The area of the trapezoid is 40 square units.
What is the height of the trapezoid?
6
3 units
5 units
10 units
10
12 units

Answer:

Step-by-step explanation:

Given the sequence that represents the diameter of a circle

2.5 cm, 3.1 cm, 3.7 cm and 4.3 cm. This sequence forms an arithmetic progression with a common difference.

nth term of an arithmetic progression is expressed as [tex]T_n = a+(n-1)d[/tex]

a is the first term of the sequence

n is the number of terms

d is the common difference.

From the sequence above, the first term a = 2.5

common difference = 3.1-2.5 = 3.7-3.1 = 4.3-3.7 = 0.6

Substituting this given values into the formula above will give;

[tex]T_n = 2.5+(n-1)*0.6\\\\T_n = 2.5+0.6n-0.6\\\\T_n = 2.5-0.6+0.6n\\\\T_n = 1.9+0.6n[/tex]

If f(n) represent diameter in centimetres and n the term number in the sequence, the equation that represents the sequence of diameters is

f(n) = 1.9+0.6n

Answer:

f(n) = 0.6n + 1.9

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

There are 3 cones and 15 flavors

Multiply the number of cones by the number of flavors

3*15

45

There are 45 possible combinations

Answer:

-2.2y - 1.8

Step-by-step explanation:

We are to simplify the expression:

1.2y + 4.5 - 3.4y - 6.3

Collect like terms:

1.2y - 3.4y + 4.5 - 6.3

Simplify:

-2.2y - 1.8

That is the answer.

Answer: D

Step-by-step explanation:

D makes a lot more sense because if you are someone who watches TV a lot then your more likely to score less on a given test.

Negative correlation means that as the x values increases the y value decrease.

So in this case hours will be on the x coordinate and y will be your test score.

Answer:

The axis of symmetry, vertex, degree of polynomial and x and y intercepts

Step-by-step explanation:

When we talk of a polynomial function, we refer to a function that involves only non-negative integer(whole number) powers of the independent variable (x in most cases). Thus, popular examples of polynomial functions include quadratic, cubic and triatic functions.

Kindly note that once a function includes a non negative power, it is not a polynomial any longer. That is why although x^2 + 2x is a polynomial function, x^2 + 2x^-1 is not a polynomial function.

Now, there are some key features that are necessary in sketching a polynomial function.

These are the vertex, axis of symmetry, x and y intercepts and the degree of the polynomial

These properties are needed to successfully make a sketch of a polynomial function.

The vertex of a polynomial function refers to that point on the curve of the function where it changes direction. For example, quadratic polynomial functions are known to have a parabolic sketch. That point in which there is a change in direction of the parabolic curve is known as the vertex of the polynomial function. A knowledge of this would ensure a proper sketch of the polynomial function curve. It helps in showcasing the concavity of the function.

The axis of symmetry applies to polynomials with even degrees. A polynomial function with an axis of symmetry will have mirror images on each side of a line that directly cuts through the polynomial.

The x and y intercepts talks about the points at which the function touches the axes of the plot

The degree of the polynomial helps to find the end behavior of the polynomial. The degree of a polynomial refers to the highest power to which the independent variable is raised. It is an important factor in determining if a polynomial function sketch will possess an axis of symmetry.

Answer:

2x⁴+x³-x²+54x+56

Step-by-step explanation:

Given the expression length of dylan room =  (x² – 2x + 8) and width = (2x² + 5x – 7), assuming the shap of the room is rectangular in nature, the formula for calculating area of a triangle is given as;

Area of rectangle = Length *Width

Area of the rectangle =  (x² – 2x + 8)(2x² + 5x – 7)

Area of the rectangle  = x²(2x² + 5x – 7) - 2x (2x² + 5x – 7) + 8(2x² + 5x – 7)

= (2x⁴+5x³-7x²)-(4x³+10x²-14x)+(16x²+40x-56)

expanding the bracket

= 2x⁴+5x³-7x²-4x³-10x²+14x+16x²+40x-56

Collecting the like terms;

= 2x⁴+5x³-4x³-7x²-10x²+16x²+40x+14x+56

= 2x⁴+x³-x²+54x+56

Hence, the expression that represents the area (lw) of Dylan's room is 2x⁴+x³-x²+54x+56

Answer:

2x^4+ x^3 - x^2 + 54x - 56 expression represents the area of Dylan’s room

Step-by-step explanation:

C on edge :)

Answer:

[tex]\boxed{V = 3591.4 \ cm^3}[/tex]

Step-by-step explanation:

Diameter = 19 cm

Radius = 19/2 = 9.5 cm

Volume = [tex]\frac{4}{3} (3.14)(9.5)^3[/tex]

V = [tex]\frac{4}{3}(3.14)(857.375)[/tex]

V = [tex]\frac{10774}{3}[/tex]

V = 3591.4 cm³

Answer:

i just wanted to delete this sorry

Step-by-step explanation:

my answer that is

lol sorry  

Answer: A. y-In x-3

explanation:

A) 22°

∡DBG = (360° - BD - BG)/2

= (360° - 170° - 146°)/2

= 44°/2

= 22°

Answer:

16 and 65536

Step-by-step explanation:

4^2 =16 and 4^8 =65536

Answer:

4^10

Step-by-step explanation:

4^2 x 4^8

When we multiply exponents with the same base, we can add the exponents

4^(2+ 8)

4^10

Answer:

Axis of Symmetry: x = 3

Vertex: (3, 5)

Step-by-step explanation:

Use a graphing calc.

Answer:

3

Step-by-step explanation:

Answer:

Becky's mistake was that she said [tex]\frac{4}{5} - \frac{5}{4} = 0[/tex], while it's actually equal to [tex]-\frac{9}{4}[/tex].

Step-by-step explanation:

[tex]\quad\begin{aligned} &\dfrac{4}{5} +7 -\dfrac{5}{4}\\\\ \\ =&\dfrac{4}{5} -\dfrac{5}{4}+7&\green{\text{Step } 1} \\\\ \\ \\ =&0+7&\blue{\text{Step } 2}\\\\ \\ \\ =&7&\purple{\text{Step } 3} \\\\ \\ \\ \end{aligned}[/tex]

Step 1 looks fine as she just rearranged the equation, keeping the negatives and positives right.

Step 2 is where she said that  [tex]\frac{4}{5} - \frac{5}{4} = 0[/tex]. This would only be true if we were multiplying one of the numbers by 0. So Step 2 was wrong.

Step 3 is right, as 0+7 = 7.

Hope this helped!

Answer:

step 2 is wrong

Step-by-step explanation:

Step-by-step explanation:

Y varies directly as cube root of x is written as

y = k³√x

where k is the constant of proportionality

when y = 3

x = 27

We have

[tex]3 = k \sqrt[3]{27} [/tex]

But ³√27 = 3

That's

3 = 3k

Divide both sides by 3

k = 1

The value of the relationship is

When x = 8

We have

Hope this helps you

Answer:

1

Step-by-step explanation:

concepts used is law of indices

where

(a^b)^c = a^bc

a^m/a^n = a^(m-n)

a^m *a^n = a^(m+n)

a^0 = 1

_______________________________________

50000)^2 = (5*10^4)^2 = 25*10^8

(0.00002)^3 = (2*10^-5)^3 = 8*10^-15

(0.0000001) = 10^-7

now

(50000)^2×(0.00002)^3\(200)×(0.0000001) =  25*10^8 * 8*10^-15/200*10^-7

  = 200*10^8-15-(-7)/200 = 10^-7 +7 = 10^0 = 1

Thus,1 is the answer

Answer:

3^6-4x=3^3x-3

Step-by-step explanation:

9^3-2x = 27^x-1  ( 9 is 3² and 27 is 3³)

(3²)^3-2x= (3³)^x-1    in case of exponential between brackets , multiply the exponents.

3^6-4x=3^3x-3

Answer:

x = 9/7

Step-by-step explanation:

9^3-2x = 27^x-1

(3^2)^3-2x = (3^3)^x-1

3^2(3-2x) = 3^3(x-1)

2(3-2x) = 3(x-1)

2(-2x+3) = 3x - 3

-4x + 6 = 3x - 3

-4x = 3x - 9

-7x = -9

x = -9/-7

x = 9/7

Answer:

36 people joined the radio control club.

Step-by-step explanation:

15-3= 12

12*3=36

Alan can conclude that the medicine given out to the treatment group does indeed work and reduces the amount of coughing and the control group with no treatment never got any better so the medicine is far better than no treatment at all.

Answer:

Trapezoid

Step-by-step explanation:

Got it right on quiz

The following that best classifies a quadrilateral with coordinates is :

A) Trapezoid

Thus, the correct answer is A.

Find out more information:

https://brainly.com/question/24200218referrer=searchResults

Answer:

Type I error

Step-by-step explanation:

Here, we are interested in knowing the type of error that stems from the hypotheses set up

in the question.

From the suggestion of the sample, we know that the food is actually safe but was wrongly labeled as being unsafe.

So in this case, the type of error committed is the type 1 error since the food is actually safe but there was a wrong suggestion of being generally unsafe by the sample

Answer: 15 cm

Step-by-step explanation:

For this problem, we can use the Pythagorean Theorem.

The legs of the triangle are 9 cm and 12 cm.

According to the theorem...

[tex]9^{2} +12^{2} =c^{2}[/tex], c being the hypotenuse.

[tex]81+144=225[/tex]

[tex]c^{2} =225\\\sqrt{225} =15[/tex]

Therefore c=15.

Answer:

15

Step-by-step explanation:

You need to find one of the other angle measures first, I will be solving for the top angle.

To find this you need to take the inverse tangent of the opposite length over the adjacent length, in this case it would be 12 over 9

tan^-1 (12/9)      

=53.1. round to the nearest degree so 53

now that you have your angle measure you can take the sine of that angle

for sine you do opposite over hypotenuse, we dont know the length of the hypotenuse so use x

sin(53) = 12/x

0.79 = 12/x  don't round the answer to sin(53) wait till the end to round and just use your calculator to remeber the exact number

0.79 = 12/x

•x          •x   multiply both sides by x

0.79x = 12

/0.79     /0.79    divide both sides by 0.79 this is when you would use the calculator to enter in the exact number not just 0.79

x = 15.02 now you can round to the nearest tenth or whole number for this one it would just be 15

x=15

Answer:

x² = 10

x = ±√10 (Take the square root of both sides)

Answer:

The pupils who are not participating in sports games are 82

Step-by-step explanation:

According to the given data we have the following:

2/31 participate in athletics

1/9 in volleyball games

Total participants=98

Therefore, pupils participate in athletics= 98*2/31

pupils participate in athletics=6

pupils participate in volleyball games=98*1/9

pupils participate in volleyball games=10

Therefore, pupils are not participating in sports games=98-16

pupils are not participating in sports games=82

The pupils who are not participating in sports games are 82

Answer: 8.94

Step-by-step explanation:

each side is the [tex]\sqrt{20}[/tex] so multiply that by 2 and you will have 8.94

Answer:

C. 18.5

Step-by-step explanation:

1/2(11 + 26) = 18.5

Answer:

x = pi/8   + pi/2  *n                    x = 3pi/8   +   pi /2 *n

Step-by-step explanation:

cos ^2 ( 2x) - sin ^2 (2x) = 0

Substitute u = 2x

cos ^2 ( u) - sin ^2 (u) = 0

We know cos ^2(x)-sin ^2(x)=cos (2x)

cos ( 2u) =0

Replacing u with 2x

cos  (2 *2x) =0

cos (4x) =0

cos u =0 when u = pi/2 + 2 pi n and 3pi/2 + 2 pi n  where n is an integer

4x = pi/2+2 pi n                    4x = 3pi/2+2pi n

x = pi/8   + pi/2  *n                    x = 3pi/8   +   pi /2 *n

Answer:

8 more unit of tiles

Step-by-step explanation:

The function is given as;

f(x) = x² - 6x + 1

Now, we want to add more unit tiles to complete the square.

The given function(f(x)) is of the order 2 due to the highest power of 2 attached to x, but the side of the square will be of the order 1.

Now, Let's make a general order 1 expression ax + b to be the side of the square.

From the function forming the square after adding some p unit tiles, we have;

f(x) + p = (side of square)²

Thus;

x² - 6x + 1 + p = (ax + b)²

x² - 6x + 1 + p = a²x² + 2abx + b²

Comparing both sides of the equation, we have;

a² = 1

2ab = 6

b² = 1 + p

From a² = 1, a = 1

From 2ab = 6,putting 1 for a, we have;

2(1)b = 6

b = 6/2

b = 3

From b² = 1 + p

Putting 3 for b, we have;

3² = 1 + p

9 = 1 + p

9 - 1 = p

p = 8

Thus, 8 more unit of tiles are required to complete the square.

Answer:

6

Step-by-step explanation:

6 appears the most

Answer:

6

Step-by-step explanation:

Put the data in order from smallest to largest

5,6,13,2,6,11,6,5,3,14

2,3,5,5,6,6,6,11,13,14

The mode is the number that appears most often

6 appears most often so it is the mode

Answer:

[tex]x = 17[/tex]

Step-by-step explanation:

According to the two tangent theory, tangent MN and tangent NP, which are both from point N, are congruent.

That is, [tex]x + 4 = 21[/tex]

Solve for x

[tex]x + 4 = 21[/tex]

Subtract 4 from both sides

[tex]x + 4 - 4 = 21 - 4[/tex]

[tex]x = 17[/tex]

Answer:

Blank 1: 3

Blank 2: 31

Step-by-step explanation:

f(x) = 2x + 7

Plug x as -2

2(-2) + 7

-4 + 7

= 3

Plug x as 12

2(12) + 7

24 + 7

= 31

Answer:

The answer is below

Step-by-step explanation:

The shape of the figure attached is the shape of a sector with an angle of 90° (quarter of a circle).

From the sector, AB = AC = radius of the sector (r) = 12. Therefore:

[tex]Area\ of\ sector=\frac{\theta}{360}*\pi r^2 = \frac{90}{360}*\pi * (12)^2 = 0.25 * \pi * 144=36\pi\\\\Area\ of\ triangle\ ABC=\frac{1}{2}*base *height= \frac{1}{2}*AB*BC=\frac{1}{2}*12*12=72\\\\Area \of\ shaded\ region = Area\ of\ sector-Area\ of\ triangle=36\pi-72\\\\Area \of\ shaded\ region =36\pi-72[/tex]

From the triangle: AC² = AB² + BC²

AC² = 12² + 12² = 144 + 144

AC² = 288

AC=√288 = 12√2

[tex]Perimeter\ of\ sector=\frac{\theta}{360}*2\pi r = \frac{90}{360}*2\pi * (12) = 0.25 * 2\pi * 12=6\pi\\\\Perimeter \of\ shaded\ region = Perimeter\ of\ sector+AC=6\pi + 12\sqrt{2}[/tex]