Answer:
So, the simplified version is
[tex]-5\sqrt{7}+7\sqrt{6}[/tex]
In words it can be written as minus 5 square root of 7 end root plus 7 square root of 6 end root
Step-by-step explanation:
[tex]5\sqrt{7}+12\sqrt{6}-10\sqrt{7}-5\sqrt{6}[/tex]
We need to simplify the above expression.
Combining the like terms of the above expression.
Like terms are those that have same variables.
[tex]=(5\sqrt{7}-10\sqrt{7})+(12\sqrt{6}-5\sqrt{6})[/tex]
[tex]=((5-10)(\sqrt{7})+((12-5)(\sqrt{6}))[/tex]
[tex]=((-5)(\sqrt{7})+((7)(\sqrt{6}))[/tex]
So, the simplified version is
[tex]-5\sqrt{7}+7\sqrt{6}[/tex]
In words it can be written as minus 5 square root of 7 end root plus 7 square root of 6
5. Write an equation for the line that is parallel to the given line and that passes through the given point. y = –5x + 3; (–6, 3)
Answer:
y = -5x - 27
Step-by-step explanation:
First and foremost, parallel lines have SIMILAR RATE OF CHANGES [SLOPES], so we keep the -5. Moving forward, we simply plug the coordinate into the Slope-Intercept Formula, y = mx + b --> 3 = -5[-6] + b. Our y-intercept is [0, -27], therefore our parallel equation is y = -5x - 27.
Can someone help me plz
Answer:
C
Step-by-step explanation:
The sign used is the greater then sign, assuming p is the variable standing for the basketball teams' points then the answer is C.
What is another name for a relation that has each element in its domain
paired with exactly one element in its range?
Answer:
Step-by-step explanation:
A function is a relation in which each element of the domain is paired with exactly one element of the range.
A relation is a set of ordered pairs. The set of the first components of each ordered pair is called the domain and the set of the second components of each ordered pair is called the range. Consider the following set of ordered pairs. The first numbers in each pair are the first five natural numbers. The second number in each pair is twice that of the first.
{(1,2),(2,4),(3,6),(4,8),(5,10)}
The domain is{1,2,3,4,5} and the range is{2,4,6,8,10}
So, this relation is a function.
Here is the histogram of a data distribution. All class widths are 1
2
3
4
5
6
7
8
9
10
What is the median of the distribution?
Answer:
6
Step-by-step explanation:
If it’s the green block from 2-6 with 6 being the tallest then it’s 6 a p e x
The median of the histogram of the data distribution where all class widths are 1 is is 6
How to determine the median?From the complete question, we have the following highlights:
The histogram has a bell shapeThe class width is 1When a histogram is bell shaped, the median of the histogram is at the highest bar in the histogram
The highest bar in the histogram has a class of 6
Hence, the median of the histogram is 6
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Andy is learning to play the guitar. Last week he recorded the minutes per day that he practiced. Find the mean absolute deviation. Round to the nearest tenth.
Day S M T W T F S
Minutes 40 55 35 60 20 50 55
Answer:
11.4
Step-by-step explanation:
Step 1: Calculate the mean.
40, 55, 35, 60, 20, 50, 55
=
315
divided by 7
=
45
Step 2: Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations.
40 - 45 = 5
55 - 45 = 10
35 - 45 = 10
60 - 45 = 15
20 - 45 = 25
50 - 45 = 5
55 - 45 = 10
Step 3: Add those deviations together.
= 80
Step 4: Divide the sum by the number of data points.divided by 7
= 11.428
Step 5: Round to the nearest tenth.
= 11.4
Answer:
The mean absolute deviation is approximately is 11.43.Step-by-step explanation:
The means absolute deviations is define by:
[tex]D_{x} =\frac{\sum |x_{i}-x| }{N}[/tex]
From the formula, we observe that we need to find the mean, and then find the different between that mean and each element. Then, we have to sum all those differences and divide this by the total number of elements.
