I just need to know if my answer is correct or not please!

Hi there!

So we are given that:-

In the third Quadrant or Quadrant III, sine and cosine both are negative, which makes tangent positive.

Since we want to find the value of cos theta. cos must be less than 0 or in negative.

To find cos theta, we can either use the trigonometric identity or Pythagorean Theorem. Here, I will demonstrate two ways to find cos.

Using the Identity

[tex] \large \displaystyle{ {tan}^{2} \theta + 1 = {sec}^{2} \theta}[/tex]

Substitute tan theta = 7/24 in.

[tex] \large \displaystyle{ {( \frac{7}{24}) }^{2} + 1 = {sec}^{2} \theta }[/tex]

Evaluate.

[tex] \large \displaystyle{ \frac{49}{576} + 1 = {sec}^{2} \theta} \\ \large \displaystyle{ \frac{625}{576} = {sec}^{2} \theta}[/tex]

Reminder -:

[tex] \large \displaystyle{ sec \theta = \frac{1}{cos \theta} }[/tex]

Hence,

[tex] \large \displaystyle{ \frac{576}{625} = {cos}^{2} \theta} \\ \large \displaystyle{ \sqrt{ \frac{576}{625} } = cos \theta} \\ \large \displaystyle{ \frac{24}{25} = cos \theta}[/tex]

Because in QIII, cos<0. Hence,

[tex] \large \displaystyle \boxed{ \blue{cos \theta = - \frac{24}{25} }}[/tex]

Using the Pythagorean Theorem

[tex] \large \displaystyle{ {a}^{2} + {b}^{2} = {c}^{2} }[/tex]

Define c as our hypotenuse while a or b can be adjacent or opposite.

Because tan theta = opposite/adjacent. Therefore:-

[tex] \large \displaystyle{ {7}^{2} + {24}^{2} = {c}^{2} } \\ \large \displaystyle{49 + 576 = {c}^{2} } \\ \large \displaystyle{625 = {c}^{2} } \\ \large \displaystyle{25 = c}[/tex]

Thus, the hypotenuse side is 25. Using the cosine ratio:-

[tex] \large \displaystyle{cos \theta = \frac{adjacent}{hypotenuse}} [/tex]

Therefore:-

[tex] \large \displaystyle{cos \theta = \frac{24}{25} }[/tex]

Because cos<0 in Q3.

[tex] \large \displaystyle \boxed{ \red{cos \theta = - \frac{24}{25} }}[/tex]

Hence, the value of cos theta is -24/25.

Let me know if you have any questions!

Answer:

[tex] {5x}^{4} + 3 {x}^{2} - 8x + 6[/tex]

Step-by-step explanation:

Math

Answer:

4th option is correct

Step-by-step explanation:

Answer: See image and explanation below

Step-by-step explanation:

The problem gives us 6 points to draw into the sketch.

The first and second point gives the domain and range of the sketch. The last 4 points tell us the coordinates.

Let's do the first two points. This tells us that the sketch should not go further (-3,0) and (3,0) of the x-axis, and should not go further (0,0) and (0,4) of the y-axis.

For the last 4 points, we can convert them to coordinates and graph them. The points would be (-2,3), (1,2), (-3,0), (3,0), and (0,4).

After we draw the 5 points listed above onto the graph, we can connect the points.

In the image I attached, the lines are straight, but when you draw it out, you should make your lines more curved.

Answer:

(0,-4)

Step-by-step explanation:

To find the y-intercept, substitute x=0

y= -3(0)^2+12(0)-4

=-4

Answer:

Step-by-step explanation:

Concept:

Quadratic equation formula: y=ax²+bx+c

Axis of symmetry formula=-b/2a

Y-intercept formula=c

Minimum or maximum is determined by the first term of the equation, which is [a]. If [a] is positive, then it is a minimum equation as the parabola heads up. If [a] is negative, then it is a maximum equation as the parabola heads down.

Given:

y = -3x² + 12x - 4

Solve:

The axis of symmetry formula = -b/2a

The Vertex

Y-intercept=c=(0, -4)

Min/Max

Hope this helps!! :)

Please let me know if you have any questions

Answer:

B

Step-by-step explanation:

The volume of any prism whose height is perpendicular to the base is

V = B * h

The base can be anything, even a 17 sided figure. As long as the base has an area that can be found, and the height is perpendicular to it, the volume can be calculated.

Answer:

How is volume calculated for a triangular prism?

Multiply the area of the triangular base by the prism’s height.

Answer:

2. 42 hrs

Step-by-step explanation:

we know that there are 60 minutes in one hour.

60 mins = 1 hour

162 mins = 162/ 60

[tex] \frac{162}{60} = \frac{120 + 42}{60} \\ = \frac{120}{60} + \frac{42}{60} \\ = 2 hrs+ \frac{42}{60} hrs[/tex]

42/ 60 hourse would mean 42 mins ( multiply the fractions with 60)

= 42 mins

therefore,

2hrs 42 mins

= 2. 42 hrs.

Answer:

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be  0  or  1  for each of its variables. In this case, the degree of variable  y  is  1  and the degree of variable  x  is  5 .

Therefore, it is not linear.

Explanation:

The probability of picking red is 0.13

The probability of picking orange is 0.20

The probability of picking either of these is 0.13+0.20 = 0.33

So the probability of picking neither of them is 1 - 0.33 = 0.67

There's a 67% of this happening.

Answer:

0.34

Step-by-step explanation:

because the probability of red is 20 and the probability of orange is 14 20 + 14 is 34.

Answer:

Answer is in attached image

I hope it help...

Answer: 5 s

Step-by-step explanation:

Given

Height of the rocket can be modelled as [tex]h=80-16t^2[/tex]

Rocket will land on earth when it's height becomes 0

[tex]\Rightarrow 80t-16t^2=0\\\Rightarrow t(80-16t)=0\\\\\Rightarrow t=0\ \text{or}\ t=\dfrac{80}{16}=5\ s[/tex]

Neglecting 0 value

Thus, rocket remains in air for 5 s.

Answer:

Length = 6

Width = 5.5

Step-by-step explanation:

Let's use the variable x to represent the width:

x = width

The question says that the length of the rectangle is "5 ft less than double the width". This length can be represented like this:

2x - 5 = length

To find the area of a rectangle, you multiply the width and length, so we are going to write an equation where we multiply the width and length and set it equal to 33 ft^2, which is the area:

(x)(2x - 5) = 33

Now use basic algebra to solve for x:

2x^2 - 5x = 33

2x^2 - 5x - 33 = 0

2x^2 + 6x - 11x - 33 = 0

(2x^2 + 6x) + (-11x - 33) = 0

2x(x + 3) - 11(x + 3) = 0

(2x - 11) (x + 3) = 0

x = 11/2, -3

x either equals 11/2 or -3. However, remember that x represents the width, and you can't have a negative number for a width, so x = 11/2 or 5.5.

Now plug in 5.5 to the length expression and simplify:

2(5.5) - 5

11 - 5 = 6

The length is 6 and the width is 5.5.

Hope this helps (●'◡'●)

Answer:

c

Step-by-step explanation:

It looks like the equation is

-sin²(x) = cos(2x)

Recall the half-angle identity for sine:

sin²(x) = (1 - cos(2x))/2

Then the equation can be written as

-(1 - cos(2x))/2 = cos(2x)

Solve for cos(2x):

-1/2 + 1/2 cos(2x) = cos(2x)

-1/2 = 1/2 cos(2x)

cos(2x) = -1

On the unit circle, cos(y) = -1 when y = arccos(-1) = π. Since cosine has a period of 2π, more generally we have cos(y) = -1 for y = π + 2nπ where n is any integer. Then

2x = π + 2nπ

x = π/2 + nπ

In the interval [-π, π], you get two solutions x = -π/2 and x = π/2.

Answer:

Step-by-step explanation:

Answer:Answer: - The Earth will be closest to Saturn. - The Earth and Saturn will be 38,800,000 miles apart in standard notation

Step-by-step explanation:

becuase the earth and saturn are pretty farr

Answer:

I hope this helps

Step-by-step explanation:

Answer:

$9.04 /gal

Step-by-step explanation:

1 gallon = 128 oz

8 * 4.23 oz = 33.84 oz

$2.39 /33.84 oz = .0707 $/oz

 .0707 $/oz * 128 = $9.04 $/gal

Answer:

Step-by-step explanation:

Total amount with Gerald = $32

Cost of fuel per gallon = $2.75

Cost of each bottle of windshield = $3

38 miles per gallon. If Gerard must fill his car with enough fuel to drive 250 miles,

Total gallons of fuel = 250 miles / 38 miles

= 6.5789473684210 gallons

Total cost of fuel = Total gallons of fuel × cost per gallon

= 6.5789473684210 × $2.75

= $18.1

Amount left for windshield = Total amount with Gerald - Total cost of fuel

= $32 - $18.1

= $13.9

what is the maximum number of bottles of windshield washer fluid Gerard can buy?

= Amount left for windshield / Cost of each bottle of windshield

= $13.9 / $3

= 4.6333333333333 bottles

Maximum number of bottles =

4 bottles

Answer:

$1,500,000

Step-by-step explanation:

Given

Principal = $1,000,000

Rate = 5%

Time = 10years

Interest = PRT/100

Interest = 1000000*5*10/100

Interest = 100000*5

Interest = $500,000

Amount after 10years =  $1,000,000+ $500,000

Amount after 10years = $1,500,000

Answer:

0

Step-by-step explanation:

Substitute b into -3.

Hence,

(b+3)(b²-5b+7)=(-3+3)(-3²-15+7)

=(0)(1)

=0

Answer & Step-by-step explanation:

We will only get a tornado if there is already a thunderstorm materializing

0.80 * 0.14 = 0.112

Probability of a tornado = 11.2%

There is a 100 - 14 = 86% chance of a tornado not being produced.

0.80 * 0.86 = 0.688

Probability of a storm and no tornado = 68.8%

Answer:

hodrvyeieiwb was the only one to win a lot

Answer:

the roots are x= -4 and x=6

the equation of the axis of symmetry is x^2-2x-24

Step-by-step explanation:

to find the roots you go to the area where the graph is touching the x axis because y is 0 on the x axis

to find the equation use the values of the x intercepts which are -4 and 6

(x+4)(x-6)

solve this into an equation by multiplying everything in the first brackets by every thing in the second the answer you are likely to come up with is x^2-2x-24

I hope this helps

Answer:

Through any three collinear points, there is exactly one plane.False [ i.e. non collinear points]

A segment is part of a line between two points on the line called the endpoints.False[I.e. mid point]

If there is a line and a point not on the line, then there exists exactly one line through the point

that is parallel to the given line.True

The midpoint of a segment is equidistant from the endpoints.True

If two angles are supplementary to the same angle, then the angles must be obtuse.True

If two angles form a linear pair, then the angles are complementary.False [I.e. supplementary]

Answer:

233 or option D

Step-by-step explanation:

In all shapes, all the angles add up to 360

So . . .

95 + x + 32 + x = 360

127 + x + x = 360

360 - 127 = 233

Therefore, your answer is 233 or option D

Answer:

233, D

Step-by-step explanation:

First, we know that the angles of a quadrilateral add up to 360 degrees. Therefore,

m∠a+m∠b+m∠c+m∠d = 360

m∠a+95+m∠c + 32 = 360

m∠a+m∠c + 127  = 360

subtract 127 from both sides

m∠a + m∠c = 233

Answer:

no change in area

Step-by-step explanation:

The original area is

A = 12*5 = 60 ft^2

The new length and width

l = 12 + .25 (12) = 12+3 =15

w = 5 - .2 (5) =5-1 = 4

The new area is

A = l*w =15*4 = 60 ft^2

The area is the same

Answer:

Students Major

Cheat reporting response

Number of Alcohols taken

Student's Height

Step-by-step explanation:

The Variables are the following:

Categorical variables

1. Major – The student's majors -

Arts & Social Science or STEM

2. Cheat - Response about reporting cheating - Yes or No

Quantitative Variables

3. Alcohol - Number of alcoholic beverages consumed in a typical week

4. Height - Self-reported height (in inches)

Answer:

15/2 that is the answer man