simplify x^2 + 7y - 4y + 9x^2.

The sine equation for the object's height is given as follows:

d = -5sin(0.24t).

The standard definition of the sine function is given as follows:

y = Asin(Bx) + C.

The parameters are given as follows:

The amplitude for this problem is of 5 inches, hence:

A = 5.

The period is of 1.5 seconds, hence the coefficient B is given as follows:

2π/B = 1.5

B = 1.5/2π

B = 0.24.

The function starts moving down, hence it is negative, so:

d = -5sin(0.24t).

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The length of BD is 18.5 units.

In the given right triangle ABC, with altitude BD drawn to hypotenuse AC, we are given the lengths AD = 22 and DC = 15. We need to find the length of BD.

Let's consider triangle ABD. Since BD is the altitude, it divides the right triangle ABC into two smaller right triangles: ABD and CBD.

In triangle ABD, we have the following sides:

AB = AD = 22 (given)

BD = ?

Now, let's consider triangle CBD. In this triangle, we have the following sides:

BC = DC = 15 (given)

BD = ?

Since triangles ABD and CBD share the same base BD, and their heights are the same (BD), we can say that the areas of these triangles are equal.

The area of triangle ABD can be calculated as:

Area(ABD) = (1/2) * AB * BD

Similarly, the area of triangle CBD can be calculated as:

Area(CBD) = (1/2) * BC * BD

Since the areas of ABD and CBD are equal, we can equate their expressions:

(1/2) * AB * BD = (1/2) * BC * BD

We can cancel out the common factor (1/2) and solve for BD:

AB * BD = BC * BD

Dividing both sides of the equation by BD (assuming BD ≠ 0), we get:

AB = BC

In triangle ABC, the lengths AB and BC are equal, which implies that triangle ABC is an isosceles right triangle. In an isosceles right triangle, the leg's length are congruent, so AB = BC = AD = DC.

BD is equal to half of the hypotenuse AC:

BD = (1/2) * AC

Substituting the given values, we have:

BD = (1/2) * (AD + DC) = (1/2) * (22 + 15) = (1/2) * 37 = 18.5

Therefore, the length of BD is 18.5 units.

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Answer:

780

Step-by-step explanation:

In this example we will call Original Price = y

72%=0.72

218.40=0.72*y

1-0.72=0.28

218.4÷0.28=780

In order to evaluate the expression 2x²+6x for x = - 2, we just have to replace -2 for x into the given formula and solve, like this:

2x²+6x

By replacing -2 for x, we get:

2(-2)²+6(-2) = 2(4) + (-12) = 8 - 12 = -4

Then, when we evaluate 2x²+6x for x = - 2 we get -4

Answer:

$155.56

Step-by-step explanation:

S.I=(PRT)÷100

$144=(P×9×1)÷100

crossmultiply

$144×100=9P

P=$14400÷9

P=$155.56

Answer:

<

Step-by-step explanation:

1) Substitute 5 into the question

2) Work out the sides

3) Put it into an inequality

5 < 7

Hope this helps, have a great day!

Answer:

8 and 16

Step-by-step explanation:

16 + 8 = 24

Answer:

a: equation is x +2x = 24 here x is the variable used for age of Bob's sister thrn Bob's age is represented by 2x.

b: x + 2x= 24

3x= 24

x = 24/3

x= 8

So Bob's sister is 8 years old and Bob is 2x = 2× 8 = 16 years old.

Each silver bead costs $0.50, and each green bead costs $1.

Let's assume the cost of each silver bead is 's' dollars, and the cost of each green bead is 'g' dollars.

According to the given information, the necklace requires 25 silver beads and 15 green beads, and the bracelet requires 10 silver beads and 5 green beads.

The total cost of the necklace beads is $27.50, and the total cost of the bracelet beads is $10.

Using this information, we can set up the following system of equations:

25s + 15g = 27.50 (Equation 1)

10s + 5g = 10 (Equation 2)

We can solve this system of equations using any appropriate method, such as substitution or elimination.

Let's use the elimination method to solve the system:

Multiplying Equation 2 by 3, we get:

30s + 15g = 30 (Equation 3)

Subtracting Equation 3 from Equation 1:

25s + 15g - (30s + 15g) = 27.50 - 30

-5s = -2.50

s = 0.50

Now, substituting the value of s into Equation 2:

10(0.50) + 5g = 10

5 + 5g = 10

5g = 5

g = 1

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Answer:

x = 8.481 or -4.481

Step-by-step explanation:

x^2 - 4x - 9 = 29

x^2 - 4x - 9 - 29 = 0

x^2 - 4x - 38 = 0

x1  

= −(−4) − √ (−4)2 − 4×1×(−38)  

2×1

= 4 − 2 × √ 42  

2

≈ −4.481

x2  

= −(−4) + √ (−4)2 − 4×1×(−38)  

2×1

= 4 + 2 × √ 42  

2

≈ 8.481

x = 8.481 or -4.481

Have a nice day!

Answer:

190

Step-by-step explanation:

Using the data points given, the equation is \(\frac{\Big(\frac{(x - 4)^2}{25}+ (y + 2)^2\Big)}{25} = 1\).

What is an ellipse?

An ellipse is a locus of a point that moves in such a way that its perpendicular distance from a fixed straight line (directrix) and its distance from a set point (focus) remain constant. which is smaller than unity, i.e. eccentricity(e).

We are given that the center of the ellipse is at (4,-2), and a vertex is at (9,-2).

We know that the distance from the center to a vertex is a, where a is the length of the semi-major axis.

Therefore, we have -

a = 9 - 4 = 5

Since the point (4,3) is on the ellipse, we can use the distance formula to find the length of the semi-minor axis -

c = distance from (4,-2) to (4,3)

c = \(\sqrt{((4-4)^2 + (3-(-2))^2}\)

c = 5

Now, we can use the equation of an ellipse -

\(\frac{\Big(\frac{(x - h)^2}{a^2}+ (y - k)^2\Big)}{b^2} = 1\)

where (h,k) is the center of the ellipse, a is the length of the semi-major axis, and b is the length of the semi-minor axis.

Plugging in the values we have found, we get -

\(\frac{\Big(\frac{(x - 4)^2}{25}+ (y + 2)^2\Big)}{25} = 1\)

Therefore, the equation for the ellipse is \(\frac{\Big(\frac{(x - 4)^2}{25}+ (y + 2)^2\Big)}{25} = 1\).

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Answer:

A 40% chance of choosing a poor or rich person

Step-by-step explanation:

The length along the x-axis is 5 - (-1) = 6. The length along the y-axis is 3 - (-1) = 4. The perimeter of this rectangle can be calculated as

\(P = 2x + 2y = 2(6) + 2(4) = 20\:\text{units}\)

The area of the rectangle can be calculated as

\(A = xy = (6)(4) = 24\:\text{units}^2\)

Therefore, the interest portion of the seventh payment is:7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7 - 7,000.

We have the following payments and their corresponding times of payment:At the end of year 1: $1,000At the end of year 2: $2,000At the end of year 3: $3,000At the end of year 4: $4,000At the end of year 5: $5,000At the end of year 6: $6,000At the end of year 7: $7,000

At the end of year 8: $8,000At the end of year 9: $9,000At the end of year 10: $10,000The present value of these payments is:PMT x [(1 - (1 + r)-n) / r]where PMT is the payment, r is the interest rate per year, and n is the number of years till payment.

For the first payment (end of year 1), the present value is:1,000 x [(1 - (1 + r)-1) / r]which equals

1,000 x (1 - 1 / (1 + r)) / r = 1,000 x ((1 + r - 1) / r) = 1,000

For the second payment (end of year 2), the present value is:2,000 x [(1 - (1 + r)-2) / r]which equals 2,000 x (1 - 1 / (1 + r)2) / r = 2,000 x ((1 + r - 1 / (1 + r)2) / r) = 2,000 x (1 + r) / r2

For the seventh payment (end of year 7), the present value is:

7,000 x [(1 - (1 + r)-7) / r]

which equals

7,000 x (1 - 1 / (1 + r)7) / r = 7,000 x ((1 + r - 1 / (1 + r)7) / r) = 7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7

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Answer:

False

True

True

False

Step-by-step explanation:

90/5 = 18 x 8 = 144 jars of paint

90/3 = 30 x 10 = 300 sketch pads

300:144 = 25:12

Answer:

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

Let the cost of the meal be x.

Adding a tip of 19%:

Answer:

Wyatt should multiply with 1.19.

Step-by-step explanation:

Forming the expression,

→ 1 + (19% of 1)

Now the required number is,

→ 1 + (19% of 1)

→ 1 + ((19/100) × 1)

→ 1 + (19/100)

→ 1 + 0.19 = 1.19

Hence, required number is 1.19.

Answer:

39  shelves needed to build

Step-by-step explanation:

To find the number of shelves needed we need to divide the number of mystery books by 34

We know that. Each shelf can hold 34.

It is given that, There are 1,326 mystery books

So, 1,326/34

39  shelves needed to build

Answer:

x = .875 y = -49

Step-by-step explanation:

(8x - y = 42)

(y = -43 - 6) or (y = -49)

Since we have our y value, we can plug it into our top equation:

8x -(-49) = 42

8x + 49 = 42

      -42   -42

8x = 7

/8    /8

x = 0.875

To check the work:

8(0.875) - 49 = 42

7 - 49 = 42

Answer:

He can buy 34 containers with a remainder of one dollar.

Step-by-step explanation:

11 x 30 = 330

375 - 330 = 45

11 x 4 = 44

45 - 44 = 1

Answer:  The answer to this is.............

                 34 containers

Step-by-step explanation:

k12

sorry if I am late

hope this helps

When the square sheet of cardboard is cut and folded to create a rectangular box with a lid, the maximum possible volume is achieved when x = 20 inches. All other values will result in a smaller volume for the box.

1. Calculate the side lengths of the box and lid:

Box: 40 inches - 2x = 40 - 2x

Lid: 2x

2. Calculate the volume of the box with a lid when x = 20 inches:

Box Volume:

(40 - 2x) x (40 - 2x) x (40 - 2x) = (40 - 2*20) x (40 - 2*20) x (40 - 2*20) = (20) x (20) x (20)

= 8000 in^3

Lid Volume: 2x x 2x x 2x = 2*20 x 2*20 x 2*20

= 8000 in^3

Total Volume: 8000 in^3 + 8000 in^3 = 16000 in^3

3. Calculate the volume of the box with a lid when x = 20/3 inches:

Box Volume: (40 - 2x) x (40 - 2x) x (40 - 2x) = (40 - 2*20/3) x (40 - 2*20/3) x (40 - 2*20/3) = (33 1/3) x (33 1/3) x (33 1/3)

= 7157.7 in^3

Lid Volume: 2x x 2x x 2x = 2*20/3 x 2*20/3 x 2*20/3

= 1365.3 in^3

Total Volume: 7157.7 in^3 + 1365.3 in^3

= 8523 in^3

4. Comparison: When x = 20 inches, the box has a minimum possible volume of 16000 in^3, while when x = 20/3 inches, the box has a volume of 8523 in^3. Therefore, the statement is true

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Answer:

B: y ≥ 2r-4.

Step-by-step explanation:

To solve for y, we need to isolate y on one side of the inequality. First, we can simplify the left side of the inequality by dividing both sides by 2:

2x - y ≤ 4

Then, we can subtract 2x from both sides to get:

-y ≤ -2x + 4

Finally, we need to isolate y by multiplying both sides by -1 and flipping the direction of the inequality:

y ≥ 2x - 4

Now we can see that the equivalent inequality is option B: y ≥ 2r-4.

The value is shown in the red circle on the number line.

The value of variable θ would be,

⇒  θ = 5π/3 and θ = 4π/3

We have to given that;

Expression is,

⇒ - 10sin θ - 8 = 5√3 - 8

Now, We can simplify as;

⇒ - 10sin θ - 8 = 5√3 - 8

⇒ - 10sin θ = 5√3

⇒ sin θ = - 5√3/10

⇒ sin θ = - √3/2

We know that sinθ = -√3/2 when θ = 4π/3 and θ = 5π/3 (among other angles).

However, since 0 ≤ θ < 2π, only the angles in the second and third quadrants are valid solutions for sinθ = -√3/2.

Therefore, the solutions are θ = 5π/3 and θ = 4π/3, option D is correct.

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Answer:

this kid grayson is deleting my answer and i dont know how when they arent even his questions and he is being a little brat

Step-by-step explanation:

so watch out for him

The elements of R4 that belong to the span of the given vectors can be found by expressing them as linear combinations of the vectors.

Let's call the elements we're looking for "y," and define y as a linear combination of Xi, X2, and X3:

y = a1Xi plus a2X2 plus a3*X3

By solving a system of linear equations with the coefficients of y and the given vectors, we can find the values of a1, a2, and a3.

y = 2Xi + 3X2 - X3 = [2, 2, -3, -3] is one element of R4 that belongs to the span of the given vectors. Another possibility is y = 4Xi + X2 + 2X3 = [4, 4, -2, -2].

The null space of the coefficient matrix formed by the given vectors can be used to find an element of IR4 that does not belong to the span of the given vectors. An element in the null space does not belong to the vectors' span.

If the rank of the coefficient matrix is less than 4, the dimension of the null space is non-zero, indicating that a non-zero solution exists that does not belong to the span of the given vectors.

Each of the given vectors has an entry sum of zero, indicating that they are orthogonal to the vector [1, 1, 1, 1]. As a result, [1, 1, 1, 1] is an IR4 element that does not belong to the given vector.

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The areas of the trapezoid is 50 units².

The trapezoid PQRS have bases 10 and 12 units respectively. The height of the trapezoid is unknown. Let's find the area of the trapezoid as follows:

area of trapezoid = 1 / 2 (a + b)h

where

Therefore,

a = 10 units

b = 15 units

Using Pythagoras's theorem,

5² - 3² = h²

h = √25 - 9

h = √16

h = 4 units

area of trapezoid = 1 / 2 (10 + 15)4

area of trapezoid = 1 / 2 × 25 × 4

area of trapezoid = 100 / 2

area of trapezoid = 50 units²

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Answer:

7.36 g/cm3

Step-by-step explanation:

Density = mass ÷ volume

Mass in grams = 9200g

Volume in cm3 = 1250cm3

9200 ÷ 7850 = 7.36

7.36 is already in 2 d.p.

you can write yd^2 or \(yd^{ \ 2}\) to indicate "square yards"

=========================================================

Work Shown:

The triangle has a base of 3+3+2 = 8, and a height of 7

A = area of triangle

A = 0.5*base*height

A = 0.5*8*7

A = 28

The rectangle has a length and width of 3 and 2

B = area of rectangle

B = length*width

B = 3*2

B = 6

The shaded area is the difference of the two areas

C = area of shaded region

C = A - B

C = 28 - 6

C = 22