what is the surface area of this square pyramid

Answer:

x=6

Step-by-step explanation:

x-2 = sqrt(28-2x)

Square each side

(x-2)^2 = (sqrt(28-2x))^2

(x-2)^2  = 28-2x

FOIL

x^2 -4x+4 = 28-2x

Subtract 28 from each side

x^2 -4x+4-28 = 28-2x-28

x^2 -4x-24=-2x

Add 2x to each side

x^2 -2x-24=-2x

x^2 -2x+2x-24=-2x+2x

x^2-2x-24 =0

Factor

(x-6)(x+4)=0

Using the zero product property

x=6  x=-4

Check for extraneous solutions

x=6

x-2 = sqrt(28-2x)

6-2 =sqrt(28-12)

4 = sqrt(16)

4=4

Solution

x=-4

x-2 = sqrt(28-2x)

-4-2 =sqrt(28+8)

-6 = sqrt(36)

-6=6

Not a solution

Answer:

Triangle (scalene)

Step-by-step explanation:

Polygon is a closed figure.

The names of polygons depends on the number of sides. Some common polygons are:

3 sides - triangle

4 sides - quadrilateral

5 sides - pentagon

6 sides - hexagon

Triangle and Quadrilaterals have their own types as well.

The points G, H , and I are shown in the attached image. As you can see, it creates a 3-sided figure, which is a triangle.

Note: Since all 3 sides have different length, we call it a "scalene triangle"

ANSWER

[tex]y (6)= \frac{20}{ {e}^{3} } [/tex]

EXPLANATION

The given equation is:

[tex] \frac{dy}{dt} = - 10 {e}^{ - \frac{t}{2} } [/tex]

We integrate with respect to t to get,

[tex]y = 20 {e}^{ - \frac{t}{2} } + k[/tex]

The initial condition is y(0)=20

We apply the initial condition to get,

[tex]20= 20 {e}^{ - \frac{0}{2} } + k[/tex]

[tex]k = 0[/tex]

This implies that;

[tex]y = 20 {e}^{ - \frac{t}{2} } [/tex]

[tex]y (6)= 20 {e}^{ - \frac{6}{2} } [/tex]

[tex]y (6)= 20 {e}^{-3} [/tex]

Or

[tex]y (6)= \frac{20}{ {e}^{3} } [/tex]

The required solution is [tex]y(6) = 20e^{-3}[/tex]

Given the following differential equation [tex]dy/dt=-10e^{-t/2}[/tex]

To get the value of y, we will integrate the equation to have:

[tex]y=-20e^{-t/2} + k[/tex]

Given that y(0) = 20, hence;

[tex]20=-20e^{-0/2} + k\\ 20 = 20 + k\\ k = 0[/tex]

Hence the solution to the given integral is [tex]y=-20e^{-t/2} [/tex]

Next is to get y(6)

[tex]y(6)=-20e^{-6/2} \\ y(6) =20e^{-3}}[/tex]

Hence the required solution is [tex]y(6) = 20e^{-3}[/tex]

Learn more on differentiation here: https://brainly.com/question/25081524

The answer is B . Please mark as brainliest :)

Answer:

The correct option is 2.

Step-by-step explanation:

It is given that Alec calculated the slope of line AC between points A and B. Avis calculated the slope of line AC between points B and C.

If a line passing through two points then the slope of the line is

[tex]slope=\frac{y_2-y_1}{x_2-x_1}=\frac{Rise}{Run}[/tex]

The coordinates of A and B are A(0,0) and B(6,2). The slope of line AB is

[tex]m_1=\frac{2-0}{6-0}=\frac{1}{3}[/tex]

The coordinates of B and C are B(6,2) and C(18,6). The slope of line AB is

[tex]m_2=\frac{6-2}{18-6}=\frac{4}{12}=\frac{1}{3}[/tex]

[tex]m_1=m_2[/tex]

Both Alec and Avis calculated the slope as 1/3. Therefore the correct option is 2.

Answer:

A

Step-by-step explanation:

The expression 5 + 2x typically means 5 plus 2 times x, or the sum of 5 and the product of 2 and x. Hence correct options are B and E.

The expression 5 + 2x can have multiple interpretations depending on the context, but most commonly, it represents the following:

The expression represents 5 plus 2 times x.

The expression represents 5 plus x plus x, which is another way of stating the distributive property of multiplication over addition.

The expression represents the sum of 5 and 2x, which can be thought of as adding the number 5 to the product of 2 and x.

It does not represent the product of 5 and 2x nor does it indicate additions of 5, 2, and x independently (without multiplication).

Answer:

D) 72

Step-by-step explanation:

The way to find the area of this figure easily is to break it down in regular shapes we know.  You can then see it as two horizontal rectangles on top and bottom, measuring 6 x 4 each, then a vertical rectangle in the middle measuring 4 x 6.

So, overall, we have 3 similar rectangles measuring 4x6 or 6x4... which are equivalent.

The area of each of those 3 rectangles is 24 units (6x4).

Since we have 3 of those: 3 * 24 = 72.

[tex]x=-10, y=5\Longrightarrow\boxed{-10, 5}[/tex]

Answer:

[tex]\frac{1}{5}\frac{in}{miles}[/tex]

Step-by-step explanation:

we know that

The original scale of the map is

[tex]\frac{2}{30}\frac{in}{miles}=\frac{1}{15}\frac{in}{miles}[/tex]

If the map is enlarged to 3 times its size

then

the new scale will be

[tex]\frac{2*3}{30}\frac{in}{miles}=\frac{6}{30}=\frac{1}{5}\frac{in}{miles}[/tex]

The scale of the original map is 2 inches to 30 miles. After enlarging the map 3 times, the new scale will be 1 inch to 15 miles, as 6 inches on the enlarged map would represent 90 miles.

The question is asking to determine the scale of a map after it has been enlarged. The original map scale is such that 2 inches represent 30 miles. If the map is enlarged 3 times its original size, each inch on the original map would now be represented by 3 inches on the enlarged map. Therefore, the 2 inches that originally represented 30 miles would now be stretched out to 6 inches on the enlarged map.

We can determine the new scale setting up a proportion:

We know the distances must remain consistent, so we set up the proportion:

By cross-multiplication, we find that:

The scale of the enlarged map will therefore be 1 inch representing 15 miles, as we can conclude from 6 inches representing 90 miles.

B.

5 squared + 12 squared = x squared

5 squared = 25

12 squared = 144

144+25 = 169

Square root of 169 = 13

Hope this helps you!! ❤️❤️

Answer: B.

Step-by-step explanation:

In B, opp=5 adj = 12 hyp=x

Using pythagoras theorem

hyp² = opp² + adj²

x² = 5² +12²

x² = 25 + 144

x² = 169

x=√(69)

x=13

B is the only triangle with a hypotenuse whose length is interger.

Looking at A,

x² = 4² +2²

x= √(20) =4.47

x is not an interger

lets take c and see,

x² = 2² +5²

x = √(29) = 5.385, its also not an interger.

Now, we will take the last one and check

x² = 8² +14²

x=√260 = 16.12, it is not an interger

There B is the only triangle with an integer hypotenuse.

Answer:

A.  2(x2 - 1) = 2(y2 - y1)

Step-by-step explanation:

Perimeter

P = 2W + 2L

W = √(x2 - x1)^2 = x2 - 1

L = √(y2 - y1)^2 = y2 - y1

So

P = 2(x2 - 1) = 2(y2 - y1)

Answer is A.

2(x2 - 1) = 2(y2 - y1)

Answer:

24 units

Step-by-step explanation:

To obtain the dimensions of this rectangle, count the number of blocks in each direction x and y.  I count 7 blocks in the x-direction and 5 in the y-direction.  Thus, the perimeter, P, is P = 2W + 2L, which here equals:

P = 2(5) + 2(7) = 24 units

Answer:

x = e³

Step-by-step explanation:

Using the property of logarithms

• [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Given

19 + 2lnx = 25 ( subtract 19 from both sides )

2lnx = 6 ( divide both sides by 2 )

lnx = 3 [ note lnx = [tex]log_{e}[/tex] x ]

x = e³

Answer:

The correct answer is D 20.09

Step-by-step explanation:

Answer:

p(A) = 0.55

p(b) = 0.45

Step-by-step explanation:

Experimental probability = [tex]\frac{Number of favorable outcomes}{Total number of outcomes}[/tex]

total students = 55 + 45   ⇒ 100

let A be the probability that students brought lunch from house = [tex]\frac{55}{100}[/tex] ⇒ 0.55

let B be the probability that students order school lunch = [tex]\frac{45}{100}[/tex] ⇒ 0.45

Answer:

B - +4.

Step-by-step explanation:

The person does not get 4.5 yards.

1/4, -1/4, and -4 do not work as well because negative numbers express loss, and not gain, and the person does not get any fractions.

Answer:

I believe the answer is B. +4

Step-by-step explanation:

Answer:

0.5

Step-by-step explanation:

Given that height of 7 year old children are normally distributed with mean =49 inches and std deviation = 2inches

Brenda is 50 inches tall

This means her X score is 50

To convert this X score to Z score we use the formula given below

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Here we know all the values of x, mu and sigma

Just substitute

Z score

=[tex]\frac{50-49}{2} =\frac{1}{2} \\=0.5[/tex]

Thus Z score of Brenda is 0.5

Answer:

0.5

Step-by-step explanation:

Answer:

110

Step-by-step explanation:

Answer:

Jesus

Step-by-step explanation:

Why all this dish soap. Sounds like that vine.

Answer:

146cm^2

Step-by-step explanation:

Area of trapezoid:

(4+14)/2*10=90

Area of triangle:

(14*8)/2=56

90+56=146

For this case we have a figure composed of a trapezoid and a triangle.

By definition we have that the area of a trapezoid is given by:

[tex]A = \frac {(B + b) * h} {2}[/tex]

Where:

B: It's the biggest side

b: It is the minor side

h: It's the height.

So:

[tex]A = \frac {(14 + 4) * 10} {2}\\A = 90 \ cm ^ 2[/tex]

For its part, the area of a triangle is:

[tex]A = \frac {b * h} {2}[/tex]

Where:

b: It's the base

h: It's the height

[tex]A = \frac {14 * (18-10)} {2}\\A = \frac {14 * 8} {2}\\A = \frac {14 * 8} {2}\\A = 56 \ cm ^ 2[/tex]

Thus, the total area is the sum of the two areas:

[tex]146 \ cm ^ 2[/tex]

ANswer:

[tex]146 \ cm ^ 2[/tex]

ANSWER

9 nickels 8 dimes

EXPLANATION

The simultaneous equations are:

1st equation: n+d=17

2nd equation: 0.05n+0.10d=1.25

Multiply through the second equation by 100.

This the equation:

3rd equation: 5n+10d=125

Make n the subject in equation (1).

n=17-d

Substitute this into equation (3)

5(17-d)+10d=125

85-5d+10d=125

-5d+10d=125-85

5d=40

Divide both sides by 5.

d=8

Put d=8 into n=17-d

This gives:

n=17-8

n=9

Answer:

8 dimes and 9 nickels

Step-by-step explanation:

In this exercise, we got a system of linear equations. We can solve this system by using several methods: substitution, reduction and equalization, and other advanced method call "Cramer's rule".

So, for this exercise we will use the substitution method.

1. Clear n for the first equation.

n + d = 17

n = 17 - d

2. Replace n in the second equation.

0.05n + 0.10d = 1.25

0.05(17 - d) + 0.10d = 1.25

0.85 - 0.05d + 0.10d = 1.25

0.85 + 0.05d = 1.25

3. We solve the obtained equation for d.

0.05d = 1.25 - 0.85

d = (1.25 - 0.85)/0.05

d = 0.40/0.05 = 8

dimes (d) = 8

4. we obtain the value of n using any of the two equations and with d = 8

Using the first equation

n + d = 17

n = 17 - d with d = 8

n = 17 - 8

n = 9

nickels (n) = 9

.

Answer:

151

Step-by-step explanation:

Answer:

755 divided by 5 would be 151

The correct answer is B

We can simply solve to see if it is correct.

Apply the distributive property.

.7*4k-.7*12

2.8k-8.4

This matches the example given in the question.

Hope this helps!

Answer:

B

It can not be c or d because you can't combine unlike factors. It is not a because 0.07 * 4K is not 2.8K

Answer:

Step-by-step explanation:

To solve indices problems you need to know the laws of indices.

The laws will guide you in answering any problem related to indices, these laws are for a ≠ 0

law 1

aᵇ * aⁿ = aᵇ⁺ⁿ

example 5³ * 5⁵ = 5³⁺⁵= 5⁸

law 2

aᵇ / aⁿ = aᵇ⁻ⁿ

example 7⁵/ 7³ = 7⁵⁻³ = 7²

law 3

(aᵇ)ⁿ = aᵇⁿ

example (5³)⁴ = 5³ * 5⁴ = 5¹²

law 4

a⁰ = 1

example 8⁰ = 1

law 5

a⁻ⁿ = 1/aⁿ

example 7⁻² = 1/7² = 1/49

law 6

a^¹/ₙ = ⁿ√a

example 27^¹/₃ = ∛27 = 3

law 7

a^ᵇ/ₙ = (ⁿ√a)ᵇ = ⁿ√aᵇ

example 8^²/₃ = (∛8)² = (2)² = 4

It’s C) , I believe..

Answer:

option C

Step-by-step explanation:

When we use the distance formula for two points ( x, y ) and ( x', y¹ )

Then formula is (distance)² = (x - x¹)² + (y - y¹)²

This is quite similar to the formula used in a right angle triangle to determine hypotenuse

(Hypotenuse)² = (base)²+(height)²

Therefore, option C is the answer.

Answer:

C!

Step-by-step explanation:

To find the the mean add all the numbers and divde by the number of numbers. The sum of all the numbers is 56. There are 7 numbers.

56/7 is 8.

B

Because I like the letter b so ha

Answer:

it's A

Step-by-step explanation:

2x-y=6+2x-2y=4 start moving the numbers

Answer:

( 4 , 2 )

Hope this helps :)

Have a great day !

5INGH

Step-by-step explanation:

2 x - y = 6

2 x - 2 y = 4

x = 4 and y = 2

(2 × 4 )- (2 × 2) = 8 - 4 = 4

( 2 × 4 ) - 2 = 8 - 2 = 6

Answer:

y = f(x) = a + bx

Step-by-step explanation:

independent variable = x

dependent variable =y

Answer:A linear function is a straight line which is just a linear function with the equation y=mx+b

Step-by-step explanation:

Answer:

3 and 7/10

Step-by-step explanation:

Answer:

Step-by-step explanation:

For this case we have the following equation of the second degree:

[tex]7x ^ 2 = 9 + x[/tex]

Rewriting:

[tex]7x ^ 2-x-9 = 0[/tex]

The solutions will be given by the following equation:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]

We have to:

[tex]a = 7\\b = -1\\c = -9[/tex]

Substituting the values:

[tex]x = \frac {- (- 1) \pm \sqrt {(- 1) ^ 2-4 (7) (- 9)}} {2 (7)}\\x = \frac {1 \pm \sqrt {(- 1) ^ 2 + 4 (7) (9)}} {2 (7)}[/tex]

Answer:

Option D

Answer:

190,208

Step-by-step explanation:

732,178 + 167 = 732,345

732,345 - 542,137 = 190,208

Question : 732,178 + 167 - 542,137

Answer : 190208

Step-by-step explanation :

732,178 + 167 = 732345

732345 -  542,137 = 190208

Hope this helps :)

Have a great day !

5INGH

Answer:

Step-by-step explanation:

I'll do them you arrange.

x +  (x - 1) > 5

If you start with 3 you will see that the answer is that the left equals the right. So 4 is the smallest number x can have

3 + (3 - 1)>5

6 - 1 = 5 not something greater than 5

4 + (4 - 1) > 5

8 - 1 > 5

7 > 5 which is true.

Answer 4

5x - 3x > 9

2x > 9          x must equal 5

2*5 > 9

10 > 9

Answer 5

6x - 14 > 3       add 14 to both sides.

6x - 14+14>3+14

6x > 17            The answer to equality is just about 3. So three is the answer

6*3 > 17

18 > 17

Answer 3

2x - 1 > 0           Add 1 to both sides.

2x > 1                 1 is the answer

2*1 > 1

2 > 1

Answer 1

So all you need do is place them in order. The last one goes first and then the second last one.

Answer:

Option A is correct.

Step-by-step explanation:

In this question the sale price and the original price of the shoe purchased is given. We need to find the amount of discount Jessica has received for purchasing shoes on sale.

Sale Price = $45.00

Original Price = $60.00

Discount she received=?

Discount received = Sale Price/Original Price

                               = 45/60

                               = 0.75

Converting it into percentage:

Discount received = 0.75 * 100

                              = 75%

So, Option A is correct.

Jessica received a 25% discount on the suede shoes she purchased during the Leather Emporium's Semi-Annual Clearance Sale.

The subject of this question is discount percent. It is inferred from the question that Jessica purchased shoes worth $60.00 at a reduced price of $45.00. To compute the discount she got, we need to subtract the sale price from the original price, and then divide that result by the original price, and multiply it by 100 to get it in percentile form.

In this case, the discount received is calculated as (($60 - $45)/$60) * 100 = 25%. So, the correct answer to the question 'If Jessica paid $45.00 for the shoes originally priced at $60.00, how much of a discount did she receive?' is B. 25%.

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Answer:

Step-by-step explanation:

Because the trapezoid is isosceles, the two diagonals are congruent. This can be shown by ASA.

ACD = BDC          Properties of parallel lines.

DC = DC               A line is equal to itself

DBA = CAB           Property of parallel lines.

AC = DB                Parts of Congruent triangles are congruent

3x + 15 = 7x - 9     Add 9 to both sides

3x + 15 + 9 = 7x

3x + 24 = 7x          Subtract 3x from both sides.

24 = 7x - 3x

24 = 4x                  Divide by 4

24/4 = 4x/4

x = 6

The value of x given that figure ADCB is an isosceles trapezoid is 6.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

AC=3x+15 BD=7x-9

Now,

In an isosceles trapezoid, the diagonals are congruent. Hence, we can set AC equal to BD and solve for x: 3x + 15 = 7x - 9. Subtracting 3x from both sides, we get: 15 = 4x - 9. Adding 9 to both sides, we get: 24 = 4x. Dividing both sides by 4, we get: x = 6.

Therefore, by algebra the answer will be 6.

More about the Algebra link is given below.

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