A second degree polynomial with zeros at 4 and at 7 passes
through the point (1,9). Its equation has the form p(x) = ax² +
bx + c.
Find the value of a.
The value of a in Quadratic function ax^2 + bx + c is 1.
In algebra, a polynomial function with one or more variables in which the highest-degree term is of the second degree is known as a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic.
the polynomial function f(x)=Ax^2+Bx+C, where A 0 and A, B, and C R. A quadratic function is a second-degree polynomial function in which all the coefficients of the terms with a degree less than 2 are zeros.
Roots of the given equation are 4 and 7.
then the quadratic function whose roots are 4 and 7 is
x^2 - (4+11)x + (4*7)
x^2-11x+28
on comparing this to the Quadratic function ax^2+bx+c
the value of a is 1.
Read more about quadratic function here :
https://brainly.com/question/18958913
#SPJ4
Which of the following statements is equivalent to 18 + 6?
We could say 18 + 6 = 2(9+3) as one example
Or 18+6 = 3(6+2) as another example
Or 18+6 = 6(3+1) as another example
There are few approaches so it depends on what answer choices you are given.
ASAP Please!
Beth purchased a $50,000 nonparticipating whole life insurance policy. The annual premium was $1,608. The cash value of the policy after 10 years will be $13,740. Assuming 5% interest rates. What is the traditional net cost of this policy, per thousand per year, over the first 10 years the policy is in force? (Round your answer to 2 decimal places)
Based on the annual premium, the cash value of the policy, and the number of years, the traditional net cost of this policy over the first 10 years is 5.76.
What is traditional net cost?First, find the net cost over 10 years:
= Total premium over 10 years - cash value
= (1,608 x 10) - 13,740
= $2,340
The net cost per year is:
= 2,340 / 10
= $234
The traditional net cost of this policy, per thousand per year for the first 10 years is:
= 234 / 50,000 x 1,000
= 4.68
Find out more on the cost of insurance policies at https://brainly.com/question/23282485
#SPJ1
Positive multiples of 4
Answer:
4,8,16,20,24,28,32,36,40,44...
Step-by-step explanation:
How many? This list goes on forever.
Answer:
4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96.
Step-by-step explanation:
(a) Write an equation in terms of x that represents the problem.
(b) Solve the problem.
The difference of a number and 16 is the same as the product of the number and 3. Find the number.
Answer:
-8
Step-by-step explanation:
x - 16 = 3x
Solve for x
-2x = 16
x = -8
What lowest terms fraction equal to 15%
Answer:
3 / 20
Step-by-step explanation:
Take only after the decimal point part for calculation.
.15
Then, divide that value by 1.
.15
1
Multiply both numerator and denominator by 100 (because there are 2 digits after the decimal point so that is 102 = 100).
.15 × 100
1 × 100
=
15
100
;
To simplify
15
100
its lowest terms, find GCD (Greatest Common Divisor) for 15 & 100, which is 5. Here's How to Find GCD of 15 and 100?
15/5
100/5
After simplify or reduce the fraction.
3
20
Find the distance between each pair of points. The points are (3,-5) and (-2,0)
Answer:
5√2
Step-by-step explanation:
The distance formula is the the square root of the difference of the x (delta x) squared plus the difference of the y (delta y) squared. So, you would do
0 - (-5) = 5 & -2 - (3) = -5
Then
5² + (-5)² = 25 + 25 = 50
Square root 50
5√2
Hope this helps! :)
if f (x) =x2-4x-6 find f(o) F(3) f(-2) show that f (1/2) f(7/2) and f(2-h) f (2+h)
If f(x) = x² ₋ 4x ₋ 6 then we get the following answers for f(0),f(3) and f(-2) respectively. And the expression f(1/2) = f(7/2) and f(2₋h) = f(2₊h) is therefore proved.
f(0) = -6
f(3) = -9
f(-2) = 6
Given the function is f(x) = x² ₋ 4x ₋ 6
we need to find for f(0):
f(0) = 0² ₋ 4(0) ₋ 6
f(0) = ₋6
f(3) = 3² ₋ 4(3) ₋ 6
f(3) = 9 ₋ 12 ₋ 6
f(3) = ₋9
f(₋2) = (₋2)² ₋ 4(₋2) ₋ 6
f(₋2) = 4 ₊ 8 ₋ 6
f(₋2) = 6
we need to prove f(1/2)f(7/2)
now, f(1/2) = (1/2)² ₋ 4(1/2) ₋ 6
f(1/2) = 1/4 ₋ 2 ₋ 6
f(1/2) = 1 ₋ 8 ₋ 24 / 4
f(1/2) = ₋31/4
f(7/2) = (7/2)² ₋ 4(7/2) ₋ 6
f(7/2) = 49/4 ₋ 14 ₋ 6
f(7/2) = 49 ₋ 56 ₋ 24 / 4
f(7/2) = ₋31/4
therefore, f(1/2) = f(7/2)
f(2₋h) = (2₋h)² ₋ 4(2₋h) ₋ 6
f(2₋h) = (4 ₊ h² ₋ 4h) ₋ 8 ₊ 4h ₋ 6
f(2₋h) = h² ₊ 4 ₋ 4h ₋ 8 ₊ 4h ₋ 6
f(2₋h) = h² ₋ 10
f(2₊h) = (2₊h)² ₋ 4(2₊h) ₋ 6
f(2₊h) = 4 ₊ h² ₊ 4h ₋ 8 ₋ 4h ₋ 6
f(2₊h) = h² ₋ 10
therefore, f(2₋h) = f(2₊h)
Hence proved.
Learn more about Functions here:
brainly.com/question/2328150
#SPJ9
What are the two equations to set up to solve the equation
Answer:
X is 21 (3x = 3*7) and 3x - 2 = 19.Step-by-step explanation:
Solve for X:
3x - 2 = 19= 3*7Solve for 19:
3 * 7 - 2 = 19= 21 - 2 = 19= 1919 = 19.So 3x - 2 = 19 is (3 * 7) - 2 = 19.(2x+3) + 7 and 2x + (3+7)? Expressions equivalent
Mariana owns a food truck and sells tacos and burritos. Each taco costs $2.50 and each burrito costs $4.00. Th
system of equations represents the results of Mariana's sales yesterday for t tacos and b burritos.
t + b = 60
2.50t + 4.00b = 175.50
How many tacos did Mariana sell yesterday?
Let the cost of one tacos = t
Let the cost of one burritos = b
So, we have this system
t + b = 60 (eq-1)
2.50t + 4.00b = 175.50 (eq-2)
We take equation-1,
We can write,
t + b = 60
t= 60-b (eq-3)
Substitute equation-3 into equation-2,
We can write,
2.50t + 4.00b = 175.50
2.50(60-b) + 4.00b = 175.50
Multiply the values,
2.5(60)-2.5b+4b = 175.5
150-2.5b+4b = 175.50
Subtract the values,
1.5b = 175.5-150
1.5b = 25.5
b = 25.5/1.5
Divide the values,
b = 17
Replace the value 'b' in equation-3,
We can write,
t= 60-b
t= 60-17
t=43
Therefore,
Mariana sell 43 tacos yesterday.
Learn more about event correlation here: brainly.com/question/14104100
#SPJ9
three lakes lost water during a drought. Lake Jensen lost 1/6 of its water, Lake parlow lost 26% of its water, and lake stockton lost 33/200. which lake lost the least amount of water whats the answer?
Answer:
lake stockton
Step-by-step explanation:
26% is equal to 26/100
you have to figure out a common denominator for all three numbers. the easiest for me was 600
to get from 1/6 to x/600 you multiply by 6 so you do the same to the top. equaling 100/600
for 26/100 you times top and bottom by 6 equaling 156/600
for 33/200 you multiply by 3 on both equaling 99/600
now you can clearly see that 99/600 is the least amount
Tomas works as an underwater photographer. He starts at a position that is 17 feet below sea level. He rises 9 feet, then descends 18 feet to take a photo of a coral reef. Enter an expression to find his position relative to sea level when he took the photo and then evaluate the expression.
Answer:
26 below sea level
Step-by-step explanation:
-17+9=-8
-18-8=26
find the measures of the angles of a triangle if the angles are resented by x, 4x, and 4x. show work
x = 20
Step-by-step explanation:Total degrees of a triangle = 180 degrees.
The three angles are x, 4x & 4x
x + 4x + 4x = 180 degrees
x + 8x = 180 degrees
9x = 180 degrees
(9x)/9 = 180/9
x = 180/9
x = 20
Question 20 of 20
The functions f(x) and g(x) are shown on the graph.
f(x) = x²
What is g(x)?
10
10
f(x)
Answer:
g(x) = - x² - 4
Step-by-step explanation:
g(x) is a reflection in the x- axis of f(x) followed by a vertical translation of 4 units down.
f(x) = x² , then
g(x) = - x² ( reflection in the x- axis )
g(x) = - x² - 4 ( a translation of 4 units down )
What is the multiplicative inverse of 1 1/3?
According to the given statement the multiplicative inverse of 4/3 is 3/4.
