Barbara has a bunny that weighs 2 pounds and gains 3 pounds per year. Her cat weighs 6 pounds andgains 1 pound per year. When will the bunny and the cat weigh the same amount?

Answer:

314.2

Step-by-step explanation:

A = pi x r^2

A = 3.142 x 10^2

A = 3.142 x 100

A = 314.2

The answer

4.16666667 yards

Answer:

On average, Tonya makes $312 more than Emily on a typical day.

Step-by-step explanation:

I was just studying that question a few hours ago

Answer:

1. 4

2. 39.3700787 (just round it up)

To find the value of x²-5x+3 when x=15-√2, we substitute the value of x into the expression:

x² - 5x + 3 = (15-√2)² - 5(15-√2) + 3

First, let's expand (15-√2)² using the formula for the square of a binomial:

(15-√2)² = (15)² - 2(15)(√2) + (√2)²

= 225 - 30√2 + 2

Simplifying further:

(15-√2)² = 227 - 30√2

Now we substitute this back into the expression:

x² - 5x + 3 = 227 - 30√2 - 5(15-√2) + 3

= 227 - 30√2 - 75 + 5√2 + 3

= 155 - 25√2

Therefore, the value of x²-5x+3 when x=15-√2 is 155 - 25√2.

Answer:

He has 68.8% of his drink left

Step-by-step explanation:

do 32 oz - 10 oz = 22 oz to get how much of his drink is left

To get the percentage, just do what left divided by original amount

so 22/32 = 0.6875 and in percent, that is about 68.8%

Answer:

28.21 = 4x + 4.61

Step-by-step explanation:

Since x equals the bags of apples and he bought 4 of them, we would multiply x by 4 like this: 4x

$4.61 were already added to the total cost of $28.21

If we wanted to find out how much each bag cost, we subtract 4.61 from both sides

28.21 = 4x + 4.61

- 4.61.         - 4.61

23.6 = 4x

Then, divide both sides by 4

23.6/4 = 4x/4

x = 5.9

Each bag of apples cost $5.90

Blanks to be filled by 4,3,8 and 3.

Multiplication in mathematics is the same as adding equal groups. As we multiply, there are more items in the group. The product, the two factors, and the product are all components of a multiplication problem. The numbers 6 and 9 are the factors in the multiplication equation 6 x 9 = 54, and 54 is the result.

Given Data

           3 __ 8

×            7 8 4

_____________

       1 _    9 2

    2 7 __ 4

_   4 3  6

_____________

 2  7 2 8 __ 2

_____________

Solving

Multiplying and adding,

           3 _4_ 8

×            7 8 4

_____________

       1 3_    9 2

    2 7 _8_ 4

_   4 3  6

_____________

 2  7 2 8 _3_ 2

_____________

To learn more about multiplying, visit:

https://brainly.com/question/620034

#SPJ13

Answer: Area 6 Perimeter 12

Step-by-step explanation:

First, you have to find the perimeter. 4+5+3=12. Then, you need to find the area, which is base*height/2. The base is 3 and the height is 4. 4*3=12. Then you need to do 12/2=6. The area is 6

Answer:

The answer for P=12cm,A=6cm²

Step-by-step explanation:

Perimeter of triangle=a+b+c

P=5+3+4

P=12cm

Area of triangle =1/2bh

A=1/2×3×4

A=2×3

A=6cm²

The names of the expressions are;

1) Monomial, quadratic

2) Monomial, constant

3) Binomial, Linear

4) Trinomial, quadratic

An algebraic expression that has one or more terms, each of which is a variable raised to a non-negative integer exponent and multiplied by a coefficient, is referred to as a polynomial. The terms are mixed by adding or removing. A polynomial may include 0 terms or more.

A particular kind of polynomial known as a trinomial has exactly three terms. Trinomials are made up of three different pieces, which are frequently denoted by the formula "ax2 + bx + c," where "a," "b," and "c" are coefficients.

Learn more about polynomials:https://brainly.com/question/11536910

#SPJ1

Vocabulary Check:

Integers are numbers that are neither fractions nor decimals.

Rational numbers are numbers that can be written as a fraction, unlike irrational numbers. Whole numbers are counting numbers, including 0.

Integers = -23, 2, 3, 16, 0, -4

Whole Numbers = 0, 2, 3, 16

Rational = -23, 2, 0.7, 5, 16, 0, 3.89, -4

Irrational: None

We get the length of AC as 14 units when we have AC = x, BC = 2 x - 18 and AB = 4 units.

We are given that the length of AB = 4.

