The equivalent expression of 2/5(s+20) is 2/5s+8 and expression (9+3)=12.
what are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, nected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between which math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now,
Given expression 2/5(s + 20)
Using distributive property
2/5s+2/5*20
2/5s+2*4
2/5s+8
and (9+3)=12
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Right question:-
Use the distributive property to write an equivalent expression for 2/5(s + 20). Then evaluate the expression (9+3).
Your students have been working on algebra equations involving inequalities. The rule for learning the > sign is:
The rule for learning the > sign is demonstrating eating with the right hand.
InequalityThe inequality signs are;
Greater than >Let was than <Equal to =Greater than or equal to ≥Less than or equal to ≤The rule for teaching your students the greater than > sign is by imagining eating with their right hand. The shape of the hand when taking food into the mouth is the greater than sign.
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Which list below shows the fractions in order from greatest to least?
A. 3/6, 4/9, 3/7, 3/10
B. 3/10, 3/7, 4/9, 3/6
C. 3/10, 4/9, 3/7, 3/6
D. 3/6, 4/7, 4/9, 3/10
Answer:
Step-by-step explanation:
Planes A and B intersect.
n
772
W
k
Mark this and return
V
19
Z
X
2
Which describes the intersection of line m and line nº
O point W
point X
point Y
O point Z
The point that describes the intersection of line m and line n is; Point W
How to interpret Intersection of Planes?
Intersection of the two lines is defined as the point where the two lines cross or meet each other.
It is given that the lines m and n intersect each other, which means that they must be intersecting each other at some point.
From the figure, it can be seen that in plane A, the lines m and n intersect each other at point W, thus point W is the point of intersection of the two line m and n.
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In 2011 the U.S. Department of Transportation reported with 95% confidence that the average length of a motor vehicle trip in the United States was 9.72 miles with a margin or error of 0.22 miles.
With 95% confidence the authors of the report are claiming that the true average length of a motor vehicle trip in the United States is between ________and_________ miles.
The level of confidence for this estimate is ________%
Using the interpretation of the confidence interval, it is found that:
With 95% confidence the authors of the report are claiming that the true average length of a motor vehicle trip in the United States is between 9.50 miles and 9.94 miles.The level of confidence for this estimate is 95%.What is the interpretation of a x% confidence interval?It means that we are x% confident that the population parameter(mean/proportion/standard deviation) is between a and b.
Considering the mean and the standard error, the bounds of the interval are:
a = 9.72 - 0.22 = 9.50 miles.b = 9.72 + 0.22 = 9.94 miles.Hence:
With 95% confidence the authors of the report are claiming that the true average length of a motor vehicle trip in the United States is between 9.50 miles and 9.94 miles.The level of confidence for this estimate is 95%.More can be learned about confidence intervals at https://brainly.com/question/25890103
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This is so confusing please help asap !
Assume that the function f is a one
-to-one function.
(a) If f (7)
= 5, find f-1 (5)
Your answer is
(b) 18 f-1 (-3) = -2, find f(-2).I
Your answer is
For the given inverse functions we have:
a) f⁻¹(5) = 7
b) f(-2) = -3
How to work with inverse functions?
Remember that if f(x) and g(x) are inverse functions, then:
[tex]f(x) = y\\then\\g(y) = x[/tex]
a) Now we know that:
f(7) = 5
Then if f⁻¹(x) is the inverse, we have:
f⁻¹(5) = 7
b) Now we know that:
f⁻¹(-3) = -2
Again, using the rule for inverse functions, we will have:
f(-2) = -3
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a brave knight traveled on his horse from one kingdom to another in 2 days the first day he rode at a speed of 10 mph and the second day he rode at a speed of 8 mph if he traveled exactly the same amount of time each day and went 180 miles find how many hors it took the knight to travel from one kingdom to another
Using the relation between velocity, distance and time, it is found that it took the knight 20 hours to traveled from one kingdom to another.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence:
v = d/t
On the first day, he traveled at a speed of 10 mph, a distance of d, hence:
10 = d/t
t = d/10
On the second day, he traveled at a speed of 8 mph, a distance of 180 - d, hence:
8 = (180 - d)/t
t = (180 - d)/8
Equaling both equations for t, we find the distance on the first day, hence:
d/10 = (180 - d)/8
8d = 1800 - 10d
18d = 1800
d = 100 miles.
The time on the first day was:
t = 0.1d = 0.1 x 100 = 10 hours.
On the second day he traveled the same amount of time, hence, in total, he traveled 20 hours.
