Applying the distance formula, the value of a is 2 or -2.
What is the Distance Formula?The distance formula is:
d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
Given the following:
d = XY = 10 units
X(a - 5, -2a) = (x1, y1)
Y(a + 1, 2a) = (x2, y2)
Plug in the values into the distance formula
10 = √[((a + 1) - (a - 5))² + (2a - (-2a))²]
10 = √[(a + 1 - a + 5)² + (2a + 2a)²]
10 = √(6² + (4a)²)
10 = √(36 + 16a²)
10² = 36 + 16a²
100 = 36 + 16a²
0 = -100 + 36 + 16a²
0 = 16a² - 64
16a² - 64 = 0
Factorize
16(a² - 4) = 0
16(a - 2)(a + 2) = 0
a = 2 or a = -2
Therefore, applying the distance formula, the value of a is 2 or -2.
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In a game of cards, 43 cards are used, including one joker. Four players are each, dealt 10 cards and the rest are put in a pile. If Greg doesn't have the joker, what is the probability that either his partner or the pile have the joker?
Probability that either his partner or the pile have the joker from the deck of 43 cards including one joker ,four players each have 10 cards and 3 cards in a pile is 13/33.
As given,
Total number of cards=43
Number of cards with each players =10
Number of cards in a pile =3
Greg doesn't have joker
Total cards left = 43-10
= 33
Probability either his or the pile have the joker = (10 +3)/33
= 13/33
Therefore, probability that either his partner or the pile have the joker is 13/33.
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may someone help meee?
The expression given by (1/2)⁻¹ is equivalent to 2
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
(1/2)⁻¹
Taking the negative one exponent gives:
= 2 / 1
Simplifying the equation gives:
= 2
The expression given by (1/2)⁻¹ is equivalent to 2
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What is the sum of each finite series?
a. Σ⁴° n=1 (3n - 8)
The sum of the given finite series is 2140
Sum notation is used to express long summation into a single formula.
Properties of sum operator:
If a is a constant, then Σₙa.b(n) = a Σₙ.b(n) Σ (a +b) = Σa + Σb[tex]\sum\limits^{40}_{n=1} {(3n-8)}=\sum\limits^{40}_{n=1} {3n}-\sum\limits^{40}_{n=1} {8}[/tex]
[tex]=3\sum\limits^{40}_{n=1} {n}-\sum\limits^{40}_{n=1} {8}[/tex]
[tex]=3\sum\limits^{40}_{n=1} {n}-8\times40[/tex]
[tex]=3(1+2+...+40)-8\times40[/tex]
[tex]=3.\frac{40}{2}. (1+40)-320[/tex]
= 2140
Hence, the sum of the given finite series is 2140
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Evaluate |c2 + b2|, given a = 5, b = -3, and c = -2.
10
6
2
13
is (36^7 + 6^13) divisible by 7?
Answer:
(36^7+6^13) is divisible by 7.
Step-by-step explanation:
(36^7+6^13)
First, solve the parentheses and exponents within it.
36^7=36*36*36*36*36*36*36=78364164096
6^13=6*6*6*6*6*6*6*6*6*6*6*6*6=13060694016
Add 78364164096 and 13060694016.
It equals 91424858112.
Divide 91424858112 by 7.
It results in 13060694016.
Hence, yes.
Hope this helps.
R-C=P solve the equation answer what the variable c equals
Answer:
C=r-p
Step-by-step explanation:
r-c=p
We need to solve the equation for Variable C
To get c alone we need to remove r from the left hand side
Subtract R from both sides
r-c=p
r-r-c=-r+P
-c=-r+P
Now divide both sides by -1 to get c alone
c=r-p
C is alone, it is solved for C
Find the midpoint of the line segment joining points A and B
A(8,- 7); B(2,3)
(5 , -2)
Step-by-step explanation:
mid point = ( (X1 + X2)/2 , (Y1 + Y2)/2 )
= ( (8 + 2)/2 , (-7 + 3)/2 )
= (5 , -2)
Simplify the quantity 7 minus one fourth times the square root of 16 end quantity squared plus the quantity 2 minus 5 end quantity squared. 27 45 324 900
The value of the expression (7 - 1/4 × ✓16)² + (2 - 5)² is 45.
How to calculate the expression?Based on the information given, the expression will be:
(7 - 1/4 × ✓16)² + (2 - 5)²
= (7 - 1)² + (-3)²
= 6² + 3²
= 36 + 9
= 45
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The lunch cost 32.00 and sales taxes was 4.45. If you plan to tip 20% find the total amount you need to pay for lunch
The total amount that you need to pay for the lunch after the sales tax and the tip will be $ 42.85.
We are given that:
The cost of lunch = $ 32
Sales tax = $ 4.45
Tip = 20 %
So, the tip will be calculated by finding the percentage of cost that you are planning to pay has a tip.
Tip = 20 % of $ 32
Tip = 20 / 100 × $ 32
Tip = 0.2 × $ 32
Tip = $ 6.4
Total amount needed to be paid for the lunch = $ 32.00 + $ 4.45 + $ 6.40
Total amount = $ 42.85
Therefore, we get that, the total amount that you need to pay for the lunch after the sales tax and the tip will be $ 42.85.
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The left and right page numbers of an open book are two consecutive integers whose sum is 253. Find these page numbers.
The consecutive page no. are 126 and 127.
WHAT ARE CONSECUTIVE INTEGERS ?An example of a run of consecutive integers is 1, 2, 3, 4. Another illustration is 7, 8, and 9. An integer sequence is a set of numbers where each term is one more than the term before it.
Continually following one another, from smallest to greatest, are consecutive numerals. For instance, the sequence of the numerals 1, 2, 3, 4, 5, and so forth.
The next two numbers are (n + 1) and (n + 2) if n is an integer. Take 1 for n as an example. Its subsequent numbers can be read as (2 and 3), or as (1 + 1) and (1 + 2).
CALCULATIONlet the consecutive page numbers be x and x+1
according to question ,
x + x + 1 = 253
2x = 252
x = 126
so the consecutive page numbers are 126 and 127.
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A foreign exchange student from Denmark would like to buy gifts for her family. She finds a special deal, 7 t-shirts for $07.93, that she would like to purchase for her family. However, her family only consists of 5 people. If she wants to purchase 5 -
shirts for her family members at that special rate, what would be the cost of these t-shirts in her currency of Krona? (Currency conversion rate is 1 U.S. Dollar 8.6064 Krona)
O 121.663 Krona
O 13.99 Krona
O 608.313 Krona
O69.95 Krona
The total cost of the shirts that the foreign student buy will be 48.71 Krona.
How to illustrate the information?From the information, the person finds a special deal, 7 t-shirts for $07.93, that she would like to purchase for her family.
Therefore, the total cost will be:
= $7.93 / 7 × 5
= $5.66
Therefore, the amount when converted to Krona will be:
= $5.66 × 8.6064
= $48.7
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Answer:
The answer is C "608.313 Krona"
Step-by-step explanation:
Got it right on my quiz.
The temperature at 1:00 pm was -7°C. By 5:00 pm the temperature increased by 11°C. What was the temperature at 5:00 pm?
What expression
can be used to add 1/2 + 5/6
Answer:
(4/3)
Step-by-step explanation:
1 5
--------- + --------
2 6
1 (3) 5
--------- + --------
2(3) 6
3 5 8
------- + ------- = -------
6 6 6
8 ÷ 2 4
------- = -------
6 ÷ 2 3
I hope this helps!
Classify each variable according to the set of numbers that best describes its values.
the number of times n a ball bounces; the height h from which the ball is dropped
The categorization of each variable according to the group of numbers that best captures its values is shown below:
Any integer from 0 to n.
Any number from 0 to h.
What is a variable?Any mathematical object can be represented by a variable in mathematics as a symbol and placeholder. A variable can, for example, represent a number, a vector, a matrix, a function, the argument of a function, a set, or a set's component.Numerous issues are resolved in a single computation by using variables in algebraic calculations as if they were explicit integers.For instance, by exchanging the variables that represent them in the quadratic formula with the numerical values of the coefficients in any given quadratic equation, the quadratic formula may solve any quadratic equation.In mathematical logic, a variable is either a sign for an undefined word of the theory (a "meta-variable") or a fundamental item of the theory that is changed without considering any potential intuitive meaning.To know more about variable, refer to the following link:
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A 12-pack of juice boxes costs $5.40. How much would an 18-pack of juice boxes cost if it is proportionate in price?
Answer: 8 dollars and 10 cents
Step-by-step explanation:
5.40 divided by 12 = .45
This means that each juice costs 45 cents
.45x18=8.10
Answer:
$8.10
Step-by-step explanation:
$5.40/12=$0.45 $0.45*18=$8.10
Malik walks 5 blocks per minute. How many blocks will he walk in 6 minutes?
5 blocks
identify all the numbered angles that are congruent to the given angle. Justify your answers.
Write an equation of a parabola with the given information.
vertex (0,0) , focus (0, 1/2)
The equation that defines the parabola with vertex at the point and focus at (0, 1/2) is
y = 2x²
What is a parabola?The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.
The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.
