The value of r is 21 when s = -1 , t = 4 and u = 1/5 for the equation r = 3s² + 5 (t - 2u).
Quadratic Equation:
Quadratic equations are the polynomial equations of degree 2 in one variable of type.
The general form of a quadratic equation is,
f(x) = ax² + bx + c = 0
where a, b, c, ∈ R and a ≠ 0.
‘a’ is called the leading coefficient and
‘c’ is called the absolute term of f (x).
Given,
Equation is,
r = 3s² + 5 (t - 2u).
Here we need to find the value of r when the values of s = -1 , t = 4 and u = 1/5.
Apply the values on the given equation then we get,
=> r = 3 (-1)² + 5 ( 4 - 2(1/5))
Expand the values,
=> r = 3 (-1)² + 5( [20 -2] /5)
Here the value 5 is getting cancelled then we get,
=> r = 3(-1)² + 18
We know that the value of (-1)² = 1
So,
=> r = 3(1) + 18
=> r = 3 + 18
=> r = 21
Therefore, the value of r is 21.
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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
A plant is already 51 centimeters tall, and it will grow one centimeter every month. The plant's height, H (in centimeters), after m months is given by the
following function.
H(m)=51+m
What is the plant's height after 18 months?
M
The height after the 18th month is 69 cm
How to determine the height after the 18th month?The function definition is given as
H(m) = 51 + m
Where m represents the number of months
In this case;
m = 18
So, we have
H(18) = 51 + 18
Evaluate the sum
H(18) = 69
Hence, the height after the 18th month is 69 cm
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What is 2.56 written as a mixed number in simplest form
Answer: 2 [tex]\frac{14}{25}[/tex]
Step-by-step explanation:
2.56=
2 + 0.56=
2 + 56/100=
2 + 14/25=2 [tex]\frac{14}{25}[/tex]
A square has an area of 90 square inches. What is the length of a side of the square in inches?
is √ 144 a natural number
No that is a rational number
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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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
A group of 408 people is going on a boat tour. If each boat holds 7 people, how many people will be on the last boat?
There will be 2 people left in the last boat
How to calculate the number of people in the last boat ?A group of 408 people are going on a boat tour
The boat hold 7 people each
408/7
= 58.2
Hence 58 boats will be complete with 7 people on each boats and the number of persons in the last boat is 2
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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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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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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
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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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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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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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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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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How would the median change if the minimum number was removed?
54,6,17,49,27,46,18,34
A. increase by 3.5
B. decrease by 3.5
C. increase by 3.25
D. decreased by 3.25
E. None of the above
The median change if the minimum number was removed is a increase by 3. 5 . Option A
What is median?Median is simply known as the middle number in a given set of data.
It is also defined as the number separating the greatest number from the least in a given set of data.
Given the data;
54,6,17,49,27,46,18,34
Arrange from least to greatest
6 , 17, 18, 27, 34, 46, 49, 54
The median = 27 + 34/ 2 = 30. 5
Removing the minimum digit which is 6, we have;
17, 18, 27, 34, 46, 49, 54
Median = 34
Find the difference in median= 30. 5 = 34 = -3. 5
Thus, the median change if the minimum number was removed is a increase by 3. 5 . Option A
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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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87.912 ÷ 40.7 with process/ procedimiento
Answer: 2.16
Step-by-step explanation:
87.912 ÷ 40.7=
87.912/40.7=
(81.4+6.512)/40.7=
81.4/40.7 + 6.512/40.7=
2+6.512/40.7=2.16
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
Refer to ®F .
If DA = 7.4 centimeters, what is EF ?
If DA = 7.4 centimeters, then the radius of the circle EF is 3.7 inches.
What is meant by the radius of a circle?A radius of a circle or sphere is any of the line segments from its center to its perimeter in classical geometry, and in more modern usage, it is also their length. The name is derived from the Latin radius, which means both ray and spoke of a chariot wheel.
The radius of a circle is the distance between the circle's center and any point on its circumference. It is usually represented by the letters 'R' or 'r'. This number is significant in almost all circle-related formulas. A circle's area and circumference are also measured in terms of radius.
Here, DA is a diameter and EF is the radius.
Radius of a circle = 1/2 diameter
Where, d = 7.4
Radius of a circle, r = 1/2 d
Radius of a circle = 1/2(7.4)
Radius of a circle = 3.7
Therefore, the radius of the circle is 3.7 inches.
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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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21 times what equals 7
Answer: -3
Step-by-step explanation:
bro i was just doing that in math class
select two adjacent angles
Answer:
Angles U and V and angles T and P
Step-by-step explanation:
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
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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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
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:
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]
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
