Answers
Answer:
a. -2x^2 + 3x+5=y
b.-x^2 +5x-4=y
c.-x^2 +6x-12=y
Step-by-step explanation:
a.y=-2x^2 +bx+c
the points P and Q lie on curve
[tex]\left \{ {{-b+c=2} \atop {b+c=8}} \right.[/tex]
=> b=3, c=5
b. delta = b^2 +4c
x1= [tex]\frac{-b+\sqrt{b^{2}+4c } }{-2}[/tex] =4
=> [tex]b-\sqrt{4c+b^{2} }[/tex]=8
x2=[tex]\frac{-b-\sqrt{b^{2}+4c } }{-2}[/tex]=1
=>2=b+[tex]\sqrt{b^{2}+4c }[/tex]
suppose : [tex]\sqrt{b^{2}+4c }[/tex] = a
=> [tex]\left \{ {{a+b=2} \atop {-a+b=8}} \right.[/tex]
=> a=-3
b=5
a=-3 => [tex]\sqrt{b^{2}+4c }[/tex] =-3 => b^2 +4c =9 =>5^2 +4c=9 => c=-4.
c.vertex (3;-3)
[tex]\frac{-b}{-2}[/tex]=3 => b =6
[tex]\frac{-D}{4a}[/tex]=[tex]\frac{-b^{2}+4ac}{-4}[/tex] =-3 =>-b^2+4ac=12 => c=-12.
Related Questions
What’s the difference between 4, 7/9 and 2 1/2
Answers
[tex]\huge \mathbb \orange{ANSWER} [/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \mathsf \purple{4 \frac{7}{9} - 2 \frac{1}{2} }[/tex]
[tex] \blue\implies \mathsf \pink{ 2(\frac{43}{9}) - (\frac{5}{2} )9 }[/tex]
[tex] \blue \implies \mathsf \purple{ \frac{86}{18} - \frac{45}{18} }[/tex]
[tex] \blue \implies \mathsf \pink{ \frac{41}{18} = 2 \frac{5}{18} }[/tex]
give me list of letter arrangement and number arangement
Answers
Answer:
what the heck question is this
Help help help help math math
Answers
Answer:
No Solution
Step-by-step explanation:
-y = -2x + 8
y = 2x - 8
2x + 8 = 2x - 8
2x - 2x = -8 - 8
0 = -16
No Solution
You can also graph y = 2x + 8 and y = 2x - 8. The slope are the same and so they are parallel
What is the equation of a circle with center (−5, −8) and radius 2?
(x − 5)2 + (y − 8)2 = 4
(x + 5)2 + (y + 8)2 = 4
(x + 5)2 + (y + 8)2 = 2
(x − 5)2 + (y − 8)2 = 2
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}☂[/tex]
Standard equation of circle ~
[tex]\qquad \sf \dashrightarrow \:(x - h) {}^{2} + (y - k) {}^{2} = r {}^{2} [/tex]
where,
h = x - coordinate of centre k = y - coordinate of centrer = radius of the circle
Now, let's plug in the values ~
[tex]\qquad \sf \dashrightarrow \:(x - (5)) {}^{2} + (y - ( - 8)) {}^{2} = {2}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:(x + 5) {}^{2} + (y + 8) {}^{2} = {4}^{} [/tex]
Therefore, the correct choice is B
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
The equation of the circle with a center of (4,5) and a radius of 2 units is (x + 5)² +(y + 8)² = 4
How to determine the circle equation?The center of the circle is given as:
Center (a,b) = (-5, -8)
The radius is given as:
Radius, r = 2
The equation of the circle is calculated using:
(x - a)² + (y - b)² = r²
Substitute values for r and (a,b)
(x + 5)² +(y + 8)² = 2²
Evaluate the square of 2
(x + 5)² +(y + 8)² = 4
Hence, the equation of the circle is (x + 5)² +(y + 8)² = 4
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what is 4 1/8 x 1/4 equal to?
Answers
Answer:1.03125
Step-by-step explanation:
Mr. Anderson decides to visit a childhood friend. His car gives him 24.82 miles to the gallon. Mr. Anderson has 4 gallons of fuel. Which of the following is true?
A.
Mr. Anderson can travel 83.28 miles.
B.
Mr. Anderson can travel 49.64 miles.
C.
Mr. Anderson can travel 115.28 miles.
D.
Mr. Anderson can travel 99.28 miles.
Answers
Answer:
D. Mr. Anderson can travel 99.28 miles.
Step-by-step explanation:
If Mr. Anderson has 4 gallons and each gallon moves him 24.82 miles you can multiply the number of miles per gallon by the gallon resulting in an equation that looks like 4*24.82=99.28.
Find the equation of a line that contains the points (2,1) and (8,7). Write the equation in slope-intercept form.
Answers
Answer:
y = x - 1
Step-by-step explanation:
First find the slope. Subtract the y's and put that on top of a fraction. Then subtract x's and put that on the bottom. Simplify if possible.
7-1 is 6 goes on top.
8-2 is 6 goes below.
6/6 is 1 when simplified.
Slope is 1.
Slope-intercept form is y = mx + b.
m is slope, so fill that in.
y = (1)x + b
Now we need to find b.
Use either one of the given points; they will give you the same answer no matter which one you choose. Let's use (2,1) because smaller numbers.
y is 1 and x is 2.
y= (1)x + b
1 = (1)2 + b
1 = 2 + b
-1 = b
Now fill in both m and b. Leave x and y as letters (variables)
y = (1)x + -1
Final answer:
y = x - 1
What is the factorization of the trinomial below?
3x^3 + 6x^2 - 24x
A. 3x(x - 2)(x + 4)
B. 3x(x - 2)(x - 4)
C. 3(x - 2)(x + 4)
D. 3(x^2 - 2)(x + 4)
Answers
Mrs. Williams' desk is located at (-5,2). The wireless internet box is halfway between her desk and the door. If the box is located at the coordinates (8, -8), what are the coordinates of the door?
Answers
Topic : Midpoint between points
desk = (-5,2)box = (8, -8)door = (x, y)formula:
[tex]\sf \bold{(x_m, y_m) = (\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})}[/tex]
=====================================
[tex]\hookrightarrow \sf \dfrac{x+(-5)}{2} ,\dfrac{y+2}{2} = (8, -8)[/tex]
separate taking coefficients:
[tex]\rightarrow \sf \dfrac{x-5}{2} =8, \ \dfrac{y+2}{2} = -8[/tex]
[tex]\rightarrow \sf x-5 =16, \ y+2 = -16[/tex]
[tex]\rightarrow \sf x =16+5, \ y= -16-2[/tex]
[tex]\rightarrow \sf x =21, \ y= -18[/tex]
coordinates of door: (21, -18)
Let that be (x,y)
So
[tex]\\ \rm\rightarrowtail (8,-8)=(\dfrac{x-5}{2},\dfrac{y+2}{2})[/tex]
[tex]\\ \rm\rightarrowtail \cfrac{x-5}{2}=8\implies x-5=16\implies x=21[/tex]
[tex]\\ \rm\rightarrowtail \cfrac{y+2}{2}=-8\implies y+2=-16\implies y=-18[/tex]
(x,y)=(21,-18)CAN SOMEBODY HELP ME SOLVE THIS EQUATION
Answers
Step-by-step explanation:
Slope m=4
Y intercept b=(-5)
formula f(x)=4x-5
If u need how to solve do let me know
LOTS OF POINTS + BRAINLIEST
Suppose p and q are both prime numbers with p > q. Prove that p-q and p+q cannot both be positive perfect squares.
FULL PROOF REQUIRED.
Answers
Answer:
The list od prime number is a quadratic sequence, each time going up by n + 2. for example, 1, 4, 9, 16, 25. they are going up by 3, then + 2 and add 2 every step. The sequence is always going up by an odd number. a negative number take away a negative number always gives you a positive number, likewise, adding does too. Therefore, you can not get both of them to fit into the sequence of increasing odd numbers.
41. Henry stands on a platform and shoots a rocket in his 10th
grade science class. He found that the motion of the rocket can be
described by the equation y = 60 + 28x – x2, where y is the
vertical distance and x is the horizontal distance traveled. If this
trajectory equation were to be graphed, find the x-intercepts of the
equation. (Fun fact: The positive x-intercept is how far away from
the platform the rocket hits the ground!)
Answers
The x-intercepts of the quadratic equation are given by x = -2 and x = 30.
What are the x-intercepts of a quadratic equation?A quadratic equation is modeled by:
y = ax² + bx + c.
The x-intercepts are the values of x when y = 0, given by:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]
[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]
In which:
[tex]\Delta = b^2 - 4ac[/tex]
In this problem, the equation is:
y = 60 + 28x - x².
Hence the coefficients are a = -1, b = 28, c = 60.
Then:
[tex]\Delta = 28^2 - 4(-1)(60) = 1024[/tex]
[tex]x_1 = \frac{-28 + \sqrt{1028}}{-2} = -2[/tex]
[tex]x_2 = \frac{-28 - \sqrt{1028}}{-2} = 30[/tex]
The x-intercepts of the quadratic equation are given by x = -2 and x = 30.
More can be learned about quadratic equations at https://brainly.com/question/24737967
Barry has two cubes of different sizes. The first cube has a volume of 1 cubic unit. The second cube has sides one-third as long as the first cube does. What is the volume of the second cube?
Answers
Answer:
1/27 units cubed or 0.037037... units cubed
Step-by-step explanation:
Volume of a cube = s*s*s : Where s is a side length.
The volume of the first cube is 1 cubed, which means that each side length is 1. (s=1)
The volume of the second cube in relation to the first cube can be found by multiplying each side length by 1/3.
Volume of second cube= (1/3s)(1/3s)(1/3)s
Volume of second cube= (1/3)(1/3)(1/3)
Volume of second cube= 1/27
5/6 of a number is 65.
Find the number.
Answers
Answer:
78 is the number
Step-by-step explanation:
(65*6)÷5 = 78.
5/6 of a number is 65.
And the number is 78.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
A phrase: 5/6 of a number is 65.
To find the number:
Let the number be n.
Applying multiplication operation,
5/6 of n is 65.
(5/6)n = 65.
Applying cross multiplication,
n = 65 x 6/5
n = 390/5
n = 78.
Therefore, the number is 78.
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pls help me in this math problem
Answers
Answer:
cUse the following equation
Step-by-step explanation:
Because of the way these angles are positioned, they must be equal to 180 together
(2x + 5) + (0.5x + 150) = 180
2.5x + 155 = 180
- 155 - 155
2.5x = 25
2.5x/2.5 = 25/2.5
x = 10
Put x into the original equations and solve
A manager drew this box-and-whisker plot to represent the number of minutes each of the company's 360 employees took on their break.
How many employees took a break that lasted between 37 and 41 minutes?
Select from the drop-down menu to correctly complete the statement.
About (blank) employees took a break that lasted between 37 and 41 minutes.
36
90
120
180
Answers
Answer:
on k12 im pretty sure its 90
Step-by-step explanation:
there is 360 minutes and between the 37 and 41 (this took me a while ) then you should get 90!!!!! hope this helped
A spinner has 16 equal-sized sections. Twelve of the sections are orange.
a. What is the probability that the spinner will land on orange?
b. Use words to describe the probability
a.
out of 16, or
.
4
b. It is
that the spinner will land on orange.
Answers
The probability that the spinner will land on orange is the likelihhood of landing on orange
The probability that the spinner will land on orange is 0.75
How to determine the probability?From the question, we have:
Spinner section = 16
Orange section = 12
So, the probability that the spinner will land on orange is:
p = 12/16
Evaluate
p = 0.75
Hence, the probability that the spinner will land on orange is 0.75
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The Length Of A Room is two time its breadth and breadth is two time its height If The volume of room is 512m2 what is the cost of plastering its wall at rs 5.50 per m2
Answers
Answer:
Rs 2464
Step-by-step explanation:
Given:
The length of a room is 2 times its breadth and breadth is 2 times its height. The volume of the room is 512 cubic metre.To find:
The cost of plastering it's wall at Rs 5.50 per square metre.Solution : A/C to given data;
[tex]Length = 2 * Breadth\\L = 2 * B[/tex]---> (1) and [tex]Breadth = 2 * Height\\B = 2 * H[/tex]----> (2)
A/C to given data let, structure of room is cuboidal.
