Point C is the center of the circle. angle ACB measures 49. What is the of arc ADB

SOH CAH TOA tells you

... cos(B) = a/c

... 4/5 = 8/c

... c = 10 . . . . . multiply by 5c/4

By the Pythagorean theorem,

... b = √c² -a²) = √(10² -8²) = √36 = 6

The lengths of the other two sides are: b = 6, c = 10.

_____

You can tell from the value of the cosine that this is a 3-4-5 right triangle. You can tell from the value of "a" that the scale factor is 2. That means the other two sides are 6 and 10.

To find the lengths of the other two sides of the right triangle, we can use the Pythagorean theorem and the cosine function. Side a is given as 8 and the cosine of angle B is given as 4/5. Using the cosine function, we can find the length of side b. Then, using the Pythagorean theorem, we can find the length of side c. The lengths of the other two sides are approximately 6.4 and 10.24, respectively.

To find the lengths of the other two sides of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. In this case, we are given that side a is opposite angle A and has a length of 8, and we are given the cosine of angle B, which is 4/5. We can use the cosine function to find the length of side b, and then use the Pythagorean theorem to find the length of side c.

Step 1: Use the cosine function to find the length of side b:
cos(B) = 4/5
b/a = cos(B)
b/8 = 4/5
b = (4/5) * 8
b = 32/5
b = 6.4

Step 2: Use the Pythagorean theorem to find the length of side c:
a² + b² = c²
8² + 6.4² = c²
64 + 40.96 = c²
104.96 = c²
c = √104.96
c ≈ 10.24

Therefore, the lengths of the other two sides of the right triangle are approximately 6.4 and 10.24, respectively.

Attendance with the higher ticket price is ...

... $1750/$7 = 250

So the percentage change in attendance is ...

... change = (new - original)/original × 100%

... = (250 -300)/300 × 100% = -1/6×100% ≈ -17%

Final answer:

The percentage change in the average number of customers after the movie theater raises ticket prices is approximately -17%.

Explanation:

The movie theater originally charges $5 per ticket and has an average of 300 customers each night. After raising the price to $7, the average nightly ticket sales amount to $1,750. To find the new number of customers, divide the total sales by the price per ticket: $1,750 / $7 = 250 customers.

The change in the number of customers is the new amount minus the original amount, which is 250 - 300 = -50. To find the percentage change, divide the change by the original amount and multiply by 100: (-50 / 300) x 100 = -16.67%. After rounding the decimal, the percentage change is approximately -17%.

ANSWER

The solution is

[tex](x=1,y=2),(x=2,y=3)[/tex]

EXPLANATION

We have

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

and

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

Let us substitute equation (1) in to equation (2). This gives us,

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

We rewrite this as a quadratic equation as the highest degree is 2.

[tex]x^2-x-1-1=0[/tex]

This implies that

[tex]x^2-x-2=0[/tex]

we factor to obtain,

[tex]x^2+x-2x-2=0[/tex]

[tex]x(x-1)-2(x-1)=0[/tex]

[tex](x-1)(x-2)=0[/tex]

This means,

[tex](x-1)=0\:\: or\:\:(x-2)=0[/tex]

[tex]x=1\:\: or\:\:x=2[/tex]

We substitute this values into any of the above equations, preferably equation (1)

When, [tex]x=1[/tex], [tex]y=1+1=2[/tex]

When, [tex]x=2[/tex], [tex]y=2+1=3[/tex]

The solution is

[tex](1,2),(2,3)[/tex]

Answer:

cos(A) = 24/25 = 0.96

Step-by-step explanation:

SOH CAH TOA tells you that ...

... cos(A) = AB/AC

We are given AB = 24, but we must calculate AC using the Pythagorean theorem.

... AC² = AB² + BC²

... AC² = 24² + 7² = 576 + 49 = 625

... AC = √625 = 25

Now, we have sufficient information to find cos(A):

... cos(A) = 24/25 = 0.96

The value of cosA is used in trigonometry and physics to calculate the horizontal component of vectors or the angle of right triangles. For example, if we have a vector A, at an angle θ, then Ax = A cos θ, where Ax is the horizontal component of the vector. So in this way, cosA provides a crucial part in vector calculations.

The value of cosA refers to the cosine of angle A. In trigonometry, this is often used in the context of right triangles or in the calculation of vectors. For example, if you have a vector A and an angle θ (theta), the horizontal component of that vector can be found by multiplying the magnitude of the vector (Ax) by cos(θ). This is often denoted as Ax = A cos θ.

To use an example, let's say we have a vector A with a magnitude of 10.3 blocks and an angle of 29.1° from the x-axis. We can find the x-component (Ax) of that vector by calculating (10.3 blocks) * cos(29.1°), which gives us a value of approximately 9.0 blocks.

Therefore, the value of cosA in this context would be used to provide a component part of a vector based on an associated angle.

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Using Pythagorean's Theorem we know that a^2 + b^2 = c^2

C is the length of the ladder, and we are given one of the sides, let's call that side b

                                                                                          _________

we have a^2 + b^2 = c^2, and a^2 = c^2 - b^2, so a = √ c^2 - b^2

       _________      ______     ____

a = √12^2-3^2 = √ 144-9 = √ 135 = 11.61895 

so the top of the ladder is 11.6 feet above the ground

here u go hope this helps

Answer:

12 sin60°

Remember SOHCAHTOA.

sinθ =

opposite

hypotenuse

sin60° =

x

12

x = 12 sin60°

I would say the low I’m just guessing so get it checked

Answer:

the answer is C

Step-by-step explanation:

The low temperatures have the greater range. The range for the highs is 6, the range for the lows is 8.

Answer: the angles are if the 30° is in the first quadrant:

30°, 150°, 30°, 150° (from quadrant one to quadrant four)

Step-by-step explanation:

If two lines intersect, and one of the angles that form is 30°, we have that:

Now, suppose that you have only a line, this is the representation of a 180° angle, then if you divide it with a line and one of the angles created is 30°, the other angle must be equal to 150°

and on the other side of the line we will have a mirrored image, right next to the 150° we should see another 30° angle, and after that another 150° angle.

Answer:

Given: ∆ABC with the altitudes from vertex B  and C intersect at point M, so that BM = CM.

To prove:∆ABC is isosceles

Proof:-Let the altitudes from vertex B intersects AB at D and from C intersects AC at E( with reference to the figure)

Consider ΔBMC where BM=MC

Then ∠CBM=∠MCB......(1)(Angles opposite to equal sides of a triangle are equal)

Now Consider ΔDMB and ΔCME

∠D=∠E.......(each 90°)

BM=MC...............(given)

∠CME=∠BMD........(vertically opposite angles)

So by ASA congruency criteria

ΔDMB ≅ ΔCME

∴∠DBM=∠MCE........(2)(corresponding parts of a congruent triangle are equal)

Adding (1) and (2),we get

∠DBM+∠CBM=∠MCB+∠MCE

⇒∠DBC=∠BCE

⇒∠B=∠C⇒AB=AC(sides opposite to equal angles of a triangle are equal)⇒∆ABC is an isosceles triangle .

Answer:

m∠MBC = m∠MCB

 by reason: Base Angles

Step-by-step explanation:

:)

Answer:

<L = 50 degrees

Step-by-step explanation:

B and C are given. There should be a one to one Correspondence. <A should = <L

Since there are 180o in any triangle

<L = <A = 180 - 35 - 95

<L = <A = 50 degrees

point slope form

y-y1 = m (x-x1)

y- (-2) = 3(x-1)

y+2 = 3(x-1)

y + 2 = 3(x - 1)

the equation of a line in point-slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = 3 and (a, b) = (1, - 2), hence

y + 2 = 3(x- 1) ← in point-slope form

The least number of gift baskets Jessica can make, given that she has 6 jars of salsa and 4 bags of tortilla chips in each case, is 12. This is calculated by finding the Least Common Multiple of 6 and 4.

Jessica is working with two different quantities: 6 jars of salsa in a case and 4 bags of tortilla chips in a case. In each gift basket, she places 1 jar of salsa and 1 bag of tortilla chips, meaning that she needs the same number of jars and bags for an even number of gift baskets.

Therefore, to find the least number of baskets she can make, we need to find the Least Common Multiple (LCM) of 6 and 4, which the smallest number that both numbers divide evenly into. The LCM of 6 and 4 is 12. Hence, the least number of gift baskets Jessica can make is 12.

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We have to write the equation of a line that is perpendicular to the line [tex]x=3[/tex] and that passes through the point [tex](0,-4)[/tex].

The general equation of a line in the slope-intercept form is given by:

[tex]y=mx+b[/tex]

Where, 'm' is the slope and 'b' is the y-intercept.

Now, we need to find the slope first,

The required line is perpendicular to the line [tex]x=3[/tex]. Slope of the line [tex]x=3[/tex] is undefined. A line perpendicular to that must have slope of '0'. That implies, our required line is parallel to the x-axis.

Therefore, m=0

Now that line is passing through the point [tex](0, -4)[/tex].

We can plug in the points to the find the value of y-intercept. After plugging the values, we get:

[tex]y=0 \times 0+(-4)=-4[/tex]

Hence, the equation of the required line is [tex]y=-4[/tex].

If you need to, you can write and solve an equation for the factor you seek.

... 6×10^10 = factor × 2×10^-3

Divide by 2×10^-3 to find the value of the factor:

... (6×10^10)/(2×10^-3) = factor

... factor = (6/2)×10^(10-(-3))

... factor = 3×10^13

The first number is 3×10^13 times the second number.

_____

An exponent signifies repeated multiplication.

... 10×10×10 = 10³

Just as you cancel common factors when you do division, you can subtract exponents.

[tex]\dfrac{10\cdot 10\cdot 10}{10\cdot 10}=\dfrac{10}{1}=10\\\\\dfrac{10^3}{10^2}=10^{3-2}=10^1=10[/tex]

The same process works regardless of the signs of the exponents. When multiplying, we add exponents; when dividing we subtract the exponent of the denominator.

The answer to "What is the P(Gate 3 and Gate 4 are both open)?" is

B: 15%

It is because they state that the chance of both gates being open at the same time is 15% and that chance is indeed the probability.

The first reflection reverses the orientation and alters the direction of the vectors representing the sides of the quadrilateral. The second reflection does the same thing. The end result is that the orientation is unchanged by two reflections, and the direction of the sides of the quadrilateral is changed.

The appropriate choice is ...

... B. The resulting image will be a rotation of the pre-image.

_____

The center of rotation will be the point where the lines cross. (That is the invariant point.)

In the attachment, the green quadrilateral RESP is reflected across the line y=2x+7 (blue) to form the blue quadrilateral R'E'S'P'. That is then reflected across the line y = -12x +5 (orange) to give the orange quadrilateral R"E"S"P", which is a rotation of the pre-image.

The amount of rotation is double the angle between the lines, about 62.7°.

Answer:

Correct options are A and D

Step-by-step explanation:

According to the synthetic division in the diagram you can write down the result of division:

[tex]2x^2+9x-7=(x-(-6))(2x-3)+11,\\ \\2x^2+9x-7=(x+6)(2x-3)+11.[/tex]

Therefore,

When [tex]x= - 6,2{x^2} + 9x -7= 11[/tex] and when [tex]2{x^2} + 9x -7[/tex] is divided by [tex]\left( {x + 6} \right)[/tex], the remainder is 11.Option (A) is correct and option (D) is correct.

Further Explanation:

Given:

Explanation:

The synthetic division can be expressed as follows,

[tex]\begin{aligned}- 6\left| \!{\nderline {\,{2\,\,\,\,\,\,\,\,\,\,9\,\,\,\,\,\,\,\,\,\,\, - 7} \,}} \right.  \hfill\\\,\,\,\,\,\,\underline {\,\,\,\,\,\,\,\, - 12\,\,\,\,\,\,\,\,\,\,\,\,18}  \hfill\\\,\,\,\,\,\,\,\,2\,\,\,\,\,\, - 3\,\,\,\,\,\,\,\,\,\,\,\,11 \hfill \\\end{aligned}[/tex]

The last entry of the synthetic division tells us about remainder and the last entry of the synthetic division is 11. Therefore, the remainder of the synthetic division is 11.

When [tex]x= - 6, 2{x^2} + 9x -7= 11[/tex] and when [tex]2{x^2} + 9x -7[/tex] is divided by [tex]\left( {x + 6} \right)[/tex], the remainder is 11. Option (A) is correct and option (D) is correct.

Learn more:

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Synthetic Division

Keywords: division, factor (x+5), remainder 12, statements, true, apply, divided, binomial synthetic division, long division method, coefficients, quotients, remainders, numerator, denominator, polynomial, zeros, degree.

Try this option:

x²+27=0;

[tex](x+\sqrt{-27})(x- \sqrt{-27})=0; \ => \ \left[\begin{array}{ccc}x=3 \sqrt{3}i\\x=-3 \sqrt{3}i \end{array}\right[/tex]

x = ± 3i√3

given x² + 27 = 0 (subtract 27 from both sides )

x² = - 27 ( take the square root of both sides )

x = ±[tex]\sqrt{-27}[/tex] = ± √(9 × 3 × -1 ) ← (i = √-1 )

  = ± (√9 × √3  ×√-1 ) = ±3i√3

(A) f(a + 2) = a² - 16

substitute x = a + 2 into f(x)

f(a + 2) = (a + 2)² - 4(a + 2) - 12

           = a² + 4a + 4 - 4a - 8 - 12

           = a² - 16

(B ) f(a + h) = a² + 2ah + h² - 4a - 4h - 12

substitute x = a + h into f(x)

f(a + h) = a² + 2ah + h² - 4a - 4h - 12

Answer:

B. 80 km/h

Step-by-step explanation:

The graph is linear and goes through the origin, so distance is proportional to time, and the constant of proportionality is speed. The desired answer can be read from the point on the graph at time = 1 hour: 80 km.

Julian's speed is 80 kilometers per hour.

B

speed = [tex]\frac{distance}{time}[/tex]

From the graph the distance travelled = 480 Km

and time taken = 6 hours

speed = [tex]\frac{480}{6}[/tex] = 80 Km / hour

The point-slope form of a line:

[tex]y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (5, 6) and (3, 4). Substitute:

[tex]m=\dfrac{4-6}{3-5}=\dfrac{-2}{-2}=1\\\\y-6=1(x-5)\\\\y-6=x-5\qquad|\text{add 6 to both sides}\\\\y=x+1\qquad|\text{subtract x from both sides}\\\\-x+y=1\qquad|\text{change the signs}\\\\x-y=-1[/tex]

Answer:

slope-intercept form: y = x + 1

point-slope form: y - 6 = 1(x - 5)

standard form: x - y = -1

Hey there!

Given points:

...(5,6) and (3,4)

Slope-intercept form:

... y=mx+b

'm' is the slope and 'b' is the y-intercept.

Slope:

... (y₂-y₁)/(x₂-x₁)

... (4-6)/(3-5)

... -2/-2

...1

:

... y = x + b

... 4 = 3 + b

... b = 1

Slope-intercept form:

... y = x + 1

Hope helps!

Answer:

14

Step-by-step explanation:

The answer us C. 9/10 minus 3/10 is 6/10 simplified to 3/5 if you need it.

"Enlargement" here implies that the two pentagons are similar.  Because of similarity, the following equation of ratios must be true:  7/15 = x/7.  Then 15x=49, and x = 49/15 = 3.27 cm, approximately.

Rounded to the nearest tenth, that comes to 3.3 cm.

Answer:

B

Step-by-step explanation:

Expressed as a fraction 56 is 56/35 of 35. That fraction can be reduced, and expressed several ways.

56/35 = 8/5 = 1 3/5 = 1.6

56 is 1 3/5 of 35

56 is 1.6 times 35

given h = 600 - 16t ( add 16t to both sides )

16t + h = 600 ( subtract h from both sides )

16t = 600 - h ( divide both sides by 16 )

t = [tex]\frac{600-h}{16}[/tex]

when h = 400

t = [tex]\frac{600-400}{16}[/tex] = [tex]\frac{200}{16}[/tex] = 12.5 seconds

Answer:

The required time is 3.54 seconds approximately or [tex]\frac{5}{2}\sqrt{2}[/tex] seconds.

Step-by-step explanation:

Consider the provided function.

[tex]h(t) = 600-16t^2[/tex]

Where t represents the time in seconds and h represents the height.

It is given that we need to find the time to reach a height of 400 feet.

Substitute h(t)=400 in the above function.

[tex]400= 600-16t^2[/tex]

[tex]400- 600=-16t^2[/tex]

[tex]-200=-16t^2[/tex]

[tex]200=16t^2[/tex]

[tex]\frac{50}{4}=t^2[/tex]

[tex]t=\sqrt{\frac{50}{4}} \\t=\frac{5}{2}\sqrt{2}[/tex]

Neglect the negative value as time should be a positive number.

Or

[tex]t\approx 3.54[/tex]

Hence, the required time is 3.54 seconds approximately.

Since the triangle is equilateral (you can tell by the tick on each side), all angles have the same measure as well.

The angles of a triangle sum up to 180 degress, so three equal angles must measure 60 degrees each.

So, in particular, we have

[tex] 7x+4 = 60 \iff 7x = 56 \iff x=8[/tex]

x = 8 and y = 6

ΔRST is an equilateral triangle

with all 3 sides equal in length and all 3 angles = 60°, hence

7x + 4 = 60 ( subtract 4 from both sides )

7x = 56 ( divide both sides by 7 )

x = 8

similarly

8y + 12 = 60 ( subtract 12 from both sides )

8y = 48 ( divide both sides by 8 )

y = 6

The answer would be 56 because 14X4 = 56

There were 56 girls who tried out for the volleyball team, found by dividing the number of girls on the team (14) by the percentage that made the team (25%), which equals 14 divided by 0.25.

The question asks us to find the total number of girls who tried out for the volleyball team if 14 girls (making up 25% of those who tried) made the team. To calculate the total number of girls who tried out, we can set up the equation based on the percentage:

25% of total girls = 14

We can rewrite 25% as 0.25 in decimal form:

0.25 × total girls = 14

To find the total number of girls, we divide both sides of the equation by 0.25:

total girls = 14 ÷ 0.25

total girls = 56

Therefore, 56 girls tried out for the volleyball team.