6th grade math , help me please :)

Answer:

1. = 8

2. =40

3. =37

Step-by-step explanation:

1. x = √(17² - 15²) = 8

2. x =√(9² +41²) = 40

3. x =√(12² + 35²) = 37

please mark brainliest

Answer:

  (F·G)(2) = 20

Step-by-step explanation:

We assume you want (F·G)(2).

  (F·G)(2) = F(2)·G(2)

  F(2) = 4 . . . . from the ordered pair (2, 4)

  G(2) = 5 . . . .from the ordered pair (2, 5)

So your product is ...

  F(2)·G(2) = 4·5 = 20

  (F·G)(2) = 20

Answer:

see explanation

Step-by-step explanation:

differentiate using the power rule.

[tex]\frac{d}{dx}[/tex]( a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex] , thus

[tex]\frac{d}{dx}[/tex](x² - x + 3 ) = 2x - 1

x = 5 → 2(5) - 1 = 10 - 1 = 9

To find the value of x for minimum , equate [tex]\frac{d}{dx}[/tex] to zero

2x - 1 = 0 , then

2x = 1 and

x = [tex]\frac{1}{2}[/tex]

Answer: 3,988.8

Usaremos la fómula: I = C * i * n

I = 72 000 * 0.05 * (1 año + 1 mes + 10 día)

I = 72 000 * 0.05 * (1 + 0.08 + 0.0028)

I = 72 000 * 0.05 * 1.108

3,988.8

Step-by-step explanation:

Podemos obtener el interés que produce un capital con la siguiente fórmula:  

I = C * i * n

Ejemplo: Si queremos calcular el interés simple que produce un capital de 1.000.000 pesos invertido durante 5 años a una tasa del 8% anual. El interés simple se calculará de la siguiente forma:

I = 1.000.000 * 0,08 * 5 = 400.000

Si queremos calcular el mismo interés durante un periodo menor a un año (60 días), se calculará de la siguiente forma:

Periodo: 60 días = 60/360 = 0,16            

I = 1.000.000 * 0,08 * 60/360 =  13.333

Espero te ayude :3

Answer:

[tex]4y - 7x - 1 = 0[/tex]

[tex]m = \frac{y2 - y1}{x2 - x1?} [/tex]

[tex]m = \frac{ - 5 - 2}{ - 6 - - 2?} [/tex]

[tex]m = \frac{ - 7}{ - 4} [/tex]

[tex]m = \frac{7}{4} [/tex]

[tex]y = m(x - x1) + y1[/tex]

[tex]y = \frac{7}{4} (x + 2) + 2[/tex]

[tex]y = \frac{7}{4} x + \frac{7}{2} + 2[/tex]

[tex]y = \frac{7}{4} x + \frac{11}{2} [/tex]

[tex]4y = 7x + 22[/tex]

[tex]4y - 7x - 22 = 0[/tex]

The equation of the line passing through the point (-2,2) and (-6,-5) is,

y = (-7/4)x +(11/2).

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the equation of a line that contains the points (−2,2) and (−6,−5).

Calculate the slope of the line,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( -5-2) / (-6 + 2 )

Slope= 7 / 4

The y-intercept is calculated as,

y = mx + c

2 = (-7/4) x 2 + c

c = 11 / 2

The equation will be written as,

y = mx + c

y = (7 / 4)x + (11/2)

Therefore, the equation of the line passing through the point (-2,2) and (-6,-5) is,

y = (-7/4)x +(11/2).

To know more about an equation of the line follow

https://brainly.com/question/18831322

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Explanation:

This is a geometric sequence because each new term is found by multiplying the last term by -4.

The common ratio is r = -4. The first term is a = -9. We want to sum up n = 9 terms.

