write the equation of a line in slope intercept form that has slope of 6 and has a y- intercept of 1/2​

Answer:

m∠2 = 56°

Step-by-step explanation:

Given;

m∠1 = 10x + 4 and m∠2 = 5x - 4

Angles 1 and 2 are supplementary angles meaning that they add up to 180°

i.e,

(10x + 4) + (5x - 4) = 180°

10x + 5x + 4 - 4 = 180°

15x = 180°

x = 180/15 = 12

m∠2 = 5(12)° - 4° = 60° - 4° = 56°

Answer:

Step-by-step explanation:

f(x) = x⁵ – 8x⁴ + 16x³

As x approaches +∞, the highest term, x⁵, approaches +∞.

As x approaches -∞, x⁵ approaches -∞ (a negative number raised to an odd exponent is also negative).

Now let's factor:

f(x) = x³ (x² – 8x + 16)

f(x) = x³ (x – 4)²

f(x) has roots at x=0 and x=4.  x=4 is a repeated root (because it's squared), so the graph touches the x-axis but does not cross at x=4.

The graph crosses the x-axis at x=0.

Answer:

Part 1. B

Part 2. 4, 0

Step-by-step explanation: Edge 2023

Answer:

factors of [tex] x^{12}y^{18}+1 = (x^4y^6+1) (x^8y^{12} -x^4y^6 +1)[/tex]

Step-by-step explanation:

We need to find factors of [tex]x^{12}y^{18}+1 can\,\,be\,\, written\,\, as\,\,\\(x^2y^3)^6 + 1\\It\,\, can\,\, be\,\, further\,\, written\,\, as\\((x^2y^3)^2)^3 +1\\Using\,\, the\,\, formula\,\, a^3+b^3 = (a+b)(a^2-ab+b^2)\\Here \,\, a = (x^2y^3)^2 and y = 1\\((x^2y^3)^2)^3 +(1)^3= ((x^2y^3)^2+1) (((x^2y^3)^2)^2 -(x^2y^3)^2 +1)\\= (x^4y^6+1) (x^8y^{12} -x^4y^6 +1)[/tex]

So, factors of [tex] x^{12}y^{18}+1 = (x^4y^6+1) (x^8y^{12} -x^4y^6 +1)[/tex]

Answer:

47%

Step-by-step explanation:

you would take the number of palomino horses and divide that by the total number of horses like this:

7 / 15 = 0.46666667

which would be rounded to 0.47

which equals 47%

so the probability of randomly choosing a palomino horse would be about 47%

i hope this helps :)

Answer:

How is that possible

Step-by-step explanation:

So..... what is the question ?

Answer:

A = 36.75 cm^2

Step-by-step explanation:

The area of a trapezoid is found by

A = 1/2 (b1+b2) *h

where b1 and b2 are the bases and h is the height

A = 1/2 (12+9) *3.5

A = 1/2(21)*3.5

A = 36.75 cm^2

Answer:

See below.

Step-by-step explanation:

The graph of the quadratic equation is a parabola or u shaped graph. It has a vertex at (-1,-3) since h=-1 and k=-3 in the vertex form. It is also facing down since the leading coefficient is negative.

The graph of the equation y = -(x + 1)2 -3 is a downward opening parabola with the vertex at (-1, -3).

The graph of the equation y = -(x + 1)2 -3 is a downward opening parabola. The coefficient in front of the quadratic term, in this case, -1, determines the direction of the opening. If the coefficient is negative, the parabola opens downward.

Additionally, the vertex of the parabola is (-1, -3) since the equation is in vertex form. The vertex is the highest or lowest point on the graph. Therefore, the graph of the equation y = -(x + 1)2 -3 will be a downward opening parabola with the vertex at (-1, -3).

y=9.64

—————

cos21=9/y

Cross Multiply

ycos21=9

Divide both sides by cos21 to isolate y

9/cos21 = 9.640304943

y=9.64

Answer:

35.25

Step-by-step explanation:

There are 4 data:

262, 313, 393, and 323

The formula for MAD (mean absolute deviation) = [tex]\frac{SUM(|x_{i}-XBar|)}{n}[/tex]

Where x_i are the each individual values (stated)

XBar is the average value

n is the number of data

First, let's find XBar, or the average. We add up all the 4 numbers and divide by 4 to get:

XBar = (262+313+393+323)/4=322.75

Now, let's calculate MAD:

MAD = [tex]\frac{|262-322.75|+|313-322.75|+|393-322.75|+|323-322.75|}{4}\\=35.25[/tex]

MAD = 35.25

Answer:

31.5

Step-by-step explanation:

ANSWER

The constant of variation is 6.

EXPLANATION

The inverse variation equation is:

[tex]xy = k[/tex]

We want to find the constant of variation, when x=-3 and y=-2.

We substitute the values for x and y to get,

[tex] - 3 \times - 2 = k[/tex]

Multiply out the left hand keeping in mind that negative times negative yields a positive result.

This implies that;

[tex]k= 6[/tex]

Hence the constant of variation is 6.

Answer:

The constant of variation k is 6.

Step-by-step explanation:

Given that there is inverse variation between x and y with equation

[tex]xy=k[/tex]

we have to find the constant of variation k when x=-3 and y=-2

The inverse variation equation is:

[tex]xy = k[/tex]

To find constant of variation we substitute the values of x and y

Put x=-3 and y=-2

[tex](-3)\times (-2)=k[/tex]

Solve LHS by multiplying

This implies

[tex]k= 6[/tex]

Hence the constant of variation is 6.

Answer:

x is less than or equal to 3.5

Step-by-step explanation:

For this you can any variable but let’s use d representing the distance that Jonathan ran.

Hmm

D_>3.5+5

In other words d is less than or equal to 3.5 plus 5

Hope this helped u :)

Answer:

The approximate difference in the growth rate of the two populations is 40%.

Step-by-step explanation:

The general exponential growth model is

[tex]y=a(1+r)^t[/tex]

Where, a is initial value, r is growth rate and t is time.

In the given graph, red curve passing through the points (2,22.5) and (3,33.75).

[tex]22.5=a(1+r)^2[/tex]           .... (1)

[tex]33.75=a(1+r)^3[/tex]           .... (2)

Divide the equation (2) by equation (1).

[tex]1.5=1+r[/tex]

[tex]0.5=r[/tex]

The graph rate of red curve is 50%.

In the given graph, purple curve passing through the points (7,19.4) and (8,21.4).

[tex]19.4=a(1+r)^7[/tex]           .... (3)

[tex]21.4=a(1+r)^8[/tex]           .... (4)

Divide the equation (4) by equation (3).

[tex]1.1031=1+r[/tex]

[tex]0.1031=r[/tex]

[tex]0.1\approx r[/tex]

The graph rate of red curve is 10%.

The approximate difference in the growth rate of the two populations is

[tex]50-10=40\%[/tex]

Therefore the approximate difference in the growth rate of the two populations is 40%.

Answer is

New perimeter = 112

See photo

Answer:

Step-by-step explanation:

(2+2i)(5+3i)

(2)5+(2)3i=10+6i

(2i)5+(2i)3i=10i+6i^2

10+6i+10i+6i^2

6i^2+6i+10i+10

6i^2+16i+10

To find the product of (2+2i)(5+3i), apply the distributive property to multiply each part. The result is 10 (real*real), 6i (real*imaginary), 10i (imaginary*real), and -6 (imaginary*imaginary, since i^2=-1), which are summed to give 4 + 16i.

The product of two complex numbers, such as (2+2i)(5+3i), can be found by using the distributive property (also known as foil - first, outer, inner, laters). In this case:

Sum these results together: 10 + 6i + 10i - 6. Thus, (2+2i)(5+3i)= 4 + 16i.

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Answer:

The answer is D

Answer:

The answer is A

Answer:

6

Step-by-step explanation:

Given data:

x=area

f(x)=the length of one side of the square

Also the model of f(x)= [tex]\sqrt{x-1} +1[/tex]

Now determining length of one side of the square f(x), when Area x of square is 26:

Putting the value x=26 in given equation of f(x)

f(x)= [tex]\sqrt{26-1} +1[/tex]

   = [tex]\sqrt{25} +1[/tex]

  = 5 +1

   = 6

Hence length of one side of the square f(x) is 6, when Area x of square is 26 !

Answer with explanation:

x= Area

f(x)= The length of one side of the square

Model Determined by Sam to approximate the side of a square is

    [tex]f(x)=\sqrt{x-1} +1[/tex]

It is given that , Area(x) = 26 Square Unit

 Substituting the value of , x in above equation

    [tex]f(x)=\sqrt{26-1} +1\\\\f(x)=\sqrt{25} +1\\\\f(x)=5+1\\\\f(x)=6[/tex]

So, Side length of Square According to model created by Sam = 6 unit

Still second graph from top down is the good one

Answer:

x = 127°

Step-by-step explanation:

We are given a polygon which has six sides but all the sides and angles are not equal so it is an irregular hexagon.

We know that the sum of the measures of the interior angles of a polygon with n sides is given by: [tex](n-2)\times180[/tex].

[tex](6-2)\times180 = 112+133+128+100+120+x[/tex]

[tex] 7 2 0 = 5 9 3 + x [/tex]

[tex] x = 7 2 0 - 5 9 3 [/tex]

x = 127°

Answer:

X = 20.6 inches

Step-by-step explanation:

Pythagorean Theorem: [tex]A^{2} =B^{2} +C^{2}[/tex]

A = 41.2 in, while B = 35.7 in and we are solving for C.

[tex]41.2^{2} = 35.7^{2} +C^{2}[/tex]

[tex]1697.44 = 1274.49 + C^{2}[/tex]

Now solve for C

[tex]422.95 = C^{2}[/tex]

Take the square root

[tex]20.5657482237 = C[/tex]

Answer:

9.2 kilo grams

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Given

q = [tex]\frac{p}{r}[/tex] + s ( subtract s from both sides )

q - s = [tex]\frac{p}{r}[/tex]

Multiply both sides by r

r(q - s) = p

Answer:

B. The price for each student ticket is the same at both theaters

Correct Option is B.

System of Linear equations:

A system of linear equations is a set of equations which are satisfied by the same set of variables.

Ex : 2x - y = 12 , x - 2y = 48

Here,

Let's take adult ticket price in theatre A = x

And the student ticket price in theatre A = y

So, (Given), 3x + 2y = $42.50 (Melanie paid)

=> 2y = $42.50 - 3x --(1)

Also given, 2x + 4y = $47 (Drew paid)

=> 4y = $47 - 2x

2(2y) = $47 - 2x

Now, substitute 2y value from eq-(1), we get

2($42.50 - 3x) = $47 - 2x

$85 - 6x = $47 - 2x

=>  $85 - $47 = 6x - 2x

=> $38 = 4x

=> x = ($38)/4 => 9.5

Substitute x value in eq-(1), we get

2y = $42.50 - 3(9.5) => y = $7.

In the given options only Option B is the correct answer.

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Answer:

2 31/32   cups used

Step-by-step explanation:

We have 4 3/8 cups cherries

Change this to an improper fraction

4 3/8 = (8*4+3)/8 = 38/8

We use 5/8 of the cherries

38/8 *5/8

190/64

Change this back to a mixed number

64 goes into 190 2 times

190 - 128 =62  left over

2 62/64

2 31/32   cups used

Go 6 units in X axis and 1 unit in Y axis and you get V.

Alternative B

Answer:

B, Point V

Step-by-step explanation:

find 6 on the x-axis and go up 1, you will find point V

Answer:

A (0,0)

Step-by-step explanation:

When a function intersects the y-axis then the point of intersection is called y-intercept of the function,

Also, for y-intercept x = 0.

