7x^2 + 8x + 1 =0 find the solution

Answer:

10 and 4.

Step-by-step explanation:

Let x be the first number.

Let y be the second number.

x + y = 2x - 6

x - y = 4y - 10

x = 4y - 10 + y

x = 5y - 10

(5y - 10) + y = 2(5y - 10) - 6

6y - 10 = 10y - 20 - 6

6y - 10 = 10y - 26

6y - 10y = -26 + 10

-4y = -16

y = 4

x - (4) = 4(4) - 10

x - 4 = 16 - 10

x - 4 = 6

x = 6 + 4

x = 10

====================================================

Explanation:

List out the multiples of 25 to get {25, 50, 75, 100, 125, 150, 175, 200}

Do the same for the multiples of 40 to get {40, 80, 120, 160, 200}

We see that the lowest common multiple (LCM) is 200

---------

Another way to get the LCM is to multiply 25 and 40 to get 25*40 = 1000. Then divide this over 5 as this is the GCF between the two original numbers. We end up with the same LCM since 1000/5 = 200.

--------

There's a third way to get the LCM

List out the prime factorization of each value

25 = 5*5

40 = 2*3*5

Note how we have the unique factors of 2, 3 and 5. Circle the unique factors such that we highlight the ones that occur the most. We have 2 occur once, 3 occur once, and 5 occurs twice. We have circled one 2, one 3, and two 5's. They multiply out to 2*3*5*5 = 8*25 = 200

-----------------

Whichever method works for you, the LCM is 200. This means that every 200 minutes, we have bus A and bus B arrive at the depot at the same time. Their cycles line up at the 200 minute mark.

Convert this to hours,minutes format.

200 minutes = 180 minutes + 20 minutes

200 minutes = 3 hours + 20 minutes

200 minutes = 3 hrs, 20 min

We can represent "3 hrs, 20 min" in 12-hour clock notation by writing 3:20

Add this onto 7:00, which is 7 AM and we get

(7:00) + (3:20) = (7+3):(00+20) = 10:20 AM

We have started at 7 AM and fast forwarded 3 hours and 20 minutes to arrive at 10:20 AM.

Answer:

Domain : all real numbers

Range: All numbers greater than 2

Step-by-step explanation:

The shark. (Haha, I'm sorry.)

There are no restrictions on the x. X can be any real number.

The range, however, does have restrictions. The range has to be a number greater than 0.

Why?

Because any number that you put in for x won't make the range less than 2. If you put in zero for x, the range is 2.

Answer:

there

Step-by-step explanation:

a) Entering this into a calculator gives us:CI = (63.876, 88.524) b) test for the population is between 63.876 and 88.524 c)  If the standard deviation of the test scores had been 42.8 instead of 21.4, the width of the confidence interval would increase. d) . If the confidence level were reduced to 90%, the interval would be narrower. e) If the sample size was increased to 75 subjects, the interval would be narrower.

a. To find a 95% confidence interval for the mean score on the test, we can use the formula:

To find the confidence interval, we need to estimate the population standard deviation with the sample standard deviation. So:

CI = 76.2 ± 1.96 * (21.4/√27)

Entering this into a calculator gives us:

CI = (63.876, 88.524)

b. The confidence interval we found tells us that we are 95% confident that the true mean score on the test for the population is between 63.876 and 88.524. In other words, if we were to take many random samples of 27 people and compute a 95% confidence interval for each one, then about 95% of those intervals would contain the true population mean.

c. If the standard deviation of the test scores had been 42.8 instead of 21.4, the width of the confidence interval would increase. This is because a larger standard deviation means that the data are more spread out, which makes it more difficult to estimate the population mean accurately.

d. If the confidence level were reduced to 90%, the interval would be narrower. This is because a higher confidence level requires a larger z-score, which widens the interval. Conversely, a lower confidence level requires a smaller z-score, which narrows the interval.

e. If the sample size was increased to 75 subjects, the interval would be narrower. This is because a larger sample size decreases the standard error (σ/√n), which makes it easier to estimate the population mean accurately and results in a narrower confidence interval.

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The area when Alex has a circular rug the radius of the rug is 5 1/4 feet is 86.625 feet².

