| y - 4 | = | y + 10|
Show how to solve too !!
Answers
Answer:
y = -3
Step-by-step explanation:
You want the solution to the absolute value equation | y-4 | = | y+10 |.
Absolute valueThe absolute value function ...
f(x) = | x |
is piece-wise defined as ...
[tex]f(x)=\begin{cases}-x&\text{for }x < 0\\x&\text{for }x\ge 0\end{cases}[/tex]
That is, the function is defined differently for argument values less than 0.
Given relationThe above observation regarding the absolute value function means the nature of the given equation changes where the absolute value arguments are zero. Those values are ...
y -4 = 0 ⇒ y = 4
y +10 = 0 ⇒ y = -10
In other words, the points y = -10 and y = 4 divide the domain of the equation into three parts. The behavior will be different in each of those parts.
To solve the equation, we must examine each region of the domain for possible solutions.
y < -10When y < -10, both of the absolute value functions change the sign of their argument. Then the equation is ...
-(y -4) = -(y +10)
Adding y to both sides of this equation gives ...
4 = -10 . . . . . false
This means there is no solution to the equation in the region y < -10.
-10 ≤ y < 4When -10 ≤ y < 4, the absolute value function |y -4| changes the sign of its argument, but the other function does not. In this region, the equation becomes ...
-(y -4) = (y +10)
-6 = 2y . . . . . . . . . add y-10 to both sides
-3 = y . . . . . . . . divide by 2. This value is in the region -10 ≤ y < 4.
The solution to the equation is y = -3.
4 ≤ yWhen 4 ≤ y, neither absolute value function changes the sign of its argument. In this region the equation becomes ...
y -4 = y +10
Subtracting y from both sides of this equation gives ...
-4 = 10 . . . . . false
This means there is no solution to the equation in the region 4 ≤ y.
__
Additional comment
The first attached graph shows the given equation rewritten as two functions. The solution is where those functions have equal values: the point(s) where the graphs intersect.
We often find it more convenient to rewrite equations like this to the form f(x) = 0. Here, that might mean we define ...
f(x) = |y -4| -|y +10|
Then the solution is found on the graph at the x-intercepts. The graph in the second attachment shows this solution, and clearly shows the changes in behavior at x = -10 and x = 4.
Related Questions
find the quotient 17 ÷ 6 8/10
Answers
The ratio of EQUATION the outcome is (17/6)/(8/10) = 3.5416667.
What in mathematics is a quotient?The quotient is the result of dividing two numbers by each other. As in the case of 8 4 = 2, when the division produced the number 2, the outcome is the quotient. The dividend is 8 and the divisor is 4.
based on the available facts;
Divide: 17/6 : 8/10
= 17/6· 10/8
= 17 · 10/6 · 8
= 170/48
= 85/ 24
= 85/24
When two fractions are divided, the first fraction is multiplied by the second fraction's reciprocal value. Finding the reciprocal of the second fraction is the first sub-step. For example, the reciprocal of 8/10 is 10/8. Multiply the two numerators after that. Multiply the two denominators after that. The intermediate step that comes after canceling by a common factor of 2 yields 85/24.
Therefore, eight tenths of seventeen sixths equal eighty-five twenty-fourths.
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A researcher who is interested in the behavior of chimps believes that temperature is related to aggression in this species of animal. She goes out to her local zoo during a particular weekend and adjusts the temperature of their climate-controlled habitat to 50-degrees, 70-degrees and 90-degrees Fahrenheit over the course of three days, noting the number of aggressive acts she observes at each temperature level.
A) What is the independent variable?
B) What is the dependent variable?
C) Is the dependent variable discrete or continuous?
D) What scale of measurement (nominal, ordinal, interval or ratio) is used to measure the dependent variable? What research method is being used (experimental or observational), and why?
Answers
The experimental research conducted by the scientist takes into account the following factors:
a)The change in temperature is the independent variable.
b) The effect of temperature on the chimp's act of aggression is the dependent variable.
c)The dependent variable is continuous.
d)The scale of measurement used to measure the dependent variable is interval.
e) The research method being used here is experimental.
In the above experiment the researcher wants to see the change in the aggression of the chimp when there is a change in temperature in the zoo.
In this experiment there are two variables that are being used, independent and dependent.The independent variable is the change in temperature as it is regulated by the researcher.The dependent variable is the change in the aggressive nature of the chimps, as the change in nature is directly affected by the change in temperature. The dependent variable(mood of the chimp) is continuous, as the value cannot be defined separately.Since the data is not discreet but continuous , the scale of measurement used is interval.The research method being used is experimental , because the researcher is controlling the variable temperature to see the effect of the temperature change on the chimps. So the researcher is directly experimenting on the chimps by changing an external factor. So the experiment is not observational.To learn more about research experiment and variables:
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62° 18’23” + 21° 47’57” =
Answers
Answer:
Note: Numbers are blocked in groups of two digits for convenience only. In using this table you can read numbers of any number of digits in any way you want.
Step-by-step explanation:
09/14/2022 9 ‑ 10 ‑ 20 ‑ 22 ‑ 52 25 3 $206 Million Roll
09/12/2022 6 ‑ 14 ‑ 16 ‑ 34 ‑ 66 25 3 $193 Million Roll
09/10/2022 38 ‑ 42 ‑ 56 ‑ 68 ‑ 69 4 2 $186 Million Roll
Scott rented a truck for one day. There was a base fee of $18.99, and there was an additional charge of 92 cents for each mile driven. Scott had to pay $150.55 when he returned the truck. For how many miles did he drive the truck?
I need to find how many miles
Answers
Answer:
143 miles
Step-by-step explanation:
Let x = number of miles
Let y = total cost
150.55 = .92x + 18.99 Multiply all the way through by 100 to clear the decimal
15055 = 92x + 1899 Subtract 1899 from both sides
13156 = 92x Divide both sides by 92
143 = x
beth bought 16 gallons of gas for $46.72. What was the unit price of the gas
Answers
Answer:
$2.92 per gallon of gas
Step-by-step explanation:
divide $46.72 and 16
$46.72 ÷ 16 gallons of gas = $2.92
$2.92 per gallon of gas
Find the circumference and area of a circle with radius 7 cm. Express your answer in terms of π.
Answers
Answer:
Circumference = 2πr=2×
7
22
×7=44 cm
Area = πr
2
=
7
22
×7×7=154 cm
2
Answer:
With a circle with radius 7 cm, the circumference of given circle is 14π (cm) and the area is 49π (cm²).
Step-by-step explanation:
Given: radius = 7 cm
Circumference of a circle: C = 2πr
C = 2πr
Substitute given value radius.
C = 2π(7)
Multiply 7 and 2.
C = 14π cm.
Area of a circle: A = πr²
A = πr²
Substitute given value radius.
A = π(7)²
Square the 7.
A = 49π cm²
Is this argument inductive or deductive?
"Whenever I get off at Valencia rather than McBean, I get to campus faster. So Valencia must be
the faster route to school."
Answers
Answer:
Step-by-step explanation:
Indutivo
4x^2-7; x= -2
4x^2-7x =
Answers
Step-by-step explanation:
f(x) = 4x² - 7 , x = -2
= 4x² - 7
= 4.(-2)² - 7
= 4.4 - 7
= 16 - 7
= 9
Find the missing coordinate (x,5) and (3,3) m= 1/2
Answers
The missing coordinate of the points is 7
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the missing coordinate?The given parameters are
Slope, m = 1/2
Points (x1, y1) = (x, 5) and (x2, y2) = (3, 3)
The slope of a linear equation is calculated as
m = (y2 - y1)/(x2 - x1)
So, we have
1/2 = (3- 5)/(3 - x)
Evaluate the differences
So, we have
1/2 = -2/(3 - x)
Cross multiply
So, we have
3 - x = -4
This gives
x = 3 + 4
Evaluate the sum
x = 7
Hence, the missing coordinate of the points is 7
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solve for x please
4 / x • 26 / 2
Answers
Answer:
x = 3.25
Step-by-step explanation:
Use the Rule of 3 to solve this
Work in picture
Janayea wanted to change 0.079 to a percent. She changed it to 79%. Which statement is true?
A) Janayea Is Correct?
B) Janayea should have moved the decimal point 0.079 two places to the left to get 0.00079%.
C) Janayea should have moved the decimal point of 0.079 two places to the right to get 7.9%.
Answers
Answer:
Janayea should have moved the decimal point 0.079 two places to the left to get 0.00079%.
Thunder from a bolt of lightning travels 1/10 mile in 1/2 second. At this rate, how many miles can it travel in one second?
Answers
Answer:
1/5 mile
Step-by-step explanation:
1/10 mile in 1/2 second
This can be written as a ratio:
1/10 mile : 1/2 second
We need the ratio in terms of 1 second, so multiply both numbers in the ratio be 2.
2 × 1/10 mile : 2 × 1/2 second =
= 2/10 mile : 1 second
= 1/5 mile : 1 second
Answer: 1/5 mile
Use an integer to describe the
situations.
6 meters
above sea level
sea level
Answers
An integer to describe 6 meters above the sea level would be [tex]+6[/tex] meters.
As per the question statement, We are supposed to use an integer to describe the following situation "6 meters above sea level".
We assume that sea level is the datum line and anything above that would be positive and below that would be negative.
So 6 meters above the sea level can be described as [tex]=6meters[/tex].
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whats the answer
to 0.75(8+e)=2-1.25e
Answers
The value of e from the given equation is -1.78
Linear functionsLinear functions are function that has a leading degree of 1
Given the expression below;
0.75(8+e)=2-1.25e
Expand to have;
0.75(8) + 0.75e = 2-1.25e
6 + 0.75e = 2 - 1.5e
6-2 = -1.5e - 0.75e
4 = -2.25e
e = 4/-2.25
e = -1.78
Hence the value of e from the given equation is -1.78
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Divide the fractions. ½÷⅞
Answers
Answer:1/2 / 7/8 = 8/14 = 4/7
Step-by-step explanation: switch the numbers on the second fraction and multiply. 1 * 8 = 8 2 * 7 = 14, 8/14 simplify: 4/7
In 2019, Company A purchased a commercial building with 8 retail units for $4,200,000. In 2021, Company A decided to sell this building for $4,500,000. Interpret the change as a percentage. Round to the nearest hundredth.
Answers
The change as a percentage is 6.7 %
How to calculate the percentage change ?The price of the building in the year 2021 is $4,200,00
The price of the building in 2021 is $4,500,000
Therefore the percentage change can be calculated as follows
= 4,500,000 - 4,200,000/4,500,000 × 100
= 300,000/4,500,000 × 100
= 0.066 × 100
= 6.7 %
Hence the percentage change is 6.7%
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Solve For x
[tex] \tt \red{4x + 2 = -8}[/tex]
Thank uh ~
Answers
Step by step explanation
Answer:
The answer will be -5/2.
Step-by-step explanation:
[tex]4x + 2 = - 8 \\ subtracting \: 2 \: from \: each \: sides \: we \: get \\ 4x + 2 - 2 = - 8 - 2 \\ 4x = - 10 \\ diving \: both \: sides \: by \: 4 \: we \: get \\ \frac{4x}{4} = \frac{ - 10}{4} \\ x = \frac{ - 5 \times 2}{2 \times 2} \\ x = \frac{ - 5}{2} [/tex]
Rectangle ABCD is shown on the grid.
A
(-1,4) 14
3
+2+
4
-6-5-4-312-3₁
(-3-b
B(3,3)
34
C(1-5)
X
What is the area of rectangle ABCD in square units?
O 3√17 square units
O 6√17 square units
O
17 square units
O 34 square units
Answers
well, we know it's a rectangle, so we know the opposite sides are perpendicular, so if we just get say the sides AD as its length and BA as its width, that'd give us its area, since it'll just be AD * BA.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-1}~,~\stackrel{y_1}{4})\qquad D(\stackrel{x_2}{-3}~,~\stackrel{y_2}{-4}) ~\hfill AD=\sqrt{(~~ -3- (-1)~~)^2 + (~~ -4- 4~~)^2} \\\\\\ ~\hfill AD=\sqrt{( -2)^2 + ( -8)^2}\implies \boxed{AD=\sqrt{68}} \\\\\\ B(\stackrel{x_1}{3}~,~\stackrel{y_1}{3})\qquad A(\stackrel{x_2}{-1}~,~\stackrel{y_2}{4}) ~\hfill BA=\sqrt{(~~ -1- 3~~)^2 + (~~ 4- 3~~)^2}[/tex]
[tex]~\hfill BA=\sqrt{( -4)^2 + (1)^2} \implies \boxed{BA=3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Area}}{(\sqrt{68})(3)\implies (\sqrt{2^2\cdot 17})(3)}\implies (2\sqrt{17})( 3)\implies \LARGE \begin{array}{llll} 6\sqrt{17} \end{array}[/tex]
Identify at least two hidden assumptions in the following argument.
I recommend giving to the Charity A because it supports so many worthwhile causes.
Which of the following are hidden assumptions for this argument? Select all that apply.
A. Giving to Charity A is better than giving to Charity B.
B. The money you give is spent on worthwhile causes.
C. Charity A does not support unworthy causes.
D. Charity A supports worthwhile causes.
Answers
Answer:
A, B, C yes
D no
Step-by-step explanation:
A. is a no-brainer. yes, that is indirectly implied.
B. this is compared to D a hidden assumption, that the money you give is guaranteed to be spent on worthwhile causes (not to mention what THAT actually means).
C. this goes combined with B. it is suggested that charity A is not engaging in unworthy causes (again, whatever that means).
D. is not hidden. that is openly said.
I need help answering question 6. I think it’s A) but my teacher told us D) ? What’s the correct answer??
Answers
As indicated below, write the equations of the line passing through the point (2, 4) and parallel to the line whose equation is y = x. Complete your work in the space provided. Part 1: Point-Slope form of the linear equation Part 2: Slope-intercept form of the linear equation Part 3: The general form of the linear equation
Answers
Part 1
[tex]y-4=x-2[/tex]
Part 2
[tex]y=x+2[/tex]
Part 3
[tex]x-y+2=0[/tex]
prove that √ 2 - 1 is irrational
Answers
Answer:
a+b/2b is an rational no. because LHS is always equal to RHS. therefore our assumption is wrong. hence , 2√2-1 is an irrational number.
Evaluate the left hand side to find the value of a in the equation in simplest form.
Answers
The value of a in the equation in the simplest form will be 17 / 6.
We are given an equation:
x³ / x^(1/6) = x^(a)
We need to evaluate the left hand side to find the value of a in the equation in simplest form.
We know that:
x^ (a) / x^ (b) = x^ ( a - b)
Using this, we get that:
x^ (3 - 1/6) = x^ (a)
x^ (17/6) = x^ (a)
By comparing the bases, we get the value of a as:
a = 17 / 6.
Therefore, the value of a in the equation in the simplest form will be 17 / 6.
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What is the simplified form of (-5+21) -(5-31)?
A
-10-i
B
-10+5i
- i
5i
WILL GIVE BRIANLIEST
Answers
Hope this helps
Points A, B, C, D, and E are collinear and in
that order. Find AC.if AE = x + 50 and
CE = x + 32.
Answers
Points A, B, C, D, and E are collinear and in that order. The value of Ac is 18.
According to the segment addition postulate, if two points on a line segment, A and C, are given, a third point, B, will only be found on line segment AC if and only if the distances between the points satisfy the conditions of the equation AB + BC = AC.
Keep in mind that a line segment is a portion of a line that has two distinct end points. There are many points between the two end points that make up the object.
The segment addition postulate can be stated more simply by saying that if point B lies on line segment AC, then AB + BC will equal AC.
by the segment addition postulate,
AC + CE = AE so AC = AE - CE
AC = (x+50) - (x+32)
AC = x+50-x-32
AC = 18
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Simplifiy the expression 1/2 cubed - 6 divide √64
Answers
Answer:-0.625
Step-by-step explanation:
The 5000 that invested in Fund A returned a 3% profit. The amount that invested in Fund B returned a 10% profit. How much did she invest in Fund B, if both funds together returned a 5% profit?
Answers
The investment in Fund B is $2000.
To understand the given question we first have to understand the logic of percentage and how it affect the return on Investment.
If an investment fund returns a profit on an investment then the profit is calculated by multiplying the investment with the profit(in decimal form).
For Example: If the investment is A and profit is x % then the profit is calculated by:
Profit =A×([tex]\frac{x}{100}[/tex])
Now in the given problem, let us consider the amount of investment into the Fund B be x.
Profit in Fund B=10%
Profit in Fund A is 3%.
Investment in Fund A=$5000
Total profit from both investments=3% of 5000+10% of x
[tex]=\frac{3}{100}\times 5000 + \frac{10}{100}\times x\\ =150+0.1x[/tex]
Now the total investment=5000+x
The combined profit for both the Investments is 150+0.1x
But the combined profit is 5% for both investments.
profit=[tex]5\% of(5000+x)[/tex]
[tex]=\frac{5}{100}\times (5000+x)\\=0.05\times5000+0.05x\\=250+0.05x[/tex]
Now the profit is same, so if we equate both the expressions of profit we get a linear equation in x.
[tex]\therefore 250+0.05x=150+0.1x\\or,250-150=0.1x-0.05x\\or,100=0.05x\\or,x=2000[/tex]
Thus we can conclude that she invested $2000 in the Fund B.
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A sloth travels about 7 feet every minute. Generate the set of ordered pairs for the ratio relationship between the total distance traveled y and the number of minutes x for a total of 1, 2, 3, and 4 minutes.
Answers
Answer:
(1, 7)
(2, 14)
(3, 21)
(4, 28)
Step-by-step explanation:
What is the slope of the line represented by the equation y =4/5x-3?
Answers
Answer:
4/5 is the slope of the line
What is an equation of the line that passes through the points (5, -3) and
(-3, -3)?
Answers
Answer:
y=-3
Step-by-step explanation:
First, we start with the basic line equation:
y=ax+b
Plugging in the two points, we get
-3=a(5)+b and
-3=a(-3)+b
Simplifying we get
b=-3-5a
b=-3+3a
Setting the two equations equal, we get
-3-5a = -3+3a
8a = 0
so a =0
plugging in a into the first equation
-3=0(5)+b
b=-3
and finally plugging a and b into y=ax+b we get
y=-3
If this was helpful pls give me brainliest <3
Equation: [tex]y=-3[/tex].
Step-by-step explanation:1. Find the slope of the equation.To find the slope of this equation, let's refer to the formula of slope:
Slope (m)= [tex]\frac{y_{2}- y_{1} }{x_{2}- x_{1} }[/tex]
Identify the points:
Let the ordered pair of (5, -3) take the number 1 for the notation. Hence:
[tex]x_{1} =5\\\\y_{1} =-3[/tex]
Note. This assigment of number 1 can be done arbitrarily, we could've named the coordinates of the other ordered pair as number 1 and the result would be the same.
Now, identify the values of the remaining ordered pair.
[tex]x_{2} =-3\\\\y_{2} =-3[/tex]
Substitute the values into the slope formula and calculate.
[tex]m=\frac{(-3)-(-3)}{(5)-(-3)} \\ \\m=\frac{-3+3}{5+3}\\ \\m=\frac{0}{8} \\ \\m=0[/tex]
2. Find the equation.To find the equation, we're going to use the formula for crafting linear equations which is the following:
[tex]y-y_{1} =m(x-x_{1} )[/tex]
Substitute the values into the formula and calculate.
[tex]y-(-3) =(0)(x-(-3) )\\ \\y+3=0\\ \\y=-3[/tex]
Note. For this formula you may use any of the ordered pairs to substitute.
3. Express your result.Equation: [tex]y=-3[/tex].
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