Factorize 21x^2 - 16-7x / 3x^2-4 = 5

let's firstly convert the mixed fractions to improper fractions.

now, 1¼ dozen of cupcakes.... well, let's keep in mind that a dozen has 12 units, so 1¼ dozen is then 12(1¼) cupcakes total.

[tex]\bf \stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}}~\hfill \stackrel{mixed}{1\frac{2}{3}}\implies \cfrac{1\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{5}{3}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \stackrel{\textit{how many cupcakes in }\frac{5}{4}\textit{ of a dozen?}}{12\cdot \cfrac{5}{4}\implies \cfrac{12}{4}\cdot 5\implies 15} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} cupcakes&\stackrel{cups}{flour}\\ \cline{1-2}\\ 15&\frac{5}{3}\\[1em] c&1 \end{array} \implies \cfrac{15}{c}=\cfrac{~~\frac{5}{3}~~}{1}\implies \cfrac{15}{c}=\cfrac{5}{3} \\\\\\ 45=5c\implies \cfrac{45}{5}=c\implies \boxed{9=c}[/tex]

In the given case, Rashida can make approximately 9 cupcakes with 1 cup of flour.

To determine how many cupcakes Rashida can make with the 1 cup of flour she has, we need to calculate the conversion factor between the given measurement of 1 2/3 cups of flour and the available 1 cup of flour.

The conversion factor is found by dividing the available amount by the required amount

(1 cup ÷ 1 2/3 cups).

We can simplify the fraction to obtain a decimal,

1 ÷ (5/3) = 3/5 ≈ 0.6.

So, Rashida can make approximately

0.6 × 1 1/4 dozen = 0.6 × 15 = 9 cupcakes.

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Answer:

A) -7.888

Step-by-step explanation:

The answer is A because it is an never ending number, which means it is irrational

The following numbers is irrational D) √0.025, which is an irrational number.

To determine which of the given numbers is irrational, we need to understand what an irrational number is. An irrational number is a real number that cannot be expressed as a fraction (i.e., it cannot be written as a ratio of two integers). Irrational numbers have non-repeating, non-terminating decimal expansions.

Let's evaluate each of the given options:

A) -7.8: This is a rational number because it can be expressed as -78/10 or -39/5, which is a ratio of two integers.

B) √25: This is a rational number because it is equal to 5, which can be expressed as 5/1. It's a ratio of two integers.

C) 25.8125: This is a rational number because it can be expressed as 258125/10000, which is a ratio of two integers.

D) √0.025: This is an irrational number. To see why, we can simplify it. √0.025 is the same as √(25/1000), which simplifies to √(1/40). The square root of 1 is 1, and the square root of 40 is a non-repeating, non-terminating decimal, making √0.025 an irrational number.

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Answer:

The possible outcome could be 4 or 3

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

There are 12 possible outcomes. Of the 12, 6 are even and 4 have B's. That would give up 10/12. But then you would subtract the possible outcomes that are BOTH even AND have a B. Only 2 possible outcomes have an even number and the letter B. So 10 minus 2 is 8. That would give you 8/12. Simplify and you will get your answer of 2/3!

Just took the test, so trust me on this fellow K12ers!

Answer:

1 meter = 39.370 inches.....so 5 meters = (5)(39.370) = 196.85 inches

Answer:

eight hundred thirty four thousand two hundred nine

All you got to do is write the places and the number.

Plzzz mark brainlest and thank em would be very much thankful

It would be 7.

Here's why:

7 + - 6 = 1

1 = 1

It's a TRUE statement!

Hope this helps you!!!! :)

The integer value that makes the sentence true is 7, as in mathematics, adding a negative number 6 to a number, to yield 1, equates deducting 6 from that number to yield 1.

This is a mathematics problem involving the concept of integer addition. In mathematics, adding a negative number is equivalent to subtracting that number's absolute value. Therefore, to find the integer that makes the addition sentence true, you would need to identify the number that, when subtracted by 6, equals 1.

So, the equation can be rewritten as X - 6 = 1. If you add 6 on both sides of the equation to isolate the variable X on one side, the equation becomes X = 1 + 6. As a result, it is clear that the integer value X that would make the equation + -6 = 1 true is 7.

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Answer:

A: There is no solution

Step-by-step explanation:

This is not a very likable question.

Y=3x-4

9x-3y=14

Put the y value from the first equation into the second.

9x - 3(3x - 4) = 14               Remove the brackets

9x - 9x + 12 = 14               Combine like terms on the left

12 = 14                                 When you get this kind of conclusion, that means there is no solution. I'll graph these two for you.

Blue: y =3x - 4

Green: 9x - 3y = 14

They never touch they never meet: they are parallel. They don't give a solution.

Answer:

x=36

Step-by-step explanation:

< CAB and <EAD are vertical angles and vertical angles are equal

<CAB = <EAD

36 = x

Answer:

0 solutions

Step-by-step explanation:

they have the same slope and different y intercepts so they never intersect

Answer:

This equation has no solution

Step-by-step explanation:

To find our many solution the system of equation has, we need to  solve simultaneously, we can either solve by substitution method, by elimination method or both method.

We will be using substitution method to solve.

Here are the system of equation;

y= -4x+2 ----------(1)

24x+6y=6---------(2)

First, we are going to substitute equation (1) in equation (3)

{what we mean by substituting equation (1) in equation (2) is then any where we see y in equation (2),  we will be replacing it by[-4x + 2]}

24x + 6(-4x + 2)  = 6

Then, we will go ahead and open the bracket

24x  -  24x  +  12  =6

This simply shows that there is no solution to this system of equation

Answer:

- 1/5

Step-by-step explanation:

the answer is the one highlighted #1

but to do this you must first change the decimal to a fraction. Personally i use a decimal calculator.

then you go to where the 3 is on the Y axes. since its positive 3 it would be 3 up instead of down.

then you count over how ever many the X is. this is 1/2 so you go over 1 time then up 2 times.

Personally I like the triangle method where u plot the +3 then draw on the line 1 over then 3 up

if u need to find out what the plot line u can keep doing that all the way up and just reverse it when u go down.

Answer:

24p -35

Step-by-step explanation:

Simplify. Remember to follow PEMDAS. First, distribute 4 to all terms within the parenthesis

4(6p - 9) 4(6p) - (4)(9) = 24p - 36

Next, simplify. Add 1 to the constant

24p - 36 + 1

24p - 35

24p - 35 is your answer

~

Answer:

A protractor.

Step-by-step explanation:

Answer:

84 lbs

Step-by-step explanation:

Answer:

the answer is D

Step-by-step explanation:

Answer:

D. 9

Step-by-step explanation:

Answer:

[tex]z_m=-\frac{1}{2}-\frac{1}{2}i[/tex]

Step-by-step explanation:

The given complex numbers are;

[tex]z_1=-8+3i[/tex]

and

[tex]z_2=7-4i[/tex].

The midpoint of any two complex numbers,

[tex]z_1=a_1+a_1i[/tex] and [tex]z_2=a_2+a_2i[/tex] is

is given by,

[tex]z_m=\frac{a_1+a_2}{2}+\frac{a_1+a_2}{2}i[/tex].

The midpoint of the complex numbers can be found by adding the corresponding real parts and imaginary parts and then dividing each by 2.

This is the same as;

[tex]z_m=\frac{z_1+z_2}{2}[/tex]

[tex]\Rightarrow z_m=\frac{-8+3i+7-4i}{2}[/tex]

[tex]\Rightarrow z_m=\frac{-8+7+3i-4i}{2}[/tex]

[tex]\Rightarrow z_m=\frac{-1-i}{2}[/tex]

[tex]\Rightarrow z_m=-\frac{1}{2}-\frac{i}{2}[/tex]

or

[tex]\Rightarrow z_m=-\frac{1}{2}-\frac{1}{2}i[/tex]

Answer:

The cost of one box of oranges = $3.3

Step-by-step explanation:

Let x be cost of one box of oranges and y be the cost of one box of grapefruit.

We have been given that Mrs. Whitten purchased 3 boxes of oranges and 2 boxes of grapefruit from a student for a total of $22.50. We can represent this information as:

[tex]3x+2y=22.50...(1)[/tex]  

Mr. Rutig purchased 1 box of oranges and four boxes of grapefruit, spending a total of $28.50. We can represent this information as:

[tex]x+4y=28.50...(2)[/tex]

We will solve our system of linear equations using substitution method.

From equation (1) we will get,

[tex]y=\frac{22.50-3x}{2}[/tex]

Substituting y's value in equation (2) we will get,

[tex]x+4*(\frac{22.50-3x}{2})=28.50[/tex]

[tex]x+2*(22.50-3x)=28.50[/tex]

Upon distributing 2 we will get,

[tex]x+45-6x=28.50[/tex]

[tex]x-6x=28.50-45[/tex]

[tex]-5x=-16.5[/tex]

[tex]x=\frac{-16.5}{-5}[/tex]

[tex]x=3.3[/tex]

Therefore, the cost of one box of oranges is $3.3.

Answer: 6x² + 4xy + 2y

Step-by-step explanation:

Polynomials are written in the order of the highest degree to the lowest degree.

Answer:

52.3 litres.

Step-by-step explanation:

The car consumption is 75/20 = 3.75 km/litre.

