Find the missing length indicated.

If Point A is located at (1, 2) and Point B is located at (4, 6), the length of the line between points A and B is 5 units.

To determine the length of the line between points A and B, we can use the distance formula, which is a formula used to calculate the distance between two points in a coordinate plane. The distance formula is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points and d is the distance between them.

Using the coordinates of points A and B, we can substitute their values into the distance formula to find the length of the line between them:

d = √((4 - 1)² + (6 - 2)²)

d = √(3² + 4²)

d = √(9 + 16)

d = √25

d = 5

Rounded to the nearest whole number, the length of the line is also 5 units.

In conclusion, we can use the distance formula to find the length of the line between two points in a coordinate plane. The distance formula uses the coordinates of the two points to calculate the distance between them. The resulting distance can be rounded to the nearest whole number, if needed.

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The expression log 3x⁹y⁴ can be written as a sum of logarithms:

log(3x⁹y⁴) = log(3) + 9log(x) + 4log(y)

To express log(3x⁹y⁴) as a sum and/or difference of logarithms, we use the logarithmic properties.

Using the power rule of logarithms, we can write the expression as:

log(3x⁹y⁴) = log(3) + log(x⁹) + log(y⁴)

we can further simplify so that the variables will be to the first degree as follows;

log(3x⁹y⁴) = log(3) + 9log(x) + 4log(y).

Therefore, the expression log(3x⁹y⁴) can be written as a sum of logarithms:

log(3x⁹y⁴) = log(3) + 9log(x) + 4log(y)

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Answer:

\(C = 25.1 \text{ cm}\)

Step-by-step explanation:

We can find the circumference of the circle by plugging the given radius value 8 cm into the formula:

\(C = \pi d\)

Note: This formula can also be written as \(C = 2\pi r\) because \(2r = d\).

↓ plugging in the given radius

\(C = 8\pi \text{ cm}\)

↓ rounding to the nearest tenth

\(\boxed{C = 25.1 \text{ cm}}\)

Answer:

\(g'(y)=3y^2-4y-8\)

Step-by-step explanation:

start by foiling out the given function

\(g(y)=(y-4)(2y+y^2)\\=2y^2+y^3-8y-4y^2\\=y^3-2y^2-8y\)

next, use the power rule to find the derivative

power rule: To use the power rule, multiply the variable's exponent n, by its coefficient a, then subtract 1 from the exponent. If there's no coefficient (the coefficient is 1), then the exponent will become the new coefficient.

\(g'(y)=3y^2-4y-8\)

The triangles ABC and DBE are similar by the SAS similarity theorem

The measure of the side lengths AC is 16 units

From the question, we have the following parameters that can be used in our computation:

The triangles ABC and DBE

These triangles have the following measures

This means that the triangles are similar by the SAS similarity theorem

Using the SAS similarity theorem, we have the following equation

(x + 1)/12 = (x + 5)/15

Cross multiply the equation

15x + 15 = 12x + 60

So, we have

3x = 45

Divide by 3

x = 15

This means that

x + 1 = 15 + 1 = 16

x + 5 = 15 + 5 = 20

Hence, the measure of the side lengths are 16 and 20 units

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The two triangles exist congruent if they contain two congruent corresponding sides and their contained angles exist congruent.

Let \($&\overline{A B} \cong \overline{D E} \\\) and \($&\overline{A C} \cong \overline{D F}\)

Angle between \($\overline{A B}$\) and \($\overline{A C}$\) exists \($\angle A$\).

Angle between \($\overline{D E}$\) and \($\overline{D F}$\) exists \($\angle D$\).

Therefore, \($\triangle A B C \cong \triangle D E F$\) by SAS, if \($\angle A \cong \angle D$$\).

Given:

\($&\overline{A B} \cong \overline{D E} \\\) and

\($&\overline{A C} \cong \overline{D F}\)

According to the SAS congruence property, two triangles exist congruent if they contain two congruent corresponding sides and their contained angles exist congruent.

Let \($&\overline{A B} \cong \overline{D E} \\\) and \($&\overline{A C} \cong \overline{D F}\)

Angle between \($\overline{A B}$\) and \($\overline{A C}$\) exists \($\angle A$\).

Angle between \($\overline{D E}$\) and \($\overline{D F}$\) exists \($\angle D$\).

Therefore, \($\triangle A B C \cong \triangle D E F$\) by SAS, if \($\angle A \cong \angle D$$\).

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The translation form of each shape is given as follows:

a) X to Z: (x, y) -> (x + 5, y + 2).

b) Z to X: (x, y) -> (x - 5, y - 2).

The four translation rules are defined as follows:

For the composition of translations, we add the coordinates, hence:

Hence the rule from X to Z is given as follows:

(x, y) -> (x + 5, y + 2).

From Z to X, we have the inverse rule, hence:

(x, y) -> (x - 5, y - 2).

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Answer:

7((x-2)(3x+4))

Step-by-step explanation:

Common factor of 7 in this quadratic formula. \(7(3x^2-2x-8)\); -8 * 3x^2 = -24x^2, now find factors of this product that equal to -2x when added. The factors that fit this is -6x and 4x. So, if you make a generic rectangle you can find the product.  You get 7((x-2)(3x+4))

Answer: 20-10

Step-by-step explanation: 486-466 is 20. Half of 20 is 10. Any expression that equals ten is 1/2 as large as 486-466.

The expression is 1/2 as large as 486-466 is with the data 10.

Fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Let us understand this concept using an example. The following figure shows a pizza that is divided into 8 equal parts. Now, if we want to express one selected part of the pizza, we can express it as 1/8 which shows that out of 8 equal parts, we are referring to 1 part.

Given:

Class = 486 - 466

We have given a class whose upper limit = 486

and, lower limit = 466

the range or difference between class

=486 - 466

=20

Thus, the 1/2 of range is 10.

Hence, expression is 1/2 as large as 486-466 is with the data 10.

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Answer:

c

Step-by-step explanation:

edg

Answer:

c

Step-by-step explanation:

Pang, Ruben, Adela, Tony

Answer:    x=67

Step-by-step explanation:

All of the angles add up to 180 for a triangle

38 + 75 + x = 180               >combine like terms (the numbers)

113 + x = 180                       >subtract 113 from both sides

x=67

Answer:

Step-by-step explanation:

We know that,

\( \sf \: By \: Using \: Angle \: sum \: property \: of \: triangle\)

\( \large \sf \: → x +38° + 75° = 180°\)

\( \large \sf \: → x + 113 = 180°\)

\( \large \sf→ x = 180°- 113°\)

\( \boxed{\large \bf→ x = 67° }\)

Answer:

55

Step-by-step explanation:

\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)

Make sure to always round up the required sample size to the nearest integer!

Answer:

8000

Step-by-step explanation:

Answer:

8,000

Step-by-step explanation:

8,000 is the same as 8 one-thousands, which is the same as 8 × 1,000

Hope that helps!

Answer:

how many ever pineapples as sandman wants...I think

Answer:

51720

Step-by-step explanation:

Answer:

31.8627

Step-by-step explanation:

The powers, (index) and coefficients of the polynomial indicates;

(A) The standard form is; 2·x⁴ + 3·x³ + 9·x² - 12·x + 6

(B) 4

(C) Positive zeroes; 2 or 0, negative zeroes; 0 or 2, complex zeroes; 0 or 2 or 4

(D) ±1/2, ±1, ±3/2, ±2, ±3, ±6

(E) Please find attached the graph of the polynomial created with MS Excel

(F) Four complex roots

A polynomial is a mathematical expression that consists of variables and coefficients joined together by addition, subtraction and multiplication, with the exponents of the variables consisting of positive integer values.

Part A) The polynomial in standard form is; 2·x⁴ + 3·x³ + 9·x² - 12·x + 6

Part B) The degree of the polynomial is 4, as the highest power of the polynomial is 4

Part C) The use of the Rule of Signs, to determine the options for the number of positive zeroes, negative zeroes and complex zeroes, can be presented as follows;

Positive zeroes options; The number of time the signs coefficients of the expression; 2·x⁴ + 3·x³ + 9·x² - 12·x + 6, changes are two as follows;

+6 to -12, and from -12 to +9, therefore, the number of possible positive zeroes are 2 or 0, positive zeroes

The negative zeroes options; The negative zeroes options can be found by changing the sign of all the coefficients as follows; -2·x⁴ - 3·x³ - 9·x² + 12·x - 6, therefore, the number of times the sign of the coefficients change are again from -6 to +12, and from +12 to -9, which is 2 times, therefore;

The possible number of negative zeros are 2 or 0, negative zeroes

Whereby there are possibly 0 negative zeros and 0 positive zeroes, the possible number of complex zeroes are 4

Whereby there are 2 negative zeros and 0 positive zeroes, the possible number of complex zeroes are 2 complex zeroes

Whereby there are possibly 0 negative zeros and 2 positive zeroes, the possible number of complex zeroes are 2 complex zeroes

Part D) The rational roots theorem indicates that for a polynomial the rational roots are in the form p/q, where p is a factor of the constant term, and q is a factor of the leading coefficient.

The constant term is 6, and the leading coefficient is 2. The factors of 6 are ±1, ±2, ±3, and ±6 and the factors of 2 are; ±1, ±2 therefore;

p/q = ±1/1, ±2/1, ±3/1, ±6/1, ±1/2, ±2/2, ±3/2, ±6/2, which can be summarized as; ±1/2, ±1, ±3/2, ±2, ±3, ±6

Part E) Please find attached a screenshot of the graph of the polynomial created with MS Excel

Part F) The attached graph of the polynomial, created with MS Excel, indicates that there are no real zeros of the polynomial, therefore, there are four complex zeroes of the polynomial

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Answer:

(x,y) = (-1,1)

Step-by-step explanation:

step 1

subsitute the given value of y into the equation

2x+7(x+2)=5

step 2

solve for x

x= -1

step 3

subsitute the value of x in to the second equation

y= -1+2

step 4

solve for y

y=1

step 5

check if there true by putting the value of x and y back in to the equation.

then configure x and y into an ordered pair.

(x,y)=(-1,1)

I hope this helped!

The Lydia has invested $3680 if the Lydia has half of her investments in stock paying a 10 % dividend and the other half in a stock paying 15% interest.

A payment made to acquire the securities of other businesses with the goal of earning a profit is referred to as an investment.

Let's suppose the invested amount is $x,

According to the problem, we can find the value of x:

(x/2)(10/100)(1) + (x/2)(15/100)(1) = 460

x/20 + 0.15x/2 =460

x = $3680

Thus, the Lydia has invested $3680 if the Lydia has half of her investments in stock paying a 10 % dividend and the other half in a stock paying 15% interest.

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Answer:

Her average was 4.9 for all three games.

Step-by-step explanation:

(5.5 + -3.6 + 12.8)/3

14.7/3

4.9

Answer: 21:9 and 42:18

Step-by-step explanation:

14:6 at its most basic form is 7:3, so find anything that could be equal to this if a number is multiplied on both sides.

21:9 is our simplified ratio multiplied by 3 on both sides.

42:18 is our simplified ratio multiplied by 6 on both sides.

But, the final ratio doesn't work, because 7 and 3 respectively cannot multiply to 13 and 8 with the same value.

Answer:

t=-4

Step-by-step explanation:

t+6=7/3.5

t+6=70/35 (I expanded 7/3.5 by multiplying both numerator and the denominator by 10)

t+6=2 (I divided 70 by 35 to get 2)

t=2-6

t=-4

Answer:

t=-4

Step-by-step explanation:

i took the test on k12

Answer:

The domain of this function is (in order of least to greatest) is [-2,-1,0,3.5,4,5.5, and 8]

The range of this function is (in order from greatest to least) is [6,5.5,4,0,-1, and -3.5]

Step-by-step explanation:

To find the domain you need to look at all of you input or x values so the question is asking to name the values of x for your domain. You look at the table to where x is and name the numbers listed in this case it's [-2,-1,0,3.5,4,5.5, and 7]

To find the range you need to look at the listed outputs or y values. You are essentially doing the same steps but instead you looking at y for the listed values. Generally when it comes to domains that have the same range (for example (4,-1) and (5.5,-1)) you would only write it once in the list of ranges so like [6,5.5,4,0,-1, and -3.5]

Answer:

-3

Step-by-step explanation:

sense its between -2 and -4

*question

Step-by-step explanation:

Here we are interested in finding the square root of \( 9 +4\sqrt5\) . So , we have

\(\longrightarrow \sqrt{ 9+4\sqrt5}\)

We can write it as ,

\(\longrightarrow \sqrt{ 5 + 4 + 4\sqrt5} \)

This can be again rewritten as ,

\(\longrightarrow\sqrt{ (\sqrt5)^2+2^2+ 2(2)(\sqrt5) } \)

Now this in the form of \( a^2+b^2+2ab \) form which is the square of \( (a+b)\) . So that,

\(\longrightarrow \sqrt{ (2+\sqrt5)^2}\)

Simplify the root ,

\(\longrightarrow 2 + \sqrt5\)

Hence we got our answer in the form of \( c +\sqrt{d}\)

And we are done!

—Rishabh

Answer:

250

Step-by-step explanation:

Answer:

All angles are different.

Internal angles can be acute, obtuse, or right angle.

The smallest side is opposite to the smallest angle and the longer side is opposite to the larger angle.

Step-by-step explanation:

Given - In ΔOPQ, PQ = 17, QO = 9, and OP = 15.

To find - Which statement about the angles of ΔOPQ must be true?

Proof -

As given,

In ΔOPQ, PQ = 17, QO = 9, and OP = 15.

As all the sides of the given triangle is different, So the given triangle is a Scalene triangle.

Now,

We know that , In Scalene triangle -

All sides are different.

All angles are different.

Internal angles can be acute, obtuse, or right angle.

The smallest side is opposite to the smallest angle and the longer side is opposite to the larger angle.

Smallest angle: ∠P

Opposite shortest side.

Middle angle: ∠O

Opposite middle side.

Largest angle: ∠Q

Opposite longest side.

Therefore:

m∠P<m∠O<m∠Q

Less than symbol goes from smallest to largest

Answer:

option B

explanation:

\(\rightarrow \sf (\dfrac{xy^2}{x^{-3}y^3} )^{-4}\)

                                                     multiply powers: \(\bold{(a^b)^c = a^{bc}}\)

\(\rightarrow \sf \dfrac{x^{-4}y^{2*-4}}{x^{-3*-4}y^{3*-4}}\)

                                               simplify the following

\(\rightarrow \sf \dfrac{x^{-4}y^{-8}}{x^{12}y^{-12}}\)

Answer:

$ 324.00

Step-by-step explanation:

Interest= principal x rate x time

First, converting R percent to r a decimal

r = R/100 = 12%/100 = 0.12 per year,

then, solving our equation

I = 2700 × 0.12 × 1 = 324

I = $ 324.00

The simple interest accumulated

on a principal of $ 2,700.00

at a rate of 12% per year

for 1 years is $ 324.00.

The answer of the question based on coordinate grid is mapped on a video game screen is option (a) StartLayout Enlarged Left-Brace 1st Row y = one-fifteenth x + 18 2nd Row y = StartFraction 5 Over 144 EndFraction (x minus 16) squared + 20 EndLayout.

A quadratic function is a function that can be written in the form:

f(x) = ax² + bx + c. The graph of a quadratic function is a parabola, which is a U-shaped curve that can either open upwards or downwards, depending on the sign of the coefficient a. If a is positive, the parabola opens upwards, and if a is negative, the parabola opens downwards.

To determine whether the paths of the helicopter and airplane cross, we need to find the coordinates where the equations of their paths intersect.

Let's start with the equation for the airplane's path, which is a linear function that can be written in slope-intercept form as:

y = mx + b

We can find the slope using the two given points:

m = (change in y) / (change in x) = (20 - 18) / (30 - 0) = 1/15

So the equation for the airplane's path is:

y = (1/15)x + 18

Next, let's consider the equation for the helicopter's path, which is a quadratic function that can be written in vertex form as:

y = a(x - h)² + k

where (h, k) is the vertex and a determines the shape of the parabola. We are given that the vertex is (16, 20), so h = 16 and k = 20. We can find a by plugging in the other given point:

25 = a(4 - 16)² + 20

5/144 = a

So the equation for the helicopter's path is:

y = (5/144)(x - 16)² + 20

To find where the two paths intersect, we need to solve the system of equations:

y = (1/15)x + 18

y = (5/144)(x - 16)²+ 20

Substituting  first equation with second, we will get:

(1/15)x + 18 = (5/144)(x - 16)² + 20

Simplifying, we get:

0 = (5/144)(x - 4)(x - 28)

So the x-coordinates of the intersection points are x = 4 and x = 28. To find the corresponding y-coordinates, we can plug these values back into either equation:

y = (1/15)(4) + 18 = 18.27

y = (1/15)(28) + 18 = 19.87

Therefore, the paths of the helicopter and airplane cross at the point (4, 18.27) and (28, 19.87).

The correct system of equations to determine whether the paths of the helicopter and airplane cross is:

y = (1/15)x + 18 (airplane's path)

y = (5/144)(x - 16)² + 20 (helicopter's path)

So the answer is:

StartLayout Enlarged Left-Brace 1st Row y = one-fifteenth x + 18 2nd Row y = StartFraction 5 Over 144 EndFraction (x minus 16) squared + 20 EndLayout

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