The base of a triangle is 9 inches more than 3 times the height. if the area of the triangle is 105 square inches, find the base and height.

Using the stated facts, the statements from the listed options which are true are given by: Option A) Circle F and circle D are similar.

Dilation of a figure will leave its size get scaled (multiplied) by same number.

Thus, suppose if a circle is dilated with its center as center of dilation, with some scale factor, that will affect its radius.

So, if the current circle is having the radius 'r' units, and the circle is dilated from its center with scale factor of S, then, we get:

New circle's radius = [tex]S \times r \: \rm units[/tex]

For the given case, the three facts to be considered are:

Since circle F is translation of circle D, 2 units right, so its all points will be shifted 2 units right, which makes coordinate (x,y) - > (x + 2, y) (since height is same, only the x coordinates shifted to right side).

Thus, center of F would be (2 + 2, 3) = (4,3).

Since there is scaling of the circle D scale factor 2, thus, radius of circle F will be twice the radius of the circle D, which will be 2 times 7 = 14 units.

Since dilated figures are similar, thus, Circle F and Circle D are similar.

(similar figures are those who look alike, although may be smaller or larger versions, but congruent figures are exact same dimension holding figures, their all properties match, but positions can be different).

Thus, the correct statement is only option A: Circle F and circle D are similar.

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Answer:

the answer is 8

Step-by-step explanation:

because if you multiply 8 times 45 it equals 360

There is your answer

Final answer:

The pitch of the roof, which rises vertically 7 ft through a horizontal run of 42 ft, is 2. This means the roof rises 2 inches for every 12 inches of horizontal run.

Explanation:

The question asks about calculating the pitch of a roof with a vertical rise of 7 ft and a horizontal run of 42 ft. The pitch of a roof is generally expressed as the amount of vertical rise per 12 inches of horizontal run. To find the pitch, we first need to calculate the rise per 12 inches of horizontal run.

Given:

Rise = 7 ft

Run = 42 ft

To find how much the roof rises for every 12 inches of run, we use the formula:

Pitch = (Rise / Run) × 12

Plugging in the given values:

Pitch = (7 / 42) × 12 = 2

Thus, the pitch of the roof is 2, meaning the roof rises 2 inches for every foot (12 inches) of horizontal run.

The reason that will complete the proof is SSS (Side-Side-Side) which states that if three corresponding sides of two triangles are congruent, then the triangles are congruent.

Out of the given options, the reason that will complete the proof is SSS which stands for Side-Side-Side. SSS is a congruence postulate that states that if three corresponding sides of two triangles are congruent, then the triangles are congruent.

In this case, since both 'o' and 'sx' are given, we can apply the SSS congruence postulate to show that the triangles are congruent. This is because two sides 'o' and 'sx' are congruent, and the third side of each triangle can be determined by adding up the length of the other sides.

The correct reason that completes the proof is "SAS" which stands for Side-Angle-Side.

SAS is a postulate in geometry that states: "If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent."

To prove two triangles congruent using the SAS postulate, you need to show that two sides of one triangle are congruent to two sides of another triangle, and the included angle (the angle formed by the two sides) of one triangle is congruent to the included angle of the other triangle.

For example, let's say we have two triangles, Triangle ABC and Triangle DEF. To prove them congruent using the SAS postulate, we need to show that AB is congruent to DE, BC is congruent to EF, and the angle at B is congruent to the angle at E.

Once we have established these congruencies, we can conclude that Triangle ABC is congruent to Triangle DEF.

Therefore, in the context of the given question, the reason that completes the proof is SAS.

The image of point B is B'(1.5,6).and this can be determined by finding the dilation factor and then multiplying point B by the dilation factor.

Given :

In order to determine the image of point B, first, determine the dilation factor. let 'x' be the dilation factor, then:

[tex]-4\times x = -6[/tex]

[tex]x = \dfrac{3}{2}[/tex]

Now, after dilation the point B becomes:

[tex]\rm B(1,4)\to B'(1\times \dfrac{3}{2},4\times \dfrac{3}{2})[/tex]

Simplify the above expression.

[tex]\rm B'\left(\dfrac{3}{2},6\right) = B'(1.5,6)[/tex]

The image of point B is B'(1.5,6).

For more information, refer to the link given below:

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Answer:

The correct option is 2.

Step-by-step explanation:

Given information: DC║AB, DC=AB.

If a transversal line intersect two parallel lines, then the alternative interior angles are equal.

In triangle ABC and CDA,

[tex]AB=DC[/tex]                          (Given)

[tex]\angle 2=\angle 3[/tex]                       (Alternative interior angles)

[tex]CA=CA[/tex]                             (Common side)

Two corresponding sides and their including angle are equal.

By SAS postulate of congruent triangles,

[tex]\triangle ABC\cong \triangle CDA[/tex]

Since both triangles are congruent by SAS postulate, therefore the correct option is 2.

Answer:

The answer is B, he can only draw one unique triangle with these side lengths.

Step-by-step explanation:

I did the quiz

The equation of the graph is [tex]y = -3 +4^{x -2[/tex]

The parent function is given as:

[tex]y = 4^x[/tex]

From the graph, we can see that the function is translated 3 units down and  2 units right.

This means that the transformation rule

(x, y) -> (x - 2, y - 3)

So, we have:

[tex]y = -3 +4^{x -2[/tex]

Hence, the equation of the graph is [tex]y = -3 +4^{x -2[/tex]

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#SPJ2

x = −10 ± 5√2

Solve. x²+ 20x + 100 = 50

Subtracting 50 from both sides

[tex] x^{2} +20x+100-50=50-50 [/tex]

[tex] x^{2} +20x+50=0 [/tex]

To solve the quadratic equation, let us use quadratic formula

For, [tex] ax^{2} +bx+c=0 [/tex] , [tex] x=\frac{-b+-\sqrt{b^{2}-4ac}}{2a} [/tex]

So, a=1, b=20, c=50

So, we get,

x=[tex] \frac{-20+-\sqrt{20^{2}-4*1*50}}{2*1} [/tex]

[tex] x=\frac{-20+-\sqrt{400-200}}{2} [/tex]

[tex] x=\frac{-20+-\sqrt{200}}{2} [/tex]

[tex] x=\frac{-20+-10\sqrt{2}}{2} [/tex]

[tex] x=\frac{-10+-5\sqrt{2}}{1} [/tex]

[tex] x=-10+-5\sqrt{2} [/tex]

Option(a) Answer

So, x=-10+5[tex] \sqrt{2} [/tex]

or, x=-10-5[tex] \sqrt{2} [/tex]

Answer:

-a^2 + 2 ab + b^2

Step-by-step explanation:

To solve this, you need to distribute the letters into the parenthesis.

Then, you sum equal things, and you get the result.

[tex]b(a+b)-a(a-b)=\\ba + b^{2} -a^{2}  + ab=\\ b^{2} + 2ab -a^{2}[/tex]

So, the rigth answer is number three: -a^2 + 2 ab + b^2

Answer: First question: b. 360°

Second question : b. 7

Third question: Yes, it is a parallelogram.

Fourth question:  It is a rhombus.

Step-by-step explanation:

1. Since,  The sum of exterior angles in a polygon is always equal to 360 degrees.

And, an octagon is also a polygon.

Therefore the sum of the all exterior angle of an octagon = 360°

2. Since, the sum of the interior angles of a polygon of n sides is (n-2)×180°

But here (n-2)×180°=900

⇒ n-2 = 5 ( After dividing both sides by 180° )

⇒ n = 5 + 2 = 7

Thus,  If the sum of the interior angles of a polygon is 900° then the polygon has 7 sides.

10. Since, In triangles XNY and WNZ,

XN≅NZ (Given)

NY≅NW ( Given)

∠XNY≅∠WNZ ( vertically opposite angles)

Thus, By SAS postulate of congruence,

ΔXNY≅ΔWNZ,

By CPCTC, XY≅WZ

Similarly, Δ XNW≅ Δ YNZ,

By CPCTC, XW≅YZ

Therefore, In quadrilateral XYZW, Opposite sides are equal.

⇒ XYZW is a parallelogram.

11. Let ABCD is a parallelogram,

In which AC is a diagonal.

Also, AB = CD and AD= BC ( By the property of parallelogram)

And, It is given that ∠DAC=∠DCA = 72°

Therefore ADC is an isosceles triangle ( By the property of isosceles triangle)

Thus, AD=DC

Similarly, ABC is an isosceles triangle.

Thus, AB= BC

Thus, AB=BC=CD=DA.

Also, ∠ADC=∠ABC  ( By the property of parallelogram)

Therefore, In ABCD all sides are equal and Opposite angles are equal.

⇒ ABCD is a rhombus. ( The diagram is shown below)

Answer: C.  0.215

Step-by-step explanation:

Given: A circle with a diameter of 124 m is inscribed in a square .

Thus side of square =124 m

Now, area of square=[tex](side)^2=(124)^2=15,376\ m^2[/tex]

Radius of circle=[tex]\frac{d}{2}=\frac{124}{2}=62\ m[/tex]

Area of circle=[tex]\pi\ r^2=3.14\times(62)^2=3.14\times3.14=12,070.16\ m^2[/tex]

Now, Area of shaded region= Area of square-Area of circle

Area of shaded region=[tex]15,376-12,070.16=3,305.84\ m^2[/tex]

Probability that a point picked at random in the square is in the shaded region

[tex]=\frac{\text{area of shaded region}}{\text{area of square}}=\frac{3305.84}{15376}=0.215[/tex]