In a trapezoid the lengths of bases are 11 and 18. The lengths of legs are 3 and 7. The extensions of the legs meet at some point. Find the length of segments between this point and the vertices of the greater base.

9 students did not study in either the cafeteria or the student lounge.

How to find the number

To find the number of students who did not study in either the cafeteria or the student lounge, we solve as follows

Let

C = 92

L = 86

C ∩ L = 40

We find the number in either C, L or C ∩ L

= (92 - 40) + (86 - 40) + 40

= 52 + 46 + 40

= 138

The number  did not study in either the cafeteria or the student lounge

= 147 - 138

= 9

Answer:

x + y = 60

Step-by-step explanation:

In the given figure, we have two lines that intersect each other at one point.

Therefore, the opposite angles are equal to each other and we can write them in the form of an equation as:

2y - 5 = 95 --- (1)

3x + 55 = 85 --- (2)

Now solving each of the equations to find the value of x and y.

For y:

2y - 5 = 95

2y = 95 + 5

2y = 100

y = 50

For x:

3x + 55 = 85

3x = 85 -55

3x = 30

x = 10

Therefore, x + y = 10 + 50 = 60.

1/3, 1/4, 1/5

40% = 40/100 = 2/5

Any fraction with a numerator of 2 and a denominator larger than 5 will be less than 40%, for example.

So, we can choose 2/6 = 1/3, 2/8 = 1/4, and 2/10 = 1/5 as some such values.

_____

We could also choose something like 39.99% = 3999/10000, or 1% = 1/100.

Answer:

6 square root of 5 end root minus 4 square root of 7

Step-by-step explanation:

[tex]3\sqrt{5}-2\sqrt{7}+\sqrt{45}-\sqrt{28}=3\sqrt{5}-2\sqrt{7}+\sqrt{3^2\cdot 5}-\sqrt{2^2\cdot 7}\\\\=(3+3)\sqrt{5}+(-2-2)\sqrt{7}=6\sqrt{5}-4\sqrt{7}[/tex]

_____

Comment on the answer form

In symbols, parentheses are preferred for grouping:

... 6√(5) -4√7

or

... 6(√5)-4√7

As with your "end root" the grouping symbols are only needed to resolve the ambiguity of what's under the radical.

Answer:

Answer:

6 square root of 5 end root minus 4 square root of 7

Step-by-step explanation:

_____

Comment on the answer form

In symbols, parentheses are preferred for grouping:

... 6√(5) -4√7

or

... 6(√5)-4√7

As with your "end root" the grouping symbols are only needed to resolve the ambiguity of what's under the radical.

Answer :

The proof is as follows :

Step-by-step explanation:

Let NC = x

⇒ AB = 3x and AN = 2x

In Δ ABN, By using Pythagoras theorem,

AB² = BN² + AN²

⇒ BN² = AB² - AN²

⇒ BN² = (3x)² - (2x)²

⇒ BN² = 5x²

⇒ BN = x√5  .......................(1)

Now in ΔANC , Using Pythagoras theorem We have,

AC² = NC² + AN²

⇒ AC² = x² + (2x)²

⇒ AC² = 5x²

⇒ AC = x√5   ....................(2)

From equations (1) and (2) We get,

AC = BN , which is our required result

Answer:

BN=AC=√5 x.

The proof is explained in step-by-step explaination.

Step-by-step explanation:

Let NC=x. It is given that AB=3NC & AN=2NC

⇒ AB=3x & AN=2x

By applying Pythagoras theorem

In triangle ANC,

[tex]AC^{2}=AN^{2}+NC^{2}[/tex]

⇒ [tex]AC^{2} = (2x)^{2}+x^{2}[/tex]

⇒ [tex]AC^{2}=4x^{2}+x^{2} =5x^{2}[/tex]

⇒ [tex]AC=\sqrt{5}x[/tex]   →    (1)

Similarly, In triangle ABN,

[tex]AB^{2}=AN^{2}+BN^{2}[/tex]

⇒ [tex](3x)^{2}=BN^{2}+x^{2}[/tex]

⇒ [tex]9x^{2} = (BN)^{2}+4x^{2}[/tex]

⇒ [tex]BN^{2}=5x^{2}[/tex]

⇒ [tex]BN=\sqrt{5}x[/tex]   →   (2)

From eq (1) & (2),    AC=BN

Answer:

The cost of the wristband for 8 rides is $35.

Step-by-step explanation:

The expression for the cost, C, for r rides is

C = 2.5r + 15

Since she wants to go on 8 rides, r is 8.

Substitute r with 8 in the cost equation and evaluate it.

C = 2.5r + 15

C = 2.5 * 8 + 15

C = 20 + 15

C = 35

The cost of the wristband for 8 rides is $35.

Using the smallest number she has, 9 daisies..

18/9 = 2

45/9 = 5

She can make 9 bouquets with 2 roses, 1 daisy and 5 tulips in each.

That means each bouquet would have 8 total flowers.

x = 8.5

The other two sides are given in the diagram.

The Pythagorean theorem tells you ...

... 19² = 17² +x²

Subtracting 17², we have ...

... x² = 361 -289 = 72

Taking the square root gives x.

... x = √72 = 6√2

... x ≈ 8.5

The correct option is the last:

[tex] a_n = -2a_{n-1}+1 [/tex]

In fact, every term in the sequence is one more than twice the opposite of the previous one:

We start with 3. Twice its opposite is -6. Plus one, we get -5.

We start with -5. Twice its opposite is 10. Plus one, we get 11.

We start with 11. Twice its opposite is -22. Plus one, we get -21.

The recursive formula is: [tex]a_n-a_{n-1} = (-8)(-1)^n \times (2)^{n-2}[/tex]

To find a recursive formula for the given sequence, we need to determine the relation between consecutive terms.

Let's denote the sequence as an, where:

[tex]a_1 = 3\\a_2 = -5\\a_3 = 11\\a_4 = -21\\[/tex]

First, let's calculate the differences between consecutive terms:

[tex]a_2 - a_1 = -5 - 3 = -8\\a_3 - a_2 = 11 - (-5) = 16\\a_4 - a_3 = -21 - 11 = -32[/tex]

We observe that each difference is a multiple of 8 and that each difference is twice the previous difference but with alternating signs.

The recursive formula can be defined as:

[tex]a_n-a_{n-1} = (-8)(-1)^n \times (2)^{n-2}[/tex]

Thus the recursive formula is: [tex]a_n-a_{n-1} = (-8)(-1)^n \times (2)^{n-2}[/tex]

Answer:

the set of all points between point F and point G, including point F and point G

Step-by-step explanation:

The definition of a line segment is the set of points on a line between two given end points, including those end points. The best description is the one that matches the definition.

Answer:

the set of all points between point F and point G, including point F and point G

Step-by-step explanation:

3 ft

The statue's height is 1.5 times the length of its shadow, so we expect the same relationship for the globe.

... 1.5 × 2 ft = 3 ft

_____

Comment on the problem

As a practical matter, with the sun high enough in the sky to cast a shadow shorter than the object's height, it will be quite difficult to measure the length of the shadow of the point at the top of the globe. The shadow of other parts of the globe will interfere.

Answer:

A = 10w

Step-by-step explanation:

In the area formula, the coefficient of width is length. Here, that is ...

... A = 7w

7 is the coefficient of the width. Increasing it by 3 makes it be 10, so we have ...

... A' = 10w

_____

Comment on the problem statement

The problem does not make it clear whether area stays the same as the coefficient increases. We have assumed that it does not.

Also, the coefficient of width in the area formula has units of inches. "Increases by 3" makes no sense in this context. It would make sense for it to increase by 3 inches. The result is very different if the increase is 3 microns, for example.

Answer:

Steplo-by-step explanation:loan is 1200.

The interest rate is 6.50

Pp 46.90

Cumulative payment $53.4

Total payments$1,282.93

Final answer:

Lane will pay a total of $156 in simple interest on the loan of $1200 over 2 years, calculated using the simple interest formula: I = PRT.

Explanation:

Lane borrowed $1200 at a simple interest rate of 6.5% for a period of 2 years. To calculate the total amount of interest that will be paid on the loan, we can use the simple interest formula, which is:

I = PRT

where I is the interest, P is the principal amount borrowed, R is the interest rate per year (expressed as a decimal), and T is the time in years the money is borrowed for.

First, we convert R to a decimal by dividing it by 100:

R = 6.5% / 100 = 0.065

Next, we substitute the values into the formula:

I = $1200 × 0.065 × 2

I = $1200 × 0.13

I = $156

Therefore, the total amount of interest that Lane will be paying on the loan over the next 2 years is $156.

2

Solve the second equation for y.

... 8x -12 = 4y . . . . add 4y -12

... 2x -3 = y . . . . . . divide by the coefficient of y

The coefficient of x is 2, so a parallel line will have an x-coefficient of 2. The line ...

... y = 2x -6 . . . . . . . . m = 2

will be parallel to the given line, so will not intersect it.

Answer:

2^(8/9) in²

Step-by-step explanation:

Make use of the identity ...

... (a^b)^c = a^(bc)

Here, you have a=2, b=4/9, c=2. There is an additional factor (units of inches) inside the parentheses on the left. For that, you use the identity

... (ab)^c = a^c·b^c

In this case a = 2^(4/9), b = in, c = 2.

So, the working of your problem is ...

... Area = (side length)^2 = (2^(4/9) in)^2 = (2^(4/9))^2 in^2

... = 2^(4/9·2) in^2 = 2^(8/9) in^2

2/5

There are 2 units of green and 5 units of "pink," so the ratio is ...

... green/pink = 2/5

Answer: No

Step-by-step explanation:

Three of the other angles are 45°. The other four are 180° - 45°, which is not 55°. At the intersection of two lines, opposite angles are equal and adjacent angles are complementary, so two adjacent angles add to 180°. Adding a parallel line gives four more angles identical to the first four.

Answer:

A = 4200 ft^2

Step-by-step explanation:

We know the formula for area is

A = l*w

We need to have the same units

convert yd to ft

1 yd = 3ft

Multiply each by 70

70 yds = 210 ft

A = 210 *20

A = 4200 ft^2

The area of the pavement section is 4200 square feet, computed by converting the length to the same unit as the width and multiplying width by length.

The subject of this question is the calculation of the area of a rectangle. The rectangle in question is a section of pavement with a width of 20 ft and a length of 70 yd. Before calculating, it's important to have the measurements in the same units. Converting 70 yards to feet (since 1 yard equals 3 feet) we get 210 feet. The formula to calculate the area of a rectangle is Area = Width x Length. Substituting the given values into the formula, we get: Area = 20 ft x 210 ft which equals 4200 square feet. Therefore, the pavement section's area is 4200 square feet.

https://brainly.com/question/34380164

#SPJ3

Answer:

2

Step-by-step explanation:

1/2 cup = 2/4 cups = 2 × 1/4 cup

Alonzo can make 2 batches that each require 1/4 cup.

Answer:

AE

Step-by-step explanation:

Pairs of letters identify line segments:

... AE, EG, AG

... AD, DE, AE

Segment AE is common to both lists.

Answer:

1: Simplify 15/20 to 3/4

y/4=3/4

Multiply both sides by 4

y=3/4×4

Simplify 3/4×4 to 12/4

y=12/4

Simplify 12/4 to 3

y=3

2: Multiply both sides by z-3

6=8/5(z-3)

Simplify 8/5(z-3) to 8(z-3)/5

8(z-3)/5

Multiply both sides by 5

6×5=8(z-3)

Simplify 6×5 to 30

30=8(z-3)

Divide both sides by 8

30/8=z-3

Simplify 30/8 to 15/4

15/4=z-3

Add 3 to both sides

15/4+3=z

Simplify 15/4+3 to 27/4

27/4=z Switch sides z=27/4

Answer:

[tex]h^{24}[/tex]

Step-by-step explanation:

[tex](\frac{h^{12}}{h^4})^3\\ (h^8)^3\\h^{24}[/tex]

When dividing two exponents (of the same bases) you subtract the exponents.  When there is an exponent to an exponent, you multiply the to exponents.

[tex]\left(\dfrac{h^{12}}{h^4}\right)^3\\\\\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=\left(h^{12-4}\right)^3=\left(h^8\right)^3\\\\\text{use}\ (a^n)^m=a^{n\cdot m}\\\\=h^{8\cdot3}=h^{24}\\\\Answer:\ \boxed{\left(\dfrac{h^{12}}{h^4}\right)^3=h^{24}}[/tex]

Answer:

56 = (0.85)w

Step-by-step explanation:

"is" translates to "=".

"of" translates to "×".

We can let "what number" translate to "w".

Then ...

56 is 85% of what number . . . . translates to ...

56 = 0.85×w

_____

Of course, you know that 85% = 85/100 = 0.85.

Answer:

‪0.155922‬

Step-by-step explanation:

Answer: 0.1562 kilograms

Step-by-step explanation: To convert 5.5 ounces into kilograms, we first convert 5.5 ounces into grams using the conversion factor 1 oz = 28.4 g.

Since we are going from a larger unit "ounces" to a smaller unit "grams" we multiply 5.5 by the conversion factor which is 28.4 to get 156.2.

This means that 5.5 ounces is equal to 156.2 grams.

Next, we convert 156.2 grams into kilograms using the conversion factor

1 kilogram = 1,000 grams. Since we are going from a smaller unit "grams" to a

larger unit "kilograms" we divide 156.2 by the conversion factor which is 1,000

and we get 0.1562 kilograms.

Therefore, 5.5 ounces is equal to approximately 0.1562 kilograms.

The angular velocity of the point is found this way:

w = v/r

w = 200/(8/2) <--the two is from 2 * Pi * r

w = 50 rad/sec.

Answer: 50 rad/sec.

fullness; live

Final answer:

After converting their completion fractions to decimal form, Jose finished more of the race than Jenna after 30 minutes, with Jose at 2/3 (approximately 0.6667) and Jenna at 7/12 (approximately 0.5833).

Explanation:

Jose and Jenna competed in a bike race. After 30 minutes, Jose had finished 2/3 of the race, and Jenna had finished 7/12 of the race. To determine who had finished more of the race, we can compare these two fractions by finding a common denominator or converting them to decimal form.

First, let's convert them to decimal form:

2/3 is approximately 0.6667

7/12 is approximately 0.5833

Comparing the decimal values, we can see that Jose's completion (0.6667) is greater than Jenna's (0.5833). Therefore, Jose had finished more of the race after 30 minutes.

Answer:

See the attached

Step-by-step explanation:

When in doubt, draw a diagram.

The orthocenter of this acute triangle will be within its bounds. That should tell you right away that the y-coordinate of it will not be 8, but must be between 2 and 6.

The line perpendicular to BC through A must have a y-intercept greater than the y-coordinate of A, so cannot be 5. Whatever it is, the y-coordinate of the orthocenter will be less, so again, your answer fails the reasonableness test.

The perpendicular line to BC through A is ...

... y = (-1/2)(x -2) +6 = -x/2 +7 . . . . . . looks like you had a sign error in (-1/2)(-2)

The intersection of that line and x=6 is ...

... y = -6/2 +7 = 4

Answer:

D. 15 and 49

Step-by-step explanation:

Numbers are relatively prime if the only positive integer  that divides both of them is 1.

A. 12 and 54

both 12 and 54 can be divided by 3

12/3 =4   54/3 = 18

B. 9 and 21

both 9 and 21 can be divided by 3

9/3 =3  and 21/3 = 7

C. 21 and 39

both 21 and 39 can be divided by 3

21/3 =7 and 39/3 = 13

D. 15 and 49

13 is 3*5    and 49 is 7*7

This is relatively prime

Answer:

-16 sqrt(3) +16i

Step-by-step explanation:

z = 2 cis (pi/6)

z^5 = 2^5 cis (5*pi/6)

z^5 = 32 cis (5pi/6)

 z^5 = 32 cos (5pi/6) + 32 i sin (5pi/6)

        = 32 * (-sqrt(3)/2) + 32i (1/2)

        = -16 sqrt(3) +16i

Answer:

it will grow 30 ft in 20 years

Step-by-step explanation:

the height will equal the growth rate times the time

height = 1.5 ft/year * 20 year

height = 30 ft