Write an addition sentence that helps you solve 51 - 9

Answer:

8 lb

Step-by-step explanation:

Use the graph relations.

Answer:

7.5 lb

Step-by-step explanation:

Look at the points on the graph.

She paid $1 for 1.5 lb.

She paid $2 for 3 lb.

She paid $4 for 6 lb.

She paid $7 for 10.5 lb.

Now divide each amount of lb by each cost.

1.5/1 = 1.5

3/2 = 1.5

6/4 = 1.5

7/10.5 = 1.5

In every case, she got 1.5 lb for each dollar.

On the day she spent $5, she got 1.5 lb for each dollar.

$5 * 1.5 lb/$ = 7.5 lb

Answer: 7.5 lb

To evaluate the indefinite integral ∫sin(9x)dx, we can use the substitution u = 9x, which leads to the integral ∫(1/9)sin(u)du.

To solve the integral, we substitute u = 9x, which implies du = 9dx. Rearranging this equation, we have dx = (1/9)du. Substituting these values into the original integral, we get:

∫sin(9x)dx = ∫sin(u)(1/9)du

Now, we can pull out the constant (1/9) outside the integral:

(1/9)∫sin(u)du

The integral of sin(u) with respect to u is evaluated as -cos(u). Therefore, the integral becomes:

(1/9)(-cos(u)) + C

where C is the constant of integration. Substituting back u = 9x:

(1/9)(-cos(9x)) + C

Hence, the indefinite integral of sin(9x)dx, using the given substitution, is (-1/9)cos(9x) + C.

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Answer: x=18/5  y=127/5

Step-by-step explanation:

For both equations

1. subtract from both sides

2. divide to find what the variable equals

Answer:

x = 77

Step-by-step explanation:

x and 103 are same- side exterior angles and sum to 180°

x + 103 = 180 ( subtract 77 from both sides )

x = 77

Answer:

w equal to 9z

or z equals to w/9

Answer:

24

Step-by-step explanation:

Okay, let's solve this step-by-step:

1) We are given: a = -8, b = 2, c = 7, d = 11

2) We are asked to solve the matrix equation: [[x + y, z], [z - x, w - y]] = [[a, b], [c, d]]

3) Matching up the elements in the matrices:

x + y = a = -8 (1)

z = b = 2 (2)

z - x = c = 7 (3)

w - y = d = 11 (4)

4) Solving the equations:

From (1): x + y = -8 => x = -8 - y

Substitute in (3): z - (-8 - y) = 7 => z - (-8) = 7 + y => z = 15 + y

Substitute (2) into the above: 2 = 15 + y => y = 13

Substitute y = 13 into (1): -8 - 13 = -21 = x

Substitute x = -21 and y = 13 into (4): w - 13 = 11 => w = 11 + 13 = 24

Therefore, the values are:

x = -21

y = 13

z = 15

w = 24

So the final value of w is:

w = 24

Answer:

the ending balance is $531.51

Step-by-step explanation:

The computation of the ending balance is shown below:

= Opening balance + all deposits - all withdrawls

= $500 + $100 + $250 + $300 - $400.32 - $100 - $55.55 - $62.62

= $531.51

hence, the ending balance is $531.51

Answer:

12.9 ft²

Step-by-step explanation:

sin = opp/hyp

sin 40 = height/ 5

5 * sin40 = height

h = 3.213938048432697

--------------------

area = (1/2)bh

a = (1/2) * 8 * 3.213938048432697

a = 12.9 ft²

AB and YX are corresponding sides, BC and XZ are corresponding sides, and AC and YZ are corresponding sides of given triangle.

What is triangle?

A triangle is a two-dimensional geometric shape that has three sides, three angles, and three vertices. It is one of the simplest polygonal shapes and is commonly studied in geometry.

Since we have:

∠A ≅ ∠Y

∠B ≅ ∠X

∠C ≅ ∠Z

We can conclude that the two triangles ABC and XYZ are similar by the Angle-Angle (AA) similarity theorem.

Therefore, the corresponding sides of the two triangles are proportional to each other. We can write this as:

AB : YX = BC : XZ = AC : YZ

where AB and YX are corresponding sides, BC and XZ are corresponding sides, and AC and YZ are corresponding sides.

In other words, the ratio of the length of each side in triangle ABC to the corresponding side in triangle XYZ is constant.

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A total of 12,000 dollars is made from the sale of 300 books at a price of $40 each. 25 fewer books are sold for every $5 increase in price.      R(x)=(40+5x)(300−25x) R ( x ) = ( 40 + 5 x ) ( 300 − 25 x )

Assumed in this instance is , At a price of 40 dollars apiece, \($(300)(40 \$)=12,000 \$$\) books generate $300 in revenue. The result is that 25 fewer books are sold if we raise the price of each book by $5. That's \($(300-25 x)$\). Due to the fact that the price always rises by five times more than the number of books, the cost is \($(40+5 x)$\).

\($R=(300-25 x) \cdot(40+5 x)$\)

\($R=12000+6000 x-1000 x-125 x^2$\\$R=-125 x^2+5000 x+12000$\\$R=125 x^2-5000 x-12000$\)

The revenue R is expressed as a function of the number x as it approaches 5. R(x)=(40+5x)(30025x) is the necessary revenue function. R(x) = (40 + 5 x)(300 25 x) is the necessary revenue function.

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The expression for  d=rt in terms of the time is t = d/r; t = 5.

Therefore,

In the equation d=rt

                          t = d/r

when distance is 40 and the rate is 8

                          t = d/r

Replace d with 40 and rate with 8

                          t = 40/8

                          t = 5

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Answer:

Assuming the numerator was 1.

\((6\sqrt{7}+1)/251\)

Step-by-step explanation:

Assuming the numerator was 1.

\(1/(6\sqrt{7} -1)\\ (6\sqrt{7}+1)/((6\sqrt{7} - 1)(6\sqrt{7} + 1))\\ (6\sqrt{7}+1)/((6\sqrt{7})^2 + 6\sqrt{7} - 7\sqrt{7} - 1)\\(6\sqrt{7}+1)/((6\sqrt{7})^2 - 1)\\(6\sqrt{7}+1)/((36*7 - 1)\\(6\sqrt{7}+1)/251\)

Answer:

x=5

Step-by-step explanation:

\(2 {x}^{2} = 50\)

\( {x}^{2} = \frac{50}{2} \)

\( {x}^{2} = 25\)

\(x = \sqrt{25} \)

\(x = 5\)

Answer:  x= \(\sqrt{x=15i} or \sqrt{x=-5\)

​

Answer:

Step-by-step explanation:

p(-4) is simply done by plugging in -4 into the equation which gets you the answer 56.

p(-4) stands for the population of the fish 4 years before 2005.

Hope that helps!

The amount of the investment at the end of the 10 years period if compounded quarterly is $2,649.6.

A = P(1 + r/n)^nt

= 1200(1 + 0.08/4)^(4×10)

= 1200(1 + 0.02)^40

= 1200(1.02)^40

= 1200(2.208)

= $2,649.6

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Answer:

10

Step-by-step explanation:

if you multiply 2 and 5 together, you get a product of 10.

Answer: it would be 2d because its the product and product means to multiply

The new inequalities are:

A) -16 < -4

B) 40 > 8

C) -45 < 15

D) 35 > -20

What is inequality?

Inequality in math is a comparison between two values, expressing that one value is greater than, less than, or not equal to the other value. It is represented by symbols such as > (greater than), < (less than), and ≠ (not equal to). For example, 5 > 3 is an inequality, which means that 5 is greater than 3.

A) When you multiply both sides of the inequality 8 > 2 by -2, you need to reverse the direction of the inequality to get the new, true inequality: -16 < -4.

B) When you multiply both sides of the inequality -10 < -2 by -4, you need to reverse the direction of the inequality to get the new, true inequality: 40 > 8.

C) When you multiply both sides of the inequality 15 > -5 by -3, you need to reverse the direction of the inequality to get the new, true inequality: -45 < 15.

D) When you multiply both sides of the inequality -7 < 4 by -5, you need to reverse the direction of the inequality to get the new, true inequality: 35 > -20.

Therefore, the new inequalities are:

A) -16 < -4

B) 40 > 8

C) -45 < 15

D) 35 > -20

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Complete question : given in the picture.

Answer:A) -16 < -4B) 40 > 8C) -45 < 15D) 35 > -20

Reverses

Step-by-step explanation:hope this helps!

have a great Thursday! :)

We must write 2 fifths as a decimal.

We know that 1 fifth is:

So 2 fifths are:

Answer: 0.4

Answer:

Step-by-step explanation:

8 and 47

The solution to the system of equations is:

X = -171, Y = -531, and Z = 363.

To solve the system of equations:

2X + 4Y + 2Z = 144 (Equation 1)

0.5X + 0.25Y = 60 (Equation 2)

1.5X + 0.5Y + Z = 36 (Equation 3)

We can use row operations to simplify and solve the system.

Let's start with Equation 2. Multiply both sides of Equation 2 by 4 to eliminate decimals:

2X + Y = 240 (Equation 4)

Now, let's solve Equations 1 and 4 using row operations. Multiply Equation 4 by -2 and add it to Equation 1:

-4X - 2Y = -480 (Equation 5)

2X + 4Y + 2Z = 144 (Equation 1)

   2Y + 2Z = -336  (Equation 6)

Next, let's solve Equations 3 and 6 using row operations. Multiply Equation 6 by -3 and add it to Equation 3:

-3Y - 3Z = 1008 (Equation 7)

1.5X + 0.5Y + Z = 36 (Equation 3)

1.5X - 2.5Z = -972 (Equation 8)

We now have a simplified system of equations:

2Y + 2Z = -336 (Equation 6)

1.5X - 2.5Z = -972 (Equation 8)

-3Y - 3Z = 1008 (Equation 7)

Now, we can solve this system by using additional row operations.

Multiply Equation 6 by 1.5 and add it to Equation 8:

-4Z = -1452

Solving for Z, we get Z = 363.

Substituting the value of Z back into Equation 6, we can solve for Y:

2Y + 2(363) = -336

2Y = -1062

Y = -531.

Finally, substituting the values of Y and Z into Equation 7, we can solve for X:

-3(-531) - 3(363) = 1008

X = -171.

Therefore, the solution to the system of equations is:

X = -171, Y = -531, and Z = 363.

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In Monogram, Robert Rauschenberg created combine-paintings by assembling everyday objects through collage and painting techniques. This artwork showcased his unique approach of combining various elements to form a cohesive artistic composition.

Robert Rauschenberg's Monogram exemplifies his innovative approach of combining different mediums and materials in his artwork. He coined the term "combine-paintings" to describe these pieces that brought together everyday objects, such as a stuffed goat, tires, and various found materials, with painting and collage techniques.

Rauschenberg's aim was to challenge traditional boundaries and definitions of art by blurring the lines between painting and sculpture, two-dimensional and three-dimensional forms. By incorporating familiar objects into his artworks, he explored themes of consumerism, popular culture, and the relationship between art and everyday life. Through his combine-paintings, Rauschenberg pushed the boundaries of artistic expression and opened up new possibilities for artistic creation.

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Answer:

It is a trapezoid

Step-by-step explanation:

Yes, the given points represent the vertices of a trapezoid.

A trapezoid is a quadrilateral with one set of parallel sides. In this case, the parallel sides are AB and CD. The other two sides, AD and BC, are not parallel.

The trapezoid is not isosceles because the two non-parallel sides are not congruent. AD has a length of 6 units, while BC has a length of 4 units.

Here is a diagram of the trapezoid:

A(-4,-1)

B((-4,6)

C(2,6)

D(2,-4)

A trapezoid is a quadrilateral with at least one pair of parallel sides. In this case, sides AB and CD are parallel because they have the same slope. So, the given points do represent the vertices of a trapezoid.

An isosceles trapezoid has two congruent legs (non-parallel sides). In this case, the length of side AD is `sqrt((-4-2)^2+(-1+4)^2)=sqrt(36+9)=sqrt(45)` and the length of side BC is `sqrt((-4-2)^2+(6-6)^2)=sqrt(36+0)=sqrt(36)`. Since `sqrt(45)` is not equal to `sqrt(36)`, the trapezoid is not isosceles.

Answer:

-1 ≤ m ≤ 9

Step-by-step explanation:

See attached image.

What you have to note about solving inequality equations like this:

Answer:

90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love u this is irrelevent but idrc lol

Step-by-step explanation:

90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love u this is irrelevent but idrc lol

The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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The reference angle would be 155 degrees.

An angle's reference angle is the measure of the smallest, positive, acute angle formed by the terminal side of the angle and the horizontal axis.

The positive reference angles have terminal sides that lie in the first quadrant and can be used as models for angles in other quadrants.

The reference angle is acute angle, it must be < 90°.

The terminal side lies in Quadrant II.

The positive measure is:

=180-25

=155°.

And the negative measure is:

= 155-360

= -205°.

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9514 1404 393

Answer:

  $81

Step-by-step explanation:

The garden is 4 yards = 12 feet by 3 yards = 9 feet. The area of it is the product of these dimensions, ...

  (12 ft)(9 ft) = 108 ft²

The cost of fertilizer for that area will be ...

  ($0.75/ft²)(108 ft²) = $81.00

They will spend $81.00 to fertilize the garden.

\(\qquad\qquad\huge\underline{{\sf Answer}}♨\)

let's solve ~

Perimeter of the composite figure :

Perimeter of rectangle + circumference of semi circle - common side.

Perimeter of rectangle :

\(\qquad \tt \dashrightarrow \:2(4 + 12)\)

\(\qquad \tt \dashrightarrow \:2(16)\)

\(\qquad \tt \dashrightarrow \:32 \: \: ft {}^{} \)

Circumference of Semicircle :

\(\qquad \tt \dashrightarrow \:\pi r\)

\(\qquad \tt \dashrightarrow \:3.14 \times 2\)

\(\qquad \tt \dashrightarrow \:6.28 \: ft\)

Length of common side = 4 feet

So, perimeter of composite figure :

\(\qquad \tt \dashrightarrow \:32 + 6.28 - 4\)

\(\qquad \tt \dashrightarrow \:34.28 \: ft\)