Triangle ABC is rotated about the origin by 270° to form the triangle A′B′C′, then translated upward 10 units to form triangle A″B″C″. Which of the following statements is true for ΔABC and ΔA″B″C″? A)There isn't enough information to identify whether ΔABC and ΔA″B″C″ are congruent or similar. B)ΔABC and ΔA″B″C″ are neither similar nor congruent. C)ΔABC and ΔA″B″C″ are similar triangles. D)ΔABC and ΔA″B″C″ are congruent triangles.

Answer:

first option

Step-by-step explanation:

Given

- 3x - 2y = 1 → (1)

- x + y = 3 → (2)

Rearrange (2) by adding x to both sides, that is

y = x + 3

Substitute y = x + 3 into (1)

- 3x - 2(x + 3) = 1 ← is the equation to be solved for x

Answer:

The correct answers are B, C ,E

Step-by-step explanation:

The correct options are a, c and e

A relationship between two expressions or values that are not equal to each other is called inequality.

Given that, the solution of 15 greater-than-or-equal-to 22 + x

1) The first one is correct because the statement is x greater-than-or-equal-to negative 7. And 22+(-7) is = to 15. This means that in order to get a number below 15 by adding 22 and 15, we need a number that is lower than -7.

2) The second one is incorrect because it is the opposite of the first one. As the first one was correct, this statement is implying the complete opposite as the first one.

3) The third one is correct because we are using greater than or equal to; this means the circle would be closed.

4) The fourth option is incorrect because we need x to be lower than -7, not higher.

5) The fifth option is also correct.

Hence, the correct options are is a, c, e.

For more references on inequality, click;

https://brainly.com/question/28823603

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Answer:

193.33333 pounds

Step-by-step explanation:

Divide 87kg by 0.45

So, it's 87 ÷ 0.45 = 193.3333333

Answer: 190

Step-by-step explanation:

Answer: 0.1457

Step-by-step explanation:

Let p be the population proportion.

Given: The proportion of Americans who are afraid to fly is 0.10.

i.e. p= 0.10

Sample size : n= 1100

Sample proportion of Americans who are afraid to fly =[tex]\hat{p}=\dfrac{121}{1100}=0.11[/tex]

We assume that the population is normally distributed

Now, the probability that the sample proportion is more than 0.11:

[tex]P(\hat{p}>0.11)=P(\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}>\dfrac{0.11-0.10}{\sqrt{\dfrac{0.10(0.90)}{1100}}})\\\\=P(z>\dfrac{0.01}{0.0090453})\ \ \ [\because z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}} ]\\\\=P(z>1.1055)\\\\=1-P(z\leq1.055)\\\\=1-0.8543=0.1457\ \ \ [\text{using z-table}][/tex]

Hence, the probability that the sample proportion is more than 0.11 = 0.1457

Answer: Resultant force = 114.96 pounds at angle 81.76°

Answer: magnitude = 114.96 lbs, direction =  88.21°

Step-by-step explanation:

Vector A: 150 lbs at  40°

Vector B: 100 lbs at 170°

Slide Vector B onto Vector A so you have a head to tail connection.

Calculate the angle between the vectors (50°).

Use Law of Cosines to find the magnitude of the resultant vector.

Use Law of Sines to find the direction of the resultant vector.

Law of Cosines:  c² = a² + b² - 2ab cos θ

Given: a = 150, b = 100, C = 50°

c² = (100)² + (150)² - 2(100)(150) cos 50°

c = 114.96

Law of Sines:

[tex]\dfrac{\sin A}{a}=\dfrac{\sin C}{c}\\\\\text{Given: a=150, c=114.96, C=50}^o\\\\\\\dfrac{\sin A}{150}=\dfrac{\sin 50^o}{114.96}\\\\\\\sin A=\dfrac{150\sin 50^o}{114.96}\\\\\\A=\sin^{-1}\bigg(\dfrac{150\sin 50^o}{114.96}\bigg)\\\\\\A=88.21^o[/tex]

Answer:

Total amount received by Mrs Khanna will be 182.5 Rs.