What is multiplicative inverse?A multiplicative inverse as well as reciprocal for a number x, indicated by 1/x or x1, is a number that produces the multiplicative identity, 1. b/a is the multiplicative inverse of either a fraction a/b. Divide 1 by the number to find the multiplicative inverse.
How Do You Find the Multiplicative Inverse?Flipping the numerator and denominator yields the multiplicative inverse of a fraction. 1's multiplicative inverse is 1. The multiplicative inverse of 0 is unknown. 1/x or x-1 seems to be the multiplicative inverse of something like a number x.
According to the given data:Given 1*(1/3)
This can be written as 4/3.
The multiplicative inverse of 4/3 is 3/4
To know more about multiplicative inverse visit:
https://brainly.com/question/13715269
#SPJ9
Richard bought 3 slices of cheese pizza and 2 sodas for $8.75. Jordan bought 2 slices of cheese pizza and 4 sodas for $8.50. How much would an order of 1 slice of cheese pizza and 3 sodas cost?
Answer:
3x+2y=8.75
2x+4y=8.5
solving above two we get
x=9/4
y=1
Then x+3y=2.25 + 3=5.25
Step-by-step explanation:
Hello can someone please help
The correct statements for this problem are given as follows:
20. Plane N contains line l.
21. Point P lies in line l.
22. PQ lies on plane N.
23. Line l and line m are coplanar.
24. Line l passes through P and Q.
25. Line m and line l intersect at P.
26. Points P and Q are colinear.
What is each thing in this problem?From the graph, we have these following items:
Plane N.Lines m and l.Segment PQ.Points P and Q.For item 20, we have that:
Line l is on plane N, hence:
Plane N contains line l.
For item 21, we have that point P is on both lines, m and l, hence:
Point P lies in line l.
For item 22, we have that points P and Q are on the plane N, hence:
PQ lies on plane N.
For item 23, we have that the lines are on the same plane, hence:
Line l and line m are coplanar.
For item 24, we have that points P and Q are both on line l, hence:
Line l passes through P and Q.
From it, we can also solve item 26, as follows:
Points P and Q are colinear.
And for item 25, the two lines intersect at point P, hence:
Line m and line l intersect at P.
More can be learned about planes, lines and points at https://brainly.com/question/28247880
#SPJ1
A quality control inspector has drawn a sample of 19 light bulbs from a recent production lot. If the number of defective bulbs is 1 or more, the lot fails inspection. Suppose 20% of the bulbs in the lot are defective. What is the probability that the lot will fail inspection? Round your answer to four decimal places.
The probability that the lot of the bulbs will fail inspection of the quality control inspector is 0.9856
How find the probability of the lot that will fail inspectionGiven data
p = 20%
sample drawn = 19 bulbs
20% of the bulbs in the lot are defective
n = 19
p = 20% = 0.20
if 20% of the bulbs are defective to find the non defective bulbs we solve as follows
q = 1 - p
= 1 - 0.20
= 0.80
Using binomial theorem,
[tex]P ( X = x) = (^n C _{x} ) * p x * (1 - p)n - x[/tex]
[tex]= 1 - P ( x < 1 )[/tex]
[tex]= 1 - P ( X = 0)[/tex]
[tex]= 1 - ( ^{19} C _{0} ) * 0.20^0 * (0.80)^{19}[/tex]
[tex]= 1 - 1 * 1 * 0.01441[/tex]
[tex]= 1 - 0.01441[/tex]
= 0.98559
= 0.9856 (to four decimal place)
Read more on binomial theorem here: https://brainly.com/question/13672615
#SPJ1
.56 x 72
Please help me find the answer to this quick
which are the partial products of 3,706×4?
The partial products of 3706 × 4 is ( 3000 × 4 ) + ( 706 × 4 ).
Calculating the product of two or more numbers is the procedure known as multiplication in mathematics. When two integers are multiplied together in mathematics, the result is a product or an expression that describes the factors to be multiplied.
The decimal numeral system is widely used to express both integer and non-integer numbers. The way of representing numbers in the decimal system is known as decimal notation.
The given product is 3706 × 4 and can be written as:-
3706 × 4 = [ 3000 + 706 ] × 4
3706 × 4 = ( 3000 × 4 ) + ( 706 × 4 )
Therefore, the partial products of the given expression is ( 3000 x 4 ) + ( 706 x 4 ).
Learn more about multiplication here:
brainly.com/question/10873737
#SPJ9
Help ASAP! 25 Points! What theorem allows you to prove line f is parallel to line g? For what value of x is line f parallel to line g?
PLEASE FIND X FOR ME TOO :) Thank you if you help!
Answer:
Theorems are stated below
x = 6
Step-by-step explanation:
The following theorems can prove that 2 lines are parallel
Two lines are parallel if they’re cut by a transversal such that
Two corresponding angles are congruent.Two alternate interior angles are congruent.Two alternate exterior angles are congruent.Two same-side interior angles are supplementary.Two same-side exterior angles are supplementary.The two angles shown are corresponding angles. They are corresponding because each is in the same position left side) in its group of four angles.
Corresponding angles are equal
Therefore,15x + 9 = 21x - 27
Subtract 9 from both sides:
15x = 21x - 27 - 9
15x = 21x - 36
Subtract 21x from both sides
15x - 21x = - 36
-6x = 36
Divide by -6 both sides
-6x/-6 = 36/-6
x = 6
The two angles are
15x + 9 = 15(6) + 9 = 90 + 9 = 99°
and
21x - 27 = 21(6) - 27 = 126 - 27 =99°
And indeed they are equal
Marty placed $4000 into an account earning 4% simple interest. At the end of the year he moved the total amount to a new account earning 5% interest. Determine the amount of money Marty would have at the end of the second year.
Simple interest , 4368 is the amount of money Marty would have at the end of the second year.
What does the term "simple interest" mean?
Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.P = $4000 R = 4% T = 1
then substitute the value into the formula = [tex]\frac{P * R * T }{100}[/tex]
= [tex]\frac{4000 * 4 * 1}{100}[/tex] = 160
So, the total amount is ( 4000 + 160) = 4160
Second year
P = 4160 , R = 5% T = 1
then substitute the value into the formula = [tex]\frac{P * R * T }{100}[/tex]
= [tex]\frac{4160 * 5 * 1}{100}[/tex] = 208
So, the total amount is ( 4160 + 208 ) = 4368
Learn more about Simple interest
brainly.com/question/25845758
#SPJ1
Michael is playing a game of chance in which he tosses a dart into a rotating dartboard with 8 equal-sized slices numbered 1 through 8. The dart lands on a numbered slice at random.
Answer:
6 I belive it should land on 6
Solve system of equations using substitution method
2x-3y=6
x + y = -12
7/11 divided by 4/5 if you can pls show the work
Answer:
please rate as brainliest
Step-by-step explanation:
7/11 divide 4/5
just intertwine the second fraction values since it is divided and you should put multiplication
=7/11 × 5/4
=35/44 or 0.7954545455
Answer:
35/44
Step-by-step explanation:
see picture above it is the answer
An albatross is flying 87 m above the surface of the ocean. Directly below the albatross, a sea gull is flying 6 m above sea level. Directly below
the birds is a shark, swimming 23 m below sea level. Determine each of the following. Explain your work for each.
a) The difference in height between the sea gull and the shark.
b) The distance between the heights of the sea gull and the shark.
Using simple addition and multiplication, we concluded that the difference in height between sea gull and shark is 17m and distance between the heights of the sea gull and the shark is 29m.
Given,
Albatross is flying 87 m above the surface of the ocean
Sea gull is flying 6 m above sea level
shark is swimming 23 m below sea level
a) The difference in height between sea gull and shark is -
23m - 6m
= 17m
b) The distance between the heights of the sea gull and the shark is -
23m + 6m
= 29m
To learn more about addition and subtraction from given link
https://brainly.com/question/20460320
#SPJ9
Evaluate Cross multiply :)
1/2|4x + 3/4|>7/8
solve the inequality. express the answer using interval notation
Answer:
2.35
Step-by-step explanation:
Ken is playing with building blocks. He wants to put all 64 blocks into the same number of stacks. How many blocks could he put in each stack
Answer: He could put 8 blocks in 8 stacks
Step-by-step explanation:
Ken could put the blocks in stacks of 1, 2, 4, 8, 16, 32, or 64.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To find out how many blocks Ken could put in each stack, we need to divide the total number of blocks by the number of stacks.
So we have:
Number of blocks = 64
Number of stacks = x
To find out how many blocks can be put in each stack, we can set up the following equation:
64 / x = y
where y is the number of blocks in each stack.
Solving for y, we get:
y = 64 / x
So if Ken wants to put all 64 blocks into the same number of stacks, he can put:
64 blocks in 1 stack
32 blocks in 2 stacks
16 blocks in 4 stacks
8 blocks in 8 stacks
4 blocks in 16 stacks
2 blocks in 32 stacks
1 block in 64 stacks
Therefore,
Ken could put the blocks in stacks of 1, 2, 4, 8, 16, 32, or 64.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2