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3 years ago

Find the values of x and y.

Mathematics

1 answer:

lara31 [8.8K]3 years ago

5 0

Answer:

x=90 y=43

Step-by-step explanation:

by looking at the diagram you can infer that the triangles are similar, this means that angle B and angle C both equal 47 degrees. you can also infer by the straight angle underneath both angles the both angle Ds add up to 180 and because they are similar triangles that means they are right angles giving you the x value, 90 degrees. after this you know that a triangle adds up to equal 180 degrees meaning if you add 90 and 47 together and subtract that from 180 you get the value of y, 43.

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Predict how many times you will roll a number less than 3 if you roll a standard number

Korvikt [17]

Answer:

about 117 times

Step-by-step explanation:

No. of possible outcomes of a cube: 6

2 out the 6 possible outcomes are less than 3,

and therefore, No. of favorable outcome: 2

P(less than 3)= No. of favorable outcome / No. of possible outcomes

=2/6 => 1/3

if you roll a standard number cube 350 times then,

Prediction= number of rolls x (P(less than 3))

=350 x 1/3

≈117 times.

4 0

2 years ago

PQR is a triangle. PR = 13 cm, PQ = 12 cm and angle QPR = 30°<br> Calculate the length of QR.

Deffense [45]

Answer:

6.55 cm

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. Types of triangles are isosceles, acute, scalene, obtuse, right and equilateral triangle.

Cosine rule is used to show the relationship between sides and angles of a triangle. If a, b, and c are sides of a triangle, while A, B, and C are angles opposite to the corresponding sides. Then:

c² = a² + b² - 2ab*cos(C)

Given that PR = 13 cm, PQ = 12 cm and angle QPR = 30°, hence:

QR² = PR² + PQ² - 2(PR)(PQ)cos(∠QPR)

QR² = 13² + 12² - 2(13)(12)cos(30) = 169 + 144 - 270

QR² = 43

QR = 6.55 cm

3 0

2 years ago

Someone please explain the difference of Multiples and Factors as well as an example.

Jlenok [28]

Answer:

A multiple is a number that can be divided by another number a certain number of times without a remainder. A factor is one of two or more numbers that divides a given number without a remainder.

Example:

2 is a factor of 8.

8 is a multiple of 2.

Step-by-step explanation:

<h2><u><em>PLEASE MARK AS BRAINLIEST!!!!!</em></u></h2>

3 0

2 years ago

Equation of the line contains the points (-3,2) and (5,-5)

makkiz [27]

For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

$y = mx + b$

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

We have the following points through which the line passes:

$(x_ {1}, y_ {1}): (- 3,2)\\(x_ {2}, y_ {2}) :( 5, -5)$

So the slope is:

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-5-2} {5 - (- 3)} = \frac {-7} {5 + 3} = - \frac {7} {8}$

Thus, the equation of the line is of the form:

$y = - \frac {7} {8} x + b$

We substitute one of the points and find "b":

$2 = - \frac {7} {8} (- 3) + b\\2 = \frac {21} {8} + b\\b = 2- \frac {21} {8}\\b = \frac {16-21} {8}\\b = - \frac {5} {8}$

Finally, the equation is:

$y = - \frac {7} {8} x- \frac {5} {8}$

Answer:

$y = - \frac {7} {8} x- \frac {5} {8}$

6 0

2 years ago

Please help me i don't know what to do <br> please show your work

Diano4ka-milaya [45]

<h3>Distributive Property</h3>

The distributive property lets you group or ungroup terms using parentheses. It lets you multiply an external factor by every term in parentheses, expressing the result as a sum:

... a(b + c) = ab + ac . . . . . . factor <em>a</em> multiplies the terms <em>b</em> and <em>c</em>

and it lets you remove a common factor from different terms, putting that factor outside parentheses:

... ab + ac = a(b + c)

The letters <em>a</em>, <em>b</em>, <em>c</em> here can stand for any number or expression.

<h3>Homework</h3>

20. To do this problem, you need to eliminate the parentheses using the distributive property. Then, "collect terms," which is another application of the distributive property. The external factor outside the parentheses is (-2/3). Multiply that by each term in parentheses, and add the results.

After that, recognize that c is a factor of two of the terms. Add their coefficients to simplify that sum to one term.

$-\dfrac{2}{3}(12c-9)+14c=\left(-\dfrac{2}{3}\right)(12c)+\left(-\dfrac{2}{3}\right)(-9)+14c=-8c+6+14c\\\\=c(-8+14)+6\\\\=6c+6$

22. You are to evaluate the expression with x=2 two ways: as is, and after you simplify it by combining like terms.

$-8x+5-2x-4+5x\\=-8(2)+5-2(2)-4+5(2)\\=-16+5-4-4+10\\=-9$

<u>Simplified:</u>

$-8x+5-2x-4+5x\\=x(-8-2+5)+(5-4)=-5x+1\\=-5(2)+1=-10+1\\=-9$

I prefer simplifying the expression first. The number of calculations and chances for error are reduced.

23. It is convenient to check for equivalence after simplifying both expressions.

<u>First Expression:</u>

$8x^2+3\left(x^2+y\right)=8x^2+3x^2+3y=11x^2+3y$

<u>Second Expression:</u>

$7x^2+7y +4x^2-4y=(7+4)x^2+(7-4)y=11x^2+3y$

The simplified forms of the expressions are identical, so we conclude the expressions are equivalent.

25. The area of a rectangle is the product of its length and width. Here, you are asked to simplify the product of (3+x) ft and 3 ft.

$((3+x)\,\text{ft})(3\,\text{ft})=(3\,\text{ft})\cdot (3\,\text{ft})+(x\,\text{ft})\cdot (3\,\text{ft})=9\,\text{ft}^2+3x\,\text{ft}^2\\\\=(3x+9)\,\text{ft}^2$

In the last form of this expression, we have used "standard form" which has the degree of the variable decreasing in terms left to right. The units are factored out to make the expression a bit less cumbersome.

3 0

2 years ago

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