Two expressions with an equal sign in between is Equation, The given equation is 168>= 7x+4y, when we solve it for y we get y<=42-7x/4..
What is Equation?
Two expressions with an equal sign in between is called as Equation.
The given equation is
168>= 7x+4y
Now we need to make y as independent variable.
Subtract 7x on both the sides
168-7x>=7x-7x+4y
168-7x>=4y
Now divide both side by 4.
42-7x/4>=y
Therefore the value of y is 42-7x/4, y<=42-7x/4.
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A Canadian goose migrated at a steady rate of 4 miles every 7 minutes.
Part 1 out of 3
Fill in the table to describe the relationship.
Time (min)
Distance (mi)
✓ Check
-7
5
14
21
28
35
9
A Canadian geese moved 4 miles every 7 minutes, consistently.
Part 1 out of 3.
Distance: 4,8,12,16,20,24,28
Time: 7,14,21,28,35,42,49
Time is an interval of time that is hours and minutes after midnight or noon.
Distance is a distance between two objects or individuals.
Given that,
A Canadian geese moved 4 miles every 7 minutes, consistently.
Distance: 4,8,12,16,20,24,28
Time: 7,14,21,28,35,42,49
Therefore, the table is
Distance: 4,8,12,16,20,24,28
Time: 7,14,21,28,35,42,49
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Find the slope of the line from the pair of points (1, -4) , (-5, 3)
A. 1/4
B. -6/7
C. -7/6
D. 7/6
Answer:
B
Step-by-step explanation:
The rise is +7, and the run is -6
so, -6, +7
If 1 x is 21 a and if 1 x is 19 b hovv much b is one a
Answer:1.052
Step-by-step explanation:
can someone help me solve for x? 2x-9=3x-1
Answer: x=−8
Evaluate
2x−9=3x−1
Move the variable to the left side
2x−9−3x=−1
Subtract the terms
−x−9=−1
Move the constant to the right side
−x=−1+9
Add the terms
−x=8
Divide both sides
−1
−x
=
−1
8
Simplify
−1
−x =
−8
Solution
x=−8
Step-by-step explanation:
Hey!
2x-9=3x-1
Lets put the x on 1 side
2x 2x
- 2x -9= 3x-1
-9= x -1
-1 -1
-8 = x
X = -8 is your answer
Hope this helps!
Use your results from Exercise 13 to determine whether the given measures define 0,1, 2, or infinitely many obtuse triangles. Justify your answers.
a=15, b=15, m
When you are given two sides but no measurement of the angle, such as a = 15 and b = 15, we can create an infinite number of triangles.
For instance:
How many different triangles can be made if we have side lengths of 15 and 15 and an angle value of 0 to 360 degrees?
Using a protractor, make one of the triangles with sides of 25 metres and 21 metres, an angle of 12 degrees, and a third side that can be changed to your preferred length. You've constructed a triangle.
Similar to this, we can create a completely different triangle by varying the third side's length and angle measurement.
It's crucial to remember that you select the side lengths and angle. This implies that you might choose differently. You may create an infinite number of distinct triangles by using the same angles.
As a result, we can make an infinite number of triangles using just one angle and one side length.
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List at least one advantage and one disadvantage of using panels to gather data.
Solve each system by elimination.
9a - 3d = 3 , -3a + d = -1
By elimination, the system of equations, 9a - 3d = 3 and -3a + d = -1, has infinite solutions.
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using the elimination method, given two equations in a and d, a variable should be eliminated by adding/subtracting the two equations.
Simplifying the first equation by dividing it by -3,
9a - 3d = 3 ⇒ -3a + d = -1 (equation 1)
-3a + d = -1 (equation 2)
Since the simplified equation of the first equation is the same as the second equation, then the two lines are exactly the same or overlapping.
Hence, the system of equations has infinite solutions.
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What is the value of 5(2x − 4) − 2y if x = −2 and y = 6?
−52
−48
−92
28
Answer:
-52
Step-by-step explanation:
fill in the x and y values and multiple it and then combine it
Find the slope of the line from the pair of points (1, 4) , (5,7)
A. 3/2
B. 3/4
C. 4/3
D. -3/4
Name the property of real numbers illustrated by the equation. - [ -(x - 10)] = x-10
The property of real numbers illustrated by the equation - [ -(x - 10)] = x-10 is Distributive property.
Distributive Property of real number is represented by the expression
a(b+c)=a*b+a*c.
For Example : 3(2+4)=3*2+3*4
=6+12
=18
In the given question ;
LHS =-[-(x-10)]
First applying distributive property in side "[ ]".
= -[-x-(-10)]
= -[-x+10]
Again applying distributive property , we get
= -(-x)-(+10)
= x-10 =RHS
Therefore , Distributive Property of Real numbers is illustrated by the equation - [ -(x - 10)] = x-10.
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Write an equation of each line in standard form.the line perpendicular to -2 x+3 y=9 through (-1,-3)
The standard form is 3/2x + y +2 = 0 for line perpendicular to -2 x+3 y=9 through (-1,-3)
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
In an equation, parallel lines have the opposite reciprocal slope. In other words, if a line's slope is a positive fraction, its reciprocal slope is negative.
Here given that -2 x+3 y=9
can also be written as
y = 2/3x + 3
Here -2/3 is the slope and 3is the y-intercept
To find a parallel line to the following equation, use the opposite reciprocal slope and point, then solve using the point-slope formula.
y - y₁ = m(x - x₁)
We have, m = -3/2 x₁ = -1 and y₁ = -3
y - (-3) = -3/2(x - (-1))
y + 3= -3/2x +1
3/2x + y +2 = 0
We have the standard form 3/2x + y +2 = 0 of a line perpendicular to y = (2/3)x - 1 through (0,6)
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A recipe for custard sauce calls for 6 egg yolks, (2/3) cup of sugar, and 1(1/2) cups of hot milk, Chelsea needs more, sauce than the recipe yields. She plans to use 1 cup of sugar. How many cups of hot milk should she use?
9/4 cups of hot milk will be used by Chelsea.
As per the given information in question about custard, we know -
For 2/3 cups of sugar, the cups of hot milk required = 1(1/2)
Converting the number of cups of hot milk from mixed fraction to improper fraction -
Number of cups = (2×1 + 1)/2
Number of cups= (2 + 1)/2
Number of cups = 3/2
So, for 1 cup of sugar, the cups of hot milk required will be = (3/2) ÷ (2/3) × 1
Number of cups of hot milk required = (3×3) ÷ (2×2)
Number of cups of hot milk required = 9/4
Hence, for 1 cup of sugar 9/4 cups of hot milk will be used by Chelsea.
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Josh is building a kaleidoscope using PVC pipe, cardboard, bits of colored paper, and a 12 -inch square mirror tile. The mirror tile is to be cut into strips and arranged to form an open prism, with a base like that of an equilateral triangle. Make a sketch of the prism, giving its dimensions. Explain your reasoning.
A sketch of the required prism is as shown below.
In this question,
Josh is building a kaleidoscope using PVC pipe, cardboard, bits of colored paper, and a 12 -inch square mirror tile.
While making a kaleidoscope, the mirror tile is to be cut into strips and arranged to form an open prism, with a base like that of an equilateral triangle.
We need to make a sketch of the prism, giving its dimensions
As the base of the prism formed is an equilateral triangle, the mirror tile must be cut into three rectangular strips of equal width.
So, the width would be 12 ÷ 3 = 4 inches
The original tile is a 12-inch square, the length of each side of the square is 12 inches.
So the each rectangular strip will be 12 inches by 4 inches.
i.e., the length = 12 inches and width = 4 inches
Therefore, a sketch of the prism is as shown below.
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Eli wants to buy a wedding cake. The original price is $80. What is the sale price?
The sale price is $80.
Here the original price is $80.
there is no any valid data to find sale price so sale price should be$80
Profit and loss are expressions used to determine whether or not a sale is economic. In our diurnal lives, we use these expressions frequently. However, the difference between the two is appertained to as profit, If the selling price is advanced than the cost price. However, the difference is appertained to as the loss, If the selling price is lower than the cost price. The cost price of a product is the price at which it's bought. The selling price of a thing is the price at which it's vended. In this essay, we will study further about profit and loss.
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1/2x+1/2x+x+1
I got to x+x+1 (if that's even right)
but how do you solve the rest?
The value of the expression ( 1/2 )x + ( 1/2 )x + x + 1 is 2x + 1.
A variable, a number, or a mix of numbers, operations, and numbers symbols make up an expression. Two expressions joined by an equal sign form an equation.
A formula called an equation uses the equals symbol (=) to denote the equality of two expressions.
Consider the expression,
1/2x + 1/2x + x + 1
Taking common out,
( 1/2 )x + ( 1/2 )x + x + 1 = ( 1/2) × [ x + x ] + x + 1
( 1/2 )x + ( 1/2 )x + x + 1 = (1/2x) × 2 + x + 1
( 1/2 )x + ( 1/2 )x + x + 1 = x + x + 1
( 1/2 )x + ( 1/2 )x + x + 1 = 2x + 1
Therefore, the value of ( 1/2 )x + ( 1/2 )x + x + 1 is 2x + 1.
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Jesse has been saving his earnings from his lemonade stand. Jesse has 47 dollars to spend. If He buys a new hat for 19 dollars, how many scarves can He buy with the remaining spending money if they cost 7 dollars each?
The remaining scarves he can spend is 4.
A mixture of constants, variables, and operators make up an algebraic expression. Algebraic expressions can be used to accomplish the four fundamental mathematical operations of addition, subtraction, multiplication, and division. Algebraic expression addition and subtraction are quite similar to addition and subtraction of numbers.
Jesse has a total of 47 dollars.
The cost of the new hat is = 19 dollars
The remaining dollars after buying the new hat is 47 dollars - 19 dollars = 28 dollars.
The cost of the scarves is 7 dollars
Thus total scarves for 28 dollars = 28/7 = 4 scarves.
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Use an algebraic equation to find the measures of the two angles described below. Begin by letting x represent the degree measure of the angle's supplement.
The measure of the angle is two times greater than its supplement.
Can someone help please
The supplementary angles are 60 degrees and 120 degrees
What are supplementary angles?Two angles are said to be supplementary when their measure add up to 180 degrees.
Therefore, if x and y are supplementary angles,
x + y = 180
x represent the degree measure of the angle's supplement.
The measure of the angle is two times greater than its supplement.
Therefore, the algebraic expression of the angles is as follows:
x + 2x = 180
3x = 180
divide both sides by 3
3x / 3 = 180 / 3
x = 60
Therefore, the supplementary angles are 60 degrees and 120 degrees.
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5|4w-1|=5w+40
Solve for x
Answer:
w1= -1.4, w2= 3
Step-by-step explanation:
I will assume that "x" is a w since there is no x within the question
Solution
w
1
=−
5
7
,w
2
=3
Alternative Form
w
1
=−1.4,w
2
=3
Evaluate
5×∣4w−1∣=5w+40
Simplify
5∣4w−1∣=5w+40
Rewrite the expression
5∣4w−1∣−5w−40=0
Separate the equation into 2 possible cases
5(4w−1)−5w−40=0,4w−1≥0
5(−(4w−1))−5w−40=0,4w−1<0
Evaluate
w=3,4w−1≥0
5(−(4w−1))−5w−40=0,4w−1<0
Evaluate
w=3,w≥
4
1
5(−(4w−1))−5w−40=0,4w−1<0
Evaluate
w=3,w≥
4
1
w=−
5
7
,4w−1<0
Evaluate
w=3,w≥
4
1
w=−
5
7
,w<
4
1
Find the intersection
w=3
w=−
5
7
,w<
4
1
Find the intersection
w=3 w=− 57
Solution
w
1
=−
5
7
,w
2
=3
Alternative Form
w 1=−1.4,w 2
=3
Which student walked at the fastest rate down the hallway?
6th grader: Walked 120 feet in
15 seconds
7th grader:walked 100 feet in 10 seconds
8th grader: Walked 180 feet in 20 secs
Answer:
8th grader
Step-by-step explanation:
They walked the the fastest since they walked 50 feet more than the 6th grader in 5 more seconds ( im sorry if you dont understand! i tried my best explaining it! hope this helps :) )
If -2+x=-6 , then -17-x= ?
A. -13
B. -4
C. 9
D. 13
E. 21
The value of -17-x is A. -13.
We are given the expression. To find the result, we need to solve the first expression. This will give the value of x. Further, we will be using the value of x to find the value of another expression.
-2 + x = -6
Shifting the value of -2 to the Right Hand Side of the equation
x = -6 + 2
Performing subtraction on Right Hand Side of the equation
x = -4
Now, keeping the value of x in second expression -
Value = -17 -(-4)
As there are two negative signs, the number 4 will be represented with positive sign
Value = -17 +4
Performing subtraction
Value = -13
Hence, the value of expression is A. -13.
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How would I solve for this?
Answer:
1
Step-by-step explanation:
replace x with -7
f(-7) = 5 - (-7)
f(-7) = 5 + 7
f(-7) = 12
Select the expressions that are equivalent to -5(-9f + 7) - 7.
-42f + 45
-9f-42
(-9f + 7)-5-7
45f - 42
Answer:
45f - 42
Step-by-step explanation:
-5(-9f + 7) - 7
Expand -5(-9f +7) = -5(-9f) + (-5)(7) = +45f -35 or simply 45f - 35
5(-9f + 7) - 7 becomes 45f - 35 - 7 = 45f - 42
Select all the points that are on the graph of the equation x+3y=12
Answer:
(1,3), (2,2), (3,1), (4,0), (-1,5), (-2,6), (-3,7), (-4,8), (-5,9), & (-6,10)
Step-by-step explanation:
First, solve to alter the equation into a slope form instead of in standard form.
x+3y=12
Because x represents the slope, we need to transfer it to the other side of the equation. By subtracting it, it'll allow the equation to only have 3y on the left side of the equation and x will become negative x which will be added on to the 12 on the right side.
x+3y=12
-x -x
+3y=-x+12
3y=-x+12
Next, you would divide the 3 underneath the y and the number 12 to allow the 3y to become y because y needs to be isolated in order for the slope intercept formula to work.
3y divided by 3 equals 3 and 12 divided by 3 is 4.
3y/3=-x+12/3
The final equation would look as follows:
y=-x+4
Hence, the y-intercept is 4 and the slope is -1.
You would then plot the origin coordinate of (0,4) and either go down one and right one or up one and left one; either way, you'll receive a negative slope looking like this: \
Some points on the graph would be: (1,3), (2,2), (3,1), (4,0), (-1,5), (-2,6), (-3,7)
Hope this helps.
Evaluate each logarithm. log₂ 16
A logarithm is a power that requires a number to be raised to another power.
The logarithmic equation given in the question can be written as
log2(16) =x
We will rewrite this equation in the exponential form by considering the definition of logarithm.
The definition states that,
If x and b are two positive real numbers and the value of b is not equal to 1, then the log of
log b (x)=y is equivalent to by=x
We will convert the given equation according to the above definition,
2x=16
The bases of all the values involved must be identical. So, we will create equivalent expressions in the equation that all have equal bases.
2x=24
Now we have the same bases; the two expressions can only be said equal if the exponents are also equal.
x=4
The variable x is equal to 4.
4
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What is the perimeter of the rectangle shown below?
Y
(0,7)
(0,1)
perimeter =
(12,7)
(12, 1)
units
The perimeter of the given rectangle is (A) 20 units.
What are rectangles?A rectangle is a quadrilateral with four right angles in Euclidean plane geometry. It can also be defined as an equiangular quadrilateral because all of its angles are equal, or a parallelogram with a right angle. A square is a rectangle with four equal-length sides.The formula of the perimeter of the rectangle: 2(l + b)
Now, substitute values:
= 2(l + b)= 2(7 + 3)= 2(10)= 20Therefore, (A) 20 units are the perimeter of the given rectangle.
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The correct question is given below:
What is the perimeter of the rectangle shown below?
Suppose that R and S are points on the number line.
If RS =5 and R lies at 14, where could S be located?
The location of S will be at 9 and ₋19 .
When speaking of a straight line in mathematics, the term "number line" refers to the placement of numbers along some or all of the breadth. Any direction can be used to postpone a number line, which is frequently displayed horizontally.
Given, on a number line R and S are points on the number line.
RS = 5 and R is located at 14.
S is located at = ?
Let x be the coordinate of the point S. Then we have:
14 ₋ x = ±5
x = ± 5 ₋ 14
x = 5 ₋ 14 or ₋5₋14
x = 9 or ₋19
Then the location of point S will be at 9 and -19.
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At a point on the ground 70 ft from the base of a tree, the distance to the top of the tree is 2 ft more than 3 times the height of the tree. Find the height of the tree.
The height of the tree is 2.22 feet so that the point on the ground is 70 ft from the base of a tree
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let h represent the height of the tree. Hence the distance to the top of tree = 3h + 2.
Using Pythagoras theorem:
(3h + 2)² = h² + 70²
9h² + 12h + 4 = h² + 70²
8h² + 12h - 66 = 0
h = 2.22 feet
The height of the tree is 2.22 feet so that the point on the ground is 70 ft from the base of a tree
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WILL GIVE 20 POINTS FAST 4521 is considered a RATIONAL number, what makes this number
rational? Explain your answer.
Answer:
4521 is a rational number because it can be expressed as the quotient of two integers: 4521 ÷ 1.
Step-by-step explanation:
Rational Numbers: Any number that can be written as a ratio (or fraction) of two integers is a rational number
Hope this helps
What is the value of 19 cubed? A: 22 B: 57 C: 361 D: 6,859
The value of 19 cubes is equal to 6859. The correct option is D.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the number is 19. The cube of 19 will be calculated as:-
19³ = 19 x 19 x 19
19³ = 6859
The cube of 19 is calculated by multiplying the number three times. Hence, the cube of 19 is 6859.
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What is 70,951 rounded to the nearest hundred?
Answer:
70,951 rounded to the nearest hundred is 71,000.
Step-by-step explanation: