How do you get -2 from
-13 = -5x -23

Answer:

17/25

Step-by-step explanation:

P(not red)=Number of Skittles Not Red/Total Number of Skittles

Answer:

13.015625

Step-by-step explanation:

Answer:

13 remainder 1.

I have attached the work to your question.

Please see the attachment below.

I hope this helps!

Answer:

X = 23

triangle angles sum = 180

67 + 49 + (3x-5) = 180

3x + 111 = 180

3x = 69

x = 23

To convert a 4L 90% acid solution to a 60% water solution we need to add 7 liters of pure water.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Assuming we have to add x liters of 100% pure water then the total solution becomes (x + 4)L.

∴ x×100% + 4×10% = (x + 4)×60%.

x×1 + 4×0.1 = 0.6x + 4×0.6.

x + 0.4 = 0.6x + 2.4.

x - 0.6x = 2.4 + 0.4.

0.4x = 2.8.

4x = 28.

x = 7.

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Answer:

18m²

Step-by-step explanation:

area = areas of top left triangle + bottom left + top right + bottom right

= (1/2 X 2 X 3) + (1/2 X 2 X 3) + (1/2 X 3 X 4) + (1/2 X 3 X 4)

= 3 + 3 + 6 + 6

= 18 m²

Answer:

\(\textsf{Equations of bisectors:}\quad \begin{cases}3x+11y-10=0\\33x-9y=0\end{cases}\)

\(\textsf{Bisector of acute angle:} \quad 33x - 9y = 0\)

Step-by-step explanation:

To determine the equations of the angle bisectors of two lines a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, we can use the formula:

\(\boxed{\dfrac{a_1x+b_1y+c_1}{\sqrt{{a_1}^2+{b_1}^2}}=\pm\dfrac{a_2x+b_2y+c_2}{\sqrt{{a_2}^2+{b_2}^2}}}\)

Let line 3x - 2y + 1 = 0 be defined by the equation a₁x + b₁y + c₁ = 0.

Let line 18x + y - 5 = 0 be defined by the equation a₂x + b₂y + c₂ = 0.

Therefore:

Substitute the values of a₁, b₁, c₁, a₂, b₂, and c₂ into both formulas.

\(\begin{aligned}\dfrac{3x-2y+1}{\sqrt{{3}^2+{(-2)}^2}}&=\dfrac{18x+y-5}{\sqrt{{18}^2+{1}^2}}}\\\\\dfrac{3x-2y+1}{\sqrt{13}}&=\dfrac{18x+y-5}{5\sqrt{13}}\\\\3x-2y+1&=\dfrac{18x+y-5}{5}\\\\5(3x-2y+1)&=18x+y-5\\\\15x-10y+5&=18x+y-5\\\\3x+11y-10&=0\end{aligned}\)

\(\begin{aligned}\dfrac{3x-2y+1}{\sqrt{{3}^2+{(-2)}^2}}&=-\dfrac{18x+y-5}{\sqrt{{18}^2+{1}^2}}}\\\\\dfrac{3x-2y+1}{\sqrt{13}}&=-\dfrac{18x+y-5}{5\sqrt{13}}\\\\3x-2y+1&=-\dfrac{18x+y-5}{5}\\\\5(3x-2y+1)&=-18x-y+5\\\\15x-10y+5&=-18x-y+5\\\\33x-9y&=0\end{aligned}\)

Therefore, the equations of bisectors of the angles between the given lines are:

\(\boxed{\boxed{\begin{aligned}3x+11y-10&=0\\33x-9y&=0\end{aligned}}}\)

\(\hrulefill\)

To identify the bisector of the acute angle, calculate the angle between any one of the bisectors and one of the lines.

The formula for the angle between two lines a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 is:

\(\tan \theta=\left|\dfrac{a_2b_1-a_1b_2}{a_1a_2+b_1b_2} \right|\)

Let's find the angle θ between the bisector 3x + 11y - 10 = 0, and the line 3x - 2y + 1 = 0.

Therefore:

Substitute the values of a₁, b₁, a₂ and b₂ into the formula for the angle between two lines:

\(\tan \theta=\left|\dfrac{3 \cdot 11-3 \cdot (-2)}{3 \cdot 3+11\cdot (-2)} \right|\)

\(\tan \theta=\left|\dfrac{33+6}{9-22} \right|\)

\(\tan \theta=\left|\dfrac{39}{-13} \right|\)

\(\tan \theta=\left|-3\right|\)

As tan θ > 1, the angle θ between the bisector and the line must be more than 45°. This means that the angle between the two given lines is more than 90°. So 3x + 11y - 10 = 0 is the bisector of the obtuse angle between the given lines. Therefore, the other angle bisector bisects the acute angle.

Therefore, the bisector of the acute angle is:

\(\boxed{\boxed{33x - 9y = 0 }}\)

Note: The attached diagram shows the given lines as black lines, the bisector of the acute angle as the red dashed line, and the bisector of the obtuse angle as the green dashed line.

The total money would Zoey have to pay in a month in which she downloaded 45 songs will be $40.75. And she has to pay if she downloaded s songs that will be y = 0.75s + 7.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

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

Zoey signed up for a streaming music service that costs $7 per month. The service allows Zoey to listen to unlimited music, but if she wants to download songs for offline listening, the service charges $0.75 per song.

Let x be the number of songs and y be the total amount. Then the equation will be

y = 0.75x + 7

The total money would Zoey have to pay in a month in which she downloaded 45 songs will be

y = 0.75 × 45 + 7

y = 33.75 + 7

y = $40.75

She has to pay if she downloaded s songs that will be

y = 0.75s + 7

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Answer:

6

Step-by-step explanation:

From the table given defining a function, the values of "x" on the table represents the input of the function, which gives us an output, f(x), which can be labelled as "y" in some instances.

Thus, the value of f(0), is simply the output value we would get, given an input value of "0".

So therefore, f(0) = 6. That is, at x = 0, f(x) = 6.

Answer: 6

Step-by-step explanation:

Answer:

I got 7920.

Step-by-step explanation:

Because 5280-2640=2640

then i added 5280+2640 and got 7920.

Answer:

The answer is

Step-by-step explanation:

The midpoint M of two endpoints of a line segment can be found by using the formula

\(M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )\)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

A(1, 2) and B(7, 8)

The midpoint is

\(M = ( \frac{1 + 7}{2} , \: \frac{2 + 8}{2} ) \\ = ( \frac{8}{2} \: , \: \frac{10}{2} )\)

We have the final answer as

Hope this helps you

Consider the following differential equation: (d^2y)/(dt^2) + 3(dy)/(dt) + 2y = 0.For this differential equation, we need to find a solution of the indicated form y = e^rt. This means that we are looking for a solution of the differential equation in the form of an exponential function.

To find a solution, we need to substitute y = e^rt into the differential equation:
(d^2(e^rt))/(dt^2) + 3(d(e^rt))/(dt) + 2e^rt = 0
This simplifies to:r^2e^rt + 3re^rt + 2e^rt = 0
Factorizing this equation by e^rt, we get:r^2 + 3r + 2 = 0
This is a quadratic equation, which can be solved using the quadratic formula:
r = (-3 ± √(3^2 - 4(1)(2))) / (2(1))r = (-3 ± √1) / 2r1 = -2, r2 = -1
We have found two solutions to the quadratic equation, r1 = -2 and r2 = -1. These are the values of r that will give us solutions of the indicated form, y = e^rt.Now that we have found the values of r, we can write down the general solution of the differential equation: y = c1e^(-2t) + c2e^(-t) where c1 and c2 are constants that depend on the initial conditions of the differential equation.

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Answer:

5. Alt ext, 6. Alt int, 7. Alt ext, 8, SS Int, 9. Corr

Step-by-step explanation:

5. Alternate exterior since they are on opposite sides of the transversal but both are exterior to parallel lines.

6. Alternate interior, opposite sides of transversal but both are inside the parallel lines.

7. Alternate exterior, same as #1

8. Same side interior since they are on the same side of the transversal and both are inside the parallel lines

9. Corresponding since they are at the same place on the 2 parallel lines.

Answer:

it rose by 0.45

Step-by-step explanation:

Answer:

Step-by-step explanation:

When you list the trigonometic ratios for both acute angles in a right triangle, you notice some interesting developments.

Let's concentrate on sine and cosine:

Observation from the table above: notice1

In a right triangle, the sine of one acute angle, A, equals the cosine of the other acute angle, B.

If ∠A and ∠B are the acute angles of a right triangle,

sin A = cos B

Since the measures of these acute angles of a right triangle add to 90º, we know these acute angles are complementary. ∠A is the complement of ∠B, and ∠B is the complement of ∠A.

If we write, m∠B = 90º - m∠A    (or m∠A = 90º - m∠B ), and we substitute into the original observation, we have:

      notice4

If θ is substituted for m∠A , we establish the following relationship between sine and cosine:

sincosrule

The sine of any acute angle is equal to the cosine of its complement.

The cosine of any acute angle is equal to the sine of its complement.

Sine and cosine are called "cofunctions", where the sine (or cosine) function

of any acute angle equals its cofunction of the angle's complement.

FYI: What about tangent?

Yes, there is a "relationship" regarding the tangent of the two acute angles (A and B) in a right triangle. It is not, however, the same type of relationship that exists between sine and cosine.

The tangent of ∠A is the reciprocal (flip over) of the tangent of ∠B.

The angles being used in the following examples are acute angles.

ex1

If sin 30º = ½ and cos θ = ½,

find θ.  Solution: Since both trig functions = ½,

30º and θ must be complementary.

θ = 60º

ex2

If sin(3x + 10)º = cos(x + 24)º,

find x.  Solution: In order for the sine and cosine to be equal, the angles must be complementary.

3x + 10 + x + 24 = 90

4x + 34 = 90

4x = 56

x = 14

ex3

If sin(15º) = 0.26 and

cos (15º) = 0.97,

find sin(75º) and the cos(75º).  Solution: The sine of an angle and the cosine of its complement are equal.

15º and 75º are complementary.

sin(75º) = cos(15º) = 0.97

cos(75º) = sin(15º) = 0.26

ex4

In right ΔABC, m∠C = 90º,

sin A = x + 0.1 and cos B = 2x - 0.4. Find x.  Solution: If A and B are the acute angles of a right triangle, sin A = cos B.

x + 0.1 = 2x - 0.4

0.5 = x

Answer:

slope: -3/4    y-intercept: 3   equation: y=(-3/4)x+3

Answer:

550

Step-by-step explanation:

It´s 550 because 612-62 is 550

The specific range depends on the material properties and the energy levels involved.

The minimum and maximum frequencies for the acoustic and optic modes depend on the specific system or material under consideration. However, I can provide some general information.

Acoustic Mode:

The acoustic mode refers to the propagation of sound waves or vibrations in a material. In a solid, the acoustic mode can have different types, such as longitudinal and transverse modes.

The minimum frequency for the acoustic mode is typically determined by the size and physical properties of the material. In general, it can be close to zero for macroscopic objects or materials with low elasticity.

The maximum frequency for the acoustic mode depends on factors such as the speed of sound in the material and the characteristic dimensions of the system. It can range from a few kilohertz to several gigahertz.

Optic Mode:

The optic mode is related to the interaction of light with a material. It typically refers to the vibrations of charged particles (such as electrons) in a solid or the oscillations of electric or magnetic fields associated with photons.

The minimum frequency for the optic mode is typically determined by the energy gap between electronic states in the material. For example, in a semiconductor, the minimum frequency is usually in the infrared range.

The maximum frequency for the optic mode is not strictly defined, as it can extend into the terahertz, infrared, visible, ultraviolet, X-ray, and even gamma-ray regions. The specific range depends on the material properties and the energy levels involved.

It's important to note that these frequency ranges are general guidelines and can vary depending on the specific system or material being studied.

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Answer:

x ≤ -3

Step-by-step explanation:

For solid lines you would do ≤ or ≥, then for shading on the right side you would need < or ≤

The sets that are equal are A = {1, 2, 3} and B = {2, 1, 3}

The order of elements does not matter when determining the equality of sets. Both sets A and B contain the same elements, namely 1, 2, and 3, even though their order is different. Therefore, we can say that A and B are equal sets.

The other sets mentioned, A = {1, 2} and B = {1}, A = {1, 2, 4} and B = {1, 2, 3}, and A = {1, 2} and B = {1, 2, 3}, are not equal because they have different elements. In the first case, set A has two elements, while set B has only one element.

In the second case, set A contains the element 4, which is not present in set B.

In the third case, set A has two elements, while set B has three elements, including the element 3, which is not present in set A.

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Answer:

sorry i needed the points for school

Step-by-step explanation:

Answer:

350

Step-by-step explanation:

350 because there are 1/12 of VIP seats and there are 600 so 600 times 1/12 is 6,600.

Then you minus off the 600 VIP seats so you get 6000

next you do 600 divided bu 12 because of the 1st tier seats and 2nd tier seats combined which then you get 50

lastly you do 50 times 7 because of the ration 7:5 1st tier seats to 2nd tier seats so then you get 350

please mark brainliest i need one last one

Answer:

b = 8.485

c = 23.995 ≈ 24

Step-by-step explanation:
Part b:

\(\sqrt{(10-4)^2+(9-3)^2}\)

√(36 + 36)

= 8.485

Part c:

Base = \(\sqrt{(6-2)^2+(1-5)^2}\)

Base = 5.656

Area = Base x Height x 0.5

Area = 5.656 x 8.485 x 0.5

Area = 23.995 ≈ 24

Answer:

320

Step-by-step explanation:

Use PEMDAS - order of operations

5(2)^2 + 3(10)^2

5 x 4 + 3 x 100

20 + 300

320

The angle between a clock's minute and hour hands changing at 10 o'clock in the morning is 5.5 degrees/minute.

what is the rate of change in calculus?

The rate of change defines the relationship between two changing variables. Consider a moving object that moves twice as much in the vertical direction (y) as it does in the horizontal direction (x). This can be expressed mathematically as y = 2x.

Let 'θ' represent the angle between the minute and hour hand.

Let θ1 be the angle between the minute hand and 12.

                     \(\frac{d\theta_2}{dt}=\frac{1}{60*12}\times2\pi\\\\\frac{d\theta_2}{dt}=\frac{\pi}{360}\)(Between hour hand and 12)

                     \(\theta=\pm(\theta_1-\theta_2)\\\\\frac{d\theta}{dt}=\pm(\frac{d\theta_1}{dt}-\frac{d\theta_2}{dt})\\\\\frac{d\theta}{dt}=\pm(\frac{\pi}{30}-\frac{\pi}{360})\\\\\frac{d\theta}{dt}=\pm5.5$ degree$\)

Hence the angle between a clock's minute and hour hands changing at 10 o'clock in the morning is 5.5 degrees/minute.

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Check the picture below.

so the center of the circle is the midpoint of that diameter, and its radius is half its length.

\(~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{7}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 4 -2}{2}~~~ ,~~~ \cfrac{ 7 -1}{2} \right) \implies \left(\cfrac{ 2 }{2}~~~ ,~~~ \cfrac{ 6 }{2} \right)\implies \stackrel{ center }{(1~~,~~3)} \\\\[-0.35em] ~\dotfill\)

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ r(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{ radius }{r}=\sqrt{(~~4 - (-2)~~)^2 + (~~7 - (-1)~~)^2} \implies r=\sqrt{(4 +2)^2 + (7 +1)^2} \\\\\\ r=\sqrt{( 6 )^2 + ( 8 )^2} \implies r=\sqrt{ 36 + 64 } \implies r=\sqrt{ 100 }\implies r=10 \\\\[-0.35em] ~\dotfill\)

\(\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{1}{h}~~,~~\underset{3}{k})}\qquad \stackrel{radius}{\underset{10}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - 1 ~~ )^2 ~~ + ~~ ( ~~ y-3 ~~ )^2~~ = ~~10^2\implies {\large \begin{array}{llll} (x-1)^2+(y-3)=100 \end{array}}\)

Answer

It is C.

Step-by-step explanation:

because you must multiply the 12 to both the A and the B. Hope this helps. Good luck!

Answer:

B. No, Hannah should have used the ratio \( \frac{adjacent}{opposite} \)

Step-by-step explanation:

✍️The formula for calculating cotangent of an angle is given as:

\( cot = \frac{adjacent}{opposite} \).

The ratio, \( \frac{opposite}{adjacent} \), used by Hannah is the formula for calculating tangent of an angle.

Therefore, Hannah did not calculate the cotangent of the angle correctly.

She should have used, the ratio, \( \frac{adjacent}{opposite} \) instead.

The probability that a customer did not order a starter is 9/10.

We have,

To find the probability that a customer did not order a starter, we can use the concept of set theory and probability.

Let's define the events:

A: Customer ordered a starter

A' (read as "A compliment"): Customer did not order a starter

Given information:

Total number of customers = 30

Customer that Ordered a starter = 3

Customer that Ordered a dessert = 5

Customer who ordered Both starter and dessert = 14

To find the probability that a customer did not order a starter (A'), we can subtract the probability of event A (customer ordered a starter) from 1.

Probability of A = Customer that Ordered a starter / Total number of customers

= 3 / 30

= 1 / 10

Probability of A' (customer did not order a starter) = 1 - Probability of A

= 1 - 1/10

= 9/10

Therefore,

The probability that a customer did not order a starter is 9/10.

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