You and your friend are selling magazine subscriptions for a fundraiser. After w weeks, you have sold (3w+8) subscriptions and your friend has sold (6w+6) subscriptions.

Answer:

Δ QRS is an obtuse triangle ⇒ according to its angle

Δ QRS is an isosceles triangle ⇒ according to its sides

Step-by-step explanation:

In Δ QRS

∵ m∠Q = 8x - 17

∵ m∠R = 19x + 4

∵ m∠S = 5x + 1

→ The sum of the interior angles of a Δ is 180°

∴ m∠Q + m∠R + m∠S = 180°

→ Substitute their values in the equation above

∵ 8x - 17 + 19x + 4 + 5x + 1 = 180

→ Add the like terms

∴ (8x + 19x + 5x) + (-17 + 4 + 1) = 180

∴ 32x + (-12) = 180

∴ 32x - 12 = 180

→ Add 12 to both sides

∵ 32x - 12 + 12 = 180 + 12

∴ 32x = 192

→ Divide both sides by 32

∵ [tex]\frac{32x}{32}[/tex] = [tex]\frac{192}{32}[/tex]

∴ x = 6

→ Substitute the value of x in each measure of angles to find them

∵ m∠Q = 8(6) - 17 = 48 - 17

∴  m∠Q = 31°

∵ m∠R = 19(6) + 4 = 114 + 4

∴  m∠R = 118°

∵ m∠S = 5(6) + 1 = 30 + 1

∴  m∠S = 31°

∵ m∠R > 90°

∴ ∠R is an obtuse angle

∴ Δ QRS is an obtuse triangle

∵ m∠Q = m∠S

→ In any Δ if two angles are equal in measures, then the two sides

  opposite to these angles are equal in length and the Δ is isosceles

∴ RQ = RS

∴ Δ QRS is an isosceles triangle

There's a pretty simple formula to follow: count of multiples [tex]*[/tex] average of the multiple.

To find the average, we take the smallest multiple of 4 which is in the range of 1 and 150 which is 4 of course. And the largest would be 148 since that's the only number in the range. So now average them: [tex]\frac{4 + 148}{2} = \frac{152}{2} = 76[/tex]

Now we find the count of the multiples which is in the range of 1 to 150. To do that, we use this formula:

[tex]\frac{\text{largest multiple} - \text{smallest multiple}}{n} \\[/tex]

Here, [tex]n[/tex] is 4 so this would be:

[tex]\frac{148-4}{4} = \frac{144}{4} = 36[/tex]

This would give you the exclusive count of all the numbers, but we want the inclusive count so, we simple add 1 so the count would be [tex]37[/tex]

Now following the 1st formula we get: [tex]37 * 76 = 2812[/tex]

So the answer would be 2812! :D

And here's the check too:

Answer:

Answer: -1

Step-by-step explanation:

The Polynomial Remainder Theorem

It states that the remainder of the division of a polynomial f(x) by (x-r) is equal to f(r).

We have the polynomial:

[tex]f(x)=x^3+x^2+x+1[/tex]

And we need to determine if x=1 and/or x=-1 are zeros of the polynomial.

Considering the polynomial remainder theorem, if we try any value for x, and the remainder is zero, then that value of x is a root or zero of the polynomial.

Find:

[tex]f(1)=1^3+1^2+1+1[/tex]

f(1)=4

Thus, x=1 is not a zero of f(x)

Now, find:

[tex]f(-1)=(-1)^3+(-1)^2+(-1)+1[/tex]

[tex]f(1)=-1+1-1+1=0[/tex]

Thus, x=-1 is a zero of f(x)

Answer: -1

Answer:

Zero lines of symmetry

Step-by-step explanation:

Answer:

Step-by-step explanation

Given

The perimeter of a rectangular painting =348 centimeter

the width of the painting=82cm

Solution

Perimeter of the rectangular painting=2(length+width)

2(Length +width)=348

2(Length+82)=348

2l+164=348

2l=348-164

2l=184

Length=184/2

So length =92cm.

Answer:

I don't get it

Step-by-step explanation:

but okay!!!!?!!?!?!?

Answer:

C. $72

Step-by-step explanation:

Answer:

A dot-plot

Step-by-step explanation:

Simply because it would be easier (someone double check my work)

Answer:

8 is the answer.

8 numbers between 8 and 65 are a multiple of 7

Answer:

23 yellow, 30 pink and 12 blue balls

Step-by-step explanation:

Let the number of yellow, pink, blue, and black balls be y, p, b, and x respectively.

From 1st sentence:

y +p +b +x= 90

"60 of them are not pink"

➜ y +b +x= 60

Given that 25 are black, x= 25.

"67 of them are not yellow"

➜ p +b +x= 67

Subst. x= 25 into the above equations:

y +p +b +25= 90

y+ p +b= 65 -----(1)

y +b +25= 60

y +b= 35 -----(2)

p +b +25= 67

p +b= 42 -----(3)

I will rewrite the 3 equations for better clarity:

y +p +b= 65 -----(1)

y +b= 35 -----(2)

p +b= 42 -----(3)

(1) -(2):

p= 65 -35

p= 30

(1) -(3):

y= 65 -42

y= 23

Substitute p= 30 and y= 23 into (1):

23 +30 +b= 65

b= 65 -53

b= 12

Thus, there 23, 30 and 12 yellow, pink and blue balls respectively.

Answer:

65 oop

Step-by-step explanation: o0iiutdgc vhy

Answer:

A

Step-by-step explanation:

The gas will increase

Have a great day

Answer:

D, B

Step-by-step explanation:

You can plug all the numbers in a calculator!! The larger the negative number, the more to the left it goes, while the larger the positive number, the more to the right it goes!

Answer:

-2/3

Step-by-step explanation:

rise over run is 4/-6 = -2/3

Answer:

54 miles

Step-by-step explanation:

86 - 22= 64. 64÷2= 32. BIANCA RAN 32 MILES. 32 + 22= 54. kiera ran 54 miles

Bianca ran 32 miles last month while Kiera ran 54 miles (22 more) for a combined total of 86 miles.

Let x = miles Bianca ran

x + 22 = miles Kiera ran

combined total of their miles is 86 miles

x + (x + 22) = 86

solving for x

2x + 22 = 86

2x = 86 - 22

2x = 64

x = 64 / 2

x = 32

therefore, Bianca ran for 32 miles.

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Answer:

b

Step-by-step explanation:

B.................

Answer:

On the test I took the correct answer is c

Step-by-step explanation:

I took the test

The modulus= 27 and Argument = π/3

The angle inclining from the real axis in the direction of the complex number shown on the complex plane is known as the argument of a complex number.

Given:

z = √3 (cos (π/18) + i sin (π/18))[tex]^{6[/tex]

Now, z = [tex](\sqrt{3}) ^6[/tex] (cos (π/18) + i sin (π/18))[tex]^{6[/tex]

z = 27 (cos (π/18) + i sin (π/18))[tex]^{6[/tex]

As, A complex equation can be expressed as:

z [tex]= |z |e^{i\theta[/tex]

where z= Modulus and [tex]\theta[/tex] is an argument

and, [tex]e^{i\theta =[/tex] cos (π/18) + i sin (π/18)

Then, z = 27 ([tex]e^{i(\(\pi/18)}^6[/tex])

and  [tex]e^{i\theta =[/tex] [tex]e^{i(\(\pi/18)}^6[/tex]

Now comparing

[tex]i\theta =i \pi/18[/tex] x 5

[tex]\theta = \pi/3[/tex]

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Answer:

its 0.12

Step-by-step explanation:

Answer:

(4,0)

Step-by-step explanation:

plz give brainliest!

Answer:

4,0

Step-by-step explanation:

Answer:

9 is the prime of it

Answer:

Prime factorization: 23 is prime. The exponent of prime number 23 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 23 has exactly 2 factors.

Answer:

The answer is 50.

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

It is TRUE to state that "A midpoint of a segment is a point that divides the segment into two congruent segments."

. The midpoint of a segment is a point that divides the segment into two congruent segments of equal length.

It is equidistant from both endpoints, meaning that the distance from either endpoint to the midpoint is the same.

The midpoint splits the segment into two equal parts, creating symmetry. This property is fundamental in geometry and is used in various geometric constructions and calculations involving segments, lines, and shapes.

Learn more about congruent segments at:

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Answer:

2

General Formulas and Concepts:

Step-by-step explanation:

Step 1: Define expression

-2y + 10 + 2y - 8

Step 2: Simplify

Answer:

Step-by-step explanation:

-2y + 10 + 2y - 8 = 20 - 8 = 2

Answer:

5 x n

Step-by-step explanation:

This is the answer because:

1) 5 times a number n is just 5 times n

Hope this helps!

Answer:

A. 7

Step-by-step explanation:

Insanely Easy

Answer:

Maybe A.

Explanation:

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions[1][2]) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena, through Fourier analysis.

Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their side lengths are proportional. Proportionality constants are written within the image: sin θ, cos θ, tan θ, where θ is the common measure of five acute angles.

The trigonometric functions most widely used in modern mathematics are the sine, the cosine, and the tangent. Their reciprocals are respectively the cosecant, the secant, and the cotangent, which are less used. Each of these six trigonometric functions has a corresponding inverse function (called inverse trigonometric function), and an equivalent in the hyperbolic functions as well.[3]

The oldest definitions of trigonometric functions, related to right-angle triangles, define them only for acute angles. To extending these definitions to functions whose domain is the whole projectively extended real line, geometrical definitions using the standard unit circle (i.e., a circle with radius 1 unit) is often used. Modern definitions express trigonometric functions as infinite series or as solutions of differential equations. This allows extending the domain of sine and cosine functions to the whole complex plane, and the domain of the other trigonometric functions to the complex plane (from which some isolated points are removed).

Contents

Right-angled triangle definitions Edit

A right triangle always includes a 90° (π/2 radians) angle, here labeled C. Angles A and B may vary. Trigonometric functions specify the relationships among side lengths and interior angles of a right triangle.

Plot of the six trigonometric functions, the unit circle, and a line for the angle θ = 0.7 radians. The points labelled 1, Sec(θ), Csc(θ) represent the length of the line segment from the origin to that point. Sin(θ), Tan(θ), and 1 are the heights to the line starting from the x-axis, while Cos(θ), 1, and Cot(θ) are lengths along the x-axis starting from the origin.

In this section, the same upper-case letter denotes a vertex of a triangle and the measure of the corresponding angle; the same lower case letter denotes an edge of the triangle and its length.

Given an acute angle A = θ of a right-angled triangle, the hypotenuse h is the side that connects the two acute angles. The side b adjacent to θ is the side of the triangle that connects θ to the right angle. The third side a is said to be opposite to θ.

If the angle θ is given, then all sides of the right-angled triangle are well-defined up to a scaling factor. This means that the ratio of any two side lengths depends only on θ. Thus these six ratios define six functions of θ, which are the trigonometric functions. More precisely, the six trigonometric functions are:[4][5]

sine

{\

Answer:

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

Use slope intercept form: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\frac{-7-5}{1-(-2)}[/tex]= [tex]\frac{-12}{3}[/tex]= -4