All categories

3 years ago

please explain to me how to solve this problem, i have my final test tomorrow and I need to know how to do it

Mathematics

1 answer:

RSB [31]3 years ago

4 0

Answers:

ST = x = 5
RT = y = 4
angle R = 88 degrees

============================================================

Explanation:

I'm assuming side PQ is parallel to side RT. If so, then triangle PQS is similar to triangle TRS.

From that, we can form the proportion below to solve for x.

PT/TS = QR/RS

15/x = 9/3

15*3 = x*9

45 = 9x

9x = 45

x = 45/9

x = 5

So ST is 5 units long.

The jump from ST = 5 to PT = 15 is "times 3". The same goes from RS = 3 to QR = 9.

We move in reverse to go from PQ = 12 to RT = y = 4, i.e. we divide by 3 to go from the larger triangle's lengths to the smaller triangle's lengths.

---------------------

Since PQ is parallel to RT, this means angles Q and R are congruent. They are corresponding angles. Angle Q is 88, and so is angle R.

Side note: Similar triangles have congruent corresponding angles.

You might be interested in

Sams brother is 7 years older than Sam. His mother is 4 less than 3 times sams age. Their combined age is 63. How old isn’t Sam,

statuscvo [17]

The answer is 14. This is because 63=3+x+3x-4. Then You just subtract it and then you get 64=4x. Then you just divide it and then you get x=16.

4 0

3 years ago

Attached as photo. Please help

Effectus [21]

By Euler's method the <em>numerical approximate</em> solution of the <em>definite</em> integral is 4.189 648.

<h3>How to estimate a definite integral by numerical methods</h3>

In this problem we must make use of Euler's method to estimate the upper bound of a <em>definite</em> integral. Euler's method is a <em>multi-step</em> method, related to Runge-Kutta methods, used to estimate <em>integral</em> values numerically. By integral theorems of calculus we know that definite integrals are defined as follows:

∫ f(x) dx = F(b) - F(a) (1)

The steps of Euler's method are summarized below:

Define the function seen in the statement by the label f(x₀, y₀).
Determine the different variables by the following formulas:

xₙ₊₁ = xₙ + (n + 1) · Δx (2)
yₙ₊₁ = yₙ + Δx · f(xₙ, yₙ) (3)
Find the integral.

The table for x, f(xₙ, yₙ) and y is shown in the image attached below. By direct subtraction we find that the <em>numerical</em> approximation of the <em>definite</em> integral is:

y(4) ≈ 4.189 648 - 0

y(4) ≈ 4.189 648

By Euler's method the <em>numerical approximate</em> solution of the <em>definite</em> integral is 4.189 648.

To learn more on Euler's method: brainly.com/question/16807646

#SPJ1

7 0

2 years ago

Given the two expressions shown below:

kobusy [5.1K]

<h2>Answer: A. Both are rational.</h2>

Step-by-step explanation:

Although both expressions have square roots, the result of each square root is an integer, which can be expressed as a fraction.

In this sense:

Rational numbers are all numbers that can be represented as the quotient (division) of two integer numbers. This means they can be represented as a fraction in which the denominator is nonzero.

If we solve both expressions, we will be able to see that the result is an integer that can be expressed as a fraction with two integers:

$\sqrt{4} + \sqrt{25}=2 + 5= 7$ The result is an integer

$7=\frac{7}{1}$

$\sqrt{4} + \sqrt{9}= 2 + 3=5$ The result is an integer

$5=\frac{5}{1}$

7 0

3 years ago

Find all constants a such that the vectors (a, 4) and (2, 5) are parallel.

Nezavi [6.7K]

Answer:

$\displaystyle a = \frac{8}{5}$ .

Step-by-step explanation:

Two vectors $(x_1,\, y_1)$ and $(x_2,\, y_2)$ are parallel to one another if and only if the ratio between their corresponding components are equal:

$\displaystyle \frac{x_1}{x_2} = \frac{y_1}{y_2}$ .

Equivalently:

$\displaystyle \frac{x_1}{y_1} = \frac{x_2}{y_2}$ .

For the two vectors in this equation to be parallel to one another:

$\displaystyle \frac{a}{4} = \frac{2}{5}$ .

Solve for $a$ :

$\displaystyle a = \frac{8}{5}$ .

$\displaystyle \frac{8}{5}$ would be the only valid value of $a$ ; no other value would satisfy the $\displaystyle \frac{x_1}{y_1} = \frac{x_2}{y_2}$ equation.

4 0

3 years ago

Helppppppppppppp meee

Darina [25.2K]

It will be 14 times 6.5

5 0

3 years ago

please explain to me how to solve this problem, i have my final test tomorrow and I need to know how to do it​

please explain to me how to solve this problem, i have my final test tomorrow and I need to know how to do it