r(x) = x^2 + 5x + 4 write r(x) in factored form. I would like an explanation as to how you get the answer please!

This mean there are infinite solutions.

Each side is equally satisfied in an endless solution. Infinite is a symbol for boundlessness or limitlessness. Typically, the sign "" is used to denote it.

Solving an equation, Henry gets to the last line of his work and is left with “3 = 3”.

Any value for the Variable would make the equation true, according to infinite solutions.

We can tell which instance it is by examining our findings. If both sides of the equal sign end up having the same word,

such as

3=3 or 3x=3x, then. Finite solutions exist.

This mean there are infinite solutions.

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Answer:

see below

Step-by-step explanation:

A prime number is a whole number that cannot be exactly divided by another number other than itself and 1.

The two largest one digit prime numbers are 7 and 5. The product of them is 7×5=35.

The two largest two digit prime numbers are: 89 and 97.

89×97=8633

The significant figure by multiplying 101 with 52 is 5000.

Here given,

101 x 52

Round 101 to 100 and 52 to 50, then multiply together to get 5000.

Significant Figures: 1

Decimals: 0

The significant notation: 5e+3

Therefore the significant notation is 5000.

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The complete equation in the slope-intercept form is y = 4x-1.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

So, the equation is,

y - y₁ = m (x - x₁)

And the standard form of the slope-intercept form:

y = mx+b,

where m is the slope and b is the y-intercept.

From the question, we have

m = 4 and coordinates of b is (0, -1).

So, the equation is,

y + 1 = 4 (x - 0)

y +1 = 4x

y = 4x-1

Therefore, the equation is y = 4x-1.

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The equation of the line, in slope-intercept form,  that passes through the given points, (6,-4) and (6,5) is: x = 6.

An vertical line can be written in slope-intercept form as x = a, because the line has no y-intercept and the change in x values in the slope formula is equal to zero.

The value of a in the equation is the point on the x-axis where the vertical line intercept, irrespective of the change in y-values up the line.

Given the line goes through the points, (6, -4) and (6, 5), it means the line is a horizontal line because they both have the same x-value, 6.

Therefore, the value of a is 6. The equation of the line would be x = 6.

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The orientation of ABCD is clockwise, as is the orientation of A'B'C'D'. This means the transformation involves a even number of reflections (may be 0).

Does the order of transformations matter in functions?

Order is not important. According to algebra, y=12f (x3). Our four transformations are (1), (3), (2), and (4); all four are in the x direction. When we combine a stretch and a translation in the same direction, the sequence counts.

The orientation of AB is North, and the orientation of A'B' is West, so a rotation of 90° CCW (or equivalent) is involved. We can find the point of intersection of the perpendicular bisectors of AA' and BB' (at (-1, -1)) to determine a suitable center of rotation.

ABCD can be transformed to A'B'C'D' by ...

rotation 90° CCW about the point (-1, -1)

Rotation by 90° can also be accomplished by reflection across a diagonal line. Since we want the orientation to remain unchanged, we need another reflection to put the figure into its final position. A suitable alternate sequence for mapping ABCD to A'B'C'D' is ...

reflection across the line y=x

reflection across the line x=-1

Complete question: A.) Describe a transformation sequence that will transform quadrilateral ABCD into quadrilateral A’B’C’D’.

b.) There is more than one way to transform quadrilateral ABCD into quadrilateral A’B’C’D’. Describe a second sequence of transformations that will accomplish this goal. Explain what tool you used as an aid in identifying a transformation sequence.

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The only two options with equations that are true for x = –2 and x = 2 are;

Option A: x² - 4 = 0

Option D: 4x² = 16

The domain of a function is the set of all input values  for which the function is possible.

Now, we are given the domain values as  x = –2 and x = 2.

a) x² - 4

f(-2) = (-2)² - 4

= 0

f(2) = (2)² - 2

= 0

b) x² = -4

f(-2) = (-2)²

= 4

f(2) = (2)²

= 4

c) 3x² + 12

f(-2) = 3(-2)²  + 12

= 24

f(-2) = 3(2)²  + 12

= 24

d) 4x²

f(-2) = 4(-2)²

= 16

f(2) = 4(2)²

= 16

e) 2(x - 2)²

f(-2) = 2(-2 - 2)²

= 32

f(2) = 2(2 - 2)²

= 0

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The total cost of the meal plus tip and tax was more than 122% of the cost of the bill.

What is percent?

A percentage in mathematics is a number or ratio that is expressed as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, though the percent sign, "%," is most frequently used. A percentage has no dimensions and no standard measurement.

Indigo goes out to lunch.

