Final answer:
To simplify the expression [tex]5^2 \times 5^4[/tex] , add the exponents to get [tex]5^{(2+4)}[/tex], which simplifies to 5^6, resulting in a final value of 15,625.
Explanation:
The question involves simplifying an expression with exponential terms. When multiplying exponents with the same base, we add the exponents according to the product of powers property. The base in this question is 5, and we have two exponential expressions:[tex]5^2[/tex] and [tex]5^4.[/tex]To simplify 5^2 x 5^4, you add the exponents since the bases are the same. This gives you[tex]5^{(2+4)} = 5^6[/tex] .
To simplify [tex]5^2 \times 5^4[/tex], we add the exponents 2 and 4, which gives us [tex]5^{(2+4).[/tex] simplifies to [tex]5^6.[/tex] Calculating this, we get [tex]5 \times 5 \times 5 \times 5 \times 5 \times 5,[/tex] which equals 15,625.
Use the figure to the right to find the value of PT. T is the midpoint of PQ overbar . PT equals 3x+3 and TQ equals 5x-7
help me find the perimeter of this triangle pls:)
one thing to be noteworthy is that this triangle has two angles, a 60° one and a 90° one, meaning the last angle will be a 30° one, thus we can use the 30-60-90 rule.
Check the picture below.
One number is 5 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 555, find the numbers.
Answer:
167
Step-by-step explanation:
Let n be your first number. Then the second number is 5n; and the third number is n+100. So:
n+5n+n+100=569
Final answer:
The three numbers in question are 65, 325, and 165, found by setting up an equation based on the given relationships and solving for the first number.
Explanation:
Finding the Three Numbers
Let's denote the first number as x. According to the problem, the second number is 5 times the first number, which can be written as 5x. The third number is 100 more than the first number and can be represented as x + 100. The sum of these three numbers equals 555, so we can set up the following equation to solve for x:
x + 5x + (x + 100) = 555
Combining like terms, we get:
7x + 100 = 555
Subtracting 100 from both sides gives us:
7x = 455
Now divide both sides by 7:
x = 65
The first number is 65. Using this value, we can find the second number:
5x = 5 × 65 = 325
And the third number:
x + 100 = 65 + 100 = 165
Therefore, the three numbers are 65, 325, and 165.
7) Katie is baking muffins for a picnic. She can bake 24 muffins in 45 minutes. At this rate, how
many muffins can she bake in 90 minutes and how do you know?
Katie can bake 48 muffins in 90 minutes because 90 minutes is twice 45 minutes, and since she can bake 24 muffins in 45 minutes, double the time means she can bake double the amount of muffins.
Katie is baking muffins at a rate where she can bake 24 muffins in 45 minutes. To determine how many muffins she can bake in 90 minutes, we simply need to set up a proportion and solve for the unknown quantity.
Step-by-Step Solution:
Identify the rate: 24 muffins per 45 minutes.Understand that 90 minutes is twice 45 minutes, so we will have two periods of this duration.Since the rate of baking is consistent, we multiply the number of muffins (24) by the number of 45-minute periods within 90 minutes (which is 2).Calculate the total: 24 muffins per period x 2 periods = 48 muffins.Therefore, Katie can bake 48 muffins in 90 minutes because the duration is double the time it takes to bake the original 24 muffins, hence she can bake twice as many.
Malik collects rare stamps and has a total of 212 stamps. Solve the system of equations.
He has 34 more domestic stamps than foreign stamps. How many foreign stamps does Malik have?
Let x represent the number of domestic stamps and let y
represent the number of foreign stamps.
foreign stamps
This system of equations models the given information
for both stamp types.
How many domestic stamps does Malik have?
x-y = 34
domestic stamps
x + y = 212
Using the two given equations:
x - y = 34
x +y = 212
Rewrite the first one in terms of x:
x = 34 + y
Now replace x in the 2nd equation:
34 + y + y = 212
Simplify:
34 +2y = 212
Subtract 34 from both sides:
2y = 178
Divide both sides by 2:
y = 178/2
y = 89
Now replace y in an equation to solve for x:
x + 89 = 212
x = 212-89
x = 123
He has 123 domestic stamps and 89 foreign stamps.
Malik has 123 domestic stamps and 89 foreign stamps
The equations are given as:
[tex]x - y = 34[/tex]
[tex]x + y = 212[/tex]
Make x the subject in [tex]x - y = 34[/tex]
[tex]x =34 + y[/tex]
Substitute 34 + y for x in [tex]x + y = 212[/tex]
[tex]34 + y + y = 212[/tex]
Evaluate like terms
[tex]34 + 2y = 212[/tex]
Subtract 34 from both sides
[tex]2y = 178[/tex]
Divide both sides by 2
[tex]y = 89[/tex]
Substitute 89 for y in [tex]x =34 + y[/tex]
[tex]x = 34 + 89[/tex]
[tex]x = 123[/tex]
Hence, Malik has 123 domestic stamps and 89 foreign stamps
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I need help, please!
