Answer:
see explanation
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio
Here a = 15, thus
[tex]a_{5}[/tex] = 15[tex](r)^{4}[/tex] = [tex]\frac{243}{125}[/tex] ( divide both sides by 15 )
[tex]r^{4}[/tex] = [tex]\frac{243}{1875}[/tex], thus
r = [tex]\sqrt[4]{\frac{243}{1875} }[/tex] = [tex]\frac{3}{5}[/tex]
Multiply the previous term by [tex]\frac{3}{5}[/tex] to obtain the next term
15 × [tex]\frac{3}{5}[/tex] = 9
9 × [tex]\frac{3}{5}[/tex] = [tex]\frac{27}{5}[/tex]
[tex]\frac{27}{5}[/tex] × [tex]\frac{3}{5}[/tex] = [tex]\frac{81}{25}[/tex]
[tex]\frac{81}{25}[/tex] × [tex]\frac{3}{5}[/tex] = [tex]\frac{243}{125}[/tex]
Thus the sequence is
15, 9, [tex]\frac{27}{5}[/tex], [tex]\frac{81}{25}[/tex], [tex]\frac{243}{125}[/tex]
PLEASE HELP
BRAINLIEST
Find the value of x in the figure.
Answer:
x = 27
Step-by-step explanation:
Using the information in the figure, we can conclude that the 3x - 17, x + 40, and 2x - 5 would be the measures of the three interior angles of the triangle. The sum of the interior angles of a triangle is 180° (use the equation: (n-2) × 180°).
By using this information, we can conclude that (3x - 17) + (x + 40) + (2x - 5) would equal 180. We can put this into the equation:
(3x - 17) + (x + 40) + (2x - 5) = 180
To find the value of x in this equation (solve for x), we would have to get the equation into the form x = _.
(3x - 17) + (x + 40) + (2x - 5) = 180
3x - 17 + x + 40 + 2x - 5 = 180
Combine like terms.
6x + 18 = 180
Subtract 18 from both sides to get rid of the +18 on the left side.
6x = 180 - 18
Simplify.
6x = 162
Divide 6 form both sides to get rid of the coefficient of 6 on the left side.
x = 162 ÷ 6
Simplify.
x = 27
x = 27
I hope this helps. :)
Find the volume of a cone that has a radius of 3 meters and a height of 6 meters.
(Use 3.14 for pi and round the answer to the nearest hundredth.)
Answer:
56.55m^3
Step-by-step explanation:
v=[tex]\pi[/tex]*r^2*h/3
What values of b satisfy 3(2b + 3)2 = 36?
b = StartFraction negative 3 + 2 StartRoot 3 EndRoot Over 2 EndFraction and StartFraction negative 3 minus 2 StartRoot 3 EndRoot Over 2 EndFraction
b = StartFraction negative 3 + 2 StartRoot 3 EndRoot Over 2 EndFraction and StartFraction negative 3 minus 2 StartRoot 3 EndRoot Over 2 EndFraction
b = StartFraction 3 Over 2 EndFraction and StartFraction negative 9 Over 2 EndFraction
b = Start Fraction 9 Over 2 EndFraction and StartFraction negative 3 Over 2 EndFraction
Answer: b=-3+2√3/2
-3-2√3/2
Step-by-step explanation: it's A on edg
The value of b which satisfies the given quadratic equation is both: A. b = (-3 + 2√3)/2 and (-3 - 2√3)/2.
How to solve a quadratic equation?
In this exercise, you're required to solve for the value of b which satisfies the given quadratic equation. Thus, we would simplify the quadratic equation as follows:
3(2b + 3)² = 36
Dividing both sides by 3, we have:
(2b + 3)² = 12
Taking the square root of both sides, we have:
2b + 3 = ±√12
2b + 3 = ±√4 × √3
2b + 3 = ±2√3
2b = -3 ± 2√3
b = (-3 + 2√3)/2 and (-3 - 2√3)/2.
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find the product of 3 and 2y-4x=8
Answer:
Step-by-step explanation:
3 * (2y - 4x) = 8
6y - 12x = 8
divide by 2 throughout
3y - 6x = 4
-6x + 3y -4 = 0
To find the product of 3 and the expression 2y - 4x, we multiply both sides of the equation by 3, resulting in 6y - 12x = 24.
The student's question asks us to find the product of 3 and the expression 2y - 4x = 8. Multiplying both sides of the equation by 3 we get:
3 * (2y - 4x) = 3 * 86y - 12x = 24The product of 3 with each term on the left side of the equation has been calculated, resulting in a new equation: 6y - 12x = 24. It is important to carry out the multiplication operation carefully, ensuring that each term within the parentheses is multiplied by 3.
Which expression is evaluated to -18-64
Answer:
-82
Step-by-step explanation:
-18 - 64
-82
Answer: -82
A triangle has a base of 5 centimeters and a height of 8 centimeters.
What is the area of the triangle?
A. 10 cm2
B. 13 cm2
C. 20 cm2
D. 40 cm2
Answer:
C. 20 cm^2 is the area. Hope this helped you.
Answer: c. 20
Step-by-step explanation:
The formula to finding a triangle is base times height over 2.
5 x 8/ 2=
40/2=
20
if measure angle MPL=63 HOW COULD I FIND THE OTHERS?
answer:
JK = 27
NJ = 153
JL = 117
KNM = N/A
MJL = N/A
JLK = N/A
step-by-step explanation:
you can see there are pairs of vertical angles which means they would be equalremember a circle adds up to 360the arc's measure and the angle's measure would be equalsince we know ∠MPL is 63°, and ∠KPL is 90°, we can find the others too∠NPM + ∠MPL = 90
∠NPM + 63 = 90
∠NPM = 27°
so, ∠JPK = 27° (since they are vertical angles)
now, add up all the ones you know to find the other angle63 + 90 + 27 + 27 + X = 360
let x be the missing angle63 + 90 + 27 + 27 + X = 360
207 + X = 360
X = 153
so, ∠JPN = 153°
now put the measures of the arcsARCS:
JK = 27
NJ = 153
JL = 117
KNM = N/A
MJL = N/A
JLK = N/A
- sorry this is the furthest i can help, i have only learnt up to that so do not know how to find the rest.
using the relationship between intercepted arc and central angle, the missing measures are:
a. m(JK) = 27°
b. m(NJ) = 153°
c. m(JL) = 117°
d. m(KNM) = 207°
e. m(MJL) = 297°
f. m(JLK) = 333°
Central Angle and measure of Intercepted ArcThe central angle is always equal to the measure of the intercepted arc.A full circle = 360 degrees.Half circle = 180 degrees.Given:
m∠MPL = 63°
a. m(JK) = 180 - 90 - 63 = 27°
m(JK) = 27°
b. m(NJ) = 180 - m(JK)
m(NJ) = 180 - 27
m(NJ) = 153°
c. m(JL) = 90 + 27
m(JL) = 117°
d. m(KNM) = 180 + 27
m(KNM) = 207°
e. m(MJL) = 27 + 180 + 90 = 297°
f. m(JLK) = 360 - 27
m(JLK) = 333°
Therefore, using the relationship between intercepted arc and central angle, the missing measures are:
a. m(JK) = 27°
b. m(NJ) = 153°
c. m(JL) = 117°
d. m(KNM) = 207°
e. m(MJL) = 297°
f. m(JLK) = 333°
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A bag contains yellow marbles and red marbles, 55 in total the number of yellow marbles is 5 less than 2 times the number of red marbles how many yellow
Answer:
35 marbles
Step-by-step explanation:
5 x 2 x2 = 20
55-20 is 35
1. Express 4 factors of -20: (-20%)(-2)(-20)(-28)
2. Expand the expression:
-2.-2.-2.-2..0.0.
3. Simplify to the exponential form: (-2)4. (4574
4. Evaluate the base 2 power: 16. (054
5. Apply the power of a power: 162"
What is the value of x in the simplified power? x=
The value of x in the simplified power is 20.
Solution:
Given expression: [tex]\left(-2 d^{5}\right)^{4}[/tex]
Step 1: Express 4 factors of [tex]-2 d^{5}[/tex]
[tex]\left(-2 d^{5}\right)\left(-2 d^{5}\right)\left(-2 d^{5}\right)\left(-2 d^{5}\right)[/tex]
Step 2: Expand the expression
[tex]-2 \cdot-2 \cdot-2 \cdot-2 \cdot d^{5} \cdot d^{5} \cdot d^{5} \cdot d^{5}[/tex]
Step 3: Simplify to the exponential form
There four -2 terms and four [tex]d^5[/tex] terms.
[tex](-2)^{4} \cdot\left(d^{5}\right)^{4}[/tex]
Step 4: Evaluate the base 2 power.
[tex](-2)^{4}=16[/tex]
[tex](-2)^{4} \cdot\left(d^{5}\right)^{4}=16 \cdot\left(d^{5}\right)^{4}[/tex]
Step 5: Apply the power of a power.
Using exponent rule: [tex](a^m)^n=a^{mn}[/tex]
So that [tex]\left(d^{5}\right)^{4}=d^{5\times4}=d^{20}[/tex]
[tex]16 \cdot\left(d^{5}\right)^{4}=16d^{20}[/tex]
[tex]16 d^{x}=16 d^{20}[/tex]
⇒ x = 20
The value of x in the simplified power is 20.
2 triangles are shown. Line M N is the line of reflection. Line segment X prime X has a midpoint at point A. Line segment Z prime Z has a midpoint at point B. Line segment Y prime Y has a midpoint at point C. Which statements must be true about the reflection of ΔXYZ across Line M N? Select three options. m∠X'Z'Y' = 90° m∠MCY = 90° XX' ≅ YY' BZ' ≅ BZ XY || X'Y'
The statements that are true with respect to the reflection of Δ XYZ are:
Option A - m∠X'Z'Y' = 90°
Option B - m∠MCY = 90° and
Option D - BZ' ≅ BZ.
What is the reflection in math?Geometrically speaking, reflection in math simply refers to a flip image of a shape, all dimensions remaining the same.
When every point in a figure is equidistant from it's equivalents points on the mirror image, both images are said to be a reflection of one another.
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Answer:
A, B, D
Step-by-step explanation:
edge 2022
Is 6/10 greater than 1/2
Answer:
No 1/2 is greater
Step-by-step explanation:
1:look at both 1/2 and 6/10
2: see which one gets to the denominator first
3: which ever one it is will be greater
4:the answer is 1/2 because if you add one more to 1/2 you get 2/2
what does a equal
5^9/5^3=5^a a=
1. Use the Quotient Rule: x^a/x^b = x^a - b
5^9 - 3 = 5a
2. Simplify 9 - 3 to 6
5^6 = 5^a
3. Simplify 5^6 to 15625
15625 = 5^a
4. Convert both sides to the same base
5^6 = 5^a
5. Cancel the base of 5 on both sides
6 = a
6. Switch sides
a = 6
The area of a playground is 266 yd. The width of the playground is 5 yd longer than its length. Find th
length and width of the playground.
a. length = 19 yd, width = 24 yd
C length = 14 yd, width = 19 yd
b. length = 19 yd, width = 14 yd
d. length = 24 yd, width = 19 yd
Answer:
C
Step-by-step explanation:
The width is 5 yds longer so we can mark out b and d if you multiply 19 and 24 is 456 so you are left with C
MULTIPLE CHOICE:
if the solution to an inequality is t < 7.4, which of the numbers below would be part of the solution?
O4.7
O5.1
O7.4
O8.2
O9.6
Answer:
4.7 and 5.1
Step-by-step explanation:
7.4 only works if it shows less than or equal to inequality
which expression is a factor of the quadratic 6x^2-11x-35?
2x-7, 2x-5, 2x+7, 2x+5
1. Split the second term in 6x^2 - 11x - 35 into two terms
6x^2 + 10x - 21x - 35
2. Factor out common terms in the first two terms, then in the last two terms
2x(3x + 5) - 7(3x + 5)
3. Factor out the common term 3x + 5
(2x - 7)
Split the second term in 6x^2 - 11x - 35 into two terms
6x^2 + 10x - 21x - 35
2. Factor out common terms in the first two terms, then in the last two terms
2x(3x + 5) - 7(3x + 5)
3. Factor out the common term 3x + 5
(2x - 7)
A passenger on a ship dropped his camera into the ocean. If it is descending at a rate of -4.2 meters per second, how long (in seconds) until it hits the bottom of the ocean, which is at -1875 meters? Round to the nearest second.
Anna baked 333 batches of cookies with ccc cookies in each batch. She then ate 888 cookies!
How many cookies does Anna have left?
Hello friend!
If each batch has three cookies (which I suppose is what the "ccc" means,
Your quick answer is 111. :)
If Anna has baked 333 batches of cookies and each batch has three cookies, then 333 multiplied by 3 is 999. If Anna ate 888 cookies then 999 minus 888 is 111.
Take care friend!
-Edge
Answer:
3c-8
Step-by-step explanation:
Which is the greatest risk when investing in stocks? A. call risk B. inflationary risk C. interest rate risk D. liquidity risk E. market risk
Answer:
E. market risk
Step-by-step explanation:
When investing in stock, an investor should be aware of three key risks which are;
The market riskThe Inflation risk Liquidity riskMarket risk involves loses that are as result of entire performance of financial markets. Examples are stock market bubbles.Inflation risk is concerned with cash used for an investment, where changes in power to purchase may cause inflation risk.Liquidity risks happens when an investor is unable to sell or buy earlier enough to prevent losses.
The correct option is E. market risk
The information regarding the market risk is as follows;
It includes the losses that leads to the overall performance of the financial markets like - stock marketSo we can say that the market risk termed to the high risk at the time of investing in the stock.Learn more: brainly.com/question/17429689
the radius of a birthday cake is 5 inches.Icing will decorate the circumference of the cake.What procedure can be used to find the approximate circumference of the cake?
Answer:
Multiply 5 by 2 and the product by 3.
Step-by-step explanation:
Which of the following sets shows all the numbers from the set {2, 3, 4, 5 that are part of the solution inequality 4n + 6> 22
Solution:
Given inequality is:
[tex]4n + 6 > 22[/tex]
Substitute n = 2
[tex]4(2) + 6 > 22\\\\8 + 6 > 22[/tex]
14 is not greater than 22
Thus, n = 2 does not satisfy the given equation
Substitute n = 3
4(3) + 6 > 22
12 + 6 > 22
18 is not greater than 22
Thus, n = 3 does not satisfy the given equation
Substitute n = 4
4(4) + 6 > 22
16 + 6 > 22
22 is equal to 22
Thus, n = 4 does not satisfy the given equation
Substitute n = 5
4(5) + 6 > 22
20 + 6 > 22
26 > 22
26 is greater than 22
Thus, n = 5 satisfies the given equation
Simplify the expression.
t+2+6t
=
Answer:
7t+ 2
Step-by-step explanation:
what is the gradient of the graph shown
The gradient of the graph is 2.
Solution:
Let the points on the graph are (-2, 0) and (0, 4).
Here [tex]x_1=-2, y_1=0, x_2=0, y_2=4[/tex].
Gradient of the graph:
[tex]$\text{Gradient }= \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]$= \frac{4-0}{0-(-2)}[/tex]
[tex]$= \frac{4-0}{0+2}[/tex]
[tex]$= \frac{4}{2}[/tex]
Cancel the common terms, we get
Gradient = 2
The gradient of the graph is 2.
How do the graphs of f(x)=x^2 and g(x)=3/4x^2
Easily putting the equation into Google, I found a graph for you! :)
Answer:
the answer is b.
the graph of g(x) is the graph of f(x) compressed vertically by a factor of 3/4
Step-by-step explanation:
why? bc i did the review
n a drawer, there are 12 pairs of socks, 6 of which are white. If you randomly select two pairs of socks, what is the probability that both are white? Express your answer as a reduced fraction.
The probability that both pairs of socks selected from a drawer containing 12 pairs, 6 of which are white, are white, is 5 out of 22.
Explanation:The subject of this question is the probability in mathematics, specifically dealing with combinations. In the problem, there are 12 pairs of socks and 6 of them are white. When we are drawing two pairs, we want both to be white which defines our event space.
To find the answer, we need to divide the number of favorable outcomes by the total number of outcomes. The favorable outcome is the probability of choosing 2 white socks out of 6 which can be calculated by combinations (represented by the formula C(n, k) = n! / [k!(n - k)!]). So, C(6, 2) = {6! / [2!(6 - 2)!]} = 15.
The total number of outcomes is the number of ways to pick 2 pairs out of 12, calculated by combinations as well, C(12, 2) = {12! / [2!(12 - 2)!]} = 66.
Now, the probability is favorable outcomes divided by total outcomes = 15/66 = 5/22.
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Solve the equation:
x² + 3x² - 4x=0
Answer: x²= 0
Step-by-step explanation:
If x² + 3x² - 4x=0
4x²-4x=0
4x² =0/4×
4x² = 0
x² = 0/4
Which expression is equivalent to 20c - 8d?
A. 2(10c + 4d)
B. 4(5c - 8d)
C. 4(5c - 2d)
D. c(20 -8d)
(explain please.)
The expression [tex]\rm 20c - 8d[/tex] is equivalent to the [tex]\rm 4(5c - 2d)[/tex] and it can be determined by using factorization.
Given that,
Expression; [tex]\rm 20c - 8d[/tex]
We have to determine
The equivalent expression to the given expression.
According to the question,
To determine the equivalent relation calculation must be done in a single unit following all the steps given below.
Expression; [tex]\rm 20c - 8d[/tex]
From the expression take out the common factor and rewrite the expression.
[tex]= \rm 20c-8d\\\\= 4 \times 5 \times c - 2\times 4 \times d\\\\= 4(5\times c - 2 \times d)\\\\= 4(5c-2d)[/tex]
Hence, The expression [tex]\rm 20c - 8d[/tex] is equivalent to the [tex]\rm 4(5c - 2d)[/tex].
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Which expression represents five less than the square of one more than a number?
(x + 1)2 - 5
5 - (x + 1)2
(x²+ 1) - 5
5-(x²+1)
Answer:
(x+1)² - 5
Step-by-step explanation:
one more than a number: x+1
the square of that (x+1)²
five less than that (x+1)² - 5
What is the decimal 89.023 in word and expanded form
Answer: Eighty Nine and Twenty Three Thousandths
Step-by-step explanation:
Answer:
eighty-nine and twenty-three thousandths <------ word form
80 + 9 + 0.02 + 0.003 <------ expanded form
The converse of a conditional statement is "If the sum of the exterior angles of a figure is 360°, then the figure is a polygon.”
What is the inverse of the original conditional statement?
If a figure is a polygon, then the sum of the exterior angles is 360°.
If the sum of the exterior angles of a figure is not 360°, then the figure is not a polygon.
If the sum of the exterior angles of a figure is 360°, then the figure is not a polygon.
If a figure is not a polygon, then the sum of the exterior angles is not 360°.
Answer:
If a figure is not a polygon, then the sum of the exterior angles is not 360.
Step-by-step explanation:
The converse of the given statement is -
"If a figure is a polygon, then the sum of the exterior angles is 360°."
What is converse of a conditional statement?You can write the converse of a conditional statement by reversing the hypothesis and conclusion with each other.
Given is the statement as -
"If the sum of the exterior angles of a figure is 360°, then the figure is a polygon.”
Converse of conditional statement can be written as -"If A then B" → "If B then A"
So, we can write the converse as -If a figure is a polygon, then the sum of the exterior angles is 360°.
Therefore, the converse of the given statement is -
"If a figure is a polygon, then the sum of the exterior angles is 360°."
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A gray wolf's sperm contains
39 chromosomes. He mates with a female gray wolf.
How many chromosomes will there be in the resulting zygote?
Answer:
The resulting zygote will have 78 chromosomes.
Step-by-step explanation:
The sperm and eggs are the sex cells of animals. These cells contain half the number of chromosomes compared to the number of chromosomes present in the somatic cell of that particular organism.
When the sperm and the egg cell unite to form a zygote, the 39 chromosomes in the wolf's sperm and the 39 chromosomes in the female wolf's egg will add up to male 78 chromosomes in the zygote.
In the process of sexual reproduction in wolves, each parent contributes 39 chromosomes. So, a zygote formed from the sperm of a male wolf and the egg of a female wolf will contain a total of 78 chromosomes.
Explanation:The concept is related to the process of sexual reproduction in mammals, which includes wolves. Since the process of sexual reproduction involves the combination of both parents' genetic material, each parent contributes half the total number of chromosomes in a zygote.
In the case of a gray wolf, the sperm contains 39 chromosomes. Therefore, the egg from the female gray wolf will also contain 39 chromosomes. When the sperm and egg meet during fertilization, they combine to form a zygote containing a total of 78 chromosomes — 39 from the male and 39 from the female.
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