Identify the initial amount a and the growth factor b in the exponential function.
f(x) = 620 - 7.8^x​

Answer:

x intercepts: (-1, 0) and (5, 0)

vertex: (2, 9)

axis of symmetry: x = 2

Step-by-step explanation:

The x intercepts are where y = 0.

0 = -(x + 1)(x − 5)

x = -1, x = 5

So the x intercepts are (-1, 0) and (5, 0).

The x coordinate of the vertex is halfway between the x intercepts.

x = (-1 + 5) / 2

x = 2

So the vertex is at (2, 9).

The axis of symmetry passes through the vertex.

x = 2

Answer: The outlier in this scatter plot is Point D.

Step-by-step explanation:

The reason its Point D because its the only one that is the farest away from the rest of the points on the plot.

The reason why "Point D" would be the correct answer because the point is no where near the "trend" of the scatter plot.

When you look at the scatter plot, you would notice that there following a "trend" when the graph increases.

However, you would notice that point D is not really near there, therefore making it an outlier.

An outlier is pretty much something that is left out, and in this case, point D would be the outlier since it's left out of the typical growth of the scatter plot.

Dotted linear inequality shaded below passes through (0, 4) & (4,3). Dotted parabolic inequality shaded above passes through points (negative 6,4), (negative 4, 0) & (negative 2, 4).

Hello! Let me help you to find the correct option to this problem. First of all, we have the following system of inequalities:

[tex]\left\{ \begin{array}{c}y< -\frac{1}{4}x+4\\y>(x+4)^{2}\end{array}\right.[/tex]

To solve this, let's write the following equations:

[tex]y=-\frac{1}{4}x+4[/tex]

This is a linear function written in slope-intercept form as [tex]y=mx+b[/tex]. So, the slope [tex]m=-\frac{1}{4}[/tex] and the y-intercept is [tex]b=4[/tex]. Since in the inequality we have the symbol < then the graph of the line must be dotted. To get the shaded region, let's take a point, say, [tex](0, 0)[/tex] and let's test whether the region is above or below the graph. So:

[tex]y< -\frac{1}{4}x+4 \\ \\ Let \ x=y=0 \\ \\ 0<-\frac{1}{4}(0)+4 \\ \\ 0<4 \ True![/tex]

Since the expression is true, then the region is the one including point [tex](0, 0)[/tex], that is, it's shaded below.

[tex]y=(x+4)^{2}[/tex]

This is a parabola that opens upward and whose vertex is [tex](-4,0)[/tex]. Since in the inequality we have the symbol > then the graph of the parabola must be dotted. Let's take the same point [tex](0, 0)[/tex] to test whether the region is above or below the graph. So:

[tex]y>(x+4)^{2} \\ \\ Let \ x=y=0 \\ \\ 0>(0+4)^2\\ \\ 0>16 \ False![/tex]

Since the expression is false, then the region is the one that doesn't include point [tex](0, 0)[/tex], that is, it's shaded above

____________________

[tex]y=-\frac{1}{4}x+4 \\ \\ \\ \bullet \ (0,4): \\ \\ y=-\frac{1}{4}(0)+4 \therefore y=4 \\ \\ \\ \bullet \ (4,3): \\ \\ y=-\frac{1}{4}(4)+4 \therefore y=3[/tex]

So the line passes through these two points.

[tex]y=(x+4)^2 \\ \\ \\ \bullet \ (-6,4): \\ \\ y=(-6+4)^2 \therefore y=(-2)^2 \therefore y=4 \\ \\ \\ \bullet \ (-4,0): \\ \\ y=(-4+4)^2 \therefore y=0 \\ \\ \\ \bullet \ (-2,4): \\ \\ y=(-2+4)^2 \therefore y=(2)^2 \therefore y=4[/tex]

So the line passes through these three points.

Finally, the shaded region is shown below.

Answer:

The factors are (3x+1)(2x+1)

Step-by-step explanation:

The expression is:

6x^2 + 5x + 1

We have to break the middle term to find its factors. For this first we have to multiply the coefficient of 1st terms with the constant term:

6*1 = 6

Now we have to find any two numbers whose product is 6 and whose sum is the middle term:

3*2=6

3+2=5

Now break the middle term by these two numbers.

6x^2 + 5x + 1

6x^2+3x+2x+1

Group the first two terms and last two terms:

(6x^2+3x)+(2x+1)

Now take out common factor from each term:

3x(2x+1)+1(2x+1)

(3x+1)(2x+1)

Therefore the factors are (3x+1)(2x+1)....

