1. Lilly has two cousins. One of the cousins is 7 years older than Lilly. The other cousin is 3 years younger than Lilly. The product of Lilly’s cousins' ages is 24. How old is Lilly?

2. Jackie is building a rectangular football field that has an area of 6000 square yards. The football field must be 40 yards longer than its width. Determine the width of the football field, in yards.

3. James is reading a book and noticed the page numbers are consecutive integers whose product is 1640. What is the value of the larger page number?

Answers

Answer 1

Answer: a. 5 years

b. 60 yards

c. 41

Step-by-step explanation:

1. Let Lily's age be x.

One of the cousins is 7 years older than Lilly. The age will be = x + 7

The other cousin is 3 years younger than Lilly. The age will be = x - 3

Therefore, (x + 7)(x - 3) = 24

x² - 3x + 7x - 21 = 24

x² + 4x - 21 - 24 = 0

x² + 4x - 45 = 0

x² + 9x - 5x - 45 = 0

(x² + 9x) - (5x - 45) = 0

x(x + 9) - 5(x + 9) = 0

(x - 5)(x + 9) = 0

(x - 5) = 0

x = 0 + 5

x = 5

Therefore, Lily is 5 years

2. Let the width be represented by x

Therefore, length will be x + 40.

Area = length × width

6000 = x(x + 40)

x² + 40x = 6000

x² + 40x - 6000 = 0

x² + 100x - 60x - 6000 = 0

x(x + 100) - 60(x + 100) = 0

(x - 60)(x + 100) = 0

x - 60 = 0

x = 0 + 60 = 60

Therefore, the width is 60 yards

3. Let the consecutive numbers be x and x+1.

Therefore, x(x + 1) = 1640

x² + x = 1640

x² + x - 1640 = 0

x² + 41x - 40x - 1640 = 0

x(x + 41) - 40(x + 41) = 0

(x - 40) = 0

x = 0 + 40

x = 40

Larger number = x + 1 = 40 + 1 = 41


Related Questions

James's Sister is arranging rows of beads. She has 56 yellow beads and 120 blue beads. She wants to arrange them so that all the beads in a row are, are the same color, and so that each row has the same number of beads. What is the least number of rows James's sister can make?

Answers

Answer:

22

Step-by-step explanation:

gcf 56, 120 = 8, 56/8=7, 120/8=15, 7+15=22. 22

Help 50 points please

Answers

The answer is

Sine(45/53)

Answer:

Sine(45/53)

Step-by-step explanation:

CHICKEN : EGG
(1 Point)

a. cow : milk

b. yesterday : today

c. boy : girl

d. toe : finger

e. hoof : mouth

Answers

Answer:

A: cow :milk bc it comes ot the cow like the egg comes out the chicken

The area of the base of a box is 825 square centimeters. It has a height of 26 centimeters. What is the volume of the box in cubic centimeters?

Answers

Answer: 4950 cubic centimeters.

Step-by-step explanation:

We know that, the volume of box = Base area x height

Given: area of the base of a box  = 825 sq. centimeters

height = 6 centimeters.

Then, Volume of the box in cubic centimeters = 825 x 6

= 4950 cubic centimeters.

hence, the volume of the box in cubic centimeters = 4950 cubic centimeters.

If Daniel pays $62.90 to fill the 17 gallon gas tank in his vehicle and he can drive 330 miles on one tank of gas, how much does he pay per mile to drive his vehicle?

Answers

He will pay per mile to drive his vehicle about 15c

In a right triangle, if a = 8 and c = 17, what is the correct setup to find the value of b?

Answers

Answer:

b = 15

Step-by-step explanation:

Assuming that the question is referring c as the hypothenuse, the Pythegorean theorem states: [tex]a^2+b^2=c^2[/tex].

Thus, [tex]b=\sqrt{c^2-a^2}=\sqrt{17^2-8^2}=15[/tex].

So b is 15.

Answer: b = 15

Step-by-step explanation:

Here, we need to know the formula for the relationship between the three sides of the right triangle: a² + b² = c².

a and b are legsc is hypotenuse

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

Given

a = 8

c = 17

Solve

a² + b² = c²

(8)² + b² = (17)²

64 + b² = 289

b² = 225

b = √225

b = 15

Hope this helps!! :)

Please let me know if you have any questions

NEED HELP ASAPPPPPPP !!!!!!!!

Answers

Answer:

6

Step-by-step explanation:

[tex]10^{2}[/tex]= 100

[tex]8^{2}[/tex]= 64

[tex]6^{2}[/tex]=36

100-64=36

b would be 36

Mrs. Williams has 3 pink pens, 2 orange pens, and 4 blue pens. What is the ratio of blue pens to total pens?

Answers

Answer:

4/9

Step-by-step explanation:

u just add all the numbers then take the blue pens

the ratio is 4:9
step by step- add all the pens together, then count the blue pens and do the blue pen amount to the whole amount

A Businessman exchange Nepali currency rupees 660000 INR to US Dollar at the rate of Dollar 1 is equal to INR rupees 110 after 4 days Nepali currency is revaluated by 10% and he has changed the dollars INR to Nepali currency again what is his gain or loss find it

Answers

Answer:

Gain = $666.67

Step-by-step explanation:

The businessman exchanged 660000 INR to US Dollar using the exchange rate of $1 = INR 110

Value of the money in dollars is;

(660000 × 1)/110 = $6000

Now, Nepali currency is reevaluated by 10%. This means it's value has gone up by 10%.

Thus, exchange rate of $1 is now;

110 - 10%(110) = INR 99

Thus, 660000 INR to US Dollar using this new exchange rate gives;

(660000 × 1)/99 = $6666.67

Therefore he made a gain.

Gain = 6666.67 - 6000

Gain = $666.67

a circle has an area of a circle circle of 108 cm squared in the sector intercepts an arc with length 12 cm find the diameter of the circle​

Answers

Answer:

formula for diameter is π®

Step-by-step explanation:

π

=22/7×108

=

What is a digit in the hundredths pace has 1/10 the value of the same digit of the same digit in the tenths pace?

Answers

Answer:

4,099 and 5,011 are the numbers whose ones place is 1/10 the value of the digit in the tens place. Step-by-step explanation: 1 : 4,099 - Yes, The digit at the ones place is 9 and the digit at the tens place is 90 (as per place value). So, 9 is one tenth of 90.

Solve the Answer)Please I need help

Answers

Answer:

178 in.

Step-by-step explanation:

14 5/6 times 12= 178 in.

A laptop computer is on sale for 10% off the original price
of $1,500 and a 7.25% sales tax is added after the
discount. What is the total cost?

Answers

Answer:

$1,252.13 I believe  or $1,252

Step-by-step explanation:

Multiply the 1500 by .10 and you'll get 150

Now subtract that from 1500 that's 1350

.0725 multiplyed by 1350 is 97.875

Subtract that from 1350 and you'll get the answer!


Ola saves $6 each week in her purse , after 6 weeks, she spent all the money she got on 4 times and each time cost the same amount. How much does each time cost?

Answers

Answer:

$1.50

Step-by-step explanation:

Divide the 6 dollars by 4 times

$6/4 = $1.50

Helppppppp
14. Rob uses free weights at the gym every 3 days and he uses the weight machines every 5 days.
Today Rob used both free weights and the weight machines. How many days will it be before he uses
both kinds of weights on the same day again?

Answers

Answer:

15 days

Step-by-step explanation:

Since he used both of the weights today, he will only do both on the day they come together.

weights: 3 days, 6 days, 9 days, 12 days, 15 days

machine: 5 days, 10 days, 15 days

Because the numbers both were the same on 15 days, then that is when he will do both of them

How do you solve 3b(9b-27)=0

Answers

Answer:0

Step-by-step explanation:3b(-27 + 9b) = 0

(-27 * 3b + 9b * 3b) = 0

(-81b + 27b2) = 0

Answer:

[tex]b=3[/tex], or [tex]0[/tex]

Step-by-step explanation:

[tex]\mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0[/tex]

[tex]b=0\quad \mathrm{or}\quad \:9b-27=0[/tex]

[tex]9b-27=0[/tex], [tex]\mathrm{Add\:}27\mathrm{\:to\:both\:sides}.[/tex]

[tex]9b-27+27=0+27[/tex]

[tex]9b=27[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}9[/tex]

[tex]\frac{9b}{9}=\frac{27}{9}[/tex]

[tex]b=3[/tex]

Which term describes the offspring of a first generation cross between parents with different forms of a trait?
A: genotype
B: hybrid
C: phenotype
D: true-breeding

Answers

the correct answer si B

Evaluate -2(|2|-(-3)(-4))

Answers

20

i hope this helps!!

Topher has of a whole pizza. How many 's of a whole pizza are there in of a whole pizza?

Answers

Answer:

huh

Step-by-step explanation:

Find the value of x in the triangle shown below.
C =
56
31
x

Answers

93 I think since tri’s add up to 180 degrees

please select the best answer from the choices provided

Answers

Answer:

[tex]\sqrt{122}[/tex]

Step-by-step explanation:

Given that,

Vector n = 4i-j

Vector m = 3i+3j

We need to find the value of m+2n.

Put all the values,

m+2n = (3i+3j)+2(4i-j)

= (3i+3j)+8i-2j

=11i+j

Magnitude of vector,

[tex]|m+2n|=\sqrt{11^2+1^2} \\\\=\sqrt{121+1}\\\\=\sqrt{122}[/tex]

So the correct option is (c).

What is the value of 0.3⁴?

Answers

It’s 0.0081 HOPE THIs helps

What is the value of x?

Answers

Answer:

C) [tex]8\sqrt{2}[/tex]

Step-by-step explanation:

Answer:

8√2

Step-by-step explanation:

The 45-45-90 triangle theorem states that the two congruent sides of an isoceles right triangle are the same, and the hypotenuse of the triangle is √2 times more than the common side. So, if the common side is 8, then the hypotenuse is 8√2.

I need help bois like i dont know what to do what to do

Answers

Answer:

the answer is A

Step-by-step explanation:

Answer:

the answer is b

Step-by-step explanation:

the two triangles are the basically the same

What is 3 1/4 x( -12.2)


Also pls answer it asap

Answers

Answer:

-39.65

Step-by-step explanation:

3 1/4 ⋅ (-12.2)

First, we must change the first fraction to a decimal.

3 1/4 = 3.25.

Now, we just multiply using standard algorithm.

3.25 ⋅ (-12.2) = -39.65.

Anytime you multiply a positive number by a negative number, the answer will ALWAYS be negative.

please answer both questions correctly!!
Don’t use files please

Answers

Answer:

Look at the image.

Step-by-step explanation:

Answer:

Not sure about the second one, but the first is x=44

Please help me asap. No links please
8th Grade

Answers

Answer:

Option P √2.5²-1.2²

Step-by-step explanation:

a = distance between Toby's House and the playground = 1.2 inches

b = distance between the playground and Toby's Friend's House = unknown

c = distance between Toby's House and Toby's Friend's House = 2.5 inches

Use the Pythagorean Theorem to calculate the side length of b:

a²+b²=c²

b²=c²-a²

b=√(c²-a²)

b=√(2.5²-1.2²)

Therefore, option P is correct.

Answer: it is p

Step-by-step explanation:

Cuál es el mayor número que cumple con todas las siguientes condiciones? Es menor que 1.000.000, todas sus cifras son números pares y solo el 8 está repetido una vez y termina en 22.

Answers

Answer:

El mayor número que cumple con las condiciones dadas es 866.622.

Step-by-step explanation:

Para determinar cuál es el mayor número que es menor que 1.000.000, todas sus cifras son números pares y solo el 8 está repetido una vez y termina en 22, se deben realizar los siguientes razonamientos lógicos:

1) Menor que 1.000.000 = Todos los números desde 0 hasta 999.999.

2)Todas sus cifras son números pares = No puede incluir los número 1, 3, 5, 7 o 9.

3) El 8 (mayor número par disponible) solo está repetido una vez = Debe iniciar con 8.

4) Termina en 22 = 8XX.X22

Con todos los datos planteados, el mayor número que cumple con las condiciones dadas es 866.622.

For a car moving at a constant speed, the distance traveled varies directly with the time spent driving. If such a car travels 500 miles in 10 hours, how long does it take to travel 400 miles?

____ hours ​

Answers

ANSWER: (8 hours)
, Thank you

This is due today please help.
What is the area of the shape.

Answer choices:
24 yd2
36 yd2
39 yd2
30 yd2

Answers

I got u
24+6=30
9-6=3
3x4=12/2=6
6x4=24

30 yd^2
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