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natima [27]
3 years ago
9

In ΔBCD, the measure of ∠D=90°, the measure of ∠B=53°, and CD = 5.5 feet. Find the length of BC to the nearest tenth of a foot.

Mathematics
1 answer:
Juli2301 [7.4K]3 years ago
5 0

Answer:

6.9

Step-by-step explanation:

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Maia's calculator displays a number as 9.125 E10. What is this number in standard form?
melomori [17]
9.125 E10 is the same as 9.125 × 10¹⁰ in standard form. 
4 0
3 years ago
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You go shopping at a local department store with your friend and cousin. You buy one pair of jeans, four pairs of shorts, and tw
VashaNatasha [74]

Answer: Cost per pair of jeans = $ 20

Cost per pair of shorts = $12

Cost per shirt = $8

Step-by-step explanation:

Let x= cost per pair of jeans

y = Cost per pair of shorts

z= cost per shirt.

For you, total cost = x+4y+2z= 84

For your friend,  total cost = 2x+y+3z=76

For cousin, total cost = x+2y+z= 52

Required system:

x+4y+2z=84\ (i)\\ 2x+y+3z=76\ (ii)\\ x+2y+z=52\ (iii)

from (i), x=84-4y-2z    (*)

put this in (ii) and (iii) we get

2\left(84-4y-2z\right)+y+3z=76\\\Rightarrow\ -7y-z+168=76\ (iv)\\\\ 84-4y-2z+2y+z=52\\\Rightarrow\ -2y-z+84=52 \ (v)

from (iv), y=-\frac{z-92}{7}\ (vi)

\mathrm{Subsititute\:}y=-\frac{z-92}{7}\ \text{in}\ (v)

-2\left(-\frac{z-92}{7}\right)-z+84=52\\\\\Rightarrow\ -2\left(-\frac{z-92}{7}\right)-z=-32\\\\\Rightarrow\ -\frac{5z}{7}-\frac{184}{7}=-32\\\\\Rightarrow\ -5z-184=-224\\\\\Rightarrow\ -5z=-40\\\\\Rightarrow\ z=8

\mathrm{Subsititute\:}z=8\text{ in (vi)}

y=-\frac{8-92}{7}\\\\\Rightarrow \ y=12

\mathrm{Subsititute\:}z=8,\:y=12\text{ in (*)}

x=84-4\cdot \:12-2\cdot \:8\\\\\Rightarrow\ x= 20

Hence, x= 20, y= 12 , z=8

So, Cost per pair of jeans = $ 20

Cost per pair of shorts = $12

Cost per shirt = $8

7 0
3 years ago
Factor the polynomial 16b^4+30b^3-12b^2
Lelu [443]

Answer:

2b²(8b²+15b-6)

Step-by-step explanation:

16b^{4}+30b³-12b²

2b²(8b²+15b-6)

This is not further factorable. If you want to find the roots, you'd have to use the quadratic formula for the polynomial in the parentheses. Therefore that is our final answer.

4 0
3 years ago
Divide. (4x^3+2x+1)÷(x+1)
stiks02 [169]

(4x^3+2x+1)\div(x+1)=4x^2-4x+6-\dfrac{5}{x+1}

8 0
3 years ago
Peter leaves Mitchell's house traveling 30 mph. Mitchell leaves 15 min later, trying to catch up to peter, going 40 mph, if they
Kruka [31]

Given :

Peter velocity , P = 30 mph .

Mitchell velocity , M = 40 mph .

Mitchell leaves 15 min later .

To Find :

If they drive along the same route how long will it take Mitchell to catch Peter.

Solution :

Distance covered by Peter in 15 min .

D = 30\times \dfrac{15}{60}=7.5\ miles

Let , time taken is x .

So , distance covered b them is equal :

7.5+30\times x=40\times x\\\\x=\dfrac{7.5}{10}=0.75\ hours\\\\x=0.75\times 60\ min\\\\x=45\ min

Therefore , time taken by them is 45 minutes .

Hence , this is the required solution .

4 0
3 years ago
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