Factor by Grouping.
The ac product of 35x² + 41x + 12 is
The factors of the ac product that add to 41 are
35x² + 41x + 12 =
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Answer:

29 small boxes

Step-by-step explanation:

[tex]\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet[/tex]

[tex]\frak{Good\;Morning!!}[/tex]

[tex]\pmb{\tt{Question\;1}}[/tex]

                 [tex]\star\boldsymbol{\rm{Given-:}}[/tex]

              [tex]\star\boldsymbol{\rm{We're\;looking\;for-:}}[/tex]

This is how it's done.

[tex]\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet[/tex]

There's a special formula that we can use if we need to find the longest side of a right triangle. Fortunately, all of these triangles are right ones! Good.

The formula is. [tex]\boldsymbol{\rm{a^2+b^2=c^2}}[/tex]. This formula is known as Pythagoras' Theorem. This formula only works for right triangles.

Since we have a and b, we can just put in the values (7 for a and 5 for b), And then simplify!

[tex]\boldsymbol{\rm{7^2+5^2=c^2}}[/tex] | 7^2 simplifies to 49, and 5^2 simplifies to 25

[tex]\boldsymbol{\rm{49+25=c^2}}[/tex]. | add

[tex]\boldsymbol{\rm{74=c^2}}[/tex] | square root both sides

[tex]\boldsymbol{\rm{8.6=c}}}[/tex]. | the answer is given to 1 decimal place, as the problem required

[tex]\orange\hspace{350pt}\above5[/tex]

[tex]\pmb{\tt{Question\;2}}[/tex]

 Once more, we're given two sides, and asked to find the third one,  

  which is still the longest side.

[tex]\boldsymbol{\rm{a^2+b^2=c^2}}[/tex] is still the formula used here

Put in 5 for a and 3 for b.

[tex]\boldsymbol{\rm{5^2+3^2=c^2}}[/tex] | 5^2 simplifies to 25, and 3^2 simplifies to 9

[tex]\boldsymbol{\rm{25+9=c^2}}[/tex] | add

[tex]\boldsymbol{\rm{34=c^2}}[/tex] | square root both sides

[tex]\boldsymbol{\rm 5.8=c}}[/tex] | once again it's given to one decimal place

[tex]\hspace{350pt}\above5[/tex]

[tex]\pmb{\tt{Question\;3}}[/tex]

This problem is solved the exact same way

[tex]\boldsymbol{\rm{a^2+b^2=c^2}}[/tex]

[tex]\boldsymbol{\rm{8.2^2+4.7^2=c^2}}[/tex]

[tex]\boldsymbol{\rm{67.24+22.09=c^2}}[/tex]

[tex]\boldsymbol{\rm{89.33=c^2}}[/tex]

[tex]\boldsymbol{\rm{9.5=c}}[/tex], rounded to one D.P.

[tex]\orange\hspace{300pt}\above2[/tex]

[tex]\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet[/tex]

[tex]\pmb{\tt{Question4}}[/tex]

Here we have the longest side and one side length-:

[tex]\boldsymbol{\rm{4^2+b^2=7^2}}[/tex] | 4^2 simplifies to 16 and 7^2 simplifies to 49

[tex]\boldsymbol{\rm{16+b^2=49}}[/tex] | subtract 16 from both sides

[tex]\boldsymbol{b^2=33}[/tex] | square root both sides

[tex]\boldsymbol{\rm{b=5.7}}[/tex]

[tex]\orange\hspace{300pt}\above3[/tex]

[tex]\pmb{\tt{Question\;5}}[/tex]

[tex]\boldsymbol{\rm{3.8^2+b^2=7.9^2}}[/tex]

[tex]\boldsymbol{\rm{14.44+b^2=62.41}}[/tex]

[tex]\boldsymbol{\rm{b^2=47.97}}[/tex]

[tex]\boldsymbol{\rm{b=6.9}}[/tex]

[tex]\orange\hspace{300pt}\above3[/tex]

[tex]\pmb{\tt{Question\;6}}[/tex]

[tex]\boldsymbol{\rm{a^2+6.1^2=7.3^2}}[/tex]

[tex]\boldsymbol{\rm{a^2+37.21=53.29}}[/tex]

[tex]\boldsymbol{\rm{a^2=16.08}}[/tex]

[tex]\boldsymbol{\rm{a=4.0}}[/tex]

[tex]\pmb{\tt{done~!!!}}[/tex]

[tex]\orange\hspace{300pt}\above3[/tex]

A histogram with frequency on the x-axis and ages on the y-axis is shown below. Then the correct option is A.

