Answer:
y = 0.4(x - 5)(x - 12)Step-by-step explanation:
Givenx- intercepts (5, 0) and (12, 0),Point P (7, - 4).SolutionThe given translates as:
p = 5, q = 12, x = 7, y = - 4Use given x - intercepts to get the equation:
y = a(x - 5)(x - 12)Use the coordinates of P to find the value of a:
- 4 = a(7 - 5)(7 - 12)- 4 = a*2*(-5)- 4 = - 10aa = -4 / - 10a = 0.4The equation of this parabola is:
y = 0.4(x - 5)(x - 12)Answer:
[tex]\textsf{Intercept form}: \quad y=\dfrac{2}{5}(x-5)(x-12)[/tex]
[tex]\textsf{Standard form}: \quad y=\dfrac{2}{5}x^2-\dfrac{34}{5}x+24[/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 (5, 0) and (12, 0) then:
p = 5q = 12Substitute the values of p and q into the formula:
[tex]\implies y=a(x-5)(x-12)[/tex]
To find a, substitute the given point on the curve P (7, -4) into the equation:
[tex]\implies -4=a(7-5)(7-12)[/tex]
[tex]\implies -4=a(2)(-5)[/tex]
[tex]\implies -4=-10a[/tex]
[tex]\implies a=\dfrac{-4}{-10}[/tex]
[tex]\implies a=\dfrac{2}{5}[/tex]
Substitute the found value of a into the equation:
[tex]\implies y=\dfrac{2}{5}(x-5)(x-12)[/tex]
Expand to write the equation in standard form:
[tex]\implies y=\dfrac{2}{5}(x^2-17x+60)[/tex]
[tex]\implies y=\dfrac{2}{5}x^2-\dfrac{34}{5}x+24[/tex]
[tex]\sf 10+2x=4[/tex]
Answer:
10+2x=4first, by using inverse operations subtract 10 on both sides.
10-10+2x=4-104-10 is -6. whys the 6 negative? because the number takes the sign of the bigge number.
2x=-6Divide by 2 to isolate x
2x÷2=-6÷2In multiplication and division one negative sign stays and 2 negative signs cancel eachother but here theres only one negative sign so;
~~~~~~~~~~~~~~~~
X=-31. Write this math statement as an algebraic expression:
The sum of one half of an unknown value and three times itself.
Answer:
Step-by-step explanation:
n = some unknown natural number
n/2 = half of that natural number
n-1 = number right before the unknown natural number
2*(n-1) = twice the number before the natural number n
Choose the correct property of addition to match the example.
3+4=7 4+3=7
The equation 3 + 4 = 7 and 4 + 3 = 7, shows the existence of Commutative Property of Addition.
What are Properties of Addition?
The properties of addition are the rules we can follow while adding numbers. Using these properties can make the calculation more straightforward and helps to solve complex problems in Math.
Solution:
Using Commutative Property of Addition the above mentioned equation can be solved.
Commutative Property of Addition - When we add two or more numbers, their sum is the same regardless of the order of the addends. We can write this property in the form of A + B = B + A.
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Four friend go out to eat and their meal cot $86. 50. The ale tax i 6. 75% and they hould tip the waiter 20%. How much do they have to pay?Round to the nearet cent
Four friends go out to eat and their meal cost $86. 50. The sales tax 6. 75% and they should tip the waiter 20%.each person must pay $27.7 for their meal
Four friends go out to eat and $86.50 for their meals.
The sales tax is 6.75%, and the waiter is tipped 20%.
M = 86.5 * 10675 / 10000 = 92.34
92.34$, and the total amount of money that four friends will give, including waiter tip, is
T=92.35 * 120 / 100 = 110.80
and each person must give
110.8/4= $27.7
each person must pay $27.7
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Look at this graph:
10
9
8
7
5
4
3
2
1
0 1 2 3 4 5 6 7 8
What is the slope?
The slope of the line is -1
First we have to choose two points
The coordinates of the first point = (9, 1)
The coordinates of the second point = (8, 2)
The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line.
The slope of the line m= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where m is the slope of the line
[tex](x_1,y_1)[/tex] is the coordinates of the first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
The slope of the line = (2-1) / (8-9)
= 1 / -1
= -1
Hence, the slope of the line is -1
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4x+y=104, x, plus, y, equals, 10
Complete the missing value in the solution to the equation.
Answer:36,37,38,39 one of the those or between
Step-by-step explanation:
IF LINE TV IS PARALLEL TO LINE ZX AND LINE ZX IS PARALLEL TO LINE QS, THEN IS LINE TV PARALLEL TO LINE QS BY TRANSITIVE PROPERTY?
Yes line TV is also parallel to line QS according to transverse property
What is transverse property?According to the transitive property, all the quantities are equal to each other if two quantities are equal to the third quantity.
When the term equal is replace by parallel it suits the case at hand hence transitive property of parallel lines is introduced
When attempting to demonstrate that several parallel lines have congruent properties, the transitive property of parallel lines can be used to create a link between numerous equal quantities.
Therefore, it can be interpreted as: if line TV || line ZX and line ZX || line QS then line TV || line ZX
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11. Tia drives 127 miles a week. Mac drives 23 times as many miles as Tia a week. How many miles does Mac drive a week?
Answer:
He drives 2921 a week.
Step-by-step explanation:
If Tia drives 127 miles in a week, and Mac drives 23 times as many miles as Tia, then we multiply. 127x23=2921.
Hope this helped :)
Mrs. Nicholas baked two batches of cookies. The first batch consisted of 120 gingerbread cookies and the second batch consisted of 150 shortbread cookies. Mrs. Nicholas saved the same fraction of cookies from each batch. If Mrs. Nicholas saved 20 more shortbread cookies than gingerbread cookies, what fraction of the cookies did she save?
I know the answer, but I don't know how to solve.
2/3 of cookies were she saved.
What is Fraction?A fraction represents a part of a whole.
The first batch consisted of 120 gingerbread cookies
Second batch consisted of 150 shortbread cookies.
And, the same fractions of cookies from each batch were saved.
Let x parts of each of cookies were saved.
Then The number of the saved gingerbread cookies = 120 x
While, The number of the saved shortbread cookies = 150 x
150x-120x=20
30x=20
x=20/30
x=2/3
Hence 2/3 of cookies were she saved.
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Which decimal is equivalent to \
{31}{9}
9
31
start fraction, 31, divided by, 9, end fraction?
3/4x - 3 = 5/6 Rewrite the equation below so that it does not have fractions.
Do not use decimals in your answer.
Answer:
18x - 72 = 20
Step-by-step explanation:
[tex] \rm \implies \dfrac{3}{4} x - 3 = \dfrac{5}{6} \\ \\ \rm \implies \dfrac{3}{4} x - 3 \times \frac{4}{4} = \dfrac{5}{6} \\ \\ \rm \implies\dfrac{3}{4} x - \frac{12}{4} = \dfrac{5}{6} \\ \\ \rm \implies \frac{3x - 12}{4} = \frac{5}{6} \\ \\ \rm \implies \frac{3x - 12}{ \cancel{4}} \times \cancel{4} = \frac{5}{6} \times 4 \\ \\ \rm \implies 3x - 12 = \frac{20}{6} \\ \\ \rm \implies (3x - 12) \times 6 = \frac{20}{ \cancel{6}} \times \cancel{6} \\ \\ \rm \implies 18x - 72 = 20 [/tex]
what is f(-3) for the function f(x) = 2x^2 + 5? need answer ASAP please!
Answer:
F(-3)= 23
Step-by-step explanation:
F(-3)= 2(-3)^2 + 5
Offering points for who can help me with this
Answer:
204 feet^2
Step-by-step explanation:
rectangle area = 18 * 10 = 180 feet^2
triangle width = 18 - 10 = 8 feet
triangle area = 6 * 8 /2 = 24 feet^2
total area = 180 + 24 = 204 feet^2
Find the inverse of the function y=2x+8
The inverse function of the given is [tex]y^-1[/tex]= [tex]\frac{x}{2}[/tex]-4 .
What is inverse function?
The domain of the original function becomes the range of the inverse function, and the range of the given function becomes the domain of the inverse function. The inverse function is denoted by the notation f-1 in relation to the original function f. Swapping (x, y) with (y, x) with reference to the line y = x yields the graph of the inverse function. Only when f is both a one-one and an onto function does it have an inverse, indicated by the symbol f-1. Keep in mind that f-1 is NOT f's inverse. The domain value of x is given by combining the function f and the reciprocal function f-1.
Here the given function is,
=> y = 2x+8
Now interchange x and y then
=> x=2y+8
Now simplify the expression with respect to y then,
=> x-8=2y
=> y = [tex]\frac{x}{2}[/tex]-4
=>[tex]y^-1[/tex]= [tex]\frac{x}{2}[/tex]-4
Hence inverse function is [tex]y^-1[/tex]= [tex]\frac{x}{2}[/tex]-4 .
