Solve 2x^2 + x - 4 = 0
X2 +

Answer:

Area of rectangle is 100 square inches.

Step-by-step explanation:

Area of rectangle = length * width

a=l*w

a=4w*w

a=4w^2............(1)

Put the value of w in (1)

a=4(5)^2

a=4(25)

a=100in^2

Answer:

100 yards

Step-by-step explanation:

the length is 4 times the width of the rectangle, so I used guess and check and figured 20 is four times greater than 5 and plugged those two numbers in and it worked.

Answer:

The factors are (4x-1) and (2x+3)

Step-by-step explanation:

The factors of 8x^2 + 10x -3 can be found by grouping terms

8x^2 - 2x  + 12x - 3

2x (4x -1)  + 3(4x-1)

(4x-1)(2x+3)

Answer:

0

Step-by-step explanation:

Solution:-

We are given two functions as follows:

                      [tex]f ( x ) = x^2 - 15\\\\g ( x ) = 2x[/tex]

We need to determine the composite function defined as ( g - f ) ( x ). To determine this function we need to make sure that both function exist for all real positive value of x.

The function f ( x ) is a quadratic function which has real values for all values of x. Similarly, function g ( x ) is a linear line that starts from the origin. Hence, both functions are defined over the domain ( -∞, ∞ )

We will perform arithmetic operation of subtracting function f ( x ) from g ( x ) as follows:

                       [tex][ g - f ] ( x ) = g ( x ) - f ( x )\\\\\\( g - f ) ( x ) = x^2 - 15 - 2x\\\\[/tex]

Now evaluate the above determined function at x = -3 as follows:

                       [tex]( g - f ) ( -3 ) = ( -3 )^2 - 2 ( -3 ) - 15\\\\( g - f ) ( -3 ) = 9 + 6 - 15\\\\( g - f ) ( -3 ) = 0[/tex]

Answer:

Mean: 46

Median: 43

Mode: 43

Step-by-step explanation:

I hope this helped. I am sorry if you get this wrong.

Answer:

C

Step-by-step explanation:

According to SohCahToa, cosine is adjacent over the hypotenuse.

The adjacent when looking from angle b, is 21.

The hypotenuse of this triangle is 29.

So Cos B=21/29

Answer:

[tex]7\frac{3}{20}[/tex]

Step-by-step explanation:

Hey there!

Well to add this we need to pu it in improper form.

7/5 + 23/4

Now we need to find the LCM.

5 - 5, 10, 15, 20, 25, 30

4 - 4, 8, 12, 16, 20, 24, 28

So the LCD is 20.

Now we need to change the 5 and 4 to 20.

5*4 = 20

7*4 = 28

28/20

4*5=20

23*5=115

115/20

Now we can add 28 and 115,

= 143/20

Simplified

7 3/20

Hope this helps :)

Answer:

Step-by-step explanation:

[tex] \mathrm{1 \frac{2}{5} + 5 \frac{3}{4} }[/tex]

Add the whole numbers and fractional parts of the mixed numbers separately

[tex] \mathrm{ = (1 + 5) + ( \frac{2}{5} + \frac{3}{4} })[/tex]

Add the numbers

[tex] \mathrm{=6 + ( \frac{2}{5} + \frac{3}{4} )}[/tex]

Add the fractions

[tex] \mathrm{=6 + (\frac{2 \times 4 + 3 - 5}{20} )}[/tex]

[tex] \mathrm{=6 + \frac{23}{20} }[/tex]

Convert the improper fractions into a mixed number

[tex] \mathrm{=6 + 1 \frac{3}{20} }[/tex]

Write the mixed number as a sum of the whole number and the fractional part

[tex] \mathrm {= 6 + 1 + \frac{3}{20} }[/tex]

Add the numbers

[tex] \mathrm{ = 7 + \frac{3}{20} }[/tex]

Write the sum of the whole number and the fraction as a mixed number

[tex] \mathrm{ = 7 \frac{3}{20} }[/tex]

Hope I helped

Best regards!

Answer:

Part A:

The probability of hitting the black circle is the ratio between the area of the black circle and the white square (including the black circle)

Area of circle:

Ac = pi x r^2 = pi x (2/2)^2 = pi (diameter = 2)

Area of square:

As = side^2 = 11^2 = 121 (side = 11)

=> P = pi/121 = ~0.025 (P = 0.025 < 0.5 => P is closer to 0 than 1)

Part B:

The probability of hitting the white portion could be calculated in a similar way as shown in part A. However, the event of hitting the white portion is the complement event of the event of hitting the black circle.

Because P(event) + P(complement of event) = 1

=> P = 1 - 0.025 = 0. 975 (P = 0.975 > 0.5 => P is closer to 1 than 0)

Answer:

Step-by-step explanation:

To find the height h we use tan

tan ∅ = opposite / adjacent

From the question

The adjacent is 2000 ft

The opposite is h

So we have

tan 15° = h / 2000

h = 2000 tan 15

h = 535.89 ft

h = 536 ft to the nearest foot

Hope this helps you

Answer:

❄️The answer is 7.0 or 7❄️

Step-by-step explanation:

It mostly depends on how many zeros will you put in 7.0

It actually doesn’t matter how many zeros you put after the decimal point.

Below I attached a picture of how to solve this kinds of problem.

Hope this helps! ^-^

By:❤️BrainlyMagic❤️

Note:if you ever need help, you can always ask me!

Answer:

It’s 7.0 or 7

Step-by-step explanation:

Trust me I got it right in my homework.

Answer:

x = -6

Step-by-step explanation:

3(x+4)-1=-7

Add 1 to each side

3(x+4)-1+1=-7+1

3(x+4)=-6  

Divide by 3

3/3(x+4)=-6/3

x+4 = -2

Subtract 4 from each side

x+4-4 = -2-4

x = -6

Answer:

Step-by-step explanation:

[tex]3(x + 4) - 1 = - 7[/tex]

Distribute 3 through the parentheses

[tex]3x + 12 - 1 = - 7[/tex]

Calculate the difference

[tex]3x + 11 = - 7[/tex]

Move constant to R.H.S and change it's sign

[tex]3x = - 7 - 11[/tex]

Calculate

[tex]3x = - 18[/tex]

Divide both sides of the equation by 3

[tex] \frac{3x}{3} = \frac{ - 18}{3} [/tex]

Calculate

[tex]x = - 6[/tex]

hope this helps

Best regards!!

Answer:

2x + y = -4

Step-by-step explanation:

standard form of equation of straight line is

ax+by = c

that  is terms containing x and y should be  on LHS and constant term should be  on RHS

______________________________________________

Given equation

y + 1 = - 2x - 3

lets bring -2x on LHS ,

add 2x on lHS and RHS

y + 1  + 2x = - 2x - 3 + 2x

=> y + 1  + 2x = -3

on lHS, 1 is there which constant term lets bring it on RHS

subtract 1 from both sides

y + 1  + 2x  - 1= -3 -1

y + 2x = -4

rearranging it

2x + y = -4  (Answer)

Answer:

x = 8.9 units

Step-by-step explanation:

We will use the theorem of intersecting tangent and secant segments.

"If secant and tangent are drawn to a circle from an external point, the product of lengths of the secant and its external segment will equal the square of the length of tangent."

8(8 + 2) = x²

x² = 80

x = √80

x = 8.944

x ≈ 8.9 units

Therefore, length of the tangent = 8.9 units

Answer:

83 cm

Step-by-step explanation:

Change meters to centimeters

1.58 m

1.58 × 100 cm

158 cm

158 cm - 75 cm

= 83 cm

Answer:

The line of best fit

y = 0.633x + 0.561

Step-by-step explanation:

The coordinates that the dart hit include

(–5, 0), (1, –3), (4, 5), (–8, –6), (0, 2), and (9, 6)

The x and y coordinates can be written as

x | y

-5|0

1 | -3

4|5

-8|-6

0|2

9|6

So, running the analysis on a spreadsheet application, like excel, the table of parameters is obtained and presented in the first attached image to this solution.

