x = 2 is the solution of the given equation: x + 3x - 4 = 10 - 3x
What is an equation?The meaning of such an equations in algebra is just a mathematical expression stating the equality between two mathematical terms. For instance, 6x + 5 = 11 is an equation where 6x + 5 and 11 are two expressions separated by the 'equal' sign.
Identity equations and conditional equations are the two types of equations. For just any value of both the variables, an equality remains true. Only such variables have values that make a condition expression true. Two expressions joined by an equals sign ("=") form an equation.
x + 3x - 4 = 10 - 3x
or, 4x - 4 = 10 - 3x
or, 4x + 3x = 10 + 4
or, 7x = 14
or, x = 14/7
or, x = 2
Thus, x = 2 is the solution of the given equation: x + 3x - 4 = 10 - 3x
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Which statement about ABC and DEF is true? A picture shows triangle A B C and triangle D E F. Triangle A B C: Side A B is 5. Side B C is 8. Side C A is 6. Triangle D E F: Side D E is 10. Side E F is 16. Side F D is 12.
Sarah runs around this track for PE. What is the distance around this track
The distance around the track is the perimeter of the given shape which would be = 572.36
What is perimeter?Perimeter of an area or an object is the total distance around that area or object.
The shape can be disintegrated as 2 semi circles(a circle) and a square.
The perimeter of a circle = 2πr
where r = 37
π = 3.14
perimeter = 2×3.14 × 37 = 232.36meters
Perimeter of square = 4 ×a
where a = 85
perimeter of square = 4×85 = 340
Therefore the distance round the track = 232.36+340= 572.36
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Solve the problem below:
6315*41=
Show your work
The value of 6315 ×41 is 260391.
What is Multiplication?Multiplication is a method of finding the product of two or more numbers
We have to find the product of 6315 times of forty one
6351
× 41
_______
6351
25404+
__________
260391
Hence, the value of 6315 ×41 is 260391.
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27. (-2,-6). О y (1,3) X how do I write this in slope intercept form
Answer:
y = 3x
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, - 6 ) and (x₂, y₂ ) = (1, 3 )
m = [tex]\frac{3-(-6)}{1-(-2)}[/tex] = [tex]\frac{3+6}{1+2}[/tex] = [tex]\frac{9}{3}[/tex] = 3 , then
y = 3x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (1, 3 ) , then
3 = 3(1) + c = 3 + c ( subtract 3 from both sides )
0 = c
y = 3x + 0 , that is
y = 3x ← equation of line
Which of the following angles is a coterminal angle with 40 degrees? -400 degrees 140 degrees -320 degrees 50 degrees
The answer choice which represents an angle which is co-terminal with the given angle 40° is; -320 degrees.
Which answer choice represents a co-terminal angle with 40°?It follows from the task content that the answer choice which represents an angle which is co-terminal with 40° is to be determined.
Co-terminal angles are related such that if x and y are co-terminal angles;
x = y - 360°n
where n represents integer values.
On this note, the angle which is co-terminal with 40° is;
x = 40° - 360°
x = -320°.
Hence, the answer choice which represents an angle that is co-terminal with 40° is; -320°.
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Amy swims for the same amount of time every morning. Every evening she swims 1 1/2 times as many minutes as she does in the morning. Each day she swims for 50 minutes. How many minutes does she swim in the evening
In the evening Amy swims for 30 minutes, as per the given condition.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let Amy swim x minutes in the morning,
So in the evening, she swims for 1 1/2 × x minutes,
According to the quesiton,
Each day she swims for 50 minutes.
x + 1 1/2 x = 50
5x/ 2 = 50
x = 20 minutes
Now,
In the evening,
= 3/2x
= 3/2{20}
= 30 minutes
Thus, in the evening Amy swims for 30 minutes.
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4. Compare using <, >, or=
.
6/8 - 3/10 ⭕️. 3/10 + 5/8
Answer:
6/8 - 3/10 < 3/10 + 5/8
Step-by-step explanation:
6/8 - 3/10 ⭕️. 3/10 + 5/8
60/80 - 24/80 ⭕️ 24/80 + 50/80
36/80 < 74/80
So, the answer is
6/8 - 3/10 < 3/10 + 5/8
Dedham bought 4 cds that were each the same price. Including sales tax, he paid a total of $63.60. Of that total, $2.80 was tax. What was the price of each CD before tax?
how to find the measure of an exterior angle geometry
The total of the measurements of the two non-adjacent internal angles of a triangle determines the size of its exterior angle.
What is Exterior Angle ?The angle created when a transversal cuts one of two lines and is located outside of the line. It describes the angle between a side of a polygon and an expanded neighboring side.
Exterior angles are those that run parallel to a polygon's inner angles but are located outside of it. The sum of the two internal opposed angles determines the size of an outside angle.
The angle between any side of a form and a line that extends from the next side is known as the exterior angle. The result of adding the interior and outside angles is a 180° straight line. "Supplementary Angles" is what they are.
The total of the measurements of the two non-adjacent internal angles of a triangle determines the size of its outer angle.
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i need help with #1-6 please!!
The inverse function returns the original value for which a function gave the output.
What is Inverse Function?A function that can reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as "f-1" or "F-1." Here, (-1) should not be confused with an exponent or a reciprocal.
If f and g are inverse functions, then f(x) = y if and only if g(y) = xIn trigonometry, the inverse sine function is used to find the measure of angle for which sine function generated the value. For example, sin-1(1) = sin-1(sin 90) = 90 degrees. Hence, sin 90 degrees is equal to 1.If you consider functions, f and g are inverse, f(g(x)) = g(f(x)) = x. A function that consists of its inverse fetches the original value.Example: f(x) = 2x + 5 = y
Then, g(y) = (y-5)/2 = x is the inverse of f(x).
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2(n + 1) = 2n
Given the equation above...what number can be replaced for n so that this equation will always be true?
There is no possible solution such that the given equation will always be true. The conclusion is drawn using concept of linear equation.
What is a linear equation?
A linear equation is one that has the highest degree of 1 possible. This indicates that there are no variables in a linear equation with exponents greater than 1. Such an equation on the graph, forms a straight line.
We are given equation- 2(n + 1) = 2n
On distributing, we get
⇒2n+2=2n
Now, subtracting 2 from both sides, we get
⇒2n+2-2=2n-2
⇒2n=2n-2
On subtracting 2n from both sides, we get
⇒2n-2n=2n-2-2n
⇒0≠2
Hence, the given equation does not have a solution.
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What is the relationship between the ratios?
0.2/2.6 and 0.3/3.6
Drag and drop a term into the box to correctly complete the statement.
Answer:
proportional
Step-by-step explanation:
test = 100%
Answer: The correct answer is that it is proportional?
Please show me how to work out these math problems. Only the ones with stairs next them please. Thank you.
On solving the provided question, we can say that the surface area of the figure 7 = 155sq units
what is surface area ?An indication of the overall space occupied by an object's surface is its surface area. A three-dimensional shape's surface area is the total amount of space that surrounds it. A three-dimensional shape's entire surface area is known as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face. As an alternative, you may use the formula below and name the box's dimensions as follows: Surface (SA) = 2lh + 2lw + 2hw. Surface area is a measurement of the entire amount of space filled by a three-dimensional shape's surface (a three-dimensional shape is a shape that has height, width, and depth).
here,
the surface area of the figure 7 =
area of square + 2*area of rectangle =
3*3 + 2*9*8 = 9 + 144 = 155sq units
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How many solutions does the system of equations below have? y = 7 10 x + 6 y = 7 10 x + 6
The number of solutions to the equation y = ( 7/10 )x + 6y is infinite number of solutions as the equations are the same
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first equation be represented as A
Now , the value of A is
y = ( 7/10 )x + 6y be equation (1)
Let the second equation be represented as B
The value of B is
y = ( 7/10 )x + 6y be equation (2)
Now , on simplifying both the equations , we get
equation (1) = equation (2)
Substituting the values in the equation , we get
( 7/10 )x + 6y = ( 7/10 )x + 6y
So, the system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept.
Hence , the number of solutions to the equations are infinite
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solve the equation 7=10s-3
Answer: s=1
Step-by-step explanation:
Nora leans a 24-foot ladder against a wall so that it forms an angle of 76∘with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary.
By using a trigonometric relation, we will see that the stari is 23.3ft high up the wall.
How high up the wall does the ladder reach?Think of a right triangle with an hypotenuse that measures 24 ft (like the length of the ladder) and we know the angle opposite to the cathetus that represent the height, which is 76°.
Then we can use the trigonometric relation:
sin(a) = (opposite cathetus)/(adjacent cathetus)
Replacing the values that we know:
sin(76°) = H/24ft
24ft*sin(76°) = H = 23.3ft
The star is 23.3ft high up the wall.
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What are the Vertical asymptotes
Answer:
Step-by-step explanation:
Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a rational function. (They can also arise in other contexts, such as logarithms, but you'll almost certainly first encounter asymptotes in the context of rationals
On average how many necklaces can Angela make each month
Angela makes 150 necklaces on average each month making necklaces for 2.5 hours each day.
What is an average of given data?
An average of a list of data is a mathematical expression for the centre value of a set of data. It is defined mathematically as the ratio of the total of all the data to the number of units in the list. In statistics, the average of a particular collection of numerical data is also known as the mean.
for e.g.
The average of 2, 3, and 4 equals (2+3+4)/3 = 9/3 = 3. As a result, the central value of 2,3, and 4 is 3. Thus, the definition of average is to determine the mean value of a set of data.
Now,
Angela works 20 days in a month making necklaces for 2.5 hours each day
so, Total hours she worked = 20*2.5
= 50 hours
She makes 3 necklaces in an hour
Hence,
Necklaces made by her on average in a month = 50*3
=150/month
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Jada is solving the equation shown below. Negative one-half (x + 4) = 6 Which is a possible first step to begin to simplify the equation? Select two options. Divide both sides of the equation by –2. Subtract 4 from both sides of the equation. Multiply both sides of the equation by –2. Distribute –2 over (x + 4). Distribute Negative one-half over (x + 4).
The first step to solve the equation -1/2(x+4) = 6 is to multiply both sides by -2
What are linear equation?A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line.
The equation -1/2( x+4) = 6 is an example of linear equation. It is a linear equation with one variable and x is the variable.
The equation -1/2(x+4) = 6
multiply both sides by -2
-1/2( x+4) ×-2 = 6 ×-2
x+4 = -12
collect like terms
x= -12-4
x = -16
therefore the first step to solve the equation is to multiply both sides by -2
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what is the slope for the graph? please help
1.2
2.-1/2
3.-5
d.-1/5
Therefore , the solution of the given problem of slope comes out to be
m = -5.
Explaining the slope.A line's slope determines how steep it is. A gradient-based equation has a phenomenon called a gradient overflow. The slope is determined by dividing the average of the run (horizontal difference) between two points by the rise (vertical difference) between those same two points. The hill variety of an equation, represented by the notation y = mx + b, is used to model the fixed path issue. The point in which the grade is m, a = b, and the line's y-intercept is located (0, b). For the trigonometric formula y = 3x - 7, the slope y and una are as follows: (0, 7). The y-intercept is situated when the slope of the line is m and b.
Here,
Given :
Points in the graph where line touches on x and y axes
So,
Point = (1,11) and (3,1)
Thus ,
By using slope formula :
=> m = y2 -y1 /x2-x1
=> m = 11 -1 / 1-3
=> m = 10/-2
=> m =-5
Therefore , the solution of the given problem of slope comes out to be
m = -5.
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If Joe currently benches a maximum of 200 lbs, but wants to reach at least 220, how much more weight does Joe need to add to his max? Remember to write this as an inequality
Joe needs to add x ≥ 20 lbs to bench at least 220 lbs
What is inequality?A linear inequality compares two values. All the ordered pairs that make the linear inequality a true statement exist on one side of the linear equation, which we get by replacing the inequality sign with the equal sign.
Given,
Joe benches maximum of 200lbs
y ≤ 200
multiplying with -1
- y ≥ - 200 -----(1)
he wants to reach at least 220lbs
y' ≥ 220 -----(2)
To reach at least 220 lbs,
Let he needs to add x lbs at max
x = y' - y
Adding inequalities (1) and (2)
y' - y ≥ 220 - 200
⇒ x ≥ 20
Hence, x ≥ 20 lbs weight should be added to reach at least 220 lbs bench-press.
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Seven times the difference of a number and eight is seven less than six times the number. Find the number. Round your answer to the nearest integer, if necessary.
Answer:
hi (●’◡’●)ﾉ blablablablablablablabla
John has a collection of 10 paise ,15 paise , 20 paise coins in the ratio of 2:5:9 and his total collection
3(x-1)2+2x-7 for x=3
Answer:
11
Step-by-step explanation:
3(3-1)2+2(3)-7 = 3(2)2+6-7 = 12-1 = 11
CP= Rs. 6000, SP= Rs. 5800!
For the given, CP and SP, Loss = 200 and Loss % = 10/3%.
How to calculate loss percentage?If a product's cost price is higher than its selling price, the business of the company is said to be losing money; yet, if the product's cost price is lower than the price at which it is being sold, the business may be making money. Loss % = 100 x Loss/CP.
Loss is equal to Cp - Sp (Cp > Sp). where S.P. is the sale price at which the product has been sold to the customer and C.P. is the actual price of the good or commodity.
Loss = CP - SP
Loss = 6000 - 5800
Loss = 200
Loss% = Loss / CP × 100
Loss % = 200 / 6000 × 100
Loss % = 10/3%
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Complete question:
What is Loss percentage when CP= Rs. 6000, SP= Rs. 5800!?
Which expression is equivalent to 3x2+(5x−8x2)+4−(5x+2)
Answer: -5x^2 + 2
Step-by-step explanation:
Question
Which system of inequalities is shown in the graph?
-5
5
-5
OA. yz 2x-2
yzx²2²-3x
OB. ys 2x-2
yz x²-3x
OC. ys-2x-2
y≤ x²-3x
OD. y≤2x-2
y≤ x²-3x
SUBMIT
The inequality system represented by the graph is Option A: y = x + 3; y = x2 - 3x.
What is the system of inequality?We can see from the inequality graph that one of the shaded zones is below the parabola and the other is between the parabola and the bottom of the line.
Due to the thickness of the boundary lines and the fact that both shaded regions are below their respective parabola and line borders, we will use the "less than or equal to" indications for each inequality.
Because both A and D use inequality signals with "less than or equal to," the correct response is between them.
Therefore, option A is the right response.
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Which expression is modeled by the number line?
O−6+(-4)
O-6+4
06-4
O-6-(-4)
Answer:
O-6-(-4)
Step-by-step explanation:
The expression O-6-(-4) is modeled by the number line. To evaluate this expression, we simplify the parentheses first. Since -4 is inside parentheses with a negative sign in front, we change the sign to positive: O-6-(+4). Then we perform the subtraction: O-(6+4) = O-10. This means that the point O is 10 units to the right of the point (-10) on the number line.
Wesley covered this figure with the unit square shown to find the area. A rectangle and square are shown. The square is labeled 1 square unit. The length of the rectangle is approximately 6 times as long as a side of the square, and the width of the rectangle is approximately 3 times as long as a side of the square. Which figure shows how he covered the square and the correct area?
The required figure shows the square of a square unit and rectangle with a length of 6 times the side of the square and a width of 3 times the side of the square.
What is a rectangle?The rectangle is 4 sided geometric shape whose opposites are equal in lengths and all angles are about 90°.
here,
Wesley covered this figure with the unit square shown to find the area. The length of the rectangle is approximately 6 times as long as the side of the square, and the width of the rectangle is approximately 3 times as long as the side of the square.
Area of square = 1 unit² [side = 1 unit]
Area fo the rectangle = [1 ×6] × [1×3] = 18 unit²
Thus, the required figure shows the square of a square unit and rectangle with a length of 6 times the side of the square and a width of 3 times the side of the square.
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A chemical company manufactures silicon carbide and silicon tetrachloride. It takes 1.5 kg of silica and 0.6 kg of carbon to make 1 kg of silicon carbide. On the other hand, 1 kg of silicon tetrachloride requires 0.35 kg of silica, 0.14 kg of carbon, and 0.84 kg of chlorine. The manufacturer has 105 kg of silica, 84 kg of carbon, and 126 kg of chlorine in stock. If they make $320 profit on 1 kg of silicon carbide and $250 on 1 kg of silicon tetrachloride, how much of each should they produce?
A percentage can be larger than 100 and a fraction can be greater than 1.
What is meant by percentage?A percentage is a figure or ratio that can be stated as a fraction of 100 in mathematics. If we need to determine a percentage of a number, multiply it by 100 and divide it by the total. So, a part per hundred is what the percentage refers to. Percent signifies for every 100. The sign "%" is used to denote it.
A percentage can be larger than 100 and a fraction can be greater than 1. We are limited to looking at the whole only when the fraction or percentage relates to a portion of it.
In addition to being stated as a decimal or a fraction, a percentage is a number that indicates how many out of 100 it is. Three for the price of one! Simply enter the % as the numerator and 100 as the denominator to convert the percentage to a fraction.
Therefore, the correct answer is 35%.
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