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4 years ago

How do you solve this equation?

Mathematics

1 answer:

ANTONII [103]4 years ago

5 0

Answer:

b=85º

a=20º

Step-by-step explanation:

Angle B is supplementary with the 45º and the 50º angle, therefore the sum of the three angles must be 180

45+b+50=180

95+b=180

b=85º

Angle A, Angle B, and the 75º angle must also add up to 180

85+75+a=180

160+a=180

a=20º

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Jose borrows $200 for 2 years at a rate of 8% simple interest calculated annually. How much will he have to pay back at the end

KatRina [158]

Annually= per year

200 at 8% the first year would be
200 • 0.08 = 16 per year
2 years = 32 dollars in interest at the end of 2 years

6 0

3 years ago

Drag the tiles to the correct boxes to complete the pairs not all tiles will be used match each quadratic graph to its respectiv

ch4aika [34]

Answer:

Part 1) The function of the First graph is $f(x)=(x-3)(x+1)$

Part 2) The function of the Second graph is $f(x)=-2(x-1)(x+3)$

Part 3) The function of the Third graph is $f(x)=0.5(x-6)(x+2)$

See the attached figure

Step-by-step explanation:

we know that

The quadratic equation in factored form is equal to

$f(x)=a(x-c)(x-d)$

where

a is the leading coefficient

c and d are the roots or zeros of the function

Part 1) First graph

we know that

The solutions or zeros of the first graph are

x=-1 and x=3

The parabola open up, so the leading coefficient a is positive

The function is equal to

$f(x)=a(x-3)(x+1)$

Find the value of the coefficient a

The vertex is equal to the point (1,-4)

substitute and solve for a

$-4=a(1-3)(1+1)$

$-4=a(-2)(2)$

$a=1$

therefore

The function is equal to

$f(x)=(x-3)(x+1)$

Part 2) Second graph

we know that

The solutions or zeros of the first graph are

x=-3 and x=1

The parabola open down, so the leading coefficient a is negative

The function is equal to

$f(x)=a(x-1)(x+3)$

Find the value of the coefficient a

The vertex is equal to the point (-1,8)

substitute and solve for a

$8=a(-1-1)(-1+3)$

$8=a(-2)(2)$

$a=-2$

therefore

The function is equal to

$f(x)=-2(x-1)(x+3)$

Part 3) Third graph

we know that

The solutions or zeros of the first graph are

x=-2 and x=6

The parabola open up, so the leading coefficient a is positive

The function is equal to

$f(x)=a(x-6)(x+2)$

Find the value of the coefficient a

The vertex is equal to the point (2,-8)

substitute and solve for a

$-8=a(2-6)(2+2)$

$-8=a(-4)(4)$

$a=0.5$

therefore

The function is equal to

$f(x)=0.5(x-6)(x+2)$

3 0

4 years ago

There are 22 rows of seats on a concert hall: 23 seats are in the 1st row, 27 seats on the 2nd row, 31 seats on the 3rd row, and

JulijaS [17]

We can model this situation with an arithmetic series.
we have to find the number of all the seats, so we need to sum up the number of seats in all of the 22 rows.

1st row: 23
2nd row: 27
3rd row: 31
Notice how we are adding 4 each time.

So we have an arithmetic series with a first term of 23 and a common difference of 4.

We need to find the total number of seats. To do this, we use the formula for the sum of an arithmetic series (first n terms):

Sₙ = (n/2)(t₁ + tₙ)

where n is the term numbers, t₁ is the first term, tₙ is the nth term

We want to sum up to 22 terms, so we need to find the 22nd term

Formula for general term of an arithmetic sequence:

tₙ = t₁ + (n-1)d,

where t1 is the first term, n is the term number, d is the common difference. Since first term is 23 and common difference is 4, the general term for this situation is

tₙ = 23 + (n-1)(4)

The 22nd term, which is the 22nd row, is

t₂₂ = 23 + (22-1)(4) = 107

There are 107 seats in the 22nd row.

So we use the sum formula to find the total number of seats:

S₂₂ = (22/2)(23 + 107) = 1430 seats

Total of 1430 seats.
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