Answer:
slope of a line perpendicular to the line -3x + 6y = -15 is -2
Step-by-step explanation:
-3x + 6y = 15
solve for y,
y = 1/2 x + 15/6
slope of a line perpendicular is the "negative reciprocal" of the slope of the original line, thus
y = -2 x + b
Solve the system by elimination. 4x=−3y−10 9x+2y=6
Answer:
x = 2, y = -6Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}4x=-3y-10&\text{add}\ 3y\ \text{to both sides}\\9x+2y=6\end{array}\right\\\\\left\{\begin{array}{ccc}4x+3y=-10&\text{multiply both sides by 2}\\9x+2y=6&\text{multiply both sides by (-3)}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}8x+6y=-20\\-27x-6y=-18\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-19x=-38\qquad\text{divide both sides by (-19)}\\.\qquad\dfrac{-19x}{-19}=\dfrac{-38}{-19}\\.\qquad \boxed{x=2}[/tex]
[tex]\text{Put the value of}\ x\ \text{to the second equation:}\\\\9(2)+2y=6\\18+2y=6\qquad\text{subtract 18 from both sides}\\2y=-12\qquad\text{divide both sides by 2}\\\dfrac{2y}{2}=\dfrac{-12}{2}\\\boxed{y=-6}[/tex]
What is the absolute value of -0.2
Answer:
0.2
Step-by-step explanation:
Absolute values are positive version of any number. So the absolute value of both 0.2 and -0.2 would be 0.2
There are 482 studemts in the school and there are two Grade 4 classes: Ms.Ashley's and Mr.Ben's classes. Mrs. Aheley's class had 15 boays and 6 girls. Mr Ben's class ahd 14 girls and 10 boys. In Ms. Ashley's class, 2/3 of the students wear glasses.
In Mr. Ben's class, 1/4 of the kids have others siblings in the school.
1. What fraction of the students in the school are in grade 4?
2. What fraction of the grade 4 students are boys?
3. What fraction of the grade 4 students are in Ms. Ashley's class?
4. What fraction of the students in Mr. Ben's class that do not have siblings in the same school?
5. In Ms. Ashley's class, are there more students that wear glasses or do not wear glasses?
Answer:
1. 45/482 of the students are in grade 4.
2. 5/9 of the students of the grade 4 are boys.
3. 7/15 of the grade 4 students are in Ms. Ashley's class
4. 3/4 of the students in Mr. Ben's class do not have siblings in the same school.
5. There are 14 students with glasses and 7 without glasses.
Step-by-step explanation:
1. Let's review the information given to us for solving the questions:
Number of students in the school = 482
Ms. Ashley's Grade 4 class = 21 students
Ms. Ashley's Grade 4 class boys = 15 students
Ms. Ashley's Grade 4 class girls = 6 students
Ms. Ashley's Grade 4 class with glasses = 2/3 * 21 = 42/3 = 14 students
Mr. Ben's Grade 4 class = 24 students
Mr. Ben's Grade 4 class boys = 10 students
Mr. Ben's Grade 4 class girls = 14 students
Mr. Ben's Grade 4 class with siblings in the school = 1/4 * 24 = 24/4 = 6 students
2. Let's answer all the questions:
1. What fraction of the students in the school are in grade 4?
(Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)/ Number of students in the school
21 + 24 / 482 = 45/482
2. What fraction of the grade 4 students are boys?
(Ms. Ashley's Grade 4 boys + Mr. Ben's Grade 4 boys)/ (Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)
15 + 10 / 21 + 24
25 / 45 = 5/9
3. What fraction of the grade 4 students are in Ms. Ashley's class?
Ms. Ashley's Grade 4 class / (Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)
21 / 21 + 24
21 / 45 = 7/15
4. What fraction of the students in Mr. Ben's class that do not have siblings in the same school?
(Mr. Ben's Grade 4 class - Mr. Ben's Grade 4 class with siblings in the school)/ Mr. Ben's Grade 4 class
24 - 6 / 24
18 / 24 = 3/4
5. In Ms. Ashley's class, are there more students that wear glasses or do not wear glasses?
There are 14 students with glasses and 7 without glasses.
Note: Same answer to question 14038475, answered by me.
Use the graph representing bacteria decay to estimate the domain of the function and solve for the average rate of change across the domain.
