For every $5 Micah saves, his parents give him $10. What is the constant of proportionality

What is f(5) if f(1) = 3.2 and f(x + 1) =5over2 (f(x))?

Lubov Fominskaja [6]

F(5) would be 16. because f(1) is only 3.2 so if you multiply 3.2 x 5 you will get 16

6 0

2 years ago

(99 POINTS) Using similarity solve for x. Show all work

Anna11 [10]

Hey there! :D

The biggest thing to remember here is the similar triangles and their side lengths.

Okay, so we can separate these triangles into 3 similar triangles. Which, we only need to do that to two for a proportion, but if you were to have more variables, you could separate the triangles even more if you needed to.

We want to find two triangles that have "x" has a value of their side, so we can solve a proportion.

The bigger triangle, (the whole two triangles combine) and the smaller triangle on the left can be used to make a proportion.

On the smaller triangle:

We have 9 cm on the shorter side and x as the hypotenuse.

On the larger triangle:

We have x as the shorter side, and then 25 as the hypotenuse. (9+16)

Note: You have to flip the larger triangle upside down to make it a similar structure to the other two triangles. It is similar, you just have to flip it.

So, now we can make a proportion.

$\frac{x}{9} = \frac{25}{x}$

Now, cross multiply.

9*25= 225

x*x= $x^{2}$

So, find the square root.

√225= 15

x= 15.

I hope this helps!
~kaikers

7 0

2 years ago

Read 2 more answers

Triangle ABC has been dilated to form triangle A'B'C'. If sides AB and A'B' are proportional, what is the least amount of additi

Ede4ka [16]

When considering similar triangles, we need congruent angles and proportional sides.

Hence
"Angles B and B' are congruent, and angles C and C' are congruent." is sufficient to prove similarity of two triangles.

"Segments AC and A'C' are congruent, and segments BC and B'C' are congruent." does not prove anything because we know nothing about the angles.

"Angle C=C', angle B=B', and segments BC and B'C' are congruent." would prove ABC is congruent to A'B'C' if and only if AB is congruent to A'B' (not just proportional).

"<span>Segment BC=B'C', segment AC=A'C', and angles B and B' are congruent</span>" is not sufficient to prove similarity nor congruence because SSA is not generally sufficient.

To conclude, the first option is sufficient to prove similarity (AAA)

3 0

3 years ago

Read 2 more answers

2 r squared + 3s cubed minus r squared + 40 squared minus r squared if R equals -2 s equals -3 and T equals 5

Flura [38]

$2r^2+3s^2-r^2+4t^2-r^2\\\\\text{simplify}\\\\(2r^2-r^2-r^2)+3s^2+4t^2=3s^2+4t^2\\\\s=-3;\ t=5\\\\3(-3)^2+4(5)^2=3(9)+4(25)=27+100=127$

6 0

3 years ago

The life in hours of a 75-watt light bulb is known to be normally distributed with standard deviation σ = 25 hours. A random sam

irina [24]

Answer: a) (1008.34,1019.658) b) (1009.24,1018.76)

Step-by-step explanation:

Since we have given that

n = 75

mean = 1014 hours

Standard deviation = 25 hours

At 95% two sided , z = 1.96

So, confidence interval would be

$\bar{x}\pm z\dfrac{\sigma}{\sqrt{n}}\\\\=1014\pm 1.96\dfrac{25}{\sqrt{75}}\\\\=1014\pm 5.658\\\\=(1014-5.658,1014+5.658)\\\\=(1008.34,1019.658)$

(b) Construct a 95% lower confidence bound on the mean life.

z = 1.65

So, confidence interval would be

$\bar{x}\pm z\times \dfrac{\sigma}{\sqrt{n}}\\\\=1014\pm 1.65\times \dfrac{25}{\sqrt{75}}\\\\=1014\pm 4.76\\\\=(1014-4.76,1014+4.76)\\\\=(1009.24,1018.76)$

Hence, a) (1008.34,1019.658) b) (1009.24,1018.76)

4 0

3 years ago