When the smaller of two consecutive integers is added to two times the larger, the result is 26. find the integers?

A family paid $142.80 which included $6.80 in taxes for 4 play tickets each ticket costs the same amount how much did each perso

borishaifa [10]

$142.80-$6.80=$136 divided by 4 equals $34

8 0

3 years ago

A carpenter has a wooden dowel that is 72 centimeters long. She wants to cut it into 2 pieces so that one piece is 5 times as lo

Jobisdone [24]

Let's say that the shorter piece is x and the longer piece is 5x (because it's 5 times as long). x+5x=72 and 6x=72. Dividing both sides by 6, we get that x=12, and 72-12=the length of the other piece (since there are only 2 pieces)=60

6 0

2 years ago

Big Ben, the famous clock tower in London, has a minute hand that is 14 feet long. How far does the tip of the minute hand of Bi

ycow [4]

Answer:

36.65 ft (2 dp)

Step-by-step explanation:

Angles around a point sum to 360°
1 hour = 60 minutes

Therefore, the minute hand of a clock travels 360° in 60 minutes

Number of degrees the minute hand will travel in 25 minutes:

$\sf =\dfrac{360}{60} \times 25=150^{\circ}$

To find how far the tip of the minute hand travels in 25 minutes, use the Arc Length formula:

$\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right)$

$\textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in degrees)}$

Given:

r = length of minute hand = 14 ft
$\theta$ = 150°

$\begin{aligned}\implies \textsf{Arc length} &=2 \pi (14)\left(\dfrac{150^{\circ}}{360^{\circ}}\right)\\ & = 28\pi \left(\dfrac{5}{12}\right)\\ & = \dfrac{35}{3} \pi \\ & = 36.65\: \sf ft\:(2\:dp)\end{aligned}$

4 0

2 years ago

Find the area: (I will give brainliest) +50 points.

scZoUnD [109]

Answer:

$A_{total} = 16\ cm^2$

Step-by-step explanation:

Step 1: Determine the area of the top rectangle

We can tell that the total shape seems like two rectangles glued together. We can separate the top rectangle and determine the area of it and then determine the area of the bottom rectangle and combine them. Lets first solve the left rectangle.

$A=l*w$

$A_{top\ rectangle}=6\ cm * 2\ cm$

$A_{top\ rectangle}=12\ cm^2$

Step 2: Determine the area of the bottom rectangle

$A=l*w$

$A_{bottom\ rectangle}=2\ cm * 2\ cm$

$A_{bottom\ rectangle}=4\ cm^2$

Step 3: Determine the total area

$A_{total}=A_{top\ rectangle}+A_{bottom\ rectangle}$

$A_{total}=12\ cm^2+4\ cm^2$

$A_{total} = 16\ cm^2$

Answer: $A_{total} = 16\ cm^2$

8 0

2 years ago

Read 2 more answers

An arithmetic sequence has this recursive formula:

ankoles [38]

Hello!

The recursive rule for an arithmetic sequence: $a_{n} = a_{n-1} + d$ .

The explicit rule for an arithmetic sequence: $a_{n}=a_{1} +d(n-1)$ .

$a_{n}$ is the value you are trying to find, or simply the answer. :)

$d$ is the common difference of the sequence.

$a_{1}$ is the first term of the sequence.

Given, $a_{1} = 8$ and $a_{n}=a_{n-1} - 6$ ...

The common difference is -6, and the first term is 8.

Plug these values into the explicit rule for an arithmetic sequence, you get:

$a_{n}=8+(-6)(n-1)$ .

Therefore, the answer is A, $a_{n}=8+(n-1)(-6)$ .

If you wondered why, $a_{n}=8+(-6)(n-1)$ is equal to $a_{n}=8+(n-1)(-6)$ , the Commutative Property of Multiplication states that when two numbers are multiplied together, the answer is the same regardless of the order of the numbers, which makes $a_{n}=8+(-6)(n-1)$ and $a_{n}=8+(n-1)(-6)$ equal to each other.

4 0

3 years ago

Read 2 more answers

When the smaller of two consecutive integers is added to two times the​ larger, the result is 26. find the integers?

When the smaller of two consecutive integers is added to two times the larger, the result is 26. find the integers?