the difference between two positive integers is 3. if the smaller is added to the square of the larger, the sum is 377. Find the integers

Answer: 70

Step-by-step explanation:

By the corresponding angles theorem, [tex]4x-50=2x+30 \longrightarrow x=40[/tex]

This means that [tex]2x+30=110[/tex].

Now, if we notice the linear pair, this means that [tex]y=\boxed{70}[/tex]

Answer:

[tex]37 - c = x[/tex]

Step-by-step explanation:

We'll use c to represent the amount taken away (subtracted) and x to represent the amount left (the answer).

We begin with 37 balloon, and take away c amount to make x.

37 - c = x

Answer:

So our unknown width is X and the unknown length is X + 3.  We know the perimeter is 2 times the length plus 2 times the width so let's set up that equation:

2 X + 2 (X+3) = 24

Now solve for X

2 X + 2 X + 6 = 24

4 X + 6 = 24

4 X = 18

X = 4.5 - this is the width

X + 3 = 4.5 + 3 = 7.5 - this is the length

Step-by-step explanation:

Answer:

Bias compare results implement treatments

Step-by-step explanation:

Answer:

By multiplying both side with the inverse of the coefficient of x

Step-by-step explanation:

coefficient of x = -6/4

inverse of coeefficient =-4/6.

multiply both sides.

x = 12(-4/6) = -8

Answer:

See below ~

Step-by-step explanation:

a)

b)

c)

Answer:

a) 4.60 (2 dp)

b)  1.31 (2 dp)

c)  8.8

Step-by-step explanation:

The "Frequency" part of a frequency table is the measure of how often the data value occurs.

To calculate the mean of data presented in a frequency table, we need to multiply each data value by its given frequency, sum these, then divide by the sum of the frequency.

The formula for mean is:

[tex]\textsf{mean}=\overline{x}=\dfrac{\displaystyle \sum fx}{\displaystyle\sum f}[/tex]

Add a row showing the values of [tex]fx[/tex]

Add a column showing the totals of [tex]f[/tex] and [tex]fx[/tex]

[tex]\large\begin{array}{| c | c | c | c | c | c | c | c |}\cline{1-8} & & & & & & & \sf Total \\\cline{1-8} x & 2 & 3 & 4 & 5 & 6 & 7 & \\\cline{1-8} \textsf{Frequency}\:f & 11 & 17 & 24 & 23 & 18 & 15 & 108\\\cline{1-8} fx & 22 & 51 & 96 & 115& 108 & 105 &497 \\\cline{1-8}\end{array}[/tex]

Now use the formula to calculate the mean:

[tex]\implies \textsf{mean}=\overline{x}=\dfrac{497}{108}=4.60\:\textsf{(2 dp)}[/tex]

Add a column showing the values of [tex]fx[/tex]

Add a row showing the totals of [tex]f[/tex] and [tex]fx[/tex]

[tex]\large\begin{array}{| c | c | c |}\cline{1-3} x & \textsf{Frequency}\: f & fx \\\cline{1-3} 0 & 35 & 0 \\\cline{1-3} 1 & 76 & 76\\\cline{1-3} 2 & 48 & 96\\\cline{1-3} 3 & 22 & 66 \\\cline{1-3} \sf Total & 181 & 238 \\\cline{1-3}\end{array}[/tex]

Now use the formula to calculate the mean:

[tex]\implies \textsf{mean}=\overline{x}=\dfrac{238}{181}=1.31\:\textsf{(2 dp)}[/tex]

Add a column showing the values of [tex]fx[/tex]

Add a row showing the totals of [tex]f[/tex] and [tex]fx[/tex]

[tex]\large\begin{array}{| c | c | c |}\cline{1-3} x & \textsf{Tally}\: f & fx \\\cline{1-3} 8 & 7 & 56\\\cline{1-3} 9 & 10 & 90\\\cline{1-3} 10 & 3 & 30\\\cline{1-3} \sf Total & 20 & 176\\\cline{1-3}\end{array}[/tex]

Now use the formula to calculate the mean:

[tex]\implies \textsf{mean}=\overline{x}=\dfrac{176}{20}=8.8[/tex]

Answer:

The number in the middle

Answer:

the answer is the one fully in line like perfect like pyramid

Step-by-step explanation:

I took the test

Answer:

9.

Step-by-step explanation:

1) the condition 'One x-intercept of y = x2 – 6x + c is 3' means, that x=3 and y=0;

2) it is possible to substitute the values x=3 and y=0 into the given equation and to calculate 'c':

0=9-18+c; ⇒ c=9.

Step-by-step explanation:

Consider the LHS, after the 5th step, consider the RHS

[tex]2 \csc(2x) = \csc {}^{2} (x) \tan(x) [/tex]

[tex]2 \frac{1}{ \sin(2x) } = \csc {}^{2} (x) \tan(x) [/tex]

[tex]2 \times \frac{1}{2 \sin(x) \cos(x) } = \csc {}^{2} (x) \tan(x) [/tex]

[tex] \frac{1}{ \sin(x) \cos(x) } = \csc {}^{2} (x) \tan(x) [/tex]

[tex] \csc(x) \sec(x) = \csc {}^{2} (x) \tan(x) [/tex]

Consider the RHS

[tex] \csc(x) \sec(x) =( 1 + \cot {}^{2} (x) ( \tan(x)) [/tex]

[tex] \csc(x) \sec(x) = \tan(x) + \cot(x) [/tex]

[tex] \csc(x) \sec(x) = \frac{ \sin(x) }{ \cos(x) } + \frac{ \cos(x) }{ \sin(x) } [/tex]

[tex] \csc(x) \sec(x) = \frac{1}{ \sin(x) \cos(x) } [/tex]

[tex] \csc(x) \sec(x) = \csc(x) \sec(x) [/tex]

Step-by-step explanation:

we can easily count this, as the diagonal lines are squares truly in half. so, 2 such cut squares are in total 1 full square.

there is one central rectangle of 4×6 squares = 24.

then in the upper left corner there is a small 2×2 square = 4.

and then we have in the bottom left 2 and the bottom right also 2 small triangles (4 in total) with each having 1 full square and 2 half-squares (2 squares in total) as area.

so, 4×2 = 8 squares.

so, the whole area is

24 + 4 + 8 = 36

Answer:

12n + 16

Step-by-step explanation:

2 (6n + 8)

= (2*6n) + (2*8) [distributive property]

= 12n + 16

Hope it helps ⚜

Answer:

12n + 16

Step-by-step explanation:

Distributive Property

Distributing the terms

Answer:

see explanation

Step-by-step explanation:

the codomain are the values of f(x) from the y- coordinate of the vertex upwards.

given a quadratic in standard form

y = ax² + bx + c ( a ≠ 0 )

then the x- coordinate of the vertex is

[tex]x_{V}[/tex] = - [tex]\frac{b}{2a}[/tex]

f(x) = 2x² + 4x - 1 ← is in standard form

with a = 2 and b = 4 , then

[tex]x_{V}[/tex] = - [tex]\frac{4}{4}[/tex] = - 1

substitute x = - 1 into f(x) for y- coordinate of vertex

f(- 1) = 2(- 1)² + 4(- 1) - 1 = 2 - 4 - 1 = - 3

vertex = (- 1, - 3 )

since the coefficient of the x² term > 0 then the graph opens up U

then codomain is [ - 3, ∞ )

Answer:

Step-by-step explanation:

1.5 x 4.5 x 4.5 = 30.375

30.375  ÷ 3 = 10.125

10.125= volume of the triangle

3 x 4.5 x 4.5 = 60.75

60.75 = volume of rectangle

60.75 + 10.125 = 70.875

70.875 = total volume

Answer:

640; 581 R 90; 90

Step-by-step explanation:

you can round 110 to 100

64000/100 is simply 640

then you do the real math

the quotient is 581 r 90

this means the remainder is 90

Answer:

We need to find 74% of 84 (that's the amount that was sold// If you would have been asked for the amount left, it would be (100%-74%), but here it's easier since it's already given to us)

Now, let's write the percentage as a fraction

74/100 of 84

**Trick, for percentages, anytime you see a "of" replace it with a multiplication symbol

74/100 x 84

Now, it's just a simple multiplication

(74x84)/100

*You can use a calculator and find your answer

It would give you 62.16 and you will need to round it to a whole number, so 62 gallons

*If you can't use a calculator, simplify the fraction as much as you can and try to approximate

Step-by-step explanation:

~62

The angle of elevation is = 70° and the distance the airplane travelled in the air is = 17,557ft

tan x° = opposite/adjacent

where opposite = 16,500 feet

adjacent = 6,000 ft

tan x° = 16,500 / 6,000

tan x° = 2.75

X = arctan ( 2.75)

X = 70°

C² = a² + b²

C² = 16,500² + 6,000²

C² = 272250000 + 36000000

C² = 308250000

C= √308250000

C= 17,557ft

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Answer:

Step-by-step explanation:

Speed is the ratio of distance to time. Speeds can be compared by comparing the times for the same distance, or by comparing the distances for the same time. A faster speed means more distance is covered in less time.

__

Here, we observe that 68 feet is a multiple of 34 feet, so it is easiest to compare the speeds of the insects by comparing their times for the same distance.

  butterfly: 68 ft in 5 seconds

  dragonfly: 2×34 ft in 2×3 seconds, or 68 ft in 6 seconds

The butterfly covers the same distance in less time, so it can fly faster.

__

Since our comparison of speeds is made using travel times, we can say the answer to "how much faster" is "1 second less over a distance of 68 feet."

_____

Additional comment

You may be expected to figure the speeds in units of feet per second. You do that by dividing feet by seconds.

  butterfly: 68 ft/(5 s) = 13.6 ft/s

  dragonfly: 34 ft/(3 s) = 11 1/3 ft/s

The difference in speeds is ...

  (13 3/5) -(11 1/3) = 2 4/15 . . . ft/s

The butterfly's speed is 2 4/15 ft/s faster than the dragonfly's speed.

__

You see time comparisons in human foot races, often with differences measured in milliseconds. Almost never are speeds compared in terms of feet (or meters) per second.

Answer:

A. 9.9%

Step-by-step explanation:

[tex] {e}^{14r} = 4[/tex]

[tex] ln(4) = 14r[/tex]

[tex]r = \frac{ ln(4) }{14} = .099 = 9.9\%[/tex]

Answer:

x²-8x-84

Using quadratic Formular -b±√b²-4ac/2a

--8±/8²-4×1×-84 /2×1

8±/64+336/2

8±/400/2

8±20/2

8+20/2, 8-20/2

28/2, -12/2

14,-6

-7+(n-1)6

-7 is the starting term

n is the term that you are looking for

6 is the common difference

The formula for the nth term in the arithmetic sequence is:

a(n) = 6n - 13

It is a sequence where the difference between each consecutive term is the same.

We have,

We are given the first four terms of an arithmetic sequence:

a₁ = -7, a₂ = -1, a₃ = 5, a₄ = 11

To find the formula for the nth term, we need to find the common difference (d) first.

We can do this by subtracting any two consecutive terms:

d = a₂ - a₁ = (-1) - (-7) = 6

Now we can use the formula for the nth term of an arithmetic sequence:

a(n) = a₁ + (n - 1)d

Substituting the values we found:

a(n) = (-7) + (n - 1)(6)

Simplifying:

a(n) = -7 + 6n - 6

a(n) = 6n - 13

Therefore,

The formula for the nth term in the arithmetic sequence is:

a(n) = 6n - 13

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Answer:

g(x) = 5|(x - 2) - 2| - 2

Step-by-step explanation:

To shift 5 units right :

⇒ f(x) = 5|(x - 2) - 2| - 7

⇒ Applied rule : a units right → f(x) = (x - a)

To shift 5 units up :

⇒ g(x) = 5|(x - 2) - 2| - 7 + 5

⇒ g(x) = 5|(x - 2) - 2| - 2

Answer:

[tex]g(x)=5|x-4|-2[/tex]

Step-by-step explanation:

Translations

For [tex]a > 0[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

Parent function:

[tex]f(x)=5|x-2|-7[/tex]

Translate 2 units right:

[tex]\begin{aligned}\implies f(x-2)& =5|x-2-2|-7\\ & =5|x-4|-7 \end{aligned}[/tex]

Then translate 5 units up:

[tex]\begin{aligned}\implies f(x-2)+5& =5|x-4|-7+5\\ & =5|x-4|-2 \end{aligned}[/tex]

Therefore:

[tex]\implies g(x)=5|x-4|-2[/tex]

The percentage of the time will Oliver get a written warning when  he is more than 16 minutes late for his shift at work is 46.7%.

The density curve is a type or way of representation of numbered distribution data over a graph. Here, the outcomes are continues. The density curve can not be below the x-axis or horizontal line of the graph.

In a density curve,

Records show that Oliver is typically 10-30 minutes late for his shift at work. The distribution for the minutes he is late forms a consistent pattern, which can be graphed as the given uniform density curve.

Oliver will get a written warning if he is more than 16 minutes late for work. The time remain after the 16 minutes is,

t=30-16

t=14 min

Thus, the percentage of the time will Oliver get a written warning is,

p=(14/30)*100

p=46.7 %

Thus, the percentage of the time will Oliver get a written warning when  he is more than 16 minutes late for his shift at work is 46.7%.

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Answer:

46.7%

Step-by-step explanation:

Answer:

y = -3x - 3

Step-by-step explanation:

The line intercepts the y-axis at -3, and moves down 3 on the y for moving to the right 1 along the x-axis

Answer:

60 miles per hour.

Step-by-step explanation:

speed = distance / time

= 750 / 12.5

= 60 miles per hour.

Answer: 6

Step-by-step explanation:

If the lines are parallel, then this means that by the corresponding angles theorem, the two angles marked in the image are congruent.

If we consider the right triangle, then by the exterior angle theorem, [tex]4x+90=11x-8 \longrightarrow x=14[/tex].

So, if [tex]x=14[/tex], then the indicated angle measures [tex]56^{\circ}[/tex], and since vertical angles are congruent, [tex]9y+2=56 \longrightarrow \boxed{y=6}[/tex]

Answer: A. No; the graph fails the vertical line test.

The vertical line test is a tool used to determine if we have a function. If we can draw a single straight vertical line through more than one point on the red curve, then the graph is said to have failed the vertical line test. Consequently, this leads to the relation not being a function.

For this circle graph, we can draw a vertical line through more than one point, which is why we don't have a function here.

Put another way, there are inputs (x) that produce more than one output (y), so that's why we don't have a function.

The measure of the unknown angle in the full circle is calculated as: 310 degrees.

The angle measure of a full circle equals 360 degrees.

The full circle given is divided into two angles, of which 50 degrees is a measure of one of the angles.

The unknown angle = 360 - 50 = 310 degrees.

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Answer:

b = 40

Step-by-step explanation:

Solve system of equations.

1) w = y

2) c + b = 90

3) y + c = 180

Since we want to solve for b, second equation would be a good starting point.

c + b = 90

b = 90 - c

But what is c?

Let's make c the subject in 3rd equation.

y + c = 180

c = 180 - y

Insert c back in second equation.

b = 90 - c

b = 90 - (180 - y)

b = 90 - 180 + y

b = -90 + y

All we need now is y. Notice that in the first equation w equals y and w is 130°, which means y is also 130°. Substitute again.

b = -90 + y

b = -90 + w

b = -90 + 130

b = 40

---

This is how it looks like if you solve it in one go (same procedure as above but in one place).

c + b = 90

b = 90 - c

b = 90 - (180 - y)

b = -90 + y

b = -90 + w

b = -90 + 130

b = 40