The distance between -57 and 13 on a number line is 70 units.
Explanation:The distance between -57 and 13 on a number line is 70 units.
To find this distance, we subtract -57 from 13:
13 - (-57) = 13 + 57 = 70.
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The distance between -57 and 13 on a number line is 70 units.
Explanation:A number line is a visual representation of real numbers arranged in order along a straight line. It extends infinitely in both directions, with zero at the center. Positive numbers are to the right, and negative numbers are to the left. Integers, fractions, and decimals are located at corresponding points.
The number line aids in understanding numerical relationships, performing arithmetic operations, and visualizing the concept of magnitude and direction in mathematics. It's a fundamental tool for teaching and learning mathematical concepts. The distance between -57 and 13 on a number line is 70 units.
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Triangle ABC is dilated by a scale factor of 4 to form triangle A′B′C′.
The coordinates of vertex A′ are?
The coordinates of vertex B′ are?
The coordinates of vertex C′ are?
Answer:
The correct answers would be
vertex A' (-8,4)
vertex B' (-12,12)
vertex C' (-4,12)
Step-by-step explanation:
I'm not 100% sure but I took this test a couple days ago and didn't do terribly:).
PLEASE HELP QUICK!!!!!!!!!!!!!!! 100 POINTS Please explain how to do this step by step. I'm super confused.
Look at the picture of a scaffold used to support construction workers. The height of the scaffold can be changed by adjusting two slanting rods, one of which, labeled PR, is shown:
A support structure is shown in which a right triangle PQR is formed with the right angle at Q. The length of PQ is shown as 14 feet, and the length of QR is shown as 6 feet..
Part A: What is the approximate length of rod PR? Round your answer to the nearest hundredth. Explain how you found your answer, stating the theorem you used. Show all your work. (5 points)
Part B: The length of rod PR is adjusted to 16 feet. If width PQ remains the same, what is the approximate new height QR of the scaffold? Round your answer to the nearest hundredth. Show all your work. (5 points)
Answer:
A: 15.23 ft, B: 7.75 ft
Step-by-step explanation:
A:
√(14² + 6²)
√(196 + 36)
√232 = 15.23
B:
√(16² - 14²)
√(256 - 196)
√60 = 7.75
NOTES:
Since Q is a right angle then PQ and QR are the legs and PR is the hypotenuse. Use the Pythagorean Theorem to solve.
********************************************************************************
Part A Answer: PR = 15.23
Step-by-step explanation:
PQ² + QR² = PR²
6² + 14² = PR²
36 + 196 = PR²
232 = PR²
15.23 = PR
************************************************************************************
Part B Answer: PR = 7.75
Step-by-step explanation:
PQ² + QR² = PR²
PQ² + 14² = 16²
PQ² + 196 = 256
PQ² = 60
PQ = 7.75
The number 124 is going to be represented on a stem-and-leaf plot that has the key 3|4 = 34. Which part of the number will be the stem?
12
1
24
4
Answer:
12
Step-by-step explanation:
Note that for the "leaf" or the right side, it is only the one's place value. The left side, or the "stem" contains the tens place as well as anything greater.
124 in a stem-and-leaf plot is seen as: 12 | 4, in which 12 is your stem, and 4 is your leaf.
~
Answer:
12 is the stem
Step-by-step explanation:
The last digit ( or the ones place) is the leaf. Everything else is the stem
So for 124, the ones digit is the leaf. 4 is the leaf
Everything else is the stem 12 is the stem
12|4
Solve for a. m=a/9-H
Answer:
9(m+H) = a
Step-by-step explanation:
m=a/9-H
The first step is to add H to each side.
m+H = a/9 -H+H
m+H = a/9
Now multiply both side by 9
9(m+H) = a/9*9
9(m+H) = a
out of 40 chocolates, ram and i shared in the ratio 1:3 . how many chocolates did ram get?
Answer:
Ram will get 10 chocolates
Step-by-step explanation:
It the chocolates are shared in the ratio of 1 to 3 then the total is 4
Ram : I
1:3
1+ 3 = total
1+ 3 =4
Our total is 40, but the ratio stays the same, we just add the variable x to the 1 and the 3
1x+ 3x =40
Combine like terms.
4x = 40
Divide each side by 4
4x/4 = 40/4
x =10
So ram will get 1 * 10 = 10 and you will get 3 * 10 = 30
Round all answer to the nearest tenth.
1. Vince wants to make a square patio in his yard. He has enough concrete to pave an area of 130 square feet. How long can a side of his patio be?
Answer:
Using the formula to calculate the area of a square, the side of the patio can be 11.4 ft.
Step-by-step explanation:
Square patio
Area: A=130 square feet= 130 ft^2
Side of the square: s=?
The formula to calculate the area of a square is:
A = s^2
Replacing A by 130 ft^2
130 ft^2 = s^2
Solving for s: Square root both sides of the equation above:
sqrt(130 ft^2) = sqrt(s^2)
11.40175425 ft = s
s = 11.40175425
Rounding to the nearest tenth:
s = 11.4 ft
To find the side length of a square given the area, take the square root of the area. So, the sides of Vince's patio will be approximately 11.4 feet long.
A square root is a mathematical operation that determines the value that, when multiplied by itself, equals a given number. It is denoted by the radical symbol (√). For example, the square root of 25 is 5, as 5 * 5 equals 25. Square roots are essential in various fields, including geometry, physics, and engineering, where they help calculate dimensions, solve equations, and analyze data. Square roots can be both real (positive or negative) and complex, depending on the input number.
To solve this problem, you need to understand that a square has four equal sides. The area of a square is calculated by squaring the length of one of its sides. So if we know the area, we can find the side length by taking the square root of the area.
Since Vince's area is 130 square feet, we calculate the square root of 130 which is approximately 11.4. Therefore, Vince can make each side of his patio 11.4 feet long, rounded to the nearest tenth.
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What is the value of the expression? −29−(−13÷3/5) Enter your answer, as a fraction in simplest form, in the box.
Answer:
-71/15
Step-by-step explanation:
Order of operations rules require that we do any work enclosed in parentheses first. Thus, we must evaluate -13÷3/5. Multiplication and division can be done in either order, but for the sake of consistency, move from left to right:
-13÷3 comes out to -13/3. Divide this result by 5, obtaining -13/15.
Then the original expression, −29−(−13÷3/5), becomes -29-(-13/15), or
-29 + 13/15.
Since -29 is negative and + 13/15 is positive, we must add 13/15 to -29:
-29
+13/15
----------
This is easily done if we rewrite -29 as -28 - 15/15.
Then we have:
-28 - 15/15 +13/15, which simplifies to -28 - 2/15, or -28 2/15.
As a single fraction, that would be -71/15.
equation is equal to .66...?
a)1/3
b)1/5
c)2/3
d)2/4
if Alice and Finn roll two number cubes. Which of the following rules will make the game fair?
1Alice wins if a total of 5 is rolled. Finn wins if a total of 9 is rolled.
2Alice wins if a total of 7 is rolled. Finn wins if a total of 8 is rolled.
3Alice wins if a total of 3 is rolled. Finn wins if a total of 10 is rolled.
4Alice wins if a total of 4 is rolled. Finn wins if a total of 11 is rolled.
Answer: Option A is correct.
Step-by-step explanation:
Since we have given that
Number of cubes Alice and Finn roll = 2
Sum of dices has outcome of 7 as the highest probability.
So,when, we move away from the probability gets equal.
Let A: Event of getting a total of 5.
Let B : Event of getting a total of 9.
So, [tex]A=\{(2,3),(3,2),(4,1),(1,4)\}[/tex]
And [tex]B=\{(5,4),(5,4),(6,3),(3,6)\}[/tex]
so, Probability of getting event A and B respectively.
[tex]P(A)=\frac{4}{36}=\frac{1}{9}\\\\and\\\\P(B)=\frac{4}{36}=\frac{1}{9}[/tex]
So, the game will make fair as both have equal possibility to win.
Hence, Option A is correct.
Answer:
Alice wins if a total of 5 is rolled. Finn wins if a total of 9 is rolled.
Step-by-step explanation:
Which of these ordered pairs could you remove to make this relation a function? {(-2,1), (-1, -5), (-1,5), (0, -7), (2, 1)}
A. (-2, 1)
B. (-1, 5)
C. (0, -7)
D. (2, 1)
Your answer would be B. (-1,5).
In order for the order pairs to be a function. All of the x coordinates must be different from each other, they can't be the same. There can't be any repeats of the x coordinates. But for the y coordinates, it's okay for them to be the same. The reason why you would eliminate (-1,5) is because there are 2 -1 x coordinates, and that would not make the ordered pairs a function. When you remove them, none of the x coordinates are the same anymore, so it would now be a function.
Hope this helps out :)
Answer:
B. (-1,5).Step-by-step explanation:
Which of these ordered pairs could you remove to make this relation a function? {(-2,1), (-1, -5), (-1,5), (0, -7), (2, 1)}
B. (-1, 5)
4,839 sq. yd. 8 sq. ft.139 sq. in.+ 7 sq. ft. 124 sq. in
The Mathematics problem involves adding areas in different units and converting them appropriately. After conversion and addition, the correct answer from the options provided is 1 acre, 7 square feet, and 119 square inches: (a) 1a 7 sqft 119 sqin.
The subject of this question is Mathematics, specifically dealing with area measurements in different units and their conversions. The student needs to solve an addition problem that involves square yards, square feet, and square inches. To solve this problem, we must first understand that there are 9 square feet in one square yard, and we use this knowledge to convert all measurements to the same unit before summing them up.
To answer the student's question, we must add the areas given in the problem:
4,839 sq yd 8 sq ft 139 sq in7 sq ft 124 sq inFirst, we convert square yards to square feet using the conversion 1 sq yd = 9 sq ft:
4,839 sq yd = 4,839 × 9 sq ft = 43,551 sq ft
Now we add the square feet:
43,551 sq ft + 8 sq ft + 7 sq ft = 43,566 sq ft
Lastly, we add the square inches:
139 sq in + 124 sq in = 263 sq in
Since there are 144 square inches in one square foot, we must convert the excess square inches into square feet and square inches:
263 sq in = 1 sq ft (144 sq in) + 119 sq in
Adding the converted square inches to the total square feet:
43,566 sq ft + 1 sq ft = 43,567 sq ft 119 sq in
Next, we convert the total square feet to acres, understanding that 1 acre = 4,840 sq yd or approximately = 43,560 sq ft.
43,567 sq ft ÷ 43,560 sq ft per acre ≈ 1 acre 7 sq ft 119 sq in
Thus, the correct answer is (a) 1a 7 sqft 119 sqin.
Complete question is here:
Solve the following problem 4,839 sq yd 8 sq ft 139 sq in + 7 sq ft 124 sq in Select one of four
a)1a 7 sqft 119 sqin
b)4a 10 sqft 145 sqin
c)3a B sqft 130 sqin
d)2a 9 sqft 150 sqin
The question asks for the addition of different area units, which requires unit conversion. Square yards are converted to square feet and then to square inches, ensuring all areas are in the same units before adding them together.
Explanation:The question involves adding areas measured in different units (square yards, square feet, and square inches) and converting between these units. To perform the calculation correctly, we need to convert all areas to the same unit. One square yard is equivalent to 9 square feet, and one square foot is equivalent to 144 square inches. Thus, to add the areas given in the question, we should first convert the 8 sq. ft. 139 sq. in. to sq. in. by multiplying 8 by 144 and then adding 139. After that, we would need to convert this total area into square yards if required. For the second part, we convert 7 sq. ft. 124 sq. in. to square inches similarly. Once both areas are in square inches, they can be added together. Additionally, it's important to remember that there is no direct conversion between square inches and square yards, so a two-step conversion is needed via square feet.
The sum of the least and greatest of three consecutive integers is 50. What is the middle integer?
x + (x + 2) = 50
Combine like terms.
2x + 2 = 50
Subtract 2 from both sides.
2x = 48
Divide both sides by 2.
x = 24
Now that we have the value of x, we can find the value of the 2nd integer by adding 1 to the value of x.
24 + 1 = 25
The middle integer is equal to 25.If a polygon is a square, then all 4 angles are right. If all 4 angles of a polygon are right, then it is a rectangle.
the main difference between a square and a rectangle is that a square has all sides of equal length, while a rectangle has opposite sides of equal length and adjacent sides of different lengths.
What is a polygon?In Mathematics, a polygon can be defined as a two-dimensional geometric figure that consists of straight line segments and a finite number of sides. Additionally, some examples of a polygon include the following:
• Triangle
• Quadrilateral
• Pentagon
• Hexagon
• Heptagon
• Octagon
• Nonagon
Given, a polygon is a square, then all 4 angles are right. If all 4 angles of a polygon are right, then it is a rectangle.
A square is a special case of a rectangle where all four sides are of equal length. So, a square is a rectangle with all right angles and all sides of equal length.
On the other hand, a rectangle is a four-sided polygon with all four interior angles equal to 90 degrees.
However, in a rectangle, the opposite sides are parallel, and the adjacent sides are of different lengths.
In summary, the main difference between a square and a rectangle is that a square has all sides of equal length, while a rectangle has opposite sides of equal length and adjacent sides of different lengths.
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Complete question:
If a polygon is a square, then all 4 angles are right. If all 4 angles of a polygon are right, then it is a rectangle. what is the difference between a square and a rectangle?
9ab over 27b = simplify
9ab
___
27b
Answer:
1A/3 OR 1/3A
Step-by-step explanation:
Please help me on #2! Could you also check the other numbers! Thank you so much!
Dani is correct. The equation can be written as y = 3x+50, which is a linear equation in the form y = mx+b. We have m = 3 as the slope and b = 50 as the y intercept
-----------------
x is the number of square feet, y is the total cost in dollars
3*x or 3x repesents multiplying the cost per square foot ($3) by the number of square feet (x). For example, if you have 10 sq ft, then so far the cost would be 3*x = 3*10 = 30 dollars.
This result is then added to 50 to get the total cost. We say that 3x is the variable cost, as it changes or varies depending on how large x gets. Additionally, the 50 is the fixed cost because this cost stays the same no matter what x is
total cost = variable cost + fixed cost
y = 3x + 50
Find the circumference of each circle. Use 3.14 for the value of π . Round answer to the nearest tenth.
Answer:
[tex]C=9.4\pi[/tex] meters
Step-by-step explanation:
Recall to find the circumference of a circle the formula is [tex]C=\pi d[/tex] or [tex]C=2\pi r[/tex].
We start by substituting 4.7m for r in the second circumference formula.
[tex]C=2\pi r\\C=2\pi (4.7)\\C=9.4\pi [/tex]. We input this value of r into the area formula.
Answer:
its C.
Step-by-step explanation:
PLEASE HELP I HAVE NO TIME AND I NEED THESE DONE!!!!!
1. 5b + 2 = 17
2. 3/8 n + 1 = -25
3. 9 + 4b = 17
4. 8x + 7 = - 7
5. 4d - 35 = -3
6. 15a - 54 = -9
Question 1. 5b + 2 = 17
Step 1. Subtract 2 from both sides of the equation.
5b+2-2=17-2
Step 2. Then simplify.
5b=15
Step 3. Finally divide by 5.
5b/5=15/5
Answer: b=3
Question 3.
Step 1. Subtract 9 from both sides.
9+4b-9=17-9
Step 2. And simplify.
4b=8
Step 3. Finally divide by 4.
4b/4=8/4
Answer: b=2
Hope this helps! :)
Answer:
With STEP
(1) 5b+2=17 move constant to the right
5b=17-2 subtract the numbers
5b=15 divide both side by 5
b=3
(2) 3/8n+1=-25 multiply both side by8
3n+8=-200 move constant to the right
3n=-200-8 divide both sides by 3
n=-208/3
Without Step just answer
(3) b=2
(4) x=-7/4
(5) d=8
(6) a=3
HOPE this HELP
a cylinder has diameter of 10 cm and a height of 20 cm what is the volume of the cylinder
Answer:
V = 1570.796327 cm^3
Step-by-step explanation:
V= pi *r^2h
diameter = 2 * radius
10 = 2r
r = 5
substitute in what we know
V = pi *( 5^2) * 20
V = pi * 25 * 20
V = pi *500
V = 1570.796327 cm^3
Answer:
Step-by-step explanation:
Surface Area of circle on top of cylinder:
= πr²
= π(d÷2)²
= π(10÷2)²
= π(5)²
= 25π
Volume of Cylinder:
= 25π × h
= 25π × 20
= 500π
= 1570.8 cm³ (to 1 decimal place)
3(x-7)
[tex]3( \times - 7[/tex]
Answer:
3x-21
Step-by-step explanation:
We want to distribute the 3
3(x-7)
3*x -3*7
3x-21
Hi there!
Answer:
3x-21
Step-by-step explanation:
Distributive property: a(b+c)=ab+ac
A=3, B=x, C=7
First, you expand.
3x-3*7
3*x=3x
3*7=21
3x-21
Final answer is 3x-21
Hope this helps!
Have a nice day! :)
:D
-Charlie
Thank you! :)
:D
REBECA HAD 9/10 OF A YARDOF RIBBON. THEN SHE GAVE 7/20 OF A YARD OF FRIEND. HOW MUCH DOES SHE HAVE LEFT?
Answer:
She has 11/20 yds left
Step-by-step explanation:
We take what she had and subtract what she gave away
9/10 - 7/20
We need to get a common denominator of 20
9/10 *2/2 - 7/20
18/20 - 7/20
11/20
She has 11/20 yds left
Solve for x and y
3x+y=6
x+y=2
3x+y=6
x+y=2
rewrite x + y = 2 as y = 2-x
Replace Y in the first equation with the re-written equation:
3x + 2-x = 6
Solve for x:
3x + 2-x = 6
subtract x:
2x +2 = 6
Subtract 2 from each side:
2x = 4
Divide both sides by 2:
x = 2
Now you have x, replace x with 2 in the second equation and solve for y:
x + y = 2
2 + y = 2
Subtract y 2 from each side:
y = 0
The answer is: X = 2, Y = 0
Rewrite the equation x^2-4x+9=5 in the form (x-p)^2=q
Answer:
(x - 2)² = 0
Step-by-step explanation:
given x² - 4x + 9 = 5 ( subtract 5 from both sides )
x² - 4x + 4 = 0
This is a perfect square of the form
(x - a)² = x² - 2a + a²
compare coefficients of the x-term
- 2a = - 4 ⇒ a = 2
⇒ (x - 2)² = 0 ← is the required form
PLEASE HELP!!!
Jason is trying to prove that this quadrilateral is a rhombus. Using the slope formula, he finds that opposite sides of the polygon are parallel. Since all of the sides appear to be congruent, Jason concludes that ABCD is a rhombus. Is Jason's reasoning correct? Why or why not?
A) correct; Jason can tell by looking at the graph that all sides are congruent.
B) correct; A rhombus has two pairs of parallel sides which may or may not be congruent.
C) incorrect; Jason must also prove that all sides are congruent by using the distance formula.
D) incorrect; A rhombus does not have two pairs of parallel sides. Jason must prove that all sides are congruent.
Answer: the correct answer is “ incorrect; Jason must also prove that all sides are congruent by using the distance formula.
Step-by-step explanation:
ΔABC is similar to ΔDEF. The ratio of the perimeter of ΔABC to the perimeter of ΔDEF is 1 : 5. If the longest side of ΔDEF measures 15 units, what is the length of the longest side of ΔABC?
Answer:
The answer is 25 units
Step-by-step explanation:
Which list of ordered pairs represents solutions to x + y = 2? (-4, 6), (0, 2), (4, 2); (-4, -6), (0, 2), (4, 2); (-4, 6), (0, 2), (4, -2)
Answer:
(-4, 6), (0, 2), (4, -2)
Step-by-step explanation:
x + y = 2?
(-4, 6), -4+6 = 2 True this is a solution
(0, 2), 0+2 = 2 True this is a solution
(4, 2); 4+2 = 6 False this is not a solution
This is not a solution set since we have a pair that is not a solution
(-4, -6), -4+-6 = 10 False this is not a solution. We do not have to check the rest since this cannot be a solution set
(0, 2),
(4, 2);
This is not a solution set since we have a pair that is not a solution
(-4, 6), -4 + 6 = 2 True this is a solution
(0, 2), 0 + 2 =2 True this is a solution
(4, -2) 4-2 =2 True this is a solution
This is a solution set since all the points are a solution
Answer:
(-4,6), (0,2), (4,-2)
Step-by-step explanation:
If you substitute the ordered pairs in the equation and all three of the ordered pairs in the list equals to 2 that is the list that represents the solution
Evaluate the following expressions giving the functions g(x)= -4x+3
g(10) is the expression
Answer:
g(10) = -37
Step-by-step explanation:
g(x)= -4x+3
g(1) means evaluate when x=10
g(10) = -4*10 +3
g(10) = -4*10 +3
g(10) = -40+3
g(10) = -37
subtract 6 from 2, then add d to the result
Answer:
The answer would be (6-2) +d
Step-by-step explanation:
That is the answer because first you subtract 6 from 2. You dont have a choice. Simplified it would be 4+d. Please give me brainliest
Alexandra purchases two doughnuts and three cookies at a doughnut shop and is charged $3.30. Brianna purchases five doughnuts and two cookies at the same shop for $4.95. All the doughnuts and cookies have the same price. Find the cost of one doughnut and the cost of one cookie.
The cost of one doughnut is $0.75 and the cost of one cookie is $0.60.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Alexandra buys two doughnuts and three treats at a donut shop and is charged $3.30. Brianna buys five doughnuts and two treats at a similar shop for $4.95. Every one of the doughnuts and treats has a similar cost.
Assume 'x' is the cost of doughnuts and 'y' is the cost of one cookie. Then the equations are given as,
2x + 3y = 3.30 ...1
5x + 2y = 4.95 ...2
Multiply equation 1 by 5 and equation 2 by 2, then we have
10x + 15y = 16.50 ...3
10x + 4y = 9.90 ...4
Subtraction equation 2 from equation 1, then we have
15y - 4y = 16.50 - 9.90
11y = 6.60
y = $0.60
Then the value of 'x' is given as,
2x + 3(0.60) = 3.30
2x + 1.80 = 3.30
2x = $1.50
x = $0.75
The expense of one donut is $0.75 and the expense of one treat is $0.60.
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Can someone help me with my math
−36+x<8
Answer:
x<44
Step-by-step explanation:
Answer:
x<-28
Step-by-step explanation:
Janelle babysat for 6 hours at an hourly rate.After she got paid she spent $12 at Walmart. She came home with $36. How much money did she make per hour?
By adding Janelle's spending to what she came home with and dividing by the hours worked, we find that she earned $8 per hour babysitting.
To find out how much Janelle made per hour babysitting, we need to add the money she spent at Walmart to the money she came home with.
This gives us the total amount she earned.
Since she spent $12 at Walmart and came home with $36, we add these two amounts together to get $48.
Janelle babysat for 6 hours, so to find out her hourly wage, we divide the total amount she earned ($48) by the number of hours she worked (6 hours).
= $48 / 6 hours = $8 per hour
Thus, Janelle earned $8 per hour for her babysitting.