MATHEMATICS HIGH SCHOOL

Complete the pairs of corresponding parts if △ RST ≅ △ TXY. ∠ R =
∠ XYT
∠ XTY
∠ TXY

Answers

Answer 1
Answer:

Solution:

Given: △ RST ≅ △ TXY

We are given ΔRST and ΔTXY are congruent to each other.

If two triangles are congruent to each other then their corresponding parts are equal.

Please see the attachment of two triangles.

  • ∠R is corresponding to ∠T

∵  ∠R=∠T By CPCT

  • ∠XYT is corresponding to ∠STR

∵  ∠XYT=∠STR By CPCT

  • ∠XTY is corresponding to ∠SRT.

∵  ∠XTY=∠SRT By CPCT

  • ∠TXY is corresponding to ∠RST

∵  ∠TXY=∠RST By CPCT

CPCT: Congruent part of congruence triangle.

Answer 2
Answer: So, two triangles are similar. Ordering of letters matters when you are writing this down. So, RST~TXY, then ∠R = ∠T, or ∠TRS = ∠YTX = ∠XTY

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Audrey wants to ride her bicycle 44 miles this week. She has already ridden 12 miles. If she rides for 5 more days, write and solve an equation which can be used to determine x, the average number of miles she would have to ride each day to meether goal.

Answers

Answer:

4

Step-by-step explanation:

Final answer:

The question involves creating and solving a basic algebraic equation. Audrey needs to cycle an average of 6.4 miles each day over the next 5 days to reach her total goal of 44 miles for the week.

Explanation:

To solve this problem, we can establish an equation based on the information given. Audrey's goal is to ride a total of 44 miles this week and she has already ridden 12. If she rides for 5 more days, we need to determine how many miles she should cover each day to reach her goal. We denote x as the average number of miles she needs to ride each day.

The communication of her plans can be expressed through this equation: 12 miles + 5 days * x miles/day = 44 miles. Next, we need to solve the equation for x. In order to isolate x, you subtract 12 from both sides of the equation resulting in: 5x = 44 - 12, which simplifies to 5x = 32.

Finally, you divide both sides of the equation by 5 to get: x = 32 ÷ 5. So, x equals 6.4. This means that Audrey needs to cycle an average of 6.4 miles each of the coming 5 days to reach her total goal of 44 miles.

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Are the graphs of the lines in the pair parallel? Explain.Find the slope of a line parallel to 5x + 2y = 6

Answers

To make it easier turn this equation into a slope. To do that you must get "y" by itself on one side of the equal sign. The "y" have to be positive. Then plot it out. Enter the "x" (1 for example) in the equation and solve to get "y". Then use the ordered pair to plot out the slope. Then you find a coefficient of "x" that matches the one in this equation and plot that out. If it's parallel then it's right. :)
The gradient of the line is - 2.5

Simplify 8^5 x 8^4

A. 16^9
B. 8^20
C. 8^9
D. 64^9

Answers

Answer:

8^9

Step-by-step explanation:

8^9

A manufacturer of metal washers needs to determine the​ cross-sectional area of each washer. If the outer radius of the washer is R and the radius of the hole is​ r, express the area of the washer as a polynomial. Factor this polynomial completely.

Answers

A=π(R+r)(R-r) is the factorization of the polynomial.

What is Polynomial?

Factoring a polynomial exists expressing the polynomial as a product of two or more factors; it stands somewhat like the reverse process of multiplying.

A polynomial exists as an expression consisting of indeterminates (also named variables) and coefficients, that concern only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

The hole in the washer will never contain an area because it does not occupy any surface of the object.

The area of any circle is$\pi r^(2)$.

To discover the area of this washer, take the area of the outer circle minus the area of the inner circle (the hole).

$A=\pi R^(2)-\pi r^(2)$

$$A=\pi\left(R^(2)-r^(2)\right)$$

The term $\left(R^(2)-r^(2)\right)$ is a difference in perfect squares.

$$A=\pi(R+r)(R-r)$$

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The c.s.a. is found by subtracting the area of the hole from the total area (including the hole):
c.s.a.=\pi R^(2)-\pi r^(2)
Factorizing completely we get:
c.s.a.=\pi(R+r)(R-r)

Algebra II
15 points

Answers

Answer:

  B.  The axis of symmetry is x=1.

  F.  The vertex is (1, 7).

  G. The y-intercept is (0, 10).

Step-by-step explanation:

A graph of the function is helpful sorting this out.

_____

For quadratic ax² +bx +c, the axis of symmetry is x=-b/(2a). Here, that is ...

  x = -(-6)/(2·3)

  x = 1 . . . . axis of symmetry

This is also the x-coordinate of the vertex. The y-coordinate of the vertex can be found by evaluating the expression for this value of x:

  3·1² -6·1 +10 = 7

so the vertex is (1, 7).

__

The y-intercept is the constant, the value of the function when x=0. Here, that is 10, so the coordinates of the y-intercept are (0, 10).

Is this correct? I have tried and want it checking

Answers

Beautifully done !  Both questions.  Really.
You do know what you're doing.
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