What is the value of sin0 given that (-3,4) is a point on the terminal side of 0?

Answer:

(I)isosceles triangle

(ii)scalene triangle,right angle triangle

(iii)scalene triangle,right angle triangle

(iv)Equilateral triangle

The expression 10√5 can be written as √500 because √(10×10) = 10 option (A) √500 is correct.

It is defined as the combination of constants and variables with mathematical operators.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have an expression:

= 10√5

We can write the above equation:

= √(10×10×5)

Because √(10×10) = 10

= √(100×5)

= √500

Thus, the expression 10√5 can be written as √500 because √(10×10) = 10 option (A) √500 is correct.

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Answer:  14

Step-by-step explanation:

We arrange the number as -3,  1, 7, 8, 18, 19, 42, the old median is 8.

But the median has change to 11 when the number is add, which means that the number is between 7 and 18.

(8 + x)/2 = 11      Where x is the new number

8 + x = 22

x = 14

BC=DE are congruent and the angles are also congruent by using CPCT.

To prove BC=DE given angle BAC=angle DAE, we can use the following steps:

Draw the circle with centre A and points B, C, D, and E on its circumference.

Draw the line segment AE, and extend it to intersect the circle at point F.

Draw the line segment BF, and extend it to intersect the circle at point G.

Draw the line segments CG and DG.

Since angles BAC and DAE are equal, we have angle BAF = angle DAF (because they are vertical angles).

Since angles BAF and BGF subtend the same arc, we have angle BAF = angle BGF.

Similarly, since angles DAF and DGF subtend the same arc, we have angle DAF = angle DGF.

Since angles BGF and DGF are both equal to angle BAC/2 + angle DAE/2, we have angle BGF = angle DGF.

Since angles BGC and DGC are both equal to angle BGF + angle CGF, we have angle BGC = angle DGC.

Since angles BDC and EDC are both equal to angle CGD, we have angle BDC = angle EDC.

Therefore, BC = BG + GC = DG + GC = DE, as desired.

To prove angle BAC=angle DAE given BC=DE, we can use the following steps:

Draw the circle with centre A and points B, C, D, and E on its circumference.

Draw the line segments AC and AD.

Draw the perpendicular bisectors of BC and DE, and let them intersect at point O.

Since BC=DE, the perpendicular bisectors of BC and DE are the same line.

Therefore, point O lies on both the perpendicular bisectors of BC and DE.

Since point O lies on the perpendicular bisector of BC, we have OB = OC.

Similarly, since point O lies on the perpendicular bisector of DE, we have OD = OE.

Since OA is a radius of the circle, we have OB = OD.

Therefore, OB = OC = OD = OE, so quadrilateral BCDE is a kite.

Since a kite has two pairs of equal adjacent angles, we have angle BOC = angle DOE and angle BCO = angle EDO.

Therefore, angle BAC = angle BOC - angle BCO = angle DOE - angle EDO = angle DAE, as desired.

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The most appropriate reason for Christie making changes to her budget at the end of every month in terms of smart financial planning is B. She is reviewing her goals and aligning the budget to work toward them.Option B is correct.

Smart financial planning involves regularly evaluating and adjusting one's budget to ensure that it reflects their financial goals and current circumstances. By reviewing her goals, Christie can assess if her budget is still aligned with those goals and make any necessary changes to stay on track.

Life circumstances, such as changes in income, expenses, or financial priorities, may warrant adjustments to the budget. Christie recognizes that her needs may change over time, and by modifying her monthly budget, she can ensure that her financial resources are allocated appropriately to meet her evolving goals.

Regularly revisiting and modifying the budget allows Christie to adapt her financial plans, optimize her spending, and make informed decisions to achieve her financial objectives. Option B is correct.

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Answer:

Choice A. $2,392 is the correct answer :)

Step-by-step explanation:

An amount of $ 2392 are withheld in a year. (Correct choice: A)

In this question we must determine the amount of money that is withheld in a year. By considering a year as a 52-week period, the total money to be withheld in a year is equal to the product of the weekly money that is withheld and the number of weeks in a year, that is to say:

\(C = (52\,weeks)\cdot \left(46\,\frac{USD}{week} \right)\)

\(C = 2392\,USD\)

An amount of $ 2392 are withheld in a year. (Correct choice: A)

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The probability that the individual must stop at at least one light that is 0.45.

Probability is the mathematical tool or procedure of predicting how likely a given event is going to happen.

Given is that there are two traffic lights on the route used by a certain individual to go from home to work. Let {E} denote the event that the individual must stop at the first light, and define the event {F} in a similar manner for the second light. Suppose that -

We can write -

P{E ∪ F} = P{E} + P{F} - P{E ∩ F}

P{E ∪ F} = 0.4 + 0.2 - 0.15

P{E ∪ F} = 0.6 - 0.15

P{E ∪ F} = 0.45

Therefore, the probability that the individual must stop at at least one light that is 0.45.

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Answer:

bru

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

Answer: So, the simple probability of reaching in and extracting a yellow marble from the bag is 0.1 or 10%.

Step-by-step explanation: To calculate the simple probability of reaching in and extracting a yellow marble from the bag, we need to divide the number of yellow marbles by the total number of marbles in the bag.

The bag contains a total of 10 marbles, and there is only 1 yellow marble. Therefore, the probability of extracting a yellow marble can be calculated as:

Probability = Number of Yellow Marbles / Total Number of Marbles

Probability = 1 / 10

Simplifying this fraction gives us:

Probability = 0.1 or 10%

Hope this helps!

The requried equation of the diagonals for which WXYZ will be rhombus is y = -x + 12 and y = x + 12.

A rhombus is a parallelogram with all sides of equal length. This means that the diagonals of a rhombus bisect each other at right angles.

Let's first find the length of the diagonals of rhombus WXYZ using the distance formula:

WY = \(\sqrt{[(9-1)^2 + (11-3)^2]]}\) = 8√2

Since the diagonals of a rhombus bisect each other at right angles, we can use the midpoint formula to find the midpoint M of the diagonal WY:

Midpoint M = ((1+9)/2, (3+11)/2) = (5, 7)

The slope of the line passing through W and Y is:

slope WY = (11-3)/(9-1) = 8/8 = 1

Therefore, the slope of the line perpendicular to WY is -1/1 = -1.

Using the point-slope form with point M and slope -1, we get:

y - 7 = -1(x - 5)

y = -x + 12

So, the equation of the line passing through M with a slope perpendicular to the line passing through W and Y is y = x + 12 equation for XZ will be the same but the slope will be +1 so the equation is y = x + 1.

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Answer: For this one, I'll use y=mx+b because that equation make the most sense in this scenario.

A) X is the number of hours, and 15, or b is the tip

B) y= 30x + 15.

Have a great day!

Stay safe and healthy!

Happy holiday seasons!

May I please have brainliest?

Answer:

B

Step-by-step explanation:

6x -8y = - 16y

6x = -8y

8y = 17x + 4

-8y = -17x - 4

6x = -17x - 4

23x = -4

x = -4/23

To calculate Swornima's annual income and the amount of tax she should pay, let's break down the information provided:

Monthly basic salary: Rs 48,000

Social security tax rate: 1%

Income tax rate on income up to Rs 5,00,000: 0% (no tax)

Income tax rate on income from Rs 5,00,001 to Rs 7,00,000: 10%

Dashain allowance: 1 month's salary

Deposit in Citizen Investment Trust (CIT): 10%

Rebate on income tax: 10%

(i) Annual Income:

Swornima's monthly basic salary is Rs 48,000, so her annual basic salary would be:

Annual Basic Salary = Monthly Basic Salary x 12

= Rs 48,000 x 12

= Rs 5,76,000

Additionally, she receives 1 month's salary as the Dashain allowance, which we can add to her annual income:

Annual Income = Annual Basic Salary + Dashain Allowance

= Rs 5,76,000 + Rs 48,000

= Rs 6,24,000

Swornima's annual income is Rs 6,24,000.

(ii) Tax Rebate:

Swornima receives a 10% rebate on her income tax. To calculate the rebate, we need to determine her income tax first.

(iii) Annual Income Tax:

First, let's calculate the income tax for the range of income from Rs 5,00,001 to Rs 7,00,000. The tax rate for this range is 10%.

Taxable Income in this range = Rs 6,24,000 - Rs 5,00,000

= Rs 1,24,000

Income Tax in this range = Taxable Income x Tax Rate

= Rs 1,24,000 x 0.1

= Rs 12,400

Now, let's calculate the total annual income tax:

Total Annual Income Tax = Income Tax in the range Rs 5,00,001 to Rs 7,00,000

= Rs 12,400

Next, we calculate the rebate on income tax:

Tax Rebate = Total Annual Income Tax x Rebate Rate

= Rs 12,400 x 0.1

= Rs 1,240

Swornima's annual income tax is Rs 12,400, and she receives a tax rebate of Rs 1,240.

To summarize:

(i) Swornima's annual income is Rs 6,24,000.

(ii) Swornima's tax rebate is Rs 1,240.

