find the vertex
(x^2)-8x+14

Answer:

Step-by-step explanation:

a. Slope of RS = [tex]-\frac{7}{5}[/tex] and slope of adjacent to RS =  [tex]-\frac{5}{7}[/tex]

b. Length of RS  = [tex]\sqrt{74}[/tex] and Length of adjacent to RS = [tex]\sqrt{74}[/tex]

c. The parallelogram PQRS is Rhombus.

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. As a result, a parallelogram's opposite sides are parallel and congruent in length, and its opposite angles are similarly congruent.

[tex]Slope = \frac{(y_{2} -y_{1})}{(x_{2} -x_{1})}[/tex]

a. for the points R (-6, 6) and S (-1, -1)

Slope of RS = [tex]\frac{-1 - (+6)}{-1 - (-6)}[/tex] = [tex]-\frac{7}{5}[/tex]

Slope of RS = [tex]-\frac{7}{5}[/tex]

Slope of adjacent side (RQ, SP) to RS = [tex]\frac{6-1}{-6-1}[/tex] = [tex]\frac{5}{-7}[/tex]

Slope of adjacent to RS =  [tex]-\frac{5}{7}[/tex]

b. Length of a line = [tex]\sqrt{({x_{2}-x_{1})^{2} } + ({y_{2}-y_{1})^{2}}[/tex]

points R (-6, 6) and S (-1, -1)

Length of RS = [tex]\sqrt{({-1- (-6))^{2} } + ({-1-6})^{2}}[/tex] = [tex]\sqrt{74}[/tex]

Length of RS  = [tex]\sqrt{74}[/tex]

Length of adjacent to RS = [tex]\sqrt{({-6- 1))^{2} } + ({6-1})^{2}}[/tex] = [tex]\sqrt{74}[/tex]

Length of adjacent to RS = [tex]\sqrt{74}[/tex]

c. All sides are equal

PQ=QR=RS=SP=√74

So, diagonal PR = [tex]\sqrt{({-6- 6))^{2} } + ({-6-6})^{2}}[/tex] = [tex]12\sqrt{2}[/tex]

and  diagonal QS = = [tex]\sqrt{({-1- 1))^{2} } + ({-1-1})^{2}}[/tex] = [tex]2\sqrt{2}[/tex]

Diagonals are unequal then parallelogram PQRS is Rhombus.

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From the quadratic equation, we found the new dimensions:

Length =  14.85 feet

Width = 18.85 feet.

What is a quadratic equation?

The polynomial equations of degree two in one variable of type

f(x) = ax² + bx + c = 0 and with a, b, c, ∈ R and a ≠ 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" is for the absolute term of

f (x).

The current dimensions of the farm are 10 feet by 14 feet.

Length l = 10 feet

Width w = 14 feet

Area a = l * w = 10 * 14 = 140 sq. feet.

Now the new area is doubled.

A = 2a = 2 * 140 = 280 sq.feet

The new dimensions are:

L = l + x = 10 + x

W = w + x = 14 +x

A = (10+x)(14+x)

280 = 140 + 10x + 14x + x²

x² + 24x - 140 = 0

This is a quadratic equation.

Solving the equation, we get

x = 4.85, -28.85

Neglecting the negative value, we get the value of x as 4.85.

Therefore from the quadratic equation, we found the new dimensions:

L = 10 + 4.85 = 14.85 feet

W = 14 + x = 14 + 4.85 = 18.85 feet.

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Answer:

2/(1/4) = 8 1/4th gallons to fill the container and 1/8 * x = 8/8 (x=8) times you can fill the tank with 1/4th gallon

Step-by-step explanation:

First let's answer the first part of the question: what fraction of the container is filled?