A tennis coach selected 5 of the 8 players he trained to represent his coaching academy in a tournament.
Which ratio is equivalent to the ratio in this situation?
A. 15 over 21
B. 20 over 32
C. 5 over 3
D. 8 over 13
Answer:
B. 20 over 32
Step-by-step explanation:
Because if you multiply both number by 4, you will get the ratio of 20:32
Final answer:
The equivalent ratio to 5 out of 8 players selected is 20 over 32, as both ratios reduce to the same value when simplified. Options A, C, and D are not equivalent to the original ratio of 5 to 3. Therefore, option(B) is correct.
Explanation:
The question asks about equivalent ratios. The tennis coach selected 5 out of 8 players to represent his academy, so the original ratio is 5 selected to 3 not selected (since 8-5 = 3). To find an equivalent ratio, we need to find multiples of both numbers that maintain the same relationship.
Option A, which presents the ratio 15 over 21, can be reduced by dividing both numbers by 3, yielding 5 over 7. This is not equivalent because 5 selected to 3 not selected is different than 5 to 7.
Option B, the ratio of 20 over 32, can also be reduced by dividing both numbers by 4, yielding 5 over 8. This is equivalent to the original ratio of 5 to 3 since the number of selected players would be scaled similarly. Therefore, the correct answer is B. 20 over 32.
Option C, 5 over 3, presents the opposite of the original scenario, where the numerator would represent the selected players, but this ratio does not need scaling, so it's not a valid equivalent ratio in this question.
Lastly, option D, 8 over 13, does not reduce to a ratio equivalent to 5 over 3 as these numbers have no common factors with 5 and 3 respectively.
[tex]6 = \frac{a}{4} + 2[/tex]
take a peek at the fractions in the expression, hmmmm let's see the LCD of all fractions will just be 4, in this case there's one fraction only anyway, so let's multiply both sides by that LCD of 4 to do away with the denominators
[tex]\bf 6=\cfrac{a}{4}+2\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4(6)=4\left( \cfrac{a}{4}+2 \right)}\implies 24=a+8\implies 16=a[/tex]
Can someone please answer this question 3[(x^2)^3]^0
Answer:
sure! Always do what's inside the brackets first and then the parentheses.
Step-by-step explanation:
anyways the answer is 3
The distance, y, in miles, traveled by a car for a certain amount of time, x, in hours, is shown in the graph below:
A graph titled Motion of a Car is shown with Time in hours labeled on x-axis and Distance from Starting Point in miles labeled on y-axis. The scale on the x-axis shows the numbers 1, 2, 3, 4, 5, 6, and the scale on the y-axis shows the numbers 0, 12, 24, 36, 48, 60, 72. There are three straight lines in the graph. The first line joins ordered pair 0, 0 with 1, 12. The second straight line joins 1,12 and 2,12 and the third straight line joins ordered pair 2,12 with the ordered pair 5,36.
Which of the following best describes the motion of the car shown?
It travels for 1 hour, then stops for 1 hour, and finally travels again for 3 hours.
It travels for 2 hours, then stops for 1 hour, and finally travels again for 2 hours.
It travels for 1 hour, then stops for 2 hours, and finally travels again for 5 hours.
It travels for 2 hours, then stops for 3 hours, and finally travels again for 5 hours.
Answer:
It travels for 1 h, then stops for 1 h, and finally travels again for 3 h.
Step-by-step explanation:
The sloped parts of the graph are where the car is moving.
For example, in the first hour the distance travelled changes from zero to 12 mi.
The horizontal part of the graph is where the car is stopped.
For example, between hours 1 and 2, the distance travelled stays the same at 12 mi.
The car travels for 1 h, then stops for 1 h, and finally travels again for 3 h.
how do u solve this.
Answer:x=-36
Step-by-step explanation:
First step: Simplify both sides of the equation by
x=1 ,so you put 1/8 and move x to the side like this 1/8x
Now you got 1/8x+1/2=-4
Step 2: Subtract 1/2 to both sides because it's the smallest constant/number
1/2-1/2=0 and -4-1/2=-9/2
-4 subtracted from 1/2 ,you put a 1 under -4, it would be like this -4/1 subtracted from 1/2
I do the butter-fly method which would be -4*2-1*1 because when you put the fractions like this -4/1-1/2 on paper then you would see why
and you multiply the denominators(bottom), so 1*2=2,and -8-1 equals -9 because -8 is larger than postive 1.
so now we have -9/2
Last step is to multiply by 8 on both sides to get rid of the 8 on the other side(left side) so x will be alone,so 8*-9/2=-36
First you will get -72/2 when you divide it you get -36
Determine which solution is correct for solving 5/7y = 6 using reciprocals
What is Reciprocal?
The reciprocal of a number is 1 divided by that number.
For example, the reciprocal of 3 is 1 divided by 3, which is 1/3.
In the question, it is given:
[tex]\frac{5}{7} y=6\\\\y=\frac{6*7}{5} \\\\y=\frac{42}{5}[/tex]
Thus, the value of y= 42/5
In terms of reciprocal, it can be written as: y=5/42.
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Answer:
This is the answer
Step-by-step explanation:
A city wants to create a garden, According to the plan below... Calculate the area of the garden.
Answer:
178 m²
Step-by-step explanation:
You want to find A - D - B + C
A = 12 * (12 + 4) = 12 * 16 = 192
D = 4 * 8 = 32
B = 4 * 3 / 2 = 12 / 2 = 6
C = 6 * 8 / 2 = 48 / 2 = 24
192 - 32 - 6 + 24 = 160 - 6 + 24 = 154 + 24 = 178
I need to find the distance between pairs of integers like 8 and 32; 15 and 64; and -27 and 18. How do I do this?
Answer:
i believe you have to divide 8 by each number to get the distance between the pairs of integers.
Step-by-step explanation:
Please help very confused
Answer:
x = -8
QR = 6
PR = 9
Step-by-step explanation:
Alrighty, this one has a lot of steps. We have to think about this logically.
The length of PR is x + 17, and the length of PQ is 3, and the length of QR is 2x + 22.
The length of PR could also be written as the length of PQ + QR, which gives us the formula PR = PQ + QR. This allows us to put all our information into one formula to solve for x.
PR = PQ + QR
x + 17 = 3 + 2x + 22
17 - 3 - 22 = 2x - x
-8 = x
so x = -8
Now we can use that x and plug it into the other two formulas:
QR = 2x + 22
QR = 2(-8) + 22
QR = -16 + 22
QR = 6
And now we plug x into PR:
PR = x + 17
PR = -8 + 17
PR = 9
Alternatively, we can use our other formula, PR = 3 + QR, which gets us the same answer:
PR = 3 + QR
PR = 3 + 6
PR = 9
Which shows the best path to find the number of centimeters in 1 yard?
yards - inches → centimeters
yards feet → centimeters
centimeters feet inches
centimeters feet HELP MEEEE
Step-by-step explanation:
1 yard equal to 91.44 centimeters (cm)
Explain the Subtraction Property of Inequalities.
Answer:Well, one of those rules is called the subtraction property of inequality, and it basically says that if you minus a number from one side of an inequality, you have to minus that same number from the other side of the inequality as well. -virtualnerd.com
Step-by-step explanation:
The Subtraction Property of Inequalities allows subtracting the same value from both sides of an inequality without altering its direction, a fundamental concept in algebra.
The Subtraction Property of Inequalities states that you can subtract the same value from both sides of an inequality without changing the inequality's direction. This property is essential in solving inequalities and maintaining the inequality relationship.
For example:
If 3 < 7, then subtracting 2 from both sides gives 1 < 5, which still holds true.
Understanding and applying this property correctly is crucial in algebra and helps in solving various mathematical problems.
Convert dotted decimal IP address into binary. 172.61.35.186
Answer:
10101100.00111101.00100011.10111010
Step-by-step explanation:
The dotted decimal IP address 172.61.35.186 converts to binary as 10101100.00111101.00100011.10111010. Each segment of the IP address is converted separately and reassembled with dots in between the binary segments.
Explanation:To convert a dotted decimal IP address to binary, it is important to understand that each segment of the IP address (divided by dots) is converted separately. Let's take for example the IP address 172.61.35.186.
The first segment is 172. Converted to binary, this becomes 10101100. The second segment is 61. In binary, it is 00111101. The third segment being, 35, turns into 00100011 in binary. Lastly, the fourth segment, 186, is transmuted into 10111010 in binary.
So, the IP address 172.61.35.186, when converted into binary, will be: 10101100.00111101.00100011.10111010.
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Write this ratio as a fraction in the simplest form 2 pounds to 28 ounces
2lbs/28oz
Divide each side by 2
1lbs/14oz
The simplest form of the ratio is: 8/7. To express the ratio of 2 pounds to 28 ounces as a fraction in simplest form, we need to convert both quantities to the same unit of measurement.
Since there are 16 ounces in 1 pound, we can convert 2 pounds to ounces:
2 pounds * 16 ounces/pound = 32 ounces
Now, the ratio becomes:
32 ounces to 28 ounces
To write this ratio as a fraction in simplest form, we can divide both numbers by their greatest common divisor (GCD), which is 4 in this case:
32 ounces ÷ 4 = 8
28 ounces ÷ 4 = 7
So, the simplest form of the ratio is:
8/7
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i need help with the work
Answer:
Step-by-step explanation:
There is an old saying that goes, Every time I go one step forward, I get bumped two steps backward. Taken literally, what would the person's forward prgess be after going through this process 23 times?
Solve the inequality:
x^2(x+2)(x-7) is greater than or equal to 0
Answer:
x² ≥ 0 for all x.
(x + 2)(x - 7) ≥ 0 when x ≤ -2 or x ≥ 7.
So x²(x + 2)(x - 7) ≥ 0 when x ≤ -2 or
x ≥ 7.
Which expression represents a perfect square monomial and it’s square root? Check all that apply
[]121; 11
[]4x2; 2x
[]9x2-1; 3x-1
[]25x; 5x
[]49x4; 7x2
Final answer:
Final answer:
The expressions that represent a perfect square monomial and its square root are: 121 and 11 since 121 is 11 squared; 4x2 and 2x as 4x2 is the square of 2x; and 49x4 and 7x2 since 49x4 is the square of 7x2.
Explanation:
The expression that represents a perfect square monomial and its square root must fulfill a specific criterion where the expression can be written as the square of a monomial. A perfect square monomial, when factored, will give the square of a binomial, which suggests that it's been multiplied by itself. The square root of such an expression will be simply the base of that monomial.
Looking at the provided options, only certain expressions fit this definition:
121; 11 - 121 is indeed a perfect square as it's 11 squared, and its square root is 11.
4x2; 2x - Here, 4x2 is the square of 2x, making 2x its square root.
49x4; 7x2 - In this case, 49x4 is the square of 7x2, hence, 7x2 is the square root of 49x4.
The other expressions listed do not represent perfect square monomials with their respective square roots. In particular, 9x2-1 is not a monomial and 25x is not a square of a monomial.
A phone company uses the equation y = 0.15x + 10 to find y, the monthly charge for a customer sending x text
messages. How many text messages are sent if the monthly charge is $77.50?
Hey!
---------------------------------------
Solution:
77.50 = 0.15x + 10
77.50 - 10 + 0.15x + 10 - 10
67.50 = 0.15x
0.15x = 67.50
0.15x/0.15 = 67.50/0.015
x = 450
---------------------------------------
Check:
77.50 = 0.15(450) + 10
77.50 = 67.50 + 10
77.50 = 77.50
---------------------------------------
Answer:
450 text messages can be sent when the monthly charge is $77.50!
---------------------------------------
Hope This Helped! Good Luck!
PLEASEEE HELP THANK YOU!
Answer:
Hi Sophia! The answer is the option 3!
Step-by-step explanation:
Check the picture!
you can read 52 pages per hour. You read for an hour and half. How many pages have you read? You must read 130 pages for homework. Can you complete the assignment in two hours? Explain your reasoning
Answer:
52*2=104
no you cannot complete the homework under two hours
Step-by-step explanation:
since 52*2 is only 104, and you need 130 pages to complete it, i would say that you can't complete the homework under two hours
how is 1.479 a rational number
Step-by-step explanation:
because it has decimal number.
Based only on the given information, it is guaranteed that AC = BC.
Answer:
What's the question?
Step-by-step explanation:
Answer: It’s true
Step-by-step explanation:
If you were asking if it’s a true and false then the answer is true.
You’re working in the sedan section of dean’s car dealership. A customer makes a down payment of 15% on a new car that costs $13,450. How much is the down payment?
Answer:
Convert 15 % to a decimal.
Then multiply 0.15 x 13450. That means the answer is $2,017.50
Please mark brainliest if this helped.
The down payment for the car is $2,017.50.
Explanation:The down payment can be found by multiplying the cost of the car by the percentage of the down payment. In this case, the down payment is calculated as follows:
Down payment = $13,450 * 15%
Thus, the down payment is $2,017.50.
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Help me please , I don’t seem to get the right answer when I do the check up point
Spiral Review (Reviews 2.6.1, 2.G.3; 3.0A.9)
3. What property describes the number
sentence?
4.
6 +0=6
Answer:
The Identity Property
Step-by-step explanation:
the Identity Property means the number's Identity stays the same; usually either itself times 1, or plus zero