Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Find the areas of the figures.
72 square units
54 square units
190 square units
36 square units
4 units
4 units
2 unitsh
1
8 units
110 units

Given:

Length of the ladder = 9.85 m

The height to the top of the ladder is 5 m more than the distance between the wall and the foot of the ladder.

To find:

The height to the top and the distance between the wall and the foot of the ladder.​

Solution:

let x be the distance between the wall and the foot of the ladder. Then the height to the top of the ladder is (x+5).

Pythagoras theorem: In a right angle triangle,

[tex]Hypotenuse^2=Base^2+Perpendicular^2[/tex]

In the given situation, hypotenuse is the length of ladder, i.e., 9.85 m. The base is x m and the height is (x+5) m.

Using the Pythagoras theorem, we get

[tex](9.85)^2=x^2+(x+5)^2[/tex]

[tex]97.0225=x^2+x^2+10x+25[/tex]

[tex]0=2x^2+10x+25-97.0225[/tex]

[tex]0=2x^2+10x-72.0225[/tex]

Here, [tex]a=2, b=10,c=-72.0225[/tex]. Using the quadratic formula, we get

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

[tex]x=\dfrac{-10\pm \sqrt{(10)^2-4(2)(-72.0225)}}{2(2)}[/tex]

[tex]x=\dfrac{-10\pm \sqrt{676.18}}{4}[/tex]

Approximating the value, we get

[tex]x=\dfrac{-10\pm 26}{4}[/tex]

[tex]x=\dfrac{-10+26}{4},\dfrac{-10-26}{4}[/tex]

[tex]x=\dfrac{16}{4},\dfrac{-36}{4}[/tex]

[tex]x=4,-9[/tex]

Distance cannot be negative so [tex]x\neq -9.[/tex]

Now we have [tex]x=4[/tex]

[tex]x+5=4+5[/tex]

[tex]x+5=9[/tex]

Therefore, the base is 4 m and the height is 9 m.

The base, height to the top of the ladder and height of the ladder when connected together we will get a triangle and then apply Pythagoras theorem we get base 4.0 m and height 9 m.

According to this theorem, the hypotenuse l,  base b and opposite side a are connected by the equation written as follows:

hypotenuse² = base² + opposite side²

l² = a² + b².

Thus if we know either two sides or the triangle we can calculate the length of the unknown side of the triangle. It is given that the length of ladder is 9.85 m. It is placed against a wall and the base that is distance between foot and wall is 5 m less than the height to the top.

Assuming a triangle connecting these three points, the hypotenuse is the length of the ladder 9.85 m and let x be the base and opposite side that is the height to the top be x + 5. Now apply Pythagoras theorem.

9.85² = (x+5)² + x²

97.02 = 2 x² + 10x + 25

2 x² + 10x -72.02 = 0

Now solve for x using quadratic equation we get x = 4.00. The base of the triangle is 4 m and opposite side that is the height = x +5 = 4 +5 = 9m.

Therefore, base is 4 m and height to the top of the ladder is 9 m.

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Answer:

2x +4 = 9

x = 5/2

Step-by-step explanation:

Let x = number

2x +4 = 9

Subtract 4 from each side

2x+4-4 = 9-4

2x = 5

Divide by 2

2x/2 =5/2

x = 5/2

Answer:

C and D have the same slope of 1

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Answer:

  A.  3.46

Step-by-step explanation:

The side ratios of a 30°-60°-90° triangle are 1 : √3 : 2. You are given the short side GF of this triangle, so its long side is GH = GF·3.

Then the area of ΔGFH is ...

  A = 1/2(GF)(GH) = 1/2(4)(4√3) = 8√3 ≈ 13.86 . . . . square units

__

Segment GI divides the area of ΔGFH in half, so that ΔGFI is half the above area. Segments GF, FI, IH, GI are all congruent, so segment GJ divides isosceles triangle GFI in half. That is. ΔGJI is half the area of ΔGFI, so is 1/4 the area of GFH.

  Area of ΔGJI = (8√3)/4 = 2√3 ≈ 3.46 . . . square units

Answer:

D. 7

Step-by-step explanation:

Apply the secant-scant product theorem. Thus, based on the theorem, we have the following equation:

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

6(10) = 5x + 25

60 = 5x + 25

Subtract 30 from each side

60 - 25 = 5x + 25 - 30

35 = 5x

Divide both sides by 5

35/5 = 5x/5

7 = x

x = 7

Answer:

look below

Step-by-step explanation:

To graph the function h(x) = -2x - 3, we can plot points on a coordinate plane using the equation and then connect the points to form the graph.

To find the points, we can choose different values of x and substitute them into the equation to calculate the corresponding values of h(x). Let's select a few values for x:

When x = -2:

h(-2) = -2(-2) - 3 = 4 - 3 = 1

So we have the point (-2, 1).

When x = 0:

h(0) = -2(0) - 3 = 0 - 3 = -3

So we have the point (0, -3).

When x = 2:

h(2) = -2(2) - 3 = -4 - 3 = -7

So we have the point (2, -7).

Now, we can plot these points on a coordinate plane and connect them to form the graph of the function h(x) = -2x - 3.

The graph will show a straight line that passes through the points (-2, 1), (0, -3), and (2, -7). The line will have a negative slope of -2, meaning it slopes downward from left to right.

Here's a rough representation of the graph:

      |

      |

 -7   |    .

      |

 -3   |

      |                  .

  1   |

      |____________________

        -2    0    2

Please note that this graph is just an approximation, and for a more accurate graph, you may use graphing software or a graphing calculator.

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9514 1404 393

Answer:

  [tex]\displaystyle\sqrt{x+7}-\log{(x+2)}[/tex]

Step-by-step explanation:

It's pretty straightforward. You want ...

  f(x) - g(x)

Substituting the given function definitions gives ...

  [tex]\displaystyle\boxed{\sqrt{x+7}-\log{(x+2)}}[/tex]

Answer:

WE reject the Null and conclude that one of the drug is more effective than the other.

Step-by-step explanation:

Given :

Diet 1 3.4 10.9 2.8 7.8 0.9 5.2 2.5 10.5 7.1 7.5

Diet 2 11.9 13.1 11.6 6.8 6.8 8.8 12.5 8.6 17.5 10.3

This is a matched pair sample :

The hypothesis :

H0 : μd = 0

H1 : μd ≠ 0

Hence, we intun the difference between the two groups of value :

Difference, d = -8.9,-2.2,-8.8,1,-5.9,-3.6,-10,1.9,-10.4,-2.8

The test statistic :

dbar ÷ (Sd/√n)

dbar = mean of difference = Σd / n = - 49.7 / 10 = - 4.97

Standard deviation of difference, Sd = 4.51

Test statistic :

-4.97 ÷ (4.51/√10)

Test statistic = - 3.485

The sample size, n = 10

df = n - 1 ; 10 - 1 = 9

Critical value (0.10, 9) = 1.833

If Test statistic > |Critical value |

Since 3.486 > 1.833 ; WE reject the Null and conclude that one of the drug is more effective than the other

Answer:

Step-by-step explanation:

This is a super simple problem. I'm going to walk through it as I do when I teach this to my students for the first time.

We are given a rectangle. We are told to find how fast the area is changing under certain conditions. That tells us that the main equation for this problem is the area formula for a rectangle which is

[tex]A=lw[/tex]. If we are looking for the rate at which the rectangle's area is changing, that means that we need to find the derivative of the area implicitly. This derivative is found using the product rule because the length is being multiplied by the width:

[tex]\frac{dA}{dt}=l\frac{dw}{dt}+w\frac{dl}{dt}[/tex] . If our unknown is the rate at which the area is changing, [tex]\frac{dA}{dt}[/tex], that means that everything else has to have a value (because you can only have one unknown in an equation). Here's what we're told:

The length of the rectangle is increasing at a rate of 7 cm/s, so that satisfies our [tex]\frac{dl}{dt}[/tex];

the width is increasing at a rate of 6 cm/s, so that satisfies our [tex]\frac{dw}{dt}[/tex];

and all of this is going on when the length = 12 and the width = 8. It looks like everything will have a value except for our unknown. Filling in:

[tex]\frac{dA}{dt}=12(6)+8(7)[/tex] and

[tex]\frac{dA}{dt}=72+56[/tex] so

[tex]\frac{dA}{dt}=128\frac{cm^2}{s}[/tex]

Answer:

1.5 cubic metres

Step-by-step explanation:

Given that in a concrete mix, cement makes up 1 part, sand makes up 2 parts and gravel makes up 3 parts.

The total number of parts = 1 + 2 + 3 = 6 parts.

The amount of marvel present the concrete mix = amount of marvel / total mix

= 3 parts / 6 parts = 1/2

Since 3 cubic metres of concrete is enough for the path, hence the amount of gravel needed is:

Amount of gravel = 1/2 * 3 cubic metres of concrete = 1.5 cubic metres

Answer:

18

Step-by-step explanation:

The sum of the angles of a triangle is 180

x+3x+6x = 180

10x = 180

Divide by 10

10x/10 =180/10

x = 18

Answer:

A. Increase speed to approximately 7.1 mph so that you cover the field more.

Step-by-step explanation:

The soil samples for the next field require more fertilizer coverage therefore there is need for more field coverage by the equipment. The speed of the tractor will be increase to 7.1 mph so that greater area can be covered in lesser time.

Answer:

X=10

Step-by-step explanation:

2x-,8<12

2x>12+ 8

2x>20

x>10

Answer:

10.6

Step-by-step explanation:

A simple sketch of the question would give a right angled triangle. So that we can easily apply the Pythagoras theorem to determine the length of the cable required.

Let the length of the cable required be represented by x.

[tex]/Hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]

[tex]x^{2}[/tex] = [tex]8^{2}[/tex] + [tex]7^{2}[/tex]

   = 64 + 49

[tex]x^{2}[/tex] = 113

x = [tex]\sqrt{113}[/tex]

  = 10.63

x = 10.6

The length of the cable required is 10.6 in feet.

The length of the cable needed to support the tenth wall is approximately 10.6 ft.

The situation forms a right angle triangle.

Right angle triangle has one of it side as 90 degrees.

Therefore,

The tent wall is the opposite side of the triangle.

The table feet from the base of the tent is the adjacent side of the triangle.

Using Pythagoras's theorem the cable needed can be found.

Therefore,

c² = 64 + 49

c = √113

c = 10.6301458127

length of the cable ≈ 10.6 feet

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Answer:

  (b)  BC = B"C"/3

Step-by-step explanation:

Choices A, C, D are all different ways of expressing the same relationship, and they are all incorrect.

B"C" is segment BC after dilation by a factor of 3, so it is 3 times as long as BC. That is, BC is 1/3 the length of B"C", choice B.

Answer:

A sample of 997 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is of:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

A previous study indicates that the proportion of left-handed golfers is 8%.

This means that [tex]\pi = 0.08[/tex]

98% confidence level

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].  

How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 2%?

This is n for which M = 0.02. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.02 = 2.327\sqrt{\frac{0.08*0.92}{n}}[/tex]

[tex]0.02\sqrt{n} = 2.327\sqrt{0.08*0.92}[/tex]

[tex]\sqrt{n} = \frac{2.327\sqrt{0.08*0.92}}{0.02}[/tex]

[tex](\sqrt{n})^2 = (\frac{2.327\sqrt{0.08*0.92}}{0.02})^2[/tex]

[tex]n = 996.3[/tex]

Rounding up:

A sample of 997 is needed.

Answer:

f(x)=27.63(1.03)^x

Step-by-step explanation:

Answer:

They must rent for less than 7 hours

Step-by-step explanation:

The charge for the room is the fee plus the hourly rate times the hour

f = 33+9.80t

This must be less than 101.60

101.60> 33+9.80t

Subtract 33 from each side

101.60-33> 33-33+9.80t

68.6> 9.80t

Divide each side by 9.8

68.8/9.8 > t

7>t

They must rent for less than 7 hours

Answer:

Statement A is correct

Step-by-step explanation:

Statement A is correct:  Model A1 (0.25) is more prefered than Model C3 (0.15)

Answer:

below

Step-by-step explanation:

hope it is well understood?

The slope is 4 and y- intercept is 13

A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics.

A slope exists Numerical calculation of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment stands as the proportion of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).

Given

Slope

y = 4x-3

dy/dx = 4

slope =  4

intercepts y = 4(4) 3

y = 16-3

y = 13

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Answer:

25%

Step-by-step explanation:

The average cost of the automobile in 2013 is $16,000

The present cost now is $20,000

Therefore the rate of increase between the two automobiles can be calculated as follows

= 20,000-16,000/16,000

= 4,000/16,000

= 0.25×100

= 25%

Hence the rate of increase is 25%

Answer:

One of these

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Add up all the frequencies given

5+6+5+6+5+8+4+4+3 = 46

The total frequencies with the missing data value should add up to 50

50 = 46 + x

x = 50 - 46

x = 4

Answer:

4

Step-by-step explanation:

The nine given values add to 5+6+5+6+5+8+4+4+3=46, so the missing frequency is 50−46=4.

Answer:

28.2 %

Step-by-step explanation:

Increase = 17.95 - 14 = $3.95

%age increase = 100 * 3.95 / 14

= 28.214

Answer:

x=9

Step-by-step explanation:

-54/x= -6

Multiply each side by x

-54/x *x= -6*x

-54= -6x

Divide each side by -6

-54/-6 = -6x/-6

9 =x

Answer:

9

Step-by-step explanation:

-54 / x = -6

-6 × ? = -54

*Must be positive

-6 × 9 = -54

The answer is 9.

m = [tex]\frac{\sqrt{3}}{2}[/tex]

theta = 60 degrees or pi/3

The best way to figure these sorts of questions out is memorizing the unit circle. There are many tricks that can help! For example, from (0,1) to the left and right, the x-values of the points go from sqrt(3) to sqrt(2) to 1.

Hope this helps!

1. Move terms to the left side

2.Subtract the numbers

3.Use the quadratic formula

4.Simplify

5.Separate the equations

6.Solve

Rearrange and isolate the variable to find each solution.

Solution,

Solution

x=5±√39