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3 years ago

A line goes through the points (1,8) and (9,12) what is the slope of the line? Plz explain

Mathematics

1 answer:

Igoryamba3 years ago

8 0

Answer:

2/3 or 0.67

Step-by-step explanation:

Slope = y2 - y1 /x2 - x1

Given

x1 = 1

y1 = 8

x2 = 9

y2 = 12

Slope = 12 - 8 /9 - 1

= 4/6

Reduce is by 2

2/3

0.67

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Your job in a company is to fill quart-size bottles of oil from a full 100-gallon oil tank. Then you are to pack 12 quarts of oi

Andreyy89

Answer:

33 cases of oil

Step-by-step explanation:

You start with 100 gallons of oil.

1 gallon = 4 quarts

100 gallons = 100 * 4 quarts

100 gallons = 400 quarts

You start with 400 quarts.

You place 12 quarts in each box.

400/12 = 33 1/3

You can pack 33 full cases plus 1/3 of another case.

The question only askes about full cases.

Answer: 33 cases of oil

5 0

3 years ago

How do I graph x squared + (y+4) squared = 9

Mashcka [7]

Answer:

I usually use this graphing calculator to graph:

www . desmos . com / calculator

3 0

3 years ago

Can you help me with my math questions

GrogVix [38]

$p^2+2(7)p+7^2=(p+7)^2$

Justification:

Given: $p^2+14p+49$

Split the middle term;

$=p^2+7p+7p+49$

Factor:

$=p(p+7)+7(p+7)$

$=(p+7)(p+7)$

$=(p+7)^2$

QUESTION 3a

The given expression for the area of the rectangle is $36x^2-12x+1$ .

This is equal to the indicated area which is $289\;in^2$

This implies that

$36x^2-12x+1=289$

$\Rightarrow (6x-1)^2=289$

$\Rightarrow (6x-1)(6x-1)=289$

$\Rightarrow l=(6x-1),w=(6x-1)$

This implies that, the dimensions of the rectangle are equal;

Using the square root method, we obtain

$\Rightarrow (6x-1)=\pm \sqrt{289}$

$\Rightarrow (6x-1)=\pm 17$

$\Rightarrow 6x=1\pm 17$

$\Rightarrow 6x=18 \:or\:6x=-16$

$\Rightarrow x=3 \:or\:x=-\frac{2}{3}$

We discard the negative value.

The side length of this rectangle is

$\Rightarrow l=(6(3)-1)=17,w=6(3)-1=17$

QUESTION 3b

The given expression for the area of the rectangle is $25x^2-50x+25$ .

This is equal to the indicated area which is $1225\;in^2$

This implies that

$25x^2-50x+25=1225$

$25(x^2-2x+1)=1225$

$(5(x-1))^2=35^2$

$5(x-1)5(x-1)=49$

$\Rightarrow l=5(x-1),w=5(x-1)$

This implies that, the dimensions of the rectangle are equal;

Using the square root method, we obtain

$\Rightarrow 5(x-1)=\pm \sqrt{1225}$

$\Rightarrow 5(x-1)=\pm 35$

$\Rightarrow x=1\pm 7$

$\Rightarrow x=8 \:or\:x=-6$

We discard the negative value.

The side length of this rectangle is

$\Rightarrow l=5(8-1)=35,w=5(8-1)=35$

QUESTION 3c

The given expression for the area of the rectangle is $49x^2-56x+16$ .

This is equal to the indicated area which is $289\;in^2$

This implies that

$49x^2-56x+16=289$

$(7x-4)^2=289$

$(7x-4)(7x-4)=289$

$\Rightarrow l=(7x-4),w=(7x-4)$

Applying the laws of indices gives;

$(7x-4)^2=17^2$

This implies that;

$7x-4=17$

$7x=21$

$x=3in.$

The side length of this rectangle is

$\Rightarrow l=7(3)-4=17\:in.,w=7(3)-4=17\:in.$

Dont forget that the square is also a rectangle.

5 0

3 years ago

Read 2 more answers

Use the quadratic formula to solve x^2+8x+9=0

Tju [1.3M]

None of your options, not via complete the square nor quadratic the formula.

Solve for x over the real numbers:
x^2 + 8 x + 9 = 0

x = (-8 ± sqrt(8^2 - 4×9))/2 = (-8 ± sqrt(64 - 36))/2 = (-8 ± sqrt(28))/2:
x = (-8 + sqrt(28))/2 or x = (-8 - sqrt(28))/2

sqrt(28) = sqrt(4×7) = sqrt(2^2×7) = 2sqrt(7):
x = (2 sqrt(7) - 8)/2 or x = (-2 sqrt(7) - 8)/2

Factor 2 from -8 + 2 sqrt(7) giving 2 (sqrt(7) - 4):
x = 1/22 (sqrt(7) - 4) or x = (-2 sqrt(7) - 8)/2

(2 (sqrt(7) - 4))/2 = sqrt(7) - 4:
x = sqrt(7) - 4 or x = (-2 sqrt(7) - 8)/2

Factor 2 from -8 - 2 sqrt(7) giving 2 (-sqrt(7) - 4):
x = sqrt(7) - 4 or x = 1/22 (-sqrt(7) - 4)

(2 (-sqrt(7) - 4))/2 = -sqrt(7) - 4:

Answer: x = sqrt(7) - 4 or x = -sqrt(7) - 4_____________________________________________________

Solve for x:
x^2 + 8 x + 9 = 0

Subtract 9 from both sides:
x^2 + 8 x = -9

Add 16 to both sides:
x^2 + 8 x + 16 = 7

Write the left hand side as a square:
(x + 4)^2 = 7

Take the square root of both sides:
x + 4 = sqrt(7) or x + 4 = -sqrt(7)

Subtract 4 from both sides:
x = sqrt(7) - 4 or x + 4 = -sqrt(7)

Subtract 4 from both sides:
Answer: x = sqrt(7) - 4 or x = -4 - sqrt(7)

4 0

3 years ago

2ln(5x)=8 solve for x

White raven [17]

$lnx=log_ex\\----------\\log_ab=c\iff a^c=b\\----------\\Domain:\\5x > 0\ \ \ |divide\ both\ sides\ by\ 5\\x > 0\\D:x\in\mathbb{R^+}\\----------------------\\2ln(5x)=8\ \ \ \ |divide\ both\ sides\ by\ 2\\\\ln(5x)=4\iff e^4=5x\\\\5x=e^4\ \ \ \ \ |divide\ both\ sides\ by\ 5\\\\\boxed{x=\frac{e^4}{5}\in D}$

8 0

3 years ago

Read 2 more answers