For the following systems of equations, match each diagram on the left with its solution on the right.

As x approaches infinity,

The function with the lowest output is graph A

The function with the greatest output is graph B

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Explanation:

As the graphs head to the right, they go up forever. However, the growth rate (how fast they go upward) varies. The red straight line (line A) goes up the slowest. The growth rate is the same throughout the entire function. The rate is the slope of the line. In contrast, the purple curve B goes up the fastest as it has the steepest increase among the four graphs. The graph steadily gets steeper as you move to the right.

The exponential graph will grow the fastest compared to a linear one or parabolic one. Graphs B and C are exponential, where graph B has a steeper curve compared to graph C.

Answer: The function with the lowest output values as x approaches infinity is Graph A.

The function with the greatest output values as x approaches infinity is Graph B.

Step-by-step explanation: I can’t give you a step-by-step explanation, but this is right!

Answer:

≈23.66

Step-by-step explanation:

Height ---> x

base ---> 5x

Formula for area of triangle: (base*height)/2

((5x)(x))/2 = 1400

[tex]5x^{2}[/tex]/2 = 1400

[tex]5x^{2}[/tex] = 1400 · 2 = 2800

[tex]x^2[/tex] = 2800/5 = 560

x= √560 ≈ 23.66

Answer:

[tex]\frac{x}{y}[/tex] = [tex]\frac{4}{9}[/tex]

Step-by-step explanation:

Given

[tex]\frac{x}{5}[/tex] = [tex]\frac{2}{3}[/tex] = [tex]\frac{5}{y}[/tex]

This can be expressed in 2 parts as

[tex]\frac{x}{5}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )

3x = 10 ( divide both sides by 3 )

x = [tex]\frac{10}{3}[/tex]

and

[tex]\frac{2}{3}[/tex] = [tex]\frac{5}{y}[/tex] ( cross- multiply )

2y = 15 ( divide both sides by 2 )

y = [tex]\frac{15}{2}[/tex]

Thus

[tex]\frac{x}{y}[/tex] = [tex]\frac{\frac{10}{3} }{\frac{15}{2} }[/tex] = [tex]\frac{10}{3}[/tex] × [tex]\frac{2}{15}[/tex] ( cancel 10 and 15 by 5 )

[tex]\frac{x}{y}[/tex] = [tex]\frac{2}{3}[/tex] × [tex]\frac{2}{3}[/tex] = [tex]\frac{4}{9}[/tex]

Answer:

= 4/9

Step-by-step explanation:

2/3 to the averall of 2/3 ans we got 5/y

sp ab- x/5 = 4/9

Answer:

B. [tex]1\frac{1}{7}[/tex]

Step-by-step explanation:

[tex]-9\frac{2}{7}[/tex]=[tex]-\frac{65}{7}[/tex]

[tex]-10\frac{3}{7}[/tex]=[tex]-\frac{73}{7}[/tex]

[tex]-\frac{65}{7}[/tex]-([tex]-\frac{73}{7}[/tex])=8/7

8/7=[tex]1\frac{1}{7}[/tex]

Hope this helped!!!

Answer:

greater than

Step-by-step explanation:

To compare 3/4 to 1/2, let's convert 1/2 so that it has a denominator of 4. This would then be 2/4. Because 3 > 2, 3/4 > 2/4 which means 3/4 > 1/2.

Answer:

Greater

Step-by-step explanation:

It is greater than 1/2 because when you divide the fractions you get- 1/2 = 0.5, 3/4 = 0.75 And this makes it greater.

Answer: -5/2 or 1/6

Step-by-step explanation:

I6n + 7I = 8

Therefore (6n + 7) = 8 or -8 because modulus means we're only getting it's absolute value, (it's positive value) meaning it could equal 8 or -8 before it's modulus'ed.

Therefore 6n + 7 = 8

or 6n + 7 = -8

Leaving us with:

6n = 1

6n = -15

So n = 1/6

or n = -5/2 (-2.5)

Answer:

n = 1/6                          n = -5/2

Step-by-step explanation:

|6n+7|=8

This has two solutions, one positive and one negative

6n+7 = 8  and 6n+7 = -8

Subtract 7 from each side

6n+7-7 = 8-7         6n+7-7 =-8-7

6n =1                        6n = -15

Divide by 6

6n/6 = 1/6                 6n/6 = -15/6

n = 1/6                          n = -5/2

Answer:

           The distance is:   [tex]\sqrt3\ cm\approx1,73\,cm[/tex]

Step-by-step explanation:

The distance of point E to the PQR plane it is the hight (vertical) of piramid PRQE

If point P is located in the middle of line EH, point Q is in the middle of line EF, and point R is in the middle of line AE than:

EP = EQ = ER = 0.5EF = 3 cm  and  m∠REQ = m∠QEP = m∠REP = 90° so triangles RQE, QPE and PRE are congruent.

RQ = QP = PR so triangle PQR is equilateral and from Pythagorean theorem (for ΔRQE):

[tex]RQ^2=ER^2+EQ^2=3^2+3^2=2\cdot3^2\ \ \implies\ \ RQ=3\sqrt2[/tex]

Then: [tex]RN=\dfrac{RQ\,\sqrt3}2[/tex]

and:  [tex]RK=\dfrac23RN=\dfrac{RQ\,\sqrt3}3=\dfrac{3\sqrt2\cdot\,\sqrt3}3=\sqrt6[/tex]

Therefore from Pythagorean theorem (for ΔERK):

[tex]EK^2+RK^2=ER^2\\\\EK^2=ER^2-RK^2\\\\EK^2=3^2-(\sqrt6)^2\\\\EK^2=9-6=3\\\\EK=\sqrt3\ cm\approx1,73\,cm[/tex]

Answer:

V = 200

Step-by-step explanation:

Cylinder

V = pi r^2 h

150 = pi r^2 h

We know that h = r

150 = pi r^2 r

150 = pi r^3

Divide each side by pi

150 /pi = r^3

Take the cube root of each side

( 150 / pi ) ^ 1/3 = r

3.627831679 = r

Rounding to 3.63

Now find the volume of the sphere

V = 4/3 pi  r^3

Replacing r^3 with 150 /pi

V = 4/3 * pi ( 150/pi)

V = 4*150 /3

V = 200

Answer:

The long of the flag is:

15 ft

Step-by-step explanation:

On a three rule:

5 ft is to 8 ft

24 ft is to  A ft

A = 24*5/8

A = 15 ft

related task:  https://brainly.com/question/17139181

Answer:

A

Step-by-step explanation:

Since a coin only has two sides, the test must be referring to the fact that she has a 50, 50 shot at passing.

Answer: w=5

Step-by-step explanation:

Answer:

0.971

Step-by-step explanation:

Given the expression (cos (arctan √3/7)) which all lies in the first quadrant. Note that all the trigonometry identities (sin, cos and tan) are all positive in the first quadrant.

From the expression given

(cos (arctan √3/7)), we need to get the expression in parenthesis first.

Let y = (cos (arctan √3/7))

If u = arctan √3/7

Then y = cos(u) .... 1

Let's get the value of u first

u = arctan √3/7

u = arctan(0.2474)

u = 13.896°

Substituting u = 13.896° into equation 1, we will have;

y = cos(u)

y = cos13.896°

y = 0.971.

Hence the expression (cos(arctan√3/7)) is equivalent to 0.971

Answer:

y = 0.971.

Step-by-step explanation:

Given the expression (cos (arctan √3/7)) which all lies in the first quadrant. Note that all the trigonometry identities (sin, cos and tan) are all positive in the first quadrant.

From the expression given

(cos (arctan √3/7)), we need to get the expression in parenthesis first.

Let y = (cos (arctan √3/7))

If u = arctan √3/7

Then y = cos(u) .... 1

Let's get the value of u first

u = arctan √3/7

u = arctan(0.2474)

u = 13.896°

Substituting u = 13.896° into equation 1, we will have;

y = cos(u)

y = cos13.896°

y = 0.971.

Answer:

0.03333 or 1/30

Step-by-step explanation:

Let A =" I go sailing" and B = "it does not rain"

P(A) = 0.03

P(B) =0.90

Since I never go sailing when it rains, P(A and B) =0.03.

Therefore, the (conditional) probability that I go sailing, given that it does not rain is:

[tex]P(A|B)=\frac{P(A\ and\ B)}{P(B)} \\P(A|B)=\frac{0.03}{0.90}=0.033333[/tex]

The probability is 0.03333 or 1/30.

Answer:

0

Step-by-step explanation:

6(-0.5) + 3 = -3 + 3 = 0

Answer:

0

Step-by-step explanation:

x= - 1/2 [given]

Now,

> 6x + 3

>6 × - 1/2 + 3

> -6/2 +3

> -3/1 + 3

> -3 + 3

> 0

Answer:

x = -7/9; y = 4/3.

Step-by-step explanation:

I will assume that the top equation is 6x + 2y = -2, and the bottom one is 3x - 2y = -5.

If you add the two...

(6x + 3x) + (2y + (-2y)) = (-2 + (-5))

9x + 0 = -7

9x = -7

x = -7/9

6(-7/9) + 2y = -2

-42/9 + 2y = -18/9

2y = 24/9

y = 24/18

y = 12/9

y = 4/3

Hope this helps!

Answer:

2/36 or 1/18

Step-by-step explanation:

There are 36 possible outcomes (6x6).

Only 2 possibilities equal 11.  (5+6 and 6+5).

So the probability is 2/36, or 1/18.

Answer:

There's no results that appear below

Answer:

The speed V = 194.03 mph

Direction = 3.6° northeast

Step-by-step explanation:

The distance of the trip = 291 miles

The direction of flight = 9.1 degrees northeast

Speed of the prevailing wind = 25 mph

Direction of wing = southeast = 45 degrees South of East

The speed heading to Ivy Cliffs = V₁

V×(sin(9.1) + cos(9.1)) + 25×(-sin(45) + cos(45))  × t₁ = 291 miles

V×(sin(9.1) + cos(9.1)) + 25×(sin(45) + -cos(45))  × t₂ = 291 miles

t₁ + t₂ = 3 hours

(V×(sin(9.1)-25×(sin(45))j + (V×cos(9.1) + 25×cos(45))i

The magnitude V² = V²+29.32·V +625= 291²/t₁²......(1)

Also on the return trip we have;

V²-29.32·V +625= 291²/(3-t₁)²..........................................(2)

Subtracting equation (2) from (1) gives;

58.64·V = 291²/t₁² - 291²/(3-t₁)² = 291²×(6·t-9)/(t²·(t-3)²)

V = 291²×(6·t-9)/(t²·(t-3)²)/58.64

Substituting the value of V in (2) with a graphing calculator gives;

t₁= 1.612 or 1.387

Given that magnitude of the speed going > return = V² for  t₁ < t₂

t₁ = 1.387, t₂ = 1.612

From  V²+29.32·V +625= 291²/t₁², we have

V²+29.32·V +625= 291²/1.387²

Which gives

V²+29.32·V -43336.5 = 0

(V + 233.35)(V-194.03) = 0

V = -233.35 mph or V = 194.03 mph

Given that V is a natural number, we have, V = 194.03 mph.

The direction is given by the relation;

V×(sin(9.1) + cos(9.1)) + 25×(-sin(45) + cos(45))  × t₁ = 291 miles

V×(sin(9.1) + cos(9.1)) + 25×(-sin(45) + cos(45))  × t₁ = 291 miles

194.03×sin(9.1 degrees)-25×sin(45 degrees)j + 194.03×cos(9.1 degrees) + 25×cos(45 degrees)i = 291/1.387

13j + 209.27i = 208.81 mph

The angle tan θ = 13/209 = 0.00622

θ = tan⁻¹(13/209.27) = 3.6°.

Answer:

12.6 units.

Step-by-step explanation:

According to cosine formula:

[tex]a^2=b^2+c^2-2bc\cos A[/tex]

Using cosine formula in triangle STU, we get

[tex](SU)^2=(ST)^2+(TU)^2-2(ST)(TU)\cos T[/tex]

[tex]t^2=(5)^2+(15)^2-2(5)(15)\cos (53^{\circ})[/tex]

[tex]t^2=25+225-150(0.60)[/tex]

[tex]t^2=160[/tex]

Taking square root on both sides.

[tex]t=\sqrt{160}[/tex]

[tex]t\approx 12.6[/tex]

Therefore, the value of t is 12.6 units.

Answer:

[tex]y\ =\ \left|\frac{1}{2}x-2.5\right|+3[/tex]

Step-by-step explanation:

Look at the image below ↓

Answer:

Check below the graph.

Step-by-step explanation:

Hi, for this function, check the graph below:

1) Note that in this function the value outside the brackets points how high the graph will be traced.

2) The value within the brackets, points since it's a negative expression how far to the right the graph will be traced.

Answer:

Step-by-step explanation:

Did you mean log (17*3)?  If so, your log (17x3) becomes log 17 + log 3.

Did you mean  log 17^3?  If so, log 17^3 = 3 log 17.

Did you mean log 17*x*3?  If so, this equals log 17 + log x + log 3

Answer:

C: 1 and 3

Step-by-step explanation:

EDGE2021

Answer:

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find an equation of a line given two points first find the slope / gradient

Slope of the line using points (-1,4) and (-2,2) is

[tex]m = \frac{2 - 4}{ - 2 + 1} = \frac{ - 2}{ - 1} = 2[/tex]

So the equation of the line using point (-1,4) is

Hope this helps you

Answer:

60

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello,

For each survey that Gwen completes she earns 10 points.

So the number of points Gwen earns for completing each survey is 10 and there is only one value.

If x is the number of surveys Gwen completed, her number of points is 10 multiplied by x.

The number of surveys Gwen completes can have several values.

And then, the total number of points Gwen earns can have several values too.

So you need to choose

The number of surveys Gwen completes.

and

The total number of points Gwen earns.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

x^2y^2(x+y)(x^2-xy+y^2)

Step-by-step explanation:

x^5y^2+x^2y^5

Factor out the greatest common factor

x^2y^2( x^3+y^3)

Apply the Sum of Cubes Formula x^3+y^3 =(x+y)(x^2-xy+y^2)

x^2y^2(x+y)(x^2-xy+y^2)

Answer:

The answer is

Step-by-step explanation:

[tex] {x}^{5} {y}^{2} + {x}^{2} {y}^{5} [/tex]

To factorize the expression first factor

x²y² out

We have

x²y²( x³ + y³)

Using the expression

Factorize the terms in the bracket

So we have

x³ + y³ = ( x + y)(x² - xy + y²)

Combine the expressions

We have the final answer as

Hope this helps you

Answer:

3/2

Step-by-step explanation:

Perpendicular lines have slopes that multiply to -1

m * -2/3  =-1

Multiply by -3/2 to isolate m

m * -2/3 * -3/2 = -1 * -3/2

m = 3/2

The perpendicular line has a slope of 3/2

Answer:

x = 5.4

Step-by-step explanation:

Multiply 7.2 by 3/4 to find the equivalent ratio.

Answer:

Step-by-step explanation:

[tex] \frac{7.2}{x} = \frac{4}{3} [/tex]

Apply cross product property

[tex]4x = 7.2 \times 3[/tex]

Multiply the numbers

[tex]4x = 21.6[/tex]

Divide both sides of the equation by 4

[tex] \frac{4x}{4} = \frac{21.6}{4} [/tex]

Calculate

[tex]x = 5.4[/tex]

Hope this helps..

best regards!!

Answer:

The probability that a man in this age category does NOT die of cancer during the course of the​ year is 0.997.

Step-by-step explanation:

Suppose the probability of an event occurring is [tex]P_{i}[/tex].

The probability of the given event not taking place is known as the complement of that event.

The probability of the complement of the given event will be,

[tex]1 - P_{i}[/tex]

In this case an events X is defined as a man, aged 55​ - 59, will die of cancer during the course of the year.

The probability of the random variable X is:

[tex]P (X) = \frac{300}{100000}=0.003[/tex]

Then the event of a man in this age category not dying of cancer during the course of the​ year will be complement of event X, denoted by X'.

The probability of the complement of event X will be:

[tex]P(X')=1-P(X)[/tex]

          [tex]=1-0.003\\=0.997[/tex]

Thus, the probability that a man in this age category does NOT die of cancer during the course of the​ year is 0.997.