The regular price of a pair of sneakers is $80. They are on sale now for $50. What is the percent decrease in the price of sneakers?

Answer:

is the 3x a expression ill comment the awnser if is

Step-by-step explanation:

Step-by-step explanation:

We need to break up the given expression into two separate fractions so that when they are added together, we will get the original expression.

Note that the denominator is made up of two factors, \((2x - 1)\) and \((x^2 + 1).\) But note that the 2nd factor is a 2nd order polynomial so as a rule, the numerator of the fraction containing this factor must be an (n - 1)-order polynomial, where n is the order. With that in mind, we can write the general form of the partial fractions as follows:

\(\dfrac{x + 7}{(2x - 1)(x^2 + 1)} = \dfrac{Ax + B}{x^2 + 1} + \dfrac{C}{2x - 1}\)

\(\:\:\:\:=\dfrac{2Ax^2 + Bx - Ax - B + Cx^2 + C}{(2x - 1)(x^2 + 1)}\)

Here, we combined the two fractions to form the equation above. Next, we compare the numerators on either side. Note that we satisfy the equality if we impose the following conditions:

\(2A + C = 0\:\:\:\:\:\:\:\:\:\:\:\:\:\:(1)\)

\(2B - \:A = 1\:\:\:\:\:\:\:\:\:\:\:\:\:\:(2)\)

\(-B + C = 7\:\:\:\:\:\:\:\:\:\:\:\:\:\:(3)\)

To find the values of the constants A, B and C, we need to solve this system of equations. We start by multiplying Eqn(3) by 2 and then adding it to Eqn(2) to get

\(-A + 2C = 15\:\:\:\:\:\:\:\:\:\:\:\:\:\:(4)\)

Then, multiply Eqn(1) by -2 to get

\(-4A - 2C = 0\:\:\:\:\:\:\:\:\:\:\:\:\:\:(5)\)

Add Eqn(4) to Eqn(5) and we will get

\(-5A = 15 \Rightarrow A = -3\)

Now that we know the value of A, we can use this in Eqn(2) to get

\(2B - (-3) = 1 \Rightarrow B = -1\)

Next, to solve for C, we use the value of A in Eqn(1) to get

\(2(-3) + C = 0 \Rightarrow C = 6\)

Therefore, the given expression can be written as

\(\dfrac{x + 7}{(2x - 1)(x^2 + 1)} = \dfrac{6}{2x - 1} + \left(\dfrac{-3x - 1}{x^2 + 1}\right)\)

As a check, let's combine the two fractions together:

\(\dfrac{x + 7}{(2x - 1)(x^2 + 1)} = \dfrac{6}{2x - 1} + \left(\dfrac{-3x - 1}{x^2 + 1}\right)\)

\(= \dfrac{6x^2 + 6 - 6x^2 - 2x + 3x + 1}{(2x - 1)(x^2 + 1)}\)

\(= \dfrac{x + 7}{(2x - 1)(x^2 + 1)}\)

As expected, we got the original expression.

Answer:

hi there!

Alrighty, so if Lucy is 3 times as old as her cousin, who is 14, you would just multiply 14 x 3

So your answer would be 42. Hope this helped!

Answer:

\(\huge\boxed{\sf Lucy's \ age = 21}\)

Step-by-step explanation:

Let Lucy age be x and her cousin's age be y.

Condition # 1:

x = 3y --------------------(1)

Condition # 2:

x - y = 14 ----------------(2)

Put Eq. (1) in (2)

3y - y = 14

2y = 14

Divide both sides by 2

y = 7

Put y in Eq. (1)

x = 3(7)

x = 21

So,

Lucy cousin's age = 7

Lucy's age = 21

\(\rule[225]{225}{2}\)

Hope this helped!

Answer:

  f(x)=40(2.25)^x

Step-by-step explanation:

You want the equation of the exponential function that goes through points (0, 40) and (1, 90).

The exponential function can be written ...

  f(x) = a·b^x

When x = 0, this is ...

  f(0) = a·b^0 = a·1 = a

Using the given point, we have a = 40.

When x = 1, this is ...

  f(1) = 40·b^1 = 40b

Using the given point, we have ...

  90 = 40b

  b = 90/40 = 2.25

The function equation is ...

  f(x) = 40(2.25^x)

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The solution to the system, as an ordered triple is: (3, -4, 6).

To solve the following given system of equations:

2x + y + 3z = 20 --> eqn. 1

x + 2y - z = -11 --> eqn. 2

3x - 2z = -3 --> eqn. 3

Multiply equation 1 by 2 to get eqn. 4:

4x + 2y + 6z = 40 --> eqn. 4

Subtract eqn. 4 from eqn. 2:

x + 2y - z = -11 --> eqn. 2

4x + 2y + 6z = 40 --> eqn. 4

-3x - 7z = -51 --> eqn. 5

Add equations 3 and 5 together:

3x - 2z = -3 --> eqn. 3

-3x - 7z = -51 --> eqn. 5

-9z = -54

z = -54/-9

z = 6

Substitute the value of z into equation 5:

-3x - 7(6) = -51 --> eqn. 5

-3x - 42 = -51

-3x = -51 + 42

-3x = -9

-3x/-3 = -9/-3

x = 3

Find the value of y by substituting the values of x and z into equation 1:

2(3) + y + 3(6) = 20 --> eqn. 1

6 + y + 18 = 20

24 + y = 20

y = 20 - 24

y = -4

The solution as an ordered triple is: (3, -4, 6).

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The critical value becomes 2.584 for two tailed test since we have to reject the null hypothesis, t >2.584 or t < -2.584 test stat lie in the rejection region.

Data;

Let's calculate the t-value

\(t = \frac{x - \mu}{\frac{s}{\sqrt{n} } }\)

Substitute the values into the equation and solve;

\(t = \frac{x - \mu}{\frac{s}{\sqrt{n} } } \\t = \frac{5.82 - 5}{\frac{4.93}{\sqrt{600} }} \\t = \frac{0.82}{0.201} \\t = 4.079\)

The t-value is 4.079.

The allowed significance value = 0.01

The degree of freedom is n -1, which becomes 600 - 1 = 599.

The critical value becomes 2.584 for two tailed test since we have to reject the null hypothesis, t >2.584 or t < -2.584 test stat lie in the rejection region, we have to reject the null hypothesis or claim incorrect.

Learn more on t-test here;

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Answer:

answer is d) $20

Step-by-step explanation:

because 2x4=8 + 2x4=8 = $16 then 4 packets for $1 is $4 16+4= $20

Answer:

D) $20

Step-by-step explanation:

Wash plus dry = $4

$4 times 4 times = $16

$1 for one detergent times the four packets = $4

Total is $20

Answer:

37

Step-by-step explanation:

n = 1st number

n+1 = next consecutive number

n + n+1 = 75

2n + 1 = 75

2n = 74

n = 37

n+1 = 38

Answer:

8

Step-by-step explanation:

4/7 = ?/14

Multiply the numerator and denominator of the left fraction by 2.

8/14 = ?/14

That means that ? = 8

Answer: 8

Answer:

8

Step-by-step explanation:

Step 1:

4/7 = x/14        Proportion

Step 2:

7x = 56       Multiply

Step 3:

x = 56 ÷ 7       Divide

Answer:

x = 8

Hope This Helps :)

The Surface area this of cylinder with radius 11cm and height 30 cm is 2833.71 cm².

Two parallel, identical bases connected by a curved surface form a 3D solid shape known as a cylinder. Similar to a disc in shape, these bases. The axis of the cylinder shape is a line drawn through the middle of, or connecting, two circular bases. Perpendicular distance is the measurement separating the two bases, and it is denoted by the letter "h," which stands for height. The distance between the two circular bases' centres and outer edges is known as the cylinder's radius and is denoted by the letter "r".

Surface area of cylinder = 2πr(r+ h)

= 2π11(11+ 30)

= 2833.71 cm²

Thus, the Surface area this of cylinder with radius 11cm and height 30 cm is 2833.71 cm².

Learn more about cylinder

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Answer: 630

Step-by-step explanation:

\(3000 * 21 /100 = 3000 * 0.21 = 630\)

Answer:

(9, -13.5)

Step-by-step explanation:

It's given in the question that a quadrilateral RSTV is dilated with a scale factor of 1.5 with respect to the origin to form R'S'T'V'.

Rule for dilation is,

(x, y) → (kx, ky)

where 'k' is the scale factor.

If vertex R of the quadrilateral is (6, -9),

By the given rule of dilation,

R(6, 9) → R'[(1.5 × 6), -(1.5 × 9)]

           → R'(9, -13.5)

Therefore, Option given in bottom right (9, -13.5) will be the answer.

all work should be in the picture, lmk if theres anything confusing

The lengths equal to 3 yards 16 inches are 3 yards, 108 inches, 3.44 yards (approximately), and 108.44 inches (approximately).

To determine the lengths that are equal to 3 yards 16 inches, we need to convert the measurements into a consistent unit. Since both yards and inches are units of length, we can convert the inches into yards or the yards into inches to find the equivalent lengths.

1 yard is equal to 36 inches (since 1 yard = 3 feet and 1 foot = 12 inches).

Therefore, 3 yards is equal to 3 * 36 = 108 inches.

Now, we can compare 108 inches to 3 yards 16 inches.

108 inches is equal to 3 yards, so it matches the given length.

To convert 16 inches into yards, we divide it by 36 since 1 yard = 36 inches. 16 inches / 36 = 0.44 yards.

Therefore, 3 yards 16 inches is equivalent to:

3 yards

108 inches

3 yards 0.44 yards (or approximately 3.44 yards)

108 inches 0.44 yards (or approximately 108.44 inches)

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Answer:

The acceleration is 2.9m/s^2

Step-by-step explanation:

Given

\(Initial\ Speed\ (u) = 6m/s\)

\(Final\ Speed\ (v) = 35m/s\)

\(Time\ (t) = 10s\)

Required

Determine the acceleration

This question will be answered using Newton's first equation of motion.

\(v = u + at\)

Substitute values for v, u and t

\(35 = 6 + 10 * a\)

\(35 = 6 + 10 a\)

Collect Like Terms

\(10a = 35-6\)

\(10a = 29\)

Solve for a

\(a = 29/10\)

\(a = 2.9\)

Hence, the acceleration is 2.9m/s^2

Answer:

C.

Step-by-step explanation:

\(\left \{ {{2x+y=10,3} \atop {3x+y=14,8}} \right.\)

\(\left \{ {{y=10,3-2x} \atop {y=14,8-3x}} \right.\)

10,3-2x=14,8-3x

x=4,5 - one hamburger

y=1,3 - one milk shake

OR:

$14,8-$10,3=$4,5 - one hamburger

2*4,5+y=10,3

y=1,3 - one milk shake

2y=2,6

Answer:

Step-by-step explanation:

Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

What is congruent?

Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.

Here,

we have to prove when can we say that the two triangles are congruent.

SSS, SAS, ASA, AAS, and HL.

These tests describe combinations of congruent sides and/or angles that are used to determine if two triangles are congruent.

Hence, two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

To learn more about the congruence from the given link

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Answer:

Step-by-step explanation:

A

Answer:

D.

Step-by-step explanation:

A statistical question can answered by collecting data and having various answers. The other options refer to a specific person/thing and give only one piece of data while the last option refers to many teachers and many pieces of data.

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

Answer:

c

Step-by-step explanation:

the surface area for spheres is

4 × π × r²

4 × π × (7²) = 196 π

Answer:

red +blue marbles :- 15 +13=28 marbles.

yellow marbles:- 50+28=22 marbles.

probability of yellow marble :- 22/50 i.e 11/25

a square is when all sides are the same and a rectangle is just if it has four sides so a rectangle cant be called a square because not all sides are the same but a square can be called a rectangle because it has four sides. i don't know if that makes sense

Answer:

144

Step-by-step explanation:

36 x 4

Answer:

144

Step-by-step explanation:

1 gallon 4

36 gallon 4*36 =144

Answer:

(5, -6)

Step-by-step explanation:

We have the two equations

\(\begin{aligned}2ax + 2y &= b \cdots\cdots [1]\\ 5 x + y &= -6 \cdots\cdots [2]\\\end{aligned}\\\)

Multiply equation [2] by 2

\(10x + 2y = -6 \cdots\cdots[3]\)

There will be an infinite number of solutions when both equations [1] and [3] are exactly the same:
For this to happen the right sides must be the same
So b = -6

Also 2ax = 10x
so 2a = 10

a = 5

So the ordered pair(5, -6) results in an infinite number of solutions

Answer:

Bill of Gemma is x

Bill of her cousin is x+5

Combined bill is: 2x + 5 <25

=> x < 10

Bill of Gemma was under $10

Step-by-step explanation: