suppose cos(A) = 4/5. use the trig identity sin^2(A)+cos^2(A)=1 to find sin(A) in quadrant IV. round to the ten-thousandth.

a. -0.3954
b. -0.6000
c. 0.6485
d. 0.4500

Answer:

80

Step-by-step explanation:

The sum of the interior angles of a triangle is 180.  Subtract out the 2 angles that you know.

180 - 70 - 30 = 80

Answer:

A

Step-by-step explanation:

point H is the point of intersection of the perpendicular bisectors of the triangle's sides and is the circumcentre.

Answer:

A. Circumcenter

Step-by-step explanation:

this is the point that has the same distance from all 3 vertexes.

being on the median line of DE, every point of that line has the same distance to D and E.

being also on the median line of FE means it has the same distance from F and E as every other point on that line.

and the same for DF.

H as the crossing point of all 3 median lines is the only point that has the same distance to D, E and F.

so, H is the center of a circle that goes through all 3 points.

The value of x in x^yz = y^2 is [tex]x = \sqrt[yz]{y^2}[/tex]

The equation is given as:

x^yz = y^2

Rewrite the equation properly as follows

[tex]x^{yz} = y^2[/tex]

Take the yz root of both sides

[tex]\sqrt[yz]{x^{yz}} = \sqrt[yz]{y^2}[/tex]

Apply the law of indices

[tex]x^{\frac{yz}{yz}} = \sqrt[yz]{y^2}[/tex]

Divide yz by yz

[tex]x = \sqrt[yz]{y^2}[/tex]

Hence, the value of x in x^yz = y^2 is [tex]x = \sqrt[yz]{y^2}[/tex]

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Answer:

e

Step-by-step explanation:

Using euler's identity we can see that e^ipi=-1 and considering that i=y and  i^2=-1 we can conclude that x=e

Answer:

60 degrees

Step-by-step explanation:

The sum of the interior angles of a triangle are 180.  The bottom triangle give you two of the angle measurements (43 and 35)  Take 180 - 43 -35 = 102.  Angle E is 102.  Vertical angles are congruent so that mean that we can use that to find angle a.  Again, the sum of the interior angles adds up to 180.  180 - 102 - 18 gives us the measurement of angle a (60)

Answer: y=[tex]-\frac{5}{2} x+2[/tex]

Step-by-step explanation:

Use the equation of the line format: y = mx + b

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

[tex]m=\frac{-3-(7)}{2-(-2)}[/tex]

[tex]m=\frac{-10}{4}[/tex]

simplified

[tex]m=\frac{-5}{2}[/tex]

in order to find B:

[tex]y = -(\frac{5}{2}) *(-2)+b[/tex]

Insert value of y:

[tex]7 = (-\frac{5}{2} ) * (-2) +b[/tex]

Rewrite:

[tex]-\frac{5}{2} * -2 - b=7[/tex]

Cancel the common factor of 2:

[tex]-5 * -1 +b = 7[/tex]

Multiply -5 by -1:

[tex]5 + b= 7[/tex]

Subtract 5 from both sides:

[tex]b = 7-5\\b=2[/tex]

Now substitute values of m, and the final answer is:

[tex]y = -\frac{5}{2}x + 2[/tex]

As per definition

In. a function every domain has an unique range of it

Here

f(10) has two corresponding values hence it's not a function

Answer:

Step-by-step explanation:

The length of the brace required is 4.3m

What is sine rule?

In a ΔABC a, b and c are the sides and A, B and C are angles then,

[tex]\frac{a}{SinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]

We can find the length, l as shown below:

Let AB=3m, BC=2m and AC=l

Let ∠A=25°

So, in ΔABC

[tex]\frac{BC}{sinA}=\frac{AB}{sinC}=\frac{AC}{SinB}[/tex]

[tex]\frac{BC}{sinA}=\frac{AB}{sinC}[/tex]

[tex]\frac{2}{sin25}=\frac{3}{sinC}[/tex]

[tex]\angle{C}=sin^{-1}(\frac{3\times sin25}{2} )[/tex]

∠C=39.34°

∠A+∠B+∠C=180°

∠B=180°-25°-39.34°

∠B=115.66°

[tex]\frac{BC}{sinA}=\frac{AC}{SinB}[/tex]

[tex]\frac{2}{sin25}=\frac{l}{sin(115.66)}[/tex]

[tex]l=\frac{2\times sin(115.66)}{sin25}[/tex]

l=4.2659

Rounding to nearest tenth of meter.

l=4.3m

Hence, the length of the brace required is 4.3m

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The graph of Lin's distance as a function of time cannot be a straight line graph because of decrease in speed.

Given that Lin walks half a mile at a constant rate i.e. Lin velocity is constant.

If the speed is low then the time will be high. If speed is high then the time will be low because of the following rule:

Speed=Distance/ time.

For the first five minutes the graph will be upward sloping because he was sprinting and his speed was high so he will cover much more distance.

But after five minutes the graph will be downward sloping as the speed becomes low and he willcover less distance.

Hence the graph of Line's distance will not look like linear curve.

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In Wagnerian music drama, a basic recurring theme representing a person, object, event, or emotion is known as Leitmotif.

What is serious opera called?

What is Wagnerian leitmotif?

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Using the Pythagorean Theorem, the perimeter of the triangle is of 58.7 cm.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

From your description, I will suppose that the legs are of 6 cm and 26 cm, hence the hypotenuse is:

[tex]h^2 = 6^2 + 26^2[/tex]

[tex]h = \sqrt{6^2 + 26^2}[/tex]

h = 26.7.

The perimeter is the sum of the lengths of the three sides, hence:

P = 26.7 + 26 + 6 = 58.7 cm.

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The cost of the Baseball is $5.

Lets take football cost as "x"

And taking baseball cost as "y"

According to given conditions,

2y + 3x = 67

x= 3y + 4

Lets put the values of x in equation (1):

2y + 3 (3y+4) = 67

=> 2y + 9y + 12 = 67

=> 11y = 55

y = 5

x = 3(5) + 4

x = 19

Hence the cost of the Baseball is $5.

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The system of linear equations can be used to find the number of nickels, n, and the number of quarters, q, yolanda used is n + q = 28

n + q = 280.05n + 0.25q = 4

n + q = 28

0.05n + 0.25q = 4

n = 28 - q

0.05n + 0.25q = 4

0.05(28 - q) + 0.25q = 4

1.4 - 0.05q + 0.25q = 4

- 0.05q + 0.25q = 4 - 1.4

0.20q = 2.6

q = 2.6 / 0.20

q = 13

Substitute into

n + q = 28

n + 13 = 28

n = 28 - 13

n = 15

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The other factor of the polynomial is a. 3x2-4x+11

Given polynomial is 3x3 + 20x2 - 21x + 88 and the factor is (x+8)

We need to find another factor using long division method

So,

We will divide the polynomial by the factor to find the another factor

Therefore,

[tex]\sqrt[x+8]{3x^3+20x^2-21x+88}[/tex]

Now calculating

First multiplying [tex]3x^2[/tex] with (x+8) so , [tex]3x^2[/tex] will be in the quotient

We get [tex]3x^3+24x^2[/tex]

simplifying the calculation for [tex]3x^3+20x^2[/tex] and [tex]3x^3+24x^2[/tex]

We get the remainder is [tex]-4x^2-21x+88[/tex]

Second we will multiply -4x with (x+8) Where -4x will be in the quotient

We get [tex]-4x^2-32x[/tex] and then we will simplify the equation

We get 11x +88 as a remainder

The quotient we get is [tex]3x^2-4x[/tex]

Third we will multiply +11 with (x+8) Where +11 will be in the quotient

we get 11x+88

Simplifying the equation we get the remainder 0

So the quotient we get is  (3x2 - 4x+11)

Hence the another factor of the polynomial is  (3x2 - 4x+11)

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Using proportions, it is found that the boat can go 6 m/s in still water.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, we have that:

He goes twice as fast down the river, hence:

v + 2 = 2(v - 2).

v + 2 = 2v - 4

2v - v = 2 + 4

v = 6.

The boat can go 6 m/s in still water.

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The statement that is true about the domain and range of each function is; A) Both the domain and range of the transformed function are the same as those of the parent function.

We are told that the graph of f(x) = |x| is reflected across the y-axis. Thus;

|-x| = x

Now, the function is translated to the left by 5 units and so the transformed function is; g(x) = |x + 5|

Thus, from the graph, we get;

Domain of both functions is the set of all real numbers.

Range of both functions is the set {y|y ≥ 0}

Thus, we conclude that Both the domain and range of the transformed function are the same as those of the parent function.

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Step-by-step explanation:

well there is a very simple point that you have mistaken tho:

484cm², 25cm²

Areas are defined in square cm but the radius is in cm

so:

[tex] \sqrt{ \frac{484 {cm}^{2} }{25 {cm}^{2} } } = \frac{7.92}{r} = = = > 4.4 = \frac{7.92cm}{x} = = > x = \frac{7.92cm}{4.4} = x = 1.8cm[/tex]

and there you go

The option B is a correct option which is y = 26x and y = -0.030(x-500)2 15,900 represent the quadratic and linear function.

According to the statement

we have given that Vertex

(h,k) = (500, 15900)

And One of the points on the graph

(x,y) = (0,8400)

FIRST PART: we have to find the quadratic function

We can find the quadratic function by parabola's equation formula

y = a (x - h)² + k  -(1)

Input the numbers to the formula, to find the value of a

y = a (x - h)² + k

8400 = a(0 - 500)² + 15900

8400 = a (500)² + 15900

8400 = 250000a + 15900

-250000a = 15900 - 8400

-250000a = 7500

a = 7500/-250000

a = 0.03

Now,

Submit a to the formula (1)

y = a (x - h)² + k

y = 0.03 (x - 500)² + 15900

this is the quadratic equation.

SECOND PART: Find the linear function

the total cost = cost each helmet × the number of helmet

y = 26x

So,

The option B is a correct option which is y = 26x and y = -0.030(x-500)2 15,900 represent the quadratic and linear function.

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Disclaimer: This question was incomplete. Please find the full content below.

Question: A company plans to sell bicycle helmets for $26 each. The company's business manager estimates that the cost, y, of making x helmets is a quadratic function with a y-intercept of 8,400 and a vertex of (500, 15900)

x= number of helmets

y = amount in dollars

Which system models this situation?

a) y = 26x and y = 8,400(x-500)2+15,900

b) y = 26x and y = -0.030(x-500)2+15,900

c) y = x/26 and y = -0.030(x-500)2+15,900

d) y = x/26 and y =8,400(x-500)2+15,900

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Answer:

B. y = 26x and y = -0.030(x-500)2+15,900

Step-by-step explanation:

The cross-section would be the same shape as the base. A cross-section cannot be a sphere because a cross-section must be two-dimensional, but a sphere is three-dimensional.

Answer:

C

Step-by-step explanation:

There are 6 outcomes and you are seeking 2 of them.  

2/6 or 1/3 1:3

The question is an illustration of combination and there are 729 potential pass codes available

The given parameters are

Symbols available = 9

Length of pass code = 3

From the question, we understand that a symbol may be entered any number of times.

This means that each of the 9 available symbols can be used three times

So, the number of potential pass codes is

Passcodes = 9 * 9 * 9

Evaluate the product

Passcodes = 729

Hence, there are 729 potential pass codes available

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Answer:

Breadth=8

Length=6

OR

breadth = 6

length=8

Step-by-step explanation:

Area of 4 walls = 2(l+b)h

112=2.4(l+b)

112/8=l+b

14=l+b

l=14-b

Area of base or ceiling=l x b

48=(14-b).b

48=14b-b²

b²-14b+48=0

factorize it and we get

(b-6)(b-8)=0

taking b-6=0

b=6

l=14-6

l=8

Question 2

1) [tex]\overline{PR} \perp \overline{QS}[/tex], [tex]\overline{PQ} \cong \overline{PS}[/tex] (given)

2) [tex]\overline{PR} \cong \overline{PR}[/tex] (reflexive property)

3) [tex]\angle PRQ[/tex] and [tex]\angle PRS[/tex] are right angles (perpendicular lines form right angles)

4) [tex]\triangle PRQ[/tex] and [tex]\triangle PRS[/tex] are right triangles (a triangle with a right angle is a right triangle)

5) [tex]\triangle PRQ \cong \triangle PRS[/tex] (HL)

Question 3

1) [tex]\angle C[/tex] is a right angle, [tex]\overline{AC} \cong \overline{AE}[/tex], [tex]\overline{DE} \perp \overline{AB}[/tex] (given)

2) [tex]\angle DEA[/tex] is a right angle (perpendicular lines form right angles)

3) [tex]\triangle ACD[/tex] and [tex]\triangle DAE[/tex] are right triangles (a triangle with a right triangle is a right angle)

4) [tex]\overline{AD} \cong \overline{AD}[/tex] (reflexive property)

5) [tex]\triangle ACD \cong \triangle AED[/tex] (HL)

6) [tex]\angle CAD \cong \angle DAE[/tex] (CPCTC)

7) [tex]\overline{AD}[/tex] bisects [tex]\angle BAC[/tex] (if a segment splits an angle into two congruent parts, it is an angle bisector)

It looks like the limit you want to compute is

[tex]\displaystyle \lim_{x\to4} \frac{f(g(x)) - f(4)}{x-4}[/tex]

Since [tex]g(4)=4[/tex], this limit corresponds exactly to the derivative of [tex](f\circ g)(x) = f(g(x))[/tex] at [tex]x=4[/tex]. Recall that

[tex]f'(a) = \displaystyle \lim_{x\to a} \frac{f(x) - f(a)}{x - a}[/tex]

By the chain rule,

[tex](f\circ g)'(4) = f'(g(4)) \times g'(4) = f'(4) \times g'(4) = 3\times7 = \boxed{21}[/tex]

Since [tex]g'(4)[/tex] exists, [tex]g[/tex] is differentiable at [tex]x=4[/tex] so it must be continuous.

Answer:

3+10 square root of 2

Step-by-step explanation:

[tex](3 + 10) \sqrt{2} [/tex]

Answer:

13.846153846

Step-by-step explanation:

Its easy Just 18:1.3=13.846153846

The item which yield the greatest level of accuracy to the true weight of rock with the least error is bricks.

A rock refers to a solid substance formed from the fusion of organic minerals.

Therefore, bricks is the item which yield the greatest level of accuracy to the true weight of rock with the least error.

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Answer:

1425

Step-by-step explanation:

Each notebook costs 40, if she buys 30 you can find the total price of notebooks by multiplying the two numbers:

[tex]40*20=1200[/tex]

Each pen costs 15, the same process can be used, multiply price by quantity:

[tex]15*15=225[/tex]

Now just sum the two numbers to find the final price:

1425

Answer:

Step-by-step explanation:

30*40+15*15=

1200+625=

Rs1625

hope this helps