If there is 1/4 a gallon of water in the container which holds 2 gallons, we can show this by adding 0/4 to 1/4 to get 1/8 as the fraction of the container filled. (Or just double the denominator for both gallons instead of 1)

To represent this with a multiplication equation, we will take the holding of the container which is 2 gallons

1/8 times x = how many times you can fill the container with 1/4 gallon of water (which is 8 total)

and then our division which is

2 divided by 1/4 = how many shares of water can fit in the container

I hope this helps :)

Answer:

Here'd how to do problems like these. For example with #1 in your image (below)

Step-by-step explanation:

The sum of the series with the general terms k + 2 from k= 1 to k= 5

All you have to do is plug in all the numbers WITHIN the interval so in this case it would be 1,2,3,4, &5. After you plug in each of those numbers into the equation, you add them up.

Like so:

(1) + 2= 3

(2) + 3= 5

(3) + 3 = 6

(4) + 3 = 7

(5) + 3 = 8

3+5+6+7+8= 30

The present value is $9,824.56.

Future value is the sum of the present value and the interest earned. When an amount earns a simple interest, it means that the present value grows at a linear rate.

Future value = simple interest + present value

Present value = future value - simple interest

Simple interest in a linear function of the present value, the interest rate and the duration of the investment.

Simple interest = present value x interest rate x time

14,000 - p = p x 0.085 x 5

14,000 - p = 0.425p

14,0000 = 1.425p

p = 14,000 / 1.425

p = $9,824.56

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the minimum number of degrees that may be rotated to satisfy rotational symmetry in this figure is 60°.

What is rotational symmetry?

Rotational symmetry is a type of symmetry where a shape or object can be rotated by a certain angle and still appear exactly the same as it did before the rotation. The smallest angle of rotation for which the shape or object appears the same is called the angle of rotational symmetry or the order of the rotational symmetry.

In light of the posed query

There is rotational symmetry in the image.

This picture can be seen as a circle. A whole circle has 360 degrees.

Six wings cover the figure.

360/6

=60°

Hence, the minimum number of degrees that may be rotated to satisfy rotational symmetry in this figure is 60°.

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Answer:

to find the height of the storage unit, we can use the formula for volume:

Volume = length x width x height

We know that the volume needs to be 400 cubic ft, the width is 10ft and the length is 8ft. So, we can plug in these values and solve for the height:

400 = 8 x 10 x height

400 = 80 x height

height = 400/80

height = 5 ft

Therefore, the height of the storage unit needs to be 5 ft.

She has 7 gallons of gas after driving for 2 hours.

What is Subtraction?

Subtraction is a mathematical operation that involves finding the difference between two numbers or quantities. It is the inverse of addition, which means that it is the opposite process of adding numbers.

In subtraction, a number or quantity (called the subtrahend) is subtracted from another number or quantity (called the minuend), resulting in the difference. The symbol used for subtraction is "-" and the resulting value is called the remainder or difference.

Katie had 12 gallons of gas.

She used 2 1/2 gallons of gas each hour.

Now, She drove 2 hours.

So, gallon of gas use for 2 hours = 2 × 2 1/2

                                                       = 2 × 5/2

                                                       = 5 gallons of gas.

Now, Gallons of gas left after 2 hours

        = total gallons of gas - Gallons used for 2 hours

        = 12 - 5

        = 7.

Hence, She is left with 7 (12-5) gallons of gas.

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Answer: 32 times

Step-by-step explanation:

there are 4 laps on a track to reach a mile

4x8=32

Correct option is D, The perimeter of the trapezoid J K L M is units 9 + StartRoot 2 EndRoot + StartRoot 5 EndRoot units (= 9 + √5 + √2 units. )

The length of a two-dimensional shape's boundary is its perimeter. It is frequently referred to as the sum of the lengths of the sides of the object. Such shape's perimeter is equal to the side lengths added together algebraically. We have formulas for the various geometric shapes.

The vertices of KLMN an isosceles trapezoid are (-7,4), (-4,4), (-2,3), (-8,3).

perimeter of trapezoid JKLM = sum of sides

Using distance formula [tex]\sqrt{(x2-x2)^2 + (y2 - y1)^2}[/tex],

Distance between the sides of trapezoid is,

(-7,4), (-4,4) =

[tex]\sqrt{(-7 + 4)^2 + (4 - 4)^2}\\= \sqrt{9}\\= 3 units[/tex]

(-4,4), (-2,3) =

[tex]\sqrt{(-2 + 4)^2 + (3 - 4)^2}\\= \sqrt{5} units[/tex]

(-2,3), (-8,3) =  

[tex]\sqrt{(-8 + 2)^2 + (3-3)^2}\\= \sqrt{6}^2\\= 6 units[/tex]

(-7,4), (-8,3)

[tex]\sqrt{(-8 +7)^2 + (3-4)^2}\\= \sqrt{-1^2 + -1^2}\\= \sqrt 2 $ units $[/tex]

So, the sum of sides will be -

= 3 + √5 + 6 + √2

= 9 + √5 + √2 units.

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Answer:

its D

Step-by-step explanation:

i took the test on edg

Answer:

Step-by-step explanation:

[tex]27=3\times 3 \times 3=3^3[/tex]

ordered: [tex]3^3[/tex]

Answer: what's so urgent?

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want the measures of the angles (5x+10°) and (10x+50°) that are divisions of an angle marked as a right angle.

The angle addition theorem tells you the whole is the sum of its parts. Here, the right angle in the diagram is divided into two parts, marked 5x+10° and 10x+50°. The measure of the right angle is the sum of these parts:

  90° = (5x +10°) +(10x +50°)

  30° = 15x . . . . . . . subtract 60°

  2° = x . . . . . . . . . divide by 15

Using this value for x, we find the angle measures to be ...

  5x+10° = 5(2°) +10° = 10° +10° = 20°

  10x+50° = 10(2°) +50° = 20° +50° = 70°

In summary, ...

The terms in the numerator and simplify the fraction, giving us: -2x² - 1/(2x + 1)

A numerator is the part of a fraction that is above the line and indicates how many parts of a whole are being considered. It is the number that is being divided.

The first step in solving this problem is to factor out the numerator. Using the distributive property, we can rewrite the numerator as:

(-3x² + 6x³ - 4 - x) = (-3x² + 6x³ - 4) - x

Now, we can factor out -3x² from the first two terms, giving us:

(-3x² + 6x³ - 4) - x = -3x²(1 + 2x - 4/3x²) - x

We can now divide the numerator and denominator by the common factor of -3x², giving us:

(-1 - 2x + 4/3x²) - (x/(-3x²)) ÷ (2x + 1)

By dividing the numerator and denominator by -3x², we can now cancel out the -3x² terms, leaving us with:

(-1 - 2x + 4/3x²) - (1/3) ÷ (2x + 1)

The next step is to simplify the fraction. To do this, we must multiply the numerator and denominator by the reciprocal of the denominator. In this case, the reciprocal is -1/(2x + 1) giving us:

[(-1 - 2x + 4/3x²) - (1/3)] × (-1/(2x + 1))

Simplifying the numerator yields:

(2x + 1 - 4/3x² + 1/3) × (-1/(2x + 1))

Finally, we can combine the terms in the numerator and simplify the fraction, giving us: -2x² - 1/(2x + 1).

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Answer:

it would be 70months when rounded up.

Step-by-step explanation:

if not then 69months 7days

Combine like terms to create an equivalent expression.[tex]\frac{9}{8} m + \frac{9}{10} - 2m - \frac{3}{5}[/tex] then we formed the equation is [tex]= \frac{1}{8} m - \frac{3}{50}[/tex]

When two expressions can be reduced to a single third expression or when one of the statements can be expressed in the same way as the other, they are said to be equivalent. When values are replaced for the variables and both expressions yield the same result, you may also tell if expressions are equal.

The final response is 2 x - 2; alternatively, you might write 2 x - 3. The ultimate response is -2 point to the right. You could see that choice d is right in this case.

In this expression, we have two terms with the variable m: [tex]9/8 m[/tex] and [tex]-2m[/tex]. We can combine these by subtracting [tex]2m[/tex] from [tex]9/8 m[/tex], which gives us [tex]1/8 m[/tex].

We also have two constant terms: [tex]9/10[/tex] and [tex]-3/5[/tex]. We can combine these by adding them, which gives us [tex]-3/50[/tex].

Putting it all together, we get:

[tex]\frac{9}{8} m + \frac{9}{10} - 2m - \frac{3}{5} = \frac{1}{8} m - \frac{3}{50}[/tex]

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Answer:-7/8m+3/10

Step-by-step explanation:

Therefore, the family drank juice at a rate of 0.8 gallons per week.

Percent is a way of expressing a fraction or a decimal as a fraction of 100. It is denoted by the symbol "%". For example, the fraction 3/4 can be written as 75% and the decimal 0.5 can be written as 50%. Percentages are commonly used in everyday life to express values such as discounts, interest rates, and success rates.

Here,

To find the rate at which the family drank juice, we need to divide the total amount of juice consumed by the time it took to consume it.

The total amount of juice consumed is 4 gallons. The time period is 5 weeks.

So, the rate at which the family drank juice is:

4 gallons ÷ 5 weeks = 0.8 gallons per week

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Answer:

? ≈ 58°

Step-by-step explanation:

since all 3 sides of the triangle are given, we can use any of the 3 trigonometric ratios.

using the sine ratio

sin ? = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{45}{53}[/tex] , then

? = [tex]sin^{-1}[/tex] ( [tex]\frac{45}{53}[/tex] ) ≈ 58° ( to the nearest degree )

Answer:

58°

Step-by-step explanation:

[tex]sin(?)=\frac{45}{53}[/tex]

[tex]?=sin^{-1} (\frac{45}{53})[/tex]

[tex]?=sin^{-1} (0.8491)[/tex]

[tex]?=58.1^{0}[/tex]

Hope this helps.

Answer: a) To find the number of working days on which under 18,000 bottles are filled, we need to calculate the z-score for this value:

z = (18,000 - 20,000) / 2000 = -1

Using a standard normal distribution table or calculator, we find that the probability of a value being less than -1 standard deviation is approximately 0.1587. Therefore, the approximate number of working days on which under 18,000 bottles are filled is:

0.1587 x 260 ≈ 41

b) To find the number of working days on which over 16,000 bottles are filled, we need to calculate the z-score for this value:

z = (16,000 - 20,000) / 2000 = -2

Using a standard normal distribution table or calculator, we find that the probability of a value being less than -2 standard deviations is approximately 0.0228. Therefore, the approximate number of working days on which over 16,000 bottles are filled is:

0.0228 x 260 ≈ 6

c) To find the number of working days on which between 18,000 and 24,000 bottles are filled, we need to calculate the z-scores for these values:

z1 = (18,000 - 20,000) / 2000 = -1

z2 = (24,000 - 20,000) / 2000 = 2

Using a standard normal distribution table or calculator, we find that the probability of a value being less than -1 standard deviation is approximately 0.1587, and the probability of a value being less than 2 standard deviations is approximately 0.9772. Therefore, the approximate number of working days on which between 18,000 and 24,000 bottles are filled is:

(0.9772 - 0.1587) x 260 ≈ 236

Step-by-step explanation:

Kayla has to purchase [tex]6[/tex] packs of cupcakes, and the dressmaker can make [tex]5[/tex] copies of the pattern.

Provide a discount on a third element in exchange for the first item's purchase, also known as purchase with purchase. Although it may also encourage sales of the side product, its primary goal is to increase sales of the main products.

The purchase accounts is a nominal account, and as per nominal account rules, business costs are debited. All purchases made on credit are noted in the purchase diary, whilst purchases made with cash are noted in the cash book.

number of packs [tex]=[/tex] (total number of cupcakes) / (number of cupcakes in each pack)

We know that there are [tex]34[/tex] people attending the party

total number of cupcakes [tex]= 34[/tex]

Plugging this into the formula above, we get:

number of packs [tex]= 34 / 6 = 5.67[/tex]

Therefore, Kayla should buy [tex]6[/tex] packs of cupcakes.

number of pattern cuts [tex]=[/tex] (total amount of material) / (amount of material used for each pattern)

We know that the seamstress has [tex]4.5m[/tex] of material and each pattern uses [tex]0.8m[/tex] of material, so we can plug these values into the formula above:

number of pattern cuts [tex]= 4.5 / 0.8 = 5.625[/tex]

Therefore, the seamstress can cut out the pattern [tex]5[/tex] times.

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Therefore, the general solution for the differential equation dy/dx cosx=ysinx+sin113x is y = log |sin(x) / sin(113x)| + C, where C is an arbitrary constant.

A differential equation explains the unknown derivative or derivatives of a function. Example: Think about the equation. The equation d y d x = x sin represents the derivative of an unknown function.

We can solve this differential equation by using separation of variables.

First, we'll rearrange the equation to isolate the y term on one side:

cos x = y sin x + sin 113x

cos x - sin 113x = y sin x

y = (cos x - sin 113x) / sin x

Now we can integrate both sides with respect to x:

∫dy = ∫(cos x - sin 113x) / sin x dx

Using integration by parts, we can integrate the second term on the right side:

∫dy = ∫cos x / sin x dx - ∫sin 113x / sin x dx

The first term on the right side can be integrated using substitution:

u = sin x, du/dx = cos x dx

∫cos x / sin x dx = ∫du/u = log |u| + C1 = log |sin x| + C1

The second term on the right side can be rewritten as:

∫sin 113x / sin x dx = - ∫sin 113x / sin 113x cos x dx

= - ∫csc x cos 113x dx

Using substitution again:

u = sin 113x, du/dx = 113 cos 113x dx

∫csc x cos 113x dx = - ∫du/u = - log |sin 113x| + C2

y = log |sin x| - log |sin 113x| + C

Simplifying:

y = log |sin(x) / sin(113x)| + C

Therefore, the general solution for the differential equation dy/dx cosx=ysinx+sin113x is y = log |sin(x) / sin(113x)| + C, where C is an arbitrary constant.

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Answer:

D-The data in Sample B is clustered around the center where Sample A is more spread out

Step-by-step explanation:

maybe sorry if wrong

Answer:

The total length of the 30 pencils in centimeters is:

30 x 16 = 480 cm

To convert centimeters to meters, we divide by 100:

480 cm / 100 = 4.8 m

Therefore, the combined length of the 30 pencils is 4.8 meters.

Step-by-step explanation:

Answer:

If 1, -5, and -1/2 are zeros of a polynomial function, then the factors of the polynomial are:

(x - 1), (x + 5), and (2x + 1)

To find the polynomial function, we multiply these factors together and simplify:

(x - 1)(x + 5)(2x + 1)

= (x^2 + 4x - 5)(2x + 1)

= 2x^3 + 9x^2 - 6x - 5

Therefore, the polynomial function of the least degree with integral coefficients that has the zeros 1, -5, and -1/2 is:

f(x) = 2x^3 + 9x^2 - 6x - 5

Based on the congruent angles theorem, the value of the variable x in the circle is 40 degrees

An angle is a figure formed by two rays that share a common endpoint, called the vertex of the angle

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

The circle with center O

In the figure, angles with the same marks are congruent angles

Using the above as a guide, we have the following:

x =40

Hence, the value of x is 40 degrees

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Answer: 1. 8.94

2. 13

3.  True

Step-by-step explanation:

Answer:

  g(x) = 2x²

Step-by-step explanation:

You want the vertical dilation of function f(x) = x² by a factor of 2.

Any function is dilated vertically by a factor of k by multiplying the function value by k:

  g(x) = k·f(x) . . . . . . dilates f(x) vertically by a factor of k

  g(x) = 2x² . . . . . . dilates f(x) = x² vertically by a factor of 2