The bill, before tax and tip, was $10.85.

A sales tax of 3% was added on.

Indigo tipped 18% on the amount after the sales tax was added.

The amount after adding sales tax is,

$10.85 x 3% = 0.3255

⇒ $10.85 + 0.3255 = $11.1755

Now to find the amount after tipped 18% on the amount after the sales tax was added.

$11.1755 x 18% = 2.01159

⇒ $11.1755 + 2.01159 = $13.18709

Hence, the amount  after tipped 18% on the amount after the sales tax was added is $13.18709.

Let x be the percent of more than the cost of the bill of $13.18709.

⇒

[tex]\frac{10.85(x)}{100} = 13.18709\\ x = \frac{100 (13.18709)}{10.85}\\ x = 121.54[/tex]

Hence, the total cost of the meal plus tip and tax was more than 122% of the cost of the bill.

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Answer:

the coordinates of the other corner are (-10/3, -1 3/4).

The four ordered pairs that represent the corners of Maya's rectangular driveway are (-1, 1), (1 1/2, -8 1/2), (-10/3, -1 3/4), and (1 1/2, -1 3/4).

Step-by-step explanation:

To plot the other two corners of Maya's rectangular driveway, we need to determine the coordinates of the points that are diagonally opposite to the points (-1, 1) and (1 1/2, -8 1/2).

Since the points (-1, 1) and (1 1/2, -8 1/2) are diagonally opposite, we can draw a line through the center of the rectangle that is perpendicular to the line connecting these two points. The center of the rectangle can be found by averaging the x-coordinates and the y-coordinates of the two points. The x-coordinate of the center is (-1 + 1 1/2)/2 = 1/4 and the y-coordinate of the center is (1 + -8 1/2)/2 = -3 3/4.

We can then use the center of the rectangle and the slope of the line connecting (-1, 1) and (1 1/2, -8 1/2) to find the coordinates of the other two corners. The slope of the line is (-8 1/2 - 1)/(1 1/2 - (-1)) = -17/3, so the slope of the line perpendicular to it is -3/17.

We can use this slope and the center of the rectangle to find one of the remaining corners by moving a fixed distance in the y-direction from the center. For example, if we move 2 units in the positive y-direction from the center, we will reach the point (1/4, -3 3/4 + 2) = (1/4, -1 3/4). We can then use the slope of the line to find the x-coordinate of the other corner by solving the equation y = mx + b for x, where m is the slope, x is the x-coordinate of the corner, y is the y-coordinate of the corner, and b is the y-intercept. The y-intercept is the y-coordinate of the center, so we can solve the equation as follows:

y = -3/17 * x + (-3 3/4)

x = (y - (-3 3/4))/(-3/17)

Substituting the coordinates of the corner we found earlier, we get:

x = (-1 3/4 - (-3 3/4))/(-3/17) = (2)/(-3/17) = -10/3

So, the coordinates of the other corner are (-10/3, -1 3/4).

The four ordered pairs that represent the corners of Maya's rectangular driveway are (-1, 1), (1 1/2, -8 1/2), (-10/3, -1 3/4), and (1 1/2, -1 3/4).

Answer:

Solve the equation for [tex]{y}[/tex].

[tex]y=\frac{5x}{2}[/tex]

Choose any value for [tex]{x}[/tex] that is in the domain to plug into the equation.

Choose [tex]{0}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.

[tex]{(0,0)}[/tex]

Choose [tex]{1}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.

[tex](1,\frac{5}{2})[/tex]

Choose [tex]{2}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.

[tex]{(2,5)}[/tex]

These are three possible solutions to the equation.

[tex]{(0,0),}[/tex] [tex](1,\frac{5}{2} )[/tex], [tex]{(2,5)}[/tex]

Answer: Y=mx+b

Step-by-step explanation:

The conclusion is that the angle which measures 120° is not Acute angle.

The construction of an angle is a type of geometric shape made by connecting two rays at their termini. Three letters that make up the form of the angle can alternatively be used to symbolise the angle, with the middle letter indicating the location of the angle (i.e.its vertex). Greek characters such θ, α, β, etc. are frequently used to denote angles.

In geometry, there are mainly six different kinds of angles. All angles have the following names and characteristics:

Angle B measures 120°.

Here the angle is more than 90° so the angle is not acute.

The conclusion is that the angle which measures 120° is not Acute angle.

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Answer:

Step-by-step explanation:

You want the length of the hypotenuse of a right triangle with sides given as 3.6×10⁶ km and 1.6×10⁷ km.

The Pythagorean theorem tells you the relationship between the side lengths and the hypotenuse of a right triangle:

  c² = a² +b²

  RQ² = PQ² +PR²

  RQ = √((3.6×10⁶)² +(1.6×10⁷)²) = 1.64×10⁷ . . . . . use numbers, take the root

The distance between planets Q and R is 1.64×10⁷ km.

__

Additional comment

The "standard form" of a number is different by location. In the US, it is written with the decimal point to the right of the units digit. In other places, "standard form" has the decimal point to the right of the most-significant digit, and a power of ten as a multiplier.

You may recognize the ratio of the given numbers is 9:40, telling you these lengths are a multiple of the {9, 40, 41} Pythagorean triple. That is, the distance RQ is 41/40 times the distance RP.

Any spreadsheet or scientific or graphing calculator can do the necessary arithmetic using the numbers in "scientific notation" format. Spreadsheets, in particular, use E() to signify ×10^(). That is, 3.6×10⁶ is entered into a spreadsheet as 3.6E6. The attached calculator display shows it can use the same sort of format.

Just use Pythagoras theorem to find the shortest distance between the two planets, (as it is along its hypotenuse)

The distance QR is :

[tex] \qquad \sf \rightarrow d = \sqrt{(1.6 \times 10 {}^{7}) {}^{2} + (3.6 \times 10 {}^{6} ) {}^{2} } [/tex]

[tex] \qquad \sf \rightarrow d = \sqrt{2.56 \times 10 {}^{14} + 12.96 \times 10 {}^{12} {}^{} } [/tex]

[tex] \qquad \sf \rightarrow d = \sqrt{256\times 10 {}^{12} + 12.96 \times 10 {}^{12} {}^{} } [/tex]

[tex] \qquad \sf \rightarrow d = \sqrt{(256 + 12.96 )\times 10 {}^{12} {}^{} } [/tex]

[tex] \qquad \sf \rightarrow d = \sqrt{(268.96 )\times 10 {}^{12} {}^{} } [/tex]

[tex]\qquad \sf \rightarrow d = 16.4\times 10 {}^{6} {}^{} [/tex]

Answer: The answer is $s$ > 7, which represents the number of seconds that can pass for the temperature in the cryotherapy chamber to drop below -20°F.

Step-by-step explanation: The temperature in the chamber will drop below -20°F when it reaches -20°F + 2.5°F = -17.5°F.

The temperature in the chamber is currently 0°F, so we can represent this situation with the inequality 0 - (2.5 * $s$) < -17.5, where $s$ is the number of seconds that can pass.

We can simplify this inequality by multiplying both sides by -1 to get the following: 2.5 * $s$ > 17.5.

Dividing both sides by 2.5, we get the final inequality: $s$ > 7.

Therefore, the number of seconds $s$ that can pass for the temperature in the cryotherapy chamber to drop below -20°F is greater than 7 seconds.

The given exponential function represents the growth in the function. The percentage of growth (increase) is 1%.

An exponential growth function is a function where the quantity increases slowly and after some time, it increases rapidly.

It is represented by the formula,

y = a(1 + r)ˣ

Here the term 'a' is the initial amount of the quantity, the term 'r' is the rate of increase and the term 'x' is the period.

The given exponential function is y = 10(1.01)ˣ

Here we can write the function as

y = 10(1.01)ˣ

⇒ y = 10(1 + 0.01)ˣ

Since 1.01 > 1, it is an exponential growth function.

So, when comparing with the formula, we get the rate of increase,

r = 0.01

Converting it into fractions, we get 1/100

Then, the percentage rate of increase is 1%.

Therefore, the given exponential function grows with a rate of 1% increase.

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The proof for the Base Angles Theorem is explained below:

A triangle's opposite angles are congruent if its two sides are congruent. We shall build the angle bisector through the vertex angle of an isosceles triangle in order to demonstrate the Base Angles Theorem. We created two congruent triangles by building the angle bisector, and then we utilized CPCTC to prove that the base angles are congruent. Base angles: The angles that include the base of an isosceles triangle are known as the "base angles."

Any triangle with at least two congruent sides is said to be isosceles. Legs are the isosceles triangle's congruent sides. The base is the other side. Base angles are the angles formed between the base and the legs.

Given: [tex]\bar{ LM}[/tex]≅ [tex]\bar{LN}[/tex]

Prove: ∠M≅∠N

According to the figure,

Given,

[tex]\bar{ LM}[/tex]≅ [tex]\bar{LN}[/tex]

By the definition of mid-point,

O is the mid-point of [tex]\bar{MN}[/tex]

Now, by joining the two points determine and draw a line of [tex]\bar{LO}[/tex]

Now, Again by the definition of mid-point

[tex]\bar{MO}[/tex]≅[tex]\bar{NO}[/tex]

Now, by using reflexive property,

[tex]\bar{LO}[/tex]≅ [tex]\bar{LO}[/tex]

By SSS rule,

ΔLMO≅ΔLNO

By CPCTC rule,

∠M≅∠N

Hence proved.

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The value of x for the expression is equal to -5 and -2.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the logarithmic expression is log₂ (x+4) + log₂ (x + 3) = 1. The value of x will be calculated as,

log₂ (x+4) + log₂ (x + 3) = 1

log₂ { (x+4)(x + 3) } = 1

x² + 7x + 12 = 2

x²+ 7x + 10 = 0

Solve the above quadratic equation,

x²+ 7x + 10 = 0

x² + 5x + 2x + 10 =0

x ( x + 5 ) + 2 ( x + 5 ) = 0

(x + 5 ) ( x + 2 ) = 0

x  = -5 and -2

The values of x are -5 and -2.

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The amount of margarine needed in Kg for making biscuits is  0.6kg

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole.

According to the definition of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilized.

The amount of margarine needed in Kg is calculated using proportions

If 225 ml or soup requires 150 g of margarine then 0.9 liters of soup will require

0.225 l  = 0.15 kg

0.9 l = ?

cross multiplying

0.225 * ? = 0.9 * 0.15

? = 0.135 / 0.225

? = 0.6

Angela will require 0.6 kg of margarine

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The points where the inequality x+ 5y <-30 intercepts is ( 30, 0 ) and (0,6).

Here given the inequality.

x + 5y ≤ 30

To find the x-intercepts.

We have to substitute 0 for y and solve x to determine the x-intercepts.

x + 5 × 0 = 30

By solving the equation.

x = 30

( 30, 0 ) is the x-intercepts.

To find the y-intercepts.

By substituting 0 for x and solving y will get the y-intercept(s).

0 + 5y = 30

5y =30

y = 30/5

y = 6

In the point form, y-intercept.

Y-intercept(s): ( 0, 6 )

(30, 0) is the x-intercept.

Y-intercepts at : ( 0, 6 ).

The points in which the inequality x+ 5y <-30 intercepts is (30, 0) and (0,6).

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As AB is the perpendicular bisector of IK so we conclude that the right option is AJ=BJ.

A precise drawing in which a line is split in half by another line that is at a 90-degree angle to the original line is known as a perpendicular bisector. To divide into two equal portions is to bisect. When two lines intersect at a straight angle, they are perpendicular.

A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.

Option J can not be true as A can not be the midpoint of IK as A is not on IK.  Because J is on the IK as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. Hence, J is assumed as the midpoint of IK.

Option H i.e IJ = JK can not be true because AJ does not necessarily equal to BJ.

Option G i.e m∠IAJ  also does not true necessarily true. The reason is simple i.e AJ is arbitrary.

So, Option f i.e AJ = BJ is the correct Answer as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. So it can be assumed that that J is the midpoint as but it doesn't necessarily mean that IJ = JK, also it is true that perpendicular lines meet at 90 degree. Hence, statement F i.e AJ = BJ  is true.

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As AB is the perpendicular bisector of IK so we conclude that the right option is AJ=BJ.

What is perpendicular bisector?

A precise drawing in which a line is split in half by another line that is at a 90-degree angle to the original line is known as a perpendicular bisector. To divide into two equal portions is to bisect. When two lines intersect at a straight angle, they are perpendicular.

What is the perpendicular of two points?

A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.

Option J can not be true as A can not be the midpoint of IK as A is not on IK.  Because J is on the IK as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. Hence, J is assumed as the midpoint of IK.

Option H) i.e IJ = JK can not be true because AJ does not necessarily equal to BJ.

Option G)  i.e  m∠IAJ  also does not true necessarily true. The reason is simple i.e AJ is arbitrary.

So, Option f)  i.e AJ = BJ is the correct Answer as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. So it can be assumed that that J is the midpoint as but it doesn't necessarily mean that IJ = JK, also it is true that perpendicular lines meet at 90 degree. Hence, statement F i.e AJ = BJ  is true.

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z-score of a value is  -5.96

What is z-score in binomial distribution?

The Z score represents the number of standard deviations above or below the mean. The Z score of the mean is 0 by definition.

What is Probability?

The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions.

Given,

A random variable, let's call it X, has parameters that fit the Binomial distribution: n (number of trials) = 50 and p (success probability) 0.76.

We must ascertain the z-score (Z) of the value 20 =  that this random variable X has chosen.

Now, for a random variable, say X, its z-score (Z) is defined as ,

Z = (X - mean of X)/ Standard deviation of X

A binomial random variable with the parameters once more n and p, its mean is given as np and its standard deviation is given as [tex]\sqrt{n*p*(1-p)}[/tex]

The standard deviation of X is provided as [tex]\sqrt{50*0.76*0.24}[/tex] = [tex]\sqrt{9.12}[/tex] = 3.0199933  while the mean of X is given as 50*0.76 = 38.

Therefore, the required z-score (Z) for X = 20, is given as,

Z = 20-38/3.0199933

Z= -5.9602781238

Z= -5.96 that is the necessary z-score.

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The carbinet has rectangular floor plan where the length is equal to 5 feet more than twice the width.  The the expression that represents the area in square feet is Option B 2w²+5. ∧where w is the width

The area of the rectangle is the floor space the rectangle can occupy at a given time.

The given parameters are

L= 2w+5

The width = w

Then area is given by the formula

A=L*W

A=2w*w+5

Simplify the expression you have

A=2w²+5 where w is the width

Therefore the area is b. 2w²+5, where w is the width

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Answer:

Step-by-step explanation:

it is c

Answer:

$9,712.12 (nearest cent)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies A=9544\left(1+\frac{0.0525}{12}\right)^{12 \cdot \frac{1}{3}}[/tex]

[tex]\implies A=9544\left(1.004375\right)^{4}[/tex]

[tex]\implies A=9544\left(1.017615179\right)[/tex]

[tex]\implies A=9712.119269[/tex]

The balance of the account at the end of August will be $9,712.12 (nearest cent).

The function g(x) = (x - 5)² has a translation of 5 units to the right.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over x-axis, (-x, y).

-f(x) = Reflection over y-axis, (x, -y).

The parent function is a quadratic f(x) = x².

Now, The transformed function g(x) = (x - 5)² is a horizontal transformation of 5 units to the right.

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Answer:

(2½,1)

Step-by-step explanation:

(-1+6/2,5+-3/2)

(5/2,2/2)

(2½,1)

A z-score tell us about an individual observation in a data set is, the number of standard deviations an observation is away from the mean.

The value of the z-score tells you how many standard deviations you are away from the mean. If a z-score is equal to 0, it is on the mean. A positive z-score indicates the raw score is higher than the mean average. For example, if a z-score is equal to +1, it is 1 standard deviation above the mean.

A z-score is the value of an observation expressed in standard deviation units. The sign of the score indicates whether it is above (positive) or below (negative) the mean, and the value quantifies how many standard deviations the score is from the mean.

The purpose of z-scores is to identify and describe the exact location of each score in a distribution & to standardize an entire distribution to understand & compare scores from different tests.

Z-scores or Z-statistics represent a statistical technique of measuring the deviation of data from the mean. There are different formula used for Z-score or Z-statistics depending upon what is measured. Z-statistics is generally used with Z-test which is a hypothesis testing statistical technique.

Therefore,

A z-score tell us about an individual observation in a data set is, the number of standard deviations an observation is away from the mean.

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Answer:

22

Step-by-step explanation:

Y is midpoint of WR.

Hence,

YR = 1÷2 of WR ( Half of WR )

So,

WR = 2YR

= 2×11

= 22

The solution of the equation is x = 6±2√11.

What is a quadratic equation?

The quadratic formula in elementary algebra is a formula that yields the answer to a quadratic problem. In addition to the quadratic formula, other methods of solving quadratic equations include factoring, completing the square, graphing, and others.

Here, we have

Given: x² - 12x = 8

Now, we factorize the given equation and find the solution.

x² - 12x = 8

x² - 12x - 8 = 0

We apply here the quadratic formula.

= (-b ±√b²-4ac)/2

= (12 ±√12²-4×1×(-8))/2

= (12±√144+32)/2

= (12±√176)/2

= (12±4√11)/2

= 6±2√11

Hence, the solution of the equation x² - 12x = 8 is 6±2√11.

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The surface area of the triangular prism is 136 square units

From the question, we have the following parameters that can be used in our computation (see attachment):

The surface area of the triangular prism is the sum of the areas of the above shapes

So, we have

Surface area = 2 * area of rectangle 1 + 1 * area of rectangle 2 + 2 * area of triangle 1

Substitute the known values in the above equation, so, we have the following representation

Surface area = 2 * 7 * 5 + 1 * 7 * 6 + 2 * 0.5 * 4 * 6

Evaluate

Surface area = 136

Hence, the surface area is 136 square units

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