Given a triangle with angles of 23, 90, 67, what type of triangle is it: acute, equiangular, obtuse, or right?

Answer:

1.33

Step-by-step explanation:

[tex] 3x({x}^{2} + 2x - 4)[/tex]

[tex]3x \times {x}^{2} = {3x}^{3} [/tex]

[tex]3x \times 2x = 6 {x}^{2} [/tex]

[tex]3x \times - 4 = - 12x[/tex]

[tex]b. \: 3 {x}^{3} + 6 {x}^{2} - 12x[/tex]

Answer:

Option B. [tex]150\°[/tex]

Step-by-step explanation:

we know that

In this problem

[tex](15+15x)=(17x-3)[/tex]

solve for x

[tex]17x-15x=15+3[/tex]

[tex]2x=18[/tex]

[tex]x=9[/tex]

Find the measure of arc BC

[tex]arc\ BC=17x-3=17(9)-3=150\°[/tex]

Answer:

The length of the rectangle is 18 cm

The width of the rectangle is 6 cm

Step-by-step explanation:

Let

x-----> the length of the rectangle

y----> the width of the rectangle

we know that

The perimeter of the rectangle is

[tex]P=2(x+y)[/tex]

we have

[tex]P=48\ cm[/tex]

so

[tex]48=2(x+y)[/tex] ------> equation A

[tex]x=2y+6[/tex] ------> equation B

Substitute equation B in equation A and solve for y

48=2(2y+6+y)

48=2(3y+6)

48=6y+12

6y=48-12

y=36/6=6 cm

Find the value of x

x=2(6)+6=18 cm

The area of the rectangle is

A=xy

A=18*6

A=108 cm^2

Final answer:

To solve for the dimensions of the rectangle, we set up a system of equations based on the given perimeter and the relationship between length and width and solve for both variables.

Explanation:

The student is asked to find the dimensions of a rectangle given the perimeter and a relationship between its length and width. Since the perimeter is 48 cm and the length (L) is 6 cm more than twice the width (W), two equations can be set up: 2L + 2W = 48 and L = 2W + 6. By substituting the second equation into the first, we get 2(2W + 6) + 2W = 48. Simplifying yields 4W + 12 + 2W = 48, which simplifies further to 6W + 12 = 48. Solving for W gives W = 6 cm, and substituting back gives L = 18 cm.

No way to know what reasons you're supposed to choose from...

By definition of tangent,

[tex]\tan\left(x-\dfrac\pi4\right)=\dfrac{\sin\left(x-\frac\pi4\right)}{\cos\left(x-\frac\pi4\right)}[/tex]

The angle sum identities give

[tex]\tan\left(x-\dfrac\pi4\right)=\dfrac{\sin x\cos\frac\pi4-\cos x\sin\frac\pi4}{\cos x\cos\frac\pi4+\sin x\sin\frac\pi4}[/tex]

[tex]cos\dfrac\pi4=\sin\dfrac\pi4=\dfrac1{\sqrt2}[/tex], so we can cancel those terms to get

[tex]\tan\left(x-\dfrac\pi4\right)=\dfrac{\sin x-\cos x}{\sin x+\cos x}[/tex]

as required.

Answer:

C

Step-by-step explanation:

You are given that

Use the rule

[tex]\lim_{x\to x_0}(f(x)+g(x))=\lim_{x\to x_0} f(x)+\lim_{x \to x_0} g(x).[/tex]

In your case,

[tex]\lim_{x\to4}(f+g)(x)=\lim_{x\to4} (f(x)+g(x))= \lim_{x\to4} f(x)+ \lim_{x\to 4} g(x)=5+0=5.[/tex]

Answer:

35 shelves

Step-by-step explanation:

If each shelf holds 36 books and there are a total of 1,260 books, divide 1,260 by 36 to get the number of shelves needed. 1,260/36 = 35 shelves. Think of it like 36 books per shelf and 35 shelves, 36*35 = 1,260.

Marc's son is 14 years old. We found this by creating the equation 3x + 4 = 46 based on the question, solving for x, and determining that x equals 14.

This is a problem that requires an understanding of simultaneous linear equations. Let's denote Marc's son's age as x.

Marc is 4 years older than 3 times his son's age. Therefore, we can write this as: 3x + 4 = 46.

To find the value of x, which represents the son's age, we first subtract 4 from both sides of the equation (3x + 4 - 4 = 46 - 4). Now we have 3x = 42. To get the value of x alone, we will then divide by 3 from both sides of the equation (3x/3 = 42/3). As a result, we'll find out that x equals 14, which means Marc's son is 14 years old.

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If

[tex]f(\theta)=10\cos\theta+5\sin^2\theta[/tex]

then the derivative is

[tex]f'(\theta)=-10\sin\theta+10\sin\theta\cos\theta[/tex]

Critical points occur where [tex]f'(\theta)=0[/tex]. This happens for

[tex]-10\sin\theta+10\sin\theta\cos\theta=0[/tex]

[tex]-10\sin\theta(1-\cos\theta)=0[/tex]

[tex]\implies-10\sin\theta=0\text{ or }1-\cos\theta=0[/tex]

In the first case, we find

[tex]-10\sin\theta=0\implies\sin\theta=0\implies\theta=n\pi[/tex]

In the second,

[tex]1-\cos\theta=0\implies\cos\theta=1\implies\theta=2n\pi[/tex]

So all the critical points occur at multiples of [tex]\pi[/tex], or [tex]n\pi[/tex]. (This includes all the even multiples of [tex]\pi[/tex].)

The critical numbers of the function will be at ([tex]\pi, n\pi[/tex])

Given the function

f(θ) = 10 cos(θ) + 5 sin2(θ)

At the turning point, [tex]\frac{df(\theta)}{d\theta} = 0[/tex]

[tex]\frac{df(\theta)}{d\theta} = -10sin \theta + 5(2sin\theta cos\theta)\\\frac{df(\theta)}{d\theta} = -10sin \theta + 10sin\theta cos\theta\\[/tex]

At the turning point,

[tex]-10sin \theta + 10sin \theta cos \theta=0\\-10sin \theta(1-cos\theta) =0\\-10sin\theta = 0 \ and \ 1-cos\theta =0\\sin\theta =0\\\theta=0 + n\pi\\\\For \ 1-cos\theta =0\\cos\theta = 1\\\theta = cos^{-1}1\\\theta = 0 + n\pi[/tex]

Hence critical numbers of the function will be at ([tex]\pi, n\pi[/tex])

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Answer:

217.01

Step-by-step explanation:

Answer:

Roughly $21.70

Step-by-step explanation:

1,205.62 times 0.018 (1.8% converted into decimal, to do so, move the decimal over to the right two places) equals 21.7

Answer:

R = 48.59 degrees

Step-by-step explanation:

We know that

sin theta = opposite / hypotenuse

sin R = 30/40

sin R = 3/4

Taking the inverse sin of each side

sin^-1 (sin R) = sin ^-1(3/4)

  R = 48.59037789

To the nearest hundredth

R = 48.59 degrees

so the difference is 975 - 828.75 = 146.25.

if we take 975 to be the 100%, how much is 146.25 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 975&100\\ 146.25&x \end{array}\implies \cfrac{975}{146.25}=\cfrac{100}{x}\implies 975x=14625 \\\\\\ x=\cfrac{14625}{975}\implies x=15[/tex]

Answer:

146.25

Step-by-step explanation:

Answer:

Step-by-step explanation:

The triangle is recognizable as a 30°-60°-90° right triangle, which has side length ratios ...

  1 : √3 : 2

Side x is thus twice the length of short side 4, so x = 8.

Side y is √3 times the length of short side x-6 = 2, so y = 2√3.

_____

If you don't happen to recognize the triangle dimensions, you can find x and y using the Pythagorean theorem.

  x = √(4² +(4√3)²) = √64 = 8

  y = √(4² -2²) = √12 = 2√3

the answer is B ln(0.0498)=-3

Answer: option c

Step-by-step explanation:

To solve this problem you must keep on mind the properties of logarithms:

[tex]log(b)-log(a)=log(\frac{b}{a})\\\\log(b)+log(a)=log(ba)\\\\a*log(b)=log(b)^a[/tex]

Therefore, knowing the properties, you can write the expression gven in the problem as shown below:

[tex]2logx-6log(x-9)\\logx^2-log(x-9)^6\\\\log\frac{x^2}{(x-9)^6}[/tex]

Answer:

c edge

Step-by-step explanation:

Answer:

2:3.

Step-by-step explanation:

The number of children = 2+ 4 = 6.

So the required ratio is 4:6 which simplifies to 2:3.

Answer:

2.3

is yo sex answer

Answer: second option.

Step-by-step explanation:

The equation  of the line in slope-intercept form is:

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

Where m is the slope of the line and b the y-intercept.

We know that we can calculate the slope with:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Therefore, keeping the above on mind, you have that:

- If the line moves upward from the left to right, then the slope is positive.

-  If the line moves down from the left to right, then the slope is negative.

Then, if the slope described moves 3 units down and 5 units to the right, the it is negative. Therefore:

[tex]m=-\frac{3}{5}[/tex]

Answer:

[tex]-\frac{3}{5}[/tex]

Step-by-step explanation:

We are to identify the slope of a line which is described as:

'down 3 and right 5'

We know that a straight line which is sloping downwards from left to right has  a negative slope.

And a straight line which goes upwards from left to right side has a positive slope.

According to the describe slope of a line, it goes 3 units down and 5 units right so it makes a negative slope which is equal to [tex]-\frac{3}{5}[/tex].

Answer:

112

Step-by-step explanation:

Answer:

b. [tex]x\approx -2.426[/tex]

Step-by-step explanation:

The given equation is;

[tex]x^3+x^2+10x+15=0[/tex]

We solve by the x-intercept method. We need to graph the corresponding function using a graphing tool.

The corresponding function is

[tex]f(x)=x^3+x^2+10x+15[/tex]

The solution to [tex]x^3+x^2+10x+15=0[/tex] is where the graph touches the x-axis.

We can see from the graph  that; the x-intercept is;

(-2.426,0)

Therefore the real solution is:

[tex]x\approx -2.426[/tex]

Answer:

b. x ≈ -2.426

Step-by-step explanation:

Given that we have possible roots we can replace these values into the equation and check if it is satisfied.

option a: 2.426^3+4*2.426^2+10*2.426+15 = 77.08 ≠ 0

option b: (-2.426)^3+4*(-2.426)^2+10*(-2.426)+15 ≈ 0

option c: 5.128^3+4*5.128^2+10*5.128+15 = 306.31 ≠ 0

option d: (-5.128)^3+4*(-5.128)^2+10*(-5.128)+15 = -65.94 ≠ 0

Answer:

The answer is 28

Step-by-step explanation:

The total number of work hours in 7 days will be 28 hours.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Randle plans to work 8 hours every two days. The total work hours in 7 days will be calculated as,

Number of hours for 6 days,

N = (6 / 2) x 8

N = 24 hours

Number of hours for 1 day,

N = 8 / 2 = 4 hours

Total hours = 24 + 4 = 28 hours

Therefore, the total number of work hours in 7 days will be 28 hours

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Answer:

[tex]0.5\frac{lb}{person}[/tex]

Step-by-step explanation:

we know that

To find out how many pounds of fries each person will receive, divide the total pounds of fries by the total number of people.

so

[tex]\frac{2}{4} \frac{lb}{persons}=0.5\frac{lb}{person}[/tex]

Each person will receive 0.5lb of fries.

To solve this problem, we need to divide the total weight of the French fries by the number of people sharing them. Carmen has prepared a 2lb bag of French fries for 4 people. To find out how much each person will get, we divide the total weight of the fries by the number of people:

[tex]\[ \text{Fries per person} = \frac{\text{Total weight of fries}}{\text{Number of people}} \][/tex]

[tex]\[ \text{Fries per person} = \frac{2 \text{lb}}{4} \] \[ \text{Fries per person} = 0.5 \text{lb} \][/tex]

So, each person will receive 0.5lb of fries.

Solve for r in the first equation:

3(r+300) = 6

Use the distributive property:

3r + 900 = 6

Subtract 900 from both sides:

3r = -894

Divide both sides by 3:

r = -894 / 3

r = -298

Now you have r, replace r in the second equation and solve:

r +300 -2 =

-298 + 300 - 2 = 0

The answer is 0.

Answer:

0 is the value of r+300-2

Solve for r in the first equation:

3(r+300) = 6

Use the distributive property:

3r + 900 = 6

Subtract 900 from both sides:

3r = -894

Divide both sides by 3:

r = -894 / 3

r = -298

Now you have r, replace r in the second equation and solve:

r +300 -2 =

-298 + 300 - 2 = 0

The answer is 0.

Only (A) and (B) are true.

Variable distributions:

X: Since we are sampling a specific number (20) of individuals with a known probability of color blindness (8%), X follows a binomial distribution with n = 20 and p = 0.08.

Y: Similarly, Y follows a binomial distribution with n = 40 and p = 0.01.

Z: Z is not a simple binomial because it combines two independent binomial variables (X and Y) with different parameters. Therefore, Z's distribution is not directly binomial.

Probability of 2 color-blind males:

Using the binomial probability formula for X, the probability of exactly 2 color-blind males (out of 20) is:

P(X = 2) = 20C2 * 0.08^2 * (1 - 0.08)^18 ≈ 0.2711

Therefore, only statements (A) and (B) are true:

(A) True: X is binomial with n = 20 and p = 0.08.

(B) True: Y is binomial with n = 40 and p = 0.01.

Statements (C), (D), and the answer choices for the probability of 2 color-blind males are incorrect.

Answer:

the answer is c for apex

Step-by-step explanation:

Answer:

a. [tex]x=-1,2,\:or\:6[/tex]

Step-by-step explanation:

The given equation is

[tex]x^3-7x^2+4x+12=0[/tex]

To find all real solutions using the x-intercept method, we to graph the corresponding function using a graphing tool.

The corresponding function is;

[tex]f(x)=x^3-7x^2+4x+12[/tex]

The real solutions to [tex]x^3-7x^2+4x+12=0[/tex], are the x-intercepts of the graph of the corresponding function.

From the graph the x-intercepts are

(-1,0),(2,0) and (6,0).

Therefore the real solutions are

[tex]x=-1,2,\:or\:6[/tex]

Answer:

350

Step-by-step explanation:

First let's see if (8, -2) can be written as a linear combination of (1, 1) and (1, -1): we want to find [tex]c_1,c_2[/tex] such that

[tex]c_1(1,1)+c_2(1,-1)=(8,-2)\implies\begin{cases}c_1+c_2=8\\c_1-c_2=-2\end{cases}[/tex]

Easily done; we find [tex]c_1=3[/tex] and [tex]c_2=5[/tex].

Since [tex]T[/tex] is linear, we have

[tex]T(8,-2)=T(3(1,1)+5(1,-1))=3T(1,1)+5T(1,-1)=3(4,3)+5(-1,1)[/tex]

[tex]T(8,-2)=(7,14)[/tex]

t(x₁, x) = (1.5x₁ + 2.5x₂, 2 x₁ + x₂). And, t(8, -2) = (7, 14)

To find the linear transformation t applied to an arbitrary vector (x₁, x₂), we begin by expressing (x₁, x₂) as a linear combination of v₁ and v₂. Given t(v₁) = (4,3) and t(v₂) = (-1,1), we can use these results to construct the transformation.

Let's express any given vector (x₁, x₂):

v₂ = (1, -1)

An arbitrary vector (x₁, x₂) can be written as a linear combination of v₁ and v₂:

(x₁, x₂) = a * v₁ + b * v₂

Hence,

x₁ = a + b

[tex]b = \frac{(x_1, x_2)}{2}[/tex]

We apply the transformation t:

t(x₁, x₂) = a * t(v₁) + b * t(v₂) = [tex](\frac{((x_1 + x_2) * (4, 3)}{ 2} + \frac{((x_1 - x_2) * (-1, 1) }{ 2})[/tex]

Expanding, Combining terms we get:

t(x₁, x) = (1.5x₁ + 2.5x₂, 2 x₁ + x₂)

To find t(8, -2):

t(8, -2) = (1.5 * 8 + 2.5 * (-2), 2 * 8 + (-2))

This gives:

t(8, -2) = (12 - 5, 16 - 2) = (7, 14)

Answer:

D

Step-by-step explanation:

The equation of the circle is (x-x0)^2 + (y-y0)^2 = r^2, where (x0,y0) is the center of the circle. Radius is the distance from any point to the center. Using distance formula you get r = 3.

The equation of the circle having center at point (4,1) and passing through the point (4,-2) is Option (D) [tex](x - 4)^{2} + (y - 1)^{2} = 9[/tex]

A circle having radius r and having center at (x0,y0) can be represented by the parametric equation as -

[tex](x - x0)^{2} + (y - y0)^{2} = r^{2}[/tex]

Any point say (x1,y1) which lies on the circle, must satisfy the given parametric equation of the circle.  

Given that the point (4,-2) lies on the circle. Also the center of circle is at (4,1). Therefore, calculating the radius of the circle which is the distance from the center to the point lying on the circle.

Using distance formula,

radius = [tex]\sqrt{(4 - 4)^{2} + (-2 - 1)^{2} }[/tex]  =  [tex]\sqrt{9 }[/tex] = [tex]3[/tex]

Thus forming the equation of circle from the general parametric equation,

⇒  [tex](x - 4)^{2} + (y - 1)^{2} = 3^{2}[/tex]

∴   [tex](x - 4)^{2} + (y - 1)^{2} = 9[/tex]

Therefore the equation of circle is Option (D) [tex](x - 4)^{2} + (y - 1)^{2} = 9[/tex]

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Answer:

The list in order from the one with least volume to the one with the greatest volume is

case C) A square pyramid with base edges 6 cm and height 6 cm

case A) A cube with edge 5 cm

case E) A rectangular prism with a 5 cm-by-5 cm base and height 6 cm

case D) A cone with radius 4 cm and height 9 cm

case B) A cylinder with radius 4 cm and height 4 cm

Step-by-step explanation:

To solve this problem calculate the volume of each solid

case A) A cube with edge 5 cm

The volume of a cube is equal to

[tex]V=b^{3}[/tex]

where

b is the length side of the cube

substitute the value

[tex]V=5^{3}=125\ cm^{3}[/tex]

case B) A cylinder with radius 4 cm and height 4 cm

The volume of a cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

substitute the value

[tex]V=(3.14)(4)^{2} (4)=200.96\ cm^{3}[/tex]

case C) A square pyramid with base edges 6 cm and height 6 cm

The volume of a pyramid is equal to

[tex]V=\frac{1}{3}Bh[/tex]

where

B is the area of the base

h is the height of the pyramid

Find the area of the base B

[tex]B=6^{2}=36\ cm^{2}[/tex] ----> is a square

substitute the values

[tex]V=\frac{1}{3}(36)(6)=72\ cm^{3}[/tex]

case D) A cone with radius 4 cm and height 9 cm

The volume of a cone is equal to

[tex]V=\frac{1}{3}Bh[/tex]

where

B is the area of the base

h is the height of the cone

Find the area of the base B

[tex]B=\pi r^{2}=(3.14)(4^{2})=50.24\ cm^{2}[/tex] ----> is a circle

substitute the values

[tex]V=\frac{1}{3}(50.24)(9)=150.72\ cm^{3}[/tex]

case E) A rectangular prism with a 5 cm-by-5 cm base and height 6 cm

The volume of a rectangular prism is equal to

[tex]V=LWH[/tex]

substitute the values

[tex]V=(5)(5)(6)=150\ cm^{3}[/tex]

therefore

The list in order from the one with least volume to the one with the greatest volume is

case C) A square pyramid with base edges 6 cm and height 6 cm

case A) A cube with edge 5 cm

case E) A rectangular prism with a 5 cm-by-5 cm base and height 6 cm

case D) A cone with radius 4 cm and height 9 cm

case B) A cylinder with radius 4 cm and height 4 cm

Answer:

Train B is traveling faster at a speed of 120 MPH

How to solve:

Train A is 840/7.5 = 112 which is the MPH so its 112 MPH

Train B is 1080/9 = 120 MPH

Final answer:

Train B is the faster train with an average speed of 120 miles per hour, compared to Train A which has an average speed of 112 miles per hour.

Explanation:

The question is asking to compare the average speed of two trains. To find the average speed, we divide the total distance traveled by the time taken. For Train A, it travels 840 miles in 7.5 hours, and for Train B, it travels 1080 miles in 9 hours.

Calculating the average speed of Train A: 840 miles / 7.5 hours = 112 miles per hour.

Calculating the average speed of Train B: 1080 miles / 9 hours = 120 miles per hour.

Therefore, Train B is traveling at the fastest speed with an average of 120 miles per hour.