The amount of oil, in ounces, in the fuel mix can be found using a proportion with the given ratio and the amount of gasoline.
Explanation:To find the number of ounces of oil, we need to use the given ratio and the amount of gasoline. The ratio of oil to gasoline is 5:18, meaning that for every 5 ounces of oil, there are 18 gallons of gasoline. Since we know that there are 36 gallons of gasoline, we can set up a proportion to find the number of ounces of oil:
5 ounces / 18 gallons = x ounces / 36 gallons
Cross multiplying, we get:
18x = 5 * 36
Simplifying further:
18x = 180
Dividing both sides by 18, we get:
x = 10 ounces
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An apple pie uses 4 cups of apples and 3 cups of flour. An apple cobbler uses 2 cups of apples and 3 cups of flour. You have 16 cups of apples and 15 cups of flour. When you sell these at the farmers market you make $3.00 profit per apple pie and $2.00 profit per apple cobbler. Use linear programming to determine how many apple pies and how many apple cobblers you should make to maximize your profit.
1. let ×= the number of apple pies you make and y= the number of apple cobblers you make. Write an inequality to show the constraint on the amount of apples you have?
2. Write an inequality to show the constraint on the amount of flour you have .
3. Write any non negativity contraints on x and y
H E L P PLEASE COME ON WHY WONT ANYONE HELP
Corey deposited $1,500 in a savings account that earns simple interest at 5.75%. What is the balance in his account at the beginning of the third quarter?
A. $1,556.78
B. $1,528.13
C. $1,543.13
D. $1,612.50
Please explain your answer CLEARLY so i can use the principles for future reference. Thanks!
2. The coordinates of the vertices of are P(-2,5), Q(-1,1) and R(7,3) . Determine whether PQR is a right triangle. Show your work.
BRAINLIEST!!!!
8. Find the glide reflection image of the black triangle where the translation is (x,y) -> (x,y - 7) and the line of reflection is x = 1.
Am I correct?
Answer:
Option D is correct.
Explanation:
From the given figure,
Labelled the black triangle as A, B and C
The coordinates of triangle ABC are;
A= (2,8) , B= (2,5) and C=(6,5)
To find the glide reflection image of the triangle ABC.
Glide Reflection: It is a composition of transformations.
In glide reflection, a translation is first performed on the figure then it is reflected over a line.
Given: The rule of translation is: [tex](x,y) \rightarrow (x, y-7)[/tex] and line of reflection is x= 1.
Now, apply the rule of translation on black triangle, we get;
[tex]A (2,8) \rightarrow (2, 8-7)[/tex] = A' (2,1)
[tex]B (2,5) \rightarrow (2, 5-7)[/tex] =B' (2,-2)
[tex]C (6,5) \rightarrow (6, 5-7)[/tex] = C' (6,-2)
Next,
Apply the rule of reflection over the line x =1,
i.e, [tex](x,y) \rightarrow (-x+2, y)[/tex]
[tex]A' (2,1) \rightarrow (-2+2, 1)[/tex] =A" (0,1)
[tex]B' (2,-2) \rightarrow (-2+2, -2)[/tex] =B" (0,-2) and
[tex]C' (6,-2) \rightarrow (-6+2, -2)[/tex] =C" (-4,-2)
You can see the graph of Glide reflection as shown below in the attachment.
A submarine is 50 meters below sea level. It goes up 15 meters, then goes down 40 meters. What is the submarine's new position relative to sea level? Write a number sentence and solve
a) -105 meters b) -75 meters c) -35 meters d) 25 meters
Please tell me how to show work also.
The bedroom of a house is 1,200 cubic meters. We know that there are 3.4 x 109 particles of dust per cubic meter. How many particles of dust are present in the bedroom of the house
To find the number of dust particles in a 1200 cubic meter bedroom with 3.4 x 10⁹ particles per cubic meter, multiply the volume by the number of particles per volume, resulting in approximately 4.08 trillion dust particles.
To calculate the number of dust particles in the bedroom, we need to multiply the volume of the bedroom by the number of dust particles per cubic meter. Given that the bedroom is 1200 cubic meters and that there are 3.4 x 10⁹ particles of dust per cubic meter, we can use the following calculation:
Number of particles = Volume of the bedroom x Number of particles per cubic meter
Number of particles = 1200 m³ x 3.4 x 10⁹ particles/m3
Number of particles = 4.08 x 10¹² particles
Therefore, there are approximately 4.08 trillion dust particles in the bedroom of the house.
what is the simplified form of 7(5x-6)
Select Repeating or Nonrepeating to correctly classify each decimal. 1.01011 2.23¯¯ 3.426¯ 4.321321… the minus signs mean like a line over the number
Answer:
2.23 3.426 4.32321... are repeating and 1.01011 is not repeating
The decimal 1.01011 is a non-repeating decimal. For the others, 2.23, 3.426, and 4.321321... are all repeating decimals because they have digits or group of digits that repeat indefinitely.
Explanation:In mathematics, decimals are either repeating or nonrepeating. A repeating decimal is a decimal that has a digit or group of digits that repeats infinitely. A non-repeating decimal doesn't have a pattern of digits that repeats infinitely.
The decimal 1.01011 is non-repeating because there's no group of digits that repeats infinitely. The decimal 2.23¯¯ is a repeating decimal. The notation with two bars above the 23 indicates that 23 is the repeating part. The decimal 3.426¯ is also a repeating decimal. The bar above the 6 indicates that the digit 6 repeats indefinitely. Lastly, the decimal 4.321321... is a repeating decimal where the group of digits 321 repeats infinitely.Learn more about Repeating and Non-Repeating Decimals here:
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The length of a rectangle is three times its width. The perimeter of the rectangle is at most 112 cm.
Which inequality models the relationship between the width and the perimeter of the rectangle?
2w+2⋅(3w)≥112
2w+2⋅(3w)<112
2w+2⋅(3w)>112
2w+2⋅(3w)≤112
Which of the following is a solution of x2 − 6x = –22?
A. -6-i√52
B. -6+i√13
C. 3-i√13
D. -3+i√52
Erica had 6 coins in her coin collection. she goes to a coin show and buys some coins. how many dose she have now?
If ABC XYZ, mA = 50°, and mY = 70°, find mC
Final answer:
Using the properties of congruent triangles and the fact that the sum of the angles in a triangle is 180°, the measure of angle C (mC) is found to be 60°.
Explanation:
Given that triangle ABC is congruent to triangle XYZ, we know that corresponding angles of congruent triangles are equal. Since the measure of angle A (mA) is given as 50°, and in triangle XYZ, the measure of angle Y (mY) is 70°, we can use the fact that the sum of the angles in a triangle is 180° to find the measure of angle C (mC).
The sum of the angles in triangle ABC would be:
mA + mB + mC = 180°
50° + mB + mC = 180°
Since triangle ABC is congruent to triangle XYZ, mB will be equal to mX, which is the same as mY, that is 70°:
50° + 70° + mC = 180°
Now, we just need to subtract the sum of mA and mB from 180° to find mC:
mC = 180° - (50° + 70°)
mC = 180° - 120°
mC = 60°
Use the distributive property to remove the parentheses -5(-6u-3x+4)
Nellie is buying bird seed to put in her bird feeders. She uses about 10 pounds of bird seed each week, but has room to store any extra that she purchases.The bird seed comes in 3 different sizes as given below: 3.5 pounds for $2.52 7.5 pounds for $5.40 11 pounds for $7.92 Nellie is trying to be a smart shopper and get the best deal on the bird seed. Which size bag of bird seed should Nellie buy? a. Nellie should buy the 3.5 pound bags because they have the cheapest unit price b. Nellie should buy the 7.5 pound bags because they have the cheapest unit price c. Nellie should buy the 11 pound bags because they have the cheapest unit price. d. Nellie should buy any size she wishes because they all have the same unit price..
Given: Nellie has to buy bird seed and the prices are as follows
3.5 pounds for $2.527.5 pounds for $5.4011 pounds for $7.92To Find: which size bag should Nellie buy (which one would have the cheapest unit price)
Solution: D. Nellie should buy any size because they all have the same unit price.
Explanation:
We begin by finding the unit price, i.e., price per pound for each of the three bags.
This is done by using the Unitary Method. We must divide the price by the volume of the bag to find the price per pound.
price per unit of the smallest (3.5 pound) bag is [tex]\frac{2.52}{3.5} =0.72 $ per pound[/tex]price per unit of the medium (7.5 pound) bag is [tex]\frac{5.40}{7.5} =0.72 $ per pound[/tex]price per unit of the biggest (11 pound) bag is [tex]\frac{7.92}{11} =0.72 $ per pound[/tex]Answer:
D
Step-by-step explanation:
Nellie should buy any size she wishes because they all have the same unit price..
6+ 4/a + b/3 a=4 b=3
The substitution property of equality allows you to say that if 7j + 14k = 28 And j = 2 then
A round cookie cake, divided into 8 equal pieces, has a diameter of 16 inches. Marty eats one piece of cake. What is the area of the piece of cake that Marty eats? Leave your answer in terms of pi. A)4π in2 B) 8π in2 C)16π in2 D) 64π in2
Answer:
8
Step-by-step explanation:
Solve the system using elimination.
x – y = –5
3x + y = 1
Answer:
(-1, 4)
Step-by-step explanation:
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1. State the domain of the rational function. (2 points)
f(x) = thirteen divided by quantity ten minus x.
a) All real numbers except -10 and 10
b) All real numbers except 13
c) All real numbers except 10
d) All real numbers except -13 and 13
2. State the vertical asymptote of the rational function. (2 points)
f(x) = quantity x minus six times quantity x plus six divided by quantity x squared minus nine.
a) x = 6, x = -6
b) x = 3, x = -3
c) x = -6, x = 6
d) None
3. State the horizontal asymptote of the rational function. (2 points)
f(x) = quantity x squared plus four x minus seven divided by quantity x minus seven.
a) None
b) y = -4
c) y = 7
d) y = 6
4. State the horizontal asymptote of the rational function. (2 points)
f(x) = quantity x squared plus eight x minus two divided by quantity x minus two.
a) None
b) y = 1
c) y = -8
d) y = 2
5. Give an example of a rational function that has a horizontal asymptote at y = 0 and a vertical asymptote at
x = 2 and x = 1.
f(x) = 13 / (10-x)
The only x value that would not produce a real number for f(x) is 10, since you
cannot divide a number by zero. Answer is C
2)
F(x)
=(x-6)(x+6)/(x2 - 9)
The vertical asymptotes are x=3 and x=-3. Graph the function on a graphing
calculator to observe the behavior of the function at these points. There is
both a positive and negative vertical asymptote a both x=3 and x=-3. Keep in
mind that the denominator approaches zero at these points, and thus f(x) approaches
either positive or negative infinite, depending on whether the denominator, however small, is a positive or
negative number. Answer is B) 3, -3
3)
F(x) = (x2
+ 4x-7) / (x-7)
Although there is a vertical asymptote as x=7, there is no horizontal asymptote.
This makes sense. As X gets bigger, there is nothing to hold y back from
getting greater and greater. X2 is the dominant term, and it’s only
in the numerator. A) none
4)
(x2 +
8x -2) / (x-2)
This function is very similar in structure to the previous one. Same rules
apply. Dominant term only in the numerator means no horizontal asymptote.
A)None
5)
Our
function approaches 0 as x approaches infinite, and has a vertical asymptote at
x=2 and x=1.
Here’s an easy example: 10 / ((x-2)*(x-1)). At x=2 and x=1, there is both a
positive and negative vertical asymptote. As x approaches infinite, the
numerator is dominated by the denominator, which contains x (actually x2 ),
and thus y approaches zero.
GEOMETRY! Need help with both please.
The perimeter of an isosceles triangle is 15.6m. Find the lengths of its sides, if: The base is 3m smaller than a leg ____m, ___m, _____m
we know that
An isosceles triangle is a triangle with two equal sides and two equal angles
Let
x-------> the length of the equal sides
y-----> the length of the base
[tex]y=x-3[/tex] -----> equation A
The perimeter of an isosceles triangle is equal to
[tex]P=2x+y[/tex]
[tex]P=15.6\ m[/tex]
so
[tex]15.6=2x+y[/tex] ------> equation B
substitute equation A in equation B
[tex]15.6=2x+[x-3][/tex]
[tex]15.6=3x-3[/tex]
[tex]3x=18.6[/tex]
[tex]x=6.2\ m[/tex]
Find the value of y
[tex]y=x-3[/tex]
[tex]y=6.2-3=3.2\ m[/tex]
therefore
the answer is
The dimensions of the triangle are
[tex]leg1=6.2\ m[/tex]
[tex]leg2=6.2\ m[/tex]
[tex]base=3.2\ m[/tex]
A maze at a county fair is made from 275 bales of hay.the maze at the state fair is made from 4 times as many bales of hay.how many bales of hay are used for the maze at the state fair?
The community center has a pottery class each month. Each student pays $15 for the class and $27 for materials. This month the pottery class brought in a total of $714. How many students are in the class this month?
If x + b > c and x > 0 have the same solutions, what is the relationship between b and c
At east zone university (ezu) there are 724 students taking college algebra or calculus. 432 are taking college algebra, 319 are taking calculus, and 27 are taking both college algebra and calculus. how many are taking algebra but not calculus?
Answer:405
Step-by-step explanation:
What is the maximum product of two numbers whose sum is 13? what numbers yield this product?
What is the product of −2 1/4 and 2 1/2?
product means multiply
-2 1/4 times 2 1/2:
-2 1/4 = -9/4
2 1/2 = 5/2
-9/4 x 5/2 = -45/8 = -5 5/8
How are hourly and salaried gross pay calculated?
Which of the following values would complete the ordered pair if the point is on the graph of ƒ(x) = -2x + 3?
(-1, ___)
-4
0
1
5
PLZ HELP ASAP
What is the measure of a base angle of an isosceles triangle if the measure of the vertex angle is 42 and the two congruent sides each measure 21 units?
Answer:
69 degrees
Step-by-step explanation: