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3 years ago

Can someone help me with this Geometry question ASAP, thanks!

Mathematics

1 answer:

slega [8]3 years ago

4 0

We are given an isosceles triangle.

An isosceles triangle has corresponding angles of corresponding sides same.

<em>Therefore, other angle is also of (3x+7) degrees.</em>

(5x+13) and (3x+7) makes a linear pair.

Therefore,

(5x+13) + (3x+7) = 180

5x +13 + 3x +7 = 180.

8x +20 = 180.

Subtracting 20 from both sides, we get

8x +20-20 = 180-20.

8x = 160

Dividing both sides by 8, we get

<h3>x = 20.</h3><h3>Therefore, correct option is 3rd option. </h3>

You might be interested in

A number q divided by 5 is 8

oee [108]

Answer:

q = 40

Step-by-step explanation:

$\frac{q}{5} = 8$

multiply 5 on boths sides:

$\frac{q}{5} x 5 = 8 x 5$

q = 40

to check:

$\frac{40}{5}$ = 8

8 0

3 years ago

Read 2 more answers

A School decides to organize field trips for all students. Tickets for first years were sold at GH¢0.40 per student and continui

Pepsi [2]

Answer:

60%

Step-by-step explanation:

You can solve this problem by setting up a system of equations.

Let's say that the number of tickets bought by students in the first year is x, and the number bought by continuing students is y. From there, you can set it up like this:

0.4x+0.2y=160

x+y=500

Now, you can multiply the first equation by 5 on both sides to get:

2x+y=800

Subtracting the second equation from the first equation now yields:

x=300

y=200

Since 300 of the 500 tickets bought were from the first year students, and 300/500 is 0.6, 60% of the students who bought the ticket were first year students. Hope this helps!

7 0

3 years ago

Arden has 15 cards and 3 of those cards are red. What percent of her cards are red? *

Kisachek [45]

Answer: 20%

Step-by-step explanation: 3/15 = 1/5 = .20 = 20%

5 0

3 years ago

Determine all prime numbers a, b and c for which the expression a ^ 2 + b ^ 2 + c ^ 2 - 1 is a perfect square .

kogti [31]

Answer:

The family of all prime numbers such that $a^{2} + b^{2} + c^{2} -1$ is a perfect square is represented by the following solution:

$a$ is an arbitrary prime number. (1)

$b = \sqrt{1 + 2\cdot a \cdot c}$ (2)

$c$ is another arbitrary prime number. (3)

Step-by-step explanation:

From Algebra we know that a second order polynomial is a perfect square if and only if $(x+y)^{2} = x^{2} + 2\cdot x\cdot y + y^{2}$ . From statement, we must fulfill the following identity:

$a^{2} + b^{2} + c^{2} - 1 = x^{2} + 2\cdot x\cdot y + y^{2}$

By Associative and Commutative properties, we can reorganize the expression as follows:

$a^{2} + (b^{2}-1) + c^{2} = x^{2} + 2\cdot x \cdot y + y^{2}$ (1)

Then, we have the following system of equations:

$x = a$ (2)

$(b^{2}-1) = 2\cdot x\cdot y$ (3)

$y = c$ (4)

By (2) and (4) in (3), we have the following expression:

$(b^{2} - 1) = 2\cdot a \cdot c$

$b^{2} = 1 + 2\cdot a \cdot c$

$b = \sqrt{1 + 2\cdot a\cdot c}$

From Number Theory, we remember that a number is prime if and only if is divisible both by 1 and by itself. Then, $a, b, c > 1$ . If $a$ , $b$ and $c$ are prime numbers, then $2\cdot a\cdot c$ must be an even composite number, which means that $a$ and $c$ can be either both odd numbers or a even number and a odd number. In the family of prime numbers, the only even number is 2.