Step-by-step explanation:

Cost of the potatoes = 25 Rs per kg

Cost of [tex]2\frac{1}{2}[/tex] kg potatoes = Weight of the potatoes × Per kg cost of the potatoes

= 2.5 × 25

= 62.5 Rs

Cost of onions = 30 Rs per kg

Cost of 3 kg onions = 3 × 30

                                 = 90 Rs

Per kg cost of Peas = 70 Rs

Cost of [tex]1\frac{1}{2}[/tex] kg Peas = 1.5 × 70

                               = 105 Rs

Per kg cost of Carrots = 40 Rs

Cost of [tex]1\frac{1}{2}[/tex] kg Carrots = 1.5 × 40

                                   = 60 Rs

Total amount of the vegetables = 62.5 + 90 + 105 + 60

                                                     = 317.5 Rs

Since she gave a note of 500 Rs

Balance amount she got = 500 - 317.5

                                         = 182.5 Rs

Therefore, total amount received by Mrs Khanna will be 182.5 Rs.

Answer:

p = 6/5

Step-by-step explanation:

-4 = 5(p - 2)

-4 = 5p - 10

-4 + 10 = (5p - 10) + 10

6 = 5p

6/5 = (5p)/5

6/5 = p

p = 6/5

Answer:

p = 6/5

Step-by-step explanation:

-4 = 5(p - 2)                       (DISTRIBUTE)

-4 = 5p - 10                        (ADD 10 TO BOTH SIDES)

6 = 5p                                (DIVIDE BY FIVE ON BOTH SIDES)

p = 6/5        

Answer:

[tex]\boxed{AC = 2.3}[/tex]

Step-by-step explanation:

AD = BD  (CD bisects AB means that it divides the line into two equal parts)

So,

AD = BD = AB/2

So,

AD = 3/2

AD = 1.5

Now, Finding AC using Pythagorean Theorem:

[tex]c^2 = a^2+b^2[/tex]

Where c is hypotenuse (AC), a is base (AD) and b is perpendicular (CD)

[tex]AC^2= (1.5)^2+(\sqrt{3} )^2[/tex]

[tex]AC^2 = 2.25 + 3[/tex]

[tex]AC^2 = 5.25[/tex]

Taking sqrt on both sides

[tex]AC = 2.3[/tex]

Answer:

[tex]\boxed{2.29}[/tex]

Step-by-step explanation:

The length of AB is 3 units.

The length of CD is [tex]\sqrt{3}[/tex] units.

D is the mid-point of points A and B.

AD is half of AB.

[tex]\frac{3}{2} =1.5[/tex]

Apply Pythagorean theorem to solve for length of AC.

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

The hypotenuse is length AC.

[tex]c=\sqrt{1.5^2 +(\sqrt{3}) ^2 }[/tex]

[tex]c=\sqrt{2.25+3 }[/tex]

[tex]c=\sqrt{5.25}[/tex]

[tex]c= 2.291288...[/tex]

Answer:

[tex]2\sqrt{14\\}[/tex] = q

Step-by-step explanation:

use geometric mean method

4/s = s/10

s^2 = 40

s = 2[tex]\sqrt{10}[/tex]

consider the triangle STR and using the Pythagorean theorem

[tex]s^{2} +16 = q^{2} \\[/tex]

[tex](2\sqrt{10})^{2} +16 = q^{2}[/tex]

40 + 16 = q^2

56 = q^2

[tex]2\sqrt{14\\}[/tex] = q

Answer:

( 4,-2)

Step-by-step explanation:

y + 2 = -3 (x - 4)

We are given y = -2

-2+2 = -3 (x-4)

0 = -3(x-4)

Divide by -3

0 = x-4

Add 4 to each side

4 = x-4+4

4 =x

Answer:4

Step-by-step explanation:

Answer:

469.4ft²

Step-by-step explanation:

We have Triangle WXY

In the question, we are given already

Angle W = 27°

Angle X = ?

Angle Y = 40°

Side w =?

Side x = ?

Side y = 38ft

Area of the triangle= ?

Step 1

We find the third angle = Angle X

Sum of angles in a triangle = 180°

Third angle = Angle X= 180° - (27 + 40)°

= 180° - 67°

Angle X = 113°

Step 2

Find the sides w and x

We find these sides using the sine rule

Sine rule or Rule of Sines =

a/ sin A = b/ Sin B

Hence for triangle WXY

w/ sin W = x/ sin X = y/ sin Y

We have the following values

Angle W = 27°

Angle X = 113°

Angle Y = 40°

We are given side y = 38ft

Finding side w

w/ sin W= y/ sin Y

w/sin 27 = 38/sin 40

Cross Multiply

sin 27 × 38 = w × sin 40

w = sin 27 × 38/sin 40

w = 26.83879ft

w = 26.84ft

Finding side x

x / sin X= y/ sin Y

x/ sin 113 = 38/sin 40

Cross Multiply

sin 113 × 38 = x × sin 40

x = sin 113 × 38/sin 40

x = 54.41795ft

x = 54.42ft

To find the area of triangle WXY

We use heron formula

= √s(s - w) (s - x) (s - y)

Where S = w + x + y/ 2

s = (38 + 26.84 + 54.42)/2

s = 59.63

Area of the triangle = √59.63× (59.63 - 38) × (59.63 - 26.84 ) × (59.63 - 54.42)

Area of the triangle = √

Area of the triangle = 469.40772706541ft²

Approximately to the nearest tenth =469.4yd²

Answer:

C

Step-by-step explanation:

0.1(x - 100)² + 250

0.1[(x - 100)(x - 100)] + 250

0.1(x² -200x + 10000) + 250

0.1x² - 20x + 1000 + 250

0.1x² - 20x + 1250

0.1x² - 25x + 5x + 1250

0.1x(x - 250) + 5(x + 250)

∴ (0.1x + 5)(x - 250) or (0.1x + 5)(x + 250)

Answer:

The owner needs 195 meters of wire

Step-by-step explanation:

If the lot is squared shaped, then its area is given by the formula:

[tex]Area =x^2[/tex]

where x is the side of the square. Then considering the value they provide for the surface, each side must be of length:

[tex]x^2=\frac{4225}{16} \,m^2\\x=\sqrt{\frac{4225}{16}} \,\,m\\x=16.25\,\,m[/tex]

Then the perimeter around this square lot is four times that side length:

Perimeter = 4 (16.25 m) = 65 m

and since the owner wants three rows of wire, the total length of wire needed is:

3 (65 m) = 195 m

Answer:

2/3q + 7/12

Step-by-step explanation:

If you are trying to simplify your expression

4/6q + 7/12

2/3q + 7/12

Answer:

at s = 10m, v(t_1) =  7.663 m/s

at s = 15m, v(t_2) = 10.041 m/s

Step-by-step explanation:

for the interval 0-10 seconds,

a(t) = t m/s^2

v(0) = 0

v(t) = v(0) + integral(a(t)dt)

= 0 +  [t^2/2]  

= (1/2) t^2

s(0) = 0      .................. arbitrary

s(t) = s(0) + integral(v(t)dt)

= 0 + integral ((1/2)t^2)

= (1/6)t^3

When s(t) = 10 m,

(1/6)t^3 = 10

t^3 = 60

t_1 = 60 ^(1/3) = 3.9149 s approx.

v(t_1) = (1/2) t_1^2 = (1/2)3.9149^2 = 7.663 m/s

When s = 15 m

(1/6)t^3 = 15

t^3 = 90

t_2 = 4.4814 s approx.

v(t_2) = (1/2)t_2^2 = (1/2)4.4814^2 = 10.041 m/s

Answer:

at s = 10m, v(t_1) =  7.663 m/s

at s = 15m, v(t_2) = 10.041 m/s

Step-by-step explanation:

I took the test and got it right

Answer:

[tex] f = 10.7 [/tex]

Step-by-step explanation:

Given ∆DEF,

<F = 36°

DF = e = 15

EF = d = 6

DE = f = ?

f can be found using the Law of Cosine as shown below:

[tex] f^2 = d^2 + e^2 - 2(d)(e)*cos(F) [/tex]

Plug in your values:

[tex] f^2 = 6^2 + 15^2 - 2(6)(15)*cos(36) [/tex]

Evaluate:

[tex] f^2 = 36 + 225 - 180*0.809 [/tex]

[tex] f^2 = 261 - 145.62 [/tex]

[tex] f^2 = 115.38 [/tex]

[tex] f = 10.74 [/tex]

[tex] f = 10.7 [/tex] (to nearest tenth)

Answer:

[tex]\huge\boxed{x=7\dfrac{23}{25}}[/tex]

Step-by-step explanation:

[tex]x\div3\dfrac{3}{10}=2\dfrac{2}{5}\\\\\text{convert the mixed number to the impropper fraction}\\\\3\dfrac{3}{10}=\dfrac{3\cdot10+3}{10}=\dfrac{33}{10}\\\\2\dfrac{2}{5}=\dfrac{2\cdot5+2}{5}=\dfrac{12}{5}\\\\x\div\dfrac{33}{10}=\dfrac{12}{5}\\\\x\times\dfrac{10}{33}=\dfrac{12}{5}\qquad\text{multiply both sides by}\ \dfrac{33}{10}\\\\x\times\dfrac{10\!\!\!\!\!\diagup}{33\!\!\!\!\!\diagup}\times\dfrac{33\!\!\!\!\!\diagup}{10\!\!\!\!\!\diagup}=\dfrac{12}{5}\times\dfrac{33}{10}\\\\x=\dfrac{396}{50}[/tex]

[tex]x=\dfrac{198}{25}\\\\x=\dfrac{175+23}{25}\\\\x=\dfrac{175}{25}+\dfrac{23}{25}\\\\x=7\dfrac{23}{25}[/tex]

Answer:

1/5

Step-by-step explanation:

The stick has a length of 5 units

The stick is broken at two points chosen at random

First break: the probability that you get a piece that is 1 unit or longer than 1 units= 1/5.

Second break, the probability that you get a piece that is 1 unit or longer than 1 units is 1/5.

Therefore,

The total probability =probability of first break * probability of second break * original stick unit

=1/5 * 1/5 * 5

= 1/25 *5

=5/25

=1/5

Answer:

19

Step-by-step explanation:

The zebra is the 10th fastest, so there are 9 zebras that are faster.

It's also the 10th slowest, so there are 9 zebras that are slower.

The total number of zebras is therefore 9 + 1 + 9 = 19.

Answer:

4/9

Step-by-step explanation:

So, the ratio of the books is 8:10:6. After 2 books were taken off of each shelf, it became 6:8:4. All of these numbers added up is 18. So that means 8/18 of the books are math books, which can be simplified to 4/9.

Answer:

4/9

Step-by-step explanation:

Answer: x = 2

Step-by-step explanation:

First, Distribute

-2+8x=3x+8

Then, Subtract 3x

-2 + 5x=8

Then, Add 2

5x=10

Then, Divide by 5

x=2

Hope it helps <3

Answer:

-2(1-4x)=3x+8

distributive property

-2+8x=3x+8

subtract 8 on both sides

-2-8+8x=3x=-10+8x

now subtract 8x on both sides which equal: -10=-5x

now it part of the step and divide -5 on both sides to leave x or solve for x

-10/-5=x=2=x

x=2

Step-by-step explanation:

Step-by-step explanation:

1. Yes  addition, subtraction, multiplication, and division can be performed on polynomials. like our everyday arithmetic dealings with mathematical operators, polynomials are no exception when it comes to math operators, the four   basic operations addition, subtraction, multiplication, and division can be performed on polynomials as well.

2. It can be less handy plus the operation can get messy if you do not have a good sense/understanding/hold of what you are doing things can get messy.

3. I personally know that the simplest is the addition of polynomials

4. I cant say which is difficult, but the operation that can get things messy  for me most time is the division operation

Answer:

4 packages of AA batteries

6 packages of AAA batteries.

Step-by-step explanation:

Let the number of packages of AA batteries bought be x

Let

the number of packages of AAA batteries bought be Y

He Brought 10 packages of AA and AAA

thus,

x+y = 10   equation 1

Given

The AA batteries are sold in packages of 6, it means one packet contains 6 batteries

Thus,

Total number of AA  batteries in x packages = 6x

The AAA batteries are sold in packages of 8, it means one packet contains 8 batteries

Thus,

Total number of AAA  batteries in y packages = 8y

Given total no. of batteries is 72

thus    

6x + 8y = 72   equation 2

x+y = 10

y = 10-x ---using this in equation 2

6x + 8(10 - x)  = 72  

=> 6x + 80 - 8x = 72

=> -2x = 72-80 = -8

=> x = -8/-2 = 4

y = 10 -x = 10 -4 = 6

y = 6

Thus,

he bought 4 packages of AA batteries

6 packages of AAA batteries.

Answer: 34°

Step-by-step explanation:

The Arc formed by segment AC:

Total measure of an arc = 360°

Measure of Major arc AC = (360° - measure of minor arc)

Minor arc = 146°

THEREFORE,

Major arc AC = (360° - 146°) = 214°

A° = B° = (214° - 146°) / 2 ( tangent - tangent theorem)

Angle formed by tangent AB and BC = difference between major and minor arcs divided by 2 : (Major arc - minor arc) / 2

(214 - 146)° / 2 = 68° / 2 = 34°

The measure of ∠ABC as shown in the circle is 34°.

A circle is the locus of a point such that all the points are equidistant from a fixed point known as the center.

∠OCB and ∠OAB = 90° (angle between a tangent and radius)

∠OCB + ∠OAB + ∠COA + ∠CBA = 360° (angles in  a quadrilateral)

90 + 90 + 146 + ∠CBA = 360

∠CBA = 34°

The measure of ∠ABC as shown in the circle is 34°.

Find out more on Circle  at: https://brainly.com/question/22965557

Answer:

The function is:

y = 150*x

where y is the number of calories consumed, and x is the number of pieces of candy consumed.

Now, the domain of a function is the possible values of x that you can input in the function.

For this particular case you can have:

x = 0 (no pieces candy)

x = 1 (one piece of candy)

x = 2 (two pieces of candy)

Notice that x can be only whole numbers because, in principle, you can't eat a fraction of a piece of candy.

So we only use x = whole numbers.

Then the domain of the function is equal to all the natural numbers plus the zero, or:

D = {x ∈ N ∪ {0}}

"x belongs to the union between the set of the natural numbers and the zero"

The amount of candies can only be positive values, hence the domain of the value exists on all natural numbers that are x≥0

The domain of a function is the input values of the function for which it exists.

Given the expression that relates the number of calories you consume after eating x pieces of candy as shown:

y = 150x

The amount of candies can only be positive values, hence the domain of the value exists on all natural numbers that are x≥0

The function is also discrete because the number of candies can be counted. Note that the domain of all discrete functions is countable.

Learn more about discrete function here:

https://brainly.com/question/25050804

Answer: [tex]U_{n} =(40)+(n-1)(10)[/tex]

Step-by-step:

[tex]U_{n} =a+(n-1)d[/tex]

a = 40

d = 10

[tex]U_{n} =(40)+(n-1)(10)[/tex] is the formula for nth hour

Answer:

-24

Step-by-step explanation:

g(-2) = 2(-2)

g(-2) = -4

h(4) = 4² + 4

h(4) = 16 + 4

h(4) = 20

g(-2) - h(4)

-4 - 20

= -24

Answer:

Step-by-step explanation:

g(x) = 2x

To find g( -2) substitute - 2 into g(x)

That's

g( -2) = 2(-2) = - 4

h(x) = x² + 4

To find h(4) substitute 4 into h(x)

That's

h(4) = (4)² + 4 = 16 + 4 = 20

So

g(-2) - h(4) is

- 4 - 20

= - 24

Hope this helps you

Answer: 20cm

Step-by-step explanation:

The perimeter of a rectangle can be calculated as 2(l+w)

2(6+4)

2(10)

20

Hope it helps, and if you want more info on perimeter, just ask <3

Answer:

20 cm

Step-by-step explanation:

Use folmula P=2(l+w)

Answer:In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. An example of a polynomial of a single indeterminate, x, is x2 − 4x + 7.

Step-by-step explanation:

might help