Solve each absolute value equation.
|x-3|+2=7
Absolute value equality entered:
|x-3|+2 = 7
Another term is moved/added to the right-hand side.
|x-3| = 7 - 2
|x-3| = 5
Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.
The Absolute Value term is |x-3|
For the Negative case, we'll use -(x-3)
For the Positive case, we'll use (x-3)
-(x-3) = 5
Multiply
-x+3 = 5
Rearrange and add up
-x = 2
Multiply both sides by (-1)
x = -2
Which is the solution for the Negative Case
(x-3) = 5
Rearrange and add up
x = 8
Which is the solution for the Positive Case
x=-2
x=8
More problems are given in the link below.
https://brainly.com/question/27648592?referrer=searchResults
#SPJ4
teh equation y=mx+b goes through the points (4,-1) and (8-7) what is the value of m
Answer:-1.5
Step-by-step explanation:
v to the 3 power =12. What does v equal been racking my brains can't figure out
Answer:
v= cube root of 12 or 2. 2894 or 2.3
Step-by-step explanation:
cube root of v³ = v
cube root of 12 = ³√12
Answer:
Step-by-step explanation:
Translate this phrase into an algebraic expression.
64 decreased by twice Greg's savings
Use the variable g to represent Greg's savings.
Answer:
64 - 2g
Step-by-step explanation:
64 decreased by twice Greg's saving (given)
↓ ↓ ↓ ↓
64 - 2 g (final equation)
64 - 2g
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
Determine whether the following statement is true or false. If true, explain your reasoning. If false, provide a counterexample.
The orthocenter of a right triangle is always located at the vertex of the right angle.
The given statement exists true that "The orthocenter of a right triangle is always found at the right angle's vertex".
What is meant by orthocenter?The orthocenter is the point at which the triangle's three altitudes cut or intersect. The altitude is the line drawn from the triangle's vertex that is perpendicular to the opposite side. There are three altitudes because the triangle has three vertices and three sides.
The given statement exists true that "The orthocenter of a right triangle is always located at the vertex of the right angle".
The altitudes from the two non-right vertices (A and B) will always be the legs of the triangle, which intersect at the vertex containing the right angle, as shown in the right triangle below (C). Because the altitude to the triangle's hypotenuse originates at the vertex, the three altitudes (the red rays) intersect there. As a result, the vertex of a right triangle is always the orthocenter.
To learn more about orthocenter refer to:
https://brainly.com/question/25688098
#SPJ4
How many triangles are in a pentagon with a star inside
Answer:
10
Step-by-step explanation:
5 outside the star 5 inside the star
The population of Midtown grows about 2% each year. In 1990 the population of Midtown was 2050.
Which equation best represents the population, y, of Midtown .x years after 1990?
A. y=2050(0.02)^x
B. y=2050(1.02)^x
C. y=2050+0.02x
D. y = 2050+1.02x
The equation best represents the population, y, of Midtown .x years after 1990 is x =518395814790971.1018 or x= 5183958147909708032 (36648831234/ 14332031746)
Based on the given conditions, stated: x *(1+2%) (199-1990) = 2050
Calculate the sum or difference: x*1.02-1791 = 2050
Divide both sides of the equation by the coefficient of variable: Inferentially, when you divide, you assume that the number you are dividing by is not equal to zero. By dividing, you rule out the chance that the given number is zero, which may result in the elimination of the right answers. x = 2050 / 1.02-1791
Simplify using negative exponent rule: For every number “a” with negative exponents “-n”, take the reciprocal of the base number and multiply the value according to the value of the exponent number. For every number “a” in the denominator with negative exponent “-n” (i.e.,) 1/a-n, the result can be written in the form of a × a ×.. n times.
a-n = 1/an : x= 2050*1.021791
Convert decimal to fraction: x = 2050* (102/100)1791
Cross out the common factor: x = 2050 * (51/50)1791
Simplify using exponent rule with same exponent: (ab) n = an. bn
x= 2050 * 511791 / 501791
Write a single fraction: x= 2050 * 511791 /501791
Hence, the equation represents the population is, x =518395814790971.1018 or x= 5183958147909708032 (36648831234/ 14332031746)
To learn more about Fraction visit:
brainly.com/question/10354322
#SPJ1
Susie and friends rent 3 life jackets and a boat. The life jacket rents for $5.00 each. The boat rents for $25.00 per hour. The total cost is $115. What is an equation that can be written to represent this situation? Explain your steps.
The equation that can be written to represent this situation is 15 + 25h = 115.
How to illustrate the equation?Let the number of hours be represented by h.
The equation will be:
(3 × 5) + (25 × h) = 115
15+ 25h = 115
It should be noted that 15 represents the cost of jackets
Therefore, the equation that can be written to represent this situation is 15 + 25h = 115.
Learn more about equations on:
brainly.com/question/13763238
#SPJ1
candace askes 100 studes what flouvor crisp they like
Answer:
This is a survey
Step-by-step explanation:
Hector's school is holding a fitness challenge. Students are encouraged to exercise at least 2 1/2 hours per week. Hector exercises about the same number of hours each week. During a 4-week period, he exercises for 11 1/2 hours. Hector wants to compare his exercise rate with the fitness challenge rate.
Hector outperformed the challenge rate as he exercised 2.88 hours a week.
It is best to convert the mixed fraction to decimals for easier calculation.
The students are encouraged to exercise 2¹/₂ hours per week. In decimals this is:
= 2 + ¹/₂
= 2 + 0.5
= 2.5 hours per week
In the 4 week period, Hector exercised 11¹/₂ hours which is:
= 11 + ¹/₂
= 11 + 0.5
= 11.5 hours
The number of hours he exercised per week is:
= Number of hours in total / Number of weeks
= 11.5 / 4
= 2.88 hours per week
When compared to the fitness challenge rate, we can conclude that Hector outperformed the challenge rate
Find out more about rates, visit brainly.com/question/17951676.
#SPJ9
Describe in words where the square root of 75 minus 13 would be plotted on a number line.
A. Between 8 and 9, but closer to 8
B. Between 8 and 9, but closer to 9
C. Between −4 and −5, but closer to −4
D. Between −4 and −5, but closer to −5
It should be noted that the place the square root of 75 minus 13 would be plotted on a number line is C. Between −4 and −5, but closer to −4.
What is square root?It should be noted that a square root simply means the numbers that can be multiplied by itself that will give the original number.
It should be noted that the square root of 75 is 8.66. Therefore, square root of 75 minus 13 would be:
= ✓75 - 13
= 8.66 - 13
= -4.3397
Therefore, it should be noted that the place the square root of 75 minus 13 would be plotted on a number line is vetween −4 and −5, but closer to −4
Learn more about square root on:
brainly.com/question/428672
#SPJ1
HELPPPPP PLEASE IM BEGGING ILL GIVE ALL MY POINTS ON ANOTHER POST BUT PLS
Einstein's mass energy relation, and the formula for finding the percentage error gives;
7) a) 9.0 × 10¹⁶ Joules
b) The bulb could be powered for approximately 47533146.96 years
8) 16.46%
9) The possible values are;
61.093 Joules and 96.77 Joules
What is a percentage error?Percentage error is the ratio of the difference between estimated value and the actual value to the actual value expressed as a percentage.
7) a) The Einstein mass energy relation is presented as follows;
E = m•c²
The speed of light, c = 3×10⁸ m/s
The mass, m = 1 kg, gives;
E = 1 kg × (3×10⁸ m/s)² = 9.0 × 10¹⁶ Joules
The energy present in 1 kg. mass is; 9.0 × 10¹⁶ Joulesb) Energy consumption of the light bulb = 60 J/sec
The duration, t, the light bulb will remain lit is therefore;
t = (9.0 × 10¹⁶)/(60) = 1.5 × 10¹⁵ s ≈ 47533146.96 years8) Percentage error, %error, is found as follows;
%error = ((Approximate value - Actual value)/(Actual value)) × 100
Appreciate value = 46,620 km
Actual value = 40,030.2 km
Which gives;
%error = ((46,620 - 40,030.2)/(40,030.2))×100 ≈ 16.46%
The percentage error of Eratosthenes estimate of the circumference of the Earth is approximately 16.46%9) The calculated value of the kinetic energy = 74.9 J
The observed error in the calculation = 22.6%
Required; The two possibilities for the correct kinetic energy
Solution;
E% = ((Approximate value - Actual value)/(Actual value)) × 100
Taking the calculated value as the approximate value, and the correct value as the actual value, we have;
22.6% = ((74.9 - Actual value)/(Actual value)) × 100
(22.6/100)×Actual value = 74.9 - Actual value
Actual value + 0.226×Actual value = 74.9
1.226 × Actual value = 74.9
Which gives;
Actual value = 74.9 J/1.226 ≈ 61.093 JThe actual value can also be given as follows;
22.6% = ((Actual value - 74.9)/(Actual value)) × 100
Actual value - 0.226×Actual value = ,74.9
Actual value = 74.9 J/(1-0.226) ≈ 96.77 J
The possible values for the kinetic energy are approximately; 61.093 J and 96.77 JLearn more about calculating percentage error in measurements here;
https://brainly.com/question/5493941
#SPJ1
What is the value of the function at x=−3?
HELP UR WORK FOR THIS and please explain with it thank you
Which expression is equivalent to 9 × 9 × 9 × 9 × 9 × 9 × 9 × 9? A. 9 B. 9 C. 99,999,999 D. 99
The expression that is equivalent to 9 × 9 × 9 × 9 × 9 × 9 × 9 × 9 is D. 9^8
How to calculate the value?It should be noted that this is a question relating to indices.
It should be noted that we have to count the number of 9s that we gave in this case.
Therefore, 9 × 9 × 9 × 9 × 9 × 9 × 9 × 9 will be equivalent to 9^8.
Learn more about expressions on:
brainly.com/question/22048677
#SPJ1
Which expression is equivalent to 9 × 9 × 9 × 9 × 9 × 9 × 9 × 9? A. 9 B. 9 C. 99,999,999 D. 9^8
Answer:
C
Step-by-step explanation:
there are 8 of 9s so it is 99,999,999 tricky question!
How many milliliters of water (d = 0.998 g/ml) are required to dissolve 25.0 g of urea and thereby produce a 1.65 m solution of urea (co(nh2)2
The term "total moles of a solute contained in a kilogram of a solvent" exists utilized to define molality. The amount of water required exists 252ml.
How to estimate the amount of water required?
Given: Mass of urea = 25 g
Required Molality = 1.65m
Density of water = 1000 kg/m³
Formula for urea = CH₄N₂O
Mass of Carbon atom = 12 u
Mass of Oxygen atom = 16 u
Mass of Nitrogen atom = 14 u
Mass of Hydrogen atom = 1 u
Molecular Mass of Urea
= (1)12 + (4)1 + (2)14 + 16
= 12 + 4 + 28 + 16
= 60 u
Molar mass = 60 g
No of moles = Given mass/Molar mass
No of moles = 25/60 = 5/12
Molality = Mass of solute / Mass of solvent(g)
Let the weight of water be x kg
1.65 = (5/12)/x
simplifying the above equation, we get
1.65 x = (5/12)
x = (5/12) / 1.65
x = 5 / 1.98
x = 0.2525
Mass of water = 0.252 kg.
Volume of water = 0.252 ÷ 1000 kg/m³
= 0.000252 m³
= 0.252 liters
= 252 ml
Therefore, the require amount of water is 252 ml.
To learn more about Molality refer to:
https://brainly.com/question/24065939
#SPJ4
12x-(4+2x)
with solution please
a. Choose two positive numbers. Find their geometric mean.
The geometric mean of two positive numbers can be determined by multiplying the numbers and taking their square root.
Geometric mean is the mean or average value which expresses the central tendency of the set of numbers by taking root of the product of their values. In other words, we multiply the n values and take the nth root of the numbers. Geometric mean can also be expressed as the nth root of the product of n numbers.
The formula for finding geometric mean is:
GM = n√ x1*x2*x3…xn
Let the two terms be 2 and 8. Hence, x1=2, x2=8 and n=2.
GM = √2*8=√16=4
Hence, the geometric mean of the two chosen positive number 2 and 8 is 4.
Learn more about geometric mean:
https://brainly.com/question/28563055
#SPJ4
f(x)=|x|+5 horizontal shrink of factor 3
The function that models the horizontal shink of f(x) by a scale factor k = 3 is:
g(x) = |3*x| + 5
How to apply a horizontal shrink to the given function?Here we want to apply a transformation to a given function where the transformation is a shrink.
For a function f(x), a horizontal shrink (or compression) of scale factor K is written as:
g(x) = f(k*x)
In this case we have the absolute value function:
f(x)= |x| + 5
And we want to apply an horizontal shrink of scale factor k = 3, so we will have a new function defined as:
g(x) = f(3*x)
If we replace f(x) by the function above we will get:
g(x) = f(3*x) = |3*x| + 5
So we conclude that the transformed function is just:
g(x) = |3*x| + 5
If you want to learn more about transformations:
https://brainly.com/question/4289712
#SPJ1
Alejandro made an error in the steps below when determining the equation of the line that is perpendicular to the line 4x – 3y = –8 and passes through the point (3, –2).
Alejandro made his first error in which step?
Step 1
Step 2
Step 3
Step 4
Alejandro stated -4/3 instead of -3/4 as the slope of the perpendicular line in step 2, therefore, his first error is in step 2.
What are the Equations of Perpendicular Lines?For any two given perpendicular lines, they must have slope (m) values that are negative reciprocals of each other. The equation of any line can be written in slope-intercept form as, y = mx + b, where m is the slope of the line.
Given the equation, 4x - 3y = -8, rewrite in slope-intercept form:
-3y = -4x - 8
-3y/-3 = -4x/-3 - 8/-3
y = 4/3x + 8/3
This means that the line has a slope of 4/3. Thus, the slope of the line that is perpendicular to the given line would be the negative reciprocal of 4/3, which is: -3/4.
Thus, we can see that Alejandro stated -4/3 instead of -3/4 as the slope of the perpendicular line in step 2, therefore, his first error is in step 2.
Learn more about slope pf perpendicular lines on:
https://brainly.com/question/1362601
#SPJ1
Write an explicit formula for each geometric sequence. Then find the first three terms. a₁ =1, r=2
FA recursive formula allows us to find each term in the geometric sequence using the previous term. Each new term is the product of the common ratio for that sequence and the previous term of that unknown or to-be-found term. If the common ratio is 9, each term is nine times the previous term.
The general term for the geometric sequence is
an= a1 * r ^ (n-1)
Where "an" refers to the nth term of the sequence, a1 is the first term known as the sequence, and r is the common ratio, n is its position or the number.
Now the term is,
where a₁ = 1 and r = 2
Sequence: 1, 2, 4, 8, 16, ....
3rd value: 4
More problems related to a similar concept are solved in the link below.
https://brainly.com/question/17102965?referrer=searchResults
#SPJ4
For all x,
17x⁵+3x²+2-(-4x⁵+3x³-2)=
A. 13x⁵+3x³+3x^2
B. 13x⁵+6x²+4
C. 21x⁵-3x³+3x²+4
D. 21x⁵+3x²+3x³
E. 21x⁵+3x³+3x²+4
21x⁵-3x³+3x²+4 will be the solution for x for the given equation 17x⁵+3x²+2-(-4x⁵+3x³-2) so option (D) will be correct.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
More than one variable may be present inside a linear b. An equation is said to be linear if the maximum power of the variable is consistently unity.
Given the equation,
17x⁵+3x²+2-(-4x⁵+3x³-2)
⇒ 17x⁵+3x²+2 + 4x⁵- 3x³+ 2
⇒ 17x⁵ + 4x⁵ - 3x³ + 3x² + 4
Hence "21x⁵-3x³+3x²+4 will be the solution for x for the given equation 17x⁵+3x²+2-(-4x⁵+3x³-2)".
For more about the equation,
brainly.com/question/10413253
#SPJ4
|1.3x+7.8|>0 what would be the answer in this inequality.
Answer:
inequality form would be x<-6 or x>-6
In your next job you are given a salary of $38,000 per annum. How much would you be paid: a) Per month
state and prove the section formula of external division
Answer:
Section formula for external division:
[tex]P(x,y)=(\frac{mx_2+nx_1}{m+n} ,\frac{my_2+ny_1}{m+n} )[/tex]
By drawing two comparable right triangles, the evidence for this result is similar to the proof for internal divisions.
What is section formula?If we know the ratio of the internal distances of any two points from the provided location, we may use the section formula to obtain the coordinates of that point.
If we were to determine the coordinates of the point P, we might use the formula below by knowing the coordinates of the points A and B and the ratio of their distances to the provided point P. (section formula).
Since all other values must be provided, any formula with two or more variables can be used to determine the value of any variable. Therefore, the formula also include the other quantities.
Another well-known coordinate geometry formula exists and is a specific instance of the section formula.
If a point is equally spaced from the provided points, the mid-point formula may be used to get its coordinates. (where the ratio of m to n is 1:1)
Thanks,
Eddie
Aplica la propiedad distributiva para crear una expresión equivalente 2(3-8y)=
Answer:
2(3-8y)=
6-16y
Step-by-step explanation:
1. Mrs. is selling tickets to a school carnival fundraiser. Adult tickets are $5 and student tickets
are $3. At the end of the fundraiser, she had made $521 and had sold a total of 145 tickets. How
many student tickets did she sell?
Taking into account the definition of a system of linear equations, she sold 102 student tickets.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.
This caseIn this case, a system of linear equations must be proposed taking into account that:
A: number of adults tickets sold.S: number of students tickets sold.Knowing that:
Adult tickets are $5 and student tickets are $3. At the end of the fundraiser, she had made $521 and had sold a total of 145 tickets.the system of equations to be solved is
[tex]\left \{ {{A+S=145} \atop {5A+3S=521}} \right.[/tex]
Of the multiple methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, isolating the variable A from the first equation:
A= 145 - S
Replacing this expression in the second equation:
5(145 - S) + 3S= 521
5×145 - 5S + 3S= 521
725 - 5S + 3S= 521
-5S + 3S= 521 - 725
-2S= -204
S= (-204)÷(-2)
S= 102
Finally, she sold 102 student tickets.
Learn more about system of equations:
brainly.com/question/14323743
brainly.com/question/1365672
brainly.com/question/20533585
brainly.com/question/20379472
#SPJ1
A four seat cessna airplane uses an average of 11 gallons of avgas per hour. if it is 28 minutes and 30 miles from olympia to hoquiam, how many miles per gallon of fuel does the plane average?
A four seat Cessna airplane does an average of 5.84 miles per gallon of fuel traveling from Olympia to Hoquiam
Given that a four seat Cessna airplane uses an average of 11 gallons of avgas per hour, and it traveled from Olympia to Hoquiam for 28minutes, then we can solve for the amount of fuel it consumed for that flight.
amount of fuel = average consumption x time
amount of fuel = 11 gallons of avgas per hour x 28 minutes
amount of fuel = 11 gallons of avgas per hour x (28/60)h
amount of fuel = 77/15 gallons
If the flight from Olympia to Hoquiam is 30 miles and the amount of fuel used by the Cessna airplane is 77/15 gallons, then
average number of miles per gallon of fuel = distance traveled / amount of fuel consumed
average number of miles per gallon of fuel = 30 miles / (77/15 gallons)
average number of miles per gallon of fuel = 450/77
average number of miles per gallon of fuel = 5.84 miles / gallon of fuel
Learn more about average here: https://brainly.com/question/22539974
#SPJ4
Please help and give me the answer and explanation could not figure this one out.
The polynomial function f(x) = (x - a)(x - b) is a quadratic function and values of a and b are 1 and - 1 respectively.
What is a polynomial?A polynomial is an algebraic expression that consists of variables and constants connected by arithmetic operations.
Given the polynomial function f(x) = (x - a)(x - b) and if we observe the graph we can see that the polynomial has two roots,
one at x = 1 and another at x = -1.
If x = 1 is a root of this polynomial we can write this in factor form as.
x = 1.
x - 1 = 0
And
x = -1.
x + 1 = 0.
∴ f(x) = (x - 1)(x + 1).
f(x) = x² - 1², So it is a quadratic function.
∴ Values of a and b are 1 and - 1.
learn more about polynomials here :
https://brainly.com/question/11536910
#SPJ1
how do you do this omg
Answer:
[tex] - 1 \geqslant x \geqslant 2[/tex]
