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4 years ago

Which transformation shows a relfection of DEF?

Mathematics

1 answer:

AfilCa [17]4 years ago

6 0

Answer:

The middle option.

Step-by-step explanation:

This is because the points on each triangle are equidistant from the imaginary line in between the two triangles. It isn't the first option because that is a rotation, and it isn't the third right option because that is a translation.

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What is the value of x in the equation 3x - 4 (2x - 5) = 15

Zepler [3.9K]

Hey there! I'm happy to help!

Here is our equation

3x - 4 (2x - 5) = 15

First, we will sue the distributive property to remove the parentheses. The term outside the parentheses is -4, so that is what we multiply the insides by.

3x-8x+20=15

We combine our like terms (our x-values).

-5x+20=15

We subtract 20 from both sides.

-5x=-5

We divide both sides by -5.

x=1

Have a wonderful day and keep on learning! :D

3 0

3 years ago

Read 2 more answers

At a lemonade stand, pink lemonade costs $2.50 and sweet tea lemonade costs $4. In one morning, the stand sells 21 drinks for $6

snow_tiger [21]

Answer:

lemonade = 11

Step-by-step explanation:

let p = pink lemonade

let t = sweet tea

create a system of equations -- one with quantity, one with associate costs

p + t = 21

2.5p + 4t = 67.5

substitution method: let t = 21 - p

2.5p + 4(21 - p) = 67.5

2.5p + 84 - 4p = 67.5

-1.5 p = -16.5

p = 11

t = 21 - 11

t = 10

4 0

3 years ago

Attached is the problem, if anyone could help me and explain this I would be grateful.

Kryger [21]

Let's say that, that equals some angle θ
thus $\bf sec^{-1}(1)=\theta \iff sec(\theta)=1\\\\
-----------------------------\\\\
sec(\theta)=\cfrac{1}{cos(\theta)}\qquad thus\\\\
-----------------------------\\\\
\cfrac{1}{cos(\theta)}=1\implies \cfrac{1}{1}=cos(\theta)\implies 1=cos(\theta)
\\\\\\
\textit{now, taking }cos^{-1}\textit{ to both sides}
\\\\\\
cos^{-1}(1)=\theta$

so.. .check your Unit Circle, what is that angle anyway?

8 0

4 years ago

Solve for x.<br> \12x + 3<br> 13x + 2<br> x = [?]

Vsevolod [243]

Answer:

x=7

Step-by-step explanation:

25x+5=180

-5 -5

25x=175

/25 /25

3 0

3 years ago

Read 2 more answers

The number of bacteria after t hours is given by N(t)=250 e^0.15t a) Find the initial number of bacteria and the rate of growth

Art [367]

Answer:

a) $N_0=250\; k=0.15$

b) 334,858 bacteria

c) 4.67 hours

d) 2 hours

Step-by-step explanation:

a) Initial number of bacteria is the coefficient, that is, 250. And the growth rate is the coefficient besides “t”: 0.15. It’s rate of growth because of its positive sign; when it’s negative, it’s taken as rate of decay.

Another way to see that is the following:

Initial number of bacteria is N(0), which implies $t=0$ . And $N(0)=N_0$ . The process is:

$N(t)=250 e^{0.15t}\\N(0)=250 e^{0.15(0)}\\ N_0=250e^{0}\\N_0=250\cdot1\\ N_0=250$

b) After 2 days means $t=48$ . So, we just replace and operate:

$N(t)=250 e^{0.15t}\\N(48)=250 e^{0.15(48)}\\ N(48)=250e^{7.2}\\N(48)=334,858\;\text{bacteria}$

c) $N(t_1)=4000; \;t_1=?$

$N(t)=250 e^{0.15t}\\4000=250 e^{0.15t_1}\\ \dfrac{4000}{250}= e^{0.15t_1}\\16= e^{0.15t_1}\\ \ln{16}= \ln{e^{0.15t_1}} \\ \ln{16}=0.15t_1 \\ \dfrac{\ln{16}}{0.15}=t_1=4.67\approx 5\;h$

d) $t_2=?\; (N_0→3N_0 \Longrightarrow 250 → 3\cdot250 =750)$

$N(t)=250 e^{0.15t}\\ 750=250 e^{0.15t_2} \\ \ln{3} =\ln{e^{0.15t_2}}\\ t_2=\dfrac{\ln{3}}{0.15} = 2.99 \approx 3\;h$

6 0

3 years ago