Answer:
An example of the quadratic function that has zeros at x = 2 and x = 4, and that takes the value 6 when x = 3 is f(x) = -6·x² + 36·x 48
Step-by-step explanation:
The general form of a quadratic function is f(x) = a·x² + b·x + c
Which gives;
When x = 3, f(x) = 6 which gives;
6 = a·3² + b·3 + c = a·9 + b·3 + c............(1)
The zeros of the function are x = 2 and x = 4 which gives
0 = a·2² + b·2 + c = a·4 + b·2 + c...............(2)
0 = a·4² + b·4 + c = a·16 + b·4 + c...............(3)
Subtracting equation (2) from (3) gives;
a·16 + b·4 + c - (a·4 + b·2 + c) = a·12 + b·2 = 0
b·2 = -a·12
b = -a·12/2 = -6·a
Substituting b = -6·a in equation (1) we have;
a·9 + b·3 + c = a·9 + (-6·a)·3 + c = 6
a·9 -18·a + c = 6
-9·a + c = 6
c = 6 + 9·a
Substituting b = -6·a and c = 6 + 9·a in equation (2), we get
0 = a·4 + b·2 + c = a·4 + (-6·a)·2 + 6 + 9·a = a·4 -12·a + 6 + 9·a
a + 6 = 0
a = - 6
b = -6·a = -6*(-6) = 36
c = 6 + 9·a = 6 + 9*(-6) = 6 - 54 = -48
The equation of the function is therefore, f(x) = -6·x² + 36·x 48.
Halla el perimetro del triangulo PQR
Answer:
Perimetro = 4 cm + 7 cm + 12 cm
= 23 cm
Step-by-step explanation:
Hello I need help can someone explain?
Answer:
As x increase, y decreases.
The rate of change for y as a function of x is not constant, therefore the function is non-linear.
For all values of x, the function y > 0.
The y-intercept of the graph is the function value y = 8.
When x = 1, the function value y = 5.
If x∝y and x=24 when y = 8. Find x when y = 16
3 points
Answer:
x= 48
Step-by-step explanation:
x∝ y
x= ky
24= 8k
k= 3
Now solve for x
x= ky
x= 3x 26
x= 48
I hope it helped
Shape s is below is exactly one quarter of solid sphere.The volume of the shape s is 1994πcm^2. Find the surface area of s.
Answer: 1035 cm^2
Step-by-step explanation:
Given that the shape s is exactly one quarter of solid sphere.
Where the volume of the shape s is 1994πcm^3.
The formula for volume of a sphere is
V = 4/3πr^3
The volume will be divided by 4 since the given solid is exactly quarter of solid sphere. Then equate it to the given value
1994π = 4/3πr^3 × 1/4
The π will cancel out
1994 = r^3/3
Cross multiply
5982 = r^3
r = cube root of 5982
r = 18.2 cm
The surface area of a sphere is
A = 4πr^2
Substitute r in the formula
A = 4× π × 18.2^2
A = 4141
Since the shape is exactly one quarter of solid sphere. Divide the answer by 4
A = 4141/4
A = 1035.3 cm^2
The surface area of s is therefore 1035.3 cm^2
The surface area of the shape s is approximately 329.53 cm².
Important information:
Shape s is exactly one-quarter of a solid sphere.The volume of the shape s is 1994π cm².Sphere:Volume of a sphere is:
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
The volume of one-quarter of a solid sphere is 1994π cm².
[tex]1994\pi=\dfrac{1}{4}\times \dfrac{4}{3}\pi r^3[/tex]
[tex]1994\pi=\dfrac{1}{3}\pi r^3[/tex]
[tex]\dfrac{1994\pi\times 3}{\pi}=r^3[/tex]
[tex]5982=r^3[/tex]
Taking cube root on both sides, we get
[tex]\sqrt[3]{5982}=r[/tex]
[tex]r\approx 18.153[/tex]
Surface area of a sphere is:
[tex]S=4\pi r^2[/tex]
Surface area of one quarter of solid sphere is:
[tex]S=\pi r^2[/tex]
[tex]S=\pi (18.153)^2[/tex]
[tex]S=329.5314\pi[/tex]
[tex]S\approx 329.53\pi[/tex]
Therefore, the surface area of the shape s is 329.53 cm².
Find out more about 'Sphere' here:
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Which of the following statements are true about checking accounts: (select all that apply) a:Some checking accounts require a low minimum balance to avoid maintenance fee. b:You can easily withdraw funds from a checking account. c:There are many types of checking accounts. d:: A Money Market account can be a type of a checking account. None of the checking accounts earn interest. Some checking accounts allow for join use. Even if you open a free checking account, a bank can charge penalties on the account. All checking accounts are free of restrictions and fees.
Answer:
A, B, C, D, F, G
Step-by-step explanation:
A. In order to stop overpayment when your account balance is low, some banks do require a low minimum balance so you don't use more money than you have
B. You can withdraw funds from a checking account easily by using an ATM or go into the bank.
C. There are many different kinds of checking accounts designed for specific activities.
D. One type of account is actually a Money Market account.
F. Some checking account can be joint so 2 or more people can access it (like wife and husband).
G. If you do overpay on your account, you will have to pay penalties for overspending.
E is incorrect because there are some few checking accounts that earn interest (very few).
H is incorrect because some banks require fees and restrictions.
Numa caixa ha 8 bolas verdes ,5 bolas vermelhas e 2 bolas azuis. Tira se ao acaso uma bola da caixa. Calcula a probabilidade da bola saida ser: verde ; vermelho; azul : verde ou azul; nao verde
Responda:
P (verde) = 8/15
P (vermelho) = 1/3
P (azul)). 2/15
P (verde ou azul) = 2/3
P (não verde) = 7/15
Explicação passo a passo:
Dado o seguinte:
Número de bolas verdes = 8
Número de bolas vermelhas = 5
Número de bolas azuis = 2
N (verde) = 8
N (vermelho) = 5
N (azul) = 2
Portanto, número total de bolas;
N (total) = 8 + 5 + 2 = 15
Probabilidade = número de resultados requeridos / Total de resultados possíveis
1.) Probabilidade de escolher uma bola verde:
P (verde) = número de bolas verdes / número total de bolas
P (verde) = 8/15
2.) Probabilidade de pegar uma bola vermelha: P (vermelho) = número de bolas vermelhas / número total de bolas
P (vermelho) = 5/15 = 1/3
3) Probabilidade de pegar uma bola azul:
P (azul) = número de bolas azuis / número total de bolas
P (azul) = 2/15
4) probabilidade de verde ou azul:
P (verde ou azul) = P (verde) + p (azul)
P (verde ou azul) = 15/8 + 2/15 = 10/15 = 2/3
P (não verde) = 1 - P (verde)
P (não verde) = 1-8/15
P (não verde) = 7/15
Just tell me the steps, not the answer please. This diagram shows the aerial view of a playground. What is the area of the playground to the nearest square yard? Use the value = 3.14.
Area of the circle = π * (35 yd)^2
Let A be the area of the sector subtended by a central angle measuring 80º. Then
A / (π * (35 yd)^2) = 80º / 360º ==> A = 2450π/9 yd^2 ≈ 854.78 yd^2
Subtract from A the area of the triangle, whose base has length 45 yd and with height 25 yd:
A - 1/2 * (45 yd) * (25 yd) ≈ 292.28 yd^2
This is the area of the missing circular segment.
Then the area of the playground is equal to the area of the circle minus this area,
π * (35 yd)^2 - 292.28 yd^2 ≈ 3554 yd^2
Question 6(Multiple Choice Worth 3 points) (03.05 MC) Find the domain for the rational function f of x equals quantity x plus 1 end quantity divided by quantity x minus 2 end quantity. (−[infinity], 2) (2, [infinity]) (−[infinity], −2) (−2, [infinity]) (−[infinity], 1) (1, [infinity]) (−[infinity], −1) (−1, [infinity])
Answer:
(A)[tex](-\infty, 2)(2, \infty)[/tex]
(−[infinity], 2) (2, [infinity])
Step-by-step explanation:
Given the rational function, f(x) such that:
[tex]f(x)=\dfrac{x+1}{x-2}[/tex]
The domain of the function are the values of x for which f(x) is defined.
A rational function is undefined when its denominator equals zero.
Denominator of f(x)=x-2
x-2=0
x=2
Therefore, f(x) is undefined at x=2.
The domain of f(x) is all therefore all real numbers excluding 2.
This is written in set notation as:
[tex](-\infty, 2)(2, \infty)[/tex]
The correct option is A.
Answer: A (-infinity,2) (2,infinity)
Step-by-step explanation:
help plsssss! picture below!
Answer:
None
Step-by-step explanation:
If one angle is 95 degrees and other is an obtuse angle (greater than 90 degrees) Say 91 (Just 1 degree greater than 90). So, no triangle would be made because a triangle can never be made from 2 obtuse angles.
¿De cuántas formas podemos cambiar un billete de 5000 por monedas de 500 y de 200,si tenemos q utilizar al menos de cada denominación?
Answer:
Existen 6 formas posibles de cambiar un billete de 5000 por monedas de 200 y 500.
Step-by-step explanation:
En primer lugar, se determina el mínimo común múltiplo de 500 y 200. Si se multiplica a 500 por 2 y a 200 por 5, se encuentra que el mínimo común múltiplo es 1000. Entonces, se encuentra las siguientes dos conclusiones:
1) Se requiere dos monedas de 500 para obtener 1000.
2) Se requiere cinco monedas de 200 para obtener 1000.
Para determinar todas las formas posibles sin considerar el orden de las monedas, se requiere estudiar tres escenarios:
(i) Todas las monedas son de 200.
(ii) Todas las monedas son de 500.
(iii) Hay monedas de 200 y 500.
Caso 1 - Todas las monedas son de 200:
Es evidente que solo existe una forma.
Caso 2 - Todas las monedas son de 500:
Es evidente que solo existe una forma.
Caso 3 - Hay monedas de 200 y 500:
Existen las siguientes formas:
- 1000 en monedas de 200, 4000 en monedas de 500.
- 2000 en monedas de 200, 3000 en monedas de 500.
- 3000 en monedas de 200, 2000 en monedas de 500.
- 4000 en monedas de 200, 1000 en monedas de 500.
En resumen, existen 4 escenarios.
Finalmente, existen 6 formas posibles de cambiar un billete de 5000 por monedas de 200 y 500.
Describe the solution of g(x) shown in the graph. parabola opening down passing through 0 comma 2, negative 1.5 comma 4.25, and negative 3.5 comma 0 All real solutions All negative solutions All whole number solutions All solutions that lie on g(x)
Answer:
Option D.
Step-by-step explanation:
It is given that function g(x) represented by the graph. In the graph parabola opening down passing through (0,2), (-1.5,4.25), and (-3.5,0).
We need find the solutions of g(x) shown in the graph.
An ordered pair is called a solution of a function if it lie on graph of that function.
So, all the points lie on graph of function g(x) are the solutions of function g(x).
Therefore, the correct option is D.
Answer:
D
Step-by-step explanation:
I took the test
Ryan is X years old. Two times his age plus fifteen equals thirty-seven minus two. ( 2X + 15=37 - 2) Write an equation showing how old Ryan is. Solve it fi you can and show your work. 10X - 8 = 9X + 8 solve and show your work
Answer:
1) 10
2) 16
Step-by-step explanation:
1) 2x+15=37-2
2x+15=35
2x=35-15
2x=20
2 2
x=10
2)10x-8=9x+8
10x-9x=8+8
x=16
Hope this helps ❤
Diana sold $150.00 worth of products and earns a commission of 3.5%. How much did she earn in commission?
Answer:
$5.25
Step-by-step explanation:
Take $150.00 times 3.5% to get $5.25
150(.035) = 5.25
Answer:
$5.25
Step-by-step explanation:
She earned 3.5% of $150.00.
To find a percent of a number, multiply the percent by the number.
3.5% * $150.00 =
= 0.035 * $150.00
= $5.25
There is 9 questions. How many do you have to get wrong to get 80%?
Answer: 1
Step-by-step explanation:
If you get a 10/10 on something, it’s 100%. If you get a 9/10, it’s 90%. If you get a 9/9, it’s 100%. So, if you get 8/9, it’s roughly 90% but not exact. It’s actually 88.8%
Answer:
7 questions
Step-by-step explanation:
if 9 = 100%
? = 80%
if less more divides
80/100 ×9
4/5×9
36/5
7.2 which is approximately 7 questions
Question 8: Please help. Line f has a slope of −63, and line g has a slope of −84.
What can be determined about distinct lines f and g?
Answer:
The answer is given below
Step-by-step explanation:
The slope of a line is the gradient of the line and is the ratio of the vertical change (change in y) to horizontal change (change in x) between two points. The slope of a line determines its steepness and direction.
A positive slope means the line slants from the right downward while a negative slope means the line slant upwards to the left. The greater the slope of for a positive slope the greater the steepness while for a negative slope the lesser the slope the greater the steepness.
Line f has a slope of −63, and line g has a slope of −84. Since both lines have negative slope, the line slant upwards to the left. The slope of line g is smaller than that of line f, therefore line g is more steeper than line f.
Select the correct answer. The table shows the altitudes of four different cities. What is the correct way to arrange the altitudes in decreasing order? City Altitude (feet) Snowvale 13 Highbridge 58 Westsilver -51 Springmoor -35 A. 58, 13, -35, -51 B. -51, -35, 13, 58 C. -35, -51, 13, 58 D. 58, 13, -51, -35
Answer:
58>13>-35>-51, so A is correct.
Step-by-step explanation:
Altitude of Snowvale: 13
Altitude of Highbridge: 58
Altitude of Westsilver: -51
Altitude of Springmoor: -35
Decreasing order means from greatest to least.
Obviously, positive numbers are greater than negative numbers, so we put the positive numbers first. 58>13>-35>-51.
(Note that with negatives, a greater number is a number closer to zero!)
Answer:
A
Step-by-step explanation:
The altitudes have to be arranged in decreasing order.
58 > 13 > -35 > -51
Please answer this question now in two minutes
Answer: x=6, y=20
Step-by-step explanation:
Since ΔBCD and ΔTUS are congruent triangles, we can set the sides equal to each other.
y=2y-20 [subtract both sides by 2y]
-y=-20 [divide both sides by -1]
y=20
--------------------------------------------------------------------------------------
3x+32=9x-4 [add both sides by 4, and subtract both sides by 3x]
36=6x [divide both sides by 6]
x=6
The World Issues club has decided to donate 60% of all their fundraising activities this year to Stephen Lewis Foundation. This foundation was created to help ease the pain of HIV/AIDS in Africa. Lewis, a Canadian, works for the United Nations trying to determine ways to stop the spread of this deadly disease from crippling an entire continent. [ /6A] Choose a variable to represent the money earned during fundraising activities and the revenue generated for the foundation. [1A] Use these variables to create an equation that will determine the amount of money the foundation will receive. [1A] In their latest bake sale, the club raised $72. Calculate the amount the foundation will receive. [2A] At the end of the year, the World Issues Club mailed a cheque to the foundation for $850. How much money did they fundraise in total? [2A]
Answer:
y=0.6x
(a)$43.20
(b)$1416.67
Step-by-step explanation:
Let:
The amount raised during fundraising activities= mThe amount the foundation will receive =nThe club donates 60% to the foundation.
Therefore, the amount of money the foundation will receive
n=60% of m
n=0.6m
(a) If the club raised $72
m=$72
n=0.6*72
The amount of money the foundation will receive, n=$43.20
(b)If the foundation received a cheque of $850
n=$850
Therefore:
850=0.6m
m=850/0.6
m=$1416.67
The club raised $1416.67 in total for the year
Which statement best describes if the relation (c, f) is a function?
Answer:
The graph is not a function of x because the line x=0 intersects the graph at two points
Step-by-step explanation:
For any function of x, x can only map to one point. What this means is that for every x value, it only results in one y value. If you can input x into the relation's equation and get two outputs, the relation is not a function.
We can check if an x value maps to two points by using a vertical line, such as x=0, and if it crosses the relation at two points, the relation is not a function.
Since x=0 crosses the line at two points, it means that this relation is not a function.
help me please, its mathwatch
Answer:
60 cm^2Solution,
Let ,
a = 13
b = 13
c= 10
then,
s = a + b + c /2
= 13 + 13 + 10 / 2
= 36/2
= 18
Now,
Area of triangle:
[tex] \sqrt{s(s - a)(s - b)(s - c)} [/tex]
[tex] \sqrt{18(18 - 13)(18 - 13)(18 - 10)} [/tex]
[tex] \sqrt{18 \times 5 \times 5 \times 8} [/tex]
[tex] \sqrt{3600} [/tex]
[tex]60 \: {cm}^{2} [/tex]
Hope this helps ....
Good luck on your assignment...
Please answer this question now in two minutes
Answer:
Side FE < Side DE < Side DF
Step-by-step explanation:
Side FE < Side DE < Side DF are in ascending order. Side FE is the shortest because it is opposite the smallest angle (47 degrees).
An inverse variation includes the point (5,10). Which point would also belong in this inverse variation?
Answer: A. (10, 5)
Step-by-step explanation:
Inverse variation means xy = k
Given: x = 5, y = 10 --> k = 5(10) = 50
A. 10(5) = 50 This works!
B. -5(10) = -50
C. -10(5) = -50
D. 5(-10) = -50
The only option that results in k = 50 is option A.
Will get lots of points!! Thank you!! Trigonometry
Answer:
Angle B = 75 degrees
AC = 35.7
BC = 9.6
Step-by-step explanation:
Angle A = 15 degrees (given)
Angle C = 90 degrees (given)
c = 37 (given)
Angle B = 90-15 = 75 degrees
AC = AB cos(A) = 37 cos(15) = 35.7
BC = AB sin(A) = 37 sin(15) = 9.6
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. A population is the collection of some outcomes, responses, measurements, or counts that are of interest.
Answer:
False
Step-by-step explanation:
This is false because a population represents all and not some. A population is the collection of all outcomes, responses, measurements, or counts that are of interest. It is not a collection of 'some' outcomes. It is a collection of 'all' outcomes.
A population data set is a set which contains all the items or elements of a specified group or data set. It is a complete list of all the possible data values.
The sample of a population are drawn out of a population. They are A subset of a population.
James is contemplating an investment opportunity represented by the function A(t)=P(1.06)t, where P is the initial amount of the investment, and t is the time in years. If James invests $5000, what is the average rate of change in dollars per year (rounded to the nearest dollar) between years 15 and 20?
Answer:
Average rate of change in dollars per year between years 15 to 20 is:
$5300 per year.
Step-by-step explanation:
Given that:
Initial Investment, P = $5000
Formula:
[tex]A(t) = P(1.06)t[/tex]
To find: If James invests $5000,
average rate of change in dollars per year (rounded to the nearest dollar) between years 15 and 20=?
Solution:
First of all, let us find out A(15) and A(20):
Putting t = 15 first,
[tex]A(15) = 5000(1.06)\times 15 ....... (1)[/tex]
Putting t = 20,
[tex]A(20) = 5000(1.06)\times 20 ....... (2)[/tex]
Average rate of change / year is defined as:
[tex]\dfrac{\text{Change in value of A}}{\text{Number of years}}[/tex]
So, required rate of change:
[tex]\dfrac{A(20)-A(15)}{5}\\\Rightarrow \dfrac{5000 \times 1.06 \times 20-5000 \times 1.06 \times 15}{5}\\\Rightarrow \dfrac{5000 \times 1.06 \times (20-15)}{5}\\\Rightarrow \dfrac{5000 \times 1.06 \times 5}{5}\\\Rightarrow 5000 \times 1.06\\\Rightarrow \$5300\ per \ year[/tex]
So, the answer is:
Average rate of change in dollars per year between years 15 to 20 is:
$5300 per year.
A
The star makes a glide reflection according to the vector (5,0) and reflection line of y = 1. What are the coordinates of A?
Select one:
O a. (-4,0)
Ob.(2,-2)
OC. (-2, 4)
O d. (0,-2)
78÷4 68÷7 98÷6
Answer me fast
Answer:
78/4=19.5, 68/7=9.71, 98/6=16.3
Step-by-step explanation:
I have the olaf needs a total of 3 cups of sugar to make 4 cakes. write and solve an equation to find the number of cups of sugar he needs for each cake. which number line shows of cups of sugar olaf needs for each cake, Wheres 3/4 cups?
Answer: 3/4 cups per cake.
Step-by-step explanation:
He needs 3 cups for 4 cakes.
Then, if you want to know the amount that he needs for each cake, you need to see the quotient between the number of cups and the number of cakes:
S = 3cups/4 cakes = (3/4) cups per cake.
In the number line, 3/4 will be:
0--I--I--(here)--1--I--I--I--2
Which fraction is not equivalent to 7/8
Answer:
C. 15/16
Step-by-step explanation:
A. Divide by 3
B. Divide by 5
C. Can't divide by anything.
D. Divide by 4
Answer:
C
Step-by-step explanation:
21/24 = 7/8
35/40 = 7/8
7/8 ≠ 15/16
14/16 ≠ 15/16
28/32 = 7/8
To solve the equation, Lorie applies the distributive property, combines like terms, then applies the addition and subtraction properties of equality to isolate the variable term on one side of the equation and the constant term on the other side. What are the possible coefficients of x after Lorie has completed these steps? 10 (one-half x + 2) minus 5 = 3 (x minus 6) + 1
The value of x after completing the steps is -16
Given the equation solved by Lorie expressed as":
[tex]10(0.5x+2) - 5=3(x-6)+1[/tex]
Expand the bracket using the distributive law as shown:
5x + 20 - 5 = 3x - 18 + 1
Collect the like terms:
5x - 3x = -18 + 1 - 20 + 5
Simplify by adding and subtracting
2x = -32
Divide both sides by 2:
2x/2 = -32/2
x = -16
Hence the value of x after completing the steps is -16
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