Answers
Answer:
[tex] A(\triangle ABC) = 7.2\: units^2 [/tex]
Step-by-step explanation:
C = (0, 7)
Since, point A lies in y-axis, so it's x coordinate will be zero. Line y = 2x + 1 passes through point A.
Therefore, plug x = 0 in y = 2x +1, we find:
y = 2*0 + 1 = 0 + 1 = 1
Hence, coordinates of point A are (0, 1).
Now, by distance formula:
[tex] AC= \sqrt{(0-0)^2 +(7-1)^2} [/tex]
[tex] AC= \sqrt{(0)^2 +(6)^2 }[/tex]
[tex] AC= \sqrt{0 +36 }[/tex]
[tex] AC= \sqrt{36 }[/tex]
[tex] AC= 6\: units[/tex]
Length of perpendicular CB dropped from point C (0, 7) to line y = 2x + 1 or 2x - y + 1 = 0 can be obtained as given below:
[tex] CB =\frac{|2\times 0+(-1)\times 7+1|}{\sqrt {2^2 +(-1)^2} } [/tex]
[tex] CB =\frac{|0-7+1|}{\sqrt {4 +1} } [/tex]
[tex] CB =\frac{|-6|}{\sqrt {5} } [/tex]
[tex] CB =\frac{6}{2.24} [/tex]
[tex] CB =2.68\: units [/tex]
By Pythagoras Theorem:
[tex] AB=\sqrt{AC^2 - CB^2} [/tex]
[tex] AB=\sqrt{6^2 - (2.68)^2} [/tex]
[tex] AB=\sqrt{36 - 7.18} [/tex]
[tex] AB=\sqrt{28.82} [/tex]
[tex] AB=5.36842621\: units [/tex]
[tex] AB\approx 5.37\: units [/tex]
[tex] A(\triangle ABC) = \frac{1}{2} \times AB\times CB[/tex]
[tex] A(\triangle ABC) = \frac{1}{2} \times 5.37\times 2.68[/tex]
[tex] A(\triangle ABC) = \frac{1}{2} \times 14.3916[/tex]
[tex] A(\triangle ABC) = 7.1958[/tex]
[tex] A(\triangle ABC) = 7.2\: units^2 [/tex]
Related Questions
A hiking trail rises 6 feet for every horizontal change of 100 feet. What is the slope of the hiking trail?
Answers
Given:
A hiking trail rises 6 feet for every horizontal change of 100 feet.
To find:
The slope of the hiking trail.
Solution:
We have,
Rise = 6 ft
Run = 100 ft
We know that
[tex]Slope=\dfrac{Rise}{Run}[/tex]
[tex]Slope=\dfrac{6}{100}[/tex]
[tex]Slope=0.06[/tex]
Therefore, the slope of the hiking trail is 0.06.
The slope of the hiking trail is equal to 0.06.
Given the following data:
Vertical distance (rise) = 6 feetHorizontal distance (running) = 100 feetTo find the slope of the hiking trail, we would use the following formula:
Slope is the ratio of the vertical distance measured to the horizontal distance measured.
Mathematically, the slope of a hiking trail is given by the formula:
[tex]Slope = \frac{Rise}{Running}[/tex]
Where:
V is the rising vertical distance of an object.H is the horizontal distance an object runs through.Substituting the given parameters into the formula, we have;
[tex]Slope = \frac{6}{100}[/tex]
Slope = 0.06
Read more on slope here: https://brainly.com/question/3514403
The angles shown are supplementary. (3x + 15)° 60° What is the value of x?
Answers
Answer:
x = 35
Step-by-step explanation:
Supplementary angles add up to 180°.
if (3x + 15)° and 60° are supplementary, then
3x + 15 + 60 = 180
now, you just have to solve the equation.
3x + 75 = 180
3x = 105
x = 35
Check
3*35 + 15 + 60 = 180
105 + 15 + 60 = 180
180 = 180
Find the sum
(w-7)+(-6w-5)
Pls answer i will give brainliest and i will give thanks pls hurry it is due soon
Answers
the answer is:
-5w - 12
-5w-12
The area of the circle is 40 yards find the area of the circle. Use 3.14 for π.
Answers
Answer:
Step-by-step explanation:
We know that the area of the circle is 40 yards, so the area of the circle would be 40 yards.
Answer:
5026.55
Step-by-step explanation:
A=πr2=π·402≈5026.54825
2(x-4) = 5 (x+24) rewrite the equation in slope-intercept form
Answers
Answer:
Since x=−128/3 is a vertical line, there is no y-intercept and the slope is undefined.
Step-by-step explanation:
Hope it helps :)
At a certain time of day, the sun causes objects to cast shadows at a 65° angle with the ground. At this time of day, a flagpole
casts a shadow that is 9 feet long. How tall is the flagpole to the nearest foot?
A.4 feet
B.7 feet
С.8 feet
D.19 feet
Answers
Answer:
D 19 feet
Step-by-step explanation:
Let x = height of flagpole
tan 65 = x/9
9tan 65 = x
x = 19.3 ≅ 19 ft. to the nearest foot
Really confused, can someone help me?
Answers
First Answer:
x = 12
First Step-by-step explanation:
12 + x = -3(4 - x)
12 + x = -12 + 3x
- x - x
—————————
12 = -12 + 2x
+ 12 + 12
—————————
24 = 2x
24/2 = 2x/2
12 = x
Second Answer:
No solution
Second Step-by-step explanation:
2(x - 1/2) = 8 + 2x
2x - 1 = 8 + 2x
+1 +1
—————————
2x = 9 + 2x
- 2x - 2x
—————————
0 = 9
^^ No solution
I just need the numbers and rule. I can’t fail this thank u sm if u help me :)
Answers
(1,5)
(2,7)
2. Rule: -3x-4
(3,-13)
(-5,11)
(-1,-1)
Answer:
I believe other question is right
Step-by-step explanation:
Jada has a meal in the Bobby Salazar's restaurant. She adds up the prices listed on the menu for everything they ordered and gets a subtotal for $48. If the tax rate is 8.7% how much is her taxes. (round to the nearest cent) $41.76 $4.76 $4.18 $3.84 $3.99
Answers
Answer:
Tax= $4.176 = $4.18
Step-by-step explanation:
Giving the following information:
She adds up the prices listed on the menu for everything they ordered and gets a subtotal for $48.
Tax rate= 8.7% = 0.087
To calculate the Tax, we need to use the following formula:
Tax= total spend*tax rate
Tax= 48*0.087
Tax= $4.176 = $4.18
does anyone know how to do this by solving with substitution
Answers
Answer:
Step-by-step explanation:
Question 1
System of equations is,
y = -6x -------(1)
y = -4x - 2 ---------(2)
Substitute the value of y from equation (1) to equation (2)
-6x = -4x - 2
-6x + 4x = -2
-2x = -2
x = 1
From equation (1)
y = -6(1)
y = -6
Question (2)
System of equations is,
-y = x --------(1)
3x + 5y = 20 ---------(2)
Substitute the value of x from equation (1) to equation (2)
3(-y) + 5y = 20
-3y + 5y = 20
2y = 20
y = 10
From equation (1)
-y = x
x = -10
Question (3)
System of the equations is,
y = -2x - 7 --------(1)
9x - 10y = 12 ----------(2)
Substitute the value of y from equation (1) to equation (2)
9x - 10(-2x - 7) = 12
9x + 20x + 70 = 12
29x = 12 - 70
29x = -58
x = -2
From equation (1)
y = -2(-2) - 7
y = 4 - 7
y = -3
3. First Street School won 12 out of 30 awards in the team competition. What percent of the awards did the school win?
HELP PLSSS
Answers
Answer:
40%
Step-by-step explanation:
(12/30)x100
Christopher is going to use a computer at an internet cafe. The cafe charges
$0.20 for every minute using a computer on top of an initial charge of $7.
Make a table of values and then write an equation for C, in terms oft,
representing the total cost of using a computer for t minutes at the internet
cafe.
Answers
Answer:
0 7
1 7.20
2 7.40
3 7.60
Step-by-step explanation:
Mr. Seoul left $48,000 to his family when he died. If he left 66 2/3% to his wife, how much did she receive?
Answers
HELP ASAP GIVING BRAINLIEST
Answers
Answer:
5: c, 3: a
Step-by-step explanation:
A store manager wants to determine how much to pay her employees. The number of hours the employees work is x, and the hourly wage that they are paid is y. The store manager is willing to pay the employees a wage given by the equation 10y-30x=20 . The business owner states that the employees should be paid a wage given by the equation 6y+30x=60. If the two equations were added then simplified to determine hourly wage, y, how much would the employees be paid?
Answers
Answer:
The employees will work for 1 hour, will earn $5 per hour and will be paid $5
Step-by-step explanation:
System of Equations
The number of hours the employees work is x.
And the hourly wage that they are paid is y. The store manager is willing to pay the employees a wage given by the equation
10y-30x=20
The business owner states that the employees should be paid a wage given by the equation
6y+30x=60
Adding both equations we have:
16y = 80
Dividing by 16:
y = 80/16 = 5
Substituting into the first equation:
10*5-30x=20
Operating and simplifying:
50-30x=20
50 - 20 = 30x
30x = 30
x = 30/30 = 1
Thus, the employees will work for 1 hour, will earn $5 per hour and will be paid $5
please help
thank u!
Answers
write an expression equivalent to 2(2x + 2y).
Answers
Answer:
4x+4y
Step-by-step explanation:
You can write an equivalent expression by simply simplifying the expression. In order to simplify this expression, distribute the numbers.
You'll get:
(2*2x)+(2*2y) = 4x + 4y
4x + 4y is an equivalent expression.
Complete the sentences. There are approximately 3,000 bass in a lake. The population grows at a rate of Complete the sentences.
There are approximately 3,000 bass in a lake. The population grows at a rate of 2% per year.
Round answers to the nearest tenth.
From Year 1 to Year 4, the average rate of change of the population was about _____
bass per year.
From Year 5 to Year 8, the average rate of change of the population was about_______
bass per year.
Answers
Answer:
From Year 1 to Year 4, the average rate of change of the population was about 61.8 bass per year.
Step-by-step explanation:
First you find 2% of 3000 which is 60
Next you find 2% of 3060 =61.2
next 2% of 3120 =62.4
last 2% of 3180 is 63.6
then you find the average of all the number combined is 61.8
Do the same with the other problem
Write a linear equation in slope Intercept form of a line with a slope of -3 and y Intercept of 0
Answers
Answer:
y=-3x
Step-by-step explanation:
THe equation formula is y=mx+b, with m being the slope and b being the y-intercept. Because the y intercept is 0, you don't need to include it.
4(6-5x)^2+11=20
quadratic equations
Answers
Answer:
(x-114.5), (x-14.05)
Step-by-step explanation:
Answer attached
5. The ratio of dog owners to cat owners is 4:3. If 320 people in a city own dogs, how many people own
cats?
Answers
4x = 320*3
4x = 960
x = 240
Check:
320/240 divide both by 80
= 4/3 :)
Answer:
240
Step-by-step explanation:
the answer is 240 bc if you divide 4 from 4:3 320/4 is 80 and use the 3 from 4:3 80x3 is 240
The school cafeteria sells two kinds of wraps: vegetarian and chicken. The vegetarian wrap costs $1.00 and the chicken wrap costs $1.50. Today they made $135.50 from the 117 wraps sold. How many of the wraps sold were vegetarian?
Answers
Answer:
Number of vegetarian wraps = 80
Number of chicken wraps = 37
Step-by-step explanation:
Let
Number of vegetarian wraps = x
Number of chicken wraps = y
x + y = 117 (1)
x + 1.5y = 135.50 (2)
Subtract (1) from (2) to eliminate x
1.50y - y = 135.50 - 117
0.50y = 18.50
y = 18.50/0.50
y = 37
Substitute y = 37 into (1)
x + y = 117 (1)
x + 37 = 117
x = 117 - 37
x = 80
Number of vegetarian wraps = 80
Number of chicken wraps = 37
Which expression is equivalent to 4 + 3 (5 + ×)
Answers
Step-by-step explanation:
[tex]4 + 3(5 + x)\\4 + (3 * 5 ) + (3 * x)\\4 + 15 + 3x[/tex]
Answer:
3x+19
Step-by-step explanation:
Let's simplify step-by-step.
4+3(5+x)
Distribute:
=4+(3)(5)+(3)(x)
=4+15+3x
Combine Like Terms:
=4+15+3x
=(3x)+(4+15)
=3x+19
x^2 + 9x + 14 I need help !
Answers
Answer:
x² + 9x + 14 can be factored as (x+2)(x+7)
Step-by-step explanation:
The general form is ax² + bx + c. If a=1, then you can start looking for two numbers that multiplied give c and added give b.
14 = 2*7
and
9 = 2+7
hence the easy factorization
(x+2)(x+7)
Keep in mind that it only works if a=1.
Answer:
( + 2 ) (x+7 )
Step-by-step explanation:
Use the sum-product pattern 2 + 9 + 1 4 2 + 7 + 2 + 1 4 2
Common factor from the two pairs 2 + 7 + 2 + 1 4 ( + 7 ) + 2 ( + 7 ) 3
Rewrite in factored form ( + 7 ) + 2 ( + 7 ) ( + 2 ) ( + 7 )
Question Help
3.3 PS-14
A salesperson at a jewelry store earns 4% commission each week. Last week, Jarrod sold $750
worth of jewelry. How much did he make in commission? How much did the jewelry store make
from his sales?
Answers
help plz i’ll give extra points
Answers
Answer:
Plot a point at the y-intercept.
Step-by-step explanation:
You start by plotting the y-intercept because you'll already have the value when you substitute x as 0 in the expression.
y = 0.5(0) -4
y = -4
Lines x and y are parallel lines cut by a transversal. If m 24 = 82°, which of the
following is true?
+
21 22
24 / 23
X
Y
25 26
28/ 27
A) m_8 = 82
B) m 25 = 82°
Answers
Can ya’ll help with answering this?
Answers
Answer:
y=2x+3 x-y=-2
substituting y=2x+3 x-(2x+3)=-2
-x=-2-3
-x=-5
x=-5/-1
x=5
now substituting x=5
y=2x+3
y=2(5)+3
=10+3
y=13
Hi I need help with this one!!!!
Answers
Answer:
Daniel can afford 12 rides
Step-by-step explanation:
So we would take his 22 dollars and subtract 4 for admission leaving us at 18\
Then we would divide 18 by 1.50 and we would get 12
Me Help ASAP or when everrr
Answers
Answer:
Base = 3√5
Step-by-step explanation:
Given:
Hypotenuse = 9
Perpendicular = 6
Find:
Base(x)
Computation:
Using Pythagorean theorem
Base = √Hypotenuse² - Perpendicular²
Base = √9² - 6²
Base = √81 - 36
Base = √45
Base = 3√5