The equivalent expressions when y = 2 and y = 5 are the expressions that have the same numeric value when y = 2 and when y = 5.
What are equivalent expressions?Equivalent expressions are expressions that have the same numeric value.
Hence, the equivalent expressions when y = 2 and y = 5 have the same value when y = 2 and y = 5.
This numeric value is calculated replacing each instance of y by 2 when y = 2 and each instance of y by 5 when y = 5.
For example:
2y + 3 at y = 2: 2(2) + 3 = 7.2y + 3 at y = 5: 2(5) + 3 = 13.Different numeric values, hence not equivalent, just an example as to how you should proceed.
You will do this for all expressions, and when you find equal values for y = 2 and for y = 5, then they will be equivalent.
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oan, omb, apb and mpn are straight lines and an = 3oa. m is the midpoint of ob. oa = a ов = b ap = kab where k is a scalar quantity. express ab and mn in terms of a and b. express mp in terms of a, b and k. finally, find the value of k.
The values of the vectors of AB = b - a , MN = 29a - b/2 and MP = b/2 + (k + 1)( b - a)
What is a triangle?A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.
We have been given that OB = b and OA = a
From ΔAOB we have;
OB + BA + AO = 0
b + (- AB ) -a = 0
AB = b - a
Now from ΔMNO we have;
MN + NO + OM = 0
MN + ( -ON) + OB/ 2 = 0
MN - (OA + AN ) + b/2 = 0
MN - ( a + 30a) + b/2 = 0
MN = 29a - b/2
Now from ΔMBP , we have;
MB + BP + PM = 0
OB/2 + (BA - PA) + PM = 0
b/2 + ( - AP/k + AP) + PM = 0
b/2 + ( -kAB /k + kAB) + PM = 0
b/2 + ( k AB + AB ) + PM ) = 0
PM = -b/2 - (k + 1) (b - a)
MP = b/2 + ( k+1) (b - a)
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5 + 7(6 −4) − 2(5 − 1)
Answer: 11
Step-by-step explanation:
5 + 7(6-4) - 2(5 - 1)
P E M/D A/S
5 + 7(2) - 2(4)
P E M/D A/S
5 + 14 - 8
P E M/D A/S
11
At his comic book store, Korey's Comics, Korey sells approximately $3,250 in comic books each month.
But as a comic book dealer, Korey only pays $1,285 for these comic books. Korey's monthly operating expenses, including labor, are $875. Calculate Korey's monthly net income.
Answer:
Korey's monthly net income is $1090Step-by-step explanation:
The spending is the cost plus expenses:
1285 + 875 = 2160Net income is the difference of money made and spent:
3250 - 2160 = 109011. Find m/Q. The diagram is not to scale.
Q/ R
77°
47°
What is the slope of the line shown?
Answer:
-11/6
Step-by-step explanation:
you can use rise over run to find your answer
4/y+2 = 10/5y
solve for y
Answer:
y = - 1
Step-by-step explanation:
[tex]\frac{4}{y}[/tex] + 2 = [tex]\frac{10}{5y}[/tex]
multiply through by 5y to clear the fractions
20 + 10y = 10 ( subtract 20 from both sides )
10y = - 10 ( divide both sides by 10 )
y = - 1
The PayDay loan company lends you $500. After 2 weeks pay you pay back $520. What is the simple interest rate? Note that the times is a fraction of a year.
Answer:
Explanation:
• Loan Amount = $500
,• Time = 2 weeks
,• The amount paid pack = $520
We want to determine the simple interest rate.
First, find the amount paid as interest:
[tex][/tex]Find the measures of the complementary angles that satisfy each case. The measure of the first angle is 40% less than the measure of the second.
The measure of the angles are 56.25° and 33.75°.
How to calculate the angles?The value in a complementary angle is equal to 90°.
Let the first angle = x
The second angle will be: 1 - (40% × x) = 1 - 0.4x = 0.6x
Therefore, they'll be added together as follows:
x + 0.6x = 90°
1.6x = 90°
Divide
x = 90/1.6
x = 56.25
The second angle will be:
= 0.6x
Since x = 56.25, this will be used in the illustration below.
= 0.6x
= 0.6 × 56.25
x = 33.75
Therefore, the second angle is 33.75.
This illustrates the concept of complimentary angles.
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Can someone please help me
May's total profit given the revenue, fixed cost and variable cost is $250.
What is the total profit?
Profit is when the difference between revenue and total cost is positive. A loss is earned when the difference between revenue and total cost is negative.
Total cost is the sum of fixed cost and variable cost. Fixed cost is the cost that remains constant regardless of the level of output. Variable cost changes based on the level of output.
