What is the tangent
ratio of angle C₂ ?

Plug the second equation (the one already solved for y) into the first equation

2x - (2x + 3) = 7

2x - 2x - 3 = 7

-3 = 7

Since the 2x's canceled out and left a false statement, this system of equations has no solution.

Hope this helps!

Step-by-step explanation:

a square has the same perimeter as a 5cm by 7cm rectangle. which of the following area of the square

Answer:

At sea level, the altimeter would read 0 feet. Any positive readings on the altimeter would indicate she is above sea level. Any negative readings on the altimeter would indicate she is below sea level.

Step-by-step explanation: PLATO

Using a system of equations, the correct statement is given as follows:

B. The equation that represents this situation is 10 + x = -18. The second number is -28.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The numbers are x and y, and their sum is -18, hence:

x + y = -18.

The number y is 10, hence:

x + 10 = -18.

x = -18 - 10 = -28.

Which means that option B is correct.

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The midpoint of the segment is (-15/2, -15/2)

The complete question is in the attached image

The points are given as:

(-8, -7) and (-7, -8)

The midpoint is calculated as:

(x,y) = 1/2 * (x1 + x2, y1 + y2)

So, we have:

(x,y) = 1/2 * (-8 - 7, -7 - 8)

Evaluate the difference

(x,y) = 1/2 * (-15, -15)

Evaluate the product

(x,y) = (-15/2, -15/2)

Hence, the midpoint of the segment is (-15/2, -15/2)

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Answer:

1

Step-by-step explanation:

any number (except zero) raised to the 0th power is equal to 1.

Answer:

1

Step-by-step explanation:

(10 - 11)⁰ = ( -1)⁰ = 1

We have a⁰ = 1

Answer:

y=7x

Step-by-step explanation:

The equation of the with a slope of m and a y-intercept of b is y=mx+b.

Options A,B and D. The correction about the area of the triangle are

Firstly this is an equilateral triangle

3 of the sides have the length of 8.7cm

b = half of 8.7

= 4.35cm

To get A we have

a² + b² = c²

a² + 4.35² = 5²

When we solve this out we would have

a² = 25 - 18.9225

a ≈ 2.5 cm.

Hence we have proved that the first option is correct.

For B,

In an equilateral triangles, each of the angles = 60 degrees

60/2 = 30 is the angle that is made from the base

a / 4.35 = tan 30

then a = 4.35 tan 30

This would also give us an approximate of 2.5

For D

The calculations we have done based on the statements in A and B shows that D is correct as 2.5.

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Answer:

A.) x = 3

Step-by-step explanation:

This equation is an example of a perfect square quadratic. This means that the quadratic can be simplified into two of the same factors.  

How can you factor the equation? The simplest way is to ask yourself, which two numbers multiply to 9 while also adding to -6? The two numbers which satisfy this question are -3 and -3. Knowing this, you can construct your factors, simplify, and then solve for "x".

x² - 6x + 9 = 0                    <----- Expanded equation

(x - 3)(x - 3) = 0                  <----- Factored equation

(x - 3)² = 0                          <----- Combine both factors

x - 3 = 0                             <----- Take square root of both sides

x = 3                                 <----- Add 3 to both sides

Step-by-step explanation:

IR = 9√3

E = 60°

I = 30°

R = 90°

• Find ER.

ER/sin(I) = IR/sin(E)

ER/sin(30°) = 9√3/sin(60°)

ER/(1/2) = 9√3/(1/2 √3)

ER/(1/2) = (9√3 . 2)/√3

ER/(1/2) = 18√3/√3

ER/(1/2) = 18 → IR/sin(E)

ER = 18 . 1/2

ER = 9 is the answer

• Find IE (There are 2 ways).

First, using a Sinus Rule.

IE/sin(R) = IR/sin(E)

IE/sin(90°) = 9√3/sin(60°)

IE/1 = 9√3/(1/2 √3)

IE = (9√3 . 2)/√3

IE = (18√3)/√3

IE = 18 is the answer

Second, using a Pythagoras Theorem.

IE = √(IR² + ER²)

IE = √((9√3)² + 9²)

IE = √(81.3 + 81)

IE = √(243 + 81)

IE = √324

IE = 18 is the answer

Answer:

by sss

Step-by-step explanation:

The property of congruence:

ΔABC ≅ ΔDCB by the SSS criterion.

The correct option is the SSS postulate.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Given information:

AB ≅ DC and AC ≅ DB.