Volume of petrol needed to travel 196 km

= 196 / 3.75 = 52.3 litres.

Answer:

1) ASA 2) In explanation 3) I cant see all of the problem

Step-by-step explanation:

For Number 1 you need one more thing to prove that the triangles are congruent. You could see that there is a pair of vertical angles and vertical angles are congruent so you could use that. Angle DEA is congruent to Angle CEB. When there is a side in between two congruent angles, that is ASA.

For Number 2 it really is almost the same as number 1. First you write the given, then you write that angle DEA is congruent to angle CEB and the reason for that is that vertical angles are congruent. Lastly, you say that triangle ADE is congruent to triangle CBE.

Answer:

Both set A and B.

Step-by-step explanation:

Set A: (-1, 0), (-2, 1), (4, 3), (3, 4)

Set B: (1, 4), (2, 3), (3, 2), (4, 1)

Set C: (2, 1), (3, 2), (2, 3), (1, 4)

In order for (x,y) to be a function, only one x get the value of y, but many x'es can get the value y.

Looking at the set A and B, and the definition above, we can say that they are functions.

What about set C? It is not a function, as x = 2 is equal 1 or 3, which does not meet the condition from the definition.

Final answer:

Both Set A and Set B are functions because each member of the domain in these sets maps to a unique value in the range. Set C is not a function because the same first element maps to different values in the range. Both set A and B are the answers.

Explanation:

To determine which set(s) represent a function, we need to ensure that each element of the domain maps to one and only one value in the range. By examining each set:

Set A: (-1, 0), (-2, 1), (4, 3), (3, 4): Every first element is unique, indicating a function.

Set B: (1, 4), (2, 3), (3, 2), (4, 1): Similarly, all first elements are unique, indicating a function.

Set C: (2, 1), (3, 2), (2, 3), (1, 4): The number 2 appears twice as a first element with different second elements, violating the definition of a function.

Therefore, both sets A and B represent functions since they each map every member of the domain to a unique member of the range, while set C does not.

The answer is b. Both Set A and Set B are functions.

Answer:

5 minutes to run 1 kilometer

Step-by-step explanation:

Alonzo takes 12 minutes to run 6 times around a 400-meter track.

6 times around a 400 m track

400 * 6 = 2400 meters

It take 12 minutes to run 2400 meters

2400 meters = 2400/1000 = 2.4km

distance = 2.4 km  and time = 12 minutes

Now we find our constant speed

[tex]Distance = speed * time[/tex]

2.4 = speed * 12

divide by 12 on both sides

speed = 0.2

so speed is 0.2 km per minute

Now we find out time when distance = 1km

Distance = speed * time

1 = 0.2 * t

divide by 0.2 on both sides

5 = t

So it take 5 minutes to run 1 kilometer

Answer:

(d) 810.34

Step-by-step explanation:

The explicit formula used for calculating the account's balance is given by:

A= P(1+R)^T

where: A= Amount (account's balance)

P= Principal  (700)

R= Rate (5%)

T= Time   (3 years) [since, the balance is calculated in the beginning of the  forth year]

A= P(1+R)^T

A = 700(1+0.05)^3

  = 700(1.05)^3

  = 700*1.157

  = 810.34

Answer: cube

Step-by-step explanation:

Think of a box .... it has 4 sides, a top, and a bottom = 6 total sides

The shape with six equal square, flat sides is known as a cube.

A cube is a three-dimensional geometric shape characterized by six equal square faces. Each face of the cube is identical, and the shape is formed by connecting these faces at right angles. This regular polyhedron is fundamental in mathematics and has practical applications in various fields. Cubes are extensively used in geometry, trigonometry, and calculus to illustrate concepts such as volume and surface area. In addition to its mathematical significance, cubes are prevalent in everyday objects like dice and building blocks. Understanding the properties of cubes is crucial in engineering and architecture, where it aids in designing structures and solving spatial problems efficiently.

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In this exercise we have to use the knowledge of equations to write the intersection equation, so we have to:

The formula for setting up an equation is given by:

[tex](y - y1) = m(x - x1)[/tex]

1.) So by the formula above, substituting for the values ​​given in the statement, then:

[tex](y - 120) = -2(x - 7)[/tex]

2.) The equation in slope intercept form will be:

[tex](y - 120) = -2(x - 7)\\(y - 120) = -2*x + (-2*-7)\\y - 120 = -2x + 14\\y = -2x + 134[/tex]

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Answer:

x = 26.4      y= 17

Step-by-step explanation:

Set up proportions.

To find x:

Set 12 over x is equal to 10 over 22.

12 times 22 = 264

264 / 10  =x

x =  26.4

To find y:

Set y over 37.4 is equal to 10 over 22.

37.4 times 10 =  374

374 / 22

y = 17