Now, we have to find out the height of the room, so we use formula of volume of the cuboid.
[tex]Volume of the room = L * B * H[from given data, and eq. {1} and eq. {2}][/tex]
[tex]512 = 2B * 2H * H[/tex]
[tex]512 = 2 * 2H * 2H * H[/tex]
[tex]512 = 4H * 2H^{2}[/tex]
[tex]512 = 8H^{3}[/tex]
[tex]H^{3} = \frac{512}{8}[/tex]
[tex]H^{3} = 64[/tex]
[tex]H = \sqrt[3]{64}[/tex]
[tex]H = 4 m[/tex]
[tex]Now, put\\ value\\ of \\H \\in \\eq. {2}[/tex]
[tex]B = 2 * H[/tex]
[tex]B = 2 * 4[/tex]
[tex]B = 8 m[/tex]
[tex]\\[/tex]Now, put value of B in eq. {1}
[tex]L = 2 * B[/tex]
[tex]L = 2 * 8[/tex]
[tex]L = 16 m[/tex]
Now, we have to find out area of the room, so we use formula of total surface area of cuboid.
[tex]Area of the room = 2*L*B + 2*L*H + 2*H*B[/tex]
[tex]Area of the room = 2 * 16 * 8 + 2 * 16 * 4 + 2 * 4 * 8[/tex]
[tex]Area of the room = 32 * 8 + 32 * 4 + 8 * 8[/tex]
[tex]Area of the room = 256 + 128 + 64[/tex]
[tex]Area of the room = 384 + 64[/tex]
[tex]Area of the room = 448 m^{2}[/tex]
Now, to find out room wall plastering cost
[tex]Room wall plastering cost = Area of the room * cost of plastering per ^{2}[/tex]
[tex]Room wall plastering cost = 448 * 5.50[/tex]
[tex]Room wall plastering cost = Rs 2464[/tex]
[tex]ence, the room wall plastering cost is Rs 2464.[/tex]
given that 10022bse 3 is equal to 155base n find the value of n show all workings
Answers
Step-by-step explanation:
log 3 (10022)
= 8.38561
log n (155)= 8.38561
n^8.38561=155
log 10 (n)= log 10 (155)
lpg 10 (155)= 2.190331698
8.38561 log10 (n)=2.190331698
log10 n = 2.190331698÷8.38561
lo^-1 (0.2612012)
=1.825
n=1.825
There are 10 questions on a true-false test. A student feels unprepared for this test and randomly guesses the answer for each of these. (a) What is the probability that the student gets exactly 7 correct? (b) What is the probability that the student gets exactly 8 correct? (c) What is the probability that the student gets exactly 9 correct? (d) What is the probability that the student gets exactly 10 correct? (e) What is the probability that the student gets more than 6 correct?
Answers
Answer:
Probability getting 7 correct :- 1/10Probability getting 8 correct :- 1/10 Probability getting 9 correct :- 1/10Probability getting 10 correct :- 1/10 → Probability getting more than 6 :- 4/10What is the value if X? and how to find exterior angles.
Answers
Change 75m to decimeters
Answers
Answer:
750 decimeters
Step-by-step explanation:
1 meter is equal to 10 decimeters.
so 75 times 10 equals your answer: 750 decimeters
Hope that helps!
Rewrite in simplest radical form
X^5/6 / X^1/6
Answers
Answer:
[tex]\sqrt[3]{x^2}[/tex]
Step-by-step explanation:
The rule of exponents says that we must use subtraction for [tex]\frac{5}{6}[/tex] and [tex]\frac{1}{6}[/tex] since we are dividing.
Thus, we have [tex]\frac{x^\frac{5}{6} }{x^\frac{1}{6} }\\\\\frac{5}{6}-\frac{1}{6}=x^\frac{4}{6}=x^\frac{2}{3}[/tex]
When dealing with fractions and radicals, we can find the simplest radical form by using the saying [tex]\frac{exponent}{index}[/tex]
Thus we have [tex]\sqrt[3]{x^2}[/tex]
Find the area of the parallelogram.
3 cm
5 cm
Answers
Answer:
Area = Base ×Height
Step-by-step explanation:
Area = Base × Height
Area = 3cm × 5cm
Area = 15cm
Area of the parrallelogram is 15cm
write balanced chemical equation for the process of photosynthesis giving the physical state of all the substances involved in the conditions of the reaction
Answers
Answer:
The process of photosynthesis is commonly written as: 6CO2 + 6H2O → C6H12O6 + 6O2.
Step-by-step explanation:
Heather planted 4 times as many tulips as Sarah planted. If Heather planted 64 tulips, how many tulips (s) did Sarah plant?
Answers
Step-by-step explanation:
let, the tulips be 'x'
According to the question,
heather=4x
& sarah=x
but heather planted 64 so,
4x=64
or, x=64/4
x=16
hence, sarah planted 16 tulips
Heather planted 4x Sarah's tulips. On the off chance that Heather has 64 tulips, Sarah has 16 tulips (64/4 = 16).
How to determine how many tulips (s) Sarah planted using algebraLet's utilize algebra to illuminate this issue. Let s speak to the number of tulips Sarah planted.
Concurring to the data given, Heather planted 4 times as numerous tulips as Sarah, so we will compose this as:
Heather's tulips = 4 * Sarah's tulips
64 = 4s
Presently, ready to fathom for s:
s = 64 / 4
s = 16
Sarah planted 16 tulips.
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Find the LCM of 20, 35 & 50.
Answers
Answer:
Answer: LCM of 20,35 and 50 is 1400
Step-by-step explanation:
I need help with this question please
Answers
Answer:
Step-by-step explanation:
As ABCD is a rectangle, ∠A = 90°.
Diagonal BD will be the hypotenuse.
[tex]Sin \ 53^{ \circ} = \sf \dfrac{opposite \ of \ angle \ 53}{hypotenuse}\\\\\\0.7986=\dfrac{AB}{42.3}\\\\\\0.7986*42.3=AB\\\\\bold{AB = 33.8}[/tex]
Length = AB = 33.8 cm
[tex]\sf Cos \ 53^{ \circ} =\dfrac{adjacent \ side \ to \ angle \ 53}{hypotenuse}\\\\\\0.6018 = \dfrac{AD}{42.3}\\\\\\0.6018*42.3 =AD\\\\\bold{AD = 25.5 }[/tex]
Width = 25.5 cm
An airline is planning its staffing needs for the next year. If a new route is approved, it will hire 837 new employees. If a new route is not granted, it will hire only 199 new employees. If the probability that a new route will be granted is 0.37, what is the expected number of new employees to be hired by the airline?
Answers
Considering a discrete distribution, it is found that the expected number of new employees to be hired by the airline is of 446.16.
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
In this problem, considering the situation described in the text, the distribution is given by:
P(X = 837) = 0.37.P(X = 199) = 0.63.Hence, the expected value is given by:
E(X) = 0.37(867) + 0.63(199) = 446.16.
More can be learned about discrete distributions at https://brainly.com/question/24855677
 Find the equation of the line that is perpendicular to 4 x + 3 y = 5 and goes through the point (3, –3)
Answers
Step-by-step explanation:
the line equation
y = ax + b
gives us slope (a) and y-interception (b).
4x + 3y = 5
3y = -4x + 5
y = -4/3 × x + 5/3
the slope of the original line is therefore -4/3.
a perpendicular slope flips x and y upside-down and flips the sign.
so, the perpendicular slope of -4/3 is 3/4.
the desired line looks like
y = 3/4 × x + b
b we get by using the given point and its coordinates :
-3 = 3/4 × 3 + b = 9/4 + b
-12/4 = 9/4 + b
b = -21/4
so our full line equation is
y = 3/4 × x - 21/4
or
4y = 3x - 21
-3x + 4y = -21