Answer:
Step-by-step explanation:
The vertex form of an equation of a parabola y = ax² + bx + c:
[tex]y=a(x-h)^2+k[/tex]
(h, k) - verex
[tex]h=\dfrac{-b}{2a},\ k=f(h)[/tex]
We have:
[tex]y=(x+5)(x+4)[/tex] use FOIL (a + b)(c + d) = ac + ad + bc + bd
[tex]y=(x)(x)+(x)(4)+(5)(x)+(5)(4)=x^2+4x+5x+20=x^2+9x+20[/tex]
a = 1, b = 9, c = 20
[tex]h=\dfrac{-9}{2(1)}=\dfrac{-9}{2}=-\dfrac{9}{2}[/tex]
For k, put the value of h to the equation y = (x + 5)(x + 4):
[tex]k=\left(-\dfrac{9}{2}+5\right)\left(-\dfrac{9}{2}+4\right)\\\\k=\left(-\dfrac{9}{2}+\dfrac{10}{2}\right)\left(-\dfrac{9}{2}+\dfrac{8}{2}\right)\\\\k=\left(\dfrac{1}{2}\right)\left(-\dfrac{1}{2}\right)=-\dfrac{1}{4}[/tex]
Finally:
[tex]y=1\bigg(x-\left(-\dfrac{9}{2}\right)\bigg)^2-\dfrac{1}{4}\\\\y=\left(x+\dfrac{9}{2}\right)^2-\dfrac{1}{4}[/tex]
The quadratic function y = (x + 5)(x + 4) in vertex form is y = (x + 9/2)^2 - 41/4, and its vertex is at (-9/2, -41/4).
Expand the given expression:
y = x^2 + 4x + 5x + 20
y = x^2 + 9x + 20
Factor out the coefficient of x^2 from the x^2 and x terms:
y = 1(x^2 + 9x) + 20
To complete the square, take half of the coefficient of x (which is 9) and square it. Add and subtract this value inside the parentheses:
y = 1(x^2 + 9x + (9/2)^2 - (9/2)^2) + 20
Factor the perfect square trinomial inside the parentheses:
y = 1((x + 9/2)^2 - (9/2)^2) + 20
Simplify the expression:
y = (x + 9/2)^2 - 81/4 + 20
Combine the constants:
y = (x + 9/2)^2 - 41/4
So, the quadratic function y = (x + 5)(x + 4) in vertex form is y = (x + 9/2)^2 - 41/4, and the vertex of the parabola is (-9/2, -41/4).
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Help with this question??
Answer:
3
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
here [ a, b ] = [ 0, 2 ] and from the graph
f(b) = f(2) = 0
f(a) = f(0) = - 6, hence
average rate of change = [tex]\frac{0-(-6)}{2-0}[/tex] = [tex]\frac{6}{2}[/tex] = 3
a teacher is holding tryouts for a school play. there are 15 students trying out for 7 parts in the play each student can play each part. in how many ways can the teacher select the students?
Answer:
6,435
Step-by-step explanation:
To find the number of ways the teacher can select the students, we can use the combination formula.
[tex]_{n}C_{k}=\dfrac{n!}{k!(n-k)!}[/tex]
n = 15
k = 7
Now let's plug it in.
[tex]_{n}C_{k}=\dfrac{n!}{k!(n-k)!}[/tex]
[tex]_{15}C_{7}=\dfrac{15!}{7!(15-7)!}[/tex]
[tex]_{15}C_{7}=\dfrac{15!}{7!8!}[/tex]
[tex]_{15}C_{7}=6,435[/tex]
So there are 6,435 ways that the teacher can select the students.
h + 6.9=11.4 what dose h= worth a lot of points please help will give brainlist
Answer: 4.5
Step-by-step explanation:
11.4-6.9=4.5
Answer:
h = 4.5
Step-by-step explanation:
You would do 11.4 - 6.9, which would equal 4.5.
Factor 1/7 out of 1/7x+46/7. 1/7x+46/7=
Final answer:
To factor 1/7 out of 1/7x+46/7, you can factor it out of each term separately and then combine like terms.
Explanation:
To factor 1/7 out of 1/7x+46/7, you can factor it out of each term separately. So you would have:
1/7(1/7x) + 1/7(46/7)
Simplifying each term gives us:
1/49x + 1/49(46)
Finally, you can combine like terms to get the answer:
1/49x + 46/49
Which point represents the center of the circle below ?
The center point is point O
17. Farimah and Helio are standing 15 ft. apart from each other and looking up at a kite that is with the flying between them. Farimah is flying the kite on a 57 ft. string at an angle of 68 ground. How far is Helio from the kite? 64.1 ft. 56.2 ft 60.0 ft. 53.2 ft.
Answer:
Helio is 53.2 feet from the kite ⇒ the last answer
Step-by-step explanation:
* Lets change this story problem to a trigonometry problem
- Assume that there is a triangle joining between the
kite, Farimah and Helio
- The name of the triangle is KFH, where K position of the kite,
F position of Farimah and H is the position of Helio
∵ Farimah and Helio are standing 15 feet apart from each other
∴ FH = 15 feet
∵ Farimah is flying the kite on a 57 feet string at an angle
of 68 with the ground
∴ FK = 57 feet
∴ m∠KFH = 68°
∵ We need to know that Helio is how far from the kite
∴ We need to calculate the length of KH
* Now lets find the best way to find the length of KH
using the trigonometry
- We have the length of two sides and the measure of the included
angle between them , then the best way is the cosine Rule
* Lets explain the cosine rule:
- In ΔABC:
∵ a is the length of the side opposite to ∠A ⇒ a is BC
∵ b is the length of the side opposite to ∠B ⇒ b is AC
∵ c is the length of the side opposite to ∠C ⇒ c = AB
∴ a² = b² + c² -2bc × cos(A)
∴ b² = a² + c² -2ac × cos(B)
∴ c² = a² + b² -2ab × cos(C)
* We will use the rule in our problem to find HK
∵ FH is k , HK is f , KF is h
∴ f² = h² + k² - 2hk × cos(F)
∵ h = 57 feet , k = 15 feet , m∠F = 68°
∴ f² = (57)² + (15)² - 2(57)(15) × cos(68) = 2833.4227
∴ f = √2833.4227 = 53.2 feet
* Helio is 53.2 feet from the kite
Plz help me with this
(-4 + 7i)(-4 - 7i)
= 16 - 49i2
Since i = √-1,
16 - 49i2
= 16 + 49
= 65
Answer: 65
Step-by-step explanation:
(-4 + 7i)(-4 - 7i)
= -4(-4 - 7i) +7i(-4 - 7i)
= 16 + 28i -28i - 49i²
= 16 - 49(-1) Note: i² = -1
= 16 + 49
= 65Tell if the slope is positive, negative , zero , or no slope
Answer:
No slope
Step-by-step explanation:
The slope of a line or segment in the Cartesian plane is zero if from left to right the value on the y-axis increases, and negative if from left to right the value on the y-axis decreases. So in this case the line is neither positive nor negative.
A slope is zero if the line is horizontal, and because the line in the figure is vertical, its slope is not zero.
For vertical lines in the plane it is said that they have no slope or that it is undefined.
What is the area?, round it to the nearest hundred where necessary.
Answer:
300 and 600
Step-by-step explanation: multiply l x w
In the given figure the area of the complete figure can be calculated as
sum of the area of the parallelogram and the area of the trapezium which is 787.5 sq.cm.
What is the area of a parallelogram?The area of a parallelogram is the product of the base and the height of the figure.
The area of a parallelogram = Base x Height
In the given figure the area of the complete figure can be calculated as
Area = area of the parallelogram + area of the trapezium
The upper figure is the shape of a parallelogram that has a height of 14cm and a base of 23cm.
The area of a parallelogram = Base x Height
[tex]14 \times 23\\\\322\:cm^{2}[/tex]
The lower figure is the shape of a trapezium that has a height of 19cm and a base of 34cm and 15 cm.
area of the trapezium
= [tex]\frac{1}{2} (a+b)h\\\\\frac{1}{2} (15+34)19\\\\465.5\:cm^2[/tex]
Therefore, Area = area of the parallelogram + area of the trapezium
Area = 322 + 465.5
=787.5 sq.cm
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(this is multiple choice and i raised points make sure to EXPLAIN !)
whats the sum of f and g ?
f(x)=10-2x and g(x)=7x+5
a) (f+g)(x)=5+5x
b) (f+g)(x)=5+9x
c) (f+g)(x)=15+5x
d) (f+g)(x)=15+9x
Answer:
C
Step-by-step explanation:
Basically (f+g)(x) = f(x)+g(x).
Following this rule you combine like terms.
7x-2x=5x and 10+5 = 15.
Therefore the answer is C.
f(x) = 10 - 2x
g(x) = 7x + 5
(f + g) (x) = (10 - 2x) + (7x + 5) //Adding two functions
= 10 - 2x + 7x + 5
= 15 + 5x
Answer: C.
//Hope it helps.
Find the value of X rounded to the nearest tenth
A)5.1
B)9.2
C)5.8
D)5.2
Answer:
B
Step-by-step explanation:
Chords which intersect have segments whose products are equal. This means the chord with lengths 5 and x has a product 5x. It is equal to the the other chords lengths 5.1 and 9 as a product 5.1*9.
5x = (5.1)(9)
5x = 45.9
x = 9.18
9.18 rounds to the tenth place as 9.2
3x+2=4x-3?
Please help me
Answer:
The answer is 5
Step-by-step explanation:
Answer:
x=5
Step-by-step explanation:
3x+2=4x-3
minus 3x from both sides
2=x-3
add 3 to both sides
x=5
Point A(-7, -2) is rotated 270° counterclockwise and then shifted down 3 units. What are to coordinates of K’?
A. (2,4)
B. (-2, -7)
C. (-2, 4)
D. (7, -5)
Answer:
C. (-2, 4)
Step-by-step explanation:
First we are going to rotate the point 270°; then we are going to shift it down 3 units.
Remember that the rule to rotate a point 270° counterclockwise about the origin is:
[tex]R_{270}(y,-x)[/tex]
In other words, we just need to switch the coordinates and change the sign of the second coordinate. Let's apply the rule to our point:
[tex]A = (-7, -2)[/tex]
[tex]A'=(y,-x)=(-2,--7)=(-2,7)[/tex]
Now we know that the coordinates of our point after the rotation are A' = (-2, 7)
The only thing left is shift that point 3 units down; to do it, we just need to subtract 3 from the y-coordinate:
[tex](x,y)-->(x,y-3)[/tex]
[tex]A'=(-2,7)[/tex]
[tex]K'=(-2,7-3)[/tex]
[tex]K'=(-2,4)[/tex]
We can conclude that after a rotation of 270° and a translation 3 units down, the coordinates of point K' are (-2, 4).
In an acute scalene triangle, one angle is 20 degrees larger than another angle and the third angle is half the sum of the other two angles. What is the measure, in degrees, of each of the three angles of the triangle?
Answer:
it could be 20 30 and 25
Step-by-step explanation:
Which of the following are possible amounts for the third check and the cash that Cindy deposited? a. no cash and a $303.68 check b. $140.50 in cash and a $267.14 check c. $99.32 in cash and a $155.55 check d. $122.04 in cash and a $205.64 check
Answer:
D. $122.04 in cash and a $206.64 check
Step-by-step explanation:
D is the correct answer :0
X = 7 sin t + sin 7t
y = 7 cos t + cos 7t
Graph this picture
Wait. You've been waiting for a year? Woah..
what is the diameter of the following circle? (x-6)^2 + (y-7)^2 =25
Answer:
d = 10Step-by-step explanation:
The standard form of an equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the equation:
[tex](x-6)^2+(y-7)^2=25[/tex]
h = 6, k = 7, r = √25 = 5
The diameter d = 2r → d = 2(5) = 10
simplify:
2/3 - 5/6 • 8
A) -4
B) -6
C) -
22
3
D) -
4
3
Step-by-step explanation:
2/3 - 5/6 * 8
You have to multiply first, then subtract:
-5/6 * 8 = -20/3
Put it back into an equation:
2/3 - 20/3
Simplify:
-18/3
= -6
Answer:
B) -6
Step-by-step explanation:
2/3 - 5/6 • 8
According to PEMDAS, we need to multiply before we subtract
5/6 *8 = 40/6
We can divide the top and bottom by 2
40/6 = 20/3
Replace 5/6*8 with 20/3 in the original equation
2/3 -20/3
-18/3
Divide the top and bottom by 3
-6/1
-6
ok these are the last ones
There are 12 months in a year
4 months that have 30 days so ratio of the months with 30 days to the months with other than 30 days = 4: 12 = 1:3
Answer:
1 to 3
--------------
24 sedans and 18 sports
Ratio of sedans to sport = 24 : 18 = 4:3
Answer:
4 to 3
---------------
30 inches to 2 feet
2 feet = 24 inches
so 30 inches to 24 inches = 30:24
simplify
= 5 : 4
Answer:
5 to 4
-------------------
36 inches to 4 feet = 36 inches to 48 inches = 36:48
simplify
= 3 : 4
Answer:
3 to 4
Answer:
1. 1 to 2 , 2. 3:2 , 3. 15:1 , 4. 6:2
Step-by-step explanation:
If (x-4) is a factor of x^2-x-w=0, then the value of w is
Step-by-step explanation:
If x-4 is factor, then one value of x is 4
4²-4-w=0
12-w=0
w=12
➷ You have to find a value that, when added to -4, gives -1
This value is +3
The factored form would be (x - 4)(x + 3)
Expand this out:
x^2 + 3x - 4x - 12
==> x^2 -x -12 = 0
w = -12
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
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A pair of sneakers with a listed price of $65 is on sale for 40% off. Which of the following is the sale price for the sneakers?
Answer:
$39
Step-by-step explanation:
65 x .40 = 26
65 - 26 = $39
Answer:
$39
Step-by-step explanation:
1st multiply: 0.40 * 0.100= 0.400
2nd multiply: 0.400 * $65 = $26 (how much you saved)
3rd subtract: $63 - $26= $39 (which is the cost of the sneakers)
what is the circumference of the circle below.use 3.14 for pi
18m
d × 3.14
18 ×3.14
c=56.52
given the similar figures name all pairs of corresponding sides and angles
Answer:
Step-by-step explanation:
Please hurry!!! Chose the equation below that represents the line that passes through the point (7,-2) and has a slope of -3
Answer:
y + 2 = -3(x - 7)
Step-by-step explanation:
Write the equation using the point slope form [tex]y - y_1 = m(x-x_1)[/tex]. Substitute m = -3 and (7,-2).
[tex]y --2 = -3(x-7)\\y + 2 = -3(x-7)\\y +2 = -3x +21\\y = -3x +19[/tex]
What does the fraction 2 1/9 minus 7/6 equal
Answer: = [tex]\frac{17}{18}[/tex]
Step-by-step explanation:
* Hopefully the work below helps:) Mark me the brainliest if this was helpful:)
The cross-section of a ramp is a triangle with side lengths of 9 inches, 40 inches, and 41 inches. Is this a right triangle?
Answer: True.
Step-by-step explanation: For this to be true, then:
[tex]9^2+40^2(=?)41^2[/tex]
[tex]81+1600 (=?) 1681[/tex]
[tex]1681=1681[/tex]
Yes, the ramp is indeed a right triangle.
Final answer:
The triangle with sides of 9 inches, 40 inches, and 41 inches is a right triangle, as it satisfies the Pythagorean theorem (9² + 40² = 41²).
Explanation:
A student asked if a ramp with a triangular cross-section and side lengths of 9 inches, 40 inches, and 41 inches is a right triangle. To determine this, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
For the triangle in question, if we square each of the side lengths and add the squares of the shorter sides, we should get the square of the longest side if it is indeed a right triangle:
9² = 8140² = 160041² = 1681Then add the squares of the two shorter sides:
81 + 1600 = 1681
Since 1681 equals 41², the triangle with sides of 9 inches, 40 inches, and 41 inches satisfies the Pythagorean theorem, confirming it is a right triangle.
What is the radius of the following circle x+y=100
Answer:
r = 10Step-by-step explanation:
The equation of a circle in standard form:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the equation:
[tex]x^2+y^2=100\\\\(x-0)^2+(y-0)^2=10^2[/tex]
Therefore we have
the center (0, 0)
radius r = 10
What is the length of AB⎯⎯⎯⎯⎯ ? Enter your answer in the box. Round only your final answer to the nearest whole number. cm Triangle A B C has angle A labeled 80.4 degrees with its opposite side labeled 17 and angle C labeled 48.9 degrees with its opposite side labeled c.
Answer:
AB = 12.99
Step-by-step explanation:
To answer this problem, use the breast theorem.
[tex]\frac{sinA}{a} = \frac{sinC}{c}[/tex]
The side opposite angle C is denoted by the letter c. It is also denoted as AB side
We know that:
A = 80.4°
a = 17
C = 48.9
Then we have that:
[tex]\frac{sin(80.4\°)}{17} = \frac{sin(48.9\°)}{c}[/tex]
Now clear the variable c from the equation
[tex]c = \frac{sin(48.9\°)}{\frac{sin(80.4\°)}{17}}[/tex]
[tex]c = 12.99[/tex]
Using the coordinates of two points (84,80) and (74,65) determine the slope of the line of best fit
Answer:
2/3
Step-by-step explanation:
Given in the question two points
(84,80) and (74,65)
Here
x1 = 84
x2 = 74
y1 = 80
y2 = 65
Slope of line means gradient of line and formula to calculate gradient of line is
gradient = [tex]\frac{x2-x1}{y2-y1}[/tex]
plug values in the formula
[tex]\frac{74-84}{65-80}[/tex]
[tex]\frac{-10}{-15}[/tex]
cancel - sign
[tex]\frac{10}{15}[/tex]
2/3 is the gradient of line having coordinates (84,80) and (74,65)
Find the area and perimeter of the following figure
Answer:
143.79
Step-by-step explanation:
The area of the figure can be found by splitting it into two shapes - a semi circle and a trapezoid.
The area of a semi-circle is found using A = 1/2πr² where r = 4.5 since the diameter is 9. A = 1/2π(4.5)² = 31.79.
The area of the trapezoid is found using A = 1/2(a+b)h = 1/2(23 + 9)(7) = 112.
Together the area is 31.79 + 112 = 143.79.