The equation of the line is:
[tex]y=\frac{-1}{2}x-26[/tex]
The point-slope equation of a line is given as:
[tex]y-y_1=m(x-x_1)[/tex]
where m represents the slope, and is calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
For the line passing through the points (-32, - 10) and (-74, 11)
[tex]x_1=-32, y_1=-10, x_2=-74, y_2=11[/tex]
Substitute these points into the slope formula to get the slope of the line
[tex]m=\frac{11-(-10)}{-74-(-32)} \\\\m=\frac{11+10}{-74+32} \\\\m=\frac{21}{-42} \\\\m=\frac{-1}{2}[/tex]
Substitute [tex]m=\frac{-1}{2}, x_1=-32, y_1=-10[/tex] into the line equation
[tex]y-(-10)=\frac{-1}{2}(x-(-32))\\\\y+10=\frac{-1}{2}x-16\\\\y= \frac{-1}{2}x-16-10\\\\y=\frac{-1}{2}x-26[/tex]
The equation of the line is:
[tex]y=\frac{-1}{2}x-26[/tex]
Learn more on equation of a line here: https://brainly.com/question/13763238
Evaluate: 3cos 80° cosec 10° + 2 sin 59° sec 31°
correct answer will be marked as Brainliest.
Given that
3 cos 80° cosec 10° + 2 sin 59° sec 31°
⇛3 cos(90°-10°) cosec 10°+2 sin (90°-31°) sec 31°
We know that
sin (90° - A) = cos A
cos (90°-A) = sin A
⇛3 sin 10° cosec 10° + 2 cos 31° sec 31°
⇛3 sin 10° (1/sin 10°) + 2 cos 31° (1/cos 31°)
⇛3 (sin 10°/sin 10°) + 2 (cos 31°/cos 31°)
⇛3 (1) + 2(1)
⇛3+2
⇛5
Answer: Therefore, 3cos 80°cosec 10°+2cos 59°sec 31° = 5.
also read similar questions: (sin teta + sec teta)^ + (cos teta+ cosec teta )^ = (1 + sec x cosec)^
https://brainly.com/question/87846?referrer
Answer:
5
Step-by-step explanation:
you can rewrite this as
3cos(90*-10*) x 1/sin(10*) + 2sin(90*-31*) x 1/cos(31*)
=3sin(10*) x 1/sin(10*) + 2cos31* x 1/cos(31*)
reduce with sin(10*) to get
3+2cos(31*) x 1/cos(31*)
cross out the cos 31* on both sides to leave you with
3+2
5
Find an equation for the perpendicular bisector of the line segment whose endpoints
are (5, 4) and (-7,-8).
Answer:
y= -x -3
Step-by-step explanation:
A perpendicular bisector of a line cuts through the line at its midpoint perpendicularly (90°).
Let's find the slope of the line segment.
[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
Slope of line segment
[tex] = \frac{4 - ( - 8)}{5 - ( - 7)} [/tex]
[tex] = \frac{4 + 8}{5 + 7} [/tex]
[tex] = \frac{12}{12} [/tex]
= 1
The product of the slopes of 2 perpendicular lines is -1.
Let the slope of the perpendicular bisector be m.
m(1)= -1
m= -1
y= -x +c
To find the value of c, substitute a pair of coordinates in which the line passes through into the above equation.
Since the perpendicular bisector cuts through the midpoint of the line segment, let's find the coordinates of this midpoint.
[tex]\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}[/tex]
Midpoint of line segment
[tex] = ( \frac{5 - 7}{2} , \frac{4 - 8}{2} )[/tex]
[tex] = ( \frac{ - 2}{2} , \frac{ - 4}{2} )[/tex]
= (-1, -2)
y= -x +c
When x= -1, y= -2,
-2= -(-1) +c
-2= 1 +c
c= -2 -1
c= -3
Thus, the equation of the perpendicular bisector is y= -x -3.
Slove the followings.
1. Use your calculator to work out the weight of rubbish in each category.
2. A household produces 1.2 t of rubbish in a year. How many adults live in the house?
3. a. How much rubbish would an adult produce in a year if he recycled the glass, paper, and card?
b. What if he also had a compost heap at foot of his garden for vegetable and decomposable material?
2. The number of adults who live in the house is 3 (1,200/400).
3.a. If an adult recycled the glass, paper, and card that have 42% of the rubbish, the adult will generate 232 kg (400 kg x (1 - 42%) of rubbish.
b. If the adult, in addition, had a composite for vegetable and decomposable material, he will generate 152 kg (400 kg x (1 - 62%).
Data and Calculations:
1 ton = 1,000 kg
Weight of rubbish produced by an adult per year = 400 kg
Total kg of rubbish produced by the family = 1,200 kg (1,000 x 1.2)
Percentage of Vegetable and decomposable material = 20%
Percentage of glass, paper, and card = 42% (33% + 9%)
Learn more: https://brainly.com/question/14954924
PLZ HELP MATH QUESTION! LOOK AT THE PICTURE BELOW!I I WILL GIVE BRAINILEST TO CORRECT FAST ANSWER!
Answer:
x<2
Step-by-step explanation:
You're answer is wrong because the circle on the number line is not closed. If it was closed, it would be x ≤ 2 , but because it is open, it would be just be x<2
HELP PLEASE I REALLY NEED IT
Answer:
18
Step-by-step explanation:
1/2 bh
1/2 (6)(6) multiply
1/2 (36) divide
18
PLZ answer correctly! Brainliest!
Answer:
[tex]A=\left(-1\dfrac{5}{5}\right)=(-2)\\\\B=\left(-\dfrac{4}{5}\right)\\\\C=\left(\dfrac{3}{5}\right)[/tex]
Step-by-step explanation:
Look at the picture.
[tex]\dfrac{2}{10}=\dfrac{1}{5}[/tex]
A 30-foot string of lights will be attached to the top of a 24-foot pole for a holiday display. How far from the base of the pole should the end of the string of lights be anchored?
Answer:
6
Step-by-step explanation:
Isn't it 6 because that the distance between 30 and 24
What is the volume if a cylinder with height 13 and radius 6?
what is c3 - 1 when c = 4
Given: (DE) is a midsegment of ∆ABC. Show all work.
Find the value of x and y.
What is the length of (AC)?
Answer:
Step-by-step explanation:
As they are similar triangles
24/AB = 24/2AD = 12/AD = (x + 2)/AD
12 = x + 2
x = 10
(y + 6) + (x - 3) / 24 = (y + 6)/(x + 2)
(y + 6) + (10 - 3) / 24 = (y + 6)/(10 + 2)
(y + 13) / 24 = (y + 6)/12
12(y + 13) = 24(y + 6)
12y + 156 = 24y + 144
12y = 12
y = 1
AC = (y + 6) + (x - 3)
AC = (1 + 6) + (10 - 3)
AC = 14
Help me out Ik you love Algebra as much as I do
Answer:
pop
yes no total
country yes 11 38 49
no 43 8 51
total 54 46 100
Hope you understand this haha
The answer is in the file. Hope it helps.
−4 1/2÷(−2 2/3) i need help
Answer:
[tex]1\frac{11}{16}[/tex]
Step-by-step explanation:
Convert mixed numbers into improper fractions.
= [tex]\frac{-\frac{9}{2}}{\left(-2\frac{2}{3}\right)}[/tex]
= [tex]\frac{-\frac{9}{2}}{\left(-\frac{8}{3}\right)}[/tex]
= [tex]\frac{\frac{9}{2}}{\frac{8}{3}}[/tex]
= [tex]\frac{9\cdot \:3}{2\cdot \:8}[/tex]
= [tex]\frac{27}{2\cdot \:8}[/tex]
= [tex]\frac{27}{16}[/tex]
Convert improper fraction into mixed number.
= [tex]1\frac{11}{16}[/tex]
what is 5y² if y= -1
Answer:
5
Step-by-step explanation:
Input all of the numbers and solve:
5×-1×-1
Start by solving -1*-1=1
5*1=5
Answer:
the answer for this question is 5
Evaluate the expression 5xy+ -2xy+y^2 when x=4 and y=-5
Answer:
-35
Step-by-step explanation:
5(4)(-5) + -2(4)(-5) + (-5)²
= -100 + 40 + 25
= -35
Answer: -35
Step-by-step explanation:
5(4)(-5)+(-2)(4)(-5)+(-5)^2
-100+40+25
-35
Simplify.
(2a2−3ab+5b2)−(a2−2ab+3b2)
A.a4−a2b2+2b4
B.3a2−5ab+8b2
C.a2−5ab+2b2
D.a2−ab+2b2
Simplify. (6x−3)−(2x−2)
A.4x2−1
B.4x−1
C.4x−5
D.4x2−5
Answer:
DBStep-by-step explanation:
You may find this easier if you distribute the minus sign first.
1)2a^2 -3ab +5b^2 -a^2 +2ab -3b^2
= (2 -1)a^2 +(-3+2)ab +(5 -3)b^2
= a^2 -ab +2b^2 . . . . . matches choice D
__
2)6x -3 -2x +2
= (6 -2)x +(-3 +2)
= 4x -1 . . . . . matches choice B
solve the system using substitution 4x+3y=23 x-5=0
Answer:
y=1, x=5
Step-by-step explanation:
Since x-5=0 is given already, give the x a value and switch the 5 to the other side x-5=0 ----> x=5
Now we have a value for x, so plug x into the original equation,
4(5)+3y=23,
20+3y=23
Subtract both sides by 20
20-20+3y=23-20
3y=3
dvide both sides by 3
y=1
use the value for x we got earlier
y=1, x=5
Solve the equation
37.86+x=53.15
A. 15.29
B. 16.39
C. 90.91
D. 90.01
Answer:
X = 53.15-37.86
X = 15.29
option A
Justin has ridden 34 miles of a bike course. The course is 40 miles long. What percentage of the course has Justin ridden so far?
85%
Step-by-step explanation:Justin has ridden 34 miles out of 40 miles. This can be expressed as a fraction, 34/40.
If you carry out the division 34 ÷ 40, you get 0.85. This is the proportion of the course that Justin has ridden, and is always less than one. To convert this to a percentage, you multiply it by 100:
0.85 * 100 = 85%
Can anyone understand what this symbol is , I'm viewing scratch work to understand what to do with a problem but I can't understand what this is, is this cursive or something?
whats 3y/2 if y = -2
Answer:
-3
Step-by-step explanation:
3(-2)/2
-6/2 = -3
can someone help me with this i’ll give you 25 points
Answer:
Um.... Wouldn't angle 1 just be 180-17 which is 163. Angle 3 would be equal to angle 1 so also 163. Angle 4 and angle 2 are equal to 17.
Step-by-step explanation:
Answer:
angle1 = 163°
angle2 = given in diagram
angle 3 = alternating angle 1, so 163°
angle 4 = alternating angle 2, so 17°
Step-by-step explanation:
noticing that the two lines intercept each other at the centre, making angles going around that interception point add up to 360° (you can use this information to check the answers).
an angle on a straight line is always 180°, so given that angle2 is 17°, you can already do 180 - 17 to get an easy answer to angle 1 and 3.
316=5
459=6
248=4
739=?
Answe
i think it's 9
Step-by-step explanation:
316 fỉst number is 3 +2 =5
459 first number is 4+2=6
2+2=4
7+2=9:)))
40 percent of students survey said that they are night owls . If 300 students said that they are night owls how many students were surveyed ?
Based on the calculations that 300 is 40%, 375 is considered 50% or halfway.. in this case, we must multiply 375 by 2 and we will discover how many students were surveyed:
375 x 2 = 750
Mary works at a local Burger King restaurant. Her regular hourly wage is $14.70. If she works overtime, she
receives an hourly rate of 14 times her regular hourly rate. If she regularly works 40 hours per week with no
overtime, what is her regular weekly pay?
$882
$2.94
$588
$294
Answer:
I’m pretty sure it’s 588
Step-by-step explanation:
14.70 * 40 = 588
Morgan Office Supply sells 8 reams of Brand X paper for $40 and 4 reams of Brand Y paper for $19. What is the cost savings per ream of paper for the cheapest brand?
Answer:
$0.25 per ream
Step-by-step explanation:
The costs per ream are ...
X: $40/(8 reams) = $5/ream
Y: $19/(4 reams) = $4.75/ream
The savings per ream is $5.00 -4.75 = $0.25 for the cheapest brand.
The sum of the measures of the angles in a triangle is 1800. If two of the angles are 72 and 76 degrees, what is the missing angle measure?
Answer:
32
Step-by-step explanation:
72 + 76 = 148
180 - 148 = 32
I hope this helps!!
An office administrator earns $16 an hour, and she works 48 hours a week.
What is her weekly wage?
Answer:
768
Step-by-step explanation:
16x48= 768
Answer:
768
Step-by-step explanation:
you multiply 16 times 48 to find the weekly wage
The height of a door is 1.8 feet longer than it's with its front area is 1496.9 ft.² find the width and height of the door
The width of the door is [tex]37.8ft[/tex] and the height of the door is [tex]39.6ft[/tex]
Let
[tex]A=\text{the front area of the door}\\h=\text{the height of the door}\\w=\text{the width of the door}[/tex]
From the question
[tex]A=w\times h=1496.9\\h=w+1.8[/tex]
We are to find both the width and the height of the door. To proceed, we have to eliminate the height, and solve for the width. Later, we calculate the value of the height from the width.
Eliminate the height;
[tex]A=w\times h\\A=w\times(w+1.8)\\w^2+1.8w-A=0[/tex]
substitute the value of the front area into the equation and solve for the width
[tex]w^2+1.8w-1496.9=0\\w\approx 37.8\text{ or }w\approx-39.6[/tex]
the width can only take positive value. Now, to get the height
[tex]h=w+1.8\\=37.8+1.8\\=39.6[/tex]
the width and height of the door are [tex]37.8ft[/tex] and [tex]39.6ft[/tex] respectively.
Another example can be found in the link: https://brainly.com/question/18625465
Lim ( 3x + 4tan2x)/x
X--》0
Answer:
where are you from me
Step-by-step explanation:
:philipines
btw ty sayo
9⁴ means _________ is multiplied by itself four times (30 points)
Answer:
9
Step-by-step explanation:
This is an example of an exponent. 9^4 means 9 is raised to itself 4 times.
If we break it down, it will look like: 9x9x9x9, which is 6561.
9⁴ =》9 multiplied by itself four times.
9⁴ = 9 × 9 × 9 × 9
9⁴ = 6561
_____
Hope it helps ⚜