Solve each equation for the variable. Show your work and check your solution.
Steps to follow:
Step 1: Distribute First
Step 2: Combine like terms
Step 3: Solve the equation
1. 5x + 4x − 6x = 24 2. 8x + 5 − 4x + 1 = 46
3. 33 = 5(x + 8) + 3 4. 2x + 3(x − 8) = 1
5. x + x − 2x + 4x = −48 6. 2(x + 5) + 3x = 25
7. 60 = 4(x + 3) + 2(x − 3) 8. 47 = 2(x + 3) + 3(x − 3)
9. −2(x + 1.4) − 1.8 = 20.6 10. 8 − 2(x + 4) = 10
11. Tyler told his friend this riddle: “I am thinking of a number. Three times my number plus twice my number is twenty. What number am I thinking of?”
a) Write an equation that models Tyler’s statement.
b) Solve the equation. What number was Tyler thinking of?
Answer:
1. This is a like term
24 = 24
2. This is not a like term
12x - 6 = 46
3. This is not a like term
33 = 5x + 43
4.This is a like term
1 = 1
5. This is not a like term
7x = -48
6. This is a like term
25 = 25
7. This is a like term
60 = 60
8. This is a like term
47 = 47
9.This is a like term
20.6 = 20.6
10.This is a like term
10 = 10
Step-by-step explanation:
1. 5x + 4x − 6x = 24
5x + 4x = 9x
9x - 6x = 24
3x = 24
We can replace x and turn it into an 8.
3(8) = 24
3 x 8 = 24
24 = 24
This is a like term.
2. 8x + 5 − 4x + 1 = 46
8x + 4x - 5 + 1 = 46
8x + 4x = 12x
12x - 5 + 1 = 46
5 + 1 = 6
12x - 6 = 46
We cannot replace the x with any number to get 46.
So this is not a like term.
3. 33 = 5(x + 8) + 3
5xX= 5x
5 x 8 = 40
33 = 5x + 40 + 3
40 + 3 = 43
33 = 5x + 43
We cannot replace any number with x and get 33.
This is not a like term.
4. 2x + 3(x − 8) = 1
3 x X = 3x
3 x 8 = 24
2x + 3x - 24 = 1
2x + 3x = 5x
5x - 24 = 1
We can replace the x with 5.
5(5) - 24 = 1
5 x 5 = 25
25 - 24 = 1
1 = 1
This is a like term
5. x + x − 2x + 4x = −48
x + x = 1x because x is always a 1
1x - 2x +4x = -48
1x + 2x = 3x
4x + 3x = 7x
7x = -48
We cannot replace x with any number.
This is not a like term.
6. 2(x + 5) + 3x = 25
2 x X = 2x
2 x 5 = 10
2x + 10 + 3x = 25
2x + 3x + 10 = 25
2x + 3x = 5x
5x + 10 = 25
We can replace the x with a 3.
5(3) + 10 = 25
5 x 3 = 15
15 + 10 = 25
25 = 25
This is a like term.
7. 60 = 4(x + 3) + 2(x − 3)
4 x X = 4x
4 x 3 = 12
60 = 4x + 12 + 2(x - 3)
2 x X = 2x
2 x 3 = 6
60 = 4x + 12 + 2x - 6
60 = 4x +2x +12 - 6
4x - 2x = 2x
60 = 2x + 12 - 6
12 - 6 = 6
60 = 2x + 6
We can replace the x with a 33.
60 = 2(33) - 6
2 x 33 = 66
66 - 6 = 60
60 = 60
This is a like term.
8. 47 = 2(x + 3) + 3(x − 3)
2 x X = 2x
2 x 3 = 6
47 = 2x + 6 + 3(x - 3)
3 x X = 3x
3 x 3 = 9
47 = 2x + 6 + 3x - 9
47 = 2x + 3x + 6 - 9
2x + 3x = 5x
47 = 5x + 6 - 9
6 - 9 = -3
47 = 5x + -3
We can replace the x with a 10.
47 = 5(10) + -3
5 x 10 = 50
47 = 50 + -3
50 + -3 = 47
47 = 47
This is a like term.
9. −2(x + 1.4) − 1.8 = 20.6
-2 x X = -2x
-2 x 1.4 = -2.8
-2x + -2.8 - 1.8 = 20.6
-2.8 - 1.8 = -4.6
-2x + -4.6 = 20.6
We can replace x with a 8.
-2(8) + -4.6 = 20.6
-2 x 8 = -16
-16 + -4.6 = 20.6
20.6 = 20.6
This is a like term.
10. 8 − 2(x + 4) = 10
2 x X = 2x
2 x 4 = 8
8 - 2x + 8 = 10
8 - 8 + 2x = 10
8 - 8 = 0
0 + 2x = 10
We can replace x with 5.
0 + 2(5) = 10
2 x 5 = 10
0 + 10 = 10
10 = 10
This is a like term.
I hope this helped. I am sorry if you get this wrong. Have a wonderful day.
can someone please help within 30 minutes :)
Answer: D
Step-by-step explanation:
It's 113 bc 180-67=113 and it's consecutive bc they are on the same side and right next to each other
Answer:
hellooo…
I think one of two options
C or D
I’ll mark Brainly! Which numerical equation could be used to describe the diagram?
A) −2 + 6 = 4
B) 4 + (−6) = −2
C) −2 + (−6) = −8
D) −6 + (−2) = −8
If y = –7 and z = –3, what is –y + z?
Answer:
4
Step-by-step explanation:
-(-)7+-3
7+(-)3
The answer is 4
A common abuse of bar graphs is
Answer:
A common abuse of bar graphs is to. replace bars by pictures and increase both height and width as the variable plotted increases. If a bar graph is to be accurate, it is essential that. the bars all have the same width.
Laura used 2 3/4 gallons of gas on Saturday and 1 2/3 gallons of gas on Sunday. How many more gallons of gas did she use on Saturday
Answer:
1 /1/12 gallons of gas.
Step-by-step explanation:
2 3/4
1 2/3
Find the common denominator: 12
33/12
20/12
33 - 20 = 13
PLZZZZZ HELP ME I WILL MAKE YOU BRAINLIEST ANWER PLZZZZZ THANKYOU!!!!!!
Answer:
1) y=1/5x +0.8
2) y= -2x +10
Step-by-step explanation:
It's been a while, but I think this is right:
1)
For 2 lines to be parallel they must have the same slope
Recall that the equation of a line is
y-y1 = m (x- x1)
m being slope
So looking at equation 1, we can tell that the slope is 1/5 because it has already been distributed to the x.
So we know our equation will look something like this
y-y1 = 1/5 (x- x1)
We also know that the line passes through the point (8,1)
So, you plug in those points to your equation
y- 1 = 1/5(x - 8)
Simplifying and distributing the equation, we end up with
y= 1/5x + 0.8
(if you would like me to explain the simplification plz ask in a comment.)
2)
First you have to move -x from the left side of the equation to the right, making the equation
2y= x+10
then divide by 2 on both sides (im writing x/2 as 1/2x, because they are the same)
y= 1/2x + 5
For 2 lines to be perpendicular they must have the opposite reciprocal slope
Meaning if you had a slope of 2, the opposite would be -2 and the reciprocal would be 1/2, so your slope would be -1/2
Knowing this and keeping in mind our equation of a line from the first question, our slope of a perpendicular line (or m in our equation) of y= 1/2x + 5
would be -2
So far we have an equation that looks like
y-y1 = -2 (x- x1)
So now we plug in our points (6, -2)
(y- -2)
y + 2 = -2 (x - 6)
Simplifying and distributing the equation, we end up with
y= -2x +10
(if you would like me to explain the simplification or have a question don't hesitate to ask in a comment.)
Answer: 1.) y = 1/5 x - 3/5
2.) y = -2x + 10
Step-by-step explanation:
1.) Keep the same slope. Substitute the y and x-values from the given coordinate into the slope-intercept form and solve for the new b
1 = 1/5(8) + b 1 = 8/5 +b .subtract 8/5 form both sides:
-3/5 = b
y = 1/5 x - 3/5
2.) Rewrite the given equation in slope-intercept form
-x + 2y = 10 becomes y= 1/2 x +10
Take the reciprocal of the slope and reverse the sign: 1/2 becomes -2
Substitute the y and x-values from the given coordinate into the slope-intercept equation and solve for b.
-2 = -2(6) + b
-2 = -12 + b Add +12 to both sides
10 = b
y = -2x + 10 Standard form: 2x + y = 10
Attachment shows the graphs and coordinates.
Write 2 x 10^-5
in standard notation.
(3.2 x 104)x(1.4 x 102)
Answer:
47523.84
Step-by-step explanation:
Can a tutor help me please
Scientists found two whales that have a combined weight of 8.4 x 105 pounds. Write this weight in standard notation.
Answer:
Step-by-step explanation:
8.4 * 10⁵ = 8.4 * 100000
= 840000.0
= 840,000
Answer:
hi
Step-by-step explanation:
8.4 * 10⁵ = 8.4 * 100000
= 840000.0
= 840,000
The perimeter of a rectangle is 24 meters. If the length of the rectangle is 8 meters, what is the width (in meters)?
Answer:
8 meters
Step-by-step explanation:
8 + 8 + 8 + 8 = 24 which is the perimeter, just trust me
OMG!!??!!?? SCIENTISTS TRANSFORM 6IX9INE INTO A RAT?!??????!!?! LOOK AT HIM!!!!!!!!
Add an equation and answer
Answer:
Currently temperature = 35°F
Rate of descend = 4°F
We have to reach = -1°F
Temperature to get cooled down = |-1 + 35| (The two lines mean absolute value)
=> 36°F
Hours = Total temperature to get cooled / Rate
=> 36 / 4
=> 9 hours
Equation = 4x = |1 + 35|
If my answer helped, kindly mark me as the brainliest!!
Thank You!!
how to find sample variance with these numbers?
4364
4459
4740
4510
4509
4666
4946
4499
4857
4022
3841
4230
Answer:
s2 = 105174.93
Step-by-step explanation:
s2=∑ni=1(xi−x¯)^2 / n−1
4. A room measures 10 meters by 15 meters. How many 30 centimeters by 30 centimeters squares of carpet are needed
to cover the floor of this room?
Answer:
1667 carpets.
Step-by-step explanation:
For this problem we have to find the
area of room,
area of 1 carpet.
Then we have to find how many such carpet's sum will be equal to area of room.
_______________________________________________
area for rectangle is given by = length * width
area of room = 10 m * 15 m = 150 m. sq.
dimension of carpet = 30 cm * 30 cm
lets converts first 30 cm in meter so that dimension of room and carpet are in same unit that is in meters
100 cm = 1 meter
30 cm = 1/100 * 30 meters = 0.3 meters
area of 1 carpet = 0.3 m * 0.3 m = 0.09 m. sq.
let there be need of x carpet to cover the floor of room.
area of x carpet = area of 1 carpet *x
area of x carpet =0.09x m. sq.
area of x carpet = area of room
0.09x m. sq. = 150 m. sq.
x = 150/0.09 = 1666.67
Thus, there will be need of 1666.67 carpets but carpets cannot be in fraction
hence rounding the number of carpet to nearest whole number.
there will be need of 1667 carpets.
I will give brainlist.
Find the slope of the line that passes through the two
points.
(12, 15 ) and (5,7)
Mrs B and Ms R plan to walk 3.75 miles to and from school every day for an entire year. If they meet their goal how many miles will they walk?
3.75 X 365 = X
or
3.75 X 366=x
or
3.75 X 180=x
I dont know what equation to use.
Solve and choose the answer in its simplest form. 3/4 ÷ 2/3 = ?
please hurry i need this fast
This triangle is congruent under the ASA congruence postulate as the two corresponding parts of this triangle which are angles are equal and there is one equal side . The equal side is the common side of both these triangles .
Find the sum. – 76 + (-124) = *
Answer:
-200
Step-by-step explanation:
[tex]-76+(-124)\\\\-76-124\\\\\boxed{-200}[/tex]
Hope this helps.
Say you own 5,715 shares of Sanden Research Labs, each of which pays a yearly dividend of $14.66. How much do you receive in dividends every year? a. $83,781.90 b. $81,729.50 c. $75,865.50 d. $93,954.60
Answer:
$83,781.90
Step-by-step explanation:
Dividend received each year is $83781.9
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
Number of shares= 5715
Yearly dividend of each share= $14.66
Now,
Total dividend of all shares
=5715*14.66
=83781.9
Therefore, by algebra the dividend will be $83781.9
More about the Algebra link is given below.
brainly.com/question/953809
#SPJ6
whats 1 + 1? (P.S this is just a joke)
which of the following statements is true, based on the graph
eye color vs. favorite color
Most of the bars are pretty close to each other.
The answer would be the first choice.
Please help! Need ASAP
Find a linear inequality with the following solution set. Each grid line represents one unit.
[asy]
size(200);
fill((-5,-3)--(5,2)--(5,5)--(-5,5)--cycle,yellow);
real ticklen=3;
real tickspace=2;
real ticklength=0.1cm;
real axisarrowsize=0.14cm;
pen axispen=black+1.3bp;
real vectorarrowsize=0.2cm;
real tickdown=-0.5;
real tickdownlength=-0.15inch;
real tickdownbase=0.3;
real wholetickdown=tickdown;
void rr_cartesian_axes(real xleft, real xright, real ybottom, real ytop, real xstep=1, real ystep=1, bool useticks=false, bool complexplane=false, bool usegrid=true) {
import graph;
real i;
if(complexplane) {
label("$\textnormal{Re}$",(xright,0),SE);
label("$\textnormal{Im}$",(0,ytop),NW);
} else {
label("$x$",(xright+0.4,-0.5));
label("$y$",(-0.5,ytop+0.2));
}
ylimits(ybottom,ytop);
xlimits( xleft, xright);
real[] TicksArrx,TicksArry;
for(i=xleft+xstep; i0.1) {
TicksArrx.push(i);
}
}
for(i=ybottom+ystep; i0.1) {
TicksArry.push(i);
}
}
if(usegrid) {
xaxis(BottomTop(extend=false), Ticks("%", TicksArrx ,pTick=gray(0.1),extend=true),p=invisible);//,above=true);
yaxis(LeftRight(extend=false),Ticks("%", TicksArry ,pTick=gray(0.1),extend=true), p=invisible);//,Arrows);
}
if(useticks) {
xequals(0, ymin=ybottom, ymax=ytop, p=black, Ticks("%",TicksArry , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));
yequals(0, xmin=xleft, xmax=xright, p=black, Ticks("%",TicksArrx , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));
} else {
xequals(0, ymin=ybottom, ymax=ytop, p=axispen, above=true, Arrows(size=axisarrowsize));
yequals(0, xmin=xleft, xmax=xright, p=axispen, above=true, Arrows(size=axisarrowsize));
}
};
draw((-5,-3)--(5,2),dashed+red, Arrows(size=axisarrowsize));
rr_cartesian_axes(-5,5,-5,5);
for( int i = -4; i 0$ or $ax+by+c\geq0$ where $a,$ $b,$ and $c$ are integers with no common factor greater than 1.)
Answer:
nobody gonna answer this for 5 points. you have to put 1 question for each 5 points
solve for x
2 1/2x−3/4(2x+5)=3/8
Answer:
x = 33/8
Step-by-step explanation:
Answer:
x = 33/8
Step-by-step explanation:
I agree with the other person.
Rihanna deposited $20.00 in her school cafeteria account. In one week she spent $16.75 on lunches. If the starting balance on her account was – $12.65, what transaction does Rihanna need to make to bring her cafeteria account to zero?
Answer:
she has to add 9.40
Step-by-step explanation:
-12.65 + 20.00 - 16.75 = -9.40
plz mark brainliest also plz try to answer my question
The microwave oven was invented in 1945 when some experiments with radar equipment failed and melted some nearby chocolate instead. The scientists realized there were other applications for this energy sirve. What is this an example of?
A. Creative thinking
B. Scientific method
C. Scientific law
D. Artistic ability
Answer:
It is an example of Scientific Law
Option C is correct...
Mark me as Brainliest if it was helpful
the diagram shows the graph of the function y=(x-r)²+4, where r is a constant.
a) find the value of r
Answer:
d
Step-by-step explanation: