Click and drag like terms onto each other to simplify fully.
-3y³-5y²+7x³+y²-5x²+7y³+5y²
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Answer:

78.8

Step-by-step explanation:

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{-5}x-14\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {-5\implies \stackrel{slope}{\cfrac{-5}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-5}\implies \cfrac{1}{5}}}[/tex]

so we're really looking for the equation of a line whose slope is 1/5 and it passes through (10, -4)

[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{1}{5}}(x-\stackrel{x_1}{10}) \implies {\large \begin{array}{llll} y +4= \cfrac{1}{5} (x -10) \end{array}}[/tex]

The probability that the mean weight of the sample babies would differ from the population mean by less than 54 grams is 0.4339.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 3316 grams - 54 grams = 3262

μ = mean = 3316 grams

σ = standard deviation = 324 grams

z-score = (3262 - 3316) / 324

z-score = -54 / 324

z-score = -0.1667

Find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score = -0.1667

Using interpolation of values,

probability = 0.4339

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Answer: ask your teacher

Step-by-step explanation:u have to multiply

Answer: 11/4n + 2 = -3 +3/2n

Step-by-step explanation:

1) Solve the given equation

-5n + 31 = -14n -5

9n = -36 (Move like terms)

n = -4

2) Solve every other equation until match

1a)

11/4n + 2 = -3 +3/2n

11/4n = -5 + 6/4n (Change fraction and move like terms)

5/4n = -5 (minus fraction)

n =  -4 Correct

Answer:

Step-by-step explanation:

y=652/4

convert decimal to a fraction

46/125=5

multiplying by both sides of the equation by 125/4

y=652/4 = 156 1/4

The point (9, 16) is on the line.

Given,

The equation of the line = y = 4/3x + 4

We have to find whether the given points are on this line or not.

For that substitute the points into the equation.

That is,

Point (6, 13)

x = 6 and y = 13

Equation;

y = 4/3x + 4

13 = 4/3 x 6 + 4

13 = 8 + 4

13 ≠ 12

That is, the point (6, 13) is not in the line.

Next,

Point (9, 16)

x = 9 and y = 16

Equation;

y = 4/3x + 4

16 = 4/3 x 9 + 4

16 = 12 + 4

16 = 16

Therefore, the point  (9, 16) is in the line.

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The value of x from the given figure is 3. Hence, proved.

Given that, ∠XVW=∠W.

When two lines cross at a point, vertical angles are created. They are always on an equal footing. In other words, four angles are created anytime two lines cross or intersect. It is evident that two opposed angles are equal and are referred to as vertical angles. They are also known as "Vertically opposite angles" due to the fact that they are perpendicular to one another.

∠XVW = ∠W   (Given)

∠XVW = ∠ZVY  (Vertical angles theorem, vertical angles are congruent.)

∠ZVY = ∠W  (Transitive property of congruence)

m ∠ZVY = m ∠W (Angle congruence postulate)

8x+13=75x+28 (Substitution property of equality)

5x=15 (Subtraction property of equality)

x=3 (Division property of equality)

The value of x from the given figure is 3. Hence, proved.

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Answer:

Jenny owes her sister 9.3 dollars.

Step-by-step explanation:

23.63 - 16.33 = 9.3

25 new teachers joined the school such that the new ratio is 1 : 20 .

In mathematics, a ratio illustrates how frequently one number appears in another. For instance, the ratio of oranges to lemons on a fruit platter would be eight to six if there were eight oranges and six lemons.

The total number of students is 2000

The ratio of teachers to students  is 3:80 .

Therefore the number of teachers = 3 × 2000 ÷ 80 = 75

Let x teachers joined the school.

Therefore new ratio = (x+75) : 2000

but the new ratio is 1 : 20

Therefore 1 : 20 = (x+75) : 2000

Simplifying we get:

x + 75 = 100

or, x = 25

Therefore the number of teachers who joined the school is 25 .

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Answer:

2:20 pm to 5:57 pm is 3 hours and 37 minutes.

Answer:

3 hours and 37 minutes.

Step-by-step explanation:

5:57

-2:20

= 3:37

1) Given that we were told that the first three terms of this Sequence. Let's find the common difference:

2) Based on that, we can do the following to find the next two terms:

Thus, the next terms are -5 and 2

The required equation of the line is 5x + y + 17 = 0.

What is an equation?

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. Equations are used to describe geometric shapes in Cartesian geometry. Because the equations under consideration, such as implicit equations or parametric equations, contain an unlimited number of solutions, the goal has shifted: instead of directly stating the solutions or counting them, which is impossible, one utilizes equations to investigate the features of figures. This is the fundamental concept of algebraic geometry, a significant branch of mathematics. An equation consists of two expressions joined by an equals sign ("="). The expressions on each side of the equals sign are referred to as the equation's "left-hand side" and "right-hand side."

The equation of the line is given below:

y - 3 = -5(x - 4)

or, y - 3 = -5x - 20

or, 5x + y + 17 = 0

Hence, the required equation of the line is 5x + y + 17 = 0.

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Answer:

d=12

Step-by-step explanation:

8d+4+6d+8 = 180 (Straight angle = 180)

14d+12=180

14d=168

d=12

:]

Answer:

D =12

Step-by-step explanation:

8d+4+6d+8 =180 (being a linear pair)

14d+12=180

14d=180-12

14d=168

d= 168/14

d=12#

Answer:

Answer is the last graph which shows 10 cookies and 5 brownies.

Step-by-step explanation:

There are more cookies (y-axis) than brownies (x-axis), the slope is 2.0 so the line must be > 45 degrees.  

Answer:

7A, 8D

Step-by-step explanation:

The compound interest formula is as followed

[tex]A = P(1+\frac{r}{n} )^{nt}\\[/tex]

A = accumulated amount

P = principle

r = interest rate

n = compounding

t = time

The accumulated amount is represented by f(x).

The principle is the amount of money you start with. In this case Tommy starts with 2000 dollars. P = 2000

The interest rate is 5%. This needs to be converted into a decimal.

5% = 0.05 = r

The money is compounded annually, thus n = 1.

The time is represented by x. x = t.

thus

[tex]f(x) = 2000(1+0.05)^{x}[/tex]

After six years, you simply find f(6), or substitute 6 into x.

f(6) = 2000(1.05)^6 = $2,680.19

Answer:

x = 12

Step-by-step explanation:

3/4x = 9

x = 9/1(4/3)

x = 12

Answer:

360 miles

Step-by-step explanation:

24*15=360

360 miles can be driven in 15 gallons gas.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For, example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

A  car has a15 gallon gas tank.

Now, per gallon = 24 miles driven

So, in 15 gallons, the miles driven

= 24 x 15

= 360 miles.

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The z-value for 29 and 34 hours is z(32) = 0, the garages take between 32 hours and 34 hours to erect 34%, the garages take between 29 hours and 34 hours to erect 77.45%, and the garages, 5% take 35.29 hours of time.

A Z-score is defined as the fractional representation of data point to the mean using standard deviations.

Weston Materials, Inc., a national manufacturer of detached garages, states that erecting the Red Barn type takes two construction workers a mean of 32 hours and a standard variation of 2 hours. Assume that the assembly times are distributed normally.

Calculating the z values for 29 and 34 hours.

z(29) = (29-32)/2 = -3/2

z(34) = (34-32)/2 = 1

z(32) = 0

The percentage of garages take between 32 hours and 34 hours to erect as:

⇒ P(32 < x < 34) = P(0< z < 1) = 0.34

The percentage of garages take between 29 hours and 34 hours to erect as:

⇒ P(29 < x < 34) = P(-1.5 < z < 1) = 0.7745

The percentage of garages take 28.7 hours to erect as:

⇒ z(28.7) = (28.7-32)/2 = -3.3

⇒ P(0 < x < 28.7) = P (-10 < z < -3.3) = 0.00048348...

The z-value corresponds to a 95% left area and only

5% to the right under the curve.

Use z-chart or InvNor(0.95) = 1.645

x-value that corresponds to the z-value.

1.645 = (x-32)/2

x-32 = 2×1.645

x = 35.29 hours

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Given,

Total distance [tex]=2\frac{1}{2}[/tex] miles

You run 1/3 of that distance on a hill.

Distance on a hill[tex]=\frac{1}{3} * 2\frac{1}{2}[/tex] miles

You run down a slope for the last 1/2 of the hill=[tex]\frac{1}{3} * 2\frac{1}{2}*\frac{1}{2}[/tex] miles[tex]=\frac{5}{12}[/tex] miles

Distance you run down the slope [tex]=\frac{5}{12}[/tex] miles

Answer:

4x²+2x-30

Step-by-step explanation:

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

(x+3) (4x-10)

4x²-10x+12x-30

4x²+2x-30

Given

Major axis of length = 12

Foci at ( 9 ,1 ) and ( -1, 1 )

Find

Equation of an ellipse

Explanation

As we know , major axis = 2a = 12

thus a = 6

the midpoint between the foci is the center , so

the distance between the foci is equal to 2c

now,

so , the equation of an ellipse is

Final Answer

The equation of an ellipse

Answer: x < -6

Step-by-step explanation:

1) Bring 1 to the other side

x/-2 > 3

2) Bring -2 to the other side. The sign flips when the number multiplied or divided is negative

x < -6

Answer:

J. - (x-7)(x + 4)

Step-by-step explanation:

The nurse should program the infusion pump to deliver 21.6ml/hour

Given the following:

Drug propofol prescribed is 8mcg/kg/min

Drug dispensed in 100mg in 50ml NS

Weight of patient is 198 pounds

Converting pounds in Kg:

198 pounds is (1 pound is 0.45Kg)

89.8 equivalent to 90Kg

Converting 8mcg/kg/min into mg/kg/min:

8mcg is 0.008mg so it becomes 0.008mg/kg/min

Patient weight is 90 kg , so required drug is:

90x0.008=0.72 mg/min

Now 50ml has 100mg, so 1ml has 2mg

We want to give 0.72mg, so if there is 2mg in 1 ml how much will be 0.72 mg for, by doing cross multiplication we get as below:

2mg in 1 ml

0.72=?

=0.72x1/2

=0.36ml

Now we have to give 0.36ml/min

Infusion pump has rate in ml/ hour, as 1 hour has 60 min, we multiply 0.36x60=21.6ml/hour

Hence, Infusion pump delivered 21.6ml/hour

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