Answer:
So the intermediate step in question is (x - 10)² = 66
Step-by-step explanation:
Let's find out:
x² + 34 = 10x
x² - 10x = -34
x² - 20x + 100 = 66
(x - 10)² = 66
x - 10 = ± √66
x = 10 ± √66
x ≈ 18.12, 1.88
Answer:
(x-5)^2=
(x−5)
2
=
\,\,-9
−9
Step-by-step explanation:
.
The residents of a city voted on whether or not to raise property taxes. The ratio of yes votes to no votes was 4 to 3. If there were 1716 no votes, what was the total number of votes?
Help!
Sarah was standing on a dock next to the ocean. She kicked a soccer ball off the dock to her friend in the water. 4 seconds after she kicked the ball it reached a height of 9 feet above the water. It hit the water 6 seconds later.
Write an equation for the path of the rock in y=a(x-h)^2+k and give the height of the dock that she kicked the ball from. Show your work!
Answer:
1) The equation for the of the ball in y = a·(x - h)² + k is;
y = -16·(x - 5)² + 25
2) The height of the dock, d = -375 feet below the water level
Step-by-step explanation:
1) The question is with regards to quadratic function representing projectile motion
The given parameters are;
The height the ball reaches 4 seconds after Sarah kicked the ball = 9 feet
The time the ball hits the water = 6 seconds after reaching the 9 feet height
The form of the quadratic equation representing the motion is given as follows;
y = a·(x - h)² + k = a·x² - 2·a·h·x + a·h² + k
Let 'x' represent the time of motion of the ball, and let 'a', represent the acceleration due to gravity, we have;
The equation for the ball, y = a·(x - h)² + k
Where;
(h, k) = The coordinates of the vertex
h = The horizontal component of the vertex coordinate = 0
Therefore, we have;
When x = 0, y = d
d = -16·(0 - h)² + k = -16·h² + k
d = -16·h² + k
When x = 4, y = 9 - d
9 - d = -16(4 - h)² + k = -16(4 - h)² + k
When x = 2, y = d
d = -16(2 - h)² + k
When x = 6, y = 9
9 = -16(6 - 5)² + k
When x = 8, y = d
d = -16(8 - h)² + k
-16(8 - h)² - (-16(2 - h)²) = 0
h = 5
From 9 - d = -16(4 - h)² + k = -16(4 - 4)² + k
d = 9 - k
9 = -16(6 - h)² + k
k = 9 + 16(6 - 5)² = 25
d = 9 - k = 9 - 25 = -16
Therefore, h = 5, k = 25
The equation for the of the ball in y = a·(x - h)² + k is therefore;
y = -16·(x - 5)² + 25
2) When x = 0, y = d, ∴ d = -16(0 - 5)² + 25 = -375 feet below the water
The height of the dock, d = -375 feet below the water level
Select that all apply.
Answer:
C. ASA E. AAS B. HA
Step-by-step explanation:
ASA - The Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
AAS - If two angles and a nonincluded side of one triangle are congruent to two angles and a nonincluded side of a second triangle, then the triangles are congruent.
HA - If the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another triangle, then the two triangles are congruent.
Answer:
c.asa
Step-by-step explanation:
only C. asa tgat correct answer
A Store charfes $0.20 per pound plus a set fee of $2 for ice.How many pounds of ice would somebody have brought if they paid $15
Answer:
65 pounds of ice
Step-by-step explanation:
15-2=13
13/0.2=65
I need help with a geometry problem
#1
[tex]\\ \tt\hookrightarrow 3x+5=1/2(2x+15+6x-37)[/tex]
[tex]\\ \tt\hookrightarrow 6x+10=8x-22[/tex]
[tex]\\ \tt\hookrightarrow 2x=32[/tex]
[tex]\\ \tt\hookrightarrow x=16[/tex]
#2
[tex]\\ \tt\hookrightarrow 7x+2+25x-14=180[/tex]
[tex]\\ \tt\hookrightarrow 32x-12=180[/tex]
[tex]\\ \tt\hookrightarrow 32x=192[/tex]
[tex]\\ \tt\hookrightarrow x=6[/tex]
You are trying to decide whether to use Uber or Lyft during a vacation. Uber charges $3 to pick up plus an additional $0.25 for each mile driven. Lyft does not charge to pick up but they have a rate of $0.75 for each mile driven.
Let x = the number of miles traveled and y = the total cost for the trip.
Answer:
Uber: y = .25x + 3
Lyft: y = .75x
Step-by-step explanation:
Classify angle X Y Z. please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!! (Last option is Isosceles triangle) !!!!!!!!!
Answer:
its C
Step-by-step explanation:
Solve the inequality: -2z - 3 < 5
Answer:
z>-4
Step-by-step explanation:
Answer:
z>4
Step-by-step explanation:
-2z-3<5
add 3 to 5: -2z < 8
divide by -2: z < -4
but since you divided by a negative number, you have to change the way the inequality is facing so the answer is z>-4
take off discount and find the sale price of 15%off of $60.00
discount sale price
Answer:
15% off of $60.00 would be $51.00
Step-by-step explanation:
(15 x 15) / 100 = 9
60-9=51
</3 PureBeauty
find the coordinates for P in the diagram given r=4 and theta=7pi/6
(the diagram is an empty unit circle)
Answer: can you please set this up differently?????
Step-by-step explanation:
the home plate at a baseball game measures 17 inches across what is the measurement in feet and inches?
a. 1 foot 7 inches
b. 1 foot 5 inches
Answer:
b. 1 foot 5 inches
Step-by-step explanation:
because one foot is 12 inches
What is the length of diagonal BD?
Answer: My answer would be 7.6
Step-by-step explanation: Hope this is correct.
Chi has a big pile of nickels. He says, “Even if I use 100 of these nickels, I’ll still have 95% of my original pile.” How many nickels does Chi have?
Answer:
2000
Step-by-step explanation:5%= 100 nickels
1%= 20 nickels
20 x 100 = 2000
Answer:
2,000
Step-by-step explanation:
If 5%=100 nickels , then 20x100=the number of nickels Chi has.
20x100=2,000
I don't really get how to do this
Answer:
you got to put them in order like you got to figure out witch one is smaller then u keep going until u figure out the bigest.....
Step-by-step explanation:
Answer:
15.5, 16 and 1/4, 16.60, 16.7, 16 and 3/4, and 16.83.
Step-by-step explanation:
Hope it helps!
What is the difference between –11x – 2 and 13x + 5?
24x + 7
-24x + 7
24x + 3
-24x - 7
____________________________
1.) Find the opposite of 13x + 5:To find the opposite of 13x+5, find the opposite of each term.[tex]13x=-13x[/tex][tex]5=-5[/tex]- We do this because when solving this they are in parenthesis, so you must get rid of the parenthesis by turning them negative.
Equation at the end of Step 1:
[tex]-11x-2-13x-5[/tex]2.) Combine −11x and −13x:[tex]-11x+-13x=-24x[/tex]- We do this since we can only have on variable at the end of the problem, so you just combine them if they have the same variable base.
Equation at the end of Step 2:
[tex]-24x-2-5[/tex]3.) Subtract 5 from −2:[tex]-2-5=-7[/tex]- We do this because we need one number left over to get a simplified version of this equation.
Equation at the end of Step 3:
[tex]-24x-7[/tex]____________________________
Mr. Rojas spent d dollars to go on vacation. He bought a plane ticket for $250 and stayed in a hotel for 5 nights. If the cost of the hotel room was the same each night, what expression can be used to find how much Mr. Rojas paid each night for the hotel?
Answer:
x = d/5 - $50
Step-by-step explanation:
Basiclly what this sentence is saying that the price d is equal to $250 + 5 prices of staying in a hotel for a night.
If we let "x" be the price per night then we can get the following..
d = $250 + 5x
5x = d - $250
[tex]x = \frac{d - 250}{5}[/tex]
x = d/5 - $50
Which graph represents an exponential function?
Answer:
b
Step-by-step explanation:
The second graph, which represents Table B, represents an exponential function.
What is an exponential function?Mathematical functions with exponents include exponential functions. f(x) = bˣ, where b > 0 and b 1, is a fundamental exponential function.
Let table A represents the first graph.
x: 0, -1, 1, 2, -2, 3, -3.
y: 0, -1, -1, -4, -4, -6, -6.
And table B represents the second graph.
x:-4, -3,-2.75, -2.
y: 2, 4, 6, 10
To determine which graph represents an exponential function, we need to recall the properties of exponential functions. An exponential function is a function of the form y = a^x, where a is a constant greater than 0 and not equal to 1.
Looking at table A, we can see that the y-values do not appear to follow an exponential pattern. For example, the y-values for x = 1 and x = -1 are both -1, but the y-value for x = 2 is -4. This is not consistent with the pattern of an exponential function.
Looking at table B, we can see that the y-values do appear to follow an exponential pattern. The y-values increase rapidly as x increases, which is consistent with the pattern of an exponential function. To confirm this, we can calculate the ratio of consecutive y-values:
For x = -4 and x = -3, y increases by a factor of 4/2 = 2.
For x = -3 and x = -2.75, y increases by a factor of 6/4 = 1.5.
For x = -2.75 and x = -2, y increases by a factor of 10/6 = 1.67.
These ratios are not exactly the same, but they are approximately equal to each other. This is consistent with the pattern of an exponential function, where the ratio of consecutive y-values is constant.
Therefore, the second graph, which represents Table B, represents an exponential function.
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Lenny bought a motorcycle. He paid 12.5% in tax. The tax added 1437.50 to the price of the motorcycle what was the price of the motorcycle not including the tax
Answer:
Amount of motorcycle = $11,500
Step-by-step explanation:
Given:
Tax rate = 12.5 % = 0.125
Amount of tax = $1,437.50
Find:
Amount of motorcycle
Computation:
Amount of motorcycle = [Amount of tax ] / Tax rate
Amount of motorcycle = [1,437.50] / 0.125
Amount of motorcycle = $11,500
Find the rate of change
Answer:
non linear
Step-by-step explanation:
you can see it doesnt go up a specific number each time, aka changes each time, therefor its non linear
Answer:
2
Step-by-step explanation:
Use the method
Change in output / Change in input
The input progresses by 1, and y progresses by 2.
We will plug the numbers in.
2/1
Then simplify.
2/1 = 2
Hence, the rate of change is 2.
Write an
explicit formula for An, the nth term of the sequence 7, -42, 252, ....
Answer:
[tex]A_n = 7(-6)^{n-1}[/tex]
Step-by-step explanation:
Key skills needed: Explicit formula, Geometric sequence
1) This is a geometric sequence, meaning a constant (like 6 or 3.5) is being multiplied to every term. First we need to find the constant.
This can be done by doing -42 ÷ 7 or 252 ÷ -42
-42 ÷ 7 equals -6.
252 ÷ -42 also equals -6.
2) This means that constant is -6.
3) The general form for an explicit formula of a geometric sequence is:
[tex]a_n = a_1(r)^{n-1}[/tex]
--> r means the constant (or common ratio) that is being multiplied.
--> [tex]a_1[/tex] means the first term
--> [tex]a_n[/tex] means the "nth" numbered term (so [tex]a_3[/tex] is the 3rd term, [tex]a_{10}[/tex] is the 10th term and so on).
--> [tex]n-1[/tex] is just the "n" in [tex]a_n[/tex] minus 1.
4) We can use this formula to create an explicit formula for the geometric sequence in the problem.
--> [tex]r = -6[/tex] (Since we got -6 as the constant/common ratio).
--> [tex]a_1 = 7[/tex] (Since 7 is the 1st term)
This means that our formula would be --> [tex]A_n = 7(-6)^{n-1}[/tex]
Hope you understood and have a nice day!! :D
Which expression represents "4 times the sum of 3 and 7?
O A 4+7=
B 4x +7
OC 4G+7)
D. 704 + x)
Answer:
associative
Step-by-step explanation:
Write 7√5 using rational exponents.
Answer:
7*(5)^0,5
Step-by-step explanation:
The value of number 7√5 in form of rational exponents will be 1561/1000.
What is Rational number?A number which can be written in the form of fraction p / q , where q is non zero, are called Rational numbers.
Given that;
The number is,
⇒ 7√5
Now,
Since, The number is,
⇒ 7√5
Solve as;
⇒ 7√5 = 7 × 2.23
= 15.61
= 1561/100
Thus, The value in rational exponents = 1561/1000
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Number 8 I need help plz
if 1 pound of candy is 3.50 how much candy can you get with one dollar?
Answer:
Step-by-step explanation:
16 divided by $3.50 = 4.5
Answer:
0.286 pounds
Step-by-step explanation:
one pound=$3.50
x pounds=$1.00
then
1/3.5=0.286 pounds
check:
0.285 pounds per dollar x $3.50=1 pound
The original price of last year's gaming system was $399. It is now selling at a 24% discounted price. What is the sale price?
Answer:
$303.24
Step-by-step explanation:
399.00x24%=95.76
399.00÷95.76=303.24
two boys decided to share their profits from a car wash job at a ratio of 2:3 how much will each boy receieve if their total profit is 35
Answer: Profit for first boy = $14
Profit for second boy = $21
Step-by-step explanation:
Given : Ratio of profits = 2:3
Let profit for one boy = 2x and for another boy = 3x
Since combined profit = $35
Then, 2x+3x= 35
⇒ 5x= 35
⇒ x= 7 [divide both sides by 5]
Profit for first boy = 2 (7)= $14
Profit for second boy = 3 (7)= $21
I need help with this ASAP
Answer:
it is D
since 6 percent of people infected by 10 day
Can someone give me the answer
Answer:
B=YZ/20A
Step-by-step explanation:
An elected official surveyed residents of a town to assess their satisfaction with city services. The survey includes
both those who own and those who rent their homes.
Level of Satisfaction
EEEE
High
Medium
Low
Total
Owners
26
34
18
78
Renters
15
12
5
22
Total
41
46
23
110
What proportion of those surveyed have low satisfaction with city services?
O 0.2091
O 0.2308
0.2644
O 0.3727
Save and Exit
Next
Submit
Answer:
A
Step-by-step explanation:
Not much of a reason but thats what i g ot
Answer:
a
Step-by-step explanation:
The number 299 is divided into two parts in
the ratio 5:8. The product of the numbers
(A) 21140
(C) 21160
(B) 21294
(D) 31294