Answer:
18.5
Step-by-step explanation:
First we plug in the number
-1 1/2 is the same as -1.5
Plugging this in we will have:
15(-1.5) + 4 =
-22.5 + 4 =
-18.5
Which equation could generate the curve in a graph below?
When you graph a system of equations what are the three possible outcomes?
Answer:
i think its a beaner
Step-by-step explanation:
What equation is parallel to
y= - 1\4x + 5 and passes through (2,-3)
QUICK
Given:
The equation of parallel line is [tex]y=-\dfrac{1}{4}x+5[/tex].
Required line passes through (2,-3).
To find:
The equation of line.
Solution:
We have,
[tex]y=-\dfrac{1}{4}x+5[/tex]
On comparing this equation with [tex]y=mx+b[/tex], where m is slope, we get
[tex]m=-\dfrac{1}{4}[/tex]
Slope of two parallel lines are always same. So, slope of required line is [tex]m=-\dfrac{1}{4}[/tex].
The required line passes through the point (2,-3) having slope [tex]m=-\dfrac{1}{4}[/tex], so the equation of line is
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-(-3)=-\dfrac{1}{4}(x-2)[/tex]
[tex]y+3=-\dfrac{1}{4}(x)-\dfrac{1}{4}(-2)[/tex]
[tex]y+3=-\dfrac{1}{4}(x)+\dfrac{1}{2}[/tex]
Subtracting 3 from both sides, we get
[tex]y=-\dfrac{1}{4}(x)+\dfrac{1}{2}-3[/tex]
[tex]y=-\dfrac{1}{4}(x)+\dfrac{1-6}{2}[/tex]
[tex]y=-\dfrac{1}{4}(x)-\dfrac{5}{2}[/tex]
Therefore, the equation of required line is [tex]y=-\dfrac{1}{4}(x)-\dfrac{5}{2}[/tex].
can anyone please help. this is my last question!!!!
9514 1404 393
Answer:
x = 3.6
Step-by-step explanation:
The angle bisector divides the triangle proportionally.
The base segment to the right of the bisector is 6-x, so we can write the proportion ...
x/6 = (6-x)/4
Multiplying by 12, we get ...
2x = 3(6 -x)
5x = 18 . . . . . add 3x
x = 18/5 . . . . divide by 5
x = 3.6
_____
Alternate solution
Since the base of the triangle is given as a left-part and a sum-of-both-parts, we can write the proportion the same way:
left-part / sum-of-both-parts = x/6 = 6/(6+4)
Then the solution is x = 6(6/10) = 36/10 = 3.6.
Doing it this way avoids having x on both sides of the equation, so makes solving the equation be "one step."
6a-2z
Please help me
Answer:
2(3a-z)
cannot be further simplified
Step-by-step explanation:
The portion of the parabola y²=4ax above the x-axis, where is form 0 to h is revolved about the x-axis. Show that the surface area generated is
A=8/3π√a[(h+a)³/²-a³/2]
Use the result to find the value of h if the parabola y²=36x when revolved about the x-axis is to have surface area 1000.
Answer:
See below for Part A.
Part B)
[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]
Step-by-step explanation:
Part A)
The parabola given by the equation:
[tex]y^2=4ax[/tex]
From 0 to h is revolved about the x-axis.
We can take the principal square root of both sides to acquire our function:
[tex]y=f(x)=\sqrt{4ax}[/tex]
Please refer to the attachment below for the sketch.
The area of a surface of revolution is given by:
[tex]\displaystyle S=2\pi\int_{a}^{b}r(x)\sqrt{1+\big[f^\prime(x)]^2} \,dx[/tex]
Where r(x) is the distance between f and the axis of revolution.
From the sketch, we can see that the distance between f and the AoR is simply our equation y. Hence:
[tex]r(x)=y(x)=\sqrt{4ax}[/tex]
Now, we will need to find f’(x). We know that:
[tex]f(x)=\sqrt{4ax}[/tex]
Then by the chain rule, f’(x) is:
[tex]\displaystyle f^\prime(x)=\frac{1}{2\sqrt{4ax}}\cdot4a=\frac{2a}{\sqrt{4ax}}[/tex]
For our limits of integration, we are going from 0 to h.
Hence, our integral becomes:
[tex]\displaystyle S=2\pi\int_{0}^{h}(\sqrt{4ax})\sqrt{1+\Big(\frac{2a}{\sqrt{4ax}}\Big)^2}\, dx[/tex]
Simplify:
[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax}\Big(\sqrt{1+\frac{4a^2}{4ax}}\Big)\,dx[/tex]
Combine roots;
[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax\Big(1+\frac{4a^2}{4ax}\Big)}\,dx[/tex]
Simplify:
[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax+4a^2}\, dx[/tex]
Integrate. We can consider using u-substitution. We will let:
[tex]u=4ax+4a^2\text{ then } du=4a\, dx[/tex]
We also need to change our limits of integration. So:
[tex]u=4a(0)+4a^2=4a^2\text{ and } \\ u=4a(h)+4a^2=4ah+4a^2[/tex]
Hence, our new integral is:
[tex]\displaystyle S=2\pi\int_{4a^2}^{4ah+4a^2}\sqrt{u}\, \Big(\frac{1}{4a}\Big)du[/tex]
Simplify and integrate:
[tex]\displaystyle S=\frac{\pi}{2a}\Big[\,\frac{2}{3}u^{\frac{3}{2}}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]
Simplify:
[tex]\displaystyle S=\frac{\pi}{3a}\Big[\, u^\frac{3}{2}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]
FTC:
[tex]\displaystyle S=\frac{\pi}{3a}\Big[(4ah+4a^2)^\frac{3}{2}-(4a^2)^\frac{3}{2}\Big][/tex]
Simplify each term. For the first term, we have:
[tex]\displaystyle (4ah+4a^2)^\frac{3}{2}[/tex]
We can factor out the 4a:
[tex]\displaystyle =(4a)^\frac{3}{2}(h+a)^\frac{3}{2}[/tex]
Simplify:
[tex]\displaystyle =8a^\frac{3}{2}(h+a)^\frac{3}{2}[/tex]
For the second term, we have:
[tex]\displaystyle (4a^2)^\frac{3}{2}[/tex]
Simplify:
[tex]\displaystyle =(2a)^3[/tex]
Hence:
[tex]\displaystyle =8a^3[/tex]
Thus, our equation becomes:
[tex]\displaystyle S=\frac{\pi}{3a}\Big[8a^\frac{3}{2}(h+a)^\frac{3}{2}-8a^3\Big][/tex]
We can factor out an 8a^(3/2). Hence:
[tex]\displaystyle S=\frac{\pi}{3a}(8a^\frac{3}{2})\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]
Simplify:
[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]
Hence, we have verified the surface area generated by the function.
Part B)
We have:
[tex]y^2=36x[/tex]
We can rewrite this as:
[tex]y^2=4(9)x[/tex]
Hence, a=9.
The surface area is 1000. So, S=1000.
Therefore, with our equation:
[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]
We can write:
[tex]\displaystyle 1000=\frac{8\pi}{3}\sqrt{9}\Big[(h+9)^\frac{3}{2}-9^\frac{3}{2}\Big][/tex]
Solve for h. Simplify:
[tex]\displaystyle 1000=8\pi\Big[(h+9)^\frac{3}{2}-27\Big][/tex]
Divide both sides by 8π:
[tex]\displaystyle \frac{125}{\pi}=(h+9)^\frac{3}{2}-27[/tex]
Isolate term:
[tex]\displaystyle \frac{125}{\pi}+27=(h+9)^\frac{3}{2}[/tex]
Raise both sides to 2/3:
[tex]\displaystyle \Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}=h+9[/tex]
Hence, the value of h is:
[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]
You seem to have left out that 0 ≤ x ≤ h.
From y² = 4ax, we get that the top half of the parabola (the part that lies in the first quadrant above the x-axis) is given by y = √(4ax) = 2√(ax). Then the area of the surface obtained by revolving this curve between x = 0 and x = h about the x-axis is
[tex]2\pi\displaystyle\int_0^h y(x) \sqrt{1+\left(\frac{\mathrm dy(x)}{\mathrm dx}\right)^2}\,\mathrm dx[/tex]
We have
y(x) = 2√(ax) → y'(x) = 2 • a/(2√(ax)) = √(a/x)
so the integral is
[tex]4\sqrt a\pi\displaystyle\int_0^h \sqrt x \sqrt{1+\frac ax}\,\mathrm dx[/tex]
[tex]=\displaystyle4\sqrt a\pi\int_0^h (x+a)^{\frac12}\,\mathrm dx[/tex]
[tex]=4\sqrt a\pi\left[\dfrac23(x+a)^{\frac32}\right]_0^h[/tex]
[tex]=\dfrac{8\pi\sqrt a}3\left((h+a)^{\frac32}-a^{\frac32}\right)[/tex]
Now, if y² = 36x, then a = 9. So if the area is 1000, solve for h :
[tex]1000=8\pi\left((h+9)^{\frac32}-27\right)[/tex]
[tex]\dfrac{125}\pi=(h+9)^{\frac32}-27[/tex]
[tex]\dfrac{125+27\pi}\pi=(h+9)^{\frac32}[/tex]
[tex]\left(\dfrac{125+27\pi}\pi\right)^{\frac23}=h+9[/tex]
[tex]\boxed{h=\left(\dfrac{125+27\pi}\pi\right)^{\frac23}-9}[/tex]
Please help! I need help on this ! I will give brainliest!
Find the equation of a line that is parallel to the line x = 12 and contains the point (-6,4).
The equation of the parallel line is . (Type an equation.)
Answer:
x = -6 and x = 12 are parallel
Step-by-step explanation:
they are both vertical lines, one crosses the x-axis at -6, the other at 12
What do you divide by 90 to get 30?
Answer:
3
Step-by-step explanation:
3 times 30 = 90 then divide 90 and 30 you get 3
A 4 inch by 6 inch picture is placed in a gram that creates a uniform border of x inches around the picture
Answer:
1.5 inches.
Step-by-step explanation:
A picture measuring 4 inches by 6 inches is placed inside a frame which has equal width around the entire picture.
The area of the frame and the picture is 63 square inches.
Mrs. Matthews wrote three math expressions on the board.
She asked her students which expression would result in a product greater than 7.
Enter the number of the expression that Mrs. Matthews's students should have chosen.
Expression
will result in a product greater than 7.
Answer:
expression 3
because expression 1 = 1
and expression 2 = 7
2x^2-20x+100 quadratic formula
Answer:10
Step-by-step explanation:
HELP ASAP PLEASE LEAVE SMALL EXPLANATION ITS DUE RLLY SOON
Answer:
1. y=3x-4
2. y=-3x+4
3. y= -1/3x+4
4. y= 1/3x-4
Step-by-step explanation:
1. slope= change in y/ change in x
slope= -1-(-4)/1-0=3
y=3x+b
-4=3(0)+b
b=-4
y=3x-4
2. slope=4-10/0-(-2)= -3
y=-3x+b
b=4
y=-3x+4
3. slope= -1/3
y=-1/3x+b
3= -1/3(3)+b
3= -1+b
b=4
y= -1/3x+4
4. y= 1/3x-4 (last one)
Investors buy a studio apartment for $140,000. Of this amount, they have a down payment of
$42,000. Their down payment is what percent of the purchase price? What percent of the purchase
price would a $49,000 down payment be?
Their down payment is % of the purchase price.
Answer:
their down payment is 30%
Step-by-step explanation:
Answer:
Step-by-step explanation:
if the price of the apartment is 140,000 dollars
lets find out how much is 1%
140,000/100=1400
42,000/1400=30
42,000 is 30% of the apt price
49,000/1400=35
49,000 is 35% of the apt price
Jada has read 3/5 of a book. She read 75 pages so far. How many pages are in the whole book
Step-by-step explanation:
3/5 of the book = 75 pages
5/5 of the book = 75 * (5/3) = 125 pages
Hence there are 125 pages in the whole book.
Answer:
Concept: Data Analysis
Jada has read 60% of the book So 60% of the book is 75 pages We want to find the whole count of pages An easy way to do this is to see that for every 20% you have 15 pages You need 40% So its 30 pages So 75+30= 105 pagesSolve for n.
below
.....................
Answer:
n = 12
I hope this helps!
PLSSSSSS I NEED HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Simplify the Expression:
[tex]\sqrt{9a^{2} }[/tex], if a<0
[tex]\sqrt{9a^{2}}=\sqrt{9}\sqrt{a^{2}}=3|a|[/tex]
As [tex]a < 0[/tex], [tex]|a|=-a[/tex], so [tex]3|a|=\boxed{-3a}[/tex]
f(x) = x2. What is g(x)?
Luke works at a shoe store. He earns a 2% commission on all shoes he sells. If he sells $50 of shoes, how much money will he make with his commission?
Answer:
$1
Step-by-step explanation:
Commission earned on sale = 2%
Total sales made = $50
Commission earned for this sale :
Commission percent * worth of sales made
0.02 * $50
= $1
Which represents the equation of the roll line?
Answer:
A) y=3x-4
Step-by-step explanation:
Which shows the use of the associative and commutative properties to make simplifying 3.2 + 20 – 3+ 4.8 + 19 easier?
Answer:
B
Step-by-step explanation:
(3.2+4.8)+[20+19+(-4)]
8. +. 47. -4
=43
backpacks originally cost $24 but if 40% back to school sale is going on determine the sale price of the backpack.
I need help right now
Really Important!!!!!!!
Answer: The price is now 14.40
Step-by-step explanation: The difference is 9.60
The dance team has three cupcake sales a
year to raise money. The amount of money
they make is a function of the amount of
people who buy cupcakes. This function is
represented by the three ordered pairs (40,
100), (70, 175) and (90, 225). What is the
domain of this function?
help
Answer:
40,70,90
Step-by-step explanation:
You run 6 miles in one hour and 24 miles in four hours.
a. 6 miles
per hour
c. 4 hours
b. 4 miles per hour
d. 6 miles
Answer:b
Step-by-step explanation:
The graphs below have the same shape. What is the equation of the red
graph?
Answer:
C. F(x) = x^2 + 4
Step-by-step explanation:
Took the test
What is the value of the expression below? 52 + (8 – 6)
Answer:
54
Step-by-step explanation:
!!! time sensitive please answer !!!
consider the sequence below. 3, 1, 1/3, 1/9
select the explicit function which defines the sequence
A. f(n) = 1/3 • 2^(n-1)
B. f(n) = 2 • (1/3)^(n-1)
C. f(n) = 3 • (1/3)^(n-1)
D. f(n) = 1/3 • 3^(n-1)
Consider the line y=5x-3.
Find the equation of the line that is parallel to this line and passes through the point (2, -5).
Find the equation of the line that is perpendicular to this line and passes through the point (2, -5).
Answer:
y=5x-15, y=-1/5x-23/5
Step-by-step explanation:
Parallel lines have the same slope, so we know the line that is parallel to y=5x-3 must have slope 5.
We now have y=5x+b. We are given the point (2, -5) so substitute the x and y coordinates into the equation.
y=5x+b
-5=5(2)+b
-5=10+b
b=-15
So the equation of the parallel line is y=5x-15.
Perpendicular lines must have slopes that multiply to -1, so we know the line perpendicular to y=5x-3 must have slope -1/5.
We now have y=-1/5x+b. We are given the point (2, -5) so substitute the x and y coordinates into the equation.
y=-1/5x+b
-5=-1/5(2)+b
-5=-2/5+b
b=-23/5
So the equation of the perpendicular line is y=-1/5x-23/5.
A certain radioactive isotope has a half-life of 50 years. A scientist determines that there are 200 grams of the radioactive material present today. How
Much of the isotope was present 200 years ago?
im guessing 800 50X4 = 200 and 200X4 = 800
i never learned this but i hope its correct.
what is 7/9 of 1 1/14
Answer:
1.5555556
1 5/9
14/9
Step-by-step explanation:
hellllllllllllllllp points if you answeer correctly
Answer:
the answer will be [-3/4,1/2]
Step-by-step explanation: