Solve please. 20 points.

Answer:

-1

Step-by-step explanation:

Given the equation :

-11 = - 12 + 2x + 3

Collect like terms

-11 + 12 - 3 = 2x

-2 = 2x

-2 /2 = 2x/2

x = - 1

Answer:

\(x = -1\)

Step-by-step explanation:

Given the equation \(-11 = -12 + 2x + 3\) find \(x\)

For resolve this you have to do basic algebraic operations in both sides of the equation, as follow:

First substract -3 in both sides of the equation

\(-14 = -12 + 2x\)

Later sum 12 in both sides of the equation

\(-2 = 2x\)

The final  step is multiply by \(\frac{1}{2}\) each side of the equation

\(-1 = x\)

So the final answer is \(x = -1\)

Answer:

x = 8

Step-by-step explanation:

By Basic Proportionality Theorem:

\( \frac{3}{x - 2} = \frac{x}{x + 8} \\ \\ x(x - 2) = 3(x + 8) \\ \\ {x}^{2} - 2x = 3x + 24 \\ \\ {x}^{2} - 2x - 3x - 24 = 0 \\ \\ {x}^{2} - 5x - 24 = 0 \\ \\ {x}^{2} - 8x + 3x - 24 = 0 \\ \\ x (x - 8) + 3(x - 8) = 0 \\ \\ (x - 8)(x + 3) = 0 \\ \\ x - 8 = 0 \: \: or \: \: x + 3 = 0 \\ \\ x = 8 \: \: or \: \: x = - 3 \\ \\ \because \: length \: can \: not \: be \: - ve \\ \\ \implies \: x \neq - 3 \\ \\ \implies \: x = 8\)

Answer:

455g

Step-by-step explanation:

The area of the largest squares that will fit on it is 441 square meters.

The greatest number that can divide the numbers in equal parts.

It is called as greatest common factor.

Given:

An area of land measures 735 meters by 756 meters.

That means,

area of land = 735 x 756

area of land = 555660.

It is to be divided up into square plots of equal size.

HCF of (735, 756),

= 21

Now, the area of the largest square,

= (a)², where a is the side of the square.

That means,

A = 21 x 21

A = 441 square meters.

Therefore, the required area is 441 square meters.

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The length of metal flashing needed to be purchase is \(1\frac{5}{8}\) feet's.

He needs 6 ½ feet of metal flashing to complete a household project.

He has two small pieces measuring 3 1/8 feet and 1 3 / 4 feet.

Therefore, the length of metals for him to purchase can be calculated as follows;

The length he has = 3 1 / 8 + 1 3 / 4

The length he has = 25  /8 + 7 / 4

The length he has =  25 + 14/ 8

The length he has = 39 / 8 feet

Therefore

length required to purchase =  \(6\frac{1}{2} - \frac{39}{8}\)

length required to purchase = \(\frac{13}{2}-\frac{39}{8}\)

length required to purchase =  \(\frac{52-39}{8}\)

length required to purchase = \(\frac{13}{8}\) feet

Therefore,

length of metal flashing required to be purchase = \(\frac{13}{8}\) feet = \(1\frac{5}{8}\) feet

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Step-by-step explanation:

Hey there!

Your answer is Option A.

Check all:

A. y = 6x-2

Comparing the equation with y = mx+b, we get;

m= 6

and b= -2

B. y= 6x+2

Comparing the equation with y= mx+b, we get;

m = 6

b= 2

C. y = 2x+6

Comparing the equation with y= mx+b, we get;

m= 2

b = 6

D. y= -2x-6

Comparing the equation with y= mx+b, we get;

m= -2

b= -6

Therefore, Option A is correct answer.

Hope it helps...

Answer

EAD= EBC true.

Step-by-step explanation:

Both triangles are equal. The line between AE and EB show the lines are equal. In turn this makes the sides AD and BC equal. DC are the same length as AE and EB. In short, all sides are equal so the triangles are the same.

Answer:

5/4 should be your answer or in decimal form 1.25

Step-by-step explanation:

Slope is rise over run

Y2-Y1 divided by X2-X1

5/4

Answer: I would say 4 centimeters

Step-by-step explanation: Well if 24 divided by 6 equals 4 then I would say 4

Based on the length of the rope and the number of pieces it is to be cut into, the length of each piece will be 25 cm long.

First covert the length of the rope to centimeters:

= 6 x 100

= 600 cm

The length of each piece will be:

= Length of rope / Number of pieces

= 600 / 24

= 25 cm

In conclusion, each piece will be 25 cm long.

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Answer:

44 pears and 52 apples

Step-by-step explanation:

pears are 8 more than apple so 52-8 = 44

Number of apples and pears in a box is equals to \(30\) and \(22\) respectively.

" Number is defined as the count of any given quantity as per given condition."

According to the question,

Given,

Total number of apples \(= 52\)

\('x'\) represents the number of pears

\('x+ 8'\) represents the number of apples

As per the given condition required equation we get,

\(x + x + 8 = 52\\\\\implies 2x = 52-8\\\\\implies x = \frac{44}{2} \\\\\implies x = 22\)

number of pears \(= 22\)

number of apples \(= 22+8\)

                              \(=30\)

Hence, number of apples and pears in a box is equals to \(30\) and \(22\) respectively.

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The data includes a concave mirror with a radius of curvature of +31.5 cm and magnification of m = 3.40. The formula for magnification is m = v/u, and the focal length is f = r/2. Substituting the values, we get u = v/m, and using the mirror formula, the distance of the object from the mirror is 10.15 cm.

Given data: Radius of curvature of a concave mirror, r = +31.5 cm Magnification produced by the mirror, m = 3.40

We know that the formula for magnification is given by:

m = v/u where, v = the distance of the image from the mirror u = the distance of the object from the mirror We also know that the formula for the focal length of the mirror is given by :

f = r/2where,f = focal length of the mirror

Using the mirror formula:1/f = 1/v - 1/u

We know that a concave mirror has a positive focal length, so we can replace f with r/2.

We can now simplify the equation to get:1/(r/2) = 1/v - 1/u2/r = 1/v - 1/u

Also, from the given data, we have :m = v/u

Substituting the value of v/u in terms of m, we get: u/v = 1/m

So, u = v/m Substituting the value of u in terms of v/m in the previous equation, we get:2/r = 1/v - m/v Substituting the given values of r and m in the above equation, we get:2/31.5 = 1/v - 3.4/v Solving for v, we get: v = 22.6 cm Now that we know the distance of the image from the mirror, we can use the mirror formula to find the distance of the object from the mirror.1/f = 1/v - 1/u

Substituting the given values of r and v, we get:1/(31.5/2) = 1/22.6 - 1/u Solving for u, we get :u = 10.15 cm

Therefore, the distance of the mirror from the face is 10.15 cm. The units are centimeters (cm).Answer: 10.15 cm.

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Answer:

14

Step-by-step explanation:

(f - g)(x)

= f(x) - g(x)

= 3x² + 1 - (1 - x)

= 3x² + 1 - 1 + x

= 3x² + x

Then

(f- g)(- 2)

= 3(- 2)² + 2

= 3(4) + 2

= 12 + 2

= 14

The quadratic $-6x^2 + 36x + 216$ can be written in the form $a(x + b)^2 + c$, where $a$, $b$, and $c$ are constants. The value of $a b c$ is -1296.

To write the quadratic in the form $a(x + b)^2 + c$, we need to complete the square. First, we factor out the coefficient of the leading term:

$-6x^2 + 36x + 216 = -6(x^2 - 6x - 36)$

Next, we add and subtract the square of half the coefficient of the $x$ term inside the parentheses:

$-6(x^2 - 6x - 36) = -6[(x - 3)^2 - 9 - 36]$

Simplifying, we get:

$-6[(x - 3)^2 - 45] = -6(x - 3)^2 + 270$

Therefore, $a = -6$, $b = 3$, and $c = 270$. The product of these constants is:

$a b c = (-6)(3)^2 (270) = -1296$.

Thus, $a b c$ is -1296.

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Answer:

w = 11.25

Step-by-step explanation:

To solve this problem, we are going to move all of the terms containing the variable w to the left side of the equation and all of the constant terms (ones with numbers only) to the right side of the equation.

w - 24 = -3w + 21

To do this, we should first add 24 to both sides of the equation.

w - 24 + 24 = -3w +21 + 24

If we simplify, we get:

w =  -3w + 45

Next, we should add 3w to both sides of the equation.

w + 3w = -3w + 3w + 45

4w = 45

Finally, we can divide both sides by 4.

4w/4 = 45/4

w = 11.25

Hope this helps!

The Perimeter of wall in inches is 4.724412 inches.

We have the Perimeter = 120 m

We know 1 m = 39.3701 inch

Then, the perimeter inches

= 39.3701 x 120

= 472.4412 inches  

and, 1 cm= 0.393701 inch

Then, perimeter

= 12 x 0.393701

= 4.724412 inches

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Answer:

A.

Step-by-step explanation:

It was trick question because they all are opinionated, but the first one should be an easy yes or no question. However, if you do not like the president then you would say no because of bias. The rest are supposed to be "biased" because they are asking what you prefer.

"Should the President of the United States serve a six-year term?" is question is biased

Survey bias is a "systematic error introduced into sampling or testing by selecting or encouraging one outcome or answer over others." Due to this "encouragement" for a particular result, surveys may be biassed and only provide one type of consumer perspective.

For first, It presumes that the responder supports the idea that the President should hold office for a six-year term, which may not apply to all respondents.

However, out of bias, you would say "no" if you didn't like the president. The others are supposedly "biassed" since they inquire about your preferences.

Thus, the biased question is Should the President of the United States serve a six-year term?.

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The statement is TRUE. Extrapolation in regression analysis refers to using the line of best fit to predict values that lie outside the range of the observed data.

It involves extending the regression line beyond the observed data points to estimate values for variables that are beyond the range of the data. However, it's important to note that extrapolation can be risky because it assumes that the relationship between the variables continues outside the observed range, which may not always be valid. Extrapolation should be done with caution and its results should be interpreted carefully.

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She has a 0.0755 chance of accurately answering three questions at most.

Given data;

A student is completing a multiple-choice exam that consists of 7 questions and 4 possible answers. Suppose the student guesses the right response with a probability of 0.75 while not knowing the topic.

The terms are expanded using the binomial theorem.

7 questions total.

The probability of doing it right is 0.75.

The chance of getting it wrong is 1 - 0.75 = 0.25

The likelihood that she will accurately respond to no more than three questions is indicated as;

\(P = ^nCr p^rq^n^-^r\)

\(P = ^nCo (0.75)^r(0.25)^n^-^r\)

Here, r ranges from (0, 1, 2, 3)

\(P = ^7Co (0.75)^o(0.25)^7+^7C1 (0.75)^1(0.25)^6+^7C2 (0.75)^2(0.25)^5+^7C3(0.75)^3(0.25)^4\)

\(P = (0.25)^7+7(0.75)^1(0.25)^6+21(0.75)^2(0.25)^5+35(0.75)^3(0.25)^4\)

P = 0.0755

Therefore, the probability that she will answer at most 3 questions correctly is 0.0755.

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The operations that results in a rational numbers are C + D, A · B and C · D.

In this problem we must determine what operations between irrational numbers are equivalent to a rational number. Real numbers are result of the union between rational and irrational numbers. We need to check if each operation is equivalent to a rational number:

Case 1: A + B

A + B = √3 + 2√3 = 3√3 (Irrational)

Case 2: C + D

C + D = √25 + √16 = 5 + 4 = 9 (Rational)

Case 3: A + D

A + D = √3 + √16 = √3 + 4 (Irrational)

Case 4: A · B

A · B = √3 · 2√3 = 2 · 3 = 6 (Rational)

Case 5: B · D

B · D = 2√3 · √16 = 2√3 · 4 = 8√3 (Irrational)

Case 6: C · D

C · D = √25 · √16 = 5 · 4 = 20 (Rational)

Case 7: A · A

A · A = √3 · √3

A · A = 3 (Rational)

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Given:

Jimmy reads a book with 21,356 words.

Bob reads a book with one-and-a-half times as many words.

To find:

The expression that represents the number of words Bob reads.

Solution:

We have,

Number of words Jimmy reads = 21,356

Bob reads a book with one-and-a-half times as many words. So,

Number of words Bob reads =  Number of words Jimmy reads × one-and-one-half

                                               \(=21,356\times 1\dfrac{1}{2}\)

Therefore, the correct option is D.

Answer:

D

Step-by-step explanation:

D

The probability of the sum of two integers is greater than the product is equal to 2 / 5.

Let 'A' be the set of positive integers less than or equal to 5.

A = { 1, 2, 3, 4, 5}

Sum of two numbers is greater than the product of the numbers.

1 × 1 = 1  and 1 + 1 = 2

1 × 2 = 2 and 1 + 2 = 3

1 × 3 = 3 and 1 + 3 = 4

1 × 4 = 4 and 1 + 4 = 5

1 × 5 = 5 and 1 + 5 = 6

2 × 1 = 2 and 2 + 1 = 3

3 × 1 = 3 and 3 + 1 = 4

4 × 1 = 4 and 4 + 1 = 5

5 × 1 = 5 and 5 + 1 = 6

2 × 2 = 4 and 2 + 2 = 4

Total possibilities = 5 × 5

                             = 25

Favourable outcomes = 10

Total number of outcomes = 25

Probability of sum of two numbers greater than the product

= 10 / 25

= 2 / 5

Therefore, the probability of the sum of two numbers is greater than the product is equal to 2/ 5.

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Answer:

The value of the given expression to the nearest integer is 114,126.

Step-by-step explanation:

\(\displaystyle \sum^{29}_{n=2}80\left(1.23\right)^{n-2}\)

The given sigma notation means

As 80(1.23)ⁿ⁻² is exponential, the series is geometric.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}\)

Therefore, the first term, a, is 80 and the common ratio, r, is 1.23.

The formula for the sum of the first n terms of a geometric series is:

\(S_n=\dfrac{a(1-r^n)}{1-r}\)

As the exponent of the sigma notation is (n - 2) rather than (n - 1), and the given values of n are from n = 2 to n = 29, we need to find the sum of the first 28 terms.

Therefore, substitute a = 80, r = 1.23 and n = 28 into the sum formula:

\(\implies S_{28}=\dfrac{80\left(1-1.23^{28}\right)}{1-1.23}\)

\(\implies S_{28}=114125.755...\)

\(\implies S_{28}=114126\)

Therefore, the value of the given expression to the nearest integer is 114,126.

if I am correct that is the solution.

Answer:

A. 4

Step-by-step explanation:

the answer is 4

i agree with the person above

The 30th term value is 2900.

A series of integers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

Given:
A sequence,

10, 110, 210, 310, …

To find the common difference:

110 - 10 = 100

So, d = 100

Remember that,

aₙ= a₁ + (n-1)d

aₙ=a₁+(n−1)d

So,

aₙ = 10 +(n−1)100.

a₃₀ = 10 + (30 - 1)100

a₃₀ = 10 + 29(100)

a₃₀ = 10 + 2900

a₃₀ = 2910.

Therefore, a₃₀ = 2910.

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formula for the tangent line is y=x-1 and differentiation of ln(x) is 1/x

A straight line without crossing the curve , it touches the curve at one single point is called tangent . Finding the derivative of a function or a variable in mathematics is called differentiation.

The ratio of the vertical to the horizontal distance between any two points on it  is called slope of ray or line or line segment in analytical geometry.

y-y1 = m(x-x1)

If the function passes through (1,0)  and the slope equals to 1 is:

y-0 = 1(x-1)

y=x-1

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Tangents are straight lines that only touch curves at a single spot rather than crossing them. Differentiation in mathematics refers to the process of determining a function's or variable's derivative.

The slope of a ray, line, or line segment in analytical geometry is the ratio of the vertical to the horizontal distance between any two locations on it.

y-y1 = m(x-x1) (x-x1)

If a function goes through the point (1, 0) and its slope is 1, then:

y-0 = 1(x-1) (x-1)

y=x-1

Answer:

A. x < 2

Step-by-step explanation:

2x - 8 < 12

2x < 12 + 8

2x < 20

x < 20/10

x < 2

3/5 = 0.6 or 3/5 as a fraction in its simplest form. 7/8 = 0.875 or 7/8 as a fraction in its simplest form. 2/3 = 0.666... or 2/3 as a fraction in its simplest form. 5/6 = 0.833... or 5/6 as a fraction in its simplest form. 1/4 = 0.25 or 1/4 as a fraction in its simplest form

To rename a fraction as a whole number or mixed number, we divide the numerator by the denominator. If the result is a whole number, then the fraction is renamed as that whole number. If the result is a mixed number, we take the integer part as the whole number and the fractional part as the numerator of the proper fraction. For example, 7/8 can be renamed as a mixed number by dividing 7 by 8, which gives 0.875. The integer part is 0, so we take the fractional part 0.875 as the numerator of the proper fraction. We can simplify it to 7/8. Similarly, we can rename the other fractions in the same way.

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Complete question:

Rename each fraction as a whole number or mixed number

3/5

7/8

2/3

5/6

1/4

Answer:

505>15+29x

Step-by-step explanation:

The equation of the line shown in this graph passing through the points (-2, 2) and (-2, -3) is x = -2

The standard equation of a line graph is expressed as \(y=mx+c\)

m is the slope of the line

c is the y-intercept

Given: coordinate points  (-2, 2) and (-2, -3)

The coordinates are in the form of (x₁,y₁) and (x₂,y₂)

Slope of the equation is \((\frac{y2-y1}{x2-x1})\)

So ,slope=\((\frac{-3-2}{-2+2})\)

               =\((\frac{-5}{0})\)

               =∝

Since the slope of infinity, this shows that the line is a vertical line. The standard equation of a vertical line is x = a

Since the x-coordinates are similar, hence a = -2

The equation of the line shown in this graph passing through the points (-2, 2) and (-2, -3) is x = -2

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Answer:

y = 2x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = A (1, 7 ) and (x₂, y₂ ) = B (- 3, - 1 )

m = \(\frac{-1-7}{-3-1}\) = \(\frac{-8}{-4}\) = 2 , then

y = 2x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (1, 7 )

7 = 2(1) + c = 2 + c ( subtract 2 from both sides )

5 = c

y = 2x + 5 ← equation of line