What is the point-slope form of a line that has a slope of 3 and passes through point (1, 4)?

Final answer:

The normal form of x + 5y - 2 = 0 is (1/√26)x + (5/√26)y - (2/√26) = 0. The length of the normal is 1, and the angle it makes with the positive x-axis can be calculated using tan θ = 5, which gives the angle as tan-1(5).

Explanation:

To rewrite the equation x + 5y - 2 = 0 in normal form, we need to express it in the form Ax + By + C = 0, where A2 + B2 = 1. The equation is already in this form, but we must divide each term by the square root of (12 + 52) to satisfy the condition for A2 + B2. After the division, the normal form becomes (1/√26)x + (5/√26)y - (2/√26) = 0.

The length of the normal is the magnitude of the vector (A, B), which in this case, is 1 due to the normalization. To find the angle θ that the normal makes with the positive x-axis, we use the relationship tan θ = B/A. For our equation, tan θ = 5/1, so θ = tan-1(5).

The analytical method of vector addition involves identifying the x- and y-components of vectors and merging them to calculate the resultant vector's magnitude and direction.

Yes, they're similar.

Step-by-step explanation:

Triangles are similar when they have the same shape but vary in sizes. This is our case here. We have two equilateral ∆s which makes them similar but what differs them is the length. One is 6 and the other is 10. Although that doesn't affect anything in the triangle. If you drew a height to any base (in either triangle) it would still be a bisector, median, and perp bisector. Their angles are alsp equal.

Carolyn wants to deposit a check into her savings account. She should sign the back of the check , complete a deposit slip, and visit the teller at the bank.

Answer:

y=15t

t is time

Answer:

[tex](4,-\frac{\pi}{3}+2n\pi)[/tex] And [tex](-4,-\frac{\pi}{3}+(2n+1)\pi).[/tex]

Hope this helps you out!

Answer:

All the polar coordinates of point P are [tex]P(4,-\frac{\pi}{3})=(4,2n\pi-\frac{\pi}{3})[/tex] and [tex]P(4,-\frac{\pi}{3})=(-4,(2n+1)\pi-\frac{\pi}{3})[/tex], where n is any integer and θ is in radian.

Step-by-step explanation:

It a polar coordinate is given as P(r,θ), then all the polar coordinates of point P  are defined as

[tex]P(r,\theta)=(r,2n\pi+\theta)[/tex]

[tex]P(r,\theta)=(-r,(2n+1)\pi+\theta)[/tex]

Where, n is any integer and θ is in radian.

The given point is

[tex]P(4,-\frac{\pi}{3})[/tex]

So, all the polar coordinates of point P  are defined as

[tex]P(4,-\frac{\pi}{3})=(4,2n\pi-\frac{\pi}{3})[/tex]

[tex]P(4,-\frac{\pi}{3})=(-4,(2n+1)\pi-\frac{\pi}{3})[/tex]

Therefore all the polar coordinates of point P are [tex]P(4,-\frac{\pi}{3})=(4,2n\pi-\frac{\pi}{3})[/tex] and [tex]P(4,-\frac{\pi}{3})=(-4,(2n+1)\pi-\frac{\pi}{3})[/tex], where n is any integer and θ is in radian.

Answer:

The correct answer is A.

trapezoid: (25+19)/2 *20 (see formula for area of a trapezoid)

and the smaller parallelogram: (10*17) (see formula for parallelogram)

and subtract the parallelogram from the trapezoid and you're done!

so we have a trapezoid with a parallelogram inside.

now, if we just get the area of the trapezoid, which includes the parallelogram, and then  get the area of the parallelogram and subtract it from that of the trapezoid, what's leftover is the shaded region, because we'd be in effect making a "hole" in the trapezoid and the area leftover is the shaded part.

[tex]\bf \stackrel{\textit{area of a trapezoid}}{A=\cfrac{h(a+b)}{2}}~~ \begin{cases} a,b=\stackrel{bases}{parallel}\\ \qquad ~~ sides\\ h=height\\ \cline{1-1} a=19\\ b=25\\ h=20 \end{cases}\qquad \stackrel{\textit{area of a parallelogram}}{A=bh}~~ \begin{cases} b=base\\ h=height\\ \cline{1-1} b=17\\ h=10 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{trapezoid}}{\cfrac{20(19+25)}{2}}~~-~~\stackrel{\textit{parallelogram}}{(17\cdot 10)}\implies 10(44)-170\implies 440-170\implies 270[/tex]

Answer:

Step-by-step explanation:

4(3-2x)=15

Distribute 4:

12-8x= 15

Subtract 12:

-8x= 3

Divide

X= -3/8 or -0.375

ANSWER

[tex]x = - \frac{3}{8} [/tex]

EXPLANATION

The given equation is:

4(3 - 2x) = 15

Expand the parenthesis to obtain:

12-8x=15

Group similar terms to get;

-8x=15-12

Combine similar terms to get:

-8x=3

Divide both sides by -8

[tex]x = - \frac{3}{8} [/tex]

Answer:

4

Step-by-step explanation:

A standard deck is composed of 52 cards, and contains 13 cards per suit. So, the theoretical probability of picking a card of any suit (and thus, in particular, a heart) is given by

[tex]P(\text{hearts}) = \dfrac{\text{\# of hearts in the deck}}{\text{\# of cards in the deck}} = \dfrac{13}{52} = \dfrac{1}{4}[/tex]

On the other hand, the experimental probability is (as the name suggests) the probability that we can deduce from our experiment: we picked 60 cards, and 12 of these were hearts. This means that it would seem to us that

[tex]P(\text{hearts}) = \dfrac{\text{\# of hearts we picked}}{\text{\# of cards we picked}} = \dfrac{12}{60} = \dfrac{1}{5}[/tex]

Answer:4 months

Step-by-step explanation:

if you go by members for each group. group A has 450 but adds in 15 members each month. group B has 25 members each month. not take 25 and multiply it by 4 it equals to 100. and multiply 15 by 4 equals 50. which makes group B 500. and group A 500.

After 5 months, Fitness Club A and Fitness Club B will have the same number of members.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have.
We can solve this problem by setting up an equation to represent the number of members at each club after a certain number of months and then solving for the number of months that makes the number of members equal.

Let's use "m" to represent the number of months:

Number of members at Club A after m months = 450 + 15m

Number of members at Club B after m months = 400 + 25m

To find when the two clubs will have the same number of members, we can set these two expressions equal to each other and solve for m:

450 + 15m = 400 + 25m

Subtracting 400 from both sides:

50 + 15m = 25m

Subtracting 15m from both sides:

50 = 10m

Dividing both sides by 10:

m = 5

Therefore,

After 5 months, Fitness Club A and Fitness Club B will have the same number of members.

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Answer:

[tex]\large\boxed{3a^n(a^n+a^{n-1})=3a^{2n}+3a^{2n-1}}[/tex]

Step-by-step explanation:

[tex]3a^n(a^n+a^{n-1})\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=(3a^n)(a^n)+(3a^n)(a^{n-1})\qquad\text{use}\ x^n\cdot x^m=x^{n+m}\\\\=3a^{n+n}+3a^{n+n-1}\\\\=3a^{2n}+3a^{2n-1}[/tex]

Answer:

The answer is .800

To round .796 to the nearest hundredth, we observe the third decimal place (6) and round up the second decimal place from 9 to 10, which effectively turns .796 into .80.

The question asks us to round .796 to the nearest hundredth. To do this, we look at the third decimal place, which is 6. Since 6 is greater than 5, we round up the second decimal place from 9 to 10. However, since the second place cannot literally take the value of 10, it effectively rolls over and adds 1 to the first decimal place, changing .796 to .80. Therefore, the answer is .80 when rounded to the nearest hundredth.

Joe is 68.4” tall. Set the ratio of 5/6=57/x, solve using the butterfly method (multiply 57 and 6, set equal to 5x) 57•6 is 342, so at this point it would be 342=5x. 342/5 is 68.4

Answer:

D.  [tex]y=\tan (x-\pi)+2.[/tex]

Step-by-step explanation:

Consider parent function [tex]y=\tan x.[/tex] The graph of this function is the same as the graph of the function [tex]y=\tan (x-\pi),[/tex] because the tangens has period of [tex]\pi.[/tex] (See first attached diagram)

Now, you can see that the graph of the function [tex]y=\tan (x-\pi)[/tex] is translated 2 units up. This translation gives you the function [tex]y=\tan (x-\pi)+2.[/tex] (see second attached diagram)

Answer: D

Step-by-step explanation: Apex

Answer:

1/5

Step-by-step explanation:

it went up one on the y axis and 5 on the X and the formula is rise/run or up/left

Answer:

55 deg

Step-by-step explanation:

In triangle ABC, angle A is a right angle, so angles B and C are complementary; their measures add to 90 deg.

m<C + m<B = 90

m<C + 35 = 90

m<C = 90 - 35

m<C = 55

Angle Z corresponds to angle C, so angles Z and C are congruent.

m<Z = m<C = 55

Answer:

Cost of shipping and handling = $23.453

Step-by-step explanation:

Given

Price of Chair=$220.59

Tax=7.9%

Invoice Price=$261.47

In order to find the cost of shipping and handling, we have to subtract the cost of chair and the tax from the invoice price of chair.

To find the tax,

Tax amount=220.59*0.079

=$17.42661

Now,

Cost of shipping and handling=$261.47-$220.59-$17.42661

=$23.453 ..

Answer:

The cost of shipping and handling is $23.45 .

Step-by-step explanation:

As given

Business services ordered a chair that cost $220.59.

if the California sales tax rate is 7.9%

7.9% is written in the decimal form

[tex]= \frac{7.9}{100}[/tex]

= 0.079

Thus

Sales tax price = 0.079 × Cost of the chair

                         = 0.079 × $220.59

                         = $ 17.43 (Approx)

Thus

Cost of the  ordered chair with sales tax price = Cost of the chair + Sales tax price .

                                                                            = $ 220.59 + $17.43

                                                                            = $ 238.02

As given

Upon arrival they received an invoice for $261.47.

Thus

Cost of  shipping and handling = Cost mentioned in invoice - Cost of the  ordered chair with sales tax price.

Put all the values in the above

Cost of  shipping and handling = $261.47 - $238.02

                                                   = $ 23.45

Therefore the cost of shipping and handling is $23.45 .

Answer:

The ball was dropped from 150 feet.

It will take the ball 3.06 seconds to reach the ground.

Step-by-step explanation:

A story is 10 feet.

You want to find the number of seconds for the ball to reach the ground, which is a height of 0.  So you can put 0 in for h(t), and then solve that.  If you need more help than that, let me know.

Answer:5-log^3 2

Step-by-step explanation:

Answer:

The answer is 5-log 3 2

Step-by-step explanation:

this is the answer on edge

you're welcome

Answer:

Tan (M) = m/p

Step-by-step explanation:

Tan (M) = Oppo. / Adj.

Tan (M) = m/p

The required value of the tanM for the given triangle is tanM = m/p.

These are the equation that contains trigonometric operators such as sin, cos.. etc. In algebraic operations.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

here,
For the given triangle,
TanM = perpendicular / base

From the figure  perpendicular =  m, base = p
Now,
tanM = m/p

Thus, the required value of the tanM for the given triangle is tanM = m/p.

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By using the counting principle in mathematics, the student can know that there are 128 possible sandwiches that can be made with one type of each ingredient.

The question you're asking is related to the counting principle in mathematics. The counting principle suggests that if you can choose one item from 4 different types of bread, one from 8 types of meat, and one from 4 different types of cheese, the number of different sandwiches you could make is the product of these choices.

To calculate it, simply multiply the choices together like this: 4 (types of bread) * 8 (types of meat) * 4 (types of cheese) = 128. So, there are 128 different sandwiches that could be created with one type of each ingredient.

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Answer:

[tex]\large\boxed{B.\ w=-\dfrac{4}{3},\ w=\dfrac{5}{2}}[/tex]

Step-by-step explanation:

[tex]6w^2-7w-20=0\\\\6w^2-15w+8w-20=0\\\\3w(2w-5)+4(2w-5)=0\\\\(2w-5)(3w+4)=0\iff2w-5=0\ \vee\ 3w+4=0\\\\2w-5=0\qquad\text{add 5 to both sides}\\2w=5\qquad\text{divide both sides by 2}\\\boxed{w=\dfrac{5}{2}}\\\\3w+4=0\qquad\text{subtract 4 from both sides}\\3w=-4\qquad\text{divide both sides by 3}\\\boxed{w=-\dfrac{4}{3}}[/tex]

Answer:

x = 5/3    or   x = -5/2

(3x-5) or (2x+5)

Step-by-step explanation:

Given in the question an equation

6x²+5x- 25

here a = 6

        b = 5

        c = -25

To solve the polynomial equation we will use quadratic equation

x = -b ±√(b²-4ac) / 2a

Plug values in the equation

-5±√(5²-4(6)(-25)) / 2(6)

-5±√(25 + 600) / 2(6)

-5±√(625) / 2(6)

-5± 25 / 2(6)

-5 + 25 / 2(6)  or -5 - 25 / 2(6)

x = 5/3    or   x = -5/2

Answer:

D???

Step-by-step explanation:

D????

stand·ard de·vi·a·tion

/ˈstandərd ˌdēvēˈāSHən/

nounSTATISTICS

a quantity calculated to indicate the extent of deviation for a group as a whole.

43.2/16= 2.7

Answer: 2.7

Your answer would be 2.7

Answer:

1. r=17

2. (-15,14) or (-15,-16)

Step-by-step explanation:

The radius of the circle is the distance from the center to the point on the circle, thus

[tex]r=\sqrt{(8-(-7))^2+(7-(-1))^2}=\sqrt{15^2+8^2}=\sqrt{225+64}=\sqrt{289}=17.[/tex]

The equation of the circle is

[tex](x-(-7))^2+(y-(-1))^2=r^2\\ \\(x+7)^2+(y+1)^2=289.[/tex]

If point lies on this circle, then its coordinates satisfy the circle's equation:

[tex](-15+7)^2+(y+1)^2=289\\ \\64+(y+1)^2=289\\ \\(y+1)^2=225\\ \\y+1=15\text{ or }y+1=-15\\ \\y=14\text{ or }y=-16[/tex]

the radius of the circle is 17 units.

the two possible points on the circle are (-15, 14) and (-15, -16).

The question requires calculating the radius of a circle given two points: the center of the circle and a point on the circumference. To find the radius, we will use the distance formula, which is derived from the Pythagorean theorem. The distance formula to find the distance between two points (x1, y1) and (x2, y2) is \\(
√{(x2 - x1)^2 + (y2 - y1)^2}\\).

Applying the distance formula with the center at (-7, -1) and a point on the circle being (8, 7), we get: \\(
√{(8 - (-7))^2 + (7 - (-1))^2}) = (√{(15)^2 + (8)^2}) = (√{225 + 64}) = (√{289}) = 17. Thus, the radius of the circle is 17 units.

To find the missing y-coordinate of the point (-15, ___) that lies on this circle, we use the circle's equation with its center at (-7, -1): ((x + 7)^2 + (y + 1)^2 = 17^2). Substituting x = -15, we solve for y.

((-15 + 7)^2 + (y + 1)^2 = 17^2)
((-8)^2 + (y + 1)^2 = 289)
64 + (y + 1)^2 = 289
(y + 1)^2 = 225
y + 1 = (√{225}) or y + 1 = -(√{225})
y = 14 or y = -16

Therefore, the two possible points on the circle are (-15, 14) and (-15, -16).

Answer:

P = 0.332

Step-by-step explanation:

The probability of having the disease is 0.08

The probability that the test predicts with accuracy is 0.7.

We need to find the probability that the test positive for the disease.

Several cases may occur.

Case 1.

You have the disease and the test predicts it accurately

[tex]P_1 = 0.08(0.7) = 0.056[/tex]

Case 2

You do not have the disease and the test predicts that you have it

[tex]P_2 = 0.92(0.3) = 0.276[/tex]

Then the probability that the test predicts that you have the disease is the union of both probabilities P1 and P2

[tex]P = P_1 + P_2\\\\P = 0.056 + 0.276\\\\P = 0.332[/tex]

Answer:

x=4, x=3

B is correct.

Step-by-step explanation:

Given: [tex]x^2-7x+12=0[/tex]

Using middle term splitting factor the left side equation.

[tex]x^2-4x-3x+12=0[/tex]

[tex](x-4)(x-3)=0[/tex]

Equate each factor to 0 and solve for x

x-4=0    or     x-3=0

x=4 and x=3

Hence, The solution of the equation is 4 or 3

Answer:

5

Step-by-step explanation:

we know that

A degree in a polynomial function is the greatest exponent of that equation

In this problem the greatest exponent is x^5

therefore

the degree of the polynomial is 5