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Answer:

1) D - 30 cm 2) 12 percents

Step-by-step explanation:

The first question was If two perpendicular sides of a right-angled triangle are 5 cm and 12 cm, its perimeter is: (A) 13 cm (B) 17 cm (C) 27 cm (D) 30 cm

two perpendicular sides are legs, find the hipotenuse of the triangle

It is equal to sqrt(5^2+12^2)= sqrt169=13

5+12+13=30 - D - the perimeter

The second question

7500 -100 percents

8400- x

7500/8400=100/x

75/84=100/x

(25/28)*x=100

(1/28)*x=4

x=4/(1/28)= 4*28= 112 percents

The profit is 12 percents

2) Option D is correct. If two perpendicular sides of a right-angled triangle are 5 cm and 12 cm, its perimeter will be 30cm.

3) None of the given options are correct. If an article is purchased for 7,500 and sold for 8,400, the profit percentage will be 12%

2) A right-angled triangle is a triangle with three sides and one of its angles is 90degrees. Find the image of a right-angled triangle attached below.

The triangle consists of 3 sides which are:

Before we can get the perimeter of the right triangle, we need to get the third side first (the hypotenuse side) using the Pythagoras theorem. According to the theorem:

[tex]c^2=a^2+b^2[/tex]

Given

a = 5 cm

b =12 cm

[tex]c^2=5^2+12^2\\c^2=25+144\\c^2=169\\c=\sqrt{169}\\c=13 cm[/tex]

Perimeter of the right triangle = a + b + c

Perimeter of the right triangle = 5 cm + 12 cm + 13 cm

Perimeter of the right triangle = 30 cm

Hence the perimeter of the right triangle is 30 cm.

3) If an article is purchased for 7,500, then;

If the same article is sold for 8,400, then:

[tex]\% profit=\frac{SP-CP}{CP} \times 100[/tex]

Substitute the given parameters

[tex]\% profit=\frac{8400-7500}{7500} \times 100\\\%profit=\frac{900}{7500} \times 100 \\\%profit=\frac{900}{75}\\\% profit = 12 \%[/tex]

This shows that the profit percent is 12%

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Step-by-step explanation:

Which correlation coefficient indicates the data set with the strongest linear correlation?

0.66

The correlation coefficient indicates the data set with the strongest linear correlation is -0.83

"It measures the strength of the relationship between two relative variables."

"When the rate of change is constant between two variables then it is said to be linear correlation."

For given example,

We have been given correlation coefficients.

We need to find the correlation coefficient that indicates the data set with the strongest linear correlation.

We know, the correlation coefficient lies between -1 to 1.

So, the strongest linear correlation is indicated by a correlation coefficient of -1 or 1.

From given correlation coefficients,

-0.83 is close to -1.

Therefore, the correlation coefficient indicates the data set with the strongest linear correlation is -0.83

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Answer:

(a) [tex]P" = (-4,-3)[/tex]

(b) [tex](x,y) \to (4,-8)[/tex]

Step-by-step explanation:

Given

[tex]P = (4,3)[/tex]

Solving (a): Reflect across x and y-axis.

Reflection across x-axis has the following rules

[tex](x,y) \to (x,-y)[/tex]

So, we have:

[tex]P' = (4,-3)[/tex]

Reflection across y-axis has the following rules

[tex](x,y) \to (-x,y)[/tex]

So, we have:

[tex]P" = (-4,-3)[/tex]

Hence, the new point is: (-4,-3)

Solving (b): Rx . Do,2 (2,4)

[tex]R_x \to[/tex] reflect across the x-axis

Reflection across x-axis has the following rules

[tex](x,y) \to (x,-y)[/tex]

So, we have:

[tex](2,4) = (2,-4)[/tex] ---- when P is reflected across the x-axis

[tex]D_{o,2} \to[/tex] dilate by a scale factor of 2

The rule is:

[tex](x,y) \to 2 * (x,y)[/tex]

So, we have

[tex](x,y) \to 2 * (2,-4)[/tex]

Open bracket

[tex](x,y) \to (4,-8)[/tex]

Answer:

14.36 AND 9.89 ===> 14 or 10

Step-by-step explanation:

Y =  Ax2 Bx C

Enter coefficients here >>>  -4 97 -568

Standard Form: y = -4x²+97x-568    

-24.25 -12.125 147.015625 -588.0625 20.0625

Grouped  Form: No valid Grouping      

Graphing Form: y = -4(x-12.13)²+20.06    

Factored Form: PRIME    

Solution/X-Intercepts: 14.36 AND 9.89    

Discriminate =321 is positive, two real solutions    

VERTEX: (12.13,20.06)     Directrix: Y=20.13    

Answer:

5(n+4)

5n+20

Step-by-step explanation:

Let n be the number

5* (n+4)

Distribute

5n+20

ABC = $425

Load = 0

Total Cost = $425

Sales Price = $850

Sales price ÷ total cost = 850/425

= 2%

DEF = $600

Load = $375

Total Cost = $975

Sales Price = $1200

Sales Price ÷ Total cost = 1200/975

= 1% (Nearest 1%)

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Answer:

8. SU = 24

9. TU = 16√3

Step-by-step explanation:

Recall: SOH CAH TOA

8. Reference angle (θ) = 30°

Opposite = 8√3

Adjacent = SU

Apply TOA,

Tan θ = Opp/Adj

Substitute

Tan 30° = 8√3/SU

Tan 30° × SU = 8√3

SU = 8√3/Tan 30°

SU = 8√3/(1/√3) (tan 30° = 1/√3)

SU = 8√3*√3/1

SU = 8*3

SU = 24

9. Reference angle (θ) = 30°

Opposite = 8√3

Hypotenuse = TU

Apply SOH,

Sin θ = Opp/Hyp

Substitute

Sin 30° = 8√3/TU

Sin 30° × TU = 8√3

TU = 8√3/sin 30°

TU = 8√3/(½) (sin 30° = ½)

TU = 8√3 × 2/1

TU = 16√3

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Answer:

click in photo

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nxndjdbbdjf

lấy x=0 ta có y= -2 => A(0;-2)

lấy y=0 ta có x=2 => B(2;0)

nối 2 điểm A và B ta có đồ thị:

Answer:

# of cases: 11

Additional units: 2

Step-by-step explanation:

If each case can hold 8 units, and we want to find the total # number of cases, we have to divide the # of units (8) for one case by the total # units (90).

As you can see, after dividing by 8, we have a total of 11 cases and a remainder of 2 units. The remainder will be the # of additional units because we cannot have another case filled with 8 units.

Answer:

14.17 kilograms

Step-by-step explanation:

Find what quantity of tomatoes was in each batch by dividing the total amount of tomatoes by the number of batches:

99.19/7

= 14.17

So, the factory put 14.17 kilograms of tomatoes in each batch.

We know

Sum of two interior angles =exterior angle

[tex]\\ \sf\longmapsto 2x+x=3x[/tex]

[tex]\\ \sf\longmapsto 3x=3x[/tex]

[tex]\\ \sf\longmapsto x=1[/tex]

Answer:

4(2e - 3)(3e + 1)

Step-by-step explanation:

Given

24e² - 28e - 12 ← factor out 4 from each term

= 4(6e² - 7e - 3) ← factor the quadratic

Consider the factors of the product of the e² term and the constant term which sum to give the coefficient of the e- term.

product = 6 × - 3 = - 18 and sum = - 7

The factors are - 9 and + 2

Use these factors to split the e- term

6e² - 9e + 2e - 3 ( factor the first/second and third/fourth terms )

= 3e(2e - 3) + 1 (2e - 3) ← factor out (2e - 3) from each term

= (2e - 3)(3e + 1)

Then

24e² - 28e - 12 = 4(2e - 3)(3e + 1) ← in factored form

Answer:

1250000cm

Step-by-step explanation:

1:500000

1x2.5 : 500000x2.5

2.5:1250000

Answer:

There is a   min     value of   376     located at (x,y) =   (9,7)  

============================================================

Explanation:

Solve the second equation for y

x+y = 16

y = 16-x

Then plug it into the first equation

f(x,y) = 3x^2+4y^2 - xy

g(x) = 3x^2+4(16-x)^2 - x(16-x)

g(x) = 3x^2+4(256 - 32x + x^2) - 16x + x^2

g(x) = 3x^2+1024 - 128x + 4x^2 - 16x + x^2

g(x) = 8x^2-144x+1024

The positive leading coefficient 8 tells us we have a parabola that opens upward, and produces a minimum value (aka lowest point) at the vertex.

Let's compute the derivative and set it equal to zero to solve for x.

g(x) = 8x^2-144x+1024

g ' (x) = 16x-144

16x-144 = 0

16x = 144

x = 144/16

x = 9

The min value occurs when x = 9. Let's find its paired y value.

y = 16-x

y = 16-9

y = 7

The min value occurs at (x,y) = (9,7)

Lastly, let's find the actual min value of f(x,y).

f(x,y) = 3x^2+4y^2 - xy

f(9,7) = 3(9)^2+4(7)^2 - 9*7

f(9,7) = 376

The smallest f(x,y) value is 376.

The 8 will end up in the "ones place".

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.

We need to find the 8 will end up in which place

A negative divided by a negative is positive, then;

2380/ 10 = 238

Therefore, The 8 will end up in the _ ones_ place.

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Answer:

just show the questions i will help

Step-by-step explanation:

Answer:

x = -1.4 and x=2

Step-by-step explanation:

The solutions are where the graphs intersect

The graphs appear to intersect at x = -1.4 and x=2

9514 1404 393

Answer:

  a) 2.038 seconds

  b) 5.918 meters

  c) 1.076 seconds

Step-by-step explanation:

For the purpose of answering these questions, it is convenient to put the given equation into vertex form.

  h = -4.9t² +9.2t +1.6

  = -4.9(t² -(9.2/4.9)t) +1.6

  = -4.9(t² -(9.2/4.9)t +(4.6/4.9)²) +1.6 +4.9(4.6/4.9)²

  = -4.9(t -46/49)² +290/49

__

a) To find h = 0, we solve ...

  0 = -4.9(t -46/49)² +290/49

  290/240.1 = (t -46/49)² . . . . subtract 290/49 and divide by -4.9

  √(2900/2401) +46/49 = t ≈ 2.0378 . . . . seconds

The ball takes about 2.038 seconds to fall to the ground.

__

b) The maximum height is the h value at the vertex of the function. It is the value of h when the squared term is zero:

  290/49 m ≈ 5.918 m

The maximum height of the ball is about 5.918 m.

__

c) We want to find t for h ≥ 4.5.

  h ≥ 4.5

  -4.9(t -46/49)² +290/49 ≥ 4.5

Subtracting 290/49 and dividing by -4.9, we have ...

  (t -46/49)² ≥ 695/2401

Taking the square root, and adding 46/49, we find the time interval to be ...

  -√(695/2401) +46/49 ≤ t ≤ √(695/2401) +46/49

The difference between the interval end points is the time above 4.5 meters. That difference is ...

  2√(695/2401) ≈ 1.076 . . . . seconds

The ball is at or above 4.5 meters for about 1.076 seconds.

__

I like a graphing calculator for its ability to answer these questions quickly and easily. The essentials for answering this question involve typing a couple of equations and highlighting a few points on the graph.

_____

Additional comment

I have a preference for "exact" answers where possible, so have used fractions, rather than their rounded decimal equivalents. The calculator I use deals with these fairly nicely. Unfortunately, the mess of numbers can tend to obscure the working.

"Vertex form" for a quadratic is ...

  y = a(x -h)² +k . . . .  where the vertex is (h, k) and 'a' is a vertical scale factor.

In the above, we have 'a' = -4.9, and (h, k) = (46/49, 290/49) ≈ (0.939, 5.918)

Answer:

Its A

Step-by-step explanation:

The tangent of the given circle is FG hence the correct option will be an option (B).

The tangent of a circle is a line that intersects the circle at the periphery of the circle.

If you draw a line that goes through the center to the tangent touching point then it will give you a 90-degree angle.

Given the circle it's clear that the tangent is only FG hence it will be the correct option  

A circle can have an infinite number of tangents.

In other words, a straight line that only touches a circle twice is said to be tangent to it. The term point of intersection refers to this location

At the tangent line, the tangent to a circle is orthogonal to the radius.

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Answer:

Hello,

Step-by-step explanation:

[tex]Let\ (u_n)\ the\ geometric\ progression.\\\\r\ is\ the\ common\ ratio.\\\\u_3=u_0*r^3\\u_6=u_0*r^6\\\\\dfrac{u_6}{u_3} =r^3=\dfrac{\frac{243}{16} }{\frac{9}{2} } =\dfrac{27}{8} =(\frac{3}{2} )^3\\\\\boxed{r=\dfrac{3}{2} }\\\\\\u_3=u_1*r^2 \Longrightarrow\ u_1=\dfrac{u_3}{r^2} =\dfrac{\frac{9}{2} }{(\frac{3}{2^2}) } =2\\\\\\u_7=u_6*\dfrac{3}{2} =\dfrac{729}{32}[/tex]

Answer:

85/100

Step-by-step explanation:

0.85 from a decimal is equal to 85/100 in fractions

Answer:

15/4

Step-by-step explanation:

sin60 =z/15

z=15sin60 =(15√3)/2

cos30 =b/z

b = zcos30 = (15√3)/2 * √3/2 = 45/4

a = 15-b = 15-45/4 = 15/4

The value of a is 15/4

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

According to the given figure,

Here is a right triangle

Let, The hypotenuse = 15

perpendicular = z and base = 15 = a + b

⇒ sin60 = perpendicular/hypotenuse = z/15

⇒ z = 15sin60 = (15√3)/2

⇒ cos30 = base/hypotenuse = b/z

⇒ b = zcos30 = (15√3)/2 * √3/2 = 45/4

⇒ a + b = 15

Substitute the value of b in the above equation,

⇒ a = 15-b = 15-45/4 = 15/4

Hence, the value of a is 15/4.

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The expected value, E(x) of the given observation is 185

The expected value is the mean of the overall observed value or random value. In other words, it is the average of the observed values.

The given parameters can be represented as:

[tex]\begin{array}{cccc}x & {100} & {200} & {300} \ \\ P(x) & {40\%} & {35\%} & {25\%} \ \end{array}[/tex]

The following formula calculates the expected value:

[tex]E(x) =\sum x * P(x)[/tex]

So, we have:

[tex]E(x) = 100 * 40\% + 200 * 35\% + 300 * 25\%[/tex]

[tex]E(x) = 40 + 70 + 75[/tex]

[tex]E(x) = 185[/tex]

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Answer:

A

Step-by-step explanation:

32 hundredths is 32/100

Side note

32/100 can be simplified to 8/25.

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

Answer:

17

Step-by-step explanation:

T4 = 4² + 1

T4 = 4² + 1 = 17

Yip yip that's all

It looks like you want to find

[tex]\displaystyle \int t^{11} e^{-t^6}\,\mathrm dt[/tex]

Substitute u = -t ⁶ and du = -6t ⁵ dt. Then

[tex]\displaystyle \int t^{11} e^{-t^6}\,\mathrm dt = \frac16 \int (-6t^5) \times (-t^6) e^{-t^6}\,\mathrm dt = \frac16 \int ue^u \,\mathrm du[/tex]

Integrate by parts, taking

f = u   ==>   df = du

dg = eᵘ du   ==>   g = eᵘ

Then

[tex]\displaystyle \frac16 \int ue^u \,\mathrm du = \frac16\left(fg-\int g\,\mathrm df\right) \\\\ =\frac16 ue^u - \frac16\int e^u\,\mathrm du \\\\ =\frac16 ue^u - \frac16 e^u + C \\\\ =-\frac16 t^6 e^{-t^6} - \frac16 e^{-t^6} + C \\\\ =\boxed{-\frac16 e^{-t^6} \left(t^6+1\right) + C}[/tex]