Find the value of z.

A.) There are many different expressions that can be equivalent to 4/2 and -2/3, but you just need one expression. 4/2 is equivalent to 2/1 and -2/3 is equivalent to -4/6.

Reason:

There are two ways you can find a fraction equivalent to another.

1.) First one is by reducing the fraction if possible.

Example: 5/10=1/2, 10/30=1/3, 9/16=3/4.

2.) The second one is by multiplying the numerator and the denominator by the same number, usually by 2 or 3.

Example: 1/2 x 2/2 = 2/4, so 1/2= 2/4. Another: 1/3 x 3/3 = 3/9, so 1/3=3/9

That said, 4/2 = 2/1 because it was reduced. While -2/3 = -4/6 because it was multiplied by 2/2.

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4/2 is equivalent to 1/2 when reduced by 2.

-2/3 is equivalent to -4/6 when multiplied by 2/2.

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[tex]g(b)=3b+13[/tex]

Hope this helps.

r3t40

To find the formula for g(b), isolate the variable a in the given equation by solving step by step. The formula for g(b) is g(b) = 3b + 13.

To write a formula for g(b) in terms of b, we need to isolate the variable a in the equation given. Let's simplify the given equation step by step:

Therefore, the formula for g(b) is g(b) = 3b + 13

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1. The first step to answering this question is to find the volume of a single spherical lead shot and then multiply this by 5000 to find the total volume of 5000 lead shots.

So, given that the lead shots are spherical, we must use the formula for the volume of a sphere:

V = (4/3)πr^3

Given that the diameter is 3mm, we can find the radius by dividing this by 2:

r = 3/2 = 1.5 mm

From here, there are two ways to proceed; we can either covert the radius into cm, or we can continue with the mm value and then convert the resulting volume in cubic mm into cubic cm (since we are given that 1 cm cubed of lead weighs 11.4g, we can already tell that we will have to finish with a volume in cubic cm). I will show both these methods as a) and b), respectively.

a) If there are 10 mm in 1 cm, and we have a radius of 1.5 mm, then to convert this into cm we need to simply divide by 10:

1.5 mm = 1.5/10 = 0.15 cm

Now that we have our radius in cm form, we can substitute this into the formula for the volume of a sphere that we specified at the very beginning:

V = (4/3)πr^3

V = (4/3)π(0.15)^3

V = (9/2000)π cm cubed, or

0.0045π cm cubed (in decimal form)

Now that we have the volume of one lead shot, all we need to do is multiply this by 5000 to find the volume of 5000 lead shots:

0.0045π*5000 = 22.5π cm cubed

Since we already have the total volume in cm cubed, there is no need to do any more conversions.

b) In this method, we will use radius = 1.5 mm and substitute this into the general formula for the volume of a sphere again:

V = (4/3)πr^3

V = (4/3)π(1.5)^3

V = (9/2)π mm cubed, or

4.5π mm cubed (in decimal form)

Thus, to calculate the volume of 5000 lead shots, we must multiply this value by 5000:

4.5π*5000 = 22500π mm cubed

Now comes the part where we must convert this into cubic cm; to do this we simply take the value in cubic mm and divide it by 10^3 (ie. 1000). Thus:

22500π/1000 = 22.5π cm cubed

As you can see, we end up with the same answer as in a). The key here is to remember that you need to convert, so maybe write a note to yourself at the start of the question and pay close attention to the different units in both the question and your working.

2. Now that we know that the volume of 5000 spherical lead shots is 22.5π cm cubed, we need to calculate their mass.

We are given that 1 cm cubed of lead weighs 11.4 g, thus to calculate the mass of 22.5π cm cubed of lead, we need to multiply this value by 11.4. Thus:

Mass = 22.5π*11.4

= 256.5π g

Note that this is the answer in exact form. I wasn't entirely sure about the rounding required or the value of π that you were specified to use (eg. exact, 22/7, 3.14), so if you wanted me to edit the answer to reflect that or had any questions, feel free to comment below.

Answer:

d. 3/6

Step-by-step explanation:7/14 simplifies to 1/2 and 3/6 also simplifies to 1/2

Using the concept of ratio and proportion to solve the problem. The ratio is 3/6. Then Option D is correct.

A ratio is an ordered couple of numbers a and b, written as a/b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

Given

7/14 is an expression.

To find

The ratio forms a proportion with 7/14.

7/14 is an expression.

On simplifying, we have

[tex]\dfrac{7}{14} = \dfrac{1}{2}[/tex]

On multiplying and dividing it by 3. then we have

[tex]\dfrac{1}{2} = \dfrac{1*3}{2*3} = \dfrac{3}{6}[/tex]

Thus, Option D is correct.

More about the ratio and the proportion link is given below.

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[tex]\bf \cfrac{9}{7}+\cfrac{7}{5}\implies \stackrel{\textit{using the LCD of 35}}{\cfrac{(5)9~~+~~(7)7}{35}}\implies \cfrac{45+49}{35}\implies \cfrac{94}{35}\implies 2\frac{24}{35}[/tex]

Answer:

94/35

Step-by-step explanation:

Least common multiples of 7 and 5.

7*5=35

9/7=9*5/7*5=45/35

7/5=7*7/5*7=49/35

Add the numbers from left to right.

49/35+45/35

49+45=94

=94/35

94/35 is the correct answer.

Answer with Step-by-step explanation:

We have to solve the equation 2x²-6x+1=0

the solution of the equation ax²+bx+c=0 is given by

[tex]x=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\ and\ x=\dfrac{-b-\sqrt{b^2-4ac}}{2a}[/tex]

Here a=2,b=-6 and c=1

[tex]x=\dfrac{6+\sqrt{6^2-4\times 2\times 1}}{2}\ and\ x=\dfrac{6-\sqrt{6^2-4\times 2\times 1}}{2}\\\\x=\dfrac{6+\sqrt{36-8}}{2}\ and\ x=\dfrac{6-\sqrt{36-8}}{2}\\\\x=\dfrac{6+\sqrt{28}}{2}\ and\ x=\dfrac{6-\sqrt{28}}{2}\\\\x=\dfrac{6+2\sqrt{7}}{2}\ and\ x=\dfrac{6-2\sqrt{7}}{2}\\\\x=3+\sqrt{7}\ and\ x=3-\sqrt{7}[/tex]

Hence, solution of 2x²-6x+1=0 is:

[tex]x=3+\sqrt{7}\ and\ x=3-\sqrt{7}[/tex]

For this case we have the following functions:

[tex]f (x) = x + 1\\g (x) = \frac {1} {x}[/tex]

By definition we have to:

[tex](f * g) (x) = f (x) * g (x)[/tex]

So:

[tex]f (x) * g (x) = x + 1 * \frac {1} {x} = \frac {x + 1} {x}[/tex]

The domain of the function is given by the values for which the function is defined. The function is not defined for x = 0.

Then, the domain is given by all real numbers except 0.

The range is the set of all values of and valid.

Then the range is given by all reals except 1.

Answer:

Option C

Answer:

C.

Step-by-step explanation:

All real numbers except y=1

Answer:

6.5 cm

Step-by-step explanation:

V = Bh for a rectangular prism where B is the area of the base

130 = 20 * h

Divide each side by 20

130/20 = 20h/20

6.5 = h

The height is 6.5 cm

Answer:

number 1

Step-by-step explanation:

Answer:

The error is in the Step 3

Step-by-step explanation:

we know that

The area of a rectangle is equal to

A=bh

where

b is the base of rectangle

h is the height of rectangle

so

The Step 1 calculating the  Base is correct

The Step 2 calculating the Height is correct

The Step 3 calculating the area of rectangle is not correct

because

A=(8)(7)=56 units² instead of 49 units²

Answer:

The error occurred in step 3

Step-by-step explanation:

The formula of a parallelogram is

A = bh

b is the base of the parallelogram

h is the height of the parallelogram

Step 1: the calculation of the base is correct

Step 2: the calculation of the height is correct

Step 3: 8 x 7 = 49 is incorrect. 8 x 7 should be equal to 56.

The bacteria population doubles in 4 hours.

So, in 1 hour it increases by x/4 of its population, where x is population.

So in 1/2 hours or 30 minutes, the increase will be x/4 × 1/2 = x/8

=> if we start with 4000 bacterias, population increase after 30 minutes is 4000× 1/8 = 500

So, 500 more bacterias were added

Total bacterias = 4000+500 = 4500 bacterias

Answer:

3 and -5

Step-by-step explanation:

(x-3)(x+5)greater than and =0​

separate

(1).

x - 3 > 0

add 3 to both sides

x > 3

(2).

x + 5 > 0

subtract 5 from both sides

x > -5

So, The solutions are 3 and -5

Answer: [tex](-\infty,-5]\ U\ [3,\infty)[/tex]

Step-by-step explanation:

Given the inequality [tex](x-3)(x+5)\geq 0[/tex], to find the solutions, we need to follow this procedure:

- First case:

[tex]x-3\geq 0[/tex] and  [tex]x+5\geq 0[/tex]

Solve for the variable "x":

[tex]x\geq 0+3\\x\geq 3[/tex]

 [tex]x\geq 0-5\\x\geq -5[/tex]

Then:

[tex]x\geq 3[/tex]

- Second case:

[tex]x+5\leq 0[/tex] and [tex]x-3\leq 0[/tex]

Solve for the variable "x":

[tex]x\leq 0-5\\x\leq -5[/tex]

[tex]x\leq 0+3\\x\leq 3[/tex]

Then:

[tex]x\leq-5[/tex]

Finally, the solution is:

[tex](-\infty,-5]\ U\ [3,\infty)[/tex]

Using the law of cosines:

Cos (angle) = Adjacent Leg /  Hypotenuse

Cos(28) = x / 64

X = 64 * cos(28)

x = 56.5 km

Answer:

D

Step-by-step explanation:

I graphed each equation on a piece of paper and on desmos.com

In a translation, the image of vertex A is represented by A’T’ in the new triangle.

In a translation, the relative positions of the points in the shape are preserved, but the shape is moved from one location to another without changing its orientation or size. So, if the translation takes triangle CAT to C’A’T’, the corresponding vertex A in the original triangle will be mapped to vertex A' in the new triangle.

Therefore, A’T’ represents the image of vertex A after the translation, and it is the corresponding vertex in the new triangle.

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A’T’ is the image of line segment AT after a geometric translation has been performed on triangle CAT. It will have the same length as AT and will be parallel to it.

In the field of mathematics, particularly in geometry, a translation is a term that describes a function that moves every point a constant distance in a specified direction. The term 'A’T’' in your question refers to the line segment connecting points A’ and T’ after the translation. Assuming that a translation takes triangle CAT to C’A’T’, A’T’ will be the image of AT after the translation.

The properties of a translation are such that the length of the segment will remain the same, and the points on the segment, A and T, will simply move, maintaining their initial orientation. So, segment A’T’ will be equal in length to segment AT of the pre-image triangle CAT and will be parallel to it.

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Answer:

$21

Step-by-step explanation:

20% of 35 is 7, then you add 7 to 35 to get 42, then you split the earnings and get 21 dollars.

Answer:

21

Step-by-step explanation:

First find the tip

35 *20%

35*.2

7

He makes 35+7 = 42

But he splits it with his friend

42/2 = 21

He will make 21 and his friend will make 21

Answer:

The answer is Both a(x) and b(x) have the same output value at x = 2.

Step-by-step explanation:

The answer is Both a(x) and b(x) have the same output value at x = 2. Because when a(x)=b(x) the lines intersect at that point lines intersect they have a point in common. Also, a(x)=b(x) means that the outcomes are the same

The statement that is true about a(x) = b(x) at x = 2 is

Both a(x) and b(x) have the same output value at x = 2.

Option B is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

a(x) and b(x)

At x = 2,

a(x) is equal to b(x)

a(x) = b(x)

This means that,

a(x) and b(x) have the same output value at x = 2.

Both a(x) and (x) have a maximum or minimum value at x = 2.

This is not true because we have to differentiate the function and put it as zero to get the maximum and minimum value at x=2.

Both a(x) and b(x) crosses the x-axis at 2.

This is not true because the function on the graph is at a point of intersection between x = 2 and the y value.

Both a(x) and (x) crosses the y-axis at 2.​

This is not true because the function on the graph is at a point of intersection between x = 2 and the y value.

Thus,

The statement that is true about a(x) = b(x) at x = 2 is

Both a(x) and b(x) have the same output value at x = 2.

Option B is the correct answer.

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Answer:

[tex]\large\boxed{(3+\sqrt{-16})(6\sqrt{-64})=-192+144i}[/tex]

Step-by-step explanation:

[tex]\sqrt{-1}=i\to i^2=-1\\\\(3+\sqrt{-16})(6\sqrt{-64})=(3+\sqrt{(16)(-1)})(6\sqrt{(64)(-1)})\\\\=(3+\sqrt{16}\cdot\sqrt{-1})(6\cdot\sqrt{64}\cdot\sqrt{-1})=(3+4i)\bigg((6)(8i)\bigg)\\\\=(3+4i)(48i)\qquad\text{use the distributive property}\ (b+c)a=ba+ca\\\\=(3)(48i)+(4i)(48i)=144+192i^2\\\\=144i+192(-1)=-192+144i[/tex]

The value of the given expression (3+√-16)(6√-64) is (-192+144i).

As the given two factors are complex numbers, therefore, we must know about the value of i

i = √(-1)

i² = (-1)

The solution of the product,

[tex](3+\sqrt{-16})(6\sqrt{-64})\\\\ = (3\times 6\sqrt{-64}) + (\sqrt{-16}\times 6\sqrt{-64})\\\\= (3+4i)(6\cdot 8i)\\\\= (3+4i)(48i)\\\\= 144i + 192(i)^2\\\\= 144i + 192(\sqrt{-1})^2\\\\= 144i + 192(-1)\\\\= -192+144i[/tex]

Hence, the value of the given expression (3+√-16)(6√-64) is (-192+144i).

Learn more about Complex Number:

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Answer:

[tex]y=-5x-27[/tex]

Step-by-step explanation:

Since we are finding a parallel line, the slopes will be the same, so the second equation will also have a slope of -5.

Then, to find the y-intercept, we can use the point given and plug in.

[tex]y=-5x+b[/tex]

[tex]3=-5(-6)+b[/tex]

[tex]3=b+30[/tex]

[tex]b=-27[/tex]

So the equation comes out to be [tex]y=-5x-27[/tex]

We can check by plugging in the given point again.

[tex]3=-5(-6)-27[/tex]

[tex]3=30-27[/tex]

[tex]3=3[/tex]

Answer:

15/56

Step-by-step explanation:

3*5=15 * 8*7=56

15/56

Final answer:

To multiply fractions 3/8 and 5/7, multiply the numerators to get 15 and the denominators to get 56, resulting in the fraction 15/56, which is in its simplest form.

Explanation:

To multiply two fractions, you multiply the numerators (the top numbers) together and then multiply the denominators (the bottom numbers) together. So for the fractions 3/8 and 5/7, you would do the following:

Therefore, the product of these two fractions is 15/56. This fraction is already in its simplest form because the numerator and the denominator do not have any common factors besides 1.

Answer:

20 bottles

Step-by-step explanation:

10*3+b=50

30+b=50

-30      -30

       b=20

Answer:

D. 0.857

Step-by-step explanation:

The coefficient of determination, R-squared, is simply the square of the  correlation coefficient;

R-squared = r^2

R-squared = 0.926^2

R-squared = 0.857

Therefore, the coefficient of determination is 0.857.

Answer:

The correct answer option is D. 0.857

Step-by-step explanation:

We are given the correlation coefficient, of a data set to be 0.926 and we are to find the coefficient of determination to three decimal places.

To find that, we will use the following formula:

Coefficient of determination = [tex] r ^ 2 [/tex]

[tex] r ^ 2 [/tex] = [tex] ( 0 . 9 2 6 ) ^ 2 [/tex] = 0.857

Answer:

48 minutes

Step-by-step explanation:

Given that;

Rosalinda can line the football field in 80 minutes

Reggie can line the football field in 120 minutes

Lets assume that if they work together, they will take T minutes to line the football field

Hence;

Thus in 1 minute, Rosalina can line 1/80 of the field where as Reggie can line 1/120 of the field

[tex]\frac{1}{T} =\frac{1}{120} +\frac{1}{80} \\\\\frac{1}{T} =\frac{2+3}{240}\\\\[/tex]

The sum of the two fractions will represent the size of the field that can be lined in 1 minute.

[tex]\frac{1}{T} =\frac{5}{240} \\\\\frac{1}{T} =\frac{1}{48} \\T= 48[/tex]

The reciprocal of the sum of the two fractions will represent the time taken for both Rosalinda and Reggie to line the field.

Answer ; It will take them 48 minutes for them to line the football field

Answer:

48 minutes

Step-by-step explanation:

Reggie can line 1/120 of a football field in 1 minute while Rosalinda can line 1/80 of a football field in 1 minute.

Therefore adding the 2 fractions we get; that BOTH of them can line 1/120+1/80 of a field in 1 minute. 1/120+1/80=1/48.

1/48 of a field can be done in a minute, so it would take them 48 minutes to do 48/48 or 1 whole field.

Answer:

4⁄9

Step-by-step explanation:

As discussed in one of my videos on my channel [USERNAME: MATHEMATICS WIZARD], whenever you are dividing mixed numbers or fractions, you multiply the first term by the divisor's multiplicative inverse [reciprocal]. So you will end up with [⅔]², which is 4⁄9. You understand?

I am joyous to assist you anytime.

Follow below steps:

To find the ratio in simplest form of 2/3 to 3/2, first identify the reciprocal relationship between the two fractions. To compare them as a ratio, we need them to have the same denominator.

Multiply the numerator and denominator of the first fraction by 2, and the numerator and the denominator of the second fraction by 3, so they both have 6 as a common denominator:

(2/3) x (2/2) = 4/6

(3/2) x (3/3) = 9/6

The ratio of 4/6 to 9/6 simplifies to 4:9, since they share the same denominator.

Therefore, the ratio of 2/3 to 3/2 in its simplest form is indeed 4:9.

There is an infinite number of common denominators, but 12 is the least common denominator.  You could also use any other number that is a multiple of 12, such as 24, 36, and 48.

12 is the least common denominator because it is the smallest number that is a multiple of both 4 and 6.

[tex]4*3=12[/tex]

[tex]6*2=12[/tex]

You can also use any other multiples of 12 because they are all multiples of 4 and 6.

The slope of the perpendicular is the negative reciprocal of the original line, so m = -1/(-2) = 1/2.

The general line of slope m through (a,b) is

[tex]y - b = m(x-a)[/tex]

So the line we seek is

[tex] y - 2 = \frac 1 2 ( x - 8)[/tex]

[tex] y = \frac 1 2 x - 2[/tex]

Answer: y = 1/2  x + -2

Answer: 29 and 8

Step-by-step explanation:

See photo attached. (:

Answer:

A + B = 37

A - B = 21    we then add the 2 equations

2A = 58

A = 29

B = 8

Step-by-step explanation: