What will be the perimeter and the area of the rectangle below if it is enlarged using a scale factor of 3.5? (1 point)

A rectangle is shown. The length of the rectangle is labeled as 8 cm, and the width is labeled as 6 cm.

1.Perimeter = 98 cm, area = 109.25 cm2
2.Perimeter = 98 cm, area = 588 cm2
3.Perimeter = 42 cm, area = 109.25 cm2
4.Perimeter = 42 cm, area = 588 cm2

The required two column proof is explained below.

A midpoint is a point which divides a line segment into two equal parts. Thus it can be referred to as the middle point of the line segment.

The two column proof for the information is given as:

M is the midpoint of CD    (Given)

CD = CM + MD   (addition property of a line segment)

CM = MD  (definition of a midpoint)

So that;

5x – 2 = 3x + 2    (Definition of midpoint)#

Then,

5x - 3x = 2 + 2 (collecting like terms)

2x = 4

x = 2

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Answer:

The answer is c

Step-by-step explanation:

Reflection involves mirroring a point over a line.

When L is reflected across the x and y axes, the new coordinates are (7,3)

Given that:

\((x,y) \to (-7,-3)\)

When a point is reflected across the x-axis, the rule is:

\((x,y) \to (x,-y)\)

So, we have:

\((-7,-3) \to (-7,3)\)

When a point is reflected across the y-axis, the rule is:

\((x,y) \to (-x,y)\)

So, we have:

\((-7,3) \to (7,3)\)

Hence, the new coordinates of L are (7,3)

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Answer:

8i+8j

Step-by-step explanation:

3i+4j+5i+4j

i(3+5) + j(4+4)

Therefore 8i +8j

HAPPY TO HELP YOU

Answer:

Step-by-step explanation:

we have :

a=3i+4j

b=5i+4i

so that : a+b=3i+4j+5i+4j

=(3i+5i)+(4j+4j)

so    a+b=8i+8j=8(i+j)

Hello!

∠AED and ∠BEC are opposite angles

so ∠AED = ∠BEC = 36°.

A partir de la definición de razón y la teoría de semejanza entre triángulos, la razón del área del triángulo AMN y el área del cuadrilátero BMNC es equivalente a 1/3.

En este problema tenemos un sistema formado por dos triángulos similares, la semejanza entre los dos triángulos se debe a la colinealidad entre los segmentos de línea AP' (triángulo pequeño) y AP'' (triángulo grande), así como de los lados AM y AB, así como los lados AN y AC, así como los mismos ángulos en la misma distribución. (Semejanza Lado - Ángulo - Lado)

En consecuencia, obtenemos las siguientes proporciones:

AP'/AP'' = MN/BC = 1/2     (1)

Finalmente, la proporción entre el triángulo AMN y el cuadrilátero BMNC es:

\(\frac{AMN}{ABC - AMN} = \frac{\frac{1}{2}\cdot a \cdot \left(\frac{1}{2}\cdot h \right)}{\frac{1}{2}\cdot (2\cdot a) \cdot h - \frac{1}{2}\cdot a \cdot \left(\frac{1}{2}\cdot h \right)} = \frac{\frac{1}{4}\cdot a\cdot h }{a\cdot h - \frac{1}{4}\cdot a \cdot h }\)

\(\frac{AMN}{ABC - AMN} = \frac{\frac{1}{4} }{\frac{3}{4} } = \frac{1}{3}\)

A partir de la definición de razón y la teoría de semejanza entre triángulos, la razón del área del triángulo AMN y el área del cuadrilátero BMNC es equivalente a 1/3.

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The probability values for the questions posed are :

A.)

Number of students Taking a public speaking class majoring in business administration.

P(PS or BA) = 55/100 = 11/20

Therefore, the probability of PS or BA is 11/20

B.)

For the survey described, P(taken a public speaking class | majoring in Business Administration) represents the probability that a selected student has taken a public speaking class given that the student is majoring in business administration.

Hence, as inferred from P(A|B) ; probability of A given B.

C.)

P(PS|BA) = n(PSnBA) / n(BA)

n(PS) = 10+20 = 30

n(PSnBA) = 10

P(PS|BA) = 10/30 = 1/3

Therefore , the probability of PS|BA is 1/3.

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The sequence of transformations that proves that the shapes are similar is given as follows:

B. a reflection across the x-axis, and then a dilation by a scale factor of 1.5

First, we have that the orientation of the figure, hence it was reflected.

The figure was reflected from the second quadrant to the third quadrant, hence the figure was reflected over the x-axis.

The base segment changes from a length of 2 units to a 3 units, hence the scale factor of the dilation is given as follows:

3/2 = 1.5.

Hence option B is the correct option for this problem.

The missing parts of the problem are given by the image presented at the end of the answer.

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Answer:

Mode is 83

Median is 85

Step-by-step explanation:

To find the median: Arrange the data points from smallest to largest.

To find the mode: Place all numbers in a given set in order; this can be from lowest to highest or highest to lowest, and then count how many times each number appears in the set

1) All of these questions are about evaluating those functions for each input.

9) So, let's check them out evaluating each one.

10)

11)

12)

Part 1

The equation is \(y=a(x+8)(x-72)\).

Using the point \((62, -490)\) to solve for \(a\),

\(-490=a(62+8)(62-72) \implies a=\frac{7}{10}\\\\\therefore \boxed{y=\frac{7}{10}(x+8)(x-72)}\)

Part 2

When \(x=-8\), \(y=0\).

When \(x=2\), \(y=-490\).

So, the average rate of change is \(\frac{-490-0}{2-(-8)}=\boxed{-49}\)

Answer:

Answer:

\sf (x+14)^2+(y+5)^2=149(x+14)2+(y+5)2=149

Step-by-step explanation:

Standard equation of a circle:  \sf (x-a)^2+(y-b)^2=r^2(x−a)2+(y−b)2=r2

(where (a, b) is the center and r is the radius of the circle)

Substitute the given center (-14, -5) into the equation:

\sf \implies (x-(-14))^2+(y-(-5))^2=r^2⟹(x−(−14))2+(y−(−5))2=r2

\sf \implies (x+14)^2+(y+5)^2=r^2⟹(x+14)2+(y+5)2=r2

Now substitute the point (-7, 5) into the equation to find r²:

\sf \implies ((-7)+14)^2+(5+5)^2=r^2⟹((−7)+14)2+(5+5)2=r2

\sf \implies (7)^2+(10)^2=r^2⟹(7)2+(10)2=r2

\sf \implies 149=r^2⟹149=r2

Final equation:

\sf (x+14)^2+(y+5)^2=149(x+14)2+(y+5)2=149

Approximation of decimals is a mathematical technique for finding or measuring approximations and minimizing the number of decimal places.

A fractional representation of a real number that comes close to representing it. Any real number a can be represented by an endless number of decimal fractions.

The number of decimal places in a decimal number is the number of digits following the decimal point. A mathematical method for locating or measuring approximations and reducing the number of decimal places is known as approximation of decimals.

Any comparison that is close but not accurate to another entity is called an approximation. By rounding, one can get a good idea of a number. By rounding the values in a computation before performing the operations, a calculation can be approximated.

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Answer:

1. Not possible

2. Possible

3. Possible

4. Possible

Step-by-step explanation:

Answer:

13.194

Step-by-step explanation:

  13.2

-   0.006

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

Just add zeros on the part where there are no numbers

  13.200

-    0.006

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

    13.194

Step-by-step explanation:

i)Initial School population,

given 15 units = 1200

1 unit =

\(1200 \div 15 \\ = 80\)

Number of teachers (initial) = 1 unit = 80.

ii)take j = number of teachers joining the school.

New teacher population = 80+j

\( \frac{3}{43} (1280 + j) = 80 + j \\ \frac{3840}{43} + \frac{3}{43} j = 80 + j \\ j - \frac{3}{43} j = \frac{3840}{43} - 80 \\ \frac{40}{43} j = \frac{400}{43} \\ 40j = 400 \\ j = 400 \div 40 \\ = 10\)

Answer:

193.4 meters squared

Step-by-step explanation:

Area of rectangle = 7 X 15 = 105

Area of semi circle = 1/2 X π X R^2

R = 7.5

R squared = 56.25

π = 3.1415932654........

1/2 X 3.1415.... X 7.5^ 2 = 88.35729338

Rounded to one decimal place = 88.4

105 + 88.4 = 193.4m^2

The surface area of each box is 0.52 square meters.

To calculate the surface area of ​​an orthohedron with 6 rectangular faces, add the areas of the 6 faces together. You can also identify the length (c), width (l) and height (a) of the orthohedron and use the formula: surface area (AS)=2cl+2ca+2al.

Knowing that:

\(2 * (L * H) + 2 * (W * H)\)

Substituting the values:

\(2 * (0.2 * 0.3) + 2 * (0.5 * 0.3) = 0.12 + 0.3 = 0.42\)

Now, the surface area of the base:

\(L * W\\0.2 * 0.5 = 0.1\)

The total surface will be:

\(0.42 + 0.1 = 0.52\)

Therefore, the surface area of each planter box is 0.52 square meters.

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The mean and the standard deviation, from the frequency table, are given as follows:

The frequency table gives the number of times that each observation appears.

The mean of a data-set is given by the sum of all observations divided by the number of observations, hence it is given as follows:

Mean = (1 x 13 + 2 x 12 + 3 x 5)/(13 + 12 + 5) = 1.73.

The standard deviation is given by the square root of the sum of the difference squared between each observation and the mean, divided by the number of observations, hence it is given as follows:

Standard deviation = sqrt((13 x (1 - 1.73)² + 12 x (2 - 1.73)² + 5 x (3 - 1.72)²)/30) = 0.73.

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One side of the cube is 2 mm, another side is 3 mm, and the remaining side is 2 mm, then the surface area of the cube is 102 mm².

A cube is a three-dimensional geometric shape that has six square faces of equal size. It is a regular polyhedron, which means that it has congruent regular polygons as its faces, and its edges and vertices are all congruent. A cube can be thought of as a three-dimensional version of a square, as all six faces are square and have equal side lengths.

The cube is a very important shape in mathematics and geometry, as it has many useful properties and applications. For example, it is used in calculating the volume and surface area of three-dimensional objects, and in modeling and visualizing three-dimensional structures in physics, chemistry, and engineering. It is also a common shape in games and puzzles, such as Rubik's Cube.

A cube has six square faces, each of which has the same area. Therefore, to find the surface area of a cube, we can calculate the area of one face and then multiply it by six.

If one side of the cube is 2 mm, then the area of one face is:

2 mm x 2 mm = 4 mm²

If one side of the cube is 3 mm, then the area of another face is:

3 mm x 3 mm = 9 mm²

If the remaining side of the cube is also 2 mm, then the area of the third face is also:

2 mm x 2 mm = 4 mm²

Therefore, the total surface area of the cube is:

6 x (4 mm² + 9 mm² + 4 mm²) = 6 x 17 mm² = 102 mm²

Therefore, if one side of the cube is 2 mm, another side is 3 mm, and the remaining side is 2 mm, then the surface area of the cube is 102 mm².

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The time it will take the money to reach $8,838.51 is 14years

The formula for calculating compound interest is expressed as:

A = P(1+r)^t

where

P = $6,680

A = $8,838.51?

r = 2% = 0.02

Substitute and calculate the time 't"

8,838.51 = 6680(1+0.02)^t
1.3231 = 1.02^t

t = ln1.3231/ln1.02

t = 14years

Hence the time it will take the money to reach $8,838.51 is 14years

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Answer:

negative

Step-by-step explanation:

Answer:

  68086.64

Step-by-step explanation:

The future value formula can be used.

  FV = P(1 +r/n)^(nt)

The future value of principal P at annual rate r compounded n times per year for t years.

  124000 = P(1 +0.02/12)^(12·30) = P·1.82120898

  P = 124000/1.82120898 ≈ 68086.64

The principal was $68,086.64.

84.13% of the printing jobs will be acceptable.

The new standard deviation required to achieve a minimum of 95% of jobs acceptable is 0.121.

The darkness of the print is measured quantitatively using an index. If the index is greater than or equal to 2.0 then the darkness is acceptable. Anything less than 2.0 means the print is too light and not acceptable. The machines print at an average darkness of 2.2 with a standard deviation of 0.20.

The mean of the darkness of the print is µ = 2.2 and the standard deviation is σ = 0.20.Therefore, the z-score can be calculated as; `z = (x - µ) / σ`.The index required for acceptable prints is 2.0. Thus, the percentage of prints that are acceptable can be calculated as follows;P(X ≥ 2.0) = P((X - µ)/σ ≥ (2.0 - 2.2) / 0.20)P(Z ≥ -1) = 1 - P(Z < -1)Using the standard normal table, P(Z < -1) = 0.1587P(Z ≥ -1) = 1 - 0.1587= 0.8413.

To find the new standard deviation, we can use the z-score formula.z = (x - µ) / σz = (2.0 - 2.2) / σz = -1Therefore, P(X ≥ 2.0) = 0.95P(Z ≥ -1) = 0.95P(Z < -1) = 0.05Using the standard normal table, the z-score value of -1.645 corresponds to a cumulative probability of 0.05. Hence,z = (2.0 - 2.2) / σ = -1.645σ = (2.0 - 2.2) / -1.645= 0.121.

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2

Step-by-step explanation:

you would first take the square root of 6 and get 2.449...

then you would round it to the nearest whole number and get 2

Given: The depth of the Trench as

To Determine: The measure of the trench in kilometers

Solution

Step 1: State the conversion rate of meters to kilometers

Step 2: Use the conversion rate to convert the given to kilometers

Hence, the depthe of the Mariana Trench in the Pacific Ocean in kilometers is 10.911kilometers

Check the picture below.

\(3x+5=\cfrac{260-100}{2}\implies 6x+10=160\implies 6x=150 \\\\\\ x=\cfrac{150}{6}\implies x=25\hspace{9em}\stackrel{\measuredangle ABC}{3(25)+5}\implies 80^o\)

Answer:

undefined

Step-by-step explanation:

to find slope it’s y2-y1/x2-x1

9-7/-2-(-2)

2/0

Undefined slope

Hopes this helps please mark brainliest

Answer:

64.58

Step-by-step explanation:

1 meter is 3.28084 so 3 meters is 9.84252 because you multiply it by 3 or add them to each other 3 times. 2 meters is 6.56168 because you multiply it by 2 or add them to each other. now that you have 6.56168 and 9.84252 multiply them with each other and you get 64.5834666336 but it was said to round to nearest hundredth so since the 3 in front of the 8 is not a 5 and above the answer is 64.58 and not 64.89