Answer:
a = 2 , r = 5
Step-by-step explanation:
The n th term of a geometric progression is
[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]
where a is the first term and r the common ratio
Given the 4 th term is 250, then
ar³ = 250 → (1)
Given the 7 th term is 31250, then
a[tex]r^{6}[/tex] = 31250 → (2)
Dividing the 2 equations gives
[tex]\frac{ar^6}{ar^3}[/tex] = [tex]\frac{31250}{250}[/tex], that is
r³ = 125 ← take the cube root of both sides
r = [tex]\sqrt[3]{125}[/tex] = 5
Substitute r = 5 into (1)
a × 5³ = 250, that is
125a = 250 ( divide both sides by 125 )
a = 2
Answer: a = 2, and r = 5
Step-by-step explanation: What we have been given here is a geometric progression. Every term in the sequence of numbers is derived by multiplying the previous term by a particular number called the common ratio, otherwise known as r. Hence if the first term is 1 for instance, the second term would be derived as 1 x r (which equals 1r), the third term would be derived as 1r x r (which equals 1r squared) and so on.
Having this in mind , we can calculate the Nth term of a geometric progression as
Nth term = a x r{to the power of n - 1}
So if we want to calculate the 4th term for instance, that would be
4th = a x r{to the power of 4 - 1} OR
4th = a x r{to the power of 3}
Similarly to calculate the 7th term would be
7th = a x r{to the power of 7 - 1}
7th = a x r{to the power of 6}
Now that we have been given the 4th (250) and 7th (31250) terms, what we now have is
a x r{to the power of 3} = 250 AND
a x r{to the power of 6} = 31250
a x r{to the power of 6}/a x r{to the power of 3} = 31250/250
After reducing both sides to their simplest form, what we now have is
r{to the power of 3} = 125
If we add the cube root sign to both sides of the equation we would have
r = 5
Having computed r as 5, we can now go back to calculate a as follows;
If a x r{to the power of 3} = 250, then
a x 125 = 250
Divide both sides of the equation by 125
a = 2
Therefore, a = 2 and r = 5
The area of a floor in square yards is one-ninth the area of the floor in square feet. Write the equation representing y, the area in square yards , to f , the area in square feet
Answer:
y = x²
f = (3x)²
Step-by-step explanation:
y = x²
f = (3x)²
check: y = 1/9 f
The required equation is [tex]y=\dfrac{1}{9}f[/tex].
Important information:
Area of a floor in square yards is one-ninth the area of the floor in square feet.We need to write an equation for the given situation.
Proportional Equation:Let [tex]y[/tex] be the area in square yards and [tex]f[/tex] be the area in square feet.
Area of a floor in square yards is one-ninth the area of the floor in square feet.
[tex]y=\dfrac{1}{9}f[/tex]
Thus, the required equation is [tex]y=\dfrac{1}{9}f[/tex].
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The area of a rectangle is 54x^9y^8 square yards. If the length of the rectangle is 6x^3y^4 yards, which expression represents the width of the rectangle in yards?
60x^12y^12
9x^3y^2
9x^6y^4
48x^6y^4
Answer:
9 x⁶y⁴
Step-by-step explanation:
for a rectangle
area = length x width, (rearranging)
width = area / length
given area = 54x⁹y⁸ and length = 6x³y⁴
width = 54x⁹y⁸ / 6x³y⁴
= (54/6) ( x⁹y⁸ / x³y⁴)
= 9 ( x⁹y⁸ / x³y⁴)
= 9 ( x⁹⁻³y⁸⁻⁴ )
= 9 ( x⁶y⁴ )
= 9 x⁶y⁴
The expression represents the width of the rectangle in yards is 9 x⁶y⁴.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
For a rectangle
width = area / length
The given area = 54x⁹y⁸ and length = 6x³y⁴
width = 54x⁹y⁸ / 6x³y⁴
= (54/6) ( x⁹y⁸ / x³y⁴)
= 9 ( x⁹y⁸ / x³y⁴)
= 9 ( x⁹⁻³y⁸⁻⁴ )
= 9 ( x⁶y⁴ )
= 9 x⁶y⁴
Hence, the expression represents the width of the rectangle in yards is 9 x⁶y⁴.
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5+15x=5( ) I'm not writing 20 characters
Answer:
(1 + 3x).
Step-by-step explanation:
We have to evaluate the missing term within the brackets in the following equation.
The equation is, 5 + 15x = 5(?)
Now, 5 + 15x
= 5 × 1 + 5 × 3x {We have to factorize the term where 5 is a factor}
= 5(1 + 3x) {This is reverse of the distributive property of multiplication}
Therefore, the missing term within the brackets is (1 + 3x). (Answer)
In September, Jerry read for 2/5 of an hour every day for 20 days. How many
hours did he read in September?
Show your work.
Answer:
Step-by-step explanation:
- 2/5 of an hour is equal to 24 min
- 24 times 20 is 480 minuets during September
- 480 minuets is 8 hours
2x - 3 greater than equal to 5
PLEASE EXPLAIN IT ;)
Answer:
x≥4
Step-by-step explanation:
We want to solve for x in
[tex]2x - 3 \geqslant 5[/tex]
Let us add 3 to both sides:
[tex]2x - 3 + 3\geqslant 5 + 3[/tex]
We simplify to get:
[tex]2x\geqslant 8[/tex]
Divide through by 2 to get:
[tex]x \geqslant 4[/tex]
Answer:
The equation means for all values of x [tex]\geq[/tex]4 this equation 2x-3[tex]\geq[/tex] 5 is true
Step-by-step explanation:
To explain
[tex]2x-3\geq 5[/tex]
let us solve this inequality and find the value of x
[tex]2x-3\geq 5\\2x\geq 5+3\\2x\geq 8\\x\geq (\frac{8}{2} )\\x\geq 4[/tex]
As
x [tex]\geq[/tex] 4
So
The equation means for all values of x [tex]\geq[/tex]4 this equation 2x-3[tex]\geq[/tex] 5 is true
Keywords: Algebra
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the length of the top of a rectangular-shaped deck is 6 meters longer than its width. if the area of the top of the deck is 72 square meters, what is it’s length in meters?
Answer:
6 meters
Step-by-step explanation:
length= 6+x
width= x
x (x+6)= 72⇔ [tex]x^{2}[/tex] + 6x - 72= 0⇔ x= (-6 ±[tex]\sqrt{6^{2} -4 *1*(-72) }[/tex]) / 2*1⇔
⇔ x= (-6±√324)/2 ⇔ x= (-6±18)/2 ⇔ x= 6 ∨ x= -12
Since the width of a rectangle can't be negative, the answer will be 6 meters.
Answer ........................
(1)
Section 3
Mr. Lenny paid $1480.00 for 4 cricket balls and 2 cricket bats. The cost of 1 cricket bat is twice as
much as a ball. What is the cost of 1 cricket ball and 1 cricket bat?
Answer.
.
.
.
.
....(
4) (answer with explanation)
Answer:
The cost of one cricket bat is $370, while the cost of one cricket ball is $185.
Step-by-step explanation:
Let's identify what we already know:
1) Mr. Lenny paid a TOTAL of $1480.00 for 4 cricket balls, and two cricket bats.
2) The cost of one cricket bat is twice as much as a cricket ball.
We can create an initial equation:
(4 times x) + (2 times y) = $1480.00
x is the price of one cricket ball, while y is the price of one cricket bat. Considering how the problem is set up, I know the 4 balls should add up to the same price as two bats.
So, the four balls should equal half of $1480, which is $740, and the two bats should also equal $740.
Calculate it out, and you'll find that one cricket bat equals $370, while one ball equals $185.
The question can be solved by representing the cost of a ball as x and bat as 2x, forming the equation 4x + 2(2x) = 1480. Solving this equation finds the cost of the individual cricket ball and bat.
Explanation:In this question, we know that the cost of one cricket bat is twice the cost of a cricket ball, and that Mr. Lenny bought 4 cricket balls and 2 cricket bats for $1480.00. To solve for the individual price of each item, we can use the method of substitution in algebra.
