Given pq || bc. Find the length of aq

What is the value of the expression shown below? 8 + (7 + 1) 2 ÷ 4 ⋅ 2

Leni [432]

The answer is 10

8+(8)2÷4·2
8+16÷4·2 4·2=8 then 16÷8
8+2=10

just use PEMDAS

6 0

3 years ago

Can someone please help me with this!?!?!

lys-0071 [83]

They are congruent because of the angles, which means the congruency reason should be SAS.

4 0

3 years ago

How do you get the answer and sketch it to this graft

Katyanochek1 [597]

F(x) = -4(x - 2)² + 2
f(x) = -4((x - 2)(x - 2)) + 2
f(x) = -4(x² - 2x - 2x + 4) + 2
f(x) = -4(x² - 4x + 4) + 2
f(x) = -4(x²) + 4(4x) - 4(4) + 2
f(x) = -4x² + 16x - 16 + 2
f(x) = -4x² + 16x - 14
-4x² + 16x - 14 = 0
x = -16 +/- √(16² - 4(-4)(-14))
 2(-4)
x = -16 +/- √(256 - 224)
 -8
x = -16 +/- √(32)
 -8
x = -16 +/- 5.66
 -8
x = -16 + 5.66 x = -16 - 5.66
 -8 -8
x = -10.34 x = -21.66
 -8 -8
x = 1.2925 x = 2.7075
f(x) = -4x² + 16x - 14
f(1.2925) = -4(1.2925)² + 16(1.2925) - 14
f(1,2925) = -4(1.67055625) + 20.68 - 14
f(1.2925) = -6.682225 + 20.68 - 14
f(1.2925) = 13.997775 - 14
f(1.2925) = -0.002225
(x, f(x)) = (1.2925, -0.002225)
or
f(x) = -4x² + 16x - 14
f(2.7075) = -4(2.7075)² + 16(2.7075) - 14
f(2.7075) = -4(7.33055625) + 43.32 - 14
f(2.7075) = -29.322225 + 43.32 - 14
f(2.7075) = 13.997775 - 14
f(2.7075) = -0.002225
(x, f(x)) = (2.7075, -0.002225)
--------------------------------------------------------------------------------------------
f(x) = 2(x - 2)² + 1
f(x) = 2((x - 2)(x - 2)) + 1
f(x) = 2(x² - 2x - 2x + 4) + 1
f(x) = 2(x² - 4x + 4) + 1
f(x) = 2(x²) - 2(4x) + 2(4) + 1
f(x) = 2x² - 8x + 8 + 1
f(x) = 2x² - 8x + 9
2x² - 8x + 9 = 0
x = -(-8) +/- √((-8)² - 4(2)(9))
 2(2)
x = 8 +/- √(64 - 72)
 4
x = 8 +/- √(-8)
 4
x = 8 +/- √(8 × (-1))
 4
x = 8 +/- √(8)√(-1)
 4
x = 8 +/- 2.83i
 4
x = 2 +/- 1.415i
x = 2 + 1.415i x = 2 - 1.415i
f(x) = 2x² - 8x + 9
f(2 + 1.415i) = 2(2 + 1.415i)² - 8(2 + 1.415i) + 9
f(2 + 1.415i) = 2((2 + 1.415i)(2 + 1.415i)) - 16 - 11.32i + 9
f(2 + 1.415i) = 2(4 + 2.83i + 2.83i + 2.00225i²) - 16 - 11.32i + 9
f(2 + 1.415i) = 2(4 + 5.66i + 2.00225) - 16 - 11.32i + 9
f(2 + 1.415i) = 8 + 11.32i + 4.0045 - 16 - 11.32i + 9
f(2 + 1.415i) = 8 + 4.0045 - 16 + 9 + 11.32i - 11.32i
f(2 + 1.415i) = 12.0045 - 16 + 9
f(2 + 1.415i) = -3.9955 + 9
f(2 + 1.415i) = 5.0045
(x, f(x)) = (2 + 1.415i, 5.0045)
or
f(x) = 2x² - 8x + 9
f(2 - 1.415i) = 2(2 - 1.415i)² - 8(2 - 1.415i) + 9
f(2 - 1.415i) = 2((2 - 1.415i)(2 - 1.415i)) - 16 + 11.32i + 9
f(2 - 1.415i) = 2(4 - 2.83i - 2.83i + 2.00225i²) - 16 + 11.32i + 9
f(2 - 1.415i) = 2(4 - 5.66i + 2.00225) - 16 + 11.32i + 9
f(2 - 1.415i) = 8 - 11.32i + 4.0045 - 16 + 11.32i + 9
f(2 - 1.415i) = 8 + 4.0045 - 16 + 9 - 11.32i + 11.32i
f(2 - 1.415i) = 12.0045 - 16 + 9
f(2 - 1.145i) = -3.9955 + 9
f(2 - 1.415i) = 5.0045
(x, f(x)) = (2 - 1.415i, 5.0045)
--------------------------------------------------------------------------------------------
f(x) = -2(x - 4)² + 8
f(x) = -2((x - 4)(x - 4)) + 8
f(x) = -2(x² - 4x - 4x + 16) + 8
f(x) = -2(x² - 8x + 16) + 8
f(x) = -2(x²) + 2(8x) - 2(16) + 8
f(x) = -2x² + 16x - 32 + 8
f(x) = -2x² + 16x - 24
-2x² + 16x - 24 = 0
x = -16 +/- √(16² - 4(-2)(-24))
 2(-2)
x = -16 +/- √(256 - 192)
 -4
x = -16 +/- √(64)
 -4
x = -16 +/- 8
 -4
x = -16 + 8 x = -16 - 8
 -4 -4
x = -8 x = -24
 -4 -4
x = 2 x = 6
f(x) = -2x² + 16x - 24
f(2) = -2(2)² + 16(2) - 24
f(2) = -2(4) + 32 - 24
f(2) = -8 + 32 - 24
f(2) = 24 - 24
f(2) = 0
(x,f(x)) = (2, 0)
or
f(x) = -2x² + 16x - 24
f(6) = -2(6)² + 16(6) - 24
f(6) = -2(36) + 96 - 24
f(6) = -72 + 96 - 24
f(6) = 24 - 24
f(6) = 0
(x, f(x)) = (6, 0)

5 0

3 years ago

PLATO: Type the correct answer in each box. The vector is first dilated by a factor of 2.5 and then rotated by pi/2 radians. If

yawa3891 [41]

Answer:

a = -1, b = -2.5

Step-by-step explanation:

Rule for the dilation of a vector $\binom{x}{y}$ by a scale factor of k is,

(x, y) → (kx, ky)

BY using this rule for a vector $\binom{-1}{4}$ by a scale factor of 2.5

$\binom{-1}{4}$ → $\binom{-2.5}{1}$

Followed by the rotation by 90° Or $\frac{\pi }{2}$ radians,

Rule for rotation of a vector by 90° is,

(x, y) → (-y, x)

By this rule vector $\binom{-2.5}{1}$ will become,

$\binom{-2.5}{1}$ → $\binom{-1}{-2.5}$

If we represent this vector by $\binom{a}{b}$ ,

Then a = -1 and b = -2.5 will be the answer.

5 0

3 years ago

Read 2 more answers

What are the solutions of the equation 9x4 – 2x2 – 7 = 0? Use u substitution to solve. tions of the equation 9

skelet666 [1.2K]

Answer:

Step-by-step explanation:

Let $u^2=x^4\\u = x^2$

Subbing in:

$9u^2-2u-7=0$

a = 9, b = -2, c = -7

The product of a and c is the aboslute value of -63, so a*c = 63. We need 2 factors of 63 that will add to give us -2. The factors of 63 are {1, 63}, (3, 21}, {7, 9}. It looks like the combination of -9 and +7 will work because -9 + 7 = -2. Plug in accordingly:

$9u^2-9u+7u-7=0$

Group together in groups of 2:

$(9u^2-9u)+(7u-7)=0$

Now factor out what's common within each set of parenthesis:

$9u(u-1)+7(u-1)=0$

We know this combination "works" because the terms inside the parenthesis are identical. We can now factor those out and what's left goes together in another set of parenthesis:

$(u-1)(9u+7)=0$

Remember that $u=x^2$

so we sub back in and continue to factor. This was originally a fourth degree polynomial; that means we have 4 solutions.

$(x^2-1)(9x^2+7)=0$

The first two solutions are found withing the first set of parenthesis and the second two are found in other set of parenthesis. Factoring $(x^2-1)$ gives us that x = 1 and -1. The other set is a bit more tricky. If