Which triangle results from a reflection across the line x = 1?

Jeanette is writing the first five terms of an arithmetic sequence. She knows that a1 is -27 and the common difference is 5. She

Musya8 [376]

No they are not correct. She should be adding 5 to the next terms instead of subtracting them. i.e. -27, -22, -17, -12, ...

6 0

4 years ago

Find the exact values of sin θ/2 and cos θ/2 for sin θ = 3/4 on the interval 0° ≤ θ ≤ 90°

timofeeve [1]

Answer:

Step-by-step explanation:

If our interval is between 0 and 90 degrees, that means that our angles are first quadrant angles. Since the formulas for the half angles of sin and cos consider both the positive and negative roots, knowing that we are in QI leaves us using only the principle, or positive, root.

Also, if we know that the sin of angle is 3/4, we can set up a right triangle in QI and find the missing side of that triangle using Pythagorean's Theorem. Sin of an angle is the ratio opposite side/hypotenuse. That means that, according to Pythagorean's Theorem,

$4^2=3^2+b^2$ and

$16-9=b^2$ and

$b=\sqrt{7}$

Now for the forula for the sin of a half-angle:

$sin(\frac{\theta}{2})=\sqrt{\frac{1-cos\theta}{2} }$

Referring to the right triangle we created and found the missing side for, we see that the cosine of that same triangle is $\frac{\sqrt{7} }{4}$

Filling in the formula then:

$sin(\frac{\theta}{2})=\sqrt{\frac{1-\frac{\sqrt{7} }{4} }{2} }$

Get a common denominator on the upper fraction:

$sin(\frac{\theta}{2})=\sqrt{\frac{\frac{4-\sqrt{7} }{4} }{2} }$

Bring up the 2 as 1/2 to multiply and get:

$sin(\frac{\theta}{2})=\sqrt{\frac{4-\sqrt{7} }{8} }$

When you do the exact same thing to find the cos of the half angle, you are using a + sign instead of a - sign under the radical. That gives you as your exact value:

$cos(\frac{\theta}{2})=\sqrt{\frac{4+\sqrt{7} }{8} }$

7 0

3 years ago

It costs $50.00 to deliver 6 floral arrangements. It costs $80.00 to deliver 12 floral arrangements. What is the constant rate o

german

The constant rate for 1 floral arrangement is $5.00 and inital value is $20.00

Equation: f(z)=20+5z

Step-by-step explanation:

Given,

Delivery cost of 6 floral arrangements = $50.00

Delivery cost of 12 floral arrangements = $80.00

Let,

x be the constant rate for each floral arrangement.

y be the initial value.

According to given statement;

6x+y=50.00 Eqn 1

12x+y=80.00 Eqn 2

Subtracting Eqn 2 from Eqn 1

$(12x+y)-(6x+y)=80.00-50.00\\12x+y-6x-y=30.00\\6x=30.00$

Dividing both sides by 6

$\frac{6x}{6}=\frac{30.00}{6}\\x=5.00$

Putting in Eqn 1;

$6(5.00)+y=50.00\\30.00+y=50.00\\y=50.00-30.00\\y=20.00$

The constant rate for 1 floral arrangement is $5.00 and inital value is $20.00

Equation for the function;

Let z be the number of floral arrangements.

f(z) = initial fee + 5*Number of floral arrangements

f(z) = 20+5z

Keywords: function, subtraction

Learn more about functions at:

#LearnwithBrainly

8 0

4 years ago

What is that slope of the line -2 -1/2 1/2 2

AnnZ [28]

Where's the data of this question?

7 0

4 years ago

PLEASE HELP FAST!!!!!

lakkis [162]

Answer:

< W ≅ < P.

Step-by-step explanation:

< W ≅ < P.

< W is the refection of < P over the x-axis.

7 0

4 years ago