WILL MARK BRAINLIEST! PLEASE HELP
In triangle PQR, mP= 43, PQ=7.5 and PR= 8.4. What is mR to the nearest degree?
A. 64
B. 52
C. 41
D. 60

In triangle ABC mA=43, mB=62 and BC=22 in. What is AB to the nearest tenth of an inch?
A. 28.5
B. 15.6
C. 14.1
D.31.2

thank you.

The answer to the above question can be explained as under -

We know that, the sum of angles of triangle is 180°.

So, vertex angle plus base angles are equal are equal to 180°.

Let the vertex angle be represented by "v" and base angles be represented by "b".

Thus,  v + b + b = 180°

So,  v + 2b = 180°

Next, the question says, the vertex angle is 20° less than the sum of base angles.

Thus, 2b - 20° = v

Thus, we can conclude that the correct option is A) v + 2b = 180°, 2b - 20° = v

The correct system of equations for an isosceles triangle where the vertex angle is 20 degrees less than the sum of the base angles is v + 2b = 180 for the sum of the angles, and 2b - 20 = v for the relationship between the base angles and the vertex angle. Option A is correct.

The correct system of equations to find the measure of the vertex and base angles of an isosceles triangle, where the vertex angle is 20° less than the sum of the base angles, is given by option A. The two equations can be described as follows:

To solve for the angles, you would substitute the expression for v from the second equation into the first and then solve for b, which represents the measure of each base angle. Once you have b, you can find v by substituting b back into the second equation.

Solution:

Given: A B CD is an inscribed polygon.

To Prove: ∠A and​ ∠C ​ are supplementary angles.

Proof: Join AC and B D.

Angle in the same segment of a circle are equal.

∠ACB=∠ADB→→AB is a segment.

Also, ∠A B D=∠A CD→→AD is a Segment.

In Δ ABD

∠A+∠ABD+∠ADB=180°→→Angle sum property of triangle.

∠A+∠A CD+ ∠ACB=180°

∠A+∠C=180°

Hence proved, that is, ∠A and​ ∠C ​ are supplementary angles.

The method Adopted by you

∠1=2 ∠A----(1)

and, ∠2=2 ∠C-------(2)

The theorem which has been used to prove 1 and 2, Angle subtended by an arc at the center is twice the angle subtended by it any point on the circle.→(Inscribed angle theorem)

Also, angle in a complete circle measures 360°.→→Chord arc theorem

∠1+∠2=360°→→Addition Property of Equality

2∠A+2∠C=360°→→[Using 1 and 2, Called Substitution Property]

Dividing both sides by 2→→Division Property of Equality

2∠A+2∠C=360°→→[Using 1 and 2]

∠A+∠C=180°

→→Correct work.

A two-column proof to prove that angles A and​ C ​ are supplementary angles should be completed as follows;

Statement                                                  Reason______________

ABCD is an inscribed polygon                   Given

mBCD = 2(m∠A)                                      Inscribed Angle Theorem

mDAB = 2(m∠C)                                      Inscribed Angle Theorem

mBCD + mDAB = 360°               The sum of arcs that make a circle is 360°

2(m∠A) + 2(m∠C) = 360°                        Substitution Property

m∠A + m∠C = 180°                                  Division Property of Equality

∠A and∠C are supplementary angles   Defintion of supplementary angles.

In Mathematics and Euclidean Geometry, the inscribed angle theorem states that the measure of an inscribed angle is one-half the measure of the intercepted arc in a circle or the inscribed angle of a circle is equal to half of the central angle of a circle.

Generally speaking, a supplementary angle refers to two angles or arc whose sum is equal to 180 degrees.

Based on the defintion of supplementary angles, we can logically deduce that angle A and angle C are supplementary angles.

The value of volume of cube is,

⇒ V = 1.728 meter³

A cuboid is the solid shape or three-dimensional shape. A convex polyhedron which is bounded by six rectangular faces with eight vertices and twelve edges is called cuboid.

Given that;

A cube has a side length of 120 cm.

Since, We know that;

1 m = 100 cm

Hence,

120 cm = 120 / 100 m

            = 1.2 m

So, Volume of cube is,

⇒ V = side³

⇒ V = 1.2³

⇒ V = 1.728 meter³

Thus,  volume of cube is,

⇒ V = 1.728 meter³

Learn more about the cuboid visit:

https://brainly.com/question/26403859

#SPJ3

Step-by-step explanation:

If the numbers can be repeated, we have such numeric codes:

10 · 10 · 10 = 1,000

If the numbers can not be repeated, then we have such numeric codes:

10 · 9 · 8 = 720

Answer:

1 and 4 i believe

Step-by-step explanation:

Answer:

Step-by-step explanation:

It is given that the base edge of the regular triangular pyramid is b=10 cm and altitude of the base h =8.66 cm. The slant height of the pyramid is k=8 cm.

Now, the lateral surface area of the pyramid is given as:

[tex]LSA={\frac{3}{2}}(b)(k)[/tex]

Substituting the given values, we have

[tex]LSA=\frac{3}{2}(10)(8)[/tex]

[tex]LSA=120cm^2[/tex]

Thus, the Lateral surface area of the pyramid is [tex]120cm^2[/tex].

Now, the surface area is given as:

[tex]SA=\frac{1}{2}bh+LSA[/tex]

[tex]SA=\frac{1}{2}bh+120[/tex]

[tex]SA=\frac{1}{2}(10)(8.66)+120[/tex]

[tex]SA=43.3+120[/tex]

[tex]SA=163.3cm^2[/tex]

Thus, the surface area of the pyramid will be [tex]163.3cm^2[/tex].

The Lateral area is 120 cubic cm, and the Surface area of the pyramid is 163.3 cubic cm.

A polyhedron that has a polygonal base and triangles for sides, is a pyramid.

The lateral area of the pyramid is equal to the area of its three triangular lateral faces is;

[tex]\rm Lateral \ Area=3 \times \dfrac{1}{2}\times b \times k\\\\ Lateral \ Area=3 \times \dfrac{1}{2}\times 10 \times 8\\\\ Lateral \ Area=120[/tex]

The surface area of the pyramid is;

[tex]\rm Surface \ area=\dfrac{1}{2}bh + Lateral \ area\\\\Surface \ area=\dfrac{1}{2}\times 10 \times 8.66 +120\\\\Surface \ area=43.3+120\\\\Surface \ area=163.3 \ cm^3[/tex]

Hence, the Lateral area is 120 cubic cm, and the Surface area of the pyramid is 163.3 cubic cm.

To know more about the pyramid click the link given below.

https://brainly.com/question/1318557

#SPJ3

Final answer:

The monthly payments would be approximately $61.02 and the total interest paid would be approximately -$764.04.

Explanation:

To calculate the monthly payments, you can use the formula for the monthly payment on a loan:

P = (r * PV) / (1 - (1 + r)^-n)

Where:

Using the given values, we can calculate:

P = (0.021 * 2469) / (1 - (1 + 0.021)^-48)

P ≈ $61.02

Therefore, the monthly payments would be approximately $61.02.

To calculate the total interest paid, you can multiply the monthly payment by the total number of payments and subtract the loan amount:

Total Interest = (P * n) - PV

Total Interest ≈ ($61.02 * 48) - $2469

Total Interest ≈ $1704.96 - $2469

Total Interest ≈ -$764.04

Therefore, the total interest paid would be approximately -$764.04. This negative value indicates that you will pay back less than the initial loan amount.

In mathematics, a conic section is a curve obtained as the intersection of the surface of a cone with a plane. The four types of conic section are the hyperbola, the parabola, the circumference and the ellipse.

For the problem we have this parametric equation:

(1) [tex]\left\{{{x=acost}\atop{y=bsint}}\right[/tex]

From geometry, we know that we can express a circumference in terms of parameters like this:

(2) [tex]\left \{ {{x=rcost} \atop {y=rsint}}\right[/tex]

being r the radius of the circumference.

On the other hands, we know that a ellipse can be expressed in terms of parameters like this:

(3) [tex]\left \{ {{x=acost} \atop {y=bsint}}\right[/tex]

Therefore, we will have three answers that are the cases for the values a and b, namely.

Case 1: Circumference

To the case of a circumference, the more simple ordinary equation is given by:

(4) [tex]x^{2} + y^{2} = r^{2}[/tex]

Substituting (1) into (4):

[tex]a^{2}cos^{2}t+b^{2}cos^{2}t=r^{2}[/tex]

But because of the equation (2), necessarily:

[tex]a = b = r[/tex]

Case 2: Ellipse (focal axis matches the x-axis) 

In this case, the simple ordinary equation is given by:

(5) [tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1[/tex]

being a and b semi-major axis and semi-minor axis respectively. 

Given that a an b are variables of the parametrization, and a and b are variables of the ellipse as well, to avoid confusion we will modify the equation (5) like this:

(6) [tex]\frac{x^{2}}{a'^{2}}+\frac{y^{2}}{b'^{2}}=1[/tex]

So, substituting (2) into (6):

[tex]\frac{a^{2}cos^{2}t}{a'^{2}}+\frac{b^{2}cos^{2}t}{b'^{2}}=1[/tex]

Necessarily:

[tex]a=a'[/tex]  and  [tex]b=b'[/tex] 

and given that the focal axis matches the x-axis, then:

[tex]a>b[/tex] 


Case 3: Ellipse (focal axis matches the y-axis) 

In this case, applying the same previous reasoning, the simple ordinary equation is given by:

(7) [tex]\frac{x^{2} }{b'^{2}}+\frac{y^{2}}{a'^{2}}=1[/tex]

being a' and b' semi-major axis and semi-minor axis respectively. 

So, substituting (2) into (7):

[tex]\frac{a^{2}cos^{2}t}{b'^{2}}+\frac{b^{2}cos^{2}t}{a'^{2}}=1[/tex]

Necessarily:

[tex]a = b'[/tex]  and  [tex]b = a'[/tex] 

and given that the focal axis matches the y-axis, then:

[tex]a<b[/tex] 

Finally, the conclusions are:

1. If [tex]a = b[/tex] then a circumference will be traced. (See Figure 1)

2. If [tex]a>b[/tex] then a ellipse will be traced with focal axis matching the x-axis. (See Figure 2)

3. If [tex]a<b[/tex] then a ellipse will be traced with focal axis matching the y-axis. (See Figure 3)

How the values of a and b determine which conic section will be traced was discussed thoroughly.

A conic section is a curve obtained as the intersection of the surface of a cone with a plane.

The given parametric equations are:

[tex]x=acos t[/tex]

[tex]\frac{x}{a} =cost[/tex]....(1)

[tex]y=bsint[/tex]

[tex]\frac{y}{b} =sint[/tex]....(2)

Adding the squares of (1) and (2)

[tex](\frac{x}{a} )^2+(\frac{y}{b} )^2=cos^{2} t + sin^{2} t[/tex]

We know [tex]cos^{2} t + sin^{2} t=1[/tex]

So, [tex]\frac{x^{2} }{a^{2} } +\frac{y^2}{b^2} =1[/tex]........(3)

If [tex]a=b[/tex], (3) will be reduced into:

[tex]x^{2} +y^{2} =a^{2}[/tex] representing a circle.

If [tex]a > b[/tex], (3) will represent an ellipse with the length of the major axis > length of the minor axis.

if [tex]a < b,[/tex] (3) will represent an ellipse with the length of the major axis < length of the minor axis.

Thus, How the values of a and b determine which conic section will be traced was discussed thoroughly.

To get more about conics visit:

https://brainly.com/question/4017703

Answer:4.8cm^3

Step-by-step explanation:I got it right on edge.

The volume of the pyramid is 1280 cubic feet.

To find the volume of a pyramid, we can use the formula:

Volume = (1/3) * Base Area * Height

Given that the pyramid has a square base with edges of 16 feet, the base area (A) is calculated as:

[tex]Base Area (A) = side^2\\A = 16^2 = 256 square feet[/tex]

The height of the pyramid can be found using the Pythagorean theorem. The height, slant height, and half the length of a side form a right triangle. The half length of a side is 16/2 = 8 feet. The slant height is 17 feet. So, using the Pythagorean theorem:

[tex]Height^2 + (Half side length)^2 = Slant height^2\\Height^2 + 8^2 = 17^2\\Height^2 + 64 = 289\\Height^2 = 289 - 64\\Height^2 = 225\\Height = \sqrt{225}\\Height = 15 feet\\[/tex]

Now that we have the base area (A = 256 square feet) and the height (h = 15 feet), we can find the volume:

Volume = (1/3) * 256 * 15

Volume = (1/3) * 3840

Volume = 1280 cubic feet

Therefore, the volume of the pyramid is 1280 cubic feet.

To know more about volume:

https://brainly.com/question/15699665

#SPJ2

Answer:

The answer is 18

Step-by-step explanation:

Subtract 115 from 180

Add 65 and 97

Subtract 162 from 180

The measure of ∠MRN  is 18°

The sum of angles of a triangle equals the straight angle which is 180°.

According to ques

∠RNM= 97°

∠RMA = 115°

∠RMA +∠RMN = 180° ( sum of angles on straight line )

115° + ∠RMN = 180°

∠RMN = 180° - 115°

∠RMN = 65°

∠RMN + ∠MRN + ∠RNM = 180° ( Sum of angles of triangle )

65° + ∠MRN + 97° = 180°

162° + ∠MRN  = 180°

∠MRN = 180° - 162°

∠MRN = 18°

Hence ,  measure of ∠MRN is 180°

To know more about Sum of angles of triangle click here

https://brainly.com/question/14780489

#SPJ2

Answer:

First box is 2, second box is 0, and the third box is 1.

Step-by-step explanation:

Final answer:

The difference between sqrt(20) and sqrt(80) is -2sqrt(5).

Explanation:

To find the difference sqrt(20) - sqrt(80), we can simplify each square root by factoring out perfect squares.

The number 20 can be factored into 4×5, and 80 can be factored into 16×5. Since 4 and 16 are perfect squares, they can be taken out of the square root as 2 and 4, respectively.

Therefore, the expressions simplify to:

sqrt(20) = sqrt(4×5) = sqrt(4) × sqrt(5) = 2sqrt(5)

sqrt(80) = sqrt(16×5) = sqrt(16) × sqrt(5) = 4sqrt(5)

Now we can find the difference:

2sqrt(5) - 4sqrt(5) = -2sqrt(5)

So the difference between sqrt(20) and sqrt(80) is -2sqrt(5).

Final answer:

To determine the number of terms in the given arithmetic sequence, we calculate the common difference and apply the formula for the nth term. With a common difference of -8 and an nth term of -225, we find that there are 31 terms in the sequence.

Explanation:

To find out how many terms are in the arithmetic sequence 15, 7, -1, -9,..., -225, we need to determine the common difference and use the formula for the nth term of an arithmetic sequence, which is an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference.

In this sequence, the common difference d is 7 - 15 = -8. Now we use the formula with an = -225, a1 = 15, and d = -8 to find n.

Plugging these values into the formula, we get:
-225 = 15 + (n - 1)(-8)
-225 = 15 - 8n + 8
-225 = 23 - 8n
-248 = -8n
n = 31

Therefore, there are 31 terms in the arithmetic sequence.