Given a polynomial function f(x)=2x²+ 7x+6 and an exponential function g(x)=2+ 5, what key features do f(x) and g(x) have in common?

Both f(x) and g(x) increase over the interval of [-4,∞)

Both f(x) and g(x) have the same x-intercepts of (-2, 0) and (-1.5, 0).

Both fox) and gox) have the same y-intercept of (0,6)

Both f(x) and g(x) have the same range of (-00.01]

The computation shows that the time before

they can no longer communicate will be 10 minutes

From the information, it was stated that two hikerd are wandering through heavy woods with walkie talkies and that the walkie talkies have a range c of 100 yards.

It should be noted that after t hours, the distance between the hikers will be:

d² = (0.24t)² + (0.17t)² - 2(0.24t)(0.17t) cos 109.10°

d = 0.0568

Therefore, we will find the time when d = 0.0568. This will give a time of 10 minutes.

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The coordinates of point F are (15/4 , -5/2)

From the image attached:

AB divided into 4 similar parts, hence

Note that the rule of the mid-point states that:

When M (x , y) is the mid-point of the segment of AB, where A (x1 , y1)  and B (x2 , y2), Then  x = (x1 + x2)/2 and that of  y = (y1 + y2)/2

Then lets solve for points E, F, D

Since A (-3 , -1) and B (6 , -3),

E is the mid-point of AB

Then  E =[(-3 + 6)/2, (-1 + -3)/2]

         = (3/2 , -2)

Since  F is the mid-point of EB,

         E (3/2 , -2) , B (6 , -3)

Then F = [(3/2 + 6)/2 , (-2 + -3)/2]

       = (15/4 , -5/2)

Since D is the mid-point of AE, A (-3 , -1), E (3/2 , -2)

Then  D = [(-3 + 3/2)/2 , (-1 + -2)/2]

           = (-3/4 , -3/2)

Note also that:

 BC is said to be an  horizontal segment due to the fact that B and C have similar y - coordinate and G can be found on BC.

Since the y-coordinate of G is similar to y-coordinate of B and C

Then  y-coordinate of G is =  -3

Since DG ⊥ BC

Then DG =  vertical segment

So  G has similar x-coordinate of D

Then  The x-coordinate of G = -3/4

The  G = (-3/4 , -3)

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Answer-

Step-by-step explanation:

The length of the function x = 2y is 2√5 units

According to the given question.

We have a function

x = 2y

Since, we know that the length of the function in the interval [a, b] is given by

l =    [tex]\int\limits^a_b\sqrt{1+(\frac{dx}{dy}) ^{2} } \,dy[/tex]

Where, l is the length of the function.

Now, differentiating the given function x = 2y w.r.t y.

Therefore,

dx/dy = 2

So, the length of the given function x = 2y  from y = -1 to y = 1 is given by

l =   [tex]\int\limits^1_{-1}{\sqrt{1+2^{2} } } \,dy[/tex]

⇒ l =   [tex]\int\limits^1_{-1} {\sqrt{1+4} } \,dy[/tex]

⇒ l =   [tex]\int\limits^1_{-1}{\sqrt{5} } \,dy[/tex]

⇒ l = √5[1 - (-1)]

⇒ l = √5(2)

⇒ l = 2√5

Hence, the length of the function x = 2y is 2√5 units.

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Answer:

x(x-1)^2

Step-by-step explanation:

x(x^2-2x+1)

x(x-1)(x-1)

(x-1)(x-1)=(x-1)^2

Answer:

The distance formula is 22.360679775

if you round it to the nearest tenth, then the answer is 22.4

Step-by-step explanation:

(-6, -12) and (4,8)

(x2 - x1)² + (y2 - y1)²

Place the x and y values

(4 - - 6)² + (8 - - 12)²

= 10² + 20²

= 100 + 400 = 500

√500 = 22.360679775

Round it to the nearest tenth, and you will get 22.4

Hope this helps!

