Use technology to obtain approximate solutions graphically. All solutions should be accurate to one decimal place. (Zoom in for improved accuracy.)
Find the intersection of the line through (0, 1) and (4.3, 2) and the line through (2.1, 3) and (5.4, 0).
(x, y) =

Answer:

64 times

Step-by-step explanation:

Multiply 0.4, the chance of getting tails, which 160, the amount of times you flip the coin, and you get 64. This is reasonable, because the probability of getting heads is 0.6, and if you flip the coin 160 times, you will get heads 96 times. Hope this helped :)

After solving the value of x is -1/6.

Given:

[tex]25^3^x^+^2[/tex] = 125

[tex]5^{2(3x+2)}[/tex] = [tex]5^3[/tex]

2(3x+2) = 3

6x + 4 = 3

6x = 3-4

6x = -1

divide by 6 on both sides

6x/6 = -1/6

x = -1/6.

Therefore after solving the value of x is -1/6.

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Step-by-step explanation:

we know the square numbers of the basic integer numbers :

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81

10² = 100

so, we see when we square the inequality, the closest numbers are

81 < 91 < 100

and therefore

9 < sqrt(91) < 10

Answer:

  (b)  15, 36, 39

Step-by-step explanation:

You want to know which sets of segment lengths could form a right triangle.

For segments to form a right triangle, the lengths must satisfy the triangle inequality and the Pythagorean theorem. The latter condition can often be determined by looking at the reduced ratios of the lengths, and comparing to known Pythagorean triples.

The ratio of lengths is 3:6:7. There are no integer side lengths that will form a right triangle when one of them is double another. Not a right triangle.

The ratio lengths is 5:12:13. These numbers are a common Pythagorean triple, so will form a right triangle.

The ratio of the smaller two numbers is 3:4. In order for these to form a right triangle, they must be part of a triangle with ratios 3:4:5. That would be 15, 20, 25. The side length 29 is too long for a right triangle. Not a right triangle.

The two short sides are too short to reach the ends of the long side. These lengths will not form a triangle.

__

Additional comment

The table in the attachment computes a²+b²-c². When that value is 0, the Pythagorean theorem is satisfied, and the triangle is a right triangle. Positive numbers indicate an acute triangle; negative numbers indicate an obtuse triangle.

The Pythagorean triples that came into play in this answer are {3, 4, 5} and {5, 12, 13}. Other triples commonly seen are {7, 24, 25} and {8, 15, 17}.

[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{3}}} \implies \cfrac{ 1 }{ -2 } \implies - \cfrac{1 }{ 2 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{- \cfrac{1 }{ 2 }}(x-\stackrel{x_1}{3}) \\\\\\ y-1=- \cfrac{1 }{ 2 }x+\cfrac{3}{2}\implies y=- \cfrac{1 }{ 2 }x+\cfrac{3}{2}+1\implies {\Large \begin{array}{llll} y=- \cfrac{1 }{ 2 }x+\cfrac{5}{2} \end{array}}[/tex]

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{3}{2}}x+4 \qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{3}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{3}}}[/tex]

so we're really looking for the equation of a line whose slope is -2/3 and that it passes through (-6 , 2)

[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{2}{3}}(x-\stackrel{x_1}{(-6)}) \implies y -2= -\cfrac{2}{3} (x +6) \\\\\\ y-2=-\cfrac{2}{3}x-4\implies {\Large \begin{array}{llll} y=-\cfrac{2}{3}x-2 \end{array}}[/tex]

Step-by-step explanation:

Jackson had 5/6 yard of ribbon. He used 2/6 yard to decorate a present. How many yards does he have left?

5/6 - 2/6 = 3/6

3/6 reduces to 1/2 yards left

Answer:

the relationship between two quantities is a proportional relationship, this relationship can be represented by the graph of a straight line through the origin with a slope equal to the unit rate. For each point (x, y) on the graph, is equal to k, where k is the unit rate.

The equation that represents the cost of the pizza is 10x where x is the cost of one slice of pizza and the value of x is $15.

According to the question,

We have the following information:

Tara eats 3 of the 10 slices and pays $4.50 for her share.

Now, let's take the cost of one slice of the pizza to be $x.

So, we have the following expression:

3x = 4.50

Dividing by 3 on both sides of the equation:

x = 4.50/3

x = $1.50

Now, there are 10 slices in pizza.

Cost of pizza = 10x

Cost of pizza = 10*1.50

Cost of the pizza = $15

Hence, the equation that represents the cost of the pizza is 10x where x is the cost of one slice of pizza and the value of x is $15.

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The partial fraction of the compound fraction [tex]\frac{x + 7}{(x - 3)(x - 5)}[/tex] is  [tex]\frac{6}{x - 5}[/tex] [tex]-\frac{5}{x - 3}[/tex]

Partial Fractions are the fractions that are formed when a complex rational expression is split into two or more simpler fractions.

When fractions become too cumbersome to solve we split them into simpler units called partial fractions so that mathematical operations can easily be carried out on them.

[tex]\frac{x + 7}{(x - 3)(x - 5)}[/tex] can be split into the form, [tex]\frac{A}{x - 3} + \frac{B}{x - 5}[/tex]

where A and B are constants.

so,

[tex]\frac{x + 7}{(x - 3)(x - 5)}[/tex]  =   [tex]\frac{A}{x - 3} + \frac{B}{x - 5}[/tex]

taking the LCM of the denominators of the split fractions, we have

(x-3)(x-5)

multiply A by x -5 and B by x - 3

fraction becomes

   [tex]\frac{x + 7}{(x - 3)(x - 5)}[/tex]  = [tex]\frac{A(x - 5) + B(x - 3)}{(x - 3)(x - 5)}[/tex]

since the denominators of the Left hand side and right hand side are same, we equate the numerators

A(x - 5) + B( x - 3) = x + 7

Using the cover up rule method,

to find A, we substitute x = 3 into the equation so that B becomes zero

A(3 - 5) = 3 + 7

-2A = 10

A = 10/-2

A = -5

To find A put x = 5 so that A = 0

B(5 - 3) = 5 = 7

2B = 12

B = 12/2 = 6

Substituting B and A into the partial fractions above

we have,

 [tex]\frac{6}{x - 5}[/tex] [tex]-\frac{5}{x - 3}[/tex]

In conclusion the partial fractions are   [tex]\frac{6}{x - 5}[/tex] [tex]-\frac{5}{x - 3}[/tex]

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Answer:

$26.33

Step-by-step explanation:

Answer:272

Step-by-step explanation:

Answer:

Luis had to make a $420 down payment

Step-by-step explanation:

10%: $2,100 / 10 = $210

20%: $210 x 2 = $420

Step-by-step explanation:

4x² + 12x + 8 = 0

this has the same solutions as

x² + 3x + 2 = 0

as we simply divided everything by 4. 0/4 = 0.

the general solution to such a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case that is

x = (-3 ± sqrt(3² - 4×1×2))/(2×1) =

= (-3 ± sqrt(9 - 8))/2 = (-3 ± sqrt(1))/2

x1 = (-3 + 1)/2 = -2/2 = -1

x2 = (-3 - 1)/2 = -4/2 = -2

so, the 2 solutions are

x = -1

or

x = -2

Answer:

d = 15

Step-by-step explanation:

(-5, 4), (4, -8)

(x₁, y₁)   (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(4 - (-5))² + (-8 - 4)²

d = √(4 + 5)² + (-12)²

d = √(9)² + (-12)²

d = √81 + 144

d = √225

d = 15

I hope this helps!

The time that initial investment be doubles is 20 year.

What is compound interest?

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest. It is the result of reinvesting interest, or adding it to the loaned capital rather than paying it out, or requiring payment from borrower, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.

Compound interest = principal (1+r/100)^n

compound interest = 3800.

3800 = 1900(1+3.5%)^n

3800/1900 = 1.035^n

taking natural log

ln(2) = n ln(1.035)

n = ln(2)/ln(1.035)

n = 20.15

Hence, time is 20 years.

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Answer:

supplementary angles

Step-by-step explanation:

1.) angle 1& angle 2 is supple. angle 2 & and angle 3 is supple.; given

2.) measure of angle 1+ measure of angle 2= 180, measure of angle 2+ measure of angle 3=180; Def. of Supple.

3.) measure of angle 1+ measure of angle 2 = measure of angle 2+measure of angle 3; Transitive

4.) measure of angle 1= measure of angle 3; Subtraction prop. of equality

5.) measure of angle 1 is congruent to measure of angle 3; Def. of Congruence

Answer:

y=4x+1

Step-by-step explanation:

Our slope is 4/1 or 4, so we know 4x is our slope. Then our y intercept is at (0,1), so we know our b=1. So we know our equation is y=4x+1.

-Hope this helped.

The amount in the account is $3499. 2

The formula for determining compound interest is given as;

A = P ( 1 + r/ n) ^nt

Given that;

Substitute the values into the formula, we have;

A = $3000 ( 1 + 0. 04 / 0. 5) ^(0.5× 4)

Find the exponential value

A = $3000 ( 1 + 0. 04 / 0. 5) ^2

A =  $3000( 1+ 0. 08)^2

Expand the bracket, we get;

A = $3000 (1. 08)^2

A = $3000(1. 17)

multiply through

A = $3499. 2

Hence, the value is $3499. 2

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Answer:

Step-by-step explanation:

You want the measures of the named angles in the given figure, given c=30°.

A right angle is 90°.

A linear pair totals 180°.

Vertical angles are congruent.

Angles that make up a right angle total 90°.

Angle 'a' is marked as a right angle, so a = 90°.

Angle b is complementary to angle c, so is ...

  b + c = 90°

  b = 90° -c = 90° -30° = 60°

Angle c is given as 30°.

Angle d is part of a linear pair with angle c, so is ...

  d = 180° -30° = 150°

Angle e is a vertical angle with respect to angle c, so is congruent to it.

  e = 30°

Answer:

116.

Step-by-step explanation:

Your welcome <3.

Answer:

116

Step-by-step explanation:

Answer:(1)  y-intercept exists 490 and the slope is -2/3x.

(2) First, I observe the point (0,490) and plot a point there. Then utilize our slope -2/3 to compute the direction and angle the line moves by measuring 2 down and 3 to the right.

(3) The equation of the function is

The diagram illustrates how many wraps could've been sold for each number of sandwich sales to maintain the identical earnings of $1,470.

(4) The graph of the equation is shown below.

(5) The profits exist the same (slope) but the y-intercept is more increased than the actual diagram.

(6) The equation is

Step-by-step explanation:

(1)

slope-intercept form of a linear equation is where one side includes only "y".

⇒

⇒

Therefore,

.

Hence, the y-intercept exists at 490 and the slope is -2/3x.

(2)  

I would graph this line using the slope-intercept method First, I observe the point (0,490) and plot a point there. Then utilize our slope -2/3 to compute the direction and angle the line moves by measuring 2 down and 3 to the right.

(3)

The equation of the function is. The diagram illustrates how many wraps could've been sold for each number of sandwich sales to maintain the identical earnings of $1,470.

(4)

The graph of the function is shown below,

(5)

Therefore,

The profits exist the same (slope) but the y-intercept is more increased than the actual diagram.

(6)

y intercept= 300

The equation will be,

Answer:

D. The denominator means three out of five are shaded

Answer: 21

Step-by-step explanation:

To simplify this, we would use Order of Operations (BEDMAS)

So, to simplify 3 + (3-8)^2 -7 we will follow the order of Operations

[tex]3 + (3-8)^{2} - 7\\3 + (-5)^{2} - 7\\3 + 25 - 7 \\28 - 7\\21[/tex]

So the answer is 21

The arithmetic sequence has the 73rd term of 306

The sequence is given as:

18,22,26,30,....

The above sequence has the following parameters

This means that the sequence is an arithmetic sequence

The nth term of an arithmetic sequence is calculated as

f(n) = a + (n - 1) * d

Substitute the known values in the above equation

So, we have the following equation

f(73) = 18 + (73 - 1) * 4

Evaluate

f(73) = 306

Hence, the 73rd term for the arithmetic sequence is 306

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He needs to buy 7 bags of fertilizer to fertilize the garden

The radius of the garden = 10 feet

The area of the garden A = π × [tex]r^2[/tex]

Where A is the area of the garden

r is the radius of the garden

Substitute the values in the equation

A = π × [tex]10^2[/tex]

= π × 100

= 314.16 feet square

Each bag of fertilizer covers 50 square feet

Then the number of bags required to fertilize the garden = The area of the garden / 50

Substitute the values in the equation

= 314.16 / 50

= 6.28

≈ 7 bags

Hence, he need to buy 7 bags of fertilizer to fertilize the garden

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The crate's density in pounds per cubic foot?

Since the crate of medicine with a density of 2050 kilograms per cubic meter will be shipped from England to the U.S, we require its density in pounds per cubic foot.

To do this, we convert the density in kilograms per cubic foot to pounds per cubic foot by using the ratios of conversion given

Since the density of the crate in kilograms per cubic meter is

2050 kg/m³, using the conversion ratios, we have

2050 kg/m³ = 2050 kg/m³ × 1 m³/35.3 ft³ × 2.2 lb/kg

= 4510 lb/m³ × 1 m³/35.3 ft³

= 127.76 lb/ft³

So, crate's density is 127.76 lb/ft³

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The exponential function relating time and money will be y = 200 (1.05)ˣ. Then the correct option is A.

Consider the function:

y = a (1 + r) ˣ

Where x is the number of times this growth occurs, a = initial amount, and r = fraction by which this growth occurs.

Leticia contributes $200 at 5% interest. Assuming that y addresses how much cash after x time spans.

Then the exponential equation is written as,

y = 200(1 + 0.05)ˣ

y = 200 (1.05)ˣ

The exponential function relating time and money will be y = 200 (1.05)ˣ. Then the correct option is A.

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Answer:

15h >= 200

>= means greater than or equal to. Just but a horizontal line underneath the >

The graph of inequalities equation on coordinate plane is given below ↓↓↓

Difference between equality and inequality equations

Both mathematical phrases, equality and inequality , are created   by connecting two expressions.The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols show that the two expressions in an inequality are not always equal: >, <, ≤ or ≥. Or in simple words the equation which has '=' sign is an equality equation while the inequality equation has the signs are >, <, ≤ or ≥.

The inequalities equation is ,

y> 2x+4

x+y≤6

so, the graph is ↓↓↓

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