All categories

3 years ago

If ABCD congruent to QRST, measure of angle A = x – 10º, and measure of angle Q = 2x – 30º, what is the measure of angle A?

Mathematics

1 answer:

belka [17]3 years ago

3 0

Congruent means they are the same,

A and Q are both the first letters, which mean they would also be the same.

Set the two equations equal to each other, solve for x then solve for angle A.

x-10 = 2x-30

Add 30 to each side:

x+20 = 2x

Subtract 1x from each side:

x = 20

Now replace x with 20 in the equation for A

A = 20-10

Angle A = 10 degrees.

You might be interested in

Describe the transformation that takes f(x)=x+1 to g(x) = -x+4. Will Mark Brainliest.

lions [1.4K]

Answer:

Reflection across y axis

Translate up by 3 units

Step-by-step explanation:

Given

$f(x) = x + 1$

$g(x) = -x + 4$

Required

Describe the transformation from f(x) to g(x)

First, take a reflection of f(x) across the y axis.

So f(x) becomes f(-x)

$f(x) = x + 1$ when reflected

$f(-x) = -x +1$

Next, translate f(-x) up by 3 units to give g(x)

$g(x) = f(-x) + k$

Where

$k = 3$

$f(-x) = -x +1$

$g(x) = -x + 1 + 3$

$g(x) = -x + 4$

Hence, the transformation from f(x) to g(x) includes:

Reflection across y axis

Translate up by 3 units

6 0

3 years ago

Help please!!!!!!!!!!!!

creativ13 [48]

Answer:

$\frac{\pi }{3},\:\frac{2\pi }{3}$

Step-by-step explanation:

Let a=THETA (angle)

$1+\sin \left(a\right)-1=\frac{\sqrt{3}+2}{2}-1\\\sin \left(a\right)=\frac{\sqrt{3}+2}{2}-1\\a=\arcsin \left(\frac{\sqrt{3}+2}{2}-1\right)+2\pi n,\:a=\pi -\arcsin \left(\frac{\sqrt{3}+2}{2}-1\right)+2\pi n\\a=\frac{\pi }{3},\:a=\frac{2\pi }{3}$

7 0

3 years ago

Find the product of f(x)=3 and g(x)=x+7

DaniilM [7]

F(x)=3 domain: negative infinity, positive infinity range: 3

g(x)=x+7 domain: - infinity, + infinity range: - infinity, + infinity

8 0

3 years ago

Two numbers N and 16 have LCM = 48 and GCF = 8. Find N.

RSB [31]

LCM=product of highest occurring primes in the numbers prime factorization.

GCF=product of shared primes in the numbers prime factorization.

16=2*2*2*2

Since the GCF is 8 N and 16 share only 2*2*2

Since the LCM is 48 and 16 has 2*2*2*2 the other number has a factor of 3

So the other number is 2*2*2*3=24

N=24

7 0

3 years ago

The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is

qwelly [4]

Answer:

Step-by-step explanation:

Given an acute triangle in which the longest side measures 30 inches; and the other two sides are congruent.

Consider the attached diagram

AB=BC=x

However to be able to solve for x, we form a right triangle with endpoints A and C.

Since the hypotenuse is always the longest side in a right triangle

Hypotenuse, AC=30 Inches

Using Pythagoras Theorem

$30^2=x^2+x^2\\900=2x^2\\x^2=450\\x=\sqrt{450}\\x=21.21$ inches$

Therefore, the smallest possible perimeter of the triangle

Perimeter=2x+30

=2(21.21)+30

=42.42+30

=72.4 Inches (rounded to the nearest tenth)

4 0

3 years ago