how is dividing mixied numbers like dividing fractions

Answer:

(a) 4n = 36

(b) n = 9

Step-by-step explanation:

(a) Kevin represents the left side, 4n, and Ivanna represents the right side, 36.

(b) Solve the equation by isolating n.

4n = 36 (divide both sides by 4)

n = 9

The sampling distribution of difference between means approximates a normal curve whose mean is zero.

The sampling distribution means the probability distribution based on the large number of samples of size n from the given population

Mean is the average of the given numbers and it is calculated by dividing the sum of observation by the number of observation. Here the term observation represents the given data.

Here they used the normal curve, sot its mean value is zero

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Answer:-4

Step-by-step explanation:

-4 x -7 = 28

28-9=19

Answer:

x=-4

Step-by-step explanation:

We are given the equation:

-7x-9= 19

We want to solve for x. Therefore, we must isolate x on one side of the equation.

9 is being subtracted. The inverse of subtraction is addition. Add 9 to both sides of the equation.

-7x-9+9= 19+9

-7x= 28

x is being multiplied by -7. The inverse of multiplication is division. Divide -7 on both sides.

-7x/-7=28/-7

x= 28/-7

x= -4

Let’s check our solution. Plug -4 in for x and solve.

-7x-9=19

-7(-4)-9=19

28-9=19

19=19

This checks out, so we know our solution is correct.

The solution to the equation -7x-9=19 is x= -4

Answer:

\(\displaystyle 1\frac{2}{5}=\frac{7}{5}\)

Step-by-step explanation:

\(\displaystyle a\frac{b}{c}=\frac{ac+b}{c}\\\\1\frac{2}{5}=\frac{(1)(5)+2}{5}=\frac{5+2}{5}=\frac{7}{5}\)

Answer:

Step-by-step explanation:

The line should be parallel to \(x = 3\), therefore, it would be a vertical line of the form \(x = a\), where `a` is a parameter representing the constant x value the line would be passing through.

We know that the line passes through (5, -7), a point whos coordinates are \(x = 5\) and \(y = -7\), though the y value has no significance as the line is vertical.

Knowing these details, we know that the line's equation is \(x = 5\), and, therefore, it is a vertical line that passes through \(x = 5\) on the x axis.

Answer:

yes, this argument uses the law of syllogism.

Step-by-step explanation

Answer:

12 feet.

Step-by-step explanation:

1 inch = 4 feet.

Multiply 3 by 4.

3×4=12

I multiplied 3 by 4 because 1-inch equals 4 feet, which means if we multiply both terms by 3, you will get 3 inch = 12 feet.

Hope this helps!

Answer:

the least common denominator is. 9

Answer:

\(\frac{2}{27}\)

Step-by-step explanation:

1) Use this rule: \(\frac{a}{b} *\frac{c}{d} =\frac{ac}{bd }\)

\(\frac{2*1}{9*3}\)

2) Simplfiy 2 · 1 to 2.

\(\frac{2}{9*3}\)

3) Simplify 9 · 3 to 27.

\(\frac{2}{27}\)

The inverse cotangent function or arccot is the angle in radians whose cotangent is a given number. Therefore, arccot(-√3) = π - π/6 = 5π/6 or 150°.

To evaluate arccot(-√3), we need to find the angle whose cotangent is -√3. Since cotangent is the reciprocal of a tangent, we can use the identity tan(x) = 1/cot(x) to get the tangent of the angle we are looking for.

In this case, tan(x) = 1/(-√3) = -1/√3.

The angle whose tangent is -1/√3 is -π/6 or -30°, because the tangent function has a period of π or 180°.

Since the range of the arccot function is (0,π), we need to add π or 180° to get the actual angle in the fourth quadrant.

Therefore, arccot(-√3) = π - π/6 = 5π/6 or 150°.

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Step-by-step explanation:

Question 10 :

3x + 6 = 4x – 12 ( reason: corresponding angles due to parallel lines)

simplify and get x, thus x = 18

to find 3x + 6 or 4x - 12(which is both the same),

3(18) + 6 = 60° , 4(18) - 12 = 60°

Question 11:

2x + 24 + x = 180 ( reason: interior angles due to parallel lines)

simplify again to get x, you will get x = 52

then find the individual by subbing in the value of x into the equation.

so 2x + 24 = 2(52)+24 = 128° and x = 52°

Answer:

$15

Step-by-step explanation:

75/5=15

Answer:

144

Step-by-step explanation:

Juliet was charged $18 for driving 120 miles.

Given,

The rent of car per day = $80

The charge for per miles driven = $0.15

Juliet was charged a total of $98 for the rental and mileage.

We have to find the total miles of driving;

Here,

Charge for miles driven = Total charge - Rent of car for a day

Charge for miles driven = 98 - 80

Charge for miles driven = $18

Now,

Total miles driven = Charge for miles driven / Charge for one mile

Total miles driven = 18/0.15

Total miles driven = 120

That is,

Juliet was charged $18 for 120 miles of driving.

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Answer:

\(\large\boxed{\tt x = 2}\)

Step-by-step explanation:

\(\textsf{We are asked to solve for x in the given equation.}\)

\(\textsf{We should know that x is cubed, meaning that it's multiplied by itself 3 times.}\)

\(\textsf{We should isolate x on the left side of the equation, then find x by cubic rooting}\)

\(\textsf{both sides of the equation.}\)

\(\large\underline{\textsf{How is this possible?}}\)

\(\textsf{To isolate variables, we use Properties of Equality to prove that expressions}\)

\(\textsf{are still equal once a constant has changed both sides of the equation. A Cubic}\)

\(\textsf{Root is exactly like a square root, but it's square rooting the term twice instead}\)

\(\textsf{of once.}\)

\(\large\underline{\textsf{For our problem;}}\)

\(\textsf{We should use the Subtraction Property of Equality to isolate x, then cubic root}\)

\(\textsf{both sides of the equation.}\)

\(\large\underline{\textsf{Solving;}}\)

\(\textsf{Subtract 1 from both sides of the equation keeping in mind the Subtraction}\)

\(\textsf{Property of Equality;}/tex]

\(\tt \not{1} - \not{1} - x^{3} = 9 - 1\)

\(\tt - x^{3} = 8\)

\(\textsf{Because x}^{3} \ \textsf{is negative, we should exponentiate both sides of the equation by}\)

\(\textsf{the reciprocal of 3, which is} \ \tt \frac{1}{3} .\)

\(\tt (- x^{3})^{\frac{1}{3}} = 8^{\frac{1}{3}}\)

\(\underline{\textsf{Evaluate;}}\)

\(\tt (- x^{3})^{\frac{1}{3}} \rightarrow -x^{3 \times \frac{1}{3} } \rightarrow \boxed{\tt -x}\)

\(\textsf{*Note;}\)

\(\boxed{\tt A^{\frac{1}{C}} = \sqrt[\tt C]{\tt A}}\)

\(\tt 8^{\frac{1}{3}} \rightarrow \sqrt[3]{8} \rightarrow 2^{1} \rightarrow \boxed{\tt 2}\)

\(\underline{\textsf{We should have;}}\)

\(\tt -x=2\)

\(\textsf{Use the Division Property of Equality to divide each side of the equation by -1;}\)

\(\large\boxed{\tt x = 2}\)

Answer:

The second option is the correct one.

Step-by-step explanation:

The algebraic expression is as such:

\(10x^{2}y+6x^{2}-7y^{2}-6\)

Step 1: Looking at the first element

The first term/element of the final expression is \(10x^{2}y\).

Only like variables can be added or subtracted from each other (\(x\) can be added to \(x\) to give \(2x\), but \(x\) added to \(y\) doesn't yield a different result).

In the options, there are two terms which have the variables \(x^{2}y\):

\(8x^{2}y\) and \(2x^{2}y\).

In the first three options, \(8x^{2}y\) is being added to \(2x^{2}y\), which would give a result of \(10x^{2}y\):

\(8x^{2}y+2x^{2}y\\=(8+2)x^{2}y\\=10x^{2}y\)

But the fourth option subtracts \(2x^{2}y\) from  \(8x^{2}y\), which wouldn't equal to \(10x^{2}y\), and so the fourth option isn't correct.

Step 2: Looking at the second element

The second term/element of the final expression is \(6x^{2}\).

In the options, there are two terms which have the variables \(x^{2}\):

\(7x^{2}\) and \(x^{2}\).

In the rest of the three options, \(x^{2}\) is being subtracted from \(7x^{2}\), which would give a result of \(6x^{2}\):

\(7x^{2}-x^{2}\\=(7-1)x^{2}\\=6x^{2}\)

So, we can't eliminate any options based on this.

Step 3: Looking at the third element:

The same thing as the second element happens with \(-7y^{2}\), so we can't use it either.

Step 4: Looking at the 3x that are being cancelled out

We can see that the options contain the term \(3x\), even though it is nowhere to be seen in the final expression.

This means that \(3x\) is subtracted from itself to produce a result of \(0\) (\(3x-3x=0\)), thus it is not present in the final expression.

In the second and third options, we can see that \(3x\) is being subtracted from itself.

But, the first option has \(3x\) being added to itself.
This would produce a result of \(6x\):

\(3x+3x\\=(3+3)x\\=6x\)

Which isn't present in the final expression.

Thus, the first option is also incorrect.

Step 5: Looking at the fourth element

The fourth term/element of the final expression is \(-6\).

In the options, there are two terms which are also integers:

\(-2\) and \(4\).

In the second option, \(4\) is being subtracted from \(-2\), which would give a result of \(-6\):

\(-2-4\\=-6\)

But in the third option, \(4\) is being subtracted from \(2\), which would give a result of \(-2\) instead of \(-6\),
So, the third option is also wrong.

Answer:

A. Look for a problem similar to the word problem you are trying to solve is the answer.

To see the graph, the inequality pairs with  y≤ −2x−1  to complete the system of linear inequalities is

y > -2x + 2.

Given,

In the question:

The inequality is given as:

y ≤ −2x−1

Now, According to the question:

The upper part of the graph must be an inequality that doesn't include the actual boundary line because such is represented with a dotted line instead of a solid one (so the equal sign must NOT be in the inequality).

The boundary line for the upper section has also the same slope as the one given (-2), and we also see that it goes through the value 2 on the y-axis, so such line in slope y-intercept form must be: y = -2x + 2

Since we need to include the (x, y) values on the plane that are "larger than" (y-value above) the boundary line we found, we need to select the "greater than" symbol for the inequality and :

y > -2x + 2.

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Answer:

I don't see any symbols, so I'll simply compare the two measurements.

Step-by-step explanation:

2 yards and 4 inches

Each yard has 3 feet.  Each foot has 12 inches.  The total inches in 3 yards is therefore:

(2 yards)*(3 feet/yard)*(12 inches/Foot) = 72 inches  [Note how the units cancel to leave only inches]

This means we have a total of 72 + 4 inches = 76 inches total

19 Inches

Compared to 19 inches, 72 inches is almost 3.79 times longer.

Answer

37 - 15

Step-by-step explanation:

Answer:

Third option

Step-by-step explanation:

Given the following question:

\(7x-4=5x+15\)

To find the answer we need to use inverse of operations to simplify the equation in till we isolate the variable and find the value of x.

\(7x-4=5x+15\)
\(-4+4=0\)
\(15+4=19\)
\(7x=5x+19\)
\(5x-5x=0\)
\(7x-5x=2x\)
\(2x=19\)
\(2x\div2=x\)
\(19\div2=\frac{19}{2}\)
\(=\frac{19}{2}\)

Your answer is the third option or "19/2."

Hope this helps.

Therefore, the rank of matrix 'a' in this case would be 5.

To find the rank of a matrix, we need to perform row reduction to obtain its row echelon form (REF) or reduced row echelon form (RREF). However, since the matrix 'a' is not provided, I cannot perform the calculations or determine its rank.

The rank of a matrix is equal to the number of non-zero rows in its row echelon form or reduced row echelon form. If the system of equations 'ax = 0' has a two-dimensional solution space, it means that the rank of matrix 'a' is less than the number of columns (6) but greater than 4 (since the solution space is two-dimensional).

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These real-world applications help young learners see the practical applications of geometry and develop a deeper understanding of geometric concepts while making learning more engaging and meaningful.

Relevance: Connecting math to real-world applications helps students see the practical value and relevance of the concepts they are learning. It provides a meaningful context and motivation for learning.

Engagement: Real-world applications make math more interesting and engaging for students. It brings concepts to life and helps students see how math is used in everyday life.

Deep understanding: By applying math concepts to real-world situations, students develop a deeper understanding of the concepts and their connections. It promotes critical thinking, problem-solving skills, and the ability to apply mathematical knowledge in different contexts.

Transferability: Real-world applications help students see how math concepts can be transferred and applied to various situations. It promotes the ability to apply learned concepts to new and unfamiliar problems.

Some real-world applications of geometry that would be appropriate for young learners include:

Measurement: Young learners can apply geometric concepts to measure and compare the lengths, areas, and volumes of objects in their environment. For example, measuring the length of a room, comparing the sizes of different shapes, or estimating the volume of a container.

Navigation and Maps: Young learners can use geometry to understand maps, directions, and spatial relationships. They can learn about reading maps, understanding coordinates, and finding distances between locations.

Architecture and Construction: Exploring geometric shapes, angles, and symmetry can help young learners understand the principles of architecture and construction. They can design and build simple structures using different shapes and understand the importance of stability and balance.

Art and Design: Geometry plays a significant role in art and design. Young learners can explore symmetry, patterns, and shapes in various art forms. They can create tessellations, explore rotational symmetry, or design patterns using geometric shapes.

Everyday Objects: Geometry is present in everyday objects around us. Young learners can identify and classify shapes in their environment, such as identifying spheres, cubes, cylinders, and cones in objects like balls, boxes, cups, and ice cream cones.

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Option C: \(y=2x+1\) is the correct option.

Answer:

Each coin has 2 outcomes when flipping (it may be head or tail), so the possibility to flip head is equal to possibility to flip tail and is .

If you are flipping three times, then using the product rule you can conclude that the possibility to get three heads is equal to possibility to get three tails and is:

Step-by-step explanation:

The given triangle is isosceles, so the two remaining angles in the triangle both have measure xº. The interior angles of any triangle sum to 180º, so that

58º + xº + xº = 180º

58 + 2x = 180

2x = 122

x = 61

Angles y and z are supplementary to angle x, so that

xº + yº = 180º

and

xº + zº = 180º

and consequently, y = z. In particular, we get

y = 180 - 61

y = 119

and so

z = 119

The fractions of all the supporters that are male and support the away

team is 1/3

The fractions of all the supporters that are female and support the away

team is 2/9.

A fraction is a value representing a part of a whole.

We have,

Supporters for the Home team = 4/9

Supporting for the away team = 1 - 4/9 = 5/9

Now,

Male supporters from the away team = 3/5 x 5/9 = 1/3

So,

Female supporters from the away team = (1 - 3/5) x  5/9 = 2/5 x 5/9 = 2/9

Thus,

The fractions of all the supporters that are male and support the away

team is 1/3

The fractions of all the supporters that are female and support the away

team is 2/9.

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Sarah's speed in kilometers per minute is 0.6 kilometers per minute.

To convert the speed from miles per hour to kilometers per minute, we need to perform the following conversions:

1 mile = 1.60934 kilometers

1 hour = 60 minutes

We will convert miles per hour to kilometers per hour:

= 22.7 miles/hour * 1.60934 kilometers/mile

= 36.525918 kilometers/hour

We will convert kilometers per hour to kilometers per minute:

= 36.525918 kilometers/hour / 60 minutes/hour

= 0.60876697

= 0.6 kilometers/minute.

Full question:

Sarah is riding her bicycle at a speed of 22.7 miles per hour. What is Sarah's approximate speed, in kilometers per minute? justify your answer

(1) 0.2

(2) 0.6

(3) 36.5

(4) 36.6​.

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Answer:

$1719.55, 61.4%

Step-by-step explanation:

Original price of stove:  $2,800

Value of stove after 1 year:  (1 - 0.15)($2,800), or 0.85($2,800) = $2,380

Value of stove after 2 years:  0.85($2,380) = $1719.55

Find the ratio of this last result to the original price and convert that to a  percentage:

$1,719.55

-------------- = 0.614, or approximately 61.4%

 $2,800

Answer:

D: find the average of 6.9 and 7.0

Step-by-step explanation:

The reason D is correct is that, 6.9 squared is around 47.6, and 7.0 squared is 49.0

48 falls between 47.6 and 49.0

So if you find the average between 6.9 and 7.0, you would then find the nearest hundredth estimate of the \(\sqrt{48}\)

Answer:

on the exam its A

Step-by-step explanation:

The vector notation <4, -5> is the same as writing \((x,y) \to (x+4, y-5)\) which in my opinion is more descriptive in saying "4 units to the right, 5 units down"

We shift 4 units to the right because of the x+4. Whatever x is, add 4 to it getting x+4. So for instance x = 10 leads to x+4 = 10+4 = 14.

The y-5 is why we shift 5 units down. Eg: y = 37 leads to y-5 = 37-5 = 32.