Answer:
Amount of 8% vinegar = 216 mL
Amount of 13% vinegar = 54 mL
Step-by-step explanation:
First, of all, let x be the amount of 8% vinegar used
Since, the scientist needs 270 mL of vinegar, then;
Let 270 - x be the amount of 13% vinegar used
Now, we are told that she needs 270 mL of a 9% vinegar.
This means that;
8%x + 13%(270 - x) = 9%(270)
Simplifying this gives;
0.08x + 0.13(270 - x) = 0.09 × 270
Expanding the bracket gives;
0.08x + 35.1 - 0.13x = 24.3
0.13x - 0.08x = 35.1 - 24.3
0.05x = 10.8
x = 10.8/0.05
x = 216 mL
Thus, she will need to use 216 mL of the 8% vinegar.
Since 270 - x is the amount of 13% vinegar used , then;
the amount of 13% vinegar = 270 - 216 = 54 mL
Distance between (-4.9(-5.3)
Use the distance formula to determine the distance between two points.
√ 37
The elevation of lake sam rayburn is 164 above mean sea level during the summer if it does not rain the elevation of the lake decreases by 0.5 feet each week
Answer:
I guess that you want to model the elevation of Lake Sam Rayburn.
During the summer, it is 165 ft above the sea level (the sea level is our position 0ft).
If it does not rain, the elevation of the lake decreases by 0.5ft each week.
So if we assume that there is no rain, we can write the elevation fo the lake as a linear relationship with slope equal to -0.5ft and y-intercept equal to 165ft.
L(w) = 165ft - 0.5ft*w
Where w is the number of weeks without rain, if we have 0 weeks without rain, then the level of the lake remains constant at 165ft above sea level,
L(0) = 165ft - 0.
Calculating the Volume of a Cylinder
Calculate the volume of this regular solid.
What is the volume of the cylinder? Round your answer
to the nearest hundredth.
cm?
В B.
13 cm
4 cm -
Answer:
The answer is 653.45
Step-by-step explanation:
1) An elevator is on the 15th floor, it goes down 18 floors
and then up 5 floors. What floor is it on now?
Answer:
The elevator is now on the 2nd floor.
Step-by-step explanation:
15 - 18 = -3
-3 + 5 = 2
Answer:2nd floor
Step-by-step explanation:
since the elevator is on the 15th floor and you go down 18 that’s equals negative 3 then you go back up 5 floors and you add 5 to negative 3 which leaves you with the 2nd floor
Jenny explained to Robert that only rational numbers are considered as a set of real numbers. Robert disagreed stating that irrational numbers could also be a set of real numbers explain which student is correct
Answer: Robert is correct, irrational numbers are part of real numbers.
Explanation:
In mathematics, numbers are classified into different groups or seats. In the case of real numbers, these are a broad category that includes all numbers that can be represented on a line. Moreover, this category includes smaller categories such as rational numbers, for example, 15, 2.4 or 6/2 that can be represented as fractions, as well as, irrational numbers such as [tex]\pi[/tex] that cannot be fractions. In this context, Jenny is incorrect and Robert is correct because irrational numbers are also real numbers.
Cynthia Besch wants to buy a rug for a room that is 21 ft wide and 34 ft long. She wants to leave
a uniform strip of floor around the rug. She can afford to buy 338 square feet of carpeting. What
dimensions should the rug have?
Answer:
Dimensions of the rug = 13 ft × 26 ft
Step-by-step explanation:
Dimensions of the room = 21 ft × 34 ft
Area of the room = 21 × 34 = 714 ft²
Cynthia wants to leave a uniform strip of floor around the rug.
Let the width of the rug = x ft
Then the dimensions of the rug will be = (21- 2x)ft × (34 - 2x)ft
Area of the rug = (21 - 2x)×(34 - 2x) square feet
338 = (21 - 2x)×(34 - 2x)
338 = 714 - 68x - 42x + 4x²
4x² - 110x + 714 - 338 = 0
4x² - 110x + 376 = 0
2x² - 55x + 188 = 0
2x² - 47x - 8x + 188 = 0
x(2x - 47) - 8(x - 47) = 0
(x - 4)(2x - 47) = 0
x = 4, [tex]\frac{47}{2}[/tex]
For x = 23.5 area of the rug will be negative.
Therefore, x = 4 ft will be the width of the rug.
Dimensions of the rug will be 13 ft × 26 ft.
Which of the following provides an object with rotational symmetry?
Answer: Choice C) Star shaped symbol
We can rotate the star symbol 90 degrees to have it line up with its original image. The before and after images would be identical after doing such a rotation. So this figure has rotational symmetry.
The other figures would change if we rotated them some angle x such that [tex]0 < x < 360[/tex], so they do not have rotational symmetry.
Find the complement and supplement of the angle with measure 40 degrees
Answer:
The complement is 50 and the supplement is 140
Step-by-step explanation:
Complementary angles add up to 90. Supplementary angles add up to 180. We simply need to subtract to find the difference to fill the gap.
90-40=50
180-40=140
The complement is 50 and the supplement is 140
Answer:
complement angle to 40 degrees is 50 and the supplement angle to 40 degrees is 140
Step-by-step explanation:
complement angle to 40 degrees is 90 - 40 = 50 degrees
Supplement angle to 40 degrees is 180 - 40 = 140 degrees.
-3x+51>13+7x-22 help
Answer:
x < 6
Step-by-step explanation:
Given
- 3x + 51 > 13 + 7x - 22 ( simplify right side )
- 3x + 51 > 7x - 9 ( subtract 7x from both sides )
- 10x + 51 > - 9 ( subtract 51 from both sides )
- 10x > - 60
Divide both sides by - 10, reversing the symbol as a result of dividing by a negative quantity.
x < 6
30 POINTS!!!!!!!!PLS COME AND LOOK!!! I NEED YOU GENIUSES!!! I WILL GIVE BRAINLIEST!!!!! AT LEAST COME AND LOOK!!!! WILL FOREVER BE GREAT FULL!!! EASY IM JUST DUMB!! The graph represents the equation 2 + 2 = 8. Use this graph to answer questions 6, 7, and 8. PART A) Look at the graph of the equation 2 + 2 = 8. Give its domain and range. PART B) Use algebraic means to show that 2 + 2 = 8 is not a function. Explain your process.
Answer:
See below.
Step-by-step explanation:
So we have the graph of:
[tex]x^2+y^2=8[/tex]
As given, the graph is a circle with a radius of 2√2 and a center of (0,0)
Part 1)
The domain of a function is the span of x-values it covers and the range of a function is the span of y-values it covers.
From the graph, we can see that the x-values the graph covers goes from -2√2 to +2√2. The graph includes these values.
Thus, the domain is, in interval notation:
[tex][-2\sqrt2,2\sqrt2][/tex]
From the graph, we can see that the y-values the graph covers also goes from -2√2 to 2√2.
Therefore, like the domain, the range in interval notation is:
[tex][-2\sqrt2,2\sqrt2][/tex]
Part 2:
First of all, we can use the vertical line test to prove that the graph is indeed not a function.
Algebraically, we have to do some more.
First, recall what it means when an equation is not a function. It means that one x maps onto two or more ys.
In other words, to prove that the equation is not a function, we can substitute an x for a value and solve for y.
For instance, let's use 0 for x (and 0 is within the domain). Thus:
[tex]x^2+y^2=8\\(0)^2+y^2=8[/tex]
Simplify:
[tex]y^2=8[/tex]
Take the square root of both sides:
[tex]y=\pm\sqrt8\\y=\pm2\sqrt2[/tex]
In other words, when x is 0, y can be either -2√2 or 2√2. So we have two different y-values with the same x-coordinate.
[tex](0,-2\sqrt2)(0,2\sqrt2)[/tex]
Therefore, the equation is not a function.
Determine for each x-value whether it is in the domain of f or not. -
Answer:
-7 is in our domain.
0 is in our domain
7 is not in our domain.
Step-by-step explanation:
So we have the rational function:
[tex]f(x)=\frac{x}{x-7}[/tex]
The domain restrictions of rational functions are the zeros of the denominator. In other words, the domain of rational functions are always all real numbers except for the zeros of the denominator.
So, solve for the denominator by setting it to 0:
[tex]x-7=0[/tex]
Add 7 to both sides:
[tex]x=7[/tex]
So, our domain is all real numbers except for 7.
(When x=7, we have 7/0, which is undefined.)
Therefore:
-7 is in our domain.
0 is in our domain
7 is not in our domain.
Answer:
the picture has it all!
whatever equals zero is not the domain and whatever doesnt equal zero is the domain!
hope i helped :)
The sum of w and fourteen is five. What is the value of w?
Answer:
w=-9
Step-by-step explanation:
14-9=5, but this is addition, so you must do a negitive
-9+14=5
Solve x(−2)3=−2(5). The solution is x=
51:26
A triangle on a coordinate plane is translated according to the rule T-3, 5(x, y). Which is another way to write this
rule?
x
(x,y) → (x - 3, y + 5)
O (x, y) - (x-3, y-5)
O(x, y) = (x + 3, y-5)
O(x, y) = (x + 3, y + 5)
Answer: x+3,y+5
Step-by-step explanation:
Pls pls pls help me!!!!
Answer:
Simplify the expression.
30.9ft
Step-by-step explanation:
you ' re welcome ! grandma loves you < 33 ; )
What is 5 1/3 ÷ 2 And explain how
Answer:
[tex]\frac{8}{3}[/tex]
Step-by-step explanation:
Convert 5 1/3 to an improper fraction, so it now looks like this: 16/3Write it out: 16/3 ÷ 2/116/3 ÷ 2/1 = 16/3 × 1/216/3 × 1/2 = 16/6 = 8/3I hope this helps!
16/6
Step-by-step explanation:
51/3= 16/3
therefore:
16/3÷2
16/3×1/2
16/6
While on beach vacation, tasha makes scale drawing of points of intererest between priers on her drawing 2 cm represents 15 MI the priers are 12 cm apart on tashas drawing. What is the actual distnace between 2 priers
Answer:
Actual distance between the 2 priers = 90 MI
Step-by-step explanation:
Ratio of Scaled drawing to actual dimension = 2 : 15
2 cm represents 15MI
2cm ≡ 15 MI
∴ 1 cm ≡ (15/2) MI
1 cm ≡ 7.5 MI
scaled distance of priers in drawing = 12cm
∴ 12 cm ≡ 7.5 × 12
= 90 MI
∴ Actual distance between the 2 priers = 90 MI
3/a x - 4 = 20. x equals -2
Answer:
[tex]\Large \boxed{a=\frac{-1}{4} }[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{3}{a} \cdot x - 4 = 20[/tex]
Let x = -2.
[tex]\displaystyle \frac{3}{a} \cdot (-2) - 4 = 20[/tex]
Solving for a.
[tex]\displaystyle \frac{-6}{a}- 4 = 20[/tex]
Adding 4 to both sides.
[tex]\displaystyle \frac{-6}{a} = 24[/tex]
Multiplying both sides by a, then dividing both sides by 24.
[tex]\displaystyle \frac{-6}{24} = a[/tex]
Simplifying.
[tex]\displaystyle \frac{-1}{4} = a[/tex]
Sara had 94 dollars to spend on 6 books. After buying them she had 16 dollars. How much did each book cost?
Answer:
each of them costed at least 16 dollars only because if you divide 94 and six your answer would be 15.6666666667 and if you round that it would be sixteen. I am confused what else the question is asking. I apologize if it did not answer your question
The sum of the angle measures of a quadrilateral is 360∘. Write and solve an equation to find the value of x.
the three nubers are 100 100 120
Answer:
x = 20
Step-by-step explanation:
360 = 100 + 100 + 120 + x
360 = 340 + x
x = 360 - 340
x = 20
Find FH
HELP
Please
Answer:
19
Step-by-step explanation:
FH is FG = GH which is 4+15=19
given that m2(n-l) m=-2 and n=3/4
Answer:
when m= -2 and n=3/4.
-2^2.(3/4-1).
-4(-1/4)
=1.
Jon was given a radical to simplify. His original problem had nothing already
simplified outside of the square root. His answer was 2xy^3z^4√3xz. What
must have been the original radical that Jon was given?
Answer:
[tex]\sqrt{12x^3y^6z^9}[/tex]
Step-by-step explanation:
[tex]2xy^3z^4\sqrt{3xz}=\sqrt{(2xy^3z^4)^2(3xz)}=\sqrt{(2^2)(3)(x^2)(x)(y^6)(z^8)(z)}\\\\=\boxed{\sqrt{12x^3y^6z^9}}[/tex]
_____
The applicable rules of exponents are ...
(a^b)^c = a^(bc)
a√b = √(a^2·b)
(a^b)(a^c) = a^(b+c)
Solve for the linear equation 3x+2+x=x+5 please show work
Answer:
3x +2 +X = X+5
4x + 2 = X + 5
3x = 3
X = 1
Step-by-step explanation:
brain list me plzzz I need it
x = 1
Step-by-step explanation:3x + 2 + x = x + 5
3x + x - x = 5 - 2
3x = 3
x = 3 : 3
x = 1
steven traveled for 10 hours at a constant rate of 53 miles per hour. Stephanie traveled at the same distance at a constant rate of 48 miles per hour. How long did it take stephanie to travel the same distance as steven, write an equation to solve.
Answer:
It took 11.04 hours by Stephanie.
Step-by-step explanation:
Concept
distance = speed*time
time = distance/time
_________________________________
Given
for Steven
time = 10 hours
speed = 53 miles per hour
Distance for steven = 53*10 = 530 miles
_____________________________________
Now ,
as Stephanie also traveled the same distance as steven
Distance = 530 miles
speed = 48 miles per hour
time = 530/48 hour = 11.04 hours
Thus, It took 11.04 hours by Stephanie.
In other way
since distance traveled by Steven and Stephanie are same
let time taken by Stephanie be x hours
Distance traveled by steven = Distance traveled by Stephanie
53*10 = 48*x
x = 530/48 = 11.04 hours
equation = 53*10 = 48*x
find ST and TR
Will mark brainest
Hello there! :D
Firstly, I want you to understand an important concept. This has something to do with absolute value. So, although distance is a number, it is neither positive nor negative. It does not necessarily involve value. So, what we are looking for today will not have a negative sign in front of it. We are simply looking for distance!
Let's start with ST, because the distance between those is smaller and therefore I can better explain this to you. T is at the point 19.1, and S is at the point 14. We need to find the amount of distance between the two. How do we do that?
Subtraction! In order to find this value we can subtract the smaller number from the larger number.
19.1-14= 5.1
ST is 5.1
Now we can look at the distance between TR. We are actually going to add numbers together! We know that T is 19.1. If we were to put a dot at zzero and measure that distance, it would be 19.1. What is the distance from R to zero? That's right! The same principle is there. If we had a dot at zero and we're measuring from 4, the distance would be 7.5 (even though it is negative on the number line).
So, we can add these numbers together!
19.1+7.5= 26.6
TR is 26.6
I hope this helped you and you have a wonderful day,
Kai xx
heeeeeeeeeeeeeeeeelllllpppppppppppp
Answer:
b = 6
I hope this helps!
The figures below represents which type of transformation?
ale
GA
Reflection across the y-acis. (x,y) --> (23)
Translation up 10 units (x, y) --> (x, y = 10)
Rotation 180°. (*--> -x, y)
Reflection across the x-axis. (x, y) --> (x, y)
Answer:Step-by-step explanation:x+2(-4) yx
A plan for a baseball diamond is drawn in a coordinate plane. The baseball diamond is in the shape of a square with vertices at approximately 0, 04105401 (0-64 and 1-6401 One unit in the coordinate plane representa 1. What is th approximate area of the baseball diamond? Show your work.
Answer:
The approximate area, of the baseball diamond is 8192 ft²
Step-by-step explanation:
The given coordinates of the baseball diamond are;
(0, 64), (64, 0), (0, -64), and (-64, 0)
The length of one unit of the coordinate plane = 1 foot
Therefore, we note that, there are two points with x-coordinate = 0 at which the y-coordinates = 64 and -64
Similarly here are two points with y-coordinate = 0 at which the x-coordinates = 64 and -64
The length of the segment are therefore the vertices of a square as we have;
A(0, 64), B(64, 0), C(0, -64), and D(-64, 0)
∠DBA = ∠DCA = tan⁻¹(64/64) = tan⁻¹(1) = 45°
∠DBA + ∠DCA = ∠ABC = 90°
The shape of the diamond is a square
The length, l of the side of the square is given by the relation;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
When, (x₁, y₁) = (0, 64), (x₂, y₂) = (64, 0)
We have;
[tex]l = \sqrt{\left (0 -64 \right )^{2}+\left (64-0 \right )^{2}} = 64\cdot \sqrt{2}[/tex]
The
The area, A, of the baseball diamond is therefore;
A = Area of a square = (Length of the side of a square)² = (64·√2)² = 8192 ft²
The area, of the baseball diamond = 8192 ft².
caroline is taking a road trip on 1-70 in kansas. she stops for gas at mile marker 36. her destination is at mile marker 353 in topeka, but she decides to stop at an attraction 3/4 of the way after stopping for gas. at about which mile marker did caroline stop to visit the attraction.
BTW not middle school
Answer:
274
Step-by-step explanation:
First stop of Caroline = At 36 mile marker
Destination of Caroline = At 353 mile marker
Distance left to be covered = 353 - 36 = 317 miles
Given that Caroline decides to stop at an attraction [tex]\frac{3}{4}[/tex] of the way after she stops for gas.
i.e. at a distance [tex]\frac{3}{4}[/tex] of 317 miles away from the Gas stop.
[tex]\frac{3}{4} \times 317 = 79.25\times 3 \approx 238\ miles[/tex]
So, Caroline stops at a point which is around 238 miles away from the gas station.
To calculate the Mile marker of her stop, we need to add the mile marker of gas station and the distance of her stop from gas station.
Mile marker location at her stop = 36+238 = 274