Write an equation in point-slope form of the line that passes through the point (4,−9) and has a slope of 6. The equation is y− = (x− )

Answer:

9 should be added to the expression to make it a perfect square

Step-by-step explanation:

Given expression:

[tex]w^2-6w+_-[/tex]

To fill in the missing term such that the expression becomes a perfect square.

Solution:

In order to make the expression a perfect square we will use completing the square method.

We have : [tex]w^2-6w[/tex]

By complete the square method we will add the square of the quotient of the co-efficient of the middle term which is [tex]-6w[/tex] and 2.  

The co-efficient of middle term = -6

Thus the number to be added will be = [tex](\frac{-6}{2})^2=(-3)^2=9[/tex]

Thus, on adding 9 the expression will become:

[tex]w^2-6w+9[/tex] which is a perfect square of the binomial [tex](w-3)[/tex]

This can be shown as:

[tex](w-3)^2=w^2-6w+9[/tex]

Thus, we add 9 to the expression to make it a perfect square.

Answer:

9

Step-by-step explanation:

Given: [tex]w^{2} -6w+[/tex]

Finding the number to make expression a perfect square.

From the expression we can see that coefficient of variable is 1 and -6.

Now, lets take a= 1 and b= -6 and finding c .

∴ c= [tex]\frac{b^{2} }{4a}[/tex]

Subtituting the value of a and b.

⇒ c= [tex]\frac{-6^{2} }{4\times 1} = \frac{36}{4}[/tex] (∵ [tex]-6\times -6= 36[/tex])

∴ c= 9

Next putting the value in the expression.

[tex]w^{2} -6w+9[/tex]

= [tex](w-3)(w-3)[/tex]

= [tex](w-3)^{2}[/tex]

Hence, 9 is a number to make the expression a perfect square.

Answer:

49x

Step-by-step explanation:

Answer:

x<-3

Step-by-step explanation:

-9x>27

x>27/-9

x>-3

The angle of elevation from point C to point A is [tex]32^{\circ}[/tex]

Solution:

Given that we have to find the angle of elevation from point C to Point A

Given in figure that, angle A = [tex]58^{\circ}[/tex]

Given is a right angled triangle ABC where angle B = [tex]90^{\circ}[/tex]

We have to find angle C

The angle sum property of a triangle states that the angles of a triangle always add up to 180°

Therefore, in given triangle ABC

angle A + angle B + angle C = 180

[tex]58^{\circ} + 90^{\circ} + C = 180^{\circ}[/tex]

[tex]148^{\circ} + C = 180^{\circ}\\\\C = 180^{\circ} - 148^{\circ}\\\\C = 32^{\circ}[/tex]

Therefore angle C = [tex]32^{\circ}[/tex]

Answer:

no because it is just a straight line. a dot is plotted at (0,-3) and a straight line is horizontal.

Answer:

The female would pay  $322.00 less for a policy of $25,000

Step-by-step explanation:

Since we have given that

Amount for policy = $25000

If she opt for 20 year life insurance at $2.90 per $1000.

so, her amount of premium becomes

[tex]25000\times \frac{2.9}{1000}[/tex]

=$72.50

If she opt for straight life insurance at $15.78 per $1000,

Then, her amount of premium becomes

[tex]25000 \times \frac{15.78}{1000}[/tex]

= $394.50

Difference between them is given by

$394.50-$72.5 = $322.00

Answer:

The answer to this question is $322.

Step-by-step explanation:

From the question, we recall the following

23-year-old female pay for a $25,000 policy less policy of 20 year life insurance.

The first step is to calculate the policy of 20 year life insurance

The number of thousands on 2500 is, 25000/1000=25

25*2.9  = 72.5

The next step is to get the straight life

Thus,

25×15.78  = 394.5

Now,

How much less  would the 23 year old pay

394.5−72.5  = $322

Real word problem ⇒ constant of proportionality

$4.16 for 4 pounds of bananas ⇒ 1.04

$16.48 for 8 pounds of potatoes  ⇒ 2.06

$18.36 for 2 pizzas  ⇒ 9.18

2 cups of flour to make 36 cookies ⇒ 18

Solution:

A proportional relationship is one in which two quantities vary directly with each other.

