If f(x)=x^2, find f(-3)

Answer:

1. [tex]\frac{x^2}{y^3}[/tex]

2. [tex]\frac{625x^{12}}{y^8}[/tex]

3. [tex]\frac{6}{x^2y^9}[/tex]

Step-by-step explanation:

Remember, when you exponent an exponent, you multiply the powers.

When you multiply exponents, you add them.

When you divide exponents, you subtract them.

1.

Step 1: Multiply exponents

[tex]x^2y^{-3}[/tex]

Step 2: Move [tex]y^{-3}[/tex] to the denominator

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

2.

Step 1: Multiply exponents

[tex]\frac{5^4(x^{3})^{4}}{(y^2)^4}[/tex]

Step 2: Power

[tex]\frac{625x^{12}}{y^8}[/tex]

3.

Step 1: Simplify

[tex]\frac{6x^3y^{-3}}{x^5y^6}[/tex]

Step 2: Remove terms

[tex]\frac{6y^{-3}}{x^2y^6}[/tex]

Step 3: Move [tex]y^{-3}[/tex] to the denominator

[tex]\frac{6}{x^2y^6y^3}[/tex]

Step 4: Combine like terms

[tex]\frac{6}{x^2y^9}[/tex]

Answer:8

Step-by-step explanation:

I’m guessing it’s like 6*x^8?

Answer:

y=-4/3x-3

Step-by-step explanation:

You look for the slope using the the slope formula (m=y2-y1/x2-x1)

You will end up with (m=1-5/3-6)

Simplify to end up with (-4/3) as your slope.

Then, pick a coordinate point. Your choices are (6,5) and (3,1). You will us it to plug into the equation.

I am picking (3,1) The y-value here is 1 and the x-value is 3.

Your equation to find b, or the y-intercept is going to be (1=-4/3(3)+b)

You will have to simplify.

1=-4/3(3)+b

You will multiply -4/3 and -3 and end up with 4 so it looks like...

1=4+b

You subtract 4 on both sides and then end up with....

-3=b

So, the final answer is: y=-4/3x-3

Answer:

a = 2 , b = 1

Step-by-step explanation:

[tex]\frac{8-i}{3-2i}*\frac{3+2i}{3+2i}[/tex]

=> [tex]\frac{(8-i)(3+2i)}{9+4}[/tex]

=> [tex]\frac{24+13i-2i^2}{13}[/tex]

=> [tex]\frac{26+13i}{13}[/tex]

Comparing it with a+bi

a = 26/13 , b = 13/13

a = 2, b = 1

Answer:

a = 2

b = 1

Step-by-step explanation:

[tex]\frac{8-i}{3-2i}[/tex]

Write the fraction in this form:

[tex]\frac{a+bi}{c+di}\:=\:\frac{\left(c-di\right)\left(a+bi\right)}{\left(c-di\right)\left(c+di\right)}=\:\frac{\left(ac+bd\right)+\left(bc-ad\right)i}{c^2+d^2}[/tex]

[tex]\frac{\left(8(3)+-1(-2)\right)+\left(-1(3)-8(-2)\right)i}{3^2+-2^2}[/tex]

Evaluate.

[tex]\frac{26+13i}{13}[/tex]

Factor the numerator.

[tex]\frac{13\left(2+i\right)}{13}[/tex]

[tex]2+1i[/tex]

Answer:

Options (B) and (C).

Step-by-step explanation:

When a quadratic function 'f' is multiplied by k,

1). If k > 0, function 'f' will be vertically stretched Or horizontally compressed.

2). If 0 < k < 1, function will be vertically compressed Or horizontally stretched.

Given quadratic function is,

f(x) = 3x² + 3x - 7

This function is multiplied by 0.5.

Since 0 < 0.5 < 1, therefore, the function will be compressed vertically Or stretched horizontally.

Therefore, Options B and C are the correct options.

Answer:

7 unique values can be created.

[tex]1,2,3,\dfrac{1}{2},\dfrac{1}{3},\dfrac{2}{3},\dfrac{3}{2}[/tex]

Step-by-step explanation:

We need to find unique values that can be created by forming the fraction

[tex]\dfrac{x}{y}[/tex]

where, [tex]x[/tex] is either 4, 8, or 12 and [tex]y[/tex] is either 4, 8, or 12.

Now, possible ordered pairs are (4,4), (4,8), (4,12), (8,4), (8,8), (8,12), (12,4), (12,8), (12,12).

For these ordered pairs the value of [tex]\dfrac{x}{y}[/tex] are:

[tex]\dfrac{4}{4},\dfrac{4}{8},\dfrac{4}{12},\dfrac{8}{4},\dfrac{8}{8},\dfrac{8}{12},\dfrac{12}{4},\dfrac{12}{8},\dfrac{12}{12}[/tex]

[tex]1,\dfrac{1}{2},\dfrac{1}{3},2,1,\dfrac{2}{3},3,\dfrac{3}{2},1[/tex]

Here, 1 is repeated three times. So, unique values are

[tex]1,2,3,\dfrac{1}{2},\dfrac{1}{3},\dfrac{2}{3},\dfrac{3}{2}[/tex]

Therefore, 7 unique values can be created.

Answer:

10

Step-by-step explanation:

Since 75 sandwiches have salad this means that 75 - 30 = 45 of them have tuna with salad. Therefore, the amount of sandwiches that have cheese without salad is 100 - (30 + 15 + 45) = 100 - 90 = 10.

Answer:

7b+21

Step-by-step explanation:

7(b+3)

Distribute

7*b + 7*3

7b+21

Answer:

5cm for  each side

Answer:

solution,

Surface area= 150 cm^2

Side of a cube(a)=?

Now,

[tex]surface \: area \: of \: cube = 6 {a}^{2} \\ or \: 150 = 6 {a}^{2} \\ or \: {a}^{2} = \frac{150}{6} \\ or \: {a}^{2} = 25 \\ or \: a = \sqrt{25} \\ or \: a = \sqrt{ {(5)}^{2} } \\ a = 5 \: cm[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

y = 86100 / w.

21 miles per gallon.

Step-by-step explanation:

If y is the consumption then:

y  = k / w   where k is some constant so we have:

28.7 = k / 3000

k = 3000 *28.7 = 86100

So the required equation is y = 86100 / w.

For a car weighing  4100 pounds:

y =  86100 / 4100 = 21 miles per gallon.

The required inverse relation is, yw = 86100.

The car will get 21 miles per gallon if it weighs 4,100 pounds.

A direct relation between two quantities implies that the increase in one increases the other and vice-versa.

If quantity a and b are directly related, then we write the relation as a ∝ b, which can be written as a = kb, where k is the constant of proportionality used to replace the proportionality symbol with the equal to sign.

An inverse relation between two quantities implies that the increase in one decreases the other and vice-versa.

If quantity a and b are inversely related, then we write the relation as a ∝ 1/b, which can be written as a = k/b, or, ab = k, where k is the constant of proportionality used to replace the proportionality symbol with the equal to sign.

In the question, we are given that the fuel consumption in miles per gallon (y) for a car inversely varies with its weight (w).

Thus we can write the relation like this:

y ∝ 1/w

or, y = k/w

or, yw = k.

The value of k can be determined using the given value of y = 28.7 miles per gallon and w = 3000 pounds.

Therefore, 28.7*3000 = k

or, k = 86100.

Thus, the required inverse relation is, yw = 86100.

Now, we are asked how many miles per gallon will a car get if it weighs 4100 pounds.

Therefore, w = 4100, y = ?

We know, yw = 86100.

or, y = 86100/w = 86100/4100 = 21.

Therefore, the car will get 21 miles per gallon, if it weighs 4,100 pounds.

Learn more about direct and inverse relations at

https://brainly.com/question/1266676

#SPJ2

Given Information:

John's mean monthly commission = μ = $10,000

Standard deviation of monthly commission = σ =  $2,000

Answer:

[tex]P(9,000 < X < 11,000) = 0.383\\\\P(9,000 < X < 11,000) = 38.3 \%[/tex]

The probability that John's commission from the jewelry store is  between $9,000 and $11,000 is 38.3%

Step-by-step explanation:

What is Normal Distribution?

We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.  

We want to find out the probability that John's commission from the jewelry store is  between $9,000 and $11,000?

[tex]P(9,000 < X < 11,000) = P( \frac{x - \mu}{\sigma} < Z < \frac{x - \mu}{\sigma} )\\\\P(9,000 < X < 11,000) = P( \frac{9,000 - 10,000}{2,000} < Z < \frac{11,000 - 10,000}{2,000} )\\\\P(9,000 < X < 11,000) = P( \frac{-1,000}{2,000} < Z < \frac{1,000}{2,000} )\\\\P(9,000 < X < 11,000) = P( -0.5 < Z < 0.5 )\\\\P(9,000 < X < 11,000) = P( Z < 0.5 ) - P( Z < -0.5 ) \\\\[/tex]

The z-score corresponding to 0.50 is 0.6915

The z-score corresponding to -0.50 is 0.3085

[tex]P(9,000 < X < 11,000) = 0.6915 - 0.3085 \\\\P(9,000 < X < 11,000) = 0.383\\\\P(9,000 < X < 11,000) = 38.3 \%[/tex]

Therefore, the probability that John's commission from the jewelry store is  between $9,000 and $11,000 is 38.3%

How to use z-table?

Step 1:

In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 1.4, 2.2, 0.5 etc.)

Step 2:

Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 0.50 then go for 0.00 column)

Step 3:

Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.

Answer:

a)

Null hypothesis : H₀:μ = $43,500

Alternative Hypothesis : H₁ : μ ≠ $43,500

b)

The calculated value t = 2.2975 < 1.7709 at 0.01 level of significance

Null hypothesis is accepted

c)

The calculated value t = 2.2975 < 1.7709

The residents of Wilmington, Delaware, have more income than the national average

Step-by-step explanation:

Step(i):-

Given mean of the Population = $43,500,

Given mean of the sample  = $50,500

Given standard deviation of the sample  = $11,400.

level of significance = 0.01

Step(ii):-

a)

Null hypothesis : H₀:μ = $43,500

Alternative Hypothesis : H₁ : μ ≠ $43,500

b)

Test statistic

[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]

[tex]t = \frac{50,500 -43,500}{\frac{11400}{\sqrt{14} } }= 2.2975[/tex]

Degrees of freedom

                           ν =n-1 = 14-1 =13

The critical value

[tex]Z_{\frac{0.01}{2} } = Z_{0.05} = 1.7709[/tex]

c)

The calculated value t = 2.2975 < 1.7709 at 0.01 level of significance

Null hypothesis is accepted

Conclusion:-

The residents of Wilmington, Delaware, have more income than the national average

160,000 / 677 = 293.88 months

Hope this helps.

Answer: 1) 21-25

               2) III

               3) II

               4) 8

               5) 4

Step-by-step explanation:

Question 1: Which numbers are missing?

            The previous interval ends at 20 the following interval starts at 26.

            The missing interval is 21 - 25

Question 2: How many tally marks to draw?

           The frequency is given as 3, so draw three tally marks: III

Question 3: How many tally marks to draw?

           The frequency is given as 2, so draw two tally marks: II

Question 4: What is the frequency?

          There are eight tally marks so the frequency is 8.

Question 5: What is the frequency?

          There are four tally marks so the frequency is 4.

Answer:

d. solid cone

Step-by-step explanation:

Solid revolution is the general method used for revolving a given figure about a reference plane to produce a required solid. This process involves the generation of a 3 dimensional shape from a 2 dimensional figure.

A triangle is a three sided figure which generates a solid or hollow cone when it revolves about a given line. If the given triangle is made to revolve about the line, the resulting object would be a solid cone.

Answer:

the answer would be a solid cone

Step-by-step explanation:

i took the test and got it right.

BRAINLIEST PLS PLS PLS PLS I RLY NEED IT

Answer:

20 miles per hour

Step-by-step explanation:

The distances traveled by each car are perpendicular, so we can find the distance between the cars using the Pythagoras' theorem between their distances traveled:

[tex]d^2 = d_1^2 + d_2^2[/tex]

Where d is the distance between the cars, d1 is the distance traveled by the first car and d2 is the distance traveled by the second car.

The distance traveled is calculated by the speed times the time traveled, so we have:

[tex]d^2 = (16t)^2 + (12t)^2[/tex]

[tex]d^2 = 256t^2 + 144t^2[/tex]

[tex]d^2 = 400t^2[/tex]

[tex]d = 20t[/tex]

The rate that the distance is increasing can be found with the derivative of the distance in relation to the time:

[tex]dd/dt = 20\ mph[/tex]

So the rate that the distance increases is always 20 miles per hour, and it's independent of the time.

Complete question is;

In a random sample of 370 cars driven at low altitudes, 43 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed. In an independent random sample of 80 cars driven at high altitudes, 23 of them exceeded the standard. Can you conclude that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard at an level of significance? Group of answer choices

Answer:

Yes we can conclude that there is enough evidence to support the claim that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard (P-value = 0.00005).

Step-by-step explanation:

This is a hypothesis test for the difference between the proportions.

The claim is that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard.

Then, the null and alternative hypothesis are:

H0 ; π1 - π2 = 0

H1 ; π1 - π2 < 0

The significance level would be established in 0.01.

The random sample 1 (low altitudes), of size n1 = 370 has a proportion of;

p1 = x1/n1

p1 = 43/370

p1 = 0.116

The random sample 2 (high altitudes), of size n2 = 80 has a proportion of;

p2 = x2/n2

p2 = 23/80

p2 = 0.288

The difference between proportions is pd = (p1-p2);

pd = p1 - p2 = 0.116 - 0.288

pd = -0.171

The pooled proportion, we need to calculate the standard error, is:

p = (x1 + x2)/(n1 + n2)

p = (43 + 23)/(370 + 80)

p = 66/450

p = 0.147

The estimated standard error of the difference between means is computed using the formula:

S_(p1-p2) = √[((p(1 - p)/n1) + ((p(1 - p)/n2)]

1 - p = 1 - 0.147 = 0.853

Thus;

S_(p1-p2) = √[((0.147 × 0.853)/370) + ((0.147 × 0.853)/80)]

S_(p1-p2) = 0.044

Now, we can use the formula for z-statistics as;

z = (pd - (π1 - π2))/S_(p1-p2)

z = (-0.171 - 0)/0.044

z = -3.89

Using z-distribution table, we have the p-value = 0.00005

Since the P-value of (0.00005) is smaller than the significance level (0.01), then the effect is significant.

We conclude that The null hypothesis is rejected.

Thus, there is enough evidence to support the claim that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard.

Answer:

6  13/16

Step-by-step explanation:

7+(10-4^2)÷4×1/2^3

PEMDAS says parentheses first

7+(10-16)÷4×1/2^3

7+(-6)÷4×1/2^3

Then exponents

7+(-6)÷4×1/8

Then multiply and divide from left to right

7+(-6)÷4×1/8

7+-3/2 *1/8

7 + -3/16

Add and subtract

6 13/16

Answer:

∠[tex]2=131[/tex]°

Step-by-step explanation:

We know that ∠[tex]4[/tex] is ≅ ∠[tex]1[/tex].

This means that ∠ [tex]1=49[/tex]°

Therefore, [tex]49+49=98[/tex]°

We know that a trapezoid is [tex]360[/tex]°.

To find ∠[tex]2[/tex] ,which is congruent to ∠[tex]3\\[/tex], we will have to subtract [tex]360[/tex]° from [tex]98[/tex]°.

[tex]360-98=262[/tex]°.

Because ∠[tex]2[/tex]≅∠[tex]3[/tex], we will have to divide [tex]262[/tex] by [tex]2[/tex] to see their measurement.

So,

[tex]\frac{262}{2}=131[/tex].

Hence, ∠[tex]2=131[/tex]°.

I really hope this helps:D

-Jazz

Answer:

The Prime Factorization of 80 is,  2 × 4 × 10, 2 × 2 × 2 × 2 × 5  and  2 × 4 × 10

Step-by-step explanation: They are correct, because they all equal 80. 2 × 4 × 10=80 and  2 × 4 × 10=80, and 2 × 2 × 2 × 2 × 5=80.

24 × 5=120, Therefore it's the only incorrect question.

The term  2 x 2 x 2 x 2 x 5 shows the prime factorization of 80.

Prime factorization is the process of dissecting a number into the prime numbers that contribute to its formation when multiplied. In other terms, it is known as the prime factorization of the number when prime numbers are multiplied to get the original number.

Given the number 80

factors of 80 are 2 x 2 x 2 x 2 x 5

and given factors,

2 x 4 x 10,

2 x 2 x 2 x 2 x 5,

2 x 5 x 8,

24 x 5

all are the factors of 80 except 24 x 5,

but the correct representation of the prime factorization of 80 is

2 x 2 x 2 x 2 x 5

Hence option B is correct.

Learn more about prime factorization;

https://brainly.com/question/29775157

#SPJ2

Answer:

You did not post the options, but i will try to answer this in a general way.

Because we have two solutions, i know that we are talking about quadratic equations, of the form of:

0 = a*x^2 + b*x + c.

There are two easy ways to see if the solutions of this equation are real or not.

1) look at the graph, if the graph touches the x-axis, then we have real solutions (if the graph does not touch the x-axis, we have complex solutions).

2) look at the determinant.

The determinant of a quadratic equation is:

D = b^2 - 4*a*c.

if D > 0, we have two real solutions.

if D = 0, we have one real solution (or two real solutions that are equal)

if D < 0, we have two complex solutions.

Answer:

This was for 5 points. not 20 my dude. Also the first answer is correct.

Step-by-step explanation:

Answer: 8n-5

Step-by-step explanation:

Answer:

Step-by-step explanation:

In general, the transformation ...

  g(x) = f(x -h) +k

translates f(x) right h units and up k units.

The transformation ...

  g(x) = f(x/a)

stretches the graph horizontally by a factor of "a".

The transformation ...

  g(x) = -f(x)

causes the graph to be reflected over the x-axis.

___

Applying the above, we have ...

f(x) = 2^x reflected over x is g(x) = -2^x

f(x) = (1/3)^x translated up 5 is g(x) = (1/3)^x +5

f(x) = 3^x translated by (-2, -3) is g(x) = 3^(x +2) -3

f(x) = (1/2)^x translated down 2 is g(x) = (1/2)^x -2

f(x) = 4^x stretched horizontally by a factor of 3 is g(x) = 4^(x/3)

f(x) = 2^x translated by (3, 4) is g(x) = 2^(x -3) +4

Answer:

-2^x

(1/3)^x +5

3^(x +2) -3

(1/2)^x -2

4^(x/3)

2^(x -3) +4

Step-by-step explanation:

In general, the transformation ...

 g(x) = f(x -h) +k

translates f(x) right h units and up k units.

The transformation ...

 g(x) = f(x/a)

stretches the graph horizontally by a factor of "a".

The transformation ...

 g(x) = -f(x)

causes the graph to be reflected over the x-axis.

___

Applying the above, we have ...

f(x) = 2^x reflected over x is g(x) = -2^x

f(x) = (1/3)^x translated up 5 is g(x) = (1/3)^x +5

f(x) = 3^x translated by (-2, -3) is g(x) = 3^(x +2) -3

f(x) = (1/2)^x translated down 2 is g(x) = (1/2)^x -2

f(x) = 4^x stretched horizontally by a factor of 3 is g(x) = 4^(x/3)

f(x) = 2^x translated by (3, 4) is g(x) = 2^(x -3) +4

Answer:

4,300

Step-by-step explanation:

Lateral area of a squared Pyramid is given as ½ × Perimeter of base (P) × slant height of pyramid

Thus, we are given,

Side base length (s) = 43 yd

height (h) = 25 yd

Let's find the perimeter

Permimeter = 4(s) = 4(43) = 172 yd

Calculate the slant height using Pythagorean theorem.

Thus, l² = s²+h²

l² = 43²+25² = 1,849+625

l² = 2,474

l = √2,474

l ≈ 50 yd

=>Lateral area = ½ × 172 × 50

= 172 × 25

= 4,300 yd

Answer:

Step-by-step explanation:

monomial, polynomial, binomial, trinomial and multinomial are the different types of algebraic expressions.

plz mark as brainliest!!!!!!!

Answer:

c) 0.1

P(5) = 0.1

Step-by-step explanation:

Given data

x  :              0      1      2       3       4      5

p(x):          0.2    0.1  0.3   0.1     0.2    ?

Given data is discrete distribution

if the numbers [tex]P(x_{i} )[/tex]  i = 1,2,3.....  satisfies the two conditions

i) [tex]P(x_{i} )\geq 0[/tex]   for all values of 'i'

ii) ∑P(x) = 1

Given data

i) [tex]P(x_{i} )\geq 0[/tex]   for all values of 'i'

ii)            ∑P(x) = 1

        P(x=1) + P(x=2) +P(x=3) +P(x=4)+P(x=5) =1

⇒      0.2 + 0.1 + 0.3 +0.1 +0.2 + p(X=5) = 1

⇒     0.9 +p(5) =1

⇒             p(5) = 1 -0.9

⇒              P(5) = 0.1

Answer:

0 (zero)

Step-by-step explanation:

A horizontal line has zero slope.

Answer:

The answer is 260 * 2 = 520

Step-by-step explanation:

520/2 = 260

Multiply both sides by 2

We have

260 × 2 = 560

Hope this helps

Answer:

131.88 cm²

Step-by-step explanation:

At = 2×Acircle + Arectangle

= 2×π·r² + w×h

w = 2π·r = 2·3.14·3 = 18.84 cm

At = 2·3.14·9cm² + 18.84cm·4cm

= 56.52cm² + 75.36cm²

= 131.88 cm²

Answer:

[tex]1.25[/tex]

Step-by-step explanation:

[tex]let \: a = x \: and \: b = y[/tex]

[tex]36x = \frac{45}{y} [/tex]

[tex]36xy = 45[/tex]

[tex]xy = \frac{45}{36} [/tex]

[tex]xy = 1.25[/tex]

[tex]therefore \: ab \: is \: 1.25[/tex]