It should be noted that the area of a circle is given the formula:

Area of a circle = πr²

where π = 22/7

r = radius = 5 1/4

Therefore, the area will be:

Area = πr²

Area = 22/7 × (5 1/4)²

Area = 22/7 × 25 1/16

Area = 86.625 feet²

The area is 86.625 feet².

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Answer:

4/9

Step-by-step explanation:

See attachment for step-by-step

Answer: C. Bisect DE at G.

Step-by-step explanation:

So, for triangle DEF , if we draw the median DG to the opposite side EF.

Here EF is the opposite side to vertex D.

So, G must be the midpoint of line segment EF.

So , we need to first mark G on EF.

i.e. we need to bisect EF at G.

So first step would be : Bisect EF at G.

The equation for the hyperbola with foci (0,±5) and asymptotes y=± 3/4 x is:

y^2 / 25 - x^2 / a^2 = 1

where a is the distance from the center to a vertex and is related to the slope of the asymptotes by a = 5 / (3/4) = 20/3.

Thus, the equation for the hyperbola is:

y^2 / 25 - x^2 / (400/9) = 1

or

9y^2 - 400x^2 = 900

The center of the hyperbola is at the origin, since the foci have y-coordinates of ±5 and the asymptotes have y-intercepts of 0.

To graph the hyperbola, we can plot the foci at (0,±5) and draw the asymptotes y=± 3/4 x. Then, we can sketch the branches of the hyperbola by drawing a rectangle with sides of length 2a and centered at the origin. The vertices of the hyperbola will lie on the corners of this rectangle. Finally, we can sketch the hyperbola by drawing the two branches that pass through the vertices and are tangent to the asymptotes.

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Answer:

1,678

Step-by-step explanation:

1030(1.05)^10 = 1677.76

The expression (3.6 * 10^-5) / (1.8 * 10^2) can be calculated as = 2 * 10^-7

A canonical, normal, or standard form of a mathematical object is a conventional manner of presenting that item as a mathematical expression in mathematics and computer science. It is frequently the one that gives the simplest representation of an item and allows it to be identified in a unique fashion.

A quantity is said to be stated in standard form if it is written as the product of a power of ten and a number higher than or equal to one but less than ten (or scientific notation).

The expression (3.6 * 10^-5) / (1.8 * 10^2) can be calculated as follows:

=3.6 * 10^-5 / (1.8 * 10^2)

= (3.6 / 1.8) * (10^-5 / 10^2)

= 2 * 10^-7

Therefore, the answer in standard form is 2 * 10^-7.

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Problem 2

Rewrite the fraction 2/3 into 4/6. This is valid because we multiply top and bottom by 2.

2/3 = 4/6

Now compare the fractions for Wednesday and Tuesday in that order. We have 4/6 and 5/6. We can ignore the denominators because they effectively cancel out. The numerators will form the answer.

=====================================================

Problem 6

7% = 7/100 = 0.07

7% of 12,500 = 0.07*12500 = 875

Answer:

m  = 2 /5

Step-by-step explanation:

Answer:

k

Step-by-step explanation:

6 is the slope im pretty sure. i followed the slope formula rise over run

( y2-y1 / x2-x1 ) and got 6

Answer:

2. Tax = 445(0.07)

3. Tax = 445(7/100)

Step-by-step explanation: Just trust me :)...I promise you'll get it right

The lowest point on the graph occurs at point (3π/2,  -1)

One of the three fundamental functions in trigonometry, along with cosine and tan functions, is the sine function.

The ratio of the opposite side of a right triangle to its hypotenuse is known as the sine x or sine theta.

The sine function graph is sinusoidal in nature. This is a sim=ne wave that have smooth periodic oscillation

The attached graph shows sine function graph plotted with the interval [0, 2pi]

The lowest point is observed to occur at  (3π/2,  -1)

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Answer:

c. Identity property

Step-by-step explanation:

edg 2020

Identity property is used in the equation a+bi+0+0i=a+bi.

The identity property of addition says that the sum of 0 and any number is that number only.

We have been given the following equation

a+bi+0+0i=a+bi

when we multiply it with 0 we get 0 and the equation becomes

a+bi=a+bi

It shows the identity property of addition.

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The area covered by the pool and the cement walkway is 304  square feet. The width of the walkway would be 5 feet

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

Let x be represent the width of the walkway.

The pool measures 25 ft by 10ft . If the walkway must have a uniform width around the entire pool, then the total length of the pool and the walkway =  25+ x + x = 25 + 2x

The total width of the pool and the walkway = 10 + x + x = 10 + 2x

The area covered by the pool and the cement walkway is 304  square feet. This means that;

(25 + 2x)(10 + 2x) = 304

250 + 50x + 20x + 4x^2 = 304

4x^2 + 70x + 250 - 304 = 0

4x^2 + 70x - 54 = 0

x(x + 20) - 5(x + 20) = 0

(x - 5)(x + 20) = 0

x = 5 or x = - 20

Thus The width cannot be negative.

Therefore, the width of the walkway is 5 feet.

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Answer:

To find the apothem of a regular polygon, we can use the formula:

A = (ns^2)/(4tan(180°/n))

Where A is the area, n is the number of sides, s is the length of each side, and tan(180°/n) is the tangent of half of the central angle.

First, we need to find the number of sides of the polygon. To do this, we can use the formula for the sum of the interior angles of a polygon:

(n - 2)180° = 1080°

Solving for n:

n = 6

So the polygon has 6 sides.

Next, we can plug in the values we have into the formula for the apothem:

A = (6s^2)/(4tan(180°/6)) = 160

Expanding the right side:

A = (6s^2)/(4tan(30°)) = 160

Using the tangent identity:

A = (6s^2)/(4(√3/3)) = 160

Multiplying both sides by 4(√3/3) to isolate s^2:

4(√3/3)A = 6s^2

Expanding the left side:

4(√3)A/3 = 6s^2

Dividing both sides by 6:

2(√3)A/3 = s^2

Taking the square root of both sides:

s = √(2(√3)A/3)

Plugging in the value for A:

s = √(2(√3) * 160/3)

Calculating:

s = √(106.667) = 3.25

So the length of each side is 3.25 inches.

Finally, we can find the apothem using the formula:

a = s/2tan(180°/n)

Expanding the right side:

a = 3.25/2tan(30°)

Using the tangent identity:

a = 3.25/2(√3/3)

Dividing both sides by √3/3:

a = 3.25√3

Calculating:

a = 5.5

So the length of the apothem is 5.5 inches.

The inequality that represents all possible combinations of x, the number of monitors, and y, the number of keyboards, the university can buy for the computer lab is 250x + 50y <= 4500

Which inequality represents all possible combinations?

The given parameters are:

Spending = At most $4,500

Cost of monitor (x) = $250 per unit

Cost of keyboard (y) = $50 per unit

The total spending is represented as

Total = 250 * x + 50 * y

This gives

Total = 250x + 50y

The spending is at most $4,500 i.e less than or equal to

So, we have

250x + 50y <= 4500

Hence, the inequality that represents all possible combinations of x, the number of monitors, and y, the number of keyboards, the university can buy for the computer lab is 250x + 50y <= 4500

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Answer:

A)  y=x+2

Step-by-step explanation:

We can see that each time x increase by 2, y also increases by 2.  The slope of the line formed by this equation is therefore 1.  But we start out with y = 2, even when x=0.  That's the definition of the y-intercept:  the value of y when x is equal to zero.

The slope-intercept form of a straight line equation is y = mx + b, where m is the slope (1, in this case) and b is the y-intercept (0 in this case).

We have y = 1x + 2, or y = x + 2

The solution is,

1.   a, 99%       b71%

2. 64%, 44%

3. Number of particles   0, 1, 2, 3, 4,  5, 6, 7,  8, 9, 10, 11, 12, 13, 14

frequencies:                 1, 2, 3, 12, 11, 15, 18, 10,  12, 4, 5, 3, 1, 2, 1

Relative frequencies  0.01, 0.02,0.03,0.12,0.11,0.15, 0.18,0.1, 0.12,0.04,                        0.05,0.03,0.01,0.02,0.01

A histogram is an approximate representation of the distribution of numerical data.

here, we have,

Number of particles: 0, 1, 2, 3, 4, , 5, 6, 7

Frequency: 1, 2, 3, 12, 11, 15, 18, 10

Number of particles: 8, 9, 10, 11, 12, 13, 14

Frequency: 12, 4, 5, 3, 1, 2, 1

we solve by saying that  . one of th smaples wafer is with  any particles. we get the proportion by subtracting 1 from the total  divided by 100

100-1/100

.99

at least five particles , then we can subtract the number of those with particles less than five from 100 , divided by 100

100-(11+12+3+2+1)=71/100

0.71 or 71%

b. those particles within 5 and 10 inclusive

15+18+10+12+4+5=64/100

0.64

0r 64%

five and 10 exclusively will be

18+10+12+4=44/100

0.44

44%

c. Draw an histogram. first we have frequency table first

Number of particles    0, 1, 2, 3, 4,  5, 6, 7,  8, 9, 10, 11, 12, 13, 14

frequencies:                 1, 2, 3, 12, 11, 15, 18, 10,  12, 4, 5, 3, 1, 2, 1

Relative frequencies  0.01, 0.02,0.03,0.12,0.11,0.15, 0.18,0.1, 0.12,0.04,                        0.05,0.03,0.01,0.02,0.01

Relative frequencies is derived by dividing each frequencies over the total frequencies

we can say that it is unimodal or say that it is slightly positively skewed

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Answer:

1 to 4

Step-by-step explanation:

First find the number of total animals

8+10+6 = 24

rabbits to total animals

6 to 24

Divide each by 6

6/6 to 24/6

1 to 4

Answer:

1 : 4

Step-by-step explanation:

ratio of rabbits to total animals.

to get the total, you must add the number of cats, dogs and rabbits.

that is...... 8 + 10 + 6 = 24 animals.

rabbits : total animals

   6       :       24

simplify the ratio to its simplest form to get the answer which is 1 : 4.

Answer:

43x+39

Step-by-step explanation:

(5)(9x)+(5)(6)+−2x+9

=45x+30+−2x+9

=45x+30+−2x+9

=(45x+−2x)+(30+9)

=43x+39

(if this helps please give brainliest and 5 stars thanks)

Answer:

43x + 39

Step-by-step explanation:

5 ( 9x + 6 ) - 2x + 9

Firstly, open up the brackets.

= 45x + 30 - 2x + 9

Now bring the like term together and simplify.

=45x - 2x + 30 + 9

= 43x + 39

Answer:

The value of x round to the nearest tenth is 12.04

Step-by-step explanation:

We have used trigonometric ratios to calculate the required value.

Answer:

Step-by-step explanation:  It means a high level of quality, with 3.4 defects per million opportunities. It is this sigma level that leads to the term Six Sigma, which is a philosophy of delivering near perfect products or services by eliminating variabilities that lead to defects.

Answer: 3,64

Step-by-step explanation:

Answer:

You didn't say from least to greatest or greatest to least but I will do both

least to greatest: 1/8, 5/9 4/5

Greatest to least: 4/5  5/9  1/8

Step-by-step explanation:

1/8 is only 1 out of eight so that is obviously the least then you can covert 5/9 and 4/5 to the same denominator which is 45. 5/9 is now 25/45 and 4/5 is 36/45 36 is bigger than 25 so 4/5 is the greatest and 5/9 is the median

Answer:

1/8 least , 5/9 , 4/5 greatest

Step-by-step explanation:

From least to greatest it is great to picture a pie chart and view on how many pieces of pie would fill the pan or if you cant do that , the divided the numerator to the denominator.

4/5 ---->  80%

5/9 ----> 55%

1/8 ----> 12%

There are 49,896 distinguishable ways to arrange the letters of the word "millimicron."

There are 30,240 distinguishable orderings of the letters of "millimicron" that begin with 'm' and end with 'n.'

There are 60,480 distinguishable orderings of the letters of "millimicron" that contain the letters 'cr' next to each other in order and also the letters 'on' next to each other in order.

What is Permutation and combination?

Permutation and combination are mathemat ical concepts that deal with counting and arranging objects in a set. Both concepts are used to calculate the number of possible outcomes or arrangements, but they are applied in different situations.

Permutation:

Permutation refers to the arrangement of objects in a specific order. It focuses on the order or sequence of the elements. In a permutation, the order of the objects matters.

Combination:

Combination refers to the selection of objects from a set without considering the order or sequence. In a combination, the order of the objects does not matter.

To find the number of distinguishable ways to arrange the letters of the word "millimicron," we can calculate the permutations considering that some letters are repeated.

The word "millimicron" contains 11 letters in total, with the following repetitions:

Letter 'i' appears twice.

Letter 'l' appears twice.

Letter 'm' appears twice.

To calculate the total number of arrangements, we divide the total number of permutations by the factorial of the repetitions. The formula is as follows:

Total arrangements = (Total letters)! / (repetition_1! * repetition_2! * ... * repetition_n!)

Let's calculate the total arrangements:

Total letters = 11

Repetitions:

'i' appears twice, so repetition_1 = 2.

'l' appears twice, so repetition_2 = 2.

'm' appears twice, so repetition_3 = 2.

Total arrangements = 11! / (2! * 2! * 2!)

Now we can calculate the value:

Total arrangements = (11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (2 * 1 * 2 * 1 * 2 * 1)

= 399,168 / 8

= 49,896

Therefore, there are 49,896 distinguishable ways to arrange the letters of the word "millimicron."

To find the number of distinguishable orderings of the letters of "millimicron" that begin with 'm' and end with 'n,' we can fix the positions of 'm' and 'n' and permute the remaining letters.

We have the following fixed positions:

First position: 'm'

Last position: 'n'

Now, we need to permute the remaining letters ('i', 'l', 'l', 'i', 'i', 'c', 'r', 'o').

We have a total of 9 letters remaining, with the following repetitions:

Letter 'i' appears three times.

Letter 'l' appears twice.

Using the same formula as before, we calculate the total arrangements:

Total letters = 9

Repetitions:

'i' appears three times, so repetition_1 = 3.

'l' appears twice, so repetition_2 = 2.

Total arrangements = 9! / (3! * 2!)

Now we can calculate the value:

Total arrangements = (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (3 * 2 * 1 * 2 * 1)

= 362,880 / 12

= 30,240

Therefore, there are 30,240 distinguishable orderings of the letters of "millimicron" that begin with 'm' and end with 'n.'

To find the number of distinguishable orderings of the letters of "millimicron" that contain the letters 'cr' next to each other in order and also the letters 'on' next to each other in order, we can treat 'cron' as a single entity.

We have the following fixed entities:

'cr'

'on'

Now, we need to permute the remaining letters ('m', 'i', 'l', 'l', 'i', 'm', 'i') and the two fixed entities ('cr' and 'on').

We have a total of 9 letters/entities, with the following repetitions:

Letter 'i' appears three times.

We have the following entities:

'cr'

'on'

And the remaining letters:

'm', 'i', 'l', 'l', 'i', 'm', 'i'

To calculate the total number of arrangements, we'll treat 'cr' and 'on' as single entities.

Total entities = 9 (7 remaining letters + 2 fixed entities)

Repetitions:

'i' appears three times, so repetition_1 = 3.

Using the formula we used before, we calculate the total arrangements:

Total entities = 9

Repetitions:

'i' appears three times, so repetition_1 = 3.

Total arrangements = 9! / 3!

Now let's calculate the value:

Total arrangements = (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (3 * 2 * 1)

= 362,880 / 6

= 60,480

Therefore, there are 60,480 distinguishable orderings of the letters of "millimicron" that contain the letters 'cr' next to each other in order and also the letters 'on' next to each other in order.

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Given the list of symbols:

x, +, ( ), ÷

Let's determine the operations that should be completed first when solving an equation.

To solve an equation, we are always required to apply the PEMDAS theorem.

PEMDAS is an acronym for:

0. P,arentheses

1. E,xponents

2. M,ultiplication

3. D,ivision

4. A,ddition

5. S,ubtraction.

This shows the order in which the operations in an equation should be solved.

We can see that the first operation which is to be completed is the parenthesis.

Therefore, using the PEMDAS theorem, the operation that should be first completed when solving an equation is the parenthesis ().

ANSWER:

C. ( )