What is the slope-intercept equation of the line below?

Answer:

Step-by-step explanation:

Answer:

use a sin cos tan calculator.

Step-by-step explanation

on calculator

2nd tan

tan x = 30/8

there's ur answer

By applying Cathetus theorem, the value of x is equal to 10 units.

In order to determine the value of x, we would apply Cathetus theorem (leg rule), which states that each leg of a right-angled triangle is the geometric mean that's directly proportional between the hypotenuse and the part of the hypotenuse that's directly below the leg.

In this context, we have:

x² = m × a

x² = (21 + 4) × 4

x² = 25 × 4

x² = 100

x = √100

x = 10 units.

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Since the lines have the same slopes, hence they are parallel lines

We can determine the relations by knowing the slopes of the line

For the line with coordinates (9, –5) and (5, –2)

Slope = -2+5/5-9
Slope = -3/4

For the line with coordinates (–4, –2) and (–8, 1)

Slope = 1+2/-8+4
Slope = -3/4

Since the lines have the same slopes, hence they are parallel lines

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Answer: 80.28 square feet

Step-by-step explanation:

[tex]2(6.1\cdot 3+3\cdot 2.4+2.4 \cdot 6.1)=80.28[/tex]

The table of inputs that satisfy the given function is (-2, 25), (-1, -30), (0, 35), (1, -40) and (2, -45).

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the function f(x) = -5(x + 7)

When x = -2; f(-2) = -5(-2 + 7) = -25

When x = -1; f(-1) = -5(-1 + 7) = -30

When x = 0; f(0) = -5(0 + 7) = -35

When x = 1; f(1) = -5(1 + 7) = -40

When x = 2; f(2) = -5(2 + 7) = -45

The table of inputs that satisfy the given function is (-2, 25), (-1, -30), (0, 35), (1, -40) and (2, -45).

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let width be 'x'

according to the question,

length = 4x

perimeter = 100 cm

we know ,

perimeter of rectangle = 2(l+b)

100= 2(4x+x)

100= 10x

x= 10

then length = 4x = 4×10= 40

and , area of rectangle = l×b

= 40 × 10 = 400

area of rectangle is 400cm

Answer:

Step-by-step explanation:

let width=x

length=4x

2(x+4x)=100

2×5x=100

x=100/10=10

width=10 cm

length=4×10=40 cm

area=l×b=40×10=400 cm²

The value of the integral is [tex]\int\limits^{}_s {9x + 2y + z^2} \, dS = \frac{4}{3}\pi[/tex]

The expression is given as:

[tex]\int\limits^{}_s {9x + 2y + z^2} \, dS[/tex]

[tex]x^2 + y^2 + z^2 = 1[/tex]

Rewrite the integral as:

[tex]\int\limits^{}_s {9x + 2y + z*z} \, dS[/tex]

As a general rule, we have:

[tex]\int\limits^{}_s {Px + Qy + R*z} \, dS[/tex]

By comparison, we have:

P = 9

Q = 2

R = z

By the divergence theorem, we have:

F = Pi + Qj + Rk

So, we have:

F = 9i + 2j + zk

Differentiate

F' = 0 + 0 + 1

F' = 1

The volume of a sphere is:

[tex]V = \frac{4}{3}\pi r^3[/tex]

Where:

r = F' = 1

So, we have:

[tex]V = \frac{4}{3}\pi (1)^3[/tex]

Evaluate

[tex]V = \frac{4}{3}\pi[/tex]

This means that:

[tex]\int\limits^{}_s {9x + 2y + z^2} \, dS = \frac{4}{3}\pi[/tex]

Hence, the value of the integral is [tex]\int\limits^{}_s {9x + 2y + z^2} \, dS = \frac{4}{3}\pi[/tex]

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Answer:

c. 12km/hr

Step-by-step explanation:

Speed = distance/time

Coffee shop: Divide distance traveled by time taken to get the speed in km/min, then convert minutes to hours, and finally simplify to calculate the speed in km/hr

4km/20min * 60min/1hr = 240km/20hr = 12km/1hr = 12km/hr

Other shop: Same task, in the question it already says he is traveling at the same rate so this is only useful to check your answer

10km/50min * 60min/1hr = 600km/50min = 12km/1hr = 12km/hr

Answer:

9. 3 acute angles

10: a) Acute Isosceles

     b) Acute Scalene  

Step-by-step explanation:

9:  Sum of Interior angle theorem: Sum of the interior angles of a Triangle = 180°

An Acute angle is a angle that is less than 90°

the sum of the two acute angles must be less than 180°

The base angles of an isosceles triangle are congruent.

So For example,

the base angles of the isosceles are ∠1 and ∠2

Lets make the three angle measure closer:

if ∠1 = 46° then ∠2 also have to be 46° and ∠3 = 88°

all three angle are less than 90° and two angles are congruent.

3) We have

[tex]f(x) = \sec\left(\dfrac{\pi x}2\right) = \dfrac1{\cos\left(\frac{\pi x}2\right)}[/tex]

which has vertical asymptotes (i.e. infinite discontinuities) whenever the denominator is zero. This happens for

[tex]\cos\left(\dfrac{\pi x}2\right) = 0[/tex]

[tex]\implies \dfrac{\pi x}2 = \cos^{-1}(0) + 2n\pi \text{ or } \dfrac{\pi x}2 = -\cos^{-1}(0) + 2n\pi[/tex]

(where [tex]n[/tex] is any integer)

[tex]\implies \dfrac{\pi x}2 = \dfrac\pi2 + 2n\pi \text{ or } \dfrac{\pi x}2 = -\dfrac\pi2 + 2n\pi[/tex]

[tex]\implies x = 1 + 4n \text{ or } x = -1 + 4n[/tex]

So the graph of [tex]f(x)[/tex] has vertical asymptotes whenever [tex]x=4n\pm1[/tex] and [tex]n\in\Bbb Z[/tex].

4) Given

[tex]h(t) = \begin{cases} t^3+1 & \text{if } t<1 \\ \frac12 (t+1) & \text{if } t\ge1 \end{cases}[/tex]

we have the one-sided limits

[tex]\displaystyle \lim_{t\to1^-} h(t) = \lim_{t\to1} (t^3+1) = 1^3+1 = 2[/tex]

and

[tex]\displaystyle \lim_{t\to1^+} h(t) = \lim_{h\to1} \frac{t+1}2 = \frac{1+1}2 = 1[/tex]

The one-sided limits don't match, so the two-sided limit [tex]L[/tex] does not exist. In other words, the limit does not exist at [tex]x=1[/tex] because the function approaches different values from the left and right side of [tex]x=1[/tex].

The dilation scale factor used to form polygon K'T'P'J' from polygon KTPJ is 1/2

An equation is an expression that shows the relationship between two or more numbers and variables.

Dilation is the increase or decrease in size of a figure by a scale factor.

The scale factor of the image = K'T'/KT = 1/2 ÷ 1 = 1/2

The dilation scale factor used to form polygon K'T'P'J' from polygon KTPJ is 1/2

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The value of g(x) = 2[f(x)]² - 1 is g(x) = 8x² + 8x + 1

f(x) = 2x+1

Find

g(x) = 2[f(x)]² - 1

Hence,

g(x) = 2[2x + 1]² - 1

g(x) = 2[4x² + 4x + 1] - 1

g(x) = 8x² + 8x + 2 - 1

g(x) = 8x² + 8x + 1

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When two straight lines or rays intersect at a shared endpoint, an angle is generated. The correct option is A.

When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."

The diagram for the given problem can be made as shown below. Therefore, the other name for angle 2 will be ∠DGE.

Hence, the correct option is A.

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Answer:

a

Step-by-step explanation:

got it right

Answer:

a) 24 [cm]; b) 30°.

Step-by-step explanation:

a) the length of full the circle is: min_arc(AB)+maj_arc(AB)=π(22+2)=24π [cm]. Then the radius is: r=L/π; ⇒ r=24π/π=24 [cm];

b) if the full circle is 360° (L=24π), then m(∠AOB):2=360°:24 and the required measure of the acute angle AOB is:

m(∠AOB)=360*(1/12)=30°.

Step-by-step explanation:

hggggggggggggggggggggg

Using the normal distribution and the central limit theorem, we have that:

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, the parameters are given as follows:

[tex]\mu = 60, \sigma = 11, n = 12, s = \frac{11}{\sqrt{12}} = 3.1754[/tex].

Hence:

The probabilities are given by the p-value of Z when X = 61.2 subtracted by the p-value of Z when X = 59.3, hence, for a single individual:

X = 61.2:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{61.2 - 60}{11}[/tex]

Z = 0.11

Z = 0.11 has a p-value of 0.5398.

X = 59.3:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{59.3 - 60}{11}[/tex]

Z = -0.06

Z = -0.06 has a p-value of 0.4761.

0.5398 - 0.4761 = 0.0637.

0.0637 = 6.37% probability that a single person consumes between 59.3 mL and 61.2 mL.

For the sample of 12, we have that:

X = 61.2:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{61.2 - 60}{3.1754}[/tex]

Z = 0.38

Z = 0.38 has a p-value of 0.6480.

X = 59.3:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{59.3 - 60}{3.1754}[/tex]

Z = -0.22

Z = -0.22 has a p-value of 0.4129.

0.6480 - 0.4129 = 0.2351 = 23.51% probability that the sample mean of the consumption of 12 people is between 59.3 mL and 61.2 mL. Since the sample size is less than 30, a normal distribution has to be assumed.

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There are 36 possible combinations that can occur when 2 dice are rolled. For the sake of this question, we'll count instances where dice 1 = 3/dice 2 = 2 and dice 1 = 2/dice 2 = 3.

Now, let's think about all of the possible ways a total of 5 could be rolled.

1 + 4

2 + 3

3 + 2

4 + 1

That's 4 possibilities to roll a total of 5 out of 36 possible outcomes.

4 / 36 = ? / 180

---Now, we need to use a proportion in order to figure out the possibilities out of 180.

36x = 720

x = 20

If you rolled a pair of fair dice 180 times, you would expect to roll a total of 5, 20 times.

Hope this helps!

Answer:

Graph 3 represents a function

Graph 4 is not a function

Step-by-step explanation:

By definition :

A function is a rule or law which relates all the elements of one set with some UNIQUE element of another set.

Which means that from a given value of the input x, there will be only one value of y in a function f(x) = y

Graphically it would represent that for a given point x , there would only be one value of y corresponding to that x.

In graph 4, we can see that for one x, there exists two values of y.

Example : at x = 5, we have y=5 AND y= -5; which is not possible in case of a function.

Now A and B are independent

Both connectors must work together to make the parallel circuit work

P(A and B)

Connectors be C1 and C2

We need P(C1.C2)

Note the formula

For independent events

[tex]\boxed{\sf P(AB)=P(A)P(B)}[/tex]

[tex]\\ \tt{:}\dashrightarrow P(C1C2)=P(C1)P(C2)[/tex]

[tex]\\ \tt{:}\dashrightarrow 0.84(0.72)[/tex]

[tex]\\ \tt{:}\dashrightarrow 0.6[/tex]

Answer:

27 cubic inches

Step-by-step explanation:

A cube by definition has all the side lengths equal to each other. Kind of like how a square has all equal sides, except with a cube, there's depth. So the volume of the cube would be the width*length*depth, but since the width=length=depth, you only need one side, and you just cube it, or raise it to the third power. So you have the equation: [tex]A=(3\text{ inches})^3=27\text{ inches}^3[/tex] which is read as 27 cubic inches

The account that yields the highest annual interest rate is account 2.

In order to determine the account that yields the highest interest, the effective annual interest has to be calculated. The effective annual interest is the interest rate that an account actually earns when compounding is accounted for.

Effective annual rate = (1 + APR / m ) ^m - 1

M = number of compounding

Account 2: (1 + 0.0325/12)^12 - 1 = 3.3%

Account 3 : (1 + 0.0310 / 52)^52 - 1 = 3.15%

Account 4: (1 + 0.0315 /365)^365 - 1 = 3.2%

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Tommy and his father will meet after 2400 seconds or 40 minutes. So they will meet at 3:40 pm.

Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.

Given that:-

The time will be calculated by using the relative speed concept.

Relative speed = Speed of father - Speed of Tommy

Relative speed = 1.65 - 1.35

Relative speed = 0.3 meter per second

Relative speed = Distance / Time

0.3 = 720 / Time

Time = 720 / 0.3

Time = 2400 seconds = 2400/ 60 = 40 minutes

We know that both departed at 3 pm they will meet at 3:40 pm.

Therefore Tommy and his father will meet after 2400 seconds or 40 minutes. So they will meet at 3:40 pm.

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Answer:

second graph

Step-by-step explanation:

looking at the y intercept. 12 is y int

Answer:

Second line

Step-by-step explanation:

our equation rearranged is y=-3x+12

meaning that y-intercept is 12, that is where the line cuts the y axis

we find that the second line cuts the y axis around that 12 therefore it is the most relevant line here

One of the two equations required in the system of equations needed to determine the dollar amount of phone and computer sales Houa made is y = x + 600.

Let x represents the dollar amount of phone sales Houa made, and y represents the dollar amount of computer sales she made.

Therefore, a system of equations that could be used to determine x and y can be written as follows:

y = x + 600 ........................................................... (1)

0.04x + 0.05y = 129 ......................................... (2)

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Step-by-step explanation:

the probability is always the number of desired cases over the number of all possible cases.

in our situation we have 15 cards.

that is the total possible cases when a random card is chosen.

how many desired cases do we have ?

a number NOT a multiple of 5.

how many are there ?

it is easier to say how many numbers there are being a multiple of 5 : 5, 10, 15

so, 3 numbers out of the 15 are multiple of 5.

that means

15 - 3 = 12 numbers of the 15 are NOT multiples of 5.

so, the probability to draw a card that is not a multiple of 5 is

12/15 = 4/5 = 0.8

the information about event B and even numbers is irrelevant for the question.

Answer:

[tex]x=6, x=-4[/tex]

Step-by-step explanation:

1) Let's solve this quadratic equation by factorizing. We need to find two numbers that multiply to -24 and add up to -2 simultaneously. If we pull out the factors of -24, two of them will be -6 and 4, which multiply to -24 as well as add up to -2.

3) Write [tex]-2x[/tex] as a sum.

[tex]x^2-6x+4x-24=0[/tex]

Now, we can factor them out by grouping.

[tex]x^2-6x+4x-24=0\\x(x-6) + 4(x-6)=0[/tex]

Since, [tex]x -6[/tex] is common in both of the factors, we only take one of the [tex]x -6[/tex] along with [tex]x[/tex] and [tex]4[/tex] and all equated to 0.

[tex](x-6)(x+4) = 0[/tex]

Solve for x: [tex]x-6=0[/tex]

[tex]x=0+6\\x=6[/tex]

Solve for x: [tex]x+4=0[/tex]

[tex]x=0-4\\x=-4[/tex]

Therefore, our solutions to this quadratic equation are  [tex]x=6, x=-4[/tex].

[tex]\huge\boxed{\textsf{A.}\ 78.5\ \text{in}^2}[/tex]

Correction to your question text: diameter, not radius.

The area of a circle is given by:

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

The radius is half of the diameter.

[tex]A=\pi\cdot\left(\dfrac{10}{2}\right)^2[/tex]

Substitute and solve.

[tex]\begin{aligned}A&=\pi\cdot\left(\frac{10}{2}\right)^2\\&=\pi\cdot5^2\\&=\pi\cdot25\\&\approx\boxed{78.5}\end{aligned}[/tex]

The set of transformations that could be applied to ABCD, to create A″B″C″D″ is a reflection over the y-axis, followed by a rotation of 180°

"It is a geometric transformation where all the points of an object are reflected on the line of reflection."

For the given question,

The Rectangle ABCD is formed by ordered pairs A at (-4, 2), B at (-4, 1), C at (-1, 1), D at (-1, 2)

The Rectangle A″B″C″D″ is formed by ordered pairs A" at (-4, -2), B" at   (-4, -1), C" at (-1, -1) and D" at (-1, -2)

We can observe that the coordinates of ABCD are of the form (-x, y)  where x, and y, are positive numbers

The form of the ordered pair of the vertices of the A″B″C″D″ will be (-x, -y)

The coordinates of the point (-x, y) after a reflection over the y-axis would be of the form (x, y)

And after rotation of 180°, the coordinates would be (-x -y).

Hence, the set of transformations that could be applied to ABCD, to create A″B″C″D″ is a reflection over the y-axis, followed by a rotation of 180°.

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