Answer:
The distance between the two given points is equal to √85.
Step-by-step explanation:
Let's recall what the distance formula is:
[tex]\displaystyle \huge\math\boxed{d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2} }[/tex]
We are defined our two points as:
(x₁, y₁) → (1, -7)(x₂, y₂) → (7, 0)We can rewrite this into our different "variables":
x₁ = 1y₁ = -7x₂ = 7y₂ = 0Now given our distance formula and our variables, we can find the distance between the two points:
[tex]\displaystyle\huge\begin{aligned}d & = \sqrt{(1 - 7)^2 + (7 - 0)^2} \\& = \sqrt{(-6)^2 + (7)^2} \\& = \sqrt{36 + 49} \\& = \math\boxed{\sqrt{85}} \\\end{aligned}[/tex]
∴ since the radical is already in its simplest form, our distance between the two points is equal to √85.
Hope this helps!
1+3+5+7+...+25 is subtracted from 2+4+6+8+...+26. The answer is
[tex]S_1 = 2+4+6+8+...+26 \\\\~~~~=2(1+2+3+4+...+13)\\\\~~~~=2 \cdot \dfrac{13(13+1)}2~~~~~~~~;\left[\text{Sum of consecutive positive integers }= \dfrac{n(n+1)}2 \right] \\\\~~~~=13 \cdot 14\\\\~~~~=182\\\\S_2 = 1+3+5+7+...+25\\\\\text{It is an arithmetic series wihere}\\\\\text{First term, a =1, ~Common difference, d = 2,~ number of terms = n} \\\\~~~~\text{Nth term} = a+(n-1)d\\\\\implies 25 = 1+(n-1)2\\\\\implies 2n-2 = 24\\\\\implies 2n = 24+2\\\\\implies 2n= 26\\\\[/tex]
[tex]\implies n = \dfrac{26}2 \\\\\implies n= 13\\\\\text{S} _2= \dfrac{\text{n(First term+ Last term)}}{2}\\\\~~~~~~=\dfrac{13(1+25)}2\\\\~~~~~~=\dfrac{13 \times 26}2\\\\~~~~~~=13 \times 13\\\\~~~~~~=169\\\\\text{Hence,}~~ S_1 - S_2 =182 - 169 =13[/tex]
Answer:
13
Step-by-step explanation:
2 + 4 + 6 + 8 + ...... + 26
n = 13
Sum of first 'n' even numbers = n( n +1)
= 13 * 14
= 182
1 + 3 + 5 + 7 + .....+25
n = 13
Sum of first 'n' odd numbers = n²
= 13 * 13
= 169
2 + 4 + 6 + 8 + ... + 26 - (1 + 3 + 5 + 7 + ......+25) = 182 - 169
= 13
If a = 12 feet, b = 6 feet, c = 2 feet, d = 15 feet, and e = 3 feet, what is the area of the object?
Answer:9282
Step-by-step explanation:
I really need help understanding when/ what situations to use sine rule and cosine rule with triangles, plssss.
thank you :)))
Answer:
See below :)
Step-by-step explanation:
If you want a missing angle or side in one pair, and you have at least one side and angle pair, use the sine rule.
If you want a remaining side, and you have the other two sides and the angle opposite the unknown side, use the cosine rule.
If you want an angle, and you have all three sides, use the cosine rule rearranged for angles.
I attached a picture to help explain better :)
Ayana's favorite brownie recipe calls for
1
2
of a cup of flour for every
1
3
of a cup of cocoa powder. For a bake sale, she plans to make a larger batch with 1 cup of cocoa powder. How much flour should she use?
Answer: 12-233 24353252345
Step-by-step explanation:
Ayana's favorite brownie recipe calls for
1
2
of a cup of flour for every
1
3
of a cup of cocoa powder. For a bake sale, she plans to make a larger batch with 1 cup of cocoa powder. How much flour should she use?
This solid is a hemisphere with a 90° slice removed and a radius of 12
Answer:
Step-by-step explanation:
u don't know this silly question
i don’t know the answer and need help
Answer:
add a screen shot
Step-by-step explanation:
The radius of a circle is 3 yards. What is the circle's circumference?
r=3 yd
Use 3.14 for .
yards
Answer: 18.84
Step-by-step explanation: Circumference is calculated as 2 × 3.14 × radius
A box of clearance clothes at a shop contains 3 red shirts and 12 black shirts. What is the probability that Ned will choose 2 red shirts randomly from the box?
12/35
1/35
2/75
3/70
The probability that Ned will choose 2 red shirts randomly from the box is 1/35.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
The probability of choosing 2 red shirts randomly from the box can be calculated using the formula for probability of independent events:
P(choosing 2 red shirts) = P(choosing 1st red shirt) × P(choosing 2nd red shirt after 1st red shirt has been removed)
The probability of choosing the first red shirt is 3/15 (since there are a total of 15 shirts in the box, of which 3 are red).
After one red shirt is removed, there will be 2 red shirts and 14 shirts remaining in the box.
Therefore, the probability of choosing the second red shirt is 2/14.
P(choosing 2 red shirts) = (3/15) * (2/14) = 1/35
Therefore, the probability that Ned will choose 2 red shirts randomly from the box is 1/35.
To learn more on probability click:
https://brainly.com/question/11234923
#SPJ2
What is the equation of a line, in point slope form, that passes through (5, 3)and has a slope of ⅔
Answer:
y - 3 = 2/3(x - 5)
Step-by-step explanation:
Formula:
y - y1 = m(x - x1)
It doesn't apply to this problem but keep in mind that two negatives make a positive so instead of writing, for example, y - (-5), you can just write y +5.
Makes it a lot cleaner and easier to work with.
Hope this helps you :)
Si se multiplica un numero por uno,¿que numero se obtiene?
Answer:
Si se multiplica un numero por uno, obtendras el numero original, por ejemplo 54x1 = 54, y 2x1= 2.
Step-by-step explanation:
3.5
B
S
A
7
ΔΑΒC ~ ΔQRS
Find the value of t.
Τ
4
C
R
Answer:
x = 0.5
Step-by-step explanation:
3.5/x = 7/4
3.5/x * 1/3.5 = 7/4 * 1/3.5
x = 7/14
x = 1/2
x = 0.5
What is the radius of the cone? 2 units 3 units 6 units 9 units
Answer:
where is the diameter?
Step-by-step explanation:
Answer:
Step-by-step explanation:
Find the median of:
21, 7, 32, 45, 28, 78
CAN SOMEBODY EXPLAIN HOW TO DO THIS IT'S MY 5TH TIME ASKING AND NOBODY EVEN HELPS ME!
i used caps to get ur attention 7u7
Answer:
10x20+10x6=260
Step-by-step explanation:
Answer:
260 cm²
Step-by-step explanation:
Area of the rectangle
= l × w
= 20 × 10
= 200 cm²
Area of the triangle
= ½bh
= ½ × 20 × 6
= ½ × 120
= 60 cm²
Area of the total figure
= Area of the rectangle + Area of the triangle
= 200 cm² + 60 cm²
= 260 cm²
________
Hope it helps ⚜
2.
Find m∠F.
a.30°
b.60°
c.15°
d.10°
Answer:
Step-by-step explanation:
[tex]\sf Sin \ F = \dfrac{Opposite \ of \ angle \ F}{hypotenuse}[/tex]
[tex]= \dfrac{9}{18}\\\\= 0.5[/tex]
[tex]F = Sin^{-1} \ (0.5)\\[/tex]
= 30°
If x - 3/x = 7 find i) x² + 9/x²
ii) x + 3/x
iii) x² - 9/x²
[tex]\text{Given that,}\\\\x-\dfrac 3x = 7\\\\\\\textbf{i).}\\\\\\x^2 + \dfrac 9{x^2}\\\\\\=x^2 + \left(\dfrac 3 x \right)^2\\\\\\=\left(x- \dfrac 3x \right)^2 + 2 \cdot x \cdot \dfrac 3x\\\\\\=7^2 +6\\\\\\=55[/tex]
[tex]\textbf{ii)}\\\\~~~~~\left(x+\dfrac 3 x \right)^2 = \left( x - \dfrac 3x \right)^2+4 \cdot x \cdot \dfrac 3x\\\\\\\implies \left(x+\dfrac 3 x \right)^2 = 7^2 +12\\\\\\\implies \left(x+\dfrac 3 x \right)^2 =61\\\\\\\implies x+ \dfrac 3x = \pm\sqrt{61}\\\\\\[/tex]
[tex]\textbf{iii)}\\\\\\x^2 -\dfrac 9{x^2}\\\\\\=x^2 - \left(\dfrac 3{x} \right)^2\\\\\\=\left( x-\dfrac 3x \right)\left( x+\dfrac 3x \right)\\\\\\=7\sqrt{61}~~ \text{or}~~ -7\sqrt{61}[/tex]
Which is the same as dividing a number by 10?
pls help I need it pls
Answer:
Splitting that number into 10 equal wholes.
Step-by-step explanation:
(fractions)
Pls help me i am st patrick
Answer:
7
Step-by-step explanation:
15+2=17
20-17=3
So, these three people definitely like lemonade
11-3=8
So, eight people like both coffee and lemonade
15-8=7
Ans: 7 people like coffee but not lemonade
HELP ME WITH THIS LOL
Find the value of X if a = 25 and b = 11, Round to the nearest tenth.
Answer:
x = 19.9
Step-by-step explanation:
These kinds of problems have a specific formula.
Formula: outside (whole) = outside (whole)
We could substitute our variables into this.
For the first line, our outside segment is b and the whole thing is a + b
For the second line, our outside segment is x, and the whole thing is x.
[tex]b (a+b) = x(x)\\11 (25+11) = x^2\\11 (36) = x^2\\396 = x^2\\\\x=\sqrt{396}[/tex]
The [tex]\sqrt{396}[/tex] = 19.8997487421
Rounding to the nearest tenth, your answer is 19.9
Question is in image below.
Answer:
-9/25, -0.bar 3, √24, 4.92
Answer:
[tex]-\frac{9}{25} < -0.3 < \sqrt{24} < 4.92[/tex]
Step-by-step explanation:
We first have to expand -0.3, -9/25, and sqrt(24). Then we determine which is least and which is greater.
-0.3 = -0.3333...
-9/25 = -0.36
[tex]\sqrt{24}[/tex] ≈ 4.8989799486
4.92
[tex]-\frac{9}{25} < -0.3 < \sqrt{24} < 4.92[/tex]
Each of the equal sides of an isosceles triangle is 5 inches more than twice the third side. If the perimeter of the triangle is 55 inches, find the sides of the triangle
Answer:
9 23 23
Step-by-step explanation:
Two sides are equal and are each 2x + 5 ( x = third side)
add the three sides to get 55 inches
2x + 5 + 2x+5 + x = 55
5x = 45
x = 9 so the sides are 9 and 23 and 23
by how much is (3/4 + 1/12 + 2/3) greater than 1
Hey there!
3/4 + 1/12 + 2/3
= 5/6 + 2/3
= 5/6 + 4/6
= 5 + 4 / 6
= 9 / 6
= 9 ÷ 3 / 6 ÷ 3
= 3/2
≈ 1.5
1.5 - 1 = 0.5
Therefore, your answer is: 0.5
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
3x + 14 / 8 = -5
And also need to do the check ♀️
distributive property
Answer:
9 x 6= 9 x ( 3+3 )
= 9 x 3 + 9 x 3
= 27 + 27
= 54
Step-by-step explanation:
Peter is packing toys into boxes each box holds 30 toys they are 94 toys and 3 boxes how many toys are there left
Answer:
4
Step-by-step explanation: You want to divide 94 by 30 and you 3 with a remainder of 4.
Answer: 4 toys
Step-by-step explanation:
We will multiply 3 by 30 for how many toys he can currently put into boxes.
3 * 30 = 90
Now we will subtract this from the total number of toys for our answer.
94 - 90 = 4
There are 4 toys left.
Stefon is paid $25 to mow a lawn. This amount is $4 less than twice the amount he received when he first began mowing. Use the model to determine x, the amount Stefon received when he first began mowing
Answer:
He used to receive $14.50.
Step-by-step explanation:
Let x = amount he used to receive.
Now he receives 2x - 4.
Now he receives $25.
2x - 4 = 25
2x = 29
x = 14.5
Answer: He used to receive $14.50.
Answer:14.5
If you want a full step explanation: https://brainly.com/question/19345016
(4×10^-1) + (4×10^-1)
Give your anwser in standard form.
Answer:
0.8
Step-by-step explanation:
Hope this helps!
Paul works at at the bucket of Cracker Barrel and makes $8.25 an hour plus tips. Paul averages $110 in tips during an 8 hour shift. Paul typically works 40 hours A week and he works 48 weeks out of the year the other 2 weeks he gets paid vacation time during this time he earns his base hourly rate for 40 hours a week what is his gross annual income?
Answer:
330.00
Step-by-step explanation:
i think thats the answer someone would have to double check but this is what i did the get that
How much overtime pay do you get for working 40 hours if you get the following pay scale:
8.25 for all hours up to 40
110 for all hours in excess of 40
Calculate Total Pay
Total Wages = Regular Rate x 40 Hours + Overtime Rate x (Hours - 40)
Total Wages = 8.25 x 40 Hours + 110 x (40 - 40) Hours
Total Wages = 8.25 x 40 Hours + 110 x (0) Hours
Total Wages = 330 + 0
Total Wages = 330.00
Taffy Twists candy company keeps the same ratio of pieces of strawberry candy to banana candy in their packs. The Mega Pack has 40 strawberry candies and 50 banana candies. The Party Pack has 20 strawberry candies.
How many banana candies are in the Party Pack?
Answer:
25 bananas
Step-by-step explanation:
You halved the strawberry number (from 40 to 20) ....half the banana number = 25
Prove that ABCD is not a parallelogram.
Answer:
Segment AD is 4 units long, while segment BC is 5 units long. If this figure was a parallelogram, these two segments would be equal to each other.
Step-by-step explanation: