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Vlad1618 [11]
3 years ago
11

A teacher has a bag of sweets. If she gives every student 8 sweets, she is left with 24 sweets. If she gives every student 10 sw

eets, she needs another 20 sweets. Find the total number of students​
Mathematics
1 answer:
alina1380 [7]3 years ago
3 0

Answer:

22

Step-by-step explanation:

<em>Please mark me as brainliest!</em>

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Triangle ABC has AB=5, BC=7, and AC=9. D is on AC with BD=5. Find the length of DC
e-lub [12.9K]

Answer:

DC=\frac{8}{3}\ units

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The triangle ABD is an isosceles triangle

because

AB=BD

The segment BM is a perpendicular bisector segment AD

so

<em>In the right triangle ABM</em>

Applying the Pythagorean Theorem

BM^2=AB^2-AM^2

we have

AB=5\ units\\AM=x\ units

substitute

BM^2=5^2-x^2

BM^2=25-x^2 -----> equation A

<em>In the right triangle BMC</em>

Applying the Pythagorean Theorem

BM^2=BC^2-MC^2

we have

BC=7\ units\\MC=AC-AM=(9-x)\ units

substitute

BM^2=7^2-(9-x)^2

BM^2=49-(81-18x+x^2)  

BM^2=49-81+18x-x^2

BM^2=-x^2+18x-32 ----> equation B

equate equation A and equation B

-x^2+18x-32=25-x^2

solve for x

18x=25+32\\18x=57\\\\x=\frac{57}{18}

Simplify

x=\frac{19}{6}

<em>Find the length of DC</em>

DC=AC-2x

substitute the given values

DC=9-2(\frac{19}{6})

DC=9-\frac{19}{3}\\\\DC=\frac{8}{3}\ units

8 0
3 years ago
14. The circle graph shows the results of an employment survey of 800
MariettaO [177]

Answer:

480 people were unemployed full time

Step-by-step explanation:

First thing to do here is to check the percentage of people that were unemployed full time

Looking at the graph, this is equal to 60%

This means that 60% of the total 800 are unemployed full time

Mathematically, that would be 60/100 * 800 = 480 people

8 0
3 years ago
Please help me with this math problem!! :)
GarryVolchara [31]

Step-by-step explanation:

the following things are clear : opposite sides are of equal length, the sum of all angles in a square, rectangle or general parallelogram is 360 degrees, and opposite angles are equal.

so,

y² + 7 = 32

y² = 25

y = 5

2y² = k

2×5² = k

50 = k

the opposite angle of 150 is also 150 degrees.

the opposite angle of x is also x.

so, we have as sum of angles

360 = 150 + 150 + x + x = 300 + 2x

60 = 2x

x = 30 degrees

4 0
2 years ago
Differentiate between Charles babbage's and Alan turing's computer designs​
inessss [21]
The Analytical Engine was a proposed mechanical general-purpose computer designed by English mathematician and computer pioneer Babbage,[2][3] with the assistance of Ada Lovelace. It was first described in 1837 as the successor to Babbage's difference engine, which was a design for a simpler mechanical computer.
6 0
3 years ago
Show tan (x) + cot (x) • sec(x)
topjm [15]
\tan x+\cot x=\csc x.\sec x

Let us change tan x and cot x to sin x and cos x

\begin{gathered} \because\tan x=\frac{\sin x}{\cos x} \\ \because\cot x=\frac{\cos x}{\sin x} \end{gathered}

Substitute them on the left side

LHS=\frac{\sin x}{\cos x}+\frac{\cos x}{\sin x}=\frac{\sin^2x+cox^2x}{\cos x\sin x}

I multiplied the denominators and multiply each numerator by the opposite denominator

\because\sin ^2x+cox^2x=1\therefore L.H.S=\frac{1}{\sin x\cos x}

Now we will work on the right hand side

\begin{gathered} \because\csc x=\frac{1}{\sin x} \\ \because\sec x=\frac{1}{\cos x} \end{gathered}

Substitute them on the right side

\because R.H.S=\frac{1}{\sin x}\times\frac{1}{\cos x}=\frac{1}{\sin x\cos x}

The L.H.S = R.H.S = 1/(sin x cos x)

4 0
1 year ago
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