Answer:
The volume of the solution with 20% acid is 27 gallons and the one with 10% acid is 18 gallons
Step-by-step explanation:
Myra needs to mix "x" gallons of the solution with 20% and "y" gallons of the solution with 10%. The volume of the final solution must be 45 gallons, therefore:
x + y = 45
The concentration of acid of the final solution is:
0.2*x + 0.1*y = 45*0.16
0.2*x + 0.1*y = 7.2
Therefore we have a system of equation:
x + y = 45
0.2*x + 0.1*y = 7.2
We need to multiply the first equation by -0.1:
-0.1*x -0.1*y = -4.5
0.2*x + 0.1*y = 7.2
We now sum both equation:
0.1*x = 2.7
x = 2.7/0.1 = 27 gallons
y = 45 - 27 = 18 gallons
At 8:00 am, it is 10 degrees outside. 12 hours later at 8:00 pm, it is -20 degrees outside. What is the difference in temperatures?
Answer:
-30
Step-by-step explanation:
Which problem is being modeled on the number line?
Answer:
Step-by-step explanation:
Determine the volume of the cylinder
Answer:
about 904.78
Step-by-step explanation:
πr^2h pi(6)^2 * 8
Please answer i'll give brainlist
AD and BE are diameters. What is the measure of arc EDC
A. 125 degrees
B. 145 degrees
C. 235 degrees
D. 215 degrees
Answer:
a
Step-by-step explanation:
When a cycle is sold allowing 10% discount on its marked
price a seller gains 5% and allowing 5% discount the profit is
Rs 351. Find the cost price of the cycle. (Ans: Rs. 3240)
The cost price of the cycle is Rs.3240
Represent the cost price of the cycle with x and the selling price with y
A gain of 5% when the marked price is at a discount of 10% implies that:
[tex]5\%=\frac{(1 - 10\%)y-x}{x}[/tex]
Express 10% as decimal
[tex]5\%=\frac{(1 - 0.10)y-x}{x}[/tex]
[tex]5\%=\frac{0.90y-x}{x}[/tex]
Express 5% as decimal
[tex]0.05=\frac{0.90y-x}{x}[/tex]
Cross multiply
[tex]0.05x=0.90y-x[/tex]
Collect like terms
[tex]x + 0.05x=0.90y\\[/tex]
This gives
[tex]1.05x=0.90y[/tex]
Make y the subject of the formula
[tex]y = \frac{1.05x}{0.90}[/tex]
Also, when the discount is 5% and the profit is 351, we have:
[tex]351=(1 - 5\%)y -x[/tex]
Express 5% as decimal
[tex]351=(1 - 0.05)y -x[/tex]
This gives
[tex]351=0.95y -x[/tex]
Make y the subject
[tex]0.95y = 351 + x[/tex]
Substitute [tex]y = \frac{1.05x}{0.90}[/tex]
[tex]0.95 \times \frac{1.05x}{0.90} = 351 + x[/tex]
[tex]\frac{0.9975x}{0.90} = 351 + x[/tex]
Subtract x from both sides
[tex]\frac{0.9975x}{0.90} -x= 351[/tex]
Take LCM
[tex]\frac{0.9975x - 0.9x}{0.90}= 351[/tex]
[tex]\frac{0.0975x}{0.90}= 351[/tex]
Multiply both sides by 0.90
[tex]0.0975x= 315.9[/tex]
Divide both sides by 0.0975
[tex]x= 3240[/tex]
Hence, the cost price of the cycle is Rs.3240
Read more about discounts and price at:
https://brainly.com/question/13651341
The measure of an angle is 17°. What is the measure of its complementary angle?
Answer:
73°
Step-by-step explanation:
the measure of two complementary angles add up to 90
so We need to solve this equation to get the measure of its complementary angle :
x + 17 = 90
then
x = 90 - 17
= 73
what is the solution of this equqtion? 1w= -17
Answer:
-17
Step-by-step explanation:
1w= -17
(1)(-17)=
-17
Answer:
-17
Step-by-step explanation:
in this situations, we normally divide both sides by the number next to the unknown.
1w is the same as saying w
so,
w = -17
The triangular prism shown below is 6 \,\text{cm}6cm6, start text, c, m, end text wide and 4\,\text{cm}4cm4, start text, c, m, end text deep. The vertical height is 7\,\text{cm}7cm7, start text, c, m, end text. What is the length of the side edge, sss, of the triangular prism? Round your answer to the nearest tenth.
Question :
The triangular prism shown below is 6 cm wide and 4 cm deep. The vertical height is 7 cm. What is the length of the side edge, s, of the triangular prism? Round your answer to the nearest tenth.
Answer: 7.62cm
Step-by-step explanation:
Given the following :
Width = 6cm
Depth = 4cm
Vertical height = 7cm
Splitting the face of the prism into two:
Thus the width becoming 6cm/2 = 3cm and vertical height = 7cm
Using Pythagoras ;
The side edge 's' equals
s^2 = width^2 + height^2
s = √(width^2 + height^2)
s = √(3^2 + 7^2
s = √9 + 49
s = √58
s = 7.62cm
Answer:
7.6
Step-by-step explanation:
the person above is correct, i took the test on khan, but you have to round to the nearest tenth
what percent of 420 is 70
Answer:
16.67
Step-by-step explanation:
Answer:
16.67
Step-by-step explanation:
70:420*100 =
(70*100):420 =
7000:420 = 16.67
What is the distance between the points (4, 5) and (10, 13) on a coordinate plane?
A. 10 units
B. 14 units
C. 12 units
D. 8 units
Answer:
10
Step-by-step explanation:
Distance = √(x2-x1)² + (y2-y1)²
d = √(10-4)² + (13-5)²
d = √6² + 8²
d = √36+364
d = √100
d = 10
help me plzzzzzzz!!!!
[tex] {y}^{2} + 14 = 3 {y}^{2} \times 5[/tex]
Answer:
[tex]y=1,\:y=-1[/tex]
Step-by-step explanation:
[tex]y^2+14=3y^2\cdot \:5\\\y^2+14-14=3y^2\cdot \:5-14\\y^2=15y^2-14\\y^2-15y^2=15y^2-14-15y^2\\-14y^2=-14\\\frac{-14y^2}{-14}=\frac{-14}{-14}\\y^2=1\\\\y=\sqrt{1},\:y=-\sqrt{1}\\y=1,\:y=-1[/tex]
Answer:
y = ± 1
Step-by-step explanation:
Given
y² + 14 = 3y² × 5, that is
y² + 14 = 15y² ( subtract y² from both sides )
14 = 14y² ( divide both sides by 14 )
1 = y² ( take the square root of both sides )
± [tex]\sqrt{1}[/tex] = y , that is
y = ± 1
Thus y = - 1 or y = 1
3. Which of the following represents a function?
O (5, 1), (5,2), (5, 3), (5, 4)
O (-1,2), (-2, 1), (-1, -2), (-2,-1)
O (3, 4), (-3, 2), (3, 8), (5,5)
O (2, 3), (4, 3), (-2, -3), (-4,-3)
Answer: D is a function.
Step-by-step explanation:
A function need to have exactly one output to each input.
Answer: D. (2, 3), (4, 3), (-2, -3), (-4,-3)
Step-by-step explanation: This represents a function because they're the opposing of each other. Hope this helps happy holidays! :)
I need help with this :/ pls help
Answer:
When you divide by 10^3, the decimal point moves three places to the right. When you multiply by 0.001, the decimal point moves three places to the right. So, both equal .0777
Step-by-step explanation:
What are the domain and range of the logarithmic
function f(x) = log7X? Use the inverse function to
justify your answers.
Answer:
The domain of f is x > 0.
The range of f is all real numbers.
The domain of the inverse function is all real numbers.
The range of the inverse function is y > 0.
The domain of f is the same as the
range of the inverse function.
The range of f is the same as the
the domain of the inverse function.
Step-by-step explanation:
this is the sample answer, make sure you rewrite in your own words!
The domain and the range of a function are the set of input and output values of the function
The domain and the range of the function are set of real numbers greater than 0
The function is given as:
[tex]f(x) = log_7(x)[/tex]
The above function is a logarithmic function.
From the properties of a logarithmic function, we have:
The x-values are always greater than 0The y-values are always greater than 0This means that, the domain and the range of the function are set of real numbers greater than 0
Read more about domain and range at:
https://brainly.com/question/10197594
find the two values that x can have if x2-12=37
Answer:
[tex]x2 - 12 = 37[/tex]
Step-by-step explanation:
Add 12 to both sides:
[tex]x2 - 12 + 12 = 37 + 12[/tex]
Simpilfy:
[tex]x2 = 49[/tex]
Simplify:
[tex]2x^{2} = 49[/tex]
Simplify:
[tex]\frac{2x^{2} }{2} = \frac{49}{2}[/tex]
[tex]x^{2} = \frac{49}{2}[/tex]
For x^2 = f(a) the solutions are x = [tex]\sqrt{f(a)} , - \sqrt{f(a)}[/tex]
x = [tex]\sqrt{\frac{49}{2} } , x = -\sqrt{\frac{49}{2} }[/tex]
-[tex]\sqrt{\frac{49}{2} } = -\frac{7\sqrt{2} }{2}[/tex]
x = [tex]\frac{7\sqrt{2} }{2} , x = -\frac{7\sqrt{2} }{2}[/tex]
Hope I helped, may I get brainliest and a thanks?
Thank you, have a good day! =)
Answer:
[tex]x = 7 \\ x = - 7[/tex]
Step-by-step explanation:
[tex] {x}^{2} - 12 = 37 \\ {x}^{2} = 37 + 12 \\ {x}^{2} = 49 \\ x = \sqrt{49} \\ x = 7 \\ x = - 7[/tex]
What is the end behavior of the polynomial function?
Answer:
D) as x approaches neg. infinity, y approaches neg. infinity
Step-by-step explanation:
This is because you get to negative x infinity which is towards the right, you see that the y value is going down sharply as well towards the direction of negative infinity in y direction (x direction is right to left and y direction is up and down)
Answer:
D one Edge 2021 ;))
Step-by-step explanation:
Benny scored 19 points in Mondays basketball game and 46 points in Fridays game.How many points did he score in the last two games?
Answer:
He scored 65 points in his last two games
Step-by-step explanation:
Here, we want to calculate the number of points Benny scored in his last two games.
We must understand that his last two games correspond to the games he played on Monday and on Friday
So to get his total points in the last two games, what we do is that we add both points together
Mathematically, that would be 19 + 46 = 65 points
A rectangular prism has a length of 12in, a height of 5in, and a width of 8in. What is its volume, in cubic in?
Answer: The volume is 480 in^3
Step-by-step explanation:
v= lwh
v= 12 * 5 * 8
v= 480 in^3
Answer:
Volume of the rectangular prism = [tex]480in.^{3}[/tex]
Step-by-step explanation:
Formula for the volume of a rectangular prism= Ah, where A= base area
& h= height
Base area(A)= Length×Width
= 12in.×8in.
= [tex]96in.^{2}[/tex]
Since height=5in.,
Volume= [tex]96in.^{2}[/tex]×5in.
= [tex]480in.^{3}[/tex]
Hope this helps!!!
Pls mark as brainliest
What is the y-intercept of the quadratic function f(x) = (x-8)(x+3)
Answer:
-24
Step-by-step explanation:
To find the y intercept, plug x in as 0.
Answer:
-24
Step-by-step explanation:
Y intercept is where graph cuts the y axis and it satisfies x=0
So put x=0 in your equation
F(0)= -8 x 3
F(0)= -24
Therefore y-intercept= -24
Need Help Asap offering 10 Points!!!!
Answer:
13 minutes 30 seconds.
Step-by-step explanation:
You just divide 10.8 by 0.8...
10.8÷0.8=13.5
Pleaaaase hellp me will mark u brainly for both answers!!!
Thank u if u do really appreciate it.
Answer:
1. Option A is correct (A = length x width)
2. Option B is correct ( A = base x height/2)
Hope this helps
:)
find the variable: n/14=3
Answer:
n=42
Step-by-step explanation:
How to determine the function with the graph?
A submarine at a depth of 675 feet below the surface rose to 1/3 this depth. Which of the following represents the new depth of the submarine below the surface?
Answer:
225
Step-by-step explanation:
Take 675/3 to find one third of its current depth. That gives you your answer. Does that make sense?
So do i divide by 2 each time?
(x - 3)² + (x - 1)² = 8
Identify the center and radius of each
Answer:
The center is at (3,1) and the radius is [tex]\sqrt{8}[/tex]
Step-by-step explanation:
I am going to assume you meant to write
[tex](x-3)^2+(y-1)^2 = 8[/tex]
Since if both variables were x it would not be a circle:
Then you can find the center and radius using the general formula of a circle:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
where the center is at (h,k) and r is the radius
Therefore:
The center is at (3,1) and the radius is [tex]\sqrt{8}[/tex]
Find the greatest common factor of 24, 40 and 60
Please answer asap ty!!
Answer:
4
Step-by-step explanation:
Answer:
GCF=4
Step-by-step explanation:
It's 4
24/4=6
40/4=10
60/4=15
You can't go any higher because there is no GCF of 6, 10, and 15.
3. Find x, y, and z.
zº
xº
y
18°
64°
Answer:
[tex]y = 18 \: \: degrees[/tex]( vertically opposite angles)
[tex]x = 64 \: \: degrees[/tex]
[tex]y + z + x = 180 \\ 18 + z + 64 = 180 \\ 82 + z = 180 \\ z = 180 - 82 \\ z = 98 \: \: degrees[/tex]
Someone help me please
Step-by-step explanation:
Step 1: Convert degrees into radians
[tex]\frac{degrees}{1}*\frac{\pi }{180}[/tex]
[tex]\frac{52}{1}*\frac{\pi}{180}[/tex]
[tex]\frac{52\pi}{180}[/tex]
[tex]\frac{13\pi}{45}[/tex]
Step 2: Find the arc length
[tex]S = r\theta[/tex]
[tex]S=(3)(\frac{13\pi}{45})[/tex]
[tex]S = \frac{39\pi}{45}[/tex]
[tex]S=\frac{13\pi}{15}[/tex]
Answer: Option B
translate (-4,5) up 3 units
then reflect the result over the y-axis
what are the coordinates of the final point?
Answer:
4,8
Step-by-step explanation:
reflecting over y axis is flipping to the other side. and you are going up 3 points so 5+3 is 8. and negative four turns to positive four
