Seventh grade

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R. 4 Evaluate linear expressions UG6

Evaluate the expression for c = 2.

40 - 7 =

Submit

Answer:

The area of x is 4

The area of the right triangle is 6

Step-by-step explanation:

The Pythagorean Theorem can be used when dealing with right triangles. So, if we use the equation a^2 + b^2 = c^2, we can find that 3^2 + x^2 = 5^2 or 9 + x^2 = 25. If we calculate, we can find that x is equal to 4. Now if we multiply by 3 and divide by 2, we can get the answer of 6 as the area of the right triangle.

The flux of F across S will be [tex]\frac{3\Pi}{2}[/tex]

A vector of magnitude 1 that is at some point perpendicular to a two-dimensional curve is referred to as the unit normal vector. Normally, you search for a function that returns not just one vector but all potential unit normal vectors of a given curve.

A vector that is perpendicular to a surface at a certain location is known as the normal vector, also referred to as the "normal" to a surface. The inward-pointing normal (pointing toward the interior of the surface) and outward-pointing normal are often distinguished when normals are taken into consideration on closed surfaces.

[tex]$Z_x=-2 x: \quad Z_y=-2 y$[/tex]

[tex]$N=\langle 2 x, 2 y, 1\rangle \quad: f=\langle x, y, z\rangle$[/tex]

[tex]f. $N=2 x^2+2 y^2+z=2 x^2+2 y^2+1-x^2-y^2$[/tex]

=1+x^2+y^2

[tex]x^2+y^2=1\\ \Rightarrow \quad x=r \cos \theta\\ \Rightarrow \quad y=r \sin \theta \\ \Rightarrow x^2+y^2=r^2 \\ 0 < r < 1: \quad 0 < \theta < 2 \pi[/tex]

[tex]$R \cdot v=\int_0^{2 \pi} \int_0^1\left(1+r^2\right)(r) dr d \theta$[/tex]

[tex]$=2 \pi \int_0^1 r+r^3 d r$[/tex]

[tex]$2 \pi\left[\frac{r^2}{2}+\frac{r^4}{4}\right]_0^1$[/tex]

[tex]$=(2 \pi)\left(\frac{1}{2}+\frac{1}{4}\right)$[/tex]

[tex]$=\frac{(2 \pi)(3)}{42}=\frac{3 \pi}{2}$[/tex]

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Answer:

[tex]80^{\circ}[/tex]

Step-by-step explanation:

The interior angles of the triangle are [tex]70^{\circ}, (14+6x)^{\circ}[/tex], and [tex](3x-3)^{\circ}[/tex].

Angles in a triangle add to [tex]180^{\circ}[/tex].

[tex]70+14+6x+3x-3=180 \\ \\ 81+9x=180 \\ \\ 9x=99 \\ \\ x=11[/tex]

So, [tex]m\angle A=14+6(11)=80^{\circ}[/tex].

Answer:

10.5 inches, 14 inches, 7 inches

Step-by-step explanation:

Let's say x is the multiplier of the ratio value and the actual length of the sides:

1/4 * x = side 1

1/3 * x = side 2

1/6 * x = side 3

Since the perimeter is the sum of all sides, the perimeter is equal to:

31.5 = 1/4 * x + 1/3 * x + 1/6 * x  ==> 31.5 inches is the perimeter

(31.5 = x/4 + x/3 + x/6)*12  ==> multiply the equation by 12 since 12 is the

                                           LCM (Least Common Multiple) of 4, 3, and 6

12 * 31.5 = 12 * x/4 + 12 * x/3 + 12 * x/6  ==> multiply each term by 12

378 = 12x/4 + 12x/3 + 12x/6 ==> simplify

378 = 3x + 4x + 2x

378 = 9x

x = 378/9 ==> divide both sides by 9

x = 42

Now find each side length [Refer to the first three equations] :

Side length 1: 1/4 * 42 = 42/4 = 10.5 inches

Side length 2: 1/3 * 42 = 42/3 = 14 inches

Side length 3: 1/6 * 42 = 42/6 = 7 inches

Answer: 10.5 inches, 14 inches, 7 inches

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The following operations are used to transform the quadratic equation y = x² into parabolas in standard form:

Case 1

Horizontal translation, vertical translation. Horizontal stretch.

Case 2

Horizontal translation, vertical translation. Reflection in the x-axis, vertical stretch.

Case 3

Horizontal translation, vertical translation. Horizontal stretch.

In this question we find three cases of parabolas in standard form, that is, quadratic equations of the form:

y - k = a · (x - h)²

Where:

This parabola is translated both horizontally and vertically by using the following definitions:

Horizontal translation

x → x - a, where a > 0 for rightward translation.

Vertical translation

y → y - b, where b > 0 for upward translation.

Horizontal dilation

f(x) → f(k · x), where k is a non-negative real number.

Vertical dilation

f(x) → k · f(x), where k is a non-negative real number.

Reflection in the x-axis

f(x) → - f(x)

The procedure is summarize below:

Finally, we summarize the procedure for each case:

Case 1

g(x) = x²

g(x) = [(1 / 2) · x²]

g(x) + 4 = [(1 / 2) · (x - 2)]²

Horizontal shift: 2 units right, vertical shift: 4 units down. Horizontal stretch.

Case 2

f(x) = x²

f(x) = - (1 / 2) · x²

f(x) - 2 = - (1 / 2) · (x - 4)²

Horizontal shift: 4 units right, vertical shift: 2 units down. Reflection in the x-axis, vertical stretch.

Case 3

h(x) = x²

h(x) = 2 · x²

h(x) - 5 = [2 · (x + 2)]²

Horizontal shift: 2 units left, vertical shift: 5 units up. Horizontal stretch.

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Triangle ABD is a right-angled triangle. The value of s which is the hypotenuse of the triangle ABD is 17 units.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane. Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees.

Here,

Given information:

From the given figure, the following information can be extracted:

Triangle ABD is a right-angled triangle.

Base AB is 8 units, Height BD is 15 units.

s is the hypotenuse of the triangle ABD.

Use the Pythagoras theorem to solve for the value of s or AD,

AD²=AB²+BD²

s²=8²+15²

s²=289

s=17 units

Therefore, the value of s which is the hypotenuse of the triangle ABD is 17 units.

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The product of 3p, 4p² and 5p 7 is 120p⁹.

Product is an item or thing that is created or produced by a business. It can refer to both physical and intangible items, such as machines, food, software, intellectual property, or services. The concept of a product is used in many different industries, including manufacturing, retail, technology, and finance. Products are typically sold in exchange for money, but can also be given away or traded. Products are an essential part of any business, as they are what generate income for a company.

This can be calculated by multiplying 3p (3 x p) with 4p² (4 x p²) and 5p 7 (5 x p x 7). The result of this multiplication is 120p⁹ (3 x 4 x 5 x p x p² x 7).

To understand this calculation better, we can break it down into its component parts.

The 3p component is 3 x p, which gives us 3p. The 4p² component is 4 x p², which gives us 4p². The 5p 7 component is 5 x p x 7, which gives us 5p 7. When these three components are multiplied together we get 3 x 4 x 5 x p x p² x 7,which is equivalent to 120p⁹.
In conclusion, the product of 3p, 4p² and 5p 7 is 120p⁹.

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We know that the area of a square/rectangle is the multiplication of its length by its width. We also know that this specific area does not include the blank region, therefore we need to subtract it from the area of the shaded region!

We can come up with two expressions:

Shaded Area:

[tex](5x + 2)(3x - 1)\\= 15x^2-5x+6x-2\\=15x^2+x-2[/tex]

Blank area:

[tex](x)(x+7)\\x^2+7x[/tex]

Now all we have to do is subtract the blank area's expression from the shaded area's and simplify since the question asks for the simplest form.

[tex](15x^2+x-2)-(x^2+7x)\\15x^2-x^2+x-7x-2\\14x^2-6x-2[/tex]

Therefore, your final answer should be:

14x^2 - 6x - 2

Answer:

accounts payable

Step-by-step explanation:

Because amount of money you owe

Right angled triangle is formed by the points (3, 2), (-2, -3) and (2,3).

Let the given points be,

A = (3, 2), B = (-2, -3) and C = (2, 3)

The formula for the distance between two points:

The length of the line segment bridging two points on a plane is known as the distance between the points.

The formula to find the distance between the two points is usually given by [tex]D = $$\sqrt{\left(X_2-X_1\right)^2+\left(Y_2-Y_1\right)^2}$$[/tex].

Therefore,

A = [tex](x_{1} , y_{1} )[/tex] = (3, 2), B = [tex](x_{2} , y_{2} )[/tex] = (-2, -3)

[tex]& \mathrm{AB}=\sqrt{(3+2)^2+(2+3)^2}=\sqrt{50}=5 \sqrt{2}[/tex]  units

B = [tex](x_{1} , y_{1} )[/tex] = (-2, -3), C = [tex](x_{2} , y_{2} )[/tex] = (2, 3)

[tex]& \mathrm{BC}=\sqrt{(-2-2)^2+(-3-3)^2}=\sqrt{52}=2 \sqrt{13}[/tex]  units

A = [tex](x_{1} , y_{1} )[/tex] = (3, 2), C = [tex](x_{2} , y_{2} )[/tex] = (2, 3)

[tex]& \mathrm{AC}=\sqrt{(3-2)^2+(2-3)^2}=\sqrt{2}[/tex]  units

By using the Pythagorean theorem:

According to Pythagoras's Theorem in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides.

Now, we can see that,

[tex]& (2 \sqrt{13})^2=(5 \sqrt{2})^2+(\sqrt{2})^2 \\[/tex]

[tex]& \mathrm{BC}^2=\mathrm{AB}^2+\mathrm{AC}^2[/tex]

Therefore, the given triangle is a right angled triangle.

Therefore, option(A) s correct.

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What type of triangle do the points (3, 2), (-2, -3) and (2,3) form a triangle? If so, name the type.

A. right triangle

B. equilateral triangle

C. isosceles triangle

D. none of these

Answer:

77.472222 etc

Step-by-step explanation:

Since you have basic knowledge of computer hardware, an action which you should take as an ethical employee include the following: A. Initiate help by offering to check the computer.

A computer hardware can be defined as a physical component of a computer system or an information technology (IT) that can be seen, touched and replaced.

In Computer technology, there are various examples of a computer hardware and these include the following:

Based on ethical principles, we can reasonably infer and logically conclude that an ethical employee should initiate help by offering to help check the colleague’s computer since he or she has basic knowledge of computer hardware.

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The values of x and y in the Simultaneous equation are 4 and 30 respectively

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 and 4x − 4y = 4.

y = -5x + 50 equation 1

y = 5x+ 10 equation 2

subtract equation 1 from 2

5x-(-5x) +10-50 = 0

10x -40 = 0

10x = 40

x = 40/10

x = 4

substitute 4 for x in equation 2

y = 5(4)+10

y = 20+10

y = 30

Therefore the value of x and y are 4 and 30 respectively

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Thus , multiplication factor answer is water desalination plant can produce 2.8 x 10⁶ gallons per day. Thus, it can produce 1.4 x 10⁷gallons in 5 days.

A multiple is a number that can be divided by another number a certain number of times without a remainder. A factor is one of two or more numbers that divides a given number without a remainder. Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In math, multiply means the repeated addition of groups of equal sizes. To understand better, let us take a multiplication example of the ice creams. Each group has ice creams, and there are two such groups.

Here,

So if there was 5 days, it would produce 5 times the amount above.

So 5 × (2.8 × 10⁶) = 14 × 10⁶

We must rewrite in scientific notation, so:

14 x 10⁶ = 1.4 x 10⁷

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Thus , multiplication factor answer is water desalination plant can produce 2.8 x 10⁶ gallons per day. Thus, it can produce 1.4 x 10⁷gallons in 5 days.

A multiple is a number that can be divided by another number a certain number of times without a remainder. A factor is one of two or more numbers that divides a given number without a remainder. Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In math, multiply means the repeated addition of groups of equal sizes. To understand better, let us take a multiplication example of the ice creams. Each group has ice creams, and there are two such groups.

Here,

So if there was 5 days, it would produce 5 times the amount above.

So 5 × (2.8 × 10⁶) = 14 × 10⁶

We must rewrite in scientific notation, so:

14 x 10⁶ = 1.4 x 10⁷

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Answer:

Step-by-step explanation:

                                                             !:}

-------------------------------------------------------------------------------------------------------------

0     1/9            2/9                   3/9     4/9        5/9   6/9   7/9   8/9  9/9

9x² + 24x + 16, which is the full quadratic trinomial expressed as (3x +4)².

