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3 years ago

Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form.

Mathematics

1 answer:

dem82 [27]3 years ago

8 0

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 4x + 3 ← is in slope- intercept form

with slope m = - 4

• Parallel lines have equal slopes, thus

y = - 4x + c ← is the partial equation

To find c substitute (- 9, - 4) into the partial equation

- 4 = 36 + c ⇒ c = - 4 - 36 = - 40

y = - 4x - 40 ← in slope- intercept form

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = - 4 and (a, b) = (- 9, - 4), thus

y - (- 4) = - 4(x - (- 9)), that is

y + 4 = - 4(x + 9) ← in point- slope form

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What are the relative frequencies, to the nearest hundredth, of the rows of the two-way table?

sveta [45]

Answer: A B

Group 1 0.25 0.75

Group 2 0.44 0.56

Step-by-step explanation:

Since we have given that

Number of people of A in group 1 = 15

Number of people of B in group 1 = 45

Total number of people in group 1 is given by

$15+45=60$

Relative frequency of people of A in Group 1 is given by

$\frac{15}{60}=0.25$

Relative frequency of people of B in Group 1 is given by

$\frac{45}{60}=0.75$

Similarly, Number of people of A in group 2 = 20

Number of people of B in group 2 = 25

Total number of people in group 2 is given by

$20+25=45$

Relative frequency of people of A in Group 2 is given by

$\frac{20}{45}=0.44$

Relative frequency of people of B in Group 2 is given by

$\frac{25}{45}=0.56$

Hence, A B

Group 1 0.25 0.75

Group 2 0.44 0.56

6 0

3 years ago

What is the annual interest rate is 1=$160.67, p=$2000, t=8 months

Sergeeva-Olga [200]

Please use " i " to denote "interest."

the formula for simple interest is i = p r t.

Here, i = $160.67 = $2000 (r) (8/12)

Solving for the interest rate, r = ($169.67)(12/8)/ $2000 = 0.127, or 12.7%

4 0

3 years ago

Someone please help me with this one quick

astraxan [27]

The length of AC is 16 km.

Solution:

Given data:

AB = c = 14 km, ∠A = 30° and ∠B = 89°

AC = b = ?

<u>Let us first find angle C:</u>

<em>Sum of all angles in a triangle = 180°</em>

m∠A+ m∠B + m∠C = 180°

30° + 89° + m∠C = 180°

119° + m∠C = 180°

Subtract 119° from both sides, we get

m∠C = 61°

<u>To find the length of AC:</u>

<em>Using sine formula:</em>

$$\frac{b}{\sin B } =\frac{c}{\sin C}$

Substitute the given values in the formula.

$$\frac{b}{\sin 89^\circ } =\frac{14}{\sin 61^\circ }$

Multiply by sin 89° on both sides.

$$\sin 89^\circ \times \frac{b}{\sin 89^\circ } =\frac{14}{\sin 61^\circ } \times \sin 89^\circ$

$$b=\frac{14}{0.8746 } \times0.9998$

$b=16$

The length of AC is 16 km.

4 0

2 years ago

Twin brothers, Billy and Bobby, can mow their grandparent’s lawn together in 63 minutes. Billy could mow the lawn by himself in

Pepsi [2]

Answer:

<h2>140 minutes</h2>

Step-by-step explanation:

this problem focuses on the combined work rate

both can finish the work under 63 minute

let bobby mow the lawn in x minute

Billy will then mow the lawn in x-25 minutes

Let the completed job = 1 (a mowed lawn)

we can now apply the combined work formula for the two boys as

$\frac{63}{x}+\frac{63}{x-25}=1$

multiplying through by x(x-25 )we have

$63(x-25)+63x= x(x-25)$

open bracket we have

$63x-1575+63x= x^2-25x$

rearranging and collecting like terms we have

$0=x^2-25x-63x-63x+1575 \\\\0=x^2-151x+1575 \\\\x^2-151x+1575=0$

we can now use the quadractic formula

$x=\frac{-b\frac{+}{} \sqrt{b^2-4ac} }{2a}$

a= 1

b= -151

c= 1575

$x=\frac{-(-151)\frac{+}{} \sqrt{151^2-4*1*1575} }{2*1}$

$x=\frac{-(-151)\frac{+}{} \sqrt{22801-6300} }{2} \\\\x=\frac{-(-151)\frac{+}{} \sqrt{16501} }{2} \\\\x=\frac{-(-151)\frac{+}{} 128.45}{2} \\\\$

$x=\frac{-(-151)+128.45}{2} \\\\\x=\frac{279.45}{2} \\\\x=139.72 \\\\\\x=\frac{-(-151)-128.45}{2}\\\\x=\frac{151-128.45}{2}\\\\x=\frac{22.55}{2}\\\\x=11.27$

the first answer x= 139.72 approximately 140 minutes mins is correct for Bobby's time

let us check

$\frac{63}{140}+\frac{63}{140-25}=1\\\\\\0.45+\frac{63}{115} =1\\\\0.45+0.5478=1\\0.997 =1$

we can see that the solution approximates to 1

8 0

3 years ago

What is 5 less than a product of 4 and a number?

Setler [38]

4x - 5
Or what kind of an answer are you looking for?

4 0

2 years ago

Read 2 more answers