Answer:
Step-by-step explanation:
Hello, we know that if the equation is
[tex]y=a(x-h)^2+k[/tex]
Then the vertex is the the point (h,k)
Here, the vertex is the point (-2,-20) so we can write, a being a real number that we will have to find,
[tex]y=a(x-(-2))^2-20=a(x+2)^2-20[/tex]
On the other hand, we know that the y-intercept is (0,-12) so we can write
[tex]-20=a(0+2)^2-12=4a-12\\\\\text{We add 12 and we divide by 4.}\\\\4a = -20+12=-8\\\\a = \dfrac{-8}{4}=-2[/tex]
So the equation becomes.
[tex]\boxed{y=-2(x+2)^2-12}[/tex]
And we can give the standard form as below.
[tex]y=-2(x+2)^2-12=-2(x^2+4x+4)-12\\\\=-2x^2-8x-8-12 \ <=>\\\\\boxed{y=-2x^2-8x-20}[/tex]
Thank you.
Answer:
this is wrong it needs to be 2 positives
Step-by-step explanation:
Three friends have been working in a garden. One has worked for 11 hours and the other 2 worked for 7 hours. The garden owner paid $500 for the work that was done. How should this money be divided fairly between the three friends?
Answer:
First should get $220, other two should get $140 each.
Step-by-step explanation:
The ratio of hours the friends worked is 11:7:7. Say that they are paid 11x, 7x, and 7x respectively, therefore:
11x + 7x + 7x = 500
25x = 500
x = 20 so the first friend should get 11 * 20 = $220 and the other two should get 20 * 7 = $140 each.
Calculate the volume of the regular triangular pyramid
with the base edges of length 17 feet and a height of
length 5 feet. (Hint: Remember that the base of a
regular triangular pyramid must be an equilateral triangle, not
necessarily congruent to the sides of the pyramid.)
Answer:
70.83 ft³
Step-by-step explanation:
The volume of a pyramid is:
[tex]\frac{bh}{3}[/tex], where b is the base area and h is the height.
Let's first find the area of the base.
[tex]17\cdot5=85\\85\div2=42.5[/tex]
Multiplying this by 5:
[tex]42.5\cdot5=212.5[/tex]
Dividing by 3:
[tex]212.5\div3=70.83[/tex].
Hope this helped!
Sally's house is located at (5, −1) and her school is located at (−9, 7). Her best friend Molly lives at the midpoint of Sally's house and school. What coordinate represents Molly's house? A. (2, −3) B. (−2, 3) C. (3, −2) D. (−3, 2)
Answer:
B. (-2, 3)Step-by-step explanation:
Given two coordinates (x₁, y₁) and (x₂, y₂), the coordinate of their midpoint is equivalent to X = (x₁+x₂)/2 and Y = (y₁+y₂)/2.
Given the coordinate of Sally's house and her school to be (5, −1) and (−9, 7) respectively, the midpoint of Sall's house and school is expressed as shown;
from the coordinates, x₁ = 5, y₁ = -1, x₂ = -9 and y₂ = 7
X = (5+(-9))/2
X = 5-9/2
X = -4/2
X = -2
Y = -1+7/2
Y = 6/2
Y = 3
The coordinate of the midpoint of Sally's house and school will be expressed as (X, Y) which is equivalent to (-2, 3).
Can you help me find all the seventh roots of unity? what do they look like graphed?
Answer:
There are seven seventh roots of unity, e2πki7 , all on the unit circle, r=1 above.
The first one is at θ=2π7=360∘7=5137 ∘ , and there are others at 4π7,6π7,8π7,10π7,12π7 and of course at 0 radians, i.e. unity itself.
How to find?
There are 4 fourth roots of unity and they are 1, i,−1 and−i
Each of the roots of unity can be found by changing the value of k k k in the expression e 2 k π i / n e^{2k\pi i/n} e2kπi/n. By Euler's formula, e 2 π i = cos ( 2 π ) + i sin ( 2 π ) = 1.
-3x8y=20
What’s the solution?
Answer:
y=-5/6
Step-by-step explanation:
-24y=20
y=-5/6
alternate:
-0.83
(1,-2),(-2,-5) find the slope and show me how u got it please
Answer:
where m= slope m= -7/3
Step-by-step explanation:
At the end of the first year, a zoo has 10 monkeys. If the number of monkeys doubles each year, how many will there be at the end of the fifth year?
A. 120
B. 160
C. 60
D. 50
I need domain and range
Answer:
Domain: all real numbers/ (-inf,inf)/ -inf<x<inf
Range: all real numbers greater than -4/ [-4,inf)/ -4≤y<inf
Step-by-step explanation:
the graphs/equations of ALL quadratics (parabolas) have a domain of all real numbers
The vertex of the parabola is at y=-4 so the range cannot be any less than that, and then both ends point up, so they will continue on for infinity.
Hope i could help!
Helen made a scale drawing of the middle school. The gym is 195 inches long in the drawing. The actual gym is 104 feet long. What scale did Helen use?
Answer:
5 inches on the drawing = 32 actual inches
Step-by-step explanation:
195 inches
104 x 12 = 1248 inches
1/39
Answer:
she used a scale of 5 inches to represent 32 inches actual length
Step-by-step explanation:
We are told that helen made the gym to be 195 inches long in the drawing.
Now, we are told that the actual length of the gym is 104 ft long.
Thus, converting to inches,
1ft = 12 inches
So, 104ft = 104 × 12 = 1248 inches
Which means that 194 inches represented 1248 inches.
So the scale is:
195:1248
Dividing both by a common factor of 39 to give a scale of (195/39):(1248/39)
This gives;
5:32
So she used a scale of 5 inches to represent 32 inches actual length
*HELP*
calculate the pay for the following day of a weekly time card given a wage of $12 an hour
Answer:
96 dollars and 50 cents
Step-by-step explanation:
Does anyone know this
=================================================
Explanation:
The graph goes on forever to the left and right. This means any real number x can be plugged into the function to get some output y. The domain is the set of all real numbers. In interval notation, we would say [tex](-\infty, \infty)[/tex] which is another way of saying [tex]-\infty < x < \infty[/tex]
The range is y > -100 because the exponential graph steadily approaches this horizontal asymptote. Think of it like an electric fence you cannot touch. Since we never actually get to this y value, this means y = -100 is not part of the range. Your teacher made a typo when they wrote [tex]y \ge -100[/tex] and instead they should have written [tex]y > -100[/tex]. So basically y can be anything larger than -100. The graph may look like it eventually reaches y = -100 itself, but it's actually just getting closer and closer to this y value. To write the range in interval notation, we would say [tex](-100, \infty)[/tex]
This function is exponential because it has the general shape all exponential growth functions do. We have a fairly flat part with very slow growth at first, but then as time goes on, the growth rate increases dramatically resulting in the very steep curve.
Quartic polynomials are 4th degree polynomials. They have the same end behavior as quadratic functions do, since both are even degree polynomials. We don't have a quartic here because the left end behavior isn't going off to positive infinity as the right end behavior is.
please help me with these
Answer:
x= -1
y= 2.5
Step-by-step explanation:
15x+6y=0
4x-6y=-19
19x = -19
x=-1
-15+6y = 0
6y=15
y=2.50
Answer:
19x = -38
x = -2
(-2,5)
Step-by-step explanation:
3(5x + 2y = 0)
2(2x - 3y = -19)
First step is to simplify the equations by using the distributive property.
3(5x + 2y = 0)
distribute the 3 by multiplying 3 by everything inside of the parenthesis
3 * 5x = 15x
3 * 2y = 6y
3 * 0 = 0
first equation simplified: 15x + 6y = 0
2(2x - 3y = -19)
distribute the 2 by multiplying 2 by everything inside of the parenthesis
2*2x = 4x
2 * -3y = -6y
2 * -19 = -38
second equation simplified: 4x - 6y = -38
We acquire the two equations
15x + 6y = 0
4x - 6y = -38
Notice how there are two 6ys, one is negative and the other is positive. When this happens we can add the two equations together and solve for x. We can do this because the two 6ys will cancel out and we will be left with one variable. when there is only 1 variable you can solve it.
So add the two equations
+ 15x + 6y = 0
4x - 6y = -38
--------------------
19x = -38
now solve for x
divide both sides by 19
19x/19 = -38/19
x = -2
Now we need to find the value of y.
To do so simply plug in the value of x into one of the equations and solve for y
4x - 6y = -38
x = -2
4(-2) - 6y = -38
multiply 4 and -2
-8 - 6y = -38
add 8 to both sides
-6y = -30
divide both sides by -6
y = 5
The solution to the system is (-2,5)
HELP ASAP ITS SO HARD! Kelsey did the following division problem. Her teacher says that the quotient she found is wrong. −2 5/6 ÷ 1 1/3 −17/6 ÷ 4/3 −6/17• 3/4 −6×3 divided by 17×4 −18/68 −9/34 A. Identify what Kelsey did wrong in her calculations. B. Find the correct quotient, showing all of your calculations.
Part A
Her steps were
[tex]-2 \frac{5}{6} \div 1 \frac{1}{3}\\\\-\frac{17}{6} \div \frac{4}{3}\\\\-\frac{6}{17} \times \frac{3}{4}\\\\-\frac{6\times 3}{17\times4}\\\\-\frac{18}{68}\\\\-\frac{9}{34}\\\\[/tex]
Kelsey made a mistake on line 3. Note how the 17/6 flips to 6/17. This is not correct. You keep the first fraction the same, but you do flip the second fraction. This only applies when you divide two fractions.
The third step should look like [tex]-\frac{17}{6}\times \frac{3}{4}[/tex]
=======================================================
Part B
Here's what she should have written
[tex]-2 \frac{5}{6} \div 1 \frac{1}{3}\\\\-\frac{17}{6} \div \frac{4}{3}\\\\-\frac{17}{6} \times \frac{3}{4}\\\\-\frac{17\times 3}{6\times 4}\\\\-\frac{51}{24}\\\\-\frac{17}{8}\\\\[/tex]
If you want to convert that improper fraction to a mixed number, then you could do something like this
[tex]-\frac{17}{8} = -\frac{16+1}{8}\\\\-\frac{17}{8} = -\frac{16}{8}-\frac{1}{8}\\\\-\frac{17}{8} = -2 \frac{1}{8}\\\\[/tex]
Or you could divide 17 over 8 using long division to get 2 remainder 1. The 2 is the quotient that goes to the left of the 1/8. The remainder of 1 is the numerator of 1/8.
The price for 2 mangoes and 3 guavas is RM 8.00. The price for 3 mangoes and a guava is RM 5.00
i) Form simultaneous linear equations in two variables based on the above situation.
ii) Represent the simultaneous linear equations graphically and explain the type of solutions obtained
here is the answer for question ii
Stewart is hiring a plumber to fit his shower. He charges a callout fee of £18.50 and then £x per hour after that. The plumber charges him £167.00 and it takes him 9 hours. How much does the plumber charge per hour?
Answer:
Step-by-step explanation:
Amount charges by plumber = £ 167.00
Call out fee = £ 18.50
Charge excluding the call out fee = 167 - 18.50 = £ 148.50
Total hours worked = 9 hours
Charge per hour = charge excluding the call out fee ÷ total hours
= 148.50 ÷ 9
= £ 16.50
Worth 20pts need help right away
Q. Make an equation that describes the table of values below
Ps pls explain work it’s worth 20 pts
Answer:
y=2x+1
Step-by-step explanation:
there's nothing to show, sorry
ask me if you have question
Please help ME ASAP!!Please explain the answer
Answer:
It seems like you misunderstood the instructions, though I don't blame you because they wrote it strangely. I believe that you're supposed to draw your own conclusion and then explain how you go there, rather than analyze a conclusion that was already drawn for you. If a long drive=a large fare, and you've been told that the driver has a long drive, you can draw the conclusion that "The fare will be large."
+
If the
sides of a triangles are
6, 8 and n. how
many integer values of n
could be the
measure of the
third side of the triangle?
Answer:
11
Step-by-step explanation:
The sum of the shortest two sides must be greater than the longest side.
If n is the longest side:
6 + 8 > n
14 > n
If 8 is the longest side:
6 + n > 8
n > 2
So n must be an integer greater than 2 and less than 14.
n can be 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, or 13.
There are 11 possible integers.
[tex] \LARGE{ \boxed{ \rm{ \purple{Answer}}}}[/tex]
We know,
Sum of two sides of a triangle > Third side
Then,
⇛ 6 + 8 > n
⇛ 14 > n
Nextly,
Difference of two sides of a triangle < Third side
Then,
⇛ 8 - 6 < n
⇛ 2 < n
Then, Range of third side:
☃️ 2 < n < 14
Possible measures of 3rd sides = 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 or 13.
There are 11 possible values of 3rd side. Out of them, any measure is the length of 3rd side.
━━━━━━━━━━━━━━━━━━━━
What is the area of this triangle?
I can't type it I have to solve on a paper for you
CAN SOMEONE PLS TELL ME DOMAIN AND RANGE
Answers:
Domain is (-4, 3]Range is (-5, 5]=====================================================
Explanation:
The domain is the set of allowed x input values, aka the set of all allowed x coordinates of the points. We see that [tex]-4 < x \le 3[/tex]. It might help to draw vertical lines through the endpoints until you reach the x axis. Note the open hole at x = -4 to indicate we do not include this as part of the domain (hence the lack of "or equal to" for the first inequality sign).
The interval [tex]-4 < x \le 3[/tex] then can be condensed into the shorthand form (-4, 3] which is the domain in interval notation.
It says: x is between -4 and 3. It can't equal -4 but it can equal 3.
So the use of parenthesis versus square brackets tells the reader which endpoint is included or not.
--------------------------------------------------
The range describes all possible y outputs. We see that y = 5 is the largest it gets and y = -5 is the lower bound. It might help to draw horizontal lines through the endpoints until you reach the y axis. The open hole means -5 is not part of the range.
The range as a compound inequality is [tex]-5 < y \le 5[/tex]. This condenses into the shorthand of (-5, 5] which is the range in interval notation.
Verbally, the range is the set of y values such that y is between -5 and 5. It can't equal -5 but it can equal 5.
Answer:
Hello,
Step-by-step explanation:
Domain(f)= ]-4;3]={x€R | -4<x≤3}
Rang(f)=]-5;5]={y€R | -5< y ≤5}
Traveling at a rate of 70 miles per hour, a car travels 26 miles per gallon of gasoline. Traveling at a rate of 45 miles per hour, the same car travels 36 miles per gallon of gasoline. Approximately how many gallons of gasoline are saved on a 300-mile trip if the car is driven at a rate of 45 miles per hour instead of at 70 miles per hour?
A) 2
B) 3
C) 12
D) 20
Answer:
B) 3
Step-by-step explanation:
Traveling at a rate of 70 miles per hour, a car travels 26 miles per gallon of gasoline.
In 300 miles journey the gallon of gasoline consumed will be
300/26= 11.54 gallons
Traveling at a rate of 45 miles per hour, the same car travels 36 miles per gallon of gasoline.
In 300 miles journey the gallon of gasoline consumed will be
300/36= 8.33 gallons
The amount of gasoline saved= 11.54-8.33
The amount of gasoline saved= 3.21
approximately 3 gallons of gasoline
Please answer this question now
Answer:
82 degrees
Step-by-step explanation:
Measure of arc ABC = 86*2 = 172 degrees.
Measure of arc DC = 360 - (145+172) = 360-317 = 43 degrees.
Measure of arc BCD = 121+43 = 164 degrees.
Measure of angle A = 164/2 = 82 degrees
All of Ralph's ranch land was divided equally among his six children whose daughter land portion of the ranch land was divided among her four children how much of Roslyn was in Inherited by 1 of Lynn's children
Complete question:
All of Ralph's ranch land was divided equally among his 6 children. His daughter Lynn's portion of the ranch land was divided equally among her 4 children. How much of Ralph's ranch land was inherited by 1 of Lynn's children?
Answer:
1 / 24
Step-by-step explanation:
Number of Ralph's children = 6
Number of Lynn's children = 4
If Ralph's land were divided equally among his six children, the fraction each child gets equals
Proportion of land / number of children
= 1 / 6
Therefore, Lynn who is also Ralph's daughter gets 1/6 portion.
If 1/6 is shared equally between her four children, then ;
Her portion ÷ 4
(1/6) ÷ 4
(1/6) × (4/1)
= 1/ 24
Each of Lynn's children gets 1 / 24
Simplify: 5 - 2(3 + 4)
Answer:
-9
Step-by-step explanation:
Hey there!
Well, to simplify,
5 - 2(3 + 4)
Wel need to use PEMDAS,
3+4=7
7 * -2 = -14
5 - 14 = -9
Hope this helps :)
Answer:
-9
Step-by-step explanation:
[tex]5 - 2(3+4)\\5 - 2(7)\\5 - 14\\-9[/tex]
Please does anyone know how to factorize x(x - 1) + 3x
Answer:
=x(x-1) +3x
= x^2-x+3x
=x^2 +2x
=x(x+2)
Step-by-step explanation:
The length of one side of a rhombus is 20 m.Find its perimeter.
Answer:
80 m
Step-by-step explanation:
Given :-
One side of rhombus = 20 m.
[ as one of the property of rhombus = all sides are equal ]
So, perimeter of rhombus = sum of all sides
= 20+20+20+20 = 80 m
...........................OR............................
Perimeter of rhombus = 4 × side
= 4 × 20 = 80 m
Hence, the perimeter of the rhombus is 80m.
Answer:
The perimeter is 80 meters
Step-by-step explanation:
The geometric characteristic of a rhombus is that it has 4 equal sides, then if one side measures 20 m, then each of the other sides measure also 20 m.Then its perimeter (addition of all the sides must render: 4 * 20 m = 80 m
plzzzz HELP ME ASAP WILL MARK AS BRAINLEIEST
Answer:
Hey there!
Part A. This is a proportional relationship because the amount of dollars she earns per hour is constant. We can divide her total income by the number of hours she works to find that she earns 12.50 dollars per hour.
Part B. Joslyn will always earn more money than Kate because she earns more money per hour, and the slope of Joslyn's line is greater.
Let me know if this helps :)
what is the length of DI? A 1.4 B 4.4 C 5.6 D 17.6
[tex]\dfrac{DI}{DR}=\dfrac{DE}{DZ}\\\\\dfrac{DI}{6+2.8}=\dfrac{3}{6}\\\\6DI=26,4\\DI=4,4[/tex]
one number is 4 less than 3 times another number. If their sum is increased by five,the result is 25. Find both the numbers.
Answer:
6 and 14
Step-by-step explanation:
let the second number=x
the first number=3x-4
(x+3x-4)+5=25
4x-4+5=25
4x+1=25
4x=25-1
4x=24
x=6
Since x is the first number,the first number is 6
second number=3•6-4
=18-4=14
Meguel does not understand which digit is in the tenths location in the number 514.196 Where would it be located at
Answer:
first number after the decimal point
Step-by-step explanation:
after the decimal point is the tenths, hundredths, and thousandths place.
0.1 - tenths
0.09 - hundredths
0.006 - thousandths