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3 years ago

HELP ASAP!!!!!!!!PLEASE Solve for x. Please explain. Thank you

Mathematics

1 answer:

Stella [2.4K]3 years ago

8 0

The values are $x=8$ and $y=10$

Explanation:

From the figure, we can see that the two quadrilaterals are similar.

Thus, by the property of quadrilateral, for similar quadrilaterals, their corresponding angles and sides are congruent. Thus, we have,

∠D = ∠S, ∠E = ∠P, ∠G = ∠R and ∠F = ∠Q

Also, GF = QR and DE = PS

Where QR = $2x-4$ and ∠D = 102°, ∠G = 84° and ∠F = 68°, ∠Q = $(6y+x)$ °

Hence, to determine the value of x for the side QR, we have,

Equating the values in GF = QR,we get,

$12=2x-4\\16=2x\\8=x$

Thus, the value of x is 8.

Substituting x in the angle Q to determine the value of y.

Thus, we have,

∠F = ∠Q

$68=6y+x\\68=6y+8\\60=6y\\10=y$

Thus, the value of y is 10.

Hence, The values are $x=8$ and $y=10$

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A research student is working with a culture of bacteria that doubles in size every

ser-zykov [4K]

Answer:

$2^{24}*1000$ bacteria

Step-by-step explanation:

The generic form of an exponential function is: $f(n)=ar^n$ , where a is the initial amount, r is the rate, and n is the time.

In this case, the initial amount is 1000, so a = 1000. Also, the rate is 2 because the culture doubles in size every 5 minutes. However, our n is not just n; it's actually n/5 because the rate is doubling per 5 minutes, not per 1 minute. If it was per 1 minute, then the time would simply be n. Unfortunately, that's not the case here, so the exponent of r should be n/5, where n is the number of minutes that have passed.

Now, we have: $f(n)=1000(2)^{n/5}$

Since n is the number of minutes, we need to convert 2 hours to minutes:

2 hours * 60 min/hour = 120 minutes.

$f(120)=1000(2)^{120/5}=1000(2)^{24}=2^{24}*1000$ $f(120)=1000(2)^{120/5}=1000(2)^{24}=2^{24}*1000$

Thus, the answer is $2^{24}*1000$ bacteria.

Hope this helps!

5 0

2 years ago

Read 2 more answers

Need help with this....

Yakvenalex [24]

Answer:

$\boxed{\dfrac{f(a+h)-f(a)}{h}=-3a^2-3ah-h^2}$

Step-by-step explanation:

$f(x)=-x^3+2\\\\\dfrac{f(a+h)-f(a)}{h}\\\\f(a+h)\to\text{substitute x = a + h}\\f(a)\to\text{substitute x = a}\\\\\dfrac{f(a+h)-f(a)}{h}=\dfrac{-(a+h)^3+2-(-a^3+2)}{h}\\\\\text{use}\ (x+y)^3=x^3+3x^2y+3xy^2+y^3\\\\=\dfrac{-(a^3+3a^2h+3ah^2+h^3)+2-(-a^3)-2}{h}\\\\=\dfrac{-a^3-3a^2h-3ah^2-h^3+2+a^3-2}{h}\\\\\text{combine like terms}$

$=\dfrac{(-a^3+a^3)-3a^2h-3ah^2-h^3+(2-2)}{h}\\\\=\dfrac{-3a^2h-3ah^2-h^3}{h}\\\\=\dfrac{h(-3a^2-3ah-h^2)}{h}\\\\=-3a^2-3ah-h^2$

6 0

2 years ago

All! Please?!!?!?!!!

balu736 [363]

What do you need help with? it helps us to know the question!

4 0

2 years ago

For what value of a are the lines of 6y=-2x+4 and 2y=ax-5 parallel? perpendicular?

masha68 [24]

Hey there!!

Parallel lines have the same slope. If they have different slope, then they are not parallel because both lines would combine at some point.

The y-intercept form:

y = mx + b

In this equation, 'm' is considered to be the slope.

The equation we have is 6y = -2x + 4

First, let's divide all the sides with 6 to isolate the value of 'y'.

... 6y = -2x + 4

... y = -1/3x + 2/3

The slope is -1/3...

... hence the slope in the other equation should be -1/3.

Equation we got...

... 2y = ax - 5

Let's divide by 2 on both sides...

... y = ax/2 - 5

The slope in this a/2

Hence, ...

... a/2 = -1/3

... 3a = -2

... a = -2/3

<h2>Hence, the value of a is -2/3. </h2><h3>Hope my answer helps!</h3>

4 0

3 years ago

What is the final reason???? I will give brainliest!

DaniilM [7]

Well CD and CB are both equal to each other because they’re the same angles , it’s a reflection

8 0

2 years ago