A diagram is made up of rectangles whose size is related to a variable's frequency and whose width is comparable to the training sample.

A large construction company wants to review the ages of its sales representatives.

A sampling of the ages of 25 sales reps are given:

50, 42, 32, 35, 41, 44, 24, 46, 31, 47, 36, 32, 30, 44, 22, 47, 31, 56, 28, 37, 49, 28, 42, 38, 45.

Then the histogram with frequency table is given as

 Range                Frequency

20 to 24                      2

25 to 29                      2

30 to 34                      5

35 to 39                      4

40 to 44                      5

45 to 49                      5

50 to 54                      1

55 to 59                      1

Then the correct option is A.

The histogram is given below.

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Answer:

4.66666666667

Step-by-step explanation:

Answer:

Step-by-step explanation:10 1/2÷ 2 1/4

solution:

=20/2 ÷ 8/4

= 10 ÷

=5

The inverse of the function f(x)= x^2 is a function.

The equation of the function is

f(x)= x^2

Rewrite as:

y = x^2

Swap x and y

x = y^2

Make y the subject

[tex]y = \sqrt x[/tex]

Rewrite as:

[tex]f^{-1}(x) = \sqrt x[/tex]

So, the inverse of f(x)= x^2 is [tex]f^{-1}(x) = \sqrt x[/tex]

See attachment for the graph

The inverse is a function.

This is so because it passes the vertical line test

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The fraction of the price of the first item is 1/19 if Roxanne bought one item for its regular price and a second item for $ 1.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

In a promotional sale, Roxanne bought one item for its regular price and a second item for $ 1.

Total money Roxanne paid = $20

First item price = 20 - 1 = $19

The fraction of the price of the first item = 1/19

Thus, the fraction of the price of the first item is 1/19 if Roxanne bought one item for its regular price and a second item for $ 1.

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A line which has the same slope as the line passing through the given points is: C. y = 2x + 8.

Given the following data:

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Substituting the given points into the formula, we have;

[tex]Slope = \frac{5\;-\;(-1)}{-1\;-\;(-4)}\\\\Slope = \frac{6}{3}[/tex]

Slope = 2.

Therefore, y = 2x + 8 is a line which has the same slope as the line passing through the given points.

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Complete Question:

Which line has the same slope as the line passing through (-4, -1) and (-1, 5)?

A. y = 3

B. 9x - 3y = 5

C. y = 2x + 8

D. the line passing through (1, 4) and (1, 7)

Answer:

Step-by-step explanation:

Givens

x2 = 4

x1 = 3

y2 = 2

y1 = 6

Formula

distance = sqrt(  (x2 - x1)^2 + (y2 - y1)^2)   )

Solution

distance = sqrt(  (4 - 3)^2 + (2 - 6)^2 )

distance = sqrt( 1^2 + 4^2)

distance = sqrt (17)

Answer

D

What is the distance between the points (3, 6) and (4, 2)?

Select the best answer from the choices provided.

Answer is: ∅ D. √17

Formula:

Distance (d) Square roots (sqrt) ( x 2 - x 1 )² + ( y2 - y1 )²

d = sqrt ( 4 - 3 )² + ( 2 - 6 )²

d = sqrt ( 1² + 4² )

d = sqrt ( 17 ) 1^2 + 4^2 = 17

CarryOnLearning <(￣︶￣)>

On the number line, -2 is not shaded and moving left to show that x is less than -2 but shaded on -6 moving right to show that x is greater than or equals to -6.

Interval Notation: [ -6, -2 ]

An inequality has an infinitely number of solution, the solution set is easily described using interval notation.

Given the set of inequality { x| -6 ≤ x < - 2}

This can easily be written in the form of interval notation as;

[ -6, -2 ]

On the number line, -2 is not shaded and moving left to show that x is less than -2 but shaded on -6 moving right to show that x is greater than or equals to -6.

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Answer:

350

Step-by-step explanation:

Let,

 x = bench

 x + 35 = garden table

EQUATION:

   (x) + (x + 35) = 735

   2x = 735 - 35

   2x = 700

   x = 350

SUBSTITUTE:

  bench costs 350 and garden table costs 385

Hello!

Based on the info we have we can form 2 equations :

(Keep in mind x is the cost of the garden table and y is that of the bench)

Now substitute x in the first equation.

⇒ y + 35 + y = 735

⇒ 2y = 700

⇒ y = 350

∴ The cost of the bench is [tex]\fbox {350}[/tex]

Answer:

[tex](-1;1)[/tex] and [tex](0;4)[/tex]

Step-by-step explanation:

First of all, even if the system is of 4th degree, by looking at the shape of the equations I am expecting up to 2 solutions.

The easiest way to solve it, since both equation are in the form y= something, is to equate both RHSs.

[tex]3x^2+6x+4=-3x^2+4\\6x^2+6x=0 \rightarrow 6x(x+1)=0[/tex]

which tells us that either [tex]x=0[/tex] or [tex]x=-1[/tex]

Now we can replace these value of x in one of the two to finish our work: [tex]x=0\rightarrow y= 4[/tex]

[tex]x=-1 \rightarrow y= -3+4=1[/tex]

The two expression 2(10x +15) and -5x ( x+6) are equivalent to given expression

Expressions are the mathematical statement consisting of variables , constants and mathematical operators .

The expression given is

-20x -30

-2(10x +15)

-20x -30

-5x ( x+6)

Therefore these two expression 2(10x +15) and -5x ( x+6) are equivalent to given expression.

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Final answer:

Height of volcano above sea level is 4205m.

Step-by-step explanation:

Step 1

Height of volcano below sea level: 5998m

Step 2

Total height of volcano below and above sea level:

10203m

Step 3

Subtract height of volcano below sea level from total height of volcano to get height of volcano above sea level:

10203 - 5998

Step 4

Subtract the terms:

10203 - 5998 = 4205

Using the Empirical Rule, the interval that contains 68% of the scores is [81.5, 90.5].

It states that, for a normally distributed random variable:

68% of the scores are within 1 standard deviation of the mean, hence the bounds of the interval are:

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Answer:

437.50 is the cost of 25kg of apple's.

Answer:

Step-by-step explanation:

The ordinary annuity and annuity due as required in the task content are; $126,498.08 and $135, 431.43 respectively.

a) The amount which would be in the account in 25 years can be evaluated by means of the annuity factor obtained from the table under column 7% and row 25 years and hence, the value in 25 years would be; $2,000 × 63.24904

= $126,498.08.

b) For the annuity due case; the future value is;

= (1+0.07) × $2000((1+0.07)^(25) - 1)/0.07

= (1.07) × $2000(5.43-1)/0.07

= $135, 431.43.

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Answer:

Definition of circle

Explanation:

All the points that lies on the circle must be same distance from the center.

This is given by the definition of a circle.

Radius is the length from the center to the points lying on the circle.

Distance formula: [tex]d =\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Diameter of circle is from one end point to another end point lying on circle.

From the shapes given, the third transformation is not an isometry.

An isometry is a mathematical function used to describe the process of moving a geometric object without a changing its size or shape from one point to another.

Thus, from the shapes given, the third transformation is not an isometry.

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The factorization if the given expression 128 + 2d³ is 2(64 + d³).

128 + 2d³

There are two parameters in the expression;

The common factors between 128 and 2d³ is 2

So,

128 + 2d³

= 2(64 + d³)

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Answer:

a₄=8n+1= -39.

Step-by-step explanation:

1) if a₁=3n; a₃=5n-6 and a₅=11n+8, then it is possible to calculate the difference according to 0.5(a₅-a₃)=0.5(a₃-a₁). Then

2) 0.5(11n+8-5n+6)=0.5(5n-6-3n); ⇔ 6n+14=2n-6; ⇔ n= -5.

3) if n=-5, then the 4th term is:

[tex]a_4=\frac{a_5+a_3}{2}; \ = > \ a_4=\frac{11n+8+5n-6}{2}=8n+1;[/tex]

or a₄=-39.

Answer:

y= -2x+2.

Step-by-step explanation:

1) according to the condition interception is '2' (point (0;2));

2) slope is: (2+4)/(0-3)= -2;

3) finally the required equation is: y=-2x+2.

P.S. the suggested option is not the only one.

Step-by-step explanation:

Well since it cost 6$ and the price was 0.36 you can calculate how many gallons you needed to fill up your tank which is calculated by dividing the price to fill the gas tank by the price per gallon

6/0.36 = 16.667 gallons

Now multiply the amount of gallons you need to fill your gas tank by the price in 2010

16.667 * 2.84 = 47.36

You could also just look at the price as a percentage relative to 1970 prices and see that the price increased by 788.9% and the find what 788.9% is of 6$. Which can be done by dividing 788.9 by 100 to convert it into decimal form which gives you 7.889 and then multiply that by the original price of 6$ to fill your gallon to get 47.33 which is slightly different although this is likely due to rounding.

Answer:

25 ft

Step-by-step explanation:

c = √a^2 + b^2 = √20^2 + 15^2 = 25ft

Hooke me up with a 5 star and a thanks :)

The points (s, t) that will maximize John's profit is; (12, 0)

We are given the inequality constraints;

s ≤ 12 - 0.5t

s ≥ 10 - t

s ≤ 20 - t

s ≥ 0

t ≥ 0

We are told that John sells the T-shirts for $6 each and the shorts for $14 each. Since the coordinate point is (s, t), when we look at the options and compare with each of the constraints, it is clear that the points (s, t) that will maximize John's profit is; (12, 0)

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The solution will be the point of intersection of the lines and since the lines are parallel to each other, there is no solution

Inequality are expressions not separated by an equal sign. Given the following inequalities

2x - y > 4

2x - y < -2

The lines for both inequality must be dashed since they do not include equal sign. The first line will be shaded in the upper part while the second in the lower portion

The solution will be the point of intersection of the lines

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Answer:

Step-by-step explanation:

Since the ladybug is [tex]3.3cm[/tex] far from each edge of the rectangle, it follows that the length of the new rectangle is [tex]3.3cm+9.5cm + 3.3cm = 16.1cm[/tex] and the width is [tex]3.3cm+7.5cm + 3.3cm = 14.1cm[/tex].

Recall a formula for the area of a rectangle: [tex]A = l \cdot w[/tex], where [tex]l[/tex] is a length and [tex]w[/tex] is a width of the rectangle.

Substitute [tex]l=16.1cm[/tex] and [tex]w=14.1cm[/tex] into the formula:

[tex]A=16.1cm\cdot 14.1cm[/tex]

Multiply the numbers:

[tex]A=[/tex] [tex]227.01cm^{2}[/tex]

Therefore, the required area is equal to [tex]227.01cm^{2}[/tex].

An equation is formed of two equal expressions. The number of questions that Lesley answered correctly is 20.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number of correct questions answered be x, while the number of questions incorrectly answered be y.

The total number of questions can be written as,

x + y = 25

Solving the equation for y,

y = 25 - x

The total marks can be written as,

3x - 1y = 55

Substitute the value of y,

3x - 25 + x = 55

4x = 80

x = 20

Hence, the number of questions that Lesley answered correctly is 20.

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Answer:

[tex]\boxed{E.~36}[/tex]

Step-by-step explanation:

Supporting drawing in the attachment.

The sum of the measures of two consecutive angles is equal to 180°.

3x° + 2x° = 180°

5x° = 180°   I ÷ 5

x° = 36°

Answer:

36

Step-by-step explanation:

I also did this for shsat

The margin of error is ±2%

A margin of error is a statistical measurement that accounts for the difference between actual and projected results in a random survey sample.

Let x be margin of error and y be the percentages of the population.  

So,

y-x =33%

y +x = 37%

Solving above equations

2y= 70

y= 35%

and x= 2%

Hence, the margin of error is ±2%.

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