Answer:
(5, - 9)
Step-by-step explanation:
Given
f(x) = (x - 8)(x - 2) ← in factored form
Find the zeros by equating f(x) to zero, that is
(x - 8)(x - 2) = 0
Equate each factor to zero and solve for x
x - 8 = 0 ⇒ x = 8
x - 2 = 0 ⇒ x = 2
The vertex lies on the axis of symmetry which is located at the midpoint of the zeros, hence
[tex]x_{vertex}[/tex] = [tex]\frac{8+2}{2}[/tex] = 5
Substitute x = 5 into f(x) for corresponding y- coordinate
f(5) = (5 - 8)(5 - 2) = (- 3)(3) = - 9
vertex = (5, - 9)
Answer: (5,-9)
Step-by-step explanation:
Make the multiplication indicated:
[tex]f(x) = x^2-2x-8x+16[/tex]
Add the like terms:
[tex]f(x) = x^2-10x+16[/tex]
Now find the x-coordinate of the vertex with this formula:
[tex]x=\frac{-b}{2a}[/tex]
In this case:
[tex]b=-10\\a=1[/tex]
Then:
[tex]x=\frac{-(-10)}{2(1)}=5[/tex]
Rewrite the expression with [tex]f(x)=y[/tex]
[tex]y = x^2-10x+16[/tex]
Now substitute [tex]x=5[/tex] into the function to find the y-coordinate of the vertex:
[tex]y = (5)^2-10(5)+16[/tex]
[tex]y =-9[/tex]
Therefore, the vertex is:
(5,-9)
Write an equation.John bought 6 note books at CVS, he spent a total of $13.50.
Hello There!
6n=13.50
This means that 6 notebooks and some amount represented as n is 13.50
Use the Exterior Angles Theorem to find the measure of each angle in degrees.
You have to begin by using the triangle sum therom. That means Angle DEC would be 64°, Angle D would be 76°, and angle C would be 40°
GENERAL QUESTION for my next math class should i take pre-calc, or intergrated math. which one is easier and which one hasmore answers on here.
Because integrated math requires skills in trigonometry, I would highly recommend pre calc first
Answer:
I would say you first evaluate your strengths by checking on both the syllabuses. Find what really interests you, your passion. Is it pre-calculus or is it integrated math.
Ability and passion go hand in hand when it comes to the performance.
Solve the inequality statement:
4r – 5 < 5r+7
Answer:
r > - 12
Step-by-step explanation:
4r – 5 < 5r+7
4r - 5r < 7 + 5
-r <12
r > - 12 (when you multiply or divide a negative number, the sign will be flipped)
Answer:D
Step-by-step explanation:
Need Help !!!!!!!!!!!!
Answer:
C
Step-by-step explanation:
The slope m of the functions give the measure of the rate of change.
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
g(x) = [tex]\frac{5}{2}[/tex] x - 3 ← is in slope- intercept form
with slope m = [tex]\frac{5}{2}[/tex] = 2.5
Calculate the slope of f(x) using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, - 3.5) and (x₂, y₂ ) = (1, - 1) ← 2 points from the table
m = [tex]\frac{-1+3.5}{1-0}[/tex] = 2.5
Hence
The slopes of g(x) and f(x) are both m = 2.5, thus
The functions increase at the same rate → C
what is the term that is used for the only number which is neither positive nor negative.
Answer:
Zero is neither positive nor negative integer and is known as origin.
Find the volume of a cylinder with a 9-inch height and a 3-inch radius
(i = 3.14).
A. 35.36 cubic inches
B. 89.78 cubic inches
C. 169.56 cubic inches
D. 254.34 cubic inches
Answer:
D. 254.34 cubic inches
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2h
Where r = 3 in and h = 9 in
V = (3.14) * (3)^2 *9
V = 254.34 in ^3
Answer:
volume of a cylinder= \pi*r^2*h
81*pi
=254.34 in^3
OFFERING A LOT OF POINTS. please write 2 or
more sentences and explain how you got the answer.
Alaska is the largest state in the United States. The state has an area of approximately 663,000 square miles. Rhode Island is the smallest state in the United States, with an area of approximately 1,000 square miles. Currently, the populations of Alaska and Rhode Island are 732,000 people and 1 million people, respectively. If Alaska had the same number of people per square mile as Rhode Island, what would its population be? In two or more sentences, explain your calculations and conclusions.
Answer:
Rhode Island has 1,000,000 people within an area of 1000 sq miles.....
1,000,000/1000 = 1000 people per sq mile
Step-by-step explanation:
If Alaska had the same number of people per square mile as Rhode Island, its population would be calculated as 663,000 mi^2 times 1,000 people = 663,000,000 people.
Simplify (a + b )(a^2 - ab + b^2)
Answer:
a^3 + b^3
Step-by-step explanation:
(a + b )(a^2 - ab + b^2)
Distribute
a*a^2 -a*ab+a*b^2 + b*a^2 -b*ab +b*b^2
Simplify
a^3 -a^2b +ab^2 +a^2b -ab^2+b^3
Combining like terms
a^3 +b^3
Answer:
a^3 + b^3
Step-by-step explanation:
hope this helps you! have a good day/night :D
can help me with this please
Answer:
Step-by-step explanation: the answer is 1 because line a and b are paralel so 1 , 5 are the same as well as (2,7)
Answer:
angle 1
Step-by-step explanation:
this is because they are alternating angles.
Plz help me with this
The minimum y-value is -7.
I'm only a few Brainliests away from ranking up, so one would be much appreciated.
Answer: A) -7
Step-by-step explanation:
The Asymptote is 1 so the range of the graph is from +1 to -1.
However, there is also a shift down of 6 units, so the range of the transformed graph is from (+1-6 = -5) to (-1-6 = -7).
Therefore, the maximum is -5 and the minimum is -7.
Solve the equation for a: ab – ac = d + e
Answer:
see explanation
Step-by-step explanation:
Given
ab - ac = d + e ← factor out a from both terms on the left side
a(b - c) = d + e ← divide both sides by (b - c)
a = [tex]\frac{d+e}{b-c}[/tex]
Answer:
Step-by-step explanation:
How do I solve each log equation
When subtracting logs you actually divide.
logx^2 = log 160 - log 2
logx^2 = log (160/2)
logx^2 = log 80
Now remove the log from each side:
x^2 = 80
x = √80
x = 4√5 and -4√5
Liliana wants to start a seventh-grade computer club at Hamden Middle School. She surveyed 20 seventh-grade students at the town park. She asked each student how many hours they spend on their computers each week. She obtained the following results.
8, 15, 0, 11, 12, 13, 16, 13, 0, 4, 17, 14, 30, 13, 5, 12, 1, 13, 12, 21
What is the ratio of the total number of students who used their computers to the total number of students surveyed?
Answer:
Ratio would be 9 : 10
Step-by-step explanation:
Liliana surveyed 20 students that how many hours they spend on their computers each week.
The results are as follows
8, 15, 0, 11, 12, 13, 16, 13, 0, 4, 17, 14, 30, 13, 5, 12, 1, 13, 12, 21
In the above results 2 students did not use computers out of 20 students.
Therefore, The total number of students who used their computers = 20 - 2 = 18
So the ratio would be 18 : 20 or 9 : 10
Answer:
C. 18/20 or 9/10
Theo starts with savings of £18
James starts with no savings
Each week from now,
Theo will save £4.50 and James will save £4
In how many weeks will Theo and James have savings in the ratio 15:8?
Answer:
6 weeks.
Step-by-step explanation:
Let x be the number of weeks to be found.
Then 4.5x + 18 / 4x = 15/8
Cross multiply:
36x + 144 = 60x
24x = 144
x = 6 (answer).
In approximately 1.67 weeks (or rounded to 2 weeks), Theo and James will have savings in the ratio 15:8.
Explanation:We can set up an equation to represent the savings of Theo and James over time. Let x be the number of weeks they have saved. Theo will have saved £4.50x and James will have saved £4x. We can set up the equation:
£4.50x / £4x = 15 / 8
Cross-multiplying the equation gives us:
8 * £4.50x = 15 * £4x
Simplifying the equation gives us:
36x = 60x
Dividing both sides by 36x gives us:
1 = 5 / 3x
Cross-multiplying again gives us:
3x = 5
Dividing both sides by 3 gives us:
x = 5 / 3
Therefore, in approximately 1.67 weeks (or rounded to 2 weeks), Theo and James will have savings in the ratio 15:8.
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HELP ASAP WILL REQARD BRAINLIEST
GRADUATING THIS WEEK NEED THIS ALL ANSWERED PLZ
1. 14k+k<30
2. 9d-3d+7 > 31
3. 13x-2x>77
4. 5y< 7y + 18
5. 3f-12-10+9f
6. 4t-8< 2t-2
7. 15h+ 16 > 6h-20
8. 4r-2r> 6-
Part A
1. 14k+k<30
Add the left hand side to get;
15k<30
Divide both sides by 15.
[tex]\frac{15k}{15}\:<\:\frac{30}{15}[/tex]
k<2
2. We have 9d-3d+7>31
Group similar terms to obtain:
9d-3d>31-7
Combine similar terms:
6d>24
Divide both sides by 6
[tex]\frac{6d}{6}\:>\:\frac{24}{6}[/tex]
This implies that:
d>4
3. We have 13x-2x>77
This implies:
11x>77[tex]\frac{11x}{11} \:>\:\frac{77}{11}[/tex]
x>7
4. We have 5y<7y+18
This implies
5y-7y<18
-2y<18
Divide both sides by -2 and reverse the sign.
[tex]\frac{-2y}{-2} \:>\:\frac{18}{-2}[/tex]
[tex]y\:>\:-9[/tex]
5. The given expression is;
3f-12>-10+9f
Group similar terms:
-12+10>9f-3f
-2>6f
Divide both sides by 6.
[tex]\frac{-2}{6}\:>\:\frac{6f}{6}[/tex]
[tex]-\frac{1}{3}\:>\:f[/tex]
[tex]f\:<\:-\frac{1}{3}[/tex]
6. We have 4t-8<2t-2
Group similar terms;
4t-2t<-2+8
2t<6
t<3
7. We have
15h+16>6h-20
Group like terms;
15h-6h>-20-16
9h>-36
Divide both sides by 9
h>-4
8. The given inequality is
4r-2r>6-r
This implies
4r-2r+r>6
3r>6
r>2
Part B
x-27=193
x=193+27
x=220
2. The given equation is
f(12)=48
or
12f=48
f=48/12
f=4
3. We have the equation 4s+2=74
4s=74-2
4s=72
s=18
4. The given equation is
9(r+1)-18=2r+12
Expand to get:
9r+9-18=2r+12
Group like terms:
9r-2r=12+18-9
7r=21
r=3
1) m SUT equals ___ Degrees.
2) m TUW equals ___ degrees
3) TUW is a(n) _____angle
4) SUT is a(n) ____angle
5) TUW and SUT are___ angles
Answer:
1. 30
2. 150
3. obtuse
4. acute
5. Adjacent
Step-by-step explanation:
The correct expression for the angles are;
1) m SUT equals 30 Degrees.
2) m TUW equals 150 degrees
3) TUW is obtuse angle
4) SUT is acute angle
5) TUW and SUT are Adjacent angles
What are obtuse acte and adjacent angles?Similar to corners, right angles have a 90° measure. Acute angles are less than ninety degrees. More than 90° but less than 180° are obtuse angles. Additionally, a straight angle is 180°, which is the point at which two lines merge into one by going in the same direction.
Any angle is composed of two rays that converge at a point known as the vertex. When two angles share a ray, it indicates that they are adjacent to one another.
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choose the correct simplification of (x^2/y^5)^4
Answer:
x^8/y^20
Step-by-step explanation:
multiply the exponents by 4.
If 1/2 of all the books at a bookstore are fiction and 3/5 of the books in fiction
are mysteries, what fraction of the store's books are fiction mysteries?
Answer:
[tex]\frac{3}{10}[/tex]
Step-by-step explanation:
we know that
To find the fraction of the store's books that are fiction mysteries, multiply 1/2 by 3/5
so
[tex](\frac{1}{2})(\frac{3}{5})=\frac{3}{10}[/tex]
which expression gives the measures of XYZ in the diagram below?
Answer:b
Step-by-step explanation:
You're answer is b. All you have to do is a measurement
Answer:
B) 1/2 (154° - 46°)
Step-by-step explanation:
Here ∠XYZ is an angle subtended by two chords from a point outside of the circle.
It is a one of the circle.
If the angle subtended by two chords from the outside point of the circle, the measure of the angle is 1/2 times difference of the major arc and minor arc.
Here Major arc = 154° and minor arc = 46°
Applying the rule, we get
m∠XYZ = [tex]\frac{1}{2} (Major arc - Minor arc)[/tex]
m∠XYZ = 1/2 (154° - 46°)
Need Help Please!!!!!!
pretty sure it’s the crickets because the others one does not make sense, crickets are known for jumping up and down a lot so i’m pretty sure it’s the cricket
PLEASE HELP RIGHT AWAY!!!!!
Answer:
1) 46.6
Step-by-step explanation:
Given Data:
s1 of Triangle ABC= 4cm
s2 of Triangle ABC=6cm
s3 of Triangle ABC=8cm
As per the side-side-side SSS of a given triangle
the corresponding angles are found by the following law of cosine formula
cos A = (b2 + c2 − a2) / 2bc
Putting the values we get
cos A= (4^2+8^2-6^2)/2(4)(8)
cos A= (16+64-36)/64
A=cos^-0.6875
A=46.57!
Find the surface area of the prism.
Answer:
376
Step-by-step explanation:
2(8x10)=2(80)=160
2(10x6)==2(60)=120
2(6x8)=2(48)=96
160+120+96=376
David wants to build a rectangular fencing with the 5 identical parts for his animals. He has 780 feet of fencing to make it. What dimensions of each part will maximize the total enclosed area?
Answer:
65 ft by 39 ft
Step-by-step explanation:
Let x ft be the length of each part and y ft be the width of each part. The total perimeter of all 5 parts is
[tex]6x+10y=780[/tex]
The length of the large rectangle is 5y ft and the width of the large rectangle is x, so the total area is
[tex]A=x\cdot 5y[/tex]
From the first equation,
[tex]y=78-0.6x[/tex]
Substitute it into the area expression:
[tex]A(x)=x\cdot 5(78-0.6x)=390x-3x^2[/tex]
Find the derivative:
[tex]A'(x)=390-3\cdot 2x=390-6x[/tex]
Equate it to 0:
[tex]390-6x=0\\ \\6x=390\\ \\x=65[/tex]
Then
[tex]y=78-0.6\cdot 65=78-39=39[/tex]
50 points!!! please have serious answers
Use the data in the following table to answer the 3 questions below. Please show all calculations needed.
Daily Earnings $25 $26.50 $20 $23.50 $20
Find:
1: Median
2: Mean
3: Mode
PLEASE SHOW ALL STEPS
Answer:
Median: 23
Mode: $20
Mean: The average of numbers added up and then divided, equalling in 23
A square garden has sides 50 ft long.
You stretch a hose exactly from one
corner of the garden to another
corner across the garden's diagonal.
How long is the hose?
Answer:
The hose is ~70.71 ft long.
Step-by-step explanation:
We need to use Pythagorean theorem to figure this out. ( A^2 + B^2 = C^2)
So we first need to square 50 two times, since that's the length and height of the garden. This equals 5000.
Then we just need to find the root of 5000! This rounds out to about 70.71 ft.
Hope I could help! :)
The length of the hose which is stretched from one corner of the garden to another corner across the diagonal of it is 70.72 ft
What is the diagonal of the square?The diagonal of the square is the distance from opposite vertices of it. There are two diagonals in a square which are equal in measure.
To find the diagonal of the square, the following formula is used.
d=a√2
Here, (a) is the length of the side of the square.
The side of a square garden is 50 ft long. One hose is stretch from one corner of the garden to another corner across the diagonal of it. Thus, the length of the diagonal is,
d=a√2
d=(50)√2
d=70.72 ft
Thus, the length of the hose which is stretched from one corner of the garden to another corner across the diagonal of it is 70.72 ft
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What is the value of v in the equation 3(2v + 1)=-15(5v + 16)
Answer:
v = -3
Step-by-step explanation:
Step 1: Use the Distributive Property
6v + 3= -75v - 240
Step 2: Isolate v
81v = -243
Step 3: Simplify
v = -3
The value of v in the equation 3(2v + 1)=-15(5v + 16) is -3 after rearranging and solving.
What is linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have a linear equation in one variable:
3(2v + 1)=-15(5v + 16)
6v + 3 = -75v -240
6v + 75v = -240 - 3
81v = -243
v = -3
Thus, the value of v in the equation 3(2v + 1)=-15(5v + 16) is -3 after rearranging and solving.
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Simplify the expression using long division. (10x2 – 85x – 10) ÷ (x – 8)
Answer: 5 • (2x2 - 17x - 2)
———————————————————
x - 8
Step-by-step explanation:
Step by step solution :
Step 1 :
Equation at the end of step 1 :
Step 2 :
10x2 - 85x - 10
Simplify ———————————————
x - 8
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
10x2 - 85x - 10 = 5 • (2x2 - 17x - 2)
Trying to factor by splitting the middle term
3.2 Factoring 2x2 - 17x - 2
The first term is, 2x2 its coefficient is 2 .
The middle term is, -17x its coefficient is -17 .
The last term, "the constant", is -2
Step-1 : Multiply the coefficient of the first term by the constant 2 • -2 = -4
Step-2 : Find two factors of -4 whose sum equals the coefficient of the middle term, which is -17 .
-4 + 1 = -3
-2 + 2 = 0
-1 + 4 = 3
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
The principal P is borrowed at a simple interest rater for a period of time t. Find the loan's future value A, or the total amount due at timet. Round answers to the
nearest cent.
P - $7000, r = 7%, t = 6 years
The loan's future amount is $9940
What is simple interest?Simple interest is based on the principal amount of a loan or the first deposit in a savings account.The formula to calculate Simple interest is :
I=PRT
where,
I(interest money created)
P(initial amount of money)
R(interest rate as a decimal)
T(time in years)
How to find the loan's future value?Loan's future value will be principle amount + the net interest.I=7000(.07)(6)
I=$2,940
So, the loan's future amount = $7000 + $2940 = $9940
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What is the function rule for the following situation? Rex paid $20 for a membership to the pool and pays $300 each time he goes to the pool
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f(x)=20+300x
Also, Rex should find a different pool because that fee is ridiculous.
The function rule in the given situation is a linear function and can be represented as C=20+300x. In this rule, 'C' is the total cost in dollars, '20' is the initial membership fee, '300' is the cost of each pool visit and 'x' is the number of pool visits.
Explanation:The function rule in this situation is called a linear function. A function rule describes how to convert an input (in this case, the number of times Rex visits the pool) into an output (the total cost).
The function rule for this specific situation could be represented as C=20+300x, where 'C' is the total cost, '20' is the initial membership fee, '300' is the cost each time Rex goes to the couple, and 'x' is the number of times Rex goes to the pool.
So, each time Rex goes to the pool, you would multiply that number by 300 (the cost per visit), and then add 20 (the initial fee) to get the total cost.
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