The following equation's linear components have no solutions.
Because they contain the same variable term on one side of the equation but distinct constant values on the other, 5-4x-7-10x=-8x-4-6x-10.
What does linear equation mean?A linear polynomial over a field with zero coefficients can be used to create a linear equation. The answers to such an equation are the numbers that, when the unknowns are replaced, make the equality true.
This particular situation, in which the variable is accurately referred to as the unknown, is commonly referred to as a "linear equation."
In the case of two variables, each solution can be thought of as a point's Cartesian coordinates on the Euclidean plane. The answers to a linear equation result in a line.
Given is an equation that reads 5-4x-7-10x=-8x-4-6x-10 and 14x-2=14x-14.
A linear equation has no solutions if both sides of the equation have different constant values but the same variable term.
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miguel has 30,000 in his savings account. sam has 40,000 in hissavings account. whatis the ratio of miguel savings to sam saving? what is the ratio of sam savings to miguel savings? what fraction of miguel savings is sam savings? what fraction of sam savings to miguel saving?
What is the inverse of f(x)=-2+(x+2)^2
Answer:f - 1 ( x ) to show the final answer. Verify if f−1(x)=x2+1 f - 1 ( x ) = x 2 + 1 is the inverse of f(x)=2x−2 f ( x ) = 2 x - 2 .
Quick loans will loan you $250 with the understanding that you will repay them $295 in two weeks. What is the APR for this loan?
The APR for this loan is equal to 468%.
What is APR?In Mathematics, APR is an abbreviation for annual percentage rate and it can be defined as a measure of an amount of money based on a yearly rate of interest, which a borrower must pay on a loan or credit card.
Mathematically, the annual percentage rate (APR) of a loan can be calculated by using this formula:
APR = [((simple interest/principal)/n) × 365] × 100
Where:
n represents the number of days.
Note: n is equal to 14 days (2 weeks).
Next, we would determine the FC for this loan as follows;
FC = $295 - $250
FC = $45.
For the two-week period, we have;
Interest = 45/250
Interest = 0.18.
Therefore, the annual percentage rate (APR) of this loan is given by;
APR = 0.18 × 52/2
APR = 468%.
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I need help with this. Can someone help?
f(x) = -x²
Find f(-10)
plug in -10 for x in -x^2
-1(-10)^2 =
10^2 = 100
Cookies baked 375 degrees for 12 minutes. Find the gas unit, g, used if t = time in minutes:
375 - 15t
g = t
To find the gas unit used in baking of cookies, we plug the values into the given equation: g = t, g = 12. Thus, the gas unit used is 12.
What is gas unit?Organic gas usage or production is measured in "gas units." It is frequently employed to estimate the price of natural gas for a predetermined time period, such as a month or a year.
British thermal units (BTUs), a measure of the energy content of natural gas, are the industry standard for quantifying this fuel. One BTU is the amount of heat necessary to raise the temperature of one pound of water by one degree Fahrenheit.
To compute the gas unit for a given time period, the total amount of natural gas used or generated is first converted into BTUs.
How to solve?
To find the gas unit used, we plug the values into the given equation:
g = t, g = 12. Thus, the gas unit used is 12.
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The area A if rectangle is represented by the formula A = lw where l is the length and w is width. The length of the rectangle is 5. What is the equation to that?
Answer:
black and white striped bass
is 7x a linear expression
Answer: Yes, it is linear expression
Step-by-step explanation:
The equation is y=mx + b
Here we have 7x, which we have the slope
We don't see the y-intercept, so it is 0
There are about 34 million gallon of water in Reervoir A and about 38 million gallon in Reervoir B. During a drought, Reervoir A loe about 0. 8 million gallon per month and Reervoir B loe about 1. 1 million gallon per month. After how many month will the reervoir contain the ame amount of water?
The water levels in reservoirs A and B, which initially had 34 million gallon and 38 million gallon water, respectively, will be equal after 13.3 months.
What is expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. No, a mathematical equation cannot be solved since it lacks the "equal to" sign $(=)$, but it can be simplified. Mathematical expressions consist of at least two numbers or variables, at least one math operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Here,
Let the number of months be x.
34-0.8x=38-1.1x
1.1x-0.8x=38-34
0.3x=4
x=40/3
x=13.33 months
After 13.3 months, The reservoir A and reservoir B will have same amount of water when initially they have 34 million gallon water and 38 million gallon water respectively.
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find the distance from point (-3,7) to the line y=1/3x-2. round your answer to the nearest 10th if necessary
The distance between the point (-3,7) and the line y=1/3x-2 is 11.0 units
How to determine the distance?Distance shows how long it is between a point and another
We can do this by drawing a segment that is perpendicular to the line
the given equation is 1/3x-2
The slope here is 1/3 That is slope =3
From the equation of slope=intercept form = y=mx+c
put m=3 to have
y=3x+c
From the given coordinates (-3,7)
7=3(-3)+c
7+9=c
c=16
This implies that y=3x+16
Find the line where the equation intersect the line
⇒3x+16=1/3x-2
Rearrange the equation
8x/3=-18
Make x the subject. x=6.75
Recall that y=1/3(6.75)-2
y=2.25
The second coordinates are (6.75,2.25) and first (-3,7)
The distance is given by
d=[tex]\sqrt({X_{2}-X_{1})^{2} +(Y_{2}-Y_{1} )^{2} }[/tex]
d= √(6.75+3)²+(2.25-7)²
d=√9.75²+(-4.75)²
d=√95.0625+22.5625
d=√117.625
d=10.8455059817
Therefore the distance is 11 units
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Identify the graph h(x)=-x^2-7
Compare the graph of h to the graph of f(x)=x^2
The function h(x) is the result of two rigid transformations, reflecting the function f(x) about the x-axis and translating it vertically 7 units down.
What is the difference between the graphs of two functions?
In this problem we must determine the difference between the quadratic functions f(x) = x² and h(x) = - x² - 7, we can infer the change necessary to derive h(x) by means of rigid transformations, that is, transformations applied on a function such that the features of the functions are conserved.
All the rigid transformations required to transform f(x) into h(x) are listed below:
Reflection about x-axis: f'(x) = - x²Vertical translation: 7 units down: h(x) = - x² - 7Now we proceed to plot the two functions. From the graph we noticed that h(x) is the result of reflecting f(x) about the x-axis and translating 7 units in the -y direction.
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To make a cake, Roe needed 2 cup of ugar. Thi i 3 cup le than the amount of flour, f , he needed for the cake. Write a ubtraction equation that could be ued to find the amount of flour he needed for the cake
He might use the equation y = (3/2) x to determine how much flour he required for the cake.
What is Equation?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including linear, quadratic, cubic, etc.
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. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.
According to our question-
Accordingly, we require 2.3 cups of sugar for every cup of flour.
It also means that you need 3 1/2 cups of flour for every cup of sugar.
Therefore, if x cups of sugar and y cups of flour, respectively, are used:
y = (3/2) x.
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identities included in Venn diagram
Answer:
Step-by-step explanation:
Aub, probability, set theory and discrete math?
The buying and selling rates of U.S. dollar ($) in a day are - Rs 115.25 and Rs 116.5 respectively. How many dollars should be bought and sold to have the profit of $ 10? Find it.
The number of dollars that should be bought and sold to have the profit of $10 is 8.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, the buying and selling rates of U.S. dollar ($) in a day are - Rs 115.25 and Rs 116.5 respectively. Let the dollars bought be illustrated as x.
This will be:
116.5x - 115.25x = 10
1.25x = 10
Divide
x = 10 / 1.25
x = 8
The number is 8.
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Hello please solve this with steps
Identify the number of solutions Or zeros of
F(x)=12x-32x^2+40-x^3
Answer:
3 solutions
Step-by-step explanation:
You want to know the number of solutions (zeros) of the cubic function ...
f(x) = -x³ -32x² +12x +40
Cubic functionAny 3rd-degree polynomial function has 3 zeros. (This is the fundamental theorem of algebra.)
Signs of rootsDescartes' rule of signs says the one sign change in the coefficients (--++) means there is one positive real root. On its face, this means there will be 0 or 2 negative real roots.
Values of rootsThe value of f(0) is positive (40), and the value of f(-1) is negative (-3), so there must be two negative real roots. (F(x) is positive for very large negative x, so there must be two x-intercepts for x < 0.)
A graph shows the roots to be irrational. The three real roots are approximately ...
−32.3328769399−0.9582093098981.29108624985__
Additional comment
The "steps" are to find the degree of the polynomial. It is 3, so there are 3 zeros. It is not complicated.
What is more complicated is finding their values. The checks we described above can tell whether there are 1 or 3 real roots. (An odd-degree polynomial always has at least 1 real root.) A graph is helpful for finding whether the roots are real or complex, rational or irrational.
Here, any rational roots must be integer divisors of the constant term, 40. We know the root between 0 and -1 is irrational, so all of them are.
The above root values were obtained by Newton's Method iteration, starting from the approximate values shown on the graph.
How do I do thi (with tep i preferred):
Suppoe you know that x = -2 i a zero of p(x) = 4x^3 10x^2 - 6x - 20. Ue ynthetic diviion to factor the polynomial and find the remaining zero
In polynomial, x - 2 is not a factor f(x) [By factor theorem]
What is Polynomials ?
Sums of terms with the pattern kxn—where k is any positive integer and n is an arbitrary number—are known as polynomials.
For instance, the polynomial 3x+2x-5. a description of polynomials. In this video, basic terms like terms, degrees, standard form, monomial, binomial, and trinomial are covered.
p(x) = 4x^3 + 10x^2 - 6x - 20
put x = -2 in equation
p(x) = 4 * (-2)³ + 10 * ( -2)² - 6 * -2 - 20
= 4 * -8 + 10 * 4 + 12 - 20
= -32 + 40 + 12 - 20
= 52 - 52
= - 2
p(x) ≠ 0
Which is not equal to zero
x - 2 is not a factor f(x) [By factor theorem]
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The equation, 687.5 = 550(1 + 0.05t), represents the amount of money earned on a simple interest savings account. What does the value 550 represent?
The value 550 represents the initial balance in the account, which means the account started with $550.
The value 550 represents the final balance in the account, which means the account balance ended with $550.
The value 550 represents the final balance in the account, which means the account balance started with $550.
The value 550 represents the amount of interest earned, which means $550 was added to the initial balance.
Answer:
(a) The value 550 represents the initial balance in the account, which means the account started with $550.
Step-by-step explanation:
You want the meaning of 550 in the simple interest expression 687.5 = 550(1 + 0.05t).
Simple interestThe formula for computing the amount A of an account earning simple interest at annual rate r on its initial balance P for t years is ...
A = P(1 +rt)
Comparing this formula to the given equation, we see ...
687.5 = 550(1 +0.05t)
A = 687.5P = 550 . . . . the initial balancer = 0.05The initial balance (starting amount) was 550.
Which pairs of rectangles are similar polygons? select similar or not similar for each pair of rectangles. similar not similar a and b similar â€"" a and b not similar â€"" a and b b and c similar â€"" b and c not similar â€"" b and c a and c similar â€"" a and c not similar â€"" a and c
The polygons from the figure given below that are similar are Polygon B and Polygon C .
In the question ,
it is given that there are three polygons ,
we have to check which polygons are similar ,
to find the similarity we compare the length of all the polygons .
Let us first check for Polygon A and Polygon B ,
105/120 = 7/8
80/90 = 8/9.
and 105/120 ≠ 80/90 ,
So , Sides are not in proportion for Polygons A and B.
Hence , the Polygons A and B are not Similar.
Let us check for Polygon A and C .
105/100 = 21/20
80/75 = 16/15.
and 105/100 ≠ 80/75
So , sides are not in proportion for Polygons A and C.
Hence , the Polygons A and C are Non Similar.
Now for Polygon B and C .
120/100 = 6/5.
90/75 = 6/5.
and 120/100 = 90/75 = 6/5
So , Sides are in proportion for Polygons B and C .
Hence , the Polygons B and Polygon C are Similar.
Therefore , the Polygon B and Polygon C are similar .
The given question is incomplete , the complete question is
Which pairs of rectangles are similar polygons ? select similar or not similar for each pair of rectangles from the figure given below .
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Are the following two functions inverse of one another ? If so tell why.
Answer: No, they are not inverses of one another.
=======================================================
Explanation:
There are at least 3 methods we can use to prove the functions aren't inverses of each other.
------------------------------------
Method 1
Let's say we plugged x = 0 into f(x).
[tex]f(\text{x}) = 2\text{x}+1\\\\f(0) = 2*0+1\\\\f(0) = 1\\\\[/tex]
The input x = 0 leads to the output y = 1.
Then let's treat y = 1 as the input of the g(x) function, so we'll plug x = 1 into here.
[tex]g(\text{x}) = -2\text{x}-1\\\\g(1) = -2*1-1\\\\g(1) = -3\\\\[/tex]
If g(x) was the inverse of f(x), then the g(1) output value should be 0 to get us back where we started. However, we get an output of -3 instead.
This is sufficient evidence to conclude that f(x) and g(x) are not inverses of each other. We only need one counter-example to disprove this claim.
------------------------------------
Method 2
Recall that if f(x) and g(x) are inverses of each other, then we have the following two properties
f(g(x)) = xg(f(x)) = xThe left hand side of each equation involves the concept of "function composition".
Let's see what f(g(x)) is equal to in this case.
[tex]f(\text{x}) = 2\text{x}+1\\\\f(g(\text{x})) = 2(g(\text{x}))+1\\\\f(g(\text{x})) = 2(-2\text{x}-1)+1\\\\f(g(\text{x})) = -4\text{x}-2+1\\\\f(g(\text{x})) = -4\text{x}-1\\\\[/tex]
We do not get an output of simply x only, so this is another way to see how we don't have inverses.
Through similar steps, you should find that [tex]g(f(\text{x})) = -4\text{x}-3[/tex] which is further confirmation that f(x) and g(x) are not inverses of each other.
------------------------------------
Method 3
Let's ignore g(x) for now. We'll start with f(x) and find the inverse of it.
The process involves this basic outline:
Replace f(x) with ySwap x and ySolve for ySo,
[tex]f(\text{x}) = 2\text{x}+1\\\\\text{y} = 2\text{x}+1\\\\\text{x} = 2\text{y}+1\\\\\text{x}-1 = 2\text{y}\\\\\text{y} = \frac{\text{x}-1}{2}\\\\f^{-1}(x) = \frac{\text{x}-1}{2}\\\\[/tex]
Unfortunately we do not end up with -2x-1 as the actual inverse.
So if [tex]g(\text{x}) = \frac{\text{x}-1}{2}[/tex] was the case, then f(x) and g(x) would be inverses of each other.
Through similar steps, the inverse of [tex]g(\text{x}) = -2\text{x}-1\\\\[/tex] is [tex]g^{-1}(\text{x}) = -\frac{\text{x}+1}{2}\\\\[/tex]
Maya wants to put fencing around her
rectangular backyard. The width of the yard
is 55 feet and the length is 75 feet. How
many feet of fencing does Maya need?
3) 260
7) 130
6) 3,905
9) 4,125
Answer:
3) 260 ft
Step-by-step explanation:
You want the perimeter of a rectangle 55 ft by 75 ft.
PerimeterThe equation for the perimeter of a rectangle is ...
P = 2(L +W)
ApplicationFor the given rectangle, the perimeter is ...
P = 2(75 ft +55 ft) = 2(130 ft) = 260 ft
Maya needs 260 feet of fencing to put fence around her rectangular yard.
What is the percent of increase from 25 to 49?
In right the hypotenuse, 117 cm and tan P= 0.51 Calculate
side lengths p and q to the nearest centimetre and all three interior angles to
the nearest degree.
For the given right triangle the measure of the remaining angles are 2.9° and 87.1° and the remaining sides are 5.9 cm and 116.85 cm respectively.
What are trigonometric ratios?The trigonometric ratios are defined for a right angled triangle.
The example of these ratios are sin, cos, tan, cosec, sec and cot.
The trigonometric ratios are useful in determining the heights and distances of the large objects.
Given that,
In a right triangle tan(P) = 0.051
And, hypotenuse = 117 cm.
The given data can be shown in the diagram as follows,
From the diagram it can be written as,
tan(P) = 0.051
=> P = 2.9°
Then, ∠Q = 180° - (90° + 2.9°)
= 87.1°
Now, Sin(P) = p/117
=> Sin(2.9°) = p/117
=> p = 117 × Sin(2.9°)
= 5.9
Similarly, Cos(P) = q/117
=> Cos(2.9°) = q/117
=> q = 117 × Cos(2.9°)
= 116.85
Hence, the measure of the remaining angles are 2.9° and 87.1° and the remaining sides are 5.9 cm and 116.85 cm respectively.
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What is the area of this square? 9 Meters and 9 Meters
Answer:
81
Step-by-step explanation:
Area is multiplying all side
9 x 9 = 81
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1/3x+3/4+2/3x-1/4-2/3x=0.66666...x+0.5
You and your friend are selling raffle tickets for a new laptop. You sell 14 more tickets than your friend sells. Together, you and your friend sell 58 tickets.
a. Write a system of linear equations that represents this situation. Let $x$x represent the number of tickets you sell and y$y$y represent the number of tickets your friend sells.
System of equations:
Question 2
b. How many tickets do each of you sell?
You sell tickets and your friend sells tickets.
Answer:
x = you sold
y = friend sold
---
x + y = 58
x = y + 14
---
put the system of linear equations into the standard form:
---
x + y = 58
x - y = 14
x= you sold 36
y= friend sold 22
Step-by-step explanation:
ALL questions are for this situation:
You are standing on a ledge and throw a ball from 10 feet above the ground. The speed the ball leaves your hand is 16 feet per second and the acceleration of gravity is -16 feet per second squared.
1. How many seconds does it take to reach the highest point (vertex)?
It takes 1 second for the ball to reach its highest point.
What is acceleration of gravity?Acceleration of gravity is the acceleration by which earth pulls
objects towards itself. Acceleration is the rate of change of speed.
Given,
The initial velocity of the ball = 16 feet/second
The initial height of the ball = 10 feet
The ball will first travel upward with an initial velocity of 16 feet/second
and the ball will reach a height of x feet from the point of release. After
that the ball will travel a total downward distance of (10+16) = 26 feet.
At highest point, velocity=0.
Applying, v = u + at
0 = 16 + (-16)t
t = 16/16
t = 1 second
Hence, the ball will take 1 second to reach the highest point.
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A fraction and a whole number with a product greater than 1
Answer: 1/2 * 6 = 3
Step-by-step explanation:
function rule to find f(3)
Answer:
f(3)=25
Step-by-step explanation:
f(3)=11(3)-8
f(3)=33-8
f(3)=25
Answer:
f(3)=25
Step-by-step explanation:
substitute 3 into the equation for x.
f(3)=11(3)-8
11×3=33 so,
33-8=25
f(3)=25
What is the greatest common factor of the terms in the polynomial 12x4 + 27x3 + 6x2?3x3x26x26x4.
The greatest common factor amongst the three factors is 3x² as it has a degree of 2 and a coefficient greater than 1.
What is polynomial?Sums of terms of the form k-x^n, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The concepts degree, standard form, monomial, binomial, and trinomial are all covered in this video. An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
Here,
The polynomial=12x⁴+27x³+6x²
On simplifying,
=3x²(4x²+9x+2)
With a degree of 2 and a coefficient larger than 1, 3x² has the highest common factor of the three components.
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Which equation represents this statement?
3 times the sum of 4 and a number is 18.
3 + 4n = 18
3⋅4+n=18
3n + 4 = 18
3(n+4)=18
Answer:
3(n+4)=18
Step-by-step explanation:
Answer:3(n+4)=18
Step-by-step explanation:
The sum of 4 and a number is 4+n
Three times the sum of 4 and a number is 3(4+n)
is means equal sign
3(n+4)=18