which of the following inequalities represents all values of x for which the quotient below is defined? sqrt 21(x-1) divided by sqrt 7x²
A. x < -1
B. x > -1
C. x < 1
D. x > 1

An example of an exponential function is given as follows:

A. Investing $1,000 at an annual interest rate of 3%, compounded monthly.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

As we saw above, the rate of change is a percent, and in this problem, only option A has a rate of change as a percent, hence it is an exponential function.

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Answer:

c = 9.7

Step-by-step explanation:

Using the law of sines

sin 55       sin 82

---------- = ---------------

8                    c

Using cross products

c sin 55 = 8 sin 82

c = 8 sin 82 / sin 55

c=9.67115

To the nearest tenth

c = 9.7

Answer:

Step-by-step explanation:

Begin by combining like terms and then factoring. Combining like terms will give you

[tex]10p^2-17p-20=0[/tex] Using the "old-fashioned" way of factoring, the a times c method, our a = 10, b = -17 and c = -20.

a * c = 10(-20) = -200 and now we need the factors of 200 (don't worry about the negative) that combine to give us that middle term, -17p (here is where the negative matters). The factors of 200 are:

1. 200;  2, 100;  4. 50;  5, 40;  8, 25;  10, 20

The combination of those numbers that can be manipulated to give us a -17p is the 8, 25 as long as we say that the 25 is negative and the 8 is positive. Rewrite the original polynomial to reflect those factors:

[tex]10p^2-25p+8p-20=0[/tex] and then factor by grouping:

[tex](10p^2-25p)+(8p-20)=0[/tex] and factor out from each set of parenthesis what is common:

[tex]5p(2p-5)+4(2p-5)=0[/tex] again factor out what is common:

(2p - 5)(5p+ 4) = 0. These are the factors; therefore the solutions are

2p - 5 = 0 so

2p = 5 and

p = 5/2  and

5p + 4 = 0 and

5p = -4 so

p = -4/5

Answer:

d=2

Step-by-step explanation:

We are given equation:

sqrt(4y-3)=d-y

Squaring both sides gives:

4y-3=(d-y)^2

Applying the identity (x+y)^2=x^2+2xy+y^2 on right:

4y-3=d^2-2dy+y^2

Now let's y=7:

4(7)-3=d^2-2d(7)+(7)^2

Simplify:

25=d^2-14d+49

Subtract 25 on both sides:

0=d^2-14d+24

Factor left:

0=(d-12)(d-2) since -2+-12=-14 and -2(-12)=24

This gives d=12 or d=2.

The d that makes d-y or I mean d-7 negative will give us y=7 as extraneous

Since 2-7 is -5, then d=2 is what we are looking for.

Check:

sqrt(4y-3)=d-y

Set d=2: sqrt(4y-3)=2-y

Now solve for y:

Square both sides: 4y-3=4-4y+y^2

Subtract 4y and 3 on both sides: 0=7-8y+y^2

Reorder right side: 0=y^2-8y+7

Factor: 0=(y-7)(y-1) since -7+-1=-8 and -7(-1)=7

This gives y=7 or y=1.

Plugging in y=7 for a check to this equation gives:

sqrt(4×7-3)=2-7

Sqrt(25)=-5

5=-5 which is not true which is what we wanted

Answer:

360cm³

Step-by-step explanation:

Volume of a triangular prism = Base area * Height of prism

Height of prism = 15cm

Base area = 1/2 * 6 * 8

Base area = 24cm²

Volume of the prism = 15 * 24

Volume of the prism = 360cm³

​

Answer:

I think C sorry if wrong

Step-by-step explanation:

9514 1404 393

Answer:

  8

Step-by-step explanation:

The matrix being multiplied is the same in all cases, so we can "collect terms" in the usual way.

  3A +5A = (3+5)A = 8A . . . . . . where A represents the 2×2 matrix

The missing number is 8.

Answer:

y=2x-8

Step-by-step explanation:

Hi there!

We want to find an equation of the line parallel to y=2x-4 but has the same x intercept as 3x-4y=12

Parallel lines have the same slope, but different y intercepts

In y=2x-4, which is written in y=mx+b form, m is the slope and b is the y intercept

2 is in the place of where the slope would be, so the slope of that line is 2

That means the slope of the line parallel to it would also have a slope of 2

Here is the equation of the parallel line so far:

y=2x+b

We need to find b, the y intercept

Typically, we'll substitute a point into the equation to solve for b, but we don't have a point, yet

We're given that the new line has the same x intercept as 3x-4y=12

The x intercept is the point where the line passes through the x axis, and so the value of y at that point is 0

Let's substitute 0 for y in 3x-4y=12 and solve for x to find the x intercept

3x-4(0)=12

Multiply

3x=12

Divide both sides by 3

x=4

So the value of the x intercept is 4. As a point, it's (4,0)

So now substitute the values of the point (4,0) into y=2x+b to find b

0=2(4)+b

Multiply

0=8+b

Subtract 8 from both sides

-8=b

Substitute -8 as b into the equation

y=2x-8

Hope this helps!  

Answer:

1 hour 33 minutes

Step-by-step explanation:

distance/speed= time

d =800/600

d=1.33

The aeroplane takes 1.33 hours to traverse a distance of 800 km.

Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time

Given here: An airplane flies a distance of 800 km with an average speed of 600 km/h

Thus the time taken by the aeroplane to cover that distance is

t=800/600

t=4/3

t=1.33 hours

Hence, The aeroplane takes 1.33 hours to traverse a distance of 800 km.

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Answer:

y=3/x

Step-by-step explanation:

^ means to the power of or exponent

logb(x) = y is b^y = x

Answer:

[tex]0.9^5=0.59049[/tex]

Step-by-step explanation:

By definition, we have:

[tex]log_ab=c\implies a^c=b[/tex]

Therefore, given [tex]log_{0.9}(0.59049)=5[/tex], assign:

Rewrite:

[tex]\boxed{0.9^5=0.59049}[/tex]

7^2 + 6^2 = h^2

49 + 36 = h^2

85 = h^2

√85 = h

h = 9.21m

Answered by Gauthmath must click thanks and mark brainliest

Answer:

I'm pretty sure it's the 3rd option

Answer:

first option is correct

Step-by-step explanation:

because there are less no. on negative side than on positive one

hopefully this answer can help you to answer the next question.

Answer:

The minimum value of f(x) is -21 and it occurs at x = 1

Step-by-step explanation:

f(x) =3x^2-6x-18

Factor out the greatest common factor out of the first two terms

f(x) =3(x^2-2x)-18

Complete the square

-2x/2 =-1  (-1)^2 = 1

Add 1  (But remember the 3 out front so we are really adding 3  so we need to subtract 3 to remain balanced)

f(x) = 3(x^2 -2x+1) -3 -18

f(x) = 3(x-1)^2 -21

This is vertex form

f(x) = a(x-h)^2 +k  where (h,k) is the vertex and a is a constant

The vertex is (1,-21)  

Since a > 0 this opens upward and the vertex is a minimum

The minimum value of f(x) is -21 and it occurs at x = 1

Answer:

3x ^ 2 + 12x-36 = 0

3(x²+ 4x-12)=0

3(x²-2x+6x-12)=0

3[x(x-2)+6(x-2)]=0

3(x-2)(x+6)=0

⇒[tex]\left \{ {{x-2=0} \atop {x+6=0}} \right.[/tex]⇔[tex]\left \{ {{x=2} \atop {x=-6}} \right.[/tex]

Answer:

¼ và 2017

Step-by-step explanation:

Answer:

x=2 is incorrect

Step-by-step explanation:

Y(2)=(3/4)*x^2=(3/4)*4=3

Isolate the variable by dividing each side by factors that don't contain the variable.

x  =  1

-6+3x+4=2-4x+3

-8+7x+1=0

7x=7

x=1

Answer:

x=1

Step-by-step explanation:

SEE IMAGE for Solution

Answer:

Common Ratio = 2.5

Step-by-step explanation:

Given

Points: (1, 1), (2, 2.5), (3, 6.25)

Required

Determine the common ratio

The points can be rewritten as:

x --- f(x)

1 ---- 1

2 --- 2.5

3 ---- 6.25

The data under the x column are the domain of the function and in this case,  they are not needed;

To calculate common ration, Lena should use data in function f(x) column

Common ratio is calculated by dividing a term by the previous term;

Hence;

Common Ratio = 2.5/1 or 6.25/2.5

Common Ratio = 2.5 or 2.5

Notice that, the results are the same;

Hence, the usable common ratio is 2.5

Answer: 2.5 or "C"

Step-by-step explanation: this is right on the edge i just did the test.....Hope this helps :D

Answer:

Cost of 1 goggles = $20

Cost of 1 mask = 15

Step-by-step explanation:

Given:

Cost of 2 goggles and 1 mask = $55

Cost of 1 goggles and 2 mask = $50

Find:

Cost of each goggles and mask

Computation:

Assume;

Cost of 1 goggles = a

Cost of 1 mask = b

So,

2a + b = 55.....EQ1

a + 2b = 50.......EQ2

EQ1 x 2

4a + 2b = 110 ......EQ3

EQ3 - EQ2

3a = 60

a = 20

Cost of 1 goggles = $20

a + 2a = 50

20 + 2b = 50

2b = 30

b = 15

Cost of 1 mask = 15

.

Answer: The range is  [tex]\{y \in \mathbb{R}\ | \ y \le -6\}[/tex]

Explanation:

The parabola opens down, forming a "frowny face" in a way (just without the eyes). Or you can think of it as a hill or mountain. This means that the vertex (-3,-6) is at the top of that mountain. It's the highest point of that parabola.

The range is the set of all possible y values. We see that y = -6 is the largest it can get. So y = -6 or y is smaller than this. We would then write [tex]y \le -6[/tex] to describe all the possible y values.

Therefore, the range is [tex]\{y \in \mathbb{R}\ | \ y \le -6\}[/tex]

This translates to "y is a real number such that y is -6 or smaller".

So the second answer you wrote is close, but you forgot the "or equal to" portion of the inequality sign.

See below for a visual example of what's going on.

Answer:

i believe it's -6? option a.

Step-by-step explanation:

okay.

60 degrees + a right angle, 90 degrees = 150 degrees

a triangle is normally 180 degrees.

180-150=30

so we need to get 30 from that equation, x + 36

x + 36 = 30

you solve.

x = -6

if im wrong, feel free to correct me + sub to gauthmath sub reddit if ya can !

Step-by-step explanation:

VERY EASY FOR ME

The real part (red) and imaginary part (blue) of the Riemann zeta function along the critical line Re(s) = 1/2. The first non-trivial zeros can be seen at Im(s) = ±14.135, ±21.022 and ±25.011. The Riemann h

ypothesis, a famous conjecture, says that all non-trivial zeros of the zeta function lie along the critical line.

SO 6+/7× and 78/+×

ANSWER

Step-by-step explanation:

r = -8/4 = -2

t1 = 4

the general formula :

tn = t1. r^(n-1)

tn = 4. (-2)^(n-1)

t12 = 4. (-2) ^(12-1)

= 4. (-2)^11

= 4. (-2,048)

= - 8,192

Answer:

5

Step-by-step explanation:

i = 5¹

5¹ = 5

The correct option is 5

Answer:

5

Step-by-step explanation:

Answer:

The expression for the height of the solid is:

[tex]\displaystyle h = x^2+x-9[/tex]

Step-by-step explanation:

Recall that the volume of a rectangular solid is given by:

[tex]\displaystyle V = \ell wh[/tex]

Where l is the length, w is the width, and h is the height.

We know that the volume is given by the polynomial:

[tex]\displaystyle V = 3x^4-3x^3-33x^2+54x[/tex]

And that the length and width are given by, respectively:

[tex]\displaystyle \ell = 3x \text{ and } w =x-2[/tex]

Substitute:

[tex]\displaystyle 3x^4-3x^3-33x^2+54x=(3x)(x-2)h[/tex]

We can solve for h. First, divide both sides by 3x:

[tex]\displaystyle \frac{3x^4-3x^3-33x^2+54x}{3x}=(x-2)h[/tex]

Divide each term:

[tex]\displaystyle x^3-x^2-11x+18=(x-2)h[/tex]

To solve for h, divide both sides by (x - 2):

[tex]\displaystyle h = \frac{x^3-x^2-11x+18}{x-2}[/tex]

Since this is a polynomial divided by a binomial in the form of (x - a), we can use synthetic division, where a = 2. This is shown below. Therefore, the expression for the height of the solid is:

[tex]\displaystyle h = x^2+x-9[/tex]

Answer:

6.82

Step-by-step explanation: