Answers
Answer's:
27. vertex: (-4, -5) and x-intercept: (√5 - 4, 0) and (-√5 - 4, 0)
28. vertex: (-5, -11) and x-intercept: (√11 - 5, 0) and (-√11 - 5, 0)
29. vertex: (1, 16) and x-intercept: (-3, 0) and (5, 0)
To find vertex, the quadratic function should be in f(x) = a(x - h)² + k form.
where:
(h, k) is the vertex27.
g(x) = x² + 8x + 11
completing square:
g(x) = (x² + 8x) + 11
g(x) = (x + 4)² + 11 - (4)²
g(x) = (x + 4)² - 5
g(x) = (x - (-4))² - 5
To find x-intercept: set y = 0
[tex]\sf (x + 4)^2 - 5 = 0[/tex]
[tex]\sf (x + 4)^2 = 5[/tex]
[tex]\sf x + 4 = \pm \sqrt{5}[/tex]
[tex]\sf x= \sqrt{5}-4, \ - \sqrt{5}-4[/tex]
Hence, the vertex is (-4, -5) and x intercepts (√5 - 4, 0) and (-√5 - 4, 0).
28.
f(x) = x² + 10x + 14
completing square:
f(x) = (x² + 10x) + 14
f(x) = (x + 5)² + 14 - (5)²
f(x) = (x + 5)² - 11
Find x intercept, so y = 0:
[tex]\sf (x + 5)^2 - 11 = 0[/tex]
[tex]\sf (x + 5)^2 = 11[/tex]
[tex]\sf x + 5 = \pm\sqrt{11}[/tex]
[tex]\sf x = \sqrt{11} -5, \ -\sqrt{11} -5[/tex]
Hence, the vertex is (-5, -11) and x intercepts (√11 - 5, 0) and (-√11 - 5, 0).
29.
f(x) = -(x² - 2x - 15)
f(x) = -((x² - 2x)) + 15
f(x) = -(x - 1)² + 15 + (-1)²
f(x) = -(x - 1)² + 16
Find the x-intercept's:
[tex]\sf -(x - 1)^2 + 16 = 0[/tex]
[tex]\sf -(x - 1)^2 = -16[/tex]
[tex]\sf (x - 1)^2 = 16[/tex]
[tex]\sf x - 1 = \pm\sqrt{16}[/tex]
[tex]\sf x - 1 = \pm4[/tex]
[tex]\sf x = -3, \ 5[/tex]
Hence, the vertex is (1, 16) and x intercepts (-3, 0) and (5, 0).
Answer:
[tex]\textsf{27.} \quad \textsf{Vertex}:(-4,-5) \quad \textsf{$x$-intercepts}: x=-4+\sqrt{5}, \:\:x=-4-\sqrt{5}[/tex]
[tex]\textsf{28.} \quad \textsf{Vertex}:(-5,-11) \quad \textsf{$x$-intercepts}: x = -5+\sqrt{11}, \:\:x=-5-\sqrt{11}[/tex]
[tex]\textsf{29.} \quad \textsf{Vertex}:(1,16) \quad \textsf{$x$-intercepts}: x = 5, \:\:x=-3[/tex]
Step-by-step explanation:
Vertex form of a quadratic function:
[tex]\boxed{y=a(x-h)^2+k}[/tex]
where:
(h, k) is the vertex.[tex]a[/tex] is some constant.Question 27Given function:
[tex]g(x)=x^2+8x+11[/tex]
Change to vertex form by completing the square.
Add and subtract the square of half the coefficient of x:
[tex]\implies g(x)=x^2+8x+11 +\left(\dfrac{8}{2}\right)^2-\left(\dfrac{8}{2}\right)^2[/tex]
[tex]\implies g(x)=x^2+8x+11 +16-16[/tex]
[tex]\implies g(x)=x^2+8x+16+11-16[/tex]
[tex]\implies g(x)=x^2+8x+16-5[/tex]
Factor the perfect trinomial:
[tex]\implies g(x)=(x+4)^2-5[/tex]
Therefore, the vertex is (-4, -5).
To find the x-intercepts, set the function to zero and solve for x:
[tex]\begin{aligned}g(x) & = 0\\\implies (x+4)^2 -5 & = 0\\(x+4)^2 & = 5\\\sqrt{(x+4)^2} & = \sqrt{5}\\x+4&=\pm\sqrt{5}\\x+4-4&=-4\pm\sqrt{5}\\x&=-4\pm\sqrt{5}\end{aligned}[/tex]
Therefore, the x-intercepts are:
[tex]x = -4+\sqrt{5}, \quad x = -4-\sqrt{5}[/tex]
---------------------------------------------------------------------
Question 28Given function:
[tex]f(x)=x^2+10x+14[/tex]
Change to vertex form by completing the square.
Add and subtract the square of half the coefficient of x:
[tex]\implies f(x)=x^2+10x+14+\left(\dfrac{10}{2}\right)^2-\left(\dfrac{10}{2}\right)^2[/tex]
[tex]\implies f(x)=x^2+10x+14+25-25[/tex]
[tex]\implies f(x)=x^2+10x+25+14-25[/tex]
[tex]\implies f(x)=x^2+10x+25-11[/tex]
Factor the perfect trinomial:
[tex]\implies f(x)=(x+5)^2-11[/tex]
Therefore, the vertex is (-5, -11).
To find the x-intercepts, set the function to zero and solve for x:
[tex]\begin{aligned}f(x) & = 0\\\implies (x+5)^2 -11 & = 0\\(x+5)^2 & = 11\\\sqrt{(x+5)^2} & = \sqrt{11}\\x+5&=\pm\sqrt{11}\\x+5-5&=-5\pm\sqrt{11}\\x&=-5\pm\sqrt{11}\end{aligned}[/tex]
Therefore, the x-intercepts are:
[tex]x = -5+\sqrt{11}, \quad x = -5-\sqrt{11}[/tex]
---------------------------------------------------------------------
Question 29Given function:
[tex]f(x)=-(x^2-2x-15)[/tex]
Change to vertex form by completing the square.
Add and subtract the square of half the coefficient of x:
[tex]f(x)=-\left(x^2-2x-15+\left(\dfrac{-2}{2}\right)^2-\left(\dfrac{-2}{2}\right)^2\right)[/tex]
[tex]f(x)=-\left(x^2-2x-15+1-1\right)[/tex]
[tex]f(x)=-\left(x^2-2x+1-15-1\right)[/tex]
[tex]f(x)=-\left(x^2-2x+1-16\right)[/tex]
Factor the perfect trinomial:
[tex]f(x)=-\left((x-1)^2-16\right)[/tex]
Simplify:
[tex]f(x)=-(x-1)^2+16[/tex]
Therefore, the vertex is (1, 16).
To find the x-intercepts, set the function to zero and solve for x:
[tex]\begin{aligned}f(x) & = 0\\\implies -(x-1)^2 +16 & = 0\\(x-1)^2 -16 & = 0\\(x-1)^2 & = 16\\\sqrt{(x-1)^2} & = \sqrt{16}\\x-1&=\pm4\\x-1+1&=1\pm4\\x&=5,-3\end{aligned}[/tex]
Therefore, the x-intercepts are:
[tex]x = 5, \quad x=-3[/tex]
Related Questions
If two rays share an endpoint,then they are opposite rays
Answers
Translate to an equation, but do not simplify or solve.
Eight more than x is equal to 53.
Solve the equation.
X =
+
Answers
Answer:
x + 8 = 53
Step-by-step explanation:
x + 8 = 53
8 more than x is x + 8 because ur adding 8 more to x. And that is equal to 53 because it literally says IS EQUAL to 53. therefore.
to solve isolate x by subtracting 8 from both side so:
x = 53-8
x = 45
(PLEASE HELP ANSWER THIS QUESTION QUICK) (and correctly please)
Analyze the following using a Venn diagram. Choose the best
answer.
"All plants have cells. Irises have cells. Therefore, irises are
plants."
1 Valid The inner circle is those with cells and the outer circle is plants
2 invalid. The inner circle is plants, and the outer circle is those with cells.
3 Invalid. The inner circle is things with cells, and the outer circle is plants
Answers
Answer: Choice 2
invalid. The inner circle is plants, and the outer circle is those with cells.
=========================================================
Further Explanation:
If we throw a dart at random, and we land in the inner circle (plants), then we automatically land in the outer circle (has cells).
Now imagine the dart landed in the "has cells" circle, but outside the smaller circle. This could be stuff like animal cells, bacteria, etc. So just because something has cells it does not automatically make it a plant. Saying "an iris has cells" is not enough info to be able to tell it's a plant or not. This means the conclusion of "irises are plants" is shaky at best.
This is why the overall argument structure is invalid.
For more information, check out the concept of "affirming the consequent" which is a common fallacy people make.
a dreidel is a four-side spinning top. each of the dreidel has a letter from the Hebrew alphabet, nun, gimmel, hay and shin.
Matthew spins the dreidel twice. he says the probability
Answers
Answer:
8 with 6
Step-by-step explanation:
A school needs 3,198 notebooks for next year. If the notebooks come in packages of 82, how many packages should the school buy?
Answers
Answer:
The school should buy 39 packages.
Step-by-step explanation:
3198 notebooks
82 notebooks = 1 package
3198÷82 = 39
(Eg: you have 4 notebooks and there are 2 in each package. How many packages are there? 4÷2 = 2 So 2 packages)
About how many pizzas does Mr. T's Pizzeria sell each week? Remember, there are 7 days in a week.
Mr. T's Pizzeria Daily Sales
Types of Pizza Number of Pizzas
Pepperoni 29
Sausage 35
Veggie 42
Cheese 28
A.
about 1,000 pizzas
B.
about 1,200 pizzas
C.
about 1,400 pizzas
D.
about 2,000 pizzas
Answers
Answer: a
Step-by-step explanation: hope it helps.
If P=5+7+9+11+...+101 and Q=9+11+13+15+...+103 are sums of arithmetic sequences, determine which
is greater, P or Q, and by how much.
Answers
In the sequence, Q is greater by 115.
How to calculate the value?From the information, P=5+7+9+11+...+101 and Q=9+11+13+15+...+103.
It should be noted that by looking at the figures the greater value will be Q as it began with a higher number.
The difference will be:
= 5 + 7 + 103
= 115
Therefore, in the sequence, Q is greater by 115.
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Plss help mee pls
Can someone answer this or look for the answer keys pls help
Answers
Answer:
11. 6
13. 73
15. 588
17. 139
19. 18
21. 18
23. 8
Step-by-step explanation:
To solve these equations, you simplify each expression. You also use the order of operations.
please help rlly fast, tysm
Answers
Answer: 27. 10 < x < 20
29. 10 < x < 20
Step-by-step explanation:
My child is struggling with the answer.
Answers
Using the relation between velocity, distance and time, the distances are given as follows:
A. d = 13/3 miles.
B. d = 4.25 miles.
C. d = M x 5/60(first five minutes) + N x 15/60(last 15 minutes).
What is the relation between velocity, distance and time?Velocity is distance divided by time, that is:
v = d/t.
Hence the distance is:
d = vt.
In item a, considering the time in hours, we have that:
v = 13, t = 20/60 = 1/3.
Hence:
d = 13/3 miles.
In item b, we have different definitions, then:
d = 15 x 5/60(first five minutes) + 12 x 15/60(last 15 minutes).
d = 15/12 + 15/5
d = 4.25 miles.
For item c, we have that:
d = M x 5/60(first five minutes) + N x 15/60(last 15 minutes).
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| y - 4 | = | y + 10|
Show how to solve too !!
Answers
Answer:
y = -3
Step-by-step explanation:
You want the solution to the absolute value equation | y-4 | = | y+10 |.
Absolute valueThe absolute value function ...
f(x) = | x |
is piece-wise defined as ...
[tex]f(x)=\begin{cases}-x&\text{for }x < 0\\x&\text{for }x\ge 0\end{cases}[/tex]
That is, the function is defined differently for argument values less than 0.
Given relationThe above observation regarding the absolute value function means the nature of the given equation changes where the absolute value arguments are zero. Those values are ...
y -4 = 0 ⇒ y = 4
y +10 = 0 ⇒ y = -10
In other words, the points y = -10 and y = 4 divide the domain of the equation into three parts. The behavior will be different in each of those parts.
To solve the equation, we must examine each region of the domain for possible solutions.
y < -10When y < -10, both of the absolute value functions change the sign of their argument. Then the equation is ...
-(y -4) = -(y +10)
Adding y to both sides of this equation gives ...
4 = -10 . . . . . false
This means there is no solution to the equation in the region y < -10.
-10 ≤ y < 4When -10 ≤ y < 4, the absolute value function |y -4| changes the sign of its argument, but the other function does not. In this region, the equation becomes ...
-(y -4) = (y +10)
-6 = 2y . . . . . . . . . add y-10 to both sides
-3 = y . . . . . . . . divide by 2. This value is in the region -10 ≤ y < 4.
The solution to the equation is y = -3.
4 ≤ yWhen 4 ≤ y, neither absolute value function changes the sign of its argument. In this region the equation becomes ...
y -4 = y +10
Subtracting y from both sides of this equation gives ...
-4 = 10 . . . . . false
This means there is no solution to the equation in the region 4 ≤ y.
__
Additional comment
The first attached graph shows the given equation rewritten as two functions. The solution is where those functions have equal values: the point(s) where the graphs intersect.
We often find it more convenient to rewrite equations like this to the form f(x) = 0. Here, that might mean we define ...
f(x) = |y -4| -|y +10|
Then the solution is found on the graph at the x-intercepts. The graph in the second attachment shows this solution, and clearly shows the changes in behavior at x = -10 and x = 4.
1/2(x + 6) = 1/2x - 9
Answers
Answer:
i think the question might be wrong.
1. Distribute
1/2 • x = 1/2x
1/2 • 6 = 3
2. Simplify
1/2x + 3 = 1/2x - 9
3. Add 3 to both sides
1/2x + 3 + 3 = 1/2x - 9 + 3
Step 4. Simplify
1/2x + 6 = 1/2x - 6
We have our solution: there is no solution. The coefficients are of a common value and the constant is comprised of opposite integers.
HELP ASAP!!!
Evaluate the polynomial for the given value by using synthetic division.
P(x) = 3x4 - x³ + 7x - 2 for x = 4 and x = -2
A.802; 52
B.-238; 32
C.730; 40
D.202; -44
Answers
Answer:
I'm assuming that is 2x squared, and not 2 multiplied by 2, as a given question usually wouldn't come in such a silly format. I do wish people would start using (2x^2) or (2x²), though.Just substitute the value of x (-3) in to the equation to find the value of y, or P(x).2(-3)² + 7(-3) - 1 = -4
Step-by-step explanation:
3/4 + 7/8 + 3/4 + 1/2 + 7/8
Answers
Answer:
=
15/4
(Decimal: 3.75)
Step-by-step explanation:
carla wrote this number:815,247 travis wrote this number: 638.571 the digit 8 in carlas number represents how many times what the digit 8 represents in travis number?(55 points)
Answers
The 8 in Carla's number is 100 times the 8 in Travis' number.
How many times what the digit 8 represents in Travis number?Here you need to understand the concept of place value. For any number, each digit is always a order of magnitude of 10 larger than the digit in the left.
For example, in 88
The first 8 is 10 times larger than the second one.
There comes the concept of place value, the first digit at the left of the decimal point represents the units, the second represents the tens, the third one the hundresd, and so on.
So, in the two given numbers:
815,247 Here the 8 represents the hundreds of thousands.
638,571 Here the 8 is in the thousands place value.
Then the relation between the first 8 and the second one is:
100,000/1,000 = 100
The 8 in Carla's number is 100 times the 8 in Travis' number.
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1. If A*B= A·B+1 and A□ B = A+B/2, then find 3 *[(7 □ 3) □ (3*4)].
2. If * represents and operation defined by a*b= a^b +b, find (1*2)*3.
Explain PLEASE!!!
Answers
The required solution would be 46 for a given problem (1).
The required solution would be 1 for a given problem (2).
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
We have been given that A * B= A·B + 1 and A □ B = A + B/2,
⇒ 3 *[(7 □ 3) □ (3*4)].
⇒ 3 *[(7 + 3/2) □ (3·4 + 1)].
⇒ 3 *[(17/2) □ (13)].
⇒ 3 *[17/2 + 13/2].
⇒ 3 *[30/2].
⇒ 3 * 15.
⇒ 3·15 + 1
⇒ 46
We have been given that * represents an operation defined by a*b= a^b +b,
find (1*2)*3.
⇒ a∗b = aᵇ + b
∴ (1 ∗ 2) ∗ 3 = (1²) ∗ 2 = (1) ∗ 2 = (1)³ = 1
Therefore, the required solution would be 46 for a given problem (1) and
the required solution would be 1 for a given problem (2).
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14. Explain how you can use multiplication to
find the quotient. Then evaluate the
expression.3/5 divided 3/15
Answers
Answer:
You can flip the second fraction and multiply the fractions so 3/5 * 15/3 = 3
Step-by-step explanation:
Helppp!
h(x)=x^2-6
Evaluate h(-3)
Answers
Answer:
3
Step-by-step explanation:
input -3 into h(x)=x^2-6
h(-3)=-3^2-6=9-6=3
A function, fx), represents the height of a plant x months after being planted. Students measure and record the height on a monthly basis.
Select the appropriate domain for this situation.
OA
the set of all integers
OB. the set of all positive real numbers
OC. the set of all positive integers.
OD. the set of all real numbers
Answers
Answer:
C. the set of all positive integers
Step-by-step explanation:
You want to know the appropriate domain of the function f(x) where x is months after a plant was planted, and f(x) is the height of the plant.
DomainThe domain of a function is the set of values of the independent variable for which the function is defined. In this case, the independent variable is x, the number of months after the plant was planted. Months are counted using the natural numbers, the set of all positive integers.
The appropriate domain is the set of all positive integers.
__
Additional comment
As a practical matter, the domain will have an upper limit, so will not actually be all positive integers.
The range of function values is likely the set of positive real numbers, though it might be integers if the measurements are recorded as integer values (mm or cm or in, for example).
Help me with this problem please
Answers
Question -: If ( 1 + tan θ ) ( 1+ ∅ ) = 2 , then what is ( θ + ∅ ) ?
a . 30⁰ b. 45⁰ c. 60⁰ d. 90⁰
Answer this question
Please Give Explanation
thanks
Answers
Correct choice is B.) 45°
The solution is in attachment ! do check it
Step-by-step explanation:
6.25 points
Find the GCF for the list.
10m4, 40m⁹
10m5
40m4
10m4
6.25 points
hey
list
Please help me I need this fast in class
Will give brainlest for help!
I got half the question solved I need help with other half please
Answers
Answer: y=-37/2
Step-by-step explanation:
y=9x/8 + (-1/2)
y=9x/8 - 1/2
y=9(-16)/8 - 1/2
y=9*(-2) - 1/2
y=-18 - 1/2
y=-(18 + 1/2)
y=-(18 + 1/2)*2/2
y=-(36 + 1)/2
y=-37/2
What is the probability of
spinning a yellow?
[?]%
Answers
Answer:
12.5 %
Step-by-step explanation:
There are 8 total sections, and only one of them is yellow. So if we spun it eight times, the possibility of getting yellow is one time. As a result, 1/8 is 12.5%
Can you help me solve for X. 4x+9=11
Answers
Answer as a fraction: x = 1/2
Answer in decimal form: x = 0.5
Work Shown:
4x+9 = 11
4x = 11-9
4x = 2
x = 2/4
x = 1/2
x = 0.5
Explanation: I subtracted 9 from both sides (step 2). Then I divided both sides by 4 to fully isolate x (step 4)
A rocket is launched vertically upward with an initial velocity of 40 ft/sec. Its height h
in ft above the ground after t seconds can be represented by the following equation.
How many seconds will it take the rocket to hit the ground? Round to the nearest
hundredth.
h = - 16t² + 40t + 8
Answers
The rocket will take a time of approximately 2.686 seconds to hit the ground.
How much time does a rocket need to hit the ground?
The height of the rocket (h), in feet, is modelled by a quadratic equation, which is used to model free fall motion, that is, the motion of an object solely due to action of gravity. In this problem we must look for the time when the rocket hits the ground:
- 16 · t² + 40 · t + 8 = 0
(t - 2.686) · (t + 0.186) = 0
Only the first root offers a realistic solution, for time is a non-negative variable. The rocket will take a time of approximately 2.686 seconds to hit the ground.
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See your levels
Mr. Camacho has 275 rubber stamps. He wants to give the same number of stamps to
each of his 8 students. If he gives away as many stamps as he can, how many stamps will be
left over?
Submit
rubber stamps
I do
Company Blog Help center User guides Tell us what you think Testimonials Contact us Terms of service Priva
IM LEARNING 2022 IXL Learning. All rights reserved.
Answers
Answer:
3 Stamps left
Step-by-step explanation:
275/8=34.375
34*8=272
275-272=3
Answer: 3
Find an equation of variation in which y varies jointly as x and z, and y= 48 when x = 8 and z=6
Answers
Answer:
y = xzStep-by-step explanation:
Joint variation equation:
y = kxz, where k- coefficient of variationGiveny = 48,x = 8,z = 6Find the value of k by plugging in the given values:
48 = 8*6k48 = 48kk = 1The equation is:
y = xzMeasures of Variation, Standard Deviation, Population Variance, Population. Can someone help?
Answers
To solve this problem one must be aware of the concepts of standard deviation and variance of raw data.
There is a direct formulae to calculate the variance of the data,
Variance = [tex]σ^{2} =\frac{Sigma(xi-m)^{2}}{n}[/tex]
Now here we need to verify ∑x and ∑[tex]x^{2}[/tex].
∑x = 21+19+15+32+27
= 114
and ∑[tex]x^{2}[/tex] = [tex]21^{2} +19^{2} +15^{2} +32^{2} +27^{2}[/tex]
= 441+361+225+1024+729
= 2780
So, the given relation is true.
Now the variance of the given data by putting the values in the formulae is equal to 45.2.
And Standard deviation=[tex]\sqrt{Variance}[/tex]
= [tex]\sqrt{45.2}[/tex]
= 6.72
And for population α²=36.16 and deviation=6.01.
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Find the equation of a line whose graph passes through the points (8,1) and (0,1)
Answers
Answer: y=1
Step-by-step explanation:
Slope formula: m=(y2-y1)/(x2-x1)
m=(1-1)/(0-8)
m=0/(-8)
m=0
y=mx+b
1=0(0)+b
b=1
y=0x+1
y=1
Refer to the number line. Find the coordinate of point X such that the ratio of MX to XJ is 3:1.
Answers
The coordinate of point X such that the ratio of MX to XJ is 3:1 is 12
How to determine the coordinate of point X?The coordinates are given as:
M = 2
J = 18
The ratio is given as:
Ratio = 3 : 1
The location of the point X is then calculated as:
X = Ratio * (J - M)
This gives
X = 3/(3 + 1) * (18 - 2)
Evaluate
X = 3/4* 16
This gives
X = 12
Hence, the coordinate of point X such that the ratio of MX to XJ is 3:1 is 12
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Step-by-step explanation:
show how to work out the question