Simplify each rational expression. State any restrictions on the variables.
49-z² / z+7

The translation sequence that maps angle ABC to angle A'B'C' is (x, y) ⇒ (x + 3, y + 6)

Transformation is the movement of a point around the coordinate plane. Types of transformations are rotation, translation, reflection and dilation.

Translation is a type of transformation which is either up, down, left or right in the coordinate plane.

The translation sequence that maps angle ABC to angle A'B'C' is (x, y) ⇒ (x + 3, y + 6)

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Following Venn diagram, the correct choice for the set is:  {2, 3, 5, 6, 8, 9}

In a Venn diagram, as used in sets, the intersect of sets refers to members that ate are common to the sets is perspective.

For the given Venn diagram, the intersect of the sets M and N is the numbers in the middle, this means the set M and N has this numbers in common.

However, the question is asking not intersect of sets M and N so knowing the intersect will help us exclude them to have {2, 3, 5, 6, 8, 9}.

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After solving the given inequality the answer is logx+log₁₀(x+1)<3.

So,

Then,

Therefore, after solving the given inequality the answer is logx+log₁₀(x+1)<3.

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Answer:

900 kilometers

Step-by-step explanation:

Convert the percentage into a decimal.

90 ÷ 100 = 0.9

Multiply 1000 by 0.9

1000 * 0.9 = 900

Reason:

The counting numbers, aka the set of natural numbers, is the set {1, 2, 3, 4, 5, ...} which is the set of positive integers

A value like 5 is the same as 5/1, which shows it is rational.

A rational number is any fraction of two whole numbers (eg: 2/3 and 4/7). The denominator cannot be zero.

Since we can rewrite the 5 as 5/1, it can be done with any counting number to show the natural numbers is a subset of the rational numbers.

Any counting number is rational, but not the other way around.

Answer:

x = 152°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle of the triangle , then

x = 79° + 73° = 152°

Based on the table given, we can infer that the table shows a proportional relationship.

A proportional relationship refers to when the value of x and y increase by the same ratio for all the values in the distribution.

In the given table, Pens is increasing by 3:
= 3, 6, 9, 12

Boxes keep increasing by 1:

= 1, 2, 3, 4

This shows that the table shows a proportional relationship because both pens and boxes are increasing by the same rate.

In conclusion, the table given shows a proportional relationship.

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Left-Skewed is the answer.

Histograms are a very common method of visualizing data, and that means that understanding how to interpret histograms is a valuable and important skill in virtually any career. There are a number of things to pay particular attention to when reading a histogram.

Bell-Shaped: A histogram with a prominent ‘mound’ in the center and similar tapering to the left and right. One indication of this shape is that the data is unimodal – meaning that the data has a single mode, identified by the ‘peak’ of the curve.

Uniform: A uniform-shaped histogram indicates data that is very consistent; the frequency of each class is very similar to that of the others.

Right-Skewed: A right-skewed histogram has a peak that is left of the center and a more gradual tapering to the right side of the graph.

Left-Skewed: A left-skewed histogram has a peak to the right of the center, more gradually tapering to the left side. It is unimodal, with the mode closer to the right and greater than either mean or median.

Undefined Bimodal: This shape is not specifically defined, but we can note regardless that it is bi-modal, having two separate classes or intervals equally representing the maximum frequency of the distribution.

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If two quantities are proportional, the true statements about the graph showing the relationship between them are-

D. The points of the graph form a straight line.

E. The points of the graph must include the origin.

F. The points must all form equivalent ratios.

In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio, which is called the coefficient of proportionality or proportionality constant.

Now let us suppose there are two quantities x and y.

A graph between two quantities is plotted.

Suppose x is directly proportional to y.

Thus, these Two variable quantities have a constant ratio

So, we can write

y ∝ x

Applying constant of proportionality,

y = kx

Where k is the constant of proportionality.

It represents a straight line.

Now,the value of x = 0 then the value of y must be equal zero, then the line which represented the direct variation must be passes through the origin

Now  If two variable quantities have a constant ratio and since y = kx is a straight line and passes through origin therefore from the given options the correct answer are-

D. The points of the graph form a straight line.

E. The points of the graph must include the origin.

F. The points must all form equivalent ratios.

Thus, If two quantities are proportional, the true statements about the graph showing the relationship between them are-

D. The points of the graph form a straight line.

E. The points of the graph must include the origin.

F. The points must all form equivalent ratios.

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For the given equations 5x+8, 2x + 1, x - 4 does not form the geometric sequence as the common ratio is not equal.

For the given sequence;

The first three terms of a sequence are given by;

a = 5x+8,

ar = 2x + 1,

ar² = x - 4

Put the value of x = 11 to check if the sequence forms and GP.

a = 5x11+8 = 63

ar = 2x11 + 1 = 23

ar² = 11 - 4 = 7

Find the common ratio;

ar/ a = ar²/ar

23/ 63 = 7/ 23

But 23/ 63 ≠ 7/ 23

As, the common ratio is not same, it will not form as geometric sequence.

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Integer -17 represents Rudy's score for 2 weeks.

Rudy's scores:

Then, add 15 and -32 as follows:

Therefore, integer -17 represents Rudy's score for 2 weeks.

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The value of x is 18.

3 × [tex] {(x - 2)}^{3/4} [/tex] = 24

Dividing the left hand side and right hand side of the equation by 3, we get

[tex] {(x - 2)}^{3/4} [/tex] = 8

Now, on the right hand side of the equation 8 can be written as

[tex] {(x - 2)}^{3/4} [/tex] = [tex] {(2)}^{3/4×4} [/tex]

Taking paper 4/3 on both the sides of the equation, we get

[tex] {(x - 2)}^{3 / 4 \times 4 / 3} = {2}^{3 / 4 \times 4 \times 4 / 3} [/tex]

x - 2 = 2⁴

x - 2 = 16

x = 16 + 2

x = 18

Thus, the value of x = 18.

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Answer:

An equivalent expression for 4 times d raised to the negative third power all over quantity 22 times d raised to the ninth power is 2d⁻³/11d⁻⁹

What is an expression?

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

What is an exponent?

An exponent can be defined as a mathematical operation that is used to raise a quantity to the power of another and it is generally written as bⁿ.

Translating the word problem into an algebraic expression, we have;

4 times d raised to the negative third power = (4 × d)⁻³ = 4d⁻³

22 times d raised to the ninth power = (22 × d)⁻⁹ = 22d⁻⁹

Next, we would write the equation as a quotient:

Expression = 4d⁻³/22d⁻⁹

Expression = 2d⁻³/11d⁻⁹

Answer:

Step-by-step explanation:

Your answer is going to be x²+4x-5=0

Answer:

94.6 m

Step-by-step explanation:

Just put in the number in the info to the formula

formula to find distance travelled, s= 1/2 (u + v) t

U = 0

V = 43

t = 4.4

s= ??

so ,

s = 1/2 (0+43) ×4.4

s = (43× 4.4) ÷ 2

s = 189.2 ÷ 2

s = 94.6 m

yay

Answer:

[tex]y = \frac{3}{4}x - 8[/tex]

Step-by-step explanation:

We know that the slope of a line perpendicular to a line with a given slope is the negative reciprocal of that given slope.  We are given that we want a line perpendicular to that of 4x + 3y = 3.  To find the slope of this given line, we put it into slope intercept form y = mx + b where m is the slope:

[tex]4x + 3y = 3[/tex]

[tex]3y = 3 - 4x[/tex]

[tex]y = 1 - \frac{4}{3}x[/tex]

So we have that the slope of our given line is -4/3. The negative reciprocal of this is 3/4. We thus have that the slope of the line we are looking for is 3/4.

We then know that the equation of the line we want fits the form [tex]y=\frac{3}{4} x + b[/tex], which we know through point slope form. We are then given that (8, -2) is a point on this line. Plugging in:

[tex]-2 = \frac{3}{4}(8) + b[/tex]

[tex]-2 = 6 + b[/tex]

[tex]b = -8[/tex]

We then get the equation of the line we are looking for as [tex]y = \frac{3}{4}x - 8[/tex].

Answer:

Steve has to save for 4 days and Maria has to save for 3 days and they will save $36 each.

Step-by-step explanation:

S = 9 x 4 = 36

M = 12 x 3 = 36

From the rules of transformation;

To get the function g, shift f upwards  by 1 unit.

Transformations simply takes the basic function and transforms it to another function.

The rules of transformation are;

Now, we want to transform f(x) = |x| into g(x) = |x| + 1

This means from the rules of transformation above, we can say that;

To get the function g, shift f upwards  by 1 unit.

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A line is an undefined term because it describes something that does not have width or depth. thus, option describes something that does not have width or depth is correct

If the ray lies onto the considered line segment(overlapping), then it can be said belonging to the considered line segment.

(Line segment has 2 fixed ends, whereas a ray has one end only, another end is not fixed)

A line segment is a straight line with finite length, and thus, have to endpoints (points on either ends).

A line can extend its length in both sides infinitely. It contains arrowheads indicating it can extend.

A line is an undefined term because it describes something that does not have width or depth. thus, option describes something that does not have width or depth is correct

According to the given figure, option (A) and option (F) are correct options which better shows ∠4 ≅ ∠6 respectively.

Let's procced to solve this question.

∠4 ≅ ∠8 by the corresponding angle postulate because two parallel lines is cut by a transversal and ∠4 ≅ ∠8 by the corresponding angle postulate. It's true.

∠6 ≅ ∠8 by the definition of vertical angles. It's true.

and by using the transitive property of congruence that ∠A ≅ ∠B and ∠B  ≅ ∠C then ∠A ≅ ∠C.

⇒ ∠4 ≅ ∠6 by the transitive property of congruence.

Hence, option (A) is correct.

Now,

∠2 ≅ ∠6 by the corresponding angle postulate because two parallel lines is cut by a transversal and ∠2 ≅ ∠6 by the corresponding angle postulate. It's true.

∠2 ≅ ∠4 by the definition of vertical angles. It's true.

and by using the transitive property of congruence that ∠A ≅ ∠B and ∠B  ≅ ∠C then ∠A ≅ ∠C.

⇒ ∠4 ≅ ∠6 by the transitive property of congruence.

Hence, option (F) is correct.

Therefore, option (A) and option (F) are correct option.

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Answer:

g = 1

Step-by-step explanation:

this is how you solve

Answer:

g = 1

Step-by-step explanation:

Add 7

[tex]-7+11g+7=9-5g+7[/tex]

Simplify it

[tex]11g=-5g+16[/tex]

Add 5g

[tex]11g+5g=-5g+16+5g[/tex]

Simplify further

[tex]16g=16\\\frac{16g}{16}=\frac{16}{16}\\= 1\\g = 1[/tex]

Using the law of cosines, the measures of the angles are given as follows:

The law of cosines states that we can find one of the sides or the angle C of a triangle according to the following equation:

c² = a² + b² - 2abcos(C)

In which:

For this problem, the parameters for the triangle are given as follows:

a = b = 12, c = 3.

We want to solve for the smallest angle C, hence:

c² = a² + b² - 2abcos(C)

9 = 288 - 288cos(C)

288cos(C) = 279

cos(C) = 279/288

C = arccos(279/288)

C = 14.36º.

The other two angles are congruent, and the sum of the internal angles of a triangle is of 180º, hence:

14.36 + x + x = 180

2x = 165.64

x = 165.64/2

x = 82.82º.

Then the measures of the angles are given as follows:

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Answer:

14

83

Step-by-step explanation:

i did it on edge

Check the picture below.

now, let's get their length of TZ and TX and thus we'll get their ratio as TX/TZ or TX : TZ

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ T(\stackrel{x_1}{-8}~,~\stackrel{y_1}{-5})\qquad X(\stackrel{x_2}{4}~,~\stackrel{y_2}{-1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ TX=\sqrt{(~~4 - (-8)~~)^2 + (~~-1 - (-5)~~)^2} \implies TX=\sqrt{(4 +8)^2 + (-1 +5)^2} \\\\\\ TX=\sqrt{( 12 )^2 + ( 4 )^2} \implies TX=\sqrt{ 144 + 16 } \implies TX=\sqrt{ 160 } \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ T(\stackrel{x_1}{-8}~,~\stackrel{y_1}{-5})\qquad Z(\stackrel{x_2}{7}~,~\stackrel{y_2}{0})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ TZ=\sqrt{(~~7 - (-8)~~)^2 + (~~0 - (-5)~~)^2} \implies TZ=\sqrt{(7 +8)^2 + (0 +5)^2} \\\\\\ TZ=\sqrt{( 15 )^2 + ( 5 )^2} \implies TZ=\sqrt{ 225 + 25 } \implies TZ=\sqrt{ 250 }[/tex]

[tex]~\dotfill\\\\ TX~~ : ~~TZ\implies \cfrac{TX}{TZ}\implies \cfrac{\stackrel{TX}{\sqrt{160}}}{\underset{TZ}{\sqrt{250}}}\implies \cfrac{\sqrt{4^2\cdot 10}}{\sqrt{5^2\cdot 10}}\implies \cfrac{4~~\begin{matrix} \sqrt{10} \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{5~~\begin{matrix} \sqrt{10} \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} \implies {\LARGE \begin{array}{llll} \cfrac{4}{5} \end{array}}[/tex]

If a 42-inch string is to be cut so that one piece is 7 inches longer than the other, then the shorter piece has a length of 17.5 inches

The length of the shorter piece can be determined by using an algebraic expression.

Any expression consisting of both numbers and letters is considered to be an algebraic expression.

Considering, x to be the length of the shorter piece

As the longer piece is 7 inches longer than the shorter piece, an algebraic expression can be given as,

x + (x + 7) = 42

x + x + 7 = 42

2x + 7 = 42

2x = 42 - 7

2x = 35

x = 35 ÷ 2

x = 17.5

Hence, the length of the shorter piece is calculated to be 17.5 inches.

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Answer:

equation: x-42=50

answer: x=8

Step-by-step explanation:

lets write the equation. We have 42 less than x is -50. 42 less than x could translate to x-42 and if it is 50, then that is what x-42 equals.

So we would have x-42=50

Now you can carry over the -42 to start solving

x-42=50

 +42    +42

(notice it is added on both sides. I add them to get rid of the -42 on the x side and whatever you do to one side you ALWAYS do to the other.)

x= 50-42

x= 8

i hope this helps :)

The product of two (I) rational numbers is always a (II) real number.

A rational number is defined as any number which can be written in the form of p\q where p, q are whole numbers and co-prime.

A real number is any a number that can be indicated on the number line.

A complex number is an imaginary number which does not reside on the number line, rather can be placed in the complex plane.

The product of any two rational numbers produces a rational number and all rational numbers belong in the superset of Real numbers.

Let us consider the possibilities of the other options as given.

A) Let us consider two complex number 2+i and 2-i . When multiplied they produce 3 which is not a complex number.

B)Product of two real numbers can never produce a complex number.

D)Imaginary and complex are same kind of numbers hence they also follow the first option and is not true.

Hence the only correct option is C as we have surmised that the product of two rational numbers will always produce a real number.

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After 12 seconds, the equipment elevator will be 204 feet under the ground while the miner's elevator will be 235 feet under the ground.

After 12 seconds, the miner's elevator is deeper.

It is the ratio of distance and time.

We have,

Equipment elevator:

Speed = 5 feet per sec

Miner's elevator:

Speed = 17 feet per sec

Now,

The position (distance) of the equipment elevator after 31 seconds and 12 seconds:

Distance = speed x time

Distance = Distance after 31 sec + Distance after 12 sec

= (31 x 5) + (16 x 5)

= 155 + 80

= 235 feet

The position (distance) of the equipment elevator after 12 seconds:

= 17 x 12

= 204 feet

Therefore, after 12 seconds, the equipment elevator will be 204 feet under the ground while the miner's elevator will be 235 feet under the ground.

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