Given the diagram below, if CD = x + 4,
DE = 2x + 7, and CE = 7x-25, what is the value
of x?

Answer:

20 glasses a day

Step-by-step explanation:

2.5litres equals 2500millilitres

2500÷125=20

Answer: 12 inches

Step-by-step explanation:

Answer: 15 cm

Step-by-step explanation:

Answer:

the answer is D

Step-by-step explanation:

Because the point of x=4 is passed through the point (0,4).

By definition of tangent,

tan(A - π/4) = sin(A - π/4) / cos(A - π/4)

Expand the numerator and denominator using the angle sum identities for sin and cos:

tan(A - π/4) = (sin(A) cos(π/4) - cos(A) sin(π/4)) / (cos(A) cos(π/4) + sin(A) sin(π/4))

Divide through everything on the right by cos(A) cos(π/4):

tan(A - π/4) = (sin(A) / cos(A) - sin(π/4) / cos(π/4)) / (1 + (sin(A) sin(π/4)) / (cos(A) cos(π/4)))

Simplify the sin/cos terms to tan:

tan(A - π/4) = (tan(A) - tan(π/4)) / (1 + tan(A) tan(π/4))

tan(π/4) = 1, so we're left with

tan(A - π/4) = (tan(A) - 1) / (1 + tan(A))

Replace tan(A) with -√15:

tan(A - π/4) = (-√15 - 1) / (1 - √15)

Then the last option is the correct one.

Answer:

Darwin is not correct.

Step-by-step explanation:

3x+4(2x+5) = 6x+5x+5

3x+8x+20 = 11x + 5

11x+20 ≠ 11x+5

Answer:

\(x= \dfrac 12 \left( -3 +i5\sqrt 3\right)\\\\x= \dfrac 12 \left( -3 -i5\sqrt 3\right)\)

Step-by-step explanation:

\(~~~~~~x^2 +3x +21 = 0\\\\\implies x^2 +3x = -21\\\\\implies x^2 + 2\cdot \dfrac 32 \cdot x + \left( \dfrac 32 \right)^2 = -21 + \left( \dfrac 32 \right)^2\\\\\implies \left(x + \dfrac 32 \right)^2 = -21+\dfrac 94\\\\\implies \left(x + \dfrac 32 \right)^2 = -\dfrac{75}4\\\\\implies x+ \dfrac 32 = \pm\sqrt{-\dfrac{75}4 \right)\\\\\implies x + \dfrac 32 = \pm i \dfrac{5\sqrt 3}{2}\\\\\implies x = -\dfrac 32 \pm i \dfrac {5\sqrt 3}2\\\\\implies x = \dfrac 12 \left( -3 \pm i5\sqrt 3\right)\)

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

The axis of symmetry of the function f(x) = x² - 6x-1 is equal to 3.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry, Xmin = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

By substituting the parameters, we have the following:

Axis of symmetry, Xmin = -b/2a

Axis of symmetry, Xmin = -(-6)/2(1)

Axis of symmetry, Xmin = 6/2

Axis of symmetry, Xmin = 3.

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Answer:

18

Step-by-step explanation:

First, I'm assuming AB=4=4x-2 was a typo and it's supposed to be AB = 4x - 2

AB=BC

AB = 4x - 2 BC = 3x + 3

4x - 2 = 3x + 3

Solve for x Add 2 to each side

4x - 2 = 3x + 3

4x - 2 + 2 = 3x + 3 + 2

4x = 3x + 5 Subtract 3x from each side.

4x - 3x = 3x- 3x + 5

4x - 3x = 5

x = 5

Now plug back in to the original equations

AB = 4x - 2                  BC = 3x + 3

AB = 4 (5) - 2               BC = 3(5) + 3

AB = 20 - 2                  BC = 15 + 3

AB = 18                        BC = 18

So AB is 18

Answer:

a) The angular velocity is 0.4π radians/second ⇒1.25664 radians/second

b) The wheel travels 124.4071 meters in 5 minutes ⇒ 39.6π meters

Step-by-step explanation:

The angular velocity ω = 2 π n ÷ t, where

The distance that moving by the angular velocity is d =  ω r t, where

a)

∵ A wheel completes 12 revolutions in 1 minute

∴ n = 12

∴ t = 1 minute

→ Change the minute to seconds

∵ 1 minute = 60 seconds

∴ t = 60 seconds

→ Substitute n and t in the rule above

∵ ω = 2 (π) (12) ÷ 60

∴ ω = 24π ÷ 60

∴ ω = 0.4π radians/second

∴ The angular velocity is 0.4π radians/second ⇒1.25664 radians/second

b)

→ To find the distance in 5 minutes multiply ω by the radius by the time

∵ The wheel has a radius of 33 cm

∴ r = 33 cm

→ Change it to meter

∵ 1 m = 100 cm

∴ r = 33 ÷ 100 = 0.33 m

∵ t = 5 minutes

→ Change it to seconds

∴ t = 5 × 60 = 300 seconds

→ Substitute them in the rule of the distance above

∵ d = 0.4π (0.33) (300)

∴ d = 39.6π meters ⇒ 124.407 meters

∴ The wheel travels 124.4071 meters in 5 minutes ⇒ 39.6π meters

Answer:

Table D

Step-by-step explanation:

I have all of the tables listed below and the correct one circled! I used to tutor my cousin about this topic!

I hope this helps and please feel free to comment, ask questions, give feedback, and correct me if I am wrong!

Have a great day!

:)

The 4th table in the option is the correct one.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Yolanda saves all the money from a regular baby-sitting job. The money in her savings account is increasing according to the equation y = 6x + 50, where x = number of hours worked and y = savings in dollars.

The given equation is y = 6x + 50

Put x = 0

y = 50

Put x = 5

y = 80

Put x = 10

y = 110

Put x = 15

y = 140

Creating the table,

                 x                                                                 y

                 0                                                                50

                 5                                                                80

                 10                                                               110

                 15                                                               140

Hence, we get the table.

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On solving the provided question ,we can say that The statement "The number of new clients (x) is 149% of the number of old clients (y)" can be written mathematically as: x = 1.49y

A sequence is a grouping of "terms," or integers. Term examples are 2, 5, and 8. Some sequences can be extended indefinitely by taking advantage of a specific pattern that they exhibit. Use the sequence 2, 5, 8, and then add 3 to make it longer. Formulas exist that show where to seek for words in a sequence. A sequence (or event) in mathematics is a group of things that are arranged in some way. In that it has components (also known as elements or words), it is similar to a set. The length of the sequence is the set of all, possibly infinite, ordered items. the action of arranging two or more things in a sensible sequence.

The statement "The number of new clients (x) is 149% of the number of old clients (y)" can be written mathematically as:

x = 1.49y

-1.49y + x = 0

-149y + 100x = 0

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The linear equation in the required form is: x - 1.49y = 0

What is linear equation?

A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:

y = mx + b

Let's start by assigning variables to the given information. We are told that "the number of new clients (x) is 149% of the number of old clients (y)."

Using this information, we can write:

x = 1.49y

To write this equation in the form ax + by = c, we need to move all the variables to one side of the equation and simplify.

Subtracting 1.49y from both sides, we get:

x - 1.49y = 0

So the linear equation in the required form is:

x - 1.49y = 0

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The solution of the system of linear equations, is (1.167, 3.667).

Given that the system of linear equations, y = -2x+6 and y = 4x - 1, we need to find the solution for the same,

y = -2x+6............(i)

y = 4x - 1.......(ii)

Equating the equations since the LHS is same,

-2x+6 = 4x-1

6x = 7

x = 1.167

Put x = 1.16 to find the value of y,

y = 4(1.16)-1

y = 4.66-1

y = 3.667

Therefore, the solution of the system of linear equations, is (1.167, 3.667).

You can also find the solution using the graphical method,

Plot the equations in the graph, the point of the intersection of both the lines will be the solution of the system of linear equations, [attached]

Hence, the solution of the system of linear equations, is (1.167, 3.667).

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Answer:

x = -1,375

y = -5

Step-by-step explanation:

{-8x + y = 6, / : (-1)

{-8x + 3y = -14;

Multiply the first equation by -1, so that we could eliminate 8x:

+ {8x - y = -6,

{-8x + 3y = -14;

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

4y = - 20 / : 4

y = -5

Now, make x the subject from the first equation (you can do it from the 2nd one instead):

8x = -6 + y / : 8

x = -0,75 + 0,125y

x = -0,75 + 0,125 × (-5) = -0,75 - 0,625 = -1,375

Answer:

Step-by-step explanation:

Lets assume that Kyle fill "a" 10-oz cups of coffee, "b" 14-oz cups of coffee and "c" 20 oz cups of coffee.

a + b + c = 16     (1)

10*a + 14*b + 20*c = 224       (2)

0.95*a + 1.15*b + 1.50*c = 18.60    (3)

Now, multiplying equation (1) by 10 and subtracting it from equation (2), we get

4b + 10c = 64  (4)

Again, multiplying equation (1) by 0.95 and substracting it from equation (3), we get,

0.2b + 0.55c = 3.4    (5)

Now,

Multiplying equation (5) by 20 and subtracting it from equation (4), we get

-c = -4,

Hence, c= 4

Putting this value in equation (4),

4b + 40 = 64

Hence, 4b = 24

So, b = 6

Again, putting the values of b and c in equation (1),

a + 6 + 4 = 16

Thus,

a = 6

Hence, the solution is

a = 6, 10oz cups of coffee

b = 6, 14 oz cups of coffee

c = 4, 20 oz cups of coffee

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Monthly Mortgage Payment is $495.88

Mortgage is a long-term amortized loan where loan is provided to buy certain capital asset and pay back total sum due in small periodic annuities. In Mortgage title of asset lies with lender and passes to borrower after complete mortgage payment.

Hence,

Mortgage Amount is $77,000

Monthly Payment for each $1,000 is $6.44

Monthly Mortgage Payment is $495.88

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Answer:

(1,5)

Step-by-step explanation:

x:

6-5=1

y:

7-2=5

This statement in the article is wrong because $2.69 is not the mean price ($2.81)

The prices from 5 gas stations surveyed are given as:

$2.79, $2.99, $2.69, $2.89, and $2.69.

There are no outliers in the dataset

So, the dataset can be summarized by the mean

The mean is

Mean = Sum/Count

So, we have

Mean = ($2.79+ $2.99+ $2.69+ $2.89+$2.69)/5

Evaluate

Mean = 2.81

The article quoted $2.69 as the typical price

This statement in the article is wrong because $2.69 is not the mean price ($2.81)

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Step-by-step explanation:

a) The x-coordinates at which f has critical values can be found by looking at the x-coordinates of the points where the graph of f' changes from increasing to decreasing or vice versa. These are the points where the graph of f' crosses the x-axis.

Based on the graph of f', we can see that the critical points occur at x = -2, -1, and 2. To determine if these are relative minimum, relative maximum, or neither, we need to examine the second derivative of f. If the second derivative is positive at a critical point, then the point is a relative minimum. If the second derivative is negative at a critical point, then the point is a relative maximum. If the second derivative is zero at a critical point, then it's neither.

b) The graph of f is concave up when the second derivative is positive, and the graph of f is decreasing when the first derivative is negative. Based on the graph of f', we can see that the graph of f is concave up on the open intervals (-3,-2) and (1,2) and decreasing on the open intervals (-infinity,-3) and (-2,-1) U (2,4) U (infinity,4)

c) The x-coordinates of all points of inflection on the graph of f are the points where the concavity of the graph changes. We can see that a point of inflection occurs at x = -1 and x = 2

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Part a: The data points appear to follow an exponential pattern. This is because the balance is increasing at a rate that is proportional to the current balance.

Part b: The equation of the best fit is y = 50(1.06)^x. This can be found using a variety of methods, including graphing the data points and fitting a curve to them, or using a statistical software package.

Part c: When x = 32, y = 50(1.06)^32 = $2,499.82.

Years since 1990, x 0 5 10 15 20 25 30

Balance, y $50 $62.31 $77.65 $96.76 $120.59 $150.27 $187.27 $2,499.82

The equation of the fitted curve is y = 50(1.06)^x.

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so the idea being, we have a system of equations of two variables and 4 equations, each one rendering a line, for this case these aren't equations per se, they're INEquations, so pretty much the function will be the same for an equation but we'll use > or < instead of =, but fairly the function is basically the same, the behaviour differs a bit.

we have a line passing through (-6,0) and (0,8), side one

we have a line passing through the x-axis and -6, namely (-6,0) and the y-axis and -4, namely (0,-4), side two

we have a line passing through (0,-4) and (6,4), side three

now, side four is simply the line connecting one and three.

the intersection of all four lines looks like the one in the picture below, so what are those lines with their shading producing that quadrilateral?

well, we have two points for all four, and that's all we need to get the equation of a line, once we get the equation, with its shading like that in the picture, we'll make it an inequality.

\((\stackrel{x_1}{-6}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-6)}}} \implies \cfrac{8 -0}{0 +6} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4}{3}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{ \cfrac{4}{3}}(x-\stackrel{x_1}{(-6)}) \implies y -0 = \cfrac{4}{3} ( x +6) \\\\\\ y=\cfrac{4}{3}x+8\hspace{5em}\stackrel{\textit{side one} }{\boxed{y < \cfrac{4}{3}x+8}}\)

\(\rule{34em}{0.25pt}\\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-6)}}} \implies \cfrac{-4 -0}{0 +6} \implies \cfrac{ -4 }{ 6 } \implies - \cfrac{2}{3}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{- \cfrac{2}{3}}(x-\stackrel{x_1}{(-6)}) \implies y -0 = - \cfrac{2}{3} ( x +6) \\\\\\ y=-\cfrac{2}{3}x-4\hspace{5em}\stackrel{\textit{side two} }{\boxed{y > -\cfrac{2}{3}x-4}} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(\stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{0}}} \implies \cfrac{4 +4}{6 -0} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4}{3}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{4}{3}}(x-\stackrel{x_1}{0}) \implies y +4 = \cfrac{4}{3} ( x -0) \\\\\\ y=\cfrac{4}{3}x-4\hspace{5em}\stackrel{ \textit{side three} }{\boxed{y > \cfrac{4}{3}x-4}} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\((\stackrel{x_1}{6}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{8}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{6}}} \implies \cfrac{ 4 }{ -6 } \implies - \cfrac{2}{3}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- \cfrac{2}{3}}(x-\stackrel{x_1}{6}) \\\\\\ y=-\cfrac{2}{3}x+8\hspace{5em}\stackrel{ \textit{side four} }{\boxed{y < -\cfrac{2}{3}x+8}}\)

now, we can make that quadrilateral a trapezoid by simply moving one point for "side four", say we change the point (0 , 8) and in essence slide it down over the line to  (-3 , 4).  Notice, all we did was slide it down the line of side one, that means the equation for side one never changed and thus its inequality is the same function.

now, with the new points for side for of (-3,4) and (6,4), let's rewrite its inequality

\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{(-3)}}} \implies \cfrac{4 -4}{6 +3} \implies \cfrac{ 0 }{ 9 } \implies 0\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{ 0}(x-\stackrel{x_1}{(-3)}) \implies y -4 = 0 ( x +3) \\\\\\ y=4\hspace{5em}\stackrel{ \textit{side four changed} }{\boxed{y < 4}}\)

Answer: (1,5)

Analysis = \(\frac{1}{2}(2,10)\)

\(=(\frac{1}{2}\times2,\frac{1}{2}\times10)\)

\(=(1,5)\)

I hope this helps you :D

Answer: 4

Step-by-step explanation:

Answer:4

2+2=4 if I have two apples and pick up two more I now have 4 total

1. d    2. a     3. c     4. b

\(1.d\ \{The\ intersection\ of\ three\ high\ lines\}\)

\(2.\ a\)

\(3.\ C\)

\(4.\ b\ \{The\ intersection\ of\ three\ angular\)

       \(bisectors\}\)

I hope this helps you

:)

Answer:

Step-by-step explanation:

Various centers are defined for a triangle, depending on how they're constructed. Here, you're asked to match the construction with the name.

__

The orthocenter is the intersection of the altitudes of the triangle. Each altitude intersects a vertex and is orthogonal to the opposite side. The orthocenter will not be inside the triangle if the triangle is obtuse. The orthocenter of a right triangle is the right-angle vertex.

Figure D depicts the intersection of altitudes.

__

The incenter is the center of an inscribed circle of a triangle. The incenter must be the same distance from each side, so will be at the point of intersection of the angle bisectors. It always lies inside the triangle.

Figure B depicts the intersection of angle bisectors.

__

The centroid is the "center of gravity" of the triangle, the point at which the triangle could be balanced. Each median divides the triangle into two equal areas, so the intersection of medians marks a spot with equal area (weight) in every pair of opposite directions.

Figure C depicts the intersection of medians.

__

The circumcenter is the center of a circle that circumscribes the triangle. It is equidistant from the three vertices, so lies on the intersection of the perpendicular bisectors of the sides. It will lie outside the triangle for obtuse triangles. It is the midpoint of the hypotenuse of a right triangle.

Figure A depicts the intersection of perpendicular bisectors of the sides.