Which expression is equivalent to this expression?

Answer:

ST is 12 meters

Step-by-step explanation:

The given triangle ΔRST = An equilateral triangle

The altitude of ΔRST = SV

The length of segment RV = 6 meters

Given that ΔRST is an equilateral triangle, the base angles of the triangles = 60°, therefore, in the formed triangles, ΔRSV, and ΔTSV, ∠RSV = ∠TSV = 90° - 60° = 30°

∴ ΔRSV, and ΔTSV are congruent, based on ASA rule of congruency

∴ Side VT in ΔTSV is congruent to side RV in triangle ΔRSV  

The midpoint of side ST

VT ≅ RV

Therefore, VT = RV = 6 meters

RT = RV + VT = 6 + 6 = 12 By segment addition property

In equilateral triangle, ΔRST, all the sides are equal, therefore;

RT = RS = ST = 12 m

ST = 12 meters.

Given:

The data points are:

(1, 0), (2, 3), (3,1), (4,4), (5,5)

To find:

The equation of best fit line in the form of [tex]y=mx+b[/tex] and then find the value of b.

Solution:

The general form of best fit line is:

[tex]y=mx+b[/tex]              ...(i)

Where, m is the slope of best fit line and b is the y-intercept of the line.

Using the graphing calculator, we get the equation for the best fit line and the equation is

[tex]y=1.1x-0.7[/tex]          ...(ii)

On comparing (i) and (ii), we get

[tex]b=-0.7[/tex]

Therefore, the value of b is equal to -0.7.

Answer: Choice B

Explanation: The rule you use is [tex]\sqrt{m*n} = \sqrt{m}*\sqrt{n}[/tex]

Answer:

Step-by-step explanation:

A: is not the answer. The answer is √144 which is 12

B: is correct. You can do it this way, by breaking the 9 and 16 apart.

C: I don't know exactly what the logic of 36 is, but it is not the right answer.

D: I can't explain why the choice would be division. It is multiplication of some sort. D is incorrect.

Answer:

The domain is all x-values or inputs of a function. hope this helps!

Step-by-step explanation:

The Answer: C I did this yesterday

Step-by-step explanation:

Answer: [tex]7.81\ km[/tex]

Step-by-step explanation:

Given

Runner A runs towards North at speed of 10 km/h

Runner B runs towards East at speed of 12 km/h

After half hour, they covered a distance of

[tex]\Rightarrow d_a=10\times 0.5\\\Rightarrow d_a=5\ km[/tex]

[tex]\Rightarrow d_b=12\times 0.5\\\Rightarrow d_b=6\ km[/tex]

They are running in perpendicular direction to each other

So, the distance between them is  given by

[tex]\Rightarrow d=\sqrt{d_a^2+d_b^2}\\\Rightarrow d=\sqrt{5^2+6^2}\\\Rightarrow d=\sqrt{61}\\\Rightarrow d=7.81\ km[/tex]

Answer:

Step-by-step explanation:

(-1, 3)

y=3

Answer:

a) 20 km away fro the starting point.

b) The bearing from P to R is 80°.

c) Q is 60 km North P.

d) Q is - 60 km west of P

Step-by-step explanation:

Stating Facts in the Question:

P to Q is 80 km and bearing 330°

It turned around, Q to R is 60 km and bearing 250°.

a) Picture a number line (Look at the first image)

You go 80 to the right. You turn around and go 60 to the left.

80 - 60 = 20

20 km away fro the starting point

b) Picture a number line (Look at the second image)

P to Q is bearing 330°

Q to R is 60 km is bearing 250°

P to Q is red

Q to R is blue

330° - 250° = 80°

The bearing from P to R is 80°

c) P to Q is 60 km

The plane went forward or North so the answer is 60 km.

Q is 60 km North P.

d) Q to P is 60 km

Q is not to the west of P

Q is - 60 km west of P

Answer:

Step-by-step explanation:

9)  (25-x^2 )(a+2) = (5-x)(5+x)(a+2)

11) 9(v-3)+u^2(3-v)

   9(v-3)+u^2( -v+3)

   9(v-3)-u^2( v-3)

   (9-u^2)(v-3)

 (3-u)(3+u)(v-3)

Answer:

I'm in 9th grade but i think i can help.

Step-by-step explanation:

Answer:

19.20

Step-by-step explanation: used

a calc

Answer:

Step-by-step explanation:

The two triangle are congruent for the rule SAS

QP congruent to TU

angle P and angle T are both right

side PR is in common

Answer:

[tex]6^4[/tex]

Step-by-step explanation:

All you have to do for this is follow PEMDAS (Parenthesis, Exponent, Multiplication, Division, Addition, Substraction) Which is the order of operations.

First you do parenthesis, [tex](2^2)^2[/tex], when you have a positive exponent outside a parenthesis like this, you add them together, and in this case, you get, [tex](2^2)^2=2^4=16[/tex]

After that, you do the rest of the exponents as well as multiplication, [tex]3^4=81[/tex].

Now we plug in the 81 from our last step along with the 16 from the first step and multiply them together. [tex]3^4*(2^2)^2=81*16=1296[/tex]

Then you just simply need to find which of the answers come out to be the result we got which is 1296. Out of these 4 possible answers, [tex]6^4[/tex] ends up being equal to 1296 which means that is the correct answer.

Answer:

6^4 is equivalent to 3^4 x (2^2)^2

Step-by-step explanation:

3^4 x (2^2)^2                  6^8 = 1679616

  3^4 x (4)^2                    6^4 = 1296

     81 x 16                       5^4 = 625

         1296                       5^8 = 390625

Answer:

1st onne I believe I couldd be wrong but thats what I got

Step-by-step explanation:

Answer:

Number of hours= 7.5

Step-by-step explanation:

Giving the following information:

Amount saved= $35

Hourly rate= $6

Total objective= $80

To calculate the number of hours to be saved, we need to use the following formula:

Number of hours= difference needed / hourly rate

Number of hours= (80 - 35) / 6

Number of hours= 45/6

Number of hours= 7.5

Step-by-step explanation:

(F-g) (X)

= f(x) - g(x)

(2x² + 2 )-(x²-1) =

3x²+3

Answer:

7_14-21-28-35-42-49 -56-63-70-77-84

Answer:

A

Step-by-step explanation:

The zero is the value of x where the line crosses the x- axis

The line crosses the x- axis at x = - 5 ← zero

Answer:

-5

Step-by-step explanation:

The zero of a function is the x-value of the location where the function intersects the x-axis.

Here I read at (-5,0), the function intersects the x-axis, so the zero of the functiion is x = -5

This is a function because each element in the domain has one and only distinct image in the co-domain.

[tex]4( \frac{1}{5} x + 7) = 2x - 2[/tex]

[tex]x = 25[/tex]

Given:

In a right angle triangle,

Hypotenuse = 25 cm

Base = x

Angle between base and hypotenuse = 18 degrees.

To find:

The value of x.

Solution:

In a right angle triangle,

[tex]\cos \theta =\dfrac{Base}{Hypotenuse}[/tex]

In the given right triangle,

[tex]\cos (18^\circ) =\dfrac{x}{25}[/tex]

[tex]\cos (18^\circ) \times 25=x[/tex]

[tex]0.9510565 \times 25=x[/tex]

[tex]23.7764125=x[/tex]

Round the answer to the nearest hundredth (two decimal).

[tex]x=23.78[/tex]

Therefore, the value of x is about 23.78 cm.

Answer:

Base = 10.5 cm

Step-by-step explanation:

GIVEN :-

TO FIND :-

GENRAL FORMULAE TO BE USED IN THIS QUESTION :-

For a triangle with height 'h' & base 'b' , its area = [tex]\frac{1}{2} \times b \times h[/tex]

SOLUTION :-

[tex]Area = \frac{1}{2} \times Base \times Height[/tex]

[tex]=> 94.5 = \frac{18b}{2}[/tex]

[tex]=> \frac{18b}{2} \times 2 = 94.5 \times 2[/tex]

[tex]=> 18b = 189[/tex]

[tex]=> b = \frac{189}{18} = 10.5[/tex]

The coordinates of the point on the unit circle at the given angle. 135° is (-√2 / 2, √2 / 2).

A circle on the Cartesian Plane with a radius of one unit and a center position is referred to as a unit circle (0, 0). When working with angles and trigonometric functions, the unit circle is a useful tool that makes reference much simpler. The Pythagorean Theorem can be used with the unit circle.

Given:

The unit circle at the given angle 135°,

Calculate the value of sin45 as shown below,

sin (180 - 135) = 1 / √2

sin 45 = 1 / √2

cos(180 - 135) =  1 / √2

cos45 = 1 / √2

Write the coordinates as shown below,

Coordinates = (1 / √2 × √2 / √2, 1 / √2 × √2 / √2 )  (Second quadrant is (-x, y))

Coordinates = (-√2 / 2, √2 / 2)

Thus, the coordinates are  (-√2 / 2, √2 / 2).

To know more about unit circle:

https://brainly.com/question/11743473

#SPJ2

Answer:

CPCTC

Step-by-step explanation:

BESTIE MY CAPS LOCK KEY IS LIKE STUCK SO YEAH

ANYWAY, THIS IS GOING TO SOUND REALLY AGGRESSIVE

SO CONGRUENT TRIANGLES HAVE 3 EQUAL SIDES AND 3 EQUAL ANGLES

THEY ARE EXACTLY THE SAME

SINCE WE KNOW ALL OF THIS AWESOME INFORMATION, NOW WE CAN THAT THE ANGLE BISECTORS WILL BE CONGRUENT BY CPCTC -

CORRESPONDING PARTS OF CONGRUENT TRIANGLES ARE CONGRUENT

WE CAN USE AN EXAMPLE TO UNDERSTAND BETTER

SAY YOU HAVE 2 CONGRUENT TRIANGLES

THE ANGLES ARE 50, 60, AND 70

SAY THAT THE ANGLE BISECTORS ARE ON 60

THEY WILL BE CONGRUENT BECAUSE THEY ARE THE CORRESPONDING ANGLES OF 2 CONGRUENT TRIANGLES

BUT WHEN YOU ARE ASKED FOR A REASON, IT IS BECAUSE OF CPCTC

CORRESPONDING PARTS OF CONGRUENT TRIANGLES ARE CONGRUENT

Answer:

M1=44 M2=136 M3=44 M4=136

Step-by-step explanation:

M3= 44 so M1=44 due to opposite angles being equal

then if two of the angles add to 88

360-88= 272

divide 272 by 2 as M2 and M4 are equal

272/2=136

Answer:

m∠1 = 44°

m∠2 = 136°

m∠4 = 136°

Step-by-step explanation:

m∠1 explanation:

I got it from m∠3 since they're both congruent

m∠2 explanation:

Since we already have the measure of 3 and 1, we can easily add both of the measures (44 + 44 = 88°) then subtract it from 360° (total) = 272°

Then since both measures (2 and 4) are congruent (measuring the exact same length and angle) we can divide 272° ÷ 2 = 136°

m∠4 explanation:

I got it from m∠2 since they're both congruent

Answer:

€270

Step-by-step explanation:

If a fruit vendor has bought 165kg of apples at € 2 per kilo, the total amount spent is expressed as;

Cost price = 165 * 2 = €330

If 15kg spoilt, the amount of fruit remaining will be 165 - 15 = 150kg

If he rests he sells for € 4 per kilo, then;

Selling price = 150 * 4 = €600

Amount earned = €600 - €330

Amount earned = €270

Answer:

See below

Step-by-step explanation:

3x < 11.75

11.75 / 3 = 3.92

x < 3.92

Answer:

41.4º

138.6º

Step-by-step explanation:

x + (x - 97.2) = 180

2x - 97.2 = 180

2x = 277.2

x = 138.6º

x - 97.2 = 41.4º