We are also given the expressions:

AC = x and BC = 2 x - 18

We need to find the value of AC

We know that:

AB + BC = AC

Substituting he values, we get that:

4 + 2 x - 18 = x

Combining the like terms, we get that:

2 x - 14 = x

2 x - x = 14

x = 14

So, we get that,

AC = x

AC = 14 units.

Therefore, we get the length of AC as 14 units when we have AC = x, BC = 2 x - 18 and AB = 4 units.

Learn more about expression here:

https://brainly.com/question/22048677

#SPJ9

Answer:

Hi, Victoria. When you are dealing with a system of equations in three variables, you want to see first if there is anyway that you can eliminate two variables in one fell swoop. Remember that for any one given equation, you can multiply both sides by the same number without making the equation untrue. Also, remember that you can add or subtract two equations.

If we add the first and second equations, we will eliminate both the x and the y.

(2x + y + z) + (2x - y - z) = (3) + (9)

The particle's acceleration a increases at a constant rate, so that its average rate of change is equal to its instantaneous rate of change, which is equal to

(4 ft/s² - 1 ft/s²) / (1 s) = 3 ft/s³

The particles starts with acceleration a (0) = 1 ft/s², so we can determine its acceleration at time t by the fundamental theorem of calculus:

a(t) = a (0) + ∫₀ᵗ (3 ft/s³) du

a(t) = 1 ft/s² + (3 ft/s³) t

It also starts from rest, so with initial velocity v (0) = 0. Integrating again gives us the velocity function,

v(t) = v (0) + ∫₀ᵗ a(u) du

v(t) = ∫₀ᵗ (1 ft/s² + (3 ft/s³) u) du

v(t) = (1 ft/s²) t + 1/2 (3 ft/s³) t ²

Taking the particle's initial position to be x (0) = 0, compute the integral again to determine the distance it travels in 1 s:

x(t) = x (0) + ∫₀ᵗ v(u) du

x(t) = ∫₀ᵗ ((1 ft/s²) u + 1/2 (3 ft/s³) u ²) du

x(t) = 1/2 (1 ft/s²) t ² + 1/6 (3 ft/s³) t ³

→   x (1 s) = 1/2 (1 ft/s²) (1 s)² + 1/6 (3 ft/s³) (1 s)³ = 1 ft

The truck driver would deliver 105 packages in a 7 hours day

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

Let y represent the number of packages delivered by the truck driver in x hours. Using the point (1, 15) and (4, 60). Hence, the equation is:

y - 15 = [(60-15)/(4-1)](x - 1)

y = 15x

For a 7 hour day (x = 7):

y = 15(7) = 105

The driver would deliver 105 packages in 7 hours

Find out more on equation at: https://brainly.com/question/29174899

#SPJ1

Answer:

75 km/hr

Step-by-step explanation:

So, if a car travels 150 km in 2hours.

Then;

f(t=0) = 0

f(t = 2 hours) = 150 km

Therefore;

f'(c) (speedometer reading) = f(t=2)-f(t=0)/(2-0)

f'(c) (speedometer reading) = 150/2  km/hr

f'(c) (speedometer reading) = 75 km/hr

SOLUTION:

Case: Polynomials

Method:

Given expression

The critical value based on the information will be zα/2 = -2.58

We want to find the critical values zα/2 and -zα/2 that correspond to these tail probabilities.

Using the standard normal distribution table for negative z scores, we can find the value that corresponds to a tail probability of 0.005. This is -2.58.

Using the standard normal distribution table for positive z scores, we can find the value that corresponds to a tail probability of 0.005. This is 2.58.

Therefore, the critical values are zα/2 = -2.58 and -zα/2 = 2.58.

Learn more about critical value on

https://brainly.com/question/14040224

#SPJ1

Projectile B begins its descent 1 seconds before Projectile A does.

In Mathematics and Geometry, the y-intercept of any graph or table such as a quadratic equation or function, generally occurs at the point where the value of "x" is equal to zero (x = 0).

By critically observing the table shown in the image attached above, we can reasonably infer and logically deduce the following y-intercept of Projectile A:

y-intercept = (0, 44).

Maximum height = (4, 300).

When t = 0, the y-intercept of Projectile B can be calculated as follows;

h(t) = -16t² + 96t

h(0) = -16(0)² + 96(0)

h(0) = 0.

For the maximum height, we have:

h(t) = -16t² + 96t

h'(t) = -32t + 96

32t = 96

t = 96/32

t = 3

Difference in time = 4 - 3

Difference in time = 1 seconds.

Read more on time and maximum height here: https://brainly.com/question/30145152

#SPJ1

Answer:

\(3^{2}+4^{2}=JH^{2} \\\\9+16=25=JH^{2} \\\\JH=\sqrt{25} =5\\\\\)

\(AB^{2} +6^{2} =10^{2} =100\\\\AB^{2} =100-36=64\\\\AB=\sqrt{64}=8\\\)

all three pairs of appropriate sides of a triangle are proportional, the ratio is the same.

10/5=8/4=6/3=2 so the triangles are similar

hope it helps

Answer:

$5.61

Explanation:

The approximate weight of each grapefruit = 165 grams

First, calculate the total weight of 40 grapefruits.

Since the orchard charges $0.85 to ship a kilogram of grapefruit, the cost of shipping 40 grapefruits will be:

Answer:

The area of the rectangle is 72 square feet

Step-by-step explanation:

The angles COA and POC are 22.5 and 67.5 degrees respectively as POA is a right angled triangle.

POA is a right angle so it is 90 degrees.

POC +COA = 90  .....(1)

Also, POC is 3 times as large as COA.

Let's take COA, "x"

POC = 3x

Substituting the values in equation (1) as follows:

x + 3x = 90

4x = 90

x= 22.5

Therefore,

COA = 22.5°

POC = 22.5*3 = 67.5°

To learn more about angles check the link below:

https://brainly.com/question/25770607

#SPJ4

divide 72 in the ratio of 4: 5

= 16

Answer:

Fraction of composite numbers = 6/10

Fraction of prime numbers = 4/10

Step-by-step explanation:

A composite number can be defined as a positive integer that will be formed when we multiply two smaller positive integers. It can also be said to be a positive integer that has at least one divisor of which 1 and itself are not included.

Thus, it means that the set of numbers given to us which is;

(11, 12, 13, 14, 15, 16, 17, 18, 19, 20), the composite numbers are;

12, 14, 15, 16, 18, 20

This is because each of them have at least one divisor that is neither itself or 1.

Thus, we have 6 out of the 10 numbers as composite.

Fraction of composite numbers = 6/10

Now, a prime number is a number that are only divisible by itself and 1.

Thus,from the given set, the prime numbers are; 11, 13, 17 & 19

We have 4 out of 10 numbers as prime numbers.

Thus, fraction of prime numbers = 4/10

Answer:

\(\textsf{A.} \quad (2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)

Step-by-step explanation:

Replace f(x) with y in the given function:

\(y=(x+2)^x\)

Take natural logs of both sides of the equation:

\(\ln y=\ln (x+2)^x\)

\(\textsf{Apply the log power law to the right side of the equation:} \quad \ln a^n=n \ln a\)

\(\ln y=x\ln (x+2)\)

Differentiate using implicit differentiation.

Place d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}\ln y=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)

First, use the chain rule to differentiate terms in y only.

In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)

Now use the product rule to differentiate the terms in x (the right side of the equation).

\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\textsf{Let}\; u=x \implies \dfrac{\text{d}u}{\text{d}x}=1\)

\(\textsf{Let}\; v=\ln(x+2) \implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{1}{x+2}\)

Therefore:

\(\begin{aligned}\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&=x\cdot \dfrac{1}{x+2}+\ln(x+2) \cdot 1\\\\\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&= \dfrac{x}{x+2}+\ln(x+2)\end{aligned}\)

Multiply both sides of the equation by y:

\(\dfrac{\text{d}y}{\text{d}x}&=y\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)

Substitute back in the expression for y:

\(\dfrac{\text{d}y}{\text{d}x}&=(x+2)^x\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)

Therefore, the differentiated function is:

\(f'(x)=(x+2)^x\left[\dfrac{x}{x+2}+\ln(x+2)\right]\)

\(f'(x)=(2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)

The given equation is:

Multiply both sides by 9/5

Subtract 32 from both sides

The domain of the relation is {1, 2, 3, 4}.

Given that, a relation R = {(1,1) (2,4) (3,9) (4,16)},

We need to find the domain of the function,

We know that the domain of the function is the set of all the input values and range is the set of all the output values.

Or we can say that the values of x are the domain of the function and the value of y is range of the function.

In the relation given

Range = {1, ,4, 9, 16}

Domain = {1, 2, 3, 4}

Hence, the domain of the relation is {1, 2, 3, 4}.

Learn more about domain, click;

https://brainly.com/question/28135761

#SPJ1

The translation -

The domain of the relation R = {(1,1) (2,4) (3,9) (4,16)} is :