Answer:
k = -3
k =5
Step-by-step explanation:
[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d = 5\\(-1,1) =(x_1,y_1)\\(2,k)=(x_2,y_2)\\[/tex]
[tex]5=\sqrt{\left(2-\left(-1\right)\right)^2+\left(k-1\right)^2}\\\\\mathrm{Square\:both\:sides}:\quad 25=k^2-2k+10\\25=k^2-2k+10\\\\\mathrm{Solve\:}\:25=k^2-2k+10:\\k^2-2k+10=25\\\\\mathrm{Subtract\:}25\mathrm{\:from\:both\:sides}\\k^2-2k+10-25=25-25\\k^2-2k-15=0\\\\\mathrm{Solve\:by\:factoring}\\\\\mathrm{Factor\:}k^2-2k-15:\quad \left(k+3\right)\left(k-5\right)\\\mathrm{Solve\:}\:k+3=0:\quad k=-3\\[/tex]
[tex]\mathrm{Solve\:}\:k-5=0:\quad k=5\\\\k =5 , k=-3[/tex]
A = (-1, 1) and B = (2, k) so:
[tex]d(A,B)=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}=\sqrt{(2-(-1))^2+(k-1)^2}=\\\\=\sqrt{3^2+(k-1)^2}=\sqrt{9+k^2-2k+1}=\sqrt{k^2-2k+10}\\\\\\d(A,B)=5\\\\\sqrt{k^2-2k+10}=5\quad|(\ldots)^2\\\\\big|k^2-2k+10\big|=25\\\\k^2-2k+10=25\qquad\vee\qquad k^2-2k+10=-25\\\\k^2-2k-15=0\qquad\vee\qquad k^2-2k+35=0\\\\\\\Delta_1=(-2)^2-4\cdot1\cdot(-15)=64>0\qquad\text{two solutions}\\\\\Delta_2=(-2)^2-4\cdot1\cdot35=-136<0\qquad\text{no solutions}\\\\\\k_1=\dfrac{2-\sqrt{64}}{2}=\dfrac{2-8}{2}=\dfrac{-6}{2}=\boxed{-3}[/tex]
[tex]k_2=\dfrac{2+\sqrt{64}}{2}=\dfrac{2+8}{2}=\dfrac{10}{2}=\boxed{5}[/tex]
The price for 2 student tickets and 4 adult tickets to a play is $50. Adult tickets are $5 more than student tickets. write an the equation
Answer:
2x + 4y = $50
x = $5, and y = $10
Step-by-step explanation:
let the price of student's ticket be represented by $x, and that of adult by $y. So that:
2x + 4y = $50 ................ 1
But, given that adult tickets are $5 more that student tickets.
i.e y = x + $5 ................. 2
Substitute equation 2 into 1, to have;
2x + 4(x + $5) = $50
2x + 4x + $20 = $50
6x = $30
x = $5
From equation 2,
y = 5 + 5
= $10
Therefore, the price of student tickets is $5 and adult tickets is $10.
If the altitude is √7, find the volume. 36√7 cu. units 18√7 cu. units 12√7 cu. units
Answer:
[tex] Volume = 12\sqrt{7} [/tex] cubic units
Step-by-step explanation:
Volume of the square pyramid is given as ⅓*area of base*height of pyramid.
Where,
Area of base = 6*6 = 36
Height of pyramid = altitude = [tex] \sqrt{7} [/tex] units
Plug the values into the formula to find volume.
[tex] Volume = \frac{1}{3}*36*\sqrt{7} [/tex]
[tex] Volume = 12*\sqrt{7} [/tex]
[tex] Volume = 12\sqrt{7} [/tex] cubic units
Explain the difference between (-5)2 and -52.
Answer:
(-5)2 would become -10, whereas -52 would just stay the same. Normally, a number next to parentheses without any other signs (+,-,×,÷) means that you multiply.
How would you round 95687 to the nearest thousand?
Answer:
96,000
Step-by-step explanation:
To round to the nearest thousand, we need to look at the digit in the hundreds place, which is 6. Since 6 > 5, we know that we need to round up (because 6 is closer to 10 than it is to 0). Currently, the number is 95 thousand so when rounding up, the answer will be 96,000.
y ÷ 5 = 2/5 . Find the value of y.
Answer:
y=2
Step-by-step explanation:
[tex] \frac{y}{5} = \frac{2}{5} \\ = > y = \frac{2}{5} \times 5 \\ = > y = 2[/tex]
Answer: Y=2
Step-by-step explanation:slove for y by simplifying both sides of the equation, the isolating the variable.
The five number summary of a dataset was found to be: 45, 46, 51, 60, 66
An observation is considered an outlier if it is below:____________.
An observation is considered an outlier if it is above:____________.
Answer/Step-by-step explanation:
Given the five summary of a data set:
45 - min
46 - Q1
51 - Median
60 - Q3
66 - Max
Thus, any number less than [tex] Q_1 - (1.5*IQR) [/tex], or any number that is greater than [tex] Q_3 + (1.5*IQR) [/tex] would be considered an outlier.
The IQR of the data set = Q3 - Q1 = 60 - 46 = 14
Thus,
[tex] Q_1 - (1.5*IQR) = 46 - (1.5*14) = 46 - 21 = 25 [/tex]
Therefore, an observation is considered an outlier if it is below: 25.
[tex] Q_3 + (1.5*IQR) = 60 + (1.5*14) = 60 + 21 = 81 [/tex]
Therefore, an observation is considered an outlier if it is above: 81.
a swimming pool is 60m long and 25m wide. it is filled with water to a depth of 7m. find the volume of water in the pool
Answer:
10500 m³
Step-by-step explanation:
60 × 25 × 7 = 10500 m³
you put $500 in your bank account. With a interest rate of 5%, how long will it take the account to reach $600?
Answer:
4 years hope this helps
Step-by-step explanation:
Answer:
4 Years
Step-by-step explanation:
t = I/Pr
Note the 600 is the total amount in the account.
Therefore Interest, I = 600 - 500 = 100.
t = 100 / (500 * 5%)
t = 100 / (500 *0.05)
t = 4
It will take 4 years.
The set of numbers whose decimal representations are neither terminating nor repeating is called the set of
Answer:
its A
Step-by-step explanation:
Answer: terminating nor repeating
Step-by-step explanation:
A teacher gave his students the four graphs below. Which graph represents a geometric sequence?
Answer:
Graph A
Step-by-step explanation:
Answer:
The Answer is Graph A on Edge
Step-by-step explanation:
Simplify 2x^2(-3x^2)^3
Answer:
[tex]-54x^8[/tex]
Step-by-step explanation:
[tex]2x^{2}(-3x^2)^3\\\\2x^2((-3)^3(x^{2*3}))\\\\2x^2(-27x^6)\\\\2(-27)(x^{2+6})\\\\-54x^8[/tex]
Answer:
[tex]-54x^{8}[/tex]
Step-by-step explanation:
[tex]2x^{2} (-3x^{2} )^{3}[/tex]
We first carry through the cube.
[tex]-3^{3} x^{2*3}[/tex]
[tex]-3^{3}[/tex] = -27 [tex]x^{2*3} = x^{6}[/tex]
Now we have [tex]2x^{2} (-27x^{6} )[/tex]
2 * - 27 = -54
[tex]x^{2} *x^{6} = x^{8}[/tex]
[tex]-54x^{8}[/tex]
I need help PWEASEEEE
Answer:
B.
Step-by-step explanation:
From the number line, we can see that the blue line points to all values to the left of 5. This means all values less than 5.
Also, note that since the blue dot is closed, the inequality includes 5.
Therefore, the inequality that represents the graph is all values less than or equal to 5.
In notation, this is:
[tex]x\leq 5[/tex]
The answer is B
Answer:
your answer is B. [tex]x\leq 5[/tex]
Step-by-step explanation:
[tex]x\leq 5[/tex] means that your arrow should be point left which means less than the line under the less than means that the don´t should be shaded in
What is 387.0642 rounded to the nearest hundredth
Answer:
387.06
Step-by-step explanation:
(0 to 5) = round down
(5 to 9) = round up
[tex]387.0642 \\ \: \: 1 \: 00[/tex]
Answer:
387
Step-by-step explanation:
387.0642 apprx. 387
0 is not equal to five nor is greater than.
Hope this helps ;) ❤❤❤
Simplify if possible
За2 + ба +2b2
solve for v
pleaseee answer and explain <333
Hi there! :)
Answer:
[tex]\huge\boxed{v = -27}[/tex]
[tex]\frac{v-3}{4} = \frac{9+2v}{6}[/tex]
Cross multiply:
[tex]6 ( v - 3) = 4 ( 9 + 2v)[/tex]
Distribute:
[tex]6v - 18 = 36 + 8v[/tex]
Isolate the "v" variable:
[tex]6v - 18 + 18 = 36 + 18 + 8v[/tex]
[tex]6v = 54+ 8v[/tex]
[tex]6v - 8v = 54+ 8v - 8v[/tex]
[tex]-2v = 54\\\\v = -27[/tex]
please help// geometry question... i will post the other picture for this question it will be under “geometry question pt.2”
Answer:
a) E
b) line segment AB
Step-by-step explanation:
a) E
b) line segment AB (It's AB with the line over it - no arrowheads)
Answer:
a)e
b)a
c)e
Step-by-step explanation:
Solve the compound - 20 ≤ 2x - 20 ≤ 10
Answer:
0≤ x ≤ 15
Step-by-step explanation:
- 20 ≤ 2x - 20 ≤ 10-20 + 20 ≤ 2x - 20 + 20 ≤ 10 + 20 ⇒ add 200 ≤ 2x ≤ 30 ⇒ divide by 20≤ x ≤ 15 ⇒ answeror x = [0,15]
Cheryl thinks that the
following expressions are
equivalent:
3x + 3 = 3 + 3x + 0
Is Cheryl right? If so,
prove that these two
expressions are
equivalent. If not, what
error(s) did Cheryl make?
Answer:
yes she is right
Step-by-step explanation:3x + 3 is the same as 3 + 3x.
the zero adds nothing to the 3x term. So this means that 3x +3 and 3 + 3 are the same.
i hope this helps you.
find the value of x and y if y-2x=3 and x+y=3
Answer:
x= 0 y = 3
Step-by-step explanation:
i hope it helped u!!
Combining liked terms. Solve these, please. 1. -6k+7k 2. 12r-8-12 3. n-10+9n-3 4. -4x-10x
Answer: 1: k 2: 12r-20 3: 10n-13 4: -14x
Step-by-step explanation:
** uestion number 2
A hardware store buys a hammer at a cost of
$6.00. The selling price of the hammer is
$12.00
The amount of markup is - and the
percent of markup based on selling price
rounded to two decimal places is
Hint: Use the formulas: Markup Selling
Price - Cost, and
Percent of Markup based on a re
Selling Price
Answer:
12 - 6 = $6 markup
marked up 200% (i think) because it is sold at twice the amount of bought price
The ratio of fiction to nonfiction books in a classroom library is 2 to 3 . If there are 24 books nonfiction books in the classroom library , how many fiction books are there?
Answer:
16Step-by-step explanation:
Given the ratio of fiction to nonfiction books in a classroom library is 2 to 3, then the total ratio of both books will be 2+3 = 5. If there are 24 books non fiction books in the library, to get the amount of fictionbooks that are there we will follow the following steps.
First we will calculate the total number of books in the shelf;
3/5 * Total number of books = total non fiction books
3/5 * Total number of books = 24
3*Total number of books = 5*24
3*Total number of books = 120
Total number of books = 120/3
Total number of books = 40
Therefore there are 40 total of books on the shelf.
Total number of fiction books = 2/5 * 40
Total number of fiction books = 2* 8
Total number of fiction books = 16 books
Hence there are 16 fiction books on the shelf.
match each statement to the reasons given for the geometric proof. Part 2
Answer: 5, 3, 2, 4, 1
Step-by-step explanation:
The proof should be written as follows:
Statement Reason
1. ABCD is a parallelogram 1. Given
2. AB||CD and AC||BD 2. Definition of a parallelogram
3. ∠EBD ≅ ∠CAB and ∠FAC ≅ ∠ABD 3. Corresponding Angles Thm
4. ∠EBD ≅ ∠CDB and ∠ACD ≅ ∠FAC 4. Transitive Property of Cong
5. ∠CDB ≅ ∠CAB and ∠ACD ≅ ∠ABD 5. Alternate Interior Angles Thm
This is the order provided in your question:
5. ∠CDB ≅ ∠CAB and ∠ACD ≅ ∠ABD 5. Alternate Interior Angles Thm
3. ∠EBD ≅ ∠CAB and ∠FAC ≅ ∠ABD 3. Corresponding Angles Thm
2. AB||CD and AC||BD 2. Definition of a parallelogram
4. ∠EBD ≅ ∠CDB and ∠ACD ≅ ∠FAC 4. Transitive Property of Cong
1. ABCD is a parallelogram 1. Given
Note: #2 & #4 might be reversed
5/4 * 6/7 Multiply. Write your answer as a fraction in simplest form. Thank you btw
Answer: 59/28
Step-by-step explanation: 59/28
What is I need it fast 3/4x = -18
Answer:
x=-24
Step-by-step explanation:
i looked it up
Answer:
X = - 1
24
Step-by-step explanation:
Solution,
3/4x = -18
or, 3/4x = -18/1
or, 3*1 = 4x*(-18) [ cross multiplication ]
or, 3 = -72x
or, -72x = 3
or, x = 3/(-72)
or, x = - 1 [ Answer ]
24
Find the indicated function for f(x) = x^2 + 3x -1 and g(x) = 3x . Question
1. (f +g) (x) =
Answer:
Step-by-step explanation:
x^2 + 3x - 1 + 3x
x^2 + 6x - 1 is the solution
What is the area of this figure? 15 yd 4 yd 7 yd 25 yd 21 yd 22 yd
Answer:
45
Step-by-step explanation:
FIND THE VALUE OF X2 FOR 20 DEGREES OF FREEDOM AND AN AREA OF .010 IN THE RIGHT TAIL OF THE CHI SQUARE
Answer:
The critical value of chi-square for 20 degrees of freedom and 0.01 level of significance is 37.57.
Step-by-step explanation:
We have to find the value of chi-square for 20 degrees of freedom an area of 0.01 in the right tail of the chi-square.
As we know that in the chi-square table; there is one vertical column represented by 'P' (the level of significance and one horizontal column represented by '[tex]\nu[/tex]' which is degrees of freedom.
Here, the degrees of freedom given to us is 20.
and the level of significance is 0.01 or 1% for the right tail of chi-square.
By looking at the chi-square table, the critical value of chi-square for 20 degrees of freedom and 0.01 level of significance is 37.57.
Suppose you toss 6 coins. What is the probability that 3 of the coins are heads and 3 of the coins are tails
Answer:
12, either it will happen or it won't. It is true that each sequence of heads and tails is equally likely to occur – with probability 164, in this case. However, the number of those sequences having exactly three heads is not 32, but (63)=20, which leads to the correct answer of 516.
Step-by-step explanation:
Answer: 50%
Step-by-step explanation: Because the likelyhood would be as likely as not then that would be half of 100, or 50%
Determine whether the statement is true or false. 12∈{18,17,15,13,12}
Answer:
True
Step-by-step explanation:
12 is the last element of the given set. The statement that it is an element of the set is true.