A rain drop hitting a lake makes a circular ripple. If the radius, in inches, grows as a function of time in minutes according to r(t)=15t+2−−−−√
, find the area of the ripple as a function of time. Find the area of the ripple at t=2
.

The median amount of time Julie's friends spend reading each week is 3 1/2 hours, which is the average of the two middle values when the given values are arranged in order.

To find the median value, we first need to put the given values in order from smallest to largest. The given values are: 1/2, 1/2, 2 1/2, 4 1/2, 7, and 12. When we arrange them in order, we get:

1/2, 1/2, 2 1/2, 4 1/2, 7, 12

The median is the middle value of the ordered list. If there is an odd number of values, the median is simply the middle value. However, in this case, we have an even number of values. Therefore, we take the average of the two middle values to find the median. The two middle values are 2 1/2 and 4 1/2. So, the median is:

(2 1/2 + 4 1/2)/2 = 3 1/2

This means that half of Julie's friends read for more than 3 1/2 hours per week and half of them read for less than 3 1/2 hours per week.

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Answer:

Multiply the numerators first together then multiply the denominators together.

Step-by-step explanation:

example  1/2(4/2) =4/4 = 1

Answer:

-16x+28

Step-by-step explanation:

Using the 2nd and 1st term in the sequence, we can find the change.

4x+4, -x+10.  Using mental math, we can see that x decreases by 5 and 4 increases by 6.  Using this, the change is -5x + 6.

The easiest way to solve this is mental math because the 5th term is very close to the last term (the 3rd).

Solving:

-6x+16 = 3rd term, so -6x+16-5x+6 = -11x+22 | -11x+22-5x+6 = -16x+28.

Answer:

9) x = 12 cm

10) x = 10.4 ft (Rounded)

11) y = 39.7 in (Rounded)

Step-by-step explanation:

Just use Pythagorean theorem

Answer and Explanation:

We can solve for x in these questions using the Pythagorean Theorem:

a² + b² = c²,

where a and b are the legs (shorter sides) of a right triangle, and c is its hypotenuse (longest side).

Applying this theorem to the problems at hand:

9. We are using (10 / 2) as one of the legs.

(10 / 2)² + x² = 13²

↓ simplifying division

5² + x² = 13²

↓ subtracting 5² from both sides

x² = 13² - 5²

↓ simplifying the right side

x² = 169 - 25

x² = 144

↓ taking the square root of both sides

x = 12

10.

6² + x² = 12²

↓ subtracting 6² from both sides

x² = 12² - 6²

↓ simplifying the right side

x² = 144 - 36

x² = 108

↓ taking the square root of both sides

x = [tex]\sqrt{108}[/tex]

↓ simplifying the square root

    [tex]\sqrt{108} = \sqrt{3 \cdot 3 \cdot 3 \cdot 2 \cdot 2} = (3\cdot 2)\sqrt{3} = 6\sqrt3[/tex]

x = 6[tex]\sqrt3[/tex]

11.

24² + 33² = y²

↓ simplifying the right side

576 + 1089 = y²

1665 = y²

↓ taking the square root of both sides

y = [tex]\sqrt{1665}[/tex]

↓ simplifying the square root

    [tex]\sqrt{1665} = \sqrt{3 \cdot 3 \cdot 5 \cdot 37} = 3\sqrt{5 \cdot 37} = 3\sqrt{185}[/tex]

y = 3[tex]\sqrt{185}[/tex]

Answer:

5x + 7(x + 10.80) = 210.00

Step-by-step explanation:

Let x be the cost of a pencil in dollars. Then, the cost of a notebook is 10.80 dollars more, which is x + 10.80 dollars.

Aldrin bought 5 pencils and 7 notebooks, so the total cost is:

5x + 7(x + 10.80) = 210.00

Simplifying and solving for x, we have:

5x + 7x + 75.60 = 210.00

12x = 134.40

x = 11.20

Therefore, a pencil costs 11.20 dollars and a notebook costs 10.80 dollars more, which is 22.00 dollars.

We can check that the total cost of 5 pencils and 7 notebooks at these prices is indeed 210.00 dollars:

5 pencils * 11.20 dollars/pencil + 7 notebooks * 22.00 dollars/notebook = 56.00 dollars + 154.00 dollars = 210.00 dollars

The correct graph of the function [tex]y=-1\sqrt{x-2-3}[/tex] is attached as picture below.

To graph a function, we need to first determine the domain and range of the function. The domain is the set of all possible input values for the function, while the range is the set of all possible output values. Once we have determined the domain and range, we can plot the points on a graph.

To plot the graph, we can choose a set of values for the independent variable (usually denoted as x) and use the function to find the corresponding values of the dependent variable (usually denoted as y). We can then plot these points on the graph and connect them to create a curve that represents the function.

Graph using the end point and a few selected points.

x       y

2    − 3

3     −4

4     −4.41

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the correct answer is (D) 8 units to the left. To find the translation direction and number of units, we need to find the vector that takes us from point R to point R'.

Vector RR' can be found by subtracting the coordinates of R from the coordinates of R':

RR' = R' - R = (-7, 4) - (1, 4) = (-8, 0)

This means that the translation moves 8 units to the left, since the x-coordinate of the vector is negative.

To determine the translation direction and number of units required to move R to R', we need to first find the distance between the x-coordinates of R and R'. We can do this by subtracting the x-coordinate of R from the x-coordinate of R': -7 - 1 = -8.

This tells us that we need to move R' 8 units to the left to get to R. However, the question is asking for the translation required to move R to R', not the other way around. Therefore, we need to reverse the direction and say that we need to move R 8 units to the right to get to R'.

We can confirm this by checking the y-coordinates of R and R'. We see that they are both 4, which means there is no vertical translation required. Therefore, the answer is C. 8 units to the right.

Therefore , the correct answer is (D) 8 units to the left.

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Answer:

I hope this helps :)

Step-by-step explanation:

its the correct answer

Answer: Let's break down the budget into different categories:

Furniture: 15% of the budget

15% of Rs. 53000 = Rs. 7950

So you can spend Rs. 7950 on furniture.

Cosmetics: 25% of the budget

25% of Rs. 53000 = Rs. 13250

So your cosmetics bill from Makeup4uonline is Rs. 13250.

Appliances: 15% of the budget at 20% discount

15% of Rs. 53000 = Rs. 7950

The appliances are at a 20% discount, so you only need to pay 80% of the price:

80% of Rs. 7950 = Rs. 6360

So you can spend Rs. 6360 on appliances.

Electric works: 5% of the total budget which is 12% of wall décor and lights

12% of the budget = 12/100 x Rs. 53000 = Rs. 6360

5% of the budget = 5/100 x Rs. 53000 = Rs. 2650

So you can spend Rs. 6360 on wall décor and lights, and Rs. 2650 on electric works.

Leftover amount for COVID-19 safety measures

The total amount spent so far is:

Rs. 7950 + Rs. 13250 + Rs. 6360 + Rs. 2650 = Rs. 30110

So the leftover amount for COVID-19 safety measures is:

Rs. 53000 - Rs. 30110 = Rs. 22890

Rate of leftover amount to total budget

The rate of leftover amount to total budget is:

(Rs. 22890 / Rs. 53000) x 100% = 43.2%

So 43.2% of the total budget is leftover for COVID-19 safety measures.

Step-by-step explanation:

Answer: would be great if you could give the options of the questions?

Answer:D=12, R=6

A=πr², C=2πr

A=36π, C=12π

A=113.04 ft²

C=37.68 ft

Answer:

AB = 14 units

BC = 11 units

CD = 14 units

AD = 11 units

Step-by-step explanation:

d=√((x2-x1)²+(y2-y1)²)

AB= (-7,6)-(7,6) √((7+7)²+(6-6)²)=√((14)²+(0)²)=√(196+0)=√(196)=14

BC= (7,6)-(7,-5) √((7-7)²+(-5-6)²)=√((0)²+(-11)²)=√(0+121)=√(121)=11

CD= (7,-5)-(-7,-5) √((-7-7)²+(-5+5)²)=√((-14)²+(0)²)=√(196+0)=√(196)=14

AD= (-7,-5,)-(-7,6) √((-7+7)²+(6+5)²)=√((0)²+(11)²)=√(0+121)=√(121)=11

Answer:

Step-by-step explanation:

The rule that relates the number of months (m) to the cost (c) of a gym membership is:

c = 15m + 25

To find the cost of a 1 year (12 months) membership, we substitute m = 12 into the equation:

c = 15(12) + 25 = 205

Therefore, the cost of a 1 year membership is $205 (which includes the $25 sign up fee).

Answer:

  (-1, 2) and (4, -8)

Step-by-step explanation:

You want the ordered pairs (x, f(x)) that satisfy both equations ...

Equating the two expressions for f(x), we have ...

  x² -5x -4 = -2x

  x² -3x -4 = 0

  (x -4)(x +1) = 0

  x = 4 or -1

Corresponding values of f(x) are ...

  f(x) = -2{4, -1} = {-8, 2}

Ordered pair solutions are ...

  (x, f(x)) = (-1, 2) and (4, -8)

Answer:

Use in² for area; use in³ for volume.

Explanation:

When you calculate the area of a rectangle, you multiply length times width. Both units are in inches so:

inches × inches = (inches)² or in²

When you calculate the volume of a box (rectangular prism), you multiply length by width by height. All three units are in inches so:

inches × inches × inches = (inches)³ or in³

The average cost per day is $90 and the average cost per km is $0.655.

To calculate the average cost per day, we need to first calculate the total cost of renting the car for both occasions and divide it by the total number of days.

The total cost of renting the car for both occasions is $180 + $180 = $360. The total number of days is 4 (2 days for each occasion).

Therefore, the average cost per day is $360 ÷ 4 = $90.

To calculate the average cost per km, we need to first calculate the total cost of renting the car for both occasions and divide it by the total number of kilometers driven.

The total cost of renting the car for both occasions is $180 + $180 = $360. The total number of kilometers driven is 550km (150km for the first occasion + 400km for the second occasion).

Therefore, the average cost per km is $360 ÷ 550km ≈ $0.655.

Correct question is " Eleni rents a car on two separate occasions. The first time, she paid $180 for 2 days and 150km. The next time, she paid $180 for 2 days and 400km. What is the average cost per day? What is the average cost per km?"

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[tex] \:\:\:\:\:\:\star\longrightarrow \sf \underline{y = 5\:x^4\:tanx}\\[/tex]

Differentiating with respect to x-

[tex] \:\:\:\:\:\:\longrightarrow \sf\dfrac{d}{dx}\:y = \dfrac{d}{dx}\: 5\:x^4\:tanx\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf\dfrac{dy}{dx}\:= 5\:\dfrac{d}{dx}\: \:x^4\:tanx\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf\dfrac{d}{dx}\:y =5\:\bigg[tanx\times \dfrac{d}{dx}\: \:x^4\:+x^4\times \dfrac{d}{dx} tanx\bigg]\\[/tex]

[tex]\pink{\star}\:\boxed{\sf\sf\dfrac{d}{dx}\bigg[f(x)\:g(x)\bigg] = f(x) \dfrac{d}{dx} g(x) + g(x) \dfrac{d}{dx} f(x)}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf\dfrac{dy}{dx}= 5\:\bigg[tanx\times 4\:x^3+ x^4 \times sec^2x \bigg]\\[/tex]

[tex] \qquad\pink{\star}\:\:\:\:\boxed{\sf \dfrac{d}{dx}x^n=nx^{n-1}}\\[/tex]

[tex] \qquad\pink{\star}\:\:\:\:\boxed{\sf \dfrac{d}{dx}tanx=sec^2x}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf\dfrac{dy}{dx}= 5\:x^3\:\bigg[4tanx+ x sec^2x \bigg]\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf\underline{\dfrac{dy}{dx}= \boxed{\sf5\:x^3\:\bigg[4tanx+ x sec^2x \bigg]}}\\[/tex]

Answer:

45/100, 0.45, 9/20

Step-by-step explanation:

Answer 1:  A percentage is part of a number is written in hundredths.  Thus, 45% is the same as 45/100

Answer 2:  To convert 45% to a decimal, you can rewrite 45% as 45.0%.  Then, you can move the decimal two places to the left, which is the same as dividing by 100.  You can also do standard division and you'll find the 45 divided by 100 = 0.45

Answer 3:  45/100 is not the simplest form of this fraction.  To simplify, we must find the greatest common factor of the numerator (45) and the denominator (100).  Both of these numbers can be divided evenly by 5 so 5 is the GCF of the two numbers.

Now, we divide both numbers by 5 to simplify the fraction:

45 / 5 = 9 and 100 / 5 = 20.  Thus, 45/100 reduces down to 9/20

Select any of the two answers available on your worksheet (if I'm reading what you wrote correctly, it seems like the two answer choices they provided were 9/20 and 45/100

The vector b is [10, 5, 10] and the general solution for [A|b] is [1, 5, -3] + [-3, 2, -1]s

To find the vector b, we need to multiply the matrix A by the vector x and solve for b in the equation Ax = b.

So, we have:

[tex]\left[\begin{array}{ccc}1&3&-3&0&1&-2&3&5&-1\end{array}\right]\left[\begin{array}{c}1&1&-2\end{array}\right] &= \left[\begin{array}{c}10&5&10\end{array}\right][/tex]

Therefore, the vector b is [10, 5, 10].

To find the general solution of [A | b], we need to perform row reduction on the augmented matrix [A | b] and express the pivot variables in terms of the free variables.

[tex]\left[\begin{array}{ccc|c}1&3&-3&10&0&1&-2&5&3&5&-1&10\end{array}\right] &\rightarrow \left[\begin{array}{ccc|c}1&0&3&1&0&1&-2&5&0&0&0&0\end{array}\right][/tex]

The third column does not have a pivot variable, so we can express x3 in terms of the free variables.

Let s be the free variable, then we have:

x3 = -s - 3

We can now express the pivot variables in terms of s:

x1 = 1 - 3s

x2 = 5 + 2s

Thus, the general solution of [A | b] is:

[tex]\left[\begin{array}{c}x_1&x_2&x_3\end{array}\right] &= \left[\begin{array}{c}1 - 3s&5 + 2s&-s - 3\end{array}\right] \&= \left[\begin{array}{c}1&5&-3\end{array}\right] + s\left[\begin{array}{c}-3&2&-1\end{array}\right][/tex]

Therefore, the general solution of [A | b] is [1, 5, -3] + [-3, 2, -1]s

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Answer:

Step-by-step explanation:

I'm a little confused where the angle is, because I don't understand English units of measurement well, but the answers must be correct!

i use formula  [tex]sin^{2} \alpha + cos^{2} \alpha =1[/tex]

The answer should be 2.The lower quartile of the number of absence is 2

0 is the lowest number and then 2 would be lower quartile, The 4 would be the Median or the middle of all the data 7 is the upper quartile and 10 would be the highest number of absences.

The lower quartile, also known as the first quartile, is a measure of central tendency that divides a dataset into four equal parts. It represents the point at which 25% of the data values fall below and 75% of the data values fall above. In other words, the lower quartile marks the boundary between the lowest 25% and the upper 75% of the data. It is often used in statistics to help summarize and analyze datasets, and can be helpful in identifying outliers or unusual values in the lower end of a dataset.

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We can use the formula for the equation of a line to determine any missing values. The formula is:

�

=

�

�

+

�

y=mx+b

where $m$ is the slope of the line and $b$ is the y-intercept.

We can use the given data points to calculate the slope of the line:

�

=

change in y

change in x

=

�

2

−

�

1

�

2

−

�

1

m=

change in x

change in y

​

=

x

2

​

−x

1

​

y

2

​

−y

1

​

​

where $(x_1, y_1)$ and $(x_2, y_2)$ are any two points on the line. Let's use the points $(-9, 3)$ and $(-6, 2)$:

\begin{align*}

m &= \frac{y_2 - y_1}{x_2 - x_1} \

&= \frac{2 - 3}{-6 - (-9)} \

&= \frac{-1}{3}

\end{align*}

Now we can use the slope-intercept form of the equation of a line to determine any missing values. Let's go through each option:

a. Missing $x:-2$, Missing $y:0$

We can use the formula $y = mx + b$ with $m = -\frac{1}{3}$ and $b = 3$ (substitute the coordinates of the point $(-9, 3)$) to find the y-value when $x = -2$:

\begin{align*}

y &= mx + b \

&= -\frac{1}{3} \cdot (-2) + 3 \

&= \frac{7}{3}

\end{align*}

So the missing value of $y$ when $x = -2$ is $\boxed{\frac{7}{3}}$.

b. Missing $x:0$, Missing $y:1$

We can use the formula $y = mx + b$ with $m = -\frac{1}{3}$ and $b = 3$ (substitute the coordinates of the point $(-9, 3)$) to find the y-intercept:

\begin{align*}

y &= mx + b \

3 &= -\frac{1}{3} \cdot (-9) + b \

3 &= 3 + b \

b &= 0

\end{align*}

So the y-intercept is $0$. Now we can substitute $b = 0$ and $m = -\frac{1}{3}$ into the formula $y = mx + b$ to find the y-value when $x = 0$:

\begin{align*}

y &= mx + b \

&= -\frac{1}{3} \cdot 0 + 0 \

&= 0

\end{align*}

So the missing value of $y$ when $x = 0$ is $\boxed{0}$.

c. Missing $x:-2$, Missing $y:2$

We can use the formula $y = mx + b$ with $m = -\frac{1}{3}$ and $b = 3$ (substitute the coordinates of the point $(-9, 3)$) to find the y-value when $x = -2$:

\begin{align*}

y &= mx + b \

&= -\frac{1}{3} \cdot (-2) + 3 \

&= \frac{7}{3}

\end{align*}

So the missing value of $y$ when $x = -2$ is $\boxed{\frac{7

Answer:

Step-by-step explanation:

Center of circle will be at the midpoint of (-2,1) and (4,3):

                     [tex]M=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]

                           [tex]=(\frac{-2+4}{2} ,\frac{1+3}{2} )[/tex]

                           [tex]=(1,2)[/tex]

Radius will be distance from circle center (1,2) to edge (4,3):

                       [tex]r=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2 }[/tex]

                           [tex]=\sqrt{(4-1)^2+(3-2)^2 }[/tex]

                           [tex]=\sqrt{3^2+1^2 }[/tex]

                           [tex]=\sqrt{10}[/tex]

Equation of circle with center (1,2) and radius [tex]\sqrt{10}[/tex]:

                      [tex](x-h)^2+(y-k)^2=r^2[/tex]        center (h,k)  radius r

                      [tex](x-1)^2+(y-2)^2=\sqrt{10}^2[/tex]

                      [tex](x-1)^2+(y-2)^2=10[/tex]

SOLUTION: [tex](x-1)^2+(y-2)^2=10[/tex]

Asymmetric: Since, for instance, (2,3) is in R but (3,2) is not, R is not asymmetric. No element in A is connected to itself under R, making R irreflexive.

The collection of output values that such a function of relation can produce is referred to as the range in mathematics. It is the distinction between the largest or smallest values within an ensemble of data or a collection of all conceivable function or relation output values.

In other terms, it is the range of possible values for a variable. For instance, the range is 21 - 3 = 18 if the integers are 3, 7, 12, 15, and 21. The set of all value of y which may be produced by a function f(x) for the given subject area of x values is known as the range.

given

We will now examine the many characteristics of the relation R:

As no element in A is connected to itself under R, R is not reflexive. For instance, R does not support (2,2).

R is not symmetric since, for instance, (3,2) is not in R yet (2,3) is.

R is transitive because, for instance, the existence of (2,3) and (3,5) in R entails the existence of (2,5) in R.

Equivalence: As R is not reflexive or symmetric, it is not an equivalence relation.

Asymmetric: Since, for instance, (2,3) is in R but (3,2) is not, R is not asymmetric. No element in A is connected to itself under R, making R irreflexive.

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Answer:

Step-by-step explanation:

r=12 in

dr=±32

A=πr²

dA=2 πr×dr=2π×12×1/32=3π/4

Possible error in computing the area=3π/4 ~square~inches.

When x is -10, the value of y is 38. This means that the point (-10, 38) is on the graph of the function y = -4x - 2.

We must determine the values of x and solve for the matching value of y in order to fill in the table using the function rule y = -4x - 2. The table can then be populated with the resulting values for x and y.

An illustration table with x values ranging from -3 to 3 is shown below:

x y

-3 10

-2 6

-1 2

0 -2

1 -6

2 -10

3 -14

We may easily change x in the function rule y = -4x - 2 to -10 to find the value of y when x is -10:

y = -4(-10) (-10) - 2 \sy = 40 - 2 \sy = 38

As a result, y equals 38 when x is -10. This indicates that the point (-10, 38) is located on the y = -4x - 2 function graph.

It's vital to remember that the numbers in the table are produced by inserting various x values into the function rule, and the resulting y-values represent the corresponding locations on the function's graph. The line passing through the point on the graph of the function y = -4x - 2 has a slope of -4 and a y-intercept of -2. (-10, 38).

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Yes,I would have made the same decision to purchase disability insurance .

What is disability insurance?

Disability insurance provides financial protection in the event that you become unable to work due to an illness or injury. It can help you pay for living expenses, medical bills, and other costs while you are unable to work.

When deciding whether or not to purchase disability insurance, it's important to consider your financial situation and your ability to manage expenses if you were to become disabled. If you have a good amount of savings or other sources of income, you may be able to manage without disability insurance. However, if you rely heavily on your income to pay for living expenses and do not have significant savings, disability insurance may be a wise investment.

It's also important to consider the cost of disability insurance and whether it fits within your budget. While the additional $22.70 a month may not seem like a lot, it can add up over time. You should evaluate whether the cost of the insurance is worth the potential benefits it provides.

Ultimately, the decision to purchase disability insurance is a personal one that depends on individual circumstances and priorities. While it's impossible to predict the future, having disability insurance can provide peace of mind and financial protection in case the unexpected happens.

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Answer:

70°

Step-by-step explanation:

280°÷4x

what is x?

x=70°

Answer:

∠h = 61°

∠g = 119°

∠m = 59°

∠k = 121°

Step-by-step explanation:

According to the Vertical Angles Theorem, when two straight lines intersect, the opposite vertical angles are congruent.

Therefore, as angle g is opposite 119°:

⇒ ∠g = 119°

As angle k is opposite 121°:

⇒ ∠k = 121°

Angles on a straight line sum to 180°.

As angle h and 119° form a straight line:

⇒ ∠h + 119° = 180°

⇒ ∠h + 119° - 119° = 180° - 119°

⇒ ∠h = 61°

As angle m and 121° form a straight line:

⇒ ∠m + 121° = 180°

⇒ ∠m + 121° - 121° = 180° - 121°

⇒ ∠m = 59°

Answer:

Step-by-step explanation:

To find:-

Answer:-

From the given figure we can see that angles k and 121° are vertically opposite angles . Also we know that vertically opposite angles are equal to each other. Hence here we can say that,

[tex]\longrightarrow \boxed{ k = 121^o}\\[/tex]

Secondly, we know the the mesure of angle of a straight line is 180° . So the sum of angles on a straight line would be 180° . If two angles are present we call them linear pair . Hence here , we can see that m and 121° are linear pairs.

So that,

[tex]\longrightarrow m + 121^o = 180^o \\[/tex]

[tex]\longrightarrow m = 180^o-121^o\\[/tex]

[tex]\longrightarrow \boxed{m = 59^o } \\[/tex]

Similarly we can see that g and 119° are vertically opposite angles. Again they will be equal. So ,

[tex]\longrightarrow \boxed{g = 119^o} \\[/tex]

Again, 119° and h form linear pair.So their sum would be 180° .

[tex]\longrightarrow h + 119^o = 180^o \\[/tex]

[tex]\longrightarrow h = 180^o - 119^o\\[/tex]

[tex]\longrightarrow \boxed{ h = 61^o }\\[/tex]

These are the required values of the unknown angles.