Answer:
The vertex form of y = x² + 24x - 15 is y = (x + 12)² - 159
Step-by-step explanation:
The vertex form of the quadratic equation y = ax² + bx + c is
y = a(x - h)² + k, where
a is the coefficient of x²(h, k) are the coordinates of the vertex pointh = [tex]\frac{-b}{2a}[/tex] , where b is the coefficient of xk = y at x = hLet us use the facts above to solve the question
∵ y = x² + 24x - 15
∵ a is the coefficient of x² and b is the coefficient of x
∴ a = 1 and b = 24
∵ h is the x-coordinate of the vertex point
∵ h = [tex]\frac{-b}{2a}[/tex]
→ Substitute the values of a and b to find h
∴ h = [tex]\frac{-24}{2(1)}=\frac{-24}{2}[/tex]
∴ h = -12
→ To find k substitute y by k and x by h
∵ y = k and x = h
∴ k = (-12)² + 24(-12) - 15 = 144 - 288 - 15
∴ k = -159
∴ The coordinates of the vertex point are (-12, -159)
→ Substitute the values of a, h, and k in the vertex form above
∵ y = 1(x - -12)² + (-159)
→ Remember (-)(-) = (+) and (+)(-) = (-)
∴ y = (x + 12)² - 159
∴ The vertex form of y = x² + 24x - 15 is y = (x + 12)² - 159
Answer:
sure.
Step-by-step explanation:
y = 6x - 10
y = 2x + 2
Answer:
1. x= 5/3 or 1.6 and y= -10
2. x= -1 and y= 2
Step-by-step explanation:
1. y= 6x - 10, 0= 6x - 10, -6x= -10, x= 5/3
2. y= 2x + 2, 0= 2x + 2, -2x= 2, x= -1
You spend 3 2/3 hours hiking and an additional 3/4 hour to rest.
A) How much time did you spend hiking and resting?
____ Hours
B) How much more time did you spend hiking than resting?
____ Hours
Explain how you got your answer.
Answer:
A: 3 hours and 55 minutes
B: 3 hours and 40 minutes more time hiking than resting.
Step-by-step explanation:
solve for R
D = RT
PLZ HELP ME
Answer:
Distance = Rate x Time
Is that what you are trying to figure out?
Answer:
R=D/T
Step-by-step explanation:
since D equals R times T, R would equal D divided by T
y = 3x - 2 what is the answer
Answer:
[tex]x = \frac{2}{3}[/tex] [tex]y = -2[/tex]I hope this helps!
what is the slope intercept formula
Answer:
y=mx+b
Step-by-step explanation:
Answer:
y=mx+b
Explanation:
The slope-intercept formula is y=mx+b. The b represents the y-intercept, which is the point where a line on a graph meets the y-axis. The coordinates for this would be (0,b). The m represents the slope, which is the rate of change. The x represents any x variable that you plug in. The y represents the y variable.
POSSIBLE POINTS: 28.57
The flight path of a volleyball is modeled by the equation h (x) = -0.034x2 + 1.3z +5.5, where h(x) is the height of the volleyball and x is the
horizontal distance measured in feet from where the ball was hit. Determine the maximum height of the volleyball
O 19.118 feet
O 18.344 feet
O 17 926 feet
O 16.982 feet
O 15.004 feet
O 14.621 feet
O 13.955 feet
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1 2 3
4
5
6
ET Review
What is the the slope of the line through the following points?(7,-4) and (3,8)
3
-3
1
o 1
Answer:
-3
Step-by-step explanation:
slope for (1,5) (3,4)
Answer:
-1,2
Step-by-step explanation:
4-5=-1
3-1=2
y2-y1
x2-x1
Need help please ASAP
Answer:
D
Step-by-step explanation:
You have 4 chairs originally, added 2 and if you separate the tables you would get T=whatever the number is. i think
what is the value of this?
Answer:
4
Step-by-step explanation:
I used desmos
[tex]\textsf{Hey there!}[/tex]
[tex]\mathsf{\dfrac{-2(7-15)}{4}}\\\\\mathsf{7-15=-8}\\\\\mathsf{\dfrac{-2(-8)}{4}}\\\\\mathsf{-2(-8)=16}\\\\\mathsf{\dfrac{16}{4} = 4}\\\\\\\boxed{\boxed{\mathsf{Thus,\ your\ answer\ is: \boxed{\boxed{\mathsf{\bf{D.\ 4}}}}}}}\checkmark[/tex]
[tex]\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Cait went apple picking with 3 friends. The 4 of them picked 17.4 lbs of
apples and want to split it equally. How many lbs of apples do they each
get?
Answer:
4.35 pounds each gets
Step-by-step explanation:
if you divide 17.4 by 4 you get 4.35 pound per each of the 4 people get
In triangle TRS, TZ = (3x) inches and WZ = (2x - 3) inches. Triangle T R S has centroid Z. Lines are drawn from each point to the midpoint of the opposite side to form line segments T W, R V, and S U. [Figure may not be drawn to scale] What is WZ? 6 inches 9 inches 18 inches 27 inches
Answer:
it is 9
Step-by-step explanation:
The value of WZ will be equal to WZ= 9 inches so the correct option is B.
What is trigonometry?
The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.
We have: U is the midpoint of TR, V is the midpoint of TS and W is the midpoint of SR
This means that.Z is the centroid of the given triangle centroid point divides any median in the triangle in the ratio of 2:1 from the vertex
This means that:
TZ = 2ZW
3x = 2(2x-3)
3x = 4x - 6
x = 6
Now, we get WZ as follows:
WZ = 2x - 3 and x = 6
WZ = 2(6) - 3
WZ = 12 - 3
WZ = 9 in
Therefore the value of WZ will be equal to WZ= 9 inches so the correct option is B.
The complete image of the triangle is attached with the answer below.
To know more about Trigonometry follow
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Don’t know answer help!!!
Answer:
Step-by-step explanation:
AA
Item 8
POSSIBLE POINTS: 11.11
In math class, the teacher asked students to randomly select a card and roll a number cube. There were 6 yellow cards, 4 blue, 8 red and 7 green cards. The number cube was numbered 1 through 6. What was the probability of choosing a green card and rolling an odd number?
14%
24%
48%
36%
Answer:
24% is the answer
Step-by-step explanation:
GEOMETRY HELP PLEASEEEEEEEEEE
Lesson 5-1 Exploring What Makes Triangles Congruent Practice and Problem Solving: A/B
Similar triangles may or may not be congruent.
The corresponding parts of XYZ and NPQ are: [tex]\mathbf{Z \cong Q}[/tex] , [tex]\mathbf{YZ \cong PQ}[/tex] , [tex]\mathbf{X \cong N}[/tex] , [tex]\mathbf{NQ \cong XQ}[/tex] , [tex]\mathbf{PN \cong YX}[/tex].The unknown values are: [tex]\mathbf{y = 18}[/tex] , [tex]\mathbf{z = 12}[/tex] , [tex]\mathbf{L = 60}[/tex] , [tex]\mathbf{C = 60}[/tex], [tex]\mathbf{AC = 24}[/tex].The congruent parts are: KL and RQ, KJ and RS, QS and LJQuestion 1 to 6:
Triangles XYZ and NPQ are similar triangles.
This means that:
Angles Z and Q, lines YZ and PQ, angles P and Y, angles X and N, lines NQ and XZ, lines PN and YX are corresponding sides and angles
Question 7 to 12:
Triangles LMN and CBA are similar triangles.
This means that:
[tex]\mathbf{7z+6 = 5y}[/tex]
[tex]\mathbf{2y-12 = z + 12}[/tex]
Collect like terms
[tex]\mathbf{2y= z + 12+12}[/tex]
[tex]\mathbf{2y= z + 24}[/tex]
Make z the subject
[tex]\mathbf{z = 2y -24}[/tex]
Substitute [tex]\mathbf{z = 2y -24}[/tex] in [tex]\mathbf{7z+6 = 5y}[/tex]
[tex]\mathbf{7(2y -24) + 6 = 5y}[/tex]
[tex]\mathbf{14y -168 + 6 = 5y}[/tex]
[tex]\mathbf{14y -162 = 5y}[/tex]
Collect like terms
[tex]\mathbf{14y -5y = 162}[/tex]
[tex]\mathbf{9y = 162}[/tex]
Divide both sides by 9
[tex]\mathbf{y = 18}[/tex]
Recall that: [tex]\mathbf{z = 2y -24}[/tex]
[tex]\mathbf{z = 2 \times 18 - 24}[/tex]
[tex]\mathbf{z = 12}[/tex]
[tex]\mathbf{L = 60}[/tex]
[tex]\mathbf{LN = 2y - 12}[/tex]
[tex]\mathbf{LN = 2 \times 18 - 12}[/tex]
[tex]\mathbf{LN = 24}[/tex]
[tex]\mathbf{C = L}[/tex]
[tex]\mathbf{C = 60}[/tex]
[tex]\mathbf{AC = LN}[/tex]
[tex]\mathbf{AC = 24}[/tex]
Question 13:
The congruent parts are: KL and RQ, KJ and RS, QS and LJ
Read more about congruent and similar triangles at:
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2xy^2 ( - 3x^2 y^2 + 4x)
Answer:-6x^3y^4+8x^2y^2
Step-by-step explanation:
Solve each system by elimination.
1) -r – 2s + t = 1
6r - + 4t = -28
-3r + 5s – 4t = 26
Answer:
s = 54/31
r= -156/31
t= -17/31
Step-by-step explanation:
If a roof is 24 feet high and if you leaned a 26 foot ladder against the side of a building how far away from the building is the base of a ladder to reach the roof
Answer: 35.4 feet.
Step-by-step explanation:
Given data:
Height of the roof = 24 feet
Height of the ladder = 26 foot
Solution:
c^2 = a^2 + b^2
a = 24
b = 26
c^2 = 24^2 + 26^2
c = √576 + 676
c = √1252
c = 35.4 feet
The foot of the ladder is 35.4 foot away from the top of the ladder.
Answer:
The distance between the base of the ladder and the building is 10 ft
Step-by-step explanation:
Here, we want to calculate the distance between the foot of the ladder and the building
To get this, we need to have a pictorial representation. Please check the attachment for this
From the pictorial representation, we can see a right angled triangle with a hypotenuse of 26 feet and the other side being 24 feet. We now need to get the third side of this triangle which represents the distance we want.
Mathematically, we can calculate the distance using Pythagoras’ theorem which states that the square of the length of the hypotenuse is equal the sum of the squares of the two other sides of the triangle.
Let the distance we are looking for be D
26^2 = 24^2 + D^2
D^2 = 26^2 - 24^2
D^2 = 100
D^2 = 10^2
D = 10 feet
Marsha is driving 600 total miles on a trip. She has already driven 2/5 of the distance. How far has Marsha driven?
A. 120 miles
B. 240 miles
C. 300 miles
D. 360 miles
Determine the GCF of 18xy and 12xy
Answer:
If im correct im pretty sure its 6xy
The GCF of 18xy and 12xy is 6xy.
What is Greatest Common Factor?The largest factor that splits both numbers is said to be the greatest common factor. List the prime factors of each integer before calculating the greatest common factor.
18 and 24 share one 2 and one 3 in common.
, so 2 x 3 = 6 is the GCF of 18 and 24.
Given:
18xy and 12xy
now, factoring the above terms
18xy = 2 × 3 × 3 × x × y
12xy= 2 × 2 × 3 × x × y
So, 18xy & 12xy = 2 x 3 xy = 6xy
hence, the GCF of 18xy and 12xy is 6xy.
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At hoffman's bike rentals,it cost $35 to rent a bike for 7 hours .How many hours of bike does the customer get per dollar?please help
Answer:
your answer is 5 dollars per hour
Step-by-step explanation:
35/7 = 5
Answer
Answer is 5 dollars per hour
Step-by-step explanation:
35/7 = 5
Question 15
Consider this set of ordered pairs: {(-2,-1), (2,1), (1,5), (-2,4)}. What is the range?
A
{-2, 1, 2}
B
All Real Numbers
С
{-1, 1,4,5)
D
{-2,-1, 1, 2, 4, 5)
Answer:
Option (C)
Step-by-step explanation:
Domain of a function is a set of x-values (input values) of the function.
Similarly, Range of a function is a set of y-values (output values).
Given set of ordered pairs is {(-2, -1), (2, 1), (1, 5), (-2, 4)}.
Domain → {-2, 2, 1, -2}
Range → {-1, 1, 4, 5}
Option C will be the correct option.
A baker has 5 bags of raisins in the cupboard. Each bag weighs 24 ounces. How many pounds of raisins does the baker have in the cupboard?
Answer:
7 1/2 pounds
Step-by-step explanation:
5 x 24 = 120
16oz = 1 pound
120oz = 7 1/2 pounds
Answer:
7.5 lbs of raisins
Step-by-step explanation:
24 x 5 = 120 ounce (oz)
1 lb = 16 oz
120 ÷ 16 = 7.5 lbs
what is the equation of the line that passes through the point (4,-5) and is parallel to the line y=1/2x+5
Answer:
y=1/2x - 7
Step-by-step explanation:
Since the lines are parallel, this means that the slopes will be the same, only the y-intercept will change. I graphed this out to find the answer.
-4(1+ 5-6- (42+5)
I really need the answer asap please and thanksss
Answer:
Read left to right
Do parenthesis first
-4 ( 1 + 5) ^2
-4 (6) ^2
Then exponent
6^2 = 6 x 6 = 36
-4 x 36 = -144
Then divide
-144 / 6 = -24
Then the next parenthesis
(42+5) = 47
-24 - 47 = -71
Step-by-step explanation:
A school wants to buy a chalkboard that measures 3 feet by 4 feet the chalkboard cost $6.14 per square foot. How much will the chalkboard cost
Answer:
$49.12
Step-by-step explanation:
Can somebody answer quick please!
Answer:27/2
Step-by-step explanation: The ratio stays the same. So 4/6 = 9/x. Solve that and get 27/2
Answer: 18 in.
Step-by-step explanation:
m to the power of 4 =
when m is 2/3
plz help me
Answer:
WAIT I MESSED UP DONT ANSWER THAT
Step-by-step explanation:
Answer:
[tex]\frac{16}{81}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3} ^{4} = \frac{16}{81}[/tex]I hope this helps!
if you have s3x 365 times how much is it a day?
this was from my math book
Answer:
Okay first okay this was not from your math book people actually need help on questions and here you are.
Step-by-step explanation:
Write the equation of the line that passes through (-3, -20) and (1,4).
Answer:
y=6x-2
Step-by-step explanation:
The equation of the line is y=mx+b
FINDING SLOPE: To find the slope of a given line use the equation [tex]\frac{y2-y1}{x2-x1}[/tex]
So x1=-3, y1=-20 and x2=1, y2=4
Plug those numbers into the equation: [tex]\frac{4-(-20)}{1-(-3)}[/tex] and we get the slope which is 6.
FINDING Y-INTERCEPT: Then we find the y intercept by plugging in our points (you can choose) I will use (1,4) and solve.
y=6x+b
4=6(1)+b
b=-2
