a). a car cost 34% more today than when it was sold. if the original cost of the car was $90000. find its price today.
b). during a sale, the price of a bicycle dropped from $160 to $125. what was the percentage decrease in price?​

Answer: True

Step-by-step explanation:

Remote interior angles are formed when a side of a triangle is extended beyond the triangle.

Answer:

[tex]c^{9}[/tex][tex]d^{15}[/tex]

Step-by-step explanation:

Answer:9

Step-by-step explanation:

13r-17=21r-89

subtract 13r from 21r so your left with

-17=8r-89

Then add 89 to -17 then you get

72=8r

divide

r=9

As the elevator climbs, the angle of depression to a certain spot on the lobby floor alters. Angle of depression increases.

the arc formed as the line of sight drops from the horizon. The angle of depression is the angle formed when an object is perceived below the observer's height between the horizon and the line of sight of the observer. The depression angle is the angle formed between the line of sight looking down at the object and the horizontal line of sight. If you are on a hill or a building and you are looking down at something, you can tell the slope. To measure these angles, a theodolite or an inclinometer might be employed.

As the elevator climbs, the angle of depression to a certain spot on the lobby floor alters. Angle of the depression increases.

∠x = 65° ≤ ∠XYZ

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The pairs of events that are disjoint and cannot occur at the same time are; Option D: Events A and C

In mathematical set problems, we usually say that two sets are said to be disjointed sets if they have no elements in common.

Since the spinner has 10 sections numbered 1 to 10, then the sample space is;

S = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

We are told that Event A is the event of the Spin of an odd number. Thus;

Event A = { 1, 3, 5, 7, 9 }

Event B: Spin a number greater than 1 Thus;

Event B = { 2, 3, 4, 5, 6, 7, 8, 9, 10}

Event C: Spin a 2. Thus;

Event C = { 2 }

Event D: Spin a multiple of 2. Thus;

Event D = { 2, 4, 6, 8, 10}

Therefore;

A ∩ B = { 3, 5, 7, 9}

B ∩ C = {2}

C ∩ D = { 2 }

A ∩ C = { }

Thus, A ∩ C does not contains any element. So A and C is a disjoint event.

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The statement that best describes Juliet's distance from her home from the graph is; C) It is decreasing in the interval 3 < x < 4 hours.

An interval on a graph is defined as a section of the x-axis that is usually examined to see whether or not the graph is increasing or decreasing throughout that section.

Now, a graph is said to be decreasing through an interval if the x-value increases as the y-value decreases. However, the graph is said to be increasing if the x-values increases as the y-values increase.

Now, looking at the given graph, we can say that between the intervals of 3 < x < 4, the graph is decreasing as it will have a negative slope. However between the intervals of 4 < x < 5, the graph is increasing as it will have a positive slope.

Thus, we can conclude that the correct option is Option C.

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If the H.C.F of Q and R is 4056,the value of a is 13

HCF or Highest Common Factor is the greatest number which divides each of the two or more numbers. HCF is also called the Greatest Common Measure (GCM) and Greatest Common Divisor(GCD).

Q = 2³ × 3 × a³ and R = R=2⁴ × 3² × a²

This means that Q = 24a³ and R = 144a²

The common factors between 24 and 144 are: 1,2,4,6,12 and 24.

And the common factors between a³ and a² are : a, a²

Therefore the highest common factors are 24 and a² = 24a²

4056 is given as the H.C.F

therefore 4056 = 24a²

divide both sides by 24

a² = 169

Therefore a = √169 = 13

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Answer:

18.5 cups

Step-by-step explanation:

There are 2 cups in 1 pint, so 9 1/4 pints is equal to 18.5 cups.

Hope this helps and if you have any more questions just ask in the comments

Answer:

17

Step-by-step explanation:

If you are trying to solve the equation "y-12=c" for y, you would begin by adding 12 to both sides of the equation to obtain "y=c+12". This means that y is equal to the value of c plus 12.

For example, if you were given the equation "y-12=5", you would have "y=5+12" or "y=17".

All measures and angles of sides and angles are:

c = 20

D ≈ 69.2

θ = 37.34°

θ = 120°

c = 11

D = 77.6

θ = 92.87°

c = 13

D = 63.5

θ = 90°

1) We are given;

m<C = 32°

a = 28

b = 13

Since two sides and the opposite angle of an unknown side are given, then we can use law of cosine which is expressed as:

c = √(a² + b² - (2ab*cos C)

Thus;

c = √(18² + 17² - (2*8*17*cos 32°)

c ≈ 19.55

c ≈ 20

2) The length of the longer diagonal of a rhombus is found by the  formula: D = 2a*cos 0.5θ

Where:

D - Length of the larger diagonal.

a - Side length.

θ - Measure of the smaller angle, in degrees.

We are given; a = 36 and θ = 32°. Thus;

D = 2 * 36 * cos (0.5 * 32°)

D ≈ 69.2

3) Using the length of diagonal of rhombus formula as above gives;

D = 2a*cos 0.5θ

We are given;

D = 36 and a = 34

Thus;

36 = 2 * 34 * cos 0.5θ

cos⁻¹36/68 = 0.5θ

18.67 = 0.5θ

θ = 18.67/0.5

θ = 37.34°

4) Applying the law of cosine, we can find the larger angle as;

18² = 10² + 12² - (2 * 10 * 12 * cos θ)

324 = 244 - (240 * cos θ)

244 - 324 = (240 * cos θ)

-120/240 = cos θ

θ = cos⁻¹(-0.5)

θ = 120°

5) By using Law of cosines, we have;

c = √(12² + 14² - (2 * 14 * 12 · cos 38°)

c ≈ 11

6) Still using formula in number 2, we have;

D = 2a*cos 0.5θ

D = 2*40*cos(0.5*28)

77.6

7)  Applying the law of cosine, we can find the larger angle as;

14² = 8² + 12² - (2 * 8 * 12 * cos θ)

196 = 208 - (192 * cos θ)

12 = (240 * cos θ)

12/240 = cos θ

θ = cos⁻¹(-0.05)

θ = 92.87°

8) Still using the using the cosine approach, we have;

We are given;

m<C = 50°

a = 14

b = 15

Since two sides and the opposite angle of an unknown side are given, then we can use law of cosine which is expressed as:

c = √(a² + b² - (2ab*cos C)

Thus;

c = √(14² + 14² - (2*8*17*cos 32°)

c ≈ 12.702

c ≈ 13

9) The length of the longer diagonal of a rhombus is found by the  formula: D = 2a*cos 0.5θ

Where:

D - Length of the larger diagonal.

a - Side length.

θ - Measure of the smaller angle, in degrees.

We are given; a = 34 and θ = 42°. Thus;

D = 2 * 34 * cos (0.5 * 42°)

D ≈ 63.5

10) Applying the law of cosine, we can find the larger angle as;

26² = 22² + 14² - (2 * 22 * 14 * cos θ)

676 = 680 - (616 * cos θ)

4 = (616 * cos θ)

4/616 = cos θ

θ = cos⁻¹(0.065)

θ = 90°

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Answer:

The first figure, fourth and fifth!

First one has 24.

Second one has 30.

Third has 16.

Fourth has 24.

Fifth has 24.

Step-by-step explanation:

Hope it helps!

Answer:

Inequality Form: g≤15

Interval Notation: (−∞,15]

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Detailed explanation and solution is available in the photo. I wish you success. If there is something you do not understand, please do not hesitate to ask.

The sum of the measures of angles D and E and the measure of angle F will be 3x + 35. Then the correct option is C.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The information is given below.

∠D = 3(x + 10)

∠E = (2x + 15)

∠F = 2(x + 10)

The sum of the measures of angle D and E than the measure of angle F is calculated as,

⇒ ∠D + ∠E - ∠F

⇒ 3(x + 10) + 2(x + 10) - (2x + 15)

Simplify the expression, then we have

⇒ 3(x + 10) + 2(x + 10) - (2x + 15)

⇒ 3x + 30 + 2x + 20 - 2x - 15

⇒ 3x + 30 + 5

⇒ 3x + 35

The sum of the measures of angles D and E and the measure of angle F will be 3x + 35. Then the correct option is C.

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The value of expression putting indicated value is -2,4,1.

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here the given expression is [tex]\frac{x}{4}[/tex] .

Now put x=-8 into [tex]\frac{x}{4}[/tex] then,

=> [tex]\frac{-8}{4}[/tex] = -2.

Now put x=16 into [tex]\frac{x}{4}[/tex] then

=>  [tex]\frac{16}{4}[/tex] = 4.

Now put x= 4 into    [tex]\frac{x}{4}[/tex] then

=> [tex]\frac{4}{4}[/tex] = 1.

Hence the value of expression putting indicated value is -2,4,1.

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The statement that is true is that the lowest score in section 2 is higher than the highest score in either of the other sections.

Professor James gave the same test to his three sections of statistics students. On the 35-question test, the highest score was 32 and the lowest was 15.

To determine this, we can look at the boxplots. In section 1, the lowest score is 15 and the highest score is 27. In section 2, the lowest score is 24 and the highest score is 32. In section 3, the lowest score is 20 and the highest score is 28.

Since the lowest score in section 2 (24) is higher than the highest score in either of the other sections (27 and 28, respectively), this statement is true. Therefore the correct option is b.

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Answer:

Step-by-step explanation:

Answer:can you please give brainliest will give answer

Step-by-step explanation:

The equation that is equivalent to the equation 4x + 41 = x + 5 is 3x + 41 = 5

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

/4x+41=x+5

Express the equation properly

So, we have the following representation

4x + 41 = x + 5

Subtract the variable x from both sides of the equation

So, we have the following representation

-x + 4x + 41 = x + 5 - x

Evaluate the difference

So, we have the following representation

3x + 41 = 5

The above equation is equivalent to the equation 4x + 41 = x + 5

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The volume of the solid is a) 1/30 and b) 1/6.

When the solid’s base is located in the xy plane and the cross-section is taken perpendicular to the x-axis with known cross sectional area given by A(x) for all the x in the interval [a,b], then the volume of the solid is given as the definite integral of these cross-sectional areas.

V = ∫_a^b▒A(x)dx

By graphing the given equations, we see that the area is bounded by the line y= x+1 and parabola y=x^2+1 on the interval on x-axis as [0,1].

a) The base of each square has length

f(x) – g(x) = (x + 1) – (x^2 + 1) = x – x^2

and the solid is square.

The area of cross section is

A(x) = (x – x^2)^2 = x^2 – 2x^3 + x^4

Hence, the volume is

∫_0^1▒A(x)dx

∫_0^1▒〖(x^2-2x^3+x^4)dx〗

[1/3 x^3-1/2 x^4+1/5 x^5]1¦0

[1/3 -1/2  +1/5]

1/30

b) The base of each rectangle has length

f(x) – g(x) = x – x^2

and the height of each rectangle is 1.

The area of cross section is

A(x) = (x – x^2)(1) = x - x^2

Hence, the volume is

∫_0^1▒A(x)dx

∫_0^1▒〖(〖x-x〗^2)dx〗

[1/2 x-1/3 x^3]1¦0

[1/2 -1/3]

1/6

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Answer:

  80 cm

Step-by-step explanation:

You want a function of the length of the perimeter belt around three packed circles of radius 10 cm.

Examination of the attached figure shows the length of the belt is the sum of the lengths of the sides of an equilateral triangle with sides 20 cm, and the circumference of a circle with diameter 20 cm.

  triangle perimeter = 3s = 3(20 cm) = 60 cm

  circle circumference = πd = π(20 cm) = 20π cm

The length of the belt is the sum of these, or

  60 cm +20π cm = (60 +20π) cm

Compared to (a +bπ) cm, we find a=60, and b=20. The desired sum is ...

  a +b = 60 +20 = 80

__

Additional comment

You will notice that equilateral triangle PQR in the attached figure has side lengths that are twice the radius of the circle. The straight segments AB, A'B', A"B" are parallel to the triangle sides, and are the same length. (ABPR is a rectangle.)

Each circular arc, BA', for example, is 1/3 of the circumference of the circle, so the total length of all the arcs is the circumference of one 20 cm circle.

The answer choice which best describes the solution of the given equation as represented above is; The equation has no solution.

It follows from the task content that the answer choice which best reflects the solution of the equation be determined.

As evident in the task content; the given equation is;

-6x = -5 ( x - 1 ) - x

-6x = -5x + 5 - x

Therefore, we have that;

-6x = -6x + 5

Add 6x both sides of the equation so that we have;

-6x + 6x = 5

0 = 5......which does not hold true.

Hence, since 0 ≠ 5; it follows that the given equation has no solution.

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Answer:

x = 19

z = 19

Step-by-step explanation:

8x - 88 + 5x + 21 = 180

13x - 67 = 180

13x = 247

x = 19

z = 19

Answer:

A

Step-by-step explanation:

If a slice of chocolate fudge cake contains 7.25 grams of sugar, thr grams of sugar in 2/3 of a slice of chocolate is 4 5/6 grams of sugar

In general, the term proportion refers to a part, share, or amount that is compared to a whole.

Using the definition of proportion, two ratios are in proportion when they are equal.

The number of grams of sugar in the chocolate is calculated using proportions

If a slice of chocolate fudge cake contains 7.25 grams of sugar

1 slice = 7.25 grams of sugar

2/3 slice  = ?

cross multiplying

1 * ? =  2/3 * 7.25

? = 29/6

? = 4 5/6 grams of sugar

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The types of triangles are -

a) Triangle ABE is a right-angled triangle.

b) Triangle BEC is an isosceles triangle.

c) Triangle DEF is an equilateral triangle.

d) Triangle CDF is a scalene triangle.

In general, triangles fall into one of two categories -

Triangles determined by the measurements of their sides - Scalene Triangle, Isosceles Triangle, Equilateral Triangle

Triangles based on their inner angles - Acute Triangle, Obtuse Triangle, Right Triangle

According to the diagram -

a) Triangle ABE has angle A which is 90°. Angle B and Angle E will be 45° each, since the sum of interior angles of the triangle should result in 180°. So, it can be classified as a right-angled triangle.

b) Line segment EC=EF+FC=5+2=7. Now, the line segment BE is also having the measurement of 7. Since, both the sides of triangle BEC are equal, hence it falls under the category of isosceles triangle.

c) Triangle DEF has all the sides equal. Hence, it is an equilateral triangle.

d) In triangle CDF, only one of the side DF=5 is known and other two sides are unknown. The sides are not marked equal and the three interior angles are also unknown. Therefore, this triangle is a scalene triangle.

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Answer:

(9,6)

Step-by-step explanation:

currently, point R is 4 units to the left of line m

after reflecting vertically over line m it must remain 4 units away

therefore R' would be at point (9,6)