athaniel is using the quadratic formula to solve 0 = x2 + 5x - 6. His steps are shown below. What are the solutions to the equation? x = –1, 6 x = –6, 1 x = –22, 27 x = –27, 22

We have two right triangles and three different rectangles.

The formula of an area of a right triangle:

[tex]A_T=\dfrac{1}{2}l_1l_2[/tex]

l₁, l₂ - legs

We have l₁ = 20cm and l₂ = 21cm. Substitute:

[tex]A_T=\dfrac{1}{2}(20)(21)=(10)(21)=210\ cm^2[/tex]

The formula of an area of a rectangle:

[tex]A_R=lw[/tex]

l - length

w - width

We have:

rectangle #1: l = 22cm, w = 29cm

[tex]A_{R1}=(22)(29)=638\ cm^2[/tex]

rectangle #2: l = 22cm, w = 21cm

[tex]A_{R2}=(22)(21)=462\ cm^2[/tex]

rectangle #3: l = 22cm, w = 20cm

[tex]A_{R3}=(22)(20)=440\ cm^2[/tex]

The total Surface Area of the triangular prism:

[tex]S.A.=2A_T+A_{R1}+A_{R2}+A_{R3}\\\\S.A.=2\cdot210+638+462+440=1960\ cm^2[/tex]

After graphing both lines, we're able to tell the solution by looking at the point where the lines cross. In this case, it's at (4, -1). And so that is the solution set.

The formula of a volume of a cuboid:

[tex]V=lwh[/tex]

l - length

w - width

h - height

We have:

l = (x + 4) cm

w = (x + 1) cm

h = 3 cm

Substitute:

[tex]V=(x+4)(x+1)(3)[/tex]      use distributive property

[tex]V=(x+4)(3x+3)[/tex]

[tex]V=(x)(3x)+(x)(3)+(4)(3x)+(4)(3)[/tex]

[tex]V=3x^2+3x+12x+12[/tex]      combine like terms

[tex]\boxed{V=3x^2+15x+12}[/tex]

When raising a monomial to a power, you multiply the exponents of each variable by that power.

When you raise a monomial to the power of 2, you multiply the exponents of each variable by 2. So in the given monomial ax6y12, you would raise each exponent to the power of 2 to get a2x12y24.

Similarly, when you raise a monomial to the power of 3, you multiply the exponents of each variable by 3. So in the given monomial ax6y12, you would raise each exponent to the power of 3 to get a3x18y36.

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Answer:

80°

Step-by-step explanation:

Three angles are equal

Let the equal angle be x

3x+120=360

3x=240

x=240/3

=80

Hence the three angles are 80∘

Answer:

Each of the three congruent angles has measure 80 deg. The fourth angle has measure 120 deg.

Step-by-step explanation:

The sum of the measures of the angles of an n-sided polygon is (n - 2)180.

A quadrilateral has 4 sides, so n = 4 in the formula above.

(n - 2)180 = (4 - 2)180 = 2(180) = 360

The sum of the measures of the angles of a quadrilateral is 360 degrees.

Three angles are congruent. Let the measures of the three congruent angles be x. The sum of the measures of the 3 angles is x + x + x = 3x.

The sum of the measures of the angles is 360 deg.

3x + 120 = 360

Subtract 120 from both sides.

3x = 240

Divide both sides by 3.

x = 80

Answer: Each of the three congruent angles has measure 80 deg. The fourth angle has measure 120 deg.

Answer: A

Step-by-step explanation: sin45(9 radical 2)

Answer: I know it’s a circle but I forget why actually sorry that doesn’t help much

Step-by-step explanation:

Answer:

$3.92  per gallon

10 gallons of gas at $3.49 a gallon will cost $34.90

Step-by-step explanation:

To find the price per gallon, we take the total cost, and divide by the number of gallons.  I will change 16 1/2 to a decimal for ease of math calculations.  

16 1/2 = 16.5

cost/gallons

$62.70/16.5

3.91875

Since we are working with money, we round to the nearest cent

$3.92  per gallon

To find the  total cost, we multiply the cost per gallon times the number of gallons.  We have a cost per gallon of $3.49.  If we multiply by 10 gallons

cost = $3.49 * 10

        $34.90

10 gallons of gas at $3.49 a gallon will cost $34.90

Answer:

2.  No it is not direction variation

3. This is direct variation with the constant being 2

Step-by-step explanation:

The equation for direct variation is y=kx

2.  8y = 3x+1

Divide each side by 8

8y/8 = 3x/8 + 1/8

y = 3/8 x + 1/8

We are adding 1/8 to each time so it is not direct variation

3.  12y = 24x

Divide each side by 12

12y/12 = 24x/12

y = 2x

This matches y= kx, where k=2

This is direct variation with the constant being 2

Answer:

y = -3x - 7

Step-by-step explanation:

Slope = (8 - 2)/(-5 + 3) = 6/-2 = -3

Equation

y - 2 = - 3(x + 3)

y - 2 = -3x - 9

y = -3x - 7

Answer

y=-3x-7

is the equation of line that passes through the points (-3,2) and (-5,8)

step by step explanation:

we are given

(x1,y1)=(-3,2)

(x2,y2)=(-5,8)

formula of slope

m=(y2-y1 )/ (x2-x1)

putting value in formula

m=(8-2) /-5-(-3)

m=6/-5+3

m=6/-2

m=-3

Formula of line slop form of equation is

y-y1=m(x-x1)

putting the values in the formula

y-2= -3(x-(-3))

y-2= -3(x+3)

y-2=-3x-9

y=-3x-9+2

y=-3x-7

is the equation of line that passes through the points (-3,2) and (-5,8)

Answer:  The​ traveler's speed off the​ walkway= 3 ft/s

The speed of the moving​ walkway= 2 ft/s

Step-by-step explanation:

Given: A traveler is walking on a moving walkway in an airport.

Let 't' be the​ traveler's speed off the​ walkway and 'w' be the speed of walkway.

Then the​ traveler's ground speed against the walkway (t-w)= 1 ​ft/s

And the​ traveler's ground speed  with the walkway (t+w)= 5 ft/s

thus we get the following equations [tex]t-w=1..........(1)\\t+w=5.............(2)[/tex]

Adding (1) and (2), we get

[tex]2t=6\\\Rightarrow\ t=3[/tex]

Subtract (2) from (1), we get

[tex]2w=4\\\Rightarrow\ w=2[/tex]

Therefore, the​ traveler's speed off the​ walkway= 3 ft/s

The speed of the moving​ walkway= 2 ft/s

Answer:

The Jar contained 5^67 pennis of nickels and quaters. Making a lot of money in 1/4 of a month. The 5he value of the pennies in the bigger than the amount of the total fitting of itself. The Largest pennies in the jar depended on the nickels and quaers inside. The 133 pennies wer the jar that contained the lesser amount of pennies, therfore the bigger jar standes with a larger value

Step-by-step explanation:

Answer:

It's 16 I just did the same question on a quiz

If the total weight of the box that contains the supplies was 10 pound.

The maximum number of copies of the book that Mr. Mateo could have ordered is 16.

Given:

The number of copies of a book = [tex]\frac{3}{5}[/tex] pound

The total weight of the box = 10 pounds

According to question,

[tex]\frac{3}{5} x<10\\3x<50\\x<\frac{50}{3}\\x<16.66[/tex]

let: x = 16

Therefore, the maximum number of copies of the book that Mr. Mateo could have ordered is 16.

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Answer:

According to the question,

Numbers are : 23 and -6

The two numbers are -6 and 23.

To find the two numbers, we can set up a system of equations based on the given information. Let the two numbers be [tex]\( x \) and \( y \), where \( x > y \)[/tex]. According to the problem, we have:

1. The sum of the two numbers is 17:

[tex]\[ x + y = 17 \][/tex]

2. The difference between the two numbers is 29:

[tex]\[ x - y = 29 \][/tex]

Now, we can solve this system of equations. We can add the two equations together to eliminate [tex]\( y \)[/tex] :

[tex]\[ (x + y) + (x - y) = 17 + 29 \] \[ 2x = 46 \] \[ x = \frac{46}{2} \] \[ x = 23 \][/tex]

Now that we have the value of [tex]\( x \)[/tex], we can substitute it back into one of the original equations to find [tex]\( y \)[/tex]. Let's use the first equation:

[tex]\[ 23 + y = 17 \] \[ y = 17 - 23 \] \[ y = -6 \][/tex]

Therefore, the two numbers are 23 and -6.

a. 0.927

We have:

0.98 – 0.053

We can re-write it as:

0. 9 8 0 -

0. 0 5 3

Moving digits to the right:

0. 9 7 10 -

0. 0 5 3

Digit-per-digit subtraction:

0. 9 2 7

b. 0.27

We have:

0.67 – 0.4

We can re-write it as:

0. 6 7 -

0. 4 0

Digit-per-digit subtraction:

0. 2 7

c. 0.298

We have:

0.3 – 0.002

We can re-write it as:

0. 3 0 0 -

0. 0 0 2

Moving digits to the right:

0. 2 10 0 -

0. 0 0 2

Again:

0. 2 9 10 -

0. 0 0 2

Digit-per-digit subtraction:

0. 2 9 8

d. 2.411

We have:

3.2 – .789

We can re-write it as:

3. 2 0 0 -

0. 7 8 9

We need to rewrite the first term by moving digits to the right several times:

3. 2 0 0 = 2. 12 0 0 = 2. 11 10 0 = 2. 11 9 10

So now we have:

2. 11 9 10 -

0. 7 8 9

Digit-per-digit subtraction:

2. 4 1 1

e. 2.232

We have:

6.53 – 4.298

We can re-write it as:

6. 5 3 0 -

4. 2 9 8

We need to rewrite the first term by moving digits to the right several times:

6. 5 3 0 = 6. 5 2 10 = 6. 4 12 10

So now we have:

6. 4 12 10 -

4. 2 9 8

Digit-per-digit subtraction:

2. 2 3 2

f. 1.68

We have:

6 – 4.32

We can re-write it as:

6. 0 0 -

4. 3 2

We need to rewrite the first term by moving digits to the right several times:

6. 0 0 = 5. 10 0 = 5. 9 10

So now we have:

5. 9 10 -

4. 3 2

Digit-per-digit subtraction:

1. 6 8

g. 4.426

We have:

7 – 3.574

We can re-write it as:

7. 0 0 0 -

3. 5 7 4

We need to rewrite the first term by moving digits to the right several times:

7. 0 0 0 = 6. 10 0 0 = 6. 9 10 0 = 6. 9 9 10

So now we have:

6. 9 9 10 -

3. 5 7 4 =

Digit-per-digit subtraction:

3. 4 2 6

h. 3.03

We have:

4.83 – 1.8

We can re-write it as:

4. 8 3 -

1. 8 0

We can immediately do the digit-per-digit subtraction:

3. 0 3

i. 2.9

We have:

3.7 – 1.8

We can re-write it as:

3. 7 -

1. 8

We need to rewrite the first term by moving digits to the right:

3. 7 = 2. 17

So now we have:

2. 17 -

1. 8 =

Digit-per-digit subtraction:

2. 9

j. 4.538

We have:

16.17 – 11.632

We can re-write it as:

1 6 . 1 7 0 -

1 1 . 6 3 2

We need to rewrite the first term by moving digits to the right:

1 6. 1 7 0 = 1 6. 1 6 10 = 1 5. 11 6 10  

So now we have:

1 5. 11 6 10 -

1 1. 6 3 2 =

Digit-per-digit subtraction:

0 4. 5 3 8

Answer:

1. a

2. d

3. b

4. it would be 7/6 NOT 6/7

Step-by-step explanation:

Answer:

Find the negative reciprocal of the slope of the original line and use the slope-intercept form

y=mx+b to find the line perpendicular to [tex]y=2x+5[/tex].

[tex]y=−12x−5[/tex]

Hope this helps!!

[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\\text{We have}\ k:y=2x+5\to m_1=2.\\\\l:y=mx+b\to m=-\dfrac{1}{2}\to y=-\dfrac{1}{2}x+b.\\\\\text{The line passes through the point (-2, -4).}\ \text{Put the coordinates to the equation:}\\\\-4=-\dfrac{1}{2}(-2)+b\\\\-4=1+b\qquad\text{subtract 1 from both sides}\\\\-5=b\to b=-5\\\\Answer:\ \boxed{y=-\dfrac{1}{2}x-5}[/tex]

recall that the slope, namely the average unit rate of change, is rise/run.

so, what's the slope for the function in the table?  well, we can simply pick any two points and get it, or just use the first point rise of 8 and a run of 7, gives us a slope of 8/7 or 1⅐.

now, let's take a peek at the lines, they all have a "rise" of 6, notice they're all lying on the y = 6 line horizontally.

1)

rise = 6, run = 2, slope 6/2 = 3.

well, 3 is more than 2, so no that one.

2)

rise = 6, run = 3, slope = 6/3 = 2.

well 2 = 2, so no that one either.

3)

rise = 6, run = 4, slope 6/4 = 3/2.

3/2 is actually larger than 8/7 and less than 2, you can check. so ✔

4)

rise = 6, run = 5, slope = 6/5.

6/5 or 1⅕ is more than 8/7, and is clearly less than 2, so ✔

5)

rise = 6, run = 6, slope = 6/6 = 1.

well, needless to say 1 is less than 2 but is less than 8/7, recall 8/7 is actually 1⅐.

Answer:

View the picture for your answer!

Have a wonderful day:))

Answer:

the answer is D because both are to the power of 8

Step-by-step explanation:

Answer:

Option D is correct

[tex](\frac{5}{9})^8=\frac{5^8}{9^8}[/tex]

Step-by-step explanation:

[tex]\text{Given the fraction }(\frac{5}{9})^8[/tex]

we have to choose the correct option which is equivalent to above.

As we know

[tex](\frac{a}{b})^x=\frac{a^x}{b^x}[/tex]

Put a=5, b=9, x=8

[tex](\frac{5}{9})^8=\frac{5^8}{9^8}[/tex]

Therefore, option D is correct

y = mx + b - it's the equation of a straight line. We need only two points to the plotting the graph of that function.

Select any two x values and calculate y values:

[tex]y=\dfrac{1}{2}x+2\\\\for\ x=0\to y=\dfrac{1}{2}(0)+2=0+2=0\to(0,\ 2)\\\\for\ x=-4\to y=\dfrac{1}{2}(-4)=-2+2=0\to(-4,\ 0)[/tex]

[tex]y=x+5\\\\for\ x=0\to y=0+5=5\to(0,\ 5)\\\\for\ x=-5\to y=-5+5=0\to(-5,\ 0)[/tex]

Look at the picture.

The solution of the system of equations is the intersection point of the line.

The slope-intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

x + y = -3      subtract x from both sides

y = -x - 3

Answer:

(a)

Given: A line passes through the points (3, -2) and (6, 2)

Point slope form: An equation of line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by:

[tex]y -y_1=m(x-x_1`)[/tex]  .....[1] where m is the slope of the line.

Calculate first the slope of the line:

Slope(m) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the given points;

[tex]m = \frac{2-(-2)}{6-3}=\frac{2+2}{3} =\frac{4}{3}[/tex]

Substitute the value of m in [1] ;

[tex]y - (-2) = \frac{4}{3}(x-3)[/tex]

[tex]y+2=\frac{4}{3}(x-3)[/tex]     ......[1]

therefore, the equation of line in point slope form is, [tex]y+2=\frac{4}{3}(x-3)[/tex]    

(b)

to find the standard form of the equation [1]

Multiply both sides by 3  in [1] we get;

[tex]3(y+2) = 4(x-3)[/tex]

using distributive property;   [tex]a\cdot (b+c) = a\cdot b + a\cdot c[/tex]

3y + 6 = 4x -12

Subtract 3y to both sides we get;  

3y + 6 -3y = 4x - 12 - 3y

Simplify:

6 = 4x - 3y -12

Subtract 6 from both sides we get;

0 = 4x - 3y -12-6

Simplify:

4x - 3y - 18 =0

Therefore, the standard form of the equation is; 4x - 3y - 18 =0

Answer:

$0.75  

Step-by-step explanation:

We have been given that a proportional relationship between the number of pounds of carrots (x) and the price in dollars (y).

We can represent this information as: [tex]y=kx[/tex].

We are also told that the ordered pair (8, 6) is on the graphed line. Let us substitute x= 8 and y= 6 in our proportional equation to find the constant of proportionality.

[tex]6=k*8[/tex]

[tex]k=\frac{6}{8}[/tex]

[tex]k=\frac{3}{4}[/tex]

Now let us substitute k=3/4 and x=1 in our proportionality equation.

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

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

[tex]y=0.75[/tex]

Therefore, the price of 1 pound of carrots will be $0.75.

Simplify 7/5x to 7x/5

3(7x/5 + 4) -2(3/2 - 5/4x)

Simplify 5/4x to 5x/4

3(7x/5 + 4) -2(3/2 - 5x/4)

Expand

21x/5 + 12 - 3 + 5x/2

Collect like terms

(21x/5 + 5x/2) + (12 - 3)

Simplify

67x/10 + 9

The simplified form of the expression 3(7/5x+4)-2(3/2-5/4x)  is (67x + 90)/10

Expression is a mathematical statement which consists of variables , constant and mathematical operators all together simultaneously.

The given expression is 3(7/5x+4)-2(3/2-5/4x)

[tex]\rm 3 ( \dfrac{7}{5} x+4) -2 ( \dfrac{3}{2}-\dfrac{5}{4}x)[/tex]

(21/5)x +12 - 3 + (5/2)x

((42+25)/10)x + 9

(67x + 90)/10

The simplified form of the expression 3(7/5x+4)-2(3/2-5/4x)  is (67x + 90)/10

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Answer:

-5x + 14y + 8

Step-by-step explanation:

2x + 4y - 7x + 10y + 8

Combine 2x and -7x because they are both being multiplied by x.

-5x + 4y + 10y + 8

Combine 4y and 10y because they are both being multiplied by y.

-5x + 14y + 8

Answer:

The square has 4-fold reflectional symmetry. The regular octagon has 8-fold symmetry.

Step-by-step explanation:

For a square,

There are two lines of symmetry along two diagonals and

two lines of symmetry along midpoints of two pairs of opposite sides.

Therefore, there are 4 lines of reflectional symmetry in total.

For a regular octagon,

There are four lines of symmetry along four diagonals and

four lines of symmetry along midpoints of four pairs of opposite sides.

Therefore, there are 8 lines of reflectional symmetry in total.

Final answer:

A square has 4-fold reflectional symmetry, while a regular octagon has 8-fold reflectional symmetry.

Explanation:

Reflectional symmetry refers to a property of a shape where it can be divided into two mirror-image halves. The -fold reflectional symmetry of a regular polygon refers to the number of lines of symmetry it possesses. A line of symmetry is an imaginary line that divides the shape into two equal halves that are mirror images of each other.

For example, a square has 4-fold reflectional symmetry because it has 4 lines of symmetry, dividing it into 4 equal halves. Each line of symmetry passes through the midpoints of opposite sides.

On the other hand, a regular octagon has 8-fold reflectional symmetry because it has 8 lines of symmetry, dividing it into 8 equal halves. Each line of symmetry passes through the midpoints of opposite sides or vertices.

Answer: Simplify the number in the square root.

Step-by-step explanation: For example, √25 can be simplified to 5 because half of 25 is 5. If x=5, graph this on the x-axis or horizontal line on the graph. Another example, √2 can be simplified to approximately 1.414. To graph this, you can use a graphing tool for accurate representation, or create a graph and place a dot right before 1.5 (in between 1 and 2).

Answer:

No.

Step-by-step explanation:

42 has the following prime factors: 2, 3, 7

105 has prime factors: 3, 5, 7

Both prime factors 3 and 7 divide 42 and 105. If 42 and 105 were relatively prime (co-prime), the set of prime factors that divide both would be empty.  

Answer:

They lost 12 games.

Step-by-step explanation:

Set up a proportion.

12/18 = x/36

36 x 12 = 432

432/18 = 24

Because 18 represents how many games they won, the 24 also represents how many games they won. Therefore, you must subtract to find the amount of times that they lost.

36 - 24 =  12

Answer:

they lost 12 games

Step-by-step explanation:

they lost 12 games