Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3

Answer:

they bought 8 candy bars and 8 + 4 = 12 packs of gum.

Step-by-step explanation:

Let's use algebra to solve this problem:

Let x be the number of candy bars they bought.

Then, the number of packs of gum they bought is x + 4.

The total cost of the candy bars is 60x cents.

The total cost of the packs of gum is 85(x + 4) cents.

We know that they spent $15.00, which is 1500 cents, so we can write an equation:

60x + 85(x + 4) = 1500

Simplifying the equation, we get:

145x + 340 = 1500

145x = 1160

x = 8

Therefore, they bought 8 candy bars and 8 + 4 = 12 packs of gum

Answer: 22

Step-by-step explanation:

The number of the gum is 13 and the number of the candy will be 22.

What is linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Jane and Sophia went to the corner store where packages of gum cost 54¢ each and candy bars cost 88¢ each.

They spent $26.38 total and bought 35 items total.

Let x be the number of the gum and y be the number of the candy.

Then the equation will be

x + y = 35 ...1

0.54x + 0.88y = 26.38 ...2

By solving the equations 1 and 2, then we have

x = 13 and y = 22

Then the number of the gum is 13 and the number of the candy will be 22.

The total space that the tiles will cover is 7x, where x is the number of tiles, and each tile has an area of 7 square inches. the maximum number of tiles that Lakita can use is  [tex]20[/tex] .

Since each tile has an area of 7 square inches, the total area that the tiles will cover is 7x, where x is the number of tiles.

Lakita wants to find the maximum number of tiles she can use, so she needs to find the largest integer value of x that satisfies the inequality 7x < y, where y is the total area of the table-top.

To find the value of y, we need to find the area of the rectangle. The rectangle is 10 inches wide and 14 inches long, so its area is:

A = length × width    [tex]= 10 \times 14 = 140[/tex] square inches

Therefore,  [tex], y = 140[/tex] square inches.

To find the maximum number of tiles, we can divide the total area of the table-top by the area of each tile:

[tex]x = y/7 = 140/7 = 20[/tex]

Therefore, the maximum number of tiles that Lakita can use is  [tex]20[/tex] .

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The confidence interval does not justify the councilman's statement because 45 minutes is greater than the upper bound of the confidence interval.

What is a confidence interval?

A confidence interval is a statistical range that is used to estimate an unknown population parameter based on a sample from that population. It is a measure of the degree of uncertainty or precision associated with the estimated value of the parameter.

The confidence interval of 34.42 ± 8.14 minutes means that we are 95% confident that the true population mean commute time falls between 26.28 minutes (34.42 - 8.14) and 42.56 minutes (34.42 + 8.14). Since the councilman's statement of 45 minutes falls outside of this range, we cannot say that it is justified by the confidence interval.

Additionally, the fact that the mean commute time from the sample of 25 adults was 34.42 minutes does not necessarily mean that the true population mean commute time is also 34.42 minutes. It only provides an estimate, and the confidence interval takes into account the variability of the sample mean.

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Answer:

A. No, because 45 minutes is greater than the upper bound of the confidence interval.

Step-by-step explanation:

Step-by-step explanation:

10b = 62 - 12

10b = 50

b = 50/10

b = 5

Answer:

5

Step-by-step explanation:

When trying to find the value of an unknown variable, it is important to take into factors on how to reverse an effect being done to the variable, which is how we can isolate b and figure out the value.

- Addition reverses subtraction

- Multiplication reverses division

We have a simple equation, [tex]10b+12=62[/tex] , and we need to work around the variable b in order to isolate it. By doing this, we are able to find the true value of b.

We can subtract 12 on each side to get the term away from the constant.

[tex]10b+12=62[/tex]

     -   12   -12

[tex]10b=50[/tex]

Then, to isolate the variable from the coefficient, which is 10, we can divide it to negate the multiplication factor on the term.

[tex]\frac{10b}{10} = \frac{50}{10}[/tex]

b=5

Therefore, the variable b=5.

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Step-by-step explanation:

pls send a picture for better clarification of the questions

According to the given information, f(125) is equal to 48479.

What is function?

A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.

To find f(125), we need to apply the recursive formula for f(n) when n is a positive integer divisible by 5. Since 125 is divisible by 5, we can use the formula:

f(125) = f(125/5) + 3(125)²

f(125/5) = f(25) = f(25/5) + 3(25)²

f(25/5) = f(5) = f(5/5) + 3(5)²

f(5/5) = f(1) = 4

Now we can substitute the values back into the formula and simplify:

f(5) = f(5/5) + 3(5)² = 4 + 75 = 79

f(25) = f(25/5) + 3(25)² = 79 + 3(625) = 2054

f(125) = f(125/5) + 3(125)² = 2054 + 3(15625) = 48479

Therefore, f(125) is equal to 48479.

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1)The number of milk chocolate that sold last week is = [tex]25\frac{2}{3}[/tex] B is correct

2)white chocolate at the candy store last week is 19.

Last week, a candy store sold [tex]5\frac{1}{3}=\frac{16}{3}[/tex] pounds of white chocolate. It sold 4 times as much milk chocolate as white chocolate.

The number of milk chocolate did the candy store sell last week.

Since the candy store sold 4 times as much milk chocolate as white chocolate, it sold:

[tex]4 *\frac{ 19}{3 } =\frac{ 76}{3}\\ pounds\ of\ milk\ chocolate.= 25 \frac{2}{3}[/tex]

option B is correct.

2)

To find out how many more pounds of milk chocolate were sold than white chocolate at the candy store last week, we can subtract the amount of white chocolate sold from the amount of milk chocolate sold:

[tex]\frac{76}{3} - \frac{19}{3} \\= \frac{57}{3}\\ = 19\ pounds.[/tex]

option C is correct

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Therefore, f(x) = g(x) when function x is approximately 0.235 or 33.765.

A quadratic equation is a polynomial equation of the second degree, which means that the highest power of the variable in the equation is 2. A general quadratic equation can be written in the form:

[tex]ax^2 + bx + c = 0[/tex]

Where 'a', 'b', and 'c' are constants, and 'x' is the variable. The value of 'x' that satisfies the equation is called the root or solution of the equation.

To find where f(x) = g(x), we need to solve the equation:

[tex]\sqrt40x = \sqrt{x} + 3[/tex]

Squaring both sides, we get:

[tex]40x = (x + 3)^2[/tex]

Expanding the right-hand side, we get:

40x = x² + 6x + 9

Bringing all terms to one side, we get:

[tex]x^2- 34x - 9 = 0[/tex]

We can solve this quadratic equation using the quadratic formula:

[tex]x = (-b± \sqrt{(b^2 - 4ac))}/2a[/tex]

where a = 1, b = -34, and c = -9.

Plugging in these values, we get:

x = (34 ± √ (34² + 419)) / 2

x = (34 ± √1165) / 2

x ≈ 0.235 or x ≈ 33.765

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Using the formula we know that the volume of the oblique rectangular prism is 1,200units³ respectively.

A prism with oblique bases is one in which the bases are not parallel to one another.

An oblique rectangular prism is a rectangular prism with bases that are not arranged one over the other.

The following qualities describe an oblique prism: It seems to be slanted or skewed. Parallelograms make up an oblique prism's faces.

The height is gauged from the outside.

The two bases are not positioned next to one another exactly.

So, the volume formula for the oblique rectangular prism:

V=l⋅w⋅h

Now, insert values:
V=l⋅w⋅h

V=15*10*8

V=1,200 units ³

Therefore, using the formula we know that the volume of the oblique rectangular prism is 1,200units³ respectively.

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The final answer is:

-1/7 < 5 < 2

Or, in interval notation:

(−1/7, 2)

What is interval?

In mathematics, an interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set. An interval can be written using interval notation, which uses parentheses, square brackets, or a combination of both to indicate whether the endpoints of the interval are included or excluded. For example:

First, let's simplify the expression inside the parentheses:

3 + 2 = 5

Now we can substitute this value into the expression and simplify further:

-14 < -7(5) < 1

-14 < -35 < 1

To solve this compound inequality, we need to isolate the variable (in this case, there is no variable) to find the range of values that satisfy the inequality. We can do this by dividing all three parts of the inequality by -7. However, we need to reverse the direction of the inequality signs since we are dividing by a negative number:

-14/-7 > -35/-7 > 1/-7

2 > 5 > -1/7

Therefore, the solution to the inequality is:

-1/7 < 5 < 2

In interval notation, this can be written as:

(−1/7, 2)

To sketch the solution, we can plot the interval on a number line. The interval does not include the endpoints, so we use open circles to indicate this:

<-------------(○======○)------------->

             -1/7    5     2

The open circle at -1/7 indicates that -1/7 is not included in the interval, and the open circle at 2 indicates that 2 is also not included in the interval. The line segment between the circles represents the range of values that satisfy the inequality.

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The value of x for the given triangle is 14 according to the question.

In triangle ABC, right-angled at B, let BM be the altitude from B to AC. Let CM be x.

Using the Pythagorean theorem in triangle ABC of the question:

[tex]AB^{2}[/tex] + [tex]BC^{2}[/tex] = [tex]AC^{2}[/tex]

Substituting AB = BM and BC = CM, we get:

[tex]BM^{2}[/tex] + [tex]CM^{2}[/tex] = [tex]AC^{2}[/tex]

Substituting the given values, we get:

[tex](2\sqrt{15}) ^{2}[/tex] +[tex]x^{2}[/tex] =[tex]16^{2}[/tex]

60 + [tex]x^{2}[/tex] = 256

[tex]x^{2}[/tex] = 196

x = 14

A line or segment that forms a straight angle or 90-degree angle with the provided line is said to be perpendicular to it. It is also known as a "orthogonal" or "normal" line.

We must first choose a point on the supplied line in order to determine the perpendicular to it. Then, a line or segment that traverses that point and is perpendicular to the specified line can be created.

The fact that the slopes of perpendicular lines are the negative reciprocals of one another is used to accomplish this. The slope of any line perpendicular to the provided line will be -1/m if the slope of the given line is m.

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The two skaters might collide at the points (1, 12) and (7, 0).

What are the collide points?

To find the points where the two skaters might collide, we need to find the values of x and y that satisfy both equations simultaneously.

Setting the two expressions for y equal to each other, we get:

-2x + 14 = -2x² + 14x

Simplifying this equation, we get:

2x² - 16x + 14 = 0

Dividing both sides by 2, we get:

x² - 8x + 7 = 0

This equation can be factored as:

(x - 1)(x - 7) = 0

Therefore, the possible values of x where the skaters might collide are x=1 and x=7.

To find the corresponding values of y, we can substitute each value of x into one of the original equations.

For x=1, we get:

y = -2(1) + 14 = 12

Therefore, one possible point of collision is (1, 12).

For x=7, we get:

y = -2(7)² + 14(7) = 0

Therefore, another possible point of collision is (7, 0).

Therefore, To find the points where the two skaters might collide, we need to find the values of x and y that satisfy both equations simultaneously.

Setting the two expressions for y equal to each other, we get:

-2x + 14 = -2x² + 14x

Simplifying this equation, we get:

2x² - 16x + 14 = 0

Dividing both sides by 2, we get:

x² - 8x + 7 = 0

This equation can be factored as:

(x - 1)(x - 7) = 0

Therefore, the possible values of x where the skaters might collide are x=1 and x=7.

To find the corresponding values of y, we can substitute each value of x into one of the original equations.

For x=1, we get:

y = -2(1) + 14 = 12

Therefore, one possible point of collision is (1, 12).

For x=7, we get:

y = -2(7)² + 14(7) = 0

Therefore, another possible point of collision is (7, 0).

Therefore, the two skaters might collide at the points (1, 12) and (7, 0).

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The answer of 2nd question Quadrilateral JUMP in a circle is  = Supplementary

What do you mean by Supplementary angle?

Supplementary angles are two angles whose measures add up to 180 degrees. In other words, if angle A and angle B are supplementary, then A + B = 180 degrees.

Supplementary angles are important in geometry and trigonometry, and they can be used to solve various problems involving angles and their measures. For example, if you know that two angles are supplementary and you know the measure of one of them, you can find the measure of the other by subtracting the measure of the known angle from 180 degrees.

According to question

Quadrilateral JUMP in a circle so opposite angle J and M is supplementary

∴ The sum of opposite angle of a circle Quadrilateral  is supplementary

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The area of the purse can be calculated using the formula for the area of a trapezoid. The purse (not including the handle) takes up 34 cm² in the magazine layout.

The formula states that the area of a trapezoid is equal to one half of the product of the length of the two parallel sides, multiplied by the height. Thus, the area of the purse can be calculated as:

Area = (1/2) x (11cm + 6cm) x 4cm

Area = (1/2) x (17cm) x 4cm

Area = 34 cm²

Therefore, the purse (not including the handle) takes up 34 cm² in the magazine layout.

It is important to note that the formula for the area of a trapezoid can be used in this instance because the purse has a shape of a trapezoid.

This is due to the fact that the line parallel to the 11cm base has a length of 6cm. The line is not parallel to the 4cm height and thus, the shape of the purse is a trapezoid and not a rectangle.

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Answer: To find the ratio of the cost of an 8-ounce box to a 16-ounce box of cereal, we can divide the cost of an 8-ounce box by the cost of a 16-ounce box:

8 oz: $12

16 oz: $20

The ratio of the cost of an 8-ounce box to a 16-ounce box of cereal is:

12/20 = 3/5

So the answer is 3:5.

Step-by-step explanation:

Answer:

The answer is A. Depreciation.

A cash budget is a financial statement that projects a company's future cash inflows and outflows. It is used to help the company manage its cash flow and avoid running out of money. The cash budget includes all of the company's expected cash receipts and payments, including sales, purchases, expenses, and taxes. Depreciation is not a cash flow, so it does not appear on a cash budget.

Depreciation is an accounting concept that allows companies to spread the cost of an asset over its useful life. It is not a cash expense, because the company does not actually pay out any money when it depreciates an asset. Instead, the company reduces the value of the asset on its balance sheet.

The cash budget is a valuable tool for businesses of all sizes. It can help businesses to plan for future cash needs, avoid running out of money, and make sound financial decisions.

Step-by-step explanation:

Answer:

Depreciation at a constant percent is exponential decay:V(t) = V0·(1-rate)tV(t) is the value at year t (we want t = 14 years)V0 is the starting value = $20,700rate is the depreciation rate expressed as a decimal = 0.05t = years = 14V(14) = $20700·(1 - 0.05)14Use your calculator to get the answer.  Round your answer to the nearest cent,  The units are $$.

Step-by-step explanation:

B. Government support for education decreasing by​ 1% per year is an example of exponential decay because the support decreases by the same percentage each year.

Exponential decay is a mathematical concept that describes the decrease of a quantity over time at a rate proportional to its current value. In other words, the amount by which the quantity decreases over a certain period of time is proportional to the current value of the quantity. This is often represented by an exponential function with a negative exponent, where the exponent is a function of time. The concept of exponential decay is used in many fields, including physics, chemistry, biology, and finance, among others.

Reasoning: It is because the support decreases by the same percentage each year. Exponential decay refers to a process in which a quantity decreases over time at a rate proportional to its current value. In this case, the government support is decreasing by a constant percentage each year, which is a characteristic of exponential decay.

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1.3.1 There are 380 pieces of 50 cents coins.

1.3.2 The total amount of cents in the money box are 23,400.

1.3.3 The amount in rands is 234.

The solution has been obtained by using unit conversion.

What is unit conversion?

Unit conversion is a multi-step procedure that requires multiplying or dividing by a numerical factor, or more specifically, a conversion factor. Furthermore, rounding and choosing the right number of significant digits may be required. Various metrics are measured using various conversion units.

1.3.1 Let the number of 50 cents coin be x.

We are given that total number of coins are 600.

This gives us an equation as x + 220 = 600.

So,

x = 600 - 220

x = 380

1.3.2 The total cents is given by the following expression

⇒ (20 * 220) + 50x

⇒ 4400 + (50 * 380)

⇒ 4400 + 19000

⇒ 23,400 cents

1.3.3 We know that 100 cents = 1 rand.

So, using unit conversion, we get

⇒ 1 cent = [tex]\frac{1}{100}[/tex] rands

⇒ 23400 cents =  [tex]\frac{1}{100}[/tex] * 23400 rands

⇒ 23400 cents = 234 rands

Hence, the required solutions have been obtained.

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The complete question has been attached below.

Answer:

2x + 3y

Step-by-step explanation:

= 3x + 2y - x + y

= 2x + 2y + y

= 2x + 3y

hope this helps

Answer:

I CANT SEE WHAT IT SAYS

Step-by-step explanation:

The number of inches the plant grew this week would be 8-x. As the length increased this week the length is substracted from this week to last week.

Subtraction (which is signified by the minus sign −) is one of the four arithmetic operations along with addition, multiplication and division. Subtraction is an operation that represents removal of objects from a collection. For example, in the adjacent picture, there are 5 − 2 peaches—meaning 5 peaches with 2 taken away, resulting in a total of 3 peaches.

Therefore, the difference of 5 and 2 is 3; that is, 5 − 2 = 3. While primarily associated with natural numbers in arithmetic, subtraction can also represent removing or decreasing physical and abstract quantities using different kinds of objects including negative numbers, fractions, irrational numbers, vectors, decimals, functions, and matrices.

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Answer: 222

Step-by-step explanation:

So you know 40% of x is 111

and we need to find 80%

80% is twice of 40%

so we multiply 111  by 2 and get 222

x=222

Step-by-step explanation:

2 hrs = 7200 seconds

       3 min 59 = 239 s    

    total seconds = 7439 s

42.195 km = 42159 m

42159 m / 7439s = 5.7 m/s

You could shade in the faces of the prism or add labels to identify different parts of the drawing.

What is Pentagonal ?

"Pentagonal" is an adjective that describes something that has five sides or angles. In geometry, a pentagon is a two-dimensional shape with five straight sides and five angles.

To draw a pentagonal prism, you'll need to follow these steps:

Draw identical pentagonal bases: Start by drawing two identical pentagons. Make sure they have the same size and shape. You can use a ruler and a protractor to help you draw the lines.

Draw five vertical lines: Connect each vertex of one pentagon to its corresponding vertex on the other pentagon using straight lines. These lines should be perpendicular to the base and have the same length. You should end up with five evenly spaced vertical lines.

Change any hidden lines to dashed lines: Identify any lines that won't be visible in the final drawing and change them to dashed lines. This will help to make the drawing easier to read and understand.

Add any additional details: Once you've completed the basic shape of the pentagonal prism, you can add any additional details or shading to make the drawing more realistic or interesting.

Therefore,  You could shade in the faces of the prism or add labels to identify different parts of the drawing.

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Answer:

y intercept = +4

slope = +2

domain = (-2,0)

range = (4,0)

Graph is increasing

x intercept = -2

Step-by-step explanation:

Line hits y axis at point 4

Slope is calculated by rise over run (2/1)

Domain is x,y listed

Range is y,x listed

Line is going up

Line hits x axis at -2

Hence, by multiplying the number of airports in California by a factor of three-quarters, we may get the number of airports in Georgia.

To find how many airports Georgia has, we need to use division. We can divide the total number of airports in California by 3 to find the number of airports in Georgia.

The key math word in the problem is "three times."

Let's say the number of airports in California is "C". Then, we can represent the number of airports in Georgia as "G," and we know that:

C = 3G

To solve for G, we can divide both sides of the equation by 3:

C/3 = G

Therefore, the number of airports in Georgia is equal to one-third of the number of airports in California.

The key math word in the problem is "three times."

We need to divide in order to determine the number of airports in Georgia. The number of airports in Georgia can be calculated by dividing the total number of airports in California by 3.

Let's say the number of airports in California is "C". Then, we can represent the number of airports in Georgia as "G," and we know that:

C = 3G

To solve for G, we can divide both sides of the equation by 3:

C/3 = G

Therefore, the number of airports in Georgia is equal to one-third of the number of airports in California.

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D. Reflection across the y-axis, translation 4 units to the right. sequence of transformation is most likely applied to figure QRSTU to form Q'R'S'T'U'.

What is transformation?

To determine the sequence of transformations applied to figure QRSTU to form Q'R'S'T'U', we can compare the corresponding vertices of the two pentagons:

Q and Q': Q' is to the right of Q and has a positive x-coordinate.

R and R': R' is to the left of R and has a negative x-coordinate.

S and S': S' is above S and has a positive y-coordinate.

T and T': T' is above T and has a positive y-coordinate.

U and U': U' is to the right of U and has a positive x-coordinate.

Based on these comparisons, it appears that the figure has been reflected across the y-axis and then translated 4 units to the right. Therefore, the most likely sequence of transformations applied to QRSTU to form Q'R'S'T'U' is:

D. Reflection across the y-axis, translation 4 units to the right.

What are vertices?

A vertex (plural: vertices) is a point where two or more line segments or curves meet. Vertices are the corner points of a polygon or the endpoints of a line segment or ray. In three-dimensional geometry, vertices are the corner points of a polyhedron or the endpoints of an edge.

Vertices are important in defining the properties of a shape, such as its angles, sides, and symmetry. They are also used in graph theory to represent points in a graph or network.

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Complete question is: D. Reflection across the y-axis, translation 4 units to the right. sequence of transformation is most likely applied to figure QRSTU to form Q'R'S'T'U'.

Answer:

it is better to buy brand B for both dish washing liquid and shoe polish.

Step-by-step explanation:

Answer:

Step-by-step explanation: