Evaluate each expression for a=3 and b=-5 . 3(a-b)

The maximum distance up the wall the ladder will reach = 19.4 ft

The total length of the ladder, L = 20 ft

Minimum distance of the base of the ladder to the wall, B = 1/4 x 20 = 5 ft

Now we need to find the maximum distance up the wall the ladder will reach. This is obtained when the base distance is the least.

i.e., when the base = 5 ft.

Now the ladder, the wall and the base distance between wall and ladder constitute a right triangle. In this right triangle, the ladder is the hypotenuse and the height of the wall up to which ladder reach, 'x' is its altitude with base = 5ft.

Then using Pythagoras theorem,

    [tex]L^2 = B^2 +x^2[/tex]

⇒ [tex]x^2 = L^2 - B^2 = 20^2 - 5 ^2[/tex]

⇒ [tex]x^2 = 375[/tex]

⇒ [tex]x=\sqrt{375}[/tex] = 19.3649

When rounded to the nearest tenth, (i.e., only one decimal place),we get,

⇒ x = 19.4 ft

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Answer:

5y =x-15

Step-by-step explanation:

yes

The equation of the line is y = -3x/5 + 1 that passes through (5, −2), and is perpendicular to y = (5/3)x - 3.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that:

The line passes through (5, −2) and is perpendicular to y = (5/3)x - 3

The slope of the line y = (5/3)x - 3

m = 5/3

The slope of the line perpendicular to the above line:

M = -3/5

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

The equation of the line

y + 2 = (-3/5)[x - 5]

y = -3x/5 + 1

Thus, the equation of the line is y = -3x/5 + 1 that passes through (5, −2), and is perpendicular to y = (5/3)x - 3.

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Answer:

Negative. Because he should run all seven weeks to get positive result.

The geometric mean between pair of numbers 7 and 11 is 8.77

We know that for a sequence of numbers x1, x2,.., xn

The formula of geometric mean is,

[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]

In this question, we have been given two numbers 7 and 11

We need to find the geometric mean between pair of numbers, 7 and 11.

Using the formula for the geometric mean,

[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]

In this question, we have two numbers.

So, the value of n is 2.

[tex]\Pi=\sqrt{7\times 11}\\\\ \Pi=\sqrt{77}\\\\ \Pi=8.77[/tex]

Therefore, the geometric mean between pair of numbers 7 and 11 is 8.77

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Answer: The prime factorization of 16 is 2 × 2 × 2 × 2, hence, the cube root of 16 in its lowest radical form is expressed as 2 ∛2.

Cube Root of 16.

Step-by-step explanation:

The solution for the cube root of 16 as a power of 2 is,

⇒ ∛16 = 2 ∛2

We have to given that,

To find the cube root of 16 as a power of 2.

The prime factorization of 16 are,

16 = 2 x 2 x 2 x 2

Take cube root,

⇒ ∛16 = ∛2 x 2 x 2 x 2

⇒ ∛16 = 2 ∛2

Therefore, The solution for the cube root of 16 as a power of 2 is,

⇒ ∛16 = 2 ∛2

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Answer:181/2

Step-by-step explanation:

90.5 as a fraction is 181/2

We conclude that MN ≅ RS under the rule in which if a = b, and b = c; then automatically a = c.

So,

Given: MN ≅ PQ, PQ ≅RS

To Prove: MN ≅ RS

This rule satisfies the above condition.

Therefore, MN ≅ RS under the rule in which if a = b, and b = c; then automatically a = c.

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With a rate of $425/day, Sherry McCoy's gross income for the year, working 180 days, is $76,500.

Gross income refers to the total salary or wages and other form of earnings before any deductions or taxes.

If as a tax consultant, Sherry McCoy charges $425 per diem for her services, then her rate is $425/day.

Rate is a ratio that compares two different quantities which have different units.

We will use this rate to find how much earnings she got if she worked for 180 days last year.

gross income = rate x time

gross income = $425/day (180 days)

gross income = $76,500

Hence, working 180 days last year, Mary has a gross income of $76,500.

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Answer:

9-x

Step-by-step explanation:

Answer:16

Step-by-step explanation:

Answer: width = 12 inches

length =  28 inches

Step-by-step explanation:

l = 4 + 2w

Perimeter = 2 ( l + w  )

80 = 2 ( 4 + 2w + w )

80 = 2 ( 4 + 3w )

80 = 8 + 6w

80 - 8 = 6w

72 = 6w

w = 72 / 6

width = 12 inches

length = 4 + 2 (12)

= 4 + 24

= 28 inches

checking

Perimeter = 2 ( 28 + 12 )

= 2 (40)

= 80 inches

correct

The actual length, if the length of the model is 10 ft and the scale factor is greater than one is Option(b) 9.5 ft.

The basic formula to find the scale factor of a figure is as:

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given:

length of the model = 10 ft

Now we determine which actual length has a scale factor greater than one.

(a) Scale factor = (10/10)

Here, we can see that the scale factor is equal to 1.

(b) Scale factor = (10/9.5) = 1.05

Here, we can see that the scale factor is greater than 1.

(c) Scale factor = (10/12) = 0.83 ( 1 yard = 3 foot)

Here, we can see that the scale factor is less than 1.

Therefore, the actual length is 9.5 ft.

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The given rational and irrational numbers can be ordered from least to greatest as follows; -2 3/5 < 10/3 < 3 7/8 < 3.9 < √20.

It follows from the task content that the numbers given are rational and irrational numbers.

To order the numbers, they should be converted to decimal numbers as follows;

Hence, the order from least to greatest is; -2 3/5 < 10/3 < 3 7/8 < 3.9 < √20.

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Answer:

x = 5

Step-by-step explanation:

3(x + 7) + 4 = 40 ( subtract 4 from both sides )

3(x + 7) = 36 ( divide both sides by 3 )

x + 7 = 12 ( subtract 7 from both sides )

x = 5

As a check

substitute x = 5 into the left side of the equation and if the value obtained is equal to the right side (40) then it is a solution

3(5 + 7) + 4

= 3(12) + 4

= 36 + 4

= 40

left side = right side

then x = 5 is the solution to the equation

A scalene triangle has at least two congruent sides is a FALSE statement.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.

In a triangle, the sum of all three angles is 180°

Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.

A scalene triangle is a triangle whose all sides are unequal.

Since congruent sides are the sides that are equal in length but in a scalene triangle, none of the sides are equal to each other.

Hence "A scalene triangle has at least two congruent sides is a FALSE statement".

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The equation in slope-intercept form y = 4/3 x + 4/3 contains the points (-1 , 0) and (2 , 4).

An equation of a line in slope-intercept form is given by the formula y = mx+ b, where m is the slope of the line and b is the y- intercept.

If you know two points on a line, you can use them to write the equation of the line in slope-intercept form.

First is to find the slope of the line using the two given points.

let Point 1(-1 , 0) and Point 2(2 , 4)

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

m = (4 - 0) / (2 - -1)

m = 4/3

Next, use the slope and one of the points to find the value of the y-intercept, b. Plug in these values in the formula for slope-intercept form.

y = mx+ b

y = 4/3 x + b

Using Point 1,

0 = 4/3 (-1) + b

0 = -4/3 + b

b = 4/3

Finally, set up the equation of the line in slope-intercept form.

y = mx+ b

where m = 4/3 and b = 4/3

y = 4/3 x + 4/3

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The given series is an arithmetic series and its sum is 36.4

The summation or sigma notation is used to express long summation into a single formula.

The series, given in a summation notation, is:

     [tex]\sum\limits^{10}_{n=4} {(0.8n-0.4)}[/tex]

The formula inside the sum notation represent the nth term, a(n).

Let evaluate the terms for some n, starts from n = 4 as indicated by the lower limit of the summation notation:

a(4) = 0.8 (4) - 0.4 = 2.8

a(5) = 0.8 (5) - 0.4 = 3.6

a(6) = 0.8 (6) - 0.4 = 4.4

This form a new arithmetic series, with the first term, let say f(1) =2.8 and common difference, d = 0.8.

The number of terms in this new geometric series is given by the upper and lower limit of the summation notation:

number of terms = 10 - 4 + 1 = 7

Use the sum formula for an arithmetic series,

S(n) = n/2 [2.f(1) + (n - 1) . d]

Substitute n = 7, f(1) = 2.8, and d = 0.8 into the formula:

S(7) = 7/2 [2. (2.8) + (7 - 1) . (0.8)]

S(7) = 36.4

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A good way to find patterns in data is to arrange it in tabular form, which acts as an "input-output" machine.

A pattern in mathematics is a recurring arrangement of numbers, forms, colors, and other elements. Any kind of event or object can be connected to the Pattern.

A pattern is referred to as a rule or a way in which a group of numbers is related to one another. Sometimes a pattern is also referred to as a sequence.

Putting data into a tabular format, which functions as an "input-output" computer, is a useful way to find patterns. It will process an input value, return an output value, and take another value as an input.

The table's process column will make it easier to comprehend how input and output are related.

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Answer:

C

Step-by-step explanation:

a number is only divisible by 4, if the number formed by the last 2 digits is divisible by 4.

   The equation that defines the parabola with vertex at the point (3, 2) and focus at (4, 2) is:

(Y - 2)² = 16(X - 3)

  A parabola is a quadratic function that can move on any axis, it is composed of:

   The equation that defines a parabola can be given by:

  This will depend on its aperture

  In this case we have the vertex of the parabola at the point (3, 2) and the focus at the point (4, 2) this is displaced on the x-axis to the right, so the parabola is of the form X = Y²

(y - 2)² = 4p(x - 3)

Focus

f = (0 + p, 0)

(y - 2)² = 4*4(x - 3)

(Y - 2)² = 16(X - 3)

Y² - 4Y + 4 = 16X - 48
X = Y²/16 - Y/4 + 13/4

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Answer: g(4b)=12b+7

Step-by-step explanation:

g(x)=3x+7

g(4b)=3(4b)+7

g(4b)=12b+7

Answer:

$3.90

Step-by-step explanation:

Expected Value formula

[tex]\boxed{\displaystytle E(x)=\sum x_iP(x_i)}[/tex]

where:

Given table:

[tex]\begin{array}{l | ccccc}\sf Payout\:(\$) & 0 & 2 & 4 & 8 & 10\\\cline{1-6} \sf Probability & 0.35 & 0.2 & 0.1 & 0.2 & 0.15\end{array}[/tex]

Substitute the given values into the Expected Value formula:

[tex]\begin{aligned}\implies E(x) & = 0(0.35) + 2(0.2)+4(0.1)+8(0.2)+10(0.15)\\& = 0+0.4+0.4+1.6+1.5\\& = 3.9\end{aligned}[/tex]

Therefore, the expected value is $3.90.

So, on average, you would expect to receive $3.90 in winnings per game.

Answer:

[tex]\textsf{a)} \quad x = 63^{\circ}[/tex]

[tex]\textsf{b)} \quad \boxed{\begin{minipage}{8.5 cm}\sf The angle between the tangent and the radius at a point \\on a circle is $90^{\circ}$.\end{minipage}}[/tex]

Step-by-step explanation:

The triangle inside the circle is an isosceles triangle, since two of its sides are the radius of the the circle (and therefore equal in length).

Therefore, its two base angles are 27°.

A tangent is a straight line that touches a circle at only one point.

The tangent of a circle is always perpendicular to the radius.

[tex]\implies x + 27^{\circ} = 90^{\circ}[/tex]

[tex]\implies x +27^{\circ}-27^{\circ}= 90^{\circ} - 27^{\circ}[/tex]

[tex]\implies x = 63^{\circ}[/tex]

The circle theorem that allows the calculation of angle x is:

[tex]\boxed{\begin{minipage}{8.5 cm}\sf The angle between the tangent and the radius at a point \\on a circle is $90^{\circ}$.\end{minipage}}[/tex]

Answer:29.3 repeating

Step-by-step explanation:Just use

calculator

The image of the point after the translation is (-4, -1)

The point is given as

(1,4)

The translation is given as

Left 5 units and down 5 units

This is represented as

(x, y) = (x - 5, y - 5)

So, we have

(x, y) = (1 - 5, 4 - 5)

Evaluate

(x, y) = (-4, -1)

Hence, the image of the point after the translation is (-4, -1)

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The given polygons that is an equilateral triangle and scalene triangle can never be similar ,as it is not possible to map equilateral triangle onto scalene triangle or vice-versa.

As given in question,

Given polygons are equilateral triangle and scalene triangle

An equilateral triangle never similar to scalene triangle.

Reason:

Therefore, the given polygons that is equilateral triangle and scalene triangle can never be similar.

The complete question is:

Determine whether the given polygons are always, sometimes, or never similar. Explain your reasoning.

An equilateral triangle and a scalene triangle

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The compound inequality that describes Tammy's test score x 85 < x < 92 and Tammy's test score is between 85 and 92

The given parameters are

Sam's test score is between 100 and 107

This means that

100 < Sam's score < 107

From the question, we have:

Tammy scored about 15 fewer points.

This means that

Tammy = Sam - 15

So, we have

Sam = Tammy + 15

Where

Tammy = x

This gives

Sam = x + 15

So, we have

100 < x + 15 < 107

Subtract 15 from the sides of the inequality

So, we have

85 < x < 92

This means that the compound inequality that describes Tammy's test score x 85 < x < 92

In part (a) of this solution, we have the following compound inequality

85 < x < 92

The above compound inequality means that Tammy's test score is between 85 and 92

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Answer:

[tex] - 8 \times |2 = - 16| [/tex]

For the given inequality x+13<41, x is less than 28

Inequality involves two algebraic expressions linked by the signs of inequality. These signs include less than (<), greater than (>) or less than equal to (<=) and greater than equal to (>=).

Let's solve the inequality

x+13<41

Move the like terms on the same side

x< 41-13

x< 28

Therefore, x is less than 28

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