Lorraine prepared a 2.5-gallon pot filled with tomatoes to be canned in jars. Each jar will hold 1.25 quarts of tomatoes. If 1 gallon equals 4 quarts, how many jars can Lorraine fill?

4 jars
5 jars
8 jars
10 jars

The value of the function f(x) at x = - 2, - 1, 0, 1 are - 4, - 1, 2, 5.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, A function f(x) = 3x + 2.

Now,

At x = - 2, f(x) = 3(-2) + 2 ⇒ f(x) = - 4.

At x = - 1, f(x) = 3(-1) + 2 ⇒ f(x) = - 1.

At x = 0, f(x) = 3(0) + 2 ⇒ f(x) = 2.

At x = 1, f(x) = 3(1) + 2 ⇒ f(x) = 5.

This can also be written in the form of ordered pairs

(- 2, - 4), (- 1, - 1), (0, 2), (1, 5).

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The volume of the storage shed is 125600 ft³.

The storage shed will be refilled after using 125600 ft³ of salt.

The cylindrical storage shed shown below is completely filled with road salt to make a town's roads safer during snow storms.

The volume of the storage shed can be found as follows;

volume of a cylinder = πr²h

where

Therefore,

r = 40 / 2  =20 ft

h = 100 ft

volume of the storage shed = 3.14 × 20² × 100

volume of the storage shed = 3.14 × 400 × 100

volume of the storage shed = 125600 ft³

Therefore, the storage shed can handle 125600 ft³ of salt before it needs to be refilled.

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Answer:

2[tex]\pi[/tex] [tex]units^{2}[/tex]

Step-by-step explanation:

BC is equal to 4 because 5*4=20.

The radius is 2. The equation for the area of a circle is [tex]\pi r^2[/tex].

Therefore, if we plug in 2 we will get [tex]4\pi[/tex].

But then we divide by 2 to get 2[tex]\pi[/tex] [tex]units^{2}[/tex] as our answer.

Hope this helped! :)

Answer:

m∠C = 67°, a = 7.37, b = 15.13

Step-by-step explanation:

There are 180° in a triangle. We know two angles in the triangle, so we can calculate the third angle.

Since this is not a right triangle, we will use the Law of Sines.

SinA/a = SinB/b = SinC/c

see image.

Answer:

1809/27=67 is your answer........

Answer:

  See attached

Step-by-step explanation:

You want various combinations of the functions g(a) = -3a+1 and h(a) = 3a³ +4a.

The functions have no common factors, so their ratio leaves the function expressions unchanged:

  [tex]\dfrac{g(a)}{h(a)}=\boxed{\dfrac{-3a+1}{3a^3+4a}}[/tex]

The like terms are combined when the functions are added.

  [tex]h(a)+g(a)=(3a^3+4a)+(-3a+1)=3a^3+(4-3)a+1\\\\=\boxed{3a^3+a+1}[/tex]

Similarly, the like terms are combined when the functions are subtracted.

  [tex]g(a)-h(a)=(-3a+1)-(3a^3+4a)=-3a^3+(-3-4)a+1\\\\=\boxed{-3a^3-7a+1}[/tex]

The product is found the way products are usually found. Each term of one of the factors is multiplied by each term of the other factor, and these products are summed. You can think of it as repeated application of the distributive property.

  [tex]g(a)\cdot h(a)=(-3a+1)(3a^3+4a)=-3a(3a^3+4a)+1(3a^3+4a)\\\\=-9a^4-12a^2+3a^3+4a\\\\=\boxed{-9a^4+3a^3-12a^2+4a}[/tex]

Answer:

40/20 & 22/11

Step-by-step explanation:

To find an equivalent fraction to 4/2, or to any other fraction, you just need to multiply (or divide, if the fraction is not yet reduced), both the numerator and the denominator of the given fraction by any non-zero natural number. For example:By dividing the original fraction by 2, we get:4 ÷ 2 / 2 ÷ 2 = 21. By multiplying the original fraction by 2, we get:4 × 2 / 2 × 2 = 8/4. Here is the full list of equivalent fractions to 4/2. 2/1, 4/2, 6/3, 8/4, 10/5, 12/6, 14/7, 16/8, 18/9, 20/10, 22/11, 24/12, 26/13, 28/14, 30/15, 32/16, 34/17, 36/18, 38/19, 40/20...

Answer: -3√3

Step-by-step explanation: Factor out the square roots from each term

2√54 -> 6√6

√27 -> 3√3

3√24 -> 6√6

The equation becomes 6√6 - 3√3 - 6√6

By combining like terms we can eliminate 6√6

This leaves us with -3√3 as the simplified solution

Answer:

-3√3

Step-by-step explanation:

do the hcf method to get all the values outside

hcf of 54= 2, 3, 3, 3

hcf of 27 = 3, 3, 3

hcf of 24 = 2,2,3,3

2✓2×3×3×3 - √3,3,3 - 3√2,2,3,3

take out the common factor and multiply it with the value we have outside leave it if it doesnt have a number

2×3√2×3 - 3✓3 -3×2×3

6√6 - 3√3 - 3×2×3

6×3 - 3√3 - 3×2×3

18-18 - 3✓3

-3√3

Answer:

no solutions

Step-by-step explanation:

   -9x-2y=5

- (-9x-2y=11)

-9x-(-9x) - 2y-(-2y) = 5 - 11  ==> subtract the top two equations

-9x + 9x - 2y + 2y = -6  ==> subtracting by a negative number is equivalent

                                       to adding by a positive number

(-9x + 9x) - 2y + 2y = -6

0 - 2y + 2y = -6

0 - 0 = -6

0 [tex]\neq[/tex] -6  ==> Hence, there is no solutions.

The probability that the team will win more than 9 games this season, given the average number of wins for the team, is 4 %

The Z-score formula is:

Z = (x - mean) / standard deviation

Where x is the number of wins we're interested in (9), mean is the average number of wins (7.6), and standard deviation is the standard deviation of the number of wins (1.3)

Z = (9 - 7.6) / 1.3

= 2.3 / 1.3

= 1.77

This means that 9 wins is 1.77 standard deviations above the mean. The result is the probability of a team winning more than 9 games this season, which is around 0.04 or 4% from the standard normal distribution table.

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Table (x, y) equals (0, 0), (6, 3), and (12, 6) represents a linear relationship that is also proportional.

In its most basic form, a ratio is a comparison between two comparable quantities.

There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.

If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.

The first option is linear but not proportional as 3 ×2 = 6 and 6×2 = 12.

By observing the given options we conclude that the third option is linear and proportional as,

6 ÷ 2 = 3 and 12 ÷ 2 = 6.

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Answer:

$10.80

Step-by-step explanation:

9 times 0.20 equals 1.80

9 + 1.80 = $10.80

The property that could be used to determine that the triangles are congruent is the SSA congruent theorem

From the question, we have the following parameters that can be used in our computation:

Triangles = QRP and XWY​

On the triangles, we can see that:

This means that we make use of the SSA congruent theorem

The SSA congruent theorem implies that  if two sides and an angle not included between them are respectively equal to two sides and an angle of the other than the two triangles are equal.

In this case, we have

Congruent sides: RQ and HG & PR and HF

Congruent angles: Angles Q and G

Hence, the additional information on the congruency of the triangles is the SSA theorem

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Answer:

7/

Step-by-step explanation:

3/4 * 7/

3 can be crossed

Leaving 7/

Answer:

Below

Step-by-step explanation:

"Lynn is making a snack. The recipes call for 3/8 cup of water for oats and 1/4 cup"

(I changed the numbers to fractions ....)

she needs   3/8 + 1/4 cup ....add them together by finding a common denominator

1/4 = 2/8    

then   3/8 + 2/8 = (3+2)/8 = 5/8 cup

  if she has one cup of water she has enough....she only needs 5/8 cup

Answer:

24,241 people

Step-by-step explanation:

To determine the attendance at the festival in the fifth year, we need to calculate the cumulative increase in attendance over five years.

1st year: 20,000

2nd year: 20,000 * 1.05 = 21,000 (5% increase from the first year)

3rd year: 21,000 * 1.05 = 22,050 (5% increase from the second year)

4th year: 22,050 * 1.05 = 23,127.50 (5% increase from the third year)

5th year: 23,127.50 * 1.05 = 24,241.38 (5% increase from the fourth year)

So, in the fifth year the festival will be attended by approximately 24,241 people.

The pound of cement used based on the information will be C. 2 pounds.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

In this case, for each pound of sand, he uses 1 2/3 pounds of gravel and for each pound of gravel, he uses 2/5 pound of cement.

The pound of cement used will be:

Gravel = 1 2/3 × 3

= 5 pounds

Cement used will be:

= 2/5 × 5.

= 2 pounds.

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The amount of white paint used by Tamara to paint the bedroom walls is 2.125.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Total amount of paint = 8.5

Three fourths of this amount is blue paint.

Amount of blue paint = (3/4) × 8.5 = 6.375

Rest is white paint.

Amount of white paint = Total paint - Amount of blue paint

                                     = 8.5 - 6.375

                                     = 2.125

Hence the amount of white paint used to paint bedroom walls is 2.125.

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let the third side be b then use the pythagoras theorem

The solution for the question found using the double angle formula for cosine is -[tex]\frac{7}{25}[/tex].

What are double angle formulae?

There are some trigonometric formulas that are known as double angle formulae because they contain double angles, such as Sin 2x, Cos 2x, and Tan 2x.

The double angle formula for cosine is

Cos 2θ = Cos²θ - Sin²θ

           =2Cos²θ – 1

            = 1 – 2Sin²θ

Given sinθ = [tex]\frac{4}{5}[/tex]

         cos(2θ) = 1-2sin²θ = [tex]1-2[/tex]×( [tex]\frac {4}{5}[/tex])² = [tex]1-[/tex] [tex]\frac{32}{25}[/tex] = [tex]\frac{-7}{25}[/tex]

Therefore Cos(2θ) fund using double angle formula is -[tex]\frac{7}{25}[/tex]

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The solution for the question found using the double angle formula for cosine is -.7/-25

There are some trigonometric formulas that are known as double angle formulae because they contain double angles, such as Sin 2x, Cos 2x, and Tan 2x.

An angle is a measure of the amount of rotation between two rays or lines that share a common endpoint, called the vertex of the angle. The two rays or lines are called the sides of the angle, and the endpoint is called the vertex. The size of an angle is typically measured in degrees or radians, with one full rotation around a point (360 degrees or 2π radians) being equal to a full circle.

The double angle formula for cosine is

Cos 2θ = Cos²θ - Sin²θ

          =2Cos²θ – 1

           = 1 – 2Sin²θ

Given sinθ = 4/5

        cos(2θ) = 1-2sin²θ = 1-2×(4/5 )² =  1-32/25 = -7/25

Therefore Cos(2θ) fund using double angle formula is -

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On solving the provided question, we cans ay that - here in triangles, triangle ABC is congruent to triangle A`B`C`

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

Here,

two triangles are there

triangle ABC and triangle A`B`C`

AB =A`B`

BC = B`C`

AC =A`C`

So, by sss property

both are congruent

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Answer:

they are intersecting.. so, there's one solution. the ordered pair is (-1,4).

Step-by-step explanation:

please refer to the sketch

The system of the equations to be used to graph the solution of the equation given is y = x² and y = 2x+3

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, is an equation, x² = 2x+3, we need to find a system of equations that can be graphed to give the solution of the equation given,

So, the equation is x² = 2x+3

We can write this as,

x²-2x-3 = 0

Now, factorize to find the solution of the equation,

x²-3x+x-3 = 0

x(x-3)+1(x-3) = 0

(x+1)(x-3) = 0

x = -1 and x = 3

So, the solution of the equation is -1 and 3

However, if we consider the equation to be two different systems combined, that is the equation of the straight line and the equation of the basic quadratic function,

y = x² and y = 2x+3

Then the solution to is the intersection of the graph of the straight line and the graph of the quadratic curve.

That is the x-coordinates of the points of intersection are the solutions.

Since, the graphs are intersecting at (3, 9) and (-1, 1) [see the graph]

Therefore, the system of equation is y = x² and y = 2x+3

Hence, the system of the equations to be used to graph the solution of the equation given is y = x² and y = 2x+3

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It will it take 56 years for the account value to reach $20,900.

This amount is calculated based on the principal amount of a loan or the first deposit in a savings account. Simple interest does not compound, thus, a creditor will only pay interest on the principal amount and a borrower would never have to pay more interest on the previously accumulated interest.

formula for calculating Simple Interest, S.I:

S.I = P * R * T

            100

Where,

S.I =  Simple Interest

P =Pricipal

R = rate ( in percentage)

T= Time

To how long will it take for the account value to reach $20,900

S.I = $20,900

R = 6.5%

P =$ 5,700

T =?

S.I = P * R * T

            100

$20,900 = $ 5,700 * 6.5 * T

                            100

Cross multiplying and Making Time, T  subject of the formula we have:

$20,900 * 100 = $ 5,700 * 6.5 * T

T=   $20,900 * 100

         $ 5,700 * 6.5

T=  56.41

T ≈  56 years

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Answer:

sq root of 21=7

Step-by-step explanation:

we need to use Pythagoras theorem

so distance(isa-jul)^2 +distance(ele-jul)^2= distance(isa-ele)^2

now just do the square root and there you go.

Answer:

no

Step-by-step explanation:

Limits of the functions shown in the graph are limx +f(x) = 0 and limx -f(x) = 0. The link between a group of inputs, each of which has a related output, is known as a function.

The study of mathematics covers a variety of topics, including numbers, formulas and related structures, forms and the environments in which they exist, quantities and their variations, and the environments in which they exist.  An easy way to think of a function is as a relationship between inputs and outputs, where each input leads to a single, distinct result. Each function has a respective domain and a codomain, or scope. Functions are typically represented by the letter f. (x). input is x. The accessible functionalities fall into four categories. based on the following elements: on functions, one-to-one functions, many-to-one functions, and within functions.

given

We first take into account how f(x) behaves as x increases unboundedly for the function in the graph below. As x can always increase because the function has no limit, it can never be zero. However, the function's behavior when x rises.

Similar to how x decreases without bound or how we move leftward on the graph, f(x) also seems to be approaching zero.

So in this case we can write:

limx → +∞f(x) = 0

limx → - ∞f(x) = 0

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Answer:

true

Step-by-step explanation:

20 away from nothing is 20

Answer:

Step-by-step explanation:

20-0=20

Example 1: Suppose you have 20 friends and they are given the choice of choosing a sport from cricket or basketball. All of them decide to play cricket and 0 chooses basketball. So, the total number of students who decided cricket is 20 students(20-0=20).

Example 2: Suppose you have 20 chocolates and you give 0 chocolates to your sister then you have a total of 20 chocolates(20-0=20).

Example 3: Suppose there are 20 students in a class and 0 were absent out of them. So, the total number of students that were present are 20 students(20-0=20).

Example 4: Suppose you have 20 clothes in your wardrobe and you gave 0 clothes for washing. So, the total number of clothes in the wardrobe is 20 clothes(20-0=20).