What is tan 30°?
1
60
90°
√3
2
30⁰
OA. √2
OB.
O C.
O D.
√√3
√√3
OE. √3
O F. 1

ΔRST was dilated and then dilated, to create ΔZXY.

The correct answer is option D.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

The statement "RST and ZXY are similar" means that the two triangles have the same shape but possibly different sizes.

Similarity means that corresponding angles are congruent and corresponding sides are proportional.

Now,

If Triangle RST was dilated to create Triangle ZXY, it means that Triangle ZXY is an enlarged or reduced version of Triangle RST, with the same shape and proportions.

This is because dilation is a transformation that changes the size of a figure while preserving its shape.

Therefore,

Triangle RST was dilated and then dilated, to create Triangle ZXY.

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Step-by-step explanation:

25 (divided by 5) 5

__ = __

40 (divided by 5) 8

[tex]|\Omega|=25+15=40\\|A|=25\\\\P(A)=\dfrac{25}{40}=\dfrac{5}{8}=62.5\%[/tex]

Step-by-step explanation:

Let the number originally be "x".

Then, According to the question,other number is 3 times [3*] greater as other.

Sum of these two numbers is 24.

ATP, equation'll be :

Solving:

Therefore,one number[x] is 6.

Other number :

The equation of the line is y = -7/5x + 56/5

The formula for expressing equation of a line is given as y = mx + b

where

m is the slope

b is the y-intercept

Given the coordinates A(8, 0) and (3, 7)

Determine the slope

Slope =7-0/3-8

Slope = -7/5

For the intercept

0 = -7/5(8) + b

b = 56/5

Hence the equation of the line is y = -7/5x + 56/5

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Answer:

7)  y⁹

9)  a⁸

Step-by-step explanation:

when we multiply two exponents (of the same base), we can add them

so, a² · a³ = a² ⁺ ³ = a⁵

let's test it out!

(a = 2 in our example)

2² · 2³ = 2⁵

4 · 8  = 32   (2⁵ = 32)

32 = 32

because this is true, we know that we can add exponents of the same base when multiplying them together

now, let's try out the question at hand:

y³ · y⁶

well, we know that 3 + 6 = 9, so y³ · y⁶ can be simplified to y⁹

--

now, we're going to be working with division. We know that division is the inverse of multiplication, so we logically know that instead of adding exponents, we subtract them when dividing

here,

a³ ÷ a² would equal a¹    (3 - 2 = 1)

let's put a = 2 again:

a³ ÷ a² = a³ ⁻ ² = a¹ = a

2³ ÷  2² =   2¹

8  ÷   4   =  2

2   =  2

once again, we have proven this shortcut to be true

now, to the problem at hand!

first, we can multiply a³ · a⁹

a³  ·  a⁹   =  a³ ⁺ ⁹  =  a¹²

so, let's rewrite the problem:

a¹² /  a⁴

because we're dividing with exponents, we can subtract 12 - 4

a¹² / a⁴

a¹² ÷  a⁴

a¹² ⁻ ⁴

a⁸

so, our simplified answer is a⁸

(note: they must be the same base, [the thing that the exponent is attached to] for this to apply)

hope this helps (and makes sense)! have a lovely day :)

The required simplification is   [tex]y^{9}[/tex]  and  [tex]a^{8}[/tex] .

To simplify the following 1 )  [tex]y^3* y^6[/tex]  2 ) [tex]\frac{a^3*a^9}{a^4}[/tex].

The process in mathematics to operate and interpret the function to make the function simple or more understandable is called simplifying and the process is called simplification.

1 )  [tex]y^3* y^6[/tex]
= [tex]y^3* y^6[/tex]
since the base of the exponents is the same so the powers of y get added
[tex]=y^{3+6}[/tex]
[tex]=y^{9}[/tex]

2 ) [tex]\frac{a^3*a^9}{a^4}[/tex]
[tex]=\frac{a^3*a^9}{a^4}[/tex]
since the base of the exponents is the same so the powers of a get added in the numerator.
[tex]=\frac{a^{3+9}}{a^4}[/tex]
[tex]=\frac{a^{12}}{a^4}[/tex]
Now, the power of the numerator will get decreased by the power of the denominator because the base is common i.e. a
[tex]=a^{12-4}[/tex]
[tex]=a^{8}[/tex]

Thus the required simplification is   [tex]y^{9}[/tex]  and  [tex]a^{8}[/tex] .

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Using Pythagorean theorem and trigonometric ratio, the resultant vector is 30.72km and the angle between is 53.1°

To determine the balloon's resultant vector, we can use the concept of Pythagorean theorem;

x² = 18.5² + 24.6²

x² = 943.72

x = √(943.72)

x = 30.72km

The resulatant vector is 30.72km

Let's calculate the angle of the vector;

To determine the angle of the vector, we can use trigonometric ratios;

tanθ = opposite / adjacent

tanθ = 24.6 / 18.5

tanθ = 1.33

θ = tan⁻¹ 1.33

θ = 53.1°

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Answer:

Step-by-step explanation:

The ratio of Anne's height: Ben's height is 7:9.

Anne's height is 1.4m.

Find Ben's height.

we can solve with an equation

7 : 9 = 1.4 : x

x = 9 * 1.4 : 7

x = 1.8 m

Answer:

17.28 cm

Step-by-step explanation:

It is 1/2 of the entire circumference of the circle

=      1/2    *   pi * d

= 1/2 * pi * 11 cm = 17.28 cm

Answer:

1. b=(d-c)/a

Step-by-step explanation:

make me a brainlist

If the length of garden is 9 feet ,breadth is 4 feet and Mark need to fence four gardens then the total fencing will be 104 feet.

Given The number of gardens is 4. The length and breadth of a garden is 9 feet and 4 feet.

We have to find total length of fencing Mark needs to surround all 4 gardens. Perimeter is the sum of all the sides of the rectangle. Length of opposite side of rectangle must be equal.

Perimeter of a rectangle=2(l+ b)

perimeter of 1 garden=2(l+ b)

=2(9+4)

=2*13

=26 feet

perimeter of 4 gardens will be 4*26

=104 feet.

Hence the total length of fencing that Mark needs to do is 104  feet.

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Answer:

[tex]6x^{2} +9x -4x+6\\[/tex]

Step-by-step explanation:

First you take 3x times 2x since its the first of both equations, which will give you 6x squared.

Then take the outer ones of both problems which is 3x times 3 which is 9x.

Then the inner, -2 times 2x which is -4x

Then the last of both individual problems which is -2 times -3 which is positive 6.

The response variable in this experiment is C. the grade received on each assignment.

The Response Variable is the result of the experiment after manipulating the explanatory variable.

The response variable can also be called the Dependent or Outcome variable.

In research, the researcher develops a question about the response variable.

Thus, the response variable in this experiment is C. the grade received on each assignment.

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The minimum sample size needed in the research of systolic blood pressure is 68.

Given standard deviation=25 mm Hg, confidence level=90%, Estimation =5 mm Hg.

We have to first find the level of alpha which is known as error.

α=(1-0.9)/2

=0.05

Now we have to find z in the z table as such z has a p value of 1-α,that is z with a p value of 1-0.05

=0.95 ,so Z=1.645.

now finding the margin of error, which is as under:

[tex]M=z st/\sqrt{n}[/tex]

in which st is standard deviation and the n is sample size of population.

By assuming the standard deviation of 25 mm Hg we get values as under:

n is sample size.

[tex]M=z* st/\sqrt{n}[/tex]

[tex]5=1.645*25/\sqrt{n}[/tex]

[tex]5\sqrt{n}=1.645*25\\[/tex]

dividing both sides by 5

[tex]\sqrt{n}=1.645*5[/tex]

squaring both sides we get

n=67.65.

Hence the sample size needed by the researcher is 68.

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The given question is incomplete as it should includes :

standard deviation= 25mm Hg

Confidence level=90%

Estimation 5 mm Hg of u.

Answer:

29ba - 7 - 5bc

Step-by-step explanation:

8ab-5bc +21ba-7

The terms 8ab, 5bc, and 21ba are made up of units multiplied by each other.  This means that each can be rewritten in a different order.  For example,

8ab is the same as:

8ba, b8a, ab8, ba8, or a8b

We may rewrite the terms to see the ones that can be combined.

8ab-5bc +21ba-7

8ba-5bc +21ba-7

8ba+21ba-7-5bc

29ba - 7 - 5bc

Using Sarai's measurements, Line 3 must be parallel to Line 5 according to (A) Converse of Alternate Exterior Angles Theorem.

Alternate Exterior Angles theorem states that, "If two lines are parallel and they are intersected by same straight line then the alternative exterior angles formed by the figure are equal to each other."

Converse of the above theorem states that, "If two lines intersected by one transverse and formed alternate exterior angles, and if they are equal to each other then that two lines are parallel to each other."

Here in Sarai's measurement we can see that Line 3 and Line 5 are intersected by one straight line and the formed alternate exterior angles both are 65, which shows they are equal to each other.

Hence by Converse of Alternate Exterior Theorem we can say that Line 3 and Line 5 are parallel to each other.

So, Line 3 must be parallel to Line 5 according to Converse of Alternate Exterior Angles Theorem.

Hence Option (A) is correct.

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The conditional probability formula is P(X|Y) = P(X and Y)/P(Y)

The conditional formula is represented as:

P(A|B) = P(A and B)/P(B)

In this case:

A = X

B = Y

So, we have:

P(X|Y) = P(X and Y)/P(Y)

Hence, the conditional probability formula is P(X|Y) = P(X and Y)/P(Y)

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Answer:

x = 2 and y = -1

Step-by-step explanation:

that is the solution above

Answer:

x = 2

y == -1

Step-by-step explanation:

     x - 10y = 12 ----------------(I)

   10x + 10y = 10 --------------(II)

We can find the value of 'x' by eliminating 'y'. To eliminate 'y', add equations (I) & (II)

           (I)             x - 10y = 12

          (II)         10x + 10y = 10   {Now add the equations}

                         11x          = 22

                                     x = 22 /11

                                  [tex]\sf \boxed{\bf x = 2}[/tex]

Now, Plugin x = 2 in equation (1)

 10*2 + 10y = 10

   20  + 10y = 10

             10y = 10 - 20

             10y = -10

                 y = -10/10

                [tex]\sf \boxed{\bf y = -1}[/tex]

The set of points which includes all of the solutions for y in the given equation is the set of all real numbers.

The equation given in the task content whose solution set is go be determined is;

y = (5/2)x + 3/2.

It therefore follows that the solution set for.tge equation includes all real numbers as the equation is linear.

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The parabola equation in the factored and standard form are f(x) = (x + 2)(x - 5), and f(x) = (x - 3/2)² - 49/4 respectivly.

It is defined as the graph of a quadratic function that has something bowl-shaped.

We have:
Parabola with zeros at (-2, 0) and (5, 0) and passes through the point (-1, -4)

In factored forms:

f(x) = (x + 2)(x - 5)

Because zeros at (-2, 0) and (5, 0)

In the standard form:

f(x) = x² - 3x - 10 or

f(x) = (x - 3/2)² - 49/4

Thus, the parabola equation in the factored and standard form are f(x) = (x + 2)(x - 5), and f(x) = (x - 3/2)² - 49/4 respectivly.

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Answer:

A.

Step-by-step explanation:

This is a 4th degree polynomial. The function has two roots at x = 0, and two more roots at x = -2 and x = 2. Since the two roots at x = 0 are just one number, the function has three distinct real roots.

Answer: A.

The numeric values for the expressions are given as follows:

The numeric value of an expression is found replacing the letters by their numeric values.

The values of the letters are given as follows: A = 5, B = 4.4, C = 4.25.

Hence the values of the expressions are:

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The total amount of money he had is $160.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given :

I had $13.00.

My Mom gave me $10.00.

My Dad gave me $30.00.

My Aunt, My Uncle, and grandma gave me $100.00.

I had another $7.00.

The initial amount of money he had

= $13 + $7

= $20

His Mom gave him $10.00.

So, the total amount of money now he had is:

= $20 + $10

= $30

His Dad gave him $30.00.

So, the total amount of money now he had

= $30 + $30

= $60

So, the total amount of money now he had

= $60 + $100

= $160

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Answer:

The answer in decimal form is 33.6.

The answer in fraction form is [tex]33\frac{3}{5}[/tex].

Step-by-step explanation:

To find 40% of 84, multiply 84 and 0.4.

84 × 0.4 = 33.6

The answer in decimal form is 33.6.

The answer in fraction form is [tex]33\frac{3}{5}[/tex].

Hope this helps!

Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "equations and expressions" The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.

Answer:

22.3

Step-by-step explanation:

By the law of Sines, since angle XYZ is 90 degrees,

[tex]\frac{XZ}{\sin 90^{\circ}}=\frac{YZ}{\sin X} \\ \\ XZ=\frac{1}{0.0448} \\ \\ XZ \approx 22.3[/tex]

The range of sales Dr. Spencer Lewis must exceed to profit the most from the second deal is 15,000 sales.

To find the range that will benefit Dr. Spencer Lewis the most with the second deal, we must perform the following operation:

We must replace the X with several numbers and buy the result, when the result of operation B exceeds the result of operation A, it means that it will be more profitable.

According to the above, if we replace the X with 15,000, the values will be the same, however, each number that we increase will mean a greater profit in agreement B.

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Answer:

E. Isosceles Triangle


Step-by-step explanation:

It is because it has 2 equal sides and 2 equal angles.

Answer:

1

Step-by-step explanation:

from sohcahtoa

tan = oppisite/ajacent

tan =5/5

tan = 1

Answer:7.07 ft

Step-by-step explanation:

use Pythagoras theorem for this one, in this question you have to find the hypotaneous, just use the formula H squared=b squared + p squared.

h squared =5 squared +5 squared

h squared =50

the squared on h will go on the other side and become the underfoot, so take the underfoot of 50

which givesus h=7.0

Answer:

A. (5, 13)

Step-by-step explanation:

The function f(x) = (x - 4) + 5 is the translation of the function f(x) 4 units right and 5 units up and the rule is:

(x, y) → (x + 4, y + 5)

Apply the rule to the given point to get:

(1, 8) → (1 + 4, 8 + 5) = ( 5, 13)

Correct choice is A