Answers
x and y are whatever you want them to be.
It can be convenient for solving a problem like this to use x and y to represent what the problem is asking for: the number of cans of cola and the number of cans of root beer. It is also convenient (less confusing) to use those variable names in the same order that the nouns of the problem are named:
... x = # of cans of cola
... y = # of cans of root beer
Then the problem statement tells you ...
... x + y = 30 . . . . . . . 30 cans total were bought
... x = 2y . . . . . . . . . . the number of cans of cola is twice the number of cans of root beer
_____
This set of equations is nicely solved by substitution: use the second equation to substitute for x in the first.
... (2y) +y = 30 . . . . . put 2y where x was
... 3y = 30 . . . . . . . . collect terms
... y = 10 . . . . . . . . . divide by 3
... 2y = x = 20
You're not done yet. You need to answer the question the problem asks.
Jared bought 20 cans of cola and 10 cans of root beer.
_____
Comment on x and y
You customarily see x and y as the variables of a problem. Personally, I like to use variables that remind me what they stand for. In this problem, I might use "c" for cans of cola and "r" for cans of root beer. Then when I've found the solution, I know exactly how it relates to what the question is asking.
Always start by writing down what the variables stand for (as we did here). Sometimes, this is called writing a Let statement: Let x = number of colas; let y = number of root beers.
Comment on problems of this type
When a proportional relationship is given between the items in a sum (2 cola cans for every root beer can), it is often convenient to work the problem in terms of groups of items. Here, a group of 3 items can consist of 2 cola cans and 1 root beer can. Then 30 items will be 10 groups, so 10 root beers and 20 colas. The problem is solved even before you can name the variables.
Even when the relationship isn't exactly proportional, you can add or subtract the extras and still work the problem this way. Had we said colas numbered 3 more than twice as many root beers, we could have our groups of 3 total 27 (30 less the 3 extra), giving 9 root beers and 21 colas (3 + 2·9).
Related Questions
Jake bought 4.08 pounds of apples he knows that 1.19 pounds are gala apples and the rest are cameo apples how many pounds of cameo apples did he buy?
Answers
Answer: He bought 2.89 pounds of cameo apples.
Step-by-step explanation:
Since we have given that
Total number of pounds of apples he bought = 4.08
Number of gala apples = 1.19 pounds
So, the rest are cameo apples.
As we know to get the remaining value we always use the subtraction operation,
Now,
[tex]4.08-1.19=2.89[/tex]
So, 2089 pounds of apple are cameo apples.
Final answer:
To find out how many pounds of cameo apples Jake bought, subtract the pounds of gala apples (1.19 pounds) from the total pounds of apples (4.08 pounds), resulting in 2.89 pounds of cameo apples.
Explanation:
Jake bought 4.08 pounds of apples. He knows that 1.19 pounds are gala apples and needs to find out how many pounds of cameo apples he bought. To find the weight of the cameo apples, we subtract the weight of the gala apples from the total weight of apples purchased.
So, the calculation will be as follows:
Total weight of apples - Weight of gala apples = Weight of cameo apples.
4.08 pounds - 1.19 pounds = 2.89 pounds.
Thus, Jake bought 2.89 pounds of cameo apples.
71.120-2.359 what is that answer please help m.
Answers
We could use the standard form of subtraction.
We put 71.120 on top and we put 2.359 at the bottom.
Then, we subtract the thousandths place. It involves a carry-over.
Then, we subtract and the answer is:
68.761
The subtraction of 71.120 and 2.359 equals 68.761.
Explanation:This question is asking for the subtraction of two decimal numbers, the first being 71.120 and the second being 2.359. To do this, you would stack the numbers on top of each other, aligning the decimal points, and subtract as you would with whole numbers.
So, your subtraction would look like this:
71.120
- 2.359
------
68.761
So, 71.120-2.359 equals 68.761.
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Which is the best estimate for the average rate of change for the quadratic function graph on the interval 4 ≤ x ≤ 8?
A)
1
B)
2
C)
3
D)
4
Answers
Answer: A:1
Step-by-step explanation:
I'd really appreciate it if anyone could help! :) I'll give Brainliest!
The graph of a function is shown below these choices.
Select ALL the statements that correctly describe this function.
The equation that represents this function is f(x)=−7x+1.
The equation that represents this function is f(x)=x−7.
The range of this function is increasing as the domain increases.
The range of this function is decreasing as the domain increases.
Answers
Answer:
The equation that represents this function is f(x)=x−7.The range of this function is increasing as the domain increases.Step-by-step explanation:
The line has a slope (m) of 1 and a y-intercept (b) of -7. Thus the equation in slope-intercept form is
... y = mx + b
... y = x - 7
For a linear function such as this, the size of the domain is equal to the size of the range (because the slope is 1). Thus when one increases, so does the other.
_____
Comments on the problem
It appears the first answer choice is a result of mixing up slope and intercept in the equation of the line. A slope (x-coefficient) of -7 is a pretty steep line going downward from left to right. The graph does not have that characteristic.
It is a bit unusual to talk about domain and range increasing or decreasing. The domain is the region over which the function is defined, so is generally fixed. The range is the corresponding set of values of the function, fixed once the domain is determined. Here, since the function is linear, if one were to define it over a larger region, the range of values produced by the function would also get larger.
made a mistake when I last posted. can someone help me .
Answers
L=3w-35
By inputting this into the equation to find the perimeter we get:
2(3w-35)+2w=190
Distribute
6w-70+2w=190
Add like terms
8w=260
Divide both sides by 8
w=32.5
The width is 32.5cm
To find the length input w into the equation for length
L=3(32.5)-35
L=97.5-35
L=62.5
The length is 62.5cm
Check that the solution is correct by inputting the solutions to the perimeter equation
2L+2w=190
2(62.5)+2(32.5)=190
125+65=190
190=190
I hope this helps :)
35 Centimeters Less than Triple the width:
190 cm. The Perimeter of the box:
W = Width of Box
L = Length of Box
Length = 3c - 35
2W + 2L = 190
Just solve to get your answer
Hope that helps!!!! : )
Mary and her brother John collect foreign coins. Mary has four times the number of coins that John has. Together they have 200 foreign coins.
Answers
x + 4x = 150
5x = 150
x = 30
John has x = 30 coins
Mary has 4x = 4*30 = 120 coins.Let the number of coins John has be "x".
The the number of coins Mary has is "4x"
John has 40 coin and Mary has 160 coins because 40 times 4 equals 160 and 160 plus 40 equals 200 so Mary has 160 and John has 40
Select the equation that represents a line with a slope of 3 and that contains the point (-4,2).
A) y - 2 = 3(x+4)
B) y+2=3(x-4)
C) x-4=3(y+4)
D)x-4=3(y+2)
Answers
Answer:
A) y - 2 = 3(x+4)
Step-by-step explanation:
Given that the equation is a line with slope =m=3 and
a point on it (x1,y1) = (-4,2)
Any line having slope m and passing through (x1,y1) has equation in point slope form as
y-y1 = m(x-x1)
We are given here x1 =-4, y1 =2 and m =3
y-y1 = y-2 and x-x1 = x-(-4) = x+4
So equation is y-2 = 3(x+4)
Verify:
The line is y = 3x+12+2 = 3x+14
Hence slope =3 is verified
Substitute the point x =-4 and y =2
2 =3(-4)+14 = 2 is true
Thus verified
Answer:
A is correct option. Equation of line: y-2=3(x+4)
Step-by-step explanation:
Slope of line is 3 and passing point (-4,2).
