Yesterday, Rachel went on a bike ride. Her average speed was 9 miles per hour. Today, she went on another ride, this time averaging 14 mlles per hour. In the two days, she biked for a combined total time of 12 hours. Let x be the number of hours she biked yesterday. Write an expression for the combined total number of miles she biked in the two days.

Circle Terminology:

Center: The point at the center of the circle.

Radius: The distance from the center to any point on the circle.

Diameter: The distance across the circle passing through the center (2 times the radius).

Chord: A line segment connecting two points on the circle.

Arc: A part of the circumference of the circle.

Sector: The region enclosed by two radii and the corresponding arc.

Circle Formulas:

Circumference (C): C = 2πr or C = πd (where r is the radius and d is the diameter).

Area (A): A = πr^2.

Central Angles and Arcs:

Central Angle: An angle whose vertex is at the center of the circle.

Arc Measure: The measure of the central angle that intercepts the arc.

Arc Length: The distance along the circumference of the circle.

Arc Length = (Arc Measure / 360) * Circumference.

Inscribed Angles and Arcs:

Inscribed Angle: An angle formed by two chords with its vertex on the circle.

Inscribed Angle Theorem: An inscribed angle is half the measure of its intercepted arc.

Intercepted Arc: The arc that lies between the endpoints of the inscribed angle.

Tangents:

Tangent: A line that intersects the circle at exactly one point (the point of tangency).

Tangent Theorem: A tangent line is perpendicular to the radius drawn to the point of tangency.

Secants:

Secant: A line that intersects the circle at two points.

Intersecting Chord Theorem: The product of the lengths of the two segments of a secant is equal to the product of the lengths of its external segment.

Relationships Between Angles and Arcs:

Angle-Arc Relationship: The measure of an inscribed angle is half the measure of its intercepted arc.

Angle in a Semicircle: An angle inscribed in a semicircle is a right angle (90 degrees).

Circle Construction:

Circumscribed Circle: A circle that passes through all the vertices of a polygon.

Incircle: A circle that is tangent to all the sides of a polygon.

Remember to practice solving problems involving these concepts, including finding angles, arc measures, lengths, and areas of circles. Additionally, review the properties and relationships between angles and arcs in different scenarios. Good luck with your study and the test!

The new price of the pants, after the discount is applied, is the one in option B:

P = $38.40

We know that the original price of the pants is $64, and we have a discount of 40%.

Then to find the new price of the pants, we need to multiply the original price by a factor (1 - 40%/100%) = (1 - 0.4) = 0.6

Then the new price of the pants, exluding the taxes, we will get that the new price is:

P = $64*0.6

P = $38.40

Then we can see that the correct option is B.

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Answer:

x ≈ 8.1

Step-by-step explanation:

using the cosine ratio in the right triangle

cos36° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{10}[/tex] ( multiply both sides by 10 )

10 × cos36° = x , then

x ≈ 8.1 ( to the nearest tenth )

The values of c  on the interval [-5, 5] are c = -[tex]5^{1/4[/tex]) and c = [tex]5^{1/4[/tex].

According to the Mean Value Theorem for Integrals, if f(x) is continuous on the interval [a, b], then there exists a value c in [a, b] such that:

f(c) = 1/(b-a) . ∫(a to b) f(x) dx

For f(x) = x⁴ on the interval [-5, 5], we have:

∫(-5 to 5) x⁴ dx = (1/5) . (5⁵ - (-5)⁵)/5

= (1/5) . (3125 + 3125)

= 1250

So we need to find c such that f(c) = 1250/10 = 125.

f'(x) = 4x³, so we can use the Mean Value Theorem for Derivatives to find a value of c that satisfies the condition.

f'(c) = (1/(5-(-5)))  . ∫(-5 to 5) f'(x) dx

= (1/10)  . [f(5) - f(-5)]

= (1/10) . [(5⁴) - ((-5)⁴)]

= 100

Therefore, by the Mean Value Theorem for Derivatives, there exists a value c in [-5, 5] such that f'(c) = 100.

Now, we need to check if there exists a value c in [-5, 5] such that f(c) = 125.

f(c) = c⁴, so we need to solve the equation c⁴ = 125.

c = ±[tex]5^{1/4[/tex]

Both of these values are in the interval [-5, 5], so they satisfy the Mean Value Theorem for Integrals.

Therefore, the values of c that satisfy the Mean Value Theorem for integrals for f(x) = x⁴ on the interval [-5, 5] are c = -[tex]5^{1/4[/tex]) and c = [tex]5^{1/4[/tex].

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Answer:

Step-by-step explanation:

Interior angle sum = 180

2x - 45  +  x  =  180

3x  -  45  =  180

x  -  15  =  60

x  =  75

The value of x in trapezoid KFGJ is 40.

Given information:

KFGJ is a trapezoid.

KF = 20

JG = x

MN is midsegment of trapezoid KFGJ.

MN = 30

To find the value of x in trapezoid KFGJ, we can use the fact that the midsegment MN of a trapezoid is parallel to the bases and its length is equal to the average of the lengths of the bases.

In this case, MN is given as 30, and we know that KF is one of the bases with a length of 20. To find the length of the other base JG, we can use the formula for the midsegment of a trapezoid:

MN = (KF + JG) / 2

Substituting the given values, we have:

30 = (20 + x) / 2

To solve for x, we can multiply both sides of the equation by 2:

60 = 20 + x

Subtracting 20 from both sides:

x = 60 - 20

x = 40

Therefore, the value of x in trapezoid KFGJ is 40.

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Reason of congruency for each of the triangle are :

(a) SAS rule

(b) Triangles are not congruent.

Given are some triangles where some of the angles and sides are given to be equal.

We have to find the reason of congruency.

(a) Given two sides are equal.

One of the triangle has an included angle of 110°.

Find the included angle of the other one.

Included angle = 180 - (40 + 30) = 110°

So two sides and included angle of one is equal to the corresponding sides and angle.

So congruency is SAS rule.

(b) Length of the hypotenuse of first triangle = √(2² + 4²) = √20 cm

Length of hypotenuse of other triangle = 4 cm

The lengths are not equal.

So they are not congruent.

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Answers:

Choice A)  Segment AC = 2*sqrt(17)

Choice B)  Segment BD is 32 units long

Choice F)  Segment AB is approximately 33 units long.

==========================================================

Explanation:

The triangles are similar, so we can form this proportion

CD/DA = DA/BD

2/8 = 8/x

2x = 8*8

2x = 64

x = 64/2

x = 32

BD is 32 units long

This means one of the answers is choice B. It rules out choice D.

--------------

The legs of right triangle ABD are

Use the pythagorean theorem to find hypotenuse AB.

a^2 + b^2 = c^2

(AD)^2 + (BD)^2 = (AB)^2

8^2 + 32^2 = (AB)^2

(AB)^2 = 64 + 1024

(AB)^2 = 1088

AB = sqrt(1088)

AB = sqrt(64*17)

AB = sqrt(64)*sqrt(17)

AB = 8*sqrt(17)

AB = 32.984845

Segment AB is approximately 33 units long.

This tells us another answer is choice F. Choice C is false because 4*sqrt(5) = 8.94427

--------------

BC = BD + DC

BC = 32 + 2

BC = 34

BC is the hypotenuse of triangle ABC

Use the pythagorean theorem to determine AC.

a^2 + b^2 = c^2

(AB)^2 + (AC)^2 = (BC)^2

(sqrt(1088))^2 + (AC)^2 = (34)^2

1088 + (AC)^2 = 1156

(AC)^2 = 1156 - 1088

(AC)^2 = 68

AC = sqrt(68)

AC = sqrt(4*17)

AC = sqrt(4)*sqrt(17)

AC = 2*sqrt(17)

Another answer is Choice A. It rules out choice E because 2*sqrt(17) = 8.2462 approximately.

The interest rate for the first period is $287.22

To obtain the first period interest, we use simple interest formula;

Simple Interest = Principal * Rate * Time

Given:

Principal = $45,687.23

Annual interest rate = 7.555%

Interest period = Monthly

Convert the annual interest rate to a monthly interest rate.

Monthly interest = Annual interest/ 12 = 7.555/12 = 0.6295%

Interest = Principal * Monthly interest rate * Time

Since it's the first period, the time is 1 month:

Interest = $45,687.23 * 0.62958333% * 1

Interest = $45,687.23 * 0.0062958333

Interest ≈ $287.22

Therefore, the first period interest is $287.22.

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given that m is parallel to n,

the angle opposite (2x + 16)° is also (2x + 16)° as vertically opposite angles are equal.

using the corresponding angle rule we know that:

2x + 16 = 96

2x = 80

so x = 40

The coefficients used to perform the synthetic division are given by the first option in this problem.

The standard format of the polynomial in this problem is given as follows:

[tex]6x^4 - 7x^3 + x^2 + 3[/tex]

Considering that x has a coefficient of zero, the order of the coefficients of  the polynomial function is given as follows:

6, -7, 1, 0 and 3.

The divisor is of:

x + 4.

Hence the term on the left box is of:

x + 4 = 0 -> x = -4.

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The similarity between the cube and cuboid is that both have 12 edges.

option C.

A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.

So a cube is a three-dimensional solid figure, having 6 square faces and 12 edges.

A cuboid is a three-dimensional geometric shape that looks like a book or a rectangular box.

A cuboid can be defined as a three-dimensional solid shape that has 12 edges, 8 vertices, and 6 faces and each of its faces is rectangular in shape.

So the similarity between a cube and cuboid is that both have 6 faces and 12 edges.

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Answer:  x+2

Step-by-step explanation:

It is not factorable through grouping method.   You can test for factors if you divide the factor and it goes in evenly (no remainder) then, it is a factor.

I will use synthetic division to test:

X-8:

8    |     1         -14        56       -64

     |                  8       -48        64        

           1          -6          8           0         =>no remainder so yes this is a factor

X+2:

-2   |     1         -14        56       -64

     |                 -2        32        -176        

           1         -16        88       -240       => remainder so NOT factor

X-2:

2    |     1         -14        56       -64

     |                  2       -24        64        

           1         -12        32           0        =>no remainder so yes this is a factor

X-4:

4    |     1         -14        56       -64

     |                  4       -40        64        

           1         -10         16           0        =>no remainder so yes this is a factor

_____________________________

_____________________________

Step-by-step explanation:

the headline says "college". that cannot be.

14 out of 33 are men.

so,

14/33 of the students are men.

that's it. nothing else can be done.

let's add a little bit more spice to this and ask also what percentage of the students are men :

for % questions, always find 100% and correspondingly 1%.

everything else can be easily calcite out of this.

100% = 33

1% = 100%/100 = 33/100 = 0.33

how many % of these 33 are 14 ?

as many as times 1% fit into these 14 :

14/0.33 = 42.42424242...%

Answer:

Step-by-step explanation:

To find out how many degrees the tank temperature should increase during the heating hours to maintain the average temperature, we need to calculate the temperature difference between the target average temperature of 67°F and the temperature during the unheated hours (50°F).

The difference in temperature is:

67°F - 50°F = 17°F

Since the heating hours account for the remaining hours of the day, which is 24 hours minus the 14 hours when no heating is required, we have:

24 hours - 14 hours = 10 hours

To maintain the average temperature of 67°F, the tank temperature should increase by 17°F during the 10 hours of heating.

To find the increase per hour, we divide the total temperature increase by the number of heating hours:

17°F / 10 hours = 1.7°F

Therefore, the tank temperature should increase by 1.7°F per hour during the heating hours to maintain the average temperature of 67°F.

The value of arc JK is determined as arc JK = 28⁰.

The value of arc JK is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.

arc JK =  m∠JNK

From the diagram, we have N = 152⁰

m∠JNK = ¹/₂ ( 360 - (152 + 152) (sum of angles at a point)

m∠JNK = 28⁰

The value of arc JK is calculated as follows;

arc JK = 28⁰

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Answer: Let me explain!

Step-by-step explanation:

Well, this is easy, I’ll explain it.
We know the value of these computers are going to go down 20% each year. So since we know that, we can multiply 20 percent by the amount of years, which is 2, so 20 times 2 is 40, so the computers decreased in value by 40 percent!

Now that that’s established, we need to subtract forty percent of 2500, from the original price, 2500.

(To do that, move the decimal place over one to get 250, which is 10%, then multiply by 4, to get 40 percent of 2500, which is 1000, in case you weren’t sure on how to do that :)

Then, subtract 1000 from 2500, and that is your answer!

$1,500

a. Natural numbers: 0, 4.2, √9

b. Whole numbers: -8, 0, 4.2, √9

c. Integers: -8, 0, 4.2, √9

d. Rational numbers: -8, 5/6, 0, 4.2, √9

e. Irrational numbers: √2, π

f. Real numbers: -8, 5/6, 0, 0.1, √2, π, 4.2, √9

We have,

a. Natural numbers:

5/6, 0, 4.2, √9 (The natural numbers are positive integers excluding zero)

b. Whole numbers:

-8, 0, 4.2, √9 (Whole numbers include zero and all positive integers)

c. Integers:

-8, 0, 4.2, √9 (Integers include positive and negative whole numbers, including zero)

d. Rational numbers:

-8, 5/6, 0, 4.2, √9 (Rational numbers can be expressed as a fraction of two integers)

e. Irrational numbers:

√2, π (Irrational numbers cannot be expressed as a fraction and have non-repeating, non-terminating decimal expansions)

f. Real numbers:

-8, 5/6, 0, 0.1, √2, π, 4.2, √9 (Real numbers include all rational and irrational numbers)

Thus,

a. Natural numbers: 0, 4.2, √9

b. Whole numbers: -8, 0, 4.2, √9

c. Integers: -8, 0, 4.2, √9

d. Rational numbers: -8, 5/6, 0, 4.2, √9

e. Irrational numbers: √2, π

f. Real numbers: -8, 5/6, 0, 0.1, √2, π, 4.2, √9

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The complete question.

-8, 5/6, 0, 0.1, √2, π, 4.2, √9

List all numbers from the given set that are a. natural​ numbers, b. whole​ numbers, c.​ integers, d. rational​ numbers, e. irrational​ numbers, and f. real numbers.

Answer:

90 minutos

Step-by-step explanation:

una hora es 60 minutos y media es 30 minutos.

If  the sum of their ages 8 years ago was 48 then the present age​ of girl is 16 years.

Mrs. Sarfo is three times as old as her daughter, so her present age would be 3J years.

8 years ago, Joyce's age would have been J - 8, and Mrs. Sarfo's age would have been 3J - 8.

The sum of their ages 8 years ago was 48:

(J - 8) + (3J - 8) = 48

Simplifying the equation:

4J - 16 = 48

Adding 16 to both sides:

4J = 64

Dividing both sides by 4:

J = 16

Therefore, the present age of Joyce is 16 years.

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Answer:

Step-by-step explanation:

3:7 = ___: 49

3 : 7 = x : 49

x = 3 × 49 ÷ 7

x = 147 ÷ 7

x = 21

3 : 7 = 21 : 49  (your answer)

Answer: Looks like its -.3

Answer:

Step-by-step explanation:

-3.6 + -0.3 = -3.9

-3.9 + -0.3 = -4.2

-4.2 + -0.3 = -4.5

you are adding - 0.3 to each number to get the next number in the sequence

=

+

Answer:

area=20ft^2

Step-by-step explanation:

3ft×4ft=12ft^2

12ft÷2=6ft is the area of the smaller triangle

7ft×4ft=28ft^2

28ft÷2=14ft is the area of the larger triangle

6ft+14ft=20ft^2

The solution of the given inequality is -3<x<4.

The given inequality is,

|6x-3| < 21

Here absolute function is applied in the given expression,

Therefore,

Case 1

⇒ (6x-3) >  -21

⇒   6x-3 > -21

Add 3 both sides,

⇒         6x > -18

⇒         6x > -3

Divide by 6 both sides we get,

⇒           x > -3

Case 2:

⇒  (6x-3) < 21

⇒    6x-3 <  21

Add 3 both sides,

⇒ 6x-3+3 <  21+3

⇒         6x <  21+3

⇒         6x <  24

Divide by 6 both sides we get,

⇒           x <  4

Now plotting the graph of this inequality we get:

-3<x<4 is the solution.

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The graph of the polynomial function y = f(x) in the xy plane could be the first graph.

Given a polynomial function f.

Range of the polynomial function is the set of all the real numbers less than or equal to 4.

So y values are y ≤ 4

So the vertex of the function will be at y = 4 and other value are less than 4.

So parabola is downwards.

Two options are there with the parabola folded downwards.

Now the zeroes of f are at -3 and 1.

Zeroes of f are the values of x where the function touches the X axis.

Hence the correct graph is first one.

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The values of  x and y is x=8 and y=12.

We are given that;

The dimensions=7 and 24

Now,

(x+y)^2= 7^2 + 24^2

x^2+y^2+2ab=49+416

x^2+y^2+2xy=465

Also, 7^2=x2+h2

49=x2+15

x2=49+15

x2=64

x=8

Substituting the values of x

8+y=20

y=12

Therefore, by Pythagoras theorem the answer will be x=8 and y=12.

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The required justification for the solution to the equation is shown in the solution part.

As per the given equation, the required solution would be as follows:

Given:

17/3 - (3/4)x = 1(/2)x + 5

Subtraction property of equality:

17/3 - (3/4)x - 17/3 = 1(/2)x + 5 - 17/3

- (3/4)x =  1(/2)x - 2/3

Addition property of equality:

- (3/4)x - 1(/2)x =  1(/2)x - 2/3 - 1(/2)x

-(5/4)x = -2/3

Multiplication property of equality:

-(5/4)x × -4/5 = -2/3 × -4/5

Simplification:

x = 8/15

The required justification for the solution to the equation is shown in the solution part.

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Answer:

Answer shown in picture.