The proof is given described as:

In triangle ABC and triangle DCB,

The two sides are congruent,

AB ≅ DC and AC ≅ DB ( As per the information provided).

And as per the diagram and reflexive property of congruence,

BC ≅ BC.

Therefore, ΔABC ≅ ΔDCB by the SSS criterion.

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Answer:

15556913140

Step-by-step explanation:

Answer:

The answer is 6 and -6

Step-by-step explanation:

The given equation is
[tex]x^2 - kx + 9 = 0 ... (1)[/tex]

where a = 1. b = -k, c = a

since the equation (1) has equal roots

[tex]\Rightarrow b^2 - 4ac = 0 \newline\\\Rightarrow (-k)^2 - 4(1)(9) = 0\\ \newline\\\Rightarrow (k)^2 - 36 = 0 \newline\\\Rightarrow k^2 = 36 \newline\\\Rightarrow k = \pm 6[/tex]

Hence volume of k = 6, -6

Answer:

23.20

Step-by-step explanation:

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Answer:

α ≈ 23.20°

Step-by-step explanation:

given all 3 sides of the triangle , then any of the trig ratios may be used, that is sine, cosine or tangent to find α

tanα = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{3}{7}[/tex] , then

α = [tex]tan^{-1}[/tex] ( [tex]\frac{3}{7}[/tex] ) ≈ 23.20° ( to the nearest hundredth )

or

sinα = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3}{\sqrt{58} }[/tex] , then

α = [tex]sin^{-1}[/tex] ( [tex]\frac{3}{\sqrt{58} }[/tex] ) ≈ 23.20° ( to the nearest hundredth )

or

cosα = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{7}{\sqrt{58} }[/tex] , then

α = [tex]cos^{-1}[/tex] ( [tex]\frac{7}{\sqrt{58} }[/tex] ) ≈ 23.20° ( to the nearest hundredth )

Answer:

x = - 5 , x = [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

the values of x that make f(x) zero are the zeros

to find the zeros let f(x) = 0 , that is

3x² + 13x - 10 = 0

consider the factors of the product of  the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 3 × - 10 = - 30 and sum = + 13

the factors are + 15 and - 2

use these factors to split the x- term

3x² + 15x - 2x - 10 = 0 ( factor the first/second and third/fourth terms )

3x(x + 5) - 2(x + 5) = 0 ← factor out (x + 5) from each term

(x + 5)(3x - 2) = 0

equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

3x - 2 = 0 ⇒ 3x = 2 ⇒ x = [tex]\frac{2}{3}[/tex]

Answer:

-∞ < x < 4

Step-by-step explanation:

→ The graph touches the y axis at 4, therefore 4 part of the range. As h ( x  ) has a vertical asymptote it will never touch the line x = 1, therefore -∞.

Answer:

[tex](x+5)^{3}[/tex]

Step-by-step explanation:

Hope this helps

The expression for the word problem is ( x + 5 )².

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The given word problem is the cube of the sum of a number and 5. The expression will be formed as below:-

Let the unknown number be x.

E = ( x + 5 )²

Therefore, the expression for the word problem is ( x + 5 )².

The complete question is given below:-

The cube of the sum of a number and 5. Write the mathematical expression.

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The true statements among the given options are written below

bc || ad

ba ≅ cd  

∠cba ≅ ∠bcd

In an isosceles trapezoid, there is one pair of legs of equal length and a pair of parallel lines.

Given that quadrilateral abcd is a isosceles trapezoid.

In the given trapezoid abcd

bc || ad ( pair of parallel sides )

So this is correct.

ba ≅ cd  ( For an isosceles trapezoid legs are equal)

So this is correct

∠cba ≅ ∠bcd (According to  the property of isosceles  trapezoid )

So this is correct.

Hence, bc || ad, ba ≅ cd, ∠cba ≅ ∠bcd are correct

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Answer:  < -4/5,  3/5>

This is equivalent to writing < -0.8, 0.6 >

======================================================

Explanation:

Draw an xy grid and plot the point (-4,3) on it. Draw a segment from the origin to this point. Then draw a vertical line until reaching the x axis. See the diagram below.

We have a right triangle with legs of 4 and 3. The hypotenuse is [tex]\sqrt{4^2+3^2} = \sqrt{16+9} = \sqrt{25} = 5[/tex] through use of the pythagorean theorem.

We have a 3-4-5 right triangle.

Therefore, the vector is 5 units long. This is the magnitude of the vector.

Divide each component by the magnitude so that the resulting vector is a unit vector pointing in this same direction.

Therefore, we go from < -4, 3 > to < -4/5,  3/5 >

This is equivalent to < -0.8, 0.6 > since -4/5 = -0.8 and 3/5 = 0.6

Side note: Unit vectors are useful in computer graphics.

The parameter to be tested is z.

We would set up the hypothesis test.

For the null hypothesis,

µ ≥ 4.2

For the alternative hypothesis,

µ < 4.2

It is a left tailed test.

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 4.2

x = 4.3

σ = 0.4

n = 37

z = (4.3 - 4.2)/(0.4/√37) = 1.53

Looking at the normal distribution table, the probability corresponding to the z score is 0.933

The p value gotten is to the right of the normal curve. Since it is a left tailed test, we need the p value to the left of the curve. Therefore,

p = 1 - 0.933 = 0.067

Since alpha, 0.05 < than the p value, 0.067, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, there is no significant evidence that mean GPA of these graduates does not exceed 4.30

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Answer:

The linear equation for tip barista gets in a day is f(n)=0.5n+20.

Step-by-step explanation:

It is given, at a noon a barista notice that she has $20 in tip jar, if she makes an average of $0.50 from each customer,

It is required to find how much will she have in her tip jar if she serves n more customers during her shift. m=0.5. Bases on this write the equation for n more customers.

Step 1 of 1

It is given, at a noon a barista notice that she has $20 in tip jar, if she makes an average of $0.50 from each customer,

To solve this let f(n) is the total tip barista has in her tip jar after a day.

When n is equal to 0 , that barista has $20,

Then if barista make 0.5 from each customer, then for the linear function m=0.5,

Bases on this write the equation for n more customers,

[tex]$$f(n)=0.5 n+20 .$$[/tex]

The quantity of wheat to be transported by the company in metric tonnes is; 1.224 metric tonnes.

Since it follows that 1 metric tonne is equivalent to 2205 lb. It therefore follows that the quantity which is equivalent to 2700lb to be transported is;

= 2700/2205 = 1.224

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Answer:

- x + 1

Step-by-step explanation:

(x² + 2x + 3) - (x² + 3x + 2) ← multiply terms inside parenthesis by - 1

= x² + 2x + 3 - x² - 3x - 2 ← collect like terms

= - x + 1

Answer:

BAC=BDC(BDX)=30°

Step-by-step explanation:

We know that BD=OD.

But OD=OB= Radius of the circle.

Therefore

BD=OD=OB

BDO is equilateral triangle.

Angle DBO= 60°

Now let us take the intersecting point of CD and AB as X.

In triangle BDX,

BXD= 90°(BXD+BXC=180°, BXD+90°=180°, BXD=90°)

BXD+DBX+BDX=180°{Angle Sum Property}

90°+60°+BDX= 180°

BDX= 30°

We also know that,

BDC(BDX)= BAC (Angles lie on the same arc{BC} are equal in measure.

Therefore,

BAC=BDC(BDX)=30°

Answer:

C

Step-by-step explanation:

In option c, the first block is divided into 3 pieces where 2 parts are shaded whereas the second block is divided into 6 pieces where 3 parts are shaded

For both to be equivalent, both of them should be the same

2/3 = x/6

x = 4

4 pieces should be shaded in in the second block to be equal to the first one, in the diagram only 3 parts are shaded thus the answer is c

Answer:

B) 18%

Step-by-step explanation:

100% - 36% - 29% - 17% = 18%

Answer:

the answer would be B) 18%

Answer:

This is always true so there are infinite solutions

Step-by-step explanation:

2(x+4)=4x+3-2x+5

To find the solution, the first step is to distribute

2x+8 =4x+3-2x+5

Combine like terms

2x+8= 2x+8

Subtract 2x from each side

2x+8 -2x = 2x+8-2x

8 = 8

This is always true so there are infinite solutions

Answer:

The answer is B.

Step-by-step explanation:

I learned this last year.

Bricklayer Ben placed a total of 462 bricks.

Bricklayer Ben places 42 bricks per hour.

Bricklayer Bob places 36 bricks per hour.

Let

x = number of hours worked by Bricklayer Bob

y = number of hours worked  by Bricklayer Ben

Therefore,

x = 2y

42y + 36x = 1254

42y + 36(2y) = 1254

42y + 72y = 1254

114y = 1254

y = 1254 / 114

y = 11

Hence,  Bricklayer Ben placed a total of 42 × 11 = 462 bricks.

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