Answer and Step-by-step explanation:
Answer:
The coordinates of C are (5 , 2)
The slope of CD is 3
The coordinates of D are (6 , 5) and (4 , -1)
Step-by-step explanation:
* Now lets study the problem
- The ends points of line AB are A = 2 , 3) and B = (8 , 1)
- CD is the perpendicular bisector of AB, and C lies on AB
- That means:
# C is the mid-point of AB
# The slope of AB × the slope of CD = -1 (one of them is a multiplicative
inverse and additive inverse of the other)
-Ex: the slope of one is a/b, then the slope of the other is -b/a
* The mid-point between two points (x1 , y1) and (x2 , y2) is:
[(x1 + x2)/2 , (y1 + y2)/2]
∵ C is the mid-point of AB
∴ C = [(2 + 8)/2 , (3 + 1)/2] = [10/2 , 4/2] = (5 , 2)
* The coordinates of C are (5 , 2)
- The slope of a line passing through points (x1 , y1) and (x2 , y2) is:
the slope = (y2 - y1)/(x2 - x1)
∴ The slope of AB = (1 - 3)/(8 -2) = -2/6 = -1/3
∵ CD ⊥ AB
∴ The slope of CD × the slope of AB = -1
∴ The slope of CD = 3
* The slope of CD is 3
- The length of a line passing through points (x1 , y1) and (x2 , y2) is:
the length = √[(x2 - x1)² + (y2 - y1)²]
∵ The length of CD = √10
∵ Point D is (x , y)
∴ (x - 5)² + (y - 2)² = (√10)²
∴ (x - 5)² + (y - 2)² = 10 ⇒ (1)
∵ The slope of CD is (y - 2)/(x - 5) = 3 ⇒ by using cross multiply
∴ (y - 2) = 3(x - 5) ⇒ (2)
- Substitute (2) in (1)
∴ (x - 5)² + [3(x - 5)]² = 10 ⇒ simplify
* [3(x - 5)]² = (3)²(x - 5)² = 9(x - 5)²
∴ (x - 5)² + 9(x - 5)² = 10 ⇒ add the like terms
∴ 10(x - 5)² = 10 ⇒ ÷ 10 both sides
∴ (x - 5)² = 1 ⇒ take √ for both sides
∴ x - 5 = ± 1
∴ x - 5 = 1 ⇒ add 5 to both sides
∴ x = 6
* OR
∴ x - 5 = -1 ⇒ add 5 to both sides
∴ x = 4
- Substitute the values of x in (2)
∴ y - 2 = 3(6 - 5)
∴ y - 2 = 3 ⇒ add 2
∴ y = 5
* OR
∴ y - 2 = 3(4 - 5)
∴ y - 2 = -3 ⇒ add 2
∴ y = -1
* The coordinates of D are (6 , 5) and (4 , -1)
PLEASE ANSWER ASAP AND PROVIDE EXPLANATION! A copy machine is set up to enlarge an original in the ratio 2:3. What is this enlargement in percent?
Answer:
50%
Step-by-step explanation:
Enlarging it in the ratio 2:3 means dividing it by 2 and multiplying it by 3.
Lest's pretend the original size was 100 in. 100/2x3=150
So in this case we enlarged it by 50 in. which is 50% of 100.
So, the enlargement as a percentage is 50%
Answer:
50% more
3-2=1
1/2=0.5
0.5=50%
You can also double check by adding half of two and checking if it is 3
2 x 0.5 = 1
2 + 1 = 3
50% increase
Hope this helps
Step-by-step explanation:
Solve for x in the triangle. Round your answer to the nearest tenth.
Answer:
x ≈ 6.9
Step-by-step explanation:
We use tan∅ to solve this:
tan21° = x/18
18(tan21°) = x
x = 6.90955
the students in Mrs. Kranger's class are holding a car wash to raise money for their end- of- year field trip. they washed 45 cars by noon, and their goal is to wash 110 cars by the end of the day. write and solve an addition equation to find c, the number of cars they still need to wash to meet their goal.
Answer:
45 + c = 110
c = 65
Step-by-step explanation:
110 - 45 = 65
Please mark as brainliest!
Answer:
They need to wash 65 more cars to reach their goal.
Step-by-step explanation:
45+c=110
subtract 45 from both sides
c=65
True/False Worth
points)
(05.02 LC)
You can draw a quadrilateral with two sets of parallel lines and no right angles.
True
O False
Answer:
the answer is true
Step-by-step explanation:
Because a parallelogram would be the result.
What is the scale factor in the dilation
2/5
1/2
2
2
1/2
Answer:
I think D, or 2 1/5
Step-by-step explanation:
Khan academy question
Step-by-step explanation:
There it is..................
Answer:
(2,5)
Step-by-step explanation:
Which represents the solution set of 5(x+5) < 85?
X<12
x>12
x<16
x>16
Answer:
x<12
Step-by-step explanation:
Divide both sides by 5
5(x+5) < 85
5 5
then simply
Answer:
x < 12
Step-by-step explanation:
[tex]5(x+5)<85\\\\5 * x = 5x\\\\5 * 5 = 25\\\\5x+25<85\\\\5x+25-25<85-25\\\\5x<60\\\\\frac{5x}{5}<\frac{60}{5}\\ \boxed{x<12}[/tex]
Generate a frequency table for the following data: 3, 12, 25, 2, 3, 6, 17, 17, 15, 13, 20, 22, 21, 18, 19.
Use the ranges listed in the table:
Range Number of Values
Relative Frequency
1-5
6 - 10
11 - 15
16 - 20
21 - 25
What is the relative frequency for the range 1 -57
a. 0.33
b. 0.4
c. 0.2
d. .27
Bud's cheeseburger and fries contained 1310 milligrams and 350 milligrams of sodium, respectively. Together they contained 66.4% of the recommended daily intake of sodium for
diet. What is the daily recommended intake of sodium for a 2,000 calorie diet?
Answer:
The recommended daily intake of sodium for a 2000 calorie diet is 2500 mg.
Step-by-step explanation:
In order to calculate the daily intake of sodium we first need to calculate the mass of sodium present in both snacks, this is given by their sum.
[tex]\text{total sodium} = 1310 + 350 = 1660 \text{ mg}[/tex]
We can now apply a rule of three for which the total sodium from the snacks is related to 66.4% in the same proportion as "x" mg, which is the value we want to know, is related to 100%. So we have:
[tex]\frac{1660}{x} \frac{mg}{mg} = \frac{66.4\%}{100\%}[/tex]
[tex]66.4*x = 1660*100\\x = \frac{166000}{66.4} = 2500 \text{ mg}[/tex]
The recommended daily intake of sodium for a 2000 calorie diet is 2500 mg.
Answer:
2,500 mg
1,310 + 350 = 1,660
1,660 is 66.4% of 2,500
A man purchased 10 pens. He sold 5 pens at 25% profit and the remaining 5
pens at [tex]16 \frac{2}{3} [/tex]% loss. If he received Rs 625 in total, find the cost price of each pen.
help!!!
Answer:
Rs 60
Step-by-step explanation:
[tex]5x \times (1+25\%)+5x \times (1-16\frac{2}{3}\%)=625[/tex]
[tex]5x(1+0.25)+5x(1-1/6)=625[/tex]
[tex]5x(1.25)+5x(5/6)=625[/tex]
[tex]10.416667x=625[/tex]
[tex]\frac{10.416667x}{10.416667}=\frac{625}{10.416667}[/tex]
[tex]x=59.99999...[/tex]
[tex]x=60[/tex]
Can someone help me please!!!
Answer:
65°
Step-by-step explanation:
180°-50°:130°
130°÷2:65°
130° divide by 2 because the shape was isosceles triangle
At a profit of 8% a shopkeeper sold a calculator for Rs 1,382.40. If he wants to increase his profit by 2%, at what price should he sell the calculator?
Answer:
Step-by-step explanation:
what’s the solution of y=x-4 and y=1/3x
Answer:
(6, 2)
Step-by-step explanation:
Step 1: Use substitution
x - 4 = 1/3x
Step 2: Isolate x
2/3x = 4
x = 6
Step 3: Plug back into original equation(s)
y = 6 - 4
y = 2
Answer:
(6,2)
Step-by-step explanation:
Let's use the substitution method.
x-4=1/3x
3x-12=x
3x=x+12
2x=12
x=6
y=6-4
y=2
Which equation is quadratic in form
Answer:
The answer is A because the quadratic equation formula
Step-by-step explanation:
because the quadratic equation formula is
ax^2+bx+c=0
and when you sub A into it, you get it in the needed form
Answer:
The Answer is A
Step-by-step explanation:
Which set of numbers is arranged in increasing order?
Answer:
B
Step-by-step explanation:
To solve this, we can make all of the numbers decimals.
π=3.14159265 and so on
Root 10 is about 3.16227766
22/7 is about 3.14285714
3.14 is already a decimal.
Now, our numbers are far easier to compare.
Let's put the numbers in increasing order.
3.14, 3.14159265, 3.14285714, 3.16227766
Substitute the original numbers in.
3.14, π, 22/7, Root 10
Therefore, option B is correct.
What is the median number of hours volunteered by the students in
the survey?
The median number of hours volunteered is hours.
Answer:
40
Step-by-step explanation:
The sum equals 80 80/2=40
Answer:
3
Step-by-step explanation: If you write out all the numbers and you cross them out in order you will find that 3 is your median.
An electrician uses the function f(x) = 60 + 40x to calculate the total cost, in dollars, for a service call that takes x hours to
complete. What does the coefficient 40 represent?
A)
The electrician works 40 hours.
B)
The electrician charges $40 per hour.
Eliminate
The electrician drives 40 miles to work.
D)
The electrician charges a $40 trip charge.
Answer:
(B) The electrician charges $40 per hour.
Step-by-step explanation:
Total cost=fixed cost + variable cost
F(x)=60+40x
Fixed cost =60
Variable cost=40x
x=hours of service
40=40 dollar per hour charge
The coefficient 40 represent the electrician charge of $40 per hour
(B) The electrician charges $40 per hour.
Solve x/2 + y/3 = 1 for x
Answer:
[tex]x[/tex] = - [tex]\frac{2y}{3}[/tex] + 2
Step-by-step explanation:
Solve for [tex]x[/tex] by simplifying both sides of the equation , isolating the variable.
Hope this helped you, Also please let me know if anything is unclear or wrong!
Answer:
Step-by-step explanation:
Help please I don’t understand the concept
Answer:
B
Step-by-step explanation:
The question is asking for what y would be when x is 2.
So, look on the graph where x = 2.
When x = 2, y = 6.
This means after 2 hours, the cost is $6
The ratio of the angle measures of a triangle is 1:2:2. What is the value of the smallest angle? 180° 90° 72° 36°
Answer:
36 degrees.
Step-by-step explanation:
All the angles in a triangle add up to be 180 degrees. Since the ratio is 1:2:2, you can say that the angles are x, 2x, and 2x.
x + 2x + 2x = 180
5x = 180
x = 180 / 5
x = 36
Since the smallest part of the ratio is 1, the smallest angle is 36 degrees.
Hope this helps!
A car travels 22 miles for every gallon of gasoline used. The table below represents this relationship. Gas Mileage Distance Traveled (miles) Gasoline Used (gallons) 22 1 44 2 x 3 88 4 Which equation correctly shows a pair of equivalent ratios that can be used to find the unknown? StartFraction 1 over 22 EndFraction = StartFraction x over 2 EndFraction StartFraction 22 over 1 EndFraction = StartFraction x over 2 EndFraction StartFraction 1 over 22 EndFraction = StartFraction x over 3 EndFraction StartFraction 22 over 1 EndFraction = StartFraction x over 3 EndFraction
Answer: The answer is the second one/b.
Answer:
D. 22/1=x/3
Step-by-step explanation:
Well what you multiply by the top you must do the bottom and opposite way also goes, sometimes so to get three as shown in (x/3) you must use the 1 from (22/1) times something to equal 3. In this it would be 1*3=3 so I multiplied three to the bottom and what I do the the bottom I haft to do to the top so 22*3=x and x is equal to 66 witch makes (D. 22/1=x/3) the correct option. If you want or need to check a good way to is to use a calculator to multiply 22*3 just as a small check up.
So I’m not great in math at all I spent 15 min crying because I don’t get it so anyone pls help
Answer:
A
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
Here b = 13 and h = 4 , thus
A = [tex]\frac{1}{2}[/tex] × 13 × 4 = [tex]\frac{1}{2}[/tex] × 52 = 26 units² → A
Answer:
A, 26
Step-by-step explanation:
Since the area of a triangle is one half base times height, and we have our height as 4, and our base as 13, we get 1/2 * 13 * 4, which is equal to 13 times 2, which is 26. Thus, our answer is A, 26.
5) A recipe for cookies calls for 2 cups of milk for 3 cups of Flour. You decide that you want to make more cookies than the recipe calls for. You have enough to use 9 cups of flour. How many cups of milk is needed if you use 9 cups of flour?
Answer: If you want to make more cookies then what is called for in this situation then you would need 6 cups of milk.
Step-by-step explanation: You have 2 cups of milk and 3 cups of flour of course. In order to make a complete batch you need 2 cups of milk and 3 cups of flour. In order to make a second batch you need the same things as you did for the first batch. Therefore two batches of cookies requires 4 cups of milk and 6 cups of flour. In this situation you want to make 3 batches of cookies. The required items are 6 cups of milk and 9 cups of flour.
James earns $1000 weekly base pay as a sales-person and gets a 10% commission on everything he sells. It is said that he sold $20,000 worth of merchandise last month, how much did he earn for the month? Provide an explanation :)) A. $4,000 B. $22,000 C. $6,000 D. $2,000
Answer:
Option C.
Step-by-step explanation:
It is given that James earns $1000 weekly base pay as a sales-person.
We know that, we have 4 weeks in a month. So, monthly salary of james is
Monthly income [tex]=\$1000\times 4=\$4,000[/tex]
It is said that he sold $20,000 worth of merchandise last month and he gets a 10% commission on everything he sells.
Commission [tex]=\$20,000\times \dfrac{10}{100}=\$2,000[/tex]
Total amount = Monthly income + Commission
[tex]=\$4,000+\$2,000[/tex]
[tex]=\$6,000[/tex]
Therefore, the correct option is C.
Stone bridge neighborhood garage sale had these cash receipts for 5 days: $214.50, $125.17, $245.30, $165.34, $58.75. What were the total cash receipts?
Answer: 809.06
Step-by-step explanation:
$214.50 + $125.17 + $245.30 + $165.34 + $58.75 = 809.06
Samantha can write 1 1⁄2 pages in 3 minutes. How many pages could she write in 12 minutes?
Answer:
[tex]6\:\mathrm{pages}[/tex]
Step-by-step explanation:
[tex]3 \times 4 = 12[/tex]
[tex]1\frac{1}{2} \times 4=6[/tex]
Answer:
6 pages
Step-by-step explanation:
1.5 pages x pages
--------------- = ------------
3 minutes 12 minutes
Using cross products
1.5 * 12 = 3x
Divide each side by 3
18 /3 = 3x/3
6 =x
6 pages
8. A goldsmith has 130 grams of a gold alloy (a mixture of gold and one or more other metals) containing 85% pure gold. How
much pure gold must be added to this alloy to obtain an alloy that is 90% pure gold?
The amount of pure gold that should be added is
grams.
(Type an integer or a decimal.)
Answer: 65 grams
Step-by-step explanation:
If 130 grams of a gold alloy (a mixture of gold and one or more other metals) containing 85% pure gold, you should first calculate the amount of gold that makes up this percentage.
That is, 85% of 130 grams.
85/100 × 130 = 110.5
Then, let X be what will be added to the above value to make 90%. So,
(110.5 + X) / ( 130 + X ) × 100 = 90
Divide both sides by 100
(110.5 + X) / ( 130 + X ) = 90/100
(110.5 + X) / ( 130 + X ) = 0.9
Cross multiply and open the bracket
110.5 + X = 117 + 0.9X
Collect the like terms
X - 0.9X = 117 - 110.5
0.1X = 6.5
Divide both sides by 0.1
X = 6.5/0.1
X = 65 grams
Therefore, the amount of pure gold that should be added is 65 grams
The radius of a circle is 9.7 m. Find the circumference to the nearest tenth?(help its urgent)
Answer:
Step-by-step explanation:
Circumference C=2πr r=radius [tex]\pi =3.14[/tex]
C=2(3.14)9.7
C=60.9
please need help I will be MARKING as BRIANILIST. thank you so much.
Answer:
C. Multiply 3 by 18
Step-by-step explanation:
Susan reads:
1 page in 3 mins
So,
1 page = 3 mins
If we want the time for 18 pages, we would multiply both sides by 18
So,
18 pages = 3×18 mins
18 pages = 54 mins
Answer:
C
Step-by-step explanation:
1 page every 3 minutes
18 pages will take 3 × 18 = 54 minutes to read.
9. How many ounces of a 25% alcohol solution must be mixed with 5 ounces of a 30% alcohol solution to make a 26% alcohol
solution?
ounces
The amount of 25% alcohol solution is
(Type an integer or a decimal.)
Answer:
27 Oz of 25% alcohol
Step-by-step explanation:
--percent ---------------- quantity
Alcohol I 30 ---------------- 18 Oz
alcohol II 25 ---------------- x Oz
Mixture 27 ---------------- 18 + x Oz
30*18+25x=27(18+x)
540+25x =486+27 x
25x-27x =486+540
-2x=-54
/ -2
x = 27
27 Oz of 25% alcohol