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3 years ago

What is the value of y?

Mathematics

1 answer:

Romashka [77]3 years ago

7 0

Answer:

y=42

Step-by-step explanation:

y+48+90=180

y=180-138

y=42

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Schach [20]

1. 27

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3 years ago

please help me, Prove a quadrilateral with vertices G(1,-1), H(5,1), I(4,3) and J(0,1) is a rectangle using the parallelogram me

mestny [16]

Answer:

Step-by-step explanation:

We are given the coordinates of a quadrilateral that is G(1,-1), H(5,1), I(4,3) and J(0,1).

Now, before proving that this quadrilateral is a rectangle, we will prove that it is a parallelogram. For this, we will prove that the mid points of the diagonals of the quadrilateral are equal, thus

Join JH and GI such that they form the diagonals of the quadrilateral.Now,

JH= $\sqrt{(5-0)^{2}+(1-1)^{2}}=5$ and

GI= $\sqrt{(4-1)^{2}+(3+1)^{2}}=5$

Now, mid point of JH= $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

= $(\frac{5+0}{2},\frac{1+1}{2})=(\frac{5}{2},1)$

Mid point of GI= $(\frac{5}{2},1)$

Since, mid point point of JH and GI are equal, thus GHIJ is a parallelogram.

Now, to prove that it is a rectangle, it is sufficient to prove that it has a right angle by using the Pythagoras theorem.

Thus, From ΔGIJ, we have

$(GI)^{2}=(IJ)^{2}+(JG)^{2}$ (1)

Now, JI= $\sqrt{(4-0)^{2}+(3-1)^{2}}=\sqrt{20}$ and GJ= $\sqrt{(0-1)^{2}+(1+1)^{2}}=\sqrt{5}$

Substituting these values in (1), we get

$5^{2}=(\sqrt{20})^{2}+(\sqrt{5})^{2} }$

$25=20+5$

$25=25$

Thus, GIJ is a right angles triangle.

Hence, GHIJ is a rectangle.

Also, The diagonals GI= $\sqrt{(4-1)^{2}+(3+1)^{2}}=5$ and HJ= $\sqrt{(0-5)^2+(1-1)^2}=5$ are equal, thus, GHIJ is a rectangle.

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3 years ago

The top of the desk is shaped like a trapezoid the bases of the trapezoid are 26.5 and 30 cm long the area of the desk is 791 CM

kotegsom [21]

Answer:

28 cm

Step-by-step explanation:

Given that :

Area = 791 cm

Base, b1 = 26.5 cm

Base, b2 = 30 cm

Area, A of trapezoid :

A = 1/2 (a + b) h

Where a and b are the bases ;

791 = 1/2(26.5 + 30)h

791 = 0.5(56.5)h

791 = 28.25h

h = 791 / 28.25

h = 28 cm

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3 years ago

A company that produces dog food claims that its bags contain 11 kg of food. From

andriy [413]

By testing the hypothesis we can conclude that the bag does not contain 11 kg of food.

Given mean of 10.6 kg, population standard deviation of 0.6 and sample size of 25.

We are required to find whether the company is right in saying that their bags contain 11 kg of food.

First we have to make hypothesis.

$H_{0}$ :μ≠11

$H_{1}$ :μ=11

We have to use t statistic because the sample size is less than 30.

t=(X-μ)/s/ $\sqrt{n}$

We will use s/ $\sqrt{n}$ =0.6 because we have already given population standard deviation of weights.

t=(11-10.6)/0.6

=0.4/0.6

=0.667

Degree of freedom=n-1

=25-1

=24

T critical at 0.05 with degree of freedom 24=2.0639

T critical at 0.05 with degree of freedom is greater than calculated t so we will accept the null hypothesis.It concludes that the bags donot contain 11 kg of food.

Hence by testing the hypothesis we can conclude that the bag does not contain 11 kg of food.

Learn more about t test at brainly.com/question/6589776

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a silk worm wind ts cocoon out of one long slik fiber. to make silk thread, 3 to 10 of these silk fibers are unwound from their

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Since the number ranges between 3 and 10, an equation can't be made because the number is always unknown or can be different every time

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