Σxᵢ = sum of all the x variables.

Σyᵢ = sum of all the y variables.

Σxᵢyᵢ = sum of the product of each x variable and its corresponding y variable.

Σxᵢ² = sum of the square of each x variable

Σyᵢ² = sum of the square of each y variable

n = number of variables = 6

The scatter plot and the line of best fit is presented in the second attached image to this solution

Then the regression analysis is then done

Slope; m = [n×Σxᵢyᵢ - (Σxᵢ)×(Σyᵢ)] / [nΣxᵢ² - (∑xi)²]

Intercept b: = [Σyᵢ - m×(Σxᵢ)] / n

Mean of x = (Σxᵢ)/n

Mean of y = (Σyᵢ) / n

Sample correlation coefficient r:

r = [n*Σxᵢyᵢ - (Σxᵢ)(Σyᵢ)] ÷ {√([n*Σxᵢ² - (Σxᵢ)²][n*Σyᵢ² - (Σyᵢ)²])}

And -1 ≤ r ≤ +1

All of these formulas are properly presented in the third attached image to this answer

The table of results; mean of x, mean of y, intercept, slope, regression equation and sample coefficient is presented in the fourth attached image to this answer.

Hope this Helps!!!

Answer:

a. y = 0.6x + 0.6

Step-by-step explanation:

Answer:

first we find the slope, m=(4-0)/(4+1)

Step-by-step explanation:

first, we find the slope, m=(4-0)/(4+1)=4/5

y-4=4/5 (x-4), y=(4/5)x+4/5

Answer:

a

The sample size is  [tex]n = 219.2[/tex]

b

The  sample size is  [tex]n = 537.5[/tex]

Step-by-step explanation:

From the question we are told  that

    The standard deviation is  [tex]\sigma = 45 \minutes[/tex]

    The  Margin of  Error is  [tex]E = \pm 5 \ minutes[/tex]

Generally the margin of  error is mathematically represented as

         [tex]E = z * \frac{\sigma }{\sqrt{n} }[/tex]

Where  n is the sample  size

    So

             [tex]n = [\frac{z * \sigma }{E} ]^2[/tex]

Now  at  90%  confidence level the z value for the z-table is  

        z =  1.645

So

       [tex]n = [\frac{1.645 * 45 }{5} ]^2[/tex]

       [tex]n = 219.2[/tex]

The z-value at 99%  confidence level is  

        [tex]z = 2.576[/tex]

This is obtained from the z-table  

   So the sample size is  

         [tex]n = [\frac{2.576 * 45 }{5} ]^2[/tex]

        [tex]n = 537.5[/tex]

For the 90% confidence interval, the sample size is 219.2 and for the 99% confidence interval, the sample size is 537.5 and this can be determined by using the formula of margin of error.

Given :

The formula of the margin of error can be used in order to determine the sample size is needed if the executive wants to be 90% confident of being correct to within 5 minutes.

[tex]\rm ME = z\times \dfrac{\sigma}{\sqrt{n} }[/tex]

For the 90% confidence interval, the value of z is 1.645.

Now, substitute the values of all the known terms in the above formula.

[tex]\rm n=\left(\dfrac{z\times \sigma}{ME}\right)^2[/tex]   --- (1)

[tex]\rm n=\left(\dfrac{1.645\times 45}{5}\right)^2[/tex]

n = 219.2

Now, for 99% confidence interval, the value of z is 2.576.

Again, substitute the values of all the known terms in the expression (1).

[tex]\rm n=\left(\dfrac{2.576\times 45}{5}\right)^2[/tex]

n = 537.5

For more information, refer to the link given below:

https://brainly.com/question/6979326

Answer:

(9, 3)  

Step-by-step explanation:

(1) 4(0.25x + 0.5 y) = 3.75 ⟶ x + 2y = 15

(2)                 4x - 8y = 12 ⟶ x  -  2y =   3

                                                   2x = 18

                                                      x = 9

                                              9 - 2y = 3

                                                  -2y = -6

                                                     y = 3

Answer:

Step-by-step explanation:

use the equation: y =50x-350 where x is the number of hours driving

hrs                

1      50            300

2      100          250

3       150          200

5       250         100

7        350           0

Answer:

1      50            300

2      100          250

3       150          200

5       250         100

7        350           0

Step-by-step explanation:

Answer:

work is shown and pictured

Answer:

It's Just 1.

Step-by-step explanation:

Check The Guys Work Above.

Answer:

option B is the right option.

Step-by-step explanation:

[tex] \frac{bc}{ab} = \frac{ab}{bd} [/tex]

Plug the values:

[tex] \frac{20}{12} = \frac{12}{x} [/tex]

Apply cross product property

[tex]20 \times x = 12 \times 12[/tex]

Calculate the product

[tex]20x = 144[/tex]

divide both sides of the equation by 20

[tex] \frac{20x}{20} = \frac{144}{20} [/tex]

Calculate:

[tex]x = 7.2[/tex]

hope this helps..

Good luck...

this is another type of lazy.... : )

Step-by-step explanation:

Answer:

125

Step-by-step explanation:

30+25+x=180

55+x=180

x=180-55

x=125

Answer:

Step-by-step explanation:

To find x we use tan

tan ∅ = opposite / adjacent

From the question

x is the adjacent

30 is the hypotenuse

So we have

tan 25 = 30/x

x = 30/tan 25

x = 64.33

x = 64.3 to the nearest tenth

Hope this helps you

Answer:

  y = √55

Step-by-step explanation:

All the triangles are similar, so the ratio of short side to hypotenuse is the same for all:

  5/y = y/(5+6)

  y^2 = 55

  y = √55

_____

Comment on the geometry

There are three "geometric mean" relationships that apply to this geometry.

If you were aware of the last of these relationships, you could write down the answer without any "work."

  y = √(5(5 +6)) = √55

__

The geometric mean is the n-th root of the product of n numbers. When there are 2 numbers, it is the square root of their product.

Answer:

48

Step-by-step explanation:

If x varies inversely as y, we have:

[tex]x \propto \frac{1}{y} \\\implies x = \frac{k}{y}[/tex]

When x=2, y=96

[tex]2 = \frac{k}{96}\\k=192[/tex]

When x=8, y=24

[tex]8 = \frac{k}{24}\\k=192[/tex]

Therefore, the constant of proportionality, k=192.

The equation connecting x and y is:

[tex]x = \frac{192}{y}[/tex]

When x=4

[tex]4 = \frac{192}{y}\\4y=192\\y=48[/tex]

The missing value in the inverse variation given in the table is 48.

Answer:

a = 8

b = -8

Step-by-step explanation:

You have the following function:

[tex]f(x)\\\\=at+b;\ \ t<2\\\\2t^2-1;\ \ 2\leq t[/tex]

A function is differentiable at a point c, if the derivative of the function in such a point exists. That is, f'(c) exists.

In this case, you need that the function is differentiable for t=2, then, you have:

[tex]f'(t)=a;\ \ \ \ t<2 \\\\f'(t)=4t;\ \ \ 2\leq t[/tex]

If the derivative exists for t=2, it is necessary that the previous derivatives are equal:

[tex]f'(2)=a=4(2)\\\\a=8[/tex]

Furthermore it is necessary that for t=2, both parts of the function are equal:

[tex]8(2)+b=2(2)^2-1\\\\16+b=8-1\\\\b=-8[/tex]

Then, a  = 8, b = -8

Answer:

Identify what you want to prove and you can test using ANOVA, Chi Square, F test ..... among many.

Step-by-step explanation:

Null and alternative hypothesis are always understood in terms of experiments.

In simple words,

  null hypothesis =    The results of your experiment are due to chance  

  alternative hypothesis = The results of your experiments are NOT due to chance

Therefore, identify what you want to prove and you can test using ANOVA, Chi Square, F test ..... among many.

Answer:

3.375

Step-by-step explanation:

Answer:

3.375

Step-by-step explanation:

Had it on Khan

Answer:

13 and -13

Step-by-step explanation:

The only factors of 169 are 1, 13, and 169.

Since the product is negative, you have to use 13 and -13. These numbers have a difference to 26. And when multiplied they equals -169

Answer:

Option (4)

Step-by-step explanation:

By the Angle of intersecting secants,

"If two lines intersect outside a circle, then the measure of the angle between these lines or secants will be one half of the difference between the intercepted arcs."

From the picture attached,

Angle between the secants = ∠1

Measure of intercepted arcs are a° and b°.

By this theorem,

m∠1 = [tex]\frac{1}{2}(a-b)[/tex]

Option (4) will be the answer.

From the odd-degree terms, take out one copy and rewrite the series as

[tex]1+6x+x^2+6x^3+\cdots=(1+x+x^2+x^3+\cdots)+5x+5x^3+\cdots[/tex]

[tex]1+6x+x^2+6x^3+\cdots=(1+x+x^2+x^3+\cdots)+5x(1+x^2+\cdots)[/tex]

Then if |x| < 1, we can condense this to

[tex]\displaystyle\sum_{n=0}^\infty x^n+5x\sum_{n=0}^\infty x^{2n}=\frac1{1-x}+\frac{5x}{1-x^2}=\frac{1+6x}{1-x^2}[/tex]

Since the series we invoked here converge on -1 < x < 1, so does this one.

The explicit formula of the function f(x) is [tex]f(x) = \frac{1 + x + 5x}{1-x^2}[/tex]

The function definition is given as:

[tex]f(x) = 1 + 6x + x^2 + 6x^3 + x^4 + ...[/tex]

Expand the terms of the expression

[tex]f(x) = 1 + 5x + x + x^2 + 5x^3 + x^3 + x^4 + ...[/tex]

Split

[tex]f(x) = (1 + x + x^2 +x^3 + .....) + 5x + 5x^3 + .. ...[/tex]

Factor out 5x

[tex]f(x) = (1 + x + x^2 +x^3 + .....) + 5x(1 + x^2) + .. ...[/tex]

Express 1 as x^0

[tex]f(x) = (x^0 + x + x^2 +x^3 + .....) + 5x(1 + x^2) + .. ...[/tex]

Express x as x^1

[tex]f(x) = (x^0 + x^1 + x^2 +x^3 + .....) + 5x(1 + x^2) + .. ...[/tex]

Also, we have:

[tex]f(x) = (x^0 + x^1 + x^2 +x^3 + .....) + 5x(x^0 + x^2) + .. ...[/tex]

Rewrite the series using the summation symbol

[tex]f(x) = \sum\limits^{\infty}_{n=0}x^n+ 5x\sum\limits^{\infty}_{n=0}x^{2n}[/tex]

The sum to infinity of a geometric progression is:

[tex]S_{\infty} = \frac{a}{1- r}[/tex]

Where:

a represents the first term, and r represents the common ratio

Using the above formula, we have:

[tex]\sum\limits^{\infty}_{n=0}x^n = \frac{1}{1 - x}[/tex]

[tex]5x\sum\limits^{\infty}_{n=0}x^{2n} = 5x * \frac{1}{1 - x^2} = \frac{5x}{1-x^2}[/tex]

So, we have:

[tex]f(x) = \frac{1}{1-x}+ \frac{5x}{1-x^2}[/tex]

Take the LCM

[tex]f(x) = \frac{1 + x + 5x}{1-x^2}[/tex]

Evaluate the like terms

[tex]f(x) = \frac{1 + 6x}{1-x^2}[/tex]

Hence, the explicit formula of the function f(x) is [tex]f(x) = \frac{1 + x + 5x}{1-x^2}[/tex]

Read more about geometric series at:

https://brainly.com/question/12563588