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Please help
Answer: (-2,2)
Step-by-step explanation:
The solution to a system of equations represented graphically is the point where the graphs intersect.
If the function is:
What is f(-4)?
Answer:
D. -11
Step-by-step explanation:
Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.
Given piecewise function:
[tex]f(x)=\begin{cases}2x-3 & \textsf{if }x \leq -4\\x^2 & \textsf{if }-4 < x < 0\\x+5 & \textsf{if }x \geq 0\end{cases}[/tex]
Therefore, the function has three definitions:
[tex]f(x)=2x-3 \quad \textsf{ when x is equal to or less than -4}[/tex]
[tex]f(x)=x^2 \quad \textsf{ when x is greater than -4 or less than zero}[/tex]
[tex]f(x)=x+5 \quad \textsf{ when x is greater than zero}[/tex]
f(-4) means to substitute x = -4 into the function.
As x = -4 satisfies the interval of the first piece of the function, substitute x = -4 into f(x) = 2x - 3:
[tex]\begin{aligned}\implies f(-4) & =2(-4)-3\\& = -8 -3\\& = -11\end{aligned}[/tex]
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Answer is D. -11
Answer:
Solution Given:
f(-4) depends on the condition x≤-4,
so
f(-4)=2*-4-3=-8-3=-11
Find the surface area of the square pyramid below if the length of the sides of the base are 10 cm, and the slant height is 15 cm.
The surface area of the square pyramid if the length of the sides of the base are 10 cm, and the slant height is 15 cm is 416.2 cm²
Surface areaSurface area of the square pyramid
= a² + 2a√a²/4 + h²
where,
a = sides of base = 10 cmh = slant height = 15 cmSurface area of the square pyramid
= a² + 2a√a²/4 + h²
= 10² + 2(10)√10²/4 + 15²
= 100 + 20√100/4 + 225
= 100 + 20√25 + 225
= 100 + 20√250
= 100 + 20(15.81)
= 100 + 316.2
= 416.2 cm²
Therefore, the surface area of the square pyramid if the length of the sides of the base are 10 cm, and the slant height is 15 cm is 416.2 cm²
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15) Mr. and Mrs. Rupe and their 4 sons are taking a 2500 mile camping trip across country. They plan to spend $120 for campsites per
day. The camper rental fee is $65 a day. While pulling the camper their car has a fuel economy of 8 miles per gallon. They estimate $85
per day for food for the 5-day trip. If gasoline is $1.92 per gallon how much will their trip cost?
O a.) $1950
Ob.) $1850
Oc.) $2950
Od.) $1750
Answer:
A $1950
Step-by-step explanation:
Food, camper rental and camp site will cost 1350
(120 + 65 + 85)5 = 1350
The trip is 2500 and the car gets 8 miles per gallon 2500/8 = 31.5. The will need to buy 31.5 gallons of gas at 1.92 a gallon or $600 (31.5 x 1.92).
When we add the cost of gas to the other costs, we get a total of 1950 (1350 + 600)
At the movie theater, child admission is $5.50 and adult admission is $9.00. on Thursday, 148 tickets were sold for a total sales of $992.50. how many adult tickets were sold that day
Answer:
51 Adult tickets were sold that day.
Step-by-step explanation:
Let c = child and a = adult
c + a = 148 5.50c + 9.00a = 992.50
Change the first equation so that it is either in the form c = or a =and then plug that number into the second equation.
I am going to change the first equation to c = by subtracting a from both sides
c = 148 - a
Now I am going to plug 148 -a for c in the second equation.
5.5(148 - a) + 9a = 992.5 Next distribute the 5.5
814 - 5.5a + 9 a = 992.5 Add the a terms together
814 + 3.5a = 992.5 Subtract 814 from both sides
3.5a = 178.5 Divide both sides by 3.5
a = 51
Write the equation of the line.
(Check image)
Options:
a. y = -2/3x + 4
b. y = 2/3x + 4
c. y = 3/2x + 4
d. y = -3/2x + 4
please show step by step
Evaluate 2a x 3 + b, if a = 5 and b = 1.
Answer:
31
Step-by-step explanation:
replace the values of a and b in the given term
=2a x 3 + b
2(5) x 3 + (1)
2x5 x 3 + 1
10 x 3 + 1
30 + 1
31
A road sign has the shape of an equilateral triangle with a side length of 48 inches. What is the height of the sign? The road sign is about 38.2 inches tall The road sign is about 38.2 inches tall The road sign is about 23.5 inches tall The road sign is about 23.5 inches tall The road sign is about 41.6 inches tall The road sign is about 41.6 inches tall The road sign is about 43.7 inches tall
The height of the equilateral triangle is 41. 6 inches. Option C
How to determine the height
The formula for finding the height of an equilateral triangle is given as;
h = (a√3)/2
we have a = 48 inches
Let's substitute the value
Height, h = [tex]\frac{48\sqrt{3} }{2}[/tex]
Height = [tex]\frac{48 * 1. 732}{2}[/tex]
Height = [tex]\frac{83. 14}{2}[/tex]
Height = [tex]41. 6[/tex] Inches
Thus, the height of the equilateral triangle is 41. 6 inches. Option C
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3^2x3^3 write on exponential form
The exponential form of the given information 3^2x3^3 is 3⁵.
What are exponential forms?The exponential form is a convenient way of expressing or writing repeated multiplication expressions concerning their bases and power.
From the information given, the given expression can be written in exponential form by using the law of indices.
= 3^2x3^3
[tex]\mathbf{=3^{2+3}}[/tex]
[tex]\mathbf{=3^{5}}[/tex]
Therefore, we can conclude that the exponential form of the given expression is 3⁵.
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A farmer harvests 70 apples and 98 peaches. They want to make baskets that have both apples and peaches to sell at the market. Each basket should contain the same combinations of fruit. They want to sell all the apples and peaches and as many baskets as possible. they can use the greatest common factor to help them divide up the fruit.
This means the farm can make x baskets of apples and y peaches.
Farmer will made 14 basket each of 5 apple and 7 peaches.
what is greatest common factor?
Greatest common factor (GCF) is largest common factor in the given number.
first find common factor of numbers 70 and 98
70 = 2*5*7
98 = 2*7*7
the common factor are 2 and 7
the greatest common factor is 2*7=14
70 apples = 14*5
98 peaches = 14*7
farmer will made 14 basket each of 5 apple and 7 peaches.
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The farmer will make 14 baskets containing each of 5 apples and 7 peaches.
How many baskets can be made which contain both apples and peaches and each basket should contain the same combinations of fruits?Given:
A farmer harvests 70 apples and 98 peaches.They want to make baskets that have both apples and peaches to sell at the market.Each basket should contain the same combinations of fruit. They want to sell all the apples and peaches and as many baskets as possible.Find:
How many baskets can the farm make having x apples and y peaches in the baskets?Solution:
So, for solving this kind of question first we have to find the greatest common factor, we get;
70 = 2*5*7
98 = 2*7*7
the common factor are 2 and 7
the greatest common factor is 2*7=14
70 apples = 14*5
98 peaches = 14*7
So, the farmer will make 14 baskets each of 5 apples and 7 peaches.
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(2^x+y , 3^x-y )= (16,9) find the value of x and y
Answer:
x=3,y=1
Step-by-step explanation:
2^x+y=16,3^x-y=9
16=2^4,9=3^2
x+y=4,x-y=2 add both
2x=6,x=3
3-y=2,y=1
Which of the following best describes both the domain and range of the distance function d=55t
Answer: All real numbers
Step-by-step explanation:
The domain and range of all linear functions is the set of real numbers.
The tomato plants in Ms. Lang's
garden grow 2 inches every 3 days. How much will they grow in 15 days?
Answer:
10 inches
Step-by-step explanation:
15 days/3 days =5
5 x 2 =10
Explain the difference between using area and volume with 2-D and 3-D figures.
The difference between Area and Volume lies in the fact that the former relates to plane shapes while the latter takes the concept of solid shapes into account.
What is the difference between Area and Volume?The distinctive characteristic of area is the space occupied by a two-dimensional, 2D flat object in a plane while Volume on the other hand is defined as the space covered by a three-dimensional, solid object. The area is quantised in square units while the volume is quantised in cubic units.
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HELP ASAPPPP PLEASE!!!!
Answer:
(c) 45°
Step-by-step explanation:
A protractor is used to measure angles by aligning one of the sides of the angle with the 0 mark on the protractor scale. Then the value of the angle is read from the same scale where it is crossed by the other side of the angle.
ApplicationHere, ray BA crosses the outer scale at 0. The other ray of the angle, BC, crosses the outer scale halfway between 40 and 50, obscuring the mark at 45°.
The measure of angle ABC is 45°.
C. 45°
Step-by-step explanation:When measuring with a protractor one of the rays should line up with the straight edge of the protractor, then match up the second ray to the tick marks. However, it can be confusing to tell how to read a protractor.
Clockwise
This angle moves clockwise. This means that the second ray is clockwise to the ray at the bottom. When using a protractor that opens up to the left like this, read the top row of the protractor. The second ray matches the 45-degree mark.
Acute vs Obtuse
There is another way to tell which row of numbers to read. By looking at the drawn angle we can tell the angle is acute (smaller than a right angle). So, the measurement must be less than 90. Therefore, the top row must apply in this situation, meaning the angle is 45°.
Which of the following best represents the linear regression equation for the
×-values and log(y)-values of the data shown below?
By using Microsoft excel to plot the data on a scatter plot, the linear regression equation can best be represented by: A. y = 12.11.1.36^x
What is a regression line?A regression line can be defined as a statistical line that best describes the behavior of a data set and such, it is a line that best fits a set of data.
By using Microsoft excel to plot the data on a scatter plot, we can logically deduce that linear regression equation for the x-values and log(y)-values is given by:
y = 12.11.0.30^x
Thus, it can best be represented by: y = 12.11.1.36^x
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What is the difference of the fractions below? 10x/3-2x/3 2x 13 3 A. 8 B. 8x C. 8x/3 D. 8/3x
The difference of the fractions is 8x/3. Option C is correct.
Given the fraction is 10x/3-2x/3.
When subtracting fractions with the same denominator, just subtract the numerators of the fractions. To find the difference between equal fractions, we subtract the smaller numerator from the larger numerator.
The given expression is 10x/3-2x/3.
Here the denominator in both the fractions are same so, we will take the LCM, we get
10x/3-2x/3=(10x-2x)/3
Now, we will simplify the numerator by subtracting the smaller term from larger, we get
10x/3-2x/3=8x/3
Hence, the difference of the fractions 10x/3-2x/3 is 8x/3 and the correct option is C.
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What is the following product 3 root 24 • 3 root 45
Answer:
54sqrt(30)
Step-by-step explanation:
3sqrt(24) can be simplified to 6sqrt(6) as 24 can be written as 4 * 6 and 4 is a perfect square
3sqrt(45) can also be written as 9sqrt(5) as 45 can be written as 5 * 9 and 6 is a perfect square
you can multiply 6sqrt(6) * 9sqrt(5) as though the square roots were variables
so
54sqrt(30)
this is your final answer
the rounded answer is 295.770181
A piece of wood is 5 m long. It is cut into pieces. The lengths of the pieces are in the ratio 4:3:2:1. The longest piece is then cut in the ratio 4:1 so that there are now five pieces. How long is the smallest piece?
Answer:
0.4
Step-by-step explanation:
4+3+2+1 =10
5m÷10 =0.5
(0.5×4=2, 0.5×3=1.5, 0.5×2=1, 0.5×1=0.5)
2 : 1.5 : 1 : 0.5
longest piece= 2 (2m)
4+1= 5
2÷5= 0.4
(0.4×4=1.6, 0.4×1=0.4)
1.6 : 0.4
so the shortest piece is 0.4!
14) Write the scientific notation.
12 million
Answer:
1.2 × 107 this is the sciencetific notation for 12 million
..
Emily purchased a bond valued at $20,000 for highway construction for $10,460. If the bond pays 7.2%
annual interest compounded monthly, how long must she hold it until it reaches its full face value?
...
Answer:
26.556192
Step-by-step explanation:
7.2×10460÷100
20000÷(7.2×10460÷100)
In ΔOPQ, m∠O = 107° and m∠P = 28°. Which statement about the sides of ΔOPQ must be true?
QO > OP > PQ.
QO > PQ > OP.
PQ > OP > QO.
OP > QO > PQ.
PQ > QO > OP.
OP > PQ > QO.
Answer:
QO < OP < QP
Step-by-step explanation:
The third angle, angle Q, must measure 45° since angles in a triangle add to 180°.
So, OQ < OP < QP.
Answer:
PQ>OP>QO
Greater than symbol goes from largest to smallest
The time taken to complete a motorcycle race is normally distributed, with an average time (µ) of 2.5 hours and a standard deviation () of 0.5 hours.
What is the probability that a randomly selected cyclist will take at least 2.45 hours to complete the race?
Using the normal distribution, there is a 0.5398 = 53.98% probability that a randomly selected cyclist will take at least 2.45 hours to complete the race.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 2.5, \sigma = 0.5[/tex]
The probability that a randomly selected cyclist will take at least 2.45 hours to complete the race is one subtracted by the p-value of Z when X = 2.45, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.45 - 2.5}{0.5}[/tex]
Z = -0.1
Z = -0.1 has a p-value of 0.4602.
1 - 0.4602 = 0.5398.
0.5398 = 53.98% probability that a randomly selected cyclist will take at least 2.45 hours to complete the race.
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