factor: d2 + 16dm + 64m2

Answer:

C

Step-by-step explanation:

The absolute value function always returns a positive value

However, the expression inside the bars can be positive or negative

| 3 | = 3 and | - 3 | = 3, hence the solution of

| x | = 3 is x = ± 3

Extending this to

| x² - 4 | = 3, then

| x² - 4 | = 3 and | - (x² - 4) | = 3

x² - 4 = 3 ; - (x² - 4) = 3 → C

Answer:

C

Step-by-step explanation:

[tex]|x^2-4|=3[/tex]

Before we say what this implies, we need to know that |-1|=1 and |1|=1.

So what I'm saying is:

[tex]|-(x^2-4)|=|-1 \cdot (x^2-4)|=|-1| \cdot |x^2-4|[/tex]

[tex]=|x^2-4|[/tex].

So [tex]|x^2-4|=3[/tex] implies:

[tex](x^2-4)=3[/tex] or [tex]-(x^2-4)=3[/tex].

Answer:

O 30, 24, and 18

Step-by-step explanation:

18^2+24^2=30^2

324+576=900

Final answer:

Using the Pythagorean theorem, only the set of lengths 24, 7, and 26 satisfy the condition for a right triangle, as 24² + 7² equals 26².

Explanation:

The question seeks to determine which set of lengths can form a right triangle. When assessing whether a given set of three lengths can form a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (the legs) is equal to the square of the length of the longest side (the hypotenuse). The formula for the Pythagorean theorem is a² + b² = c², where a and b are the lengths of the legs, and c is the length of the hypotenuse.

We will check each set of given lengths:

Therefore, the lengths that would form a right triangle are 24, 7, and 26.

Answer:

C

Step-by-step explanation:

When both the numerator and denominator of a rational function have the same degree, you divide the highest powered term's coefficients. That is the horizontal asymptote.

Since this function has third degree in both the numerator and denominator, we divide the respective coefficients to find the horizontal asymptote.

So, y = 9/7

Correct answer is C

Note:  horizontal asymptote is always in the form y = a (where a is the constant)

Your mouse pointer is covering the number at the hypotenuse, but I assume that it is 10.

We can test to see if the triangle is a right angled triangle by using Pythagoras' Theorem. This is because the Pythagorean Theorem only works with right angled triangles.

The theorem is:

[tex]a^{2} + b^{2} = c^{2}[/tex]

where:

a = length of one leg of the triangle

b = length of the other leg of the triangle

c = the length of the hypotenuse.

If triangle FGH is a right triangle then:

[tex]\sqrt{51}^ {2} + 7 ^{2} = 10^{2}[/tex]

[tex]\sqrt{51} ^{2}[/tex] is just 51

[tex]7^{2}[/tex] is 49

and [tex]10^{2}[/tex] is 100

if we add up 51 and 49 we get 100. And of course, 100 = 100,

Since the theorem works, then the FGH is a right triangle

______________________________________

Answer:

True: FGH is a right angled triangle

Answer:

Angle 1 equals 90 degrees. Angle 2 equals 38 degrees.

Step-by-step explanation:

Angle 1 is at the cross of two perpendicular lines, making it 90 degrees. Angle 2 can be found by making the two equal side lengths and the middle line into one triangle. This means that two of the angles are 52 degrees. This leaves 76 degrees to be split in the triangle. The middle line cuts the angle in half, making it 38 degrees

Answer:

Step-by-step explanation:

Use the Pythagorean theorem:

[tex]leg^2+leg^2=hypotenuse^2[/tex]

We have

[tex]leg=56\ m,\ hypotenuse=65\ m,\ leg=x\ m[/tex]

Substitute:

[tex]56^2+x^2=65^2[/tex]

[tex]3136+x^2=4225[/tex]          subtract 3136 from both sides

[tex]x^2=1089\to x=\sqrt{1089}\\\\x=33\ m[/tex]

Answer:

33

Step-by-step explanation:

We need to use the Pythagorean Theorem.

65 is the length for the hypotenuse.

So we do a^2+b^2=c^2 where a and b are legs and c is the hypotenuse.

x^2+56^2=65^2

x^2+3136=4225

Subtract 3136 on both sides

x^2         =1089

Square root both sides

x=33

The answer is 33 meters.

Answer:

23

Step-by-step explanation:

f(x)=3 − 4x

Let x=-5

f(-5) = 3-4(-5)

       = 3 -(-20)

      = 3+20

     =23

The correct equivalent expression for 3√x⁵y=3 is option c. x⁵/³y

Therefore, after simplification, the equivalent expression to 3√x⁵y is x⁵/³y.

The expression 3√x⁵y​ represents the cube root of x⁵y. To simplify this expression, let's break it down step by step.

First, we can express 3√x⁵y in exponential form:

3√x⁵y =(3x⁵y)¹/³

Using the property (ab)ⁿ=aⁿ⋅bⁿ, we can separate the terms inside the cube root:

(3x⁵y)¹/³ =3(x⁵/³, y¹/³)

Now, let's look at the options provided:

a. x⁵/³y

b. x⁵/³y¹/³

c. x⁵/³y

d.x⁵/³y³

Comparing the simplified expression 3√x⁵y=3(x⁵/³, y¹/³) to the given options: correct equivalent expression for 3√x⁵y=3 is option c. x⁵/³y.

[tex]-1=\dfrac{5+x}{6}\\\\-6=5+x\\\\x=-11[/tex]

"Solve for x" means get an equation that says " X = something ".  It has nothing but X all alone on one side, and the other side tells exactly what X is equal to.

How do you get such an equation ?  

-- Take what they gave you in the question.

-- Do anything you want on one side of it, to get X all by itself on that side.

BUT . . .

-- Whatever you do to one side, you must immediately do the same thing on the other side.

Here's how that goes:

Given in the question:  -1 = (5 + X) / 6

Multiply each side by 6 :  -6 = 5 + X

Subtract 5 from each side:  -11 = X

And there you are.  It's over almost as soon as it started.

Answer:

5 x 2 = 10

(10^20)^5 = 10^100

(10) x (10^100) = 10^101 which is 1 followed by 101 zeroes.

Answer:

10 ^101

Step-by-step explanation:

(5 x 2)(10^20)^5

5*2 = 10

We know a^b^c = a^(b*c)

(10^20)^5 = 10 ^ (20*5) = 10 ^ 100

10 * 10^100

Replacing 10 with 10^1

10^1 * 10^100

We know that a^b * a^c = a^ (b+c)

10^1 * 10^100 = 10 ^(100+1) = 10 ^101

Answer:it’s the number that appears most often,so the answer would be 2,4,and 0.

Step-by-step explanation:

The modes of the data set are 0, 2, and 4

In this question, it is asking you to find the mode of the given data set.

We would be using the data set in the question in order to find out what the mode is.

The mode would be the number that "occurs" the most. In other words, the number(s) that are more "frequent."

Data set:

2, 2, 1, 4, 4, 2, 3, 0, 0, 4, 1, 0, 4, 0, 2

Now, we could count how many of each numbers there are.

0 = 4 (Most)

1 = 2  

2 = 4 (Most)

3 = 1

4 = 4 (Most)

When you're done counting the numbers, you would notice that 0, 2, and 4 have the highest number of occurrence in the data set.

This means that the modes of the data set are 0, 2, and 4

Answer:

Part 1) [tex]cos(\theta)=(+/-)\frac{\sqrt{7}}{4}[/tex]

cosine theta equals plus or minus square root of seven over 4

Part 2) [tex]tan(\theta)=(+/-)\frac{3}{\sqrt{7}}[/tex]

tangent theta equals plus or minus three over square root of seven

or

[tex]tan(\theta)=(+/-)3\frac{\sqrt{7}}{7} [/tex]

tangent theta equals plus or minus three times square root of seven over seven

Step-by-step explanation:

we have that

The sine of angle theta is equal to

[tex]sin(\theta)=\frac{3}{4}[/tex]

Is positive

therefore

The angle theta lie on the I Quadrant or in the II Quadrant

Part 1) Find the value of the cosine of angle theta

Remember that

[tex]sin^{2} (\theta)+cos^{2} (\theta)=1[/tex]

we have

[tex]sin(\theta)=\frac{3}{4}[/tex]

substitute and solve for cosine of angle theta

[tex](\frac{3}{4})^{2}+cos^{2} (\theta)=1[/tex]

[tex]cos^{2} (\theta)=1-(\frac{3}{4})^{2}[/tex]

[tex]cos^{2} (\theta)=1-\frac{9}{16}[/tex]

[tex]cos^{2} (\theta)=\frac{7}{16}[/tex]

[tex]cos(\theta)=(+/-)\frac{\sqrt{7}}{4}[/tex]

cosine theta equals plus or minus square root of seven over 4

Part 2) Find the value of tangent of angle theta

we know that

[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]

we have

[tex]sin(\theta)=\frac{3}{4}[/tex]

[tex]cos(\theta)=(+/-)\frac{\sqrt{7}}{4}[/tex]

substitute

[tex]tan(\theta)=\frac{\frac{3}{4}}{(+/-)\frac{\sqrt{7}}{4}}[/tex]

[tex]tan(\theta)=(+/-)\frac{3}{\sqrt{7}}[/tex]

tangent theta equals plus or minus three over square root of seven

Simplify

[tex]tan(\theta)=(+/-)3\frac{\sqrt{7}}{7} [/tex]

tangent theta equals plus or minus three times square root of seven over seven

The correct values for cosine and tangent when sine theta equals 3/4 are, cosine theta equals plus or minus 3/4, and tangent theta equals plus or minus 3/7. These values are found using the Pythagorean identity and the definitions of tangent in terms of sine and cosine.

To solve for cos θ and tan θ when given that sin θ = ¾, one can use the Pythagorean identity, which states that sin2 θ + cos2 θ = 1. Substituting the known value of sin θ, we get (¾)2 + cos2 θ = 1. Solving this equation yields cos2 θ = 1 - (¾)2 = ¹⁄16, so cos θ is either the positive square root of ¹⁄16 or its negative counterpart. Since the square root of ¹⁄16 is ³⁄4, cos θ can be either ³⁄4 or -³⁄4.

For tan θ, which is defined as sin θ/cos θ, we use the positive and negative values found for cos θ. Therefore, tan θ can be 3/4 divided by ³⁄4, which simplifies to ³⁄7 or, when using the negative cosine value, tan θ will be -³⁄7.

Answer: 34 miles

Step-by-step explanation:

First multiply the 2 miles she power walked by the 7 days. (14 miles)

Next, multiply the 5 miles by the 4 days. (20)

Add both numbers, 20+14=34 miles

Answer:

-5x+13 given (-x+3)-(4x-10)

Answer:-5x+13

Step-by-step explanation:

We are going to distribute to get rid of the ( ):

-x+3-4x+10

Pair up like terms:

-x-4x+3+10

Combine the like terms:

-5x+13

Answer:

-5x+13

Step-by-step explanation:

( - x + 3) - (4x - 10)

Distribute the minus sign

( - x + 3) - 4x + 10

Combine like terms

-5x +13

Answer:

0.012

Step-by-step explanation:

The probability of more than 7 customers arriving within a minute is obtained by taking the probability at X equal to 0, 1, 2, 3, 4, 5, 6, and 7 then subtracting from the total probability. It can be expected about 1.2% of times that more than 7 customers arriving within a minute.

Answer: 0.0216

Step-by-step explanation:

Given : Average arrivals of customers at a local grocery store = 3 per minute

The Poisson distribution formula :-

[tex]\dfrac{e^{-\lambda}\lambda^x}{x!}[/tex], where [tex]\lambda[/tex] is the mean of the distribution.

If X = the number of arrivals per minute, then the probability of more than 7 customers arriving within a minute will be :-

[tex]\dfrac{e^{-3}(3)^7}{7!}=0.0216040314525\approx0.0216[/tex]

Hence, the probability of more than 7 customers arriving within a minute = 0.0216

Answer:

[tex]20x^{4}-39x^{3} +26x^{2}-6x\\[/tex]

Step-by-step explanation:

Multiply the two polynomials by multiplying each term

[tex](5x^{2} -6x+2)(4x^{2} -3x)\\5x^2*4x^2+5x^2(-3x)+(-6)*4x^2+(-6x)(-3x)+2*4x^2+2(-3x)\\20x^{4}-39x^{3}  +26x^{2} -6x\\[/tex]

To multiply the given expressions, use the distributive property and combine like terms. The final result is 20x⁴ - 39x³ + 26x² - 6x.

To multiply the expression (5x²-6x+2) (4x²-3x), we can use the distributive property. Multiply the first term in the first binomial (5x²) by each term in the second binomial (4x², -3x), and then multiply the second term in the first binomial (-6x) by each term in the second binomial. Finally, multiply the third term in the first binomial (2) by each term in the second binomial. Combine like terms and simplify as needed to get the final result.

Applying this process, we get:

5x² × 4x² = 20x⁴

5x² × -3x = -15x³

-6x × 4x² = -24x³

-6x × -3x = 18x²

2 × 4x² = 8x²

2 × -3x = -6x

Combining all the terms, we have:

20x⁴ - 15x³ - 24x³ + 18x² + 8x² - 6x

Simplifying further, we get:

20x⁴ - 39x³ + 26x² - 6x

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Answer:

r= 9

Step-by-step explanation:

;/

The solution to the equation 21 + 3r = 48 is r = 9.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

3x + 5 = 9 is an equation.

We have,

21 + 3r = 48

Subtract 21 on both sides.

3r = 48 - 21

3r = 27

Divide both sides b 3.

r = 9

Thus,

The value of r is 9.

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Answer:

[tex]\large\boxed{x=\dfrac{7}{8}}[/tex]

Step-by-step explanation:

[tex]4^{(4x-1)}=32\\\\(2^2)^{4x-1}=2^5\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{2(4x-1)}=2^5\iff2(4x-1)=5\ \ \text{use the distributive property}\ a(b+c)=ab+ac\\\\(2)(4x)+(2)(-1)=5\\\\8x-2=5\qquad\text{add 2 to both sides}\\\\8x=7\qquad\text{divide both sides by 8}\\\\x=\dfrac{7}{8}[/tex]

Answer:

2) Yes, each x-coordinate is only used once.

3) {1,2,3,4}

4) {25,45,60,70}

5) (3,60)

6) No because (4,7) and (4,25) share the same x-coordinate.

Step-by-step explanation:

A relation is a function if there is no more than one y-value assigned to an x.

Any x used can only be used once in an order pair.

You that here.

(1,25)

(2,45)

(3,60)

(4,70)

So basically because all of the x-coordinates are different, this is a function.

The domain is the x-coordinate of each pair (the first of each pair):

{1,2,3,4}.

The range is the y-coordinate of each pair (the second number of each pair):

{25,45,60,70}.

One ordered pair that I see in the table is (3,60). There are 3 others you can choose and I named them above.

{(4,10),(3,15),(1,5),(2,25),(4,25)} is not a function because there are more than one pairs with the same x-coordinate,4.  

Answer:

17mL

Step-by-step explanation:

Convert 0.85 gr to miligrams

If 100 mg is 1 gr. Then, 0.85 gr is 850 mg

So, 850 multiply for 5ml and divide for 250 ml

or [tex]850mg  \frac{5ml}{250mg}[/tex]

So all mg is gone and the amount of mililiters is 17

Answer:

17 milliliters of dose should be poured into a prescription bottle.

Step-by-step explanation:

Amount of dose in liquid antiboitic = 0.85 g = 850 mg

1 g = 1000 mg

Concentration of antibiotic = 250 mg/5 ml = 50 mg/mL

So, in 1 mL of liquid we have 50 mg of antibiotic.

Then in 0.85 mg of antibiotic will be:

[tex]\frac{1}{50}\times 850 mL=17 mL[/tex]

17 milliliters of dose should be poured into a prescription bottle.

Answer:

r = 4.2 cm; d = 8.4 cm

Step-by-step explanation:

The radius is the distance from the centre of the circle to the circumference.

r = 4.2 cm

The diameter is the length of a straight line that passes through the centre with each end at the circumference.

d = 2r = 2 × 4.2 cm = 8.4 cm

Answer:

radius=4.2

diameter=8.4

Step-by-step explanation:

Answer:

the answer of this question is 3/5

Answer: the answer is

0.04444

Answer:

im trying to find this answer too dont worry :(

Step-by-step explanation:

I dont know

Answer:

Option B, [tex]3.27[/tex]

Step-by-step explanation:

Given -

The submerged vessel travel horizontal distance above the shipwrecked hull

[tex]= 400[/tex]

[tex]= 0.4[/tex] kilometers

The vertical distance from the the shipwrecked hull to the ground is equal to [tex]7[/tex] kilometers

There forms a right angled triangle with

Base [tex]= 7[/tex] kilometer

Perpendicular [tex]=[/tex] 0.4 kilometer

Tan (angle) [tex]= \frac{Perpendicular}{Base}[/tex]

Substituting the given values we get -

Angle of depression

[tex]= tan^{-1}(\frac{0.4}{7})\\= 3.27[/tex]

Hence, option B is correct.

Answer:

XY=10 cm

Step-by-step explanation:

Finding limits by direct substitution means simply means to evaluate the function at the desired value: in the first case, we have to evaluate [tex]f(x)=x^2-3[/tex] at [tex]x=0[/tex]: we have

[tex]f(0)=0^2-3 = 0-3=-3[/tex]

Similarly, in the second example, we have

[tex]f(x)=x^2+3x-1 \implies f(3) = 3^2+3\cdot 3-1 = 9+9-1 = 17[/tex]

Going on, we have

[tex]f(x) = \dfrac{x^2-16}{x-4} = \dfrac{(x+4)(x-4)}{x-4} = x+4[/tex]

And thus we have

[tex]f(4) = 4+4=8[/tex]

Finally, we have

[tex]f(x) = \dfrac{x^2-2x}{x^4} = \dfrac{x(x-2)}{x^4} = \dfrac{x-2}{x^3}[/tex]

So, we can't evaluate this function at 0.

The limits of the functions are determined and the values are:

5) -3

6) 17

7) 8

8) does not exist.

Given data:

5)

The limit function is expressed as  [tex]\lim_{x \to 0} (x^{2} -3)[/tex].

So, when x = 0, the limit is:

L = 0² - 3

L = -3

6)

The limit function is expressed as  [tex]\lim_{x \to 3} (x^{2} +3x - 1)[/tex].

So, when x = 3, the limit is:

L = 3² + 3 ( 3 ) - 1

L = 9 + 9 - 1

L = 17

7)

The limit function is expressed as  [tex]\lim_{x \to 4} \frac{(x^{2} -16)}{x-4}[/tex].

So, when x = 4, the limit is simplified as:

[tex]\lim_{x \to 4} \frac{(x^{2} -16)}{x-4}=\lim_{x \to 4} \frac{(x-4)(x+4)}{x-4}[/tex]

[tex]\lim_{x \to 4} \frac{(x-4)(x+4)}{x-4}=\lim_{x \to 4} (x+4)[/tex]

L = 4 + 4

L = 8

8)

The limit function is expressed as  [tex]\lim_{x \to 0} \frac{(x^{2} -2x)}{x^{4} }[/tex].

So, when x = 0, the limit is simplified as:

L = 0/0 and the limit does not exist.

Hence, the limits are solved.

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Answer:

This system has one solution (-1,1)

Step-by-step explanation:

The attached picture shows the solutions for the system

If we equalize the eq. obtain the following

-x=2x+3

From we obtain that x= -1

Using the first equation y=-x, we obtain that y=1

so (-1,1)

The correct equation for the given graph will be option A that is

y=[tex]x^{2} +9x+18[/tex]

It is a relationship between two variables and having a equal to sign in between.

Firstly we need to find the points of the respective equations.

y=[tex]x^{2} +9x+18[/tex]

y=[tex]x^{2}[/tex]+6x+3x+18

y=x(x+6)+3(x+6)

y=(x+3)(x+6)

Put  this equal to 0 and we get x=-3 and x=-6

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

It is a wrong equation.

y=(x-3)(x-6)

put this equal to 0 we get x=3 and x=6

Now we have to check in the graph whether points (-3,0)(-6,0) satisfies or (3,0)(6,0)

We can easily see that (-3,0)(-6,0) satisfies the graph.

Hence the correct equation is y=x2+9x+18

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Answer:

left 1 unit, reflection about the x-axis, up 1 unit

Step-by-step explanation:

This is a cubic that has been moved left 1 unit because of the (x+1)^3 part.

It also has been moved up one unit because of the plus 1 on the outside of the cube.

There has also been a reflection across the x-axis because of the -1 in front of the -(x+1)^3 part.

In general, g(x-h)+k means:

1) the function g has been moved right (if h is positive) or moved left (if h is negative).

2) the function g has been moved up (if k is positive) or down (if k is negative)

The graph that represents the given piecewise function is the one on the right. Therefore the correct answer is option b.

The piecewise function f(x) is defined as follows:

f(x) = -x if x ≤ 3

f(x) = 2 if x > 3

To graph this piecewise function, you would draw two separate segments:

For x values less than or equal to 3, you would graph the line y = -x, which has a negative slope and goes through the point (3, -3). This line represents the function f(x) = -x for x ≤ 3.

For x values greater than 3, you would graph the horizontal line y = 2. This line represents the function f(x) = 2 for x > 3.

The transition from the first segment to the second occurs at x = 3. At this point, you would typically draw an open circle to indicate that the function is defined separately for x ≤ 3 and x > 3.

The graph will consist of a line sloping downward to the left (y = -x) for x ≤ 3 and a horizontal line at y = 2 for x > 3.

Therefore, the correct answer is option b.

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