A side of the triangle below has been extended to form an exterior angle of 158º. Find
the value of x.

Answer:

[tex]\angle DFE = \angle DFG[/tex]

Step-by-step explanation:

Given

See attachment for complete question

Required

What makes DEF and DGF congruent

We have:

[tex]EF = GF[/tex] --- this is indicated by the single line on both sides

Also:

[tex]DF = DF[/tex] --- both triangle share same side

For SAS to be true;

2 sides and 1 angle must be equal in either triangles

So far, we have:

[tex]EF = GF[/tex] ---- S

[tex]DF = DF[/tex] ---- S

The additional to complete the proof is:

[tex]\angle DFE = \angle DFG[/tex] ---- angle between the above sides

Reflection is a type of rigid transformation which requires the turning of an object, shape or figure about a reference point or line. Therefore, the needed additional information is ∠DFE ≅ ∠ DFG. Option B.

Reflection implies turning the given triangle DEF about its side DF, so as to produce an image with the same dimensions but different orientation.

The required proof by Side-Angle-Side (SAS) implies that the relations will be in respect of two of its sides and their included angle.

So that,

GF ≅ FE (given)

DF is the common side to triangles DEF and DFG.

DFG is the included side.

Thus;

∠DFE ≅ ∠ DFG (Side-Angle-Side postulate, SAS)

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Answer:

B. point B

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

B(-1, -3)

y = 3x

When x = -1,

y = 3(-1) = -3

Answer: B.

Answer:

4/200 is the answer

Answer:

Both the answers will be B

Answer:

Option C.

Step-by-step explanation:

For a given set of N elements:

{x₁, x₂, ..., xₙ}

The mean is given by:

[tex]M = \frac{x_1 + x_2 + ... + x_n}{N}[/tex]

And the variance is given by:

[tex]v = \frac{(x_1 - M)^2 + (x_2 - M)^2 + ... + (x_n - M)^2}{N}[/tex]

Then for our set:

{70, 80 ,75, 75, 80}

We have 5 elements, then N = 5

The first thing we need to find is the mean.

[tex]M = \frac{70 + 80 + 75 + 75 + 80}{5} = 76[/tex]

Then the variance will be:

[tex]v = \frac{(70 - 76)^2 + (80 - 76)^2 + (75 - 76)^2 + (75 - 76)^2 + (80 - 76)^2}{5} = 14[/tex]

The correct option is C, 14.

Answer:

the function for y=-4x+3

= soln,

y=mx+b"

Answer:

true

Step-by-step explanation:

idek

Answer:

True

Step-by-step explanation:

If we say x-1=0

x=1

F(1)=(1)^3-7(1)^2+15(1)-9

=1-7+15-9

=-6-9+15

=0

So this proves that it's a factor by factor theorem

A factor must give 0 if it's substituted to the equation

Answer:

150 different committees can be formed

Step-by-step explanation:

We have 6 boys and 5 girls and we want to select 5 members

Out of these 5 members, two boys are selected

Since two boys are selected, we are left with three girls

So, out of 6 boys, we select 2 boys and out of 5 girls, we select 3 girls

Mathematically, we know that the number of ways in which we can select r items from a total n follows the combinatorial formula;

nCr = n!/(n-r)!r!

With this, we have;

6C2 * 5C3

= (6!/(6-2)!2!) * (5!/(5-3)!3!) = 150 different committees can be formed

B

the number doubles by itself

Answer:

Marcela tardó 6 horas y Roberto tardó 8 horas.

Step-by-step explanation:

Dado que Marcela tardó dos horas menos que Roberto en recorrer una distancia en bicicleta, y sabiendo que el producto de los dos tiempos es de 48 horas, para determinar cuánto tardó cada uno se debe realizar el siguiente cálculo:

M = X

R = X + 2

X x (X + 2) = 48

8 x 6 = 48

Por lo tanto, Marcela tardó 6 horas y Roberto tardó 8 horas.

Answer:

the coordinates of point B are (-5, 2)

Step-by-step explanation:

1. use midpoint formula to find the midpoint (equation attached below)

2. plug in the numbers

[tex](\frac{-8+(-2)}{2},\frac{3+1}{2})[/tex]

3. solve

[tex](\frac{-8-2)}{2},\frac{3+1}{2})[/tex]

[tex](\frac{-10}{2},\frac{4}{2})[/tex]

[tex](-5,2})[/tex]

Answer:

10

Step-by-step explanation:

the small engine tanks that Harvey have = 5 ÷ ½ = 10

Answer:

-3.855

Step-by-step explanation:

Not sure if you need the weight of each screw! but you just subtract 80.955-84.81

Answer:

1

Step-by-step explanation:

itnisbbsndnfnfnfnnfnfnfncjcjccjcj

Answer:

this involves dividing numbers by making use of their place values or value

Step-by-step explanation:

hope this is helpful

Answer:

105

Step-by-step explanation:

l is parallel m so angle 3+angle 6=180

Answer:

3

Step-by-step explanation:

Volume of sphere:

4/3 * pi * r^3

Surface Area of Sphere:

4 * pi * r^2

So if V = SA

4/3 * pi * r^3 = 4 * pi * r^2

4/3 * pi * r^3 = 4 * pi * r^2

1/3 * r^3 = r^2

1/3 * r = 1

r = 3

Volume is a three-dimensional scalar quantity. The radius of the ball is equal to 3 units.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of the sphere is given by the formula,

V = (4/3)πR³

The surface area of the sphere is given by the formula,

Surface area = 4πR²

Also, it is mentioned that the numerical value of the volume in cubic inches was the same as the numerical value of the surface area in square inches. Therefore,

(4/3)πR³ = 4πR²

R³/3 = R²

R = 3

Hence, the radius of the ball is equal to 3 units.

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Given:

The equation is:

[tex]24+12=\_\_\times (8+4)[/tex]

To find:

The missing value.

Solution:

We have,

[tex]24+12=\_\_\times (8+4)[/tex]           ...(i)

Taking left hand side, we get

[tex]24+12=3\times 8+3\times 4[/tex]

Taking 3 common, we get

[tex]24+12=3\times (8+4)[/tex]             ...(ii)

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

Missing value = 3

Therefore, the missing value in the given equation is 3.

Answer: conducting quantitative research

Step-by-step explanation:

Quantitative research refers to the collection and the analysis of numerical data. Quantitative research can be used in making predictions, and testing casual relationships.

Quantitative research methods emphasize the numerical analysis of data which can be collected through questionnaires, polls, surveys etc.

Answer:

12y² + 9y + 7

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

4y² + 5y + 2 + 8y² + 4y + 5

Step 2: Simplify

Answer:

12y² + 9y + 7

Step-by-step explanation:

4y² + 5y + 2 + 8y² + 4y + 5

Simplify :-

4y² + 5y + 2 + 8y² + 4y + 5

4y² + 8y² + 5y + 4y + 2 + 5

12y² + 9y + 7

Note: Consider the given equation is [tex]2(a+b)=8.1[/tex] instated of [tex]2(a+b)-8.1[/tex].

Given:

The expression [tex]2(a+b)=8.1[/tex] for certain values of a and b.

To find:

The value of [tex]3(a+b)[/tex] for the same value of a and b.

Solution:

We have,

[tex]2(a+b)=8.1[/tex]

Divide both sides by 2.

[tex](a+b)=\dfrac{8.1}{2}[/tex]

[tex](a+b)=4.05[/tex]

Multiply both sides by 3.

[tex]3(a+b)=3\times 4.05[/tex]

[tex]3(a+b)=12.15[/tex]

Therefore, the value of [tex]3(a+b)[/tex] is 12.15.

Answer:

Step-by-step explanation:

1) Slope of the given line = -3

slope of the perpendicular line = 1/3

y - 0 = 1/3(x-9)

y = 1/3x - 3

2) slope of the parallel line = -3

y - 0 = -3(x-9)

y = -3x + 27

Answer:

1). y = 1/3x - 3       2).y = -3x + 27

Step-by-step explanation:

1). y = 1/3x + b

0 = 1/3(9) + b

0 = 3 + b

-3 = b

y = 1/3x - 3

2)/ y = -3x + b

0 = -3(9) + b

0 = -27 + b

27 = b

y = -3x + 27

Answer:

Diameter: the straight distance from one edge of a circle to the other

Radius: the straight distance from one edge of a circle to the center

I hope this helps :)

Answer:

Diameter - a straight line that goes straight through the center of the circle to one point on its outline to another point on it's outline

Radius - a line that starts at the center and goes to anywhere on the circles circumference

Answer:

x= -7

Step-by-step explanation:

f(x) = -5(x+7)

0 = -5x -35

5x = -35

equals to x= -7

Step-by-step explanation:

hope this will help you mark me as brinalist friend please

The amount paid for the 5 pound of almond by Nachelle is $27.75.

Let 'p' be the number of pounds of almonds purchased by Nachelle.

Let 'c' be the total cost paid.

The cost of per pound of the almonds is $6.50 per pound.

The amount of the coupon is $4.75.

Thus, the equation will be ;

c = 6.50p - 4.75   ......equation.

For number of pounds p = 5.

c = 6.50×5 - 4.75

c = $27.75

Thus, the amount paid for the 5 pound of almond by Nachelle is $27.75.

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Answer:

None of the above

Step-by-step explanation:

Distance is the difference between two positions. That is x1- x2  Since both numbers were negative, you would want the absolute value of one plus the other, because subtracting a negative results in a positive. For this example the distance would look more like this:

| -4.7 - ( -3.9 ) | = .8