Answer:

(2x + 1)(3x + 1)

Step-by-step explanation:

Given

6x² + 5x + 1

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 6 × 1 = 6 and sum = + 5

The factors are + 3 and + 2

Use these factors to split the x0 term

6x² + 3x + 2x + 1 ( factor the first/second and third/fourth terms )

= 3x(2x + 1) + 1 (2x + 1) ← factor out (2x + 1) from each term

= (2x + 1)(3x + 1) ← in factored form

Answer:

The basic answer to your question is that we have to start somewhere.

The essence of mathematics (in the sense the Greeks introduced to the  

world) is to take a small set of fundamental "facts," called  

postulates or axioms, and build up from them a full understanding of  

the objects you are dealing with (whether numbers, shapes, or  

something else entirely) using only logical reasoning such that if  

anyone accepts the postulates, then they must agree with you on the  

rest.

It can sometimes be proven.

Answer: Third Option

[tex]Q_1=3[/tex]

[tex]Q_3=6[/tex]

Step-by-step explanation:

Notice that we already have the data sorted from least to greatest.

Now to find Q1 and Q3 we can use the following formulas

For a set of data ordered from least to greatest of the form [tex]X_1, X_2, ..., X_n[/tex]

Where n is the total number of data

[tex]Q_1=X_{\frac{1}{4}(n+1)}[/tex]

In this case [tex]n=10[/tex]

So:

[tex]Q_1=X_{\frac{1}{4}(10+1)}[/tex]

[tex]Q_1=X_{2.75}[/tex]

Round the nearest whole and get:

[tex]Q_1=X_{3}[/tex]

[tex]Q_1=3[/tex]

For [tex]Q_3[/tex] we have:

[tex]Q_3=X_{\frac{3}{4}(n+1)}[/tex]

[tex]Q_3=X_{\frac{3}{4}(10+1)}[/tex]

[tex]Q_3=X_{8.25}[/tex]

Round the nearest whole and get:

[tex]Q_3=X_{8}[/tex]

[tex]Q_3=6[/tex]

Answer:

So 67 degrees is one value that we can take the sine of such that is equal to cos(23 degrees).

(There are more values since we can go around the circle from 67 degrees numerous times.)

Step-by-step explanation:

You can use a co-function identity.

The co-function of sine is cosine just like the co-function of cosine is sine.

Notice that cosine is co-(sine).

Anyways co-functions have this identity:

[tex]\cos(90^\circ-x)=\sin(x)[/tex]

or

[tex]\sin(90^\circ-x)=\cos(x)[/tex]

You can prove those drawing a right triangle.

I drew a triangle in my picture just so I can have something to reference proving both of the identities I just wrote:

The sum of the angles is 180.

So 90+x+(missing angle)=180.

Let's solve for the missing angle.

Subtract 90 on both sides:

x+(missing angle)=90

Subtract x on both sides:

(missing angle)=90-x.

So the missing angle has measurement (90-x).

So cos(90-x)=a/c

and sin(x)=a/c.

Since cos(90-x) and sin(x) have the same value of a/c, then one can conclude that cos(90-x)=sin(x).

We can do this also for cos(x) and sin(90-x).

cos(x)=b/c

sin(90-x)=b/c

This means sin(90-x)=cos(x).

So back to the problem:

cos(23)=sin(90-23)

cos(23)=sin(67)

So 67 degrees is one value that we can take the sine of such that is equal to cos(23 degrees).

Answer:(6,12)

Step-by-step explanation:

[tex]\bf \textit{recalling that }~\hfill i^4=1~\hfill i^3=-i~\hfill i^2=-1 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 5i^4+2i^3+8i^2+\sqrt{-4}\implies 5(1)+2(-i)+8(-1)+\sqrt{-1\cdot 4} \\\\\\ 5-2i-8+\sqrt{-1}\cdot \sqrt{2^2}\implies -2i-3+i\cdot 2\implies ~~\begin{matrix} -2i \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~-3~~\begin{matrix} +2i \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill -3+0i~\hfill[/tex]

Answer:

X intercepts (3,0) Y (0, -6/5)

Step-by-step explanation:

X intercepts: -6-2x/5=0

                       5(-6-2/5)=0*5

                         -6+2x=0

                          -6+6+2x=0+6

                          2x=6

                           2x/2=6/2

                            x=3

Y intercepts: y=-6-2*0/5

                      y=6-2*0=6

                        6-2*0/5

                         6-0/5

                          6/5

Answer:

X= 5y/2+3

Step-by-step explanation:

First add 5y to both sides

2x-5y+5y=6+5y

2x=5y+6

Step 2

Divide both sides by 2

2x/2=5y+6/2

X=5y/2+3

Answer:

The correct answer would be option A, Don't you agree that the financial crisis is essentially over.