So, the mean is
[tex]x=\frac{\sum x_{i} }{N}\\ x=\frac{40+55+35+60+20+50+55}{7}=45[/tex]
Now, each difference would be
[tex]40-45=-5\\55-45=10\\35-45=-10\\60-45=15\\20-45=-25\\50-45=5\\55-45=10[/tex]
The sum of all differences, using their absolute value, would be:
[tex]5+10+10+15+25+5+10=80[/tex]
Then, we divide this result by the total number of elements which is 7:
[tex]\frac{80}{7} \approx 11.43[/tex]
Therefore, the mean absolute deviation is approximately is 11.43.
the hastings family drove 12/25 of the distance to yellowstone national park on the first day of their vacation. what percent of the distance to the park remained for them to drive?
Step-by-step explanation:
They drove 12 out of 25, so the remaining is 13/25. To convert to percent:
13 / 25 = x / 100
x = 52
52% of the distance remains.
A. Jenna wants to buy a new tablet computer. Top Quality, an electronics store, is selling them at a 15% discount off the list price.
Using t as the list price of the tablet, write two different expressions representing the discounted price.
B. Explain how each expression represents the discounted price.
C. While at Top Quality, Jenna sees a smartphone on sale for 14 off its list price. Her friend tells her to wait and buy it at Big Value, a discount chain, where the same phone is selling for only 75% of the list price.
Should Jenna buy the smartphone at Top Quality or Big Value? Support your answer with mathematical evidence. (Assume that getting the lowest price is Jenna's only consideration.)
Answer:
Step-by-step explanation:
Part A
Cost = T - (15/100) * T
Cost = (85/100)*T
Part B
You are asked to take 15% off the cost of something. The first equation is very clear how to do that -- just take 15% of T away from T
The second part is not so obvious if you are not familiar with it, but the result will be the same.
Start with the first equation
Cost = T - (15/100) T Change 1 T to 100 / 100
Cost = 100*T/100T - 15/100T
Cost = 85 /100 * T
Part C
Cost = Phone - 14 at Top quality. Red in Graph below
Cost = 75/100 * Phone at Big value. Blue in Graph belos
The graph below is a good way to answer this. I won't solve it algebraically when the graph will give you a much better idea which phone to get.
Answer: Up to a phone cost of 55 dollars, the red phone is the better buy.
After 55$ the blue phone is better.
Try this with a couple of values for phone,
What is the correct answer
Answer:
c
Step-by-step explanation:
just took the test
Answer:
B
Step-by-step explanation:
The domain of the function are the input values on the left and the corresponding values on the right are the output values, the range
domain is { 1, 2, 3, 4 }
How long must a ladder be to reach the top of 20” wall if the ladder and the wall form a 32 angle at the top
Answer: 23.58
Step-by-step explanation:
[tex]cos\theta=\dfrac{adjacent}{hypotenuse}\\\\\\cos(32^o)=\dfrac{20}{x}\\\\\\x=\dfrac{20}{cos(32^o)}\\\\\\x=23.58[/tex]
Answer:
23.97 ft
Step-by-step explanation:
In this question apply the expression for determining cosine of an angle.
Cosine of an angle x°=length of the adjacent side÷hypotenuse
[tex]Cos\alpha =\frac{A}{H}[/tex]
where α is the angle in degrees, A is the adjacent side length, and H is the hypotenuse
Given α=32° and A=20ft H=?
Applying the expression
[tex]Cos\alpha =\frac{A}{H} \\\\Cos32=\frac{20}{H} \\\\0.8342=\frac{20}{H}\\ \\H=\frac{20}{0.8342} =23.97[/tex]
In this case, the length of the ladder represents the hypotenuse side of the triangle which will be 23.97 ft
X+3y=28 when x =28 find the value for y plz help
Answer:
y = 0
Step-by-step explanation:
Plug in 28 for x. Solve for the equation:
x + 3y = 28
(28) + 3y = 28
Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. First, subtract 28 from both sides:
28 (-28) + 3y = 28 (-28)
3y = 0
Isolate the variable, y. Divide 3 from both sides:
(3y)/3 = (0)/3
y = 0
y = 0 is your answer.
~
Multiply X to the 2/5 power times X to the 2/9 power
Answer:
[tex] x^{\frac{28}{45}} [/tex]
Step-by-step explanation:
To multiply powers with the same base, add the exponents.
[tex] x^{\frac{2}{5}} \times x^{\frac{2}{9}} = [/tex]
[tex] = x^{\frac{2}{5} + \frac{2}{9} [/tex]
[tex] = x^{\frac{2 \times 9}{5 \times 9} + \frac{2 \times 5}{9 \times 5}} [/tex]
[tex] = x^{\frac{18}{45} + \frac{10}{45}} [/tex]
[tex] = x^{\frac{28}{45}} [/tex]
If you were asked to solve a system of equations in which there are no linear equation to start with you can sometimes begin by isolating and substituting a veritable there a square in both equations true or false
Answer:
The correct answer option is true.
Step-by-step explanation:
The given statement is true that if there is no linear equation to start with, you can isolate and substitute a variable that is squared in both the equation.
For instance, if we have a non linear equation, start by dividing both sides by coefficient of the variable.
Once you do that and isolate a variable, continue solving by substituting that variable into the other equation.
This graph shows the solution to which inequality?
[tex]m=\frac{y2-y1}{x2-x1} \\ \\ m=\frac{2-(-6)}{3-(-3)} \\ \\ m=\frac{8}{6} \\ \\ m=\frac{4}{3}[/tex]
The y-intercept of the graph is -2
The graph is shaded upwards, so we will be using the greater than symbol, but since the line is dotted we will not be using any of the "equal to" symbols.
Hence, the solution of the graph is [tex]y>m=\frac{4}{3} x-2[/tex]
Option: C is the correct answer.
C. [tex]y>\dfrac{4}{3}x-2[/tex]
Step-by-step explanation:By looking at the graph we observe that the line is dotted this means that the inequality will be strict.
Also, this line passes through the point (-3,-6) and (3,2).
Hence, the equation of line is calculated by using a two point form i.e. a line passing through two points (a,b) and(c,d) is calculated with the help of formula as:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
Here (a,b)=(-3,-6) and (c,d)=(3,2)
i.e.
[tex]y-(-6)=\dfrac{2-(-6)}{3-(-3)}\times (x-(-3)}\\\\i.e.\\\\y+6=\dfrac{2+6}{3+3}\times (x+3)\\\\i.e.\\\\y+6=\dfrac{8}{6}\times (x+3)\\\\i.e.\\\\y+6=\dfrac{4}{3}\times (x+3)\\\\i.e.\\\\y+6=\dfrac{4}{3}x+4\\\\i.e.\\\\y=\dfrac{4}{3}x-2[/tex]
Also, the shaded region is towards the origin.
Hence, the inequality is:
[tex]y>\dfrac{4}{3}x-2[/tex]
Jerry has a spinner with 4 sections numbered 1 through 4. He suspects that the spinner is not fair because it seems to land on 2 more often than any other number.
To test this, he spins the spinner 250 times and records the relative frequency of each outcome.
Outcome 1 2 3 4
Relative frequency 0.26 0.24 0.24 0.26
Select from the drop-down menus to correctly complete each statement.
For the spinner to be fair, each outcome will be .
The relative frequencies in the table are .
This means it is likely that the spinner is
♡ The Question ♡
Jerry has a spinner with 4 sections numbered 1 through 4. He suspects that the spinner is not fair because it seems to land on 2 more often than any other number. To test this, he spins the spinner 250 times and records the relative frequency of each outcome. Outcome 1 2 3 4 , Relative frequency 0.26 0.24 0.24 0.26 Select from the drop-down menus to correctly complete each statement.
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ The Answer ♡
For the spinner to be fair, each outcome will be equally likely.
The relative frequencies in the table are relatively close to equal.
This means it is likely that the spinner is fair.
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ The Explanation/Step-By-Step ♡
No Explanation/Step-By-Step provided!
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ Tips ♡
No Tips provided!
The true statements are for the spinner to be fair, each outcome will be equal, the relative frequencies in the table are relatively close and this means it is likely that the spinner is fair.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.
Given that,
Outcome 1 2 3 4
Relative frequency 0.26 0.24 0.24 0.26
The spinner has 4 sections
This means that the probability of landing in a section is:
p = 1/4
p = 0.25
So, for the spinner to be fair, each outcome will be equal
The relative frequencies in the table are relatively close is the true statement.
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What is the cube root of -729a9b6
ANSWER
[tex]\sqrt[3]{- 729{a}^{9} {b}^{6} } = - 9 {a}^{3} {b}^{2} [/tex]
EXPLANATION
We want to find the cube root of
[tex] - 729 {a}^{9} {b}^{6} [/tex]
We express this symbolically as:
[tex] \sqrt[3]{- 729 {a}^{9} {b}^{6} } [/tex]
The expression under the radical called the radicand.
We need to express this radical in exponential form using the property,
[tex] {x}^{ \frac{m}{n} } = \sqrt[n]{ {x}^{m} } [/tex]
Applying this rule gives us:
[tex]\sqrt[3]{- 729 {a}^{9} {b}^{6} } = ({- 729 {a}^{9} {b}^{6}})^{ \frac{1}{3} } [/tex]
[tex]\sqrt[3]{- 729{a}^{9} {b}^{6} } = ({- {9}^{3} {a}^{9} {b}^{6}})^{ \frac{1}{3} } [/tex]
Recall that
[tex] ({a}^{m} )^{n} = {a}^{mn} [/tex]
We apply this rule on the RHS to get,
[tex]\sqrt[3]{- 729{a}^{9} {b}^{6} } = ({- {9}^{3 \times { \frac{1}{3} } } {a}^{9 \times { \frac{1}{3} } } {b}^{6 \times { \frac{1}{3} } }})[/tex]
This simplifies to
[tex]\sqrt[3]{- 729{a}^{9} {b}^{6} } = - 9 {a}^{3} {b}^{2} [/tex]
Answer:
-9a3b2
Step-by-step explanation:
The expression log1/3/log2 is the result of applying the change of base formula to a logarithmic expression. Which could be the original expression?
Answer:
Option C. [tex]log_{2}\frac{1}{3}[/tex]
Step-by-step explanation:
The given logarithmic expression is [tex]\frac{log(\frac{1}{3} )}{log2}[/tex]
Rule of logarithm says
[tex]\frac{log_{e}a }{log_{e}b}=log_{b}a[/tex]
So by this rule,
expression [tex]\frac{log(\frac{1}{3} )}{log2}[/tex] will become [tex]log_{2}\frac{1}{3}[/tex]
Therefore, Option C. [tex]log_{2}\frac{1}{3}[/tex] will be the answer.
To solve the problem we must know about the rule to change the base of any logarithmic expression.
The solution of the given expression [tex]\dfrac{log\dfrac{1}{3}}{log 2}[/tex] is [tex]\rm log_2\dfrac{1}{3}[/tex].
What is the rule for changing the base of a logarithm expression?The formula which helps us to change the base of any logarithm expression,
[tex]\rm log_ab = \dfrac{log_cb}{log_ca}[/tex]
Given to us
[tex]\dfrac{log\dfrac{1}{3}}{log 2}[/tex]
As we have already discussed the formula for the change of the base of any logarithm expression, comparing the formula with that expression,
[tex]\rm log_ab = \dfrac{log_cb}{log_ca} = \dfrac{log\dfrac{1}{3}}{log 2}[/tex]
[tex]\rm log_2\dfrac{1}{3} = \dfrac{log\dfrac{1}{3}}{log 2}[/tex]
Hence, the solution of the given expression [tex]\dfrac{log\dfrac{1}{3}}{log 2}[/tex] is [tex]\rm log_2\dfrac{1}{3}[/tex].
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Question 4
Line c has a slope of 3/4. Line d is perpendicular to c and line d has a slope of --1. True or False
True
False
O
Answer:
False
Step-by-step explanation:
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex]
Given a line with m = [tex]\frac{3}{4}[/tex]
Then the slope of the line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{\frac{3}{4} }[/tex] = - [tex]\frac{4}{3}[/tex]
ne height of Zak is 1.86 metres.
The height of Fred is 1.6 metres.
Write the height of Zak as a fraction of the height of Fred.
Give your answer in its simplest form.
To write the height of Zak as a fraction of the height of Fred, divide Zak's height by Fred's height and simplify the fraction to its simplest form.
Explanation:To write the height of Zak as a fraction of the height of Fred, divide Zak's height by Fred's height. Zak's height is 1.86 metres and Fred's height is 1.6 metres. So the fraction becomes 1.86/1.6.
