A piece of ribbon of length 1m 10cm was cut off from a length 5m. What length remained?.​

The measure of the ∠PQS will be 71° , and the measure of the ∠PQR will be 142°.

What is an angle bisector ?

The angle bisector is the line or line segment that divides the angle into two identical portions.

Given that line, QS is bisecting the angle PQR into two angles RQS and PQS.

We know that the angle bisector bisects the two angles into two equal halves , i.e.,

∠ PQS = ∠ RQS

So ; the measure of ∠ PQS will be :

∠ PQS = 71°

So , if we want to calculate the measure of ∠PQR then it can be represented as the sum of two angles.

∠ PQR = ∠PQS + ∠RQS

or

∠PQR = 71° + 71°

or

PQR = 142°

Therefore, the measure of the ∠PQS will be 71° , and the measure of the ∠PQR will be 142°.

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Hey there!

9 - 3x + x - 15

= 9 - 3x + 1x - 15

COMBINE the LIKE TERMS

= (9 - 15) + (-3x + 1x)

= (-3x + 1x) + (9 - 15)

= (-3x + x) + (9 - 15)

= -3x - x + 9 - 15

= -2x - 6

Therefore, your answer should be:

-2x - 6

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

Yes they are equivalent.

In fact any value of x will make both equations equivalent.

Step-by-step explanation:

The simplified expression is [tex]-\sqrt{2} x^{2} \sqrt{x}[/tex].

English expressions, also commonly known as expressions, are words, or groups of words that when used in a certain way convey a certain meaning. Expressions come in many forms, for instance, some of them are collocations, others are common phrases, while others are idioms or even phrasal verbs.

The written expression refers to a highly complex, cognitive, self-directed process. Higher-order components include planning, translating (drafting), reviewing, and revising.

Emotional expression is simply the acknowledgment of these emotions we are built to feel. Healthy expression allows us to understand emotions, truly feel them, and move on.

[tex]\sqrt{8x^{5} } =2\sqrt{2} x^{2} \sqrt{x}\\\sqrt{18x^{5} }=\sqrt{2} 3x^{2} \sqrt{x}\\=2\sqrt{2} x^{2} \sqrt{x}-\sqrt{2} 3x^{2} \sqrt{x}\\=-\sqrt{2} x^{2} \sqrt{x}[/tex]

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[tex]5^{2x}[/tex] = 56 => x = 1.252, by properties of logarithm.

Given: [tex]5^{2x}[/tex] = 56

Taking logarithm on both sides:

=>log([tex]5^{2x}[/tex])  = log (56)

As [tex]log_b(a)^m = m (log_b(a))[/tex],

=> 2x ( log 5) = log (56)

=> 2x = [tex]\frac{log56}{log5}[/tex]

=> 2x = [tex]\frac{1.748}{0.698}[/tex]

=> 2x = 2.504

=> x= 1.252

Hence, [tex]5^{2x}[/tex] = 56 => x = 1.252, by properties of logarithm.

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Answer:

Step-by-step explanation:

The slope is defined as the ratio of the “rise” divided by the “run” between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line.

The inclination of a straight line is the angle that the line makes with the positive direction of the x-axis. The tangent of the angle that a line makes with the positive direction of the x-axis is called the slope or gradient of the line. The slope of a line is generally denoted by m.

Given two points (x1, y1) and (x2, y2) on a line, the slope m of the line is y = (y2 – y1)/(x2 – x1)

The slope-intercept form of a line is given by y = mx + b gives the slope of line m and the y-intercept of line b. The inclination of the line with the horizontal axis is called the slope of the line. The point at which the curve cuts or crosses the y – axis is called the y-intercept.

The extraneous solution for the equation √3 x + 3 - 1 = x is x = - 1 ± √ 3.

We are given an equation:

√3 x + 3 - 1 = x

√3 x + 2 = x

Subtract 2 from both the sides, we get that:

√3 x = x - 2

Raise both sides to the power 2, we get that:

3 x² = x² + 4 - 4 x

2 x² = 4 - 4 x

x² = 2 - 2 x

x² + 2 x - 2 = 0

x = - 1 ± √ 3

Therefore, we get that, the extraneous solution for the equation √3 x + 3 - 1 = x is x = - 1 ± √ 3.

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Answer:

2/5+9+7+4+11 or 2/11

Step-by-step explanation:

2 is the smallest then we just add everything on the bottom together

Or just 2/11 since 2 is the smallest and 11 is the biggest

If you have a question ask

The difference in price between the two brands when buying 800 g of hot chocolate is 0.

What is arithmetic operation?

A field of mathematics known as arithmetic operations deals with the study of numbers and the operations on those numbers that are relevant to all other branches of mathematics. The basic operations included in it are addition, subtraction, multiplication, and division.

For brand A

For 160g of hot chocolate is $2.85

For 1g of hot chocolate is 2.85/160

For 800g of hot chocolate is [tex]\frac{2.85}{160} \times 800[/tex]

                                             = 2.85 [tex]\times[/tex] 5

                                             = $14

For brand B

For 200g of hot chocolate is $3.40

For 1g of hot chocolate is 3.40/200

For 800g of hot chocolate is [tex]\frac{3.40}{200} \times 800[/tex]

                                             = 3.40 [tex]\times[/tex] 4

                                             = $14

Difference of brand A and brand B of hot chocolate of 800g is $14 - $14 = 0.

Therefore, the difference in price between the two brands when buying 800 g of hot chocolate is 0.

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Answer:

Step-by-step explanation:

33

The given quotient ( ∛8 x⁶ y¹² ) / ( √4 x⁴ y⁸ ) is x² y⁴.

This question can be easily solved by using the concept of roots. The two root terms mentioned in the question are ∛8 ( cubic root of 8 ) and  √4 (square root of 4 ). This question can be solved in 4 easy steps

Determining the power of the root and find the LCM of those numbers..

In this case, the powers of root for ∛8 and √4 are 3 and 2, respectively. Take LCM of 3 and 2.

LCM = 3 x 2 = 6

=> We get the LCM of 3 and 2 as 6.

Writing the given numbers as fractional powers.

∛8 = 8¹ˡ³  => The power of 8 = 1/3

√4 = 4¹ˡ²  => The power of 4 = 1/2

Step 3 : Multiply and divide the powers of the base number ( in this case 8 and 4 ) with a number such that you get the denominator as the LCM's ( in this case 6 )

1/3  can be multiplied and divided by 2 to get the denominator as 6

=> 1 * 2 / 3 * 2 = 2/6

1/2  can be multiplied and divided by 3 to get the denominator as 6

=> 1 * 3 / 2 * 3 = 3/6

Step 4 : Divide the two terms

6√8² x 6√4³ = 6√( 4 x 2 x 4 x 2 / 4 x 4 ) = 6√1 = 1

Also,  x⁶ y¹² / x⁴ y⁸ = x² y⁴

Therefore, using the concept of roots and fractions, we get The quotient ( ∛8 x⁶ y¹² ) / ( √4 x⁴ y⁸ ) as x² y⁴.

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The length is greater then width with degree one so f(x) = x + 7 and g(x) = x + 3 represents length and width respectively so option (A) will be correct.

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Perimeter of rectangle = 2( length + width).

A rectangle has two dimensions of size one is greater called length and another is small known as width.

The length and width both are on units of length only such that meter, cm.

In the given option

x + 7 > x + 3 so f(x) will be length and g(x) will be width.

In the option (B) x - 7 < x - 3 so it will not.

Option (C) x² + 7 can not be a unit of length.

Option (D) x - 7 < x - 3 so it will not.

Hence "The length is greater then width with degree one so f(x) = x + 7 and g(x) = x + 3 represents length and width respectively".

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Answer: is A

Step-by-step explanation:

I did that

Answer:

81 times.

Step-by-step explanation:

A dice has 6 sides.

The dice is fair, so each side has a 1/6 chance of being rolled.

The are 3 numbers greater than 3 - 4, 5 and 6.

Each of those numbers have a 1/6 chance of being rolled.

Together, their chance of being rolled is:

1/6 + 1/6 + 1/6 = 3/6 = 1/2

The dice is rolled 162 times.

162 x 1/2 = 81

Gordon should roll a number greater than 3 81 times.

The graph given below y = -x + 2 have a negative slope and a positive y intercept. The point (2, 1) lies on the line 3y = 2x - 1

An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The graph given below have a negative slope and a positive y intercept. The graph is given by y = -x + 2

Given the equation

3y = 2x - 1

When x = 2:

3y = 2(2) - 1

y = 1

Therefore, The point (2, 1) lies on the given line 3y = 2x - 1

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[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ B(\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad C(\stackrel{x_2}{4}~,~\stackrel{y_2}{-1}) ~\hfill BC=\sqrt{(~~ 4- 0~~)^2 + (~~ -1- 3~~)^2} \\\\\\ ~\hfill BC=\sqrt{( 4 )^2 + ( -4)^2}\implies \boxed{BC=\sqrt{32}}[/tex]

[tex]C(\stackrel{x_1}{4}~,~\stackrel{y_1}{-1})\qquad E(\stackrel{x_2}{2}~,~\stackrel{y_2}{-3}) ~\hfill CE=\sqrt{(~~ 2- 4~~)^2 + (~~ -3- (-1) ~~)^2} \\\\\\ ~\hfill CE=\sqrt{( -2)^2 + ( -2)^2}\implies \boxed{CE=\sqrt{8}} \\\\\\ E(\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad F(\stackrel{x_2}{-2}~,~\stackrel{y_2}{1}) ~\hfill EF=\sqrt{(~~ -2- 2~~)^2 + (~~ 1- (-3)~~)^2} \\\\\\ ~\hfill EF=\sqrt{( -4)^2 + ( 4)^2}\implies \boxed{EF=\sqrt{32}}[/tex]

[tex]F(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{0}~,~\stackrel{y_2}{3}) ~\hfill FB=\sqrt{(~~ 0- (-2)~~)^2 + (~~ 3- 1~~)^2} \\\\\\ ~\hfill FB=\sqrt{( 2)^2 + ( 2)^2}\implies \boxed{FB=\sqrt{8}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Perimeter} }{\sqrt{32}+\sqrt{8}+\sqrt{32}+\sqrt{8} ~~ \approx ~~ \text{\LARGE 16.97}}[/tex]

Answer:

x = -7

Step-by-step explanation:

to solve this first subtract 5 to both sides

5 - x - 5 = 12 - 5

- x = 7

now multiply -1 to both sides

-x(-1) = 7(-1)

x = -7

that is your answeer

Real and complex zeros of a polynomial function can be find as:

A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc. For example, 2x+5 is a polynomial that has exponent equal to 1.

Given:

We have to find all real and complex zeros of a polynomial function.

first convert the polynomial to factored form. Once all factors are found, set each individual factor equal to zero to solve for the real zeros

So, according to fundamental theorem of Algebra

It states that every polynomial equation of degree n with complex number coefficients has n roots, or solutions, in the complex numbers.

A complex zero is a complex number that is a zero of a polynomial. For example, i (the square root of negative one) is a complex zero of the polynomial x² + 1, since i² + 1 = 0.

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It should be noted that the scientist could use the data to estimate the proportion of fish affected by copper toxicity in the entire population along this portion of the river by dividing the number of fishes affected by the fishes collected

Let the number of fish collected in sample be represented as N.

Let the number of fish affected in it be represented by X.

Therefore, the proportion will be;

= X/N

Therefore, this can be used by the scientist to estimate the proportion of fish affected by copper toxicity in the entire population.

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An asymptote of the tangent occurs at θ=π/2 , and repeats every π units.

Asymptote of the tangent

Due to the fact that tan(x)=sin(x)cos(x), the tangent function is undefined for cos(x)=0. In light of this, whenever cos(x)=0 the tangent function exhibits a vertical asymptote. Similar to the sine function, the tangent function has zeros for integer multiples of because tan(x)=0 when sin(x)=0.

Typically, dashed lines are used to separate asymptotes from the function itself. The vertical lines that frequently appear on the tangent function's graph are spaced 180 degrees apart from one another.

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Answer:

39.13%

Step-by-step explanation:

14/23=60.87%

Since the question asks how much has miss Taylor cohort fallen by we do this:

100%-60.87%=39.13%

Answer = 39.13%

Hope this helps :)

The solved logarithmic functions are log y = log 2 + 4 log x and log y = 2 log 2 - log x for y = 2x⁺⁴ and y - 4x⁻¹ = 0 respectively.

What is a logarithmic and exponential function?

Logarithmic functions and exponential functions are inverses of each other. The logarithmic function is denoted by using the word log while exponential by using the alphabet,  e. For example log 10 = 1 and e^2.

Solving the given expressions: y = 2x⁺⁴, y - 4x⁻¹ = 0

Applying given properties of logarithmic and exponential function;

log a + log b = log (ab)

4 log x = log x⁴

e^(log x) = 1

e^(x + y) = (e^x) × (e^y)

Take expression y = 2x⁺⁴

Applying log on both sides, we get,

log y = log (2x⁺⁴)

log y = log 2 + log x⁺⁴

log y = log 2 + 4 log x

To Check Results,

Taking exponential,

y = e^[log 2 + 4 log x]

y = e^(log 2) × e^[4 log (x)]

y = 2 × e^(log x⁴)

y = 2x⁴

Thus, the answer is verified.

Take expression y - 4x⁻¹ = 0

Applying log on both sides, we get,

log y = log (4x⁻¹)

log y = log 4 + log x⁻¹

log y = 2 log 2 - log x

To Check Results,

Taking exponential,

y = e^[2 log 2 - log x]

y = e^(2 log 2) × e^[-log (x)]

y = e^(log 4) × e^(log x⁻¹)

y = 4x⁻¹

y - 4 x⁻¹ = 0

Thus, the answer is verified.

Hence, the solved expression is log y = log 2 + 4 log x and log y = 2 log 2 - log x for y = 2x⁺⁴ and y - 4x⁻¹ = 0 respectively.

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Answer:

61

Step-by-step explanation:

It should be noted that converting 11/20 to a decimal through division will gives 0.55.

This can be illustrated as follows. It should be noted that the quotient is the value obtained by dividing one value by another. The quotient is 11.

The divisor is the value that divides. It should be noted that in this case, this is illustrated as 20.

It should be noted that 11 is the numerator and 20 is the denominator.

Therefore, it should be noted that converting 11/20 to a decimal through division will gives 0.55.

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The volume of the triangular prism that is 16 ft long is calculated as: 288 ft³

A triangular prism has two triangular bases. The volume of the triangular prism can be found by using the formula below:

Volume of triangular prism = 0.5 * b * h * L, where:

Given the parameters below:

Length of the the base of the triangular face (b) = 4 ft

Height of the triangular face (h) = 9 ft

the length is triangular prism (L) = 16 ft

Volume of the triangular prism = 0.5 * 4 * 9 * 16

Volume of the triangular prism = 288 ft³

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Answer:

75

Step-by-step explanation:

there is a pattern in which you can get your answer 75 to 79 you are counting in three 75,76,77,78,79 if you look closely you will see the pattern and you continue to his sixth test and that is how you will get your answer

Answer:  55 degrees

Step-by-step explanation: If the Whole is 180 and you subtract 125 degrees you are left with 55.

Answer:

neither ordered pair is a solution

Step-by-step explanation:

to determine if the pairs are a solution, substitute the x- coordinate into the left side of the equation and if equal to the right side then they are a solution.

(- 9, 3 ) with x = - 9

6(- 9) = - 54 ≠ 14 ← not a solution

(2, - 4 ) with x = 2

6(2) = 12 ≠ 14 ← not a solution

The statements that completes the two column proof table, obtained through the use of complementary, and angle addition postulates, arranged using the numbering on the given table are as follows;

The reasons that completes the two column proof table are as follows;

1. ‹PQR is a right angle; Given ‹PQR is a right angle

2. m‹PQR = 90°; Definition of Right Angles

3. m‹PQS + m‹SQR = m<PQR; Angle addition postulate

4. m‹PQS + m‹SQR = 90°; Substitution

5. ‹PQS and ‹SQR are complementary angles; Definition of Complementary Angles

6. ‹TQP and <SQR are complementary angles; Given ‹TQP and <SQR are complementary angles

7 [tex] \angle PQS \cong \angle TQP[/tex]

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Answer:

X = 4

Step-by-step explanation: