(a) 10^5/10^2 = 1000
(b) x^2/x^6 = 1/(x^4)
(c) x^4y/xy^8 = x^3/y^7
a) To rewrite the expression 10^5/10^2 as the product of two fractions, we can write it as (10^5)/(10^2) = (10 * 10 * 10 * 10 * 10) / (10 * 10).
Next, we can simplify this expression by canceling out the common factors in the numerator and denominator. Since both the numerator and denominator have 10 as a common factor, we can simplify further to get (10 * 10 * 10 * 10 * 10) / (10 * 10) = 10 * 10 * 10 = 1000.
Therefore, the equivalent and simpler expression for 10^5/10^2 is 1000.
(b) For the expression x^2/x^6, we can rewrite it as (x * x) / (x * x * x * x * x * x).
Next, we can simplify this expression by canceling out the common factors in the numerator and denominator. Since both the numerator and denominator have x as a common factor, we can simplify further to get (x * x) / (x * x * x * x * x * x) = 1 / (x * x * x * x).
Therefore, the equivalent and simpler expression for x^2/x^6 is 1/(x^4).
(c) To rewrite the expression x^4y/xy^8 as the product of two fractions, we can write it as (x * x * x * x * y) / (x * y * y * y * y * y * y * y).
Next, we can simplify this expression by canceling out the common factors in the numerator and denominator. Since both the numerator and denominator have x and y as common factors, we can simplify further to get (x * x * x * x * y) / (x * y * y * y * y * y * y * y) = (x^3) / (y^7).
Therefore, the equivalent and simpler expression for x^4y/xy^8 is x^3/y^7.
Complete question :-
Rewrite each expression as the product of two fractions, one of which is equal to . Then, write it as an equivalent, but simpler, expression.. (a) 10^5/10^2 (b) x^2/x^6 (c) x^4y/xy^8
a 0.5 kg ball is kicked with a force of 40 N. what is the resulting acceleration of the ball?
Answer: The resulting acceleration of the ball is 80m/s² .
Step-by-step explanation:
Formula for force : [tex]F= ma[/tex]
,where m = mass pf object and a = the resulting acceleration of object.
As per given , we have
The mass of ball : m= 0.5 kg
Force = 40 N
Let 'a' be the resulting acceleration of the ball.
Substitute all values in formula , we get
[tex]40=(0.5)a\\\\\Rightarrow\ a=\dfrac{40}{0.5}=80\ m/s^2[/tex]
Hence, the resulting acceleration of the ball is 80m/s² .
The acceleration of the ball is 80 Newton per kg.
Given that
A 0.5 kg ball is kicked with a force of 40 N.
We have to determine
What is the resulting acceleration of the ball?
According to the question
The acceleration of the ball is determined by the following formula;
[tex]\rm Acceleration = \dfrac{Force}{Mass}[/tex]
The mass of the ball is 0.5 kg.
The force applied to the ball is 40 N.
Therefore,
The acceleration of the ball is,
[tex]\rm Acceleration = \dfrac{Force}{Mass}\\ \\ \rm Acceleration = \dfrac{40}{0.5}\\ \\ \rm Acceleration = 80 \ Newton \ per \ kg[/tex]
Hence, The acceleration of the ball is 80 Newton per kg.
To know more about Acceleration click the link given below.
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C = 5/9 x ( F - 32)
176*F = ?? *C
The original temperature conversion equation is Tc = 5/9 x (T-f - 32). When converting 176 degrees Fahrenheit, it is multiplied by 5/9 to get approximately 108.89 degrees Celsius.
The equation provided by the student, C = 5/9 x (F - 32), is used to convert a temperature from Fahrenheit (F) to Celsius (C). To find the factor to convert Fahrenheit to Celsius directly, we can manipulate the given formula. The request seems to be asking for the conversion factor that is applied to Fahrenheit to get Celsius. However, the original equation needs to be rewritten correctly as: TC = (5/9) × (T-F - 32). From this, we infer that each degree Fahrenheit is equivalent to 5/9 of a degree Celsius. Therefore, 176°F would convert to 176 × (5/9) = 980/9 or approximately 108.89°C.