Let's represent the cost of a ball as x and a bat as 2x. This becomes an equation of 4x (cost of 4 balls) + 2(2x) (cost of 2 bats) = 1480.
Solving for x will give us the cost of one cricket ball, and multiplying the value of x by 2 will offer the cost of a single cricket bat.
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The first term of a geometric sequence is 32, and the 5th term of the sequence is 818 .
What are the geometric means between these terms?
Enter your answer by filling in the boxes to correctly complete the geometric sequence. Enter any fractions as simplified fractions.
Answer:
[tex]32,24,18,\frac{27}{2} ,\frac{81}{8}[/tex]
Step-by-step explanation:
Let x, y , and z be the numbers.
Then the geometric sequence is [tex]32,x,y,z,\frac{81}{8}[/tex]
Recall that term of a geometric sequence are generally in the form:
[tex]a,ar,ar^2,ar^3,ar^4[/tex]
This implies that:
a=32 and [tex]ar^4=\frac{81}{8}[/tex]
Substitute a=32 and solve for r.
[tex]32r^3=\frac{81}{8}[/tex]
[tex]r^4=\frac{81}{256}[/tex]
Take the fourth root to get:
[tex]r=\sqrt[4]{\frac{81}{256} }[/tex]
[tex]r=\frac{3}{4}[/tex]
Therefore [tex]x=32*\frac{3}{4} =24[/tex]
[tex]y=24*\frac{3}{4} =18[/tex]
[tex]z=18*\frac{3}{4} =\frac{27}{2}[/tex]
Answer:
Step-by-step explanation:
Find the solution(s) to the system of equations represented in the graph. They intersect at 0, negative 4 and 4, 0 (0, 4) and (4, 0) (0, 4) and (−4, 0) (0, −4) and (4, 0) (0, −4) and (−4, 0)
Answer
(0,-4) and (4,0).
Step-by-step explanation:
The solutions of a system of equation from a graph is where the graphs intersect.
From the question, you mentioned that the graphs intersect at (0,-4) and (4,0).
Therefore the solutions to the system are (0,-4) and (4,0).
Probably, you might have a straight line and a quadratic graph interesting or two quadratic graphs.
Micah is preparing for a piano recital. He practices for 50 minutes on Monday and 90 minutes on Wensday
Answer:
She increased 80% the practise time
Step-by-step explanation:
The question is incomplete, the following is missing:
by how much did she increase the time she practised each day?
From Monday to Wednesday she increased 90 - 50 = 40 minutes the practise time.
To compute the increment as a percentage use: increment/reference *100
In this case, that is: 40/50*100 = 80%, where 50 minutes is taken as a reference.
Answer: increased by 40
she increased by 80%
Step-by-step explanation:
How to work out -31-4x=-5-5(1+5x)
Answer: x = 1
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
−31−4x=−5−5(1+5x)
−31+−4x=−5+(−5)(1)+(−5)(5x)(Distribute)
−31+−4x=−5+−5+−25x
−4x−31=(−25x)+(−5+−5)(Combine Like Terms)
−4x−31=−25x+−10
−4x−31=−25x−10
Step 2: Add 25x to both sides.
−4x−31+25x=−25x−10+25x
21x−31=−10
Step 3: Add 31 to both sides.
21x−31+31=−10+31
21x=21
Step 4: Divide both sides by 21.
21x/21 divided by 21/21
Get x = 1
Answer:
x=1
Step-by-step explanation:
*I underlined everything we are working with at that moment
- 31 - 4x = - 5 - 5(1+5x)
-5(1+5x)=5-25x
-31-4x=-5-5-25x
-31=-10-21x
-21=-21x
x=1
300,000+900+4
write this number in standard form
Answer:
300,904
Step-by-step explanation:
The profit a hamburger vendor earned, in dollars, is proportional to the number of hamburgers sold. This equation represents the proportional relationship between the profit earned and number of hamburgers sold. 2p = 3H
Answer:
The hamburger earns $ 1.50 for each hamburger he sells
Correct statement and question:
The profit a hamburger vendor earned, in dollars, is proportional to the number of hamburgers sold. This equation represents the proportional relationship between the profit earned and number of hamburgers sold.
2p = 3H.
Enter the profit, in dollars, earned for each hamburger sold.
Source:
Previous question that can be found at brainly
Step-by-step explanation:
Let's find the value of p, profit earned when H = 1:
2p = 3H
2p = 3 * 1
2p = 3
p = 3/2
p = 1.5
The hamburger earns $ 1.50 for each hamburger he sells
5. Mrs. Neri works part time at an electronics store. She is paid a weekly salary plus a
commission based on her total sales. The table shows her total sales and her total pay
for the last two weeks.
Week/1
Total Sales
/ $500
to
Total Pay
$425
Week/2
Total sales
$350
Total pay 395
Based on the data in the table, which equation represents Samantha's total pay, y, as
a function of her total sales, x?
A) y = 0.6x + 125
B) y = 0.2% + 325
C) y = 1.6% -95
Answer:
The equation that represents Samantha's total pay as a function of her total sales is B. y = 0.2x + 325
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Total Sales Total Pay
Week 1 $ 500 $ 425
Week 2 $ 350 $ 395
2. Let's find out the equation that represents Samantha's total pay as
a function of her total sales, this way:
Week 1:
A) y = 0.6x + 125 = 0.6 * 500 + 125 = 300 + 125 = 425 Correct
B) y = 0.2x + 325 = 0.2 * 500 + 325 = 100 + 325 = 425 Correct
C) y = 1.6x - 95 = 1.6 * 500 - 95 = 800 - 95 = 705 Incorrect
Week 2:
A) y = 0.6x + 125 = 0.6 * 350 + 125 = 210 + 125 = 335 Incorrect
B) y = 0.2x + 325 = 0.2 * 350 + 325 = 70 + 325 = 395 Correct
C) y = 1.6x -95 = 1.6 * 350 - 95 = 560 - 95 = 465 Incorrect
The equation that represents Samantha's total pay as a function of her total sales is B. y = 0.2x + 325
Write the absolute value function as a piecewise function. y=6∣x−3∣
Answer:
Step-by-step explanation: y=6 x - 3
(6 X x) - (6 x 3)
6x - 18
-12
The absolute value function y = 6 |x - 3| can be written as a piecewise function. For x < 3, y = 6 * (3 - x) and for x >= 3, y = 6 * (x - 3). This takes into account the always-positive relationship of the absolute value function.
Explanation:The absolute value function y = 6 |x - 3| can be written as a piecewise function as follows:
if x < 3 then y = 6 * (3 - x)if x ≥ 3 then y = 6 * (x - 3)This is because the absolute value function defines a relationship where distance is always positive. For values of x less than 3, the expression within the absolute value brackets is negative, so we have to change the sign. For values of x greater than or equal to 3, the expression is already positive, so it stays as it is.
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1/3(z+4)-6=2/3(5-z)
Find the answer
Step-by-step explanation:
[tex] \frac{1}{3} (z + 4) - 6 = \frac{2}{3} (5 - z) \\ \\ \therefore \: \frac{ (z + 4) - 6 \times 3}{3} = \frac{2(5 - z) }{3} \\ \\ \therefore \: \frac{ z + 4 -18}{3} = \frac{10 - 2z }{3} \\ \\ \therefore \: \frac{ z - 14}{3} = \frac{10 - 2z}{3} \\ \\ \therefore \: z - 14 = 10 - 2z \\ \\ \therefore \: z + 2z = 10 + 14\\ \\ \therefore \: 3z =24 \\ \\ \therefore \: z = \frac{24}{3} \\ \\ \: \: \: \: \: \: \: \: \huge \orange{ \boxed{ \therefore \: z = 8}}[/tex]
which value of x is in the solution set of the following inequality?
The right answer is Option 2.
Step-by-step explanation:
Given inequality is;
-3x+5>17
Solving the inequality
Subtracting 5 from both sides of the inequality;
[tex]-3x+5-5>17-5\\-3x>12[/tex]
Dividing both sides of inequality by -3;
[tex]\frac{-3x}{-3}>\frac{12}{-3}\\\\x>-4[/tex]
The solution to the inequality is -4.
The right answer is Option 2.
Keywords: subtraction, division
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Solutions to -8x + 5 less than or equal to 11
Answer:
[tex]x\geq -\frac{3}{4}[/tex]
Step-by-step explanation:
[tex]-8x+5\leq 11\\\\1. -8x\leq 11-5\\ -8x\leq 6[/tex]
Isolate the parts of the equation with the x variable
[tex]2. \frac{-8}{-8} x\geq\frac{6}{-8} \\x\geq -\frac{3}{4}[/tex]
When you divide or multiply by a negative number in inequalities, you must flip the sign of the inequality.
Hello there!
Im assuming you're solving for X!
Answer:
Your answer in Inequality Form comes to:
x > -3/4
Explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
what is (4x + 3) + (-2x + 4)
Answer:
(4x + 3) + (-2x + 4) = 2x + 7
Step-by-step explanation:
(4x + 3) + (-2x + 4) = you then collect like terms
(4x + -2x) + (3 + 4)= like this, and you add what's inside perenthesis
= 2x + (3 + 4). step-by-step
= 2x + 7. then that is how you get =2x+7
Answer:
The answer to your equation would be 2x + 7.
Step-by-step explanation:
4x + 3 + -2x + 4
= (4x + -2x) + (3 + 4)
= 2x + (3 + 4)
= 2x + 7
Therefor, your answer would be 2x + 7.
A boy is 8 years older than his brother four years from now the boy will be twice as old as his brother how old is each boy
Answer:32
Step-by-step explanation:
8 times 4
Answer:
Boy: 12 Brother: 6
Step-by-step explanation:
If a boy was 8 years old and in 4 years from the boy was twice is brothers age you would first have to add 4 to the 8 to get how many years old the boy was (8+4=12)
When you get these answer, you would have to divide bye 2 bceause the boy was twice his age and therefore, we would find out how many years old the brother was
(12/2=6)
The sides 5, 6, and 12 form a triangle. True or False
Answer:
False
Step-by-step explanation:
According to the The Triangle Inequality Theorem, the sum of any two sides of a triangle must be greater then the measure of the third side. So use this theorem to solve:
6+12=18 and 18>5
so far it is following the theorem but we need to make sure all of the sides follow it so lets continue.
6+5= 11 and 11<12
This does not follow the theorem, so the sides 5,6, and 12 cannot form a triangle.
Answer:
False
Step-by-step explanation:
If 130 is invested in a savings account that earns 4% interest per year, which of the following is closest to the amount in the account at the end of 10 years
In may, Xia made 5 flower planters with f flowers in each planter. in June, she made 8 flower planters with f flowers in each planter. Write an expression in simplest form that gives the number of flowers Xia has in the planters.
13f is the expression in simplest form that gives the number of flowers Xia has in the planters
Solution:
Given that,
In may, Xia made 5 flower planters with f flowers in each planter
Therefore,
Number of flowers planted in May: [tex]5 \times f = 5f[/tex]
In June, she made 8 flower planters with f flowers in each planter
Therefore,
Number of flowers planted in June: [tex]8 \times f = 8f[/tex]
Write an expression in simplest form that gives the number of flowers Xia has in the planters
Total number of flowers planted = Number of flowers planted in May + Number of flowers planted in April
Total number of flowers planted = 5f + 8f = 13f
Thus, the expression is 13f
Julia bought 12 bags of cucumber seeds. each bag contains 42 seeds. if she plant one half of the seeds how many seeds does she have left
Answer:
She will have 252 seeds left.
Step-by-step explanation:
12 x 42 = 504
504 ÷ 2 = 252
So, she will have planted 252 seeds and she will have 252 seeds left to plant.
Final answer:
Julia has 252 seeds left after planting half of the seeds.
Explanation:
To find out how many seeds Julia has left, we first need to determine the total number of seeds she has. Julia bought 12 bags of cucumber seeds, and each bag contains 42 seeds. So the total number of seeds she has is 12 bags × 42 seeds per bag = 504 seeds.
If Julia plants one-half of the seeds, she would be planting 504 seeds × 1/2 = 252 seeds.
To find out how many seeds she has left, we subtract the number of seeds she planted from the total number of seeds she initially had. 504 seeds - 252 seeds = 252 seeds left.
complete the square x^2-6x+__= -13+__
Answer:
Step-by-step explanation:
x^2 - 6x + __ = -13 + __
take half of the coefficient in ur x term, square it, and add it to both sides
so take half of -6.....which is -3......and square it....-3^2 = 9. Now add 9 to both sides.
x^2 - 6x + 9 = -13 + 9
(x - 3)^2 = - 4
To complete the square for the equation x^2-6x+__= -13+__, add the square of half the coefficient of x to both sides. The completed square equation is (x-3)^2 = -4.
Explanation:The student is asking how to complete the square for the equation x^2-6x+__= -13+__. Completing the square is a method used in Mathematics to solve quadratic equations, reorganize expressions, and is important for calculus. Here are the steps to solve this:
First, we take half of the coefficient of x, which is -6, square it, and add it to both sides of the equation. This gives us (x^2-6x+9) = -13+9. Simplify the left side into (x-3)^2. The right side simplifies to -4. This gives us the completed square equation: (x-3)^2 = -4.Learn more about Completing the Square here:
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Plz help ASAP!!!
What is the correlation coefficient between the variables? Round to three decimal places. Enter your answer in the box.
Items purchased: 40, 29, 108, 35, 62, 50, 8
Bags used: 6, 5, 11, 7, 14, 10, 2
r ≈ ____
The correlation coefficient between the given variables is determined as 0.771 (three decimal places).
Correlation coefficient between the variablesThe correlation coefficient between the variables is calculated as follows;
[tex]r = \frac{n\Sigma xy - \Sigma x\Sigma y}{\sqrt{[n\Sigma x ^2 \ - (\Sigma x)^2][n\Sigma y^2- (\Sigma y)^2]} }[/tex]
∑xy = (40 x 6) + (29 x 5) + (108 x 11) + (35 x 7) + (62 x 14) + (50 x 10) + (8 x 2)
∑xy = 3202
n∑xy = 7(3202)
n∑xy = 22,414
∑x = 40 + 29 + 108 + 35 + 62 + 50 + 8 = 332
∑y = 6 + 5 + 11 + 7 + 14 + 10 + 2 = 55
∑x∑y = 332 x 55 = 18,260
∑x² = 40² + 29² + 108² + 35² + 62² + 50² + 8² = 21,738
n∑x² = 7(21,738) = 152,166
(∑x)² = (332)² = 110,224
∑y² = 6² + 5² + 11² + 7² + 14² + 10² + 2² = 531
n∑y² = 7(531) = 3,717
(∑y)² = (55)² = 3,025
Correlation coefficient[tex]r = \frac{22,414-18,260}{\sqrt{(152,166-110,224) (3,717 - 3025)} } \\\\r = \frac{4154}{\sqrt{29,023,864} } \\\\r = 0.771[/tex]
Thus, the correlation coefficient between the given variables is determined as 0.771 (three decimal places).
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what ordered pair is a solution of this equation 3x-7y=28
help
put it in slope intercet form then take the number before the x and the number after the x and put them into an ordered pair.
A rectangle has a area of 1/6 square centimeters and a length of 1.5 centimeters. What is the width? What is the perimeter?
Answer:
Step-by-step explanation:
width is 9 and the perimiter is 21
Solve for x: 14-14x^1/3 =2
Answer: 216/343 or 0.6297
Step-by-step explanation:
[tex]14-14x^{1/3} = 2\\14 -2 = 14x^{1/3}\\12 = 14x^{1/3}\\\frac{12}{14} =x^{1/3}\\\frac{6}{7} =x^{1/3}\\(\frac{6}{7})^3 =(x^{1/3})^3\\\frac{6^3}{7^3} =x\\\\\frac{216}{343} = 0.629737609 = x[/tex]
I WILL GIVE BRAINLIEST!!!
Which is the definition of the root qua- (from the word quadrilateral)?
Option 1. one
Option 2. two
Option 3. three
Option 4. four
Answer the answer is 4
Step-by-step explanation:
Easy way means four