If point d is placed on AC how will the measure of DAB relate to the measure of CAB

When we simplify (3 + √5)(3 + √2), the result obtained is:

9 + 3√2 + 3√5 + √10

a√b × c√d = (a × c)√(b × d)

(3 + √5)(3 + √2)

Expand by clearing the bracket

3(3 + √2) + √5(3 + √2)

9 + 3√2 + 3√5 + √10

Thus,

(3 + √5)(3 + √2) = 9 + 3√2 + 3√5 + √10

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Answer:

(-2, -4)

Step-by-step explanation:

You can complete the square of the equation to get

y+(4/2)^2 = x^2+4x+(4/2)^2

y+4 = x^2 + 4x + 4

y+4 = (x+2)^2

y = (x+2)^2 - 4

This gives the form y = a(x-h)^2 + k where (h, k) is the vertex of the equation. You can also arrive at the same conclusion by making some observations of the equation. (x+2)^2 minimum value is going to be 0 since and negative values resulting from x+2 is going to become positive because of the square. So the minimum value is when x+2 is 0 or when x is equal to -2 and when it's at that minimum value of 0 it's going to have 4 subtracted from it which gives the vertex of (-2, -4)

In total 180 chairs are ordered for the cost $6000.

The total cost of chairs=$6,000.

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Let x be the chairs ordered each at $20 and y be the chairs ordered each at $40.

Then equation will be 20x+40y=6000-------(1)

Given that, twice as many $20 chairs as $40 chairs were ordered.

That is 2x=y⇒2x-y=0--------(2)

Multiply equation (2) by 40.

That is 80x-40y=0--------(3)

By adding equation (2) and (3) we get

20x+40y+80x-40y=6000

⇒100x=6000

⇒x=60

Substitute x=60 in equation (2)

That is, 2x=y

⇒y=120

Total number of chairs=x+y=60+120=180 chairs.

Hence, in total 180 chairs are ordered for the cost $6000.

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Answer:

The function h(x) = -5√x is decreasing on the interval (–∞, 0) is true, Option A is correct.

A relation is a function if it has only One y-value for each x-value.

The given function h of x equals negative 5 times the square root of x.

h(x) = -5√x

The value of h(x) decreases as the value of x increases.

The function h(x) is a decreasing function over the interval (–∞, 0) because it is a negative function over the interval.

Hence, the function is decreasing on the interval (–∞, 0) is true.

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Reason:

I'm assuming that the swimmer travels along the 50 meter side

Divide 1500 over 50 to get 1500/50 = 30, which tells us that the swimmer must make 30 trips.

Answer:

See below.

Step-by-Step Explanation:

5) 8x+9-6x-7

8x + 2 - 6x (Subtract the numbers)

2x + 2 (Combine like terms)

2 (x + 1)  (Common factor - Factor by grouping twice)

6) 2y-6+5y+9

2y + 3 + 5y (Add the numbers)

7y + 3 (Combine like terms)

7) 3x+8+4x-9

3x - 1 + 4x (Subtract the numbers)

7x - 1      (Combine like terms)

8) 9y+16-12y+24

9y + 40 - 12y (Add the numbers)

-3y + 40 (Combine like terms)

9) 7g-5-8g+12

7g + 7 - 8g (Add the numbers)

-g + 7 (Combine like terms)

10) 11c-8+5c-8

11c - 16 + 5c (Subtract the numbers)

16c - 16 (Combine like terms)

16 (c - 1)   (Common factor - Factor by grouping twice)

11) 5(2x + 3) (This one was a bit blurry, I am assuming that's a addition sign.)

10x + 15 (Distribute)

12) 5(-2x+3)

-10x + 15 (Distribute)

Hope this helps!

Answer: those are the answers its a long time.

Question  5  Answer: 2(x+1)

8x+9−6x−7

Multiply and combine like terms.

2x+2

Factor out 2.

2(x+1)

Questio 6 Answer : 7y + 3

2y−6+5y+9

Combine 2y and 5y to get 7y.

7y−6+9

Add −6 and 9 to get 3.

7y+3

Question 7  Answer: 3x+8+4x−9

Combine 3x and 4x to get 7x.

7x+8−9

Subtract 9 from 8 to get −1.

7x−1

Question 8 Answer: - 3y + 40

9y+16−12y+24

Combine 9y and −12y to get −3y.

−3y+16+24

Add 16 and 24 to get 40.

−3y+40

Question 9 Answer: -g + 7

7g−5−8g+12

Combine 7g and −8g to get −g.

−g−5+12

Add −5 and 12 to get 7.

−g + 7

Question 10 Answer: 16 ( c - 1 )

11c−8+5c−8

Combine 11c and 5c to get 16c.

16c−8−8

Subtract 8 from −8 to get −16.

16c - 16

Question 11 Answer: 10x +15

5(2x+3)

Use the distributive property to multiply 5 by 2x+3.

10x+15

Question 12 Answer: 15 - 10x

5(−2x+3)

Use the distributive property to multiply 5 by −2x+3.

−10x+15

The probability of P(20s | Chocolate) and P(chocolate | 30s) x P(vanilla | 30s) will be 0.26 and 0.25, respectively.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

Adults were polled to determine whether they preferred vanilla or chocolate ice cream. The survey findings for three age groups are displayed in the table.

There are 127 people who enjoy chocolate, and 33 of them are in their 20s is given as,

P(20s | Chocolate) = 33 / 127 = 0.26

There are 122 persons in their 30s, and 53 of them prefer chocolate 69 others prefer vanilla is given as,

P(chocolate | 30s) x P(vanilla | 30s) = 53/122 x 69/122 = 0.25

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Answer:

the answer is C.64

Step-by-step explanation:

Answer:

the answer is C

Step-by-step explanation:

because the

The expression for P(red) is (x - 5)/x

The given parameters are:

Apple = x

Green = 5

The number of red apples is:

Red = Apple - Green

This gives

Red = x - 5

The expression for P(red) is then calculated as:

P(Red) = Red/Apple

This gives

P(Red) = (x - 5)/x

Hence, the expression for P(red) is (x - 5)/x

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Answer:

45

Step-by-step explanation:

Answer:

07698+96965#5_(-&)!:86539'6";

The solution to the given expression will be [tex]\dfrac{-8\pm\sqrt{180}}{6}[/tex].

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

The given equation will be solved as:-

= 3x² + 8x - 10  

Using the formula of factors:-

x = [tex]\dfrac{-b\pm\sqrt{b^-4ac}}{2a}[/tex]

x = [tex]\dfrac{-8\pm\sqrt{64-(-120)}}{2\times 3}[/tex]

x = [tex]\dfrac{-8\pm\sqrt{180}}{6}[/tex].

Therefore the solution to the given expression will be [tex]\dfrac{-8\pm\sqrt{180}}{6}[/tex].

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C. For the first card, there are three ways to choose the number of card.

For the another, there two options, and likewise there's only 1 choice of card. So there are 3 × 2 × 1 = 6 ways that the calculation can be chosen.

Doing this for the other attributes, we get 6 × 6 × 24 × 6 ways. But the order of cards does not count in a set of card, so we divide by 3! 6 * 6 * 24 × 6 ÷ 3! = 864. It means there are 864 sets for part.

D. The cards may have the same number, color, shapess, orshading.

However, also there are 6 × 24 × 6 × 3! = 144 sets of cards, If all the colors are thesame. How ever, also there are 144 sets of cards.

If all the calculation are the same. We get the same number for shape and shadings, so there are 4 × 144 = 576 sets of cards.

what is Probability?

Probability is branches of mathematics concerning numerical descriptions of how to the likely an event is to occurs, or how to the likely it is that a proposition is true. The probability of an event is a numbers between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the events and 1 indicates certain of cards.

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An expression can either be an equation or an inequality.

The correct classification of the terms are:

Expression; 4x+20

Inequality: 4x+20>40

Equation: 4x+20=40

We have given that,

{20,18,8,18,10,8,4}

{12,14,16,20,4,8,10}

{12,16,4,20,8,6,8}

To determine the correct classification, we make use of the following highlights

When an expression has the =, then the expression is an equation.

When an expression has any of the following signs>, <, >=, <= or != , then the expression is an inequality.

When the expression is neither an equation nor an inequality, then it is just an expression.

Hence, the correct classifications are:

Expression; 4x+20

Inequality: 4x+20>40

Equation: 4x+20=40

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The constant of proportionality is 0.1

Find the constant of proportionality (r)in the equation y=rx.

r =

x    y

14  1.4

16  1.6

21  2.1

The equation is given as:

y = rx

When x = 14 and y = 1.4, we have:

1.4 = r * 14

Divide both sides by 14

r = 0.1

Hence, the constant of proportionality is 0.1

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Step-by-step explanation:

[tex] = { ({16}^{ \frac{3}{2} } )}^{ \frac{1}{2} } [/tex]

[tex] = { ({( {2}^{4}) }^{ \frac{3}{2} } )}^{ \frac{1}{2} } [/tex]

[tex] = {2}^{4 \times \frac{3}{2} \times \frac{1}{2} } [/tex]

[tex] = {2}^{ \frac{12}{4} } [/tex]

[tex] = {2}^{3} [/tex]

[tex] = 2 \times 2 \times 2[/tex]

[tex] = 8[/tex]

The answer is B.

72

x varies directly as y

hence x=k y

k=6

y=12

x=6×12

x=72

Answer:

x = (√10  -3)/2  and (-√10  -3)/2

Step-by-step explanation:

(2x+3)^2 = 10

To solve the equation, take the square root of each side

sqrt((2x+3)^2) = ±√10

2x+3 = ±√10

Subtract 3 from each side

2x+3-3 = ±√10  -3

2x = ±√10  -3

Divide each side by 2

2x/2 = (±√10  -3)/2

x = (±√10  -3)/2

There are two solutions

x = (√10  -3)/2

and (-√10  -3)/2

Answer:

[tex]\large {\textsf{A and D}}\ \implies \sf \sf \bold{x_1}=\dfrac{-\sqrt{10}-3}{2},\ \bold{x_2}=\dfrac{\sqrt{10}-3}{2}[/tex]

Step-by-step explanation:

Given: (2x + 3)² = 10

In order to find the solutions to the given equation, we can take the (square) roots of the equation to find the zeros, which are also known as the x-intercepts. This is where the zeros intersect the x-axis.

Note: when taking the square roots of a quadratic equation, remember to use both the positive and negative roots.

Step 1: Square both sides of the equation.

[tex]\sf \sqrt{(2x + 3)^2} = \sqrt{10}\\\\\Rightarrow 2x+3=\pm\sqrt{10}[/tex]

Step 2: Separate into possible cases.

[tex]\sf x_1 \implies 2x+3=-\sqrt{10}\\\\x_2 \implies 2x+3=\sqrt{10}[/tex]

Step 3: Solve for x in both cases.

[tex]\sf \bold{x_1} \implies 2x+3=-\sqrt{10}\ \ \textsf{[ Subtract 3 from both sides. ]}\\\\\Rightarrow 2x+3-3=-\sqrt{10}-3\\\\\Rightarrow 2x=-\sqrt{10}-3\ \ \textsf{[ Divide both sides by 2. ]}\\\\\Rightarrow \dfrac{2x}{2}=\dfrac{-\sqrt{10}-3}{2}\\\\\Rightarrow x_1=\dfrac{-\sqrt{10}-3}{2}\\\\[/tex]

[tex]\sf \bold{x_2}\implies 2x+3=\sqrt{10}\ \ \textsf{[ Subtract 3 from both sides. ]}\\\\\Rightarrow 2x+3-3=\sqrt{10}-3\\\\\Rightarrow 2x=\sqrt{10}-3\ \ \textsf{[ Divide both sides by 2. ]}\\\\\Rightarrow \dfrac{2x}{2}=\dfrac{\sqrt{10}-3}{2}\\\\\Rightarrow x_2=\dfrac{\sqrt{10}-3}{2}[/tex]

Therefore, the solutions to this quadratic equation are: [tex]\sf \bold{x_1}=\dfrac{-\sqrt{10}-3}{2},\ \bold{x_2}=\dfrac{\sqrt{10}-3}{2}[/tex]

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The value of n is 12. and m is 6root5

We have given the diagram,

The measurement of m,

n = 12

According to the altitude theorem

The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the hypotenuse in a right triangle and the two-line segments it creates on the hypotenuse.

24/n = n/6

The Cross multiply

24 * 6 = n²

144 = n²

n² = 144

n = √144

n = 12

[tex]m^2=6^2+n^2[/tex]

[tex]m^2=6^2+12^2\\m^2=36+144\\m^2=180[/tex]

[tex]m=\sqrt{180} \\m=2\cdot \:3\sqrt{5}\\m=6\sqrt{5}[/tex]

Hence the value of n is 12.

