∠A and ​ ∠B ​ are vertical angles with m∠A=x and m∠B=3x−60 .

What is m∠A ?

Enter your answer in the box.

Answer-

[tex]\boxed{\boxed{y^{\circ}=26^{\circ}\ 45'}}[/tex]

Solution-

As the triangle ABC is an isosceles triangle, with AC = BC.

So the angles A and B will be same, i.e

[tex]\Rightarrow \angle A=\angle B[/tex]

[tex]\Rightarrow 34^{\circ}=(x-5)^{\circ}[/tex]

[tex]\Rightarrow x^{\circ}=34^{\circ}+5^{\circ}[/tex]

[tex]\Rightarrow x^{\circ}=39^{\circ}[/tex]

As sum of all angles in a triangle is 180°, so

[tex]\Rightarrow \angle A+\angle B+\angle C=180^{\circ}[/tex]

[tex]\Rightarrow 34^{\circ}+39^{\circ}+4y^{\circ}=180^{\circ}[/tex]

[tex]\Rightarrow 4y^{\circ}=180^{\circ}-34^{\circ}-39^{\circ}[/tex]

[tex]\Rightarrow 4y^{\circ}=107^{\circ}[/tex]

[tex]\Rightarrow y^{\circ}=\dfrac{107^{\circ}}{4}[/tex]

[tex]\Rightarrow y^{\circ}=26.75^{\circ}[/tex]

[tex]\Rightarrow y^{\circ}=26^{\circ}\ 45'[/tex]

The angle measures 40 degrees, and its complement, which is 25% larger than the angle, measures 50 degrees. This is solved using elementary algebra by setting up an equation with the angle as 'x' and its complement as '90-x', and then simplifying the equation to solve for 'x'.

The question involves finding the measure of an angle and its complement when given that the complement exceeds the measurement of the angle by 25%. To solve this, let's use algebra. Let the measure of the angle be x degrees.

Since the complement of an angle adds up to 90 degrees with the angle itself, the complement can be represented as 90 - x degrees. According to the problem, the complement is 25% more than the angle, so we can write the equation:

90 - x = x + 0.25x

Simplifying, we get:

90 - x = 1.25x

90 = 2.25x

Dividing both sides by 2.25 gives us the measure of the angle x:

x = 40 degrees

Since the complement is 90 - x, we find:

Complement = 90 - 40 = 50 degrees

Therefore, the angle measures 40 degrees, and its complement measures 50 degrees.

When cosθ >0 then , b² + c² > a².

" Triangle is a 2 dimensional shape which is having three sides and three vertices. Sum of all the interior angles of a triangle is 180°."

Formula used

As per Cosine Rule

For a given ΔABC,

cosθ = [tex]\frac{b^{2} + c^{2} - a^{2} }{2bc}[/tex]

According to the question,

cosθ >0

⇒ [tex]\frac{b^{2} + c^{2}-a^{2} }{2bc}[/tex] >0

⇒ b² + c² >a²

Hence, we conclude that Option D is correct.

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To solve the system by substitution, substitute the value of z in the equations and solve them simultaneously.

To solve the system by substitution, we need to substitute the value of z in the other equations. Given that z=5, we can substitute this value in the first and third equations:

2x - y + 5 = -4

-2x + 3y - 5 = 10

Now, we can solve these two equations simultaneously to find the values of x and y.

To solve a system of equations by substitution, express one variable in terms of the other and substitute it into the other equations to eliminate that variable before solving for the remaining variables.

To solve this system of equations by substitution:

By following these steps, you can find the values of x, y, and z that satisfy the system of equations.

None of the given points is the solution to the inequality y < -|x|.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given inequality,

y < -|x|

As per the given below, the dotted line is not included in the region thus, point (1,-1) is not included.

Hence "None of the given points is the solution to the inequality y < -|x|".

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Answer:

Hmmm... interesting on my final I answered B: a=14, b=8 and got it wrong but, when I did it again I got C: a=17, b=6

Step-by-step explanation

Answer:

The value of a=17 cm and b=6 cm

C is correct option.

Step-by-step explanation:

Given: FGHJ is a kite.

Kite has property their adjacent sides are equal. Top two side of the kite is equal and bottom two side of the kite is equal.

FG=GH because ∠F=∠H.

30=2a-4

2a=34

a=17 cm

Similarly, ∠F=∠H

FJ=HJ

3b+6=24

3b=18

b=6 cm

Hence, The value of a=17 cm and b=6 cm

Answer: Certain

Step-by-step explanation:

A probability is from 0 - 1, if not 0 or 1 it is a fraction, percentage, or decimal. 100% also equal to 1 is the highest amount you can get, therefore the answer is certain.

Answer:

[tex]h=\frac{25}{b+r}[/tex]

Step-by-step explanation:

Given equation,

[tex]bh+hr=25[/tex]

For solving this equation for h,

We need to isolate h in the left side of the equation,

We can write,

[tex]h(b+r) = 25[/tex]    ( by the converse of distributive property ),

Divide both sides by b + r,

[tex]h=\frac{25}{b+r}[/tex]

Which is the required equation.

Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

If Jolinda scored 21 points of 28 total, the fraction is:

[tex]\frac{21}{28}=\frac{3}{4}= 0.75(or75\%)[/tex]

Remember that a fraction is the representation of a portion among the total.

In addition, this fraction also would represent the effectiveness of Jolinda, we could say that she is able to score a 75% of team's points.

The correct expression representing the volume of the pyramid is:

[tex]\[ \frac{1}{3} \times x^2 \times y \[/tex]. Therefore the correct option is 2.

The volume [tex]\( V \)[/tex] of a pyramid is given by the formula:

[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]

For a square pyramid, the base area is given by [tex]\( \text{Base Area} = \text{side length}^2 \)[/tex].

In this case, the side length is [tex]\( x \)[/tex] and the height is [tex]\( y \)[/tex]. Therefore, the expression for the volume [tex]\( V \)[/tex] is:

[tex]\[ V = \frac{1}{3} \times x^2 \times y \][/tex]

Now, let's compare this with the given options:

1. [tex]\( \frac{1}{3}xy \)[/tex] cm³

2. [tex]\( \frac{1}{3}x^2y \)[/tex] cm³

3. [tex]\( \frac{1}{2}xy^2 \)[/tex] cm³

4. [tex]\( \frac{1}{2}x^2y \)[/tex] cm³

Now, we can see that the correct expression representing the volume of the pyramid is:

[tex]\[ \frac{1}{3}x^2y \, \text{cm}^3 \][/tex]

So, the correct option is option 2: [tex]\( \frac{1}{3}x^2y \)[/tex] cm³.

The correct expression representing the volume of the pyramid is:

[tex]\[ \frac{1}{3} \times x^2 \times y \[/tex]

Complete question:

A solid right pyramid has a square base with an edge length of x cm and a height of y cm. Which expression represents the volume of the pyramid?

1. [tex]\( \frac{1}{3}xy \)[/tex] cm³

2. [tex]\( \frac{1}{3}x^2y \)[/tex] cm³

3. [tex]\( \frac{1}{2}xy^2 \)[/tex] cm³

4. [tex]\( \frac{1}{2}x^2y \)[/tex] cm³

Answer:

c

Step-by-step explanation:

ratio is 5:4

5+4 =9

54 pounds divided by 9 = 6

6*5 = 30

6*4 = 24

Sam gets 30 pounds Bethan gets 24 pounds

Answer:  The required scale factor that is used for the dilation is 3.

Step-by-step explanation:  Given that the rectangle ABCD is transformed to A'B'C'D' by a dilation.

We are to find the scale factor that is used for the dilation.

We know that

the scale factor of dilation is defined as

[tex]S=\dfrac{\textup{the length of a side of the dilated figure}}{\textup{the length of the corresponding side of the original figure}}.[/tex]

From the graph, we see that

in rectangle ABCD, the length the side AB is 2 units

and

the length of the corresponding side A'B' in the dilated rectangle A'B'C'D' is 6 units.

Therefore, the scale factor of dilation is given by

[tex]S=\dfrac{A'B'}{AB}=\dfrac{6}{2}=3.[/tex]

Thus, the required scale factor that is used for the dilation is 3.