We say the variable y varies directly as x,

if for x ∝ y

then,  x = y k

Where "k" is called constant of proportionality

[tex]k = \frac{x}{y}[/tex]

$4.16 for 4 pounds of bananas

x = 4.16 and y = 4

[tex]k = \frac{4.16}{4} = 1.04[/tex]

Thus constant of proportionality is 1.04

$16.48 for 8 pounds of potatoes

x = 16.48 and y = 8

[tex]k = \frac{16.48}{8} = 2.06[/tex]

Thus constant of proportionality is 2.06

$18.36 for 2 pizzas

x = 18.36 and y = 2

[tex]k = \frac{18.36}{2} = 9.18[/tex]

Thus constant of proportionality is 9.18

2 cups of flour to make 36 cookies

x = 36 and y = 2

[tex]k = \frac{36}{2} = 18[/tex]

Thus constant of proportionality is 18

Answer:

[tex]x \approx 31.8[/tex]

Step-by-step explanation:

[tex]\frac{\sin(75)}{22}=\frac{\sin(x)}{12}[/tex]

Cross multiply:

[tex]\sin(75) \cdot 12=\sin(x)\cdot 22[/tex]

Divide both sides by 22:

[tex]\frac{\sin(75) \cdot 12}{22}=\sin(x)[/tex]

Take [tex]\sin^{-1}( )[/tex] of both sides:

[tex]\sin^{-1}(\frac{\sin(75) \cdot 12}{22}=x[/tex]

Put left hand side into a calculator now:

[tex]31.7941 \approx x[/tex]

To the nearest tenth that is: [tex]x \approx 31.8[/tex]

Answer:

[tex]\frac{4}{11}[/tex]

Step-by-step explanation:

The total length of KN is 11 units and the length of LM is 4 units. This means that the probability would be [tex]\frac{4}{11}[/tex]

Answer : The probability that p on LM is, [tex]\frac{4}{11}[/tex]

Step-by-step explanation :

Probability : It is defined as the extent to which an event is likely to occur. That means, it is measured by the ratio of the favorable outcomes to the total number of possible outcomes.

[tex]\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of favorable outcomes}}[/tex]

Favorable outcomes on line KN are, 2, 4, 5

Favorable outcomes on line LM is, 4

Number of favorable outcomes = 4

Total number of outcomes = 2 + 4 + 5 = 11

[tex]\text{Probability}=\frac{\text{Number of favorable outcomes for a multiple of 3}}{\text{Total number of favorable outcomes}}[/tex]

[tex]\text{Probability}=\frac{4}{11}[/tex]

Therefore, the probability that p on LM is, [tex]\frac{4}{11}[/tex]

Answer:

The area of the pool increasing at the rate of 653.12[tex]cm^2/min[/tex]  when the radius is 13 cm

Step-by-step explanation:

Given:

radius of the pool increases at a rate of 8 cm/min

To Find:

How fast is the area of the pool increasing when the radius is 13 cm ?

Solution:

we are given with the circular pool

hence the area of the circular pool =

A =[tex]\pi r^2[/tex]-----------------------------(1)

The area of the pool os increasing at the rate of 8 cm/min, meaning that the arae of the pool is changing with respect to time t

so differentiating eq (1)  with respect to t , we have

[tex]\frac{d A}{d t}=\pi \cdot 2 r \cdot \frac{d r}{d t}[/tex]

we have to find  [tex]\frac{d A}{d t}[/tex] with [tex]\frac{d r}{d t}[/tex] = 8 cm/min and  r =  13cm

substituting the values

[tex]\frac{d A}{d t}=\pi \cdot 2 (13) \cdot 8[/tex]

[tex]\frac{d A}{d t}=\pi \cdot 26 \cdot 8[/tex]

[tex]\frac{d A}{d t}=\pi \cdot 208[/tex]

[tex]\frac{d A}{d t}= 208 \pi[/tex]

[tex]\frac{d A}{d t}=653.12[/tex]

Answer:

208pi cm^2/min

Step-by-step explanation:Take the derivative of the formula for Area and substitute the values

The most accurate measurement of the boiling point of water is  option B: 212.1 degrees F.

The most accurate measurement of the boiling point of water is option B: 212.1 degrees F.

When measuring the temperature of boiling water, it is important to consider the accuracy and precision of the measuring instrument. The given options range between 205.46 and 213.15 degrees F, but the boiling point of water is widely accepted to be 212 degrees F at standard atmospheric pressure.

Therefore, the measurement closest to this accepted value is the most accurate, which is option B: 212.1 degrees F.

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Answer:

The principal amount invested is $4395.93 .

Step-by-step explanation:

Given as :

The Amount that saved for future = A = $5,000

The bank applied rate of interest = r = 4.3% compounded monthly

The time period of loan = t = 3 years

Let the principal amount invested = $p

Now, From monthly Compound Interest method  

Amount = principal × [tex](1+\dfrac{\textrm rate}{12\times 100})^{12\times time}[/tex]

Or, A = p × [tex](1+\dfrac{\textrm r}{12\times 100})^{12\times t}[/tex]

Or, $5000 = p × [tex](1+\dfrac{\textrm 4.3}{12\times 100})^{12\times 3}[/tex]

Or, $5000 = p × [tex](1.003583)^{36}[/tex]

Or, $5000 = p × 1.137414

∴ p = [tex]\dfrac{5000}{1.137414}[/tex]

i.e p = $4395.93

So, The principal amount invested = p = $4395.93

Hence, The principal amount invested is $4395.93 . Answer

Answer:

[tex]B=\frac{4}{3}A[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem we have a proportional relationship because the line passes through the origin (0,0)

Find the value of k

[tex]k=\frac{B}{A}[/tex]

take the point (3,4)

A=3,B=4

substitute

[tex]k=\frac{4}{3}[/tex]

The equation of the line is

[tex]B=\frac{4}{3}A[/tex]

Answer:

The probabilities are 0.4 and 0.6 respectively.

Step-by-step explanation:

We are given two spinning wheels with numbers on it and we have to find the probability of getting 3.

In the first wheel, there are 5 slots and the numbers are 3, 3, 2, 5 and 4.

So the probability of getting 3 =[tex]\frac{number of 3's}{total number of slots}[/tex]

                                            = [tex]\frac{2}{5}[/tex]

                                            = 0.4

In the second spinner there are three 3's and total of 5 slots.

So probability of getting 3 = [tex]\frac{number of 3's}{total number of slots}[/tex]

                                             = [tex]\frac{3}{5}[/tex]

                                             = 0.6

Hence the probabilities are 0.4 and 0.6 respectively.

Answer:

[tex]A=6.33\ cm^2[/tex]

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The circumference of a circle is equal to

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

we have

[tex]C=\frac{28}{3.14}\ cm[/tex]

[tex]\pi=3.14[/tex]

substitute the values

[tex]\frac{28}{3.14}=2(3.14)r[/tex]

[tex]r=\frac{28}{19.7192}\ cm[/tex]

[tex]r=1.42\ cm[/tex]

step 2

Find the area of the circle

The area of the circle is equal to

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

substitute the values

[tex]A=(3.14)(1.42)^{2}[/tex]

[tex]A=6.33\ cm^2[/tex]

Answer: -47 - 48x

Step-by-step explanation: When you first take a look at this problem, it's tempting to want to subtract -7 - 8 to get -15 and then distribute the -15 through the parentheses.

You wouldn't want to subtract however before you distribute because the distributive property is a form of multiplication and remember from your order of operations that multiplication comes before subtraction.

So the first thing you want to do here is distribute and change the minus sign in front of the -8 to plus a negative 8 so that you know you are distributing a -8 through your parentheses.

So we have -7 + -8 times 6x which is -42x + -8 times 5 which is -40.

Now we have -7 + -48x + -40.

Now just combine your like terms. -7 + -40 is -47 and plus a negative 48x can be written as -48x so we have -47 - 48x.

So your answer is just -47 - 48x.

Answer:

The Length of side of park is 20 meter.

Step-by-step explanation:

Given:

Shape of a Park is SQUARE

Area of a square park = 400 sqm

To Find:

The length of side of park = side =  ?

Solution:

We know For a SQUARE

All the sides are equal

And Area of a square is given as

[tex]\textrm{Area of Square Park}= (Side)^{2} \\[/tex]

Substituting the given values we get

[tex]400=(side)^{2} \\\\\textrm{Square rooting we get}\\\\side=\sqrt{400} \\\\\therefore side = 20\ meter[/tex]

The Length of side of park is 20 meter.

Answer:

a = -2  and  b = 7

Step-by-step explanation:

We need to solve for the value of "a" and "b".

We need to distribute and make the left side of the equation same form as the right side of the equation and match the coefficients, simple.

We will use the distributive property shown below to expand the left side and simplify.

Distributive Property:  a(b-c) = ab - ac

Now, simplifying left hand side:

5x - 7(x - 1)

= 5x -7(x) -7(-1)

= 5x -7x +7

= -2x + 7

The right hand side is "ax + b".

If we match left-hand side and right-hand side, we see that:

a = -2

and

b = 7

THese are the only solution.

Answer:

3r-5r

Step-by-step explanation:

Answer:

m=16/39

Step-by-step explanation:

-5(4m-2)=-2/3+6m

-20m+10=-2/3+6m

-20m-6m=-2/3-10

-26m=-2/3-30/3

-26m=-32/3

26m=32/3

m=(32/3)/26

m=(32/3)(1/26)

m=32/78

m=16/39

Answer

THE REAL ANSWER IS c and f

Step-by-step explanation:

I just finished and they are the only 2 and I got it right

Nikki's and Dylan's Both proposed placements will light the same sized area.

A = 1/2 × b × h.

The steps are as follow:

A= 1/2×60×38

A= 30×38

A = 1,140ft.

So, Nikki's and Dylan's Both proposed placements will light the same sized area.

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Answer:

This board of 24.5 inches long is not enough to be cut into the four walls of the bird house.

Step-by-step explanation:

Hodi is building a birdhouse. Each of the four walls of the birdhouse needs to be 5.5 inches long.

So, to get four 5.5 inches long walls we need to have (5.5 × 4) = 22 inches ling board from which four equal 5.5 inches board can be made.

Now, Hodi has a piece of a board that is 24.5 inches long.

Therefore, this board is not enough to be cut into the four walls of the birdhouse. (Answer)

Answer:

[tex]-5c[/tex]

Step-by-step explanation:

To find: The sum of [tex]6c-5c[/tex] and opposite of [tex]6c[/tex]

Opposite of [tex]6c[/tex] means taking the opposite sign.

[tex]6c[/tex] is positive. So, opposite sign is [tex]-6c[/tex].

Therefore, the addition is given as:

[tex]=6c-5c+(-6c)[/tex]

Opening the parenthesis, we get:

[tex]6c-5c-6c[/tex]

Now, as per PEDMAS rule, we subtract [tex]6c\ and\ 5c[/tex], we get

[tex]6c-5c=(6-5)c=1c[/tex]

Now, we are left with [tex]1c-6c[/tex]

Subtracting a bigger number from a smaller number will give a negative answer.

So, [tex]1c-6c=(1-6)c=-5c[/tex]

Therefore, the final answer is [tex]-5c[/tex]

Answer:

2

2x + 3 = 5x - 3

Move x to one side:

[tex]2x-2x+3=5x-2x-3\\3=3x-3[/tex]

Remove the -3:

[tex]3x-3(+3)=(3+3)[/tex]

[tex]3x=6[/tex]

Remove the 6 to get x by itself:

[tex]\frac{3x}{3} =\frac{6}{3} \\x=2[/tex]

The number 2 from the number set would solve the equation.

2(2) + 3 = 5(2) - 3

4 + 3 = 10 - 3

7 = 7

The statement is true.

An equation is formed of two equal expressions. The number(s) from the set that will satisfy the given equation is 2.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given equation can be simplified as shown below,

2x + 3 = 5x - 3

Subtract 2x from both sides of the equation,

2x + 3 - 2x = 5x - 3 - 2x

3 = 5x - 3 - 2x

Add 3 on both sides of the equation,

3 + 3 = 5x - 3 - 2x + 3

6 = 3x

3x = 6

Divide both the sides of the equation by 3,

3x/3 = 6/3

x = 2

Hence, the number(s) from the set that will satisfy the given equation is 2.

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Answer:

Therefore the value of x is 15.

Step-by-step explanation:

Given:

AD || BC

m∠ B = (9x + 15)°

m∠ A = (3x - 15)°

To Find:

x = ?

Solution:

AD || BC       ...............Given

If two lines are parallel and sum of the interior angles are supplementary.

i.e m∠ B and m∠ A are interior between Parallel lines.

∴ [tex]\angle B + \angle C =180\\[/tex]

Substituting the given values we get

∴ [tex](9x + 15)+( 3x - 15)=180\\12x=180\\\\x=\frac{180}{12} \\\\\therefore x =15[/tex]

Therefore the value of x is 15.

Cost of admission for a group of 3 people is $ 120

Solution:

Given that amusement park charges an admission fee of 40 dollars per person

The cost, C (In dollars), of admission for a group of p people is give by the following expression:

C = 40p

Here "p" denotes the number of people

To find: cost of admission for a group of 3 people

For a group of 3 people, p = 3

Substituting p = 3 in given cost formula, we get the cost of admission for a group of 3 people

[tex]c = 40p\\\\c = 40(3) = 120[/tex]

Thus cost of admission for a group of 3 people is $ 120

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

We have the following points:

[tex](x_ {1}, y_ {1}) :( 4,6)\\(x_ {2}, y_ {2}): (- 2, -9)[/tex]

We can find the slope:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-9-6} {- 2-4} = \frac {-15} {- 6} = \frac {5} {2}[/tex]

Thus, the equation is of the form:

[tex]y = \frac {5} {2} x + b[/tex]

We substitute one of the points and find "b":

[tex]6 = \frac {5} {2} (4) + b\\6 = 10 + b\\6-10 = b\\b = -4[/tex]

Finally, the equation is:

[tex]y = \frac {5} {2} x-4[/tex]

Thus, it is observed that the lines have the same y-intercept

Answer:

Option D

Answer:

No.

Step-by-step explanation:

Because perpendicular means negative reciprocal of the slope. So 4 and -1/4 are perpendicular.

Answer:

20,000

Step-by-step explanation: