Which transformations were used to create A’B’C’?

Chloe is painting on a stretched canvas that has an area of 108 square inches. The length of the canvas is 12 inches. The width

Stolb23 [73]

Answer: Width of canvas = 9 inches

Area left for painting after painting the border = 70 square inches.

Explanation :

Since we have given that

Area of painting = 108 square inches

Length of canvas = 12 inches

As we know that

$\text{Area of rectangle} = length\times breadth$

$108=12\times breadth\\\\\frac{108}{12}=breadth\\\\9=breadth$

So, breadth of canvas = 9 inches .

Now, Chloe paints a 1 inch wide blue border on the canvas.

$\text{So, remaining length left for painting after painting the border} = 9-1-1=9-2=7\text{ inches}$

$\text{ Remaining breadth left for painting after painting the border }= 12-1-1=12-2= 10\text{ inches}$

$\text{So , area of remaining portion }= length\times breadth \\\\ \text{ area of remaining portion }=7\times 10\\\\\text{ area of remaining portion }=70 \text{ square inches}$

Hence, remaining area = 70 square inches .

6 0

3 years ago

Which of the following mathematical statements contains a quotient? A. 7 + 6 = 13 B. 7 × 6 = 42 C. 7 − 6 = 1 D. 42 ÷ 6 = 7

Black_prince [1.1K]

B: 7 x 6 = 42 and the only reason that B is the answer is because a quotient is the word used for a answer when you multiply c:

7 0

3 years ago

Read 2 more answers

If arc VY = 132° and ∠YUV = 41°, what is the measure of arc XV?

Tom [10]

Answer:

50

Step-by-step explanation:

Use this equation

$\frac{b - a}{2} = angle \: yuv$

where b is arc VY, A is arc XV.

Substitute the equation in

$\frac{132 - a}{2} = 41$

$132 - a = 82$

$- a = - 50$

$a = 50$

so our arc measure is 50

5 0

3 years ago

Can you help me write proofs for these, PLEASE!!!

brilliants [131]

Exterior angle theorem and properties of the isosceles triangles are used

prove the specified relations.

Correct responses:

9. ΔPAT ~ ΔPTB by AA similarity postulate

15. $\overleftrightarrow{HM}$ ║ $\overleftrightarrow{JK}$ by basic proportionality theorem

<h3>Detailed methods used to prove response</h3>

9. A two column proof is presented as follows;

Statement ${}$ Reasons

1. ∠PTA = ∠B ${}$ 1. Given

2. ∠PAT = ∠ATB + ∠B ${}$ 2. Exterior angle of a triangle theorem

3. ∠BTP = ∠ATB + ∠PTA ${}$ 3 Angle addition postulate

4. ∠BTP = ∠ATP + ∠B ${}$ 4. Substitution property of equality

5. ∠PAT = ∠BTP ${}$ 5. Substitution property

6. ΔPAT ~ ΔPTB ${}$ 6. AA similarity postulate

The Angle-Angle, AA, similarity postulate states that two triangles are similar if two angles in one triangle are each equal to two angles in the other triangle.

15. A two column proof is presented as follows;

Statement ${}$ Reasons

$\displaystyle 1. \hspace{0.3 cm} \frac{GJ}{HK} = \frac{GK}{GM}$ ${}$ 1. Given

2. ∠1 ≅ ∠G ${}$ 2. Given

3. ΔKHG is an isosceles triangle ${}$ 3. Definition

4. HK = HG ${}$ 4. Legs of an isosceles triangle

$\displaystyle 5. \hspace{0.3 cm} \frac{GJ}{HG} = \frac{GK}{GM}$ ${}$ 5. Substitution property

6. $\overleftrightarrow {HM}$ ║ $\overleftrightarrow{JK}$ ${}$ 6. BPT, Basic Proportionality Theorem

Basic Proportionality Theorem, BPT, states that if a line parallel to one of the sides of a triangle, intersects the other two sides, then the line divides the other two sides in the same proportion.

Learn more about basic proportionality theorem, AA similarity postulate here:

brainly.com/question/14417137

brainly.com/question/17003791

4 0

3 years ago

Which expression is equivalent to the given expression?

Keith_Richards [23]

The right answer is of option B

Look at the attached picture ⤴

Hope it will help u.

8 0

3 years ago