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40 quarts of a 50% solution of acid must be added to 20 quarts of a 20% solution of acid to obtain a mixture containing a 40% solution of acid

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let, The quart of the solution must be added be 'x'.

Therefore, According to the given information,

0.5x + 0.2(20) = 0.4(x + 20).      (0.5 represents 50% solution)

0.5x + 4 = 0.4x + 8.

0.1x = 4.

x = 40.

So, 40 quarts of acid must be added.

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Answer:

Step-by-step explanation:

To get the y values all you need to do is substitute the x value in the equation y=-2/3x+7.

For example:

y=-2/3(-6)=7

-2/3x6=-4

-4+7=3

(-6,3)

You can double check your work by filling the x and y coordinates in the equation and when solved if it it true you know you were correct.

To get the x value, you need to fill in the y in the equation y=-2/3x+7

for example:

5=-2/3x+7

-2=-2/3x

3=x

(3,5)

y=-2/3x+7

y=-2/3(15)+7

y=-10+7

y=-3

(15,-3)

y=-2/3x+7

15=-2/3x+7

8=-2/3x

-12=x

(-12,15)

Step-by-step explanation:

Tulis 689.802.473 dalam angka

six hundred eighty nine million eight hundred two four hundred and seventy three

sorry if wrong

Trigonometric ratios relate the angles of a triangle to the length of the sides.

Given a triangle as shown below

The side opposite the angle θ is referred to as the Opposite and the side opposite the right-angle is referred to as the Hypotenuse. The remaining side is the Adjacent.

The Sine ratio is given as

The Tangent ratio is given as

The Cosine ratio is given as

A mnemonic to easily remember is SOH CAH TOA.

Answer:

y = 3x + 3

Step-by-step explanation:

Rise: 3   Run: 1

slope (m) = 3/1 = 3

y intercept (b) = 3

y = mx + b = 3x + 3

The fraction of the sweets that are blue given the ratios is 13/40.

A fraction is a non-integer that is made up of a numerator and a denominator. An example is 2/3. 2 is the numerator and 3 is the denominator.

Ratio shows the relationship between two or more numbers. It is the number of times that one value is contained in other value(s). Ratios are used to compare two or more numbers.

We would be assuming the numbers of sweet based on the given ratios.

The number of hard sweets = 30

The number of soft sweets = 50

Number of hard sweets that are blue = (1/5) x 30 = 6

Number of soft sweets that are blue = (2/5) x 50 = 20

Total number of blue sweets =20 + 6 = 26

Total number of sweets = 30 + 50 = 80

Fraction of blue sweets = 26/80 = 13 /40

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The depth of the aquarium is approximately 4 feet when rounded to the nearest whole number (since 3.64 is closer to 4 than it is to 3 when rounded to the nearest whole number).

To calculate the depth of the aquarium, we need to use the formula for volume of a rectangular prism,

which is V = lwh where V is the volume, l is the length, w is the width, and h is the height (or depth, in this case).

Given that the aquarium holds 11.35 cubic feet of water, the volume of the aquarium can be represented by V = 11.35 cubic feet.We are also given that the length of the aquarium is 2.6 feet and the width is 1.1 feet.

Substituting these values into the formula for volume,

we get:11.35 = 2.6 × 1.1 × h

Simplifying this expression:

11.35 = 2.86h

Dividing both sides by 2.6 × 1.1,

we get:h ≈ 3.64 feet (rounded to two decimal places)

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Answer:

d i think

Step-by-step explanation:

Answer:

The correct answer is D:-15,120

\(^{n}P_{r}=\dfrac{n!}{(n-r)!}\\\\\implies ^{9}P_5 = \dfrac{9!}{(9-5)!} =\dfrac{9!}{4!} = 15120\)

The answer is D.

The equivalent expression of -14 - 6 is -14 - (+6)

Equivalent expressions are expressions that have the same value when evaluated

The expression is given as:

-14 - 6

Put the terms of the expression in brackets

-14 - (6)

Rewrite 6 as +6

-14 - (+6)

Hence, the equivalent expression of -14 - 6 is -14 - (+6)

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Let:

x = space covered by the couch

y = space covered by the rug

T = total space

so:

Answer:

0.6 as a decimal and 60 percent

9514 1404 393

Answer:

  (x, y) = (1/2, 1)

Step-by-step explanation:

Subtract twice the second equation from the first to eliminate the x-variable.

  (2/x +3/y) -2(1/x -4/y) = (7) -2(-2)

  11/y = 11 . . . . . . . simplify

  y = 1 . . . . . . . . multiply by y/11

__

Substituting into the second equation gives ...

  1/x -4/1 = -2

  1/x = 2 . . . . . . add 4

  1/2 = x . . . . . . multiply by x/2

The solution is (x, y) = (1/2, 1).

_____

Additional comment

The attached graph seems to show that the graphs of the two equations also intersect at (x, y) = (0, 0). However, careful consideration of these equations leads to the conclusion that x=0 and y=0 are not in the domain of either equation. (Division by 0 is undefined.) So, the only solution is (x, y) = (1/2, 1).

If you were to multiply both equations by xy to eliminate fractions, you would, indeed, arrive at the conclusion that (x, y) = (0, 0) is a solution. As we noted, that "solution" is extraneous. Whenever you multiply an equation by an expression that can have the value 0, you need to be careful to exclude any "solution" that makes that expression 0.

The equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is: R(x) = 250000 + 375x - 2.5x²

Equations are mathematical statements with two algebraic expressionsοn either sideοf an equals (=) sign. It illustrates the equality between the expressions writtenοn the left and right sides. To determine the valueοf a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

N(x) = 625 + 2.5x

The revenue R(x) will be the productοf the numberοf students enrolled and the fee charged per student. The fee charged per student will be (400 - x) dollars. So, the revenue function can be represented as:

R(x) = (625 + 2.5x)(400 - x)

Simplifying the expression, we get:

R(x) = 250000 + 375x - 2.5x²

Therefore, the equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is:

R(x) = 250000 + 375x - 2.5x²

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y=-2x+5 is the slope-intercept equation for a line that goes through the point (4,-3) and 5 is the value of b.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We have to find the slope-intercept equation for a line that goes through the point (4,-3)--with a slope of -2

m=-2

Now let us find the y intercept

-3=-2(4)+b

-3=-8+b

-3+8=b

5=b

Hence, y=-2x+5 is the slope-intercept equation for a line that goes through the point (4,-3) and 5 is the value of b.

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Answer:

I found 8 matrices for you to choose the three you want.

Step-by-step explanation:

What are Matrices? Matrices or matrix is commonly used its mathematics, matrix, a set of numbers arranged in rows and columns to form a rectangular array. The numbers are called the elements, or entries, of the matrix. Matrices have wide applications in engineering, physics, economics, and statistics as well as in various branches of mathematics.

1. Encryption: Use to scramble data for security purposes to encode, and to decode this data we need matrices. There is a key that helps encode and decode data which is generated by matrices.

2. Games especially 3D: Use to alter an object, in 3d space. They use the 3d matrix to 2d matrix to convert it into different objects as per requirement.

3. Economics and business: Study the trends of a business, shares, and more. To create business models etc.

4. Construction: Buildings that are straight but sometimes architects try to change the outer structure. This can be done with matrices.  A matrix is made of rows and columns you can change the number of rows and columns within a matrix.  Matrices can help support various historical structures.

5. Dance – contra dance: It is used to organize complicated group dances.

6. Animation:  It can help make animations more precise and perfect.  

7. Physics: Matrices are applied in the study of electrical circuits, quantum mechanics, and optics. It helps in the calculation of battery power outputs, resistor conversion of electrical energy into another useful energy. Therefore, matrices play a major role in calculations.  Especially in solving the problems using Kirchoff’s laws of voltage and current. It helps in studying quantum physics and in using it.

8. Geology:  Matrices are used for taking seismic surveys.

-Hope this helps.

Answer:

The midpoint between A(-7, 5) and B (7, 3) is: (0, 4)

Step-by-step explanation:

Given the points

Determining the midpoint between A(-7, 5) and B (7, 3)

\(M.P_{AB\:}=\:\:\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\)

\(\left(x_1,\:y_1\right)=\left(-7,\:5\right),\:\left(x_2,\:y_2\right)=\left(7,\:3\right)\)

             \(=\left(\frac{7-7}{2},\:\frac{3+5}{2}\right)\)

             \(=\left(0,\:4\right)\)

Therefore, the midpoint between A(-7, 5) and B (7, 3) is: (0, 4)

Answer:

x=1

Step-by-step explanation:

y=3x so just add 1+3=4 then add veriable y=4x

Answer:

262 feet²

Step-by-step explanation:

2(5×8 + 5×7 + 8×7)

2(40+35+56)

2(131)

262

---

hope it helps

After answering the provided question, we can conclude that Rounding triangle to the nearest meter, the height of the building is 74 m.

A triangle is a closed, double-symmetrical object composed of three line segments known as sides that intersect at three points known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are less than 90 degrees), okay (one angle is equal to 90 degrees), or orbicular (all angles are greater than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.

The ratio of the height of the pole to the length of its shadow is:

2.7 m / 1.71 m = 1.5789

The ratio of the height of the building to the length of its shadow is:

\(h / 46.75 m = x\\1.5789 = x\\x = h / 46.75 m\\1.5789 = h / 46.75 m\\h = 73.794 m\)

Rounding to the nearest meter, the height of the building is 74 m.

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Answer: its 49

Step-by-step explanation:

Answer

Measure the shape yourself and follow the explanation.

Step-by-step explanation:

Measure each side of the Triangles with your ruler. Record it.

For example,

I measured and got 3cm, 3.5cm, 3.5cm.

Multiply by scale factor r 2.

for example, 3cm × 2 = 6cm

3.5cm × 2 = 7.0cm

3.5cm × 2 = 7.0cm

Use your pencil to draw your new numbers to form the new Triangle.

As for the second shape, measure each four sides using ruler

for example, I measured and had 4cm, 6cm, 4cm, 6m.

Multiply by scale factor r 2.

for example, 4cm × 1/4 = 1 cm

6cm × 1/4 = 1.5cm

4cm × 1/4 = 1 cm

6cm × 1/4 = 1.5cm

Use your ruler to measure 1cm, 1.5cm, 1cm and 1.5cm, then to draw your new shape

Answer:

B 1/2

Step-by-step explanation:

This is right

The probability that the sum of the two numbers is odd, given that the product is 6 will be 2/3. Option C is correct.

Probability is synonymous with possibility. It is concerned with the occurrence of a random event. Probability can only have a value between 0 and 1.

Ethan cranks the arrow on the spinner after rolling the number cube. There is a list of all conceivable outcomes.

{(1, 1), (1, 2), (1,3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (4,1),(4,2), (4,3), (5, 1), (5,2), (5,3), (6, 1), (6,2), (6,3)}

The no of sets having the sum of the number is odd=9

The no of sets having the product of the number is 6=3

The total number including the two conditions=3+9=12

Probability is found as;

P=12/18

P=2/3

The probability that the sum of the two numbers is odd, given that the product is 6 will be 2/3.

Hence, option C is correct.

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Answer:

y=26.67

Step-by-step explanation:

The given equation is 0.75x+1.5y=40.

We need to show the result of substituting x=0 in above equation.

0.75x+1.5y=40

Put x = 0

0.75(0)+1.5y=40

0+1.5y=40

⇒ 1.5y=4

\(y=\dfrac{40}{1.5}\\\\y=26.67\)

So, the value of y = 26.67 when x = 0.

Answer:

-1/6.38

Step-by-step explanation:

Answer:

0.01m=10km

25m=25000km

1m=1000km

0.0015m=1.5km

If this is incorrect forgive me plz

I hope this will help you

Answer:

21000,14000,and14000

Step-by-step explanation:

3x+2x+2x=49000

7x=49000

x=7000

3×7000=21000

2×7000=14000

2×7000=14000