The compound inequality in this problem is represented by:
y > -(x + 2)² + 6.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
For this problem, the vertex is at (-2,6), hence:
h = -2, k = 6.
y = a(x + 2)² + 6.
When x = 0, y = 2, hence we use it to find a as follows:
2 = 4a + 6
a = -1.
Hence:
y = -(x + 2)² + 6.
The inequality is the interior of the parabola, hence values greater, and the parabola is dashed, hence it is an open interval and the inequality is given by:
y > -(x + 2)² + 6.
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Approximate + √50 to the nearest hundredth.
07.07
10.14
11.14
10.21
Answer:
7.07
Step-by-step explanation:
think about some perfect square values
7x7=49, which is very close to 50
so 7.07
Answer:
7.07
Step-by-step explanation:
√50≈7.07 because 7*7=49
The probability that a car has two doors, given that it is red, is 0.6 . The probability that a car has two doors and is red is 0.2 . What is the probability that a car is red?
The probability that a car is red is 1/3
What is the probability that a car is red?The given parameters are
P(Car has two doors, given that it is red) = 0.6
P(car has two doors and is red) = 0.2
The probability that a car is red is
P(Red) = P(car has two doors and is red)/P(Car has two doors, given that it is red)
This gives
p(Red) = 0.2/0.6
Evaluate
p(Red) = 1/3
Hence, the probability that a car is red is 1/3
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Evaluate the related serious of eatch sequence
1. The sequence will be 13 + 2( n - 1).
2. The sequence will be 22 + 6(n - 1).
How to illustrate the information?1. It should be noted that the common difference is 15 - 13 = 2
First term = 13
Therefore, the sequence will be:
= a + (n - 1)d.
a = first term
d = difference
n = numbers
= 13 + 2( n - 1).
2. Common difference = 28 - 22 = 6
First term = 22
The sequence will be:
a + (n - 1)d
= 22 + 6(n - 1)
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Suppose y varies directly with x . If x is 30 when y is 10 , what is x when y is 9 ?
a. 3
b. 27
c. 29
d. 300/9
Answer: Maybe D I'm not sure
Step-by-step explanation:
Convert 10 weeks to minutes
O 1.008 x 10² min
1.008 x 105 min
1.008 x 10³ min
O 1.008 x 104 min
6 cm
6 cm
18 cm
9.5 cm
3cm
11cm
9cm
6cm
Answer: 68.5
Step-by-step explanation:
6 cm + 6 cm + 18 cm+ 9.5cm + 3cm + 11cm+ 9cm+ 6cm= 68.5
~Hope this helps ;0~
If the faster stone takes 10.0 s to return to the ground, how long will it take the slower stone to return? t = nothing s
The slower stone will take 3.33 seconds if the faster stone takes 10s to return to the ground.
What is linear acceleration?It is defined as the rate of change in linear velocity with respect to time. It is also known as linear acceleration.
From the motion equation:
s = ut + at²/2
From the data given:
s = 0
0 = 3u(10) - 9.8(10)²/2
After solving:
u = 16.33 m/s
To calculate for time:
s = ut + at²/2
s = 0
u = 16.33
0 = 16.33t + 9.8t²/2
t = 3.33 seconds
Thus, the slower stone will take 3.33 seconds if the faster stone takes 10s to return to the ground.
The complete question is:
Two stones are thrown vertically upward from the ground, one with three times the initial speed of the other.
(a) If the faster stone takes 10s to return to the ground, how long will it take the slower stone to return?
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A square has an area of 90 square inches. What is the length of a side of the square in inches?
PLEASE HELP
PLEASE SHOW HOW U CHECKED UR WORK
Answer:
x = 3
Step-by-step explanation:
2(4 + 3x) + 6 = 32 ( subtract 6 from both sides )
2(4 + 3x) = 26 ( divide both sides by 2 )
4 + 3x = 13 ( subtract 4 from both sides )
3x = 9 ( divide both sides by 3 )
x = 3
As a check
substitute x = 3 into the left side of the equation and if value obtained is equal to the right side (32) then it is a solution to the equation.
2(4 + 3(3)) + 6
= 2(4 + 9) + 6
= 2(13) + 6
= 26 + 6
= 32
left side = right side
then x = 3 is the solution to the equation
Answer:
[tex] \sf \: x = 3[/tex]
Step-by-step explanation:
[tex] \sf \rightarrow \: 2(4 + 3x) + 6 = 32[/tex]
Apply the distributive property
[tex] \sf \rightarrow8 + 6x + 6 = 32[/tex]
Combine like terms
[tex] \sf \rightarrow 14 + 6x = 32[/tex]
Rearrange variables to the left side of the equation
[tex] \sf \rightarrow 6x = 32 - 14[/tex]
Calculate
[tex] \sf \rightarrow 6x = 18[/tex]
Divide both sides by the coefficient of 6
[tex] \sf \rightarrow \frac{6x}{6} = \frac{18}{6} [/tex]
Calculate
[tex] \sf \rightarrow x = \frac{18}{6} [/tex]
[tex] \sf \rightarrow \: x = 3[/tex]
Find a₁ for a geometric sequence with the given terms. a₅ = 112 and a₇ = 448
The first term of the geometric sequence is a(1) = 7.
The nth term of a geometric sequence is given by:
a(n) = a(1) . rⁿ⁻¹
Where:
a(1) = the first term
r = ratio
Parameter given in the problem:
a(5) = 112
Plug n = 5 into the formula
a(1) . r⁵⁻¹ = 112
a(1) . r⁴ = 112 ....... (1)
a(7) = 448
Plug n = 7 into the formula
a(7) = a(1) . r⁶
448 = a(1) . r⁶ ..... (2)
Divide (2) by (1)
448 : 112 = r⁶ : r⁴
4 = r²
Since r² = 4, then r⁴ = ( r² )² = 4² = 16.
Substitute r⁴ = 16 into equation (1):
a(1) . 16 = 112
a(1) = 112/16 = 7
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Suppose y varies directly with x , and y=2 when x=-2 . Find the constant of variation. Then find the value of x when y=3 .
The value of x when y=3 is x=-3.
y ∝ x
y=kx
where k is the constant of proportionality.
put x=-2, y=2
2=k*-2
k=-1
now it's given that y=3 putting in the equation
y=kx
3=-1*x
x=-3
The value of x when y=3 is x=-3.
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Yama stated that △KLM≅△PLN by the HL Theorem. what mistake did yama make?
The triangles are congruent by the SAS theorem not the HL Theorem
How to determine the mistake in Yama's solution?The statement is given as
Yama stated that △KLM≅△PLN by the HL Theorem
From the figure, we can conclude that the triangles are truly congruent
This is evident by the marks on the corresponding angle and the corresponding sides of the triangles
From the figure, we have
1 corresponding angle
2 corresponding sides
This means that the triangles are congruent by the SAS theorem not the HL Theorem
Hence, the triangles are congruent by the SAS theorem not the HL Theorem
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21 times what equals 7
Answer: -3
Step-by-step explanation:
bro i was just doing that in math class
mariah is reading a book. the number of pages shhe has left to read can be modeled by the equation p = 300 - 50h where p is the number of pages she has left to read and h is the number of hours she has read. Based on this model, how many hours of reading does it take Mariah to read 200 pages
This Question will be worth 20 points and a Thank you bc ion know how to give brainliest
It takes 10 hours to read 200 pages
How to determine the number of hours?The function is given as
P = 300 - 50h
When she reads 200 pages, we have
300 - 50h = 200
Subtract 300 from both sides
-50h = -500
Divide by -50
h = 10
Hence, it takes 10 hours to read 200 pages
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Write an equation for the line on the graph below:
Answer:
x=4
Step-by-step explanation:
This line has an undefined slope since it goes straight up
The line falls on the x coordinate 4
Use the given statement to find the measure of numbered angle.
∠6 and ∠ 8 are; complementary m ∠8=47 .
∠6 = 43°
If two angles sum to 90 degrees, they are said to be complementary angles. In other terms, a right angle is created when two complementary angles are combined (90 degrees). Angles 1 and 2 are complementary if their total of angles equals 90 degrees (i.e., ∠1 + ∠2 = 90°), and as a result, they are referred to as each other's complements.
Now as per the question the given angle is
∠8 = 47°
It is also given that ∠6 and ∠8 form are complementary angles. Therefore it means that the sum of both the angles will be 90°
∠6 + 47° = 90°
Now subtracting 47 from both sides we will get :
∠6 = 90 - 47 = 43°
Therefore, ∠6 = 43°
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3x - 16=54 what is the value of x
Answer:
I think it is 23.333
Step-by-step explanation:
I added 16 to both sizes and got 3x=70
then divide 70 by 3 and got 23.333
Solve each system.
0.02a - 1.5b = 4 , 0.5b - 0.02a = 1.8
Answer: (-235, -5.8)
Step-by-step explanation:
elimination
Example 1 PR00F Write the specified type of proof.two-column proof
Given: AB ≅ED, CA ≅ CE ; AC bisects BD .
Prove: Δ A B C≅ΔE D C
In the accompanying diagram of ABC, AB ≅ AC,. BD = 1. 3. BA, and CE = 1. 3. CA. Triangle EBC can be proved congruent to triangle.
What do you mean by congruent?
Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.Triangles. Congruent
∆ABC ≅ ∆ DEF.
1. AB ≅ DE
2. BC ≅ EF
3. AC ≅ DF
4. ∠ A ≅ ∠ D
5. ∠ B ≅ ∠ E
6. ∠ C ≅ ∠ F
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Which expression is equivalent to 8x^3 − 64 when factored completely?
a
(2x − 4)(4x^2 + 8x + 16)
b
(2x − 4)(4x^2 − 8x + 16)
c
(2x + 4)(4x^2 + 8x + 16)
d
(2x + 4)(4x^2 + 8x − 16)
The expression that iis equivalent to 8x³ − 64 when factored completely will be A. (2x − 4)(4x² + 8x + 16)
How to calculate the expression?It should be noted that (2x − 4)(4x² + 8x + 16) will be:
= (2x − 4)(4x² + 8x + 16)
= 8x³ + 16x² + 32x - 16x² - 32x - 64
= 8x³ - 64
Therefore, the correct option is A.
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Given f(x)=(x−2)2+15 what is the the value of f(11)
The output value of f(11) in the given function f(x) = ( x − 2 )2 + 15 is 33
What is the output value of f(11) in the given function?Given the data in the question;
f(x) = ( x − 2 )2 + 15f(11) = ?To determine the output value of f(11), replace all the occurrence of x with 11 in the function.
f(x) = ( x − 2 )2 + 15
f(11) = (11−2)2 + 15
f(11) = (9)2 + 15
Remove the parenthesis
f(11) = 9×2 + 15
f(11) = 18 + 15
f(11) = 33
Therefore, the output value of f(11) in the given function f(x) = ( x − 2 )2 + 15 is 33.
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Solve for X on the triangle.
When Rachel stands next to her cousin, Rachel's shadow is 2 feet long and her cousin's shadow is 1 foot long. If Rachel is 5 feet 6 inches tall, how tall is her cousin?
When measuring height, it is necessary to represent both the vertical position and the separation between the minimum and maximum place or location. Rachel is 5 feet 6 inches tall, the tall is her cousin exists 2 feet 9 inches.
What is meant by tall?In math, tall can be defined as the vertical distance from the top to the base of the object. Tall is the distance between an object's highest and lowest points.
The measurement of an object's height from the base to the top is known as tall. It is sometimes referred to as altitude in geometry. The vertical distance between the lowest and highest point is measured. In coordinate geometry, it is often the measurement along the y-axis of an object.
Rachel/Cousin = Rachel's shadow / Cousin's shadow
5 feet 6/x = 2/1
simplifying the above equation, we get
5ft 6 = 2x
x = 5ft 6/2
x = 66in/2
x = 33 in
x = 2ft 9inch
Therefore, the value of x = 2ft 9inch.
Rachel is 5 feet 6 inches tall, the tall is her cousin exists 2ft 9inch.
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Find the missing term of each geometric sequence. It could be the geometric mean or its opposite. 9180,-1-255, . . . . . . .
The missing term of the GP is: 1530.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Given: 9180, ___, 255.
To find: the missing term of the geometric sequence.
Finding:
The geometric mean of a geometric sequence is used to find the term between two term of a geometric sequence.
Thus, Let the missing term by x.
Then, x = [tex]\sqrt{9180\times255} = \sqrt{2340900}=1530.[/tex]
Hence, the missing term of the geometric sequence is 1530,
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Use the quadratic formula to solve for x.
2x² +7x+1=0
Answer:
Step-by-step explanation:
you can use the slide divide bottoms up method for this.
slide the 2 over to the 1 which gives:
x²+7x+2=0
then apply the quadratic formula to get
-7±√7²-4(1)(2)
______________
2
then we have
-7±√41÷2
Find the sum of each finite arithmetic series. 7+14+21+ . . . . . . +105
The sum of the given finite arithmetic series 7+14+21+ . . . . . . +105 is S(5) = 840
The formula for the nth term in an arithmetic series is given by:
a(n) = a(1) + (n-1) . d
Where:
a(1) = the first term
d = the common difference = a(n) - a(n-1)
The given arithmetic series:
7+14+21+ . . . . . . +105
We can infer that:
a(1) = 7
d = 14 - 7 = 7
Find n that lead to a(n) = 105 by substituting a(1) = 7 and d = 7 into the formula:
a(n) = a(1) + (n-1) . d
105 = 7 + (n-1) . 7
105 = 7n
n = 15
Use the sum formula for n = 15.
S(n) = n/2 [a(1) + a(n)]
S(15) = 15/2 (7 + 105)
S(15) = 15 . 56 = 840
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B is between A and C. If AC = 31, AB = x–6, and BC = 2x+10, find the value of x.
Answer:
Step-by-step explanation:
The answer is I.D.K
Simplify each expression. 8 . 7 . 6 . 5 .4
Answer:
6720
Step-by-step explanation:
[tex](8)(7)(6)(5)(4) \\ \\ =(56)(30)(4) \\ \\ =56(120) \\ \\ =6720[/tex]
HELP ASP SHOW UR WORK ILL GIVE BRAINILEST
Answer:
Step-by-step explanation: 2x+12x = 14x
14x=70
70/14 = 5
x = 5
Answer: x=29
Step-by-step explanation:
12=70-2x
12=-2x+70
Subtract 70 from both sides: 12-70=-2+70-70
-58=-2x
Divide both sides by the same factor: -58/-2=-2x/-2
x=29
A runner charted how long it took her to run certain distances. Here is the information she gathered: 0 8 16 24 0 1 2 3 At this pace, how long will it take her to run 6 miles?
It will take 48 min . to run 6 miles .
Given : In 0 min 0 miles .
In 8 min . 1 mile .
In 16 min . 2 miles .
In 24 min . 3 miles .
To find : how long will it take to run 6 miles
Calculation :
0 mile = 0 min
1 mile = 8 min
2 mile = 16 min
3 mile = 24 min
Therefore , avg . is of 8 min . per mile .
Hence , it will take ( 6 * 8 ) min . = 48 min . to run 6 miles .
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