An exponential function titled Bacteria Decay with x axis labeled Time, in Minutes, and y axis labeled Amount of Bacteria, in Thousands, decreasing to the right with a y intercept of 0 comma 60 and an x intercept of 18 comma 0.
0 ≤ x ≤ 18, −3.33
0 ≤ x ≤ 18, −0.3
0 ≤ y ≤ 60, −3.33
0 ≤ y ≤ 60, −0.3
Mr. Anderson drove 168 miles in 3 hours. He then drove the next 2 hours at a rate
of 5 miles an hour faster than the first rate,
How many miles did Mr. Anderson drive during th
hours?
Answer:
If you were asking how many miles in total: 290 miles.
If you were asking how many miles in the 2 hours: 122 miles
Step-by-step explanation:
In the first 168 miles,
[tex]Since \\v_1=168miles/3h=56 miles/h\\\\Thus \\v_2=v_1+5=56+5=61miles/h\\\\X_1=168miles\\X_2=v_2*2h=61*2=122miles\\X_1+X_2=168+122=290miles\\\\[/tex]
solve for w: -5(3-w)+4=-5/6(24-6w)
Answer:
no solution
Step-by-step explanation:
well first you gotta distribute
-5(-3 - w) + 4 = -5/6(24 - 6w)
15 + 5w + 4 = -20 + 5w
19 + 5w = -20 + 5w
+20 +20
39 + 5w = 5w
-5w -5w
39 ≠ 0
therefore there is no solution (which is the answer)
Hey circular trampoline has an area of 132.2 ft.² what is the radius of the trampoline rounded to the nearest tenth
Final answer:
To find the radius of the circular trampoline, we can use the formula for the area of a circle and rearrange it to solve for the radius. The radius of the trampoline is approximately 6.5 ft (rounded to the nearest tenth).
Explanation:
To find the radius of the circular trampoline, we can use the formula for the area of a circle, which is A = πr². In this case, the area is given as 132.2 ft². We can rearrange the formula to solve for the radius:
r² = A/π
r² = 132.2/π
r ≈ √(132.2/π)
r ≈ √(42)
r ≈ 6.5 ft (rounded to the nearest tenth)
Final answer:
To find the radius of the trampoline, we use the formula for the area of a circle and rearrange it to solve for the radius. After substituting the given area and approximating π as 3.14, we find that the radius is approximately 6.5 ft when rounded to the nearest tenth.
Explanation:
The area of a circle is given by the formula A = πr², where A is the area and r is the radius of the circle. Given the area of the trampoline as 132.2 ft², we can solve for the radius using the area formula. We rearrange the formula to solve for the radius: r = √(A/π).
Substituting the given area and the approximate value for π (3.14), we get r = √(132.2/3.14). This simplifies to r = √(42.085...), which is approximately r = 6.487 ft. Rounding to the nearest tenth gives us a radius of 6.5 ft.
Given that LON is a right angle, find the measure of x.
Answer:
[tex]x=30\°[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
m∠LOM+m∠MON=m∠LON ----> by angle addition postulate
we have
m∠LOM=2x°
m∠MON=x°
m∠LON=90° ----> is a right angle
substitute the values
[tex]2x+x=90[/tex]
solve for x
[tex]3x=90[/tex]
[tex]x=30\°[/tex]
What happens to the energy that is stored in cells? Check all that apply.
A: It is released slowly.
B: It is released quickly.
C: It is released in a single reaction.
D: It is released in a series of reactions.
E: It is used by cells for repair and growth.
This is worth 20 points.
A, D & E
Cells store energy in the form ATPs. These molecules power al the biochemical activities that would not occur spontaneously. Examples of these bioactivities are the contraction of actin filaments, glycolysis cycle, replication of DNA, cell division, gene expression, cell repair and etcetera.
Step-by-step explanation:
All ATPs are not spent at the same time, and futhermore, they are constantly replaced by the continuous process of cellular respiration that captures the chemical energy in the glucose molecules and stores them in ATP. During the release of this energy to power the biochemical reactions, much of it is lost as heat energy and this is why living organisms are always warm.
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Answer: The multiple choice answers would be, A, D, and E.
Step-by-step explanation:
decide whether the pair of lines is parallel, perpendicular, or neither. 3x-6y=2 and 18x+9y=8
Answer: perpendicular
Step-by-step explanation:
Final answer:
The slopes of the two lines given by the equations 3x-6y=2 and 18x+9y=8 are 1/2 and -2 respectively. Since these slopes are neither equal nor negative reciprocals, the lines are neither parallel nor perpendicular.
Explanation:
To decide whether the pair of lines is parallel, perpendicular, or neither, we need to find the slopes of the lines. The lines are given by the equations 3x-6y=2 and 18x+9y=8. To find the slope of each line, we must rewrite the equations in slope-intercept form (y=mx+b), where m represents the slope
For the first line, 3x-6y=2, we isolate y:
3x - 6y = 2-6y = -3x + 2y = (1/2)x - 1/3So the slope of the first line is 1/2.
For the second line, 18x+9y=8, we isolate y:
18x + 9y = 89y = -18x + 8y = -2x + 8/9The slope of the second line is -2.
Since the slopes of the two lines are not equal and not negative reciprocals of each other, the lines are neither parallel nor perpendicular.
What is the unit rate of (30,24) expressed in price per pound?
Answer:
80cents per pound
Step-by-step explanation:
24 divided by 30 is .8
3
Select the correct answer.
A square field was enlarged by adding 5 feet to the length and width of the original field. If the area of the enlarged field is 576 square feet, what
was the side length of the original field?
A.
29 feet
19 feet
C.
6 feet
D.
36 feet
Answer:
The answer is 19 feet or B.
Step-by-step explanation:
First you should know that a square has equal sides.
Then it tells you to add 5 feet on the original field. So you add 5 to 19 and you get 24. After that, you multiply the 24 by itself to get 576 feet.
In order to play at the Cape Gerbil City Miniature Golf Club, a player has to pay the membership fee and pay for each round played. The total cost is represented by the function
T = 33.47r + 17.72, where T = the total cost (in dollars) and r = the number of rounds played.
Which of the following statements must be true?
A .The slope is the cost per round $33.47, and the y-intercept is the membership fee of $17.72.
B.The total cost is $51.19.
C.The slope is the cost per round $17.72, and the y-intercept is the membership fee of $33.47.
D.The slope is the membership fee of $17.72, and the y-intercept is the number of rounds played.
E.I don't know
Please answer
Final answer:
The correct statement must be that the slope of the equation is the cost per round of $33.47, and the y-intercept is the initial membership fee of $17.72, since the slope represents the additional cost per round and the y-intercept the initial cost at zero rounds.
Explanation:
In the function T = 33.47r + 17.72, which represents the total cost T of playing miniature golf as a function of the number of rounds played r, the coefficient of r represents the slope and the constant term is the y-intercept. The slope indicates the additional cost for each additional round of golf played, while the y-intercept represents the initial cost when no rounds are played, which can be interpreted as the membership fee. Therefore, the correct statement about the cost structure of the Cape Gerbil City Miniature Golf Club is A: The slope is the cost per round $33.47, and the y-intercept is the membership fee of $17.72.
The measure of the vertex angle of an isosceles triangle is 92. Find the measure of a base angle
Answer:
44°
Step-by-step explanation:
The sum of the angles in a triangle = 180°
In an isosceles triangle the base angles are equal, thus
base angle = [tex]\frac{180-92}{2}[/tex] = [tex]\frac{88}{2}[/tex] = 44°
If the sum of a number and -3 is doubled the result is 1 half
times the number. Find the number
Answer:
-3
Step-by-step explanation:
2(x+-3)=1/2x
2x+6=1/2x
6=-1/2x
x=-3
Answer:
-3 is the write answer
Step-by-step explanation:
2(x+3)=1/2x
2x+6=1/2x
6=-1/2x
x=-3
AB contains points (2, 1) and (-1, -8). What is the equation of the line parallel to AB that contains point (0, 2)?
For this case we have that by definition, the equation of a line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
We have two points that belong to the AB line:
[tex](x_ {1}, y_ {1}) :( 2,1)\\(x_ {2}, y_ {2}): (- 1, -8)[/tex]
We can find the slope:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-8-1} {- 1-2} = \frac {-9} {- 3} = 3[/tex]
By definition, if two lines are parallel then their slopes are equal. Thus, a line parallel to AB will have slope [tex]m = 3[/tex], then the equation will be of the form:
[tex]y = 3x + b[/tex]
We substitute the given point and find b:
[tex](x, y) :( 0,2)\\2 = 3 (0) + b\\2 = b[/tex]
Finally, the equation is:
[tex]y = 3x + 2[/tex]
Answer:
[tex]y = 3x + 2[/tex]
A barn silo, excluding the top, is a cylinder. The silo is 7 m in
diameter and the height is 12 m. What is the volume of the silo?
The volume of the silo is 461.81 m³
Step-by-step explanation:
A barn silo, excluding the top, is a cylinder
The silo is 7 m in diameterIts height is 12 mWe need to find the volume of the silo
∵ The silo is shaped a cylinder
∵ The volume of a cylinder = base area × height
∵ The base is shaped a circle
∵ Area a circle = π r², where r is the radius of the circle
∴ The volume of the silo = π r² × h
∵ The diameter of the silo = 7 m
∵ The radius of a circle is half the diameter
∴ The radius of the silo = [tex]\frac{1}{2}[/tex] × 7 = 3.5 m
∵ The height of the silo = 12 m
- Substitute the values of r and h in the rule of volume
∴ The volume of the silo = π (3.5)² × 12
∴ The volume of the silo = 147 π = 461.81 m³
The volume of the silo is 461.81 m³
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Final answer:
The volume of a barn silo that is shaped like a cylinder with a diameter of 7 meters and a height of 12 meters is approximately 461.7 cubic meters.
Explanation:
To calculate the volume of the silo which is in the shape of a cylinder, we use the formula V = πr²h, where V is the volume, r is the radius, and h is the height. The diameter of the silo is given as 7 meters, so the radius is half of that, which is 3.5 meters. The height of the silo is 12 meters. Plugging these values into the formula gives:
V = π × (3.5 m)² × 12 m
V = π × 12.25 m² × 12 m
V = π × 147 m³
Assuming π to be approximately 3.14159, the calculation results in:
V = 3.14159 × 147 m³ = 461.7 m³ (approx)
So, the volume of the silo is approximately 461.7 cubic meters.
The product of 3! is
The product of 3 factorial is 6.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
We have to find the value of 3 factorial.
By the definition of factorial, factorial of any natural number can be defined as,
a factorial = 1 × 2 × ....... × (a - 1) × a
Here we have to find 3 factorial.
3 factorial can be written as,
3 factorial = 3 × 2 × 1 = 6 × 1 = 6
Hence the required product of 3 factorial is 6.
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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. The function below represents the monthly expenses for an event planning company where f(x) represents the total monthly expenses for planning x events. If at the end of one month the expenses for the company were $12,350, then ___ events were planned
f(x) = 50(2x=1) + 300
Answer:
There were 120 events planned.
Step-by-step explanation:
We are given the following information in the question:
f(x) represents the total monthly expenses for planning x events.
[tex]f(x) = 50(2x+1) + 300[/tex]
Cost of expenses for the company at the end of one month = $12,350
We have to find the number of events planned that is we have to find the value of x.
[tex]f(x) = 50(2x+1) + 300 = 12350\\50(2x+1) + 300 = 12350\\100x + 50 + 300 = 12350\\100x + 350 = 12350\\100x = 12350-350\\100x = 12000\\\\x = \displaystyle\frac{12000}{100} =120[/tex]
Thus, there were 120 events planned.
Answer:
120
Step-by-step explanation:
i actually did just guess on that answer i didnt know what to put
Which table shows the relationship y= 1/2x?
Using the approximation 3.14 for \pi what is the radius of a circle with circumference 75.4m
Answer:
The radius of the circle is 12.006 m.
Step-by-step explanation:
Let us assume the radius of the circle = r
Circumference = 75.4 m
Now, CIRCUMFERENCE OF A CIRCLE = 2 π r
⇒ 75 .4 m = 2 π r
Now, putting π = 3.14, we get:
75 .4 m = 2 (3.14) r
⇒ 75.4 = 6. 28 r
or, r = 75.4/6.28 = 12.006
or, r = 12.006 m
Hence, the radius of the circle with circumference 75.4 m is 12.006 m.
You work 37 1/2 hours and earn $352.50. What is your hourly wage
Answer:
$9.40
Step-by-step explanation:
well since you work 37.5 hours and you earn $352.50 you divide them to get your hourly wage
352.5 ÷ 37.5 = 9.4
so your hourly wage is $9.40
Final answer:
To calculate the hourly wage, the total earnings of $352.50 should be divided by the total work hours of 37.5. The hourly wage comes out to be $9.40.
Explanation:
To find out your hourly wage, you need to divide your total earnings by the number of work hours. In this instance, you worked 37.5 hours (since 1/2 an hour is equivalent to 0.5 hours) and earned $352.50. So, your hourly wage would be calculated as follows:
Hourly Wage = Total Earnings ÷ Number of Work Hours
Hourly Wage = $352.50 ÷ 37.5 hours
Hourly Wage = $9.40 per hour
Therefore, your hourly wage is $9.40.
How to simplify the fractions
Answer:
[tex]\large\boxed{\dfrac{3x+6}{x-4}\div\dfrac{2x^2+9x+10}{x^2+4x}=\dfrac{3x(x+4)}{(x-4)(2x+5)}}[/tex]
Step-by-step explanation:
Just like that
[tex]\dfrac{3x+6}{x-4}\div\dfrac{2x^2+9x+10}{x^2+4x}=\dfrac{3x+6}{x-4}\cdot\dfrac{x^2+4x}{2x^2+9x+10}\\\\=\dfrac{3(x+2)}{(x-4)}\cdot\dfrac{x(x+4)}{2x^2+4x+5x+10}=\dfrac{3(x+2)}{(x-4)}\cdot\dfrac{x(x+4)}{2x(x+2)+5(x+2)}\\\\=\dfrac{3(x+2)}{(x-4)}\cdot\dfrac{x(x+4)}{(x+2)(2x+5)}\qquad\text{cancel}\ (x+2)\\\\=\dfrac{3x(x+4)}{(x-4)(2x+5)}[/tex]
Given A(5,3) and O(0,0), find a point B that makes the following true: m(A,B)=3
A point B is (1 , -9)
Step-by-step explanation:
The formula of the slope of a line is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
where [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are two points
lie on the line
A (5 , 3) and O (0 , 0) are two pointsm(A , B) = 3 ⇒ (the slope of AB = 3)We need to find a point B that makes that true
Assume that point B is (x , y)
∵ Point A = (5 , 3)
∵ Point B = (x , y)
∴ [tex]x_{1}=5[/tex] and [tex]x_{2}=x[/tex]
∴ [tex]y_{1}=3[/tex] and [tex]y_{2}=y[/tex]
- Substitute these values in the formula of m
∴ [tex]m=\frac{y-3}{x-5}[/tex]
∵ m(A , B) = 3
- Equate the formula of the slope by 3
∴ [tex]\frac{y-3}{x-5}=3[/tex]
- By using cross multiplication
∴ y - 3 = 3(x - 5)
- Simplify the right hand side
∴ y - 3 = 3x - 15
- Add 3 for both sides
∴ y = 3x - 12
To find point B chose any value for x and substitute it in the
equation to find y
∵ x = 1
∴ y = 3(1) - 12 = 3 - 12
∴ y = 9
∴ Point B = (1 , -9)
V.I.N: You can find many values of point B by chose different values of x and find the corresponding values of y
A point B is (1 , -9)
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Can someone help me with these problems? The majority of them I have answers but I don't understand them. Thanks!
What is the area of the triangle with a base of 5 1/2 cm and a height of 3 1/2 cm?
My answer - 11 1/2
919÷ 2
Round to the nearest whole
My answer-?
What is the area of a parallelogram with a base of 14.5 m and a height of 21 m?
The cafeteria sold 200 grilled cheese sandwiches, 100 tacos, and 150 grilled chicken salads. What is the ratio in simplest terms of grilled chicken salads sold to the total number of lunches sold?
My Answer- 1:3
What is the ratio of odd to even digits in the following number:
7,208,631
My Answer- 3:4
Given that one ton is equal to 2000 pounds, what is 5 tons?
My Answer- 400 or 1000
A table measures 3 feet across. How many inches is this?
My Answer-36
Answer:
The corresponding answers to the questions are 9.625 cm² , 459, 304.5m², 1 : 3 , 3:4 , 10,000 pounds , 36 inches.
Step-by-step explanation:
1.
Area of triangle = 0.5 x base length x height
Here base length = 5.5cm and height = 3.5cm
So area will be 0.5 x 5.5 x 3.5 cm² = 9.625 cm²
2.
919/2 rounding off to nearest whole
We know that the value of 919/2 = 459.5 .
So the nearest whole number value to which it can be rounded off is 459.
3.
We know that area of parallelogram is base length x height
Here, base length =14.5m and height = 21m
So area = 14.5 x 21 m² = 304.5m²
4.
No. of grilled cheese sandwiches sold = 200
No. of tacos sold = 100
No. of grilled chicken salads sold = 150
Total lunches sold = 200 + 100 + 150 = 450
So, ratio of chicken salads to lunches sold is 150 : 450 = 1 : 3
5.
Given number : 7,208,631
Odd digits here - 7,3,1 - 3 digits
Even digits here - 2,0,8,6 - 4 digits
So, ratio of odd digits to even digits is 3:4
6.
One ton = 2000 pounds
So 5 tons = 5 x ( 1 ton) = 5 x 2000 pounds = 10,000 pounds
7.
Table length = 3 feet
We know that 1 foot = 12 inches
So table length = 3 foot = 3 X 12 inches = 36 inches
The line segment shown is rotated 90° clockwise about the origin. What are the new coordinates of point B?
(3, - 4)
Imagine a rectangle with one corner on the origin and the opposite on the point. Rotate the rectangle about the origin and see where the point lands.
To find the new coordinates of point B after a 90° clockwise rotation around the origin, you apply the rotation rule: (x, y) becomes (y, -x). The original coordinates are needed to calculate the exact new position of point B.
Explanation:The student is asking about the result of a 90° clockwise rotation of a point around the origin in the Cartesian coordinate system. To find the new coordinates of point B after the rotation, we use the rule for 90° clockwise rotation, which is (x, y) becomes (y, -x). If the original coordinates of point B are (x₂, y₂), the new coordinates after the rotation will be (y₂, -x₂).
Without knowing the original coordinates of point B, we cannot give the exact new coordinates. However, if the student provides the initial coordinates, the new coordinates can be calculated using the rotation rule mentioned.
5x - 9y=1
-7x + 2y = -5
9514 1404 393
Answer:
(x, y) = (43/53, 18/53)
Step-by-step explanation:
If we want to eliminate the x-terms, we multiply the first equation by 7 (opposite of the x-coefficient in the second equation), and we multiply the second equation by 5 (x-coefficient in the first equation). Then we add the result.
7(5x -9y) +5(-7x +2y) = 7(1) +5(-5)
35x -63y -35x +10y = 7 -25
-53y = -18 . . . . simplify. Note the x-terms are gone.
y = 18/53 . . . . . divide by -53
__
Putting this value of y in the first equation, we get ...
5x -9(18/53) = 1
5x = 1 + 162/53 = 215/53 . . . . . add 9y to both sides, simplify
x = 43/53 . . . . . . . . . . divide by 5
The solution is (x, y) = (43/53, 18/53).
3x + 2 = x + 4 ( x + 2 )
Answer:
x = -3Step-by-step explanation:
[tex]3x+2=x+4(x+2)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\3x+2=x+(4)(x)+(4)(2)\\\\3x+2=x+4x+8\qquad\text{combine like terms}\\\\3x+2=(x+4x)+8\\\\3x+2=5x+8\qquad\text{subtract 2 from both sides}\\\\3x+2-2=5x+8-2\\\\3x=5x+6\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\3x-5x=5x-5x+6\\\\-2x=6\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2x}{-2}=\dfrac{6}{-2}\\\\x=-3[/tex]
10. A toy store received a shipment of 17 cases of
teddy bears. Use compatible numbers to estimate
the total number of teddy bears in the shipment.
12 bears per case
Answer: 204 teddy bears
Step-by-step explanation:
Answer:
17 x 12 = 204 teddy bears
Step-by-step explanation:
17 cases, 12 bears in each case
You could round 17 --> 20
You could round 12 --> 10
20×10=200
using the piling method, which of the following can be constructed from polygons alone? check all that apply
A. circle
B. pyramid (including the vertex)
C. cylinder
D. pyramid (not including the vertex)
E. prism
F. cone
Answer:
D. pyramid (not including the vertex)
E. prism
Step-by-step explanation:
D and E are the answers to this question.
D. pyramid (not including the vertex)
E. prism