Step-by-step explanation: So this one can be a little confusing, but I think I can help. You see if 'y'= number of feet and 'x'= number of meters then y=3.28x is a way for you to figure out how many feet are constant to every meter.
Look at it more like, Number of Feet= 3.28 times the number of meters.
If you want to figure out many feet are constant to let's say...2 meters, then you would replace the 'x' variable with 2 and multiply it by 3.28.
It would look something like this:
y=3.28(2)
y= 6.56
Thus, every 1 feet there are 6.56 meters, or 6.56 meters equals 1 foot.
Hope this helps a little, tell me if you need anymore help with this!
PLEASE ANSWER CORRECTLY ASAP!!THE OTHER OPTION IS 4 7/12 !
As a salesperson at trading cards unlimited Justin receives a monthly base pay Plus commission on all of that he sells. If he sells for $100 worth of merchandise in one month he is paid $500 if he sells $700 of merchandise in one month he is paid $575 find Justin’s salary when he sells $2500 worth of merchandise
Answer:
If he sells $2500 worth of merchandise, his salary is $800.
Step-by-step explanation:
You can find a function that gives you his salary as a function of the sales.
You have two points: (100, 500) and (700, 575).
y = mx + b
m = (575 - 500)/(700 - 100) = 75/600 = 0.125
Now use point (100, 500) to find b.
y = mx + b
500 = 0.125(100) + b
500 = 12.5 + b
b = 487.5
y = 0.125x + 487.5
If he sells $2500, then x = 2500.
y = 0.125x + 487.5
y = 0.125(2500) + 487.5
y = 800
If he sells $2500 worth of merchandise, his salary is $800.
plz help Pru, Piper, and Phoebe share spices in the ratio 5:3:4. If Pru has 24 more spices than Piper, how many spices does Phoebe have?
Answer:
Step-by-step explanation:
Pru, Piper, Phoebe ratio 5:3:4vadded = 12
What this means is Pru has 5/12 of the total amount, Piper has 3/12 of the total amount, and Phoebe has 4/12 of the total amount of spices.
pru = piper + 24
5/12x = 3/12x + 24
5/12x - 3/12x = 24
2/12x = 24
x = 24 / (1/6)
x = 24 * 6
x = 144 spices in total
Pru has : 5/12(144) = 720/12 = 60 spices
Piper has : 3/12(144) = 432/12 = 36 spices
Phoebe has : 4/12(144) = 576/12 = 48 spices
I hope this can help.
Answer:
48
Step-by-step explanation:
Pru, Piper, and Phoebe share spices in the ratio 5:3:4
5+3+4=12
So Pru has 5/12 share of spices, Piper has 3/12 share of spices, and Phoebe has 4/12 share of spices.
If Pru has 24 more spices than Piper, (5/12 - 3/12)=2/12 share of spices =24
Total spices = 24x12/2 = 144
Phoebe has 4/12x144 = 48 spices
If the speed limit of the highway is 60 mph which car exceed the speed limit assume other cars were traveling at a constant speed a car traveled at 183 miles in three hours a car that travel 236 miles in four hours a car that traveled 290 miles in five hours or a car that traveled 342 miles in six hours
Answer:
The first car
Step-by-step explanation:
183/3 = 61mph
Answer:
183/3 or Option A
Step-by-step explanation:
Edge 2021
thats where i got the correct answer plus i took the test
what functions equation does the sentence describe? every y-value is 5 less then the corresponding x-value
Answer:
The sentence describes this function equation:
y=x-5
Step-by-step explanation:
Every y-value is 5 less than the corresponding x-value:
y=x-5
You travel 12 miles north and then 5 miles west from your home. How far are you from home?
Answer:
13 Miles
Step-by-step explanation:
This problem could be solved using the Pythagorean theorem.
a² + b² = c²
a = 12 b = 5
12² + 5² = 169
√169 = 13
Therefore, you are 13 miles away from your house!
the equation cos-1 3.4/10 =x can be used to determine the measure of angle BAC. What is the degree of measure angle BAC? Round to the nearest whole degree.
Answer:
70°
Step-by-step explanation:
x = [tex]cos^{-1}[/tex]([tex]\frac{3.4}{10}[/tex]) ≈ 70°
Answer:
<BAC= 70 degrees.
Step-by-step explanation:
The given equation to find angle BAC that is x is :
x=[tex]cos^{-1} \frac{3.4}{10}[/tex]
Or ,[tex]x=cos^{-1} 0.34[/tex]
Using calculator to find the arc of cosine0.34 we have :
x=70.1231
This when rounded to nearest whole degree is 70 degrees.
