Is the following shape a right triangle? How do you know?

Answer:

(4/3, 4  5/9) and (-32, -53)

Step-by-step explanation:

When a curve is given as a set of parametric equations, as this one is, then the slope of the tangent line to the curve is

              dy/dt

dy/dx = ------------

               dx/dt

which here is

              dy/dt        8 - 20t

dy/dx = ----------- = --------------

               dx/dt         12t^2

If the slope at a certain point on this curve is 1, then we conclude that:

8 - 20t = 12t^2, or

12t^2 + 20t - 8 = 0, or

3t^2 + 5t - 2 = 0

We have to solve this equation for the parameter, t:

Here a = 3, b = 5 and c = -2, and so the discriminant is

b^2 - 4ac = 25 - 4(3)(-2), or 49, and the square root of that is 7.

Thus, the roots are:

     -5 ± 7

t =  --------- = 1/3 and t = -2

        2(3)

Evaluate x and y twice, once each for each t value.

Case 1:  t = 1/3

x = 4(1/3) and y = 3 + 8(1/3) - 10(1/3)^2, or

x = 4/3 and y = 3 + 8/3 - 10/9:  (4/3, 4  5/9)

Case 2:  t = -2

x = 4(-2)^3 and y = 3 + 8(-2) - 10(-2)^2, or y = 3 - 16 - 40, or y = -53.

This gives us the point (-32, -53)

To find the points where the tangent line has a slope of 1 on the given curve, we derive expressions for dx/dt and dy/dt, set dy/dx equal to 1, and solve for t.

The given equation defines a parametric curve with x = 4t3 and y = 3 + 8t − 10t2. To find the points on this curve where the tangent line has a slope of 1, we'll first need to find expressions for dx/dt and dy/dt, which represent the rates of change of x and y with respect to the parameter t.

By differentiating x = 4t3 with respect to t, we find dx/dt = 12t2. Similarly, by differentiating y = 3 + 8t − 10t2 with respect to t, we find dy/dt = 8 - 20t.

The slope of the tangent line at a particular point on the curve corresponds to dy/dx, which we can find by dividing dy/dt by dx/dt, yielding (8 - 20t) / (12t2). We can set this equal to 1 (since we want a slope of 1) and solve for t to find the points on the curve where the tangent line has slope 1.

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Answer:

y = 3(x + 2) + 2 and y = -3(x + 2) + 2

Step-by-step explanation:

* Lets revise the equation of the hyperbola with center (h , k) and

 transverse axis parallel to the y-axis is (y - k)²/a² - (x - h)²/b² = 1

- The coordinates of the vertices are  (h , k ± a)

- The coordinates of the co-vertices are (h ± b , k)  

- The coordinates of the foci are (h , k ± c) where c² = a² + b²

- The equations of the asymptotes are  ± a/b (x - h) + k  

* Lets solve the problem

∵ The equation of the hyperbola is (y - 2)²/9 - (x + 2)² = 1

∵ The form of the equation is (y - k)²/a² - (x - h)²/b² = 1

∴ h = -2 , k = 2  

∴ a² = 9

∴ a = √9 = 3

∴ b² = 1

∴ b = √1 = 1

∵ The equations of the asymptotes are y = ± a/b (x - h) + k  

∴ The equations of the asymptotes are  y = ± 3/1 (x - -2) + 2

∴ The equations of the asymptotes are  y = ± 3 (x + 2) + 2    

* The equations of the asymptotes of the hyperbola are

  y = 3(x + 2) + 2 and y = -3(x + 2) + 2

Answer: I just did this quiz in Plato the correct answer is in the pic I did this question 3 times because I listened to the other people and finally got the answer which is the correct one, Hope this helps :)

Step-by-step explanation:

Answer:

x = 11.79

? = 6.25

Step-by-step explanation:

Using the law of sines

[tex]\frac{10}{sin58}[/tex] = [tex]\frac{x}{sin90}[/tex]

x = sin 90° x [tex]\frac{10}{sin58}[/tex] = 11.79

by Pythagorean theorem,

?² + 10² = x²

? = √  (x²- 10²)

? = √  (11.79²- 10²) = 6.25

Answer:

-10.5 deg

Step-by-step explanation:

Yesterday's temp = 7-1/2 deg (or 7.5 deg)

Today's temp = -3 deg

net change = today's temp - yesterday's temp

= -3 - 7.5 = -10.5 deg

Answer:

-10.5

Step-by-step explanation:

I listened to the other person and they helped me get it right. I'm just here to confirm it. Stay safe!! <3

Check the picture below.

so, the vertex at N, is noticeably not a right angle is an acute angle, so is less than 90°, so we don't need to check that one.

now, is the angle at L 90°?

well, if that's true LM and LN are perpendicular, and if they're indeed perpendicular, their slopes are negative reciprocal, meaning the slope of one is the same as the other but negative and upside down, well, let's check.

[tex]\bf L(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad M(\stackrel{x_2}{2}~,~\stackrel{y_2}{2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{2-0}{2-0}\implies \cfrac{2}{2}\implies 1 \\\\[-0.35em] ~\dotfill\\\\ L(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad N(\stackrel{x_2}{2}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-0}{2-0}\implies \cfrac{-1}{2}\implies -\cfrac{1}{2}[/tex]

[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope~of~LM}{1\implies \cfrac{1}{\underline{1}}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{\underline{1}}{1}}\qquad \stackrel{negative~reciprocal}{-\cfrac{\underline{1}}{1}\implies -1}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{slope of LM}}{1}\qquad \stackrel{\textit{negative reciprocal of LM}}{-1}\qquad \stackrel{\textit{slope of LN}}{-\cfrac{1}{2}}~\hfill -1\ne -\cfrac{1}{2}[/tex]

so that means Lydia put too much espresso on her last cup.

Answer:

Step-by-step explanation:

If you observe the image, you deduct that the polygon ABCD was increased in size, that means the scale factor applied dilated the figure. In other words, there was applied a factor of dilation.

To find the exact factor of dilation, we just have to divide each prime coordinate by the original ones.

For example, you can observe that coordinates [tex]A(3,0)[/tex] was changed to [tex]A'(6,0)[/tex], [tex]B(1,0)[/tex] was changed to [tex]B'(2,0)[/tex], [tex]C(1,2)[/tex] was changed to [tex]C'(2,2)[/tex] and [tex]D(3,2)[/tex] was changed to [tex]D'(6.2)[/tex].

Now, observe that the dilation was horizontal, that is, the scale factor was only applied to x-coordinates, and this factor is 2, beacuse each x-coordinate was increase by a factor of 2.

Therefore, this transformation is a horizonta dilation by a factor of 2.

Answer:

2y

Step-by-step explanation:

-2y + 3y x 2  – 3y + y

= -4y + 3 x 2y

= 4y + 6y

= 2y

Answer: I hope it's right :3

Step-by-step explanation:

Answer:

Shaded to the left

Step-by-step explanation:

I cannot see the illustration, but I know for a fact that after using the zero-interval test [plug 0 in for BOTH y and x], you get 0 < 4, which is a genuine statement, so it gets shaded on the left hand side, otherwise shaded on the right of it were false statement.

I am joyous to assist you anytime.

Answer:

Lol you answered your own question but yes it is -4 thanks!

Step-by-step explanation:

Answer:

D. 66.

Step-by-step explanation:

There has to be 3 even multiples in the 5 numbers so we try:

22+33+44+55+66

= 220.

Answer:

Option D. 66

Step-by-step explanation:

A multiple is an exact number of times to another number.

The five consecutive multiples of 11 are:

22 -> 11/22 = 2 times, no remainder

33 -> 33/11 = 3 times, without remainder

44 -> 44/11 = 4 times, without remainder

55 -> 55/11 = 5 times, without remainder

66 -> 66/11 = 6 times, without remainder

Of those five multiples of 11 (22, 33, 44, 55, 66), the greatest is 66.

Answer:

Factored form of A-B is: (5-3p^4)(25+15p^4+9p^8)

Option A is correct.

Step-by-step explanation:

Given:

A= 125

B = 27p^12

To find: A-B

A-B = 125 - 27p^12

A-B=(5)^3-(3p^4)^3

We know that, a^3 - b^3 = (a-b)(a^2+ab+b^2)

Using this formula and finding factored form of A-B:

=(5-3p^4)((5)^2+(5)(3p^4)+(3p^4)^2)

=(5-3p^4)(25+15p^4+9p^8)

So, factored form of A-B is: (5-3p^4)(25+15p^4+9p^8)

Option A is correct.

Answer:

C. The system has no solution.

C. The system has no solution.

A system of linear equations has no answer whilst the graphs are parallel. A coordinate plane. The x- and y-axes both scale by way of one-1/2. A graph of a line is going through the factors 0, one and a half of and three, two.

No solution would suggest that there's no answer to the equation. it's miles not possible for the equation to be proper regardless of what price we assign to the variable. infinite answers would suggest that any value for the variable would make the equation authentic.

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f(x)=(x-5)(x-4)(x-2)

x-5=0

x-5+5=0+5

x=5

x-4=0

x-4+4=0+4

x=4

x-2=0

x-2+2=0+2

x=2

Answer: 5,4,2 -C

The zeros of the function f(x) = (x-5)(x-4)(x-2) are 5, 4, 2

Option C is correct

Note that:

The zeros of a function f(x) are the values of x that makes f(x) to be equal to zero

If f(x)  =  (x - a)(x - b)(x - c), then the zeros of the function f(x) are:

x  = a,  x  =  b,  x  =  c

Therefore, the zeros of f(x)=(x-5)(x-4)(x-2) are found by equating f(x) to zero

(x - 5)(x - 4)(x - 2)  =  0

Equate each of the terms to zero

x  -  5  =  0

x  =   5

x  -  4  =  0

x   =  4

x  -  2  =  0

x   =  2

The zeros of the function f(x) = (x-5)(x-4)(x-2) are 5, 4, 2

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Answer:

  C.  0.006 g/cm³

Step-by-step explanation:

As the units tell you, density is the ratio of mass to volume. The volume of the container is found from ...

  V = πr²h = π(10 cm)²(25 cm) = 2500π cm³

Then the density is ...

  ρ = (50 g)/(2500π cm³) = 1/(50π) g/cm³

  ρ ≈ 0.006 g/cm³

_____

Comment on the problem

The "liquid" has about the same density as air pressurized to 75 psi.

Can someone confirm is this answer is right?

Answer:

[tex]f(x)=x^{4}+x^{3}-7x^{2}-x+6[/tex]

Step-by-step explanation:

The zeros of the polynomial are: -3, -1, 1, 2

According to the factor theorem, the factors of the polynomial will be:

(x - (-3)) = x + 3

(x - (-1)) = x + 1

(x - 1)

(x - 2)

Since we have the factors, we can multiply them to obtain the equation of the polynomial.

So,

[tex]f(x)=(x+3)(x+1)(x-1)(x-2)\\\\ f(x)=(x+3)(x^{2}-1)(x-2)\\\\ f(x)=(x^{2}-1)(x^{2}-2x+3x-6)\\\\ f(x)=(x^{2}-1)(x^{2}+x-6)\\\\ f(x)=x^{4}+x^{3}-6x^{2}-x^{2}-x+6\\\\ f(x)=x^{4}+x^{3}-7x^{2}-x+6[/tex]

The above equation give the polynomial with integer coefficients and a leading coefficient of 1

The polynomial of degree 4 that has -3, -1, 1, and 2 as its real zeros and integer coefficients with a leading coefficient of 1 can be expressed in its factored form as f(x) = (x + 3)(x + 1)(x - 1)(x - 2).

To form a polynomial with the given real zeros and degree, we must first understand that each real zero corresponds to a factor of the form (x - a), where a is the zero.

Therefore, given the zeros -3, -1, 1, and 2,

the corresponding factors of the polynomial are (x + 3), (x + 1), (x - 1), and (x - 2).

The polynomial of degree 4 with these zeros can then be written as the product of these factors,

obtaining f(x) = (x + 3)(x + 1)(x - 1)(x - 2).

Since it's required that polynomial has integer coefficients and a leading coefficient of 1,

we leave it in this factored form.

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Answer:

164 legs all together

Step-by-step explanation:

There are 144 legs out of all the numbered creatures together.

Spiders = 8 legs

8 x 8 = 64

Cockroaches = 6 legs

6 x 5 = 30

Bees = 6 legs

7 x 6 = 42

Deer = 4 legs

3 x 4 = 12

Cows = 4 legs

4 x 4 = 16

Answer:

yes

Step-by-step explanation:

this is right i think

The correct answer is line HJ .

1. **Line AB**: The slope of line AB is not the negative reciprocal of 1/2, so it is not perpendicular.

2. **Line CD**: The slope of line CD is not the negative reciprocal of 1/2, so it is not perpendicular.

3. **Line FG**: The slope of line FG is not the negative reciprocal of 1/2, so it is not perpendicular.

4. **Line HJ**: The slope of line HJ is the negative reciprocal of 1/2, which makes it perpendicular.

A line with a slope of **-3/5** can be represented by the equation:

[tex]\[ y = -\frac{3}{5}x + b \][/tex]

where \(b\) is the y-intercept. To find points on this line, we need to consider different values of \(x\) and calculate the corresponding \(y\).

Let's explore some potential points:

1. **Point A (x, y)**:

  - Assume \(x = 0\):

  [tex]\[ y = -\frac{3}{5} \cdot 0 + b = b \] - So, point A is \((0, b)\).[/tex]

2. **Point B (x, y)**:

  - Assume \(x = 5\):

  [tex]\[ y = -\frac{3}{5} \cdot 5 + b = -3 + b \] - So, point B is \((5, -3 + b)\).[/tex]

3. **Point C (x, y)**:

  - Assume \(x = 10\):

  [tex]\[ y = -\frac{3}{5} \cdot 10 + b = -6 + b \] - So, point C is \((10, -6 + b)\).[/tex]

These are just a few examples. You can find more points by choosing different values of \(x\). Remember that any point on the line will satisfy the equation [tex]\(y = -\frac{3}{5}x + b\).[/tex]

Now, let's explore the concept of parallel lines. Two lines are parallel if they have the **same slope**. If we have another line with a slope of 1/2, we can find points on that line as well.

Answer:

m = 3, n = 4

Step-by-step explanation:

Solve using the substitution process. First, start with the second equation:

2m + 2n = 14

Simplify. Divide 2 from all terms within the equation. What you do to one side, you do to the other:

(2m + 2n)/2 = (14)/2

m + n = 7

Isolate the variable m. Subtract n from both sides:

m + n (-n) = 7 (-n)

m = 7 - n

Plug in 7 - n for m in the first equation:

-5m + 9n = 21

-5(7 - n) + 9n = 21

Solve. First, distribute -5 to all terms within the parenthesis:

(-35 + 5n) + 9n = 21

Simplify. Combine like terms:

-35 + (5n + 9n) = 21

-35 + 14n = 21

Isolate the variable, n. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. First, add 35 to both sides:

14n - 35 (+35) = 21 (+35)

14n = 21 + 35

14n = 56

Isolate the variable n. Divide 14 from both sides:

(14n)/14 = (56)/14

n = 56/14

n = 4

Plug in 4 to n in one of the equations, and solve for m.

2m + 2n = 14

2m + 2(4) = 14

2m + 8 = 14

Isolate the variable, m. Do the opposite of PEMDAS. First, subtract 8 from both sides:

2m + 8 (-8) = 14 (-8)

2m = 14 - 8

2m = 6

Divide 2 from both sides:

(2m)/2 = (6)/2

m = 6/2

m = 3

Your answers: m = 3, n = 4

~

Answer:

(3, 4)

Step-by-step explanation:

Please include the instructions.  I'm assuming that you want to solve this system of linear equations.

If that's the case, let's use elimination by addition and subtraction.

Multiply the first equation, -5m + 9n = 21, by 2:  -10m + 18n = 42, and

multiply the second equation, 2m + 2n = 14, by 5:  10m + 10n = 70

Next, combine these two "new" equations:

-10m + 18n = 42

10m + 10n = 70

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

          28n = 112.  Dividing both sides by 28, we get  n = 4.

Subbing 4 for n in the second equation, we get 2m + 2(4) = 14, or

2m = 6.  Then m = 3, and the solution is thus

(3, 4).

Answer:

x-intercept (-3,0)

y-intercept  (0,-9)

Step-by-step explanation:

The x-intercepts can be found by setting y to 0 and solving for x.

y=-3x-9

0=-3x-9

Add 9 on both sides:

9=-3x

Divide both sides by -3:

9/-3=x

-3=x

The x-intercept is (-3,0).

The y-intercepts can be found by setting x to 0 and solving for y.

y=-3x-9

y=-3(0)-9

y=0-9

y=-9

The y-intercept is (0,-9).

Answer:

Step-by-step explanation:

x-intercept is for y = 0.

y-intercept is for x = 0.

y = -3x - 9

x-intercept (put y = 0):

0 = -3x - 9            add 9 to both sides

9 = -3x          divide both sides by (-3)

-3 = x → x = -3

y-intercept (put x = 0):

y = -3(0) - 9

y = 0 - 9

y = -9

Answer:

Step-by-step explanation:

It all depends upon what the terms are.  If each term of the 3 all have a variable you can factor out, then you'd do that first.  For example, if your trinomial looks like this:

[tex]x^3+3x^2+4x[/tex]

you would begin by factoring out the common x, reducing the third degree polynomial to a quadratic which can then be factored many ways.

[tex]x^3+3x^2+4x=x(x^2+3x+4)[/tex]

If that is not the case, then you are factoring higher degree polynomials, and the way I always recommend to my students is the Rational Root Theorem and then synthetic division.

Answer:

  ABCDEADBEC

Step-by-step explanation:

A path that traverses all streets exactly once is called an Euler path. It is only possible for a graph that has an even number of streets coming together at each vertex, or one that has an odd number of streets at only two vertices.

This map has an odd number of streets at vertices A and C, so those are suitable starting and ending points for the path. I find it convenient to travel the outside ring first, then fill in the inner paths that weren't previously traveled. The list of vertices for one possible path is shown above.

Answer:

c

Step-by-step explanation:

5/12, 1, 1/3, 5/6. 1/3 is the smallest.

Answer with Step-by-step explanation:

Mixture A-

Blue Paint - 5 cups

White Paint - 12 cups

Ratio of blue paint to white paint=5:12

Mixture B-

Blue Paint- 6 cups

White Paint- 6 cups

 Ratio of blue paint to white paint=6:6=12:12  

(on multiplying numerator and denominator by 12 i.e.6/6=12/12)

Mixture C-

Blue Paint - 4 cups

White Paint - 12 cups

 Ratio of blue paint to white paint=4:12

Mixture D-

Blue Paint - 5 cups

White Paint - 6 cups

Ratio of blue paint to white paint=5:6=10:12

(on multiplying numerator and denominator by 12 i.e.5/6=10/12)

The denominator of the ratios are same in each mixture now,to determine the lowest ratio we have to see the numerator with smallest value which is 4

Hence, Mixture C has the lowest ratio of blue paint to white paint

Since the graph above shows a proportional relationship between x and y, an equation of the line is y = -1/4(x).

In Mathematics and Geometry, a proportional relationship is a type of relationship that passes through the origin (0, 0) and produces equivalent ratios as represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = -1/4 = -2/8 = -12/3

Constant of proportionality, k = -1/4.

Therefore, the required linear equation for y(x) is given by;

y = kx

y = -1/4(x)

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Answer:

37°

Step-by-step explanation:

By definition all internal angles of a triangle add up to 180°

Hence,

98° + 45° + x = 180°

x = 180° - 98° - 45° = 37°

Answer:

Angles congruent to angle 2 is first. Angles congruent to angle 6 is second. Angles congruent to angle 1 is third. Angles congruent to angle 7 is last.

Step-by-step explanation:

Opposite angles are always equal. Alterbate interior/exterior angles are always equal.

Answer:

0.88 feet

Step-by-step explanation:

The tire covers 0.88 feet in 1 rotation.

1 rotation means the whole tire moves, which is basically its circumference. So, the distance it covers in moving 1 rotation IS ITS CIRCUMFERENCE.

Hence, 0.88 feet is the circle's circumference.

Answer:

The top tag price you could pay for the shorts = $32.71....

Step-by-step explanation:

Total amount = $ 60.00

Cost of jacket = $25.50

Sales tax = 7% = .07

First of all find the total price of the jacket including sales tax.

25.50* .07 = 1.79( this is the sales tax)

Now add this sales tax into the original price.

25.5 + 1.79 = 27.29

Total price of a jacket = $27.29

Now subtract the total amount by the amount of the jacket.

$60.00 - $27.29 = $32.71

Thus the top tag price you could pay for the shorts = $32.71....

Answer:

b/x=y/b

Step-by-step explanation:

Switch it over and get the y.

Answer:

(a) Five

(b) Thirteenth

Step-by-step explanation:

We have the mean is 12.6 and

that 11 occurs 4 times, 12 occurs 7 times, 13 occurs 9 times, and 14 occurs f times.

How many children are there in all (that is the sum of the frequencies).

4+7+9+f

20+f

Alright so the mean could be found by doing:

[tex]\frac{4(11)+7(12)+9(13)+f(14)}{20+f}[/tex]

But we are given this is also equal to: 12.6.

So we have

[tex]\frac{4(11)+7(12)+9(13)+f(14)}{20+f}=12.6[/tex]

I'm going to simplify what I can on top.

[tex]\frac{245+14f}{20+f}=12.6[/tex]

I'm going to write 12.6 as [tex]\frac{12.6}{1}[/tex] because I want to cross multiply:

[tex]\frac{245+14f}{20+f}=\frac{12.6}{1}[/tex]

[tex](245+14f)(1)=12.6(20+f)[/tex]

Distribute:

[tex]245+14f=252+12.6f[/tex]

Subtract 12.6f on both sides:

[tex]245+1.4f=252[/tex]

Subtract 245 on both sides:

[tex]1.4f=7[/tex]

Divide both sides by 1.4:

[tex]f=5[/tex]

There are five 14 years old.

(b) I would say 13 is good age to represent this bunch.

The means was 12.6 which when rounded is 13.

The mode is 13 because it is the most occurring

The median is also 13. Why? If you list out the data 13 will be the middle number. Or you could say there are 25 kids and if I divide it by 2, I get 12.5.  This means you only need to count to the 13th kid with the ages in order to tell with the median is.

There are 4 eleven yr olds.

There are 7 twelve yr olds.  That is 11 kids so far.

So the median has to be included in the 9 thirteenth yr olds.

Answer:

5

Step-by-step explanation:

Given

Original Measurement = 11*9 inches

Measurement after enlargement = 55 * 45 inches

In order to find the scale factor, we can choose one side of the figure or the whole area and find the ratio between the measurement before enlargement and after enlargement.

In case of a side the answer will be the scale factor while in case of finding scale factor using areas the answer will be the square of scale factor.

So,

[tex]Scale\ factor =s^2= \frac{55*45}{11*9} \\s^2 = \frac{2475}{99} \\s^2=25[/tex]

As we know that this is the square of scale factor.

Hence the scale factor will be:

[tex]\sqrt{s^2}=\sqrt{25}  \\s=5[/tex]

So, the scale factor is 5 ..