Using modern methods, the first step in solving the quadratic equation x2 + 7x = 8 would be to put it in standard form by

We have been given a graph that shows a line of best fit for data collected on the cost of hardwood flooring, from different vendors, as a function of area. We are asked to find the equation of line of best fit.

First of all, we will find the slope of line using point (0,0) and (400,1500) using slope formula.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{1500-0}{400-0}[/tex]

[tex]m=\frac{1500}{400}[/tex]

[tex]m=\frac{15}{4}[/tex]

So the slope of line is [tex]\frac{15}{4}[/tex].

We can see that line starts at origin (0,0), so y-intercept will be 0.

Now we will slope-intercept form of equation [tex]y=mx+b[/tex], where m represents slope and b represents the y-intercept.

[tex]y=\frac{15}{4}x+0[/tex]

[tex]y=\frac{15}{4}x[/tex]

Therefore, our required equation would be [tex]y=\frac{15}{4}x[/tex] and option B is the correct choice.

Answer:

12 tiles

Step-by-step explanation:

First we need to find the area of the parallelogram, which can be found by the product of the two dimensions.

If the parallelogram has 6 cm and 10 cm, the area is 6 * 10 = 60 cm2

Then to find how many tiles are needed to fill the area of 720 cm2. we can do a rule of three:

1 tile -> 60 cm2

x tiles -> 720 cm2

x = 720 / 60 = 12 tiles

Answer:

(143/74, -65/148)

Step-by-step explanation:

We have the equations:

4x - 12y = 13

14x + 32y = 13

Let's use elimination, so multiply the first equation by 8 and the second equation by 3:

8 * (4x - 12y = 13)  ⇒  32x - 96y = 104

3 * (14x + 32y = 13)  ⇒  42x + 96y = 39

Add those two equations:

    32x - 96y = 104

+   42x + 96y = 39

________________

    74x  +  0y  =  143

Divide both sides by 74:

x = 143/74

Plug this into an equation to find y:

4x - 12y = 13

4 * (143/74) - 12y = 13

12y = 572/74 - 13 = -390/74

y = -65/148

The answer is (143/74, -65/148).

Answer:

x = 143/74

y = -65/148

Step-by-step explanation:

4x-12y= 13

4x = 13 + 12y

x = 13/4 + 3y

32y+14x=13

32y + 14(13/4 + 3y) = 13

32y + 91/2 + 42y = 13

74y = 13 - 91/2

74y = -65/2

y = -65/148

x = 13/4 + 3(-65/148)

x = 143/74

x = 143/74

y = -65/148

Answer:

The answer is A

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

If the area of a circle is 562 in², then the radius of the circle is about 13 inches long.

Step-by-step explanation:

[tex]A = r^2\pi[/tex]

[tex]r = \sqrt{\frac{A}{\pi } }[/tex]

[tex]r = \sqrt{\frac{562}{\pi } }[/tex]

[tex]r = \sqrt{179}[/tex]

[tex]r[/tex] ≈ [tex]13[/tex]

Answer:

13 inches

Step-by-step explanation:

The area of a circle is given by the equation A = πr²

To solve for r, we must first divide both sides by π to get [tex]\frac{A}{\pi }=r^{2}[/tex]

We must then take the square root of both sides to get r by itself

Doing so, we get [tex]r=\sqrt{\frac{A}{\pi } }[/tex]

Now plugging in our values that we have we can solve for r:

[tex]r=\sqrt{\frac{562}{\pi } }=13.37[/tex] and rounding to the nearest inch gives us 13 inches

Answer:

1. 55.23   2. 52.31   3. 27.49   4. 347.05   5. 7.57

Step-by-step explanation:

Pretty self explanatory when viewing my answers, there is no trick question within this problem, you simply add 10 to the first 3 numbers, but leave the range and standard deviation the same.

Mean = $55.23

Median = $52.31

Mode = $27.49

Range = $347.05

Standard Deviation = $7.57

Mean: The mean represents the average value of the dataset.

Median: Median is the middle value of the dataset in which the dataset is arranged in the ascending order or in descending order.

Mode: The mode represents the frequently occurring value in the dataset.

Range: Range is the difference between the largest and smallest value in the data set

Standard Deviation: Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists.

