Answer:
[tex]T_n=-1(-5)^n^-^1[/tex]
Step-by-step explanation:
We are given;
A geometric sequence;
-2,10,-50
Required to determine the nth term
The nth term in a geometric sequence is given by the formula;
[tex]T_n=a_1r^n^-^1[/tex]
where [tex]a_1[/tex] is the first term and r is the common ratio;
In this case;
[tex]a_1=-2[/tex]
r = 10 ÷ -2
= -5
Therefore;
To get the nth term in the given geometric sequence we use;
[tex]T_n=-1(-5)^n^-^1[/tex]
Thus, the nth term is [tex]T_n=-1(-5)^n^-^1[/tex]
If a circle has a diameter of 18cm, how long is the circumference?
Answer:
56.52
Step-by-step explanation:
C=3.14 * D
whats is 38.96×15.7
What is the equivalent expression for 6(x-7)+50
Answer:
3x+4
Step-by-step explanation:
Solve the system of linear equations by substitution.What is the solution to x=2y+y and 3x+2y=3
Answer: the first one is 3y
Step-by-step explanation:
Go to the website mathpapa , type in the problem and it gives you the answer with steps
The perimeter of a rectangular atrium is 104 inches. The length of the atrium is three times the width. Find the length and the width.
Answer:
Length = 39 inches , breadth = 13 inches
Step-by-step explanation:
Given:
The perimeter of a rectangular atrium is 104 inches.
The length of the atrium is three times the width.
Question asked:
The length and the breadth of rectangular atrium = ?
Solution:
Let breadth of rectangular atrium = [tex]x[/tex]
Then, the length of rectangular atrium = [tex]3x[/tex] (given)
Perimeter of rectangle = [tex]2\times(length + breadth)[/tex]
[tex]104 = 2\times( 3x + x )[/tex]
[tex]104 = 2\times 4x[/tex]
[tex]104 = 8x[/tex]
Dividing both side by 8
[tex]13 = x[/tex]
breadth of rectangular atrium = [tex]x[/tex] = 13 inches
length of rectangular atrium = [tex]3x[/tex] = [tex]3 \times13 = 39[/tex] inches
Thus, length and the breadth of rectangular atrium are 39 and 13 inches.
kevin uses each of the digits 6,4,3 and 8, once and once only to make four digit numbers.
what is the smallest odd number that he can make?
Answer:
3468
Step-by-step explanation:
We can make four digit number from the digits 6,4,3,8
Smallest digit for thousands is 3=3000
Smallest digit for hundreds (out of remaining 6,4,8) is 4 = 400
Smallest digit for tenths (out of remaining 6,8) is 6= 60
And unit digit is 8
So the smallest number is 3000+400+60+8=3468 answer
A + 6 equals 3 a - 8
Answer:
7
Step-by-step explanation:
Let's solve your equation step-by-step.
a+6=3a−8
Step 1: Subtract 3a from both sides.
a+6−3a=3a−8−3a
−2a+6=−8
Step 2: Subtract 6 from both sides.
−2a+6−6=−8−6
−2a=−14
Step 3: Divide both sides by -2.
−2a
−2
=
−14
−2
a=7
Answer:
a=7
a collection of dimes an nickels is worth $3.30. if there are 42 coins in all, how many of each kind of coin is there ?
==============================
Work Shown:
d = number of dimes
n = number of nickels
10d = value of all the dimes in cents
5n = value of all the nickels in cents
10d+5n = total value of all the coins in cents
$3.30 = 3.30*100 = 330 cents
so one equation is 10d+5n = 330
-------
Let's set up the second equation
we have 42 coins, so n+d = 42
subtract d from both sides to get n = 42-d
-------
Go back to the first equation and apply substitution to solve for d.
10d+5n = 330
10d+5(42-d) = 330 ... plug in n = 42-d
10d+5(42)+5(-d) = 330 ... distribute
10d+210-5d = 330
5d+210 = 330
5d = 330-210 ... subtract 210 from both sides
5d = 120
d = 120/5 ... divide both sides by 5
d = 24
-------
Now we can use that to find n.
n = 42-d
n = 42-24 ... plug in d = 24
n = 18
------
Check:
n = 18 nickels
5*n = 5*18 = 90 cents from just the nickels
d = 24 dimes
10*d = 10*24 = 240 cents from just the dimes
5n+10d = 90+240 = 330 cents = $3.30 total from all the coins
n+d = 18+24 = 42 coins total
Answers are confirmed
Final answer:
To solve the question, set up a system of linear equations based on 0.10d + 0.05n = 3.30 and d + n = 42. Solve the system to find there are 33 dimes and 9 nickels in the collection.
Explanation:
The question involves solving a system of linear equations based on the given conditions involving dimes and nickels. To find out how many of each kind of coin there are, we can set up the following equations using the facts provided:
Let d be the number of dimes.
Let n be the number of nickels.
Since the total value is $3.30, we can write the equation: 0.10d + 0.05n = 3.30 (since a dime is worth 10 cents and a nickel is worth 5 cents).
We are also told that there are 42 coins in total, which gives us the equation: d + n = 42.
Now we have a system of equations:
0.10d + 0.05n = 3.30
d + n = 42
To solve this system, we can multiply the second equation by 0.10 to make the coefficient of d the same in both equations:
0.10d + 0.05n = 3.30
0.10d + 0.10n = 4.20
We then subtract the first equation from the second to eliminate d:
0.10n = 0.90
n = 9 nickels
Plugging n = 9 into the second original equation d + 9 = 42, we get:
d = 42 - 9
d = 33 dimes
Therefore, there are 33 dimes and 9 nickels in the collection.
What is the translation shown in the following graph?
(x + 3, y - 4)
(x - 3, y + 4)
(x + 4, y - 3)
(x - 4, y + 3)
Answer:
(x - 4, y + 3)
Step-by-step explanation:
This is because when you follow the movement of the individual points you can see that they have moved 3 spaces up which is shown as y + 3, and they have moved 4 spaces to the left which is shown as x - 4
Answer:
The correct answer is: D
Step-by-step explanation:
(x - 4, y + 3)
Hope this helps! :)
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What’s the distributive property of 12(x+5)?
Answer:
12x+60
Step-by-step explanation:
12 gets multiplied with x
12 gets multiplied with 5
Which gives 12x + 60
A customer at the grocery store purchased 27 apples and an unknown number of bananas. The customer purchased a total of 58 apples and bananas. Write an equation with a variable that represents this situation. Explain your process for determining this equation, then solve for how many bananas the customer purchased.
Answer:
The equation is
(x+27)= 58
Therefore the customer purchased 31 bananas
Step-by-step explanation:
Given , A customer at the grocery store purchased 27 apple and unknown number of bananas. The customer purchased a total of 58 apple and bananas.
Let the number bananas be x
He purchased a total (x+27) apples and bananas.
According to the problem,
(x+27)= 58
⇔x= 58-27
⇔x = 31
Therefore the customer purchased 31 bananas
what is the soulution to the system
(-9,-9)
(-36,-9)
(-9,-36)
(9,-9)
Answer:
(-9,-9)
I Agree
Step-by-step explanation:
A shopper buys cat food in bags 4 lbs. her cat eats 3/4 lb each week. How many weeks does one bag last? Draw a diagram
Answer:
5 weeks
Step-by-step explanation:
how do i find the imaginary unit?
[tex]\bf \pm\sqrt{-14}\implies \pm\sqrt{(-1)(14)}\implies \pm\sqrt{-1}\cdot \sqrt{14}\implies \stackrel{\sqrt{-1}}{\pm\stackrel{\downarrow }{i}\sqrt{14}}[/tex]
Enter the value for x that makes the equation true
36(x-5)=9x-18
Answer:
x = 6
Step-by-step explanation:
Solve for x:
36 (x - 5) = 9 x - 18
Expand out terms of the left hand side:
36 x - 180 = 9 x - 18
Subtract 9 x from both sides:
(36 x - 9 x) - 180 = (9 x - 9 x) - 18
36 x - 9 x = 27 x:
27 x - 180 = (9 x - 9 x) - 18
9 x - 9 x = 0:
27 x - 180 = -18
Add 180 to both sides:
27 x + (180 - 180) = 180 - 18
180 - 180 = 0:
27 x = 180 - 18
180 - 18 = 162:
27 x = 162
Divide both sides of 27 x = 162 by 27:
(27 x)/27 = 162/27
27/27 = 1:
x = 162/27
The gcd of 162 and 27 is 27, so 162/27 = (27×6)/(27×1) = 27/27×6 = 6:
Answer: x = 6
Finding the Median from a Dot Plot
Highlands
The dot plots show rainfall totals for several spring
in highland areas and lowland areas.
What is the median rainfall for the highland storms?
4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
Rainfall (mm)
Lowlands
median rainfall for the lowland storms?
LLLLLLL
2
4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
Rainfall (mm)
Answer:
16mm and 12mm
Step-by-step explanation:
Final answer:
The median rainfall for the highland storms is 19 mm and for the lowland storms is 13 mm.
Explanation:
To find the median rainfall for the highland storms, we need to locate the middle value in the dot plot. Since there are 14 observations, the median is between the seventh value, 18, and the eighth value, 20. To find the median, add the two values together and divide by two: (18 + 20) / 2 = 19.
To find the median rainfall for the lowland storms, we also need to locate the middle value in the dot plot. Since there are 14 observations, the median is between the seventh value, 12, and the eighth value, 14. To find the median, add the two values together and divide by two: (12 + 14) / 2 = 13.
I need help please and thank you
Answer:
20 degrees.
Step-by-step explanation:
The 3 angles of a triangle add up to 180 degrees.
Therefore the third angle in this triangle
= 180 - (120 + 40)
= 180 - 160
= 20 degrees.
What is the median for 5, 5, 5, 10, 10, 15, 15, 20, 25, 30, 35, 40, 40, 45, 50, 50?
Answer:
22.5
Step-by-step explanation:
1) Arrange the numbers in order by size.
(5,5,5,10,10,15,15,20,25,30,35,40,40,45,50,50)
2) If there is an odd number of terms, the median is the center term.
3) If there is an even number of terms, add the two middle terms and divide by 2.
(25+20=45)
45 divided by 2 is 22.5
22.5 is your median
Ann thought of a number N, multiplied it by 5 and added 7. Then she told the result R to Jim. Write a formula that will tell you the value of R for any value of N
Answer:
[tex]R=5N +7[/tex]
Step-by-step explanation:
We want to write a formula for the statement:
Ann thought of a number N, multiplied it by 5 and added 7.
When we multiply N by 5, we get 5N
When we add 7 to 5N we get 5N+7
Our formula now becomes:
R=5N +7
Which expression could be used to find the volume of the prism shown below?
A rectangular prism with length of 12, height of 10, and width of 4.
(4 times 12) times 10
(4 + 12) times 10
(10 + 4) times 12
(10 + 12) times 4
Answer:
The answer is A
Step-by-step explanation:
The volume is found by [tex]l*w*h[/tex]
Therefore you multiply, 4*12*10
Answer:
The answer is A
Step-by-step explanation:
The sum of 21, 1.7,0.25
21+1.7+0.25=22.95
You add 21+1.7, which equals 22.7, then add 0.25 to get 22.95.
Mara spent 3/5 of her vacation in British Columbia. While in that province, she spent 1/2 of her time in Vancouver. What fraction of her vacation did Michaela spend in Vancouver? If her vacation lasted 20 days, how many days did she spend in Vancouver?
Answer:
6 days
Step-by-step explanation:
Data given:
Vancouver is in the British Columbia
3/5 of the vacation was spent in British Columbia
1/2 of the time spent in British Columbia was spent in Vancouver.
The whole vacation was 20 days long
total days spent in British Columbia = 3/5 *20
total days spent in British Columbia = 12
Since the 1/2 of the time in British Columbia was spent in Vancouver then
time spent in Vancouver = 1/2 * 12
time spent in Vancouver =6 days
Mara spent [tex]\(\frac{3}{10}\)[/tex] of her vacation in Vancouver. If her vacation lasted 20 days, she spent 6 days in Vancouver.
Mara spent [tex]\(\frac{3}{10}\)[/tex]of her vacation in British Columbia. While in British Columbia, she spent [tex]\(\frac{1}{2}\)[/tex] of her time in Vancouver.
To find the fraction of her entire vacation that Mara spent in Vancouver, we multiply the two fractions:
[tex]\[ \text{Fraction of vacation in Vancouver} = \frac{3}{5} \times \frac{1}{2} = \frac{3 \times 1}{5 \times 2} = \frac{3}{10} \][/tex]
So, Mara spent [tex]\(\frac{3}{10}\)[/tex] of her vacation in Vancouver.
Next, to find out how many days she spent in Vancouver, we take the total number of days of her vacation, which is 20 days, and multiply it by the fraction of the vacation spent in Vancouver:
[tex]\[ \text{Days in Vancouver} = 20 \times \frac{3}{10} \][/tex]
[tex]\[ \text{Days in Vancouver} = 6 \][/tex]
Therefore, Mara spent 6 days in Vancouver.
2. A sweater costs $35. Find the total cost of the
sweater if the sales tax is 5%.
The total cost of the sweater will be $36.75.
What is Percentage?Percentage is a number or ratio which is a fraction of hundred.
Given,
Cost price of sweater =$35.
Sales tax= 5%.
The total cost of the sweater can be calculated as,
Total cost price = CP of sweater + sales tax
= 35 + (5/35)*100
=$36.75
Hence, The total cost price of sweater would be $36.75.
Learn about Percentages:
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Given: a ∥ b and ∠1 ≅ ∠3
Prove: e ∥ f
Horizontal and parallel lines e and f are intersected by parallel lines a and b. At the intersection of lines a and e, the bottom left angle is angle 1. At the intersection of lines b and e, the uppercase right angle is angle 2. At the intersection of lines f and b, the bottom left angle is angle 3 and the bottom right angle is angle 4.
We know that angle 1 is congruent to angle 3 and that line a is parallel to line b because they are given. We see that __________ by the alternate exterior angles theorem. Therefore, angle 2 is congruent to angle 3 by the transitive property. So, we can conclude that lines e and f are parallel by the converse alternate exterior angles theorem.
Which information is missing in the paragraph proof?
∠2 ≅ ∠4
∠1 ≅ ∠2
∠2 ≅ ∠3
∠1 ≅ ∠4
Answer:
∠1 ≅ ∠2
Step-by-step explanation:
As shown in the figure:
We need to prove e ∥ f using the congruent angle.
So, check the options:
A) ∠2 ≅ ∠4 ⇒ (Wrong)
B) ∠1 ≅ ∠2 ⇒ (True) because a ∥ b (Given)
C) ∠2 ≅ ∠3 ⇒ It is required to prove that to prove e ∥ f , it can't be used.
D) ∠1 ≅ ∠4 ⇒ (Wrong)
The complete sentence will be:
We see that ∠1 ≅ ∠2 by the alternate exterior angles theorem.
Therefore, angle 2 is congruent to angle 3 by the transitive property.
The missing information in the paragraph proof is: ∠2 ≅ ∠4.
In the given proof, it is correctly established that angle 1 is congruent to angle 3 because lines a and b are parallel, and this is due to the alternate exterior angles theorem.
Furthermore, it is correctly deduced that angle 2 is congruent to angle 3 through the transitive property.
However, to conclude that lines e and f are parallel using the converse alternate exterior angles theorem, it is essential to establish that angle 2 is congruent to angle 4.
Without this information, the proof is incomplete because it doesn't demonstrate the congruence between the corresponding angles on lines e and f at their intersection with line b.
To complete the proof, you would need to show that ∠2 ≅ ∠4, thereby demonstrating that all pairs of corresponding angles between lines e and f are congruent.
This additional congruence statement would justify the application of the converse alternate exterior angles theorem, allowing you to conclude that e ∥ f.
for such more questions on angle
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Is 7% sales tax or 1/20 sales tax bigger
Answer: 7%
Step-by-step explanation:
5) A stereo speaker in the shape of a triangular pyramid has a height of 6 inches. The area of the base of the speaker is 11 square inches. What is the volume of the speaker in cubic inches?
volume of the speaker= 22 cubic inches
Step-by-step explanation:
The formula to find this question is V= 1/3 BHWHERE H =6 INCHESArea of base = 11 square inchestherefore,v= 1/3 (11) (6)volume of the speaker= 22 cubic inchesthe sum of 4 numbers is 771. the ratio of the first to second number is 2:3. the ratio of the second to third is 5:4. the ratio of the third to the fourth is 5:6. find the value of the second number
Answer:
The second number is 225.
Step-by-step explanation:
Consider the provided information.
Let the first number is x.
Second number
[tex]\dfrac{x}{\text{Second number}} =\dfrac{2}{3}\\\\\text{Second number}=\dfrac{3}{2}x[/tex]
Third number is:
[tex]\dfrac{\text{Second number}}{\text{Third number}} =\dfrac{5}{4}\\\\\text{Third number}=\dfrac{3}{2}x\times\dfrac{4}{5}=\dfrac{6}{5}x[/tex]
Fourth number is:
[tex]\dfrac{\text{Third number}}{\text{Fourth number}} =\dfrac{5}{6}\\\\\text{Fourth number}=\dfrac{6}{5}x\times\dfrac{6}{5}=\dfrac{36}{25}x[/tex]
The sum of 4 numbers is 771.
[tex]x+\dfrac{3}{2}x+\dfrac{6}{5}x+\dfrac{36}{25}x=771[/tex]
[tex]50x+75x+60x+72x=38550[/tex]
[tex]257x=38550\\x=150[/tex]
First number is 150.
[tex]\text{Second number}=\dfrac{3}{2}\times150=225[/tex]
Hence, the second number is 225.
The value of the second number is 165.21.
Step 1: Understand the problem.
We have four numbers whose sum is 771. The ratios between consecutive numbers are given. We need to find the value of the second number.
Step 2: Construct equations using the provided ratios.
Let the four numbers be represented as 2x, 3x, 4x, and 5x respectively (using the smallest common multiple of the ratios).
Step 3: Create an equation using the total of the numbers.
2x + 3x + 4x + 5x = 771
Step 4: Solve for x.
[tex]\(2x + 3x + 4x + 5x = 771\)[/tex]
[tex]\(14x = 771\)[/tex]
[tex]\(x = \frac{771}{14}\)[/tex]
[tex]\(x = 55.07\)[/tex]
Step 5: Find the value of the second number.
The second number is 3x.
[tex]\(3x = 3 \times 55.07 = 165.21\)[/tex]
So, the value of the second number is 165.21.
How do u do this with a guess check revise graph?
Answer:
12 inches by 15 inches
Step-by-step explanation:
Let
Width of the painting = x inches, then
Length of the painting [tex]=1\dfrac{1}{4}x[/tex] inches
The area of the painting:
[tex]A=\\ \\=\text{Width}\times \text{Length}=\\ \\=x\times 1\dfrac{1}{4}x=\\ \\=\dfrac{5}{4}x^2\ in^2[/tex]
Hence,
[tex]\dfrac{5}{4}x^2=180\\ \\x^2=\dfrac{4}{5}\times 180=4\times 36=144\\ \\x=12\ inches\\ \\\text{Width}=12\ inches\\ \\\text{Length}=\dfrac{5}{4}\times 12=15\ inches[/tex]
please answer both with work,please use a paper and picture, thanks
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Answer:
a. [tex]$ \frac{\textbf{17}}{\textbf{4}} $[/tex]
b. [tex]$ \frac{\textbf{3}}{\textbf{8}} $[/tex]
Step-by-step explanation:
a. [tex]$ \textbf{3} \hspace{1mm} \textbf{+} \hspace{1mm} \textbf{1}\frac{\textbf{1}}{\textbf{4}} $[/tex]
A mixed fraction of the form [tex]$ a\frac{x}{y} = a + \frac{x}{y} $[/tex]
[tex]$ \therefore 3 + 1\frac{1}{4} = 3 + 1 + \frac{1}{4} $[/tex]
[tex]$ = 4 + \frac{1}{4} $[/tex]
[tex]$ = \frac{\textbf{17}}{\textbf{4}} $[/tex]
b. [tex]$ \textbf{2} \hspace{1mm} \textbf{-} \hspace{1mm} \textbf{1}\frac{\textbf{5}}{\textbf{8}} $[/tex]
A mixed fraction of the form [tex]$ -c\frac{a}{b} = - c - \frac{a}{b} $[/tex]
[tex]$ \therefore 2 - 1\frac{5}{8} = 2 - 1 - \frac{5}{8} $[/tex]
[tex]$ = 1 - \frac{5}{8} $[/tex]
[tex]$ = \frac{8 - 5}{8} $[/tex]
[tex]$ = \frac{\textbf{3}}{\textbf{8}} $[/tex]
Hence, the answer.
Square root of -4 simplified by using the imaginary number i
Answer:
2i
Step-by-step explanation:
The square root of -4 is equal to 2i.
The square root of -4 can be simplified using the imaginary number i. Since the square root of a negative number is not defined in the set of real numbers, we use i to express it, where i is defined as the square root of -1. Thus, the square root of -4 is calculated as follows:
√-4 = √(-1*4)
= √(-1) * √(4)
= i * 2
= 2i
This result shows that 2i is the simplified form of the square root of -4 using the imaginary number i.