[tex]~~~~~~~~y = (x-4)^2 +6\\\\\implies (x-4)^2 = y-6 \\\\\implies x -4 = \pm\sqrt{y-6}\\\\\implies x = \pm\sqrt{y-6} +4[/tex]
Given the pattern rule Tn=n2-1
what are the first 3 terms of the pattern
Answer:
0, 3 , 8
Step-by-step explanation:
substitute n = 1, 2, 3 into the pattern rule
T₁ = 1² - 1 = 1 - 1 = 0
T₂ = 2² - 1 = 4 - 1 = 3
T₃ = 3² - 1 = 9 - 1 = 8
Sketch the graph of y = negative 2 x squared + x + 1 using your graphing calculator. What are the x-intercepts of this graph? a. (1, 0) and (-0.5, 0) c. There are no x-intercepts b. (-2.5, 0) and (-2, 0) d. (-1.5, 0) and (-0.5, 0)
The x-intercept is (1, 0) and (-0.5, 0).
The correct option is (a)
What is intercept?The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
Given function is:
f(x)= [tex]-2x^{2}+x+1[/tex]
So, The graph of this equation is attaches below.
The x- intercepts of this graph
[tex]\mathrm{X\:Intercepts}:\:\left(-\frac{1}{2},\:0\right),\:\left(1,\:0\right)[/tex]
or
X intercepts: (1, 0) and (-0.5, 0)
Hence, the x-intercept is (1, 0) and (-0.5, 0).
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Solve for system of equations. y = x²-3x + 4
x + y = 4
Answer:
Step-by-step explanation:
x²-3x+4+x=4
x²-3x+x=4-4
x²-2x=0
x²-x=0/2
x²-x=0
x=0
3b - c +5 if c= - 4, b=2.
Answer:
15
Step-by-step explanation:
To find the answer, plug the values of each variable into the equation and simplify. It may be easiest to plug one variable in at a time, simplify, then plug the next variable in. Remember, if the equation is asking you to subtract a negative number, the negatives cancel and you want to add the numbers.
b = 2 c = -4
3b - c + 5 <----- Original expression
3(2) - c + 5 <----- Plug 2 in for "b"
6 - c + 5 <----- Multiply 3 and 2
11 - c <----- Add 6 and 5
11 - (-4) <----- Plug -4 in for "c"
15 <----- Add 11 and 4
The Raymond family is building a pool in their backyard. If the contractor
chargest $2 per cubic foot to excavate, how much money will it cost to dig out
the hole for the pool?
19 ft
14.5 ft
4 ft
5 ft
12 ft
Answer:
2020
Step-by-step explanation:
(12×5×14.5+7×4×5)×2=
2020
Type the probability notation for choosing a blue disk or a green disk.
The probability notation for choosing a blue disk or a green disk is P ( B U G).
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Probability = (number of blue discs / total number of discs) + (number of green discs / total number of discs)
3/8 + 5/8
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Wich inequality represents the phrase “a number b is atleast 16”?
Answer: B
Explanation: Key word: Atleast. This shows that you can still get 16 but it's the lowest you can get. Meaning, if you were to say, atleast get a 16% done. It'll mean that getting 16% is good but also, you'll want to get a higher number of course.
If x is a positive integer, for how many different values of x is the square root of 48/x a whole number?
The number of values x for which the square root of 48/x a whole number are two.
What is the number?The square root of a number can be described as number that when multiplied with itself yields the number.
The first step is to determine the factors of 48. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
The factors of 48 that will yield a perfect square when divided by 48: 3 and 12.
48 divided by 3 would give a value of 16.
48 divided by 12 would give a value of 4.
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A toy giraffe was made using
a scale factor of 1:8. If the toy
giraffe is 2 feet long, how many
feet long is the real giraffe?
For what value of x is the rational expression below undefined?
1-x
——
x+1
Answer:
x = - 1
Step by step explanation:
The rational expression will be undefined if the denominator is zero.
x+1 = 0
x = -1
Hence, for x = -1, the given expression will be undefined.
How does the rate of change work
A radioactive isotope has a rate of decay of 84%. that is, every day,
84% of the isotope remains. how many days is its half-life? round to
the nearest tenth.
The half life of the radioactive isotope to the nearest tenth is 0.83 days.
What is rate of radioactive decay?The rate of radioactive decay is the rate at which a radioactive isotope is disintegrated. The half life is the time taken for half of the original amount of radioactive isotope to remain.
Given that;
t/12 = 0.693/k
Where;
t1/2 - half life
k =decay constant
t/12 = 0.693/0.84
t/12 = 0.83 days
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show how to solve the equation in the picture
[tex]\left(3\cdot8\cdot x\right)^7\\\\\left(3\cdot2\cdot4\cdot x\right)^7\\\\\left((3\cdot2)\cdot4\cdot x\right)^7\\\\\left(6\cdot4\cdot x\right)^7\\\\6^7\cdot4^7\cdot x^7\\\\[/tex]
In the second step, I rewrote 8 as 2*4. Then after that I regrouped terms so that the (3*2) can pair up together. This of course turns into 6. After that point, we have 6, 4 and x multiplied together as the base.
The last step uses the rule that [tex](a*b*c)^d = a^d*b^d*c^d[/tex], in other words, we apply the exponent d to each term inside the parenthesis. Each term inside gets its own exponent.
An example: [tex](2*4*6)^3 = 2^3*4^3*6^3[/tex]
The starting line for a race in Cass is 2.4 miles from the finish line. On a map of the course,
the starting and finish lines are 6 inches apart. What scale does the map use?
Write your answer in simplest form using whole numbers.
__ inches = __ miles
Answer:
5 in. = 2 mi.
Step-by-step explanation:
2.4mi = 6in
1 mi = 2.5in
2.5 inches = 1mile
Convert to whole #'s as the question asks
5 in. = 2 mi
-- Gage Millar, Algebra 1/2 Tutor (Pending Pre-Calc Tutor)
Answer:
3 inches = 1 miles
Step-by-step explanation:
The first scale you get is with the information that is given:
6 inches = 2.4 miles
Then you simplify, dividing both sides by 2.4:
2.5 inches = 1 miles
Rounding up: 3 inches = 1 miles
Hope it helps!
For an upcoming field trip to the science center, the school will allow students to select one extra activity. The school surveys a random sample of 25 students to determine about how many tickets of each kind they will need to buy.
The total amount that would be spent on all the activities is $1605.40.
What is the total amount?The total amount that would be spent on movies = (14/25) x 1200 x 1.55 = $1041.60
The total amount that would be spent on planetarium tickets = (7/25) x 1200 x 1.05 =352.80
The total amount that would be spent on backstage passes = (4/25) x 1200 x 1.10 =211.20
Total amount = 211.20 + 352.80 + $1041.60 = $1605.40
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[tex]\sqrt{29-12\sqrt{5}[/tex] simplify this
[tex] \sqrt{29 \: - \: 12 \sqrt{5} } [/tex]
Factor the indicated expression:[tex] \sqrt{(3 \: - \: 2 \sqrt{5}) ^{2} } [/tex]
Simplified the index the root and also the exponent using the number 2.[tex] \boxed{ \bold{2 \sqrt{5} \: - \: 3}}[/tex]
MissSpanish[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt{29-12\sqrt{5}} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{20-12\sqrt{5}+9} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{4\cdot \:5-12\sqrt{5}+9} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{\left(\sqrt{4}\right)^2\left(\sqrt{5}\right)^2-12\sqrt{5}+\left(\sqrt{9}\right)^2} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt{4}=2 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt{9}=3 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf 2\cdot2\cdot3\sqrt{5}=12\sqrt{5} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{2^2\left(\sqrt{5}\right)^2-2\cdot \:2\cdot \:3\sqrt{5}+3^2} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Apply\:the\:formula\:from\:binomial\:to\:square:(a-b)^2=a^2-2ab+b^2 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf 2^{2}(\sqrt{5})^{2}-2\cdot2\cdot3\sqrt{5}+3^{2}=(2\sqrt{5}-3)^{2} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{\left(2\sqrt{5}-3\right)^2} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Apply \ the \ laws \ of \ exponents:\sqrt[n]{a^{2} }=a \end{gathered}$}[/tex]
[tex]\sqrt{(2\sqrt{5}-3)^{2} } =2\sqrt{5 }-3.[/tex]
[tex]\red{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \red{=2\sqrt{5}-3 } \end{gathered}$}}} \ \ \red{\Rightarrow} \ \ \bf{\red{Answer}}[/tex]
↓
[tex]\red{\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\red{MyHeritage}} \end{gathered}$}}}}[/tex]
evaluate q-r if q= -14 and r=-6
Answer:
- 8
Step-by-step explanation:
substitute q = - 14 and r = - 6 into the expression
q - r
= - 14 - (- 6)
= - 14 + 6
= - 8
Type the correct answer in the box. Use numerals instead of words.
What is the length of the diagonal shown in the rectangular prism? Round your answer to the nearest tenth.
The length of the diagonal shown in the rectangular prism is; 9.5 ft
How to Use Pythagoras Theorem?First of all, we have to find the length of the diagonal base to get;
x = √(4² + 7²)
x = √65
Thus;
Length of the diagonal shown = √(5² + (√65)²)
Length of the diagonal shown = √90
Length of diagonal shown = 9.4868
Length of diagonal shown ≈ 9.5 ft
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Answer:
got 100% on Plato
Step-by-step explanation:
√x-1=4
I need the answer for this question
Answer:
25
Step-by-step explanation:
First we add 1 to both sides :
√x = 5
Now we square both sides :
x = 5²
x = 25
To check this answer we substitute our answer back into the original equation:
√25 - 1 = 4
5 - 1 = 4
4 = 4
✅
Hope this helped and brainliest please
10 out of 15
Which is the equation of the line passing through (0, 8) and (4, 0)?
Answer:
y=-2x+8
Step-by-step explanation:
We want an equation of the form y=mx + b, where m is the slope and b is the value of y when x=0.
The slope of a line through the two given points:
(4,0) and (0,8)
Rise = (8-0) = 8
Run = (0-4) = -4
Slope = 8/-4 = -2
The y-intercept is given by the point (0,8), which tells us that b=8.
The equation is y = -2x + 8
Answer:
Which is the equation of the line passing through (0, 8) and (4, 0)?
The one that you are on is correct
y = -2x + 8Step-by-step explanation:
You're welcome.
The graph shows the functions f(x), p(x), and g(x): 6.98 Ax) 1 p(x) 8(xx) US -9.06 10.94 -6.35 Courtesy of Texas Instruments Part A: What is the solution to the pair of equations represented by p(x) and f(x)? (3 points) Part B: Write any two solutions for f(x). (3 points) Part C: What is the solution to the equation p(x) = g(x)? Justify your answer.
Answer:
See the attached graph.
Step-by-step explanation:
The A.M. between two numbers exceeds their G.M. by 2 and the G.M. exceeds the H.M by 1.8. Find the numbers.
The numbers based on the information will be 4 and 16.
How to compute the numbers?Let the numbers be a and b.
Therefore, a - g = 2
(a + b)/2 - ✓ab = 2 or
(✓a - ✓b( = 4
g - h = 1.8
✓ab = 2ab/a + b = 1.8
5✓ab(✓a - ✓b)² = 8(a + b)
2a - 5✓ab + 2b + 0
✓a = 2✓b
a = 4b
b = 4.
✓a = 2✓b = 4
a = 16
Therefore, the numbers based on the information will be 4 and 16.
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what is the value of x
The value of x in the triangle is 20
How to determine the value of x?From the triangle, we have the following equivalent ratios:
5x+ 10 : 121 = 10 : 11
Express as fraction
5x + 10/121 = 10/11
Multiply both sides by 121
5x + 10 = 110
Subtract 10 from both sides
5x = 100
Divide both sides by 5
x = 20
Hence, the value of x in the triangle is 20
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given f(x)=2/x^2+3x-10.
which of the following is true?
Of(x) is positive for all x < -5
Of(x) is negative for all x < -5
Of(x) is positive for all x < 2
Of(x) is negative for all x > 2
The function f(x)=2/x²+3x-10 is negative for all x < -5 option second "is negative for all x < -5" is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
[tex]\rm f\left(x\right)=\dfrac{2}{x^2}+3x-10[/tex]
f(x) is positive for all x < -5
Plug x = -4
f(-4) = -21.875
The above statement is not true
f(x) is negative for all x < -5
Plug x = -4
f(-4) = -21.875
The above statement is true
f(x) is positive for all x < 2
Plug x = 1
f(1) = -5
The above statement is not true
f(x) is negative for all x > 2
Plug x = 3
f(3) = -0.777
The above statement is not true
Thus, the function f(x)=2/x²+3x-10 is negative for all x < -5 option second "is negative for all x < -5" is correct.
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A standard die is rolled and a month
of the year is chosen at random.
What is the probability of rolling a
number that is at least
then
choosing a month that does not
begin with the letter M?
200
Answer:
The probability is [tex]\frac{5}{9}[/tex]
Step-by-step explanation:
First we will find the probability of having a roll that is at least 3
1 2 3 4 5 6
this means there is a [tex]\frac{4}{6}[/tex] chance we will roll at least 3
Next we will find which months of the year are applicable
January February March April May June July August September October November December
This means there is a [tex]\frac{5}{6}[/tex] chance we will pick a month that does not begin with the letter M.
Now we can multiply these chances together to see what the total probability is.
[tex]\frac{4}{6} * \frac{5}{6} = \frac{20}{36} \rightarrow \boxed{\frac{5}{9}}[/tex]
That is the answer
- Kan Academy Advance
The two tables show the number of copies of albums x, y, and z sold in outlets a, b, c, and d of a company. which outlet sold the greatest number of copies of album x in july and august?
Outlet A sold the greatest number of copies of album x in July and August
How to determine the outlet?The tables of values are given as:
July
Album X Album Y Album Z
Outlet A 14 8 6
Outlet B 7 13 4
Outlet C 2 11 1
August
Album X Album Y Album Z
Outlet A 12 14 10
Outlet B 5 12 8
Outlet C 16 12 7
In July, the total sales of album x are:
Outlet A = 14
Outlet B = 7
Outlet C = 2
In August, the total sales of album x are:
Outlet A = 12
Outlet B = 5
Outlet C = 16
Add both sales
A = 14 + 12 = 26
B = 7 + 5 = 12
C = 2 + 16 = 18
26 (in outlet A) is greater than 12 and 18
Hence, outlet A sold the greatest number of copies of album x in July and August
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Answer:
Outlet D
Step-by-step explanation:
they sold 28 of album x
outlet a only sold 26
An adult mamenchisaurus dinosaur was about 24 feet tall . if a toy model of the dinosaur is made to the scale of 1 inch to 9 inches , how tall will the toy dinosaur be
The height of the toy dinosaur will be 32 inches.
What is scaling?In mathematics scaling is defined as the enlarging or contracting of the size of an object by reducing or increasing the units of the measurements of the object.
Given that:-
An adult mamenchisaurus dinosaur was about 24 feet tall. if a toy model of the dinosaur is made to the scale of 1 inch to 9 inches.
The new height of the dinosaur will be calculated as:-
We know that the size of the dinosaur is scaled as 9 inches to 1 inch the actual height of the dinosaur is 24 feet so the scaled height will be:-
Actual height = 24 ft = 24 x 12 = 288 inches
9 inches → 1 inch
288 inches → 288 / 9 = 32 inches.
Therefore the height of the toy dinosaur will be 32 inches.
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Hi can anybody answer this please !
Answer:
7ft; 8 minutes
Step-by-step explanation:
a. to find the height the person boarded at, plug in t=0 since this is right when the person got on the Ferris wheel. we then get:
h(0) = -45 * cos ((pi/4)*0) + 52 = 7 ft
b. to find the period, we have pi/4 * t = 2*pi, solve for t to get t=8
Help please i need this
Answer:
i can't see the question i would love to help though
Step-by-step explanation:
The difference between two numbers is 17 and twice the smaller of these is 26. What are the numbers?
Does anyone know the answer?
Answer:
13 and 30
Step-by-step explanation:
the smaller of the two numbers is 13.
If there is a 17 number difference, then that means that the second number is 30.
give brainliest, please!
hope this helps :)