To simplify this fraction, find the greatest common divisor (GCD) of 1.86 and 1.6, which is 0.02. Divide both the numerator and denominator of the fraction by the GCD to write the height as a fraction in its simplest form.
The simplified fraction is 93/80.
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What is the formula for scientific notation
Answer:General Formula of Scientific Notation. The general from of a number in scientific notation is: a ×10n where 1 ≤ a ≤ 10 and n is an integer. In other words the number that we'll call "a" is is multiplied by 10, raised to some exponent n.
Step-by-step explanation:
Final answer:
The formula for scientific notation involves expressing a number as the product of a coefficient (a number between 1 and 10) and a power of ten. The sign of the exponent is determined by the direction the decimal point is moved to create the coefficient.
Explanation:
The formula for scientific notation is a method of writing very large or very small numbers as a product of two parts: a coefficient and a power of ten. The coefficient must be a number greater than or equal to 1 and less than 10, while the power of ten reflects how many places the decimal point is moved to convert the number to the coefficient. In scientific notation, for example, the Earth's distance from the Sun, which is 150,000,000,000 meters, is expressed as 1.5 × 1011 m.
When converting a number to scientific notation, count the number of places you moved the decimal point to get a number between 1 and 10 for your coefficient. If the decimal point is moved to the left, the exponent will be positive, and if moved to the right, it will be negative. For instance, 2386 can be converted to 2.386 × 103 because the decimal is moved 3 places to the left.
Solve the following quadratic equations by extracting square roots.Answer the questions that follow.
1. x²=16
2. t²=81
3. r²=100=0
4. x²-144=0
5. 2s²=50
Answer:
1. x=±4
2. t=±9
3. r=±10
4. x=±12
5. s=±5
Step-by-step explanation:
1. x^2 = 16
Taking square root on both sides
[tex]\sqrt{x^2}=\sqrt{16}\\\sqrt{x^2}=\sqrt{(4)^2}\\[/tex]
x=±4
2. t^2=81
Taking square root on both sides
[tex]\sqrt{t^2}=\sqrt{81}\\\sqrt{t^2}=\sqrt{(9)^2}[/tex]
t=±9
3. r^2-100=0
[tex]r^{2}-100=0\\r^2 =100\\Taking\ Square\ root\ on\ both\ sides\\\sqrt{r^2}=\sqrt{100}\\\sqrt{r^2}=\sqrt{(10)^2}[/tex]
r=±10
4. x²-144=0
x²=144
Taking square root on both sides
[tex]\sqrt{x^2}=\sqrt{144}\\\sqrt{x^2}=\sqrt{(12)^2}[/tex]
x=±12
5. 2s²=50
[tex]\frac{2s^2}{2} =\frac{50}{2}\\s^2=25\\Taking\ Square\ root\ on\ both\ sides\\\sqrt{s^2}=\sqrt{25}\\\sqrt{s^2}=\sqrt{(5)^2}[/tex]
s=±5 ..
Answer:
[tex]1.+4,-4\\2. +9,-9\\3. +10,-10\\4. +12, -12\\5. +5, -5[/tex]
Step-by-step explanation:
IN order to solve the quadratic equations you just have to solve the square root of the numeric part of the equation:
[tex]x^{2} =16\\x=\sqrt{16}\\ x= +4, -4[/tex]
[tex]t^{2} =16\\t=\sqrt{81}\\ x= +9, -9[/tex]
[tex]r^{2} =100\\r=\sqrt{100}\\ x= +10, -10[/tex]
[tex]x^{2} -144=0\\x=\sqrt{144}\\ x= +12, -12[/tex]
[tex]2s^{2}=50\\s^{2}=\frac{50}{2} \\s=\sqrt{25}\\ s= +5, -5[/tex]
Just remember that the solution for any square root will always be a negative and a positive number.
The slope intercept form of the equation of a line that passes through (-2,13) is y =5x-3what is the point slope form of the equation for this line
Answer:
y - 13 = 5(x + 2)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Given y = 5x - 3 in slope- intercept form
with slope m = 5, then
m = 5 and (a, b) = (- 2, 13)
y - 13 = 5(x - (- 2)), that is
y - 13 = 5(x + 2) ← in point- slope form
The length of a rectangle is 8 mm longer than its width. Its perimeter is more than 32 mm. Let w equal the width of the rectangle.
a. Write an expression for the length in terms of the width.
b. Use expressions for the length and width to write an inequality for the
perimeter, on the basis of the given information.
c. Solve the inequality, clearly indicating the width of the rectangle.
Part A
w = width
L = length
L = w+8 since the length is 8 mm longer than the width
Answer: w+8====================================================
Part B
P = perimeter of rectangle
P = 2*(L+W) = 2L + 2W
We want the perimeter to be more than 32 mm, so we want P to be greater than 32
This means we write P > 32
Replace P with either 2(L+W) or 2L+2W. I'll pick 2L+2W
So we go from
P > 32
to
2L+2W > 32
After this, replace L with W+8 (refer to part A above)
We now have
2(W+8) + 2W > 32
Answer: 2(w+8) + 2w > 32====================================================
Part C
Let's solve the inequality found in part B to get...
2(w+8) + 2w > 32
2w + 16 + 2w > 32
4w + 16 > 32
4w + 16-16 > 32-16 ....... subtracting 16 from both sides
4w > 16
4w/4 > 16/4 ......... dividing both sides by 4
w > 4
Answer: w > 4; The width of the rectangle must be larger than 4 mmTranslate the following phrase into an algebraic expression using the variable x to represent the cost of the puck. Do not simplify the cost of purchasing a hockey stick and puck if the stick costs $7 less than twice the cost of the puck
Final answer:
The algebraic expression for the cost of purchasing a hockey stick and a puck, where the stick costs $7 less than twice the cost of the puck, and using x to represent the cost of the puck, is x + (2x - 7).
Explanation:
To translate the given phrase into an algebraic expression using the variable x to represent the cost of the puck, let's follow the instructions provided in the phrase very carefully. The cost of the hockey stick is described as "$7 less than twice the cost of the puck." Therefore, we first consider "twice the cost of the puck" which is 2x, and then subtract 7 from it to account for the phrase "$7 less than." Hence, the final expression for the cost of the hockey stick is 2x - 7.
Now, to find the cost of purchasing both the hockey stick and the puck, we simply add the cost of the puck (x) to the expression for the cost of the hockey stick (2x - 7), giving us a total cost expression of x + (2x - 7).
Notice that we are not simplifying the expression; we're just writing the combined cost as requested. So the final untranslated expression for the cost of purchasing a hockey stick and a puck based on the given conditions is x + (2x - 7).
Find all numbers whose absolute value is 8.
Answer:
8 or -8Step-by-step explanation:
The absolute value of number a:
|a| = a for a ≥ 0
|a| = -a for a < 0
|a| = 8 ⇔ a = 8 or a = -8
The numbers that have an absolute value of 8 are 8 and -8. This is because the absolute value refers to a number's distance from 0 on a number line, which includes both positive and negative numbers.
Explanation:The absolute value of a number refers to its distance from zero on the number line, ignoring whether it is to the left or right (negative or positive). When we speak of the absolute value of 8, we're looking for numbers whose distance from zero is 8 units. This means we are looking for two numbers: +8 and -8 since they are both 8 units away from 0, but in opposite directions.
So, the numbers whose absolute value is 8 are 8 and -8.
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Choose the correct simplification of the expression 8 time b over a to the power of -5. a to the power of 5 time b all over 8 8 over a to the power of 5 times b 8a5b Already simplified
Expression to simplify: [tex]\frac{8b}{a^{-5} }[/tex]
Remember, when a number has a negative power, it reciprocates (flips over)
First lets write the expression so that the a is in a fraction by itself:
[tex]\frac{8b}{a^{-5} }[/tex] = [tex]8b[/tex] × [tex]\frac{1}{a^{-5} }[/tex]
So to simplify, all we do is reciprocate [tex]\frac{1}{a^{-5} }[/tex] and make the power positive:
[tex]8b[/tex] × [tex]\frac{1}{a^{-5} }[/tex] = [tex]8b[/tex] × [tex]a^{5}[/tex]
=[tex]8a^{5}b[/tex]
----------------------------------------------
Answer:
[tex]8a^{5}b[/tex]
The correct simplification Expression is [tex]8b/a^-5[/tex]
The correct simplification of the expression "8 times b over a to the power of -5" is [tex]8b/a^-5[/tex]. This can be simplified by using the following rule:
[tex]x^m \times x^n = x^ \ (m + n)[/tex]
Therefore, we can rewrite the expression as:
[tex]8b/a^-5 = 8b \times a^5[/tex]
We can then multiply the numerator and denominator by 8 to get:
[tex]8b \times a^5 = 64b \times a^5[/tex]
Finally, we can rearrange the factors to get:
[tex]64b \times a^5 = 8a^5 \times b[/tex]
Therefore, the simplified expression is [tex]8a^5 \times b.[/tex]
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-2(x+5)=4 sole using distributive property
Answer:
x = -7
Step-by-step explanation:
-2x - 10 = 4
-2x = 14
x = -7
Verification:
-2(-7 + 5) = 4
-2(-2) = 4
4 = 4
The cost, (x), for parking in a city lot is given by c(x) = 3x + 4.00, where x is
the number of hours. What does the slope mean in this situation?
A. The rate of change of the cost of parking in the lot is $3.00 per
hour.
B. The rate of change of the cost of parking in the lot is $4.00 per
hour.
C. It costs a total of $4.00 to park in the lot.
D. Parking in the lot costs $3.00 per car.
Help
Answer:
A) The rate of change of the cost of parking in the lot is $3.00 per hour
Step-by-step explanation:
for y=mx+b:
b is the base "cost" ($4)
x is the number of hours parked in the parking lot
m is the slope or how much it costs to be parked PER hour
therefore, for x hours, the cost would be 3*#of hours + $4, so the rate of change of the cost of parking in the lot is $3 per hour (which is shown by m or the slope)
Answer:
Option A
Step-by-step explanation:
we have
x -----> is the number of hours
c(x) ----> is the cost for parking in a city lot
we know that
c(x)=3x+4.00
This is a linear equation in slope intercept form
where
the rate of change or slope m is equal to m=$3 per hour
the y-intercept is equal to b=$4.00 (this is the cost when the number of hours is equal to zero)
therefore
The rate of change of the cost of parking in the lot is $3.00 per
hour
What is the first quartile of this data set?
10, 11, 12, 15, 17, 19, 22, 24, 29, 33, 38
A. 12
B. 19
C. 29
D. 10
Answer:
12
Step-by-step explanation:
find the median:
19
find median of 10, 11, 12, 15, 17
median: 12
Answer: 12
Step-by-step explanation: Apex said so
The similarity ratio of two similar polygons is 2:5. What is the ratio of their areas
Answer:
4 : 25
Step-by-step explanation:
Given the ratio of 2 similar figures = a : b, then
ratio of areas = a² : b²
Given the similarity ratio = 2 : 5, then
ratio of areas = 2² : 5² = 4 : 25
To determine the ratio of areas of two similar polygons, square the similarity ratio. For a ratio of 2:5, the area ratio is 4:25.
The ratio of the areas of two similar polygons is found by comparing the squares of their linear dimensions.
For example, if the similarity ratio of two polygons is 2:5, the ratio of their areas will be (2^2):(5^2), which simplifies to 4:25.
Therefore, the ratio of areas of polygons with a similarity ratio of 2:5 is 4:25.
Given ΔJKL : ΔXYZ, find x.
A)10
B)12
C)16
D)20
Answer: 12
Step-by-step explanation:
Triangle JKL is dilated by a scale factor of 1.5 to get triangle XYZ. You can find this out by dividing 9 by 6, which will give you 1.5. To get the answer, you multiply 8 by 1.5 to get 12
ANSWER
EXPLANATION
We have that ΔJKL is similar to ΔXYZ.
The corresponding sides will therefore
be in the same proportion.
This implies that,
[tex] \frac{XY}{JK} = \frac{YZ}{KL} [/tex]
From the diagram,XY=9, JK=6, KL=8, and YZ=x.
We plug in the known values into the formula to get:
[tex] \frac{9}{6} = \frac{x}{8} [/tex]
Multiply both sides by 8
[tex] \frac{9}{6} \times 8=\frac{x}{8} \times 8[/tex]
[tex]12 = x[/tex]
The correct answer is B.