All categories

2 years ago

the ratio of the measures of the three angles in a triangle is 10:3:7 find the measure of the largest angle

Mathematics

1 answer:

UNO [17]2 years ago

6 0

Answer:

The largest angle is 90 degrees

Step-by-step explanation:

The three angles of a triangle add to 180

The ratio is 10 : 3: 7

Multiply each by x

10x, 3x 7x

Add them together and set equal to 180

10x+3x+7x = 180

Combine like terms

20x = 180

Divide by 20

20x/20x =180/20

x = 9

The largest angle is 10x

10*9 = 90

The largest angle is 90 degrees

You might be interested in

Maya reads 1/8 of a newspaper in 1/28 of a minute.how many minutes does she need to read an entire paper

zepelin [54]

8/20 of a minute or 2/5 of a minute

5 0

3 years ago

The plot below shows the graphs of three functions, f, g, and h, all of which determine the population of three different cities

monitta

So, here we have an exponential function.

Remember that an exponential function has the form:

$y=a(b)^x=a(1\pm\frac{r}{100})^x$

Where a represents an initial amount, and r is the rate of this amount to change. (Increase, or decrease).

So, given that the population of City A in 2000 was 40 thousand people and the population increased by 13% each year, we can say that

$\begin{gathered} a=40 \\ b=1+\frac{13}{100}=1.13 \end{gathered}$

So,

$f(x)=40(1.13)^x$

For city B:

$\begin{gathered} a=40 \\ b=1+\frac{16}{100}=1.16 \\ g(x)=40(1.16)^x \end{gathered}$

But something different happens with city C. This is not an exponential function, this is a linear function.

So,

$h(x)=40+10x$

7 0

7 months ago

Lia must work at least 5 hours per week in her family’s restaurant for $8 per hour. She also does yard work for $12 per hour. Li

Fittoniya [83]

Answer:

(a)

$r\geq 5$

$r+y\leq 15$

$8r+12y\geq 120$

$y\geq 0$

(c)Maximum number of hours Lia can work at the restaurant and still meet her earnings goal = 15 hours

(d)Maximum Earning = $160

Step-by-step explanation:

Let r be the number of hours worked at the restaurant.

Let y be the number of hours of yard work,

Lia must work at least 5 hours per week in her family’s restaurant for $8 per hour.

$r\geq 5$

Since she does yard work, $y\geq 0$

Lia’s parents allow her to work a maximum of 15 hours per week overall.

$r+y\leq 15$

Lia’s goal is to earn at least $120 per week.

The restaurant, r pays $8 per hour

Yard work, y pays $12 per hour.

Therefore:

$8r+12y\geq 120$

The system of inequalities that represent this problem is therefore:

$r\geq 5$

$r+y\leq 15$

$8r+12y\geq 120$

$y\geq 0$

(b)The graph of the inequality is attached below

(c)When the graph is plotted, the vertices of the feasible region are:

(5,10)
(5, 6.7)
(15,0)

Where the first term is for the number of hours worked in the restaurant.

The maximum value of r possible is 15 from the three points.

Therefore, she can work at the restaurant for 15 hours and still meet her earning goal.

(d)Maximum Amount Lia can earn in 1 Week

At (5,10), Earning=(5X8)+(10X12)=40+120=$160

At (5, 6.7), Earning=(5X8)+(6.7X12)=40+80.4=$120.4
At (15,0) Earning=(15X8)+(0X12)=$120

Since she has to work at least 5 hours at the restaurant, the maximum amount possible is $160.

8 0

2 years ago

Item 9 a flight averages 460 miles per hour. the return flight averages 500 miles per hour due to a tailwind. the total flying t

Ksenya-84 [330]

Let us say that the variables for flight is designated by 1, while the return flight by 2, since the distance travelled are equal, therefore:

v1 t1 = v2 t2

460 t1 = 500 t2

Since t1 + t2 = 4.8, therefore: t1 = 4.8 – t2

460 (4.8 – t2) = 500 t2

2208 – 460 t2 = 500 t2

960 t2 = 2208

t2 = 2.3

t1= 4.8 – t2 = 4.8 – 2.3

t1 = 2.5

Answer:

The flight took 2.5 hours while the return flight took 2.3 hours.

8 0

2 years ago

A dentist polls his patients and finds that 83 percent brush their teeth at least twice a day, 47 percent floss daily, and 19 pe

puteri [66]

Answer:

The correct option is B. 23%

Step-by-step explanation:

Let the event that patient brushes his teeth at least twice a day is denoted by A

So, P(A) = 0.83

Let the event that patient flosses daily is denoted by B

So, P(B) = 0.47

Now, it is given that 19 percent patients brush at least twice a day and floss daily.

⇒ P(A and B) = 0.19

Now, we need to find conditional probability of occurring event B given A has occurred.

$\implies P(B|A) =\frac{P(A\: and\: B)}{P(A)}\\\\\implies P(B|A) = \frac{0.19}{0.83}\\\\\implies P(B|A) = 0.2289\approx 0.23$

Hence, Nearest required percentage = 23%

Therefore, The correct option is B. 23%

4 0

2 years ago

Read 2 more answers