Answer:
6
Step-by-step explanation:
A=5-x^2+2x
Rewriting
A = -x^2 +2x+5
This is a downward opening parabola so the maximum value is at the vertex
Factor out the negative sign out of the first two terms
A = -(x^2 -2x) +5
Complete the square
-2/2 = -1 -1^2 = 1
Add 1 inside the parentheses Remember the negative sign out front so -1(1) is really adding -1 so we need to add 1 outside of the parentheses
A = -(x^2-2x+1) +1 +5
A = -(x-1)^2 +6
This is in vertex form
y = a(x-h)^2 +k where (h,k) is the vertex
The maximum occurs at x=h and the value is k
The maximum is 6
A group of students is arranging squares into layers to create a project. The first layer has 5 squares. The second layer has 10 squares. Which formula represents an arithmetic explicit formula to determine the number of squares in each layer ?
Answer: Its B i just took the test
Step-by-step explanation:
What is the area
Help quick pls
Answer:
22 cm
Step-by-step explanation:
just add
Answer:
50 + [tex]5\sqrt{6}[/tex] =
62.24744871
Step-by-step explanation:
10* 5 = 50
triangle 5^2 + x^2 = 7^2
x = [tex]\sqrt{24 }[/tex]
area triangle = 1/2 * [tex]\sqrt{24 }[/tex] *5
[tex]\sqrt{24} = 2\sqrt{6}[/tex]
area triangle = [tex]5\sqrt{6}[/tex]
There are 135 people in a sport centre. 73 people use the gym. 59 people use the swimming pool. 31 people use the track. 19 people use the gym and the pool. 9 people use the pool and the track. 16 people use the gym and the track. 4 people use all three facilities. How many people didn't use any facilities?
Answer:
24 people
Step-by-step explanation:
((The numbers are up there, so I am not going to define each variable.))
For starters, there is no overlap between the double facilities groups, except the triple facility users, so:
19 + 9 + 16 - 4 = 40 people
Since there is overlap between single and double groups, you will need to subtract, so:
Gym: 73 - 19 - 16 = 38
Pool: 59 - 19 - 9 = 31
Track: 31 - 9 - 16 = 6
Total for 1 facility: 38 + 31 + 6 - 4 = 71 people
((Minus 4 because the 4 triple facility users overlap the double facility users (problem is in layers: layer 1 minus layer 2, then minus layer 3).))
Next, add the totals:
71 + 40 = 111 people (using facilities)
135 - 111 = 24 people (who didn't use any)
(((I'm not 100% sure on this answer, so if someone could check my work, that would be much appreciated.)))
Instructions: Find the missing side of the triangle.
24 and 7
If 24 and 7 are the lengths of the legs of the right triangle, the missing side, which is the hypotenuse, has a length of 25.
To find the missing side of the triangle, we need more information about the triangle. Specifically, we need to know which side is missing: the hypotenuse (longest side) or one of the legs.
If 24 and 7 are the lengths of the legs of a right triangle, we can use the Pythagorean theorem to find the length of the hypotenuse.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
Let's label the hypotenuse as 'c' and the legs as 'a' and 'b'.
Using the Pythagorean theorem:
[tex]c^2 = a^2 + b^2[/tex]
Substituting the given values:
[tex]c^2 = 24^2 + 7^2\\c^2 = 576 + 49\\c^2 = 625[/tex]
Taking the square root of both sides:
c = √625
c = 25
Therefore, if 24 and 7 are the lengths of the legs of the right triangle, the missing side, which is the hypotenuse, has a length of 25.
To know more about lengths , here
https://brainly.com/question/28322552
#SPJ2
Find the y-intercept of the following equation. Simplify your answer.
y = -10x -3/7
Answer: (0, -3/7)
Step-by-step explanation:
The Y-intercept would be the value of y when x is at 0, which is when the Y axis is intercepted. -3/7 is the starting position of the function when the the X = 0.
What are the solutions to the system of equations?
{y=x²−4x+8
y=2x+3
Answer:
x = 1, y = 5
x = 5, y = 13
Step-by-step explanation:
y = x² − 4x + 8 .......(1)
y = 2x + 3 .......(2)
Substitute the value of y in equation 2 into equation 1
y = x² − 4x + 8
y = 2x + 3
x² − 4x + 8 = 2x + 3
Rearrange
x² − 4x − 2x + 8 − 3 = 0
x² − 6x + 5 = 0
Solve by factorization
Find the product you x² and 5. The result is 5x²
Find the factors of 5x² such that their sum will result in −6x. The factors are −x and −5x.
Replace −6x in the equation above with −x and −5x. This is illustrated below:
x² − x − 5x + 5 = 0
x(x − 1) − 5(x − 1) = 0
(x − 1)(x − 5) = 0
x − 1 = 0 or x − 5 = 0
x = 1 or x = 5
Substitute the value of x into equation 2 to obtain the value of y.
y = 2x + 3
x = 1
y = 2(1) + 3
y = 2 + 3
y = 5
x = 5
y = 2x + 3
y = 2(5) + 3
y = 10 + 3
y = 13
SUMMARY:
x = 1, y = 5
x = 5, y = 13
ABC is a right-angled triangle. Angle B = 90. Angle A = 36. AB = 8.7 cm. Work out the length of BC. Give your answer correct to 3 significant figures.
Answer: About 6.321 cm
Step-by-step explanation:
[tex]tan(x)=\frac{opposite}{adjacent}[/tex]
[tex]tan(36)=\frac{x}{8.7} \\\\x=8.7*tan(36)=6.3209...[/tex]
Write an equation
in slope y-intercept form A(2,6),m=0
Solve for b:
y = 0x + b
6 = 0 + b
b = 6
The answer is y = 0x + 6
is (the number in the photo) rational or irrational?
Answer:
irrational
Step-by-step explanation:
Find the area of a regular pentagon
with a side length of 10 cm. Round to
the nearest tenth.
10 cm
[? ] cm2
Step-by-step explanation:
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I neeeddddd helppppp it’s urgenttttttt!!!!!!!!
Answer:
x=7
Step-by-step explanation:
The sum of the arc of a circle is 360 degrees
85+5x+5+10x+5+-7+6x+6+17x = 360
Combine like terms
38x+94=360
Subtract 94 from each side
38x+94-94 = 360-94
38x = 266
Divide each side by 38
38x/28 = 266/38
x = 7
Find the distance between K(9, 2) and L(-3, 9) to the nearest tenth
Answer:
≈ 13.9
Step-by-step explanation:
Calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = K(9, 2) and (x₂, y₂ ) = L(- 3, 9)
d = [tex]\sqrt{(-3-9)^2+(9-2)^2}[/tex]
= [tex]\sqrt{(-12)^2+7^2}[/tex]
= [tex]\sqrt{144+49}[/tex]
= [tex]\sqrt{193}[/tex]
≈ 13.9 ( to the nearest tenth )
The slopes of two lines. Determine the value of ‘a’ that will make the lines
parallel
and perpendicular
Instructions: Find the measure of the indicated angle to the nearest
degree.
19
?
8
=
Answer:
? ≈ 65°
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos? = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{8}{19}[/tex] , then
? = [tex]cos^{-1}[/tex] ([tex]\frac{8}{19}[/tex] ) ≈ 65° ( to the nearest degree )
PLEASE HELP WITH BOTH SEPRATE QUESTIONS
1 Your mom asks you to take the family car to the gas station and put no more than 8 gallons of gas in it. Write an inequality for this scenario.
2Translate this statement into an inequality.
A number less than 5 is greater than 7
Answer:
(1) question no.1
x<=8
(2) question no.2
5<x<7
Answer:
1. 8≥g
2. A-5≥7
Step-by-step explanation:
Sin theta = 9/15. Find tan theta. A. 15/12. B. 9/12 C. 12/15 D. 12/9
Answer:
B
Step-by-step explanation:
[tex]Sin \ theta = \frac{9}{15}=\frac{Opposite \ side}{hypotenuse}\\[/tex]
Pythagorean theorem,
Adjacent side ² = hypotenuse² - opposite side²
= 15² - 9²
= 225 - 81
= 144
Adjacent side = √144 = √(12*12) = 12
[tex]Tan \ theta = \frac{opposite \ side}{adjacent \ side}= \frac{9}{12}[/tex]
v2 = u? + 2as
u = 12
a = -3
S =
= 18
(a) Work out a value of v.
Answer:
6√7 m/s
Step-by-step explanation:
Given,
u = 12
a = - 3
s = 18
v^2 = u^2 - 2as
= 12^2 - 2 ( - 3 ) ( 18 )
= 144 + 108
v^2 = 252
v = √252
v = 6√7 m/s
Step-by-step explanation:
hope it helps you...:)....
Which of the following is a geometric sequence?
ES EL PUNTO A. RPBHCGNDGE
{24a - 18b} =24a−18b I neeed help
0
(24a - 18b) = 24a - 18b
24a - 18b = 24a - 18b
collect like terms
24a - 24a = -18b + 18b
0 = 0
x(x - 2) = 4 please help
Answer:
[tex]x = 1 + \sqrt{5} x = 1 - \sqrt{5} [/tex]
see ss below
please show all work
Answer:
Solution given:
since Rosie walked 18 km INA first day.
so
first term[a]=18km
again
she walked 90% of what she walked the day before which means
common ratio decreasing
common ratio[r]90%=0.9
sum of 10th day[tex]S_{10}[/tex]=?
no of term (n)=10
now
we have
[tex]Sum_{10}=\frac{a(r^{n}-1)}{r-1}[/tex]
substituting value:
=[tex]\frac{18(0.9^{10}-1)}{0.9-1}[/tex]
=117.28km
in nearest 10 it is 117km
the total distance Rosie had travelled by the end of 10 days is 117km.
what is bigger 35% or 2/5
Answer:
35% = .35
2/5 = 4/10 = .4
.4 >.35
Step-by-step explanation:
Consider this equation. tan) 19 17 If 8 is an angle in quadrant II, what is the value of Cos() OA. 19 6 OB. 17 6 O c. V18 6 OD. 17
Using trigonometric identities, it is found that the value of [tex]\cos{\theta}[/tex] is given by:
B. [tex]\cos{\theta} = \frac{\sqrt{17}}{6}[/tex]
What is the tangent of an angle?It is given by the division of it's sine by it's cosine, that is:
[tex]\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}[/tex]
In this problem, the equation given is:
[tex]\tan{\theta} = -\sqrt{\frac{19}{17}}[/tex]
That is:
[tex]\frac{\sin{\theta}}{\cos{\theta}} = -\sqrt{\frac{19}{17}}[/tex]
[tex]\sin{\theta} = -\sqrt{\frac{19}{17}}\cos{\theta}[/tex]
The following identity is applied:
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
Then:
[tex]\left(-\sqrt{\frac{19}{17}}\cos{\theta}\right)^2 + \cos^2{\theta} = 1[/tex]
[tex]\frac{36}{17}\cos^2{\theta} = 1[/tex]
[tex]\cos^2{\theta} = \frac{17}{36}[/tex]
[tex]\cos{\theta} = \frac{\sqrt{17}}{6}[/tex]
More can be learned about trigonometric identities at https://brainly.com/question/24496175
Answer:
Hi sorry I just wanted to ask is it B or D? positive or negative?
Step-by-step explanation:
edmentum is the worst
The base of a triangular prism has an area of 35 m2. This triangular prism has a height of 7 m. What is the volume of this triangular prism?
Answer:
The volume is 245 m^2
Step-by-step explanation:
the volume formula is aways base time height, or V = bh
so plot the number in, 35 x 7 = 245
james cuts his 2 of his neighbor's lawn the first is 1000 m long and 100 m wide what is the area
Answer:
100,000m^2
Step-by-step explanation:
The area formula is length multiplied by width:
A=l x w
Substitute in the values for length and width
A= 1000 x 100
Solve for A
A= 100,000m^2
Answer: 100,000 m² or 1 × 10⁵ m²
Step-by-step explanation:
Concept:
Here, we need to know how to calculate the area of a rectangle.
Area = w · l
w = width
l = length
Solve:
Width = 100 m
Length = 1000 m
Area = w · l
Area = (100) (1000)
Area = 100,000 m²
Hope this helps!! :)
Please let me know if you have any questions
Find the angle between the hands of a clock at 5:15
Answer:
67.5
Step-by-step explanation:
Answer:
the hour hand and minute hand on a 12-hour clock at 5:15. Again, the two angles created by the hour hand and minute hand at five-fifteen are 292.5 degrees and 67.5 degrees.
Step-by-step explanation:
Given HM = 24 and mHK = 66 , find x and y
Answer:
x=24,y=33
hopefully this answer can help you to answer the next question
Helpppp pleaseeee !!!!!!
Answer:
149 inches squared
Step-by-step explanation:
top rectangle: 25 * 7 = 175
second rectangle: 8 * (25 - 17) = 8^2 = 64
triangle in bottom right: 1/2 * (13 - 8) * (15 - 11) = 10
175 + 64 + 10 = 149 sq in
hopefully got this right!
Find the value of x. Round to the nearest tenth.
Answer:
x=400 m is the correct answer
find the equation of the line passing through (-4,1) and perpendicular to the line y=x/4+2
Answer:
y = -4x
Step-by-step explanation:
First, for an equation of form y=mx+b, m represents the slope. Therefore, for y=x/4+2 = (1/4)*x + 2, 1/4 is the slope. For perpendicular lines, the negative reciprocal of the slope is the slope of the line perpendicular to it. Therefore, the slope of our line is the negative reciprocal of 1/4.
To find the reciprocal of something, we can just divide 1 by it (another way to do this would be to flip the numerator and denominator, so 1/4 turns into 4/1). Therefore, 1/(1/4) = (1/1)/(1/4) = (1/1) * (4/1) = 4. The negative reciprocal is thus -4.
Our equation is therefore of form y = (-4) x + b. To solve for b, we can plug in the point given and solve for b in our equation. We have
-4 = (-4) * 1 + b
-4 = -4 + b
add 4 to both sides to isolate the b
0 = b
Therefore, our equation is
y= (-4)x + 0
y = -4x
