The first term of an arithmetic progression of 4 terms and ratio equal to 4 whose sum is 100 is 19.
How to calculate arithmetic progression?The first term of an arithmetic progression can be calculated using the following expression:
Sn = n/2 [2a + (n − 1)d]
Where;
a = first termUn = sumn = no of termsd = common ratio100 = 2 [2a + (4 - 1)4]
100 = 4a + 24
4a = 100 - 24
a = 76/4
a = 19
Therefore, the first term of an arithmetic progression of 4 terms and ratio equal to 4 whose sum is 100 is 19.
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rationalize the denominator of the fraction (6)/(4+\sqrt(5))
The rationalization the denominator of the fraction (6)/(4+\sqrt(5)) is [tex]\dfrac{6(4-\sqrt(5))}{11}[/tex].
How to rationalize a fraction?Suppose the given fraction is [tex]\dfrac{a}{b+c}[/tex]
Then the conjugate of the denominator is given by b - c
Thus, rationalizing the fraction will give us
[tex]\dfrac{a}{b+c} \times \dfrac{b-c}{b-c} = \dfrac{a(b-c)}{b^2 - c^2}[/tex]
The given expression is
[tex]\dfrac{6}{4+\sqrt(5)}\\\\[/tex]
By rationalizing the denominator of the fraction
[tex]\dfrac{6}{4+\sqrt(5)}\times \dfrac{4-\sqrt(5)}{4-\sqrt(5)} \\\\\\\dfrac{6(4-\sqrt(5))}{4^2-(5)}\\\\\\\dfrac{6(4-\sqrt(5))}{11}[/tex]
Thus, the rationalization the denominator of the fraction (6)/(4+\sqrt(5)) is [tex]\dfrac{6(4-\sqrt(5))}{11}[/tex].
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need help with this graphing question please
Step-by-step explanation:
12 . The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Thinking about intercepts helps us graph linear equations..
How many liters each of a 24% iodine solution in a 40% iodine solution must be used to produce a total make sure of 100 L of 28% iodine solution
By weighted average, we need 75 liters of 24 % iodine solution and 25 liters of 40 % iodine solution to obtain 100 liters of 28 % iodine solution.
How to determine the volume associated with a given concentrationPhysically speaking, concentration is equal to the amount of solute divided by the volume of solution. We have two solutions with same solute and different concentration and can find the right proportion between the 24 % solution and the 40 % solution by concept of weighted average:
x · 24 + (1 - x) · 40 = 28
40 - 16 · x = 28
16 · x = 40 - 28
16 · x = 12
x = 3/4
By weighted average, we need 75 liters of 24 % iodine solution and 25 liters of 40 % iodine solution to obtain 100 liters of 28 % iodine solution.
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12. Find the solution to the system of equations by
using
substitution.
y = -2x + 13
4x + 8y = 20
A)(-7,-1)
B)(4,5
C)(7,-1)
D)(-3,7)
An auto weighing 2,000 pounds is on a street inclined at 10° with the horizontal. Find the force necessary to prevent the car from rolling down the hill. (Round your answer to the nearest whole number.)
347 pounds
14,397 pounds
2,462 pounds
Force (F) = WSin(angle)
F = 2000×Sin(10)
Therefore, F = 347lb.
what equation is equivalent to 2^3^x =10
Answer:
[tex]log_2(10)[/tex]
how to findSimplify the equation using logarithms.
part 1[tex]2^3x=10[/tex]
[tex]log_1_0(2^3x)=log_1_0(10)[/tex]
log rule ⇩
[tex]log_a(x^y)=y*log_a(x)[/tex]
move exponent out of log.
[tex]x*log_1_0(2)=log_1_0(10)[/tex]
part 2isolate variable further
[tex]x*log_1_0(2)=log_1_0(10)[/tex]
[tex]x=\frac{log_{10}(10)}{log_{10}(2)}[/tex]
formula for combining logs. ⇩
[tex]\frac {log_b(x)}{log_b(a)}=log_a(x)[/tex]
the result ⇩
[tex]x=log_2(10)[/tex]
How many classrooms would be necessary to hold 1,000,000 inflated balloons? (Assume one balloon is about 1 ft3 and a typical classroom is about 35 ft × 50 ft × 15 ft. Round your answer to the nearest number of classrooms.)
To hold 1,000,000 inflated balloons,
38 classrooms are needed.
What is volume?In three-dimensional space,
the amount of space taken by an object is the volume of that object.
The volume of the cubic,
= length x width x height
Given:
The dimensions of the normal classroom are 15 ft × 50 ft × 35 ft.
The volume of the classroom,
= 15 ft by 50 ft by 35 ft.
= 26250 cubic feet.
The number of classrooms,
= 1,000,000 / 26250
Simplifying the fraction,
we get,
= 38.09
≈ 38 to the nearest whole number.
Therefore, 38 classrooms are required.
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PLEASE HELP!!!!!!!!!! I'll NAME BRAINLIEST!!!!!!
Classify the expression by the number of terms.
5y^2-8+6y^4
Answer:
5x2-2x+1 The highest exponent is the 2 so this is a 2nd degree trinomial.
Step-by-step explanation: Also pls answer by question
Julian calculates the volume of a rectangular prism with the dimensions 3/4ft by 4 feet by 1/2 ft. His work is shown here.
What error did Julian make?
He multiplied the numerators incorrectly.
He multiplied the denominators incorrectly.
He simplified 12/6 incorrectly.
He wrote 4 as a fraction incorrectly.
Answer:
He multiplied the denominators incorrectly
Step-by-step explanation:
we know that
The volume of a rectangular prism is given by the formula
V=LWH
we have
L=3/4 ft
W=5/1 ft
H=1/2
substitute
V=(3/4)(5/1)(1/2)= 3x5x1= 15
₋₋₋₋₋₋₋₋ ₋₋₋₋ ft³
4x1x2= 8
therefore
He multiplied the denominators incorrectly
What is the y-intercept for this function?
a
(0, −3)
b
(3, 0)
c
(−9, 0)
d
(0, −9)
Answer:
d
Step-by-step explanation:
the y- intercept is the point on the y- axis where the graph crosses
the graph crosses the y- axis at point (0, - 9 )
then y- intercept = (0, - 9 )
The average profit on each car sold was $2430, correct to the nearest $10. Calculate the lower bound for the total profit. Write down the exact answer.
The lower bound for the profit is $2425.
What is the lower bound?When a number of rounded off to the nearest $10, it means that the value of the number in the units place, if greater than 5 becomes zero and one is added to the $10 number. If the number is less than 5, there is no change in the $10 number and the units number becomes 0
The possible values of the average profit are 2425, 2426, 2427, 2428, 2429, 2430. 2431. 2432, 2433, 2434
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EASY POINTS
What is the slope-intercept equation of this line?
Answer:
B
Step-by-step explanation:
The y-intercept is 8
The slope is -2x
Therefore the slope-intercept is y = -2x + 8
Fahari kicks a ball on the ground into the air. One
second after being kicked, the ball reaches its
maximum height of 16 feet above the ground, and
2 seconds after being kicked, the ball is back on the
ground. A quadratic function models the height h(t) ,
in feet, of the ball t seconds after Fahari kicks it.
Which equation defines this relationship?
The equation that defines the relationship between the height and the time and models the position of the ball in time is the quadratic function y = - 8 · t² + 24 · t.
How to derive a quadratic function for the height of a ball
Quadratic functions are polynomials of grade 2 of the form y = a · t² + b · t + c, where t and y are the time and the height of the ball, in seconds and feet, respectively. To determine the value of the three coefficients we need to know three different points of the form (t, y).
If we know that (t₁, y₁) = (0 s, 0 ft), (t₂, y₂) = (1 s, 16 ft) and (t₃, y₃) = (3 s, 0 ft), then the quadratic function is:
a · 0² + b · 0 + c = 0 (1)
a · 1² + b · 1 + c = 16 (2)
a · 3² + b · 3 + c = 0 (3)
The solution to this system is a = - 8, b = 24, c = 0.
The equation that defines the relationship between the height and the time and models the position of the ball in time is the quadratic function y = - 8 · t² + 24 · t.
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WHAT IS THIS HELP
if u put a bad answer i'll report
Answer:
C
Step-by-step explanation:
Two negatives cancel out and turn into a positive.
In the expression 11 - ( -3 5/8 ) there are two negative signs. If the parenthesis are removed, the two negative signs cancel out and turn into a positive and we are left with 11 +3 5/8
So the answer is C
If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be ______ that when the population is not highly skewed a. different from b. the same as c. larger than d. smaller than
Answer:
2
Step-by-step explanation:
the same as...
(2) is the answer
If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be the same as that when the population is not highly skewed.
What is the central limit theorem?The central limit theorem states in probability theory that, in many instances, when independent random variables are added together, their correctly normalized sum tends toward a normal distribution, even if the original variables are not normally distributed.
If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be the same as that when the population is not highly skewed.
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Compare 3.5 • 10^4 to standard form
Answer:
35,000
Step-by-step explanation:
^4 means 4 zeros
10^4 = 10,000
3.5 times 10,000 =
35,000
what is a variable in mathematics?
Answer:
variable, In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).
Answer:
variable, In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).
Step-by-step explanation:
In Maths, a variable is an alphabet or term that represents an unknown number or unknown value or unknown quantity. The variables are specially used in the case of algebraic expression or algebra. For example, x+9=4 is a linear equation where x is a variable, where 9 and 4 are constants.
Multiply:
(x+y)by (x+y)
a+b by a^2-b^2
(a+5) by (a^2-2a-3)
(a^2-ab+b^3) by (a+b)
Answer:
Multiply:
[tex](x+y)by (x+y)[/tex]
[tex] : \implies(x + y)(x + y)[/tex]
[tex] : \implies \: x(x + y) + y(x + y)[/tex]
[tex] : \implies {x}^{2} + xy + xy + {y}^{2} [/tex]
[tex] : \implies{x}^{2} + 2xy + {y}^{2} [/tex]
Multiply:
[tex]a+b \: by \: a^2-b^2[/tex]
[tex]: \implies( {a}^{2} + {b}^{2} ) \times (a + b)[/tex]
[tex]: \implies \: {a}^{2} (a + b) - {b}^{2} (a + b)[/tex]
[tex]: \implies \: {a}^{3} + {a}^{2} b - {ab}^{2} - {b}^{3} [/tex]
Multiply:
[tex](a+5) by (a^2-2a-3)[/tex]
[tex]: \implies{(a + 5) \times ( {a}^{2} - 2a - 3) }[/tex]
[tex]: \implies \: a({a}^{2} - 2a - 3) + 5( {a}^{2} - 2a - 3)[/tex]
[tex]: \implies(a \times {a}^{2} - a \times 2a - a \times 3) + (5 \times {a}^{2} - 5 \times 2a - 5 \times 3)[/tex]
[tex]: \implies{a}^{3} - {2a}^{2} - 3a + 5 {a}^{2} - 10a - 15 [/tex]
[tex]: \implies{ {a}^{3} + {3a}^{2} - 13a - 15}[/tex]
Multiply:
[tex](a^2-ab+b^3) by (a+b)[/tex]
[tex]: \implies{(a + b) \times ( {a}^{2} - ab + {b}^{3} )}[/tex]
[tex]: \implies \: a( {a}^{2} - ab + {b}^{3}) + b( {a}^{2} - ab + {b}^{3} ) [/tex]
[tex]: \implies {a}^{3} - {a}^{2} b + a {b}^{3} + {a^2b} - {ab}^{2} + {b}^{4} [/tex]
[tex]: \implies{ {a}^{3}+ab^3 - ab^2+ {b}^{4} }[/tex]
Step-by-step explanation:
[tex] \blue{ \frak{Seolle_{aph.rodite}}}[/tex]
Please help we’re stuck
Answer:
Divide 12 by -6
In order to qualify for a role in a play, an actor must be taller than 64 inches but shorter than 68 inches. The inequality 64 < x < 68, where x represents height, can be used to represent the height range. Which is another way of writing the inequality?
x > 64 and x < 68
x > 64 or x < 68
x < 64 and x < 68
x < 64 or x < 68
Lila invested 10000 in one of long life insurance company annuity contracts. When issued, the contract was paying a 5 percent rate of return
The kind of annuity does Lila own is: variable immediate annuity.
What is variable immediate annuity?Variable immediate annuity can be defined as the type of annuity that vary or fluctuate based on the type of investment you choose or pick.
In this type of annuity the payment you will receive will not be fixed reason being that payments that will made to you will always increase or decrease.
Therefore the kind of annuity does Lila own is: variable immediate annuity.
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What is the median of the data set?
16, 21, 28, 30, 40, 45, 54, 58
A. 58
Β. 35
C. 10
D. 19
Answer:
I think 10 is the answer it's not sure.
please help! acellus
find the missing side of this right triangle.
30
3
x
x= [?]
Answer:
The number that belongs in the green box is equal to 909.
General Formulas and Concepts:
Algebra I
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityTrigonometry
[Right Triangles Only] Pythagorean Theorem:
[tex]\displaystyle a^2 + b^2 = c^2[/tex]
Step-by-step explanation:
Step 1: Define
Identify given variables.
a = 30
b = 3
c = x
Step 2: Find x
Let's solve for the general equation that allows us to find the hypotenuse:
[Pythagorean Theorem] Square root both sides [Equality Property]:Now that we have the formula to solve for the hypotenuse, let's figure out what x is equal to:
[Equation] Substitute in variables:∴ the hypotenuse length x is equal to √909 and the number under the square root, our answer, is equal to 909.
___
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Topic: Trigonometry
In which table does yvary directly with x?
The table in which y varies directly with x is table C.
What is direct variation?
When a variable varies directly with another variable, it means that as one variable increases, the other variable also increases.
The equation that is used to represent direct variation is:
y = kx
Where y is the constant of proportionality
In table c, k is equal to 26
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Donovan is paying for gym classes. Each type of class has its own weekly fee. He signed up for x weeks of yoga classes and y
weeks of kickboxing classes. He paid a total of $136. The equation below describes the relationship between the number of weeks
of yoga classes and the number of weeks of kickboxing classes Donovan signed up for.
8x + 12y
-
136
The ordered pair (5,8) is a solution of the equation. What does the solution (5.8)
Considering the given function, the ordered pair (5,8) means that the signed up for 5 weeks of yoga classes and 8 weeks of kickboxing classes.
What does the function represent?
The function that represents the relationship between the number x of yoga classes that Donovan signs up for and the number y of kickboxing classes is given by:
8x + 12y = 136.
Hence the ordered pair (5,8) means that the signed up for 5 weeks of yoga classes and 8 weeks of kickboxing classes.
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If you help me you get a lot of points
Answer:
Step-by-step explanation:
#a
pattern 0 will include 4 reds in square
Because it's independent of pattern no
#b
Figure 1 has 4+4=8
Figure 2=4+8+2=14
Figure 3=4+12+3=19
The pattern n rule is
n²+3n+4So for 13th n
13²+3(13)+4169+39+4212squares#c
attached
y=x²+3x+4#d
Already given in c
What are the domain and range of g(x)= √x-3?
A. D: [3, ∞) and R: [0, ∞)
B. D: [–3, ∞) and R: [0, ∞)
C. D: (–3, ∞) and R: (–∞, 0)
D. D: (3, ∞) and R: (–∞, 0)
Answer:
I guess, A is the wanted answer, but
A and D together are the really correct answer.
Step-by-step explanation:
if I understand this correctly, then
g(x) = sqrt(x - 3)
the domain of a function is the definition of all valid x (input) values.
the range of a function is the definition of all valid y (result) values.
well, the content (the arguments) of a square root cannot be negative (at least not while dealing with real numbers).
so, the answer options B and D are automatically out, because the domain contains values that would make the arguments of the square root negative.
I guess your teacher wants to focus only on the positive results of the square root, so A is the correct number.
BUT formally, without designated restrictions, a square root has always 2 solutions : a positive and a negative one.
because (-x)² = (x)² = x².
so, I would have to say that the really correct answer is
A + D, because the range contains both, the positive and the negative numbers.
Find the height of a trapezium below with are 90cm and parallel sides 6 and 19.
Answer:
7.2 cm
Step-by-step explanation:
The height of the trapezium can be found by making use of the area formula with known values filled in.
__
solve for heightThe area of a trapezium is given by ...
A = 1/2(b1 +b2)h . . . . b1, b2 are the parallel sides, h is the height
Using the given values, we have ...
90 cm² = 1/2(6 cm +19 cm)h . . . . . . use the known values
(90 cm²)/(12.5 cm) = h = 7.2 cm . . . . divide by the coefficient of h
The height of the trapezium is 7.2 cm.
what is the transformation
(x,y) (x+5,y -3)
(x -5, y+3)
(x+3 y-5 )
x-3,y +5
A bag contains 2 red, 5 blue, and 3 green marbles. A marble is chosen at random. What is the probability of NOT choosing a red marble
Step-by-step explanation:
Number of red = 2Number of blue = 5Number of green = 3total number of marbles = 10probability of not choosing a red marble = 1--choosing a red marble.Because probability is always one(1).
Probability =
[tex]1 - \frac{2}{10} [/tex]
[tex] \frac{8}{10} [/tex]
[tex] \frac{4}{5} [/tex]
Is the probability of not choosing a red marble.