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Why is the following no solution?
|x| = -5
A basketball has a volume of about 452.1 cubic inches. Fine the radius of the basketball in inches
The radius of the basket ball having volume 452.1 cubic inches is 4.76 inches.
What is the volume?
Volume is the 3 dimentional occupied space by any object. It is measured in SI units [tex]\textnormal{m}^3[/tex] and other derived units like [tex]\textnormal{in}^3[/tex].
All properties of a spherical shape is defined by its radius. The shape of a basketball is spherical hence, the formula of the volume is given by the followin expression:
[tex]V=\frac{4}{3}\pi r^3[/tex]
Here, V is the volume of the basket ball and r is the radius of the basket ball.
Rearrange the above equation for [tex]r[/tex].
[tex]3V=4\pi r^3\\\frac{3V}{4\pi}= r^3[/tex]
[tex]r=[\frac{3V}{4\pi}]^{1/3}[/tex]
Substitute values.
[tex]V=[\frac{3(452.1 \ \textnormal{cubic inches})}{4\pi}]^{1/3}\\=4.76 \ \text{inches}[/tex]
Hence, the radius of the basket ball is 4.76 inches.
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Two angles of a quadrilateral measure 260° and 15º. The other two angles are in a ratio of 7:10. What are the measures of those two angles?
The measures of those two angles are 35° and 50°.
How to calculate the angle?It's important to note that the sum of angles on a quadrilateral is 360°. In this case, two angles of a quadrilateral measure 260° and 15º.
The remaining angles will be:
= 360° - (260° + 15°)
= 85°
Since the other two angles are in a ratio of 7:10, the measure will be:
= 7 / (7 + 10) × 85°
= 7/15 × 85°
= 35°
Also, 10/17 × 85°
= 50°
The angles are 35° and 50°.
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Could I get help with this?
Answer: convergencnt
Step-by-step explanation:
What did I do wrong?
Step-by-step explanation:
I gone through your work and I don't see anything wrong.
Try reaching out to your teacher.
Answer:
You answered every question correctly. All ten of them. The program you are using has some issues. lol
Step-by-step explanation:
[tex]\sf x+ (-9) =-18[/tex]
what's the value x ?
Answer:
x = -9
Step-by-step explanation:
Below:-
Answer:
x = -9
Step-by-step explanation:
Given equation,
→ x + (-9) = -18
Now the value of x will be,
→ x + (-9) = -18
→ x - 9 = -18
→ x = -18 + 9
→ [ x = -9 ]
Hence, the value of x is -9.
The area of a circle is 25pieft2. What is the circumference, in feet? Express your answer in terms of pie
The circumference of the circle in feet is 10π feet.
According to the question,
We have the following information:
Area of the circle = 25π square feet
We know that the following formula is used to find the area of circle:
π[tex]r^{2}[/tex] where r is the radius of the circle
π[tex]r^{2}[/tex] = 25π
Dividing by π on both the sides:
[tex]r^{2}[/tex] = 25
r = 5 feet ...(1)
We know that the following formula is used to find the circumference of circle:
2πr
Putting the value of r from equation 1:
2π*5
10π feet
Hence, the circumference of the circle in feet is 10π feet.
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A board 65 inches long is sawed into two pieces. One of the pieces in 7 inches shorter than twice the length of the other piece. Find the length of the two pieces.
Answer:
24 and 41 inches.
Step-by-step explanation:
Let the lengths of the two pieces be a and b.
The total length of the two-piece should be the length of the original board.
Therefore:
a + b = 65
One piece, say b, is 7 inches shorter than twice the length of the other, a.
Therefore, we can write the following equation:
b = 2a - 7
The “2a” represents the twice, and the “-7” represents the 7 shorter inches.
We now have a system of equations:
a + b = 65
b = 2a - 7
We can solve using substitution. Substitute the second equation with the first. Hence:
a + (2a - 7) = 65
Combine like terms:
3a - 7 = 65
Add 7 to both sides:
3a = 72
Divide both sides by 3:
a = 24
So, the shorter piece is 24 inches.
Then, we can use our second equation again:
b = 2a - 7
Since we now know a substitute 24 for a and evaluate. Hence:
b = 2(24) - 7
= 48 - 7
= 41
Therefore, the length of the other two pieces is 24 and 41 inches.
Simplify:
[tex]\frac{4-i\sqrt{2}}{4+i\sqrt{2}}[/tex]
(7-4i)√2/7 is the simplified form of (4-i√2)/(4+i√2)
What is complex number?a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit
The given expression is
(4-i√2)/(4+i√2)
Now we have to rationalize the above expression
((4-i√2)/(4+i√2))×((4-i√2)/(4-i√2))
(4-i√2)(4-i√2)/(4+i√2)(4-i√2)
16-4i√2-4i√2-2/16-2
16-8i√2-2/14
14-8i√2/14
2(7-4i√2)/2(7)
(7-4i)√2/7
Hence (7-4i)√2/7 is the simplified form of (4-i√2)/(4+i√2)
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Suppose we are given the following.
Line 1 passes through (-3, 8) and (0,4).
Line 2 passes through (4, 4) and (-4,-2).
Line 3 passes through (4, 1) and (8,4).
(a) Find the slope of each line.
Slope of Line 1-
Slope of Line 2-
Slope of Line 3-0
(b) For each pair of lines, determine whether they are parallel, perpendicular, or neither.
Line 1 and Line 2: OParallel
Line 1 and Line 3:
OParallel
Line 2 and Line 3:
OParallel
Operpendicular ONeither
Operpendicular
ONeither
OPerpendicular
Neither
Slope of line 1 is -4/3, slope of line 2 is 3/4, slope of line 3 is 3/4, and Line 1 and Line 2 are perpendicular, Line 1 and Line 3 are also perpendicular, Line 2 and Line 3 are parallel.
What is slope of a line?
The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate points and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates on a line in order to determine its slope.
Slope of a line can be calculated using the formula:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here, m = slope and (x1, y1), (x2, y2) are two points on the line,
Calculating the slope of line 1 whose points are (-3, 8), (0, 4)
[tex]m = \frac{4 - 8}{0 - (-3)}[/tex]
m = -4/3
Calculating the slope of line 2 whose points are (4, 4), (-4, -2)
[tex]m = \frac{-2 - 4}{ -4 - 4}[/tex]
m = 3/4
Calculating the slope of line 2 whose points are (4, 1), (8, 4)
[tex]m = \frac{4 - 1}{ 8 - 4}[/tex]
m = 3/4
Now we know that if lines are parallel that their slope is equal and when lines are perpendicular the product of their slope is -1,
Therefore, Line 1 and Line 2 are perpendicular, Line 1 and Line 3 are also perpendicular, Line 2 and Line 3 are parallel.
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it would be great if someone could help me with these please?
Answer:
Find the angle measurement like a 90 degree angle or something for both of them and then find the solution following it. If you need further help post the question with the name where these questions are posted!
PLEASE GIVE BRAINLIEST THANK YOU!!!
an experiment may have: a. only one outcome b. only two outcomes c. two or more outcomes d. several events
Using the concepts of probability, we got that an experiment may have d) several events
Event is called one or more outcomes of an experiment. Example of this is -rolling a dice, we get a possible outcomes as {1,2,3,4,5,6}.
In an experiment there can be one outcome, two outcomes, more than two outcomes or several outcomes.
An event is the collection of one or more of the outcomes of an experiment. An event that actually includes one and only one of the (final) outcomes for an experiment is called the simple event and is denoted by Ei.
Hence, an experiment may have d)several events
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Question
Forty-five people are going on a road trip. Each car seats 5 people.
How many cars are needed for 45 people?
a car dealer buys a car for $500, gives it a clean new, is sold for $100. what is the percentage of loss
Answer:
Step-by-step explanation:
1. Find decrease.
If the car dealer bought the car for 100$ and only received 100$ for selling the car, he had 400$ in disadvantage!
2. Caculate Percent Loss:
400/ 500*100=
400/5=
80
There was a 80% decrease from the starting value!
Answer: 80% decrease!
I really need help for interpreting the remainder. Here is the question.
The student in class of 24, share 48 apple slices end 36 orange slices equally among them. How many pieces of fruit did each student get.
Whoever is going to be answering this question, please give me a valid answer and show your work
Answer:
so that means they would each get 2 and a half of apple and orange slices
Step-by-step explanation:
48 ÷ 24 =2
36 ÷ 24 =1.5
=2 1.5
Find the fourth degree polynomial that contains the origin and to which the line x+2y=14 is tangent at both x=4 and x=-2.
Answer: 60,30,180, and 37
Step-by-step explanation: