What is the area of the obtuse triangle given below?

Hello There!

Your answer would be “B”

Forget about the -5 and just do 5 multiplied by 3 and you get a product of 15.

Then, make it negative and it would be 4^-15

Answer: The population in Eric's survey is the high school seniors.

Answer:

all high school seniors at Eric’s school

Step-by-step explanation:

Answer:

Option A.

Step-by-step explanation:

step 1

we know that

The equation of the solid line is

[tex]y=5[/tex]

The solution is the shaded area above the solid line

so

The equation of the first inequality is

[tex]y\geq 5[/tex]

step 2

The equation of the dashed line is

[tex]y=x^{2} -5x+6[/tex]

The solution is the shaded area above the dashed line

so

The equation of the second inequality is

[tex]y>x^{2} -5x+6[/tex]

therefore

The system of inequalities could be

[tex]y\geq 5[/tex]

[tex]y>x^{2} -5x+6[/tex]

Answer:

Yes

Step-by-step explanation:

We need to determine the sides of the squares

Area = 9

A = s^2

9 = s^2

Taking the square root of each side

sqrt(9)= sqrt(s^2)

3 =s

Perimeter of a square = 16

P =4s

16 =4s

Divide each side by 4

16/4 =4s/4

4 =s

Side = 5 in

Right triangles obey the Pythagorean theorem

a^2 + b^2 = c^2

Putting the smaller sides in for a and b

3^2 +4^3 = 5^2

9+16=25

25=25

Since this is true, we can arrange the squares to make a right triangle

Answer:

Yes, due to the Pythagorean theorem.

Leg A would be 3

Leg B would be 4

Hypotenuse C would be 5

Explanation:

When making the right triangle, only one side length value is needed.

If the area of square one is 9, 9 divided by 2 is 3.

If the perimeter of square two is 16, 16 divided by 4 is 4.

The single side length for square three is given, which is 5.

The Pythagorean theorem consists of a^2 + b^2 = c^2.

Plug in the values.

3^2 + 4^2 = 5^2

9 + 16 = 25

Hope this helps! :)

Answer:

coordinate of the other endpoint is (-9,-2)

Step-by-step explanation:

Given that a segment has endpoints at (1, -2). The midpoint is at (-4, -2).

Now we need to find about what are the coordinates of the other endpoint.

let the coordinates of other end points are (x,y)

Then mid point of (1,-2) and (x,y) is given by mid point formula:

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

[tex]\left(\frac{x+1}{2},\frac{y-2}{2}\right)=(-4,-2)[/tex]

[tex]\Rightarrow \frac{x+1}{2}=-4, \frac{y-2}{2}=-2[/tex]

[tex]\Rightarrow x+1=-8, y-2=-4[/tex]

[tex]\Rightarrow x=-9, y=-2[/tex]

hence coordinate of the other endpoint is (-9,-2)

Answer:

what the otherperson said

Step-by-step explanation:

just read what the other person said

Answer:

Asin(wt + φ) = c2sinwt +c1coswt

Step-by-step explanation:

Proof:

wt here is periodic where as φ is constant

taking left hand side

Asin(wt + φ)

Using trigonometric identity sin(θ+φ) = sinθcosφ +sinφcosθ

Asin(wt +φ) = A[sinwtcosφ +sinφcoswt]

                  = Asinwtcosφ +Asinφcoswt

Now as we know φ is constant

so will Asinφ and Acosφ will also be constant

let     Asinφ= c1

and Acosφ=c2

Putting in above expression, we get

Asin(wt +φ) = c2sinwt +c1coswt !

Answer:

x = 14; x = 0  

Step-by-step explanation:

(x)(6 + 8) = x²

(x)(14) = x²

14x = x²

14x - x² = 0

(x)(14 - x) = 0

x = 14; x = 0  

Answer:

number2

Step-by-step explanation:

Answer:

f(x) = |x|

Step-by-step explanation:

function is even if and only if f(-x) = f(x)

f(x) = |x| ; regard to its sign f(x) = x

f(-x) = |-x| ; regard to its sign f(-x) = x

So answer is f(x) = |x| is the even function

Answer:

Step-by-step explanation:

The way that this function looks when graphed could be similar to the seismic waves recorded when an earthquake hits.

A logarithmic measure known as the Richter scale is used to quantify the overall energy generated during an earthquake. Each number higher on the Richter scale denotes a ten-times-stronger intensity. For instance, a magnitude 5 earthquake is ten times more powerful than a magnitude 4 earthquake.

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.

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Answer:

(x + 3)^2 + (y + 1)^2 = 25

Step-by-step explanation:

Equation of a circle with center (h, k) and radius, r.

(x - h)^2 + (y - k)^2 = r^2

The center is (-3, -1), so h = 1, and k = 2.

(x - (-3))^2 + (y - (-1))^2 = r^2

(x + 3)^2 + (y + 1)^2 = r^2

Now we substitute x and y with the values of x and y from the given point, and we solve for r^2.

(1 + 3)^2 + (2 + 1)^2 = r^2

4^2 + 3^2 = r^2

16 + 9 = r^2

r^2 = 25

Now that we know r^2, we substitute it into the equation above.

(x + 3)^2 + (y + 1)^2 = 25

Answer:

The correct answer is,

(x + 3)² + (y +1)² = 25

Step-by-step explanation:

It is given that, What is the equation of a circle with center (-3,-1) that contains the point (1,2)

Formula;-

Equation of the circle passing through the point ( x₁,y₁) with radius r is given by,

(x - x₁)² + (y - y₁)² = r²

To find the radius of circle

r =√[ (1 --3)² + (2 --1)²]

 =√(4² + 3²)

 = √(16 + 9)

 =√25 = 5

To find the equation of the circle

(x₁, x₁) = (-3, -1) and r = 5

(x - x₁)² + (y - y₁)² = r²

(x - -3)² + (y - -1)² = 5²

(x + 3)² + (y +1)² = 25

Answer:

120 votes

Step-by-step explanation:

So one way to solve this is by creating an equation to solve for x.

So we are given 4/7, that will be one side of the equation.  

And we are trying to figure out how many votes out of the 210 she received, so on the other side of the equation we will have x/210, since we are solving for x.  

So 4/7 = x/210

We want to get x alone, so we can multiply 4/7 by 210, which equals 120.

So x equals 120!

Isabel received 4/7 of the 210 votes for class treasurer, which equals 120 votes when the total is multiplied by the fraction.

The student is asking for help with a mathematics problem related to finding a fraction of a whole number. Isabel received 4/7 of the total votes cast for class treasurer, and the total number of votes cast was 210. To find how many votes Isabel received, we simply multiply 210 by 4/7:

Isabel's votes = (210) * (4/7)

Isabel's votes = 840 / 7

Isabel's votes = 120

Therefore, Isabel received 120 votes.

9. Area = 59.755[tex]cm^{2}[/tex] square cm. when the area to nearest tenth then, area = 60 square cm.

10. Area = 22.9813[tex]mi^{2}[/tex]. When the area to nearest tenth then, area = 20 square mi.

Area of the Triangle:

Area of the triangle is = half of (base x height)

=> (1/2) x (b x h)

Trigonometry:

sinθ = opposite side / hypotenuse

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The area of the triangles are 59.8 square cm and 23.0 square miles

From the question, we have the following parameters that can be used in our computation:

The triangle

The area of each triangle is calculated using the following sine equation

Area = 1/2absin(C)

Using the above as a guide, we have the following

Area of triangle 1 = 1/2 * 11 * 11 * sin(99 degrees)

Area of triangle 1 = 59.8 square cm

Area of triangle 2 = 1/2 * 5 * 12 * sin(50 degrees)

Area of triangle 2 = 23.0 square miles

Hence, the area of the triangles are 59.8 square cm and 23.0 square miles

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Answer:

see explanation

Step-by-step explanation:

0.97 is the value of cos14° to 2 dec. places

Use your calculator ( ensuring it is in degree mode )

press cos14 then = to obtain value 0.97

Answer:

336 ft squared

Step-by-step explanation:

Looking for face area, not volume

So...

10*12=120

6*12=72

8*12=96

6*8/2=24

6*8/2=24

24+24+120+72+96=336ft squared

Answer:

D

Step-by-step explanation:

5 divided by 3 is 1.6666 which is the same as 1 and 2/3

The correct answer is D

A quantity is proportional to 18/3 if it simplifies to the same value, which is 6. The proportional quantities are 90/15, 36/6, 72/12, and 6/1, as they all simplify to 6. The quantity 36/12 is not proportional since it simplifies to 3.

To determine which quantities are proportional to 18/3, we need to find what 18 divided by 3 equals and then compare this to the given fractions to check for equivalence. Calculating 18/3 gives us 6. Now, let's examine each option:

90/15: This fraction reduces to 6, which is proportional to 18/3.

36/6: This fraction also equals 6 after simplification, so it is proportional to 18/3.

72/12: Simplifying 72/12 gives us 6, making it proportional to 18/3

6/1: 6 divided by 1 is just 6, so this too is proportional to 18/3.

36/12: Simplifying 36/12 results in 3, which is not equal to 6, so it is not proportional to 18/3.

Answer:

Part A) The equation is [tex]t=3.50z+40[/tex]

Part B) Kristina did go to the gym 20 times

Step-by-step explanation:

Let

t-----> the total amount

z----> the number of times that Kristina go the health club

Part A) Write an equation

we know that

The linear equation that represent this situation is

[tex]t=3.50z+40[/tex]

Part B) For [tex]t=\$110.00[/tex]

Substitute the value of t in the linear equation and solve for z

[tex]110.00=3.50z+40[/tex]

[tex]3.50z=110.00-40[/tex]

[tex]3.50z=70.00[/tex]

[tex]z=70.00/3.50[/tex]

[tex]z=20\ times[/tex]

C.yes, because of ASA or AAS

Answer:

Part 1) The area of the shaded region is [tex]2.1\pi\ m^{2}[/tex]

Part 2) The length of the arc AB is [tex]2.5\pi\ in[/tex]

Part 3) The area of the shaded region is [tex]56.53\pi\ in^{2}[/tex]

Step-by-step explanation:

Part 1) Find the area of the shaded region

step 1

Find the area of the circle

The area is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=3\ m[/tex]

substitute

[tex]A=\pi (3)^{2}[/tex]

[tex]A=9\pi\ m^{2}[/tex]

step 2

we know that

The area of complete circle subtends a central angle of 360 degrees

so

by proportion

calculate the area of the shaded region with a central angle of 84 degrees

[tex]\frac{9\pi }{360} =\frac{x }{84}\\ \\x=(9\pi)*84/360\\ \\x=2.1\pi\ m^{2}[/tex]

Part 2) What is the length of arc AB?

step 1

we know that

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=5\ in[/tex]

substitute

[tex]C=2\pi (5)[/tex]

[tex]C=10\pi\ in[/tex]

step 2

we know that

The length of complete circle subtends a central angle of 360 degrees

so

by proportion

calculate the length of the arc AB with a central angle of 90 degrees

[tex]\frac{10\pi }{360} =\frac{x }{90}\\ \\x=(10\pi)*90/360\\ \\x=2.5\pi\ in[/tex]

Part 3) Find the area of the shaded region given that XY measures 8 in

step 1

Find the area of the circle

The area is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]XY=r=8\ in[/tex]

substitute

[tex]A=\pi (8)^{2}[/tex]

[tex]A=64\pi\ in^{2}[/tex]

step 2

we know that

The area of complete circle subtends a central angle of 360 degrees

so

by proportion

calculate the area of the shaded region with a central angle of (360-42)=318 degrees

[tex]\frac{64\pi }{360} =\frac{x }{318}\\ \\x=(64\pi)*318/360\\ \\x=56.53\pi\ in^{2}[/tex]

The correct answer is b

The height of rectangle is 10 inch

Answer:

10 inches

Step-by-step explanation:

Answer:

B 1/5 1/4 1/3

Step-by-step explanation:

The first digit Maggie's bank picked from the 5 digit available, so 1/5.

The second digit will be picked from the 4 remaining digits available, so 1/4.

For the final digit, the bank will have only 3 options to choose from, so 1/3.

So the possibility for the 3-digit assigned PIN to be 123 is

[tex]\frac{1}{5} * \frac{1}{4} *\frac{1}{3} =\frac{1}{60}[/tex]

1/60, so the formula is the one presented in the B option: 1/5 1/4 1/3

Answer:

Option B. [tex]x=-\frac{9}{28}(+/-)\frac{\sqrt{479}}{28}i[/tex]

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]14x^{2}+9x+10=0[/tex]

so

[tex]a=14\\b=9\\c=10[/tex]

substitute in the formula

[tex]x=\frac{-9(+/-)\sqrt{9^{2}-4(14)(10)}} {2(14)}[/tex]

[tex]x=\frac{-9(+/-)\sqrt{-479}} {28}[/tex]

Remember that

[tex]i=\sqrt{-1}[/tex]

substitute

[tex]x=\frac{-9(+/-)\sqrt{479}i} {28}[/tex]  

[tex]x=-\frac{9}{28}(+/-)\frac{\sqrt{479}}{28}i[/tex]

The surface of the ocean is 0 meters.

Because the fish is below the surface it would be a negative number. ( it is less than 0)

The elevation of the fish would be -12 meters.

Answer:

-12 meters

Step-by-step explanation:

Elevation is the height above a given level, most often the sea. Therefore, elevation is like a vertical numerical line. If the sea level is 0, and to the right of the 0 is positive numbers, then the left has to be negative.

Therefore, the fish is -12 meters below sea level.

Answer:

x=30

Step-by-step explanation:

Add up all of the values of the angles and set it equal to 180 degrees since a triangle is always made up of angles that have a sum of 180 degrees.

x+2x+3x=180

6x=180

x=30

Answer: [tex]f(2)=25[/tex]

Step-by-step explanation:

You know that the given function is:

[tex]f(x)=4x^3-x^2-5x+7[/tex]

You know that you must evaluate this function for [tex]x=2[/tex].

Then, to evaluate the function for [tex]x=2[/tex], you need to substitute this value into the given function and simplify it.

Therefore, you get:

[tex]f(x)=4x^3-x^2-5x+7\\f(2)=4(2)^3-(2)^2-5(2)+7\\f(2)=4(8)-(4)-10+7\\f(2)=32-4-10+7\\f(2)=25[/tex]

So, the answer is: [tex]f(2)=25[/tex]

Final answer:

The range of a cosine function is the set of output values the function can take, which is always between -1 and +1. This applies to the standard cosine function and is unaffected by horizontal or phase shifts. This range is consistent with the definition of the cosine function as the ratio of the adjacent side to the hypotenuse in a right triangle.

Explanation:

The range of a cosine function refers to the set of possible values that the function can output. In mathematical terms, the cosine function oscillates between +1 and -1 irrespective of any horizontal shifts or phase shifts. A horizontal shift, demonstrated in Figure 15.8 (b), where the function is shifted by an angle φ (phase shift), does not alter the range of values of the function, which remain – from its minimum value of -1 to its maximum of +1.

Similarly, in Figure 16.10, a sine function, which is related to the cosine function, also oscillates between +1 and -1 every 2π radians (a complete cycle). This oscillation represents the wave function amplitude, which in cases other than a cosine can fluctuate between +A and -A.

As illustrated in Figure 2.18, the cosine function can be visualized as the ratio of the adjacent side to the hypotenuse (Ax/A = cos A) in a right triangle, further highlighting that this ratio (and thus the range of the cosine function) is between -1 and 1.

For example, when √(1+1)* approaches 1, it is indicative that cos 0 = 1, representing one end of the cosine function's range.

Answer:

a. [tex]u=\frac{4\sqrt{41}i }{41}-\frac{5\sqrt{41}j}{41}[/tex]

Step-by-step explanation:

The given vector is v= 4i - 5j

The magnitude of this vector is;

[tex]|v|=\sqrt{(-4)^2+(-5)^2}[/tex]

[tex]|v|=\sqrt{16+25}[/tex]

[tex]|v|=\sqrt{41}[/tex]

The unit vector u in the direction of v is;

[tex]u=\frac{v}{|v|}[/tex]

[tex]u=\frac{4i - 5j}{\sqrt{41}}[/tex]

[tex]u=\frac{4i }{\sqrt{41}}-\frac{5j}{\sqrt{41}}[/tex]

We rationalize to get

[tex]u=\frac{4\sqrt{41}i }{41}-\frac{5\sqrt{41}j}{41}[/tex]

Answer:

C.

Step-by-step explanation:

A - Perpendicular lines always touch each other at least once.

B - Parallel lines never touch.

D- Not always true.

C is true. If they are not in the same plane they are skewed lines.

The true statement is C: Parallel lines are always in the same plane. Perpendicular lines do intersect, while parallel lines do not, and perpendicular lines can certainly be in the same plane. Hence, correct option C.

The question seeks to determine the accuracy of given statements about geometric relationships between. Perpendicular lines and parallel lines. Based on the provided theorems, the true statement is: C. Parallel lines are always in the same plane.

This is because if two lines are parallel, they will be equidistant from each other at all points, which can only occur if they are in the same plane. Statements A, B, and D are false.

Perpendicular lines do intersect at a 90-degree angle.

Parallel lines, by definition, never intersect as they are always equidistant.

Perpendicular lines can be in the same plane or in different planes, although a line that is perpendicular to a plane must lie in another plane.

Answer:

1) d. 2400

2) d.4200

Step-by-step explanation:

As per given data:

F(x) represents number of fish

x represents number of weeks

Relation between F(x) and x is given as

F(x)= 500 (1.2)x

Now part 1:

How many fish are in the pond after 4 weeks=?

x=4

Putting in given equation  F(x)= 500 (1.2)x

F(x)= 500(1.2)(4)

     = 2400

Now part 2:

How many fish are in the pond after 7 weeks?

x=7

Putting in given equation  F(x)= 500 (1.2)x

F(x)= 500(1.2)(7)

     = 4200 !

Answer:

Correct choice is b. 1036 fish.

and c. 1791 fish.

Step-by-step explanation:

Given equation is [tex]f(x)=500(1.2)^x[/tex].

There x represents number of weeks. We need to find about wow many fish are in the pond after 4 weeks.

To find that we will plug x=4 into above formula and simplify

[tex]f(x)=500(1.2)^x[/tex]

[tex]f(x)=500(1.2)^{4}[/tex]

[tex]f(x)=500(2.0736)[/tex]

[tex]f(x)=1036.8[/tex]

Which is approx 1036

Hence correct choice is b. 1036 fish.

------

We can repeat same process with x=7 for 2nd problem

[tex]f(x)=500(1.2)^{7}=1791.5904[/tex]

Hence correct choice is c. 1791 fish.