The measure of two supplementary angles are x+10 and 2x-5. Find the values of x and then find the angles
Answer:
68 1/3, 111 2/3
Step-by-step explanation:
The sum of two supplementary angles is 180°, so ...
(x +10) +(2x -5) = 180
3x +5 = 180 . . . . . collect terms
x +5/3 = 60 . . . . . divide by 3
x = 58 1/3 . . . . . . . subtract 5/3
The first angle is ...
x +10 = 58 1/3 +10 = 68 1/3
The second angle is ...
2x -5 = 2(58 1/3) -5 = 116 2/3 -5 = 111 2/3
The angles measure 68 1/3 and 111 2/3.
A customer gets a 14% discount on monthly internet service. If the customer pays $51.60 a month after the discount, what is the original price of the internet service?
Answer:
60
Step-by-step explanation:
I used the guess and change method and subtracting every guessed number for 51.6. I found out that if you subtract 60 by 14%, you'll get 51.6.
Hope this helps :)
The expression LaTeX: -5t^2+40t
−
5
t
2
+
40
t
predicts the height, in meters of an object t seconds after a person launches it into the air.
It will take _ seconds for the object to hit the ground.
Answer:
8 seconds
Step-by-step explanation:
Given
h = - 5t² + 40t
When the object hits the ground then h = 0
Substitute h = 0 into the function and solve for t
- 5t² + 40t = 0 ← factor out - 5t from each term
- 5t(t - 8) = 0
Equate each factor to zero and solve for t
- 5t = 0 ⇒ t = 0
t - 8 = 0 ⇒ t = 8
t= 0 denotes the time of launch
t = 8 denotes the time it hits the ground
if f(x) = 5x - 7, what is f(3)?
A. 22
B. 8
c. 2
D. 1
Answer:
B
Step-by-step explanation:
To evaluate f(3), substitute x = 3 into f(x)
f(3) = 5(3) - 7 = 15 - 7 = 8 → B
What is the slope of the line described by the equation below?
у= 5x - 22
оооо
Explanation: Linear equations can be written in the form y = mx + b where the multiplier, m, or the coefficient of the x term represents the slope of the line and b represents the y-intercept of the line.
The linear equation y = 5x - 22 has a slope equal to 5
and a y-intercept equal to -22.
The diameter of a circle is 40 m. Find the aread of the circle in terms of π
Answer:
40π
Step-by-step explanation:
Circumference Formula: C = 2πr
Step 1: Divide diameter by 2 to get the radius
40 / 2 = 20 m -> Radius
Step 2: Plug into the Circumference Formula
C = 2π(20)
C = 40π
Answer: 40π
Answer:
Step-by-step explanation:
The radius of the circle is d/2
The Area of the circle is pi*r^2
The Area of the circle is pi * (d/2)^2
The Area of the circle is A = pi * (40/2)^2
The Area of the circle is A = 400 * pi
Tim answered all the questions on his math yes but got 10 wrong. He received 4 points for every correct answer, and no penalty for wrong answers. His score was 76 points write an equation and find the total number of questions on the test
Answer: (a) 4x + 10(0) = 76
(b) 29questions
Step-by-step explanation: let the correct answer = x.
4points for correct answer each total 4xpoints
Since no penalty for wrong answers, his total points were 76points.
Equation: 4x = 76
x = 19. He scored 19 correct answers.
Total number of questions on the test = 19 correct answers + 10 wrong answers
29 questions
Solve the equation below for x.
log2x + log(2x - 1) = log3x
Answer:
x = 5/4
Step-by-step explanation:
1. cancel x for log 3x and 2x
2. multiply log 2x-1 by log 2
3.simplify to log 4x-2 = log3
4.logs will cancel out and leave you with 4x-2 = 3
5. solve and get 5/4
Answer:
x = 5/4
Step-by-step explanation:
find the values of a and b such that x^4 +ax^3 -7x^2 - 8x +b is exactly divisible by(x+2) and (x+3)
Answer:
a = 2 ; b = 12
Step-by-step explanation:
p(x)=x⁴ + ax³ - 7x² - 8x +b
p(x) is exactly divisible by (x + 2). So p(-2)=0
(-2)⁴ + a(-2)³ - 7(-2)² - 8(-2) +b = 0
16 - 8a - 7*4 +16 + b =0
16 - 8a - 28 + 16 + b =0
4 - 8a + b = 0
-8a + b = -4 -----------(i)
p(x) is exactly divisible by (x + 3). So p(-3)=0
(-3)⁴ + a(-3)³ - 7(-3)² - 8(-3) +b = 0
81 -27a - 63 + 24 + b =0
42 - 27a + b = 0
-27a + b = -42 ------------(ii)
-8a + b = -4 -----------(i)
-27a + b = -42 ------------(ii)
subtract 19a = 38
a = 38/19 = 2
a=2
Substitute a value in equation (i)
-8*2 + b= -4
-16 + b = -4
b = -4 + 16
b = 12
The length of a rectangle is 5 m less than twice the width, and the area of the rectangle is 52 m^2. Find the dimensions of the rectangle.
length is 8m
Width is 6.5m
Explanation:
Let, width = b
So, length = 2b-5
area = 52[tex]m^{2}[/tex]
We know,
area of rectangle = length X width
So, [tex]52m^{2}[/tex] = [tex](2b-5) X b[/tex]
On solving the above equation, we get
Width, b = 6.5m
length, l = 8m
identify this coefficient 8x
Answer:
8
Step-by-step explanation:
The term 8x is a product (as is any term). It is the product of a constant coefficient (8) and a variable (x). The "coefficient" is the multiplier of the variable of interest, so is 8 in this term.
_____
The word "coefficient" is often used to refer to the constant multiplier in any term. For example, in the term 6xy, if we just ask for the coefficient, we are interested in the value 6.
On the other hand, if we ask for the coefficient of y in that term, we expect to be told it is 6x. That is, the "coefficient" is the multiplier of the specified variable or constellation of variables.
The coefficient in the expression 8x is the number 8, which is the numerical factor that multiplies the variable x.
Identifying the Coefficient in the Expression 8x
To identify the coefficient in the expression 8x, we need to recognize that a coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression. In the case of 8x, the coefficient is 8. This means that 8 is the number by which the variable x is being multiplied. Coefficients play a crucial role in equations and functions, as they determine the proportionality and scale of the variable's effect within the expression.
For example, if x represents the number of units sold, and each unit contributes 8 units of value, the expression 8x would represent the total value contributed by all units combined.
Solve for t
-7/4=2/5t
Answer:
Step-by-step explanation:
-7/4 = 2/5t
*5 *5
-35/4 = 2t
-8.75 = 2t
-4. 37
2 times 5 with a expont of 2 minus (4+1)
Answer:
2([tex]5^{2}[/tex])-5
45
Step-by-step explanation:
Answer:
45
Step-by-step explanation:
2x5^2-(4+1)
2x25-5
50-5
45
0.63 ÷ 1.638 what is ir
Answer:
[tex]0.3846154[/tex]
Step-by-step explanation:
We want to perform the following division:
0.63 ÷ 1.638
Let us convert everything to fraction to get:
[tex]\frac{63}{100}\div \frac{1638}{1000}[/tex]
We multiply by the reciprocal of the second fraction to get:
[tex]\frac{63}{100}\times \frac{1000}{1638}[/tex]
[tex]=\frac{63}{1638}*10[/tex]
[tex]=0.03846154*10=0.3846154[/tex]
Final answer:
To find the result of 0.63 divided by 1.638, you multiply both numbers by 1000 to remove the decimals and then divide, resulting in approximately 0.384612.
Explanation:
The question asks for the result of dividing 0.63 by 1.638. To solve this problem, you perform division as you would with any two numbers. The steps are as follows:
Set up the division problem: 0.63 ÷ 1.638.
To make the division simpler, you can multiply both the divisor (1.638) and the dividend (0.63) by powers of 10 to remove the decimals. In this case, multiply both by 1000 to get 630 ÷ 1638.
Perform the division: 630 divided by 1638 equals approximately 0.384612.
Thus, 0.63 ÷ 1.638 is approximately 0.384612.
Tina owns a florist shop. She charges 2.99 cents for each flower plus a delivery fee of 5.
y=_____________, only type what goes in the blank.
Answer:
Charges per flower delivered by Tina is, y= 2.99 (x) + 5
Step-by-step explanation:
Given:
Tina's charges per flower = 2.99 cents
Delivery charged by Tina = 5 units or 5$
We have fill the blank in terms of 'y'.
We know slope intercept form that is : y = m(x)+b
So here we have to fill numbers according to the slope intercept form.
Let the numbers of flowers sold by Tina be 'x'.
Here slope (m) will be the charge of each flower charged by the florist.
The delivery charge is the fixed rate so its the constant value and will be treated equivalent to y-intercept or b values.
Arranging our values:
[tex]m=2.99[/tex] cents , [tex]b=5\$[/tex]
Then the slope-intercept form :
⇒ [tex]y=m(x)+b[/tex]
⇒ [tex]y= 2.99(x) + 5[/tex]
We have to type only that goes in the blank and that is 2.99(x) +5.
y = 2.99(x) + 5 is our final answer.
Prove that the value of the expression: (5^18–25^8)(16^4–2^13–4^5) is divisible by 30 and 44.
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
Find f(100) and show how to solve
The area of a rectangle is 56 cm. The length is 2 cm more than x and the width is 5 cm less than
twice x. Solve for x. Round to the nearest whole number.
Answer:
x = 6, length = 8 cm and width = 7 cm
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Area of a rectangle = 56 cm²
Length of the rectangle = x + 2
Width of the rectangle= 2x - 5
2. Solve for x. Round to the nearest whole number.
Area of a rectangle = Length * Width
(x + 2) (2x - 5) = 56
2x² + 4x - 5x -10 = 56
2x² - x - 66 = 0
Factoring, we have:
(2x + 11) * (x - 6) = 0
x₁ = 2x + 11 = 0 ⇒ 2x = -11; x₁ = - 5.5
x₂ = x - 6 = 0 ⇒ x₂ = 6
We picked x₂ because x₁ will give us negative values for length and width.
Length = 6 + 2 = 8 cm
Width = 2 * 6 - 5 = 12 - 5 = 7 cm
The Murphy family is on a road trip. On the first day, they traveled 30% of their total distance. On the second day, they traveled another 1/4 of the total distance. What fraction of the total distance do they have left after the second day? What percent? ANSWER ASAP!
Answer:
[tex] \frac{11}{20} [/tex]
On the first day, they traveled 30 percents of the total distance. On the second day they traveled one fourth of the total distance. One fourth converted into percentage is 25 percent. Then you add 30 plus 25 because that is the to a
total distance that Murphy's family traveled for 2 days. It will be 55 percents, and you convert 55 percents into fraction will be 55/100, and you simplify it, will be 11/20.
On a coordinate plane, a line is drawn from point J to point K. Point J is at (1, negative 10) and point K is at point (7, 2). What is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1? y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1 –8 –5 0 6On a coordinate plane, a line is drawn from point J to point K. Point J is at (1, negative 10) and point K is at point (7, 2). What is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1? y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1 –8 –5 0 6On a coordinate plane, a line is drawn from point J to point K. Point J is at (1, negative 10) and point K is at point (7, 2). What is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1? y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1 –8 –5 0 6
Lines can be divided into different segments of different lengths using ratios.
The y-coordinate of the point at this ratio is 0
The coordinates of J and K are given as:
[tex]\mathbf{J = (1,-10)}[/tex]
[tex]\mathbf{K = (7,2)}[/tex]
The ratio is given as:
[tex]\mathbf{m:n =5:1}[/tex]
The y-coordinate of the point at this ratio is calculated using:
[tex]\mathbf{y_p = \frac{my_2 + ny_1}{m+n}}[/tex]
So, we have:
[tex]\mathbf{y_p = \frac{5 \times 2 + 1 \times -10}{5+1}}[/tex]
[tex]\mathbf{y_p = \frac{10 -10}{5+1}}[/tex]
Simplify the numerator, and the denominator
[tex]\mathbf{y_p = \frac{0}{6}}[/tex]
Divide the fraction
[tex]\mathbf{y_p = 0}[/tex]
Hence, the y-coordinate is 0
Read more about line segment ratios at:
https://brainly.com/question/20075110
The y-coordinate of the point is 0.
The formula for the section formula is
x [tex]= \frac{mx_2 + nx_1}{m + n}[/tex]
y [tex]= \frac{my_2 + ny_1}{m + n}[/tex]
Substituting in the points, we get
x = [tex]= \frac{5(7) + 1(1)}{5 + 1} = \frac{36}{6} = 6[/tex]
y [tex]= \frac{5(2) + 1(-10)}{5 + 1} = \frac{0}{6} = 0[/tex]
Therefore, the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1 is 0.
Which symbol makes the number sentence true?
A. <
B. >
C. =
Answer:
solution is c
Step-by-step explanation:
look at picture
Part II: What is 5,290,000,000,000 written out in words? What is it in scientific
notation?
Answer:
5,290,000,000,000 written in words would be
five trillion, two hundred and ninety billion
Written in scientific notation would be
5.29*10^12
Step-by-step explanation:
When writing numbers in words you always want to go from left to right, the last three of your digit was in the hundreds place, then the next three were in the thousands place, than the millions, then the billions, and last was the trillions which is where we got five trillion to start out with, you next number was two hundred and ninety billion, because your next place value was in the billions.
When writing numbers using scientific notation you always want just one number to the left of the decimal point. When adding a decimal we put it right after the 5 because then we only have one number in front of the decimal point. Then you would go times 10 to the whatever power it is. In our case it was 12 because you go from your decimal point and count backwards til you get to the correct number that you want
-Hope this helps ;)
Find the circumference and area of a circle with radius 8 cm. Express
your answer in terms of pi
Answer:
c=16*pi
a=64*pi
Step-by-step explanation:
The circumference and area of a circle with a radius of 8 cm are 16 pi cm and 64 pi [tex]cm^2[/tex], respectively.
Explanation:To find the circumference and area of a circle with radius 8 cm, we can use the following formulas:
Circumference = 2 * pi * radius
Area = [tex]pi * radius^2[/tex]
Plugging in the given value, we have:
Circumference = 2 * pi * 8 cm = 16 pi cm
Area =[tex]pi * 8^2 cm^2[/tex] = [tex]64 pi cm^2[/tex]
Learn more about Circumference here:https://brainly.com/question/31885235
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The sum of 8 and a number h is 12 into an equation
Answer: 4
Step-by-step explanation:
The sum of 12 and 8 is 12 add 8 which is 20. The difference between 12 and 8 is 12 minus 8 which is 4.
I don't know if this is right but if it is not tell me plz.
:) Thx
HELPPP PLEASEE
QUICKK
Answer:
i forgot
Step-by-step explanation:
please help me
7)
Multiply.
2x(x2 + 2x - 6)
A) 2x3 + 4x2 - 12x
B) 2x2 + 4x - 12
C) 2x3 + 4x - 12x
D) 2x3 + 4x2 - 6
Multiply the 2x by each term inside parentheses:
2x x x ^2 = 2x^3
2x x 2x = 4x^2
2x x -6 = -12x
Answer: A) 2x^3 + 4x^2 - 12x
Answer:
please mark me brainliest!
Step-by-step explanation:
What is the answer to -12=4+c
Answer:
c=-16
Step-by-step explanation:
We want to solve for c in the equation:
-12=4+c
We add the additive inverse of 4 to both sides of the equation to obtain:
[tex] - 12 + - 4 = 4 + - 4 + c[/tex]
We simplify to obtain:
[tex] - 12 - 4 = 4 - 4 + c[/tex]
We simplify further to get:
[tex] - 16= 0 + c[/tex]
Therefore
[tex] - 16 = c[/tex]
Or
[tex]c = - 16[/tex]
An airplane flies 600 km in 1 hour. What is it’s average speed in kilometers per hour.