A cat is running away from a dog at a speed of 3 m/s. Originally, the distance between them was 48 meters. What should be the speed of the dog to catch up with the cat in 1 minute?

Given:

The expression is:

[tex]\dfrac{25x^2}{2x+6}\cdot \dfrac{2}{5x}[/tex]

To find:

The simple product.

Solution:

We have,

[tex]\dfrac{25x^2}{2x+6}\cdot \dfrac{2}{5x}[/tex]

It can be written as:

[tex]=\dfrac{5\times 5\times x\times x}{2(x+3)}\cdot \dfrac{2}{5x}[/tex]

Cancel out the common factors.

[tex]=\dfrac{5\times x}{x+3}[/tex]

[tex]=\dfrac{5x}{x+3}[/tex]

Therefore, the correct option is C.

Answer:

option C.

Step-by-step explanation:

roots of a function are the values of x for which the corresponding value of f(x) is 0.

since f(x) is being plot on the y axis it's value being zero signifies the intersection of the curve with the x axis.

so the roots of g(x) are :-

2, and 10

for roots of f(x) :-

f(x) = 0

x² - 9 = 0

(x+ 3)(x - 3) = 0

either x = 3 or x = -3

so the roots of f(x) are

3, and -3

Comparing their roots one can very well see both the functions share no roots in common.

Answer:

62+75+85+63+69+72+76+84+87+88 = 761

total scores is 10 then divde 761 by the total number of scores which is 10

761÷10 = 76.1

Answer:

... i dont know what that means... i would comment this but i dont know how to.... so yeah

Step-by-step explanation:

Answer:

Eric can either charge $10 or $40 in order to break even.

Step-by-step explanation:

Eric has a summer lawn mowing business and the equation:

[tex]p=-3x^2+150x-1200[/tex]

Models his total profit p by charging x dollars per lawn.

We want to determine what price Eric needs to charge in order to break even.

The price Eric charges to break even means that his total profit will be zero. Hence, we can let p = 0 and solve for x. Thu:

[tex]0=-3x^2+150x-1200[/tex]

We can divide both sides by -3:

[tex]0=x^2-50x+400[/tex]

Factor:

[tex]0=(x-10)(x-40)[/tex]

Zero Product Property:

[tex]x-10=0\text{ or } x-40=0[/tex]

Solve for each case. Hence:

[tex]x=10\text{ or } x=40[/tex]

Therefore, Eric can either charge $10 or $40 in order to break even.

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

see this attachment

Step-by-step explanation:

age of grandpa=72

age of grandson =16

Last year He was 7 years old.

His father is 4 times the age 7 x 4 = 28

Last year his dad was 28, so this year he is 29.

Combined age this year = 29 + 8 = 37

51 - 37 = 14 years

14/ 2 people = 7 years

8 + 7 = 15

29 + 7 = 36

15 + 36 = 51

It will take 7 years.

Answer:

H0 : The mean difference in strikes between pre and post strike is equal to 0

H1 : The mean difference in strikes between pre and post strike is not equal to 0

Step-by-step explanation:

The scenario described abibe meets the condition for a paired (dependent) sample t test as the same subject is involved in both the pre and post strike data. Therefore measurement from the strike(pre) must be paired with measurement from the strike(post) data.

For a paired test involving a single subject ; The mean difference in the two sample is 0 ; that is both are the same while the alternative negates the null by claiming that the mean difference is not equal to zero.

Answer:

<RQP

Step-by-step explanation:

The vertex must either be the name of the angle or in the middle of the letters

<PQR  or <RQP

We can also just call it <Q since there is only one angle

Given:

The number is 93.

To find:

The square root of 93.

Solution:

We need to find the square root of 93.

The square root of 93 by division method is:

         9.6436

_____________

9     |     93

9     |      81

__________

186 |    1200

  6 |      1116

___________

1924 |  8400

    4  | 7696

__________

19283 | 70400

       3 | 57849

____________

192686 | 1255100

         6 | 1156116

______________

192692 | 98984

And so on.

[tex]\sqrt{93}\approx 9.645[/tex]

Therefore, the square root of 93 is about 9.645.

Answer:

9.643

Step-by-step explanation:

Got it right, checked answer on calculator

Answer:

$1,281.00

Step-by-step explanation:

We start by calculating the value $50 added each month after the first month

= $50 × 11

= $550

Calculation:

First, converting R percent to r a decimal

r = R/100 = 5.5%/100 = 0.055 per year.

P = Principal = 500 + 550

= $1050

Calculation:

First, converting R percent to r a decimal

r = R/100 = 5.5%/100 = 0.055 per year.

Solving our equation:

A = 1050(1 + (0.055 × 4)) = 1281

A = $1,281.00

Therefore, there would be $1,281.00 after 4 years.

Answer:

(D) 100

Step-by-step explanation:

(A) 16 = 1+3+5+7

(B) 40 =7+9+11+13

(C) 72=15+17+19+21

(D) 100

(E) 200=47+49+51+53

Answer:

Trapezium (An acute trapezium to be exact)

Step-by-step explanation:

Draw all four co-ordinates on a cartesian plane. We know these co-coordinates are the vertices (corners), so draw a line connecting all four points and observe what shape you have.

Your reasoning for why it is a trapezium can include the following points.

Trapeziums are a flat, closed shape, having 4 straight sides, with one pair of parallel sides.

We can say its an acute trapezium since the bottom two angles are unequal and both measure less than 90 degrees

Answer:

[tex]AB^{2} =AD^{2} +BD^{2}[/tex]

[tex]AB^{2} =(7.5)^{2} +(4.9)^{2}[/tex]

[tex]AB=\sqrt{80.26}[/tex]

[tex]=8.96[/tex]

ΔABC tan C=AB/BC

⇒ tan 55.8= 8.96/BC ⇒BC= 8.96/tan 55.8

BC=x= 6.09

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

Hope it helps...

Have a great day!!

Option 4 is correct

The relationship is:

y = 3/4 x

Answer:

Pedro make 6 m of wall, Juan make 18 m of the wall and Luis make 36 m of the wall.

Step-by-step explanation:

Juan, Pedro and Luis build a 60 meter long wall. Juan builds triple the size of Pedro and Luis double the size of Juan. How many meters did each one build?

Total length of the wall is 60 m.

Let Pedro make p length of the wall.

Juan make = 3 p

Luis make = 6 p

So,

According to the question

60 = p + 3 p + 6 p

60 = 10 p

p = 6

So, Pedro make 6 m of wall, Juan make 18 m of the wall and Luis make 36 m of the wall.  

Answer:

QR ≈ 16.3

Step-by-step explanation:

Since the figures are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{MN}{QR}[/tex] = [tex]\frac{MP}{QT}[/tex] , substitute values

[tex]\frac{40.3}{QR}[/tex] = [tex]\frac{57}{23}[/tex] ( cross- multiply )

57 QR = 926.9 ( divide both sides by 57 )

QR ≈ 16.3 ( to the nearest tenth )

Step-by-step explanation:

The second option is the answer.

Answer:

147˚, 33˚

Step-by-step explanation:

supplementary angles means those angles add up to 180˚

so A+B = 180

substitute A and B with the values given.

(4a+7) + (a-2) = 180

combine like terms

5a + 5 = 180

5a = 175

a = 35

Now that we have a, substitute in the actual value of a into the expressions for each angle.

for <A: 4(35) + 7 = 147˚

for <B: 35 - 2 = 33˚

Answer:

<A =147

<B =  33

Step-by-step explanation:

Supplementary angles add to 180

4a+7 + a-2 = 180

5a+5 = 180

5a+5-5 = 180-5

5a = 175

Divide by 5

5a/5 = 175/5

a = 35

<A = 4a+7 = 4*35 +7 = 140+7=147

<B = a-2 = 35-2 = 33

Answer:

25

Step-by-step explanation:

Answer:

p = 26.3

Step-by-step explanation:

Using the law of sines

sin 101        sin 38

---------  = ------------

42               p

Using cross products

p sin 101 = 42 sin 38

p = 42 sin 38 / sin 101

p=26.34175

To the nearest tenth

p = 26.3

Answer:

40 pupils speak French and English

5 pupils speak only English

Step-by-step explanation:

**The grammar has some errors, but I hope I understood it correctly to answer your question correctly!**

Here's what we know about the question:

- 1/10 of the 50 pupils speak only FRENCH

- 4/5 of the 50 pupils speak FRENCH and ENGLISH

- rest of the pupils speak only ENGLISH

Here's what we're trying to find:

- # of pupils that speaks FRENCH and ENGLISH

- # of pupils that speak only ENGLISH

Let's start of with find how many pupils speak French:

1/10 of the 50 pupils speak French. To find the # of pupils, divide 50 by 10:

50/10 = 5

5 pupils speak only French

Now let's find out how many pupils speak French and English:

4/5 of the 50 pupils speak French and English. We are going to divide 50 by 5 and then multiply the result by 4:

50/5 = 10

10 * 4 = 40

40 pupils speak French and English

Finally, let's find the number of pupils that speak only English:

The question only says that the rest of the 50 pupils speak only English.

We are going to add the other pupils who don't speak only English, then subtract that value from 50:

40 + 5 = 45

50 - 45 = 5

5 pupils speak only English

Hope that helps (●'◡'●)

Answer:

d. The APR helps compare loans with the same payback period, but with different monthly rates and different fees.

Step-by-step explanation:

A loan can be defined as an amount of money that is being borrowed from a lender and it is expected to be paid back at an agreed date with interest.

Generally, the financial institution such as a bank lending out the sum of money usually requires that borrower provides a collateral which would be taken over in the event that the borrower defaults (fails) in the repayment of the loan.

An annual percentage rate (APR) is an amount of money paid as interest by borrowers or earned on loans by lenders such as banks, expressed as a percentage of the amount borrowed or invested over a 12-month period i.e on an annual basis.

Generally, the annual percentage rate (APR) helps compare loans with the same payback period, but with different monthly rates and different fees.

Answer:

A- If you have good credit, you will get a higher APR

Step-by-step explanation:

Answer:

mean = 8.4

Step-by-step explanation:

Mathematically, we have the mean as np

This is the product of the number of items per batch by the probability that each of the products will germinate

Mathematically, we have this as:

0.7 * 12 = 8.4

Answer:

75 in^2

Step-by-step explanation:

The surface area is the sum of the areas

Area of the square:

A = s^2 = 5^2 =25

Area of one triangle

A = 1/2 bh = 1/2 (5)(5) = 25/2

There are 4 triangles

4* (26)/2 = 50

The sum is 25+50 = 75

Answer:

75 in2

Step-by-step explanation:

[tex]===========================================[/tex]

Formulas:

Area of a rectangle/square:

[tex]A=lw[/tex]

Area of a triangle:

[tex]A=bh\frac{1}{2}[/tex]

[tex]===========================================[/tex]

Square:

5*5= 25 in.

Triangles (4):

[tex]5*5*\frac{1}{2} =12.5[/tex]

Multiply by 4.

12.5*4= 50 in.

Add all them up.

25+50= 75

Answer:

Step-by-step explanation:

So, yearly $2100 is paid, plus the 1.73% interest, so 1.73% interest is $2136.33every year interest stacks on itself so youll take 1.73% of the year 1 total with interest.  

Year 1 total: $2136.33

Year 2 total:$2173.29

Year 3 total:$2210.89

Year 4 total:$2249.14

Year 5 total:$2288.05

Total Paid After 5 years:$11057.70

Year 1 total interest:$36.33

Year 2 total interest:$36.96Year 3 total interest:$37.60Year 4 total interest:$38.25Year 5 total interest:$38.91

Total Interest paid after 5 years:$188.05

Answer:

4 > [tex]-\frac{n}{4}[/tex]

-16 > n

Step-by-step explanation:

Greater than would mean that the "arrow" is not facing the number. It would mean it is larger than the other number. Also, you have to construct the other part of the inequality which would be [tex]-\frac{n}{4}[/tex].

4×4 > [tex]-\frac{n}{4}[/tex]×4

16 > -n

-16 > n

Answer:

I think its 40 I could be wrong

Step-by-step explanation:

I had subtract 80 and 40