Answer:
The vertex is at (-1, -16).
Step-by-step explanation:
We are given the quadratic equation:
[tex]y = (x-3)(x+5)[/tex]
And we want to find its vertex.
Recall that the x-coordinate of the vertex is also the axis of symmetry. Since a parabola is symmetric about the axis of symmetry, the axis of symmetry is halfway between the two roots.
From the equation, we can see that our two roots are x = 3 and x = -5.
Hence, the axis of symmetry or the x-coordinate of the vertex is:
[tex]\displaystyle x = \frac{(3) + (-5)}{2} = -1[/tex]
To find the y-coordinate of the vertex, evaluate the equation at x = -1:
[tex]\displaystyle \begin{aligned} y(-1) &= ((-1)-3)((-1)+5)\\ &= (-4)(4) \\&= -16\end{aligned}[/tex]
Hence, the vertex is at (-1, -16).
Which expression is equivalent to 36÷3+3?
22÷3⋅3
3⋅22÷3
3⋅22+3
22+3⋅3
Answer:
None.
Step-by-step explanation:
36 ÷ 3 + 3 = 15
22 ÷ 3 × 3 = 22
3 × 22 ÷ 3 = 22
3 × 22 + 3 = 69
22 + 3 × 3 = 31
Which numbers are solutions of each inequality?
Answer:
45. -7.1, -7 1/7
46. 3.7
Step-by-step explanation:
45. y < -7
Answer: -7.1, -7 1/7
46.
z > 3 2/3
Answer: 3.7
help lol i forgot everything of the summer time
fill in the table using this function rule
Answer:
hope it help you
Step-by-step explanation:
mark me brailiest answer
Algebra 1 need help ASAP
Answer:
first one ( x ≥ -12)
Step-by-step explanation:
when you divide by -12 for both sides, the inequality reverses as the value is negative.
First one is the answer I think so
If a school camp has enough food for 150 students over 5 days
How long would the food last for is only 100 students are there
Answer:
It is over 7 days
hope it helps
Does the graph represent a function? Why or why not?
Answer:
D. Yes, because it passes the vertical line test.
Step-by-step explanation:
In order to be a function, it needs to pass the vertical line test as a function can not have multiple y's for one x. However, functions can have multiple x's for one y such as in a quadratic function.
Answer:
D.
Brainliest, please!
Step-by-step explanation:
This function passes both the horizontal and vertical line tests. But when determining if it is a function or not, the vertical line test is the only one that matters. If we wanted to know if this function had an inverse or not, then B. would be right.
WILL GIVE BRAINLIEST, PLEASE ANSWER ASAP, URGENT!! I ONLY NEED 3 AND 4
Answer:
Step-by-step explanation:
85 which is <UTY is vertically opposite <RTS makes RTS = 85
So 3 is + 85 = 180 Substitution
2x + 3x + 85 = 180
5x = 95
x = 95/5
x = 19
3 1/2 + (-5 2/3 ) ÷ ( 1 3/4)²
Which term can be used in the blank of 36x3−22x2−__ so the greatest common factor of the resulting polynomial is 2x? Select two options.
2
4xy
12x
24
44y
Answer:
[tex]4xy[/tex][tex]12x[/tex]-------------
[tex]36x^3,\:22x^2,\:4xy[/tex]
Factor 36x³
[tex]2\cdot \:2\cdot \:3\cdot \:3\cdot \:x\cdot \:x\cdot \:x\\[/tex]Factor 22x²
[tex]11\cdot \:2\cdot \:x\cdot \:x[/tex]Factor 4xy
[tex]2\cdot \:2\cdot \:x\cdot \:y[/tex]Common factor
[tex]2x[/tex]---------------------
[tex]36x^3-22x^2-12x[/tex]
Factor 36x³
[tex]2\cdot \:2\cdot \:3\cdot \:3\cdot \:x\cdot \:x\cdot \:x[/tex]Factor 22x²
[tex]11\cdot \:2\cdot \:x\cdot \:x[/tex]Factor 12x
[tex]2\cdot \:2\cdot \:3\cdot \:x[/tex]Common factor
[tex]2x[/tex]OAmalOHopeO
round 2.034 to the nearest whole number
Answer:
2
Step-by-step explanation:
2.034
We are rounding to the ones place.
To round, look at the digit to the right of which we are rounding. In this case, it is 0.
0 is less than 5, so we just keep the 2.
I hope this helps!
pls ❤ and mark brainliest pls!
Answer:
2
Step-by-step explanation:
2.034 can be rounded to 2.000, or 2. This is because the digit after the two in the tenths place, 0, is less than 5.
Brainliest, please!
Find two different integers such that the square of the integer is 12 less than seven times the integer
9514 1404 393
Answer:
3, 4
Step-by-step explanation:
If x represents the integer, then the relationship required is represented by the equation ...
x^2 = 7x -12
x^2 -7x +12 = 0 . . . . put in standard form
(x -3)(x -4) = 0 . . . . . factor
The values of x that make this relation true are x=3 and x=4.
The two integers are 3 and 4.
Use the function f(x) = 2x3 - 3x2 + 7 to complete the exercises.
f(−1) =
f(1) =
f(2) =
Answer:
2, 6, 11
Step-by-step explanation:
To evaluate f(- 1) substitute x = - 1 into f(x)
f(- 1) = 2(- 1)³ - 3(- 1)² + 7 = 2(- 1) - 3(1) + 7 = - 2 - 3 + 7 = 2
Similarly
f(1) = 2(1)³ - 3(1)² + 7 = 2(1) - 3(1) + 7 = 2 - 3 + 7 = 6
f(2) = 2(2)³ - 3(2)² + 7 = 2(8) - 3(4) + 7 = 16 - 12 + 7 = 11
Answer:
f(-1) = 2
f(1) = 6
f(2) = 11
Step-by-step explanation:
Got it right on Edge (⌣_⌣”)
I need help with this question
Answer:
m
Step-by-step explanation:
3,125 subtracted by what can give me 514
Answer:
2611
Step-by-step explanation:
3125-2611= 514
for more answers check my bio
Find the surface area of the composite figure
Answer:
144 cm²
Step-by-step explanation:
This figure is formed by rectangles and triangles, so we need to find the surface area of they and add all to have the surface area of the figure:
area of the rectangles:
4×3 = 12, and there are two of these rectangles
6×3 = 18, and there are just one of that
4×6 = 24, and there are two of these
5×3 = 15, and there are two of these
Now the area of a triangle:
6×4/2 = 12, and there are two of these
12×2 + 18 + 24×2 + 15×2 + 12×2 = 144 cm²
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
In a basketball game, Noli scored 3 points by shooting the ball at a horizontal distance of 7 feet from the 10-feet-high hoop. Noli threw the ball 6 feet above the ground and the ball went twice as high as its initial horizontal distance from the hoop. What was the horizontal distance of the ball from Noli when it reached its maximum height?
Answer:
The horizontal distance of the ball from Noli when it reached maximum height is approximately 4.1 feet
Step-by-step explanation:
The horizontal distance from the hoop at which Noli threw the ball, y₀ = 7 feet
The height of the hoop = 10 feet
The height from which the ball was thrown = 6 feet
The height to which the ball is thrown = 2 × The initial horizontal distance from the hoop
∴ The height to which the ball is thrown, [tex]y_{max}[/tex] = 2 × 7 feet = 14 feet
The coordinates of points on the path of the ball are;
(0, 6), (7, 10), (x, 14)
The projectile in vertex form is y = a·(x - h)² + k
Where;
(h, k) = The x, and y-coordinate of the maximum height
The y-coordinate of the maximum height reached = k = 14 feet
The x-coordinate of the maximum height = h = The horizontal distance of the ball from Noli when it reached maximum height
At y = 6, x = 0, therefore, we get;
6 = a·(0 - h)² + 14 = a·h² + 14
6 = a·h² + 14
a = -8/h²
At y = 10, x = 7, we get;
10 = a·(7 - h)² + 14 = (-8/h²)·(7 - h)² + 14
10·h² = -8·(7 - h)² + 14·h²
-4·h² = -8·(7 - h)²
4·h² - 8·(7 - h)² = 0
-4·h² + 112·h - 392 = 0
h = (-112 ± √(112² - 4 × (-4) × (-392)))/(2 × -4)
h ≈ 4.1, or h ≈ 23.9
We reject the value, h ≈ 23.9 feet given that the distance between the where the Noli threw the ball and the hoop = 7 feet
Therefore, the horizontal distance of the ball from Noli at which the ball reached its maximum height, h ≈ 4.1 feet
Find the value of x and y
[tex]\\ \rm\Rrightarrow \dfrac{x}{2}=3[/tex]
[tex]\\ \rm\Rrightarrow x=2(3)[/tex]
[tex]\\ \rm\Rrightarrow x=6[/tex]
And
[tex]\\ \rm\Rrightarrow \dfrac{y}{2}+1=3[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{y}{2}=3-1=2[/tex]
[tex]\\ \rm\Rrightarrow y=2(2)[/tex]
[tex]\\ \rm\Rrightarrow y=4[/tex]
Answer:
x=6 y=4
Step-by-step explanation:
Equating corresponding terms , we get
x/2=3
or, x=6
Also,
y/2+1=3
or, (y+2/2)=3
or, y+2=6
or, y=6-2
y=4
Therefore, x=6 and y=4.
please solve it
find the value of x
Answer:
The measure of angle x is 25 degrees.
Step-by-step explanation:
Since triangle ABC is an isosceles triangle, the measure of angle BAC is equal to the measure of angle ACB. Angle ABC = 80 degrees, leaving 100 degrees to be divided equally for the measures of the other two angles. Now that you know that angle ACB = 50 degrees, you can calculate the value of angle ACD and determine that angle ACD = 130 degrees. Triangle ACD is also an isosceles triangle, and the two equal legs are AC and CD. Since angle ACD = 130 degrees, the other two angles have a total of 50 degrees. Splitting the 50 degrees equally between the two angles gives you 25 degrees as the value of angle CAD, which is labeled "x."
HELP!!!!! PLEASE!!!!
Can someone help me on this please
Answer:
105
Step-by-step explanation:
y=75. 180-z=2y, z=180-2*75=30. As the triangle is isosceles, the other two angles are 75 and 75 and x+75=180, x=105
A circle has a circumference of C inches and an area of A square inches. inches. fC = 2/5 * A what is the diameter of the circle?
0.4 in.
0.8 in
2.5 in
10in
[tex]\it R=circle's \ radius;\ \ D=diameter;\ \ D=2R\\ \\ \mathcal{C}=2\pi R\\ \\ \mathcal{A}=\pi R^2\\ \\ \mathcal{C}=\dfrac{2}{5}\cdot\mathcal{A} \Rightarrow 2\pi R=\dfrac{2}{5}\pi R^2|_{\cdot\frac{5}{2}} \Rightarrow 5\pi R=\pi R^2|_{:(\pi R)} \Rightarrow 5=R|_{\cdot2} \Rightarrow 10=2R\\ \\ But,\ 2R=D,\ so\ \ D=10\ in[/tex]
The question is
"Mia has a large bag of sweets, If i share the sweets equally among 1,2,3,4,5 or 6 people, there will always be 1 sweet left over"
with step by step pls :(
Answer:
61
or
421
Step-by-step explanation:
Find the L.C.M. of 2,3,4,5,6 and add 1.
2| 2-3-4-5-6
-------------------
2| 1-3-2-5-3
---------------------
3| 1-3-1-5-3
----------------------
5| 1-1-1-5-1
----------------------
| 1-1-1-1-1-1
L.C.M.=2×2×3×5=60
reqd. number=60+1=61
if i distribute between 2,3,4,5,6 people then reqd number is 61
if Mia is also among those people or she gets also share
then the people are2,3,4,5,6 or 7
L.C.M. of 2,3,4,5,6,7=60×7=420
so reqd number is 420+1=421
What is the answer in scientific notation?
(5.1 × 106) x (4.3 × 105)
A 0.8 × 106
B 0.8 × 105
C 4.67 × 105
D 4.67 × 106
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\boxed{\star \ (5.1 \times10^6) \times (4.3 \times 10^5)\ \star}[/tex]
[tex]\huge\boxed{10^6}[/tex]
[tex]\huge\boxed{= 10 \times 10 \times10 \times10 \times10 \times 10}[/tex]
[tex]\huge\boxed{= 100\times 100\times100}[/tex]
[tex]\huge\boxed{= 10,000\times100}[/tex]
[tex]\huge\boxed{= \bf 1,000,000}[/tex]
[tex]\huge\boxed{\star\ (5.1 \times 100,000) \times(4.3 \times 10^5)\ \star}[/tex]
[tex]\huge\boxed{10^5}[/tex]
[tex]\huge\boxed{= 10 \times 10 \times10 \times 10 \times 10}[/tex]
[tex]\huge\boxed{= 100\times100\times 10}[/tex]
[tex]\huge\boxed{= 10,000\times10}[/tex]
[tex]\huge\boxed{= \bf 100,000}[/tex]
[tex]\huge\boxed{\star \ (5.1 \times 1,000,000) \times (4.3\times 100,000)\ \star}[/tex]
[tex]\huge\boxed{5.1 \times 1,000,000}[/tex]
[tex]\huge\boxed{= \bf 5,100,000}[/tex]
[tex]\huge\boxed{4.3 \times 100,000}[/tex]
[tex]\huge\boxed{= \bf 430,000}[/tex]
[tex]\huge\boxed{\star\ 5,100,000 \times 430,000\ \star}[/tex]
[tex]\huge\boxed{= \bf 2,193,000,000,000}[/tex]
[tex]\huge\boxed{0.8 \times 10^6}[/tex]
[tex]\huge\boxed{= \bf 800,000}[/tex]
[tex]\huge\boxed{0.8 \times 10^5}[/tex]
[tex]\huge\boxed{= \bf 80,000}[/tex]
[tex]\huge\boxed{4.67\times10^5}[/tex]
[tex]\huge\boxed{= \bf 467,000}[/tex]
[tex]\huge\boxed{4.67 \times 10^6}[/tex]
[tex]\huge\boxed{= \bf 4,670,000}[/tex]
[tex]\huge\boxed{\textsf{Therefore, this makes the answer: \bf NONE}}\\\hug\boxed{\textsf{of the \bf ABOVE}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\huge\boxed{\frak{Amphitrite1040:)}}}[/tex]
What is the solution of the system of equations?
y = –3x + 7
y = 2x – 8
Answer:
(3,-2)
Step-by-step explanation:
The easiest way to solve this is to realize that in both equations, the ys must have the same value. So the right side of each equation can be equal.
-3x + 7 = 2x - 8 Add 8 to both sides
-3x + 7 + 8 = 2x Combine
-3x + 15 = 2x Add 3x to both sides
15 = 2x + 3x Combine and exchange sides
5x = 15 Divide by 5
x = 15/5
x = 3
Use y = 2x - 8 to solve for y
y = 2(3) = 8
y = 6 - 8
y = - 2
Which cannot be a value of 0 ? Help pls
Answer:
B.
Step-by-step explanation:
Since i is in the denominator, if i = 0, then the result will be undefined. Therefore, B cannot be a value of θ.
Find the height of the triangle
Answer:
The height is 12 cm
Step-by-step explanation:
Hi there!
We are given a triangle with the 3 sides marked as 15, 20, and 25 and we want to find the height of it (marked as x in the problem).
This problem can seem a bit difficult, but let's see if the triangle is a right triangle first off.
One way to figure out if it is a right triangle is to apply the converse of the Pythagorean theorem.
Let's label the sides, where a is the shortest side, b is the second shortest side, and c is the longest side:
a=15
b=20
c=25
Now square a and b, then add the result together. If it's the same as c squared, then the triangle is a right triangle
15²+20²=25²
225+400=625
625=625
So we can safely say that the triangle is a right triangle
This makes the problem way easier, as there are 2 ways to find the area of a right triangle:
The first way is to multiply the legs (the sides that make up the right angle) together, then divide the result by 2
The other way is to multiply the height and the hypotenuse (the side OPPOSITE to the right angle) together, and then divide the result by 2
First, we need to figure out which sides are the legs, and which side is the hypotenuse
By the triangle inequality theorem, the hypotenuse of a right triangle is the longest side, which means that the 25 cm side is the hypotenuse, and that leaves 15 cm and the 20 cm sides as the legs
So let's find the area of the triangle using the legs
A=[tex]\frac{15*20}{2}[/tex]=[tex]\frac{300}{2}[/tex]=150
So the area of the triangle is 150 cm²
However, as mentioned above, we can also find the area of the triangle by multiplying the hypotenuse by the base, then dividing the result by 2
Which means that the area is also:
A=[tex]\frac{25x}{2}[/tex] cm²
As these both equal the area of the triangle, we can set them equal to each other. This is possible via a property known as transitivity (if a=b and b=c, then a=c)
[tex]\frac{25x}{2}=150[/tex]
Multiply both sides by 2
25x=300
Divide both sides by 25
x=12 cm
So the height of the triangle is 12 cm
Hope this helps!
Emma is making posters by hand to advertise her school play, but her posters are not the same
length as a standard sheet of paper (the width is the same, though). She has 3 1/2 sheets of paper
left over, which she says is enough to make 2 1/3 posters. How many sheets of paper (and parts of
a sheet) does each poster use?
Answer:
1 1/2 sheets
Step-by-step explanation:
7/3 x = 7/2
x=3/2
The exchange rate between dollars ($) and pounds (£) is $1 = £0.65 . The exchange rate between euros (€) and pounds is €1 = £0.74 . Khan changes €520 into pounds. He spends £260 and then changes the rest into dollars. Work out how many dollars he receives
Answer:
€520=£442.83
=£442.83-£260
=£182.83 into dollars=$251.52
Therefore he receives $251.52
melanie is cutting a 6 1/2 inch piece of yarn from a string that is 15 3/4 inches long how much yarn will be left
Answer:
9 1/4 inches would be left
Step-by-step explanation: