Answer:
[tex]\bold{x=\dfrac{a^2+ab}{a-b}}[/tex]
Step-by-step explanation:
[tex]\bold{a(x-b)=a^2+bx}\\\\\bold{ax-ab=a^2+bx}\\\\{}\ \ +ab\qquad+ab\\\\\bold{ax\ =\ a^2+bx+ab}\\\\ -bx\qquad-bx\\\\\bold{ax-bx=a^2+ab}\\\\\bold{(a-b)x\ =\ a^2+ab}\\\\\div(a-b)\quad\ \,\div(a-b)\\\\ \bold{x=\dfrac{a^2+ab}{a-b}}\qquad\qquad\qquad a\ne b[/tex]
Clyde’s truck travels an average distance of 12 miles per gallon of gas. When full, his truck’s tank holds 40 gallons of gas. If the tank is 8 7 empty, about how many more miles can the truck travel before the tank is completely empty?
The truck can travel 60 miles before the tank is completely empty
How to determine the number of miles?The capacity of the truck is;
Capacity = 40 gallons
When it is 7/8 empty, the amount of gas in the truck is:
Amount = (1 - 7/8) * 40 gallons
Amount = 5 gallons
The rate is given as:
Rate = 12 miles per gallon
So, the number of miles it can travel from this point is:
Miles = Amount * Rate
Miles = 5 * 12
Miles = 60
Hence, the truck can travel 60 miles before the tank is completely empty
Read more about rate at:
https://brainly.com/question/14335655
#SPJ9
A business man bought a car at rs 550000 and sold it rs 533500 find his loss percentage
Answer:
Cost price (c.p) = Rs. 550000
selling price (s.p) = Rs. 533500
Loss (l) = c.p - s.p
= Rs. 550000 - Rs. 533500
= Rs. 16500
Now,
Loss percentage = Actual loss * 100%
c.p
= Rs. 16500 * 100%
Rs. 550000
= 3%
Answer:
loss%=3.09%
Step-by-step explanation:
given,s.p=550000
c.p=533500
Now,loss percent= Actual loss /c.p×100%
=16500/53500×100%
=3.09%
determine whether the fractions 3/6 and 2/4 are equivalent
Answer:
They are equivalent
Step-by-step explanation:
3/6 is equal to 1/2
2/4 is equal to 1/2
what is the equation of the line
Answer:
y = -7
Step-by-step explanation:
the value of -7 is constant at the x coordinates
y = -7
x | y
-8 | -7
-6 | -7
-4 | -7
-2 | -7
0 | -7
2 | -7
4 | -7
6 | -7
8 | -7
When you roll a dice you are more likely to get a 2 than a 6
Answer:
You are just as likely to get a 2 as a 6
Step-by-step explanation:
There are six sides on a die 1,2,3,4,5,6
Assuming a fair normal die
P(2) = number of 2's / total = 1/6
P(6) = number of 6's / total = 1/6
You are just as likely to get a 2 as a 6
Given__________
there is one,
and only one, line perpendicular to the plane through that point.
Answer:
plane containing a line
Step-by-step explanation:
In accordance with a plane postulate corollary, it is concluded that, for a given PLANE CONTAINING A LINE, there is one and only one perpendicular line through a given point on the line.
Hence, in this case, the correct complete statement is written as: Given PLANE CONTAINING A LINE there is one, and only one, a line perpendicular to the plane through that point.
What is the midpoint between each pair (-1, -5) and (-5, 9)
==============================================
Explanation:
The x coordinates are -1 and -5. They add to -6. Which is then cut in half to -3
The y coordinates are -5 and 9. They add to 4. This is cut in half to 2.
The midpoint is therefore (-3, 2)
-------
A symbolic way to write this is if you had endpoints (a,b) and (c,d), then the midpoint is [tex]\left(\frac{a+c}{2}, \frac{b+d}{2}\right)[/tex]
Evaluate the expression below when x = 5.
3(2x - 7)
Answer:
9
Step-by-step explanation:
Hello!
They want us to find x when x is 5 so we put 5 in for x
3(2(5) - 7)
Now we follow PEMDAS
3(10 - 7)
3(3) = 9
The answer is 9
Hope this helps!
Given the equation 3x+25 =7x-5 which order of operations completely solves for x?
What is the cost of 18 toy cars?
Answer:
$27
Step-by-step explanation:
Assuming this price list, ...
4 toy cars cost 6 dollars
6 toy cars cost 9 dollars
8 toy cars cost 12 dollars
We recognize that 18 cars is 3 times 6 cars, so the cost will be ...
cost of 18 cars = 3(cost of 6 cars) = 3($9) = $27
The cost of 18 toy cars is $27.
A bucket has 16 inches of water in it but there is a hole in the bottom. Use interval notation to write the domain and range of the function H(x) = 16 - 1.25x, where x is the time the water has been leaking for (in minutes) and is the height of the water (in inches). *
Answer: range: {0in, 16in}
domain {0min, 12.8 min}
Step-by-step explanation:
When we have a function:
f(x) = y.
The range is the set of possible values of y and the domain is the set of all the possible values of x.
In this case, our function is:
H(x) = 16 - 1.25*x
which is a linear equation, and we know that the linear equations are defined (for range and domain) in the set of all the real numbers, but this is a physical situation, so we must see at the real problem.
The bucket can not have more water than the initial amount, 16 inches, so this is the maximum in the range.
The minimum height of water that we can find in the bucket is 0 inches (so the bucket is empty) then this is the minimum of the range.
Then we can write the range as:
R: 0in ≤ y ≤ 16in. = {0in, 16in}
Now we can find the extremes of the domain by using the extremes of the range:
y = 16 = 16 - 1.25*x
0 = -1.25*x
then we have x = 0min, this will be the minimum of the domain.
Now using the minimum of the range y = 0 we have:
y = 0 = 16 - 1.25*x
1.25*x = 16
x = 16/1.25 = 12.8 mins
This is the maximum time in the domain (because after this time, there is no water in the bucket)
Then the domain is:
D: 0min ≤ x ≤ 12.8 min
how to solve slope intercept form with 4y=x+3
m = 1/4 = slope
b = 3/4 = y intercept
===================================================
Explanation:
The goal is to solve for y.
Divide both sides by 4 and simplify like so
4y = x+3
4y/4 = (x+3)/4
y = (x+3)/4
y = x/4 + 3/4
y = (1/4)x + 3/4
This equation is in slope intercept form y = mx+b
m = 1/4 is the slope
b = 3/4 is the y intercept
The graph is a straight line that goes through (1,1) and (5,2)
The size of a television is the length of the diagonal of its screen in inches. The aspect ratio of the screens of older televisions is 4:3, while the aspect ratio of newer wide-screen televisions is 16:9. Find the width and height of an older 35-inch television whose screen has an aspect ratio of 4:3.
Answer:
The width and height of the old 35-inch television are 28 inches and 21 inches, respectively.
Step-by-step explanation:
35-inch television is a television whose screen has an hypotenuse ([tex]l[/tex]) of 35 inches and the aspect ratio of 4 : 3 means that 4 inches width per each 3 inches height. And by Pythagorean Theorem:
[tex]r_{l} =\sqrt{r_{w}^{2}+r_{h}^{2}}[/tex]
Where:
[tex]r_{l}[/tex] - Hypotenuse rate, dimensionless.
[tex]r_{w}[/tex] - Width rate, dimensionless.
[tex]r_{h}[/tex] - Height rate, dimensionless.
If [tex]r_{w} = 4\,in[/tex] and [tex]r_{h} = 3\,in[/tex], the hypotenuse rate is:
[tex]r_{l} = \sqrt{4^{2}+3^{2}}[/tex]
[tex]r_{l} = 5[/tex]
The width and height of the old television can be found with the help of trigonometric functions:
Width of 35-inch old television ([tex]w[/tex])
[tex]w = l\cdot \cos \theta[/tex]
[tex]w = l\times\left(\frac{r_{w}}{r_{l}} \right)[/tex]
Height of 35-inch old television ([tex]h[/tex])
[tex]h = l\cdot \sin \theta[/tex]
[tex]h = l\times\left(\frac{r_{h}}{r_{l}} \right)[/tex]
Where [tex]\theta[/tex] is the direction of the hypotenuse with respect to width, measured in sexagesimal degrees.
If [tex]r_{w} = 4[/tex], [tex]r_{h} = 3[/tex] and [tex]r_{l} = 5[/tex] and [tex]l = 35\,in[/tex], the width and height of the old 35-inch television:
[tex]w = (35\,in)\times \left(\frac{4}{5} \right)[/tex]
[tex]w = 28\,in[/tex]
[tex]h =(35\,in)\times \left(\frac{3}{5} \right)[/tex]
[tex]h = 21\,in[/tex]
The width and height of the old 35-inch television are 28 inches and 21 inches, respectively.
Help urgent, which functions are bounded below but not above? Choose all answers that apply.
Answer:
c, e, f, and i
Step-by-step explanation:
a. is bounded above at y = 1 and below at y = 0
b. is unbounded both above and below
c. is bounded below at y = 0 and unbounded above
d. is unbounded both above and below
e. is bounded below at y = 0 and unbounded above
f. is bounded below at y = 0 and unbounded above
g. is bounded below at y = 0 and bounded above at y = 1
h. is unbounded both above and below
i. is bounded below at y = 0 and unbounded above
j. is unbounded both above and below
can someone help me in kinda dumb
Answer:
[tex]\Huge \boxed{\mathrm{d}}[/tex]
Step-by-step explanation:
y is equal to $1.67 per pounds of peanuts
pounds of peanuts = x
y is equal to $1.67 per x
per is for each
y = $1.67 × x
The equation that correctly describes this relation is option d.
How the exponent can be multiplied?
Answer:
D
Step-by-step explanation:
The answer is D, because it is saying for you to do,
2⁶ multiplied 5 times in a row,
2⁶×2⁶×2⁶×2⁶×2⁶ and this is equal to 2³⁰.
Answer:
Option D
Step-by-step explanation:
Whenever we multiply the same numbers with different exponents, we write the same number and add the exponents.
Example: (1/5)^2 x (1/5)^6
=> (1/5)^2 + 6
=> (1/5)^8
Example: 7^3 x 7^8
=> 7^3+8
=>7^11
Whenever we divide the same number with different exponents, we write the same number and subtract the exponents.
Example: 9^3 / 9^4
=> 9^3-4
=> 9^-1
Whenever there is an number with the exponent, and there is an exponent outside the bracket, then we multiply.
Example: (2^6)^-5
=> 2^6 x -5
=> 2^-30
So, the Answer is D.
The first four terms of a sequence are shown below:
7,4, 1, -2
Which of the following functions best defines this sequence?
Of(1) = 7, f(n + 1) = f(n) + 3; for nx 1
O f(1) = 7, f(n + 1) = f(n) - 3; for nx 1
O f(1) = 7, f(n + 1) = f(n) – 4; for n 2 1
Of(1) = 7, f(n + 1) = f(n) + 4; for n > 1
Answer:
second option
Step-by-step explanation:
Given the sequence
7, 4, 1, - 2
There is a common difference d between consecutive terms, that is
d = 4 - 7 = 1 - 4 = - 2 - 1 = - 3
Thus to obtain any term in the sequence from the previous term, subtract 3
Thus
f(1) = 7 , f(n + 1) = f(n) - 3 for n ≥ 1
Solve for 6x when x=6. I need your guys and girls' help.
Answer:
36
Step-by-step explanation:
if x=6 you are multiplying 6 by 6..
you substitute 6 in for x in the problem (6x) so it becomes 6 x 6
the you multiply and get 36
Answer: 36
Step-by-step explanation: 6x means the same thing as 6 · x.
In this case, we are given that x = 6.
So we have 6 · 6 which is 36.
Rewrite the number in standard form. 3.4 x 10^8
Answer:
340000000
Step-by-step explanation:
3.4 x 10^8 is in scientific notation.
To change this to standard form you have to multiply 3.4 by 10 to the 8th power. You would be multiplying 3.4 by 10 eight times. It's a positive 8 so you move the decimal point 8 times to the right. If it were a negative then you'd move the decimal to the left.
3.4
↑ moving the decimal 8 times to the right would then make it 3400000002. The radius of a circle is 9 cm. Find the area of the circle
(Use 3.14 as the approximation of T.)
Answer:
Area of a Circle = 254.34 cm²
Step-by-step explanation:
Area of a Circle = π r²
Area of a Circle = 3.14 * 9²
Area of a Circle = 254.34 cm²
What is y = -3x+4 and y=-7x
Answer:
x=-1 , y=7
Step-by-step explanation:
y = -3x+4 and y=-7x
substitute y=-7x in the equation y = -3x+4
-7x=-3x+4 ( put variable(x) together)
-7x+3x=4
-4x=4
x=-4/4
x=-1
find y: y=-7x ⇒ y=-7(-1) ⇒ y=7
check :y = -3x+4
7=-3(-1)+4
7=7 ( correct)
Given x=-3, y=6, and z=-4
-15+(-x)+y=
x = -3 , y = 6 , z = -4
Take Given equation :
⇒-15 + (-x) + y = 0
substitute values of x and y
⇒-15 + [- ( -3)] + 6
⇒-15 + (3) + 6
⇒-15 + 9
⇒-6
Hence, value of -15 + (-x) + y = - 6
0
The commission rate at Toys R Us
is 4%. If the salesman sold $450
in toys how much did he make in
commission?
Answer:
$18
Step-by-step explanation:
To find a percent of a number, change the percent to a decimal by dividing it by 100, and multiply the decimal by the number.
4% of $450 = 4% * $450 = 0.04 * $450 = $18
Which image shows a rotation?
Answer:
c is the best answer in my mind
Brainliest for whoever gets this right!
Make x the subject of the formula
a(x-b)=a^2+bx
Answer:
[tex]x=\frac{(a^2+ab)}{a-b}[/tex]
Step-by-step explanation:
So we want to make x the subject of the formula:
[tex]a(x-b)=a^2+bx[/tex]
First, distribute the left side:
[tex]a(x)-a(b)=a^2+bx\\ax-ab=a^2+bx[/tex]
Combine all the terms with x with it on one side. To do this, first subtract bx from both sides. The right side cancels:
[tex](ax-ab)-bx=(a^2+bx)-bx\\ax-ab-bx=a^2[/tex]
Remove the -ab from the left. Add ab to both sides. The left side cancels:
[tex](ax-ab-bx)+ab=a^2+ab\\ax-bx=a^2+ab[/tex]
Now, distribute out the x from the left side:
[tex]ax-bx=a^2+ab\\x(a-b)=a^2+ab[/tex]
Divide both sides by (a-b). The left side cancels:
[tex]\frac{(x(a-b))}{a-b}=\frac{(a^2+ab)}{a-b} \\x=\frac{(a^2+ab)}{a-b}[/tex]
Therefore:
[tex]x=\frac{(a^2+ab)}{a-b}[/tex]
Answer:
Step-by-step explanation:
ax -ab = + bx
collect like terms
ax-bx= +ab
factorise
x(a-b)=a(a+b)
x=[tex]\frac{a(a+b)}{a-b}[/tex] or [tex]\frac{a^{2} + ab}{a -b}[/tex]
what is 40 x 90 in multiplacation
Answer:
3600
Step-by-step explanation:
We multiple 40 x 90 which is equal to 4 x 10 x 9 x 10.
4 x 9 = 36 and 10 x 10 = 100, so 40 x 90 = 36 x 100 = 3600.
Answer:
The answer is 3,600
Step-by-step explanation:
40x90=3,600
Look at picture for step by step!
Hope this helps!
By: BrainlyAnime
Brainliest would be appreciated!
If 5 becomes 11 and 12 becomes 25, what does 15 become?
Answer:
31
Step-by-step explanation:
5---11
12---25
hmmm
isn't that jsut x * 2 + 1?
soooo
15 would be
15*2+1
which is 31
Answer:
31.
Step-by-step explanation:
5+5 = 10 + 1 = 11
12 + 12 = 24 +1 = 25
15 + 15 = 30 + 1 = 31
I don't know I tried to see if that was the pattern. It checks out math wise.
Which of the following best describes the term constructions in geometry?
The options in this question are missing; here is the complete question:
Which of the following best describes the term constructions in geometry?
A. Combining two or more figures together to create a new figure or shape.
B. A way to draw precise figures using a compass and a straightedge.
C. Creating a figure or shape by hand.
D. Places where things are being built that often slow down traffic.
The answer to this question is B. A way to draw precise figures using a compass and a straightedge.
Explanation:
Geometry is a sub-field of mathematics that studies figures, lines, angles, and related features. In this, the term "construction" describes the creation of figures by using a straight edge such as a ruler, a compass (object to draw circles or arcs and measure distances), and a pen, pencil, or similar instrument to draw. For example to draw or construct a circle a compass is mainly used while the construction of a hexagon requires a straight edge and compass. According to these ideas, the correct answer is B.
A new Youth Activity Center is being built in Hadleyville. The perimeter of the rectangular playing field is 442 yards. The length of the field is 4 yards less than quadruple the width. What are the dimensions of the playing field?
Answer:
45 yards and 176 yards
Step-by-step explanation:
Perimeter of a rectangular playing field = 2(Length + width)
P = 2(L+W)..................... Equation 1
From the question,
Let the width of the rectangular playing field = x yards,
The the Length = 4x-4 yards.
Given: P = 442 yards.
Substitute these values into equation 1
442 = 2(4x-4+x)
442/2 = 5x-4
221 = 5x-4
5x = 221+4
5x = 225
x = 225/5
x = 45 yards.
Width = 45 yards.
Length = (45×4)-4 yards = 176 yards
Hence the dimensions of the playing field are, 45 yards and 176 yards
how do reference angles work and how do you find them?
A 200-degree angle is between 180 and 270 degrees, so the terminal side is in QIII.
Do the operation indicated for that quadrant. Subtract 180 degrees from the angle, which is 200 degrees.
You find that 200 – 180 = 20, so the reference angle is 20 degrees.
hope this helped!
o(*￣▽￣*)ブ