Answer:
f(x) = -(x + 8)(x -14)
= -(x2 - 112 - 6x)
= -x2 + 6x + 112 --- (1)
We know the graph of an equation y = ax2 + bx + c where a ≠ 0 is a parabola. The parabola opens upwards if a > 0 and opens downwards if a < 0. The vertex of the parabola is the point where the axis and parabola intersect. Its x coordinate x = -b/2a and its y coordinate is found out by substituting x = -b/2a in the parabola equation.
The parabola given in the problem statement has a negative coefficient of x2 and hence it is a parabola which opens downwards. Also for the equation
a = -1, b = 6 and c = 112. Therefor the x-coordinate of the vertex is
x = -b/2a
= -(6)/[2(-1)]
= 3
Substituting the value of x = 3 in equation (1) we get,
Now y = -(3)2 + 6(3) + 112
= -9 + 18 + 112 = 121
So the vertex point coordinates are (3, 121) and the y value is 121.
The graph below verifies the vertex point.
vertex of the graph
What is the y-value of the vertex of the function f(x) = -(x + 8)(x - 14)?
Summary:
The y-value of the vertex of the function f(x) = -(x +
Answer:
Step-by-step explanation:
D or 121 got it right on edgenuty
Complete the table of values below so that it represents a line with a constant rate of change of `-\frac{3}{4}.`
Use the empty sketch area for any figuring you do.
Then, explain how you know your table values are correct.
To find values of the table, plug in the given corresponding values of x or y, and constant rate of change (m) = -3/4 into y = mx.
What is the Constant Rate of Change?Constant rate of change of any table or function is a comparison of how two variables are changing, which can be determined using the formula, m = change in y/change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].
Where x and y are the coordinates of a table or functions, and m is the constant rate of change, the equation that models the relationship would be, y = mx.
The image of the table is missing, however, to complete the given table, plug in any of the given values of x or y, and constant rate of change (m) = -3/4 into y = mx.
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Rachel currently has $836 in a savings account that has earned 4. 5% annual compound interest for the past year. What was Rachel’s beginning balance one year ago if she has made no other deposits during the year?
Rachel's beginning balance one year ago was $800.
What is compound interest?Compound interest is applicable when there will be a change in the principle amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.
Given that,
The current balance is $836 which is the result of compound interest of 4.5 % annually.
The original amount was a priciple amount P on which interest was applied and the final amount $836 made.
Compound interest formula;
A = P[ 1 + RT/100]^T
Where A is the final amount and T is the time period.
Here,
A = 836 , R = 4.5% and T = 1 year.
So,
836 = P[1 + 4.5/100]^1
P = 836/1.045 = $800
Hence "Rachel's beginning balance one year ago was $800".
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The ratio of rides to games at the fair is 3 to 4. If there are 27 rides at the fair, how many games are there?
Answer: 36
Step-by-step explanation: Ratio 27:36 is also 3:4
Answer:
36 games
Step-by-step explanation:
since the ratio is 3:4 we must get what the original is.
27/3=9
27+9=36
27:36
this make no sense:
find the distance between the pair of points.
(2, 0) and (-1, 1)
A. 0
B. 2
C. 1.4
D. 3.2
Answer:
D is correct.
Step-by-step explanation:
Hoped this helped!
Hoped this helped!Hoped this helped!Hoped this helped!Hoped this helped!Hoped this helped!Hoped this helped!Hoped this helped!
Answer:
3.2
Step-by-step explanation:
Distance forumla
[tex]y = \sqrt{(x1 - x2)^2 + (y1-y2)^2}[/tex]
[tex]y = \sqrt{(2 - (-1))^2 +(0-1)^2} \\ y = \sqrt{10} \\y = 3.2[/tex]
What is the missing value in the table below?
Number of Books
3. $10.00
9. $30.00
18. $60.00
$80.00
Answer:
24 books
Step-by-step explanation:
Books are valued at $10/3 books. 18 books would have a value of (18books)*($10/3books) = $60, and so on.
X books would have a value of X($10/3)=$80
X = ($80)*(3/$10)
X = 24 books
What is the lower quartile of the following data set
53,49,43,59,63,76,40,71,47,66,57,30,48,58,35
The lower quartile is 43.
Find the Area of the figure below, composed of a rectangle and two semicircles. Round to the nearest tenths place.
Melinda kept a record of her spending for the week. she spent $25 to put gas in the car, bought a new shirt for a total of $22.38, played putt-putt golf with some friends that cost $6.95 and paid $38.71 for a few groceries. what was the total of melinda’s expenses for the week? a. $68.24 b. $86.09 c. $91.94 d. $93.04 please select the best answer from the choices provided a b c d
The total of Melinda's expenses for the week is $93.04 option (c) $91.94 is correct.
What is expenses?It is defined as the money spends on the utility, the amount of money is required to buy something in other words it is the outflow of money from the solely earners income or the money incurred by any organization.
Melinda kept a record of her spending for the week as follows:
The amount she spent money to put gas in the car = $25
The amount to buy a new shirt = $22.38
The amount to play putt-putt golf with some friends = $6.95
The amount to buy groceries = $38.71
To calculate the total expenses for the week, we must add all the expenses:
= $25+$22.38+$6.95+38.71
= $93.04
Thus, the total of Melinda's expenses for the week is $93.04 option (c) $91.94 is correct.
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Find the product of (–d e)(4e d). which statements are true? check all that apply. there are 2 terms in the product. there are 3 terms in the product. there are 4 terms in the product. the product is degree 1. the product is degree 2. the product is degree 4.
The product of the given expression is -3ed + 3e^2 showing that they contain two terms and the product has a degree of 2.
How to find the product of expressions?
Equations are expressions separated by an equal sign.
Given the following expression
(–d + e)(4e + d).
We are to take the product of both expressions.
Expand to have:
(–d + e)(4e + d) = -4ed - d^2 + 4e^2 + de
(–d + e)(4e + d) = -3ed + 3e^2
Hence, there are two terms in the solution and the product is degree 2.
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Answer:
B and E
Step-by-step explanation:
I need this done quick.
A portion of the graph of f(x) = −x2 − 10x − 21 is shown. Which of the following describes all solutions for f(x)? a partial parabola opening down and passing through negative 7 comma 0 and negative 3 comma zero with endpoints at negative 8 comma negative 5 and negative 2 comma negative 5 (x, −x2 − 10x − 21), where −7 ≤ x ≤ −3 (x, y), where −7 ≤ x ≤ −3 (x, −x2 − 10x − 21), where −8 ≤ x ≤ −2 (x, y) for all real numbers
Let's solve for solutions i e zeros
-x²-10x-21=0x²+10x+21=0x²+7x+3x+21=0(x+7)(x+3)=0x=-7 OR -3Answer:
(x, −x2 − 10x − 21), where −8 ≤ x ≤ −2
Step-by-step explanation:
because x is greater then it.
What is the quotient?
5^-6/5^3
Heyo!
SaddySokka is here to help!!
Let's do this step-by-step explanation!
[tex]=\frac{5^-^6}{5^3}[/tex]
[tex]=5^-^6^-^3[/tex]
[tex]=5^-^9[/tex]
[tex]=\frac{1}{5^9}[/tex]
Answer:
A. [tex]\frac{1}{5^9}[/tex]
Hopefully, this helps you!!
Have a great day!!
SaddySokka~
Why did the 1979 iran hostage crisis happen?
yes it is uses in1979 there ie big tsunami
Answer:
the American Embassy in Tehran was overrun and its employees taken captive.
Step-by-step explanation:
Which of the following choices is the y-intercept of the equation -3x − 2y = 10?
Hey everybody how are you doing do you have any plans for Easter? What is your favorite holiday or book? What is your favorite subject in school do you like school?
Answer:
hey i am doing god how are you and i dont know what i am doing for easter. My favorite holiday is christmas and easter. My favorite subjects in school are math and reading. I love school.
Step-by-step explanation:
Help!! I need to pass this class by the end of this week!!!!
Answer:
It's not clear can you show clearly
Answer: c
Step-by-step explanation:
please help me please
Answer:
Step-by-step explanation: y axis is 6units up (y=+6)
X axis is 2units to the right. (×=+2)
Find the Area of the figure below, composed of a rectangle and a semicircle. The radius of the circle is shown. Round to the nearest tenths place.
What is the center of a circle represented by the equation (x 9)2 (y−6)2=102? (−9,6) (−6,9) (6,−9) (9,−6)
The center of the circle (x + 9)² + (y − 6)² = 10² is at (-9, 6) and the radius of the circle is 10 units.
What is a circle?It is a locus of a point drawn an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
The equation of the circle is given as
(x + 9)² + (y − 6)² = 10²
Then the center of the circle is at (-9, 6) and the radius of the circle is 10 units.
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Answer:
A. (-9, 6)
Step-by-step explanation:
i did it B)
What is Limit of (x cubed + 3 x squared + 4 x minus 12) as x approaches negative 3? –78 –24 30 54
All polynomials are continuous, so the limit can be evaluated by direct substitution:
[tex]\displaystyle \lim_{x\to-3} (x^3+3x^2+4x-12) = (-3)^3+3(-3)^2+4(-3)-12 = \boxed{-24}[/tex]
The Limit of (x cubed + 3 x squared + 4 x minus 12) as x approaches negative 3 is -24.
What are polynomials?Polynomials are those algebraic expressions that consist of variables, coefficients, and constants. The standard form of polynomials has mathematical operations such as addition, subtraction, and multiplication.
All polynomials are continuous, so the limit can be evaluated by direct substitution:
[tex]\lim_{x \to {-3}} x^3 + 3 x ^2+ 4 x - 12\\\\= (-3)^3 + 3 (-3)^2+ 4 (-3)- 12\\\\= -24[/tex]
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What is the value of x?
Enter your answer in the box.
x =
Answer:
x= 26°
Step-by-step explanation:
it's a 90 degree angle as a whole so just subtract 64° from 90° to get the other angle.
Answer:
x=26
A line is 180 degrees
the square at the bottom left means 90 degrees
90+64=154
180-154=26 degrees
ABC ~ DEF. What sequence of transformations will move ABC onto DEF?
The transformation that is implemented is clockwise rotation by 270° about the origin and dilation by a scale factor of 1/2 .
The process of transformation an existing graph or equation into a new graph is known as graph transformation . The alteration of algebraic equations is a typical form of algebraic challenge.
A transformation modifies the graph of a parent function. Dilations, reflections, and translations are the three distinct types of transformation . The y-values of a function can be changed vertically, or the x-values can be changed horizontally (affects the x-values).
In the given figure we can see that the length of the side BC of the figure is 4 units, where as the length of the corresponding side in the image is
2 units . Hence the image is dilated buy a scale factor of 1/2 .
And from the transformation figure it is clear that the image has rotated either 270° clockwise or 90 ° counterclockwise.
Hence the second option on transformation is correct.
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Answer:
D). A dilation by scale factor of 1.2, centered at the origin, followed by a 270 clockwise rotation about the origin
Step-by-step explanation:
I keep trying but it won't accept my answers for some reason I think I'm doing it wrong
Answer
In the box, put "12" shots attempted.
Step-by-step explanation:
I learned this already and I am 100%it is correct. btw i love basketball.
5. If your father earns Rs. 40,000/-, mother earns Rs. 35,000/- and your brother earns Rs. 25,000/- per month and your friend's father earns Rs. 45,000/-, mother Rs.30,000/- and brother earns Rs. 15,000/- then whose monthly income is more and by what percent.
Answer:
✏The correct option is B Rs 73,333
Per capita income is the sum of all income sources, divided by the total number of people. Here the gross income of the family is = Rs (1,80,000+ 40,000) = Rs 2,20,000, the pocket money won't be added as it is an expense for the family. Then the per capita income of the family= Gross income / 3 (as the family has three members) = Rs 73,333.
Step-by-step explanation:
Percent is a relative quantity. Earning of our family is more than our friend's family (on monthly basis), by 11.11% approximately. (compared to friend's family's monthly income)
How to find how much percent 'a' is of 'b'?Percent is a relative quantity, as it is the measure of one quantity per 100 units of other quantity.
Suppose a number is 'a'Suppose another number is 'b'We want to know how much percent of 'b' is 'a'.
Then, it is calculated as:
[tex]\dfrac{a}{b} \times 100[/tex]
(in percentage)
For this case, we're specified that:
For our family:
Income of father = ₹ 40,000Income of mother = ₹ 35,000Income of brother = ₹ 25,000Total monthly income = ₹(40000 + 35000 + 25000) = ₹100,000
For friend's family:
Income of father = ₹ 45,000Income of mother = ₹ 30,000Income of brother = ₹ 15,000Total monthly income = ₹(45000 + 30000 + 15000) = ₹90,000
Thus, we see that friend's family's monthly is monthly ₹10,000 less than our family's monthly income.
We need to find how much percent this ₹10,000 is of their family because we need to find by how much percent our family's income is more than the friend's family's monthly income (so comparison is with respect to the monthly income of friend's family).
Let P be the percent the ₹10,000 is of the amount ₹90,000
Then, we get:
[tex]P = \dfrac{10000}{90000} \times 100 = \dfrac{100}{9} \approx 11.11 \%[/tex]
Thus, earning of our family is more than our friend's family (on monthly basis), by 11.11% approximately. (compared to friend's family's monthly income)
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Please help me on this!!
Answer:
Pretty sure it's "only i"
Step-by-step explanation:
A constant rate of change means that something changes by the same amount during equal intervals.
$30 is the same amount whereas 10% could vary.
Hope this helps.
Please help me with this problem! Also, please stop posting scam links under my questions.
Answer:
the second option is correct, the one that you picked
Step-by-step explanation:
The diagram below is used to sort out numbers.
Type each number in the correct location on the diagram.
7 8 9 10
7, 7, 9, 27, 27, are the numbers that we can fill these boxes starting from left.
What is a prime number?A prime number is not a composite number, prime numbers are only divisible by the number itself and one.
An example of a prime number is 2 which is only divisible by 2 and 1 it is also the only even prime number.
The only prime number is 7.
The intersection of prime and odd numbers is 7.
The only odd number is 9.
The intersection of odd and cube numbers is 27.
The only cube number is 27.
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sin^2θtanθ+cos^2θcotθ+2sinθcosθ=tanθ+cotθ
[tex]\text{L.H.S}\\\\=\sin^2 \theta \tan \theta + \cos^2 \theta \cot \theta+2\sin \theta \cos \theta \\\\\\=\sin^2 \theta \cdot \dfrac{\sin \theta}{\cos \theta} + \cos^2 \theta \cdot \dfrac{\cos \theta}{\sin \theta} + 2\sin \theta \cos \theta\\\\\\=\dfrac{\sin^3 \theta}{\cos \theta}+ \dfrac{\cos^3 \theta}{\sin \theta}+ 2\sin \theta \cos \theta\\\\\\=\dfrac{\sin^4 \theta + \cos^4 \theta}{\cos \theta \cdot \sin \theta}+ 2\sin \theta \cos \theta\\\\[/tex]
[tex]=\dfrac{(\sin^2 \theta)^2 + (\cos^2 \theta)^2 }{\cos \theta \sin \theta}+ 2\sin \theta \cos \theta\\\\\\=\dfrac{(\sin^2 \theta + \cos^2 \theta)^2-2\sin^2 \theta \cos^2 \theta}{\cos \theta \sin \theta}+ 2\sin \theta \cos \theta\\\\\\=\dfrac{1-2 \sin^2 \theta \cos^2 \theta}{\cos \theta \sin \theta}+ 2\ sin \theta \cos \theta\\\\\\=\dfrac{1-2\sin^2 \theta \cos^2 \theta+2\sin^2 \theta \cos^2 \theta}{\cos \theta \sin \theta}\\\\=\dfrac 1{\cos \theta \sin \theta}\\\\[/tex]
[tex]=\dfrac{\sin^2 \theta + \cos^2 \theta}{\sin \theta \cos \theta}\\\\\\=\dfrac{\sin^2 \theta}{\cos \theta \sin \theta}+\dfrac{\cos^2 \theta}{\cos \theta \sin \theta}\\\\\\=\dfrac{\sin \theta}{\cos \theta}+\dfrac{\cos \theta}{\sin \theta}\\\\\\=\tan \theta + \cot \theta\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]
Delta Math
(Brainlist if right :)
Answer:
123°Step-by-step explanation:
It is assumed GE and DA are parallel
EFH and FCA are same side interior angles and therefore supplementary
m∠EFH + m∠FCA = 180On the other hand, ∠HBA is exterior angle of triangle CHB, so it is
m∠HBA = m∠FCA + m∠CFB143 = m∠FCA + 90m∠FCA = 147 - 90m∠FCA = 57Now, find the value of m∠EFH
m∠EFH + 57 = 180m∠EFH = 180 - 57m∠EFH = 123<C
147-90[Sum of interiors=Exterior]57°Now
<C+<EFH=180
<EFH
180-57123°Triangle LMN is similar to triangle OPQ. Find the measure of side PQ. Round your answer to the nearest tenth if necessary.
The measure of PQ if the triangle LMN is similar to triangle OPQ is 69.4
What are similar triangles?Similar triangles are triangles that have equal sides and angles. The ratio of the similar sides is a constant.
According to the triangle given:
PQ/17 = OQ/LM
PQ/17 = 49/12
12PQ = 833
PQ = 69.4
Hence the measure of PQ if the triangle LMN is similar to triangle OPQ is 69.4
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