Given, information about online purchases:

Mean = $45.23

Median = $42.31

Mode = $17.49

Range = $347.05

Standard Deviation = $7.57

After adding Shipping Charge of $10 to each purchase:

Since $10 is added to each value then,

New Mean = (∑x + n($10) )/n = ∑x/n + n ($10)/n

New Mean = $45.23 + 10

New Mean = $55.23

To find median, $10 will be added to the value of median.

New Median = $42.31 + $10

New Median = $52.31

To find mode, $10 will be added to the value of mode.

New Mode = $17.49 + $10

New Mode = $27.49

Range and Standard Deviation don't change if we add same value to each data point, It will remain same.

New Range = $347.05

New Standard Deviation = $7.57

Hence, the new mean, new median and new mode are $10 increased than the original ones, there is no change in value of range and standard deviation.

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Answer: 0.0

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Because think about it if there’s no one working in a business then there’s no work and no one gets paid in their business that’s how technology affects places where people work.

The answer is option C - More people are working from a remote location rather than an office building.

Technology has enabled a significant shift in the way people work, allowing many to perform their tasks remotely from locations outside of traditional office settings. With advancements in communication technology, internet connectivity, and collaboration tools, individuals can now work from virtually anywhere with an Internet connection. This trend towards remote work has been accelerated by factors such as the COVID-19 pandemic, which necessitated remote work arrangements for many organizations.

As a result, more people are opting to work from home, co-working spaces, or other remote locations rather than commuting to and working in traditional office buildings. This shift has several implications, including increased flexibility for workers, reduced commuting time and expenses, and the ability for companies to tap into talent from diverse geographical areas without the need for physical relocation.

While some individuals still prefer or require the structure and social interaction of a traditional office environment, the rise of remote work options has fundamentally changed the landscape of where and how people work.

Answer:

C

Step-by-step explanation:

Answer:

the answer is 1/12

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

Answer:

y=−2/3x+3

Step-by-step explanation:

I graphed the point and the equation given below. I used the same slope in the new equation as the original equation. The y-intercept is 3 because the line goes through (0,3).

Thus option C :  [tex]y = -\dfrac{2}{3}x + 3[/tex]  is correct.

Given that:

Equation of considered straight line:

[tex]y = -\dfrac{2}{3}x + 53[/tex]

Let the equation of the straight line that has to be found is given by:

[tex]y = mx + c[/tex]

It is given that the line is parallel to previous straight lines.

Which means  that slope of both the lines are same

or

[tex]m = -\dfrac{2}{3}[/tex]

Now since the second line passes through (-3,5), thus we have:

[tex]5 = -\dfrac{2}{3}\times -3 + c\\or\\c = 3[/tex]

Thus the needed equation of straight line is given by:

[tex]y = -\dfrac{2}{3}x + 3[/tex]

Thus option C :  [tex]y = -\dfrac{2}{3}x + 3[/tex]  is correct.

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Answer:

y = -6 * x^3

Step-by-step explanation:

We can model the new function as:

f(x) = ax^3

the function y = x^3 have positive values of y for positive values of x, and negative values of y for negative values of x.

As the negative values of x have positive values of y and vice-versa, the first change is to put a negative sign in front of x^3, so we know that 'a' is negative.

Then, for x=1 we have y = -6, so:

-6 = a*1^3

a = -6

So the equation of the transformed function is:

y = -6 * x^3

Answer:

Area = 15 m²

Step-by-step explanation:

Area of A rectangle is length * breadth or height.

Length = 2 m

Height = 7.5 m

So the area = 2*7.5

Area = 15 m²

Answer:

[tex]t \approx 750550.12\,yr[/tex]

Step-by-step explanation:

The time constant of the isotope is:

[tex]\tau = \frac{1.3\times 10^{9}\,yr}{\ln 2}[/tex]

[tex]\tau \approx 1.876 \times 10^{9}\,yr[/tex]

The decay of the isotope is described by the following model:

[tex]\frac{m}{m_{o}} = e^{-\frac{t}{\tau} }[/tex]

Now, the time is cleared in the equation:

[tex]t = -\tau \cdot \ln \frac{m}{m_{o}}[/tex]

[tex]t = - (1.876\times 10^{9}\,yr)\cdot \ln 0.9996[/tex]

[tex]t \approx 750550.12\,yr[/tex]

The rock from Maui with 99.96% of its parent K-40 remaining is significantly younger than 1.3 billion years, the half-life of K-40. The precise age calculation would yield a time much less than the half-life, indicating the rock's relative youth.

The age of a rock that has 99.96% of its parent K-40 remaining can be calculated using the half-life of K-40, which is 1.3 billion years. Since such a small percentage (0.04%) of K-40 has decayed to form Ar-40, the rock sample from Maui is very young relative to the half-life of K-40. We can estimate the age of the rock by using the concept of half-lives in radioactive decay.

The formula for radioactive decay is: N(t) = N0 (1/2)^(t/T), where N(t) is the amount of the parent isotope remaining, N0 is the initial amount of the parent isotope, t is the time that has elapsed, and T is the half-life of the isotope.

In the case of Maui's rock, with N(t)/N0 being approximately 0.9996 (or 99.96/100), we can set up the equation as follows: 0.9996 = (1/2)^(t/1.3 billion years). Solving for t gives an age that is much less than 1.3 billion years, indicating that the rock is relatively young and has experienced only a fraction of a half-life period.

However, because the amount of decay is so small, it would fall within the uncertainties of practical measurement and thus would only give us an approximation that the age of the rock is significantly less than one half-life, or markedly younger than 1.3 billion years.

Answer:

Step-by-step explanation:

Next time, please share the possible answer choices.

A quadratic function with one real zero actually has TWO real, identical zeros.  The vertex of the graph lies on the x-axis (touching it in only one place).

Answer:

a

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

if the term to term rule is to divide by two and the third term in the sequence is 3, you work backwards by multiplying by 2

So 3x2=6

6x2= 12

Thus the first number is 12.

working forward again, you can check your answer. Divide 12 by 2, then divide 6 by 2 and you get 3, the third term if the sequence

The first term of the sequence will be 12.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The term to term rule is divide by 2 the third term of the sequence is 3.

Now,

Since, The term to term rule is divide by 2 the third term of the sequence is 3.

So, We get the second number by multiply the 2 in the third number 3.

Second number = 2 x 3

                         = 6

And, We get the first number by multiply the 2 in the second number 3.

So, First number = 6 x 2

                          = 12

Thus, The first term of the sequence will be 12.

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hi,  

you have  then :   2100 * 1.045 ^n  = 47 200

                                         1.045^n = 47200 /2100

                                          1.045^n = 472/21

                                                    n =  ln ( 472/21 )  / ln ( 1.045)

                                                    n ≈71 years

let's check :   2100 *1.045^70 = 45746,68   and  2100 *1.045^71 = 47805.28

Answer:

[tex]\frac{x+5}{x+3}[/tex]

Step-by-step explanation:

hope this helps!

Answer:

C - 5/y+5

Step-by-step explanation:

edge 2020

YO MY N E  G G GA ITS 40 RACKS ON KEEP IT A ON GANG FORREAL MY N I 6 G A F5CK 12

Answer:

2,316 cu inch

Step-by-step explanation:

.

Answer:

69 ounces of water

Step-by-step explanation:

Answer:

Step-by-step explanation:

its 69 ounces.  

i did the test and got 100% it works :)

Answer:

A

Step-by-step explanation:

Looking at the function, we have;

V(t) = 1,000(1.06)^t

Mathematically, the amount earned on an investment that offers a particular constant percentage return to a particular number of years can be written as;

V = I(1 + r)^t

where V is the value of the investment after some certain number of years

I is the initial amount invested

r is the constant percentage increase

and t is the number of years.

Let’s now re-write what we can deduce in the question.

This is;

V(t) = 1000(1 + 0.06)^t

Thus what this 0.06 represents is r which is the constant interest rate

Answer:

5.5lb of strawberries cost $10.78

Step-by-step explanation:

We can use ratios to solve this problem.

 lb : $$$

0.5 : 0.98

  5 : 9.8

5.5 : 10.78

5.5lb of strawberries cost $10.78

You can also divide 5.5 by 0.5 (pounds) and multiply the quotient by how much a 0.5 pound of strawberries cost.

To find the total cost of 5.5 pounds of strawberries, determine the cost of one pound by doubling the cost for a half-pound. Then multiply the cost of one pound by the quantity of pounds purchased to get the total cost, which is $10.78.

The question asks us to calculate the total cost of 5.5 pounds of strawberries when given the price for a half-pound. The first step is to determine the cost of one pound of strawberries by doubling the cost of the half-pound.

If a 1/2 pound of strawberries costs $0.98, then one pound would cost $1.96 (since 0.98 x 2 = 1.96).

Next, to find out how much 5.5 pounds would cost, multiply the cost of one pound by 5.5:

5.5 pounds of strawberries x $1.96 per pound = $10.78.

Therefore, if you bought 5.5 pounds of strawberries, you would have spent $10.78.

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Answer:

length*width*height?

Step-by-step explanation:

12 three credit classes and two 2 credits

The number of two-credit and three-credit classes that students need to take is 5 and 10 respectively.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

As per the given,

Let's say the number of 2-credit classes is x while 3-credit classes are y.

Total classes, x + y = 15

Total credit 2x + 3y = 40

Solving both equations,

2(15 - y) + 3y = 40

30 - 2y + 3y = 40

30 + y = 40

y = 10

So, x = 15 - 10 = 5

Hence "The number of two-credit and three-credit classes that students need to take is 5 and 10 respectively".

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Answer:

60%

Step-by-step explanation:

To know the discount, we must know how much that $ 18 represents of the original price, as follows:

18/45 = 0.4

That is, $ 18 is 40% of $ 45

Therefore, to calculate the discount we must subtract what represents 45%, that is, 100%

100% - 40% = 60%

In other words, the discount is 60%

Answer:

60

Step-by-step explanation:

Answer: [tex](2x+5)(x+3)[/tex]

Step-by-step explanation:

[tex](2x^2+6x)+(5x+15)\\2x(x+3)+5(x+3)\\(2x+5)(x+3)[/tex]

Answer:

EDG 2021

Step-by-step explanation:

Step 2: C. 2x

Step 3: B. 5

Step 4: C. x + 3

Step 5: A. (x + 3) (2x + 5)

Answer:

L = 17 m W = 12 m

Step-by-step explanation:

Here is the answer.

The width of the rectangle is 12 meters, and the length is 17 meters, obtained by setting up equations based on the perimeter and the given relationship between length and width.

To find the length and width of the rectangle, we need to set up equations based on the given information. The question states that the length is 5m longer than the width, and the perimeter is 58m. Let's denote the width as w and the length as l. According to the problem, l = w + 5m.

The formula for the perimeter P of a rectangle is P = 2l + 2w. We can substitute the expression for the length into this formula:

P = 2(w + 5m) + 2w

Since we know the perimeter is 58m:

58m = 2(w + 5m) + 2w

58m = 2w + 10m + 2w

58m = 4w + 10m

48m = 4w

w = 12m

Now we can find the length:

l = w + 5m

l = 12m + 5m

l = 17m

The width of the rectangle is 12 meters and the length is 17 meters.

Answer: The price for the product is R$5.

Step-by-step explanation: Suppose the unit price of the product is X.

T is all the money I have.

In the first option, 20 units spend all my money, so:

T = 20x

In the second option, if I buy 14 of it, I have a remaining of R$30, so:

T = 14.x + 30

To determine the unit valor:

20x = 14x + 30

20x - 14x = 30

x = [tex]\frac{30}{6}[/tex]

x = 5

The product costs R$5.

Answer:

O valor unitário deste produto é de R$ 5.

Step-by-step explanation:

Ao comprar 14 unidades do produto, restam 30 Reais, ao comprar 20 unidades, não resta dinheiro, podemos afirmar que para comprar 6 unidades são necessários 30 Reais.

Portanto, para determinar o valor unitário do produto, devemos dividir os 30 Reais da troco pelas 6 unidades que não foram compradas.

Portanto, como 30/6 resulta em 5, esse é o valor unitário do produto. Cada produto vale 5 Reais.

Answer:

The answer is C. 103

Step-by-step explanation:

180 - 110 = 70

So, the measurement of angle z is 70.

Since parallelograms have a sum of 360°, then...

360 - (100 + 87 + 70)

360 - 257

103