Total cost = variable cost + fixed cost
$9,000 + $300 = $9,300
Profit = revenue - total cost
$9,950 - $9,300 = $250
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Which of the following values are solutions to the
inequality 9 ≤ 3x +4?
I. - 7
II. 8
III. 2
Answer:
II. 8
III. 2
Step-by-step explanation:
Solving an inequality
9 ≤ 3x +4
Subtract 4 from each side
9-4 ≤ 3x +4-4
5 ≤ 3x
Divide each side by 3
5/3 ≤ 3x/3
5/3 ≤ x
x must be greater than or equal to 5/3
I. - 7 this is not greater than or equal to 5/3
II. 8 this is greater than or equal to 5/3
III. 2 this is greater than or equal to 5/3
1. Alex and chris share sweets
In ratio Alex : Chris= 7:3
Work out the number of
Sweets chris recieves.
Using ratios, we can conclude that Chris gets 12 sweets.
What are ratios?In mathematics, a ratio shows how many times one number is represented by another. If there are eight oranges and six lemons in a bowl of fruit, the proportion of oranges to lemons would be eight to six. 8:14 for oranges and 6:8 for lemons, respectively, are the ratios of oranges to the total amount of fruit.So, a number of sweets Chris receive:
Alex : Chris = 7:3Let, Chris sweets be 'x' and Alex sweets be 'x + 20'Now, 7:3 = x+20:x, solve as follows:
7:3 = x+20:x7/3 = x+20/x7x = 2x + 607x - 2x = 605x = 60x = 60/5x = 12
Therefore, using ratios, we can conclude that Chris gets 12 sweets.
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The correct question is given below:
Alex and Chris share sweets in the ratio Alex: Chris = 7 : 3. Alex receives 20 more sweets than Chris. Work out the number of sweets Chris receives.
A groundskeeper needs grass seed to cover a circular field 290 ft in diameter a store sells 50-pound bags of grass seed. One pound of grass seed covers about 400 square ft. What is smallest number of bags there groundskeeper must buy to cover the circular field
Using the concept of area, we got 165 bags is the smallest number of bags there groundskeeper must buy to cover the circular field.
The branch of mathematics which deals with measuring is known as Mensuration. It was basically first used for land surveys and other civic works in Egypt. The father of mensuration is known as Archimedes. Mensuration is a discipline of mathematics which studies the measurements of various geometrical forms possible and their areas, perimeters, and volumes, among other things.
Diameter of the field = 290 feet, radius = 145 feet
Area of the circular field =[tex]\pi r^{2}[/tex]
=>[tex]\pi[/tex]×145×145 =66018.5 square feet.
No of bags to be brought = 66018.5/400=165bags,
Hence, the smallest number of bags is 165 which groundskeeper must buy to cover the circular field.
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the following data are from a simple random sample. 5 8 10 7 10 14 a. what is the point estimate of the population mean? b. what is the point estimate of the population standard deviation?
The point estimate of the population mean is 9
The point estimate of the population standard deviation is 2.83
Part a
Point estimate of population mean:
Given the sample data is 5,8,10,7,10,14
Number of samples, n is 6
Population mean=[tex]\frac{\sum x }{n}[/tex]
=(5+8+10+7+10+14)/6
=54/6
=9
Point estimate of mean=9
Part b
Point estimate of population standard deviation:
Mean=9
Data (x) (x-mean)^2
5 16
8 1
10 1
7 4
10 1
14 25
Total 48
Standard deviation=√(x-mean)^2/n
=√48/6
=√8
=2.83
Hence, the point estimate of population standard deviation is 2.83
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17. A container is partially filled with 12 liters of whole milk containing 4% butterfat. How
much 1% milk must be added to get a mixture that is 2% butterfat? Construct a table,
then solve.
Step-by-step explanation:
a table ? why? what kind ?
it is relatively simple to solve :
x liters of 1% had to be mixed with 12 liters of 4% to get 12+x liters of 2%
x×0.01 + 12×0.04 = (12+x)×0.02 = 12×0.02 + x×0.02
12×0.02 = x×0.01
x = 12×0.02/0.01 = 12×2 = 24 liters
so, 24 liters of 1% had to be added to the 12 liters of 4% to get a 2% mixture (12 + 24 = 36 liters).
101x^2+231x-334=-2 find the A,B,C
The roots of the equation is 1 and 3.28
The given equation is a quadratic
To find the roots of a quadratic equation, the formula is
[tex]\frac{-b + \sqrt{b^{2} - 4ac } }{2a}[/tex]
The equation is 101x^2+231x-334=-2 we need to find the A,B,C
101x^2+231x-332 = 0
here a is 101, b is 231, and c is -332
[tex]\frac{-b + \sqrt{b^{2} - 4ac } }{2a}\\\frac{-231 + \sqrt{231^{2} - 4(101)(-332) } }{2(101)}\\\frac{-231 + \sqrt{53361 + 134128 } }{202}\\\frac{-231 + \sqrt{187489 } }{202}\\\\\frac{-231 + \sqrt{187489 } }{202}\\\\\frac{-231 + 433 }{202}\\\\=\frac{202}{202}\\\\ 1[/tex]
[tex]\frac{-b - \sqrt{b^{2} - 4ac } }{2a}\\\frac{-231 - \sqrt{231^{2} - 4(101)(-332) } }{2(101)}\\\frac{-231 - \sqrt{53361 + 134128 } }{202}\\\frac{-231 - \sqrt{187489 } }{202}\\\\\frac{-231 - \sqrt{187489 } }{202}\\\\\frac{-231 -433 }{202}\\\\=\frac{664}{202}\\\\ 3.28[/tex]
Therefore, the roots of the equation is 1 and 3.28
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A savings account increases from 250$ to 265$. What is the percent increase of the savings account?
suppose that a tall child with arm span 120 cm and height 118 cm was added to the sample used in this study. what effect will this addition have on the correlation and the slope of the least-squares regression line?
A tall child with an arm span of 120 cm and height of 118 cm was added to the sample used in this study then the correlation will increase whereas the slope stays the same.
Correlation is a relation between two variables, by shifting one independent variable, how the dependent variable will shift, that's the degree of correlation since Correlation can be fitted in any shape or condition. It can be fitted nonlinear, straight or curvy straight, etc whereas slope is related to a straight variety of two variables, it is characterized as the rate of altering of the dependent variable in order with the independent variable. By and large you'll discover equation incline =( y2-y1)/(x2-x1).
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*IMAGE ATTACHED* (What’s the perimeter of the shaded figure below?
Answer:
The perimeter is 12 units.
Step-by-step explanation:
The answer would be 12 units because each side is 1 unit. If you count all the sides together, you get 12 units.
Answer: 12 units
Step-by-step explanation:
The perimeter is the length around a 2D shape. We will count the units that make up this shape's outline. See attached. Please note that as long as you count every side for this shape, it doesn't matter the order you count.
The perimeter is 12 units, the last option.
You have a TV that is 30 inches tall and 40 inches wide. What is the length of the diagonal of the TV. (The measure from bottom left to top right of the TV) 2500 inches/ 1250 inches/ 50 inches/ 26.5 inches
The length of the diagonal of the TV is 2500 inches
Calculating your TV size is less complicated than you might think. A TV's size refers to its diagonal length, which comes from measuring from the upper left hand corner of the actual TV screen to the lower right hand corner.
How do you measure the diagonal of a TV?TV that is 30 inches tall and 40 inches wide.
The length of the diagonal of the TV of the equation is
[tex]30^{2} + b^{2} =40^{2}[/tex]
Then
[tex]30^{2} +40^{2} =2500[/tex]
so
The length of the diagonal of the TV is 2500 inches
Calculating your TV size is less complicated than you might think. A TV's size refers to its diagonal length, which comes from measuring from the upper left hand corner of the actual TV screen to the lower right hand corner. Most are expressed in inches.
The screen surface's diagonal length is calculated from one corner to the other corner (bottom left to top right or top left to bottom right)
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Help ASAP!! Which algebraic expression is equivalent to the expression below?
The algebraic expression is equivalent to the expression below is 36x+110
Simplifying expressions using the distributive law.According to the Distributive Law, multiplying a number by a collection of numbers is equivalent to performing each multiplication independently.
For instance, given the standard expression C(D + E). Using the distributive law;
C(D + E) = CD + DE
Using this rule to the given expression shown below;
11(4x + 10) - 8x
Apply the distributive property;
11(4x + 10) - 8x
11(4x) + 11(10) - 8x
44x + 110 - 8x
Collect the like terms
44x + 110 - 8x
44x-8x+110
36x+110
This gives the resulting equation of the linear function after expansion
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Find the perimeter and area of the figure, rounding to the nearest tent. Use 3.14 for pie 7 ft 25 ft 4 ft Perimeter = 89.12 feet Area = feet squared
According to the picture, you can find the area of the figure by susbtracting the area of the segments of the circles to the area of the rectangle. We can observe that these segments are a quarter of a circle, together they would be a complete circle, then to find the area of the figure we can substract the area of one of the circles to the area of the rectangle.
1. Find the area of the circle:
[tex]\begin{gathered} A=\pi r^2 \\ A=\pi(4)^2 \\ A=16(3.14) \\ A=50.24 \end{gathered}[/tex]2. Find the area of the rectangle:
To do it, you need to find the length and the width first, do it this way:
[tex]\begin{gathered} l=25+4+4=33 \\ w=7+4+4=15 \end{gathered}[/tex]Now, find the area of the rectangle:
[tex]\begin{gathered} A=l\cdot w \\ A=33\cdot15 \\ A=495 \end{gathered}[/tex]3. Find the area of the figure:
[tex]\begin{gathered} A=495-50.24 \\ A=444.76 \end{gathered}[/tex]The area of the figure is 444.76 feet squared.
What sets does -√3,1 and 0 belong to
√2 and -√3 belong to the set of Irrational Numbers.
1 belong to the following sets:
• Rational
,• Whole
,• Natural
,• Integers
0 belongs to the following sets:
• Rational
,• Whole
,• Integers
quick sell outlet sold a total of 40 televisions, each of which was either a model p television or a model q television. each model p television sold for $p and each model q television sold for $q. the average (arithmetic mean) selling price of the 40 televisions was $141. how many of the 40 televisions were model p televisions? (1) the model p televisions sold for $30 less than the model q televisions. (2) either p
Model P televisions made up 12 of the 40 televisions when Quick Sell outlet sold a total of 40 television, each of which was either a model P television or a model Q television.
Price plus quantity equals revenue.
Let x be the quantity of sold TVs of model p.
40 - x units of the model q TV would have been sold.
Profits from model p TV sales are
px
Sales of the type q TV bring in money.
(40 - x)q
Total income equals px plus (40 - x)q
The average price calculation formula is written as
Total revenue / total number of TVs sold equals average price.
The 40 televisions sold for an average (arithmetic mean) price of $141. It follows that
141 = (px + (40 - x)q)/40
141 × 40 = px + (40 - x)q
5640 = px + (40 - x)q
p = q - 30
5640 = x(q - 30) + (40 - x) (40 - x)
q
30x + 40q - xq = 5640
5640 = - 30x + 40q
Since q = 120,
5640 = - 30x + 40 × 120
5640 = - 30x + 4800
5640 - 4800 = - 30x
840 = - 30x
x = 840/- 30 = - 28
Q cannot equal 120 since x cannot be negative.
Again,
5640 = px + (40 - x)q
If q = 30 + p, then
5640 = px + (40 - x)(30 + p)
5640 = px + 1200 + 40p - 30x - px
5640 = 1200 + 40p - 30x
Therefore,
If p = 120, then
5640 = 1200 + 40 × 120 - 30x
5640 = 6000 - 30x
30x = 6000 - 5640
30x = 360
x = 360/30
x = 12
Therefore, out of 40 televisions 12 tv are of model p
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PLEASE HELP QUICK!!!!!!!
Answer:
D
Step-by-step explanation:
Translation 4 units right and 1 unit up
angles in a triangle
Answer:
i = 74
j = 47
Step-by-step explanation:
to find "i" add 16 & 90 which is 106. subtract 106 from 180 to get 74.
to find "j" add 43 & 90 which is 133. subtract 133 from 180 to get 47
Let n =2 and z=4. Evaluate the following (8/n)n -✓z
Airfare from Atlanta, GA to Nashville, TN was decreased from $250 to $180. By what percentage did the cost of the airfare change
this is junior high math
Step-by-step explanation:
100% = $250
1% = 100%/100 = 250/100 = $2.50
the price decreased by
250 - 180 = $70
how many % are $70 ?
as many as how many times 1% ($2.50) fits into $70 :
70 / 2.50 = 28%
it changed (decreased) by 28%.
If x=5,solve for y.(Recall you can ue either original equation).y=x-6-2x+3y=-13
Using first equation
y=x-6
substitute x = 5 into the equation
y = 5-6
y = -1
Or
Using second equation
-2x+3y=-13
substitute x = 5 into the equation
-2(5) + 3y = -13
-10 + 3y = -13
3y = -13 + 10
3y = -3
y = -3/3
y = -1
Which of the following could be the first step when solving the equation 4-3(x+6)=28
Answer:
I don't know the options, but the first step would definitley be distributing the -3 over the parantheses --> -3x - 18
What is x in this equation
2(x-7)=-4
x = 5
2x - 14 = -4
2x = -10
x = 5
Answer: 5
Step-by-step explanation: First I took away the 2 on the left which was multiplying the brackets. Then because I did this I had to do the opposite to the other side. -4÷2
Then I just filled in the gaps 5-7=-2