In this case we have the vertex of the parabola at the point (0,0) and the focus at the point (0, 1/2) this is displaced on the y-axis upward, so the parabola is of the form.
y = x²
Canonical equation
(y - yo) = 4p(x - xo)
Vertex (0, 0)xo, yo = (0 , 0)
Focus:
f = (0, 0 + p)
(y- 0) = 4*0.5(x - 0)²
y = 2x²
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pls answer these two questions ASAP
Answer:
Step-by-step explanation:
[tex]\displaystyle\\\frac{10px^2}{3c^2d} \div\frac{5px}{6c^2d^2} =\\\\\frac{10px^2}{3c^2d}*\frac{6c^2d^2}{5px} =\\\\\frac{60c^2d^2px^2}{15c^2dpx^2} =\\\\4d\\\\\\\frac{3}{x+7} \div\frac{8x^2-8x}{x^2+6x-7} =\\\\\frac{3}{x+7} \div\frac{8x(x-1)}{x^2-x+7x-7} =\\\\\frac{3}{x+7} \div\frac{8x(x-1)}{x(x-1)+7(x-1)} =\\\\\frac{3}{x+7} \div\frac{8x(x-1)}{(x-1)(x+7)} =\\\\\frac{3}{x+7} \div\frac{8x}{x+7} =\\\\\frac{3}{x+7} *\frac{x+7}{8x} \\\\\frac{3(x+7)}{8x(x+7)}=\\\\\frac{3}{8x}[/tex]
diego compro 12 cuadernos que le costaron 96. 000 ¿cuanto le costo cada uno ?
Simplify it.
Show steps please
√16x^2
Answer:
4[tex]x^{2}[/tex]
Step-by-step explanation:
1st seperate the equation
[tex]\sqrt{16}[/tex] and [tex]x^{2}[/tex]
square root of 16 is 4, and x squared stays the same, so the equation becomes
4[tex]x^{2}[/tex]
An investor puts $1760.25 into
an insurance policy that pays
6.5% simple annual interest.
If no additional investment is made
into the policy, how much interest
should the investor expect at the end
of 15 years?
(Round to the nearest cent.)
The investor should expect $1716.24375 at the end of 15 years .
Formula for calculation of Simple Interest :
Simple Interest = ( Rate * Principal * no . of years ) / 100 , when no additional investment is made .
Here , principal = $1760.25 , rate = 6.5 , no . of years = 15 .
Substituting values in formula above ,
SI = ( 6.5 * 1760.25 * 15 ) / 100
= 1716.24375
Hence , the investor should expect $1716.24375 at the end
of 15 years .
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i need help solving this problem
Step-by-step explanation:
or, 55° = (4x - 1)° [ vertically opposite angle ]
or, 55° + 1° = (4x)°
or, 56° = (4x)°
or, 56°/4° = x
or, x = 14°
Therefore the value of x is 14° .
help please.
-1/3 - (-3/5)
Answer:
Step-by-step explanation:
93959453
julia ordered 2 hamburgers and steve ordered 3 hamburgers. If their total bill was $7.50, how much did each hamburger cost?
Answer:
$1.50
Step-by-step explanation:
there are 5 burgers since 2+3 is five. Divide 7.50 by five. The answer is 1.50.
$1.50
Because 2+3=5 and once you 7.5÷5 it equals 1.5.
solve 2x + 5y = -1for y. Then find the value of y when x=-2
solve 2xy - x = 3for y. Then find the value for y when x=2
In equation (1) the value of y = 3/5 and In equation (2) the value of y = 5/4
In the given statement is
Solve 2x + 5y = -1 for y.
To find the value of y when x= -2
Now, Equation is 2x + 5y = -1 …..(1)
Put the value of x = -2 in eq. 1
2 (-2) + 5y = -1
-4 + 5y = -1
5y = -1 + 4
y = 3/5
Again, Solve 2xy - x = 3 for y
To find the value of y when x = 2
Now, Equation is : 2xy - x = 3 ….(2)
Put the value of x = 2 in eq. (2)
2(2)y - 2 = 3
4y - 2 = 3
4y = 5
y = 5/4
Hence, In equation (1) the value of y = 3/5 and In equation (2) the value of y = 5/4
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how do I write the domain and range as an inequality here.
Check the picture below.
notice, the function namely f(x) or "y", has a hole at (-3 , 2), that means that the values for the range are anything less than 2, but never 2, so 1.1 is ok, 1.99 is also good, 1.999999999999999 is also ok, but never 2, thus y < 2.
Let's also notice, the arrowhead means the graph keeps on going to the left as well as to the bottom.
Please tell me the angles of x and y on letter B
Answer:
x = 100, y = 80
Step-by-step explanation:
100° and x° are alternate interior angles and are congruent , so
x = 100
x° and y° are a linear pair and sum to 180° , that is
100 + y = 180 ( subtract 100 from both sides )
y = 80
Find the GCF of 45, 27, 72
how much was the original price of the ticket? Pls help answer with detailed explanation
Answer: the original price of the ticket was $42
Step-by-step explanation:
[tex]Let's\ make\ a\ proportion:[/tex]
$44.92 - 107%
$x - 100%
[tex]\displaystyle\\x=\frac{44.92*100}{107} \\\\x=\frac{4492}{107} \\\\x=42[/tex]