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Answer: Distance = 10√2

Step-by-step explanation:

Given formula

[tex]Distance~=~\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Given information

(x₁, y₁) = (-6, -12)

(x₂, y₂) = (4, 8)

Substitute given information into the formula

[tex]Distance~=~\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]Distance~=~\sqrt{((4)-(-6))^2+((8)-(-12))^2}[/tex]

Simplify values in the parenthesis

[tex]Distance~=~\sqrt{(4+6)^2+(8+12)^2}[/tex]

[tex]Distance~=~\sqrt{(10)^2+(20)^2}[/tex]

Simplify the exponents

[tex]Distance~=~\sqrt{100+400}[/tex]

Simplify the radical number

[tex]Distance~=~\sqrt{500}[/tex]

[tex]Distance~=~\Large\boxed{10\sqrt{5}}[/tex]

Hope this helps!! :)

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The other names used to identify the transformation of geometric figures is translation or reflection and rotation.

Given that the types of transformations of geometric figures in the coordinate plane can be described as a slide, a flip, or turn.

We are required to find the other names used to identify the above transformations.

The other names used to identify the transformation of geometric figures is translation or reflection and rotation.

Translation means the displacement of a figure from one place to another. In translation a figure can move upward, downward,right , Iift or anywhere in the coordinate system. In translation, the position of the object changes, its size remains the same.

Reflection is a type of transformation that flips a shape in a mirror line so that each point is the same distance from the mirror line as its reflected point.

Rotation is a motion of a  space that preserves at least one point.

Hence the other names used to identify the transformation of geometric figures is translation or reflection and rotation.

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    Let's say you want to go on a vacation this summer because you finally saved enough money for it. While at the store to buy more hairbands (you just can't seem to figure out where they all went) you see something that you have been wanting for ages. The item is a bit on the more expensive side but you don't know when you will see it again. You decide to buy the item but you had to use some of the money planned for your trip to pay for it. But because you bought the item you now can't do all the activities you wanted on your trip.

The choice of buying the item affected your choices available on your trip.  

Answer:

dependent events

Step-by-step explanation:

The volume of the composite solid in terms of pi and using 3.14 as pi are 1125π cubic inches and 3532.5 cubic inches respectively

A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes

The volume of the composite cylinder is expressed as shown below;

V = πr²h

where

r is the radius

h is the height

According to the given diagram;

V = Vl - Vs

V = π(10)²*15 -  π(5)²*15

V = 1500π - 375π

V = 1125π cubic inches

If the value of π is 3.14, hence;

V = 1125(3.14) cubic inches

V = 3532.5 cubic inches

The volume of the composite solid in terms of pi and using 3.14 as pi are 1125π cubic inches and 3532.5 cubic inches respectively

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The missing number in the given series is 24.

Missing numbers are the numbers that have been missed in the given series of a number with similar differences among them. The method of writing the missing numbers is stated as finding similar changes between those numbers and filling the missing terms in the specific series and places.

Given the series,

4, ?, 144, 864, 5184, 31104

Multiplying with 6 in each term in the given sequence.

4×6 = 24

24×6 = 144

144×6 = 864

864×6 = 5184

5184×6 = 31104

Following the above sequence, we get the 2nd term is 24.

Hence the missing number is 24.

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Isolate y

Compare to slope intercept form y=mx+b

Slope=m=5/3

Answer:

[tex]\dfrac{5}{3}[/tex]

Step-by-step explanation:

To find the gradient (slope) of the given linear relation, use arithmetic operations to isolate y:

Given relation:

[tex]3y-5x=10[/tex]

Add 5x to both sides:

[tex]\implies 3y-5x+5x=10+5x[/tex]

[tex]\implies 3y=5x+10[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{3y}{3}=\dfrac{5}{3}x+\dfrac{10}{3}[/tex]

[tex]\implies y=\dfrac{5}{3}x+\dfrac{10}{3}[/tex]

Slope-intercept form of a linear equation

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

where:

Comparing the rewritten equation with the slope-intercept formula, the gradient (slope) of the given linear relation is ⁵/₃.

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Answer:

5/52 i think

Step-by-step explanation:

there are 52 cards in desk ,with26red and black cards.There 2red and 2 blackthree and. 1 six of hearts .

.

.

.

.

.

.

.

Answer:

n=2

Step-by-step explanation:

Create an equation.

9n=18

Divide 9 from both sides.

9n/9=18/9

n=2

Hope this helps!

a. Expressing y in terms of x, y = 20/(x + 3)

b. When x = 5, the value of y is 2.5

The question has to do with inverse variation.

Inverse variation is variation in which one quantity varies inversely as the other.

Given that y is inversely as x + 3 and that y = 4 when x = 2.

Since y varies inversely as x + 3, we have

y ∝ 1/(x + 3)

y = k/(x + 3)

When y = 4, x = 3. So

y = k/(x + 3)

4 = k/(2 + 3)

4 = k/5

k = 4 × 5

k = 20

So, y = k/(x + 3)

y = 20/(x + 3)

So, expressing y in terms of x, y = 20/(x + 3)

Since  y = 20/(x + 3)

Substituting x = 5 into the equation, we have

y = 20/(x + 3)

y = 20/(5 + 3)

y = 20/8

y = 5/2

y = 2.5

So, when x = 5, the value of y is 2.5

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Answer:

x = -6, y = -8

Step-by-step explanation:

8x - 5y = -8

-7x - 5y = 82

minus them

15x = -90

x = -90 / 15

x = -6

8(-6) - 5y = -8

-48 - 5y = -8

-5y = -8 + 48

-5y = 40

5y = -40

y = -40 / 5

y = -8

Answer:

The first choice.  

Step-by-step explanation:

The second choice is a translation and the third choice is a reflection.

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

A linear function is an equation of the form:

[tex]\sf{y=mx+b}[/tex]

▪ [tex]\sf{m= \: slope}[/tex]

▪ [tex] \sf{b= \: y-intercept}[/tex]

First, pick any two pairs of points from the table.

[tex]\small\longrightarrow \sf{(x_1,y_1)(-1.13)}[/tex]

[tex]\small\longrightarrow \sf{(x_2,y_2)=(0,10)}[/tex]

Using these points, find the slope.

[tex]\small\longrightarrow \sf{m= \dfrac{y _{2 } - y_1}{x_2-y_1} }[/tex]

When x=0, y=10, therefore, the y-intercept, b=10.

[tex]\leadsto[/tex] Substitute m=-3 and b=10 into the slope-intercept form given above:

[tex]\small\longrightarrow \sf{m=m = \dfrac{10 - 13 }{0 -( - 1) } = - \dfrac{3}{1} = - 3}[/tex]

▪ [tex]\small\longrightarrow \sf{y= -3x+10}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

[tex]\large\boxed{\bm{y= -3x+10}}[/tex]

Answer:

We multiply by 2 and add 4

Step-by-step explanation:

To find the pattern,  we find the slope

m = ( y2-y1)/(x2-x1)

m = ( 10-6)/(3-1)

m = 4/2

m =2

We are multiplying by 2

y = mx+b  where m is the slope and b is the y intercept

y = 2x+b

Using the point (1,6)

6 = 2(1)+b

6 = 2+b

The y intercept is 4

y = 2x+4

We multiply by 2 and add 4

[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=562\\ r=5 \end{cases}\implies 562=\cfrac{\pi (5)^2 h}{3}\implies 1686=25\pi h \\\\\\ \cfrac{1686}{25\pi }=h\implies 21.47\approx h[/tex]

Answer: 9 cm² : 25 cm²

Step-by-step explanation:

    The area of a square can be found with x² where x is the length of one side.

    x² : x²

    3² : 5²

    9 : 25

           9 cm² : 25 cm²

Proficiency in statistics is an important skill for a data analyst because it is needed in  identifying patterns and correlations in data.

Data analysis can be regarded as the  process of collecting as well as modeling, and analyzing data so as to be able to extract insights that support decision-making.

Some Types of Data Analysis are:

It should be noted that Proficiency in statistics is an important skill for a data analyst because it is needed in  identifying patterns and correlations in data.

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The value of A such that cos A = 0.7715 is 39.5 degrees

The equation is given as:

cos A = 0.7715

Where the angle is in degrees

There are several ways to solve this equation, some of which include:

In this case, we make use of the first option; using a scientific calculator

Recall that the equation is represented as:

cos A = 0.7715

Next, we take the arccos (or anti cosine) of the above equation.

This is represented as

arccos(cos A) = arccos(0.7715)

Evaluate the expression on the left-hand side

A = arccos(0.7715)

Evaluate the expression on the left-hand side using the scientific calculator

A = 39.5112207183

Approximate the above expression

A = 39.5

Hence, the value of A such that cos A = 0.7715 is 39.5 degrees

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Step-by-step explanation:

we have

B = J + 2

as the number of laps Bill ran.

to get the number of laps Jill ran we need to transform this equation, so that we get

J = ...

or

... = J

J has to be on one side, and the rest on the other (just as it is with B = ...).

so,

B = J + 2

B - 2 = J

or

J = B - 2

hey ! we are finished already !

=======================================================

Explanation:

Replace x with 4 and y with 5.

Then use the order of operations (PEMDAS) to simplify until you get a single number.

Something like 9x means "9 times x", and a similar situation happens with the 8y term as well.

---------

Here's what the steps look like:

9x + 8y

9*4 + 8*5

36 + 40

76

Therefore, 9x+8y = 76 when x = 4 and y = 5.

The point (4,5) is located on the line 9x+8y = 76

Answer:

  58.25

Step-by-step explanation:

A "moving average" is a "boxcar average," the unweighted average over the specified number of days.

The 4-day moving average ending on day 7 is ...

  4-day average = (day 4 +day 5 +day 6 +day 7)/4

  = (60 +59 +55 +59)/4 = 233/4

  4-day average = 58.25

The four-day moving average for the price of the stock for the end of day 7 is 56.00

What is moving average?

The moving average on a particular day  is the average of prices on the days prior to the pricing day.

In other words, four-day moving average on day 7 is the sum the prices of four days prior to day 7 divided by the number of days whose prices were considered.

In computing the four-day moving average for day 7, we would sum the prices for days 3-6, then divide the sum by 4 since prices of 4 days were made use of.

four-day moving average on day 7=(50.00+60.00+59.00+55.00)/4

four-day moving average on day 7= 56.00

Note, as the day of pricing changes, the input prices would also change

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The graph for the given system of equations is shown below

From the question, we are to determine the graph that describes the given system equations

First, we will graph the given system of linear equations.

The given equations are

Y equals four over X +3

and

Y equals negative 2X subtract four

That is,

y = 4/(x+3)

y = -2x -4

The graph for the given system of equations is shown below

The statement that best describes the graph of the two equations is the statement that describes the graph of the system of equations as shown below

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The rhombus ABCD has an area of 72 square units. Diagonals AC and BD intersect at E. Given EC = 8 units and DB = x - 1, the value of x is 10 units. The correct option is B).

We are given a rhombus ABCD with area 72 square units. The diagonals AC and BD intersect at point E.

Since all sides of the rhombus are congruent, we can assume that the length of each side is "s" units.

We are also given that EC (a part of diagonal AC) is 8 units long.

As diagonals of a rhombus bisect each other, we can deduce that the other half of diagonal AC is also 8 units. So, the full diagonal AC is 16 units (8 units + 8 units).

Now, we are told that DB (a part of diagonal BD) is x - 1 units long.

To find the value of x, we need to find the length of the other half of diagonal BD, which is also x - 1 units. So, the full diagonal BD is

(x - 1) units + (x - 1) units = 2x - 2 units.

The area of a rhombus is given by the formula:

Area = 1/2 × Product of Diagonals.

Substituting the given values, we have:

72 = 1/2 × 16 × (2x - 2).

Now, we can simplify the equation:

72 = 8x - 8.

Move the constant term to the right side:

8x = 72 + 8.

Combine the constants:

8x = 80.

Finally, solve for x by dividing both sides by 8:

x = 80 / 8 = 10.

So, the value of x is 10 units. The correct answer is B).

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--The given question is incomplete, the complete question is given below " Rhombus A B C D is shown. Lines are drawn from point A to point C and from point D to point B and intersect at point E. All sides are congruent.

The area of rhombus ABCD is 72 square units. EC = 8 units and DB = x – 1.

What is the value of x?

9

10

14

16 "--

This is reverse percentage

8.4% = 420

÷8.4 both side

1% is now 50

1% =50

x100

100% is 5000

Check:

8.4/100 = 0.084 our decimal multiplier

5000 x 0.084 = 420

Thus, x is 5000

Hope this helps!