trigonometry help (angles of evaluation and depression)

Answer:

The solution is the point (2,-2)

Step-by-step explanation:

we have

[tex]-4x+8y=-24[/tex] -----> equation A

[tex]7x-5y=24[/tex] -----> equation B

step 1

Multiply by 7 equation A both sides

[tex]7(-4x+8y)=7(-24)[/tex]

[tex]-28x+56y=-168[/tex] -----> equation C

step 2

Multiply equation B by 4 both sides

[tex]4(7x-5y)=4(24)[/tex]

[tex]28x-20y=96[/tex] -----> equation D

step 3

Adds equation C and equation D

[tex]-28x+56y=-168\\28x-20y=96\\-----------\\56y-20y=-168+96\\36y=-72\\y=-2[/tex]

Find the value of x

substitute the value of y in any equation

equation A

[tex]-4x+8(-2)=-24\\4x=-16+24\\4x=8\\x=2[/tex]

therefore

The solution is the point (2,-2)

Answer:

  yes, they are

Step-by-step explanation:

y = -5 is a horizontal line.

x = 5 is a vertical line.

Horizontal and vertical lines are perpendicular to each other. These lines are perpendicular.

The amount of pencils she bought could be 20p.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. The unitary method is a technique by which we find the value of a single unit from the value of multiple devices and It is a method that we use for most of the calculations in math.

We are given Grace bought a book for $8 and some pencils that cost $.50 each. and spent a total of $18.

when the notebook is $8 and you spend $18 which means bringing 10 worth of pencils.

50c - 1pencil

$1 - 2 pencils

$1.50 is 3

Then we have spent $5 on pencils then have 20p for $10

then $10 + 8 is $18 then spent $18 x

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Answer:

The value of the expression is 19

Step-by-step explanation:

We want to find the value of the expression: [tex]-8+19+8[/tex]

We regroup the numbers to make the computation very easy for us.

[tex]-8+8+19[/tex]

Recall that -x+x  are  zero pairs.

This implies that:

[tex]-8+8+19=0+19[/tex]

Also zero is the identity element of addition of of real numbers

[tex]0+19=19[/tex]

Hence the correct answer is 19

The value of the expression and correct answer is 19

Answer:

Therefore,

[tex]m\angle A =28\°\\\\m\angle C =99\°\\\\c=21\ units[/tex]

Step-by-step explanation:

Consider a Δ ABC with

m∠ B = 53°

BC = a = 10

AC = b = 17    

To Find:  

AC = c = ?  

m∠ A = ?

m∠ C =  ?

Solution:

We know in a Triangle Sine Rule Says that,  

In Δ ABC,

[tex]\dfrac{a}{\sin A}= \dfrac{b}{\sin B}= \dfrac{c}{\sin C}[/tex]

substituting the given values we get

[tex]\dfrac{a}{\sin A}= \dfrac{b}{\sin B}[/tex]

[tex]\dfrac{10}{\sin A}= \dfrac{17}{\sin 53}\\\\\sin A=0.469\\A=\sin^{-1}(0.469)=28.02\approx 28\°[/tex]

Therefore m∠A = 28°

Triangle sum property:

In a Triangle sum of the measures of all the angles of a triangle is 180°.

[tex]\angle A+\angle B+\angle C=180\\\\28+53+\angle C=180\\\therefore m\angle C =180-81=99\°[/tex]

Therefore m∠C = 99°

Now From Sine rule we have

[tex]\dfrac{b}{\sin B}= \dfrac{c}{\sin C}[/tex]

Substituting the values we get

[tex]\dfrac{17}{\sin 53}= \dfrac{c}{\sin 99}\\\\c=21.02\approx 21\ unit[/tex]

Therefore,

[tex]m\angle A =28\°\\\\m\angle C =99\°\\\\c=21\ units[/tex]

Answer:

Right and isosceles

Step-by-step explanation:

Apex

Answer:

176 square yards

Step-by-step explanation:

The picture of the question in the attached figure N 1

we know that

The area of the walkway around the rectangular pool, is equal to the area of two trapezoids (#1 and #2), plus the area of two smaller rectangles (#3 and #4)

see the attached figure N 2 to better understand the problem

step 1

Find the area of the two trapezoids (#1 and #2)

[tex]A=2[\frac{1}{2}(b_1+b_2)h][/tex]

simplify

[tex]A=(b_1+b_2)h[/tex]

we have

[tex]b_1=12\ yd\\b_2=4+12+4=20\ yd\\h=4\ yd[/tex]

substitute

[tex]A=(12+20)(4)=128\ yd^2[/tex]

step 2

Find the area of the two smaller rectangles (#3 and #4)

[tex]A=2[LW][/tex]

we have

[tex]L=4\ yd\\W=6\ yd[/tex]

substitute

[tex]A=2[(4)(6)]=48\ yd^2[/tex]

step 3

Find the area of the walkway around the rectangular pool

[tex]128+48=176\ yd^2[/tex]

Answer:

176 sq yards

Step-by-step explanation:

Answer:

1,500

Step-by-step explanation:

Find x in proportional form.

Answer: 1,500

Step-by-step explanation:

use the is/of = %/100 proportion

Answer:

Step-by-step explanation:

V=πr²h

=3.14*6*6*10

=1130.4 cm³

New cylinder:

h = 15cm

V= 1130.4  cm³

πr²h = 1130.4

3.14*r²*15=1130.4

r²=1130.4/15*3.14

r²=24

r=√24

r=4.898 = 4.9 cm

The radius be to meet the client's need is 4.9 cm.

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies.

Volume is sometimes referred to as capacity.

We have,

Radius of cylinder (r)= 6 cm

Height of cylinder (h) = 10 cm

and, Height of new cylinder (H)  = 15 cm

Radius of new cylinder = R cm

Now, Volume of cylinder can be compared as

πr²h = πR²H

6 x 6 x 10 = R² x 15

360 / 15 = R²

R² = 24

R= 4.9 cm

Thys, the radius is 4.9 cm.

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Paolo wrote the following equation for the perimeter of a rectangle.

P=2(l+w)

Which equation is equivalent to the equation Paolo wrote?

The equivalent equations are:

[tex]w = \frac{p-2l}{2}\\\\l = \frac{p-2w}{2}\\\\p = 2l+2w[/tex]

Given that:

The equation for perimeter of rectangle written by Paolo is:

P = 2(l + w)

where

l = length side of rectangle

w = width side of the rectangle

We have to find the equivalent equation

Let us solve the equation for "w"

[tex]P = 2(l + w)[/tex]

Divide by 2 both sides

[tex]\frac{P}{2} = \frac{2(l+w)}{2}\\\\\frac{P}{2} = l + w[/tex]

[tex]\text{Subtract L on both sides of equation }[/tex]

[tex]\frac{P}{2} - l = l + w - l\\\\\frac{P}{2} - l =w[/tex]

[tex]w = \frac{p-2l}{2}[/tex]

Similarly solving for "l" we get,

[tex]l = \frac{P-2w}{2}[/tex]

Also, given equation can be written as,

[tex]P = 2(l+w)\\\\P = 2l + 2w[/tex]

Thus the equivalent equations are found

Final answer:

The equivalent equation to Paolo's originally written P=2(t+W) for a rectangle's perimeter should be P=2t+2u, assuming 't' stands for width and 'u' for length. The area function a(t) for the rectangle based on width and fixed perimeter is valid within the domain 0 <= t <= L/2.

Explanation:

The question pertains to the formation of equivalent equations to express the perimeter of a rectangle. Paolo wrote the equation P=2(t+W). However, it seems there may have been a typographical error as the correct variables should have been 't' for width and 'u' for length. Given this, the equivalent equation to Paolo's should be P = 2t + 2u, also stated as P = 2(t + u) which confirms the relationship between perimeter, length, and width for a rectangle.

From the provided context, it's also understood that the function representing the area of the rectangle, when written in terms of width (t), is a(t) = t(L/2 - t), which is valid within the domain 0 <= t <= L/2. This function helps in determining the maximum area of the rectangle for a given perimeter (L).

Answer:

Answer 4/5 or class 2

Step-by-step explanation:

4/5=0.80    Class 3 is 70% 75+5=80, or 80%

Final answer:

After converting the pass rates of the classes to percentages, none of the classes have a pass rate that is exactly 5% greater than another class's pass rate.

Explanation:

The student's question pertains to comparing the pass rates of different math classes to determine which class had a pass rate that was exactly 5% greater than another class's pass rate. To answer this, we need to convert the pass rates for each class to a percentage and then compare them.

For class 1, the pass rate is 16 out of 24, which can be converted to a percentage by dividing 16 by 24 and then multiplying by 100, resulting in approximately 66.67%. Class 3 has a pass rate of 75%, as provided. Class 4 has a pass rate of 0.81, which is already in a decimal format comparable to a percentage; it is simply 81% when expressed as a percentage.

By comparing these percentages, we find that Class 3's pass rate is exactly 5% greater than Class 1's pass rate (75% - 66.67% = 8.33%, which is more than 5%). Therefore, none of the classes have a pass rate that is exactly 5% greater than another class's pass rate.

Answer:

Step-by-step explanation:

2x + 2y = -10

Making y as subject

2y = -2x - 10

Dividing by 2

y = -2x/2 - 10/2

y = -x - 5

Comparing with y = mx + c

Slope m = -1, y intercept c = -5

The equation is first rewritten in slope-intercept form as y = -x - 5, revealing that the slope is -1 and the y-intercept is -5.

To find the slope and y-intercept of the given equation 2x + 2y = -10, you need to rewrite it in the slope-intercept form, which is y = mx + b, where m represents the slope, and b represents the y-intercept. First, let's separate the y-term on one side by subtracting 2x from both sides of the equation:

2y = -2x - 10

Now divide the entire equation by 2 to solve for y:

y = (-2x/2) - (10/2)

y = -x - 5

Comparing this with the slope-intercept form y = mx + b, we can see that the slope (m) is -1, and the y-intercept (b) is -5.

Final answer:

In the given algebraic expression, 4n³ and 2n³, 2m and 6m, and 5n and 2n are identified as like terms.

Explanation:

The question asks to identify like terms in a given algebraic expression. Like terms in algebra are terms that have the exact same variables raised to the same powers, although they can have different coefficients.

For example, 4n³ and 2n³are like terms because they both contain the variable n to the third power.

On the other hand, 2m and 6m are like terms because they both contain the variable m to the first power.

Lastly, 5n and 2n are like terms because they contain the variable n to the first power.

Answer:

Step-by-step explanation:

This line goes through the y-axis at 6; therefore, the coordinate at this point is (0, 6).

This line goes through the x-axis at 2; therefore, the coordinate at this point is (2, 0).

The rate of change of a linear function (aka a line) is the slope of the line.  We can use the slope formula to solve for the slope:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Filling in with our coordinates:

[tex]m=\frac{0-6}{2-0}=-\frac{6}{2}=-3[/tex]

The rate of change is -3.  This means that y decreases 3 with every increase in x of 1.

Answer: $22.03

Step-by-step explanation: 15% 67.8= 10.17. 67.8+10.17=77.97. x=remain balance. x=100.00-77.97=22.03.

Answer:

Step-by-step explanation:

40 hours per week*20 dollars per hour=800 dollars per week. This job makes 200 more dollars than the other job.  

The amount of generation of the most income in the second job offer will be more which is $800 per week.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

An employee working 40 hours per week earns a salary of $600 per week. Then the rate is given as,

Rate = $600 per week

But gets a second job offer to work 40 hours per week, hourly at $20 an hour. Then the rate is given as,

Rate = $20 x 40

Rate = $800 per week

The amount of generation of the most income in the second job offer will be more which is $800 per week.

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The sum of the series [tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)[/tex] is 44.

Step-by-step explanation:

The given series is [tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)=44[/tex]

To find the sum of the series, we need to substitute the values for k in the series.

[tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)=\left[2(1)^{2}-4\right]+\left[2(2)^{2}-4\right]+\left[2(3)^{2}-4\right]+\left[2(4)^{2}-4\right][/tex]

Now, simplifying the square terms, we get,

[tex][2(1)-4]+[2(4)-4]+[2(9)-4]+[2(16)-4][/tex]

Multiplying the terms,

[tex][2-4]+[8-4]+[18-4]+[32-4][/tex]

Subtracting the values within the bracket term, we get,

[tex]-2+4+14+28[/tex]

Now, adding all the terms, we get the sum of the series,

[tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)=44[/tex]

Thus, the sum of the series is [tex]\sum_{k=1}^{4}\left(2 k^{2}-4\right)=44[/tex]

Hes right its 44

444444444444444444444

All isosceles trapezoids have congruent base angles.

Option A

Explanation:

An isosceles trapezoid is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides.

Properties of isosceles trapezoid:

Note: Refer the attached file for the image of an isosceles trapezoid.

All isosceles trapezoids come into the category of trapezoids but all trapezoids cannot be marked as isosceles. Clearly, if a trapezoid has congruent legs, it is an isosceles trapezoid.

If a trapezoid has one pair of congruent base angles, then the trapezoid is isosceles. A trapezoid is isosceles if and only if its diagonals are congruent.

In the case of quadrilaterals, if the quadrilateral is an isosceles trapezoid, then each pair of base angles are congruent.

The shape that has congruent base angles is all isosceles trapezoids, as they have two pairs of congruent sides which result in two pairs of congruent base angles due to their geometric properties.

After excluding options such as all trapezoids, all kites, and all quadrilaterals which do not necessarily have congruent base angles, it becomes evident that the correct answer is all isosceles trapezoids.

An isosceles trapezoid is defined as a trapezoid where the non-parallel sides (legs) are congruent. According to geometric properties, these congruent non-parallel sides imply that the base angles are also congruent. So, an isosceles trapezoid always has two pairs of congruent base angles.

To support this, consider the Theorem, in an isosceles triangle the angles opposite the equal sides are equal. Similarly, by applying this to the two triangles that form when dividing an isosceles trapezoid along the line of symmetry, it becomes clear why the base angles are congruent.

Answer:

20 units

Step-by-step explanation:

Let the equal sides of the triangle be x.

Then the third side will be (x+5) units

Since the perimeter is 50, we have:

[tex]x + x + (x + 5) = 50[/tex]

We simplify to get:

[tex]3x + 5 = 50[/tex]

This implies that:

[tex]3x = 50 - 5[/tex]

[tex]3x = 45[/tex]

Divide both sides by 3 to get:

[tex]x = \frac{45}{3} = 15 [/tex]

The length of the third side is:

15+5=20

Answer:

f(x) = 6x² -25x -9

Step-by-step explanation:

6x² - 25x -9 = (2x - 9) (3x + 1)

x = (2/9) or (- 1/3)

Answer:

The second species is slower , flying at 21mph

Step-by-step explanation:

18.9/42x60=27mph

20.3/58x60=21mph

The second species is slower , flying at 21mph

Answer:

I would eliminate both of the -4x because they are identical.

Step-by-step explanation:

Cancel out the both of the -4x by eliminating them. Then subtract the 3y - y. Subtract the -19 - 15. You then will be left with 2y = -34. Solve for y. Then plug y back into the equation to solve for the x.

Hope this helped. :^)

Answer:

x = 20

Step-by-step explanation:

    2x + 7x = 180

⇔ 9x = 180

⇔ x = 180/9 = 20

Answer: 1 hour

Step-by-step explanation: if he travels 12 mph, it will take 1 hour to travel 12 miles.

Answer:

add up the numbers and divide by the counting of the numbers. so the answer will be 56/7 equal to 8

Answer:

5/6

Step-by-step explanation:

[tex]1-\frac{2}{12}=1-\frac{1}{6}=\frac{1*6}{1*6}-\frac{1}{6}\\\\=\frac{6}{6}-\frac{1}{6}=\frac{6-1}{6}=\frac{5}{6}[/tex]

0x + 1y = -5 is the standard form of equation

Solution:

Given that we have to write the equation of line passing thorugh (6, -5) and has slope 0

The equation of line in slope intercept form is given as:

y = mx + c ---------- eqn 1

Where, "m" is the slope of line and "c" is the y - intercept

Given that, m = 0

Given point is (6, -5)

To find the y - intercept:

Substitute (x, y) = (6, -5) and m = 0 in eqn 1

-5 = 0(6) + c

c = -5

Substitute c = -5 and m = 0 in eqn 1

y = 0x + (-5)

y = -5

The standard form of equation is given as:

The standard form of an equation is Ax + By = C

In this kind of equation, x and y are variables and A, B, and C are integers

y = -5

0x + 1y = -5 is the standard form of equation

The question is about comparing Angela's 12% commission structure against her friend's $750 fixed salary plus 5% commission. The answer examines how the volume of sales would affect their respective incomes.

This problem is about comparing commission rates and overall income. If Angela worked on a straight 12% commission, it means that she earns 12% of the total sales she makes. Her friend, however, has a fixed salary of $750, in addition to earning 5% of his total sales as commission. To compare their incomes, we would need to know the total sales each of them makes. Generally, the more sales they make, the more beneficial the commission system becomes.

For example, if Angela made $1000 in sales, she would earn $120 (12% of $1000). If her friend made the same amount in sales, he would earn $800 ($750 salary + $50 from 5% of $1000). However, if they only made $100 in sales, Angela would earn $12, and her friend would earn, $755. So, the best system depends on the volume of sales.

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