Devon made a scale drawing of a triangle. He used a scale factor 1/4 to draw the new triangle. How does each side of the new triangle compare to the original?

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:

Step-by-step explanation:

A is correct answer

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:

Step-by-step explanation:

The slope-intercept form y = mx + b

m - slope

b - y-intercept → (0, b)

We have the equation

y - 2x = -3              add 2x to both sides

y = 2x - 3

slope m = 2

y-intercept b = -3

We need two points to draw a graph of this linear function.

One is y-intercept (0, -3). The second one is calculated by choosing any value of x and put it to the equation:

for x = 2 → y = 2(2) - 3 = 4 - 3 = 1 → (2, 1).

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.

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:

110

Step-by-step explanation:

Answer:

Jesus

Step-by-step explanation:

Why all this dish soap. Sounds like that vine.

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:

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:

Minimum balance account requires an amount of money to left in it all times in order to avoid fees.

Step-by-step explanation:

We have "many types of account" available in the banking sectors. As per the convenience of the customer, they opt from them. The minimum balance account is the type of account in which the customer has to maintain a standard amount prescribed by the bank in his account, failing to maintain it will lead to the gathering of fine or fee.

Answer:

Minimum Balance account.

Step-by-step explanation:

A minimum balance account is an account type that requires a minimum balance as set by the bank, at all times, in order to waive maintenance fees.

Failing this, certain amount is charged when money is deposited in that account. It can range from few dollars to 500 dollars in some banks.

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

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

The answer is A. $18,600 because $620,000 × 3% = $18,600

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.

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:

Its C

hope this helps!!

The correct answer is A .)1

Answer:

270,000

Step-by-step explanation:

So, you have a number of people (15) that can stand comfortably within a certain area (5x8 ft = 40 sq feet).  And you need to find out how many people can fit in the whole park area.

First step is to find out how big the park is, in square feet, so we can then evaluate the number of people that we can fit in.

You had the right number for calculating the area of the park:

A = 400 yards x 200 yards = 1,200 feet x 600 feet = 720,000 sq feet

Now, how many people can we fit in there?  Let's use a simple cross-multiplication (x being the number of people fitting in the whole park, what we are looking for):

[tex]\frac{x}{720 000} = \frac{15}{40}[/tex]

By isolating x, we have x = (720,000 * 15) / 40 = 10,800,000 / 40 = 270,000

So, the park could accommodate 270,000 people.

That is of course if there are no trees, no benches, no kids playground or any other infrastructure in the park.

Answer:

3 and 7/10

Step-by-step explanation:

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

[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

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:

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

Anwer:

1/7^2

explantion:

The expression equivalent to 7^3 • 7-^5 is 1 / 7^2.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now the given expression is,

7^3 • 7-^5

Now using the exponential property,

n^a . n^b = n^(a+b)

Therefore, we can write as,

7^3 • 7-^5 = 7^(3-5)

Solving we get,

7^3 • 7-^5 = 7^-2

Since, n^-a = 1/n^a

⇒7^-2 = 1 / 7^2

Therefore, we can write

7^3 • 7-^5 = 1 / 7²

this is the required equivalent expression.

Thus, the expression equivalent to 7^3 • 7-^5 is 1 / 7^2.

To learn more about equivalent expression :

brainly.com/question/10188283

#SPJ2

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:

[tex]h=15.73\ in[/tex]

Step-by-step explanation:

we know that

The volume of a cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]V=1,000\ in^{3}[/tex]

[tex]r=9/2=4.5\ in[/tex] ----> the radius is half the diameter

substitute and solve for h

[tex]1,000=(3.14)(4.5)^{2} h[/tex]

[tex]h=1,000/[(3.14)(4.5)^{2}][/tex]

[tex]h=15.73\ in[/tex]

Answer:

r = 11 in V =968 pi in3

Step-by-step explanation:

got it right on edge

Answer:

The area of two pieces is [tex]51.28\ in^{2}[/tex]

Step-by-step explanation:

step 1

Find the area of the circle (large pizza)

The area is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=14/2=7\ in[/tex] ----> the radius is half the diameter

assume

[tex]\pi =3.14[/tex]

substitute

[tex]A=(3.14)(7)^{2}[/tex]

[tex]A=153.86\ in^{2}[/tex]

step 2

Divide the area into 6 pieces

[tex]153.86/6=25.64\ in^{2}[/tex]

step 3

Find the area of two pieces

[tex]25.64*2=51.28\ in^{2}[/tex]

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:

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:

A. Use straightedge to connect vertex B to right-most vertex of the equilateral triangle.

Step-by-step explanation:

The process is to create a bisector of angle ABC... so it means cutting angle at vertex/summit B in half.

Drawing a line from the vertex B to the right-most vertex of the equilateral triangle will deliver you the bisector.

The only answer choice that includes vertex B is the answer A, all other answers are dealing with vertex A and C... which will not help you to draw the bisector or angle ABC.

Answer:

Option A is right

Step-by-step explanation:

Given in the picture is an angle B formed by line segments AB and BC

To construct bisector of angle B

First with centre at B a circle is drawn which meets AB and BC at D and E respectively. With same radius equal to DE and centres of D and E two circles are drawn which intersect at the right most point.

The next step is join B to the rightmost vertex of equilateral triangles

This will be the angle bisector of angle ABC

Hence option A is right