Use the geometric nth partial sum formula below to plug in the terms mentioned

[tex]S_n = \frac{a*(1-r^n)}{1-r}\\\\S_9 = \frac{-9*(1-(-4)^9)}{1-(-4)}\\\\S_9 = \frac{-9*(1-(-262144))}{1+4}\\\\S_9 = \frac{-9*(1+262144)}{1+4}\\\\S_9 = \frac{-9*(262145)}{5}\\\\S_9 = \frac{-2359305}{5}\\\\S_9 = -471,861\\\\[/tex]

Answer:

-471,861

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

Company A f(x) = 15(7x)

Company B g(x) = 100x + 5

If Marguerite rents for 2 weeks, it will cost her more if she rents from Company B

A = 105(2) = 210

B = 100(2) + 5 = 205   B costs less  False

f Marguerite rents for 2 weeks, it will cost her less if she rents from Company B

A = 105(2) = 210

B = 100(2) + 5 = 205   B costs less  True

If Marguerite rents for 1 week, it will cost her the same at either company

A = 105(1) = 105

B = 100(1) +5 = 105   True

If Marguerite rents for 1 week, it will cost her more if she rents from Company A  

A = 105(1) = 105

B = 100(1) +5 = 105    False

h(x) = 5x – 5  

h(x) = f(x) – g(x)

      =15(7x) - ( 100x + 5)

      = 105x - 100x -5

      = 5x-5   True

h(x) = 5x + 5  False

Answer:

If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B.

If Marguerite rents for 1 week, it will cost her the same at either company.

h(x) = 5x - 5.

Step-by-step explanation:

Company A: f(x) = 15(7x)

Company B: g(x) = 100x + 5

h(x) = f(x) - g(x)

So, the function h(x) is the difference between Company A's rental and Company B's rental.

h(x) = (15(7x)) - (100x + 5)

= (105x) - (100x + 5)

= 105x - 100x - 5

= 5x - 5

h(x) = 5x - 5.

Let's say that Marguerite rents for 1 week. In Company A, that will cost her 15 * 7 = 105. In Company B, it will cost her 100 + 5 = 105. So, if Marguerite rents for 1 week, it will cost her the same at either company.

Let's say that Marguerite rents for 2 weeks. In Company A, that will cost her 15 * 7 * 2 = 30 * 7 = 210. In Company B, it will cost her 100 * 2 + 5 = 200 + 5 = 205. So, if Marguerite rents for 2 weeks, it will cost her less if she rents from Company B.

Hope this helps!

Answer:

f(x) = 60(2)ˣ

Step-by-step explanation:

f(x) = a(b)ˣ

After one month:

120 = a(b)¹

After four months:

960 = a(b)⁴

Divide the second equation by the first:

8 = b³

b = 2

Plug into either equation and find a.

120 = a(2)¹

a = 60

Therefore, f(x) = 60(2)ˣ.

Answer:

1. k=0

2. yes, result is still a polynomial.

3. yes, f and g must have the same degree to have deg(f+g) < deg(f) or deg(g)

Step-by-step explanation:

1. for what constant k must f(k) always equal the constant term of f(x) for any polynomial f(x)

for k=0 any polynomial f(x) will reduce f(k) to the constant term.

2. If we multiply a polynomial by a constant, is the result a polynomial?

Yes, If we multiply a polynomial by a constant, the result is always a polynomial.

3. if deg(f+g) is less than both deg f and deg g, then must f and g have the same degree?

Yes.  

If

deg(f+g) < deg(f) and

deg(f+g) < deg(g)

then it means that the two leading terms cancel out, which can happen only if f and g have the same degree.

2×y = 2×6= 12 so 2×x = 2×23 = 43 = 113

Step-by-step explanation:

Is this what you are looking for?

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Work Shown:

x = speed of train A

y = speed of train B

"train A travels 4/5 the speed of train B" (I'm assuming "train one" is supposed to read "train B"). So this means x = (4/5)y

distance = rate*time

d = x*7

d = (4/5)y*7 = (28/5)y represents the distance train A travels

d = y*7 = 7y represents the distance train B travels

summing those distances will give us 693

(28/5)y + 7y = 693

5*(  (28/5)y + 7y ) = 5*693

28y + 35y = 3465

63y = 3465

y = 3465/63

y = 55

Train B's speed is 55 mph

4/5 of that is (4/5)y = (4/5)*55 = 4*11 = 44 mph

Train A's speed is 44 mph

Answer:

[tex]\boxed{\sf \ \ \ [-7,0] \ \ \ }[/tex]

Step-by-step explanation:

Hello

[tex]y=x^2+7x=x(x+7) >0\\<=> x>0 \ and \ x+7 >0 \ \ or \ \ x<0 \ and \ x+7<0\\<=> x>0 \ \ or \ \ x<-7\\[/tex]

So values of x which is not in this domain is

[tex]-7\leq x\leq 0[/tex]

which is [-7,0]

hope this helps

Answer:

Correct option: D

Step-by-step explanation:

In the figure we have a right triangle, that is, one of the angles is a 90° angle. Therefore, we can use the Pythagoras' theorem to find the relation between the sides of the triangle:

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

Where b and c are cathetus of the triangle (sides adjacent to the 90° angle) and a is the hypotenuse (opposite side to the 90° angle).

So in our case, we have that x is the hypotenuse, and 40 and 42 are cathetus, so we have:

[tex]x^2 = 40^2 + 42^2[/tex]

[tex]x^2 = 1600 + 1764[/tex]

[tex]x^2 = 3364[/tex]

[tex]x = 58[/tex]

So the correct option is D.

Hello!

Answer:

Choice 1.

Step-by-step explanation:

We can go through each answer choice and examine whether it represents the question:

1) This does not represent the question because 10% of 6 is 0.6. The question is asking to find a number that 6 = 10% of, not finding 10% of 6.

2) Correct because a number multiplied by 10%, or 0.1, should be equal to 6 to answer the question.

3) Correct because 6 is equivalent to 10% of the answer, which is stated in this answer choice.

4) Correct because 6 should be 10% of the answer.

Therefore, the incorrect choice would be Choice 1.

Answer:

5,000

Step-by-step explanation:

If it decreases by 5% a year, it'll decrease by 75% in 15 years

i.e 1 year = 5%

15 years = x

Cross multiply

x = 75%

Therefore, since it decreases by 75%

100 - 75 x 20,000 = 5,000

100

Answer:

-5/3 -2/5

im pretty sure

Answer:

[tex]5^{7[/tex] or 78125

Step-by-step explanation:

5^2 ( 5^3 · 5^2 )

= 5^2 ( 5^5 ) = 5^7

or, 78125

Answer:

A) 22 cans required to paint

B) Including 13% tax, cost of painting = $633.93

Step-by-step explanation:

As we check the figure, we have a composite figure.

Cuboid on the base and a pyramid on the top of it.

To find the area to be painted, we have 4 rectangular faces of cuboid with dimensions 6m [tex]\times[/tex] 3m.

And 4 triangular faces of pyramid with Base = 6m and Height 5m.

So, total area to be painted = 4 rectangular faces + 4 triangular faces

Area of rectangle = Length [tex]\times[/tex] Width = 6 [tex]\times[/tex] 3 = 18 [tex]m^2[/tex]

Area of triangle = [tex]\frac{1}{2}\times Base \times Height =\frac{1}{2}\times 6 \times 5 = 15\ m^{2}[/tex]

Total area to be painted = 4 \times 18 + 4 \times 15 = 72 + 60 = 132 [tex]m^2[/tex]

A) Area painted by 1 can = 6 [tex]m^2[/tex]

Cans required to paint 132 [tex]m^2[/tex] = [tex]\frac{132}{6} = 22\ cans[/tex]

B)

Cost of 1 can = $25.50

Cost of 22 can = $25.50 [tex]\times[/tex] 22 = $561

Including tax of 13% = $561 + $561 [tex]\times \frac{13}{100}[/tex] = $561 + $72.93 = $633.93

So, the answers are:

A) 22 cans required to paint

B) Including 13% tax, cost of painting = $633.93

Answer:

A. $500.00

Step-by-step explanation:

IRS popularly known as  Internal revenue service charges an IRS fee under the authority of the Federal Law and policy agencies. This implementation of IRS fee is to recuperate the cost of rendering a service to the masses.  

From the given information in the question:

Suppose you invest $15,000 at the age of 35 and agree to start receiving  payments at the age of 45.

At age 41, you decide you want to withdraw $5000  from your account.

Since the investor is still 41 years of age ; IRS will charge 10% of the withdrawal amount.

IRS fee = 10% of $5000

IRS fee = 0.1 × $5000

IRS fee = $500

Answer:

6227020800

Step-by-step explanation:

There are 13 ways to choose the first person in the first group, 12 ways to choose the second person in the first group and so on until we get 1 way to choose the second person in the last group so the answer is 13 * 12 * 11 * ... * 3 * 2 * 1 = 13! = 6227020800.

Answer:

I believe the interquarrile range is 5

Answer:

H₀ is accepted, we don´t have evidence to claim valves produces more than 4,1 pounds/square inch

Step-by-step explanation:

Normal Distribution

Population mean   μ₀  = 4.1

Population standard deviation  σ = 0,9

Sample size   n  = 260

Sample mean     μ  =  4,2

Level of significance 0,02       α = 0,02 form z-table we find z score

z(c) = 2,05  (critical value)

Test hypothesis      

Null hypothesis                       H₀            μ  =  μ₀

Alternative hypothesis           Hₐ            μ   >  μ₀

Is a one tail-test ( to the right. Values have a mean over the population mean)

z(s) = (  μ  -  μ₀ )/ σ /√n

z(s) =  4,2 - 4,1 / 0,9/√260

z(s) = 0,1 *16,1245 / 0,9

z(s) =  1,7916

To compare  z(s)   and z(c)

z(s) < z(c)

Then  z(s) is in the acceptance region, we accept H₀

An exponential has the base at the bottom, or the lower portion. Think of "basement" to help remember this. The exponent is the number up top, so 12 is the exponent.

Answer:

The person above me is correct ( :

Step-by-step explanation:

B

Answer:

a dilation by One-fourth and a translation

Step-by-step explanation:

For determining the sequence first we have to find out the scale factor which is shown below:

We can calculate the scale factor to obtain  

[tex]= \frac{1.5}{6} \\\\ = \frac{1}{4}[/tex]

Now as we know that the triangle XYZ and the triangle ABC are similar to each other but in the triangle XYZ is smaller in size and it is a shift to upward and right

Therefore the last option is correct

Answer:

B) Conclusions drawn using inductive reasoning are always valid, while conclusions drawn using deductive reasoning may or may not be valid.

Step-by-step explanation:

Inductive reasoning uses logic and uses more evidence to draw conclusions. In deductive reasoning, WE decide whether a deductive statement is true by assessing the strength of the link between the premises and the conclusion. But some deductive reasoning may appear to make sense without pointing to a truth

Answer:

The answer is D. Conclusions drawn using deductive reasoning are always valid, while conclusions drawn using inductive reasoning may or may not be valid.

Step-by-step explanation:

I took the test

Answer:

Step-by-step explanation:

To get theta, we will apply the formula for calculating the length of an arc as shown;

Length of an arc = theta/360 * 2πr

theta is the central angle (required)

r is the radius of the circle

Given r = 9 inches and length of the arc PQ = 6π in

Substituting this given values into the formula to get the central angle theta;

6π = theta/360 * 2πr

Dividing both sides by 2πr

theta/360 = 6π/2πr

theta/360 = 3/r

theta/360 = 3/9

theta/360 = 1/3

cross multiplying;

3*theta = 360

theta = 360/3

theta = 120°

Since 180° = π rad

120° = x

x = 120π/180

x = 2π/3 rad

Hence the measure of the central angle in radians is 2π/3 rad

[tex]\frac{1}{30}[/tex]

From the question, in the bag there are;

4 red balls

6 green balls

10 balls in total.

Now, reaching in the bag and taking out 3 balls without looking, the probability that all three balls are red, can be analyzed as follows;

All three red means;

The first ball is red,

The second ball is red and;

The third ball is red.

i. First you take out a ball from a total of 10 balls. The probability P⁰(R) of having a red ball is given as;

P⁰(R) = [tex]\frac{possible-space}{total-space}[/tex]

Since there are 4 red balls, the possible-space is 4

Also, since there are a total of 10 balls, the total-space is 10

P⁰(R) = [tex]\frac{4}{10} = \frac{2}{5}[/tex]

ii. Secondly, you take out a ball from a remaining total of 9 balls. The probability P¹(R) of still having a red ball is given as;

P¹(R) = [tex]\frac{possible-space}{total-space}[/tex]

Since there are 3 red balls remaining, the possible-space is 3

Also, since there are a remaining total of 9 balls, the total-space is 9

P¹(R) = [tex]\frac{3}{9} = \frac{1}{3}[/tex]

iii. Thirdly, you take out a ball from a remaining total of 8 balls. The probability P²(R) of still having a red ball is given as;

P²(R) = [tex]\frac{possible-space}{total-space}[/tex]

Since there are 2 red balls remaining, the possible-space is 2

Also, since there are a remaining total of 8 balls, the total-space is 8

P²(R) = [tex]\frac{2}{8} = \frac{1}{4}[/tex]

Therefore, the probability P(R) of taking out three red balls without looking is given by the product of the probabilities described above. i.e

P(R) = P⁰(R) x P¹(R) x P²(R)

P(R) = [tex]\frac{2}{5} * \frac{1}{3} * \frac{1}{4} = \frac{1}{30}[/tex]

Answer:

The  confidence interval is  [tex]-11.34 < \mu_1 -\mu_2 < -10.86[/tex]

Step-by-step explanation:

From the question we are told that

    The first sample size is  [tex]n_1 = 146[/tex]

    The second sample size is [tex]n_2 = 180[/tex]

    The first sample mean is [tex]\= x_1 = 51.6[/tex]

    The second  sample  mean is  [tex]\= x_2 = 62.7[/tex]

     The first standard deviation is  [tex]\sigma _1 = 9.42[/tex]

     The second standard deviation is  [tex]\sigma _2 = 14.5[/tex]

Given that the confidence level is  98% then the significance level is mathematically evaluated as

      [tex]\alpha = (100 -98 )\%[/tex]

       [tex]\alpha = 2 \%[/tex]

        [tex]\alpha = 0.02[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the z-table , the value is  [tex]Z_{\frac{\alpha }{2} } = 2.33[/tex]

The reason we are obtaining critical value of  

 [tex]\frac{\alpha }{2}[/tex]

instead of  

[tex]\alpha[/tex]

is because  

 [tex]\alpha[/tex]

represents the area under the normal curve where the confidence level interval (

[tex]1-\alpha[/tex]

) did not cover which include both the left and right tail while  

 [tex]\frac{\alpha }{2}[/tex]

is just the area of one tail which what we required to calculate the margin of error

NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)

Generally the margin of error is mathematically represented as

      [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\sigma_1^2}{n_1^2} + \frac{\sigma_2^2}{n_2^2} }[/tex]

substituting values

      [tex]E = 2.33 * \sqrt{ \frac{9.42^2}{146^2} + \frac{14.5^2}{180^2} }[/tex]

substituting values

     [tex]E = 2.33 * \sqrt{ \frac{9.42^2}{146^2} + \frac{14.5^2}{180^2} }[/tex]

     [tex]E = 0.2405[/tex]

The 98% confidence interval is mathematically represented as

      [tex](\= x _ 1 - \= x_2 ) - E < \mu_1 -\mu_2 < (\= x _ 1 - \= x_2 ) + E[/tex]

substituting values

      [tex](51.6 - 62.7) - 0.2405 < \mu_1 -\mu_2 < (51.6 - 62.7) + 0.2405[/tex]

     [tex]-11.34 < \mu_1 -\mu_2 < -10.86[/tex]

Answer:

2

Step-by-step explanation:

The degree of this polynomial is 2, since a parabola is drawn. A parabola is a graph of a quadratic equation which has the highest degree of 2.