9514 1404 393
Answer:
10. (x, y) = (-3/8, 2 9/16)
11. k = -1
Step-by-step explanation:
10. The value of x at the vertex is ...
x = -b/(2a)
x = -(-3)/(2(-4)) = -3/8
The corresponding value of y is ...
y = 2 +(-3/8)(-3 +(-3/8)(-4)) = 2 +(-3/8)(-3/2) = 2 +(9/16)
The vertex is (x, y) = (-3/8, 2 9/16).
__
11. The discriminant is zero when the roots are equal.
b² -4ac = 0
(k-1)² -4(1)(-k) = 0
k² -2k +1 +4k = 0
k² +2k +1 = 0 . . . . . collect terms
(k +1)² = 0 . . . . . . . . write as a square
k = -1 . . . . . . . . . . . . the value of k that satisfies
Check
x² -2x +1 = (x -1)² = 0 . . . . has equal roots: x=1.
In the first week of July, a record 1,060 people went to the local swimming pool. In the second week, 100 fewer people went to the pool than in the first week. In the third week,140 more people went to the pool than in the second week. In the fourth week, 146 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
Answer:
there was a total of 954 people at the pool
Step-by-step explanation:
Answer: 246
Step-by-step explanation:
4(3xy^4)^3/(2x^3y^5)^4
Answer:
[tex]\frac{4\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}=\frac{27}{4x^9y^8}[/tex]
Step-by-step explanation:
Given the expression
[tex]\:\:\frac{4\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}[/tex]
solving the expression
[tex]\:\:\frac{4\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}=4\cdot \:\frac{\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}[/tex]
[tex]=4\:\frac{27x^3y^{12}}{16x^{12}y^{20}}[/tex]
[tex]=4\cdot \frac{3^3}{2^4x^9y^8}[/tex]
The multiply fractions are defined as
[tex]\:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}[/tex]
so the expression becomes
[tex]=\frac{3^3\cdot \:4}{2^4x^9y^8}[/tex]
[tex]=\frac{3^3\cdot \:2^2}{2^4x^9y^8}[/tex]
[tex]=\frac{3^3}{2^2x^9y^8}[/tex]
Refining
[tex]=\frac{27}{4x^9y^8}[/tex]
Therefore,
[tex]\frac{4\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}=\frac{27}{4x^9y^8}[/tex]
What is the length of side BC of the triangle?
Enter your answer in the box.
units
Answer:
BC is 28
Step-by-step explanation:
Please help me out with this question please...
Answer: B) No, every x-value does not have exactly one y-value
Explanation:
We have the input x = 3 map to the outputs y = 2 and y = 8 at the same time. A function is only possible if any given x value goes to exactly one y value.
Put another way, if x repeats itself, then we don't have a function. This assumes we don't repeat the same y value when we repeat the x value.
Steven has 10 1/4 pages of homework. If he finishes 2 1/2 pages every ten minutes, how many pages will Steven have left after 10 minutes?
A. He has completed all pages of homework.
B. 12 3/4 pages
C. 7 3/4 pages
D. 2 1/2 pages
Answer: 7 3/4
Step-by-step explanation:
From the question, we are informed that Steven has 10 1/4 pages of homework and that he finishes 2 1/2 pages every ten minutes.
The number of pages that Steven will have left after 10 minutes will be:
= 10 1/4 - 2 1/2
= 7 3/4
He'll have 7 3/4 pages left
(24-2)180 whats the answer?
Answer:
3960 is the answer
Step-by-step explanation:
Answer:
3960
Step-by-step explanation:
...........................
...........................
answer is 3960
what is the vertex of the parabola using this equation y=-x^2+4x+5
Answer:
(2, 9)Step-by-step explanation:
[tex]y=-x^2+4x+5\quad \implies\quad a=-1\,,\ b=4\,,\ c=5\\\\h=\dfrac{-b}{2a}=\dfrac{-4}{2(-1)}=2\\\\k=c-\dfrac{b^2}{4a}=5-\dfrac{4^2}{4(-1)}=5-\dfrac{16}{-4}=5+4=9[/tex]
Or by completing the square:
[tex]y=-x^2+4x+5\\\\y=-(x^2-4x)+5\\\\y=-(\underline{x^2-2\cdot x\cdot 2+2^2}-2^2)+5\\\\y=-\left((x-2)^2-4\right)+5\\\\y=-(x-2)^2+4+5\\\\y=-(x-2)^2+9\quad\implies\quad h=2\,,\ k=9[/tex]
If f(y) = 2y - 2/5,
what is f(f^-1(1024))?
Answer:
-0.399
Step-by-step explanation:
f^-1(1024)=(2*1024-2/5)^-1= 0.000488
f(0.000488)=2*0.000488-2/5= -0.399
Which of the following represents the graph and y-intercept of the function 3x + y = -2?
determine the equation of the quadratic function represented by the table of values below: x -4 -3 -2 -1 0 1 y -20 -13 -8 -5 -4 -5
Answer: y = -1*x^2 - 4
Step-by-step explanation:
A generic quadratic equation is written as:
y = a*x^2 + b*x + c
we need to find the values of a, b, and c
We have the table:
x y = f(x)
-4 -20
-3 -13
-2 -8
-1 -5
0 -4
1 -5
In the table we can see two things:
y(0) = a*0^2 + b*0 + c = c = -4
Then we know that:
y(x) = a*x^2 + b*x - 4
Now we only need to find a and b.
We also can see that we have symmetry around the point x = 0, this means that x = 0 is the vertex of the quadratic equation, and for a general case the vertex is at:
x = -b/2a
and this is equal to zero:
-b/2a = 0
then we must have b = 0.
So for now, the equation is:
y = a*x^2 -4
Now we can just replace the values of any of the points to find the value of a, for example we can use the point (1, -5)
this means that:
y = -5 = a*1^2 - 4
-5 = a - 4
-5 + 4 = a
-1 = a
Then the quadratic equation is:
y = -1*x^2 - 4
What is the slope of the line that
passes through these two points?
(-3, 2)
(4, 2)
Remember, Slope
rise (y2-yı)
run (x2-x1)
Simplify your answer completely.
Answer:
The line has a slope of zero which means the line is a horizontal line.
Step-by-step explanation:
Given that:
The two points are (-3,2) and (4,2)
Slope of a line is given by the formula,
[tex]m = \frac{Rise}{Run} = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Here,
[tex]x_{1}=-3,\ y_{1}=2\\x_{2}=4,\ y_{2}=2[/tex]
Putting these values in formula;
[tex]m=\frac{2-2}{4-(-3)} \\m = \frac{0}{4+3}\\m = \frac{0}{7} = 0[/tex]
Hence,
The line has a slope of zero which means the line is a horizontal line.
If one angle equals 130 in a triangle and the other equals 96 then what does the angle labelled X equal
Answer:
x = 46
Step-by-step explanation:
This is basic trigonometry, so we can apply this procedure...
- The total sum of all angles in a triangle is 180 (no angle should be more than 180, this is the limit) and we only need to know just one angle labeled as x, this is represented as:
130 + 96 + x = 180
x = 130 + 96 - 180
- Now we just need to obtain x:
x = 130 + 96 - 180
x = 226 - 180
x = 46
7th grade math need asap. Lilliana is training for a marathon. She runs the same distance every day for a week. On Monday, Wednesday, and Friday, she runs 2 laps on a running trail and then runs 6 more miles. On Tuesday and Sunday, she runs 4 laps on the trail and then runs 2 more miles. On Saturday, she just runs laps. How many laps does Lilliana run on Saturday?
Answer:
5 Laps
Step-by-step explanation:
The question says that she runs the same distance everyday. This shows us that...
2 laps on a running trail and 6 more miles = 4 laps on a running trail and 2 more miles
We can turn laps into the variable L and miles into the variable M to create an equation
2 L + 6 M = 4 L + 2 M
We can start by subtracting 2 M from both sides to get:
2 L + 4 M = 4 L
Now, we can subtract 2 L from both sides
4 M = 2 L
This tells us that 2 laps are 4 miles which means that 1 lap is 2 miles.
Now, we can break down either side of the equation. Let's break down
2 L + 6 M
First, we can turn the miles into laps. We know that 2 miles is one lap so we can divide 6 by 2. Our Equation:
2 L + 3 L
Now, we can simplify this :
5 L
Now we know that she ran 5 laps on saturday.
Hope this Helps!!! :)
Let me know in the comments if this answer was perfect or if I should change anything!!!
Rob loves to snowboard in the winter, so he is looking at the cost of ski lift tickets for different mountains. Peak Point is selling 5-day packs for $275.60. Grand Mountain is selling 3-day packs for $174.75. Which mountain offers the better deal?
Answer: Peak Point offers the better deal.
Step-by-step explanation:
To find which has the best price, we need to know the cost for one day at each mountain. To do this, we would divide the cost of each pack by the number of days it pays for, so
$275.60/5 days
and $174.75/3 days.
Peak Point costs $55.12 per day while Grand mountain costs $58.25 for each day. This shows that Peak Point clearly has the better deal, costing $3.13 less for every day included in the pack.
Substitute the given values into the formula, and solve for the unknown variable.
1
A= 2h(B+b); A=44, B = 2, b= 9
h=
Step-by-step explanation:
44 = 2 * h * 11
44 = 22 * h
divide 22 on both sides, and you get the answer
2 = h
A = 2h(B + b)
Disregard my first reply.
Here is the math work.
44 = 2h(2 + 9)
44 = 4h + 18h
44 = h(4 + 18)
44/(4 + 18) = h
44/22 = h
Divide top and bottom by 11.
4/2 = h
2 = h
Done!
1
what is the domain of g?
Answer:
(4,-5) is the answer
hope it helps you!!!!!!!
Step-by-step explanation:
.
Answer:
actual answer
Step-by-step explanation:
What's the gcf of 47 and 17
Answer:
The GCF of 47 and 17 is 1
Step-by-step explanation:
What is the value of y?
Answer:
Step-by-step explanation:
(12,5)
Divide. Reduce the answer to lowest terms.
3/4 ÷ 1/3
Answer:
when dividing fractions folow these steps:
first, you need to switch the denom and num of the second fraction:
3/4 ÷ 1/3---> 3/4 ÷ 3/1
Next you just switch the sign of the negative to a multiplication sign and multiply:
3/4 ÷ 3/1---> 3/4 x 3/1
3/4 x 3/1 -----> 9/4
9/4, 2 1/4 - these are your answers. Either are correct
Step-by-step explanation:
Answer:
2 1/4
Step-by-step explanation:
Please help will mark brainliest
Answer: The awnser is B
Step-by-step explanation: ive went over the problem and checked
Someone help me with this please
Graph y = 5/3x - 9
Answer:
The answer is in the attached screenshot
the Y intercept is 9
the slop is 5/3
hope this helps.
Step-by-step explanation:
May I have brainliest please? :)
Answer:jdjej
Step-by-step explanation: so u can give him brainliest
Which is the answer???
This homework is really confusing me. PLEASE HELP SOON. i also haven't been able to understand this topic that well so if someone could explain some stuff that would be good
I've been having some problems too
:/
Drag the tiles to the correct boxes to complete the pairs. Match each population trend to a contributing factor. government-sponsored family control programs agricultural economies medical advancements Industrial Revolution high birthrate arrowRight low death rate arrowRight increase in food supply arrowRight low birthrate arrowRight Reset Next
Answer:
Matching the population trend to a contributing factor:
Contributing Factors Population Trends
government-sponsored family control programs Low birth rate
agricultural economies increase in food supply
medical advancements low death rate
Industrial Revolution high birth rate
Step-by-step explanation:
a) Contributing factors are some negative or positive factors that influence or cause a single event or chain of events that result to the incident.
b) Defining population trends:
1) High birth rate: the industrial revolution triggered high birth rate, following increased food supply and medical advancements.
2) Low death rate: medical advancements brought about low death rate as better healthcare is provided to the sick.
3) Increase in food supply: large-scale agricultural economies ensured increasing food production and supply.
4) Low birth rate: when governments started sponsoring family control programs, the resulting effect was low birth rate.
Answer:
The first one is children and adolescents
the second one is adults
the third one is pregnancy
the last one is indivisuals with brittle bones
Step-by-step explanation:
hope this helps :D
Help!!! I need the answer!!
Answer:
Step-by-step explanation:
3/4a>-16=
a >- 64/3 or -21 1/3
5x+4=x+44 solve for x
Answer:
x=10
Step-by-step explanation:
hope this helps
5x = x + 44 - 4
5x = x + 40
5x - x = 40
4x=40
x=40/4
x = 10
Please help with this question ASAP I will give brainliest !!!
Answer:
(2).
Step-by-step explanation:
We have the expression:
[tex]\displaystye{\ln(\displaystyle{\frac{\sqrt{e}}{y^3})}[/tex]
First, we can use the difference property of logarithms:
[tex]\ln(x/y)=\ln(x)-\ln(y)[/tex]
Hence, this is equivalent to:
[tex]=\ln(\sqrt{e})-\ln(y^3)[/tex]
We can rewrite the left as:
[tex]=\ln(e^\frac{1}{2})-\ln(y^3)[/tex]
Now, we can use the power property:
[tex]\ln(a^b)=b\ln(a)[/tex]
Essentially, we move the exponent to the front.
Hence, this yields:
[tex]=\frac{1}{2}\ln(e)-3\ln(y)[/tex]
The natural log of e is simply 1. Hence:
[tex]=\frac{1}{2}-3\ln(y)[/tex]
Combine fractions:
[tex]\displaystyle{=\frac{1}{2}-\frac{6\ln(y)}{2} \\ =\frac{1-6\ln(y)}{2}}[/tex]
Hence, our answer is (2).
Wilfred is feeding his goats. He gives 56% of the bag of feed to the goats in field A and the rest to the goats in field B. If the bag has 21kg of feed, how much do the goats in field A get?
Answer:
[tex]Feeds = 11.76kg[/tex]
Step-by-step explanation:
Given
[tex]Field\ A= 56\%[/tex]
[tex]Field\ B= The\ rest[/tex]
[tex]Bag = 21kg\ feed[/tex]
Required
Determine how much goats in field A, get.
To do this, we simply multiply the percentage feed received by goats in field A by the actual bags of feeds
i.e.
[tex]Feeds = 56\% * 21kg[/tex]
Convert percentage to decimal
[tex]Feeds = 0.56 * 21kg[/tex]
[tex]Feeds = 11.76kg[/tex]
Hence, goats in field A get 11.76kg of feeds
Divide. Reduce the answer to lowest terms.
14/3 ÷ 4
Answer:
Work shown below!
Step-by-step explanation:
[tex]\frac{14}{3}[/tex] ÷ [tex]\frac{4}{1}[/tex] = [tex]\frac{14}{3}*\frac{1}{4} = \frac{14}{12}=\frac{7}{6}[/tex]
Answer:
the correct answer is 1 1/6
I WILL GIVE BRAINLIEST! Parallelogram WXYZ has vertices W(-5, 3), X(-2, 0), Y(-4, -2), and Z(-7, 1), as shown in the graph below.
Which statement about parallelogram WXYZ is true?
A. Since two adjacent sides are congruent and have slopes that are negative reciprocals, WXYZ is a square.
B. Since two adjacent sides are not congruent, WXYZ is not a rhombus.
C. Since two adjacent sides have slopes that are negative reciprocals, WXYZ is a rectangle.
D. Since two adjacent sides have slopes that are not negative reciprocals, WXYZ is not a rectangle.
Answer:
d
Step-by-step explanation: