Triangle ΔABC has side lengths of a = 18, b=[tex]18\sqrt{3}[/tex], and c = 36 inches.

Part A: Determine the measure of angle A.

Part B: Show how to use the unit circle to find tan A.

Part C: Calculate the area of ΔABC.

Area of a triangle is 1/2 x base x height.

area of triangle = 1/2 x 20 x 17 = 170 square feet.

the image shows 4 triangles, total area = 170 x 4 = 680 square feet.

the answer is A. 680 sq. ft.

Answer:

Area of a triangle is 1/2 x base x height.

area of triangle = 1/2 x 20 x 17 = 170 square feet.

the image shows 4 triangles, total area = 170 x 4 = 680 square feet.

the answer is A. 680 sq. ft.

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Answer:

Matrix  1:  -4269

Matrix 2:  1768

Matrix 3:  647.3561

Step-by-step explanation:

Matrix 1: [tex](7*19)-(31*142)=-4269[/tex]

Matrix 2:  1768

[tex]\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right][/tex]

Determinant = [tex]a(ei-fh)-b(di-fg)+c(dh-eg)[/tex]

Matrix 3:  647.3561

[tex]\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right][/tex]

Determinant = [tex]a(ei-fh)-b(di-fg)+c(dh-eg)[/tex]

Answer:

-4

Step-by-step explanation:

Answer: If f(x) = -x2 - 3x + 5, then the value of f(-3) is -4.

Answer:

f(-3) = 14

Step-by-step explanation:

f(-3) just means to fill in -3 for x.

2x^2 + 3x + 5

becomes

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

Exponent first.

2(9) + 3(-3) + 5

Multiplication

18 + -9 + 5

Add.

14

Answer

A: $28,000

B: 15 years

Step-by-step explanation:

A: Since $25,000 is deposited in the bank and you earn 4% interest annually over 3 years you would earn 12% interest. 12% of 25,000 is 3,000. The sum of 25,000 and 3,000 is 28,000 having you earn $28,000 over 3 years.

B: Since every year you earn 4% annual interest and you have $25,000 deposited in the bank you have to find what percentage of 25,000 equals 15,000. Since 25,000 isn't exactly easy to find multiply it by 4. That leaves you with 100,000 which we know you don't have in the bank but it will make it easier to find the percentage. You will also have to multiply 15,000 by 4 giving you 60,000. Now divide the 60,000 by 1,000 which equals 60. What's the point of the number 60? Well, that's the percentage it takes. Now divide 60 by the annual interest which is 4 and that gives you 15. 15 is the number of years it will take for the balance to reach $40,000.

Hope this helps!

Answer:

Line R

Step-by-step explanation:

Answer:

h is the horizontal translation

k is the vertical translation

a is the stretch parallel to the y-axis

Step-by-step explanation:

Parent equation:  [tex]y=x^2[/tex]

Translate [tex]h[/tex] units right:  [tex]y=(x-h)^2[/tex]

(if [tex]h < 0[/tex], then the translation is [tex]h[/tex] units left)

Stretched parallel to the y-axis by a factor of [tex]a[/tex]:  [tex]y=a(x-h)^2[/tex]

(if [tex]a < 0[/tex], the graph is also reflected in the x-axis)

Translated k units up:  [tex]y=a(x-h)^2+k[/tex]

(if [tex]k < 0[/tex] then the translation is k units down)

Example attached for [tex]y=2(x-3)^2+4[/tex]

Answer:

585

Step-by-step explanation:

Explanation in picture below.

Using linear equations, the number of minutes that both would read for them to read equal number of pages is: 30 minutes.

Equation of a linear graph is given as, y = mx + b, where m and b are the slope and y-intercept of the graph respectively.

Equation for Emily's graph:

Slope (m) = rise/run = 1/3

y-intercept (b) = 2

Substitute m = 1/3 and b = 2 into y = mx + b

y = 1/3x + 2

Equation for Serena's graph:

Slope (m) = rise/run = 2/5

y-intercept (b) = 0

Substitute m = 2/5 and b = 0 into y = mx + b

y = 2/5x + 0

y = 2/5x

To find how many minutes for both of them to read the same number of pages, make both equations equal to each other.

2/5x = 1/3x + 2

2/5x - 1/3x = 2

1/15x = 2

Multiply both sides by 15

x = (2)(15)

x = 30

The answer is 30 minutes for both to read the same number of pages.

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Answer:

Step-by-step explanation:

Find the horizontal asymptotes by comparing the degrees of the numerator and denominator.

Vertical Asymptotes:

x=1

Horizontal Asymptotes:

y=0

No Oblique Asymptotes

Answer:

300 cents in pennies

1000 cents in nickles

2000 cents in dimes

3000 cents in quarters

the answer would be B. 63.00

Answer:

D

Step-by-step explanation:

In order to find a non-real number we look for a part of the expression that cannot exist.

Answer choice D stands out as you cannot take a square root of a negative number.

That's our answer!

Option D is correct,  the given number 3√(7/5) + √-(9/5)  is a  non real complex number.

The complex number is basically the combination of a real number and an imaginary number.

3√(7/5) +√(-9/5) is a non real complex number

We know that a+ib is a complex number where a is real number and b represents the imaginary number

3√(7/5) +√i²(9/5)

3√(7/5) + i√9/5 it is in the form of a+ib.

where a is 3√(7/5) and b is √9/5

3√(7/5) + √-(9/5) is non real complex number

Hence, among the given numbers 3√(7/5) + √-(9/5)  is a  non real complex number.

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Answer:

A: (-3,4) (-3,6) (-5,6) (-7,4)

B: The transformation would be described as a reflection over the y axis

C:  The transformation does result in a congruent figure because the shape doesn't change in size or shape and in length or width

Step-by-step explanation:

So our plots from the figure are: (3,4)  (3,6)  (5,6)  (7,4)

So using the rule (x, y) → (-x, y) are new points would be:

(-3,4)

(-3,6)

(-5,6)

(-7,4)

This rule (x, y) → (-x, y) is used for the type of transformation that is a reflection but over the y axis.

Answer:

6 gallons because 3/4 is the same as 6/8 so therefore 6 gallons would be 3/4 full

The amount of water in gallons in the fish tank is A = 6 gallons

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

If Levi wants to fill the fish tank so it is only 3/4 full, then he only needs to fill it with 3/4 of its total capacity.

A = (3/4) x 8

On simplifying the equation , we get

A = 6 gallons

Hence , Levi should put 6 gallons of water in the fish tank to fill it to 3/4 of its total capacity

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Answer:

buying a book of 9 round trip bus tickets from Houston to Austin for a total of $702 is a better deal because 702/9 = 78 which is less than 522/6 = 87

Step-by-step explanation:

Answer: Abby would be able to make 12 hamburgers.

Step-by-step explanation:

You have to divide 2.28 and 0.19 and you would get 12 so the answer is 12.

Therefore, the production cost for a packet of Super tea is $923.91.

Since Brenya Estate produces a high quality tea branded Super by blending three types of tea coded A, B and C in the ration 1½ : 5 : 1, and originally Type A tea costs GHS 1,600 type B costs GHS 800 and type C costs GHS 1,700 per Kg to produce, and Brenya Tea Estate packs Super tea in packets of 825g each. Blending and packing costs are 40 per Kg, to determine the production cost for a packet of Super tea, the following calculation must be made:

Therefore, the production cost for a packet of Super tea is $923.91.

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Answer:

the discriminant of g positive

Step-by-step explanation:

the discriminant of g positive because the graph of g cross the x-axis in two points.

Answer:

30112.50. 15x22x91.20+26.50

Answer:

819

Step-by-step explanation:

The mean is the average. Add up all the values and then divide that by the total amount of values. 1500+338+588+850=3276. 3276/4=819.

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1 (#3)

The formula for a regular octagon inscribed in a circle of radius [tex]r[/tex] is [tex]A=2\sqrt{2}r^2[/tex]. Hence, [tex]A=2\sqrt{2}(4)^2=16*2\sqrt{2}=32\sqrt{2}\approx45.255m^2[/tex].

Thus, C is the correct answer

Problem 2 (#4)

Using the co-function identity [tex]\displaystyle \sin\biggr(x+\frac{\pi}{2}\biggr)=\cos(x)[/tex], the equation can be rewritten as [tex]cos(x)=\frac{\sqrt{3}}{2}[/tex]. Using a unit circle, it's easy to see that the answer is [tex]\displaystyle\biggr\{\frac{\pi}{6},\frac{11\pi}{6}\biggr\}[/tex].

Thus, C is the correct answer

Problem 3

[tex]f(x)=g(x)\\\\2\sin^2 x-1=-\cos(x)\\\\2(1-\cos^2 x)-1=-\cos(x)\\\\2-2\cos^2 x-1=-\cos(x)\\\\1-2\cos^2 x=-\cos(x)\\\\2\cos^2x-\cos(x)-1=0[/tex]

Let [tex]u=\cos(x)[/tex], hence:

[tex]2u^2-u-1=0\\\\(2u+1)(u-1)=0[/tex]

[tex]\displaystyle2u+1=0\\\\2u=-1\\\\u=-\frac{1}{2}\\ \\\cos(x)=-\frac{1}{2}\\ \\x=\biggr\{\frac{2\pi}{3},\frac{4\pi}{3}\biggr\}[/tex]

[tex]u-1=0\\\\u=1\\\\\cos(x)=1\\\\x=\{0\}[/tex]

So, the solution set is [tex]\displaystyle\biggr\{0,\frac{2\pi}{3},\frac{4\pi}3}\biggr\}[/tex]

Thus, B is the correct answer

Problem 4 (#8)

If we construct a right triangle in Quadrant I with an opposite leg length of 1 unit and an adjacent leg length of 1 unit, this shows that [tex]\displaystyle\tan\theta=\frac{opposite}{adjacent}=\frac{1}{1}=1[/tex]. Since [tex]\displaystyle \csc\theta=\frac{1}{\sin\theta}[/tex] and [tex]\displaystyle\sin\theta=\frac{opposite}{hypotenuse}[/tex], we must solve for the hypotenuse with the Pythagorean Theorem:

[tex](opposite)^2+(adjacent)^2=(hypotenuse)^2\\1^2+1^2=(hypotenuse)^2\\1+1=(hypotenuse)^2\\2=(hypotenuse)^2\\\sqrt{2}=hypotenuse[/tex]

Therefore, since [tex]\displaystyle \sin\theta=\frac{opposite}{hypotenuse}=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}[/tex], then [tex]\displaystyle \csc\theta=\frac{1}{\sin\theta}=\frac{1}{\frac{\sqrt{2}}{2}}=\frac{2}{\sqrt{2}}=\frac{2\sqrt{2}}{2}=\sqrt{2}[/tex].

Thus, B is the correct answer

Problem 5 (#9)

As no angles are given and only side lengths, we are forced to use the Law of Cosines to solve for the angles:

Angle A:

[tex]a^2=b^2+c^2-2bc\cos(A)\\400^2=500^2+600^2-2(500)(600)\cos(A)\\160000=250000+360000-600000\cos(A)\\160000=610000-600000\cos(A)\\-450000=-600000\cos(A)\\\frac{3}{4}=\cos(A)\\ A\approx41.410^\circ[/tex]

Angle B:

[tex]b^2=a^2+c^2-2ac\cos(B)\\500^2=400^2+600^2-2(400)(600)\cos(B)\\250000=160000+360000-480000\cos(B)\\250000=520000-480000\cos(B)\\-270000=-480000\cos(B)\\\frac{9}{16}=\cos(B)\\B\approx55.771^\circ[/tex]

Angle C:

By the Triangle Angle-Sum Theorem, [tex]C\approx82.819^\circ[/tex]

Hence, we can conclude that angle A is the smallest angle the swimmers must turn between the buoys.

Thus, C) 41.410° is the correct answer

Problem 6 (#unknown)

As we are given two angles and a side length, we can use the Law of Sines to find side length "b". Firstly, we need angle C so we can set up the proportion to find "b". By the Triangle Angle-Sum Theorem, [tex]m\angle C=60^\circ[/tex].

[tex]\frac{\sin(B)}{b}=\frac{\sin(C)}{c}\\\\\frac{\sin(64^\circ)}{b}=\frac{\sin(60^\circ)}{8}\\\\8\sin(64^\circ)=b\sin(60^\circ)\\\\b=\frac{8\sin(64^\circ)}{\sin(60^\circ)}\\ \\b\approx8.303[/tex]

Thus, B is the correct answer (how ironic lol)

Problem 7 (#13)

[tex]\displaystyle\sqrt{2}\cos2x=\sin^2x+\cos^2x\\\\\sqrt{2}\cos2x=1\\\\\cos2x=\frac{1}{\sqrt{2}}\\\\\cos2x=\frac{\sqrt{2}}{2}\\ \\2x=\frac{\pi}{4},\frac{7\pi}{4}\\ \\x=\frac{\pi}{8},\frac{7\pi}{8}[/tex]

Hence, B is the correct answer

Problem 8 (#14)

[tex]\displaystyle \sec\theta=2\\\\\frac{1}{\cos\theta}=2\\ \\\cos\theta=\frac{1}{2}\\ \\\theta=\frac{\pi}{3}+2\pi n,\frac{5\pi}{3}+2\pi n[/tex]

Thus, D is the correct answer

Problem 9 (#19)

The bottom graph looks correct as the period of the tangent function is [tex]\frac{\pi}{|b|}=\frac{\pi}{2}[/tex].

Answer:

70

Step-by-step explanation:

2 quarters are 50¢

4 dimes are 40¢

1 nickel is 5¢

if you add it all together you will get 70¢

Answer:

A, B, and C.

Step-by-step explanation:

The square root of 25 is 5. 5 is rational, a whole number, and an integer.

Answer:

10.19

Step-by-step explanation:

Answer:

5*3*2=30ways

Step-by-step explanation:

Since we have 5 different manufacturers who manufactures the drug in 3 different forms and 2 type of strengths, then;

Number of ways in which a nurse can administer the drug for a patient

are; Ways=5*3*2=30ways

the answer would be supplementary angle, as an angle is supplementary when the measurements add up to 180 degrees

Answer:

1.97 day; 1 day.

Step-by-step explanation:

0.07*100 = 7

31.91x - 7 = 70

70 - 7 = 63

31.91x = 63

63 / 31.91 = 1.97

Hudson can afford to drive the car for 2 days and stay under his budget.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

We know that it costs $0.07 for every mile driven and we plan to drive 100 miles, that means we can set the inequality as:

31.91x + 0.07(100) ≤ 70

31.91x + 7 ≤ 70

Rearranging the inequality so we have the variable isolated on one side, we get:

31.91x ≤ 63

Divide both sides by 31.91 to get x alone.

x ≤ 1.97430

x ≤ 2

From obtaining the solution, Hudson can afford to drive the car for 2 days and stay under his budget.

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The question seems incomplete, the complete question would be as:

A rental car company charges $31.91 per day to rent a car and $0.07 for every mile driven. Hudson wants to rent a car, knowing that:

• He plans to drive 100 miles.

• He has at most $70 to spend.

Which inequality can be used to determine, the maximum number of days Hudson can afford to rent for while staying within his budget?

Applying the formula for the area of a sector and length of an arc, the value of k is calculated as: 27.

Area of a sector of a circle = ∅/360 × πr²

Length of arc = ∅/360 × 2πr

Given the following:

Find ∅ of the sector using the formula for length of acr:

∅/360 × 2πr = 6π

Plug in the value of r

∅/360 × 2π(9) = 6π

∅/360 × 18π = 6π

Divide both sides by 18π

∅/360 = 6π/18π

∅/360 = 1/3

Multiply both sides by 360

∅ = 1/3 × 360

∅ = 120°

Find the area of the sector:

Area = ∅/360 × πr² = 120/360 × π(9²)

Area = 1/3 × π81

Area = 27π

Therefore, the value of k is 27.

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