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2 years ago

Richard walks every day for exercise at a rate of 1 kilometer every 12 minutes

1 answer:

8 0

He coud walk 5 meters in one hour because i did 60-12-12-12-12 and then you have a extra 12 so he got 5 meters in one hour part b he can 1 more further because 1 meter because before it was 12 hope explained it right

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What is the greatest common factor of the two expressions? 7a^2 8a^3b^2

Andreyy89

Answer:

a²

Step-by-step explanation:

(see attached for reference)

We can find GCF by expressing each expression into their prime factors

7a² = 7 x a x a

8a³b² = 8 x a x a x a x b x b

by observation, we can see that a x a or a² shows up in both expressions, highlighted in bold here:

7a² = 7 x a x a

8a³b² = 8 x a x a x a x b x b

Hence the greatest common factor is a x a = a²

6 0

2 years ago

If Janice works overtime, she receives an hourly rate of 1½ times her regular hourly rate of $14.00 an hour. What is her overtim

ankoles [38]

$21.00 per hour. $14.00 * 1.5 = $21.00

6 0

2 years ago

Frank has a 2-digit number on his baseball uniform. The number is a multiple of 10 and has 3 for one of its factors . What three

White raven [17]

Frank could have 30, 60 , 90 on his uniform

Solution:

Given that, Frank has a 2-digit number on his baseball uniform

The number is a multiple of 10 and has 3 for one of its factors

To find: Three numbers that Frank have on his uniform

Given that,

It's a multiple 10 and has 3 for one of its factors and its a 2-digit number

Let us first find the multiples of 10

The two digit multiples of 10 are:

{10, 20, 30, 40, 50, 60, 70, 80, 90}

From the above list, find the numbers which has 3 as one of its factors

Which means, find the numbers which are divisible by 3

The possible numbers = 30, 60, 90

Thus frank could have 30, 60 , 90 on his uniform

3 0

2 years ago

A hardware supplier manufacturers 3 kinds of clamps types AB &c production restrictions force it to make 10 more type C clam

hichkok12 [17]

Answer:

Hardware supplier will manufacture 60 Type A clamps, 180 Type B clamps and 150 Type C clamps.

Step-by-step explanation:

Given:

Company produces 3 types of clamp

Type A

Type B

Type C

production restrictions force it to make 10 more type C clamps in the total of the other types

Hence We can say that Clamp C is equal to sum of Clamp A and Clamp and 10

framing in equation form we get;

$C=A+B+10 \ \ \ \ \ equation \ 1$

Also Given:

3 times as many Type B clamps as type A clamps

Hence we can say that Clamp B is equal to thrice of Clamp A.

$B=3A \ \ \ \ equation\ 2$

Also Given

Total Number of Clamps = 490

Hence Total Number of Clamps is equal to sum of number of Clamps of Type A, Type B and Type C.

Framing in equation form we get;

$A+B+C =490 \ \ \ \ equation \ 3$

Substituting the equation 1 and Equation 2 in equation 3 we get

$A+B+C=490\\\\A+3A+A+B+10=490\\\\A+3A+A+3A+10=490\\\\8A = 490-10\\\\8A=480\\\\A=\frac{480}{8}=60$

Now Substituting the Value of A in equation 2 we get;

$B=3A = 3\times60 =180$

Now Substituting the values of A and B in equation 1 we get:

$C=A+B+10 = 60+180+10= 250$

Now checking the same we get;

$A+B+C=490\\60+180+250=490\\490=490$

Hence the Hardware supplier will manufacture 60 Type A clamps, 180 Type B clamps and 150 Type C clamps.

5 0

2 years ago

Given: mTP= 70°,m∠EPT = 54° Find: Angles of △SPT

Zigmanuir [339]

Answer:

The Angles of △SPT are

$m\angle STP=35\°$

$m\angle SPT=126\°$

$m\angle PST=19\°$

Step-by-step explanation:

step 1

Find the measure of angle PET

we know that

The inscribed angle is half that of the arc it comprises.

$m\angle PET=\frac{1}{2}(arc\ PT)$

substitute the given values

$m\angle PET=\frac{1}{2}(70\°)$

$m\angle PET=35\°$

step 2

Find the measure of angle PTE

we know that

The sum of internal angles of a triangle must be equal to 180 degrees

In the triangle PET

$m\angle PET+m\angle EPT+m\angle PTE=180\°$

substitute the given values

$35\°+54\°+m\angle PTE=180\°$

$m\angle PTE=180\°-89\°=91\°$

step 3

Find the measure of angle STP

we know that

The inscribed angle is half that of the arc it comprises.

$m\angle STP=\frac{1}{2}(arc\ TP)$

substitute the given values

$m\angle STP=\frac{1}{2}(70\°)=35\°$

step 4

Find the measure of angle SPT

we know that

$m\angle SPT+m\angle EPT=180\°$ ----> by supplementary angles

$m\angle SPT+54\°=180\°$

$m\angle SPT=180\°-54\°=126\°$

step 5

Find the measure of angle PST

we know that

The sum of internal angles of a triangle must be equal to 180 degrees

In the triangle SPT

$m\angle STP+m\angle SPT+m\angle PST=180\°$

substitute the given values

$35\°+126\°+m\angle PST=180\°$

$m\angle PST=180\°-161\°=19\°$

5 0

2 years ago