(iii) Swornima should pay an annual income tax of R

The equation of the line that is parallel and perpendicular to y = -8x + 6 and passes through the point (7, 5) are y = -8x + 61 and  \(y = \frac{1}{8}x + \frac{33}{8}\) respectively.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the original line:

y = -8x + 6

Using the slope intercept:

Slope m = -8

Since the desired line is parallel, it will have the same slope.

Therefore, the slope of the parallel line is also -8.

Plug in the slope m = -8 and the poin (7,5) into the point-slope form:

( y - y₁ ) = m( x - x₁ )

( y - 5) = -8( x - 7 )

Simplify

y - 5 = -8x + 56

y = -8x + 56 + 5

y = -8x + 61

The equation of the parallel line is y = -8x + 61.

For the perpendicular line:

The slope of the perpendicular line will be the negative reciprocal of -8, which is 1/8.

Hence, plug slope m = 1/8 and point (7,5) into the point-slope form:

( y - y₁ ) = m( x - x₁ )

\(y - 5 = \frac{1}{8} ( x + 7 )\\\\y - 5 = \frac{1}{8}x + \frac{7}{8} \\\\y = \frac{1}{8}x + \frac{7}{8} + 5\\\\y = \frac{1}{8}x + \frac{33}{8}\)

Therefore, the perpendicular line is \(y = \frac{1}{8}x + \frac{33}{8}\).

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Answer:

B

Step-by-step explanation:

Given y and x vary directly then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 27 when x = 4 , then

27 = 4k ( divide both sides by 4 )

\(\frac{27}{4}\) = 6.75 = k

y = 6.75x ← equation of variation

When x = 12 , then

y = 6.75 × 12 = 81

Answer:

-1562500

Step-by-step explanation:

15625 × (-2) + (-15625) × 98 = -31250 + (-1531250)

                                              = -31250 - 1531250

                                              = -1562500

Answer:

\(-1562500\)

Step-by-step explanation:

\(5625\left(-2\right)+\left(-15625\right)\times \:98\)

\(15625\left(-2\right)\)

\(=-31250\)

\(15625\times \:98\)

\(=1531250\)

\(-31250-1531250\)

\(-1562500\)

Answer:

\(q=45\)

Step-by-step explanation:

Notice that \((q+2)^{\circ}\) and \((3q-2)^{\circ}\) form a linear pair, that is, they sum to \(180^{\circ}\) as follows:

\((q+2)^{\circ}+(3q-2)^{\circ}=180^{\circ}\\(q+2+3q-2)^{\circ}=180^{\circ}\\(4q)^{\circ}=180^{\circ}\\4q=180\\q=\frac{180}{4}\\q=45\)

Answer:

1.) inverse proportion : 1kx = y

2) direct proportion. y = kx

Answer:

\(y=6(x-8)-2\qquad\text{point-slope form}\)

\(y=6x-50\qquad\text{slope-intercept form}\)

Step-by-step explanation:

The equation of a line can be written in several forms. Two of the most-used forms are the point-slope and the slope-intercept forms.

The point-slope form requires to have one point (xo, yo) through which the line passes and the slope m. The equation expressed in this form is:

\(y=m(x-xo)+yo\)

The slope-intercept form requires to have the slope m and the y-intercept b, or the y-coordinate of the point where the line crosses the y-axis. The equation is:

\(y=mx+b\)

The line considered in the question has a slope m=6 and passes through the point (8,-2). These data is enough to find the point-slope form of the line:

\(\boxed{y=6(x-8)-2\qquad\text{point-slope form}}\)

To find the slope-intercept form, we operate the above equation:

\(y=6x-48-2\)

\(\boxed{y=6x-50\qquad\text{slope-intercept form}}\)

Salt remaining at the end of the basketball game will be 3/10lb

It is given that, the amount of salt at the beginning of the basketball game was 8/10lb

During the game, he made 20 batches of popcorn using salt. The amount of salt used is given as 1/2lbs.

To find the remaining salt at the end of the game we will have to subtract the amount used for making popcorn from the original amount. So, we get :

    => Total = Original - Used

    =>  Total = 8/10 - 1/2    => (16-10)/20

    =>  Total = 6/20 => 3/10

Hence, the salt remaining at the end of the basketball game will be 3/10lb

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Answer:

Step-by-step explanation:

Either way works. It comes to the same thing.

(2x-5)(x+1)=9

F: 2x*x = 2x^2

O: 2x*1 = 2x

I: -5 * x = -5x

L: -5*1 = -5

2x^2 + 2x - 5x - 5 = 9    Subtract 9 from both sides

2x^2 - 3x - 14 =0            Divide by 2 (it makes life easier).

Factoring you get

(2x - 7)(x + 2)

2x - 7 = 0

2x = 7

x = 3.5

x + 2 = 0

x = -2

The x intercepts = (3.5,0) and (-2,0)

I've put a graph up for the given equation.

Answer:

2.221992

Step-by-step explanation:

can i have the crown pls ૮ ♡ﻌ♡ა

Answer:

2.221

Step-by-step explanation:

Answer:

y = - 2x + 13

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (3, 7) and (x₂, y₂ ) = (5, 3)

m = \(\frac{3-7}{5-3}\) = \(\frac{-4}{2}\) = - 2, thus

y = - 2x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (3, 7), then

7 = - 6 + c ⇒ c = 7 + 6 = 13

y = - 2x + 13 ← equation of line

Answer:

\(-3(x-2)^2+5\)

Step-by-step explanation:

First we can factor a -3 from the \(x^2\) term and the \(x\) term to get \(-3(x^2-4x)-7\).

Then we want the stuff in the parentheses to have the form of \((x+b)^2\), or equivalently, \((x^2+2b+b^2)\) . So we can let \(2b = -4\). By solving it, we get \(b = -4/2 = -2\). Then our \(b^2\) term should be \(b^2 = (-2)^2 = 4\).

In order to make our \(b^2\) term appear in the parentheses, we need to add and subtract our \(b^2\) term, so we get \(-3(x^2 - 4x + 4 - 4) -7\).

What we to keep inside our parentheses is \((x^2 - 4x + 4)\) , so we can factor the \(-4\) out of parentheses to get \(-3(x^2-4x+4-4)-7 = -3(x^2-4x+4)+(-3)(-4) - 7 = -3(x^2 - 4x + 4) + 12 - 7 = -3(x^2 - 4x + 4) + 5\)

Finally, plugging  \(b = -2\)  that we computed earlier into the equation \((x^2+2b+b^2) = (x+b)^2\), we get  \((x^2 - 4x + 4) = (x-2)^2\).

So we have \(-3(x^2-4x+4)+5 = -3(x-2)^2+5\).

In summary, the procedure is

\(-3x^2+12x-7 \\= &-3(x^2-4x) -7 \\= &-3(x^2-4x+4-4)-7 \\= -3(x^2-4x+4) + (-3)(-4)-7\\=-3(x^2-4x+4)+12-7\\= -3(x^2-4x+4)+5 \\= -3(x-2)^2+5\)

Answer:

y-b-w+x+12

Step-by-step explanation:

yea

Answer: 5x

Step-by-step explanation: 5(1) = 5

The system of inequalities for the graph is

a) y < 3x - 4

b) y = x + 3

Given data ,

Let the inequality equations be represented as A and B

where

Let the first point be P ( 0 , 3 )

Let the second point be Q ( -3 , 0 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 3 - 0 ) / ( 0 + 3 )

m = 1

Now , equation of line is y - y₁ = m ( x - x₁ )

y - 0 = 1 ( x + 3 )

y = x + 3

And , the second equation is

Let the first point be R ( 0 , -4 )

Let the second point be S ( 2 , 2 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( -4 - 2 ) / ( 0 - 2 )

m = -6/-2

m = 3

Now , equation of line is y - y₁ = m ( x - x₁ )

y - 2 = 3 ( x - 2 )

Adding 2 on both sides , we get

y = 3x - 4

Since , it is a dotted line ,

y < 3x - 4

And , the solution to the inequality is point of intersection

where A ( 3.5 , 6.5 ) is the solution

Hence , the inequality equations are solved and A ( 3.5 , 6.5 ) is the solution

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A set of numbers that can represent the side lengths, in centimeters, of a right triangle is any set that satisfies the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

A right triangle is a type of triangle that contains a 90-degree angle. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's consider a set of numbers that could represent the side lengths of a right triangle in centimeters.

One possible set could be 3 cm, 4 cm, and 5 cm.

To verify if this set forms a right triangle, we can apply the Pythagorean theorem.

Squaring the length of the shortest side, 3 cm, gives us 9. Squaring the length of the other side, 4 cm, gives us 16.

Adding these two values together gives us 25.

Finally, squaring the length of the hypotenuse, 5 cm, also gives us 25. Since both values are equal, this set of side lengths satisfies the Pythagorean theorem, and hence forms a right triangle.

It's worth mentioning that the set of side lengths forming a right triangle is not limited to just 3 cm, 4 cm, and 5 cm.

There are infinitely many such sets that can be generated by using different combinations of positive integers that satisfy the Pythagorean theorem.

These sets are known as Pythagorean triples.

Some other examples include 5 cm, 12 cm, and 13 cm, or 8 cm, 15 cm, and 17 cm.

In summary, a right triangle can have various sets of side lengths in centimeters, as long as they satisfy the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

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Answer:

29 1/4 ft^2

Step-by-step explanation: