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netineya [11]
3 years ago
10

Find an equation of the line with x-intercept 8 and y-intercept 4

Mathematics
2 answers:
kifflom [539]3 years ago
7 0

Answer:

Step-by-step explanation:

eq. of line with intercepts a and b is

\frac{x}{a} +\frac{y}{b} =1\\here ~eq. ~of ~line~ is ~ \frac{x}{8} +\frac{y}{4} =1\\or x+2y=8\\

DerKrebs [107]3 years ago
5 0

Answer:

 y = -1/2x + 4

Step-by-step explanation:

We have two points ( 8,0) and ( 0,4)

We can find the slope

m =(y2-y1)/(x2-x1)

    = (4-0)/(0-8)

    4/-8

   -1/2

We can use the slope intercept form

 y = mx+b where m is the slope and b is the y intercept

 y = -1/2x + 4

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2. Factor f(x) = x4 + 10x3 + 35x2 + 50x + 24 completely showing all work and steps with synthetic division. Then sketch the grap
telo118 [61]

We need to use rational root theorem to find out roots here.

The rational root theorem states that if p(x) is a polynomial with integer coefficients and if \frac{p}{q} is a zero of p(x) then p is a factor of constant term and q is a factor of leasing term coefficient.

Here factors of constant term are 1,2,3,4,6,8,12,24,-1,-2,-3,-4,-6,-8,-12, and -24.

And factors of leading coefficient is -1,1.

Hence possible roots may be -1,1,-2,2,-3,3,-4,4,-6,6,-8,8,-12,12,-24 and 24.

Let us plugin these in f(x) to find zeroes.

f(-1)=(-1)^{4}+10(-1)^{3}+35(-1)^{2}+50(-1)+24 =1-10+35-50+24=0

Hence x=-1 is a zero which means x-(-1)=x+1 is a factor.

Let us use synthetic division to find quotient.

-1 | 1  10  35  50  24

  <u>| 0  -1  -9  -26   -24</u>

   <u> 1    9  26  24    0</u>

Hence quotient is x^{3} +9x^{2} +26x+24

Since all coefficients are positive, root must be negative. Let's plugin all remaining negative numbers in the quotient.

(-2)^{3}+9(-2)^{2}+26(-2)+24 = 0

Hence x+2 is another factor.

Let us find quotient again using synthetic division.

-2 | 1   9  26   24

   <u>| 0  -2  -14   -24</u>

   <u>  1    7    12     0</u>

Hence quotient is x^{2} +7x+12

Again we got quotient with all positive coefficients, let us plugin remaining negative numbers from rational root theorem.

(-3)^{2}+7(-3)+12=-9-21+12=0

Hence x+3 is also a factor.

Let us find quotient using synthetic division.

-3 | 1  7  12

   <u>| 0 -3  -12</u>

    <u> 1    4    0</u>

Hence quotient is x+4.

So, f(x)=x^{4}+10x^{3}+35x^{2}+50x+24 =(x+1)(x+2)(x+3)(x+4)

Please have a look at the graph attached.

4 0
3 years ago
Which property states that if a = b, then b = a?
yawa3891 [41]
Symmetric or communative
6 0
3 years ago
Read 2 more answers
A rectangle has length 127.3 cm and width 86.5 cm, both correct to 1 decimal place. Calculate the upperbound and the lowerbound
Mnenie [13.5K]

Answer:

Correct to 1dp

127.3 cm = 127.0 cm

86.5 cm = 87.0 cm

Upper limits:

127.0 cm = 127.05 cm

87.0 cm = 87.05 cm

Lower Limits:

127.0 cm = 126.95 cm

87.0 cm = 86.95 cm

upper limit of perimeter of rectangle:

P = 2(l+w)

= 2(127.05 + 87.05)

= 2(214.1)

= 428.2 cm

lower limit of perimeter of rectangle:

P = 2(l+w)

= 2(126.95 + 86.95)

= 2(213.9)

= 427.8 cm

therefore;

427.8 cm \leqslant perimeter < 428.2cm

8 0
3 years ago
Sonja's house is 4 blocks west and 1 block south of the center of town. Her school is 3 blocks east and 2 blocks north of the ce
dexar [7]

If the center of town is the origin then 4 blocks west and 1 block south would be 4 blocks to the left and 1 block down or (-4, -1) house 3 block east and 2 blocks north would be 3 blocks to the right and 2 blocks up or (3, 2) use the distance formula to find the distance between two points. That's all I know! hope this helps!~ just remember to use the distance formula to find the distance between two points.

5 0
3 years ago
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Find the area of the trapezoid. points are (-5,-3)(4,-3)(6,-7)(-7,-7)​
Olegator [25]

Answer:

44 square units

Step-by-step explanation:

The area of a trapezoid with bases b₁ and b₂ and height h is given by the formula

A=\left(\dfrac{b_1+b_2}{2}\right)h

If you're wondering how we get this formula, check the attached illustration (remember the area of a parallelogram is its base multiplied by its height)! Moving on to our trapezoid, the pairs of points (-5,-3)(4,-3) and (6,-7)(-7,-7) form two horizontal segments, which form b₁ and b₂, and our height is the distance between the y-coordinates -3 and -7, which is 4. We can find b₁ and b₂ by finding the distance between the x coordinates in their pairs of points:

b_1=|-5-4|=|-9|=9\\b_2=|6-(-7)|=|6+7|=13

Putting it altogether:

A=\left(\dfrac{9+13}{2}\right)(4)=\left(\dfrac{22}{2}\right)(4)=(11)(4)=44

So the area of our trapezoid is 44.

4 0
3 years ago
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