The midsegment of a trapezoid is 11 cm in length. If one of the trapezoid's bases is 17 cm long, what is the length of the other base?

Answer:

2h+2f=10.50

4h+3f=19.50

Step-by-step explanation:

2h+2f=10.50

4h+3f=19.50

• To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

{2h2f=10.5,4h3f=19.5}

• Choose one of the equations and solve it for h by isolating h on the left hand side of the equal sign.

2h+2f=10.5

• Subtract 2f from both sides of the equation.

2h=−2f+10.5

• Divide both sides by 2.

h=1/2 (−2f+10.5)

• Multiply 1/2  times −2f+10.5.

h=−f+21/4

• Substitute −f+21/4  for h in the other equation, 4h+3f=19.5.

4(−f+21/4)+3f=19.5

• Multiply 4 times −f+21/4.

−4f+21+3f=19.5

• Add −4f to 3f.

−f+21=19.5

• Subtract 21 from both sides of the equation.

−f=−1.5

• Divide both sides by −1.

f=1.5

• Substitute 1.5 for f in h=−f+21/4. Because the resulting equation contains only one variable, you can solve for h directly.

h=−1.5+21/4

• Add 21/4  to −1.5 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

h=15/4  

Answer:

A)

62/3 = 20.67 hours

B)

60.00 hours

C)

2074.29 miles

Step-by-step explanation:

If we assume the earth is a perfect circle, then in a complete rotation the earth covers 360 degrees or 2π radians.

A)

In 24 hours the earth rotates through an angle of 360 degrees. We are required to determine the duration it takes to rotate through 310 degrees. Let x be the duration it takes the earth to rotate through 310 degrees, then the following proportions hold;

(24/360) = (x/310)

solving for x;

x = (24/360) * 310 = 62/3 = 20.67 hours

B)

In 24 hours the earth rotates through an angle of 2π radians. We are required to determine the duration it takes to rotate through 5π radians. Let x be the duration it takes the earth to rotate through 5π radians, then the following proportions hold;

(24/2π radians) = (x/5π radians)

Solving for x;

x = (24/2π radians)*5π radians = 60 hours

C)

If the diameter of the earth is 7920 miles, then in 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle we have;

circumference = 2*π*R = π*D

                         = 7920π miles

Therefore, the speed of the earth is approximately;

(7920π miles)/(24 hours) = 330π miles/hr

The distance covered by a point in 2 hours will thus be;

330π * 2 = 660π miles = 2074.29 miles

Answer:

Step-by-step explanation:

The quotient in each case can be found by any of several means, including synthetic division (possibly the easiest), polynomial long division, or graphing.

1. The graph shows you the quotient is (x-1)^2 +2 = x^2 -2x +3.

2. The graph shows you the quotient is (x+1)^2 +2 = x^2 +2x +3.

The range would only include positive integers.

Answer B

Answer:

- The maximum value is 86 occurs at (8 , 7)

Step-by-step explanation:

* Lets remember that a function with 2 variables can written

 f(x , y) = ax + by + c

- We can find a maximum or minimum value that a function has for

 the points in the polygonal convex set

- Solve the inequalities to find the vertex of the polygon

- Use f(x , y) = ax + by + c to find the maximum value

∵ 3x + 4y = 19 ⇒ (1)

∵ -3x + 7y = 25 ⇒ (2)

- Add (1) and (2)

∴ 11y = 44 ⇒ divide both sides by 11

∴ y = 4 ⇒ substitute this value in (1)

∴ 3x + 4(4) = 19

∴ 3x + 16 = 19 ⇒ subtract 16 from both sides

∴ 3x = 3 ⇒ ÷ 3

∴ x = 1

- One vertex is (1 , 4)

∵ 3x + 4y = 19 ⇒ (1)

∵ -6x + 3y = -27 ⇒ (2)

- Multiply (1) by 2

∴ 6x + 8y = 38 ⇒ (3)

- Add (2) and (3)

∴ 11y = 11 ⇒ ÷ 11

∴ y = 1 ⇒ substitute this value in (1)

∴ 3x + 4(1) = 19

∴ 3x + 4 = 19 ⇒ subtract 4 from both sides

∴ 3x = 15 ⇒ ÷ 3

∴ x = 5

- Another vertex is (5 , 1)

∵ -3x + 7y = 25 ⇒ (1)

∵ -6x + 3y = -27 ⇒ (2)

- Multiply (1) by -2

∴ -6x - 14y = -50 ⇒ (3)

- Add (2) and (3)

∴ -11y = -77 ⇒ ÷ -11

∴ y = 7 ⇒ substitute this value in (1)

∴ -3x + 7(7) = 25

∴ -3x + 49 = 25 ⇒ subtract 49 from both sides

∴ -3x = -24 ⇒ ÷ -3

∴ x = 8

- Another vertex is (8 , 7)

* Now lets substitute them in f(x , y) to find the maximum value

∵ f(x , y) = 2x + 10y

∴ f(1 , 4) = 2(1) + 10(4) = 2 + 40 = 42

∴ f(5 , 1) = 2(5) + 10(1) = 10 + 10 = 20

∴ f(8 , 7) = 2(8) + 10(7) = 16 + 70 = 86

- The maximum value is 86 occurs at (8 , 7)

Answer:

B  (5, 1)

Step-by-step explanation:

Answer:

Here's what I get.

Step-by-step explanation:

Question 4

The general equation for a sine function is

y = a sin[b(x - h)] + k

where a, b, h, and k are the parameters.

Your sine wave is

y = 3sin[4(x + π/4)] - 2

Let's examine each of these parameters.

Case 1. a = 1; b = 1; h = 0; k = 0

y = sin x

This is a normal sine curve (the red line in Fig. 1).

(Sorry. I forgot to label the x-axis, but it's always the horizontal axes)

Case 2. a = 3; b = 1; h = 0; k = 0

y = 3sin x

The amplitude changes from 1 to 3.

The parameter a controls the amplitude of the wave (the blue line in Fig. 1).

Case 3. a = 3; b = 1; h = 0; k = 2

y = 3sin x - 2

The graph shifts down two units.

The parameter k controls the vertical shift of the wave (the green line

in Fig. 1).

Case 4. a = 3; b = 4; h = 0; k = 2

y = 3sin(4x) - 2

The period decreases by a factor of four, from 2π to π/2.

The parameter b controls the period of the wave (the purple line in Fig. 2).

Case 5. a = 3; b = 4; h = -π/4; k = 2

y = 3sin[4(x + π/4)] - 2

The graph shifts π/4 units to the left.

The parameter h controls the horizontal shift of the wave (the black dotted line in Fig. 2).

[tex]\boxed{a = 3; b = 4; h = \frac{\pi}{2}; k = -2}}[/tex]

[tex]\text{amplitude = 3; period = } \dfrac{\pi}{2}}[/tex]

[tex]\textbf{Transformations:}\\\text{1. Dilate across x-axis by a scale factor of 3}\\\text{2. Translate down two units}\\\text{3. Dilate across y-axis by a scale factor of } \frac{1}{4}\\\text{4. Translate left by } \frac{\pi}{4}[/tex]

Question 6

y = -1cos[1(x – π)] + 3

[tex]\boxed{a = -1, b = 1, h = \pi, k = 3}[/tex]

[tex]\boxed{\text{amplitude = 1; period = } \pi}[/tex]

Effect of parameters

Refer to Fig. 3.

Original cosine: Solid red line

m = -1: Dashed blue line (reflected across x-axis)

 k = 3: Dashed green line (shifted up three units)

 b = 1: No change

h = π: Orange line (shifted right by π units)

[tex]\textbf{Transformations:}\\\text{1. Reflect across x-axis}\\\text{2. Translate up three units}\\\text{3. Translate right by } \pi[/tex]

Answer:

  D)  √3/3

Step-by-step explanation:

The coordinates of the point at the angle π/6 are shown as (√3/2, 1/2). The tangent of the angle is the ratio of the y-coordinate to the x-coordinate:

  tan(π/6) = (1/2)/((√3)/2) = 1/√3 = (√3)/3 . . . . matches choice D

B. x=5

Two shapes are congruent if you can turn one into the other by moving, rotating or flipping. So if we rotate 180 degrees, say, trapezoid WXYZ and then moving it to the left, it will match trapezoid ABCD. If so, it will be true that:

[tex]\angle BAD=\angle XWZ \\ \\ \angle BAD=4x-7 \\ \\ \angle XWZ=2x+3 \\ \\ 4x-7=2x+3 \\ \\ Solving \ for \ x: \\ \\ 4x-2x=7+3 \\ \\ 2x=10 \\ \\ \boxed{x=5}[/tex]

Answer:

Answer is B x=5

Step-by-step explanation:

Hope this helps!!

Answer:

see below

Step-by-step explanation:

sin x                                 1

-------------------              = -----------

sec^2 x - tan ^2 x               csc x

Sec = 1/cos   and tan = sin/cos

sin x                                         1

-------------------                     = -----------

1/ cos ^2 x -sin^2/cos ^2 x       csc x

Factor the denominator

sin x                                         1

-------------------                     = -----------

(1-sin^2 x)/ cos ^2 x                csc x

We know that 1 - sin^2 x = cos ^2

sin x                                         1

-------------------                     = -----------

(cos^2 x)/ cos ^2 x                csc x

sin x                                         1

-------------------                     = -----------

1                                               csc x

Multiply the top and bottom of the left hand side by 1/ sin x

sin x  * 1/ sin x                              1

-------------------                     = -----------

1     * 1 sin x                             csc x

1                                                1

-------------------                     = -----------

       1 sin x                             csc x

We know that 1/sin x = csc

1                              1

---------               = -----------

csc (x)                   csc x

Answer:

The hourly fee is $ 3.

Step-by-step explanation:

Given,

The initial fee = $ 43,

Let x be the additional hourly fee ( in dollars ),

Thus, the total additional fee for 7 hours = 7x dollars,

And, the total fee for 7 hours = Initial fee + Additional fee for 7 hours

= ( 43 + 7x ) dollars,

According to the question,

43 + 7x = 64

7x = 21      ( Subtracting 43 on both sides )

x = 3          ( Divide both sides by 7 )

Hence, the hourly fee is $ 3.

Answer:

7h+43=64

$3

Step-by-step explanation:

did it on edge

Answer:

  74.8 square yards

Step-by-step explanation:

The centerline of the path is a rectangle 5.3+2 = 7.3 yards wide and 9.4+2 = 11.4 yards long. The perimeter of that rectangle is 2(7.3+11.4) = 37.4 yards long. The area of the path is this length times the width of the path:

  path area = (37.4 yd)(2 yd) = 74.8 yd²

The area of the path is 74.8 square yards.

First, we calculate the area of the garden:

[tex]\[ A_{\text{garden}} = \text{length} \times \text{width} = 9.4 \text{ yards} \times 5.3 \text{ yards} \][/tex]

[tex]\[ A_{\text{garden}} = 49.82 \text{ square yards} \][/tex]

Next, we need to find the area of the entire region including the path. The path adds an additional width of 2 yards on all sides of the garden.

The total length and width of the region including the path are:

[tex]\[ \text{Total length} = 9.4 \text{ yards} + 2 \times 2 \text{ yards} = 13.4 \text{ yards} \][/tex]

[tex]\[ \text{Total width} = 5.3 \text{ yards} + 2 \times 2 \text{ yards} = 9.3 \text{ yards} \][/tex]

Now we calculate the area of the entire region including the path:

[tex]\[ A_{\text{total}} = \text{Total length} \times \text{Total width} = 13.4 \text{ yards} \times 9.3 \text{ yards} \][/tex]

[tex]\[ A_{\text{total}} = 124.62 \text{ square yards} \][/tex]

Finally, we subtract the area of the garden from the total area to find the area of the path:

[tex]\[ A_{\text{path}} = A_{\text{total}} - A_{\text{garden}} \][/tex]

[tex]\[ A_{\text{path}} = 124.62 \text{ square yards} - 49.82 \text{ square yards} \][/tex]

[tex]\[ A_{\text{path}} = 74.8 \text{ square yards} \][/tex].

Answer:a reflection across the line containing AB

Step-by-step explanation:

The correct option is A).

Step-by-step explanation:

Given :

First Transformation is a translation of vertex B to vertex R.

AB = RQ   (refer the given figure)

Solution :

The second transformation is obviously a reflection across the line containing AB because AB = RQ and there is translation of vertex B to vertex R therefore there is also a translation of vertex A to vertex Q and through observing the given diagram we can say that there is a reflection across the line containing AB.

Hence, the correct option is A).

For more information, refer the link given below

https://brainly.com/question/21454252?referrer=searchResults

Answer:

rate=1.28571428571.. (1.29) miles per minute, or 77.1428571429.. (77.14) mph

Step-by-step explanation:

"use distance = rate time (d=rt) to find the number of miles per hour Etty must drive to go 45 miles in 35 minutes. ( remember time is written in hours?"

distance=rate*time--- we know distance and time

45 mi= rate*35

rate=45/35

rate=1.28571428571 miles per minute, or 77.1428571429 mph

Answer:

Step-by-step explanation:

77/14mph

Answer:

[tex]\frac{5}{2}x^3-\frac{9}{4}x^2+\frac{7}{2}x-\frac{3}{2}[/tex]

Step-by-step explanation:

Given polynomials are [tex]\frac{1}{2}x-\frac{1}{4}[/tex] and [tex]5x^2-2x+6[/tex].

Now we need to find their product which can be done as follows:

[tex]\left(\frac{1}{2}x-\frac{1}{4}\right)\left(5x^2-2x+6\right)[/tex]

[tex]=5x^2\left(\frac{1}{2}x-\frac{1}{4}\right)-2x\left(\frac{1}{2}x-\frac{1}{4}\right)+6\left(\frac{1}{2}x-\frac{1}{4}\right)[/tex]

[tex]=\frac{5}{2}x^3-\frac{5}{4}x^2-x^2+\frac{1}{2}x+3x-\frac{3}{2}[/tex]

[tex]=\frac{5}{2}x^3-\frac{9}{4}x^2+\frac{7}{2}x-\frac{3}{2}[/tex]

Hence final answer is [tex]\frac{5}{2}x^3-\frac{9}{4}x^2+\frac{7}{2}x-\frac{3}{2}[/tex].

Answer:

C.

Step-by-step explanation:

The topic is on: 'impossible geometric construction"

The three areas of concern are : Trisecting an angle, squaring a circle and doubling a cube.

In double a cube the , when the edge in 1 unit will give the equation will give the equation x³=2 whose solution yields cube root of 2. This problem can not be solve because cube root of 2 is not an Euclidean number.

Answer:

C. Doubling the cube.

Step-by-step explanation:

Geometric construction is majorly a two dimensional drawing, excluding some form of projections (isometric and oblique drawing) which are three dimensional. Essential instruments to use in construction are; a pair of compass and straightedge (eg ruler).

From the options stated in the given question, doubling the cube is difficult to construct using the instruments given. A cube is a three dimensional shape that has all sides to be equal. It is a prism formed from a square, and it has six faces.

Answer:

B 18*2/9 =4

Step-by-step explanation:

To determine the number of mixed nuts that were almonds, take the number of nuts and multiply by the fraction that were almonds

nuts * 2/9= almonds

18 * 2/9

36/9

4

Answer: Option B.  Ellipse

[tex]\frac{(x-\frac{1}{4})^2}{\frac{129}{16}}+\frac{(y-0)^2}{\frac{129}{32}}=1[/tex]

Step-by-step explanation:

To know what type of conic section the function is

[tex]2x ^ 2-9x + 4y ^ 2 + 8x = 16[/tex] we must simplify it.

[tex]2x ^ 2-9x + 4y ^ 2 + 8x = 16\\\\2x^2 -x +4y^2 =16[/tex]

complete the square of the expression:

[tex]2x ^ 2 -x\\\\\\2(x^2 -\frac{1}{2}x)\\\\2(x^2-\frac{1}{2}x +\frac{1}{16})-2\frac{1}{16}\\\\2(x-\frac{1}{4})^2 -\frac{1}{8}[/tex]

So we have

[tex]2(x-\frac{1}{4})^2 -\frac{1}{8}+4y^2 =16\\\\2(x-\frac{1}{4})^2+4y^2 =\frac{129}{8}\\\\\frac{8}{129}[2(x-\frac{1}{4})^2] +\frac{8}{129}[4y^2] =1\\\\\frac{16(x-\frac{1}{4})^2}{129}+\frac{32(y-0)^2}{129}=1[/tex]

[tex]\frac{(x-\frac{1}{4})^2}{\frac{129}{16}}+\frac{(y-0)^2}{\frac{129}{32}}=1[/tex]

We know that the general equation of an ellipse has the form

[tex]\frac{(x-h)^2}{a^2} +\frac{(y-k)^2}{b^2}=1[/tex]

Then the equation

[tex]\frac{(x-\frac{1}{4})^2}{\frac{129}{16}}+\frac{(y-0)^2}{\frac{129}{32}}=1[/tex]

is an ellipse with center [tex](\frac{1}{4}, 0)[/tex]

[tex]a =\sqrt{\frac{129}{16}}[/tex]  and  [tex]b=\sqrt{\frac{129}{32}}[/tex]

Observe the attached image

Answer:

b = 6√3.

Step-by-step explanation:

Use trigonometry.

cos 30 = adjacent side / hypotenuse = b / 12

√3 / 2 = b / 12

2b = 12√3

b = 6√3 answer.

Answer:

Step-by-step explanation        

∣

∣

∣

x

{x|x≥8/3}

Answer:

im pretty sure its d

Step-by-step explanation:

-35/5 is the answer

Answer:

17 days

Step-by-step explanation:

For each day she works, she earns +55 and each day she DOES NOT work she earns -66. Total 30 days.

Let number of days she works be x

thus, number of days she DOES NOT work is 30 - x

We can setup an equation as:

55(x) + -66(30-x) = 77

This means, she works x days for 55 each and 30 - x days getting -66 each, totalling 77.

We can solve for x to find number of days she worked. Work shown below:

[tex]55(x) + -66(30-x) = 77\\55x-66(30)+66x=77\\121x -1980 = 77\\121x = 77+1980\\121x = 2057\\x=\frac{2057}{121}\\x=17[/tex]

Thus, she worked 17 days

Answer:

A B = {x | x < 5}

Step-by-step explanation:

The domain of A B will be given by {x | x < 5}

The domain of A is given as  {x | x < 5} while that of B is {x | x ≤ 7}. From this we can infer that the domain of A is a subset of B since A is contained in B. The domain of A B is simply the intersection of these two sets which is A.

Answer:

[tex]\frac{13}{5}[/tex]

Step-by-step explanation:

we know that

[tex]csc(\theta)=\frac{1}{sin(\theta)}[/tex]

In this problem

[tex]sin(\theta)=\frac{1.5}{3.9}[/tex]

substitute

[tex]csc(\theta)=\frac{3.9}{1.5}[/tex]

Multiply by 10 both numerator and denominator

[tex]csc(\theta)=\frac{39}{15}[/tex]

Divide by 3 both numerator and denominator

[tex]csc(\theta)=\frac{13}{5}[/tex]

Answer:

hexagonal pyramid

Step-by-step explanation:

Answer:

Final answer is approx 1622.48 square kilometers.

Step-by-step explanation:

Given that a certain forest covers an area of 2600 km 2 suppose that each year this area decreases by 9% . Now we need to find about what will the area be after 5 years.

So we need to plug these values into decay formula which is given by:

[tex]A=P(1-r)^t[/tex]

Where P=2600

r= rate = 9%= 0.09

t=time = 5 years

Plug these values into above formula, we get:

[tex]A=2600(1-0.09)^5[/tex]

[tex]A=2600(0.91)^5[/tex]

[tex]A=2600(0.6240321451)[/tex]

[tex]A=1622.48357726[/tex]

Hence final answer is approx 1622.48 square kilometers.

Final answer:

Using the exponential decay formula, A = A_0 (1-r)^t, the forest area after 5 years with an annual decrease of 9% is approximately 1622.4 km².

Explanation:

To calculate the forest area after 5 years with an annual decrease of 9%, we can use the formula for exponential decay. The original area of the forest is 2600 km2.

So, if the forest continues to decrease by 9% annually, the area will be approximately 1622.4 km2 after 5 years.

Answer: 10) 615° & -105°

               12) -440° & 280°

Step-by-step explanation:

Coterminal means it is in the exact same spot on the Unit Circle but one or more rotations clockwise or counterclockwise.

Since one rotation = 360°, add or subtract that from the given angle until you get a positive or negative number.

10) 255° + 360° = 615°     (this is a POSITIVE coterminal angle to 255°)

     255° - 360° = -105°     (this is a Negative coterminal angle to 255°)

12) -800° + 360° = -440°   (this is a Negative coterminal angle to -800°)

    -440° + 360° =  -80°      (this is a Negative coterminal angle to -800°)

      -80° + 360° = 280°     (this is a POSITIVE coterminal angle to -800°)

Final answer:

Coterminal angles for 255° are 615° (positive) and -105° (negative) by adding or subtracting 360° respectively. For -800°, the coterminal angles are -80° (positive) and -1160° (negative).

Explanation:

To find a positive and a negative angle coterminal with the given angle of 255°, we can add or subtract multiples of 360° (the total degrees in a circle). For a positive coterminal angle, we can add 360° to 255°:

255° + 360° = 615°

For a negative coterminal angle, we subtract 360° from 255° until we get a negative result:

255° - 360° = -105°

Similarly, for -800°, to find a positive coterminal angle, we keep adding 360° until we get a positive result:

-800° + 360° = -440°
-440° + 360° = -80°

For a negative coterminal angle, we can subtract 360° from -800°:

-800° - 360° = -1160°

Answer:

3,105

Step-by-step explanation:

the answer is 3,105 because you simply take the total number that was eaten in 3 months and divide it by 3 since they only want to know what was eaten in 1 month

The sum of two number a and b is [tex]a+b[/tex]

Its square is [tex](a+b)^2[/tex]

Half of c is [tex]\frac{c}{2}[/tex]

And we have to subtract this from what we got before:

[tex](a+b)^2-\dfrac{c}{2}[/tex]

Finally, we multiply everything by 5:

[tex]5\left[(a+b)^2-\dfrac{c}{2}\right][/tex]

Queremos, a partir de una frase, escribir la correspondiente expresión algebraica.

Obtendremos:

[tex][(a + b)^2 - c/2]*5[/tex]

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

Lo que nos dan es:

"Si al cuadrado de la suma de dos números a y b le restamos la mitad de c y la diferencia resultante la multiplicamos por 5"

Veamos esto en partes, la primera dice:

"Si al cuadrado de la suma de dos números a y b..."

El cuadrado de la suma de dos números a y b se escribe como:

[tex](a + b)^2[/tex]

Ahora tenemos:

"Si al cuadrado de la suma de dos números a y b le restamos la mitad de c ..."

Ahora le restamos la mitad de c a lo que encontramos antes:

[tex](a + b)^2 - c/2[/tex]

Finalmente:

"Si al cuadrado de la suma de dos números a y b le restamos la mitad de c y la diferencia resultante la multiplicamos por 5"

Es decir, debemos multiplicar por 5 a la diferencia (la resta) de arriba:

[tex][(a + b)^2 - c/2]*5[/tex]

Está es la expresión que queriamos encontrar.

Si quieres aprender más, puedes leer:

https://brainly.com/question/24758907

But in cost

(50×4)-(42.5×4)

Rs30

Answer:

its D

Step-by-step explanation:

Answer:it would be c because the stock increased by 5.74 over yesterday’s price

Step-by-step explanation: