Answer:
1) The smaller t is -6
The larger t is 7
2) The vertex of the parabola is (1/2, -42.25)
Step-by-step explanation:
Hey there!
To find the zeros of a function, you need to find two values that add up to "b" and multiply together to get "ac"
The b and ac come from the standard form of a parabola which this statement is given to us right now
t^2-t-42
1 is the "a" value, -1 is the "b" value, and -42 is the "c" value
What are two numbers that multiply together and get -42 and those same two numbers add up to -1
Those two numbers are -7 and 6
When you multiply those numbers together, you get -24
And when you add them together, you get -1
Now you can split the -t in the equation
The new equation after splitting the original equation will look like this
t^2-7t+6t-42
Now we group the equation into two parts
(t^2-7t) + (6t-42)
Since t is the common variable in the first set of parentheses, we can take it out
t(t-7)+(6t-42)
Now in the second pair of parentheses, 6 is the constant term
You can also take that out
t(t-7)+6(t-7)
Now we have our zero pairs
We take one of the parentheses and the terms that are outside of the parentheses
Now we have
(t+6)(t-7)=0
Now we can find our two zeros
The smaller t is -6
The larger t is 7
Now we have to find the vertex
The formula to solving the x-coordinate of the vertex is -b/2a
The "b: value is -1 and the "a" value is 1
So, the x-coordinate of the vertex is 1/2
Now we plug that into the equation
(1/2)^2 - 1/2 - 42
1/4 - 1/2 - 42
-1/4 - 42
-169/4 --> -42.25
So, the y-coordinate of the vertex s -42.25
This means,
The vertex of the parabola is (1/2, -42.25)
You are playing a game that uses two fair number cubes. If the total on the number cubes is either 2 or 5 on your next turn, you win the game. What is the probability of winning on your next turn? Express your answer as a percent. If necessary, round your answer to the nearest tenth.
Answer:
13.9%
Explanation:
Rolling for 2 : (1, 1)
Rolling for 5 : (1, 4), (4, 1), (2, 3), (3, 2)
So, there are (4 + 1) = 5 possible outcomes out of 36 outcomes
Note: There are 36 outcomes when rolling a two fair cubes.
[tex]\sf Probability = \dfrac{possible \ outcomes}{Total \ outcomes}[/tex]
[tex]\rightarrow \sf \dfrac{5}{36} \ x \ 100[/tex]
[tex]\rightarrow \sf \dfrac{125}9} \%[/tex]
[tex]\rightarrow \sf 13.9 \%[/tex]
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Answer:
i think its D.
Step-by-step explanation:
i just counted
A new car is purchased for \$49,000$49,000 and over time its value depreciates by one half every 5 years. What is the value of the car 11 years after it was purchased, to the nearest hundred dollars?
YOUR HELP WOULD BE MUCH APRECIATED!!!!!!!!!
[tex]y = 4^{-2}[/tex] = [tex]\frac{1}{16}[/tex]
[tex]y = 4^ {1}[/tex] = [tex]\\ 4[/tex]
[tex]y = 4^{3}[/tex] = [tex]\\ 64[/tex]
Write the standard form equation for circle
Step-by-step explanation:
(x - h)² + (y - k)² = r²
with (h, k) being the center and r the radius.
in our case the center is (1, 3), the radius is 3.
so, the right answer is the third answer option
(x - 1)² + (y - 3)² = 9
How do you write 7.4 × 10–2 in standard form?
Answer:
740
Step-by-step explanation:
10^2 = 100
So 7.4 * 10^2
= 740
What is the slope of the line that contains the points in the table?
X
4
-1
2
8
Y
-9
-9.75
-10.5
-12
Answer:
[tex]\frac{3}{20}[/tex]
Step-by-step explanation:
slope/gradient=[tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
=[tex]\frac{-9.75+9}{-1-4}[/tex]
=[tex]\frac{3}{20}[/tex]
The expression above can also be written in the form a=, b=,c=. 3 6/5
The expression above can also be written in the form .
For this expression, a =
, b =
, and c =
.
The value of a, b, and c are 3, 6, and 5 respectively because we can write the provided expression as ⁵√(3)⁶
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have:
[tex]\rm = 3^{\dfrac{6}{5}}[/tex]
We can write it as:
[tex]\rm = \sqrt[5]{3^6}[/tex]
The value of a = 3,
The value of b = 6, and
The value of c = 5
Thus, the value of a, b, and c are 3, 6, and 5 respectively because we can write the provided expression as ⁵√(3)⁶
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I need help with this, and a step by step explaination would be very helpful! Thank you!
Answer:
18
Step-by-step explanation:
The summation symbol is telling you there are 4 terms of the sum. The values of x in the terms range from 1 to 4.
__
The expanded form of the sum is ...
(1 +2) +(2 +2) +(3 +2) +(4 +2)
= 3 +4 +5 +6 = 18
The sum is 18.
_____
Additional comment
The sum can be rewritten as ...
[tex]\displaystyle \sum_{x=1}^4{(x+2)}=\sum_{x=1}^4{x}+\sum_{x=1}^4{2}=\dfrac{4(4+1)}{2}+4\times2=10+8=\boxed{18}[/tex]
This way, you need to know the sum of integers from 1 to n is (n/2)(n+1). It may be easier just to write the terms out as we have done above.
9. Use the Desmos graphing calculator to find slope and y-intercept for the least-squares
regression line for the dataset in the table:
xy
31
45
8 11
10 21
m= 2.55, b= 6.435
m=1.477, b=1.477
m= 1.698, b-0
m=2.55, 6-6.435
Answer:
D) m=2.55, b=-6.435
Step-by-step explanation:
See attached file ("a" represents the slope and "b" represents the y-intercept).
A recipie requires 3/4 lbs of onions to make 3 servings of soup. Mark has 1 1/2 lbs of onions. How many servings can Mark make?
Answer:
4 1/4 lbs of onions = 1llb so there are 4 x 3 servings = 12 servings in 1 lb 6 servings in 1/2 lb total of 12+6= 18 servings you can also use ratio and proportion converted to decimals to eliminate fractions ,25/3= 1.5/x cross multiply .25x= 4.5 x=18 hope this helps
Step-by-step explanation:
6. Abbi invested $1,000 in a certificate of deposit with a simple interest rate of 4%. Find the interest earned in 8 years. Then find the total of principal plus interest.
Answer:
$1320
Step-by-step explanation:
4%=0.04
Intrest = 0.04x8
Intrest = 0.32
Intrest = 1000x0.32
Intrest = 320
Then add 1000+320=1320
For how many values of x does f(x) = g(x), on the graph shown
below?
a. 0
b. 2
c. 3
d. 6
Answer:
the answer is C
Step-by-step explanation:
as you can see f(x) cut g(x) 3 time ( sorry for my bad English )
1.3b + 2 = 12.4 what is b?
Answer:
b = 8
Step-by-step explanation:
1.3b + 2 = 12.4
- Subtract 2 from both sides
1.3b = 12.4 - 2
- Subtract 2 from 12.4 to get 10.4.
1.3b = 10.4
- Divide both sides by 1.3.
b = [tex]\frac{10.4}{13}[/tex]
- Expand [tex]\frac{10.4}{13}[/tex] by multiplying both numerator and the denominator by 10.
[tex]b = \frac{104}{13}[/tex]
- Divide 104 by 13 to get 8.
christian is trown into a swimming pool his mass is 62,000g and his volume is 68,000cm3 what would his density be? (Show solution)
Answer:
0.91 g/cm³
Step-by-step explanation:
Density Formula
Density = Mass/VolumeSolving
Density = 62,000 g / 68,000 cm³Density = 31/34 g/cm³Density = 0.91 g/cm³Can you use Pythagorean Theorem to find the missing side?
Answer:
b=20
Step-by-step explanation:
[tex] {b}^{2} = {c}^{2} - {a}^{2} \\ b = \sqrt{ {25}^{2} - {15}^{2} } \\ b = 20[/tex]
GR. 9 QUESTION 1/ VRAAG 1: Simplify the following: / Vereenvoudig die volgende: 1.1 -8xy-6xz + 10xy + 9xz - 4yx
1.2 m² - 4m - 1 + m² - 8m + 5-6m² +3m - 1
Answer:
Below in bold.
Step-by-step explanation:
-8xy-6xz + 10xy + 9xz - 4yx (Note 4yx = 4xy)
Bringing like terms together we have:
-8xy + 10xy - 4xy - 6xz + 9xz
= -2xy + 3xz.
m² - 4m - 1 + m² - 8m + 5-6m² +3m - 1
= m² + m² - 6m² - 4m - 8m + 3m - 1 + 5 - 1
= -4m² - 9m + 3.
How many integers are between the numbers a = - 6.52 and b = 6.98?
Answer:
-13.5
Step-by-step explanation:
-6.52-6.98=-13.5
°116°
56
f
What is the degree measure of f?.
Answer:
C. 60
Step-by-step explanation:
if one angle of a triangle is 63 and the other two are 7x degrees and 6x degrees what is X worth
Answer:
x = 9
Step-by-step explanation:
Sum of all angles of a triangle = 180
63 + 7x + 6x = 180
63 + 13x =180
13x = 180 - 63
13x = 117
x = 117/13
x = 9
Answer:
X= 9
Step-by-step explanation:
The angles in a triangle all add up to 180°
Hence we can form this equation :
63 + 7x + 6x = 180°
Subtracting 63 from both sides:
7x + 6x = 117°
Adding together to find the total X:
13x = 117°
Finally, diving by 13 on both sides:
X = 9
Answer the one you would like thank you.
Answer: 1.9
Step-by-step explanation:
Question 11
9.88 rounds to 10
5.2 rounds to 5
10/5 = 2
A ream of A4 paper contain 500 sheets the size of each paper is 297mm long and 210mm wide the volume of the ream is 3742.2cm find the thickness of each sheet of paper answer in millimeters
The thickness of each sheet of paper is 0.0012mm.
To find the thickness of each sheet of paper answer in millimeters.
What is mensuration?The act of measuring geometry applied to the computation of lengths, areas, or volumes from given dimensions or angles.
Given that:
A ream of A4 paper contain 500 sheets the size of each paper is 297mm long and 210mm wide the volume of the ream is 3742.2cm.
To convert cm in mm.
3742.2cm=37422 mm
Surface 1 sheet:
(297mm) X 210mm) =
62370[tex]mm^{2}[/tex]
Volume 1 sheet:
37422mm : 500 =
74.844mm
Thickness of 1 sheet:
74.844mm : 62370mm =
0.0012mm
So, the thickness of each sheet of paper is 0.0012mm.
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Calculate the range of the data set
33,38,35.5,39.25,31.75
The range of the given data set, 33, 38, 35.5, 39.25, 31.75, is 7.5. The range represents the spread or the difference between the highest and lowest values in the data set.
To calculate the range of a data set, you need to find the difference between the maximum and minimum values.
Given the data set: 33, 38, 35.5, 39.25, 31.75
To determine the maximum value, we can compare the numbers in the data set and identify the highest one. In this case, 39.25 is the largest number.
To find the minimum value, we compare the numbers and identify the smallest one. Here, 31.75 is the smallest number.
Now, we can calculate the range by subtracting the minimum value from the maximum value:
Range = Maximum value - Minimum value
= 39.25 - 31.75
= 7.5
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Which describes the process of finding the volume of a cylinder? (Help ASAP)
GIVING BRAINLIEST!!!!!
Answer:
The first answer is correct
Step-by-step explanation:
< O Z Q = < O Z P + < Q Z P
Given that,
< O Z Q = 12x - 4
< O Z P = 6x + 4
< Q Z P = 3x + 10
Let us solve it now.
< O Z Q = < O Z P + < Q Z P
12x - 4 = 6x + 4 + 3x + 10
Combine like terms and make the x as the subject.
12x - 4 = 9x + 14
12x - 9x - 4 = 14
3x - 4 = 14
3x = 14 + 4
3x = 18
Divide both sides by 3.
x = 6
Becky spent h hours studying
plus an additional 2 hours
typing a report for the week. If
her total studying and work
time was 6.5 hours, how many
hours did she study for?
Write an equation to solve.
Answer:
6.5 = h + 2
h = 4.5
Step-by-step explanation:
We are given h and since she did 2 additional hours of work, we add the 2 hours. and since we are trying to find h, we set the equation equal to 6.5
please help i have no idea what to do
Answer: D) 80 degrees
Step-by-step explanation:
Quadrilateral CDEF is similar to quadrilateral GHIJ. Find the measure of side JG.
Round your answer to the nearest tenth if necessary.
Answer: 30.5
Step-by-step explanation:
If f(1)=1f(1)=1 and f(n)=f(n-1)^(2)-1f(n)=f(n-1)
2
-1 then find the value of f(4)f(4).
Answer:
f(4) = 0
Step-by-step explanation:
For many sequences that involve recursive formulas, the quickest way to find the value of a given term is to evaluate those leading up to it. That seems to be the case here.
givenf(1) = 1f(n) = f(n -1)² -1findf(4)solutionThe next term after the one given is ...
f(2) = f(1)² -1 = 1² -1 = 0
Then we have ...
f(3) = f(2)² -1 = 0² -1 = -1
f(4) = f(3)² -1 = (-1)² -1 = 0
The value of f(4) is 0.
_____
Additional comment
Now that we have seen a few terms of the sequence, we can write an explicit formula for the terms after the first:
f(n) = (-1 +(-1)^n)/2 . . . integer n ≥ 2
Hi! really need help with my math and its due tmrw please helppp Also make sure
to slide over to see the other problems sorry if its glitchy.
Answer:
The value of x is equal to 109