Into how many equal parts can the same cake be cut if the cuts can only be made along the gridlines?

Tony has $20. He wants to buy at least 4

snacks. Hot dogs (x) are $3 each.

Peanuts (y) are $2 each.​

Answer:

To solve the above question, we use the below inequality equations

x + y ≥ 4 snacks .........Inequality equation 1

3x + 2y ≤ $20 ..........Inequality equation 2

Step-by-step explanation:

We can make use of the inequality equations

Hot dogs = (x) are $3 each.

Peanuts = (y) are $2 each.​

He wants to buy at least 4

x + y ≥ 4 snacks .........Inequality equation 1

3x + 2y ≤ $20 ..........Inequality equation 2

From the above inequality equations, Tony can buy at least 4 snacks but he can only spend $20.

Let take a random number, where x = 4, and y = 4. This means Tony can buy

a) 4($3) + 4($2) = 12 + 8 = $20

The total number of snacks = 4 + 4 = 8 snacks.

b)

This answer above confirms the inequality equations 1 and 2

x + y ≥ 4 snacks .........Inequality equation 1

8 snacks ≥ 4 snacks

3x + 2y ≤ $20 ..........Inequality equation 2

$20 ≤ $20

Answer:

4 is the first one and the second one is ---->

Total Price: 3x + 2y ≤ 20

Step-by-step explanation:

Let's complete the inequalities that represent Tony's situation.

Given:

Tony wants to buy at least 4 snacks.

Hot dogs (x) are $3 each.

Peanuts (y) are $2 each.

We can form the following inequalities:

Total Snacks: Tony wants to buy at least 4 snacks, which can be represented by the inequality:

x + y ≥ 4

This inequality ensures that the sum of hot dogs (x) and peanuts (y) is greater than or equal to 4, indicating that Tony wants to buy at least 4 snacks in total.

Total Price: To represent the total price, we need to consider the cost of each snack. Hot dogs are $3 each, and peanuts are $2 each. Thus, the total price can be represented by the inequality:

3x + 2y ≤ 20

This inequality accounts for the total cost of the snacks Tony wants to buy. The left-hand side represents the cost of x hot dogs ($3 each) and y peanuts ($2 each), and the inequality ensures that the total cost does not exceed Tony's available budget of $20.

Therefore, the completed inequalities are:

Total Snacks: x + y ≥ 4

Answer:

length of side of square = (4x - 5) inches

Step-by-step explanation:

We are given;

Area of square = 16x² – 40x + 25

Let's find the roots of this quadratic equation [-b ± √(b² - 4ac)]/2a

Thus;

x = [-(-40) ± √((-40)² - 4(16 × 25)]/(2×16)

x = [40 ± √(1600 - 1600)]/32

x = (40 ± 0)/32

x = 40/32

x = 5/4

Thus, the factors of the polynomial are;

(4x - 5)²

So,

Area = 16x² – 40x + 25 = (4x - 5)²

Since, the right hand side is (4x - 5)² and area of square is (length of side)², thus we can say that length of side of square is (4x - 5) inches

Answer:

4√5

Step-by-step explanation:

√80 = √16 times √5

√16 = 4

4 times √5

4√5

Answer:

A=4  B=5

Step-by-step explanation:

Answer:

5. 8

6. 18

Step-by-step explanation:

5.

a(a^2 + a - 1) + 7 =

= a^3 + a^2 - a + 7

For a = -1,

= (-1)^3 + (-1)^2 - (-1) + 7

= -1 + 1 + 1 + 7

= 8

6.

2ab(a + b) - 3ab(a - b) =

= 2a^2b + 2ab^2 - 3a^2b + 3ab^2

= -a^2b + 5ab^2

For a = 1 and b = 2,

= -(1)^2(2) + 5(1)(2)^2

= -1(2) + 5(4)

= - 2 + 20

= 18

Answer:

Step-by-step explanation:

a(a^2 + a -1) +7

a^3+a^2-a+7

f(-1)=(-1)^3+(-1)^2-(-1)+7

f(-1)=-1+1+1+7

f(-1)=0+1+7

f(-1)=8

2ab(a+b)-3ab(a-b)

2a^2*b+2ab^2-3a^2*b+3ab^2

−a^2*b+5ab^2

when a=1 and b=2

−a^2*b+5ab^2

−(1)^2*2+5*1*2^2

-1*2+5*1*4

-2+5*4

-2+20

18

Answer:

6 sq. units

Step-by-step explanation:

The area of a triangle is base times height divided by 2.

[tex]\frac{bh}{2}[/tex]

[tex]\frac{6 \times 2}{2}[/tex]

[tex]\frac{12}{2} =6[/tex]

Answer:

D. 6

Step-by-step explanation:

The formula for the area of a triangle is A=1/2bh. In this case, the base is 6 and the height is 2. The work is below:

A=1/2bh

A=1/2(6)(2)

A=1/2(12)

A=6

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer:

D

Step-by-step explanation:

Out of the 0 + 3 + 1 + 2 + 2 + 4 = 12 trials, the numbers 4, 5, and 6 (the numbers greater than 3) appeared 2 + 2 + 4 = 8 times so the probability is 8 / 12.

Answer: it’s D 8/12

Step-by-step explanation:

I did the quiz

Answer:

Brainliest!!!

Step-by-step explanation:

A:B

1:2

B:C

4:3

B is both 4 and 2

In B:C, B is double (in ratio) than when B is in A:B

2:4:2

A:B:C

this would mean there is a total of 8

A would get  1/4 of the 90 pounds

CHECK THE COMPLETE QUESTION BELOW:

Supervisor: "Because you are working a late shift, you will get an increase in your wage. You will get an additional 10% per hour from 6:00 PM to 12:00 AM and additional 15% from 12:00 AM to 1:00 AM." Employee: "I am working from 2:00 PM to 12:00 AM. Between 2:00 PM and 6:00 PM, I will make $12.00 per hour. Between 6:00 PM and 12:00 AM, I will make __________ per hour

Answer:

I will make $13.2 per hour

Explanation:

It can be deducted from the question that that the money Employee gets money for Working from 2.00 PM to 6.00 PM = $12per hour

Also the Employee gets additional 10% of money for working from 6.00 PM to 12.00 AM which implies that

10% = (10/100)*$12per hour

=$1.2per hour

Again, Employee gets additional 15% of the money for working from 12.00 AM to 01.00 AM which can be calculated as:

15% = (15/100)*$12per hour

=$1.8 per hour

which means that Employee gets additional $1.8 per hour

of the money for working from 12.00 AM to 01.00 AM

Therefore, if Employee works from 2.00 PM to 12.00 AM,

Employee will gets money for Working from 2.00 PM to 6.00 PM as well as the 10\% extra wage which

= $12 + $1.2 = $13.2

= \$ 12 + \$ 1.2 = \$ 13.2

Answer:

1/3

Step-by-step explanation:

7/12 - 3/12= 4/12= 1/3

Answer:

1170

Step-by-step explanation:

Total Population = 900

Annual rate of increase = 30 % of 900

=> [tex]\frac{30}{100}*900[/tex]

=> 30 * 9

=> 270

Population next Year = 900+270

=> 1170

Answer:

He has 8 possible choices

Step-by-step explanation:

Here, we want to know the number of choices Jill has.

He wants to buy either of the 2 pens.

In the first set , he has 4 styles to choose from

In the second set, he has also 4 styles to choose from

So his total number of possible choices would be 4 + 4 = 8 possible choices

Answer:

100 sq. m

Step-by-step explanation:

So, first, we need to know the formula for the area of a triangle.

A=BH/2

In this case, we know the base and the height (B and H respectively), and we just fill it out.

A=10*20/2

A=200/2

A=100.

Lastly, don't forget the units, so, A=100 sq. m

Answer:

c 100

Step-by-step explanation:

Answer:

B) 6 inches

Step-by-step explanation:

==>Given that ∆JKL ~ ∆TUV, it therefore means the ratio of proportion of the corresponding sides of ∆JKL and ∆TUV are equal.

Thus:

JK/TU = JL/TV = KL/UV

10/7.5 = 8/x = 13/9.75

Let's find x

10/7.5 = 8/x

=>Cross multiply

10*x = 8*7.5

10x = 60

Divide both sides by 10

x = 6 inches

Our answer is B) 6 inches

Step-by-step explanation:

Angle XBC = 55 degrees because it is a corresponding angle with Angle AXC

and corresponding angles are equal or congruent.

Ok so angle XBC = 55 degrees and since this an isosceles triangle

XBC = XCB which means XCB = 55 degrees

Now to find angle BXC we know that all angles of a triangle add up to 180 degrees.

Angle XBC + Angle XCB + Angle BXC = 180 degrees

Let x represent angle BXC

55 + 55 + x = 180

110 + x = 180

x = 180 - 110

x = 70

∴ Angle BXC = 70 degrees

Answer:

$460

Step-by-step explanation:

let the number of melons be x

4x + 3x + 3x = 200 melons

10x = 200 so, x will be 20

4x = 80 melons

3x = 60

3x = 60

amount made by 1st child = 80 × $2 = 160$

the remaining melons are 60 + 60 = 120

amount collected: they sold them in groups of 2 and each group was $5. so,

120÷2 × $5 = $300

total amount = 300 + 160 = $460.

Answer:

Answer choice A) About 38.47 square units

Step-by-step explanation:

Since all four sides of a square have the same length, the perimeter of a square is just 4 times one of the side lengths. The perimeter of the square and therefore the circumference of the circle is 5.5*4=22. The circumference of a circle is 2 times the radius multiplied by pi. The radius of this circle is therefore:

[tex]\dfrac{22}{2\pi}\approx 3.503[/tex]

Since the area of a circle is [tex]\pi r^2[/tex], the area of this circle is:

[tex]\pi \cdot 3.503^2= 3.14\cdot 12.271\approx 38.47[/tex]

Hope this helps!

The area of a circle with a circumference that equals the perimeter of the square is  about 38.47 square units

Since all four sides of a square have the same length, the perimeter of a square is just 4 times one of the side lengths.

The perimeter of the square and therefore the circumference of the circle is [tex]5.5*4=22.[/tex]

The circumference of a circle is 2 times the radius multiplied by pi. The radius of this circle is, therefore

[tex]22/2\pi=3.503[/tex]

The area of a circle is [tex]\pi r^2[/tex],

the area of this circle is:

=[tex]\pi \times 3.305^2[/tex]

[tex]=3.14(12.27)[/tex]

=38.47 unit^2

Thus, The area of a circle with a circumference that equals the perimeter of the square is about 38.47 square units.

To learn more about the circle visit:

https://brainly.com/question/24375372

#SPJ2

Answer:

Less than 13 pounds of grapes,

as 14 pounds of grape exceeds $35.80,

If you order as low as zero pounds of grapes, then the price of apple pounds would be $35.80/20 =$1.79 per pound

Step-by-step explanation:

Let

Quantity of Apple and grapes=20

Cost of apple=$2.19

Cost of grape=$2.60

Total cost of apple and grape=$35.80

a+g=20

a=20-g

PaQa+PgQg=35.80

2.19(20-g)+2.60g=35.80

43.8-2.19g+2.60g=35.80

0.41g=35.80-43.8

0.41g=-8

g=-8/0.41

g= -19.51

PaQa+PgQg=35.80

2.19a+2.60(-19.51)=35.80

2.19a-50.726=35.80

2.19a=35.80+50.726

2.19a=86.526

a=86.526/2.19

=39.51

PaA+PgG=35.80

Pa(20-G)+2.60G=35.80

35.80/2.60 = 13.77 pounds of grapes, but no money will be left to buy apples, unless Pa=0

G<13.77

It would be

[tex] \sqrt{ \frac{x - 2}{ 2} } [/tex]

I hope this is what you're looking for!

Step-by-step explanation:

here first you have to find the perimeter of square

given that perimeter of circle is equal to perimeter of square,,,,, therefore with the perimeter of square you have to find the radius of the circle.....

now you have the radius of the circle so by applying the formula of area of circle the answer will be finded

Please follow

Answer:

38.47 units²

Step-by-step explanation:

I got it right on the test...

Answer:

Step-by-step explanation:

Answer:

The 3rd option

Step-by-step explanation:

To prove that 2 triangles are similar, we need to prove that 2 pairs of their angle measurements are congruent.

This is because all triangles have 180 degrees, so if 2 pairs are congruent, the remaining angles will also be congruent

We know that m<D=m<E

We also know that m<DCA=m<ECB because they are vertical angles.

Vertical angles are always congruent.

Therefore, the triangles are similar.

The correct similarity statement would be 1, since <D corresponds with <E.

Now let's look at the 3rd Statement. To prove that two lines are similar, we would have to prove that their alternate interior angles are congruent.

A pair of alternate interior angles would be <D and B or or <E  and <A

There is no way to prove this, since we do not know any of the angle  or that measurements or if the triangles are isosceles triangles.

Hence, the correct choice would be 1 only.

Answer:

b

Step-by-step explanation:

Answer:

b or The value will be greater than 1 because (negative 3) minus (negative 9) = 6. A number in scientific notation with a positive exponent is greater than 1.

Step-by-step explanation:

Answer:

13.3

Step-by-step explanation:

The triangles are similar so we can use ratios to solve

AM             AN

---------- = ------------

AM+AB          AC

6             8

---------- = ------------

6+4          AC

Using cross products

6AC = 8 * 10

6AC = 80

Divide by 6

AC = 80/6

AC =13 1/3

AC = 13.33333

Answer:

11

Step-by-step explanation:

add

Answer:

70

Step-by-step explanation:

well you know that angles in the same segment are equal so angle VWZ also= 38

triangle VWZ is a triangle so the sum of interior angles sums to 180

180-72-38=70

Step-by-step explanation:

_2x _3x+3+64-4=

_5x+63

Answer:

D.) If soccer balls are sold for $2.05 or $14.61 each, the store will break even but will not make a profit.

Step-by-step explanation:

Let us assume x = selling price of each soccer ball

y = daily profit earned from selling of soccer balls

Given that

Y= [tex]-6x^2+100x-180[/tex]

where,

a = -6

b = 100

c = -180

Now we have to applied the formula which is as follows

x [tex]= \frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]

[tex]= \frac{-100\pm\sqrt{100^2-4\times -6\times -180}}{2\times -6}$[/tex]

[tex]= \frac{-100\pm\sqrt{10,000 - 4,320}}{-12}$[/tex]

[tex]= \frac{-100\pm\sqrt{5.680}}{-12}$[/tex]

[tex]= \frac{-100 + 75.3658}{-12}$[/tex]

[tex]= \frac{24.6342}{-12}[/tex]

x^1 = -2.05285

Now

x^2  [tex]= \frac{-100 - 75.3658}{-12}$[/tex]

[tex]= \frac{- 175.3658}{-12}[/tex]

x^2 = 14.6138

Based on this the option D is most appropriate as per the given situation

Answer:

If soccer balls are sold for $2.05 or $14.61 each, the store will break even but will not make a profit.

Answer:

b

Step-by-step explanation:

Answer:

(a)The solution set is: [tex]x \in [6, \infty) \forall x \in R[/tex]

(c) [tex]6 \leq x[/tex]

Step-by-step explanation:

Given the inequality: [tex]12+\dfrac{11}{6}x\leq 5+3x[/tex]

We solve by collecting like terms

[tex]12+\dfrac{11}{6}x\leq 5+3x\\12-5\leq 3x-\dfrac{11}{6}x\\7\leq \dfrac{18x-11x}{6}\\42 \leq 7x\\$Divide both sides by 7\\6 \leq x\\$We can re-write this as:\\x\geq 6[/tex]

The solution set is therefore: [tex]x \in [6, \infty) \forall x \in R[/tex]

Answer:

2x/4y = x/2y = x : 2y

Step-by-step explanation:

The question only gave us the cost of each white tiles and blue tiles respectively . The cost of each white tiles is £2  while the cost of each blue tiles is £4. The total cost of the blue tiles and the white tiles can only be calculated if we know the number of blue and white tiles available.

Let us assume

the number of white tiles = x

the number of blue tiles = y

total cost of white tiles = 2 × x = 2x

total cost of blue tiles =  4 × y = 4y

Therefore, the ratio of the total cost of white tiles to the total cost of the blue tiles can be expressed as follows

2x/4y = x/2y = x : 2y

If the number of white and blue tiles is known it can be replaced in the ratio to find the ratio of the total cost of the white tiles to the total cost of the blue cost.