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Answer:

12

Step-by-step explanation:

definetly not a

Step-by-step explanation:

because it is an incompetent answer

The time it takes = 3 hours 12 minutes

Rate is a ratio which compares two quantities of different units.

Analysis:

Speed = 5 miles/hour

distance covered = 16 miles

speed taken = distance covered/time taken

time taken = 16/ 5 = 3.2 hours = 3 hours 12 minutes

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Answer:

-1

Step-by-step explanation:

The y-intercept is where the line crosses the y-axis.

Answer:

[tex]\huge\boxed{\sf y-intercept = -1}[/tex]

Step-by-step explanation:

Here,

Since, this is the point where x = 0 and where the line passes through the y-axis.

[tex]\rule[225]{225}{2}[/tex]

Answer:

has no x^2 term

Step-by-step explanation:

Has no x^2 term   <====== that would make it an exponential function, not linear

Answer:

  f(-2) = 0

Step-by-step explanation:

The value of the function for a particular x-value can be read from the graph.

The graph is a map showing the value of f(x) for each value of x for which the function is defined. The x-values are identified by the numbers on the horizontal x-axis. The corresponding function values are found by referencing the vertical y-axis.

To find the function value f(x) for x=-2, we locate the vertical grid line marked with -2 at the x-axis. We then locate the point on the graph of the function where it crosses that vertical grid line. Tracking horizontally from that point to the vertical y-axis, we can read the function value from the vertical scale.

The attachment has a red arrow pointing to the intersection of the graph with the grid line x=-2. That point of intersection lies on the x-axis, where the y-value is 0. That means ...

  f(-2) = 0

__

Additional comment

On this graph, the axis crossing point (x=0, y=0) is not labeled. It is halfway between x=-1 and x=1. Similarly, it is halfway between y=-1 and y=1. Based on this and on experience with similar graphs, you can assume that the axis crossing has coordinates (x, y) = (0, 0).

The solutions of the given equation are x= (√5+3)/2 & x= (-√5+3)/2

If ax²+bx+c = 0 is a quadratic equation ,where a,b,c are real numbers, Then the solution is x = (-b±√(b²-4ac))/2a , where a≠0

The given equation is, 4x²-12x+9 = 5

So, 4x²-12x+9 = 5

⇒ 4x²-12x+9-5 = 0

⇒ 4x²-12x+4 = 0

Comparing this equation with ax²+bx+c = 0 we get,

a = 4, b = -12, c = 4

Applying sridharacharya formula we get,

x = (-(-12)±√((-12)²-4×4×4))/(2×4)

  = (12±√(144-64)/8

  = (12±√80)/8

  = (3±√5)/2

The values of x are (√5+3)/2 & (-√5+3)/2

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Step-by-step explanation:

2y+9= 4

2y=-5

y=-5/2

y= -2and 1/2

A figure can be graphed on a coordinate plane as a set of points located on specific places, specified by  their coordinates.

The cartesian coordinate plane is an infinite 2 dimensional plane and each point of a cartesian plane is tracked by a location.

Now, the perpendicular distance of point from the horizontal axis and vertical axis are respectively usually named x-axis and y-axis. The location is then written as (a,b) where;

a is that point's shortest distance from the y-axis and called x-coordinate of that point.

b is that point's shortest distance from the x-axis, and called y-coordinate of that point.

Thus, those given geometric figures can be graphed on a coordinate plane as a set of points located on specific places, specified by  their coordinates.

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Based on the calculations, the length of side AB is equal to 13.93 units.

Since the points of tangency are at A and B, we would determine the side length of the point lying between side A and D as follows:

AM = AD - BC

AM = 7 - 2

AM = 5 units.

Now, we can determine the length of side AB by applying Pythagorean's Theorem:

AB² = BM² + AM²

AB² = 13² + 5²

AB² = 169 + 25

AB = √194

AB = 13.93 units.

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Answer:

135

Step-by-step explanation:

Depending on where you start, the protractor can read in different ways. Since the measure of this angle started from the left, you read the numbers at the top. If the measure would have started from the right, you read the numbers below.

A good rule of thumb is that if the angle appears to be greater than 90 degrees, or an obtuse angle, you would choose the only answer choice that is above 90 degrees.

Hope this helps!