A trinomial expression is an algebraic expression containing three distinct terms, hence the name "trinomial expression". An algebraic expression called a trinomial expression contains three nonzero terms. A trinomial expression is formed when three monomials are added or subtracted from each other. A quadratic trinomial has the form: ax² + bx + c, where a, b, and c are nonzero real values.

Given that

9x² + 24x + 16

= (3x)² + 2(12x) + 16

= (3x)² + 2(3x)(4) + 4²

This is similar to a² + 2ab + b² = (a + b)².

So you can write:

= (3x + 4)²

= (3x +4) (3x + 4)

So this is a complete quadratic trinomial.

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9.6 quarts

First, find the unit rate, which is that when you divide 16 and 5 and you will get 3.2, then you multiply it with 3 for the 3 flower pots, and that's how you end up with the answer

Answer:

8

Step-by-step explanation:

the cubed root of 8 equals 2

if you quadruple 2 (multiply it by 4), you will get 8

Answer: (-4, -6)(9, 2):

y=8/13x - 46/13 (Point slope form: y + 6 = 8/13 *(x+4)

The ladder would reach a distance of 6 feet up the wall.

This is a theorem that can be used to determine the unknown side of a right angled triangle. It is given as:

/hyp/^2 = /opp/^2 + /adj/^2

In the given question, the ladder is placed a against a vertical wall of a building. Given that the bottom of the ladder is 8 feet to the base of the building. Therefore this is would form a right angled triangle, such that the Pythagorean theorem can be applied.

So that, let the height of the ladder on the wall be represented by t. Then;

10^2 = t^2 + 8^2

100 = t^2 + 64

t^2 = 100 -64

     = 36

t = (36)^1/2

t = 6 feet

Thus the ladder is placed 6 feet up the vertical wall.

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Answer:

74,779,038,221

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given

[tex]5^3*7^5+9^8+0+0+0+0+0+0+9^7*5^6[/tex]

We can eliminate all the zeroes.

[tex]5^3*7^5+9^8+9^7*5^6[/tex]

Evaluate each term.

Raise 5 to the power of 3.

[tex]125*7^5+9^8+9^7*5^6[/tex]

Raise 7 to the power of 5.

[tex]125*16807+9^8+9^7*5^6[/tex]

Raise 9 to the power of 8.

[tex]125*16807+43046721+9^7*5^6[/tex]

Raise 9 to the power of 7.

[tex]125*16807+43046721+4782969*5^6[/tex]

Raise 5 to the power of 6.

[tex]125*16807+43046721+4782969*15625[/tex]

Multiply 125 by 16807.

[tex]2100875+43046721+4782969*15625[/tex]

Multiply 4782969 by 15625.

[tex]2100875+43046721+74733890625[/tex]

Add 2100875 and 43046721.

[tex]45147596+74733890625[/tex]

Add 45147596 and 74733890625.

[tex]74779038221[/tex]

A calculator would help but here you go.

Answer:

[tex] \sqrt{a {}^{2} + b {}^{2} }[/tex]

Graphing exponential functions and logarithms involves understanding the key characteristics of these functions and how they are represented on a graph.

Asymptotes: The graph of an exponential function does not have any asymptotes.

Domain and range: The domain and range of an exponential function are all real numbers.

Increasing or decreasing: An exponential function is always increasing.

Shape: The graph of an exponential function is concave up.

y-intercept: The y-intercept is (0,1)

x-intercept: The x-intercept does not exist.

To graph an exponential function, you can start by plotting the y-intercept (0,1) on the graph. Then, you can use the information about the shape of the graph (concave up) and the increasing nature of the function to determine the general shape of the graph.

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The probability of a lion living longer than 10.1 will be 0.1585.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The lifespans of lions in a particular zoo are normally distributed. The average lion lives 12.5 years; the standard deviation is 2.4 years.

The lifespan of a lion in a particular zoo is normally distributed with average lion lives:

Mean u = 12.5 years

Standard deviation s = 2.4 years

We are to use the empirical rule ( 68-95-99.7% ) to estimate the probability of a lion living between 5.3 and 10.1.

The empirical rule ( 68-95-99.7% ) states:

P ( u - s < X < u + s ) = 68%

P ( u - 2s < X < u + 2s ) = 95%

P ( u - 3s < X < u + 3s ) = 99.7%

The test has the following number of standard deviations (s):

u - s < X < u + s  = 12.5 - 2.4 < X < 12.5 + 2.4  = 10.1 < X < 14.9

u - 2s < X < u + 2s = 12.5 - 4.8 < X < 12.5 + 4.8  = 7.7 < X < 17.3

u - 3s < X < u + 3s = 12.5 - 7.2 < X < 12.5 + 7.2  = 5.3 < X < 19.7

Then the probability is calculated as,

P ( 10.1 < X < 14.9 ) = 0.68

P ( 7.7 < X < 17.3 ) = 0.95

P ( 5.3 < X < 19.7 ) = 0.997

We need P ( X < 10.1 ) and P ( X < 5.3 ):

P ( X < 10.1 ) = [ 1 - P ( 10.1 < X < 14.9 ) ] / 2

P ( X < 10.1 ) = [ 1 - 0.68 ] / 2

P ( X < 10.1 ) = 0.16

P ( X < 5.3 ) = [ 1 - P ( 5.3 < X < 19.7 ) ] / 2

P ( X < 5.3 ) = [ 1 - 0.997 ] / 2

P ( X < 5.3 ) = 0.0015

P ( 5.3 < X < 10.1 ) = P ( X < 10.1 ) - P ( X < 5.3 )

P ( 5.3 < X < 10.1 ) = 0.16 - 0.0015

P ( 5.3 < X < 10.1 ) = 0.1585

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The percent that the new frame is bigger than the original frame if the width of the frame remains the same is 9.1%.

From the information, the painting, square in shape, is placed in a wooden frame with width of 10% of the length of the side of the paining. The painting was enlarged by 10%.

Let the length be Illustrated as 10cm.

Width = 10% × 10cm

= 1cm

New Length = 10cm + (10% × 10cm)

= 11cm

The old perimeter will be:

= 2(1 + 10)

= 22cm

New perimeter will be:

= 2(1 + 11)

= 24cm

The percentage increase will be:

= (24 - 22) / 22 × 100

= 2/22 × 100

= 9.1%

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The kilogram of fruits sold each day are 135 kg, 110 kg and 70 kg

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

Day 2 = Day 1 - 25

Day 3 = 2/7 * (Day 1 + Day 2)

Total weights = 315

Next, we use the following representations

x = Day 1, y = Day 2 and z = Day 3

So, we have the following equations

y = x - 25

z = 2/7(x + y)

x + y + z = 315

Substitute y = x - 25 in z = 2/7(x + y) and x + y + z = 315

z = 2/7(x + x - 25) = 2/7(2x - 25)

x + y + z = 315 ⇒ x + x - 25 + z = 315

So, we have

z = 2/7(2x - 25)

2x + z = 340

Substitute z = 2/7(2x - 25) in 2x + z = 340

2x + 2/7(2x - 25) = 340

So, we have

7x + 2x - 25 = 1190

Evaluate the like terms

9x = 1215

Divide by 9

x = 135

So, we have

y = x - 25 = 135 - 25 = 110

z = 2/7(x + y) = 2/7 *(135 + 110) = 70

Hence, the amounts are 135 kg, 110 kg and 70 kg

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The Least Common Multiple (LCM) of 2, 6, and 11 is 66.

We shall divide the numbers (6, 11) by their prime factors in order to determine the LCM of 6 and 11 using the division method (preferably common). The LCM of 6 and 11 is determined by the product of these divisors.

Step 1:Find the smallest prime number that at least one of the numbers, 6, or 11, can be factored into. As indicated by the ladder arrangement, place this prime number (2) to the left of the supplied numbers (6 and 11).

Step 2: Divide any of the supplied integers (6, 11) by 2 and write the quotient below it if it is a multiple of 2. Any number that is not divisible by the prime number should be brought down.

Step 3: Continue the procedure until there are only 1s left in the

The LCM of 6 and 11 is the product of all prime numbers on the left, i.e. LCM(6, 11) by division method = 2 × 3 × 11 = 66

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