That is, if f(x) is the function then its y-intercept is (0, f(0) )

By the given table for x = 0, f(x) = 0

Hence, the y-intercept of the given function is (0,0),

Option A is correct.

Answer:

A trust

Step-by-step explanation:

Answer:

Step-by-step explanation:

By showing that 0.20 is greater than 0.18 by doing 0.20-0.18 which gives a positive 0.02, thich means that its greater.

0.2 is greater than 0.18.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

We have to Compare 0.2 and 0.18.

First we have two digits in 0.18 after decimal.

Then, make 0.2 with two digits after decimal as 0.20.

Now, compare the after decimal value

20 > 18

So, 0.2 is greater than 0.18.

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Answer:

see explanation

Step-by-step explanation:

The exponential function is of the form

y = a [tex]b^{x}[/tex]

Substitute the given points into the equation to find a and b

Using (0, 4), then

4 = a[tex]b^{0}[/tex] ⇒ a = 4

Using (1, 24), then

24 = 4 [tex]b^{1}[/tex] ⇒ b = 6

Exponential function is

y = 4 × [tex]6^{x}[/tex]

The equation of the exponential function that passes through the points (0,4) and (1,24) is y = 4(6)^x.

To find the equation of the exponential function that passes through the points (0,4) and (1,24), we can use the general form of an exponential function: y = ab^x, where a is the initial value and b is the growth/decay factor.

Using the point (0,4), we plug in x=0 and y=4 to get the equation 4 = ab^0, which simplifies to a = 4.

Using the point (1,24), we plug in x=1, y=24, and a=4 to get the equation 24 = 4b^1, which simplifies to b = 6.

Therefore, the equation of the exponential function is y = 4(6)^x.

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hope it helps you!!!!!!!!!!!

Answer: option B

Step-by-step explanation:

The circumference of a circle can be calculated with this formula:

[tex]C=2\pi r[/tex]

Where "C" is the circumference of the circle and "r" is the radius of the circle.

The area of a circle can be calculated with:

[tex]A=\pi r^2[/tex]

Where "r" is the radius.

Knowing the area, you can solve for the radius:

[tex]r^2=\frac{9\pi cm^2}{\pi }\\\\r=\sqrt{\frac{9\pi cm^2}{\pi } }\\\\r=3cm[/tex]

Substituting into  [tex]C=2\pi r[/tex], you get that the circumference of this circle is:

 [tex]C=2\pi (3cm)=6\pi\ cm[/tex]

Answer:

B

Step-by-step explanation:

The area (A) of a circle = πr² ← r is the radius

here A = 9π, hence

πr² = 9π ( divide both sides by π )

r² = [tex]\frac{9\pi }{\pi }[/tex] = 9

r = [tex]\sqrt{9}[/tex] = 3

The circumference (C) of a circle is C = 2πr, hence

C = 2π × 3 = 6π → B

Answer:

Flat 12,885.68

Compound 13,876.90

Step-by-step explanation:

Flat rate (6% of only the amount you invested originally per year (based on investment) -

(8706.54*.06)*8+8706.54=12885.68 (rounded)

Compound interest (6% interest on total money earned per year(based on amount invested previous year).)

(((((((8706.54*1.06)*1.06)*1.06)*1.06)*1.06)*1.06)*1.06)*1.06)=13,876.90

The future value of the investment is $13876.90 and the interest earned is $5170.36.

We can use the following formulas:

Future value = [tex]Principal * (1 + Interest rate)^N^u^m^b^e^r ^o^f^ y^e^a^r^s[/tex]

Interest earned = Future value - Principal

Substituting the known values into the formulas, we get:

Future value =[tex]$8706.54 * (1 + 0.06)^8 = $13876.90[/tex]

Interest earned = $13876.90 - $8706.54 = $5170.36

Therefore, the future value of the investment is $13876.90 and the interest earned is $5170.36.

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