Students were asked to write an expression equivalent to the expression below:
30a+12b-6a+ 2(9b+c+15)
Their answers are as follows:
36a-30b+2c +30
Ben wrote: 36a - 30b + 2c + 30
Martin:
24a+30b+2c +30
Sara wrote: 24a + 30b + 2c + 15
Martin wrote: 24a + 30b+2c +30
Which, if any, of those students wrote expressions that are equivalent to the original expression?
In the space provided below, either prove why each student's response is equivalent, or explain and correct the student's error.
Sara
| Ben:
Allie wrote: 2(12a + 15b+c+15)
24a+30b+ac+15
Allie:
2(13a +156+c+15)
The equivalent is 24a + 30b +2c + 30
How to determine the equivalent expressionGiven the original expression as;
30a+12b-6a+ 2(9b+c+15)
First, expand the bracket, we have
30a + 12b -6a + 18b + 2c + 30
Then, collect like terms
30a -6a + 12b + 18b + 2c + 30
24a + 30b +2c + 30
The equivalent is 24a + 30b +2c + 30
From the result, we have that Martin is correct.
Sara wrote the equivalent as 24a + 30b +2c + 15
She made a mistake in expand the bracket = 2( 9b +c +15) = 18b + 2c + 30
Ben wrote 36a - 30b + 2c + 30. He made a mistake in issuing the sign for 30b = 12b + 18b = +30b
Thus, the equivalent is 24a + 30b +2c + 30
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Which best explains if quadrilateral WXYZ can be a parallelogram?
A quadrilateral in which opposite sides are parallel is called a parallelogram. The correct option is A.
What is a parallelogram?A quadrilateral in which opposite sides are parallel is called a parallelogram. Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
For a parallelogram, the pair of opposite sides are equal and parallel. Therefore,
1.) For the first pair.
(x+8) = 15
x = 7
2.) For the second pair
(x+2)=(2x-5)
x + 2 = 2x - 5
2 + 5 = 2x - x
x = 7
(x+2) = (7+2) = 9
Since the measure of the pair of opposite sides is 15 units, the pair of the other two sides measure 9 units.
Hence, the correct option is A.
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Which expression is equivalent to (4 + 6)²?
Answer:
A) -20+48i
Step-by-step explanation:
[tex](4+6i)^2\\(4+6i)(4+6i)\\16+24i+24i+36i^2\\**i^2=-1*\\16+48i+36i^2(-1)\\16+48i-36\\-20+48i[/tex]
A six sided die is rolled and a coin is tossed. Find P(odd and T).
The probability of getting tails and rolling an odd number is P = 0.25
How to get the probability?
The probability of getting tails on the coin is 0.5
On the dice, there are 6 numbers and 3 are odd, so the probability of rolling an odd number is:
p = 3/6 = 0.5
The joint probability (of getting tails and rolling an odd number) is equal to the product between the individual probabilities:
P(odd and T) = 0.5*0.5 = 0.25
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The following data set is the age of customers at the ice cream shop:
18, 52, 42, 36, 5, 31, 29, 22
Find the mean.
Answer: About 29
Step-by-step explanation: First you need to add all the numbers together. Then you divide the sum, 235, by however many numbers you have (8). And BOOM: you got your answer :)
PS: If you have a decimal number, just round it up or down ( 5 and above give it a shove; 4 and below let it lie low)!
PLEASE HELP thank you!!!!
Answer:
The answer is C: 3/4
Step-by-step explanation:
Your equation is equal to (3/2)/(4/2) due to absolute value (all numbers are positive even if negative symbol is infront of it) which is equal to 3/4.
Step-by-step explanation:
what is the real problem definition ?
is there now an absolute value around the top "-2", or not ?
in any case, remember, when we divide 2 rational numbers like this :
a/b / c/d
the result is
"outer multiplication" over "inner multiplication" :
a×d / b×c
as alternative you can always also say
a/b / c/d = a/b × d/c = a×d / b×c
so,
if the problem is
3/-2 / |-4/-2|
the result is
3×2 / 4×-2 = 6/-8 = - 3/4
if the problem is
3/|-2| / |-4/-2|
the result is
3×2 / 4×2 = 6/8 = 3/4
please pick the solution based on the actual problem.
Random assignment to treatments helps control for lurking variables ? true ? false.
It is true that Random assignment to treatments helps control for lurking variables
The main purpose for using randomization in an experiment is to create sure that the results are accurate. you wish to avoid biasis and lurking variables. Having a randomized experiment will facilitate your to create sure that your information is correct
The main purpose for using randomization in an experiment is to manage the lurking variable and establish a cause and effect relationship. Also, by randomizing an experiment the evidence is more supported
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If you anwser the question i give you brainly
A function assigns the value of each element of one set to the other specific element of another set. The correct option is A.
What is the inverse of a function?Suppose that the given function is
[tex]f:X\rightarrow Y[/tex]
Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is
[tex]f^{-1}: Y \rightarrow X[/tex]
such that:
[tex]\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X[/tex]
(and vice versa).
It simply means that the inverse of 'f' is an undone operator, that takes back the effect of 'f'
The graph that represents the inverse of the given function is option A because graph A is showing more rapid growth as compared to the given graph.
Hence, the correct option is A.
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how do you find the angle of 2/5ths of a circle
Answer:
You divide 360 by 5 which is 72 & Then muiltiply that by 2.
Your answer would be 144 tho.
If g(x) = 4x² - 16 were shifted 9 units to the right and 1 down,
what would the new equation be?
[tex]9 \: units \: to \: the \: right \: = x - 9[/tex]
[tex]1 \: unit \: down \: = - 1[/tex]
[tex]g(x) = 4x {}^{2} - 16 \\ h(x) = 4(x - 9) {}^{2} - 17[/tex]
Letter ASimplify, state all restrictions.
The simplified expression is [tex]\frac{1 - x - y}{x + y}[/tex]and the restriction is [tex]y \ne -x[/tex]
How to simplify the expression?The expression is given as:
[tex]\frac{x - y}{4x^2 - 8xy + 3y^2} \div \frac{2x + y}{2x - 3y} \times \frac{4x^2 - y^2}{x^2 - y^2} -1[/tex]
Express x^2 - y^2 as (x + y)(x - y) and factorize other expressions
[tex]\frac{x - y}{(2x - y)(2x - 3y)} \div \frac{2x + y}{2x - 3y} \times \frac{4x^2 - y^2}{(x - y)(x + y)} -1[/tex]
Rewrite the expression as products
[tex]\frac{x - y}{(2x - y)(2x - 3y)} \times \frac{2x - 3y}{2x + y} \times \frac{4x^2 - y^2}{(x - y)(x + y)} -1[/tex]
Cancel out the common factors
[tex]\frac{1}{(2x - y)} \times \frac{1}{2x + y} \times \frac{4x^2 - y^2}{(x + y)} -1[/tex]
Express 4x^2 - y^2 as (2x - y)(2x + y)
[tex]\frac{1}{(2x - y)} \times \frac{1}{2x + y} \times \frac{(2x - y)(2x + y)}{(x + y)} -1[/tex]
Cancel out the common factors
[tex]\frac{1}{x + y} -1[/tex]
Take the LCM
[tex]\frac{1 - x - y}{x + y}[/tex]
Hence, the simplified expression is [tex]\frac{1 - x - y}{x + y}[/tex]and the restriction is [tex]y \ne -x[/tex]
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Question 2
Consider a right angled triangle where one of the non-hypotenuse sides has
length 3 and the angle it makes with the hypotenuse is 65. What is the area of
this triangle?
A: 3cos65/2 B: 9tan65/2 C: 9sin65/2 D: 9cos65/2 E: 3sin65/2
Using relations in a right triangle, the area of the triangle is given by:
B. 9tan(65º)/2.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.In this problem, we have one leg(length 3) and the angle with the hypotenuse(65º), hence the other leg can be found as follows:
[tex]\tan{65^\circ} = \frac{x}{3}[/tex]
x = 3tan(65º).
What is the area of a right triangle?The area of a right triangle is half the multiplication of it's legs, hence in this problem:
A = 1/2 x 3 x 3tan(65º) = 9tan(65º)/2.
Which means that option B is correct.
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The perimeter of an equilateral triangle is 38 centimeters. Find the length of an
altitude of the triangle. Round to the nearest tenth.
Answer:
11.0 cm
P=38 cm
38/3=12.67cm length of one side
Base of triangle = 12.67/2 =6.34 cm
Use formula [tex]a^2+b^2=c^2[/tex]
[tex]6.34^2+x^2=12.67^2\\\\=11.0 cm[/tex]
x = altitude of triangle
Pleaseeee helppppppp
Answer:
The second choice (-6, -5 2/5, -4 1/5)
Step-by-step explanation:
1) Find the nth term by using the rule given. Foil them out.
A(n) = -6 + 1/5n - 1/5
A(n) = 1/5n - 31/5
2) Find the first term by substituting 1 into n.
a1 = 1/5(1) - 31/5
a1 = -6
3) Find the fourth term by substituting 4 into n.
a4 = 1/5(4) - 31/5
a4 = -27/5 or -5 2/5
4) Find the tenth term by substituting 10 into n.
a10 = 1/5(10) - 31/5
a10 = -21/5 or -4 1/5
Therefore, the second choice (-6, -5 2/5, -4 1/5) is correct.
Calculate XY, if UV=25 and WZ=39
Answer:
Step-by-step explanation:
UV = [tex]\frac{XY+WZ}{2}[/tex]
[tex]\frac{XY+39}{2}[/tex] = 25
XY + 39 = 50
XY = 11
A given gas powered water pump delivers 42.50 gallons of water per minute. This value can also be expressed as _____________ L/s (Liters per second).
The rate at which the gas powered pump deliver water is 160.9 litres per seconds
How to convert rate?The gas powered water pump delivers 42.50 gallons of water per minute.
Therefore,
1 gallon = 3.78541 litres
42.50 gallons = ?
cross multiply
volume = 42.50 × 3.78541 = 160.879925 litres
Hence,
60 seconds = 1 minutes
1 second = ?
time = 1 / 60 = 0.01666666666 seconds
Hence,
rate = 160.9 litres per second
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For which function is f(5) = 2?
By evaluating the linear function f(x) = x - 3 at x = 5 and discarding the another function in the table given, we conclude that f(5) = 2 belongs to that linear equation.
What function contains a given relationship?
In this problem we must check if the given relationship between the independent variable (x) and the dependent variable (y) exists in any of the two functions: (i) a table, (ii) an expression.
After a quick analysis, we conclude that f(5) = 2 is a point of the linear function f(x) = x - 3. Here is the proof:
f(5) = 5 - 3
f(5) = 2
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Answer:A which is x-3
Step-by-step explanation:
Use the Pythagorean identity
to find cos X.
15
19
?]√
sin x =
COS X =
Answer:
Step-by-step explanation:
So sin is defined as [tex]\frac{opposite}{hypotenuse}[/tex]. and cosine is defined as [tex]\frac{adjacent}{hypoteunse}[/tex]. So we need the adjacent side. Since we already have the opposite, and hypotenuse, you can use the Pythagorean identity to solve for the missing side: [tex]a^2+b^2 = c^2[/tex]
[tex]15^2 + b^2 = 19^2[/tex]
[tex]225 + b^2 = 361[/tex]
[tex]b^2 = 136[/tex]
[tex]b = \sqrt{136}[/tex]
[tex]b = \sqrt{4} * \sqrt{34}[/tex]
[tex]b = 2\sqrt{34}[/tex]
This is the adjacent side, so now plug this into the cosine equation and you get: [tex]\frac{2\sqrt{34}}{19}[/tex]
What fraction of £1 is 31p?
The fraction of 1 pound to 31 penny is 31/100.
Given that, £1 and 31 p.
What is metric conversion?Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.
We know that, 1 pound = 100 penny
Now, the fraction of £1 is 31 p is
31/100
Therefore, the fraction of 1 pound to 31 penny is 31/100.
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I don’t know what to do pls help me
Answer:
35
Step-by-step explanation:
Basically, since the angle HGF consists of HGE and EGF, then that means that HGF = HGE + EGF, and since EGF and HGF is given we plug this into the equation to get: 145 = HGE + 110, so HGE = 35.
Answer: 35°
Step-by-step explanation:
Hi!
The total angle is 145°
part of the angle is 110°
to find the missing angle, do 145 - 110 = 35°
Hope this helped :)
The ratio of the area of the shaded part to the unshaded part is______.
Answer: 1 : 3
Shaded area:
[tex]\Longrightarrow \sf Length \ \times \ Breadth = \dfrac{x}{4} \ \times \ x \ = \ \dfrac{1}{4}x^2[/tex]
Unshaded area:
[tex]\Longrightarrow \sf Length \ \times \ Breadth = (x - \dfrac{x}{4}) \ \times \ x \ = \ \dfrac{3}{4}x^2[/tex]
Ratio of shaded to unshaded:
[tex]\Longrightarrow \sf \dfrac{1}{4} x^2 \ : \ \dfrac{3}{4} x^2 = 1 : 3 \quad (simplified)[/tex]
Which interval is the solution set to 0.35x – 4.8 < 5.2 – 0.9x? (–[infinity], –8) (–[infinity], 8) (–8, [infinity]) (8, [infinity])
(-∞,8) is interval is the solution to set 0.35x – 4.8 < 5.2 – 0.9x.
How to solve the inequality?0.35x - 4.8 < 5.2 - 0.9x
Adding 0.9x to both sides of equation.
0.35x - 4.8 + 0.9x < 5.2 - 0.9x + 0.9x
1.25x - 4.8 < 5.2
Adding 4.8 to both sides of equation.
1.25x - 4.8 + 4.8< 5.2 + 4.8
1.25x < 10
Dividing both sides of equation by 1.25
x < [tex]\frac{10}{1.25}[/tex]
Hence x < 8
Thus, (-∞,8) interval is the solution to given set 0.35x – 4.8 < 5.2 – 0.9x.
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A florist made 4 bouquets of flowers. each bouquet had "c" carnations and 9
daisies. 4(c+9) this expression can be used to represent the total number of flowers the florist used for the bouquets.
The equivalent expression without parenthesis that can be used to determine the total number of flowers the florist used is 4c + 36
How to find equivalent expression?The equivalent expression without parenthesis that can be used to determine the total number of flowers the florist used.
total number of flower the florist used for the bouquet = 4(c + 9)
Therefore,
total number of flower the florist used for the bouquet = 4c + 36
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two numbers that multiply to equal 20 and that also equal -12
Answer:
-10 and -2
Step-by-step explanation:
ONLY IF ITS two number that mutiply to equal 20 and their sum is -12
to solve the system of equations below, Becca isolated x^2 in the firs equation and then substituted it into the second equation
The resulting equation if Becca isolated x² in the first equation and then substituted it into the second equation is (9-y²) / 25 - y²/36 = 1
Equationx² + y² = 9
x²/25 - y²/36 = 1
From (1)
x² = 9 - y²
substitute x² = 9 - y² into (2)
x²/25 - y²/36 = 1
(9-y²) / 25 - y²/36 = 1
Therefore, the resulting equation is option C; (9-y²) / 25 - y²/36 = 1
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Answer:
(9-y²) / 25 - y²/36 = 1
Step-by-step explanation:
19) Find the surface area of the solid shown that has a square base. 9 in 7 in 3 in
The surface area of the composite shape is: 315 in.².
What is the Surface Area of the Composite Shape?Surface area = surface area of square pyramid + surface area of square prism - 2(base area)
Surface area of square pyramid = Area of base + 1/2(perimeter of base × slant height) = 9² + 1/2[4(9) × 7] = 207 in.²
Surface area of square prism = 2a² + 4ah = 2(9²) + 4(9)(3)
Surface area of square prism = 2(9²) + 4(9)(3) = 270 in.².
Base area = 9² = 81 in.².
Surface area of the composite shape = 207 + 270 - 2(81) = 315 in.².
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Answer:
315 in.²
Step-by-step explanation:
Recall:
area of rectangle = length × width
area of triangle = base × height / 2
Base of prism: 9 in. × 9 in. = 81 in.²
4 sides of prism: 4 × 9 in. × 3 in. = 108 in.²
Lateral area of pyramid: 4 × 9 in. × 7 in. / 2 = 126 in.²
Total area = 81 in.² + 108 in.² + 126 in.² = 315 in.²
Please Help Asap Please And Thank You.
Answer:
m (slope) = -1/10; the slope means that every 1/10 minute the candle goes down 1/100 centimeters OR every 10 minutes the candle goes down 1 centimeter; the y intercept is how tall the candle is at the beginning
Step-by-step explanation:
to find the slope of this line we can simply use the (y2 - y1) / (x2 - x1) formula
that gives us
(0 - 25) / (250 - 0)
or
-25/250
or
-1/10
the slope means that every 1/10 minute the candle goes down 1/100 centimeters OR every 10 minutes the candle goes down 1 centimeter
the y intercept is how tall the candle is at the beginning
Describe how to determine the average rate of change between x = 2 and x = 4 for the function f(x) = 2x3 + 1. Include the average rate of change in your answer.
The average rate of change of the function given is 56
Rate of change of a functionThe formula for calculating the rate of change of a function is expressed as;
f'(x) = f(b)-f(a)/b-a
where
b = 4
a = 2
f(4) = 2(4)^3 +1
f(4) = 129
f(2) = 2(2)^3 + 1
f(2) = 17
Substitute
f'(x) = 129-17/4-2
f'(x) = 112/2
f'(x) = 56
Hence the average rate of change of the function given is 56
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A customer ordered 15 pieces of gourmet chocolate. The order can be packaged in small boxes that contain 1, 2 or 4 pieces of chocolate. Any box that is used must be full. How many different combinations of boxes can be used for the customer's 15 chocolate pieces
There are 20 combinations of boxes that can be used for the customer's 15 chocolate pieces.
In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or an expression; it is usually a number, but may be any expression. When the coefficients are themselves variables, they may also be called parameters.
It is given that a customer ordered 15 pieces of gourmet chocolate. The order can be packaged in small boxes that contain 1, 2 or 4 pieces of chocolate. Any box that is used must be full.
The coefficient of [tex]x^{15}[/tex] from the steps shown in the image is 20.
Hence, there are 20 possibilities.
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take a deck of playing cards form following sets out of those
A=Set of playing cards
B=SET OF RED COLOURED FACE CARD
The information given about the probability shows that the cardinality of D is 18.
How to calculate the probability?From the complete information, the number of red-colored cards is 26.
Also, the number of red-colored number cards will be 18.
The cardinality of a set is a measure of a set's size, meaning the number of elements in the set.
Here, the cardinality of set D is 18.
Here is the complete question:
Take a deck of playing cards. Form following sets out of those:
A = Set of Face Cards
B = Set of Red Coloured Face cards
C = Set of Black Coloured Face Cards
D = Set of Red Coloured Number Cards
Find the Cardinality of set D
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