QUESTION 10 of 10 The slope of the line below is -4. Use the coordinates of the labeled point to find a point slope equation of the line. ​

The solutions to the nearest tenth are x = -0.1 and x = 1.3

From the question, we have the following parameters that can be used in our computation:

5x² - 2x - 1 = 4x

Evaluate the like terms

So, we have

5x² - 6x - 1 = 0

Next, we solve using a graph

The graph of 5x² - 6x - 1 = 0 is added as an attachment

From the attached graph, we can see that the curve intersects with the x-axis at x = -0.1 and x = 1.3

This means that the solutions are x = -0.1 and x = 1.3

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Answer:

The solutions to the equation 5x^2-2x-1=4x to the nearest tenth are x ≈ 1.3 or x ≈ -0.4.

Step-by-step explanation:

To solve the equation 5x^2-2x-1=4x to the nearest tenth, we can start by moving all the terms to one side of the equation.

5x^2-2x-1=4x

5x^2-6x-1=0

Next, we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 5, b = -6, and c = -1.

Plugging these values into the formula gives:

x = (-(-6) ± sqrt((-6)^2 - 4(5)(-1))) / 2(5)

x = (6 ± sqrt(56)) / 10

Answer:

x = - 9

Step-by-step explanation:

2x + 7 = - 11 ( subtract 7 from both sides )

2x = - 18 ( divide both sides by 2 )

x = - 9

The answer is:

x = -9

Work/explanation:

The point of equations is to find the variable's value by isolating it step-by-step.

For this equation, the variable is x.

To isolate it, I will perform a few operations.

First, I will subtract 7 from each side:

\(\sf{2x+7=-11}\)

\(\sf{2x=-11-7}\)

\(\sf{2x=-18}\)

Divide each side by 2

\(\sf{x=-9}\)

Hence, x = -9.

\(\rule{350}{4}\)

To find the total in the retirement account after 38 years of investing with monthly contributions and an interest rate of 4.99%, we can use the compound interest formula.

The formula for the future value of an investment with regular monthly contributions is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value or the total in the retirement account.

P is the monthly contribution amount.

r is the monthly interest rate (annual interest rate divided by 12).

n is the number of monthly contributions (years invested multiplied by 12).

Let's calculate the total:

P = $225

r = 4.99% / 100 / 12 = 0.0041583 (monthly interest rate)

n = 38 * 12 = 456 (number of monthly contributions)

FV = $225 * [(1 + 0.0041583)^456 - 1] / 0.0041583

Using a financial calculator or spreadsheet, we can evaluate this expression to find the future value or total in the retirement account.

The calculated total may vary depending on the compounding frequency and rounding used.

b) The 99% confidence interval for the population proportion is given as follows: (0.57, 0.68).

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.

The parameters for this problem are given as follows:

\(n = 520, \pi = \frac{325}{520} = 0.625\)

Then the lower bound of the interval is given as follows:

\(0.625 - 2.575\sqrt{\frac{0.625(0.375)}{520}} = 0.57\)

The upper bound of the interval is given as follows:

\(0.625 + 2.575\sqrt{\frac{0.625(0.375)}{520}} = 0.68\)

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The balance sheet attached shows the Total Assets to be $55.968M  and Total Liabilities and Capital to be $252M respectively.

1. Assets:

  a. Cash in Reserves:

The required reserves are 5.4% of checkable deposits.

Therefore, the required reserves amount to 5.4% of $92 million, which is:

(0.054 * $92 million) = $4.968 million.

This amount is considered a liability for the bank, but it is held as an asset in the form of cash reserves.

  b. Loans: The bank made a $28 million commercial loan and a $23 million mortgage loan. Therefore, the total loans amount to:

total loan =  $28 million + $23 million

                 = $51 million.

2. Liabilities:

  a. Checkable Deposits:

The bank received $92 million in checkable deposits.

  b. Required Reserves:

As mentioned above, the required reserves amount to $4.968 million.

3. Capital:

  The bank started with $155 million in capital.

Based on the above information, the bank's balance sheet would look as attached.

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Answer:

#1  (0,-4)

#2  (5,0)

#3  (3,1)

Step-by-step explanation:

#1.  (-3, 2) (0, y)  slope = -2

slope = rise/run    therefore slope = -2/1  or down 2 and over 1

so from -3 to 0 you are going over 3 units (or 3 times)  Therefore to find y at x=0, you have to move three steps, or 3 times -2 = -6      so 2-6 = -4

so y intercept (b)  = -4 0r (0,-4)

#2   (-7,-4)  (x,0)  slope (m) = 1/3   -7+12=5    x=5

#3   (4,-3)   (x, 1)   slope (m) = -4   (4/-1)   Moving one unit in slope  means

-3=4=1 for Y and 4-1=3 for X    therefore the point is (3, 1)

Answer:

83 kids total

Step-by-step explanation:

There are 54 girls on the playground. There are 25 fewer boys than girls on the playground. How many kids are on the playground?

girls = 54

boys = 54 - 25 = 29

54 + 29 = 83 kids total

kids that are on the playground are 83.

Merging objects and identifying them since one big bunch is done through addition. In arithmetic, addition is the technique of adding two or more integers together. The product can meet are the quantities that are included, and the outcome of the operation, or the final response, is referred to as the sum.

The total number of girls that are present is 54

The data given is that there are

25 fewer boys taht are4 present

The total number of boys will be

boys = 54 - 25 = 29

The number of kids that are present will be the total of boys and girls that are present.

Kids = boys + girls

54 + 29 = 83 kids total

The quantity of kids that are present in the playground is 83.

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Answer:

does anyone know

Step-by-step explanation:

That is hard

Find:

step 1: open the bracket,

step 2: simplify step-wise

The answer is 17

Answer:

dggdhdhdhshsjshdhdhhshshshshdhdhsbsbsbd

The simplified value of the expression given is 3a⁴b/ 7

Given the fraction :

divide the coefficients by 5

From division rule of indices, subtract the powers of values with Equivalent coefficients.

Hence,

Finally we have :

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Answer:

Step-by-step explanation:

B because after having the star and the circle comes the square.

Answer:

when Riley starts selling her $h1t

Answer:

Debbie runs 9 feet per second: 9 ft/s

Jessica runs 1 mile  in 440 seconds: 414/50 ft/s = 207/25 ft/s = 8 7/25 ft/s

jesssica runs 131 feet in 10 seconds: since 1 mile = 5280 ft we have 1/470 mi/s = 5280/470 ft/s = 528/47 ft/s = 11 11/47 ft/s

ron runs 603 feet in 1 minute: 547 ft/min = 603/60 ft/s = 201/20 ft/s = 10 1/20 ft/s

Since:

11 11/47 > 10 1/20 > 9 > 8 7/25

Emily runs the fastest.

Answer:

b

Step-by-step explanation:

pls mark me as brainliest pls

The required 7,000 gallons of gasoline which are 9% ethanol must be added to 2,000 gallons of gasoline with no ethanol to get a mixture that is 7% ethanol.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
To solve the problem, we can use the following formula:

(amount of ethanol in the final mixture) / (total amount of gasoline in the final mixture) = 7%

To find the amount of ethanol in the 2,000 gallons of gasoline with no ethanol:

ethanol in 2,000 gallons of gasoline with no ethanol = 0 × 2,000 = 0 gallons

Then, find the amount of ethanol in the final mixture:

ethanol in final mixture = (0.09x + 0 * 2,000) / (x + 2,000)

Notice that we use 0 gallons for the ethanol in the 2,000 gallons of gasoline with no ethanol, since it contains no ethanol.

Ethanol in the final mixture / total amount of gasoline in the final mixture = 7%

(0.09x + 0) / (x + 2,000) = 0.07

0.09x + 0 = 0.07(x + 2,000)

0.09x = 0.07x + 140

0.02x = 140

x = 7,000

Therefore, 7,000 gallons of gasoline which is 9% ethanol must be added to 2,000 gallons of gasoline with no ethanol to get a mixture that is 7% ethanol.

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Answer:

\(\Huge \bold{\boxed{\boxed{\text{5\%}}}}\)

Step-by-step explanation:

To calculate the margin of error for the survey, we need to use the formula:

\(\large \text{Margin of error} = \large \text{$\frac{\text{Range of values}}{2}$}\)

The range of values is the difference between the upper and lower bounds of the interval. In this case, the lower bound is 22% and the upper bound is 32%, so the range of values is:

\(\large \text{Range of values = 32\% - 22\% = 10\%}\)

Substituting this value into the formula, we get:

\(\large \text{Margin of error = $\frac{10\%}{2}$ = 5\%}\)

Therefore, the margin of error on the survey is 5%.

Answer: 3^3 Square root 3

Step-by-step explanation:

Answer:

180 - 90 = 90

half of 90 = 45

40 and 50??

Step-by-step explanation:

Answer:

A) y = 4

Step-by-step explanation:

Line AB is a vertical line, so a line perpendicular to it would have to be a horizontal line (perpendicular lines make an "x" shape with one another). Horizontal lines are written as y = ___ .

The perpendicular line also has to pass through the point (2,4). Points are written as (x, y). Therefore, the y-value in (2,4) is 4.

The perpendicular line has to be y=4 since it passes through both the Line AB and the given point.

Answer:

Check explanation section.

Step-by-step explanation:

So, we have the following parameters or information from the question above:

=> that the regression equation is Score = 31.55 + 10.90 Years.

So, the regression equation is in the form of mx + c.

Thus, the coefficient that is constant = 31.55 and the coefficient that shows or represents the years = 10.90.

=> Also, we have the value which is most important in this question that is the coefficient of Determination which is represented as R-sq and has the value of 83%.

The percentage of the total variation in test scores is NOT explained by the linear relationship between years of study and test scores = 100% - 83% = 17%.

For the percentage of the total variation in test scores is explained by the linear relationship between years of study and test scores = R- sq = 83%.

Answer:

Refer to the step-by-step explanation, please follow along very carefully. Answers are encased in two boxes.

Step-by-step explanation:

Given the following function, find it's derivative using the definition of derivatives. Evaluate the function when θ=1, 11, and 3/11

\(p(\theta)=\sqrt{11\theta}\)

\(\hrulefill\)

The definition of derivatives states that the derivative of a function at a specific point measures the rate of change of the function at that point. It is defined as the limit of the difference quotient as the change in the input variable approaches zero.

\(f'(x) = \lim_{{h \to 0}} \dfrac{{f(x+h) - f(x)}}{{h}}\)\(\hrulefill\)

To apply the definition of derivatives to this problem, follow these step-by-step instructions:

Step 1: Identify the function: Determine the function for which you want to find the derivative. In out case the function is denoted as p(θ).

\(p(\theta)=\sqrt{11\theta}\)

Step 2: Write the difference quotient: Using the definition of derivatives, write down the difference quotient. The general form of the difference quotient is (f(x+h) - f(x))/h, where "x" is the point at which you want to find the derivative, and "h" represents a small change in the input variable. In our case:

\(p'(\theta) = \lim_{{h \to 0}} \dfrac{{p(\theta+h) - p(\theta)}}{{h}}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11(\theta + h)} - \sqrt{11\theta} }{h}\)

Step 3: Take the limit:

We need to rationalize the numerator. Rewriting using radical rules.

\(p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11(\theta + h)} - \sqrt{11\theta} }{h} \\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11\theta + 11h} - \sqrt{11\theta} }{h}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} }{h}\)

Now multiply by the conjugate.

\(p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} }{h} \cdot \dfrac{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} } \\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{(\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} )(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )}{h(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )} \\\\\\\)

\(\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{11h}{h(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{11}{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }\)

Step 4: Simplify the expression: Evaluate the limit by substituting the value of h=0 into the difference quotient. Simplify the expression as much as possible.

\(p'(\theta)= \lim_{h \to 0} \dfrac{11}{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{\sqrt{11}\sqrt{\theta+(0)} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{\sqrt{11}\sqrt{\theta} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11\theta} }\)

\(\therefore \boxed{\boxed{p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta} }}}\)

Thus, we have found the derivative on the function using the definition.

It's important to note that in practice, finding derivatives using the definition can be a tedious process, especially for more complex functions. However, the definition lays the foundation for understanding the concept of derivatives and its applications. In practice, there are various rules and techniques, such as the power rule, product rule, and chain rule, that can be applied to find derivatives more efficiently.\(\hrulefill\)

Now evaluating the function at the given points.  

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}; \ p'(1)=??, \ p'(11)=??, \ p'(\frac{3}{11} )=??\)

When θ=1:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(1)= \dfrac{\sqrt{11} }{2\sqrt{1}}\\\\\\\therefore \boxed{\boxed{p'(1)= \dfrac{\sqrt{11} }{2}}}\)

When θ=11:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(11)= \dfrac{\sqrt{11} }{2\sqrt{11}}\\\\\\\therefore \boxed{\boxed{p'(11)= \dfrac{1}{2}}}\)

When θ=3/11:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(\frac{3}{11} )= \dfrac{\sqrt{11} }{2\sqrt{\frac{3}{11} }}\\\\\\\therefore \boxed{\boxed{p'(\frac{3}{11} )= \dfrac{11\sqrt{3} }{6}}}\)

Thus, all parts are solved.

Answer:

\( y = -6x^2 -17 x -12\)

And since the higher exponent for the x term is 2 we can classify the equation  as quadratic

Quadratic term: -6

Linear term: -17

Constant term: -12

Step-by-step explanation:

For this problem we have the following equation:

\( y = (3x+4)(-2x-3)\)

And we can distribute the terms and we got:

\( y = -6x^2 -9x -8x -12\)

And solving we got:

\( y = -6x^2 -17 x -12\)

And since the higher exponent for the x term is 2 we can classify the equation  as quadratic

Quadratic term: -6

Linear term: -17

Constant term: -12

Answer:

35%

Step-by-step explanation:

14÷40= 0.35 (35%)

0.35 × 40= 14

Answer:

2/3=0.66
7/8=0.875
1 2/5= 1.4

Step-by-step explanation:

It's pretty simple if you have a calculator to divide 2/3 along with 7/8 and 1 2/5

Answer:

353/120 or 2 113/120

Step-by-step explanation:

The cost of gas is proportional to the volume of gas because a constant rate of $3.15 to 1 gallon of gas.

From the given table;

The volume of the first gas Layla bought = 3 gallons.

The cost of the 3 gallons = 9.45

Therefore the cost of 1 gallon = ?

That is:

3 gallons = $9.45

1 gallon = X

Make X the subject of formula:

X = 9.45/3 = $3.15

Therefore, the cost of 11 gallons of gas would be = 11×3.15 = $34.65. This is because the cost of 1 gallon would be = $3.15.

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