Answer:
max = 150
Step-by-step explanation:
the maximum height is the value of the y- coordinate of the vertex.
given a quadratic equation in standard form : y = ax² + bx + c = 0 ( a ≠ 0 )
then the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
- 16x² + 64x + 86 = 0 ← is in standard form
with a = - 16 and b = 64 , then
[tex]x_{vertex}[/tex] = - [tex]\frac{64}{-32}[/tex] = 2
substitute x = 2 into the quadratic for corresponding y- coordinate
- 16(2)² + 64(2) + 86 = - 16(4) + 128 + 86 = - 64 + 128 + 86 = 150
vertex = (2, 150 )
then maximum height is 150 units
4 The following stem plot shows the number of text
messages that students send in one day. Draw a pie
chart that represents this data.
Number of Text Messages Students Sent in One Day
Stem
Leaves
o 37
1
0011223445 77 88 89
2 013557
Key: 10 = 10
The pie chart of the number of text messages sent by the students represents the stem plot using a circle graph
How to represent the stem plot on a pie chart?The stem plot is given as:
0 | 37
1 | 0011223445 77 88 89
2 | 013557
From the above stem plot, we have the following frequency table
SMS Frequency
0 - 9 2
10 - 19 16
20 - 29 6
Total 24
Next, we determine the relative frequency table
SMS Frequency Relative Frequency
0 - 9 2 2/24 = 8.33%
10 - 19 16 16/24 = 66.67%
20 - 29 6 6/24 = 25.0%
Total 24 100%
Next, we plot the pie chart
See attachment for the pie chart
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In ΔLMN, l = 3. 9 cm, m = 2. 7 cm and ∠N=133°. Find the area of ΔLMN, to the nearest 10th of a square centimeter
Answer:
3.9 cm²
Step-by-step explanation:
The area formula for a triangle when sides 'a' and 'b' and angle C are known is ...
A = 1/2ab·sin(C)
__
The area of the specified triangle is ...
A = 1/2(3.9 cm)(2.7 cm)sin(133°) ≈ 3.85058 cm²
The area of ΔLMN is about 3.9 square centimeters.
A population of 75 foxes in a wildlife preserve quadruples in size every 15 yr. the function is y = 75 x 4^x, where x is the number of 15-yr periods, models the population growth. How many foxes will there be after 45 yr? Help asap
Answer:
4800
Step-by-step explanation:
→ Find how 15yr periods there are in 45 years
45 ÷ 15 = 3
→ Substitute this value as x into the equation
75 × 4³ = 4800
10x -3 = -33
please help lol
Answer:
-3
Step-by-step explanation:
10x=-33+3 isolate the variable
10x=-30 divide by 10
X=-3
x=-3
Solution:First, add 3 to both sides:10x-3=-3310x=-33+310x=-30Now, divide both sides by 10:x=-3The value of x=-3Hope it helps.
Do comment if you have any query.
Find the lateral area of this cone.
Leave your answer in terms of a.
3 cm
+ 4cm
LA = [ ? ]7 cm2
=
T
Hint: Lateral Area of a Cone = tre
Where e = slant height
Step-by-step explanation:
For Slant Height (l)
(l)^2=(3)^2+(4)^2
Using Pythagoras Theroem,
(l)^2=9+16
(l)^2=25
l=5cm
For lateral surface area (pi*r*l)
pi*4*5
20pi cm^2
MARK ME AS BRAINLISTThe lateral area of the cone in terms of π, given that the cone has a radius of 4 cm is 20π cm²
How to determine the lateral area of the cone?First, we shall obtain the slant height of the cone. This is shown below:
Height (h) = 3 cmRadius (r) = 4 cmSlant height (L) = ?L² = r² + h²
L² = 4² + 3²
L² = 16 + 9
L² = 25
Take the square root of both side
L = √25
= 5 cm
Finally, we shall obtain the lateral area of the cone. This is shown below:
Radius (r) = 4 cmSlant height (L) = 5 cmLateral area (LA) =?LA = πrL
= π × 4 × 5
= 20π cm²
Thus, the lateral area of the cone is 20π cm²
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The table shows the estimated number of lines of code written by computer programmers per hour when x people are working. a 2-column table with 6 rows. the first column is labeled people working with entries 2, 4, 6, 8, 10, 12. the second column is labeled lines of code written hourly with entries 50, 110, 160, 210, 270, 320. which model best represents the data? y = 47(1.191)x y = 34(1.204)x y = 26.9x – 1.3 y = 27x – 4
The estimated number of lines of code written by computer programmers per hour when x people are working & the correct option is y = 27x - 4.
Table showing the estimated number of lines of code written by computer programmers per hour when x people are working & option given y= 47 * 1.191ˣ y= 34 * 1.204ˣ y=26.9x - 1.3 y = 27x - 4
To Choose the model which best represents the data.
What is choosing the best model data?To understand a set of data, it is helpful to organize it and provide summary descriptions of the set.
People Working lines of code
2 50
4 110
6 160
8 210
10 270
12 320
x y= 47 * 1.191ˣ y= 34 * 1.204ˣ y=26.9x - 1.3 y = 27x - 4
2 66.66 49.3 52.5 50
4 94.57 71.44 106.3 104
6 134.14 103.57 160.1 158
8 190.27 150.14 213.9 212
10 269.91 217.64 267.7 266
12 382.85 315.5 321.5 320.
Below 2 0 4 1
on line 0 0 0 2
Above 4 6 2 3
Therefore y = 27x - 4 is the best fit
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Answer:
y = 27x - 4
mark me as brainliest
Step-by-step explanation:
Matthew and his mom are sharing an apple pie. Matthew ate 2/3 of it and his mom ate 2/6 of it. How much more did Matthew eat than his mother
Answer:
2/6th or 1/3rd of the pie
Step-by-step explanation:
Subtract 2/6 from 2/3: convert 2/3 to 4/6. Then 4/6 less 2/6 is 2/6.
Matt ate 2/6th, or 1/3rd, more pie than did his mother.
Find the perimeter of the isosceles triangle with points A (0,0); B (3,3); and C (6,0)
Answer:
3+3+6=12
Step-by-step explanation:
the sides are both3 and bottomed is 6
rationalise 1/√7-√3
PLEASE GIVE ANSWER IT'S URGENT
[tex]\dfrac 1{\sqrt 7- \sqrt 3}\\\\\\=\dfrac{\sqrt 7 + \sqrt 3}{\left ( \sqrt 7 -\sqrt 3\right) \left( \sqrt 7 + \sqrt 3\right)}\\\\\\=\dfrac{\sqrt 7 + \sqrt 3}{\left(\sqrt 7 \right)^2 - \left(\sqrt 3 \right)^2}\\ \\\\=\dfrac{\sqrt 7 + \sqrt 3}{7-3}\\\\\\=\dfrac 14\left(\sqrt 7 + \sqrt 3\right)[/tex]
What is the missing statement in the proof? ∠BAC ≅ ∠DEC ∠ACD ≅ ∠ECB ∠ACB ≅ ∠ECD ∠BCA ≅ ∠DCA
It is Given that two lines segment, AC and BD bisect each other at C.
The missing statement is ∠ACB ≅ ∠ECD
What is the congruent triangle?Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
Given two lines segment, AC and BD bisect each other at C.
We have to prove that ΔACB ≅ ΔECD
In triangle ACB and ECD
AC=CE (Given)
BC=CD (Given)
so, as seen in options the angle ∠ACB ≅ ∠ECD due to vertically opposite angles
hence, the missing statement is ∠ACB ≅ ∠ECD
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Answer:
C.∠ACB ≅ ∠ECD
Step-by-step explanation:
please help please please
Answer:
1) 27
2) 63
Step-by-step explanation:
cos-1(17/38)= 63.425...= 63= angle C
90-63= 27=angle A
Let () = −22 − 8 + 4. Then (a) write the function in vertex form. (b) identify the vertex. (c) determine the x-intercept(s). (d) determine the y-intercept. (e) sketch the function. (f)
determine the axis of symmetry. (g) determine the minimum or maximum value of the function. (h) write the domain and range
Answer:
Graph the parabola y=x2−7x+2 .
Compare the equation with y=ax2+bx+c to find the values of a , b , and c .
Here, a=1,b=−7 and c=2 .
Use the values of the coefficients to write the equation of axis of symmetry .
The graph of a quadratic equation in the form y=ax2+bx+c has as its axis of symmetry the line x=−b2a . So, the equation of the axis of symmetry of the given parabola is x=−(−7)2(1) or x=72 .
Substitute x=72 in the equation to find the y -coordinate of the vertex.
y=(72)2−7(72)+2 =494−492+2 =49 − 98 + 84 =−414
Therefore, the coordinates of the vertex are (72,−414) .
Now, substitute a few more x -values in the equation to get the corresponding y -values.
x y=x2−7x+2
0 2
1 −4
2 −8
3 −10
5 −8
7 2
Plot the points and join them to get the parabola.
pls help me thank you
Answer:
C
Step-by-step explanation:
a and b add to 180 degrees also known as a straight line
Answer:
supplimentarry
Step-by-step explanation:
add up to be 180
The distance between San Francisco and Los Angeles is about 387 miles. If Takara leaves San Francisco and travels 6 hours at an average speed of 55 miles per hour, will she reach Los Angeles? How far will she travel?
Select the correct answer.
What is the solution to this system of equations?
x-2y = 15
2x+4y=-18
OA. x = 1, y=-6
OB. X= 1, y=-7
ОС. Х 3, y= -6
OD. x= 3, y=-7
Reset
Next
Answer:
O C. x = 3, y = -6
Step-by-step explanation:
x - 2y = 152x + 4y = -18Take Equation 1 and equate to x.
x - 2y = 15x = 2y + 15Now, substitute in Equation 2.
2x + 4y = -182(2y + 15) + 4y = -184y + 30 + 4y = -188y = -48y = -6x = 15 + 2(-6)x = 3Option CAnswer:
C) x = 3, y = -6
Step-by-step explanation:
[tex]\textsf{Equation 1}:x-2y=15[/tex]
[tex]\textsf{Equation 2}:2x+4y=-18[/tex]
Rewrite Equation 1 to make x the subject:
[tex]\implies x=15+2y[/tex]
Substitute into Equation 2 and solve for y:
[tex]\implies 2(15+2y)+4y=-18[/tex]
[tex]\implies 30+4y+4y=-18[/tex]
[tex]\implies 8y=-48[/tex]
[tex]\implies y=-6[/tex]
Substitute found value of y into Equation 1 and solve for x:
[tex]\implies x-2(-6)=15[/tex]
[tex]\implies x+12=15[/tex]
[tex]\implies x=3[/tex]
Therefore, the solution to the system of equations is:
x = 3, y = -6
Which expression represents the volume of the prism? x(x – 2) cubic units x(x 1) cubic units x2(x – 2) cubic units x2(x 1) cubic units
The expression that represents the volume of the prism is x²(x-2).
Given side of the base =[tex]x[/tex]
So, the area of the base =[tex]x^{2}[/tex]
Given the height of the prism = [tex]x-2[/tex]
What is the volume of the prism?The volume of the prism with base area A and height h is Ah.
So, the volume of the given prism with the base area [tex]x^{2}[/tex] and height [tex](x-2)[/tex] will be:
V= [tex]x^{2} *(x-2)[/tex]
V= [tex]x^{2} (x-2)[/tex]
Hence, the expression that represents the volume of the prism is x²(x-2).
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Answer:
its C trust me
Step-by-step explanation:
If log_b x = 2, log_b y = 5, log_b z = 4
What's log_b (x · y)
What's log_b ( xy^2/z^2)
[tex]\text{Given that,}\\\\\log_b x =2,~~ \log_b y=5,~~ \log_b z = 4\\\\\\\log_b(x\cdot y)\\\\=\log_b x + \log_b y~~~~~~~~~~~~~~~;[\log_b(MN) = \log_b M+ \log_b N ] \\\\=2+5\\\\=7\\\\\\\log_b\left( \dfrac{xy^2}{z^2}\right)\\\\=\log_b (xy^2) - \log_b z^2~~~~~~~~~~;\left[\log_b\left(\dfrac MN \right) = \log_b M - \log_b N \right] \\\\=\log_b x +\log_b y^2 - 2\log_b z\\\\=\log_b x + 2 \log_b y - 2 \log_b z\\\\=2+2 \cdot5 - 2 \cdot 4\\\\=2+10-8\\\\=10-6\\\\=4[/tex]
At a store, a 26 oz box of cereal costs $6.65, and a 38 oz box of cereal costs $10.98. What is the unit price of the box that is the better deal? Round your answer to the nearest cent.
Answer:
3.75.../ $1
Step-by-step explanation:
25 ounces ÷ 6.65
6.65 dollars ÷ 6.65
=
3.759398 ounces/1 dollar
solve for w and y
Please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
w = 10√2
y = 20
Step-by-step explanation:
Sum of interior angles of a triangle = 180°
Therefore, the triangle on the left (with side length 10) is a right triangle,
since 180° - 45°- 45° = 90°
As this triangle is also an isosceles triangle (since it has 2 equal angles), then it will have 2 sides of the same length.
So the legs of the right triangle are both 10 units.
Using Pythagoras' Theorem to calculate the hypotenuse of this triangle:
⇒ 10² + 10² = c²
⇒ 200 = c²
⇒ c = √200
⇒ c = 10√2
The triangle with side w and base y is also isosceles triangle with base angles of 45°.
Therefore, the sides are equal in length.
So w = hypotenuse of the left triangle = 10√2
We know that the horizontal distance between the left base vertex and the top vertex of this triangle is 10, therefore y = 10 + 10 = 20
Max goes to school which is 5 miles away he skips 3/14 of the way and then walk the rest of the way how many miles does he skip
Answer:
1.07142857143 (1 rounded)
Step-by-step explanation:
3/14 of 5 is 1.07142857143
Emma incorrectly gave the sum as 8 100 . explain what emma did incorrectly and use the model to correct her work. solve the problem in your answer.
Using the fraction model, Emma made a mistake by adding 5 and 3 to get 8/100, instead of 3/100 + 5/10 = 53/100.
What are Fractions?Fractions can be referred to as a part of a whole number.
The following are the information given that was omitted:
1 grid having 10 equal columns. 5 are shaded.
This can be expressed as a fraction, as 5/10.
Another identical grid shows, 100 squares with 3 of them shaded, which can be represented in fraction, as 3/100.
The model for the addition problem would be solved as:
3/100 + 5/10 = 53/100
Therefore, using the fraction model, Emma made a mistake by adding 5 and 3 to get 8/100, instead of 3/100 + 5/10 = 53/100.
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Solve the following exponent:
70
Answer 70 = 7070
Step-by-step explanation: denotes how many times to multiply the base (70)
4.2 divided by 6 blank tenths divided by 6
Answer: 0.11
Step-by-step explanation:
I hope i helped TvT
They got to an altitude of 500 feet. The balloon is tethered to the ground by a cable and the angle between the ground and the cable is 53º. Find the length of the cable
Answer:
about 626.1 ft
Step-by-step explanation:
The geometry of the problem can be modeled by a right triangle. The given angle is opposite the given side, and we are asked to find the hypotenuse. The relevant trig relation is ...
Sin = Opposite/Hypotenuse
__
Solving for the hypotenuse, we get ...
Hypotenuse = Opposite/Sin
cable length = (balloon height)/sin(53°) = (500 ft)/0.79864
cable length ≈ 626.1 ft
What type of triangle is defined by the following set of side lengths
10, 9, 5
Acute
Obtuse
Right
Not a triangle
Answer:
Acute
Step-by-step explanation:
Hope it helps you in your learning process.
Hello there.
Question:What type of triangle is defined by the following set of side lengths
10, 9, 5
Answer:
Acute
Step-by-step explanation:
The triangle perimeter is the sum of the lengths of its three sides.
[tex]p=a+b+c=10+9+5=24[/tex]
The semiperimeter of the triangle is half its perimeter. The semiperimeter appears in formulas for triangles to be given a separate name. the triangle inequality, the longest side length of a triangle is less than the semi perimeter.
[tex]s=\frac{p}{2} =\frac{24}{2} =12[/tex]
using Heron's formula
Heron's formula gives the area of a triangle when the length of all three sides is known.
[tex]T=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]T=\sqrt{12(12-10)(12-9)(12-5)}[/tex]
[tex]T=\sqrt{504}=22.45[/tex]
There you go :) I even calculated it for you.
Hope this helps!
If you have any questions please ask.
How many square feet of outdoor carpet will
we need for this hole?
Answer:
18
Step-by-step explanation:
If you x 12x6 the area would get you 72 you already used 6 and 12 you just times 6x3 and that gets 18. If this didnt help im sorry!
Tineka has a sack that contains 7/12 lb of jellybeans. If she splits the jellybeans into 2 piles of equal weight, how much will each pile weigh?
F 3/16
H 1 1/16
G 7/24
J Not here
The weight of each of the two piles Tineka split the jellybeans in the sack to is 7/24 lb.
What is the weight of each pile?
Division is when two numbers are grouped into equal parts using another number. The sign used to denote division is ÷.
In order to determine the weight of each pile, divide the weight of the sack by 2.
Weight of each sack = 7/12 ÷ 2
7/12 x 1/2 = 7/24
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(24x³y⁶)² divided by 4y²
show ur work
A golf ball is hit so that it travels a horizontal distance of 440 feet and reaches a maximum height of 190 feet. Determine a quadratic equation that models the path of the golf ball, assuming it starts at the origin. (4 points) Round the coefficient of x2 to the nearest ten-thousandths place, and round the coefficient of x to the nearest thousandths place. Using your understanding of parametric equations for projectile motion, what is the angle the ball takes off? Show your steps.
(1) A quadratic equation that models the path of the golf ball, is 16.0850t² - 110.560t - 190 = 0.
(2) The angle the ball takes off is 64.4⁰.
Equation of motion of the golf ballThe equation that models the motion of the gofl ball is calculated as follows;
Vertical motionVf² = V₀² - 2gh
at maximum height, Vf = 0
V₀² = 2gh
V₀ = √2gh
V₀ = √(2 x 32.17 x 190)
V₀ = 110.56 ft/s
Equation of motionh = V₀t - ¹/₂gt²
-190 = 110.56t - ¹/₂(32.17)t²
-190 = 110.56t - 16.0850t²
16.0850t² - 110.560t - 190 = 0
Horizontal motion440 = Vxt
Vx = 440/t
The time of motion, t is determined as follows;
16.0850t² - 110.560t + 190 = 0
a = 16.0850, b = -110.560, c = 190, solve using formula method
t = 8.3 s
Vx = 440 /8.3
Vx = 53.01 ft/s
Angle of projectiontan θ = (Vy) / (Vx)
tan θ = (110.56)/(53.01)
tan θ = 2.086
θ = tan⁻¹(2.086)
θ = 64.4⁰
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You’re given two side lengths of 3 cm and 5 cm. Which measurement can you use for the length of the third side to construct a valid triangle?
1. 8cm
2. 6cm
3. 4cm
4. 10cm
5. 2cm