Answer:
See explanation
Step-by-step explanation:
Given the expression
[tex](5^{18}-25^8)(16^4-2^{13}-4^5)[/tex]
First, simplify all terms:
[tex]25^8=(5^2)^8=5^{2\cdot 8}=5^{16}\\ \\16^4=(2^4)^4=2^{4\cdot 4}=2^{16}\\ \\4^5=(2^2)^5=2^{2\cdot 5}=2^{10}[/tex]
Then the expression is
[tex](5^{18}-5^{16})(2^{16}-2^{13}-2^{10})[/tex]
Use distributive property in both factors:
[tex](5^{18}-5^{16})(2^{16}-2^{13}-2^{10})=\\ \\=(5^{16}(5^2-1))(2^{10}(2^6-2^3-1))=\\ \\=(5^{16}(25-1))(2^{10}(64-8-1))=\\ \\=5^{16}\cdot 24\cdot 2^{10}\cdot 55=\\ \\=5^{16}\cdot 4\cdot 6\cdot 2^{10}\cdot 5\cdot 11=\\ \\=5^{16}\cdot 2^{10}\cdot (4\cdot 11)\cdot (5\cdot 6)=\\ \\=5^{16}\cdot 2^{10}\cdot 44\cdot 30[/tex]
Therefore, this expression is divisible by 30 and by 44
What are the angle measures of triangle ABC?
mA= 30°, m ZB = 60°, m 2C = 90°
mZA= 90°, m ZB = 60°, m 2C = 30°
mZA= 60°, m ZB = 90°, m2C = 30°
mZA= 90°, m ZB = 30°, m2C = 60°
∠A = 90°, ∠B = 60° and ∠C = 30°
Step-by-step explanation:
Step 1: Find whether the triangle is a right angled triangle by using Pythagoras theorem. Given sides are a = 24 (opposite to ∠A), b = 12√3 (opposite to ∠B) and c = 12 (opposite to ∠C).⇒ 12² + (12√3)² = 144 + 432 = 576
⇒ √576 = 24 = a. This shows that the triangle is a right angled triangle.
So ∠A = 90°
Step 2: Use trigonometric equations to determine the other angles.⇒ cos B = AB/BC = 12/24 = 1/2
⇒ ∠B = 60°
Step 3: The sum of the angles in a triangle is 180°. To find ∠C,⇒ ∠C = 180° - (90° + 60°) = 180° - 150°
⇒ ∠C = 30°
The angle measures of triangle ABC is therefore;
mZA= 90°, m ZB = 60°, m ZC = 30°
Angle measures of Right trianglesBy testing for Pythagoras triple;
24² = 12² + (12√3)²576 = 144 + 432576 = 576.Hence, the triangle is a right-angled triangle.
We can then evaluate mZC as follows;
Sin C = 12/24 = 0.5C = Sin-¹(0.5) = 30°And angle B = 180 - 30 -90Angle, B = 60°Read more on angle measures in triangles;
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can someone please help been trying to figure this out for 2 days -.-
Answer:
PC=40 units
Step-by-step explanation:
we know that
The circumcenter is the center of the triangle's circumcircle (the circle that passes through all three of the triangle's vertices)
That means
PC=RC=QC----> is the radius of the circumcircle
step 1
Find the value of x
equate PC and RC
[tex]3x+7=5x-15[/tex]
solve for x
[tex]5x-3x=7+15\\2x=22\\x=11[/tex]
Verify
substitute the value of x
[tex]PC=3x+7=3(11)+7=40\ units[/tex]
[tex]RC=5x-15=5(11)-15=40\ units[/tex]
[tex]QC=51-x=51-11=40\ units[/tex]
so
[tex]PC=RC=QC[/tex] ----> is ok
Which expression is equivalent to the following complex fraction?
2 minus StartFraction 1 Over y EndFraction divided by 3 + StartFraction 1 Over y EndFraction
StartFraction 3 y + 1 Over 2 y minus 1 EndFraction
StartFraction (2 y minus 1) (3 y + 1) Over y squared EndFraction
StartFraction y squared Over (2 y minus 1) (3 y + 1) EndFraction
StartFraction 2 y minus 1 Over 3 y + 1 EndFraction
i hope this will help :)
Answer:
2y-1/ 3y+1
Step-by-step explanation:
over a month the weight of a turkey increases from 20kg to 24kg calculate the increase as a percentage
Answer:
%120
Step-by-step explanation:
Step 1: Divide the new weight by the original weight.
24/20 = 1.2
Step 2: Change 1.2 into percent
To make a percent, multiply the number by 100
1.2 * 100 = %120
Answer: %120
Hugo is pumping regular gas into his truck.Write and wolve an absolute value equation to represent how many galloons of gas will he pumped when the total is $25 plus or minus $0.50
Please, find attached the picture with the whole question.
Answer:
[tex]9.8gallons\leq x\leq 10.2gallons\\ \\ \ [9.8gallons,10.2gallons][/tex]
Both are different forms to represent the same: the amount of gas is between 9.8 gallons and 10.2 gallons, including the borders.
Explanation:
1. Relation between the number of gallons of gas pumped and the total amount paid:
[tex]Number\text{ }of\text{ }gallons=amount\text{ }paid(\$)/price(\$/gallon)[/tex]
2. Conversion
The amount paid is said to be $ 25 ± $0.50
To transform that into number of gallons, divide by the price of the regular gas: $2.50/gallon
[tex]Number\text{ }of\text{ }gallons=\$25/(\$2.50/gallon)\pm$0.50/(\$2.50/gallon)[/tex]
[tex]Number\text{ }of\text{ }gallons=10gallons\pm0.2gallon[/tex]
3. Absolute value equation (inequality)
10 gallons ± 0.2 gallons converted to an absolute value inequality is:[tex]|x-10gallons|=0.2gallons[/tex]
Solution:
[tex]-0.2\leq x-10\leq 0.2[/tex]
[tex]-0.2+10\leq x\leq 0.2+10[/tex]
[tex]9.8\leq x\leq 10.2[/tex]
Hence, the solution is:
[tex]9.8gallons\leq x\leq 10.2gallons\\ \\ \ [9.8gallons,10.2gallons][/tex]
The absolute value equation that represents how many gallons of gas Hugo will pump, assuming a cost of $1.60 per gallon, is |1.6g - 25| ≤ 0.50. Solving this, we find Hugo will pump between approximately 15.31 and 15.94 gallons of gas based on his budget of $25 plus or minus $0.50.
Explanation:Given that Hugo is pumping regular gas into his truck and the total amount he is willing to spend varies between $24.50 and $25.50, we can create an absolute value equation to model this. Assuming the cost per gallon is $1.60, we want to find the number of gallons, represented by 'g', such that the absolute difference between the cost of g gallons and $25 is not more than $0.50.
The absolute value equation would, therefore, be: |1.6g - 25| ≤ 0.50. We can solve this as a compound inequality: -0.50 ≤ 1.6g - 25 ≤ 0.50.
Solving for 'g' in this inequality, we find: 15.3125 ≤ g ≤ 15.9375. This means Hugo will pump between approximately 15.31 and 15.94 gallons of gas.
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How many times can 2 go into 405
Answer:
202 times with a remainder of 5 but if you need an exact number that i would go with 203 because if you round it up
Step-by-step explanation:
Area of a triangle = 1/2 bh
Yo sup??
we know that area of a triangle is given by the formula
A=1/2*b*h
where
b=lenght of base
h=height of the triangle
in the given figure
h=x
b=5x/6
plugging in the values, we get
A=1/2*x*5x/6
A=5x²/12
Please name the triangle as ABC and you will get full credit.
Hope this helps
r(x)=2[tex]\sqrt{x}[/tex] s(x)=[tex]\sqrt{x} \\[/tex]
Step-by-step explanation:
We have,
[tex]r(x)=2\sqrt{x}[/tex] and [tex]s(x)=\sqrt{x}[/tex]
and [tex](rs)(4)=8[/tex]
To find, the value of [tex](\dfrac{r}{s})(3) =?[/tex]
∴ [tex]r(x)s(x)=2\sqrt{x} \sqrt{x}[/tex]
[tex](rs)(x)=2x[/tex]
Also,
[tex](\dfrac{r}{s})(x) =\dfrac{2\sqrt{x} }{\sqrt{x} }[/tex]
[tex]=2[/tex]
∴ The value of [tex](\dfrac{r}{s})(3)[/tex] = 2
Thus, the value of [tex](\dfrac{r}{s})(3)[/tex] is equal to 2.
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HELP! Write the equation of the line using function notation.
f(x) = -3x + 3
f(x) = 3x + 3
f(x) = 2x + 3
f(x) = 1/3x + 3
f(x) = 3x + 3
Solution:
Let us take f(x) = y.
The points indicated in the graph are (0, 3) and (–2, –3).
Slope(m) of the line passing through two points formula:
[tex]$m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the given points in the above formula,
[tex]$m=\frac{-3-3}{-2-0}[/tex]
[tex]$=\frac{-6}{-2}[/tex]
m = 3
constant is the y-intercept which implies c = 3.
The equation of a line standard form is y = mx + c.
y = 3x + 3
The equation of a line is
f(x) = 3x + 3
Perimeter of a rectangle is 52 feet. If the length is 10 less than 2 times the width, what is the width?
Step-by-step explanation:
Let the width be x feet.
Therefore, length = 2x - 10
Perimeter of rectangle = 52
[tex]2(2x - 10 + x) = 52 \\ 2(3x - 10) = 52 \\ \therefore \: 3x - 10 = \frac{52}{2} \\ \therefore \: 3x - 10 = 26\\ \therefore \: 3x = 26 + 10\\ \therefore \: 3x = 36 \\ \therefore \: x = \frac{36}{3} \\ \therefore \: x = 12 \\ \purple{ \boxed{\therefore \: width \: of \: rectangle = 12 \: feet }}[/tex]
Which expression is equivalent to 4/147
283
12V7
please help!
Option A: [tex]28\sqrt{3}[/tex] is the expression equivalent to the expression [tex]4\sqrt{147}[/tex]
Explanation:
The expression is [tex]4\sqrt{147}[/tex]
To find the equivalent expression, let us solve the expression [tex]4\sqrt{147}[/tex]
The square root of 147 can be written as,
[tex]\sqrt{147} =\sqrt{49*3}[/tex]
Since, we know that 49 is a perfect square, we can write the above expression as,
[tex]\sqrt{147} =7\sqrt{3}[/tex]
Multiplying this value with the expression [tex]4\sqrt{147}[/tex], we have,
[tex]4\sqrt{147}=4(7\sqrt{3} )=28\sqrt{3}[/tex]
Thus, the expression which is equivalent to the expression [tex]4\sqrt{147}[/tex] is [tex]28\sqrt{3}[/tex]
Hence, Option A is the correct answer.
Smith chose the underlined words for a reason. What
effect did she hope to have on the audience by using
words with strong negative connotations?
This was one of the matters that motivated Charlotte
Smith to declare that the bicycle had brought about "the
alarming increase of immorality among young women in
the United States" because of the "evil associations and
opportunities" it made possible.
-Wheels of Change,
Sue Macy
She wanted to encourage cycling for women's
health.
She wanted to persuade others that women should
not ride bicycles
She wanted to evoke patriotic feelings in citizens.
She wanted to convince men to ride bicycles.
Answer:
She wanted to persuade others that women should not ride bicycle
Answer:
B.
Step-by-step explanation:
The square root of -1 is:
The United States Air Force has 19 women for every 81 men enlisted. If a squadron has 750 members, approximately how many are women?
Answer: 143
Step-by-step explanation: 19 x 7.5 = 142.5 rounds to 143
Hope this helps
family has an annual income of $23 comma 400. Of this, one fourth
is spent for food, one fifth
for housing, one tenth
for clothing, one ninth
for savings, one fourth
for taxes, and the rest for other expenses. How much is spent for each?
$
nothing is spent for food.
Amount spent for food = $5850, housing = $4680, clothing = $2340, savings = $2600, taxes = $5850, expenses = $2080.
Step-by-step explanation:
Step 1:
Given details are Total Income = $23,400
Step 2:
Amount spent for food, F= 1/4th of 23,400 = [tex]1/4 \times 23400[/tex]
= $5850
Step 3:
Amount spent for housing, H = 1/5th of 23,400 = [tex]1/5 \times23400[/tex]
= $4680
Step 4:
Amount spent for clothing, C = 1/10th of 23,400 = [tex]1/10 \times 23400[/tex] = $2340
Step 5:
Amount spent for savings, S = 1/9th of 13,400 = [tex]1/9\times 23400[/tex] = $2600
Step 6:
Amount spent for taxes, T = 1/4th of 23,400 = [tex]1/4 \times 23400[/tex] =$5850
Step 7:
Find amount spent on other expenses by totaling all expenditures and subtracting from the annual income.
Annual Income = F + H + C + S + T + E
Amount spent on other expenses, E = 23400 - (5850 + 4680 + 2340 + 2600 + 5850)
E = 23400 - 21320
E = $2080
x-9/3=56/x+4 solve for x
Answer:
x = sqrt(273)/2 - 1/2 or x = -1/2 - sqrt(273)/2
Step-by-step explanation:
Solve for x:
x - 3 = 56/(x + 4)
Cross multiply:
(x - 3) (x + 4) = 56
Expand out terms of the left hand side:
x^2 + x - 12 = 56
Add 12 to both sides:
x^2 + x = 68
Add 1/4 to both sides:
x^2 + x + 1/4 = 273/4
Write the left hand side as a square:
(x + 1/2)^2 = 273/4
Take the square root of both sides:
x + 1/2 = sqrt(273)/2 or x + 1/2 = -sqrt(273)/2
Subtract 1/2 from both sides:
x = sqrt(273)/2 - 1/2 or x + 1/2 = -sqrt(273)/2
Subtract 1/2 from both sides:
Answer: x = sqrt(273)/2 - 1/2 or x = -1/2 - sqrt(273)/2
To solve the equation x - 9/3 = 56/x + 4 for x, multiply both sides by x, distribute and simplify, factor out x, set each factor equal to zero, and solve for x to get the solutions 0 and 63.
Explanation:To solve the equation x - 9/3 = 56/x + 4 for x:
Multiply both sides by x to get rid of the fraction: x(x) - 9/3(x) = 56 + 4(x)Distribute and simplify: [tex]x^2 - 3x = 56x + 4x[/tex]Combine like terms: [tex]x^2 - 63x = 0[/tex]Factor out x: x(x - 63) = 0Set each factor equal to zero: x = 0 or x - 63 = 0Solve for x: x = 0 or x = 63Therefore, the solutions for x are 0 and 63.
At the beach, Malia measured the footprints of the people who passed by. The line plot displays the length of each footprint. What fraction of the footprints measure more than afoot?
Length of Footprints
Answer:
still need the answer g?
a factory can fill 225 bottles of orange juice each hour. each bottle of juice contains 24 fluid ounces of juice. each bottle of juice sells for $5.50 how many fluid ounces of juice are filled in each 12 hours shift
Answer:
64800 fluid ounces of juice.
Step-by-step explanation:
Given:
A factory can fill 225 bottles of orange juice each hour.
Each bottle of juice contains 24 fluid ounces of juice.
Question asked:
How many fluid ounces of juice are filled in each 12 hours shift ?
Solution:
By applying unitary method:
A factory can fill number of bottles in 1 hour = 225 (given)
A factory can fill number of bottles in 12 hours = [tex]12\times 225 = 2700\\[/tex]
Each bottle contains = 24 fluid ounces of juice (given)
2700 bottles contain = [tex]24 \times2700 = 64800[/tex] fluid ounces of juice.
Thus, 64800 fluid ounces of juice are filled in each 12 hours shift.
Give the 46th term of the following sequence: -2, -5,-8, -11, -14, ...
[A] -137
[B] 44
[C] -134
[D] -138
Answer:
d
Step-by-step explanation:
it the 46 one in the pattern
Can someone please help me
Answer:
544 units^2
Step-by-step explanation:
Please see attached picture for full solution.
Lee earns $1,075 each month. How much does he earns in 6 months?
Answer:
6450
Step-by-step explanation:
1075*6=6450
Answer:
$6450.00
Step-by-step explanation:
1075 x 6 = 6450
add the .00 because the unit is dollars
reduce to simplest form
6/3+(- 1/6)
Answer:
11/6
Step-by-step explanation:
6/3+(-1/6)
2+(-1/6)
2-1/6
12/6-1/6
11/6
Answer: 11/6
Step-by-step explanation:
is 54183 divisble by 5,6,and 9
Answer: No.
Step-by-step explanation:
If you divide 54183 by each number, it would be in decimal form.
Answer:
No
Step-by-step explanation:
A car travels at a constant speed. The table shows the distance y
(in miles) that the car travels after x
minutes. How far does the car travel after 12 minutes
?
the car trave after 12 minute in mile
the car travels 8 miles after 12 minutes.
To find out how far the car travels after 12 minutes, we first need to determine the time interval that includes 12 minutes. From the table, we see that the time intervals are spaced by 10 minutes each.
Since 12 minutes falls between 10 and 20 minutes, we need to find the corresponding distance for this time interval.
Given that the car travels at a constant speed, we can see that the distance traveled in each time interval is constant.
From the table:
- From 0 to 10 minutes, the car travels 8 miles.
- From 10 to 20 minutes, the car also travels 8 miles.
Therefore, if the car travels 8 miles in the first 10 minutes, it would also travel 8 miles in the next 2 minutes (from 10 to 12 minutes).
So, the car travels 8 miles after 12 minutes.
The complete Question is given below:
A car travels at a constant speed. The table shows the distance y (in miles) that the car travels after x minutes. How far does the car travel after 12 minutes?
Time(minutes), x 0 | 10 | 20 | 30
Distance(miles), y 0 | 8 | 16 | 24
A shipping container is in the shape of a right rectangular prism with a length of 8 feet, a width of 3.5 feet, and a height of 14.5 feet. The container is completely filled with contents that weigh, on average, 0.65 pound per cubic foot. What is the weight of the contents in the container, to the nearest pound?
Answer:
Volume = 8 * 3.5 * 14.5 =
406 cubic feet
.65 pounds / cubic foot * 406 =
263.9 pounds
Step-by-step explanation:
Answer:
264 pound if you had to round it
Step-by-step explanation:
Rajeev walked 7/8 of a mile in 1/4 of an hour. What was the speed in miles per hour?
Answer:
Rajeev walked at 3.5 miles per hour of speed
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Distance Rajeev walked = 7/8 of a mile = 0.875 miles
Time of walking = 1/4 of an hour = 15 minutes
2. What was the speed in miles per hour?
Let's use the Direct Rule of Three for answering this question, as follows:
Distance in miles Time in minutes
0.875 15
x 60
*************************************************
15x = 0.875 * 60
15x = 52.5
x = 52.5/15
x = 3.5
Rajeev walked at 3.5 miles per hour of speed
How do i slove 6=m/7 -3
Answer:
m=63
Step-by-step explanation:
6=m/7-3
m/7=6+3
m/7=9
m=9*7
m=63
I WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWER
Every month, Midtown Grocery Store donates 8-ounce cans of vegetables to a food bank. The food bank's volunteers fill bags with these cans and deliver the bags to families in need.
There is a proportional relationship between the number of bags the food bank's volunteers can fill, x, and the total number of cans they deliver, y.
x (bags) y (cans)
5 50
7 70
8 80
9 90
What is the constant of proportionality? Write your answer as a whole number or decimal.
cans per bag
Answer:8 80
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
Find the missing number:
QUICKLY PLEASE
Answer:
10
Step-by-step explanation:
Jack deposited $1,400 in his bank account. After 3 years, the account earned
$294 in interest. Find the simple
interest rate.
Answer:
his intrest rate is 7%
Step-by-step explanation:
294/1400=0.21
0.21/3 years = 0.07
0.07=7%
1400*0.07=98
98*3 years = 294
The rate of simple interest the account earned is 7%.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
Given, P = 1400, t = 3 and SI = 294.
∴ 294 = (1400×3×r)/100.
29400 = 4200r.
42r = 294.
r = 7%
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