|4x + 7| − 4 = 20
Can anyone help me with this
Answer:
x = -31/4 or x = 17/4
Step-by-step explanation:
|4x + 7| − 4 = 20
⇔ |4x + 7| − 4 + 4 = 20 + 4
⇔ |4x + 7| = 24
⇔ 4x + 7 = 24 or 4x + 7 = -24
⇔ 4x = 24 - 7 or 4x = -24 - 7
⇔ 4x = 17 or 4x = -31
⇔ x = 17/4 or x = -31/4
Answer:
x = [tex]\frac{17}{4}[/tex] (17/4 = 4.25)
or x = [tex]-\frac{31}{4}[/tex] (-31/4 = -7.75)
Step-by-step explanation:
| | is notation for absolute value
absolute value - the distance that a number is from 0
> essentially, you can think of absolute value as the "positive version" of whatever is inside of the | |
if we have | x | = 20, we could really have (without the | | ) two versions of x
either | x | = 20 ; or | -x | = 20 {because a negative x inside of the | | has the same value as positive x}
we set this up as two equations:
x = 20 or -x = 20
^ {multiply by -1}
x = 20 or x = -20
now, let's plug our understanding into the equation
|4x + 7| - 4 = 20
first, we should simplify our equation to:
|4x + 7| - 4 = 20
+ 4 + 4
|4x + 7| = 24
now, let's separate this absolute value equation into two separate equations:
4x + 7 = 24:
- 7 - 7 {subtract 7 from both sides to isolate x}
4x = 17
÷4 ÷4 {divide both sides by 4 to get 1x}
x= [tex]\frac{17}{4}[/tex]
or,
4x + 7 = -24:
- 7 -7 {subtract 7 from both sides to isolate x}
4x = -31
÷4 ÷4 {divide both sides by 4 to get 1x}
x = [tex]-\frac{31}{4}[/tex]
so, we know that
x = [tex]\frac{17}{4}[/tex] (17/4 = 4.25)
or x = [tex]-\frac{31}{4}[/tex] (-31/4 = -7.75)
hope this helps!!
(7 + 7i)(2 − 2i)
(a) Write the trigonometric forms of the complex numbers. (Let
0 ≤ < 2.)
(7 + 7i) =
(2 − 2i) =
(b) Perform the indicated operation using the trigonometric forms. (Let
0 ≤ < 2.)
(c) Perform the indicated operation using the standard forms, and check your result with that of part (b).
The complex number -7i into trigonometric form is 7 (cos (90) + sin (90) i) and 3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)
What is a complex number?It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
We have a complex number shown in the picture:
-7i(3 + 3i)
= -7i
In trigonometric form:
z = 7 (cos (90) + sin (90) i)
= 3 + 3i
z = 4.2426 (cos (45) + sin (45) i)
[tex]\rm 7\:\left(cos\:\left(90\right)\:+\:sin\:\left(90\right)\:i\right)4.2426\:\left(cos\:\left(45\right)\:+\:sin\:\left(45\right)\:i\right)[/tex]
[tex]\rm =7\left(\cos \left(\dfrac{\pi }{2}\right)+\sin \left(\dfrac{\pi }{2}\right)i\right)\cdot \:4.2426\left(\cos \left(\dfrac{\pi }{4}\right)+\sin \left(\dfrac{\pi }{4}\right)i\right)[/tex]
[tex]\rm 7\cdot \dfrac{21213}{5000}e^{i\dfrac{\pi }{2}}e^{i\dfrac{\pi }{4}}[/tex]
[tex]\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}[/tex]
=21-21i
After converting into the exponential form:
[tex]\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}[/tex]
From part (b) and part (c) both results are the same.
Thus, the complex number -7i into trigonometric form is 7 (cos (90) + sin (90) i) and 3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)
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One positive number is 8 times another number. Their difference is 70.
Which of the following equations could be used to find the numbers?
Answer:
X equals 10.
8x - x = 70
Step-by-step explanation:
8 x 10 = 80
80 - 10 = 70
Find an equation for the line that passes through the point P(-5,-3) and is parallel to the line
7x + 4y
10. Use exact values.
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{y = -1.75x - 11.75}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Goes through (-5, -3) and parallel to 7x + 4y = 10}[/tex]
Find: [tex]\textsf{The equation in slope-intercept form}[/tex]
Solution: We need to first solve for y in the equation that was provided so we can determine the slope. Then we plug in the values into the point-slope form, distribute, simplify, and solve for y to get our final equation.
Subtract 7x from both sides
[tex]\textsf{7x - 7x + 4y = 10 - 7x}[/tex][tex]\textsf{4y = 10 - 7x}[/tex]Divide both sides by 4
[tex]\textsf{4y/4 = (10 - 7x)/4}[/tex][tex]\textsf{y = (10 - 7x)/4}[/tex][tex]\textsf{y = 10/4 - 7x/4}[/tex][tex]\textsf{y = 2.5 - 1.75x}[/tex]Plug in the values
[tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex][tex]\textsf{y - (-3) = -1.75(x - (-5))}[/tex]Simplify and distribute
[tex]\textsf{y + 3 = -1.75(x + 5)}[/tex][tex]\textsf{y + 3 = (-1.75 * x) + (-1.75 * 5)}[/tex][tex]\textsf{y + 3 = -1.75x - 8.75}[/tex]Subtract 3 from both sides
[tex]\textsf{y + 3 - 3 = -1.75x - 8.75 - 3}[/tex][tex]\textsf{y = -1.75x - 8.75 - 3}[/tex][tex]\textsf{y = -1.75x - 11.75}[/tex]Therefore, the final equation in slope-intercept form that follows the information that was provided is y = -1.75x - 11.75
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex] \texttt{ \:The absolute maxima of f is f(-8) = 6} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Absolute maxima is the maximum possible value for a given x, of a function.
and here, the maximum value is at -8, and the maximum value is 6.
[tex]\qquad \tt \rightarrow \: maximum - \: \: f( - 8) = 6[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
The solution set to 6 + 2n > 12 is n > 3. Which are correct representations of this solution? Select two options.
{n | n < 3}
{n | n ≥ 3}
A number line going from negative 5 to positive 5. An open circle appears at positive 3. The number line is shaded from positive 3 to positive 5.
A number line going from negative 5 to positive 5. An open circle appears at positive 3. The number line is shaded from positive 3 to negative 5.
(3, ∞)
The correct representations of this solution is {n | n > 3} an open circle appears at positive 3.
Solution to inequality expressionInequalities are expressions not separated by an equal sign. Given the inequality
6 + 2n > 12
Subtract 6 from both sides
2n > 12 - 6
2n >6
Divide both sides by 2
2n/2 >6/2
n >3
Hence the correct representations of this solution is {n | n > 3} an open circle appears at positive 3.
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The Strikers soccer team has 20 members, and 8 of them play offense. What percent of the team members play offense?
Answer:
40%
Step-by-step explanation:
We already have our first value 20 and the second value 8. Let's assume the unknown value is Y which answer we will find out.
As we have all the required values we need, Now we can put them in a simple mathematical formula as below:
Step 1 ⇒ Y = 8/20
By multiplying both numerator and denominator by 100 we will get:
Step 2 ⇒ Y = 8/20 × 100/100 = 40/100
Step 3 ⇒ Y = 40
Finally, we have found the value of Y which is 40 and that is our answer.
To purchase 13700 worth of restaurant equipment for her business Maria made a down payment of 1500 and took out a business loan for the rest after 3 years of paying monthly payments of 371.16 she finally paid off the loan
What was the total amount Maria ended up paying for the equipment
How much internet did Maria pay on the loan
The total amount Maria ended up paying for the equipment will be $14,861.76. And The interest of Maria on the loan will be 8.48%.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
To purchase 13700 worth of restaurant equipment for her business.
Maria made a down payment of 1500 and took out a business loan for the rest, after 3 years of paying monthly payments of 371.16 she finally paid off the loan.
The total amount Maria ended up paying for the equipment will be
Total amount = 371.16 × 3 × 12 + 1500
Total amount = $14,861.76
The interest of Maria on the loan will be
Interset = [(14861.76 – 13700) / 13700] x 100
Interset = 8.48%
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What formula should be entered in A3 to compute A1 times B1?
A =A1 B1
B =A1/B1
=B1*83
=A1*B3
123
2
A B
2
10
8
8458
U375
C
The formula that should be entered in A3 is = A1 * B1
How to determine the formula?The question implies that:
A3 = A1 times B1
In mathematics, the term "times" means *
So, we have:
A3 = A1 * B1
Remove the variable A3
= A1 * B1
Hence, the formula that should be entered in A3 is = A1 * B1
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What are the solutions to the equations y= 4x^2+5x-6
Answer:
D. x = -2; x = 3/4
Step-by-step explanation:
Read the values of a, b, and c from the quadratic equation: a is the number in front of x^2, b is the number in front of x, c is the number at the end. In our case: a = 4,b = 5,c = −6 The formula for the roots is = [tex]\frac{-b +-\sqrt{b^{2}-4ac } }{2a\\}[/tex]four big water bottles can hold 8 gallaons how much can 10 big water gallons hold
A woman passed gas silently. I said "it stinks", and she said "I apologize. Excuse me". Why did she say both of those things?
Which of the following terms best fits this definition?
The angle between two sides of a triangle.
Select one:
AAS Theorem
SAS Postulate
Included Side
ASA Postulate
HL Congruence Theorem
Included Angle
SSS Postulate
Step-by-step explanation:
hope you can understand
What are m and b in the linear equation y=16+6x
Answer: B=16 and m=6
Step-by-step explanation:
in y=mx+b the number next to x is always the m/slope and the number without a variable is always the b.
How many pounds of candy that sells for $0.82 per lb must be mixed with candy that sells for $1.36 per lb to obtain 9 lb of a mixture that should sell for $0.91 per lb?
7.5 pounds of the $0.82 per lb candy must be used in the mixture.
How many pounds of each candy should we use?First, let's define the variables:
x = pounds of the $0.82 candy used.y = pounds of the $1.36 candy used.We want to make 9 lb of mixture, then:
x + y = 9.
And the price of these 9 pounds must be $0.91, then we can write:
x*$0.82 + y*$1.36 = 9*$0.91 = $8.19
Then we have a system of equations:
x + y = 9.
x*$0.82 + y*$1.36 = $8.19
We can isolate y on the first equation so we get:
y = 9 - x
Now we can replace that on the other equation:
x*$0.82 + (9 - x)*$1.36 = $8.19
And now we can solve this for x.
x*($0.82 - $1.36) = $8.19 - 9*$1.36
-x*$0.54 = -$4.05
x = (4.05/0.54) = 7.5
So 7.5 pounds of the $0.82 per lb candy must be used in the mixture.
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A woman passed gas silently. I said "it stinks", and she said "I apologize. Excuse me". Why did she say both of those things?
Answer:
one possible way was because she knew what she did and started playing innocent
Select the correct answer.
x
f(x)
2.0 2.8
2.5 1.1
3.0 –0.8
3.5 –1.2
4.0 –0.3
4.5 0.7
For the given table of values for a polynomial function, where must the zeros of the function lie?
A.
between 2.0 and 2.5 and between 4.0 and 4.5
B.
between 2.5 and 3.0 and between 4.0 and 4.5
C.
between 2.0 and 2.5 and between 3.5 and 4.0
D.
between 2.5 and 3.0 and between 3.5 and 4.0
Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients. The correct option is B.
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication, and non-negative exponentiation of variables involved.
Example:
x² + 3x + 5
In order to find the values at which the given polynomial will have zeros of the function, we need to find the values at which f(x) changes from positive to negative or vice versa. Since this is the range at which the function must have crossed the x-axis on the graph.
As per the given table, the value of f(x) is changing from negative to positive and positive to negative are between 2.5 and 3.0 and between 4.0 and 4.5.
Hence, the correct option is B.
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find the slope of the line that passes through (3,10) and (1,17)
Answer:
[tex]m=- \frac{7}{2}[/tex]
Step-by-step explanation:
The slope of a line passing through the two points [tex]\displaystyle{\large{{P}={\left({x}_{{1}},{y}_{{1}}\right)}}}[/tex] and[tex]\displaystyle{\large{{Q}={\left({x}_{{2}},{y}_{{2}}\right)}}}[/tex] is given by [tex]\displaystyle{\large{{m}=\frac{{{y}_{{2}}-{y}_{{1}}}}{{{x}_{{2}}-{x}_{{1}}}}}}[/tex].
We have that [tex]x_1=3[/tex], [tex]y_1=10[/tex], [tex]x_2=1[/tex], [tex]y_2=17[/tex].
Plug the given values into the formula for slope: [tex]m=\frac{\left(17\right)-\left(10\right)}{\left(1\right)-\left(3\right)}=\frac{7}{-2}=- \frac{7}{2}[/tex]
Answer: the slope of the line is [tex]m=- \frac{7}{2}[/tex].
Answer:
slope = - [tex]\frac{7}{2}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{x_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 10 ) and (x₂, y₂ ) = (1, 17 )
m = [tex]\frac{17-10}{1-3}[/tex] = [tex]\frac{7}{-2}[/tex] = - [tex]\frac{7}{2}[/tex]
Create and solve a linear equation that represents the model, where circles and a square are shown evenly balanced on a balance beam.
A linear equation that represents the model is: x + 6 = 10; x = 4
How to solve linear equations?Let us first define the variables based on the attached image of the ball balance:
Let x = number of balls that contains the square.
On the left side, we have; square + 6 balls
On the right side, we have; 10 balls
To balance this, we have;
x + 6 = 10
x = 10-6
x = 4
Thus, a linear equation that represents the model is:
x + 6 = 10; x = 4
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Find the range of the function.
f(x) = 10-x²
a. [5,00)
c. (-∞0, 10]
b. (-∞, -1) U [0, 00)
d.
Please select the best answer from the choices provided
(-∞, -1) U [∞o, 10)
Answer: hard to tell but I think D is correct (−∞,10],{y| y ≤ 10}
Step-by-step explanation:
Range:
(−∞,10] or {y| y ≤ 10}
because there is a vertex at (0, 10)
(found this by using -b/2a giving us 0 for x coord and plugging in 0 to 10-x² giving us (0, 10)
Then understanding since -x² is negative, the parabola goes down. And we know that the range is anything less or equal to 10
Question 10 of 10
Rewrite the following linear equation in slope-intercept form. Write your
answer with no spaces.
v+2=4(x-3)
Answer here
A rectangular parking lot has a perimeter of 820 ft. The area of the parking lot measures 42,000 ft2. What is a dimension of the parking lot?
By solving a system of equations, we will see that the parking lot is 210ft by 200ft.
How to get the dimensions of the parking lot?For a rectangle of length L and width W, the perimeter is:
P = 2*(L + W)
And the area is:
A = L*W
Here we know that the perimeter is 820 ft and the area is 42,000 ft²
Then we can write the two equations (ignoring units).
820 = 2*(L + W)
42,000 = L*W
We can isolate L in the first equation to get:
820/2 = L + W
410 - W = L
Now we can replace that in the other equation:
42,000 = (410 - W)*W = 410*W - W^2
Now we want to solve the quadratic equation:
-W^2 + 410*W - 42,000 = 0
The solutions are given by:
[tex]W = \frac{-410 \pm \sqrt{410^2 - 4*(-1)*(-42000)} }{-2} \\\\W = \frac{-410 \pm 10 }{-2}[/tex]
Then the solutions are:
W = (-410 + 10)/(-2) = 200
W = (-410 - 10)/2 = 210
If we take W = 200, then:
L = 410 - W = 410 - 200 = 210
So we can conclude that the parking lot is 200ft by 210ft.
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Answer: C, 210 ft
Step-by-step explanation: edge :)
Read the following two statements. Then, if possible, use the Law of Detachment to draw a conclusion. The doctor recommends rest if the patient has the flu. The doctor recommends rest. not possible The patient does not have the flu. If the doctor recommends rest, the patient has the flu. The patient has the flu.
The doctor recommends rest if the patient has the flu. Then the correct option is A.
What is decision-making?Determining the proper option, acquiring evidence, and exploring various options are all steps in the decision-making process.
Read the following two statements.
Then, if possible, use the Law of Detachment to draw a conclusion.
Then the correct option is A.
The doctor recommends rest if the patient has the flu.
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A hyperbola centered at (7, 0) has a focus at (7, 5) and vertex at (7, 4). Which is the equation of the hyperbola in standard form?
quantity x minus 7 end quantity squared over 16 minus y squared over 9 equals 1
quantity x minus 7 end quantity squared over 25 minus y squared over 16 equals 1
y squared over 16 minus quantity x minus 7 end quantity squared over 9 equals 1
y squared over 25 minus quantity x minus 7 end quantity squared over 16 equals 1
Based on the calculations, the equation of this hyperbola in standard form is: A. [tex]\frac{x\;-\;7}{16} + \frac{y}{9} = 1[/tex].
How to determine the equation of a hyperbola?Mathematically, the equation of a hyperbola in standard form is given by:
[tex]\frac{x\;-\;h}{a^2} + \frac{x\;-\;k}{b^2} = 1[/tex]
Given the following data:
Center (h, k) = (7, 0)
Vertex (h+a, k) = (7, 4)
Focus = (h+c, k) = (7, 5)
Also, we can deduce that the value of a and c are 4 and 5 respectively.
For the value of b, we would apply Pythagorean's theorem:
c² = a² + b²
b² = c² - a²
b² = 5² - 4²
b² = 9.
Substituting the parameters into the standard equation, we have:
[tex]\frac{x\;-\;7}{4^2} + \frac{y\;-\;0}{3^2} = 1\\\\\frac{x\;-\;7}{16} + \frac{y}{9} = 1[/tex]
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a.The product of two integers is -20.Find the largest possible sum of the two integers?b.The product of two integers is -30.Find the largest possible sum of the two integers.c.Can you generalize the result of a and b?
Step-by-step explanation:
first express the second function in terms of the other and find the critical point(which is the point that makes the graph to have a slope of 0). then you get the first number.
Which of the following best describes the expression below when i = √-1?
3+4i
A. Complex number
B. Real number
C. Irrational number
D. Rational number
The answer is A. Complex number
1
2
3
5
10
Two runners are saving money to attend a marathon.
The first runner has $110 in savings, received a $45 gift
from a friend, and will save $25 each month. The
second runner has $50 in savings and will save $60
each month.
After how many months will both runners have the
same amount of money?
02
O 3
Answer:
3 months
Step-by-step explanation:
The first runner: $110 + $45 = $155 starting out, plus 25x for $25 each month.
The second runner: $50 starting out, plus 60x for $60 each month.
To find out when both runners have the same amount of money, we will set the expressions equal to each other and solve.
155 + 25x = 60x + 50
105 = 35x
x = 3
Brainliest, please :)
March 8, 2017, one U.S. dollar was worth 66.79 Indian rupees.
a) On that date, how many dollars was 110.66 rupees worth?
Round your answer to the nearest hundredth of a dollar. I need help with this question.
[tex] \huge \tt \underline {\green{Answer}}[/tex]
If on March 8, 2017 , one U.S. dollar worth 66.79 Indian rupees
ie. $1 = Rs 66.79
$ 1 = 66.79 × 1
$ ? = 110.66
$ = New / old
$ = 110.66 / 66.79
$ = 1.65683485552
or
$1.66 = 110.66
Need help with the following question
what is the ratio of the radius of circle a to the radius of circle b?
Answer:
3:1
Step-by-step explanation:
Assuming that the edges of the circle are supposed to line up with the dotted lines of the graph, all you have to do is count how many lines are between the middle of the circle and the edge (either directly vertical or horizontal due to the graph we are using). We can see that the radius of circle A is approximately 3 units, while the radius of circle B is approximately 1 unit. So the ratio of the radius of circle A to the radius of circle B is 3:1.
Answer:
3:1
Step-by-step explanation:
because once count the radius of the big circle that is 3 unit and the radius of small circle is 1 unit
