What is the equation of the following line? Be sure to scroll down first to see all answer options

The given expressions written in standard form are;

A) 21 × 10⁷

B) 5 × 10²

This is about expression of given algebra in standard form making use of laws of indices.

A) We are given;

(7 × 10⁵) × (3 × 10²)

Now according to the law of indices, when we want to multiply 2 numbers with same bases and different exponents, we retain the bases and add the exponents.

Also, when we want to multiply 2 numbers with different bases and same exponent, we multiply the bases and retain the exponent.

Applying that to our question gives;

(7 × 3)¹ × (10)⁽⁵ ⁺ ²⁾

⇒ 21 × 10⁷

B) We are given;

(2 × 10⁵)/(4 × 10²)

According to the law of indices, when we want to divide 2 numbers with same bases and different exponents, we retain the bases and subtract the exponents.

Also, when we want to divide 2 numbers with different bases and same exponent, we divide the bases and retain the exponent.

Thus;

(2/4)¹ × (10)⁽⁵ ⁻ ²⁾ = 0.5 × 10³

0.5 can also be expressed as; 5 × 10⁻¹

Thus, 5 × 10⁻¹ × 10³ = 5 × 10²

Read more at; brainly.in/question/18681990

Answer:

5.29

Step-by-step explanation:

Answer:

To solve this question, we just need to observe the given graph.

Each little square is equivalent to 0.5 units, so there are 5 students who fot more than 8. Specifically, 1 got 8 points and 4 students got 10.

There are 33 pupils in total, remember that each little square is equivalent to 0.5 units.

The assumption was that the majority of pupils scored less than 8.

The complete question is;

Lourdes is making a frame in the shape of a parallelogram. She adds diagonal braces to strengthen the frame. Parallelogram A B C D is shown. Diagonals are drawn from point A to point C and from point D to point B and intersect at point E. The length of D E is (3 y + 6) centimeters, the length of E B is (5 y minus 10) centimeters, and the length of E C is (2 y + 4) centimeters. How long is the brace that connects points B and D? 8 cm 16 cm 30 cm 60 cm

Answer:

60 cm. Option D is the correct answer

Step-by-step explanation:

From the image, the diagonals of the parallelogram bisect each other. Thus;

AE = EC and BE = ED

We are given that;

DE = 3y + 6 cm and BE = 5y - 10 cm, thus;

3y + 6 = 5y - 10

Rearranging, we have;

5y - 3y = 6 + 10

2y = 16

y = 16/2

y = 8 cm

The brace that bisects point B and D is BD. So, BD = BE + DE

So, BD = 5y - 10 + 3y + 6

BD = 8y - 4

Putting 8 for y to obtain;

BD = 8(8) - 4

BD = 64 - 4

BD = 60cm

Answer:

60 cm

Step-by-step explanation:

tan X = |YZ| / |XZ| = 20/8 = 5/2

X = arctan(5/2) = 68.2°

Answer: 68.2°

The size of angle ∠YXZ is 68.3° given that sides YZ=20cm and XZ=8cm by using trigonometric ratios.

In a right angled triangle, if A is an angle other than right angle then trigonometric ratios are

sin A =[tex]\frac{opposite side}{hypotenuse}[/tex]

cos A=[tex]\frac{adjacent side}{hypotenuse}[/tex]

tan A =[tex]\frac{opposite side}{adjacent side}[/tex]

Given YZ=20cm and XZ=8cm

Since the triangle is right angled, and opposite side and adjacent side are given we can find tan(∠YXZ )

tan (∠YXZ ) =20/8 =2.5

∠YXZ = arctan (2.5) =68.2°

Hence the size of angle ∠YXZ is 68.2° given that sides YZ=20cm and XZ=8cm.

Learn more about trigonometric ratios here :

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Answer:

Options B, C and D.

Step-by-step explanation:

Those are the answers because when you solve the equation, the same values are on both sides of the equation. example option B;

-19x -19 = -19x-19

Add 19 to both sides of the equation to get rid of -19

-19x -19 +19 =-19x -19 +19

Divide both sides by -19

[tex]\frac{-19x}{-19} = \frac{-19x}{-19}[/tex]

x = x

Answer:

a=24.65 sq.m

Step-by-step explanation:

A=[tex]a^{2} or l^{2}[/tex]

608=[tex]a^{2}[/tex]

[tex]a=\sqrt{608}[/tex]

[tex]a=24.65[/tex]

To check your answer

[tex]A=a^{2} \\A=24.65^{2}\\A=24.65*24.65\\A=607.6225=608[/tex]

Answer:

y= -x^2+5

Step-by-step explanation:

It normally expontionally goes up, so across the x axis is down so it is negative, and is is all scales up, so the start is 5 up from the origin on the y axis, so it would be y=-x+5

Hope this helped!

Answer:can you put some angle degrees on it plz

Step-by-step explanation:

Answer:

  a.  16%

Step-by-step explanation:

The difference from the mean is ...

  (x - µ) = 4420 lb -3550 lb = 870 lb

Then the minimum Z-score of the traffic of interest is ...

  (x - µ)/σ = (870 lb)/(870 lb) = 1

__

The "empirical rule" tells you that 68% of a normal distribution is within 1 σ (Z = ±1) of the mean. If 68% is inside that range, then the remaining 32% is outside that range. The normal distribution is symmetrical about the mean, so half that quantity is below Z = -1, and the other half, 16%, is above Z=1.

About 16% of the cars have weights more than 4420 pounds.

Answer:

2.5

Step-by-step explanation:

I'm sorry I don't know how to explain it but I'm pretty sure the answer is a. 2.5

Answer:

180 meters

Step-by-step explanation:

The function you have here is negative function meaning the function has a concave down parabola (if you graph it on desmos or a graphing calculator you'll see what I'm talking about).

So they gave it to you in factored form and asked you to find the max. The max of this function is at the vertex of the parabola. In order to find the vertex you have distribute or multiply to get the original polynomial.

-5(x-8)(x+4)

-5(x^2+4x-8x-32)

-5(x^2-4x-32)

-5x^2-20x-160

Vertex formula is: -b/2a

b = 20

a = -5

[tex]\frac{-20}{2(-5)}[/tex]

= 2

The x-coordinate of the vertex is 2.

Plug 2 into the equation

-5(2)^2+20(2)+160

= 180 meters

Answer:

39

Step-by-step explanation:

From left to right but first parenthesis

11-6=5

5+2=7

7x5=35

12/3=4

35+4=39

Answer:

39

Step-by-step explanation:

1. Never forget to use P.E.M.D.A.S

11 - 6 = 5

2 + 5 (5) + 12/3

39

Answer:

The logo has an area of 5.7 cm².

Step-by-step explanation:

The area of the logo must be equal to the sum of the square's area and the triangle's one, therefore we will calculate each individually. The triangle is attached to the square, this means that its base has the same length as the side of the square.

[tex]square = side^2 = 2^2 = 4 \text{ cm}^2[/tex]

[tex]triangle = \frac{b*h}{2} = \frac{2*1.7}{2} = 1.7 \text{ cm}^2[/tex]

The total area of the figura is:

[tex]total = square + triangle = 4 + 1.7 = 5.7 \text{ cm}^2[/tex]

The logo has an area of 5.7 cm².

Corrected Question

The triangular prism shown has 1, 2, 3 or 5 triangular faces and 1,2,3, or 5 lateral faces.

The area of one triangular face is 7.5,8.125,15,or 17  [tex]mm^2[/tex]

The surface area of the triangular prism is 55.5,127.5,135,or 150  [tex]mm^2[/tex]

Answer:

(B)2 triangular faces

(C)3 lateral faces.

(A)Area of one Triangular Face [tex]=7.5mm^2[/tex]

(C)Total Surface Area of the Triangular prism [tex]=135mm^2[/tex]

Step-by-step explanation:

The triangular prism is attached.

The triangular prism shown has 2 triangular faces and 3 lateral faces.

Base of the triangle =2.5mm

Height of the Triangle =6mm

Area of one Triangular Face [tex]=\frac{1}{2}*6*2.5=7.5mm^2[/tex]

The dimensions of the lateral rectangles are:

Therefore, total surface area of the triangular prism

=2(Area of one Triangular Face)+Area of 3 rectangular faces

[tex]=2(7.5)+ (2.5 X 8+ 6 X 8 + 6.5 X 8)\\=15+120\\=135mm^2[/tex]

Total Surface Area of the Triangular prism [tex]=135mm^2[/tex]

Answer:

A....2

B....3

C.....7.5

D......135

Step-by-step explanation:

We know that the area of each tile is 3 1/2in^2

All we need to do is divide.

210 / 3.5 = 60

So, she will need 60 tiles to cover the entire bathroom floor.

Best of Luck!

Answer:

-8

Step-by-step explanation:

1+5=6

6-8=-2

4x-2=-8

Answer:

8

Step-by-step explanation:

Answer:

x= 8, 3

Step-by-Step Explanation:

[tex]x= \frac{-(-5)^{2} +\sqrt{(-5)^2-4*1(-24)} }{2*1} =8[/tex]

[tex]x= \frac{-(-5)-\sqrt{(-5)^2-4*1(-24)} }{2*1} : -3[/tex]

To find the volume of a box-shaped fish trap, we have to multiply the three dimensions of it: 

(1/4 m)* (2/3 m)* (3/5 m)

= (1*2*3)/ (4*3*5) m^(3)

= 6/ 60 m^(3)

= 1/10 m^(3)

= 0.1 m^(3)

The volume of the box-shaped fish trap is 0.1 m^(3).

Hope this is helpful~

Answer:

[tex]\frac{\sqrt[3]{19} }{\sqrt[3]{x} }[/tex]

So A is the answer

Step-by-step explanation:

[tex]y=\frac{19}{x^3}\\\mathrm{Interchange\:the\:variables}\:x\:\mathrm{and}\:y\\x=\frac{19}{y^3}\\\mathrm{Solve}\:x=\frac{19}{y^3}\:\mathrm{for}\:y\\y=\sqrt[3]{\frac{19}{x}}\\\sqrt[3]{\frac{19}{x}}\\\frac{\sqrt[3]{19} }{\sqrt[3]{x} }[/tex]

Answer:

3 to 5 This is because if you simplify the ratio by dividing each number in the ratio by 4, therefore for every group of 5 birds 3 of them are parrots

Step-by-step explanation:

Answer:

answer d

Step-by-step explanation:

edg 2020

Answer:

D 49

Step-by-step explanation:

just did it

Step-by-step explanation:

pythagorean theorem states

c²=a²+b² where c is the longest line a is the base while b is the height thus

example

1)c²=a²+b²

12²=a²+8²

144=a²+64.

144-64=a²

80=a² a=√80. =8.9

2)c²=a²+b²

15²=4²+b²

225=16+b²

225-16=b²

209=b² b=√209. =14.45

3)c²=a²+b²

c²=5²+9²

c²=25+81

c²=106. c=√106. =10.295

I hope you have understood I will do the other ones simply

4)26²=18²+a²

676-324=a²

√352=a. a=18.761

5)10²-6²=b²

100-36=b² b²=64. b=8

6)c²=12²+9²

=144+81.

c² =225. c=15

1...

Formula=  A=C^2-B^2

A=12^2-8^2

A=144-64

144-64=80

√80 = 8.944

Rounded = 8.9

2...

Formula=  A=C^2-B^2

A=15^2-4^2

A= 225-16

225-16=209

√209=  14.456

Rounded= 14.5

3...

Formula= A^2+B^2=C^2

9^2+5^2=C^2

81+25=106

√106=  10.295

Rounded= 10.3

4...

Formula=  A^2=C^2-B^2

A^2= 26^2-18^2

A^2=676-324

676-324=352

√352=18.761

Rounded= 18.8

5...

A^2=C^2-B^2

A^2=10^2-9^2

100-91=9

√9=3

6...

Formula= A^2+B^2=C^2

9^2+12^2=C^2

81+144=225

√225=15

Code= 8.9, 14.5, 10.3, 18.8, 3, 15.

Step-by-step explanation:

The first term is 6x3

Because he subtracted like terms 8x3 and 2x3

Answer:

6x³

Step-by-step explanation:

2x²y + 8x³ – xy² – 2x³ + 3xy² + 6y³=

6x³+2x²y+2xy²+6y³

Answer:

there are 62 prime numbers with squares

Answer:

i believe it is 3...?

11, 13, and 17

Step-by-step explanation:

11 = 121

13= 169

17 = 289

these are prime numbers

Answer: B. 72ᴼ alternate exterior angles theorem

Step-by-step explanation:

Alternate exterior angles because they’re angles on the outside of the transversal.

Alternate exterior angles are also congruent to each other, so that’s why 2 is congruent to 72ᴼ

Answer:-637

Step-by-step explanation:

Answer:

It will be true when a ≤ 4

Step-by-step explanation:

You can plug in the number to see if it is correct. 4(4) ≤ 16. Sorry, I'm not the best at explaining things.

Answer:

g(-4) =1

Step-by-step explanation:

g(-4) we want to find the value of the graph when x = -4

Got over to x=-4

Got up to the blue line

read the value of the y coordinate

y=1

g(-4) =1

Answer:

x = -2

Step-by-step explanation:

-5x - 7 = 3

-5x = 10

x = 10/-5

x = -2