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denis23 [38]
2 years ago
9

The first 4 terms and the 10th term for 3n+4

Mathematics
1 answer:
topjm [15]2 years ago
5 0

Answer:

first 4 terms =7,10,13,16

10th term = 34

Step-by-step explanation:

3n+4

3(1)+4=7

3(2)+4=10

3(3)+4=13

3(4)+4=16

7,10,13,16

10th term = 3(10)+4= 34

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Angle D has a measure between 0° and 360° and is coterminal with a –920° angle. What is the measure of angle D?
topjm [15]
Take -920/360 = -2.55555
Take the fraction part -0.5555555 * 360 = -200
The positive of that would be 160 degrees
7 0
3 years ago
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A rectangular piece of metal is 25 in longer than it is wide. Squares with sides 5 in long are cut from the four corners and the
Licemer1 [7]

Answer:

The original length was 41 inches and the original width was 16 inches

Step-by-step explanation:

Let

x ----> the original length of the piece of​ metal

y ----> the original width of the piece of​ metal

we know that

When squares with sides 5 in long are cut from the four corners and the flaps are folded upward to form an open box

The dimensions of the box are

L=(x-10)\ in\\W=(y-10)\ in\\H=5\ in

The volume of the box is equal to

V=(x-10)(y-10)5

V=930\ in^3

so

930=(x-10)(y-10)5

simplify

186=(x-10)(y-10) -----> equation A

Remember that

The piece of metal is 25 in longer than it is wide

so

x=y+25 ----> equation B

substitute equation B in equation A

186=(y+25-10)(y-10)

solve for y

186=(y+15)(y-10)\\186=y^2-10y+15y-150\\y^2+5y-336=0

Solve the quadratic equation by graphing

using a graphing tool

The solution is y=16

see the attached figure

Find the value of x

x=16+25=41

therefore

The original length was 41 inches and the original width was 16 inches

3 0
3 years ago
A pentagon has angle measures of 12x°, 7x°, 16x°, 9xº, and 10x°. Find the<br> value of x.
Musya8 [376]

Answer:

10

Step-by-step explanation:

one interior angle in a pentagon is 108^o.

5 interior angles are 540^o.

If we add 12+7+16+9+10, we get 54x=540^o

That means x=10

3 0
3 years ago
Please help me 33/2 + 3y/5 = 7y/10 + 15
8090 [49]

We are given with an equation in <em>variable y</em> and we need to solve for <em>y</em> . So , now let's start !!!

We are given with ;

{:\implies \quad \sf \dfrac{33}{2}+\dfrac{3y}{5}=\dfrac{7y}{10}+15}

Take LCM on both sides :

{:\implies \quad \sf \dfrac{165+6y}{10}=\dfrac{7y+150}{10}}

<em>Multiplying</em> both sides by <em>10</em> ;

{:\implies \quad \sf \cancel{10}\times \dfrac{165+6y}{\cancel{10}}=\cancel{10}\times \dfrac{7y+150}{\cancel{10}}}

{:\implies \quad \sf 165+6y=7y+150}

Can be <em>further written</em> as ;

{:\implies \quad \sf 7y+150=165+6y}

Transposing <em>6y </em>to<em> LHS</em> and <em>150</em> to<em> RHS </em>

{:\implies \quad \sf 7y-6y=165-150}

{:\implies \quad \bf \therefore \quad \underline{\underline{y=15}}}

8 0
2 years ago
Solve each quadratic equation. Show your work 15. x2 + 3x = 10
OLEGan [10]
X² + 3x = 10

Convert to standard form.
x² + 3x - 10 = 0

factor x² = x * x
factor -10 = 5 * -2

(x + 5) (x - 2) = 0
x(x -2) + 5(x-2) = 0
x² - 2x + 5x - 10 = 0
x² + 3x - 10 = 0

x + 5 = 0               x² + 3x = 10
x = -5               -5² + 3(-5) = 10
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x - 2 = 0            x² + 3x = 10
x = 2               2² + 3(2) = 10
                             4 + 6 = 10
                                 10 = 10
4 0
3 years ago
Read 2 more answers
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