Step-by-step explanation:

A survey questionnaire is a series of question which is set formally to be asked from a specific sample of a population to gather, analyze and interpret the data obtained from the sample population. So the questions in the survey must be structured, to the point, clear, short and straight. Survey questions are desirably closed ones and the ones which do not need much explanation by the person who is doing the survey. So the first question in this question require an explanation, and also the question is not structured, clear and to the point and thus is not a good survey question. Comparatively, the second question is more structured, clear and to the point and such questions are normally desirable in the surveys.  

Answer:

See image

Step-by-step explanation:

Plato

Answer:360

Step-by-step explanation:

1 ton = 2000 pounds

8000/2000 =4

4x90= 360.00

Answer is 360.00 for shipping

[tex]\huge{\boxed{\$360}}[/tex]

Each pound contains [tex]2000[/tex] pounds, so divide [tex]8000 \div 2000[/tex] to find the number of tons. [tex]8000 \div 2000=4[/tex]

Now, just multiply [tex]\$90*4=\boxed{\$360}[/tex]

Answer:

96π units²

Step-by-step explanation:

area of shaded sector (A) = area of circle × fraction of circle

A = πr² × [tex]\frac{\frac{3\pi }{4} }{2\pi }[/tex]

   = 16² × [tex]\frac{3\pi }{8}[/tex]

   = 256 × [tex]\frac{3\pi }{8}[/tex]

   = 32 × 3π

   = 96π units²

Answer:

Area of sector : 96 π unit².

Step-by-step explanation:

Given : The measure of central angle XYZ is 3pi/4 radians.

To find : What is the area of the shaded sector?

Solution: We have given central angle XYZ is 3pi/4 radians.

Area of sector : [tex]\frac{1}{2}[/tex] (radius)²* central angle.

Plug the values central angle  = [tex]\frac{3\pi }{4}[/tex] , radius = 16 units.

Then ,

Area of sector : [tex]\frac{1}{2}[/tex] (16)²* [tex]\frac{3\pi }{4}[/tex].

Area of sector : [tex]\frac{1}{2}[/tex] * 256 * [tex]\frac{3\pi }{4}[/tex].

Area of sector :  128 * [tex]\frac{3\pi }{4}[/tex].

Area of sector : 32 * 3 π

Area of sector : 96 π unit².

Therefore, Area of sector : 96 π unit².

Answer:

Option B [tex]g\left(x\right)=\left|x-4\right|+6[/tex]

Step-by-step explanation:

we have

[tex]f\left(x\right)=\left|x\right|[/tex]

The vertex is the point (0,0)

If to the parent function apply

Shift 4 units to the right and Shift 6 units up

The rule of the translation is

(x,y) ------> (x+4,y+6)

so

The vertex of the new function is (4,6)

therefore

the equation of the new function is

[tex]g\left(x\right)=\left|x-4\right|+6[/tex]

Answer:

just entered the answer and it was |x-4|+6

hope that helps!

Step-by-step explanation:

Check the picture below.

notice, on the first 2 lines, we used the quadrilateral conjecture.

on the lines 3 and 4 we used the inscribed angle theorem.

line 5, if we add those 3 arcs, we end up with 427°, mind you that the surplus is arcYW or "b", since it's added twice by XW and YZ.

line 6, if we subtract a full circle from it, we have the surplus.

line 7, we simply subtract YW from XW, leaving the leftover of arc "a".

Check the picture below.

The distance across the lake is 210 meters, and this is found using the concept of similar triangles and proportionality.

The correct answer is option B.

To find the distance across the lake, we can use the concept of similar triangles. Given that the triangles are similar, we can set up a proportion to find the missing side length.

Let's label the sides of the larger triangle as A, B, and C and the sides of the smaller triangle as X, Y, and Z. The given values are:

A = 70 m (the length of the larger triangle)

X = 20 m (the length of the smaller triangle)

Y = 60 m (the width of the smaller triangle)

We want to find side C, which represents the distance across the lake.

We can set up a proportion between the corresponding sides of the two similar triangles:

A / X = B / Y = C / Z

Plugging in the given values:

70 m / 20 m = C / 60 m

Now, solve for C by cross-multiplying:

70 m * 60 m = 20 m * C

4200 m² = 20 m * C

To isolate C, divide both sides by 20 m:

C = 4200 m² / 20 m

C = 210 m

So, the distance across the lake (side C) is 210 meters. This is the solution based on the concept of similar triangles and the given side lengths.

Therefore, from the given options the correct one is B.

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Answer:

y - 4 = 3(x- (-1)     --->      y-4 = 3(x+1)

Step-by-step explanation:

y - 4 = 3(x + 1)

y - 4 = 3x + 3

y = 3x + 7

then plug in (-1,4)

4 = 3(-1) + 7

4 = -3 + 7

4 = 4

Point slope form looks like:

y - y₁ = m(x - x₁)

Answer:

Y-4=3[(x-(-1)]

Step-by-step explanation:

This answer is corect i got it right on my questions

Answer:

The answer is def. A.

Answer: OPTION A.

Step-by-step explanation:

By definition:

A number is Rational when it can be written as a simple fraction.

A number is Irrational when it cannot be written as a simple fraction.

Notice that:

[tex]\frac{2}{5}[/tex] is a Rational number.

[tex]\sqrt{88}=2\sqrt{2}[/tex] It is an irrational number.

Therefore, the sum of these numbers is an Irrational number:

[tex]\frac{2}{5} + \sqrt{88}=\frac{2}{5} + 2\sqrt{22}=9.78083151...[/tex]

Problem #1= 7 5/12- 6 1/12= 1 4/12 which is simplified to 1 1/3

The answer to the first problem is 1 1/3 feet.

Problem #2= 28(3/4)= 84/4= 21

The answer to the second problem is 21 points.

Hope this helps!

Answer:

Step-by-step explanation:

[tex]B=(\frac{-9-1}{2},\frac{-4+6}{2} ) (midpoint formula)\\B=(-5,1)\\\\Then using midpoint formula again,\\E=(-4,3)=(\frac{-5+x}{2} =-4,\frac{1+y}{2} =3)\\so \\x=-3\\y=5\\\\D=(-3,5)[/tex]:

Answer:

[tex]sinx+cosx=\frac{cosx}{1-tanx}+\frac{sinx}{1-cotx}\\[/tex] proved.

Step-by-step explanation:

[tex]sinx+cosx=\frac{cosx}{1-tanx}+\frac{sinx}{1-cotx}\\[/tex]

Taking R.H.S

[tex]\frac{cosx}{1-tanx}+\frac{sinx}{1-cotx}\\[/tex]

Multiply and divide first term by cos x and second term by sinx

[tex]=\frac{cosx*cosx}{cosx(1-tanx)}+\frac{sinx*sinx}{sinx(1-cotx)}[/tex]

we know tanx = sinx/cosx and cotx = cosx/sinx

[tex]=\frac{cos^2x}{cosx(1-\frac{sinx}{cosx} )}+\frac{sin^2x}{sinx(1-\frac{cosx}{sinx})}\\=\frac{cos^2x}{cosx-sinx}+\frac{sin^2x}{sinx-cosx}[/tex]

Taking minus(-) sign common from second term

[tex]=\frac{cos^2x}{cosx-sinx}-\frac{sin^2x}{cosx-sinx}[/tex]

taking LCM of cosx-sinx and cosx-sinx is cosx-sinx

[tex]=\frac{cos^2x-sin^2x}{cosx-sinx}[/tex]

We know a^2-b^2 = (a+b)(a-b), Applying this formula:

[tex]=\frac{(cosx+sinx)(cosx-sinx)}{cosx-sinx}\\=cosx+sinx\\=L.H.S[/tex]

Hence proved

Answer:

Step-by-step explanation:

x = 1, y = 12

x = 2, y = 9

x = 3, y = 6

x = 4, y = 3

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\dfrac{9-12}{2-1}=\dfrac{-3}{1}=-3[/tex]

Answer:

=60 the second option.

Step-by-step explanation:

Given the trigonometric ratio, we can find the value of the angle by simply finding the inverse of the given ratio.

If for example Cos ∅= a, then ∅=Cos⁻¹a

If Cos (x)= 0.5, then x= Cos⁻¹ 0.5

Cos⁻1 0.5=60°

The angle whose sine is 0.5 is ∅=60°

Answer: second option.

Step-by-step explanation:

You have that:

[tex]cos(x)=0.5[/tex]

Then, to find the value of "x", you need to apply Arccosine ( This is the inverse function of the cosine).

Therefore, applying this in the procedure, you get that the value of "x" is the following:

[tex]cos(x)=0.5\\\\x=Arccos(0.5)\\\\x=60\°[/tex]

You can observe that this matches with the second option.

For this case we have that the area of the figure is given by the area of a rectangle plus the area of a square. By definition, the area of a rectangle is given by:

[tex]A = a * b[/tex]

According to the figure we have:

[tex]a = 9 \sqrt {2}\\b = 8 \sqrt {2} -2 \sqrt {2} = 6 \sqrt {2}[/tex]

So, the area of the rectangle is:

[tex]A = 9 \sqrt {2} * 6 \sqrt {2} = 54 (\sqrt {2}) ^ 2 = 54 * 2 = 108[/tex]

On the other hand, the area of a square is given by:

[tex]A = l ^ 2[/tex]

Where:

l: it is the side of the square

According to the figure we have:

[tex]l = 2 \sqrt {2}[/tex]

So:

[tex]A = (2 \sqrt {2}) ^ 2 = 4 * 2 = 8[/tex]

Finally, the area of the figure is:

[tex]A_ {t} = 108 + 8 = 116[/tex]

Answer:

116

[tex]\text{Hey there!}[/tex]

[tex]\huge\text{Decimals, fractions, \& negatives are below 0!}[/tex]

[tex]2\dfrac{21}{30}\ = 2\times30+21 \ = 2\times 30 = 60+21= 81\rightarrow \dfrac{81}{30}[/tex]

[tex]2\dfrac{1}{2}\ = 2\times2+1=2\times2=4+1=5\rightarrow\dfrac{5}{2}[/tex]

[tex]-\dfrac{32}{40}=-\dfrac{32}{40}[/tex]

[tex]\boxed{\boxed{\huge\text{Answer:}-\dfrac{32}{40}, \ 2\dfrac{1}{2}, \ 2\dfrac{21}{30}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

B

Step-by-step explanation:

Using the Sine Rule in ΔABC

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]

∠C = 180° - (82 + 58)° = 180° - 140° = 40°

Completing values in the above formula gives

[tex]\frac{a}{sin58}[/tex] = [tex]\frac{b}{sin82}[/tex] = [tex]\frac{8.4}{sin40}[/tex]

We require a pair of ratios which contain b and 3 known quantities, that is

[tex]\frac{b}{sin82}[/tex] = [tex]\frac{8.4}{sin40}[/tex]

OR

[tex]\frac{sin40}{8.4}[/tex] = [tex]\frac{sin82}{b}[/tex] → B

Answer:

B

Step-by-step explanation:

[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{-2})~\hspace{10em} slope = m\implies -2 \\\\\\ \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-(-2)=-2(x-3) \\\\\\ y+2=-2x+6\implies y=-2x+4[/tex]

For this case we must convert 21 hours to seconds!

We have that by definition, 1 hour equals 3600 seconds. Then, making a rule of three we have:

1h ------------> 3600s

21h ----------> x

Where "x" represents the number of seconds equivalent to 21 hours.

[tex]x = \frac {21 * 3600} {1} = 75600[/tex]

Thus, 21 hours represent 75600 seconds.

Answer:

75600 seconds.

Answer:

D. Cannot be determined​

Step-by-step explanation:

there is not enough information for you to answer this question. A picture would be helpful to answer this question, but there isn't one.

The correct option is,

D. Cannot be determined.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Since, We are given that two triangle PQR and XYZ are similar.

AA-Similarity postulate: Two angles of one triangle is equal to its corresponding angles of other triangle. Then, the two triangles are similar by AA postulate.

SSS similar: When three sides of two triangles are in the same ratio.

SAS similar: When two sides of two triangle are in the same ratio and one angle between two proportional sides of two triangles is congruent.

But we have not enough information by which we can determine triangle PQR and triangle XYZ is similar.

Hence, option D is true.

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Answer:

Step-by-step explanation:

31 is prime. It can't be factored. The way I'm reading the directions, you should enter 31.

Answer:

31

Step-by-step explanation:

The prime factorization of 31 is 1 x 31 = 31.

You have to multiply the number by 1 to find its prime factorization.

However, it is usually written as just 31.