If slope and passing point given then we have an equation of line
[tex]y-y_1=m(x-x_1)[/tex]
where,
[tex](x_1,y_1)\rightarrow (-4,2)[/tex]
Slope (m)=3
Equation of line:
y-2=3(x+4)
This equation match with option A
Thus. option A is correct.
In how many ways can the 19 members of a chess club fill the offices of King, Knight, Bishop, and Rook?
Answers
Solution:
This problem is a permutation because the order matters here. This means that choosing A as King, B as Knight, C as Bishop and D as Rook results in a different arrangement from B as King, A as Knight, D as Bishop and C as Rook. We would count them both because in the first case A is King, but in the second case A is Knight.
Therefore, the possible number of ways are given below:
[tex]19P4=\frac{19!}{(19-4)!} =\frac{19 \times 18 \times 17 \times 16 \times 15!}{15!} =19 \times 18 \times 17 \times 16 =93024[/tex]
Hence there will be 93024 ways 19 members of a chess club fill the offices of King, Knight, Bishop, and Rook.
There are 19 members in the chess club, and they can fill the offices of King, Knight, Bishop, and Rook in 38760 ways.
In how many ways can the 19 members of a chess club fill the offices of King, Knight, Bishop, and Rook.
To determine the number of ways to fill the offices, we use the concept of permutations. Since each office must be filled by a different member, the number of ways is calculated as 19P4 = 19! / (19-4)! = 38760 ways.
Find the length of the side of the square.
Answers
6x-1=4x+6
subtracting 4x from each side
2x-1=6
adding 1 to each side
2x=7
divide by 2
x=7/2 or 3.5
check: 6(7/2) -1 =4(7/2)+6
21-1 =14+6
20=20 correct
The length of a side of the square can be found using the Pythagorean theorem. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, we find the length of a side of the square to be the square root of half of the square of the hypotenuse.
Explanation:To find the length of the side of the square, we are going to use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².
Consider a square with a hypotenuse labeled as 's'. If we bisect this square diagonally, we form two right triangles. Since the sides of the square are equal, we can denote the other two sides of the right triangle as 'D' and 'L'. So, the Pythagorean theorem becomes: D² + D² = s², since D = L. Solving this, we find that s² = 2D².
Therefore, the length of a side of the square 'D'= √(s²/2).
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Graph the following lines and using the graph determine several values of x for which the graph is positive (negative):
y = -0.5x - 2
y is positive when BLANK
x is positive when BLANK
Answers
Answer:
Step-by-step explanation:
Given equation is,
y=-0.5x-2
when x=-2 , y=-0.5(-2)-2=1-2=-1
when x=0 , y=-0.5(0)-2=0-2=-2
when x=2 , y=-0.5(2)-2=-1-2=-3
So, we get the points (-2,-1) , (0,-2) , (2,-3)
Now, using the points on the graph and adding them, we will get the graph of given line.
Please check image for the graph.
Now for the second part- we have to find values of x , for which y is positive.
That means, y will be above the x-axis.
From the graph we can see that- when x<-4,
then the graph is above the x-axis.
So, for all values of x, which are less than -4,
we will get the positive graph.
Which number is not divisible by either of the numbers 3 and 5?
A.
5000
B.
2374
C.
1203
D.
2505
Answers
Which postulate or theorem proves that △PNQ and △QRP are congruent?
SAS Congruence Postulate SSS Congruence Postulate HL Congruence Theorem ASA Congruence Postulate
Answers
Answer:
SSS Congruence Postulate
Step-by-step explanation:
we know that
The SSS Congruence Postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
In this problem
PN≅QR
NQ≅RP
PQ≅QP -----> is the same side
so
Three sides of triangle PNQ are congruent with three sides of triangle QRP
therefore
△PNQ and △QRP are congruent by SSS Congruence Postulate
SSS Congruence Postulate or theorem proves that △PNQ and △QRP are congruent
Explanation:According to the dictionary, congruent (of figures) is identical in form; coinciding exactly when superimposed. Two figures or objects are congruent if they have the same shape and size.
According to the picture attached, the answer is SSS Congruence Postulate Because I have three pairs of congruent sides such as
PR = NQ is one pair, QR = NP is another pair, then PQ = PQ is the third pair
SSS Congruence Postulate or theorem proves that △PNQ and △QRP are congruent
Which postulate or theorem proves that △PNQ and △QRP are congruent?
a. SAS Congruence Postulate b. SSS Congruence Postulate c. HL Congruence Theorem d. ASA Congruence Postulate .
The other example can be seen in the second attachment of picture. The question is still the same: Determine which postulate or theorem can be used to prove that ABC = DCB!
Then AC = DB
AB = DC
BC = BC, This side is equal to itself
Therefore the three sides of one triangle equal to 3 sides of the other. It means that the triangles are congruent. Therefore the answer is SSS
Hope it helps you to learn more about triangle.
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Use compatible numbers to find two estimates that the quotient is between 1045÷2
Answers
Answer: The two estimates of quotient is 522 and 523 .
Step-by-step explanation:
Compatible numbers are numbers which are close in value to the given numbers, and make it easy to calculate the answer for any given arithmetic problem .
To find two estimates that the quotient is between in 1045÷2
We now that 1045 is greater than 1044 and less than 1046 i.e.1044<1045<1046
Dividing 2 from all sides ,we get
1044÷2<1045÷2<1046÷2
⇒522<1045÷2<523
As the quotient of 1045÷2 is lying between 522 and 523.
Therefore, the two estimates of quotient is 522 and 523
To estimate the quotient of 1045 divided by 2 using compatible numbers, one can use 1040 (which gives an estimate of 520) and 1050 (which gives an estimate of 525) as they are easily divisible by 2. Hence, the quotient should fall between 520 and 525.
The student is asked to find two estimates that the quotient 1045 ÷ 2 falls between using compatible numbers. To estimate, we look for numbers that are easy to divide. Compatible numbers to 1045 that are close to it and divisible by 2 could be 1040 and 1050. So our two estimates for 1045 ÷ 2 are:
1040 ÷ 2 = 5201050 ÷ 2 = 525Therefore, the quotient of 1045 ÷ 2 should be between 520 and 525.
Bill wants to put a large mural on a wall that is 9 1/3 feet long and 8 1/8 feet wide. Find the area of the wall. If the mural is 100 sq feet, will it fit on the wall?
Answers
the area of a rectangle is: lxw
1. plug in our values: length: 9.3 - width: 8.125
9.3x8.125 = area of the wall
2. multiply and solve for the area of the wall:
9.3x8.125 = 75.5625 square feet
now that we found the area of the wall we need to compare that to our mural
our mural is 100 square feet and our wall is 75.5625 square feet
therefore our wall has a smaller area than our mural meaning our mural will NOT fit on the wall
Please help!!!! I just need help with part c.
A pumpkin is being grown for a contest at the state fair. Its growth can be modeled by the equation P=25(1.56)^n, where P is the weight of the pumpkin in pounds and n is the number of weeks the pumpkin has been growing.
a. By what percentage does the pumpkin grow every week?
(my answer) The pumpkin grows 156% percent every week.
b. After how many weeks will the pumpkin be 80 pounds?
(my answer)The pumpkin will be 80 pounds after 3 weeks.
c. What if the growth percentage changed to 32, after how many weeks will the pumpkin be 80 pounds?
Answers
A) the growth is 56% per week. The 1.56 is multiplying the weight of the pumpkin now by the 56% to get the total weight after the 56% increase.
B) Replace P with 80 and solve for n:
80 = 25(1.56)^n
Divide each side by 25:
80/25 = 1.56^n / 25
3.2 = 1.56^n
Take the natural logarithm of both sides:
ln(3.2) = ln(1.56^n)
Remove the exponent:
ln(3.2) = n(ln(1.56)
Divide both sides by ln(1.56)
n = ln(3.2) / ln(1.56)
n = 2.6 weeks, round to 3 weeks.
C) Change 1.56 to 1.32 and redo the same calculation from B.
80 = 25(1.32)^n
80/25 = 1.32^n /25
3.2 = 1.32^n
ln(3.2) = ln(1.32^n)
ln(3.2) = n(ln(1.32)
n = ln(3.2) / ln(132)
n = 4.2, round to 4 weeks.
Sweet t has 2 orange picks for every 5 green if there 21 picks in all ow many orange picks are there
Answers
I think the answer would be 6?
Consider two functions: g(x)=−x2−6x and the quadratic function f(x) shown in the table.
Which statements are true?
Select each correct answer.
The average rate of change of f(x) is greater than g(x) on the interval [0,3] .
g(x) has a greater y-intercept than f(x) does.
f(x) is greater than g(x) on the interval (0,3) .
g(3) is less than f(3) .
Answers
Answer:
Hence average rate of change is greater for f(x) in (0,3).
Yes. f(x) is greater than g(x) in the interval (0,3)
Yes. g(3) <f(3)
Step-by-step explanation:
To find average rate of change of f and g in (0,3)
f(3)-f(0)/3 = (9-0)/3 =3
g(3) = -9-18 = -27
g(0) = 0
Rate of change in(0,3) of g(x) = -27/3 =-9
Hence average rate of change is greater for f(x) in (0,3)
---
Both f and g have intercepts of y as 0
Hence both are equal.
3) Yes. f(x) is greater than g(x) in the interval (0,3)
Because g(x) <0 for all x in (0,3) while f(x) >0
4) g(3)= -9-18=-27 <f(3)
Answer:
1). g(3) is less than f(3).
2). The average rate of change of f(x) is greater than g(x) on the interval [0,3] .
Step-by-step explanation:
g(x) = -x^{2} - 6x
so f(3) = 9
let's solve for g(3)
3^{2} = 9
g(3) = - 9 - 18 = -27
so -27 is less than 9
g(3) < f(3)
So our answer is correct: g(3) is less than f(3).
In second option:
put the value from 0 to 3 in function g(x) = - x^{2} - 6x
g(0) = 0
g(1) = -7
g(2) = -16
g(3) = -27
on the other hand values of f(x) are:
f(0) = 0
f(1) = 1
f(2) = 4
f(3) = 9
So average values of f(x) are greater than g(x) so our option is correct.
The average rate of change of f(x) is greater than g(x) on the interval [0,3] .
i hope you get the idea.
PLEASE HELP with vocabulary
This means to move a graph vertically and/or horizontally around the coordinate plane.
It’s NOT Shifting Or just translation by itself.
It’s 20 letters
Answers
joe has twelve more coins than brenda. together they have 64 coins. how many coins does each have
Answers
brenda: 26
your welcome
long division x^3 - 6x^2 + 13x -12 over x - 3
Answers
Complete solution is given in attachment below.
Solve the equation.
9x2 + 4 = 0
Answers
Answer: [tex]x = \frac{2}{3}i , -\frac{2}{3}i[/tex]
Step-by-step explanation:
9x² + 4 = 0
-4 -4
9x² = -4
[tex]\frac{9x^{2} }{9} = \frac{-4}{9}[/tex]
x² = [tex]\frac{-4}{9}[/tex]
[tex]\sqrt{x^{2} } = \sqrt{-\frac{4}{9} }[/tex]
[tex]x = +/- \frac{2}{3}i[/tex]
Which equations are correct
-6^4(4y^2+2)=-24y^8-12y^4
-4x^2(2x^2+5)=-8x^4-20x^2
-4b^3(5b^2+3)=-20b^6-12b^3
-5a^4(2a^2+4)=-10a^6-20a^4
Answers
Answer:
2nd, 3rd and 4th equations are correct.
Step-by-step explanation:
[tex]-4x^2(2x^2+5)=-8x^4-20x^2\\\\[/tex]
is right because each term inside is multiplied by -4x square and we find the answer is right.
[tex]-4b^3(5b^2+3)\\\\\\= -4(5)(b^3)(b^2) =-20b^6-12b^3\\[/tex]
Hence correctly done.
[tex]-5a^4(2a^2+4)= (-5)(2)(a^4)(a^2)+(-5)(4)(a^4\\-10a^6-20a^4\\[/tex]
Correctly done.
[tex]-6^4(4y^2+2)=-24y^8-12y^4\\= -(6)(6)(6)(6) 4y^2 -(6)(6)(6)(6) (2)[/tex]
should be the right answer.
But instead only 6 is multiplied by inner terms. Hence wrong.
I answer is wrong and others are right.
Autumn is paying for college in monthly installments. The college requests that a $1000 down payment be made. Autumn will then continue to pay $500 per month to pay for her tuition. a) write an equation that represents Autumn’s payment to her college. b) after 4 months, how much will she have paid?
Answers
a. 500 X 12 =
b. 20,000
Can someone explain step by step how to do this? thanks. I know some but not understanding what you do with the vto the power if 3
Answers
See the attached picture for the steps:
Explain how the cartons and boxes for table tennis balls are like the digits for numbers in our base-10 number system.
Answers
Answer:
To explain the cartoons and the boxes for table tennis balls are like the digits for numbers in base-10 number system
Here we know that, the number of table tennis balls in one box =10 balls
and the number of table tennis balls in boxes in each cartoon = 10 balls
Therefore, The number of table tennis balls in each cartoon =10×10=100 balls
Hence for the number of balls ,the hundreds place tells the number of cartoons and tens place tells the number of boxes which left as remainder or without cartoon.
For example if the total tennis balls =540 then its hundreds place i.e 5 tells the number of cartoons and its tens place i.e.4 tells the number of boxes which left as remainder or without cartoon.
Answer:
Base 10 Number System = (0,1,2,3,4,5,6,7,8,9)
In a Carton of table tennis there are 10 boxes.
And Each Box can Hold 10 Balls.and if i mark boxes from 0 to 9, then
then there are 10 boxes , Total number of Balls=100
So if I represent a single Carton by A, then
A[single carton] ={0,1,2,3,4,5,6,7,8,9}= 10 boxes =100 balls
B [2 carton]= 20 boxes=200 balls
C[ 5 cartons + 3 Boxes] = 5× 100+ 3×10 =530 balls
D[ 12 cartons + 8 Boxes]= 12×100+8×10=1280 balls
Now you can see,
Each carton is holding the balls in decimal number system.
Boxes = Ten's place in number system,
Number of cartons = either Hundred place or thousand place or more than that
In this way we can represent Carton and Box for table tennis balls in decimal number system having base 10 .
Ari walked 2 3/4 miles at a constant speed of 2 1/2 miles per hour. Beth walked 1 3/4 miles at a constant speed of 1 1/4 miles per hour. Cindy walked for 1 hour and 21 minutes at a constant speed of 1 1/8 miles per hour. List the three people in order of the times they spent walking from least to greatest.
Answers
[tex]speed = \frac{distance \: covered}{time \: taken} [/tex]
[tex]2 \frac{1}{2} mph = \frac{ 2\frac{3}{4} }{time} [/tex]
[tex]time= \frac{ 2\frac{3}{4} h }{ 2 \frac{1}{2} mph } [/tex]
[tex]time= \frac{ \frac{11}{4} }{ \frac{5}{2} }hours[/tex]
[tex]time= \frac{11}{10} hours[/tex]
[tex]time =1 \frac{1}{10} hours = 1.1 \: hours[/tex]
Time Beth spent
[tex]1 \frac{1}{4} mph = \frac{ 1\frac{3}{4} }{time} [/tex]
[tex]time = \frac{ 1\frac{3}{4} }{1 \frac{1}{4} mph} [/tex]
[tex]time = \frac{ \frac{7}{4} }{ \frac{5}{4}} hours[/tex]
[tex]time = \frac{7}{5} hours[/tex]
[tex]time = 1 \frac{2}{5} hours = 1.4 \: hours[/tex]
Time Cindy Spent
We convert Cindy's time to hours.
[tex]1 \: hour \: 21 \: minutes \: = 1 \frac{21}{60} hours = 1 \frac{7}{20} hours = 1.35hours[/tex]
In order of time spent,
Ari, Cindy, Beth
The order of their time spent from least to greatest is; Ari, Cindy, Bety
What is the time spent for the distance covered?
Distance covered by ari = 2³/₄ miles
Speed of ari = 2¹/₂ miles per hour
Formula for time is;
time = distance/speed
Thus;
Time spent by ari = 2³/₄/2¹/₂
Time spent by ari = 1.1 hours
Distance covered by beth = 1³/₄ miles
Speed of beth = 1¹/₄ miles per hour
Formula for time is;
time = distance/speed
Thus;
Time spent by beth = 1³/₄/1¹/₄
Time spent by beth = 1.4 hours
Distance covered by cindy = 1 hour 21 minutes = 1⁷/₂₀ miles
Speed of cindy = 1¹/₈ miles per hour
Formula for time is;
time = distance/speed
Thus;
Time spent by cindy = 1⁷/₂₀/1¹/₈
Time spent by cindy = 1.35 hours
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what is 168 cm in feet
Answers
5.51181 in feet. Hope this helps
Solve for d.
0.5(7d+4)=7-1.5d0.5(7d+4)=7−1.5d
Answers
ANSWER
[tex]d=1[/tex]EXPLANATION
We want to solve
[tex]0.5(7d+4)=7-1.5d[/tex]
Let us first multiply through by [tex]10[/tex] to clear the decimal.
[tex]10\times 0.5(7d+4)=7\times 10 -1.5d\times 10[/tex]
This implies that;
[tex]5(7d+4)=70 -15d[/tex]
We now expand to obtain;
[tex]35d+20=70 -15d[/tex]
We group like terms to obtain;
[tex]35d+15d=70 -20[/tex]
[tex]50d=50[/tex]
Dividing through by 50 gives;
[tex]d=1[/tex]
Answer:
The value of the equation for d is 1.
Step-by-step explanation:
Consider the provide equation.
[tex]0.5(7d+4)=7-1.5d[/tex]
We need to solve the equation for d.
Open the parentheses.
[tex]3.5d+2=7-1.5d[/tex]
Add 1.5d both sides.
[tex]3.5d+1.5d+2=7-1.5d+1.5d[/tex]
[tex]5d+2=7[/tex]
Subtract 2 from both sides.
[tex]5d+2-2=7-2[/tex]
[tex]5d=5[/tex]
Divide both the sides by 5.
[tex]d=1[/tex]
Hence, the value of the equation for d is 1.
I need an expression for the area of the outer square, thanks
Answers
The area of a square is calculated suing the formula x^2, where x is a side length of the square. This is just like length times width because a square has equal side lengths.
Take the left side and add the two lengths together because they form one side length of the square. A side length of the square is x + 4.
To find the area using the side length x + 4, you would square the side length. Your answer is (x + 4)^2.
What variable expression represents the phrase 25 decreased by the sum of 6 and a number
Answers
The variable expression represents the phrase '25 decreased by the sum of 6 and a number' is 25-(6+x).
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically.
For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and methods can be used to convert description to mathematical expressions.
We have to find the variable expression represents the phrase '25 decreased by the sum of 6 and a number'
Let the number be x then decrease mean subtract, sum means add
by means parenthesis;
The expression becomes as;
25 - (6 + x)
Learn more about expression here;
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