A triangle has side lengths:
5,13,12 Is this triangle a right triangle, an acute triangle of an obtuse triangle?

Answer:

The conic is ellipse of equation (x - 1)²/22 + (y + 4)²/44 = 1

Step-by-step explanation:

* Lets revise how to identify the type of the conic  

- Rewrite the equation in the general form,  

 Ax² + Bxy + Cy² + Dx + Ey + F = 0  

- Identify the values of A and C from the general form.  

- If A and C are nonzero, have the same sign, and are not equal  

 to each other, then the graph is an ellipse.  

- If A and C are equal and nonzero and have the same sign, then  

 the graph is a circle  

- If A and C are nonzero and have opposite signs, and are not equal  

then the graph is a hyperbola.  

- If either A or C is zero, then the graph is a parabola  

* Now lets solve the problem

The equation is 4x² + 2y² - 8x + 16y - 52 = 0

∴ A = 4 and C = 2 ⇒ same sign and different values

∴ The equation is ellipse

* The standard form of the ellipse is

  (x - h)²/a² + (y - k)²/b² = 1

- Lets try to make this form from the general form

- Group terms that contain the same variable, and move the

  constant to the opposite side of the equation

∴ (4x² - 8x) + (2y² + 16y) = 52

- Factorize the coefficients of the squared terms

∴ 4(x² - 2x) + 2(y² + 8y) = 52

- Complete the square for x and y

# To make completing square

- Divide the coefficient  of x (or y) by 2 and then square the answer

- Add and subtract this square number and form the bracket of

 the completing the square

# 2 ÷ 2 = 1 ⇒ (1)² = 1 ⇒ add and subtract 1

∴ 4[(x² - 2x + 1) - 1] = 4(x² - 2x + 1) - 4

- Rewrite as perfect squares ⇒ 4(x -1)² - 4

# 8 ÷ 2 = 4 ⇒ (4)² = 16 ⇒ add and subtract 16

∴ 2[(y² + 8y + 16) - 16] = 2(y² + 8y + 16)² - 32

- Rewrite as perfect squares ⇒ 2(y + 4)² - 32

∴ 4(x - 1)² - 4 + 2(y + 4)² - 32 = 52

∴ 4(x - 1)² - 4 + 2(y + 4)² = 32 + 4 + 52

∴ 4(x - 1)² + 2(y + 4)² = 88 ⇒ divide all terms by 88

∴ (x - 1)²/22 + (y + 4)²/44 = 1

Answer:

The lateral area is [tex]4,608\pi\ in^{2}[/tex]  or  [tex]32\pi\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The lateral area of a cylinder (pillar) is equal to

[tex]LA=2\pi rh[/tex]

Remember that

1 ft=12 in

Find the lateral area in square inches

we have

[tex]r=8\ in[/tex]

[tex]h=24\ ft[/tex] ----> convert to inches

[tex]h=24*12=288\ in[/tex]

substitute the values

[tex]LA=2\pi (8)(288)[/tex]

[tex]LA=4,608\pi\ in^{2}[/tex]

Find the lateral area in square feet

we have

[tex]h=24\ ft[/tex]

[tex]r=8\ in[/tex] -----> convert to feet

[tex]r=8/12=(2/3)\ ft[/tex]

substitute the values

[tex]LA=2\pi (2/3)(24)[/tex]

[tex]LA=32\pi\ ft^{2}[/tex]

Answer:

11.1 years

Step-by-step explanation:

The formula for interest compounding continuously is:

[tex]A(t)=Pe^{rt}[/tex]

Where A(t) is the amount after the compounding, P is the initial deposit, r is the interest rate in decimal form, and t is the time in years.  Filling in what we have looks like this:

[tex]2000=1150e^{{.05t}[/tex]

We will simplify this first a bit by dividing 2000 by 1150 to get

[tex]1.739130435=e^{.05t}[/tex]

To get that t out the exponential position it is currently in we have to take the natural log of both sides.  Since a natural log has a base of e, taking the natual log of e cancels both of them out.  They "undo" each other, for lack of a better way to explain it.  That leaves us with

ln(1.739130435)=.05t

Taking the natural log of that decimal on our calculator gives us

.5533852383=.05t

Now divide both sides by .05 to get t = 11.06770477 which rounds to 11.1 years.

Answer:

There is no real number root

Step-by-step explanation:

There is no real number root because there is a negative number inside the root.

No real number root

Answer:

i have provided some pictures to help you i cant post the graphs though cuz they dont allow me to but if you need them i can send link pictures  :)

i also love you're Naruto profile picture uwu

Jeanne can use a system of inequalities to make at least $75.

Let X represent babysitting hours = $6 per hour.

Y represent tutoring hours = $10 per hour.

If she will work more 7.5hours or more than 7.5 hours she can make $75 easily.

$10 per hour × 7 hours = $70

& $6 per hour × 1 hour = $6

so, $70 + $6 = $76.

In the above way she can make easily $75.

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Answer:

She will receive [tex]\$5[/tex]

Step-by-step explanation:

step 1

Find the total cost

The total cost is equal to

[tex]5(\$6.00)+4(\$7.50)=\$60[/tex]

step 2

Find the difference

[tex]\$65-\$60=\$5[/tex]

Answer:

$5

Step-by-step explanation:

65-6x5-4x7.5=5

No there is no variability cause the answers will always be the same

this would be a non-stat question

Answer:

its going to have to be option c

Step-by-step explanation:

because it shows all the listings of cars next to her

Answer:  D) sample: local listings and internet sites

                    population: all used passenger cars

Step-by-step explanation:

A sample is a subset of items from a larger population.

A population includes all of the elements from a set of data.

Cynthia wants to buy a used passenger car.

All available used cars is the POPULATION

Cynthia looks at local listings and on internet sites.

This is a subset of all available used cars so this is the SAMPLE

Furthermore, she may not find what she is looking for and may expand her subset to include used car lots, etc.

1.Observation study

2.Survey

3.Experiment

4.Survey

Hope thiz help:)

In choosing between a survey, experiment, or observational study, consider the requirements of your study and the nature of the data you hope to collect. Surveys are good for widespread data, experiments allow control of variables, and observational studies are good for observing natural behavior.

The best way to gather information in research scenarios depends on the nature of the scenarios in question. However, here are brief descriptions for each method:

Depending on the scenario, choose the method that fits best with the data needed and the practical considerations of conducting the study.

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Answer:

B

Step-by-step explanation:

The intercepted angle is given as "34x+4"

The arc is 196.

Any intercepted angle of an arc that falls in the opposite circumference, it will have a measure half that of the arc intercepted.

Hence,

34x+4 = (0.5)(196)

34x + 4 = 98

34x = 98 - 4

34x = 94

x = 94/34 = 2.76

Answer choice B is right.

For this case we have that, by definition, the volume of the cylinder is given by:

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

Where:

h: It's the height

A: It's the radio

We have to:

[tex]h = 15\\r = 12[/tex]

Substituting:

[tex]V = \pi * (12) ^ 2 * 15\\V = \pi * 144 * 15\\V = 2160 \pi \ units ^ 3[/tex]

Answer:

Option B

Answer: 2160

Step-by-step explanation:

apex

Answer:

d = 7.071068

Step-by-step explanation:

[tex]\vec r(t)=t^2\,\vec\imath+t^3\,\vec\jmath-2t\,\vec k[/tex]

[tex]\mathrm d\vec r=(2t\,\vec\imath+3t^2\,\vec\jmath-2\,\vec k)\,\mathrm dt[/tex]

[tex]\vec f(x,y,z)=(x+y^2)\,\vec\imath+xz\,\vec\jmath+(y+z)\,\vec k[/tex]

[tex]\vec f(x(t),y(t),z(t))=(t^2+t^6)\,\vec\imath-2t^3\,\vec\jmath+(t^3-2t)\,\vec k[/tex]

The line integral is

[tex]\displaystyle\int_C\vec f\cdot\mathrm d\vec r=\int_0^2\bigg((t^2+t^6)\,\vec\imath-2t^3\,\vec\jmath+(t^3-2t)\,\vec k\bigg)\cdot(2t\,\vec\imath+3t^2\,\vec\jmath-2\,\vec k)\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^2(2t^7-6t^5+4t)\,\mathrm dt=\boxed{8}[/tex]

Given:

[tex]\to \bold{\int_{c} \ F \cdot dx}[/tex]

Where

[tex]\to \bold{F(x,y,z)=(x+y^2)i+xzj+(y+z)K}[/tex] and C is given by the vector function [tex]\bold{r(t)}[/tex].

[tex]\to \bold{r(t)=t^2i+t^3j-2tk,\ \ 0\leq t\leq 2}\\\\\to \bold{dx=(2ti+3t^2j-2k)dt}\\\\[/tex]

therefore

[tex]\to \bold{x=t^2}\\\\ \to \bold{y=t^3}\\\\ \to \bold{z=2t}\\\\\to \bold{F(r)=(t^2+(t^3)^2)i+t^2(-2t)j+(t^3-2t)k}\\\\[/tex]

            [tex]\bold{=(t^2+t^6)i-2t^3j+(t^3-2t)k}\\\\[/tex]

[tex]\bold{\therefore}\\\\\bold{F(r).dx=((t^2+t^6)i-2t^3j+(t^3-2t)k).(2ti+3t^2j-2k)}\\\\[/tex]

             [tex]=\bold{((t^2+t^6)2t-2t^3(3t^2)+(t^3-2t)(-2)]dt}\\\\=\bold{(2t^3+2t^7-6t^5-2t^3+4t)dt}\\\\=\bold{(2t^7-6t^5+4t)dt}\\\\[/tex]

Calculating the line integral:

[tex]\bold{\int_{c}\ F .dx=\int^{2}_{t=0} (2t^7-6t^5+4t)dt}\\\\[/tex]

               [tex]=\bold{[\frac{t^8}{4}-t^6+2t^2]^{2}_{0}}\\\\=\bold{\frac{2^8}{4}-2^6+2(2)^2}\\\\=\bold{\frac{256}{4}-64+2(4)}\\\\=\bold{64-64+8}\\\\=\bold{8}[/tex]

Therefore the final answer "8".

Learn more:

line integral: brainly.com/question/16571684

Answer:

  b = 10

Step-by-step explanation:

a) Solve by inspection. b=10 makes both fractions equal to 1.

Both the numerator and denominator of the fraction on the right are 2 greater than those of the fraction on the left. The fractions will be equal when numerator and denominator are equal.

__

b) Multiply by 60 and solve in the usual way.

  6b = 5(b+2)

  b = 10 . . . . . . . . . . subtract 5b

__

c) Expand the fraction on the right, subtract the variable term.

  b/10 = b/12 + 2/12

  b(1/10 - 1/12) = 1/6

  b/60 = 1/6 . . . . simplify

  b = 60/6 = 10 . . . . multiply by 60

_____

Comment on the question

There is no "y", so you cannot solve for y. This is another example of poor quality control (editing) of math curriculum materials. It is my sincere wish that you not have to put up with that. Math is tough enough without this added confusion.

Answer:

b=10

Step-by-step explanation:

Answer:

option C

y = 2

Step-by-step explanation:

Given in the question,

a co-ordinate = (-2,2)

x = -2

y = 2

Equation of the straight line

y = mx + c

here m = gradient of the line

        c = y - intercept

plug value in the equation above

y = (0)x + 2

y = 2

The true annual interest rate for this loan is approximately 1.44 or 144%.

The Breakdown

To calculate the true annual interest rate, we can use the formula for calculating the interest rate on a loan:

True Annual Interest Rate = [(Monthly Payment Amount × Number of Payments) / Loan Amount - 1] × 12

Given the information provided:

Loan Amount = $3,000

Number of Payments = 36

Monthly Payment Amount = $93.33

Substituting these values into the formula:

True Annual Interest Rate = [(93.33 × 36) / 3000 - 1] × 12

Calculating this expression:

True Annual Interest Rate = [(3360 / 3000) - 1] × 12

True Annual Interest Rate = (1.12 - 1) × 12

True Annual Interest Rate = 0.12 × 12

True Annual Interest Rate = 1.44

Therefore, the true annual interest rate for this loan is 1.44 or 144%.

Answer:

Vol. of the composite figure is 189 m³

Step-by-step explanation:

Find the volume of the larger figure by mult. together its 3 dimensions:

V = (9 m)(8 m)(3 m) = 216 m³.

Next, find the volume of the "notch," which is (3 m)³, or 27 m³.

Finally, subtract the "notch" volume from the 216 m³ volume found earlier:

216 m³ - 27 m³ = 189 m³

Answer:

see explanation

Step-by-step explanation:

There are 2 possible positions for n, that is

- 2 - 1.5 = - 3.5

OR

- 2 + 1.5 = - 0.5

Both are 1.5 units distance from - 2

The possible values of n are -0.5 and -3.5

Step-by-step explanation:

Analyze two cases

1) n-(-2)=1.5

Solve for n

n+2=1.5

n=1.5-2

n=-0.5

2) -2-n=1.5

n=-2-1.5

n=-3.5

Answer:

The length of the escalator ≈ 1088.8 ft ⇒ answer (b)

Step-by-step explanation:

* Lets explain the problem

- Consider the escalator and the vertical raise formed a right

 angle triangle

- The length of the escalator is the hypotenuse

- The vertical rise is on leg of the right triangle

- The angle of elevation is the angle between the hypotenuse

  and the horizontal

* Now lets solve the problem

∵ Angle of elevation = 10° 21' 36"

∵ Vertical distance = 195.8 feet

* The vertical is opposite to the angle of elevation

∴ sin angel of elevation= the vertical/the length of the escalator

∴ sin(10° 21' 36") = 195.8/the length of the escalator

- By using cross multiplication

∴ The length of the escalator = 195.8/sin(10° 21' 36") = 1088.8 feet

* The length of the escalator = 1088.8 ft

approximately 0.3 or 3/10 pizza was left for Julio to eat.

mind you some numbers were rounded. if you want the exact number then it's 9/28 which is equal to 0.32.

hope this helps

After accounting for the amounts of pizza eaten by Julio's family (parents, brothers, and sisters), you find that there was approximately 0.36 pizzas left for Julio to eat.

This question deals with some basic arithmetic and fractions. Start by counting how many pizzas Julio's family ate altogether. His parents ate 3/7 of one pizza, his brothers ate 2 3/4 pizzas, and his sisters ate 2 1/2 pizzas.

To add these amounts together, you might find it easiest to convert all the fractions to sevenths. The brothers ate 2 4/7 pizzas (as 4/7 is equivalent to 1/2) and the sisters ate 2 3.5/7 pizzas (as 3.5/7 is equivalent to 1/2). Add these to the 3/7 pizza the parents ate, you find the family ate a total of approximately 5.64 pizzas.

Since Julio's family ordered 6 pizzas in total, you then subtract the total amount eaten by the family from 6, which is approximately 0.36 pizzas. Therefore, Julio was left with 0.36 pizzas to eat.

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Answer:

The equation of the curve is y = x² + 3x

Step-by-step explanation:

I get your drift, but wish you had stated specifically that you wanted to find the equation of this curve.

Slope of tangent line to curve is dy/dx = 2x + 3.

Integrating that with respect to x yields y = x² + 3x + C.

The point (-3, 0) must satisfy this equation:

0 = (-3)² + 3(-3) + C, so C = 0.

The equation of the curve is y = x² + 3x

The equation of the curve where the slope at any point is 2x + 3 and it passes through the point (-3, 0) is y = x² + 3x.

The student's question involves finding the equation of a curve given that at each point (x, y) on the curve, the slope is 2x + 3, and the curve passes through the point (-3, 0). This is a problem that involves differential equations, as it asks us to find a function y(x) whose derivative with respect to x is given.

To find the equation of the curve, we integrate the slope function. Since the slope at any point is 2x + 3, we have:
∂y/∂x = 2x + 3
Integrating both sides with respect to x gives:
y = x² + 3x + C

To find the constant of integration C, we use the fact that the curve passes through (-3, 0). Substituting these values into the equation gives:
0 = (-3)² + 3(-3) + C
0 = 9 - 9 + C
Thus, C = 0, and the equation of the curve is:
y = x² + 3x.

Check the picture below.

Answer: 414.48

Step-by-step explanation:

r: the radius of the base

h: height

The volume of a cone is given by:

V = π ∙ r2 ∙ h / 3,

where π ∙ r2 is the base area of the cone.

π defines the ratio of any circle's circumference to its diameter and is approximately equal to 3.141593, however the value 3.14 is often used.

Answer:

V = 414.7 m3

Step-by-step explanation:

Thats your answer :))

Answer:

Median

Step-by-step explanation:

This set of data has an extreme outlier, which will throw off the mean. The median, on the other hand, does not change or changes minimally whether or not the outlier is there.

By default, the mean is always better, but if an outlier, such as this one, is too large, the median is better.

Answer:

B

Step-by-step explanation:

This is easier to follow if you write it out the long way.

g(x) = (x + 3)/x

g(f(x)) = (f(x) + 3)/f(x)

g(x^2 - 7) = (x^2 + 7 + 3)/(x^2 + 7)

g(x^2 - 7) = (x^2 +10 ) / (x^2 + 7)

g(-5) = ( (-5)^2 + 10) / ( (-5)^2 + 7)

g(-5) = ( 25 + 10) / (25 + 7)

g(-5) = 35/32

The answer is D. 36pi units^3

Hope this helps!

The formula for cylinder volume is: pi*r^2*h

For this case we have that the volume of the cylinder is given by:

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

Where:

h: It is the height of the cylinder

A: It is the radius of the cylinder

We have to, according to the given data:[tex]h = 4\\r = 3[/tex]

Substituting:

[tex]V = \pi * (3) ^ 2 * 4\\V = \pi * 9 * 4\\V = 36 \ pi[/tex]

[tex]36 \pi \ units ^ 3[/tex]

ANswer:

Option D

[tex]36 \pi \ units ^ 3[/tex]

Answer:

the total available area = (3x^2 + 4x + 1) - (2x^2 + 8x + 8) = x^2 - 4x - 7

Step-by-step explanation:

The question seems to ask available area and not how much wallpaper is required. Let's calculate the area of the rectangular window. Area of a rectangle = Length * Breath Area = (x + 2) * (x + 1) = x^2 + 3x + 2 The wall also has a built- in shelving unit that occupies an area of (x^2 + 5x + 6). So total area occupied by the rectangular wall and shelf is (x^2 + 3x + 2) + (x^2 + 5x + 6) = 2x^2 + 8x + 8. If the wall is to be covered with wallpaper

Sorry for the wait

Answer: I believe it is 33 seats

Step-by-step explanation:

Answer:

516

Step-by-step explanation:

Answer:

46°

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you ...

Cos = Adjacent/Hypotenuse

You are given the lengths of the hypotenuse of the triangle and the side adjacent to the angle you want to find. So, the cosine function describes the relationship:

cos(B) = AB/CB = (20 cm)/(29 cm)

B = arccos(20/29) ≈ 46.397°

B ≈ 46°

The student is looking for the value of an angle, m∠B, which requires solving an equation and rounding to the nearest integer. The provided information does not give a direct method or equation for calculating m∠B, thus an answer cannot be given confidently.

The student is asking to calculate the value of an angle, denoted as m∠B, to the nearest degree. This is a mathematics problem likely involving geometry or trigonometry.

In the information provided, different equations and scenarios for calculating angles and magnitudes are given, but they seem to be disconnected, and the specific question regarding m∠B isn't directly addressed by the provided equations and examples.

Without a direct relationship or equation including m∠B, or a diagram to reference, it is not possible to confidently provide the value of m∠B. However, the excerpts suggest that if we had an equation and needed to find an angle such as m∠B, we would solve the equation and then round the result to the nearest integer, as angles are typically given in integers when degrees of freedom are considered.

Since tan is negative in the second quadrant, hence the direction angle for v is 98.13 degrees

The direction of a vector is the degree at which the vector is moving with respect to the horizontal.

Given the coordinate point (-3, 21), the direction is expressed as:

theta = arctan(y/x)

Substitute

theta = arctan(21/-3)
theta =arctan(-7)

theta = -81.7 degrees

Since tan is negative in the second quadrant, hence the direction angle for v is 98.13 degrees

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