Answer:
Below
Step-by-step explanation:
a(x-p)(x-q) p = -2 q = 5
a ( x- - 2)(x - 5) sub in the values of the point given (3,6) to calculate 'a'
6 = a (3+2)(3-5)
a = -6 /10 = - 3/5
y = -3/5 (x+2)(x-5)
Answer:
[tex]\textsf{Intercept form}: \quad y=-\dfrac{3}{5}(x+2)(x-5)[/tex]
[tex]\textsf{Standard form}: \quad y=-\dfrac{3}{5}x^2+\dfrac{9}{5}x+6[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
If the x-intercepts are (-2, 0) and (5, 0) then:
p = -2q = 5Substitute the values of p and q into the formula:
[tex]\implies y=a(x-(-2))(x-5)[/tex]
[tex]\implies y=a(x+2)(x-5)[/tex]
To find a, substitute the given point on the curve P (3, 6) into the equation:
[tex]\implies 6=a(3+2)(3-5)[/tex]
[tex]\implies 6=a(5)(-2)[/tex]
[tex]\implies 6=-10a[/tex]
[tex]\implies a=\dfrac{6}{-10}[/tex]
[tex]\implies a=-\dfrac{3}{5}[/tex]
Substitute the found value of a into the equation:
[tex]\implies y=-\dfrac{3}{5}(x+2)(x-5)[/tex]
Expand to write the equation in standard form:
[tex]\implies y=-\dfrac{3}{5}(x^2-3x-10)[/tex]
[tex]\implies y=-\dfrac{3}{5}x^2+\dfrac{9}{5}x+6[/tex]
Savio leaves his home 9.00 to drive to a work appointment. He drives a distance of 40miles.
Savio thinks he drives at an average speed of 60 miles per hour.
If Savio is correct what time will he arrive at his appointment
Answer:
9:40
Step-by-step explanation:
Distance = rate x time
Let t = time
40 = 60t Divide both sides by 60
[tex]\frac{40}{60}[/tex] = t An hour would be 60 minutes so the number of minutes out of the total would be 40.
Janet buys 4 bags of potatoes.
The first bag has 8 potatoes in it.
The second bag has 6 potatoes in it.
The third bag has 10 potatoes in it.
She has not yet counted the number of potatoes in the fourth bag.
To represent the total number of potatoes she has, Janet writes (8+6+10)
+x, where x is the number of potatoes in the fourth bag. Which expression
also represents the total number of potatoes Janet has?
2(4+3+5+x)
O 25+1+B)4x
O (8+6)(10+x)
O (8+6)+(10+x)
Answer:
(8+6)+(10+x)Step-by-step explanation:
2(4+3+5+x) Not valid since x represents the total number of potatoes in the fourth bag. The expression expands to (8+6+10 + 2x), not just x.25+1+B)4x Not valid as written, the expression has a new, undefined variable, B. Plus the 25+1 are not related to the actual inforamation. (8+6)(10+x) Not valid since there is no logic in multiplying the two expressions.(8+6)+(10+x) Valid: The expression can also be writte as 8+6+10+x, which matches the potatoe count in the four bags.b to the power of −6 times b to the power of 11
Answer: B^5
Step-by-step explanation: truss
Translate this sentence into an equation.
Six more than the quotient of a number and 7 is equal to 9.
I need help please!!!
The slope of the line that passes through (9, 1) and (-8, 2) is -1/17
How to find the slope?If we have a linear equation or a segment that passes through two points (x₁, y₁) and (x₂, y₂), then the slope is given by the formula:
slope = (y₂ - y₁)/(x₂ - x₁)
In this case, we know that the two points are (9, 1) and (-8, 2), using the above formula we can find the slope to be:
slope = (2 - 1)/(-8 - 9)
slope = 1/-17 = -1/17
That is the slope of the line or segment that passes through the given points.
Learn more about slopes.
https://brainly.com/question/3493733
#SPJ1
Given that 25% of a certain volume is 30cm^3, calculate the total volume
Answer:
Step-by-step explanation:
[tex]x[/tex] x 25/100=30
25/100[tex]x[/tex]=30
25[tex]x[/tex]=3000
[tex]x[/tex]=300/25
[tex]x[/tex]=120
Algbra 2 help please asap
Answer:
3√10 units
Step-by-step explanation:
[tex] \sqrt{250} = \sqrt{25 \times 10} = \sqrt{25} \sqrt{10} = 5 \sqrt{10} [/tex]
[tex]3x + 2x = 5 \sqrt{10} [/tex]
[tex]5x = 5 \sqrt{10} [/tex]
[tex]x = \sqrt{10} [/tex]
So the length of the longer piece is 3√10 units.
Francesca has 2615 comic books.
She wants to put them into groups of 8.
How many comic books would be left over
after putting them into groups?
Answer: 7 comic books would be left after putting them into groups of 8.
Step-by-step explanation: There will be 326 groups of comic books. 326 x 8 = 2,608 which means that there will be 7 comic books left after putting them all into groups of 8.
Figure CC is the result of a transformation on Figure BB. Which transformation would accomplish this??????
Can someone please help me
(1). A translation 1 unit down
(2). A reflection over the y -axis
(3) A reflection over the x -axis
(4) A translation 1 unit up
Translation 1 unit up is the transformation which accomplish the graph.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given,
Figure C is the result of a transformation on Figure B
We need to find which transformation is used for this.
Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.
and A vertical reflection reflects a graph vertically across the x-axis, while a horizontal reflection reflects a graph horizontally across the y-axis
Horizontally translating a graph is equivalent to shifting the base graph left or right in the direction of the x-axis.
The graph is just shifted slightly to right.
Figure B undergoes a translation of translation 1 unit up.
Hence translation 1 unit up is the transformation which accomplish the graph.
To learn more on Graphs click:
https://brainly.com/question/17267403
#SPJ1
How do I solve this Quadratic expression by factoring?
Answer:
Step-by-step explanation:
Step-by-step explanation:
the highest exponent is 2, so, we expect to get 2 factors in x (as the multiplication of x×x = x²).
3 is a prime number, and the only factors to get 3 are 3 and 1
3 = 3×1
so, we expect to get factors that look like
(3x + a)(x + b)
when we do the multiplication, we get
3x² + 3bx + ax + ab = 3x² +(3b + a)x + ab
now we compare this to our original expression
3x² +(3b + a)x + ab = 3x² - 13x + 12
3b + a = -13
ab = 12
so, we know a and b must both be negative
(-×- = +, - - - = -).
the negative factors of 12 are
-12 × -1
-6 × -2
-4 × -3
which one of these pairs can make
3b + a = -13
be true ?
3×-12 + -1 = -37 no
3×-1 + -12 = -15 no
3×-6 + -2 = -20 no
3×-2 + -6 = -12 no
3×-4 + -3 = -15 no
3×-3 + -4 = -13 yes
so, our factors are
(3x - 4)(x - 3)
(a)Bill invests Rs 75000 for 10 years at a rate of 6 % per year simple interst. Calulate the total interest he will receive.
(b) Harry invests Rs 24 000 at a rate of 7 % per annum at simple interest.After how many months will Ravi gain Rs 1260 as interst?
Answer:
Step-by-step explanation:
A = 75000(1 + (0.06 × 10)) = 120000
A = $120,000.00
B = 24000(1 + (0.07 × 0.75)) = 25260
B = $25,260.00
B=9 months
I need help please!!
Answer:
-5/3 or -1.67
Step-by-step explanation:
Answer:
-5/3
Step-by-step explanation:
Oh it's you again, I am just gonna copy paste my format from your previous question.
Use the slope formula: s=(y2-y1)/(x2-x1)
It doesn't matter the order.
Let's say -6 is x2 and 8 is y2; 3 is x1 and -7 is y1
Plug in the equation: s=[(8)-(-7)]/[(-6)-(3)]
Simplify and solve: s=[8+7]/[-9]
s = -15/9
s = -5/3
Use front-end estimation to place the decimal point in each answer. a) 32.47 6.75 2 5 7 2 b) 118.234 19.287 1 3 7 5 2 1 c) 17.9 0.8 1 7 1
Using front end estimation, the solutions to the given problems are;
1) 25.72
2) 137.521
3) 17.1
How to use front end estimation?
Front-end estimation is defined as a particular way of rounding numbers to estimate sums and differences.
The procedure for using front- end estimation, is to add or subtract only the numbers in the greatest place value. Thereafter, we add the decimals rounded to the nearest tenth.
1) 32.47 - 6.75
First of all, let's deal with the whole numbers part;
32 - 6 = 26
Next is to deal with the decimal part to get;
0.47 is approximately 0.5 while 0.75 is approximately 0.8. Thus;
0.5 - 0.8 = - 0.3
Thus, we have;
26 + (-0.3) = 25.70
Therefore, our given solution can be written as; 25.72
2) 118.234 + 19.287
First of all, let's deal with the whole numbers part;
118 + 19 = 137
Next is to deal with the decimal part to get;
0.234 is approximately 0.2 while 0.287 is approximately 0.3. Thus;
0.2 + 0.3 =0.5
Thus, we have;
137 + 0.5 = 137.5
Therefore, our given solution can be written as; 137.521
C) 17.9 - 0.8
First of all, let's deal with the whole numbers part;
17 - 0 = 17
Next is to deal with the decimal part to get;
0.9 - 0.8 = 0.1
Thus, we have;
17 + 0.1 = 17.1
Therefore, our given solution can be written as; 17.1
Read more about front end estimation at; https://brainly.com/question/14261571
#SPJ1
How is p-value calculated with example?
To calculate the p-value, we have to follow the following steps:
First, identify the correct test statistic.Then, calculate the test statistic using the relevant properties of the sample.Specify the characteristics of the test statistic’s sampling distribution.Then, place test statistics in the sampling distribution to find the p-value.To calculate the p-value, we need
p = sample proportion
p' = assumed population proportion in the null hypothesis
n = sample size
Example
Given, n =40, σ = 32.17 and X = 105.37. calculate p-value.
σₓ = σ/ √n
σₓ = 32.17 / √40
= 5.0865
Now, by applying the test static formula, we get
t = (105.37 – 120) / 5.0865
t = -2.8762
Using the table, we find the value of P(t>-2.8762)
From the table, we get
P (t<-2.8762) = P(t>2.8762) = 0.003
If P(t>-2.8762) = 1- 0.003 = 0.997
P- value = 0.997 > 0.05
To learn more about the p-value from the given link
https://brainly.com/question/13786078
#SPJ4
Choose the multiplication equation that is represented by the model (will give brainlist thingy)
0.9 x 0.8 = 0.72
0.9 x 0.2 = 0.18
0.1 x 0.8 = 0.08
0.9 x 0.6 = 0.54
Answer:
0.9*0.8=0.72
Step-by-step explanation:
there are 9 squares across the top and 8 square downward so the only equation similar to this is the first equation.
Answer: 0.9 x 0.8 = 0.72
Step-by-step explanation:
dark gray is 9 x 8, divide both numbers by 10, you get 0.9 x 0.8 = 0.72
The equation y = mx + b is used to express the equation of a line. Which solution is a correct way to solve this equation for x in terms of y?
By first subtraction b and then dividing by m, the solution of the linear equation for x is:
(y - b)/m = x
How to solve the linear equation for x?Here we have a linear equation that defines the variable y in terms of the variable x:
y = m*x + b
Where m and b are real numbers.
Now we want to find x in terms of the variable y, this means that we need to isolate the variable x.
if first we subtract b in both sides, we get:
y - b = m*x + b - b
y - b = m*x
If now we divide both sides by m, we get:
(y - b)/m = m*x/m
(y - b)/m = x
This is the linear equation solved for x.
Learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
Answer:If you’re using imagine math it will be the the third one
Step-by-step explanation:
2[3x] = [1/2(4x+20)]2
Answer:x=10
Step-by-step explanation:
Answer:
x=10
Step-by-step explanation:
Multiply the numbers
2⋅3x=[12(4x+20)]⋅22⋅3=[12(4+20)]⋅2
6x=[12(4x+20)]⋅26=[12(4+20)]⋅2
Combine multiplied terms into a single fraction
6x=[12(4x+20)]⋅26=[12(4+20)]⋅2
6x=[1(4x+20)2]⋅26=⎣⎡1(4+20)2⎦⎤⋅2
Multiply by 1
6x=[1(4x+20)2]⋅26=⎣⎡1(4+20)2⎦⎤⋅2
6x=[4x+20/2]⋅26=[4+20/2]⋅2
Re-order terms so constants are on the left
6x=4x+20/2⋅26=4+20/2⋅2
6x=2⋅4x+20/2
Cancel multiplied terms that are in the denominator
6x=2⋅4x+20/2
6x=4x+20
Subtract 4x from both sides
6x=4x+20
6−4=4+20−4
Simplify
6x-4x=4x+20-4x
2x=4x+20-4x
Combine like terms
2x=20
Divide both sides by the same factor
2x=20
2x/2=20/2
cancel 2 on both sides
20 divided by 2 is 10
so therefore,
x=10
(-5,6)
(-3,3)
(-1,0)
(1,-3)
(3,-6)
Find the range of the relation.
(-6, -3, 0, 3, 6)
(-5, -3, -1, 1, 3)
(-6, -5, -3, -1, 0, 3, 6}
(-6,6)
The range of the given relation is (-6, -3, 0, 3, 6).
Range:
Basically the set contains 2 elements in it, in which set contains all the second elements, on the other hand, is known as the range of the relation.
Given,
Here we have the relation (-5,6), (-3,3), (-1,0), (1,-3) and (3,-6)
Here we need to find the range of the relation.
According to the definition of the relation,
Range refers the y values of the coordinates,
So, based on this the value of the given coordinates are extracted as,
(-5, 6) => 6
(-3, 3) => 3
(-1, 0) => 0
(1, -3) => -3
(3, -6) => -6
Now we have arrange the range values from the smallest to largest,
Therefore, the range of the relation is (-6, -3, 0, 3, 6).
To know more about Range here.
https://brainly.com/question/28696000
#SPJ1
pleaseeeee help me asap
Answer: x=30 degrees
Step-by-step explanation:
A triangle has 180 degrees, so:
90+x+20+x+10=180
90+2x+30=180
2x+30=90
2x=60
x=30
Justin wants to find the volume of a rectangular box. He starts by placing a layer of cubes in the bottom of the box (as shown).
Each cube has a length, width, and height of `1/2` inches. He continues placing cubes in the box until it is full. What is the volume of the box?
The volume of the given rectangular box is given by 225 cubic inches.
We know that the volume of the rectangular box with length L and width W and height H is given by,
V = LWH
So given the length of rectangular box is = 12 1/2 inches = 25/2 inches
The width of rectangular box is = 4 1/2 inches = 9/2 inches
The height of box is = 4 inches
So the volume of the rectangular box = (25/2)*(9/2)*4 = 25*9 = 225 cubic inches.
To know more about Volume refer to:
https://brainly.com/question/463363
#SPJ1
An elevator can carry 24 adults or 40 children at one time during the course of a day the elevator Carrie’s a full passenger load 74 times if all the passengers were children how many people would the elevator Carry than if all the passengers were adults
Using simple mathematical operations, we know that the lift will carry 1,120 more children than adults in a day.
What do we mean by mathematical operations?A mathematical function known as an operation converts zero or more input values into a precisely defined output value.
The quantity of operands affects the operation's arity.
parentheses, exponents, multiplication, division, and PEMDAS.
So, to calculate how many more children the lift carries in a day:
The number of adults the lift can carry is 24.
The number of children the lift can carry is 40.
The lift carries people at full capacity 70 times.
Now, calculate as follows:
24 × 70 = 1,680
40 × 70 = 2,800
Difference:
2,800 - 1,680 = 1,120
Therefore, using simple mathematical operations, we know that the lift will carry 1,120 more children than adults in a day.
Know more about mathematical operations here:
https://brainly.com/question/28937023
#SPJ1
Tasha plants seeds in clay pots. She has 40 seeds to plant. She plants 6 seeds in each pot. How many seeds does Tasha have left over?
she would have four seeds left because 6 seeds times six pots would equal 36 seeds so subtract 36 from forty to get four
Step-by-step explanation:
Answer:4
Step-by-step explanation:6x6=36+4=40
Do this thing please I will be very thankful
An ostrich egg has a width of 12.9 cm to the nearest tenth of a centimeter. Find the minimum and maximum possible measurements.
The minimum measurement is 12.85 and the maximum measurement is 12.94 that would be equal to 12.9.
What is rounding of decimal numbers?
Look at the next digit in the correct position to determine how to round a number; if it is less than 5, round down, and if it is 5 or more, round up. The term "rounding decimals" describes the accurate rounding of decimal figures. To the nearest whole, tenth, or hundredth, we can round decimals.
Given, An ostrich egg has a width of 12.9 cm to the nearest tenth of a centimeter.
We have to find the minimum and maximum possible measurements.
If you're rounding to the nearest tenth of a centimeter, 12.85 centimeters is the smallest measurement that would equal 12.9 centimeters.
And 12.94 centimeters is the maximum measurement that would be equal to 12.9.
Therefore, the minimum measurement is 12.85 and the maximum measurement is 12.94.
To know more about the rounding of decimal numbers, click on the link
https://brainly.com/question/28393353
#SPJ1
Vani went to the store to buy some chicken. The price per pound of the
chicken is $3.50 per pound and she has a coupon for $3.25 off the final
amount. With the coupon, how much would Vani have to pay to buy 3 pounds
of chicken? Also, write an expression for the cost to buy p pounds of chicken,
assuming at least one pound is purchased.
PLEASE PROVIDE THE AMOUNT FOR P AND FOR 3 POUNDS
The cost is the cost per pound times the number of pounds minus the coupon.
If [tex]p[/tex] pounds are purchased, she will pay [tex]3.50p-3.25[/tex].
If 3 pounds are purchased, she will pay 3.50(3)-3.25=7.25.
Guided Problem Solving You have a class photo that is 10 in. long and 8 in. wide. If you want to enlarge your photo to be 15 in. long, how wide will the photo be?
Understand the Problem You know the dimensions of the original photo and the length of the enlarged photo. Find the width of the enlarged photo.
Make a Plan Draw the figures and label their sides.
The width of the enlarged photo is 12 inches
The length of the original photo = 10 inches
The width of the original photo = 8 inches
The length of the enlarged photo = 15 inches
The width of the enlarged photo = x
Then the proportion of the length and width of the original and enlarged photo will be
10 / 8 = 15 / x
Cross multiply the terms
10x = 15 × 8
Multiply the terms in the equation
10x = 120
Divide both side of the equation by 10
10x / 10 = 120 / 10
x = 120 / 10
Divide the terms
x = 12 inches
Hence, the width of the enlarged photo is 12 inches
Learn more about proportion here
brainly.com/question/24374571
#SPJ1
A company claims that the mean weight per apple they ship is 120 grams with a standard deviation of 12 grams. Data generated from a sample of 49 apples randomly selected from a shipment indicated a mean weight of 122. 5 grams per apple. Calculate and interpret a 95% confidence interval for the mean weight per apple.
The average apple weight's 95% confidence interval is (119.14, 125.86).
According to one manufacturer, an apple weighs 120 grams on average with a 12-gram standard variation. According to statistics generated from a sample of 49 apples randomly selected from a shipment, the average weight per apple was 122. 5 grams.
Let,
n = 49
x = 122.5
σ = 12
To figure up and analyze a 95% confidence interval for the average apple weight;
The formula for a 95% confidence interval is
(x ± 1.96*σ√n)
(122.5 ± 1.96*12/√49)
(119.14, 125.86)
Consequently, a 95% confidence interval for the average apple weight is (119.14, 125.86).
To learn more about Confidence interval click here:
brainly.com/question/24131141
#SPJ4
PLEASE I REALLY NEED THIS ANSWER
Which equation represents the line parallel to the line whose equation is 2y=4x+14
The parallel line has an equation of y = 2x + 3
How to determine the line equation?The equation is given as
2y = 4x + 14
Make y the subject
2y = 4x + 14
Divide through by 2
y = 2x + 7
The equation of a line can be represented as
y = mx + c
Where
slope = m
By comparing the equations, we have:
m = 2
This means that the slope of 2y = 4x + 14 is 2
The slopes of parallel lines are equal
This means that the slope of the other line is 2
i.e. m = 2
Recall that:
The equation of a line can be represented as
y = mx + c
Where
slope = m
So, we have
y = 2x + c
Assume any value for c
This gives
y = 2x + 3
Hence, the equation of the parallel line is y = 2x + 3
Read more about linear equations at
brainly.com/question/4074386
#SPJ1
What’s the value of (a)?
Answer:
a=5
a=2x-5
Step-by-step explanation:
hope it helps
have a nice day!
or night