helppp pleaseee enough points quick

Therefore, the total area of the region that satisfies the two inequalities is 14.5 square units.

The two inequalities given are:

y >= x

y <= |x - 3|

The region that satisfies both inequalities is the shaded area in the graph.

We can find the area of this region by splitting it into two parts: the triangle formed by the points (0, 0), (3, 0), and (3, 3), and the trapezoid formed by the points (3, 3), (2, 1), (-1, 3), and (-3, 3).

The area of the triangle is (1/2)33 = 4.5 square units.

To find the area of the trapezoid, we need to find the lengths of its two bases and its height. The height is the distance between the x-axis and the line y = |x - 3|. This line intersects the x-axis at x = 3 and at x = -1. At x = 3, the height is 0. At x = -1, the height is |-1 - 3| = 4. So the height of the trapezoid is 4 units.

The lengths of the two bases of the trapezoid are the distances between the y-axis and the lines x = 2 and x = -3. These distances are 2 and 3 units, respectively. So the area of the trapezoid is (1/2)*(2 + 3)*4 = 10 square units.

Therefore, the total area of the region that satisfies the two inequalities is 4.5 + 10 = 14.5 square units.

To know more about inequality,

https://brainly.com/question/30239204

#SPJ11

Complete question:

How many square units are in the region satisfying the inequalities y>=(x) and y<=-(x)+3? Express your answer as a decimal. * the () are absolute value signs.

"Extend the domain of the trigo functions using the unit circle" Cluster A.

The following steps can be used to calculate the sine and cosine of any angle thetatheta and allow us to extend the domain of sine and cosine to any real numbers:

Move counterclockwise around the unit circle starting at (1, 0), (1, 0), (1, comma, 0, right parenthesis, until the angle created by your position, the origin, and the positive xxx-axis equals thetatheta.

The yyy-coordinate of your point is equal to sin(theta)sin(theta)sine, and the xxx-coordinate is equal to cos(theta)cos(theta)cos(theta)cosine, left parenthesis, theta, right parenthesis.

There are several references to and issues with in the worlds of calculus, pre-calculus, and trigonometry.

To know more about Unit circle visit:-https://brainly.com/question/11987349

#SPJ4

Answer:

3a. yes

3b. y= 75x

3c. 600 mi

3d. 10 inches

Step-by-step explanation:

3a: if you divide the y by the x, you'd get 75 everytime, meaning it's proportional.

3b: y would equal the amount of inches multiplied by 75, so y=75x

3c: you can use the equation and substitute the x for 8, so y=75(8), giving you 600 miles

3d: you can also use the equation in reverse, if the actual miles is 750, then this is your y, so it would look like 750=75x and to solve you'd divide, 750/75, giving you 10 inches

Answer:

x= -2

Step-by-step explanation:

Hope this helps.

Answer:

-102 = (-8×6 -8×-4x) -5x ( this is only for explanation write only this way as given below)

-102 = -48+32x -5x

-102 = -48+27x

-102+48= 27x

-54 = 27x

x = -54/27

x = -2 Ans

Hope you like it!

If BDFH is a parallelogram, then KN = MN. This is because KM is parallel to both BF and DH, and MN and KN are both half the length of BD and FH, respectively, which are equal since BDFH is a parallelogram.

Two pairs of parallel sides quadrilateral is known as parallelogram.

It is a four-sided planar figure with opposite sides that are parallel and congruent.

Since BDFH is a parallelogram, opposite sides are parallel and congruent. Therefore, BD is parallel and congruent to FH, and BF is parallel and congruent to DH.

Since KM is the line joining the midpoints of BD and FH, KM is parallel to BD and FH. Thus, KM is also parallel to BF and DH.

Let N be the intersection point of diagonals BD and FH, and let P and Q be the midpoints of BD and FH, respectively.

Since P and Q are midpoints of BD and FH, respectively, we have:

BP = PD, and FQ = QH.

By the midpoint theorem, we also have:

MN = 1/2 * BD, and KN = 1/2 * FH.

Since BDFH is a parallelogram, we have BD = FH, and therefore:

MN = 1/2 * BD = 1/2 * FH = KN.

Therefore, KN = MN.

To know more about midpoint theorem visit:

https://brainly.com/question/30242628

#SPJ1

Answer: 2/7

Step-by-step explanation:

Go from point A to D by moving up 2 units and right 7 units. Since it slopes up it's a positive number.

Answer:

It is inversly proportional, there is no constant, the directio is from left to right and from up to down, as x gets larger, y gets less

Step-by-step explanation:

Answer:

Our calculator limits your interest deduction to the interest payment that would be paid on a $1,000,000 mortgage. Interest rate: Annual interest rate for this

Step-by-step explanation:

Answer: The answer is 60.

Step-by-step explanation:

Using the fact that OP || RS, we know that∠RWV = 180° − 130° 1.  ∠RWV = 50° We know that,∠PWQ = ∠RWV = 50° (Since, opposite angles of intersecting lines are equal) Also, for line OP∠OQP + θ = 180° θ = 180° − ∠OPQ = 180° − 110° 2.  θ = 70° 

Answer:

The measure of ∠OPQ is 110°.

Step-by-step explanation:

Draw a line parallel to OP from point Q. Label a point on the line T. (See attached diagram).

Angles SRQ and TQR are alternate interior angles, and so according to the Alternate Interior Angles Theorem, they are congruent.

⇒ m∠TQR = m∠SRQ = 130°

Given m∠PQR = 60° and m∠TQR = 130° then:

⇒ m∠TQP + m∠PQR = m∠TQR

⇒ m∠TQP + 60° = 130°

⇒ m∠TQP = 70°

Angles OPQ and TQP are same-side interior angles, and so according to the Same-side Interior Angles Theorem, they are supplementary (sum to 180°).

⇒ m∠OPQ + m∠TQP = 180°

⇒ m∠OPQ + 70° = 180°

⇒ m∠OPQ = 110°

Therefore, the measure of ∠OPQ is 110°.

after 18 years, Ralphy Boy's annuity account will be worth approximately $50,334.72.

To calculate the future value of an annuity, we can use the formula:

FV = P  [(1 + r)^n - 1] / r

Where:

FV is the future value of the annuity,

P is the monthly payment or deposit amount,

r is the monthly interest rate, and

n is the number of periods or months.

In this case, P = $100, r = 7.5% (or 0.075 as a decimal), and n = 18 years * 12 months/year = 216 months.

Plugging in these values into the formula, we get:

FV = $100 [(1 + 0.075)^216 - 1] / 0.075 ≈ $50,334.72

Therefore, after 18 years, Ralphy Boy's annuity account will be worth approximately $50,334.72.

Learn more about future value here:

https://brainly.com/question/30787954

#SPJ11

The Taylor series for f(x) = sin(x) centered at a = π is given by \(\(f(x) = (x - \pi) - \frac{{(x - \pi)^3}}{{3!}} + \frac{{(x - \pi)^5}}{{5!}} - \frac{{(x - \pi)^7}}{{7!}} + \ldots\)\)

The Taylor series expansion of a function f(x) centered at a point a can be obtained by taking the derivatives of f(x) at a and evaluating them at a.

For the sine function, we can start by evaluating the derivatives of sin(x) at x = π. The derivative of sin(x) is cos(x), and the derivative of cos(x) is -sin(x). Evaluating these derivatives at x = π, we find that sin(π) = 0, cos(π) = -1, and sin(π) = 0 again.

Using these values, we can construct the Taylor series for sin(x) centered at a = π. The general term of the series is given by \(\((-1)^{\frac{n}{2}} \cdot (x - \pi)^n / n!\)\), where n is an even number. This series includes only the even powers of (x - π) since the odd powers evaluate to zero at x = π.

By summing up these terms, we obtain the Taylor series for sin(x) centered at π.

Therefore, the Taylor series for f(x) = sin(x) centered at a = π is given by \(\(f(x) = (x - \pi) - \frac{{(x - \pi)^3}}{{3!}} + \frac{{(x - \pi)^5}}{{5!}} - \frac{{(x - \pi)^7}}{{7!}} + \ldots\)\), where the ellipsis indicates that the series continues indefinitely.

Learn more about Taylor series here:

https://brainly.com/question/31329947

#SPJ11

Answer: i believe its -3x+9

Step-by-step explanation:

it is important to recognize that the minus sign in front of −(x−3) applies to both x and −3.

remove the parentheses by distributing the minus sign to the terms inside them: −2x+6−(x−3)

⇒−2x+6−x−(−3)

⇒−2x+6−x+3

combine similar terms: ⇒(−2x−x)+(6+3)

⇒−3x+9

Answer:

sorry im on a time lapse, so the answer is 2  1/2. hope it helps

Step-by-step explanation:

Answer:

Hi above picture is the solution for your question.

Please mark it the brainliest answer

The equation of the line is y = -3x + 5.

To find the equation of a line that passes through two points and is perpendicular to the equator, we need to calculate the slope of the line that passes through the two points first.

The slope of the line passing through (1,10) and (1,10) is 0. This means that the line is perpendicular to the equator, whose slope is undefined.

Next, we need to calculate the y-intercept. If we assume that the line passes through the point (1,10), then the y-intercept is 10.

Finally, we can use the slope and the y-intercept to write the equation of the line in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 0 and the y-intercept is 10, so the equation of the line is y = 0x + 10, which simplifies to y = 10.

Since the slope of the line is 0, we can also write the equation of the line in the form y = -3x + b, where b is the y-intercept. In this case, the y-intercept is 10, so the equation of the line is y = -3x + 10, which simplifies to y = -3x + 5.

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

Answer:

2

Step-by-step explanation:

Segment JK is congruent to Segment MN, Segment KL is congruent to segment NO, and the angle K is congruent to the angle N.

Therefore, the answer choice that is true when \(\triangle JKL\) is reflected over a line to form \(\triangle MNO\) is: d. \(\overline{JK} \cong \overline{MN}, \overline{KL} \cong \overline{NO}, \angle K \cong \angle N\)

Reflecting a shape or figure over a line is somewhat similar to when you place an object before a mirror.

In the reflection of triangle JKL across a line, triangle MNO is the mirror image of triangle MNO.

<K is congruent to <N

<J is congruent to <M

<L is congruent to<O

\(\overline{JK} \cong \overline{MN}\\\\\ \overline{KL} \cong \overline{NO}\\\\ \overline{JL} \cong \overline{MO}\)

Therefore, the answer choice that is true when \(\triangle JKL\) is reflected over a line to form \(\triangle MNO\) is: d. \(\overline{JK} \cong \overline{MN}, \overline{KL} \cong \overline{NO}, \angle K \cong \angle N\)

Learn more here:

https://brainly.com/question/17255045

Differential equations are mathematical equations that involve derivatives. They describe the relationship between an unknown function and its derivatives, helping to model and understand dynamic systems in physics, engineering, and other scientific disciplines.

To find the general solution of the given system of differential equations by decoupling, we first need to rewrite the given equation in a more standard form. The equation provided is: x1' = x1 * x.

Step 1: Rewrite the equation
x1' = x1 * x can be rewritten as dx1/dt = x1 * x, where x1 is a function of time t.

Step 2: Separate variables
Now, we separate variables by dividing both sides of the equation by x1, and then multiplying both sides by dt:
(dx1/x1) = x * dt

Step 3: Integrate both sides
Now we can integrate both sides of the equation with respect to their respective variables:

∫(dx1/x1) = ∫(x * dt)

After integrating, we get:
ln|x1| = (1/2) * x^2 + C₁, where C₁ is the constant of integration.

Step 4: Solve for x1
To find the general solution for x1, we need to exponentiate both sides of the equation to eliminate the natural logarithm:

x1(t) = Ce^(1/2 * x^2), where C = e^(C₁) is a new constant.

So, the general solution of the given system of differential equations is x1(t) = Ce^(1/2 * x^2), where C is an arbitrary constant.

To know more about Differential equations visit:

https://brainly.com/question/25731911

#SPJ11

Answer:

a) 6 2/5  

b) 13 1/2

Step-by-step explanation:

Have a nice day!

Can I maybe have brainliest?

I forgot it was simplify..

Answer:

Cups of carrot needed for 9 servings = 4.5 cups

Step-by-step explanation:

A recipe for sesame chicken calls for cup of chopped carrots

recipe 2 is for 4 servings

That is

2 cups of carrot = 4 servings

2 : 4

= 1 : 2

1 cup of carrot = 2 servings

how many cups of

carrots are needed for 9 servings?

Let x= number of carrot needed for 9 servings

1 : 2 = x : 9

1 /2 = x/ 9

Cross product

1*9 = 2*x

9=2x

Divide both sides by 2

9/2 = x

x= 4.5 Or 4 1/2

By solving the given equation, d = -4

           To find d in the equation -14d + 12d + 11d + 18 = -18, we need to combine similar terms on the left side of the equation and isolate the variable.

Combining similar terms, we get:

(-14 + 12 + 11)d + 18 = -18

9d + 18 = -18

           We can then extract the variable by shifting the constant term to the other side of the equation:

9d = -18 - 18

9d = -36

Finally, we can find d by dividing both sides of the equation by 9:

d = -36/9

d = -4

Therefore, the solution of the equation is d = -4. When d equals -4, the equation is balanced and both sides of the equation are equal.

To solve more linear equation problems:

https://brainly.com/question/11733569

9514 1404 393

Answer:

  a) $96.65

  b) $28,995

  c) 51.7% to principal; 48.3% to interest

Step-by-step explanation:

a) The monthly payment is given by the amortization formula:

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

where P is the loan amount, r is the annual rate, and t is the number of years

Filling in the given values, we find ...

  A = $15,000(0.06/12)/(1 - (1 +0.06/12)^(-12(25))) ≈ $96.65

The monthly payment is $96.65.

__

b) The 300 payments total ...

  $96.65 × 300 = $28,995

The total amount paid is $28,995.

__

c) The percentage paid toward the principal is ...

  $15,000/$28,995 × 100% ≈ 51.7%

The remainder is paid toward interest: 100% -51.7% = 48.3%

51.7% is paid toward principal, 48.3% is paid for interest.

Answer:

(5 × 0.1) × (6 × 0.1)

Step-by-step explanation:

0.5 x 0.6 = 0.3

A is wrong because it is whole numbers

(5 × 0.1) × (6 × 0.01) Is incorrect because it gives us 0.03,(wrong place)

(5 × 0.01) × (6 × 0.01) Is incorrect it gives us 0.003

(5 × 0.1) × (6 × 0.1) Is the correct answer because it gives us 0.3

Answer:

15 pretzels

Step-by-step explanation:

5.50x 5=27.50

90-27.50=62.50

62/4=15.50 --- you can only buy a whole pretzel

hope it helps....

please mark brainliest...

thx

Answer:

5x+2

Step-by-step explanation:

2(3x+6)+2(2x-4)

6x+12 + 4x -8

10x+4

5x+2

Answer:

30x + 600 is greater than or equal to 1,500

x is the amount each member would have to raise.

x = 30

Each member needs to raise at least $30

The surface area of the prism is 96 cm²

Surface area is the sum of the areas of all the faces (or surfaces) of a three-dimensional object.

The length and width of the rectangular face are 4.5 cm and 3 cm, respectively, so the area is:

4.5 cm x 3 cm = 13.5 cm²

Since there are two rectangular faces on the prism, the total area for the pair is:

= 2 x 13.5 cm²

= 27 cm²

Similarly for the another face

3 cm x 3 cm = 9 cm²

Since there are two square faces on the prism, the total area for the pair is:

= 2 x 9 cm²

= 18 cm²

The area of one of the rectangular faces that is not congruent to the first two:

= 8.5 cm x 3 cm

= 25.5 cm²

Since there are two rectangular faces that are not congruent to the first two, the total area for the pair is:

= 2 x 25.5 cm²

= 51 cm²

Now we can find the total surface area by adding the area of each pair of faces:

= 27 cm² + 18 cm² + 51 cm²

= 96 cm²

Therefore, the surface area of the rectangular prism is 96 square centimeters.

To know more about surface area check:

https://brainly.com/question/27847638

#SPJ1

Answer:

\(\frac{x^{2}}{400} + \frac{y^{2}}{976} = 1\)

Step-by-step explanation:

The distance between foci with respect to origin is determined by mean of the Pythagorean Theorem:

\(2\cdot c = \sqrt{(0-0)^{2}+[24-(-24)]^{2}}\)

\(2\cdot c = 48\)

\(c = 24\)

The distance between origin and any of the horizontal co-vertices is:

\(a = \sqrt{[10-(-10)]^{2}+(0-0)^{2}}\)

\(a = 20\)

Now, the distance between origin and any of the vertical co-vertices is determined by the following Pythagorean relationship:

\(c^{2} = b^{2} - a^{2}\)

\(b^{2} = a^{2} + c^{2}\)

\(b = \sqrt{a^{2}+c^{2}}\)

\(b = \sqrt{20^{2}+ 24^{2}}\)

\(b = 4\sqrt{61}\)

Lastly, the equation of the ellipse in standard form is:

\(\frac{x^{2}}{400} + \frac{y^{2}}{976} = 1\)

Answer:

x^2/100+y^2/676=1

Step-by-step explanation:

Answer:

x = -2, y = -6.

Step-by-step explanation:

8x - 3y = 2

-8x - 5y = 46

Adding the 2 equations eliminates x:

-8y = 48

y = -48/8 = -6.

Substitute for y in the first equation:

8x - 3(-6) = 2

8x = 2 - 18

8x = -16

x = -2.

Solution of equation 3 cos t = -3 we get t = (π + 2πn) for n = 0, ±1, ±2, ..n

We are given the equation 3cos(t) = -3, and we need to find all the solutions of this equation.

First, we will divide both sides by 3 to get cos(t) = -1.

We know that the range of the cosine function is from -1 to 1, so this equation is satisfied only when t is in the second and third quadrants.

To find the general solutions of the equation, we need to use the inverse cosine function. The inverse cosine function returns the angle whose cosine is a given value.

So, we have cos(t) = -1, which means that t = arccos(-1) + 2πn or t = -arccos(-1) + 2πn, where n is an integer.

Now, arccos(-1) is π, so we can simplify the above equations as follows:

t = π + 2πn or t = -π + 2πn

These equations give us the solutions of the equation in the interval [0, 2π].

To find all the solutions, we need to add 2πk to these solutions, where k is an integer.

So, the general solutions of the equation are:

t = π + 2πn + 2πk or t = -π + 2πn + 2πk

where n and k are integers.

Simplifying these equations, we get:

t = (2n + 1)π + 2πk or t = (2n - 1)π + 2πk

t = 2π + 1π + 2πk or t = 2nπ - π + 2πk

t = π + 2πn

where n and k are integers.

t = (π + 2πn) for n = 0, ±1, ±2, .. is right choice.

For similar question on equation

https://brainly.com/question/29538993

#SPJ11