The number you thought of is -1.
To solve this problem, you can use algebra to represent the unknown number as a variable (let's call it x) and the given information as equations. The first step is to determine what the problem is asking for. In this case, it is asking to find the original number before it was doubled and 3 was added. To do this, you can use the information given in the problem to set up equations.
The first equation is (2x+3)*4 = 52. You can then solve this equation for x. First, you can simplify the left side of the equation by distributing the 4 to the 2x and the 3: 4x + 12 = 52. Then, you can subtract 12 from both sides to get 4x = 40. Finally, you can divide both sides by 4 to get x = 10. however, this is not the solution, since the problem does have not a unique solution. x=-1 is also the solution.
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During two games, the number of points scored by a basketball team Increased from 75 to 87. By what percentage
did the number of points scored increase?
The percentage of increase in the number of points is 16 %
What Does Percent Mean?
A ratio or figure stated as a fraction of 100 is called a percentage. The percent marker is frequently used to indicate it,%
given the data,
The basketball team's total point total was 75.
The basketball team's enhanced point total was 87.
The difference between the basketball team's total points scored and its increased points are the increase in points.
The increase in points = 87 - 75
= 12 points
So, the percentage increase in points = ( increase in points/number of points scored by the basketball team ) x 100
The percentage increase in points = ( 12 / 75 ) x 100
= 0.16 x 100
= 16 %
Therefore, the percentage increase is 16 %
Hence, the percentage of increase in the number of points is 16 %
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expert that helps you learn core concepts.
See Answer
Raul works at a movie theatre. The function f(x) represents the amount of money Raul earns per ticket, where x is the number of tickets he sells. The function g(x) represents the number of tickets Raul sells per hour, where x is the number of hours he works. Show all work to find f(g(x)), and explain what f(g(x)) represents.
f(x) = 2x2 + 16
g(x) = √5x^3
The required function that gives [tex]f(g(x))[/tex] that represents the total amount of money Raul earned is
[tex]f(g(x)) = 10x^{3}+16[/tex]
What is a function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
Mostly functions are written as f(x) where x is the input of the function.
Given,
[tex]f(x) = 2x^{2}+16[/tex]
[tex]g(x)[/tex] = [tex]\sqrt{5x^{3} }[/tex]
If [tex]f(x)[/tex] represents amount of money Raul earns per ticket and [tex]g(x)[/tex] represents number of tickets Raul sells per hour, where x is the number of hours he works, then,
[tex]f(g(x))[/tex] represents the total amount of money Raul earned in a day.
To find [tex]f(g(x))[/tex], substitute value of [tex]g(x)[/tex] in the place of x in function [tex]f(x)[/tex] .
[tex]f(g(x))[/tex] = [tex]f[/tex]([tex]\sqrt{5x^{3} }[/tex])
= 2( [tex]\sqrt{5x^{3} }[/tex])² +16
= 10x³ + 16
Therefore the required function is [tex]f(g(x)) = 10x^{3}+16[/tex].
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Jacqueline is buying grapes and apples from the Walmart produce section. Grapes are $3
per pound and apples are $4 per pound. Jacqueline’s mother gave her $20 to spend. To
determine the combinations of grapes and apples that she can afford to purchase,
Jacqueline wrote the inequality 3 + 4 ≤ 20.
1. Define the variables Jacqueline used based on the context.
Let represent _______________________________________________.
Let represent _______________________________________________.
2. Explain why the inequality sign ≤ makes sense in this context.
3. Graph the inequality 3 + 4 ≤20.
4.The ordered pair (3, −4) is a solution to the inequality 3 + 4 ≤ 20.
Explain why
this is not a viable solution in the context of buying grapes and apples.
5. The ordered pair (4, 2) is a point on the boundary line. Explain what the ordered
pair represents in the situation.
Therefore , the solution to the given problem of inequality comes out to be Part a:where x is the no of apples and y is the no of grapes , Part b:Inequality sign and Part c: ordered pair (3, −4) isn't solution.
What is inequality, exactly?An unbalanced connection between two expressions or values is referred to in mathematics as an inequality. So, inequity results from imbalance. In mathematics, an inequality defines the connection between two non-equal quantities. Egality and inequality do not mean the same thing. Use the not equal sign whenever two values are not equal (). It is possible to compare values of any size using a variety of inequalities. By changing both sides until only the variables are left, it is possible to solve many straightforward inequality problems.
Here,
Given : 3x + 4y ≤ 20.
where x is the no of apples
and y is the no of grapes
Thus,
Part a:
where x is the no of apples
and y is the no of grapes
Part b:
Inequality signs means that 20 will be the maximum amount of the no of apples and no of grapes summation.
Part c: ordered pair (3, −4)
Thus,
putting in the inequality we find:
=> 3(-3)+ 4(-4)
=> -6 -16
=> -22
Thus , it is not a solution for inequality.
Therefore , the solution to the given problem of inequality comes out to be Part a:where x is the no of apples and y is the no of grapes , Part b:Inequality sign and Part c: ordered pair (3, −4) isn't solution.
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What is an intractable problem?
Answer: A problem is said to be intractable if there is no efficient algorithm to solve it.
Intractable problems are common. We need to discuss how we approach it when we actually encounter it.
Step-by-step explanation:
How many colours do you need to colour a graph such that no adjacent vertices are of the same colour showed in the image below?
Conclusion : Provided the graph with a large number of vertices, we see that we are again faced with resorting to a systematic tracing of all paths, comparison of the neighbour's colours, backtracking, etc resulting in exponential time complexity once again.
32x^6-4
how do yo factor this
What is the solution to the system Y 3x 7 and 6x 2y 12?
The system of equations y = 3x - 7 and 6x - 2y = 12 has no solution. That is the lines of the equation is parallel.
To solve a system of equations, you can use substitution or elimination.
One method to find the solution for this system of equations is substitution. To use this method, you can solve one equation for one variable in terms of the other variable, and then substitute this expression into the other equation.
Solving for y in the first equation:
y = 3x - 7
Then substitute the result in the second equation:
6x - 2(3x - 7) = 12
6x - 6x + 14 = 12
14 = 12
That clearly is not true and this system of equations has no solution.
--The question is incomplete, answering to the question below--
"What is the solution to the system y = 3x - 7 and 6x - 2y = 12?
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Please help me! Find the circumference of the circle
Answer:
convert to cmthen write the perimeter of the circle and solveFind the greatest common factor of $144$ and $405$.
Answer:The answer to your question is 9
Question content area top Part 1 Without using paper and pencil, how would you find the sum of 8.8 and 5.5 and ?
The sum of 8.8 and 5.5 is 14.3
What is addition?Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.
To find the sum of 8.8 and 5.5 without using pen and pencil:
First, we break the term in simple manner.
8.8 = 8 + 0.3 + 0.5
And 5.5 = 5 + 0.5
And now adding the terms one by one,
0.5 + 0.5 = 1.0
0.3 = 0.3
8 + 5 = 13
Addition,
13 + 1 + 0.3 = 14.3
Therefore, the value is 14.3
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Using long division convert 1/4 to a decimal
Using long division convert 1/4 to a decimal
To convert a fraction into a decimal, we'll just divide the numerator by the denominator:
4√1
we'll divide 1 by 4.
1 divided by 4 equals 0
0
4√1
To keep dividing, we'll add a decimal point and a zero after the 1, we'll also add a decimal point after the 0 on top
0.
4√1.0
Now we can divide 10 by 4, 10 divided by 4 equals 2.
0.2
4√1.0
Now we'll multiply 4 by 2, 4 times 2 equals 8. So we'll subtract 8 from 10.
0.2
4√1.0
-8
______
2
Since 2 is greater than 0, we're not finished dividing yet. We'll add another 0 after the decimal point and bring it down.
0.2
4√1.00
-8
________
20
20 divided by 4 equals 5.
0.25
4√1.00
-8
______
20
Now we'll multiply. 4 times 5 equals 20. When we subtract 20 from 20, we get 0. The 0 means we're done dividing.
0.25
4√1.00
-8
______
20
20
________
0
So 1/4 is equal to 0.25.
(X-5)-1 substitute the 9 for x and evaluate
Therefore , the solution of the problem of linear equation comes out to be the value after substituting is 3.
The definition of a linear equation.A linear equation is one that satisfies the algebraic formula y=mx+b. m is the y-intercept, while B is the slope. The foregoing sentence is sometimes referred to as a "linear equation with two variables" because y and x are variables. Bivariate linear equations are two-variable linear equations. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. An equation is said to be linear if its formula is y=mx+b, where m denotes the slope and b the y-intercept.
Here,
Given : (X-5)-1
Thus,
after substituting the value of x with 9
We get,
=> (X-5) -1
=>(9-5)-1
=> 4 -1
=> 3
Therefore , the solution of the problem of linear equation comes out to be the value after substituting is 3.
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ESSENTIAL QUESTION CHECK-IN
17. Tell how you can determine whether a number is a solution of an
equation.
324 Unit 4
Answer:
Step-by-step explanation:
1. Substitute the number for the variable in the equation.
Quentin is filling a glass that holds cups of water. He is using a cup measuring cup. How many times will he have to fill the smaller measuring cup to equal cups
So, by fraction, number of times he will have to fill the smaller measuring cup to equal 1 3/4 cups is 7 times.
What is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
Glass holds = 1(3/4) cups of water
One cup holds = 1/4 cup of water
number of 1/4 cups needed to fill the 1(3/4) cups of water glass.
[tex]\frac{1}{4xC}=1(\frac{3}{4})\\\\\frac{C}{4} = \frac{7}{4} \\\\C=\frac{7}{4x4}\\ \\C= 4[/tex]
number of times the smaller cup fills the glass is 7.
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Complete Question: Quentin is filling a glass that holds 1 3/4 cups of water. he is using 1/4 cup measuring cup. how many times will he have to fill the smaller measuring cup to equal 1 3/4 cups?
How do you find the missing side of a triangle?
The missing sides of the triangle can be found by applying the Pythagoras Theorem .
What is Pythagoras Theorem ?
The Pythagoras Theorem states that square of hypotnuse (that is longest side) is equal to sum of the square of perpendicular and base .
that means : [tex]Hypotnuse^{2} = Perpendicular^{2} +Base^{2}[/tex] ;
let missing side of the Right triangle be hypotnuse ;
So , missing side is written as : [tex]Hypotnuse = \sqrt{Perpendicular^{2} +Base^{2}}[/tex] .
For Example : Let a right triangle has sides lengths of perpendicular = 6 and hypotnuse = 10 .
let , the length of side "base" be unknown.
So , in order to find length of side b (base) , we substitute the known values into Pythagoras theorem:
[tex]10^{2} =6^{2} +Base^{2}[/tex] ;
[tex]Base = 100-36[/tex] ;
So , missing side "base" is = 8 ;
Therefore , the missing side can be found by using the Pythagoras Theorem .
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Lemon quah ha 2 part of concentrate to 5 part of water, if you put 90ml of concentrate in a gla, how much water hould be added?
Based on the 2:5 quantity of concentrate and water, the amount of water required for 90 mililitres will be 225 mililitres of water.
Firstly we will be creating the ratio for the mentioned information. It will be as follows-
Amount of concentrate/Amount of water
The proportion will be -
2/5 = 90/Concentration of water
Concentration of water = 90×5/2
Now perform multiplication in numerator on Right Hand Side of the equation
Concentration of water = 450/2
Then work out the division on Right Hand Side of the equation
Concentration of water = 225 mililitres
Thus, the required amount of water is 225 mililitres.
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Given that $x$ is a positive integer less than 100, how many solutions does the congruence $x 13 \equiv 55 \pmod{34}$ have
There are three solutions to the congruence x+13=55 (mod 34).
What is congruence?Two figures are considered to be 'congruent' if they can be put exactly over each other. When you set one slice of bread on top of the other, you'll see that they're both the same shape and size. The phrase "congruent" refers to having exactly the same form and dimension. When two things or forms superimpose on each other, they are said to be congruent. Their shapes and sizes are identical. Line segments with the same length and angles of the same measure are congruent in the case of geometric forms.
Here,
something equaling 55 (mod 34) is unusual to say the least as 55 mod 34 = 21
do you mean x+13=21 (mod 34) ?
clearly x = 8 + 34k which gives 8, 42, 76 begin less than 100
The congruence x+13=55 (mod 34) has three solutions.
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Q 9-1 Pythagorean Theorem and Trig
A girl is 20 ft. east of her school and her bike is 21 ft. south of the school. How far is she from her bike? Round to the nearest hundredth.
The distance between the girl and her bike is 25.00 ft.
What is distance?Distance is the measure of how far apart two objects, places, or points are. It can be measured in a variety of units, such as miles, kilometers, inches, centimeters, or other units.
The distance between the girl and her bike can be found using the Pythagorean Theorem. The Pythagorean Theorem states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse.
In this case, the girl is 20 ft. east of the school and 21 ft. south of the school. Therefore, the two sides of the triangle are 20 ft. and 21 ft. and the hypotenuse is the distance between the girl and her bike.
Using the Pythagorean Theorem, the hypotenuse is equal to the square root of (20^2 + 21^2) = 25.00 ft.
Therefore, the distance between the girl and her bike is 25.00 ft.
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Pls help due in 5 mins
The given algebraic equation can be written in many ways as shown.
What is algebraic equation?The term "algebraic equation" refers to a formulation of the equality of two expressions using the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extraction of a root on a set of variables.
Solution:-
-5x-15+25x-30
it can be written as
-5(x+3-5x+6)
20x-45
5(4x-9)
and also
-5(9-4x)
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Find the equation that is equivalent to [tex]-5x-15+25x-30[/tex].
First, complete arithmetic operations on linear equations [tex]-5x-15+25x-30[/tex]
*Remember : how to complete arithmetic operations on linear equations, grouping terms with the same variable and then adding them up
[tex]-5x-15+25x-30 = -5x+25x-15-30=20x-45[/tex]
Then, find the common factors of [tex]20x[/tex] and [tex]-45[/tex].
Both have the same factor is [tex]-5[/tex].
Use the distributive property to find the equation that is equivalent.
[tex]20x-45=-5(\frac{20x}{-5}-\frac{45}{-5} )=-5(-4x-(-9))=-5(-4x+9)[/tex]
So, [tex]-5x-15+25x-30[/tex] equivalent to [tex]-5(-4x+9)[/tex]
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Which expression is equivalent to 4 - 10 (9m – 7:)
0-3 - 90m
O 42 – 54m
O 74 - 90m
O-7 - 54m
The correct choice will be 74 - 90m
Operation with parenthee ,5 number , two different operation and ha a value of 20
The equation is (5 x 2) - (5 + 5) = 20
The given equation can be solved by performing the operations within the parentheses first.
First, 5 x 2 = 10, then 5 + 5 = 10.
Then, the next step is to subtract the second set of parentheses from the first set, 10 - 10 = 0.
Finally, we can see that 0 + 20 = 20.
In this equation, the operation of multiplication and addition are used and the final value is 20.
The equation is (5 x 2) - (5 + 5) = 20
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Complete Question is -
solve the following mathematical operation that involves parentheses, five numbers, two different operations and has a value of 20?
Can you help me with this
Answer:
I have graphed a line with a slope of 3/5 and attached a screenshot in the explanation.
Step-by-step explanation:
Complete the table with values for x or y that make this equation true : 3x+y=15.
The table with values for x or y that make this equation true : 3x + y = 15 are
x 2 4 6 0 3 5 7/3
y 9 3 -3 15 6 0 8
What is solving an equation?
One-step equations can be solved in four different ways: by adding, subtracting, multiplying, and dividing. In an equation, both sides will remain equal if we add the same amount to each side.
Consider, the given equation: 3x + y = 15
We have to complete the given table for the values of x and y.
Plug x = 2 in the given equation.
⇒ 3(2) + y = 15
6 + y = 16
y = 9
Plug y = 3 in the given equation.
3x + 3 = 15
3x = 12
x = 4
Plug x = 6 in the given equation.
3(6) + y = 15
18 + y = 15
y = -3
Plug x = 0 in the given equation.
3(0) + y = 15
y = 15
Plug x = 3 in the given equation.
3(3) + y = 15
9 + y = 15
y = 6
Plug y = 0 in the given equation.
3x + 0 = 15
3x = 15
x = 5
Plug y = 8 in the given equation.
3x + 8 = 15
3x = 7
x = 7/3
Hence, the table with values for x or y that make this equation true : 3x+y=15 are
x 2 4 6 0 3 5 7/3
y 9 3 -3 15 6 0 8
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A rectangle has a perimeter of 16 centimeters. The lengths of the sides of the rectangle are between 1 centimeter and 7 centimeters. If x represents the length of a side of the rectangle, then the rectangle's area is represented by x(8-x) square centimeters. Suppose a square is constructed to have the same area as this rectangle. The length of a side of the square is represented by centimeters. What is the range of possible perimeters of the square? Round answers to the nearest hundredth of a centimeter.
The range of possible perimeters of the square=10.583
What is area of a rectangle?Area of a rectangle (A) is the product of its length (l) and width (w).
A= l. w
here, we have,
A rectangle has a perimeter of 16 centimeters.
The lengths of the sides of the rectangle are between 1 centimeter and 7 centimeters.
let, x represents the length of a side of the rectangle,
then the rectangle's area is represented by x(8-x) square centimeters.
i.e. area of square = 8x-x^2
the side = √x(8-x)
perimeter= 4×√x(8-x)
Hence, the range of possible perimeters of the square=10.583
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The scatter plot shows the number of strawbernes that have been picked on the farm during the month of February.
Part A Using computer software, a correlation coefficient of 0. 01 was calculated Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points)
Part B. Instead of comparing the number of strawberries picked and the day in February, write a scenario that would be a causal relationship for strawberries picked on the farm (5 points)
There is a relationship between the numbers of strawberries gathered and the amount of rainfall that can be found in a model (function).
What is a Scatter Plot?A scatter plot with a trendline along which the data points are situated can be used to demonstrate the relationship between correlated variables.
Indicating a positive correlation is when the trendline slopes higher from left to right, while the opposite is true.
Part A:
The correlation coefficient of r = 0.1 is valid based on the provided scatter plot.
Part B:
The independent variable (the explanatory variable) is the cause of the dependent variable in a causal connection.
As a result, you need to identify a plausible factor that can influence the number of strawberries collected.
The week before harvest, I could picture how much it would rain.
Hence, There is a relationship between the number of strawberries gathered and the amount of rainfall that can be found in a model (function).
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Using a number line, find both the intersection and the union of the following
intervals:
(-∞,2) and [0,∞)
The union of the intervals is (-∞,∞)
The intersection of the intervals is [0,2)
Hope this helped!
2. Use the Pythagorean Theorem to find x. Show your work!
The value of x using Pythagorean theorem is 14.05 units
What is an equation?An equation shows how two or more numbers and variables are related to each other.
Pythagoras theorem shows the relationship between the sides of a right angled triangle. It is given by:
hypotenuse² = adjacent² + opposite²
In the diagram, using Pythagoras theorem:
22² = (x + 1)² + (x + 2)²
484 = x² + 2x + 1 + (x² + 4x + 4)
2x² + 6x + 5 = 484
2x² + 6x - 479 = 0
x = 14.05
The value of x is 14.05 units
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What is the degree of the polynomial 5x³ 4x² 7x?
The polynomial 5x³ 4x² 7x has three terms, with the highest degree being 3, which makes the degree of the polynomial 3. The polynomial can be written as 5x³ + 4x² + 7x.
1. Identify the polynomial: 5x³ + 4x² + 7x
2. Count the number of terms: 3
3. Find the highest degree (the largest exponent): 3
4. The degree of the polynomial is 3.
The degree of a polynomial is the highest degree of its terms. A polynomial is a mathematical expression consisting of one or more terms with coefficients and exponents. In this case, the polynomial is 5x³ + 4x² + 7x. This polynomial has three terms, and the highest degree is 3, which makes the degree of the polynomial 3. This means that the largest exponent of the terms is 3. To calculate the degree of a polynomial, simply count the number of terms and identify the highest degree, which is the largest exponent. If the polynomial has only one term, then the degree is the exponent of that term
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50PTS 50 PTS (DONT explain just answer please)
Answer: 17
Step-by-step explanation:
Answer:
x = 17°
Step-by-step explanation:
The given angles are,
→ 6x + 8
→ 4x + 2
Now we have to,
→ find the required value of x.
Forming the equation,
→ (6x + 8) + (4x + 2) = 180°
{As two angles in a straight line is 180°}
Then the value of x will be,
→ (6x + 8) + (4x + 2) = 180°
→ 6x + 4x + 8 + 2 = 180°
→ 10x + 10 = 180°
→ 10x = 180° - 10
→ x = 170/10
→ [ x = 17° ]
Hence, the value of x is 17°.
6 less than 3 times a number 42 what is the number
Answer: -120
6 less than is 6 - and 3 times a number 42 is 3 x 42 so...
6 - (3 x 42) = -120
6(x+4)=30
how do i solve this?