percentage represents the remaining storage space available?
Answer
87.5
Step-by-step explanation:
An ice cream factory makes 160 quarts of ice cream in 5 hours. How many
quarts could be made in 36 hours? What was that rate per day?
Answer:
1152
Step-by-step explanation:
5 hours = 160 quarts
1 hour = 32 quarts
and finally
36 hours = 32×36
= 1152
Which equation describes the line shown in the graph?
y = - 5x +5/8
y = - -1/5x+8/5
y = - 5x +3/2
y= -1/5x+3/2
Determine the number of real solutions to the quadratic equation -9m^2-8m-3=0
Step-by-step explanation:
Let's solve your equation step-by-step.
−9m2−8m−3=0
For this equation: a=-9, b=-8, c=-3
−9m2+−8m+−3=0
Step 1: Use quadratic formula with a=-9, b=-8, c=-3.
m=
−b±√b2−4ac
2a
m=
−(−8)±√(−8)2−4(−9)(−3)
2(−9)
m=
8±√−44
−18
Answer:
No real solutions.
The given equation has no real solutions.
We have given that the quadratic equation
[tex]-9m^2-8m-3=0[/tex]
For this equation: a=-9, b=-8, c=-3
[tex]-9m^2-8m-3=0[/tex]
Step 1: Use quadratic formula with a=-9, b=-8, c=-3.
What is the formula for the quadratic roots?[tex]x=\frac{-b \±\sqrt{b^2-4ac}} {2a}[/tex]
Therefore we have,
[tex]x=\frac{-b \±\sqrt{b^2-4ac}} {2a}[/tex]
[tex]x=\frac{-(-8)\±\sqrt{(-8)^2-4(-9)(-3)} }{2(-9)}[/tex]
[tex]x=-\frac{4}{9} -i\frac{\sqrt{11} }{9}[/tex] and [tex]x=-4/9+i\frac{\sqrt{11} }{9}[/tex]
This equation has no real solutions.
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plz help thank you thank you
Answer:
B
Only one that goes over once and up twice
Answer:
b is the answer I believe
Gwen bought a hardcover book for $16.50 not including taxes. Her mother told her the tax was 8% on all purchases. What was the amount of tax Gwen paid? ( I need thiissss)
Answer chooses:
1.48, 1.32, 1.28, 0.88
Answer:
1.32
Step-by-step explanation:
because if you multiply it you get 1.32
What is the difference between a credit score and a credit rating? a. A credit score and a credit rating are the same thing. b. Acredit score is a measure of how much debt you have, anda credit rating is a measure of your creditworthiness. C. A credit score is a number indicating your creditworthiness, and a credit rating is a measurement of how your credit score compares to others. d. Acredit score is a measurement of your creditworthiness from one major credit bureau, and a credit rating is a measurement of your creditworthiness from all three major credit bureaus. whats the answer
Credit rating is expressed with alphabets, whereas credit score is expressed with numbers.
given s=3x+t/r, rearrange the equation for x, in terms of r,s, and t
9514 1404 393
Answer:
x = (rs -t)/(3r)
Step-by-step explanation:
[tex]s=3x+\dfrac{t}{r}\\\\s-\dfrac{t}{r}=3x\\\\\dfrac{rs-t}{3r}=x\\\\\boxed{x=\dfrac{rs-t}{3r}}[/tex]
Which of the following is the product of the complex numbers below?
(7+41)(2-31)
OA. 26+29/
OB.
26-13
1.26-13
OC. 2+29/
D. 2-13/
What is the equivalent of 6 3/10?
Answer:
63/10
Step-by-step explanation:
This is a mixed freaction therefore you would multiply the whole number by the denominator and add the numerator. The answer then being:
6x10+3
(63)
Good luck on your assignment!
Select all the relations which represent a function.
A. (1,3), (2,5), (2,7), (4,9)
B. (1,3), (2,5), (3,7), (4,9)
C. (1,3), (1,5), (1,7), (4,9)
D. (1,3), (2,3), (3,3), (4,3)
E. (1,2), (2,5), (2,1), (4,5)
please help
Answer:
(B), (D)
Step-by-step explanation:
A. (1,3), (2,5), (2,7), (4,9) NOT a function
B. (1,3), (2,5), (3,7), (4,9) - YES, it's a function
C. (1,3), (1,5), (1,7), (4,9) NOT a function
D. (1,3), (2,3), (3,3), (4,3) - YES, it's a function
E. (1,2), (2,5), (2,1), (4,5) NOT a function
find the value of this expression is x=1
x^2+4/x-6
Answer:
x
−
3
x
−
2
Step-by-step explanation:
If f(x) = -2x + 6, then find (3).
Answer:
f(3) = 0
Explanation:
To find f(3) substitute x = 3 in the equation.
Given equation:
f(x) = -2x + 6
By substituting x = 3:
f(3) = -2(3) + 6
f(3) = -6 + 6
f(3) = 0
Four different stores sell packages of organic brown rice. The prices at each store are shown in the table.
Which store has the lowest price per pound?
A. Eat Right Grocery
B. Good Food Market
C. Health First Store
D. Food for Life Market
================================
Work Shown:
For each store, divide the cost over the size to get the unit price.
Eat Right Grocery: 2.32/2 = 1.16Good Food Market: 3.70/3 = 1.23Health First Store: 5.65/4 = 1.41Food for Life Market: 7.28/5 = 1.46Round each result to the nearest penny. We see that Eat Right Grocery has the lowest unit price, or price per pound.
----------------------
Further explanation:
Let's look at the first row of the table. This says that 2 pounds of rice cost 2.32 dollars. We can form an equation of sorts
2 pounds = 2.32 dollars
Divide both sides by 2 to turn that "2 pounds" into "1 pound". This is because "price per pound" really means "price per 1 pound" or "price for each 1 pound"
So we get
2 pounds = 2.32 dollars
2/2 pounds = 2.32/2 dollars
1 pound = 1.16 dollars
Telling us the unit cost for Eat Right Grocery is $1.16 per pound. The other stores unit prices are calculated the same way.
A box shaped like a cube has an edge that is 28 cm long. How much space is available to pack inside the box?
Answer: 21,952 cm³
Step-by-step explanation:
Answer:
There are 21952cm of room in the middle
Step-by-step explanation:
To find the volume
LxHxW=volume
Mohammed used an area model to show 4x35
What is the missing number
Answer: 140
Step-by-step explanation:
An account is opened with an initial deposit of \$3,000 and earns 4.1\% interest compounded quarterly What the account worth in 2 years?
Answer:
After 2 years the account worth will be $3225
Step-by-step explanation:
Initial Deposit (Principal Amount P) = $3000
Rate r = 4.1% = 0.041
Compounded quarterly = n = 4
Time t = 2 years
We need to find future value A
The formula used is: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Putting values in formula and calculating A
[tex]A=P(1+\frac{r}{n})^{nt}\\A=3000(1+\frac{0.041}{4})^{4*2} \\A=3000(1+0.01025)^{8} \\A=3000(1.01025)^8\\A=3000(1.085)\\A=3225[/tex]
So, After 2 years the account worth will be $3225