Answer:
g(1)=7 1/5
Step-by-step explanation:
vertex (-5,0) , y intercept(0,5)
the quadratic equation is in the form of a parabola: y=ax²+bx+c
y=a(x-h)²+k find a and b and c
5=a(0-(-5))²+0
5=a(5)²+0
5=25a ⇒ a=5/25 ⇒ a=1/5
-b/2a=h
-b=2ah ⇒=-b=2(1/5)(-5) ⇒ -b=-2⇒ b=2
y=c=5 ( when x=0, y intercept)
y=1/5x² + 2x + 5
g(1)=1/5(1)²+2(1)+5
g(1)=1/5+2+5
g(1)=7 1/5
A quadratic function has a degree of 2, and it is represented as: [tex]y = ax^2 + bx + c[/tex]. The value of g(1) is -7.2
Given that:
[tex](h,k) = (-5,0)[/tex] --- the vertex
[tex](x,y) = (0,-5)[/tex] --- the y-intercept
The quadratic function in vertex form is:
[tex]y = a(x - h)^2 + k[/tex]
Where:
[tex](h,k) = (-5,0)[/tex] --- the vertex
So, we have:
[tex]y = a(x - -5)^2 + 0[/tex]
[tex]y = a(x +5)^2[/tex]
Substitute [tex](x,y) = (0,-5)[/tex] to calculate the value of a
[tex]-5 = a(0 +5)^2[/tex]
[tex]-5 = a(5)^2[/tex]
[tex]-5 = a \times 25[/tex]
Divide both sides by 25
[tex]a = -\frac 15[/tex]
So, the quadratic equation is:
[tex]y = a(x +5)^2[/tex]
[tex]y = -\frac 15(x +5)^2[/tex]
Rewrite as a function
[tex]g(x) = -\frac 15(x +5)^2\\[/tex]
To calculate g(1), we simply substitute 1 for x
[tex]g(1) = -\frac 15(1 +5)^2[/tex]
[tex]g(1) = -\frac 15(6)^2[/tex]
[tex]g(1) = -\frac 15 \times 36[/tex]
[tex]g(1) = -7.2[/tex]
Hence:
The value of g(1) is -7.2
Read more about quadratic functions at:
https://brainly.com/question/4119784
A graduated cylinder is filled to an initial volume of 20ml. A ball is dropped into the graduated cylinder. The final volume of the graduated cylinder is 29 ml. If the has a mass of 27 g. What is the density of the ball?
Hey there! I'm happy to help!
A graduated cylinder is basically a cylinder with little measurements on it.
If we drop the ball into the cylinder and the final volume in 29 instead of 20, this means that the ball has a volume of 9 mL as it took up 9mL of the water, pushing it up 9 mL.
Density is mass divided by volume. The ball has a mass of 27 g and a volume of 9mL. So, the density is 3 g/mL.
Have a wonderful day! :D
Describing How to Format Tables Using Table and Border Styles
Which tasks did Tristan do to format his table? Check
all that apply
Page 1
Page 2
Tristan's modified table is shown below.
O He clicked the Design tab.
Use
O He selected the whole table.
Percentage
17.5
9.5
O He changed the Table Style.
He used the No Border option.
He used the same Border Style.
He clicked the Banded Rows option.
9.2
9.1
Space cooling
Water heating
Lighting
Space heating
Refrigerators and freezers
Television and related
equipment
All other uses
8.8
5.9
40.0
He then formats his table using Table and
Answer:
He clicked the design tab
He selected the whole table
He changed the table style
Step-by-step explanation:
Just did the assignment :)
Therefore, the answer is as follows:
He clicked the design tab.He selected the whole table.He changed the table style.Know more about Tables and borders here:
https://brainly.com/question/14078371
#SPJ2
solve the following in simultaneous equations with the help of steps. x/7 + y/3 = 5,x/2 - y/9 = 6
Answer:
(14, 9 )
Step-by-step explanation:
Given
[tex]\frac{x}{7}[/tex] + [tex]\frac{y}{3}[/tex] = 5 ( multiply through by 21 to clear the fractions )
3x + 7y = 105 → (1)
[tex]\frac{x}{2}[/tex] - [tex]\frac{y}{9}[/tex] = 6 ( multiply through by 18 to clear the fractions )
9x - 2y = 108 → (2)
Multiplying (1) by - 3 and adding to (2) eliminates the term in x
- 9x - 21y = - 315 → (3)
Add (2) and (3) term by term to eliminate x
- 23y = - 207 ( divide both sides by - 23 )
y = 9
Substitute y = 9 into either of the 2 equations and evaluate for x
Substituting into (1)
3x + 7(9) = 105
3x + 63 = 105 ( subtract 63 from both sides )
3x = 42 ( divide both sides by 3 )
x = 14
Solution is (14, 9 )
3) Choose the prime factorization of 15.
O 11,4
O 5,5,5
O 3,5
O 2, 2, 11
05.10
Hey there! I'm happy to help!
A prime number is a number whose only factors are one and itself. 5 is a prime number because the only whole numbers you can multiply to get 5 are 1 and 5.
Prime factorization is finding the prime numbers that multiply to make that number.
To do this, you see what numbers it divides by. 15 is divisible by 1, giving us 15. It is not divisible by 2, but it is divisible by 3, which gives us 5.
Now, we see if 3 and 5 can be factorized even more, but they cannot as they are both prime numbers. Therefore, the prime factorization of 15 is 3,5.
Have a wonderful day! :D
what is the equation of the line perpendicular to the line y=3x+2 and passing through the point (3, -4)
A: y=3x-4
B: y=3x-2
C: y=-(1/3)x-5
D: y=-(1/3)x-3
HELP
Answer:
D: y= -(1/3)x -3Step-by-step explanation:
[tex](3, -4)=(x,y)\\y=3x+2\\\\m_1 =3\\In\: perpendicular\: line ;\\\\m_2 = \frac{-1}{m_1} \\m_2 = \frac{-1}{3} \\m_2 = -1/3\\\\Substitute \:new\:values\:into\: ;y=mx+b\\\\-4 = -\frac{1}{3} (3) + b\\-4 = -1 +b\\-4+1 =b\\-3 =b\\Substitute \:new\:values\:into\: ;y=mx+b\\y =-\frac{1}{3}x -3[/tex]
what are dense rational numbers
Answer:
The rational numbers are a dense subset of the real numbers because every real number either is a rational number or has a rational number arbitrarily close to it.
Answer:
Informally, for every point in X, the point is either in A or arbitrarily "close" to a member of A — for instance, the rational numbers are a dense subset of the real numbers because every real number either is a rational number or has a rational number arbitrarily close to it (see Diophantine approximation).
What is the range of the function represented by the graph?
Answer:
B) {1,2,3,4}
Step-by-step explanation:
Since they are separate points and not on a function, you take the y value of each
Se quieren repartir 21 chocolates entre 4 chicos en partes iguales y sin que sobre nada, cuantos chocolates recibira cada uno?
Answer: Cada chico recibira 5.25
A circular region has population of about 15,500 people and a population density of about 775 people per square kilometer find the radius of the region
Answer:
Radius of the region = 2.5 km (Approx)
Step-by-step explanation:
Given:
Total population = 15,500
Density = 775 people per square kilo meter
Find:
Radius of the region
Computation:
Total ares = 15,500 / 775
Total ares = 20 km
Total ares = πr²
20 = (22/7)r²
r² = 6.363636
r = 2.52
Radius of the region = 2.5 km (Approx)
There are 2 pizzas for 8 guests. How much of a pizza will each guests receive?
Answer:
1/4
Step-by-step explanation:
2 divided by 8 is .25 which is equal to 1/4
3(c-1)+2(3c+1)=-(3c+1)
Answer:
c=0
Step-by-step explanation:
3(c-1)+2(3c+1)=-(3c+1)
Distribute
3c -3 +6c +2 = -3c -1
Combine like terms
9c -1 = -3c -1
Add 1 to each side
9c = -3c
Add 3c to each side
12c = 0
Divide by 12
c = 0
Answer:
Step-by-step explanation:
3c-3+6c+2= -3c-1 ( 3c+6c =9c) and (-3+2 = -1) so
9c -1 = -3c-1 = so add 3c to both sides to get rid of the 3c on the right side
9c-1 +3c = -3c +3c -1 =
12c-1 = -1 add +1 to both sides
12c-1 +1 = -1 +1
12c=0
c = 0/12
so c= 0
can someone help me out please and explain?
====================================================
Explanation:
Notice how the point to the very far right is an outlier. See the diagram below. The line of best fit in red goes through (or close to) the cluster of points to the left of this outlier location. It's not the best fit ever, but it's close enough. The drawing I did is my best guess. Without knowing the actual numbers, it's impossible to get the actual regression line.
The location of this outlier is (x,y) = (7,4). This means x = 7 and y = 4 pair up together. Since x is the width and x = 7, this means a width of 7 is an outlier.
Write and solve an equation to determine how many degrees the temperature T fell. The temperature at 5 P.M. Is 20∘F. The temperature at 10 P.M. Is −5∘F.
Temperature fell 25° [tex]\\[/tex]
5 PM => 20
10 PM => -5
Find the difference between both temperatures at 5 PM and 10 PM
T = 20 - ( -5) = 20 + 5 = 25
The reason we subtracted 10 PM from 5 PM (20 - ( -5)) and not the other way around is because 5 PM obviously comes before 10 PM.
Si el divisor de una división es 67, el cociente es 495 y el residuo es 31, ¿cuál es el valor del dividendo? A. 33.196 B. 33.264 C. 34.412 D. 34.528
Answer:
Divisor = 67, Cociente = 495
Resto = 31
Dividendo = Cociente × Divisor + Resto
Dividendo = 495 × 67+ 31
= 33165 +31
= 33,196
Step-by-step explanation:
What is the quotient and remainder of 21÷6
Answer:
3 remainder 3
Step-by-step explanation:
Integrated science, kinda need help. Take your time!
Answer:
Your friends data
Step-by-step explanation:
The rule of statistics is: the more exact the data, the better.
Here it seems that you got less precise data, as you can see. This also causes the possibility of mistakes.
This is because when you have data that is more exact, you get a better estimation for mean, median, etc. This can help make patterns in your data.
This means that your friend had better data than you.
Hope this helped!
Explain what the y-intercept of a line is
Answer:
The Y intercept happens when x = 0
Step-by-step explanation:
When x = 0, it lands on the y coordinate, creating the Y intercept
Caroline is going to an amusement park. The price of admission into the park is $10, and once she is inside the park, she will have to pay $2 for every ride she rides on. How much money would Caroline have to pay in total if she goes on 8 rides? How much would she have to pay if she goes on rr rides?
Answer:
Step-by-step explanation:
The base price is 10 dollars.
(10)
For every ride she goes on, Caroline must pay 2 dollars.
(2r)
So, add them together.
10 + 2r
For 8 rides, replace r for 8.
10 + 2 x 8
10 + 16
$26
Hope this helped, please mark Brainliest so that everyone can see
Estimate the product of 53 x 73.
Answer:
3500
Step-by-step explanation:
53 is closer to 50 and 73 is closer to 70, so 50*70 is 3500, which is the closer bet.
4 intersecting lines are shown. Line m contains points Y, K, and B. Another line contains points C, Y, and W. Another line contains points B, A, and C. The fourth line contains points J, A, K, and W. Points P and X are not on the lines. Points W, K, and are collinear. Line CA and line YK intersect at . Point is not contained on line m.
Answer:
Points W, K, and
✔ J
are collinear.
Line CA and line YK intersect at
✔ point B
.
Point
✔ W
is not contained on line m.
Step-by-step explanation:
Answer:
Ray C E is contained on line m.
Ray AD is the same as ray AC.
∠ECB is created from Ray C E and Ray C B.
Step-by-step explanation:
i took the test
Explain the general steps to adding any two polynomials.
Answer:
Below
Step-by-step explanation:
● Make sure you write the polynomials correctly. Pay attention to the + and - signs.
● Combine like terms: variables with variables and constants with constants
● Combine the variables with the same power. For example 2x^2 with 5x^2
● write the terms left after combining
Solve.
5
4
The discount at WalMart is 20%. The bill for
If the TV was originally $800 how before tax
much did I actually pay?
9.5% wha
Answer:
$700.8
Step-by-step explanation:
discount = 0.20
You actually pay full price (100% or 1) - discount (20% or 0.20), so 1 - 0.20 = 0.80
If the TV was originally $800, then you pay 0.80 (80%) of it, or
(800)(0.80) = $640.00 dollars.
Tax, 9.5% or 0.095, of $640 is added to the $640, so
Tax = 0.095 + 640 = $60.8
$60.8 + $640 = $700.8
(17+3)/10x(3-1) please help
Answer:
I think this is the right answer: 1/x
Step-by-step explanation:
Solve the equation t - 8 = -3.
Answer: [tex]t=5[/tex]
Add 8 to both sides
[tex]t-8+8=-3+8\\t=5[/tex]
Answer:
The correct answer is t = 5.
Step-by-step explanation:
To solve this question, we must first recognize that our goal is to get the variable t by itself. To do this, we should add 8 to both sides of the equation to get rid of the -8 on the left side of the equation. This is modeled below:
t - 8 = - 3
t - 8 + 8 = -3 + 8
t = 5
Therefore, the correct answer is t = 5.
If we want to check our answer, we can plug in 5 for t in the original equation. If we do this, we get: 5 - 8 = -3, which is a true statement, so we know that we did the problem correctly.
Hope this helps!
5(x^3)^2(-2x^4)^-3
Simplify and write with positive exponents
P.s that isn’t minus 3, it is exponent -3
Answer:
20480x^18
Step-by-step explanation:
first of all, solve 5(x^3)^2
(x^3)^2 means 3x2=6, so x^6. 5 times x^6 = 5x^6
(16x^4)^-3 = 1/4096x^-12
when theres a negative in exponent, make it 1/y.
when negative exponent appears in 1/y just flip it again to make it y. So...
5x^6 ( 4096x^12) = 20480x^18
hope this helps.
Sarah is expanding her landscaping business. She currently has three regions in which she provides landscaping services, and intends to increase that by two regions every month. Each region begins with eight clients, and she intends to increase the number of clients by three every month. The estimate for the total number of clients is given by the expression below, where x is the number of months after Sarah begins the expansion.
Complete question is;
Sarah is expanding her landscaping business. She currently has three regions in which she provides landscaping services, and intends to increase that by two regions every month. Each region begins with eight clients, and she intends to increase the number of clients by three every month.
The estimate for the total number of clients is given by the expression below, where x is the number of months after Sarah begins the expansion.
6x² + 25x + 24
Use the information given to determine how best to complete the following sentences.
The constant of the expression represents the:
A.) increase in number of regions each month
B.) number of clients before the expansion
C.) maximum number of clients
D.) increase in the number of clients each month
The binomial (8 + 3x) is a factor of the expression, which represents the
A.) number of clients per region
B.) total number of clients
C.) total number of regions
per .
Answer:
A) Option B - number of clients before the expansion.
B) Option A - number of clients per region
Step-by-step explanation:
A) We are told that each region begins with eight clients, therefore it is a constant. Since she tends to increase this number by additional 3 each month, it means that this constant represents the number of clients before the expansion.
B) The binomial (8 + 3x) represents the new number of clients per region since each region begins with eight clients, and that she tends to increase this number by additional 3 each month.
8b - 5r use b = 6 and r = 3
Answer:
33
Step-by-step explanation:
8b - 5r
Let b = 6 r = 3
8*6 - 5*3
48 - 15
33
Answer:
33
Step-by-step explanation:
So we have the expression:
[tex]8b-5r[/tex]
And we want to evaluate it when b is 6 and r is 3. Substitute:
[tex]=8(6)-5(3)[/tex]
Multiply:
[tex]=48-15[/tex]
Subtract:
[tex]=33[/tex]
And that's our answer :)
Make p the subject of the formula
y = 3p2 - 4
Answer:
p =√(y+4)/3
Step-by-step explanation:
y=3p^2-4
so 3p^2=y+4
then p^2=(y+4)/3
so p =√(y+4)/3
Answer:
Step-by-step explanation:
y=3p^2-4
so 3p^2=y+4
then p^2=(y+4)/3
so p =√(y+4)/3
The area of a rectangle is 70 in2 and the length of the rectangle is 3 in longer than the width
Answer:
w(w+3)= 70
hope it helps.
determine the final price of an item that costs $75 and is 10% off show working
Answer:
67.5$
Step-by-step explanation:
75$ x .10 = 7.5$
75$ - 7.5$ = 67.5$
Answer:
$67.50
Step-by-step explanation:
First, find the discount.
Multiply the discount rate by the cost.
discount rate * cost
The discount rate is 10% and the cost is $75.
$75 * 10%
Convert 10% to a decimal. Divide 10 by 100 or move the decimal place two spots to the left.
10/100 = 0.10 or 10.0 --> 1.0 --> 0.10
$75 * 0.10
$7.5
Now, find the final price.
Since it is a 10% discount, we must subtract the discount amount from the cost.
cost - discount
The cost is $75 and the discount is $7.5
$75 - $7.5
$67.50
The final price of a item that costs $75 with a 10% discount is $67.50