5-2x2=-15
Two solutions were found :
x = ± √10 = ± 3.1623
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
5-2*x^2-(-15)=0
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(5 - 2x2) - -15 = 0
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
20 - 2x2 = -2 • (x2 - 10)
Trying to factor as a Difference of Squares :
3.2 Factoring: x2 - 10
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 10 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
Equation at the end of step 3 :
-2 • (x2 - 10) = 0
Step 4 :
Equations which are never true :
4.1 Solve : -2 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
4.2 Solve : x2-10 = 0
Add 10 to both sides of the equation :
x2 = 10
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ 10
The equation has two real solutions
These solutions are x = ± √10 = ± 3.1623
Two solutions were found :
x = ± √10 = ± 3.1623
To solve the equation 5 - 2x^2 = -15 using inverse operations, we need to isolate the variable x on one side of the equation.
1. Start by adding 15 to both sides of the equation to eliminate the constant term on the right side:
5 - 2x^2 + 15 = -15 + 15
20 - 2x^2 = 0
2. Next, divide both sides of the equation by -2 to isolate the x^2 term:
(20 - 2x^2) / -2 = 0 / -2
-10 + x^2 = 0
3. Now, move the constant term to the other side by adding 10 to both sides:
-10 + x^2 + 10 = 0 + 10
x^2 = 10
4. To solve for x, we need to take the square root of both sides of the equation:
√(x^2) = √(10)
x = ±√(10)
To check the solutions, substitute them back into the original equation and see if they make it true:
For x = √(10):
5 - 2(√(10))^2 = -15
5 - 2(10) = -15
5 - 20 = -15
-15 = -15 (True)
For x = -√(10):
5 - 2(-√(10))^2 = -15
5 - 2(10) = -15
5 - 20 = -15
-15 = -15 (True)
So, the solutions to the equation 5 - 2x^2 = -15 are x = √(10) and x = -√(10).
Place the following in order from least to greatest. 74.6, -74.69,-74.069, 74.59
Answer:
-74.069, -74.69, 74.59, 74.6
Step-by-step explanation:
negative numbers are smaller than positives
Answer:
-74.69, -74.069, 74.59, 74.6
Step-by-step explanation:
The product of 9 and x is less than or equal to -17
Answer:
9+x< -17
(make sure there's a line under the less than sign to make it work to)
Step-by-step explanation:
the product of 9 and x describes an addition problem, so it would be 9+x. after you put the less then or equal to sign and then -17.
Hope this helps
To solve the inequality 9x ≤ -17, divide both sides by 9 to find x ≤ -17/9, meaning x can be any value less than or equal to approximately -1.888.
The student's question pertains to an inequality in mathematics involving a variable x and requires an understanding of algebraic inequalities. To solve the inequality 9x ≤ -17, we need to isolate the variable x. We can do this by dividing both sides of the inequality by 9, which gives us x ≤ -17/9. It is important to note that dividing by a positive number does not change the direction of the inequality sign.
The value of x must satisfy this inequality, so any number less than or equal to -17/9 is a solution to the inequality. That means x could be -2, -3, or any other value that is less than or equal to approximately -1.888... (since -17/9 is a decimal approximation of -1.888...).
Write the equation in slope intercept form.
[tex]\bf y+2=\cfrac{1}{3}(x-6)\implies y+2=\cfrac{1}{3}x-2 \\\\\\ y=\cfrac{1}{3}x-4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
Answer:
[tex]y = \frac{1}{3} x - 4[/tex]
Step-by-step explanation:
Given equation :-
[tex]y + 2 = \frac{1}{3} (x - 6)[/tex]
• Slope intercept form is
y = mx + c
where , m is slope of the straight line
and c is y intercept of the line !
Solving and simplifying the given equation ,
[tex]3y + 6 = x - 6 \\ \\ 3y = x - 6 - 6 \\ \\ 3y = x - 12[/tex]
[tex]y = \frac{1}{3} x - \frac{12}{3 } \\ \\ y = \frac{1}{3} x - 4[/tex]
So, m = 1/3 and c = ( -4 )
hence , the required slope intercept form of the equation is
[tex]y = \frac{1}{3} x - 4[/tex]
model the number 5.55 on the place value chart
Answer:
Here's what I get
Step-by-step explanation:
Each digit in a number has a place value, based on its distance from the decimal point.
The value of a digit is the digit multiplied by its place value.
The place value of a digit increases by a factor of 10 as we move left on the place value chart and decreases by a factor of 10 as we move right.
Numbers to the left of the decimal point increase in the order: ones, tens, hundreds, thousands, etc.
Numbers to the right of the decimal point decrease in the order: tenths, hundredths, thousandths, etc.
So, we put the digits of 5.55 on the chart according to their place value.
How much does 8.20 X 10-3dm3 (1dm3 = 1L) sample of aluminum weigh in grams?
centimeters?
Answer:
8.20 grams ; 8.20 cm³
Step-by-step explanation:
At first convert it to m³ from dm³
we know,
1 dm³ =10⁻³ m³
∴ 8.20 X 10⁻³dm3 = 8.20 X 10⁻³ x 10⁻³ m³
=8.20 X 10⁻⁶ m³
m³ to gram :
1 m³ = 10⁶ grams
∴ 8.20 X 10⁻⁶ m³ = (8.20 X 10⁻⁶x10⁶) grams
= 8.20 grams
m³ to cm³ :
1m³ = 10⁶ cm³
∴8.20 X 10⁻⁶ m³ = (8.20 X 10⁻⁶ x 10⁶) cm³
=8.20 cm³
Note:
1 cm³ = 1 gram
One positive number is 3 times another number. The difference between the two numbers is 62. Find the numbers
Answer:
31
93
Step-by-step explanation:
Let the larger number = y
Let the smaller number = x
y = 3x
y - x = 62
3x - x = 62
2x = 62
2x/2 = 62/2
x = 31
y = 3x
y = 3*31
y = 93
Final answer:
To find two positive numbers where one is 3 times the other and their difference is 62, let one number be x, then solve the equation 3x - x = 62 to find the numbers 31 and 93.
Explanation:
To find the numbers:
Let one number be x, then the other number is 3x.
Form an equation: 3x - x = 62.
Solve for x: 2x = 62, x = 31.
So, the two numbers are 31 and 93.
Please help with this math question!
Answer:
74 feet in total. All it is is the perimeter
Write an even number between 7 and 16 draw a picture and the write a sentence to explain why it is an even number
The even number I picked was 6, here is why it is an even number.
You can put each in even groups, without having one group be more or less then the other, if I picked an odd number like 7, one group would had more, and the other 2 groups would have less.
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Hope this helped, have a great day!
BRAINLIEST ASAP
solve for x
2x+9=35
Hey!
---------------------------
Solution:
2x + 9 = 35
2x + 9 - 9 = 35 - 9
2x = 26
2x/2 = 26/2
x = 13
---------------------------
Answer:
x = 13
---------------------------
Hope This Helped! Good Luck!
Answer:
x = 13
Step-by-step explanation:
Given
2x + 9 = 35 ( isolate 2x by subtracting 9 from both sides )
2x = 26 ( divide both sides by 2 )
x = 13
Which of the following transformations is shown?
A. Translation 1 unit down
B. Translation 2 units down
C. Translation 3 units to the right
D. Reflection across the line y-axis
Answer:
B. Translation 2 units down
Step-by-step explanation:
Each time you start from a certain y-intercept, its prime gets translated two below each time:
n[1, 0] to n'[-1, 0]
m[4, 0] to m'[2, 0]
Now, it does not look perfectly shifted down for m' and m, but it it is definitely translated.
I am joyous to assist you anytime.
Find the value of W and please show step by step working out
Answer:
w = 60
Step-by-step explanation:
Given
[tex]\frac{4w}{10}[/tex] + 28 = 52 ( subtract 28 from both sides )
[tex]\frac{4w}{10}[/tex] = 24
Multiply both sides by 10 to clear the fraction
4w = 240 ( divide both sides by 4 )
w = 60
The first three steps in writing f(x) = 40x + 5x2 in vertex form are shown.
The answer is f(x)=5(x+8)-80f ( x ) = 5 ( x + 8 ) − 80
The expression above can also be written in the form of
Answer:
a= 7
b=9
c=4
Step-by-step explanation:
Answer:
a= 7
b=9
c=4
Step-by-step explanation:
lol
% of 50 shirts is 35 shirts.
Answer:
35/50
= x/100
3500=50x
x=3500/50=70
70%
Answer:
Step-by-step explanation:
% of 50 s:hirts is 35 shirts: (35×50)/100 = 17.5
8. Minnie has 6 country CDs and 5 rock CDs.
Amanda has 5 rock CDs and 6 country CDs.
Who has more CDs? Explain.
Answer: They have the same amount (11 )
Step-by-step explanation: just because the numbers are switched, doesn’t mean anything( no difference in the numbers.
-7 1/3 written as a fraction is
- 10/3
- 21/3
- 22/3
Answer:
-22/3
Step-by-step explanation:
Multiply the whole number by the denominator, and then add the numerator to get the improper fraction.
What is the slope of (5,3) and (5,-9)
The slope is the change in Y over the change in X.
A point is written as ( X,Y), where the first number is the X and the second number is the Y.
You have:
(5,3) and (5,-9)
The change in Y is -9 - 3 = -12
The change in X is 5-5 = 0
The slope becomes -12/0
Because you have a 0 on the bottom of the fraction the slope is undefined because you cannot divide by 0.
The slope is undefined.
Jordan will hike the trail shown at a rate of 4 mi/h. Write a linear equation to represent the distance Jordan still has to walk after x hours.What does the y-intercept of the equation
represent?
What we know:
Start of trail:
0 miles
End of trail:
25 miles
Answer:
Y=25-4x
Y means the distance Jordan still has to walk after x hours
Step-by-step explanation:
Answer:
y = 25 - 4*x
The y-intercept represents the total distance Jordan has to walk
Step-by-step explanation:
By Definition, speed = distance/time. We are interested in distance, then:
distance = speed*time
Calling x the hours of walking, and knowing that his speed is 4 mi/h, then:
distance = 4*x
The trail length is 25 miles, so if he walked 1 mile, 25 - 1 = 24 miles are left, in general:
y = 25 - 4*x
where y is the distance Jordan still has to walk.
The y-intercept is found replacing with x = 0, then:
y = 25 - 4*0
y = 25
which represents the total distance Jordan has to walk
What is the slope of the line in the graph?
Answer:
The slope is 1
Step-by-step explanation:
Slope is change in y over change in x.
You have point (1,2) and point (0,1)
change in y = 2-1 = 1
change in x = 1-0 = 1
change in y over change in x = 1/1 = 1
a cone has a radius of 5 m and a height of 3 m.What is the volume of the cone?
Answer:
78.54 [tex]m^3[/tex]
Step-by-step explanation:
Use the formula for the volume of a cone of circular base with radius "R" and height "H", using the given values for the radius R (5 meters), and the cone's height (3 meters)
[tex]Volume= \pi R^2 \frac{H}{3} \\Volume = \pi 5^2 \frac{3}{3} m^3 = 78.539816.... m^3[/tex]
And we round the answer to two decimals:
Volume = 78.54 [tex]m^3[/tex]
Write .46 as a fraction
Which equations represent the line that is perpendicular to the line 5x - 2y = -6 and passes through the point
(5, -4)? Select three options.
y=-2 X-2
2x +hoy = -10
L2x - 5y = -10
y+ 4 = _{(x - 5)
y- 4 = 5(x+5)
Answer
See below
Step-by-step explanation:
The given line has equation
[tex]5x - 2y = - 6[/tex]
The slope intercept form is
[tex]y = \frac{5}{2} x + 3[/tex]
The slope of this line is
[tex] m = \frac{5}{2} [/tex]
The line perpendicular to this line has slope
[tex] - \frac{2}{5} [/tex]
If this line passes through (5,-4), the point-slope form is
[tex]y + 4 = - \frac{2}{5} (x - 5)[/tex]
The slope-intercept form is
[tex]y = - \frac{2}{5} x- 2[/tex]
The standard form is
2x+5y=-10
I’d like for you to Show work please:)
Find the slope and the y-intercept of the line.
y=9x-1
slope:
y-intercept:
Hey!
------------------------------------------------
Solution:
The equation is written in slope-intercept form!
~Formula
y = mx + b
~Terms
m = slope
b = y-intercept
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Answer:
[tex]\large\boxed{9~=~slope!}\\\large\boxed{1~=~y~intercept!}[/tex]
------------------------------------------------
Hope This Helped! Good Luck!
Hi, let me help you out!
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
We are given an equation in slope-intercept form:
[tex]\longrightarrow\tt{y=mx+b}[/tex]
Where m is the slope, and b is the y-intercept.
Now let's find the slope of the given line.
Note: The slope is the coefficient of x.
The slope is 9, and the y-intercept (the constant term added to or subtracted from the slope) is -1.
I hope this helps you! Have an awesome day!
If you need any explanation or clarification, feel free to ask! :D
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Find the length of segment CD with points C(2,2) and D (-1,8)
A. 8.1
B. 5.2
C. 4.3
D. 6.7
Answer:
D
Step-by-step explanation:
Calculate the length using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = C(2, 2) and (x₂, y₂ ) = D(- 1, 8)
CD = [tex]\sqrt{(-1-2)^2+(8-2)^2}[/tex]
= [tex]\sqrt{(-3)^2+6^2}[/tex]
= [tex]\sqrt{9+36}[/tex] = [tex]\sqrt{45}[/tex] ≈ 6.7 → D
Norma's credit card has an APR of 16%, calculated on the previous monthly
balance, and a minimum payment of 2%, starting the month after the first
purchase. Her credit card record for the last 7 months is shown in the table
below.
Norma's credit card balance at the end of the 7th month is $1,487.22.
How to solveCalculate the interest for each month.
Interest = (Previous month's balance * APR) / 12
Calculate the new balance for each month.
New balance = Previous month's balance + Purchases + Interest - Payments
Here's the calculation for each month:
Month 1:
Interest: 0 (No interest on the first month)
Balance: $500 + $0 = $500
Month 2:
Interest: ($500 * 0.16) / 12 = $6.67
Balance: $500 + $200 + $6.67 - $10 = $696.67
Month 3:
Interest: ($696.67 * 0.16) / 12 = $9.29
Balance: $696.67 + $300 + $9.29 - $20 = $986.29
Month 4:
Interest: ($986.29 * 0.16) / 12 = $13.15
Balance: $986.29 + $100 + $13.15 - $20 = $1079.44
Month 5:
Interest: ($1079.44 * 0.16) / 12 = $14.39
Balance: $1079.44 + $150 + $14.39 - $10 = $1233.83
Month 6:
Interest: ($1233.83 * 0.16) / 12 = $16.45
Balance: $1233.83 + $0 + $16.45 - $15 = $1235.28
Month 7:
Interest: ($1235.28 * 0.16) / 12 = $16.47
After all the computations, taking into consideration the amount spent and paid earlier,
Norma's credit card balance at the end of the 7th month has amounted to $1,487.22.
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Norma's credit card has an APR of 16%, calculated on the previous monthly balance, and a minimum payment of 2%, starting the month after the first purchase. Her credit card record for the last 7 months is shown in the table below.
Month Purchases Payments
1 $500 $0
2 $200 $10
3 $300 $20
4 $100 $20
5 $150 $10
6 $0 $15
7 $250 $15
Calculate Norma's credit card balance at the end of the 7th month.
Answer: 389.46
Step-by-step explanation:
Add all payments received.
trust
Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Select three options. y = –Two-fifthsx – 2 2x + 5y = −10 2x − 5y = −10 y + 4 = –Two-fifths(x – 5) y – 4 = Five-halves(x + 5)
The three linear equations that represent the line perpendicular to the line 5x - 2y = -6 and passing through the point (5, -4) are: y = -2/5x - 2, 2x + 5y = -10, and y + 4 = -2/5 * (x - 5).
Explanation:Firstly, to find a line perpendicular to another line, we need to find the negative reciprocal of the slope of the original line. The equation 5x - 2y = -6 can be rewritten in slope-intercept form (y = mx + b) as y = 2.5x + 3, so its slope is 2.5. The negative reciprocal of 2.5 is -2/5. Therefore, the slope of the line we are looking for is -2/5.
Secondly, a line passes through a given point (5, -4), so we can use the point-slope form of the equation, which is y - y1 = m(x - x1). By substituting the values, we get y - (-4) = -2/5 * (x - 5), which simplifies to y + 4 = -2/5 * (x - 5).
Lastly, to find other representations of the same line, the standard form of a linear equation is Ax + By = C. Converting y + 4 = -2/5 * (x - 5) to standard form gives us 2x + 5y = -10. So, the three equations that represent the line are: y = -2/5x - 2, 2x + 5y = -10, and y + 4 = -2/5 * (x - 5).
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What is (f ° g)(2) and (g ° f)(2) with the set of points f: {(0,4), (1,2), (2,0), (3,2), (4,4)} and g: {(0,4), (1,3), (2,2), (3,1), (4,0)}
Answer:
[tex]\large\boxed{(f\circ g)(2)=0}\\\boxed{(g\circ f)(2)=4}[/tex]
Step-by-step explanation:
[tex]f:\{(0,4), (1,2), \underline{(2,0)}, (3,2), (4,4)\}\\\\g:\{\underline{(0,4)}, (1,3), \underline{(2,2)}, (3,1), (4,0)\}\\\\(f\circ g)(x)=f\bigg(g(x)\bigg)\\\\g(2)=2\qquad/from\ (2,2)/\\f\bigg(g(2)\bigg)=f(2)=0\qquad/from\ (2,0)/\\\\(g\circ f)(x)=g\bigg(f(x)\bigg)\\\\f(2)=0\qquad/from\ (2,0)/\\g\bigg(f(2)\bigg)=g(0)=4\qquad/from\ (0,4)/[/tex]
x + (-y)= -y + x
What’s the property
hm
Step-by-step explanation:
I'd go with associative because its re grouping
Answer:
Step-by-step explanation:
the property is : a+b= b+a comutative for +
Esther works for a marketing company. She earns $12 per hour, and she gets $50 travel allowance every month. Which linear equation could be used to find her monthly pay rate?
Answer:
y = 12x + 50
Step-by-step explanation:
Given,
The fixed amount of monthly allowance = $ 50,
Also, the earning per hour = $ 12,
If she works x hours in a month,
Then her total earning in x hours = 12x,
Also, total earning for a month ( say y ) = earning for x hours + fixed allowance
⇒ y = 12x + 50
Which is the required linear equation.
Answer:
y = 12x + 50
Step-by-step explanation:
Just took post-test 15/15