Ben has a barrel in his garden to collect rainwater. The barrel can hold less than 42 gallons of water. Which inequality represents this situation? Ow> 42 Ow< 42 w² 42 Ow≤ 42​

Yes , the triangles ΔSTU and ΔSRQ are similar triangles

What are similar triangles?

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be ΔSTU

Let the second triangle be ΔSRQ

Now , for the triangles to be similar , the corresponding sides of the triangles should be in the ratio

So , on simplifying , we get

The measure of side ST = 21

The measure of side SU = 35

The measure of side SQ = 6

The measure of side SR = 10

Now , for similar triangles ,

ST / SQ = SU / SR

Substituting the values in the equation , we get

21 / 6 = 35 / 10

3.5 = 3.5

Therefore , the corresponding sides of the triangles are equal

Hence , the pair of triangles are similar triangles

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a. Harold's monthly payment is given as follows: $164.13.

b. The total amount paid is given as follows: $9,847.8.

c. The finance charge is of: $847.8.

The monthly payment formula is defined as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which the parameters are listed as follows:

The values of these parameters for this problem are given as follows:

P = 9000, r = 0.036, n = 5 \times 12 = 60.

Then:

r/12 = 0.036/12 = 0.003.

Then the monthly payment is calculated as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 9000\frac{(0.003)(1.003)^{60}}{(1.003)^{60} - 1}[/tex]

A = $164.13.

Then the total amount paid is of:

Total = 60 x 164.13 = $9,847.8.

Meaning that the finance charge is given as follows:

9847.8 - 9000 = $847.8.

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Answer:

volume of cube= l^ 3

=(4x)^3

=64x^3 cubic units

1. In the simple interest equation, 687.5 = 550(1 + 0.05t), A. The value 550 represents the initial balance in the account, which means the account started with $550.

2. The account balance of a savings account opened with an initial deposit of $425.00, after 9 years if the account earns 2.7% simple interest annually, is C. $528.28.

3. The formula for the arithmetic sequence which begins with 56, 59, 62, 65, 68, … is C. f(n) = 56 + 3(n).

4. The equation, 816 = 600(1 + 9r), represents the amount of money earned on a simple interest savings account, where r is A. r = 0.04.

The simple interest system operates without compounding the interest.

Compounding implies that interest attracts interest.

1) 687.5 = 550(1 + 0.05t)

Principal = $550

Final amount after t years = $687.50

Simple interest rate = 0.05 or 5%

Time, t = [$687.5/$550 - 1]/0.05

= 5 years

2) Principal = $425.00

Time = 9 years

Simple interest rate = 2.7%

Amount after 9 years = $528.28 ($425 x 1 + (9 x 2.7%)

f(n) = 56 + 3(n)

Where n = 1:

f(n) = 56 + 3(1)

= 56 + 3

= 59

Where n = 2:

f(n) = 56 + 3(2)

= 56 + 6

= 62

4) Principal = $600

Amount after 9 years = $816

Simple interest rate = r

r = ($816/$600 - 1)/9

= 0.04

= 4%

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Answer:

Answer below

Step-by-step explanation:

1. The value 550 represents the initial balance in the account, which means the account started with $550.

2. (C) 528.28

425.00 x  2.7% x 9 = 103.275

Then we add 103.275 to the initial deposit of $425.00

425.00 + 103.275 = 528.275

Therefore the answer is (C) 528.28

3. The answer for this one is (A) f(n) = 56 + 3(n − 1)

So, as we can see the first value is 56 and the common difference is 3 and the rule for the nth term is [tex]a_{n} =a_{1} +d(n-1)[/tex] .

Therefore, its 56 + 3(n − 1)

4. For this one we solve for r and using a calculator its (A) r = 0.04

5. Oh also he doesn't have this one but its (C) 102

An auditorium has 30 seats in the first row, 38 seats in the second row, 46 seats in the third row, and so on. How many seats are in the 10th row?

60

93

102

110

As we can see the common difference is 8.

Then we use the rule for nth term which is [tex]a_{n} =a_{1} +d(n-1)[/tex]

[tex]a_{n} =30+8(n-1)[/tex]

[tex]a_{n} =30+8n-8[/tex]

[tex]a_{n} =22+8(10)[/tex]

[tex]a_{n} =22+80[/tex]

[tex]a_{n} = 102[/tex]

So therefore, the answer is (C) 102.

Therefore ,0.62097 % proportions  of students scored at least 27 points on this test

The Z-score provides information on how far a given value deviates from the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations above or below the mean a specific data point falls. The level of variability within a particular data collection is effectively reflected in the standard deviation.

Here,

z = (x - μ)/σ

here ,raw score =x ,standard deviation=σ   and mean= μ  

μ = 22, σ = 2

For x > 27:

z = (27 - 22)/2 = 1

P(z > 1) = 1 - P(z < 1) = 1 -  0.99379  =  0.0062097

Therefore , 0.62097 % of students scored at least 27 points on this test

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The equations found for the number of tickets sold when 22 tickets are sold on Monday and 30 per day after are sold by Madelyn, and 53 tickets are sold on Monday and 20 per day after that are;

Tickets sold by Madelyn is; y = 22 + 30·x

Tickets sold by Kaia is; y = 53 + 20·x

A system of equation obtained from the details in the question can be presented as follows

y = 22 + 30·x...(1)

y = 53 + 20·x...(2)

The appropriate method for solving the system is to equate equivalent values of one of the variable obtained from each equation in the system.

The solution of the system of equation is; x = 3.1, which indicates that it takes about 3.1 days for the number of tickets sold by Madelyn and Kaia to be equivalent.

An equation consists of two expressions that are joined by the 'equals to' (=) sign.

The number of tickets for the Winter Dance Madelyn sold = 22

Number of tickets per day Madelyn sold after that = 30 per day

Number of tickets Kaia sold on Monday = 53

Number of tickets per day Kaia sold after that = 20 per day

Let x represent the number of days since Monday, and let y represent the number of tickets sold

Therefore;

The number of tickets Madelyn sold, y = 22 + 30·x

The number of tickets Kaia sold, y = 53 + 20·x

The system of equations from the specified information is the equation for the number of tickets Madelyn sold and the number of tickets Kaia sold combined, which can be presented as follows;

y = 22 + 30·x...(1)

y = 53 + 20·x...(2)

The method of solving the equations is by plugging in the value of y from equation (1) in equation (2), as follows;
22 + 30·x = 53 + 20·x

30·x - 20·x = 53 - 22 = 31

10·x = 31

x = 31 ÷ 10 = 3.1

The meaning of the solution of the system of equation, x = 3.1, is that the number of days for the number of tickets sold by Madelyn and Kaia to be the same is about 3 days

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The number of quizzes still need to be graded is 17quizzes.

There are many different ways to define an equation. In terms of algebra, an equation is a claim that demonstrates the equality of two mathematical expressions.

For instance, the two equations 5x + 4 and 16, which are separated by the 'equal' sign, make up the equation 5x + 4 = 16.

Algebraic equations in mathematics frequently have one or more variables.

It is given that,

grades of the teacher out of 48 quizzes before school = 16

grades of the teacher of the remaining quizzes after school = 15

Let us assume 'X' as the number of quizzes still need to be graded.

then X= 48-16+15

          =48-31

          =17

Hence, The number of quizzes still need to be graded is 17quizzes.

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The number of quizzes still need to be graded is 17 quizzes.

   then X= 48-=48-31

    =17

Hence, The number of quizzes still need to be graded is 17 quizzes.

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Answer:

i think that answer is correct

Step-by-step explanation:

The equation Sharon can use to find c, the average amount the cable company charges per channel is 300(c - 0.20) = 180.

The cable company charges an average of $0.80 per channel.

An equation involves two expressions or statement on two sides connected with an equal sign.

Total number of channels = 300

Let c be the cable company charges per channel.

Then the charge satellite company charges per channel = c - 0.20

Monthly charge of satellite company = 300(c - 0.20)

Monthly satellite bill = $180

So,  300(c - 0.20) = $180

⇒ c - 0.20 = 180/300

⇒ c - 0.20 = 0.60

⇒ c = 0.60 + 0.20

⇒ c = 0.80

Hence the equation used to find the cable company charge per channel is 300(c - 0.20) = 180 and the cable company charge per channel is $0.80.

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Answer:

144cm²

Step-by-step explanation:

If the square is perfectly even on all sides, the you first need to divide 48 by 4, as a square has 4 sides.

48/4 = 12cm

Then, to find the area, you need to multiply 12 by 12.

12 cm x 12 cm = 144cm²

Hope this helps :)

Answer: x = 0.375

Step-by-step explanation:

Equation: 8x + 4 = 7

Subtract 4 on both sides

8x = 3

Divide by 8 on both sides

x = 3/8 is 0.375 decimal

x = 0.375 (0.38 round-up)

Answer:

Step-by-step explanation:

Four more than the product of a number and 8 is equal to 7.

4 + 8x = 7

8x = 7 - 4

8x = 3

x = 3/8

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

check

4 + 8 x 3/8 = 7

4 + 3 = 7

7 = 7

the answer is good

The expression that represents c in terms of A, h, and d would be c = (2A/h) - d.

What is the area of the trapezium?

The formula for the area of a trapezium is A = h(c + d)/2, where h is the height of the trapezium, c is the length of one of the bases, and d is the length of the other base.

To find an expression for c in terms of A, h, and d, we can start by rearranging the formula to solve for c:

A = h(c + d)/2

2A = h(c + d)

2A/h = c + d

c + d = 2A/h

Then, we can subtract d from both sides of the equation to solve for c:

c = (2A/h) - d

Hence, the expression that represents c in terms of A, h, and d would be c = (2A/h) - d.

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The expression that represents c in terms of A, h, and d would be c = (2A/h) - d.

What is the area of the trapezium?

The formula for the area of a trapezium is A = h(c + d)/2, where h is the height of the trapezium, c is the length of one of the bases, and d is the length of the other base.

To find an expression for c in terms of A, h, and d, we can start by rearranging the formula to solve for c:

A = h(c + d)/2

2A = h(c + d)

2A/h = c + d

c + d = 2A/h

Then, we can subtract d from both sides of the equation to solve for c:

c = (2A/h) - d

Hence, the expression that represents c in terms of A, h, and d would be c = (2A/h) - d.

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The transformations that took for mapping ΔA onto ΔB are:

a) Translated the triangle A 2 units to the right,

b) Reflected the ΔA' (translated A) over the y-axis,

c) Reflected the ΔA'' (reflected A) over the x-axis, resulting in ΔB.

The transformation rules are:

a) Translation: (x, y) ⇒ (x + 2, y) (In the right side direction)

b) Reflection over the y-axis: (x, y) ⇒ (-x, y)

c) Reflection over the x-axis: (x, y) ⇒ (x, -y)

The given vertices of triangle A are: (-2, 3), (-5, 3), and (-5, 5).

a) Applying translation by 2 units to the right to triangle A:

(-2, 3) → (-2 + 2, 3) → (0, 3)

(-5, 3) → (-5 + 2, 3) → (-3, 3)

(-5, 5) → (-5 + 2, 5) → (-3, 5)

So, triangle A is translated to triangle A'.

b) Applying reflection over the y-axis to the triangle A':

(0, 3) → (0, 3)

(-3, 3) → (3, 3)

(-3, 5) → (3, 5)

So, triangle A' is reflected as triangle A''.

c) Applying reflection over the x-axis to triangle A'':

(0, 3) → (0, -3)

(3, 3) → (3, -3)

(3, 5) → (3, -5)

Thus, the formed triangle is B at the vertices (0, -3), (3, -3), and (3, -5).

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The number of petals that the flower should have is of:

8 petals.

A figure has rotational symmetry when it can be rotated by an angle measure which is greater than 0º and less than 360º and the rotated image is equals to the original figure, that is, the image is equals to the pre-image.

In this problem, we want the flower to have a rotation symmetry of 45 degrees.

The total angle measure of the flower is given as follows:

360º.

Then the number of petals needed for the flower to have a rotational symmetry of 45º is calculated as follows:

360/n = 45.

Applying cross multiplication, we have that:

45n = 360

n = 360/45

n = 8 petals.

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Answer:

Step-by-step explanation:

Answer:

6. Scalene, No congruent sides

7. Isosceles, 2 congruent sides

8. Equilateral, All congruent sides

Answer:

True

Step-by-step explanation:

The point [tex](0,3)[/tex] lies on the graph.

Alyssa has the money of worth $660

Eric has the money of worth $245

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

Let x be the amount Alyssa has.

Let y be the amount  Eric has.

alyssa has $75 less than three times eric

=> x= 3y - 75

Together they have $905

=> x + y =905

Substitute x

=> 3y - 75  +y = 905

    4y = 905 +75 = 980

    y = 980 /4 = 245

x= 3y - 75  = 3(245) - 75 = 660

Alyssa has  $660

Eric has  $245

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Answer:

New price = 0.06 x Original price

New price $1,968

Answer:

All Real Numbers

Step-by-step explanation:

I assume you are solving for x.
The Interval Notation would be: (-∞,∞)

Age, BMI, creatinine, and the amount of time between conception and death are a few examples of quantitative characteristics.

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Answer:

Step-by-step explanation: To solve the problem, we can use the given information to set up a system of equations and solve for the values of $x$ and $y$. Specifically, we are given that one number is 4 less than 3 times a second number, and that two times the first number decreased by two times the second is 8.

Let $x$ represent the larger number, and $y$ represent the second number. We can write the given information as a system of equations as follows:

x &= 3y - 4

2x - 2y &= 8

Solving this system of equations, we find that $x = 12$ and $y = 2$. Therefore, the value of the larger number is 12

It will take 38 weeks a student to save enough money for the ticket.

Mathematical operations come in several types, with division being one. The phrases or numbers are divided into the same number of components during this operation.

Given,

a student must save at least $675 plus 3% tax to buy a round-trip ticket to London.

3% of 675

= 3 x 675 / 100

= 20.25

The student has $98 saved already.

Now student needs ($675 - $98) + 20.25 = $577 + 20.25

= $597.25

If the student earns $32 per week and plans to save half of the earnings each week toward the ticket cost.

That means, $32 / 2 = $16 per week.

To find the amount of enough money:

Divide $597.25 by $16.

597.25 /16

= 37.328125

≈ 38 weeks

Therefore, student will save for 38 weeks.

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a. 4(x - 5)^2

= 4 * (x - 5)^2

= 4 * ((x - 5) * (x - 5))

= 4x^2 - 40x + 100

b. 3(x + 1) (2x - 9)

= (3(x + 1)) (2x + −9)

= (3(x + 1))(2x) + (3(x + 1))(−9)

= 6x^2 + 6x − 27x − 27

= 6x^2 − 21x − 27

c. -2(4x + 2)^2

= -2 * (4x + 2)^2

= −2 * ((4x + 2) * (4x + 2))

= 32x^2 − 32x − 8

or d. -2(4x + 2)^2 - 5 (with subtracting 5)

= −32x^2 + −32x + −8 + −5

= (−32x^2) + (−32x) + (−8 + −5)

= −32x^2 + −32x + −13

d. -3(5x - 2)^2 + 5 (with negative)

= 75x^2 + −60x + 12 + 5

= 75x^2 + −60x + 12 + 5

= (75x^2) + (−60x) + (12 + 5)

= 75x^2 + −60x + 17

or d. 3(5x - 2^2 + 5 (without negative)

= (3)(5x + −4 + 5)

= (3)(5x) + (3)(−4) + (3)(5)

= 15x − 12 + 15

= 15x + 3

Answer:

-5/3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)  ==> (x1, y1), (x2, y2) are the coordinates and

                                   m is the slope

  (x1, y1), (x2, y2)  ==> (x1=-4, y1=7), (x2=5, y2=-8)

m=(-8-7)/(5-(-4))  ==> plug in known values

m=(-15)/(5+4)  ==> simplify

m=-15/9

m=-5/3

The coordinate location of the hill halfway between them is  (1, -1).

Jack's house is located at the point (-2, 3) and Jill's house is located at the point (4, -5).  They plan to meet up at the hill located halfway between there two houses.

The coordinate location of the hill can be calculated as follows:

using mid point formula,

(x, y) = (x₁ + x₂ / 2, y₁ + y₂ / 2)

using the end points (-2, 3) and (4, -5)

(x, y) = (-2 + 4 / 2, 3 - 5 / 2)

(x, y) = (2 / 2. -2 / 2)

(x, y) = (1, -1)

Therefore, the coordinate location of the hill is (1, -1).

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Answer:

2xy + 3x + 6y + 9

Step-by-step explanation:

2y times x = 2xy

3 times x = 3x

2y times 3 = 6y

3 times 3 = 9

Answer:12

Step-by-step explanation:

270/3=90, this is the amount it costs for 1 person to go

1080/90=12

12 people can go for $1080

Answer:

y = 1/3x + 8/3

Step-by-step explanation:

The slope of a line that is perpendicular to the line y = -1/3x + 7 is the negative reciprocal of the slope of the given line, which is -3. So, the slope of the perpendicular line is 1/3.

The point where the perpendicular line intersects the given line is also the point where the two lines intersect, which is (4,2) in this case. So, we can use this point to find the equation of the perpendicular line using the point-slope form of a line:

y - y1 = m(x - x1)

where m is the slope of the line and (x1,y1) is a point on the line.

In our case, the equation of the perpendicular line is:

y - 2 = 1/3(x - 4)

We can simplify this equation to obtain:

y = 1/3x + 8/3

Therefore, the equation of the perpendicular line is y = 1/3x + 8/3.