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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

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