<BAC= 70 degrees.
Which table represents a nonlinear function?
Answer:
The table that represents the nonlinear function is the one where the x-values are -7, -5 and 0 and the y-values are -3, 0 and 3.
Step-by-step explanation:
In order for a table to represent a linear function, there needs to be a consistent change in y-values divided by the change in x-values. For example, for any two points on the table when we subtract two y-values and divide by the number we get when we subtract two x-values, this change should be represented throughout the table. So, in the case of the other three tables, when we choose two points from the table, such as (-5, 7) and (-2,6) and put them into an equation (y2-y1/x2-x1) or (6-7)/(-2-(-5)) we would get a change of -1/3. However, when we apply this concept to the table where x-values are -7,-5, and 0, we see that the change is not consistent between points, so the function must be nonlinear.
Which statement about the graph y= 4x - 10 is NOT true?
A. The slope of the line can be written as 4/1
B. The graph crosses the y-axis 10 units below the origin
C. The line has a constant rate of change
D. The graph contains the point (4, -10)
Answer:
D. The graph contains the point (4, -10)
Step-by-step explanation:
We have been given an equation of a function: [tex]y=4x-10[/tex]. We are asked to find which of the given statements are not true about our given function.
A. The slope of the line can be written as 4/1.
We can see from our given equation that slope is 4 we can write 4 as 4/1 as it will not change value of 4, therefore, option A is true.
B. The graph crosses the y-axis 10 units below the origin.
Since we know that b represents y-intercept, where line crosses y-axis. y-intercept for our given equation is -10, which means that our given line crosses y-axis at -10 (10 units below the origin), therefore, option B is true.
C. The line has a constant rate of change.
We can see that slope of line is 4 which means with each increase in x, y will increase by 4 units, which remains constant, therefore, option C is true indeed.
D. The graph contains the point (4, -10)
Since we know that y-intercept is -10, which occurs at x equals 0, therefore, the graph does not contain the point (4,-10) and option D is not true.
15 Points!
I have tried multiple times on this question and I don't understand it. Matikas is writing a coordinate proof to show that the midpoints of a quadrilateral are the vertices of a parallelogram. He starts by assigning coordinates to the vertices of quadrilateral RSTV and labeling the midpoints of the sides of the quadrilateral as A, B, C, and D.
Enter the answers, in simplified form, in the boxes to complete the proof.
Answer:
coordinate of point A is (a,b)
coordinate of point C is (2c,d)
slope of AD and BC =[tex]\frac{b}{a-c}[/tex]
Step-by-step explanation:
According to midpoint formula
If we have points P [tex](x_{1} ,y_{1} )[/tex] and Q [tex](x_{2} ,y_{2} )[/tex]
then the coordinate (x,y) of mid point of line PQ is given by
[tex]x=\frac{x_{1} +x_{2} }{2}[/tex] and [tex]y=\frac{y_{1} +y_{2} }{2}[/tex]
now from the given diagram A is the mid point of line joining R(0,0) and S(2a,2b)
Using midpoint formula, coordinates of point A is given by
[tex]x=\frac{0+2a}{2}= a[/tex] and [tex]y=\frac{0+2b}{2} =b[/tex]
so we have
coordinate of point A is (a,b)
Also C is the midpoint of line joining T (2c,2d) and V(2c,0)
coordinate of point C is given by
[tex]x= \frac{2c+2c}{2} =2c[/tex] and [tex]y=\frac{2d+0}{2} =d[/tex]
so we have
coordinate of point C is (2c,d)
it is given that coordinate of point B is (a+c, b+d) and coordinate of D is (c,0)
If we have points P [tex](x_{1} ,y_{1} )[/tex] and Q [tex](x_{2} ,y_{2} )[/tex]
then the slope of PQ =[tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
hence slope of AD= [tex]\frac{0-b }{c-a} [/tex]
=[tex]\frac{-b}{c-a}[/tex]
=[tex]\frac{-b}{-(a-c)}[/tex]
=[tex]\frac{b}{a-c}[/tex]
and slope of BC =[tex]\frac{d-(b+d)}{2c-(a+c)}[/tex]
=[tex]\frac{d-b-d}{2c-a-c}[/tex]
=[tex]\frac{-b}{c-a}[/tex]
=[tex]\frac{b}{a-c}[/tex]
so we have
slope of AD and BC =[tex]\frac{b}{a-c}[/tex]
Answer:
Co-ordinates of A are ( a, b )
Co-ordinates of C are ( 2c, d )
Slope of line segments AD and BC is [tex]\frac{-b}{c-a}[/tex]
Step-by-step explanation:
We know that, the co-ordinates of the mid-point of a line segment having end points (x,y) and [tex](x_{1} , y_{1} )[/tex] is [tex](\frac{x+x_{1} }{2} , \frac{y+y_{1} }{2} )[/tex]
Now as 'A' is the mid-point of the line segment RS having end points (0,0) and (2a,2b).
The co-ordinates of A will be ( [tex]\frac{0+2a}{2}[/tex], [tex]\frac{0+2a}{2}[/tex] ) i.e [tex]( a, b )[/tex]
Now as 'C' is the mid-point of the line segment TV having end points (2c,2d) and (2c,0).
The co-ordinates of C will be ( [tex]\frac{2c+2c}{2}[/tex], [tex]\frac{2d+0}{2}[/tex] ) i.e. [tex]( \frac{4c}{2} , \frac{2d}{2})[/tex] i.e. [tex]( 2c, d )[/tex].
Further, we need to find the slope of line segments AD and BC.
AD has end points [tex]( a, b )[/tex] and [tex]( c, 0 )[/tex]. Then the slope of AD will be [tex]\frac{0-b}{c-a}[/tex] i.e [tex]\frac{-b}{c-a}[/tex]
Similarly, BC has end points [tex]( a+c, b+d )[/tex] and [tex]( 2c, d )[/tex]. Then the slope of BC will be [tex]\frac{d-b-d}{2c-a-c}[/tex] i.e [tex]\frac{-b}{c-a}[/tex]
Hence, the slope of AD and BC is [tex]\frac{-b}{c-a}[/tex].
Calvin goes shopping over the weekend and buys a new pair of shoes,a T-Shirt, a pair of sunglasses, and a hat that costs $9. The shoes are twice as much as the shirt, and the sunglasses are half as much as the shirt. The total cost of his purchase is $65. How much does each cost?
Answer:
I got you :)
Step-by-step explanation:
okay so if the hat is 9$ there is only 56$ left . it says the shoes are twice as much as the shirt , so i just went in and seen how much ill have left if i split it all. So i said 32$ for the shoes , because half of 32$ for shoes would mean 16$ for the shirt which would be 48. Then it says the sunglasses are half as much as the shirt and half of 16 is 8. When we add 32+16+8+9 we get 65$.
what is the greatest possible integer solution of the inequality 8.904x < 18.037
Answer:
2
Step-by-step explanation:
8.904x < 18.037 Divide each side by 8.904
x < 2.026
The largest integer that satisfies the inequality is 2.
Miguel has two same size rectangles divivded into the same number of equal parts. One rectangle has 3/4 of the parts shaded, and the other has 5/8 of the parts shaded. Into how many parts could each rectangle be divided?
Final answer:
Each rectangle can be divided into 8 equal parts, allowing [tex]\frac{3}{4}[/tex] and [tex]\frac{5}{8}[/tex] to be expressed with the same denominator for comparison.
Explanation:
To determine how many parts each rectangle can be divided, we need to find a common denominator that allows us to express [tex]\frac{3}{4}[/tex] and [tex]\frac{5}{8}[/tex] using the same size parts. The smallest number that both denominators 4 and 8 can divide into without a remainder is 8. Therefore, the first rectangle can be divided into 8 equal parts, with 6 of those parts being shaded (since [tex]\frac{3}{4}[/tex] is equivalent to [tex]\frac{6}{8}[/tex]). The second rectangle is already divided into 8 equal parts with 5 of those parts being shaded.
The probability that Gavyn wins a raffle is given by the expression o/p
.
Is there another part to this question? What should we answer?
Answer:
i've literally got this same question and i have no idea what to putt
Step-by-step explanation:
Your car averages 34 miles per gallon on the highway. If gas costs $2.10 per gallon, how much does it cost in dollars per mile, to drive your car on the highway?
(A) $.06/mi (B) 16 mi/dollar (C) $16/mi (D) 0.06 mi/dollar
Answer:
Your answer is (A) $.06/mi
Step-by-step explanation:
In an ordinary annuity, when does the interest on a yearly investment start building interest?
Answer:
The interest on a yearly investment start building interest - at the end of the first period.
Step-by-step explanation:
In an ordinary annuity, the interest on a yearly investment start building interest - at the end of the first period.
An ordinary annuity is a series of payments, where all the payments are of the same amount and are paid at the same intervals of time. The interest is calculated at the end of first period.
Find (f • g) when f(x) = x^2 + 5x + 6 and g(x) = 1/x+3
Answer:
option D
Step-by-step explanation:
[tex]f(x) = x^2 + 5x + 6[/tex]
[tex]g(x)= \frac{1}{x+3}[/tex]
(fog)(x) = f(g(x))
Plug in g(x) in f(x)
We plug in 1/x+3 in the place of x in f(x)
[tex]f(g(x))= f(\frac{1}{x+3})= (\frac{1}{x+3})^2 + 5(\frac{1}{x+3}) + 6[/tex]
To simplify it we take LCD
LCD is (x+3)(x+3)
[tex]\frac{1}{(x+3)(x+3)}+5\frac{1*(x+3)}{(x+3)(x+3)}+\frac{6(x+3)(x+3)}{(x+3)(x+3)}[/tex]
[tex]\frac{1}{x^2+6x+9}+\frac{(5x+15)}{x^2+6x+9}+\frac{6x^2+36x+54}{x^2+6x+9}[/tex]
All the denominators are same so we combine the numerators
[tex]\frac{1+5x+15+6x^2+36x+54}{x^2+6x+9}[/tex]
[tex]\frac{6x^2+41x+70}{x^2+6x+9}[/tex]
Option D is correct
Answer:
The correct option choice is D. 6x^2 + 41x + 70 / x^2 +6x + 9
In May, 2018 a store had a furniture with a listed price of $550, having a sales tax of 3% on the listed price. Next month the price increased by 33 1/3 %. What sales tax should be paid in dollars on the new price?
The sales tax that should be paid in dollars on the new price is $22
Further explanationOrder of Operations in Mathematics follow this following rule :
ParenthesesExponentsMultiplication and DivisionAddition and SubtractionThis rule is known as the PEMDAS method.
In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.
Let us tackle the problem !
Given:
Initial Price = $550
Sales Tax = 3%
Percentage of Price Increase = 33¹/₃ %
Unknown:
Final Sales Tax = ?
Solution:
[tex]\texttt{Final Price} = \texttt{Initial Price} \times (100\% + \texttt{Percentage of Price Increase} )[/tex]
[tex]\texttt{Final Price} = \$550 \times (100\% + 33\frac{1}{3}\% )[/tex]
[tex]\texttt{Final Price} = \$550 \times (100\% + \frac{100}{3}\% )[/tex]
[tex]\texttt{Final Price} = \$550 \times (\frac{300}{3}\% + \frac{100}{3}\% )[/tex]
[tex]\texttt{Final Price} = \$550 \times (\frac{400}{3}\%)[/tex]
[tex]\texttt{Final Price} = \$550 \times (\frac{4}{3})[/tex]
[tex]\texttt{ }[/tex]
[tex]\texttt{Final Sales Tax} = 3\% \times \texttt{Final Price}[/tex]
[tex]\texttt{Final Sales Tax} = 3\% \times \$550 \times (\frac{4}{3})[/tex]
[tex]\texttt{Final Sales Tax} = \frac{3}{100} \times (\frac{4}{3}) \times \$550[/tex]
[tex]\texttt{Final Sales Tax} = \frac{4}{100} \times \$550[/tex]
[tex]\texttt{Final Sales Tax} = 4 \times \$5.5[/tex]
[tex]\texttt{Final Sales Tax} = \$22[/tex]
[tex]\texttt{ }[/tex]
Learn moreInfinite Number of Solutions : https://brainly.com/question/5450548System of Equations : https://brainly.com/question/1995493System of Linear equations : https://brainly.com/question/3291576Student's Shirt : https://brainly.com/question/909783Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Percentage
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent , cookies , chocolate , chip , paper , fourth , pieces
The sales tax should be paid in dollars on the new price is [tex]\boxed{\$ 22}.[/tex]
Further Explanation:
Given:
The listed price of furniture is [tex]\$550.[/tex]
The sales tax is of [tex]3\%[/tex] on the listed price.
The price is increased by [tex]33\dfrac{1}{3}\%.[/tex]
Calculation:
The increased price of the furniture can be obtained as follows,
[tex]\begin{aligned}{\text{Increased price}} &= 550 + \left( {33\frac{1}{3}\% \times 550} \right)\\&= 550 + \left( {\frac{{33.34}}{{100}} \times 550} \right)\\&= 550 + 0.3333 \times 550\\&= 550 + 183.32\\&= 733.32\\\end{aligned}[/tex]
The new price of the furniture is [tex]\$ 733.32.[/tex]
The sales tax is of [tex]3\%[/tex] on the listed price.
The sales tax can be obtained as follows,
[tex]\begin{aligned}{\text{Sales tax}} &= 3\% {\text{ of new price}}\\&= \frac{3}{{100}} \times 733.32\\&= \$ 22\\\end{aligned}[/tex]
The sales tax should be paid in dollars on the new price is [tex]\boxed{\$ 22}.[/tex]
Learn more:
Learn more about inverse of the function https://brainly.com/question/1632445 Learn more about range and domain of the function https://brainly.com/question/3412497 Learn more about profit and loss https://brainly.com/question/2479097
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Investment and return
Keywords: May, 2018, store, furniture, listed, price, listed price, $550, sales, sales tax, 3%, tax on listed price, next month, price increased, increased price, month[tex], 33 1/3%[/tex], paid, dollars, new price.
the first term of a sequence is 13 the term-to-term rule is take away 5 workout the 4th term
Answer:
[tex]a_{4}[/tex] = - 2
Step-by-step explanation:
given the term to term rule is subtract 5, then
[tex]a_{2}[/tex] = 13 - 5 = 8
[tex]a_{3}[/tex] = 8 - 5 = 3
[tex]a_{4}[/tex] = 3 - 5 = - 2
The fourth term is -2.
Given that,
the first term of a sequence is 13.The term-to-term rule is take away 5Based on the above information, the calculation is as follows:
Second term is
= 13 - 5
= 8
Third term is
= 8 -5
= 3
And, the fourth term is
= 3-5
= -2
Therefore we can conclude that The fourth term is -2.
Learn more: brainly.com/question/6201432
HELP !!! Use the elimination method to solve the system of equations.
4x + 3y = 11
x - y = 8
Answer:
C. (5, -3)
Step-by-step explanation:
4x + 3y = 11
x - y = 8 (multiply by 3) --> 3x - 3y = 24
4x + 3y = 11
3x - 3y = 24
---------------------add
7x = 35
x = 5
5 - y = 8
y = 5 - 8
y = -3
(5, -3)
Answer:
C. (5, -3)
Step-by-step explanation:
Rewrite the first equation.
Multiply the second equation by 3 and write it under the first equation.
4x + 3y = 11
3x - 3y = 24
Now add the equations.
7x = 35
Divide both sides by 7.
x = 5
Substitute 5 for x in the original first equation:
4(5) + 3y = 11
20 + 3y = 11
3y = -9
y = -3
Solution: (5, -3)
Give an example of an opposite integers
Answer:
-2, 2
Step-by-step explanation:
they are both the same distance from zero but one is positive and one is negative
Answer:
3- and 3+
Step-by-step explanation:
Basically just have your positive number and have the same number but just it being negative.
4. FLOWERS Bethany placed a bouquet of roses in a vase full of water. Each day she recorded how much water had evaporated from the vase before refilling it. The results are shown in the table below. Over the course of five days how much water had evaporated? Use mental math to find your answer.[Day-1=0.8][Day-2=0.2][Day-3=1.1][Day-4=0.9][Day-5=1]
Answer:
4 is the answer
Step-by-step explanation:
the quotient of 32 times a number and 4 is 16
Answer:
x=2
Step-by-step explanation:
32x ÷ 4 = 16
32x = 64
x = 2
Answer:
x = - 3.5
Step-by-step explanation:
32 * ( x + 4 ) = 16
x + 4 = 16 / 32
x + 4 = 0.5
x = 0.5 - 4
x = - 3.5
Donna is ordering chocolate chip cookies for her company's picnic. The cookies are sold in packages of 6. She needs 336 cookies. How many packages should Donna buy?
Answer:
56 packs
Step-by-step explanation:
just divide
One number is equal to two times a second number. Two times the first number plus two times the second number is 24. If you let x stand for the first number and y for the second, what are the two numbers? A. x = –24, y = –12 B. x = 12, y = 6 C. x = 8, y = 4 D. x = 24, y = 12
Answer:
C, x = 8 and y = 4
Step-by-step explanation:
Let's isolate y.
x = 2y
Divide both sides by 2.
x/2 = y
Now plug it in to the other equation.
2x + 2(x/2) = 24
Simplify.
2x + x = 24
Simplify.
3x = 24
Divide both sides by 3.
x = 8
Now plug x back into the original equation.
8/2 = y
Simplify.
4 = y
Therefore, the answer is C, x = 8, y = 4.
vector is flying his helicopter at 200 miles per hour. how long has he been flying if he has traveled 1,200 miles?
Answer:
6 hours
Step-by-step explanation:
200mph
1200 miles
200X=1200
X=6
jacie can swim 3/4 of a mile in 3/8 of an hour.how far can she swim in one hour?
Answer:
2 miles
Step-by-step explanation:
convert 3/4 into 6/8. With this you have a ratio of 6/8 miles to 3/8 hours. Meaning 2/8 mile is equal to 1/8 of an hour. With this you can find that Jacie can swim 2 miles in a hour
Jacie can swim 2 miles in one hour, based on her speed of swimming 3/4 of a mile in 3/8 of an hour.
The student has asked how far Jacie can swim in one hour if she can swim 3/4 of a mile in 3/8 of an hour. To find out how far she can swim in one hour, we need to calculate her swimming speed and then use that speed to determine the distance she can cover in one full hour.
First, we determine Jacie's speed by dividing the distance by the time:
Speed = Distance / Time
Speed = (3/4) mile / (3/8) hour = 2 miles per hour
Now that we know Jacie swims at a speed of 2 miles per hour, we can find out the distance she swims in one hour simply by considering the speed:
Distance in one hour = Speed / Time
Distance in one hour = 2 miles per hour / 1 hour = 2 miles
Therefore, Jacie can swim 2 miles in one hour.
Phillip bought 12 used cds and dvds. CDs cost 2 each and dvds cost 3 each. He spent 32 not including tax. How many dvds did Phillip buy?
Answer:
Eight
Step-by-step explanation:
We have two conditions:
(1) C + D = 12
(2) 2C + 3D = 32 Subtract D from each side of Equation (1)
C = 12 - D Multiply both sides by 5
2(12 – D) + 3D = 32 Remove parentheses
24 – 2D + 3D = 32 Combine like terms
24 + D = 32 Subtract D from each side
D = 8
Philip bought eight DVDs.
a file is 284 megabytes is being downloaded. If the download is 15.3% complete how many megabytes have been downloaded
Answer:
43.452
Step-by-step explanation:
284 times .153 = 43.452
What is the solution set of x2 – 10 = 30x?
So for this, I will be completing the square to solve for x. Firstly, add 10 and subtract 30x on both sides of the equation:
[tex]x^2-30x=10[/tex]
Next, we want to make the left side of the equation a perfect square. To find the constant of this soon-to-be perfect square, divide the x coefficient by 2 and square the quotient. Once you get that result, add it to both sides of the equation:
[tex]30\div 2 = 15\\15^2=225\\\\x^2-30x+225=235[/tex]
Now, factor the left side:
[tex](x-15)^2=235[/tex]
Next, square root both sides:
[tex]x-15=\pm\ \sqrt{235}[/tex]
Now, add 15 to both sides of the equation:
[tex]x=15\pm \sqrt{235}[/tex]
This is the exact solution. To find the approximate solution, solve the left side twice -- once with the plus sign, once with the minus sign:
[tex]x=30.33,-0.33[/tex]
Answer:In short:
Exact Solution: [tex]x=15\pm\sqrt{235}[/tex]Approximate Solution (Rounded to the hundredths): [tex]x=30.33,-0.33[/tex][tex]x^2-10=30x\qquad\text{subtract 30x from both sides}\\\\x^2-30x-10=0\\\\\text{Use the quadratic formula}\\\\ax^2+bx+c=0\\\\x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a},\ x_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\\text{We have}\ a=1,\ b=-30,\ c=-10\\\\\text{Substitute.}\\\\b^2-4ac\to(-30)^2-4(1)(-10)=900+40=940\\\\\sqrt{b^2-4ac}=\sqrt{940}=\sqrt{4\cdot235}=\sqrt4\cdot\sqrt{235}=2\sqrt{235}\\\\x_1=\dfrac{-(-30)-2\sqrt{235}}{2(1)}=\dfrac{30-2\sqrt{235}}{2}=15-\sqrt{235}\\\\x_2=\dfrac{-(-30)+2\sqrt{235}}{2(1)}=\dfrac{30+2\sqrt{235}}{2}=15+\sqrt{235}[/tex]
[tex]Answer:\ \boxed{x=15-\sqrt{235}\ and\ x=15+\sqrt{235}}[/tex]