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4 years ago

The third term of an arithmetic sequence is 21, and the eighth term is 56. The first term is_______

Mathematics

1 answer:

Aleks04 [339]4 years ago

8 0

The first term is 7 because they both can be divided by 7.

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What's 51 correct and 9 incorrect as a fraction

pentagon [3]

Yes because it's a improper fraction

4 0

3 years ago

The outlier, 78, is removed from the data set shown. 23, 23, 25, 27, 34, 34, 35, 41, 45, 45, 78 How does this affect the range?

KATRIN_1 [288]

Hello.

The range with 78 is 55

without 78 is 22

So the range goes down

Have a nice day

6 0

3 years ago

Read 2 more answers

Select the correct answer from each drop-down menu. A parabola is given by the equation y = x2 − 2x − 3. The directrix of the pa

choli [55]

Answer:

Part 1) The directrix of the parabola is y=-4.25

Part 2) The focus of the parabola is F(1,-3.75)

Step-by-step explanation:

we have

$y=x^{2}-2x-3$

This is a vertical parabola open upward

we know that

If a parabola has a vertical axis, the standard form of the equation of the parabola is

$(x - h)^{2}=4p(y - k)$

where

p≠ 0

The vertex of this parabola is at (h, k).

The focus is at (h, k + p).

The directrix is the line y = k - p.

The axis is the line x = h.

step 1

Convert the equation of the parabola in standard form

$y=x^{2}-2x-3$

$y+3=x^{2}-2x$

$y+3+1=x^{2}-2x+1$

$y+4=x^{2}-2x+1$

$y+4=(x-1)^{2}$

$(x-1)^{2}=(y+4)$ ----> equation in standard form

The vertex is the point (1,-4)

4p=1 ------> p=1/4

step 2

Find the directrix of the parabola

The directrix is the line y = k - p

we have

k=-4

p=1/4

substitute the values

y = k - p

y=-4-(1/4)=-17/4

y=-4.25

step 3

Find the focus of the parabola

we know that

The focus is at (h, k + p).

we have

h=1

k=-4

p=1/4

substitute

F(1,-4+1/4)

F(1,-3.75)

4 0

4 years ago

Perimeter, Area And Volume

Maslowich

$\large\huge\green{\sf{Answer:-}}$

<h3>area of shaded figure= </h3>

<h2>area of whole rectangle</h2>

= lengthx breadth=15x30= 450 cm²

<h3>area of unshaded region= lengthx breadth= (30-8)x 15cm²= 22x 15cm²= 330cm²</h3>

<h3>are of shaded region</h3>

= area of whole rectangle -area of unshaded region= 450cm²-330cm²= 120cm²

therefore 120 is correct answer

6 0

3 years ago

a student answered 86 problems on a test correctly and received a grade 98% how many problems were on the test if all the proble

maxonik [38]

98% Grade was achieved, so 0.98 of the questions were answered correctly.

n = number of problems

$\frac{86}{n} = 0.98 \\ \\ n = \frac{86}{0.98} \\ \\ n = 87.755...$

Our final answer can't be a decimal, so we round it to:

$n = 87$

4 0

3 years ago