The distance between (-4,3,-6) and the origin is [tex]\sqrt{61[/tex]
How to determine the distance?The point is given as:
(x, y, z) = (-4,3,-6)
The origin is
(x, y, z) = (0,0,0)
The distance between the point and the origin is calculated as:
[tex]d = \sqrt{x^2 + y^2 + z^2[/tex]
So, we have:
[tex]d = \sqrt{(-4)^2 + (3)^2 + (-6)^2[/tex]
Evaluate
[tex]d = \sqrt{61[/tex]
Hence, the distance between (-4,3,-6) and the origin is [tex]\sqrt{61[/tex]
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Given: x is the midpoint of MN¯¯¯¯¯¯¯¯¯¯ and MX=RX
Prove: XN=RX
A midpoint of a line segment implies a point on the line that is equidistant to its two ends. So that the required proof is shown below:
Given: line segment MN
x, the midpoint of MN
MX = RX
Then;
MX = XN (midpoint property of a line)
So that,
MN = MX + XN
= MX + MX (since XN = MX)
MN = 2MX
Thus,
MX = XN = RX (given that MX = RX)
Therefore, it can be concluded that;
XN = RX
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If a soccer team made 28 penalty shots out of 100, what fraction and what
percentage of penalty shots did the team miss? Choose two answers.
Which statement about the function represented by this graph is true? A curve rises from (0, 2), (2, 3 point 9), (4, 4), (5, 4 point 1), (6, 4 point 9), (8, 5), (9, 5), and (10, 5) on the x y coordinate plane. A. The function has an inverse because it passes the vertical line test. B. The function does not have an inverse because it does not pass the horizontal line test. C. The function does not have an inverse because it never crosses the x-axis. D. The function has an inverse because it passes the horizontal line test.
The true statement about the function which is represented by this graph is: D. the function has an inverse because it passes the horizontal line test.
What is the horizontal line test?The horizontal line test states that if the graph of function (f) is intersected by any horizontal line more than once, then, the function (f) doesn't have an inverse.
Conversely, if the graph of function (f) isn't intersected by any horizontal line more than once, then, the function (f) has an inverse.
By critically observing the graph of the given function (f) shown in the image attached below, we can logically deduce that it has an inverse because it passed the horizontal line test.
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Answer: D. The function has an inverse because it passes the horizontal line test.
Step-by-step explanation:
Got it right on test.
A pole that is 2.8 tall casts a shadow that is 1.79 long. At the same time, a nearby building casts a shadow that is 42.25 long. How tall is the building? Round your answer to the nearest meter.
Answer:
The building is around 47 meters tall
Step-by-step explanation:
Pole:
tall/long
2.8/1.79
Building:
tall/long
x/42.25
Solve for x:
2.8/1.79 = x/42.25
1.79x = 84.5
x ≈ 47
Find NM=
Help me please thanks
A triangle is a three-edged polygon with three vertices. The length of the side MN is 3 cms.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
The triangle formed by MN, MO, NO is an equilateral triangle, with the length of each side of the triangle equal to the radius of the triangle. Therefore, the length of MN will be,
MN = r
Now, the length of arc MN can be written as,
2 × π × r × (60° /360°) = π
r = 360 / (60 × 2)
r = 3
Hence, the length of the side MN is 3 cms.
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I need help pls WILL GIVE BRAINLIEST
Answer: (1, -3)
Step-by-step explanation:
[tex]8x+4y=-4\\-4x-5y=11[/tex]
[tex]2(-4x-5y)=11(2)\\-8x-10y=22[/tex]
new system:
[tex]8x+4y=-4\\-8x-10y=22[/tex]
add.
[tex]-6y=18\\y=-3[/tex]
plug in -3 for y
[tex]8x+4(-3)=-4\\8x-12=-4\\8x=8\\x=1[/tex]
system:
[tex](1,-3)[/tex]
Answer:
Make one of the variable in one of the equations the subject of the formular first.[tex]4y = - 4 - 8x[/tex]to leave y independent divide the whole equation by the coefficient of y at this point it is 4.Then divided the whole equation by 4.[tex] \frac{4y}{4} = \frac{ - 4}{4} - \frac{8x}{4} [/tex]therefore the new equation will be[tex]y = - 1 - 2x....(3)[/tex]substitute the new equation in the other equation N.B not the one you extracted the new equation from.you will use -4x-5y=11 in substituting y=-1-2y[tex] - 4x - 5( - 1 - 2x) = 11 \\ - 4x + 5 + 10x= 11 \\ \\ - 4x + 10x = 11 - 5 \\ 6x = 6 \\ \frac{6x}{6} = \frac{6}{6} \\ x = 1[/tex][tex]y = - 1 - 2(1) \\ y = - 1 - 2 \\ y = - 3[/tex]HOPE THIS HELPS!Solve the following proportion by cross multiplying:
x / 8 = 28 / 32
Answer: x = 7
Step-by-step explanation:
[tex]\frac{x}{8} =\frac{28}{32}[/tex]
We cross multiply, and we get:
32x = 8(28)
32x = 224
x = 7
Select the correct answer.
Which function is the inverse of function f if the domain of f is ?
The inverse function of f(x) is [tex]f^{-1}(x) = \sqrt{x - 6}[/tex] and the domain is x > 6
How to determine the inverse function?The function is given as:
f(x) = x^2 + 6
Rewrite as:
y = x^2 + 6
Swap x and y
x = y^2 + 6
Subtract 6 from both sides
y^2 = x - 6
Take the square root
[tex]y = \sqrt{x - 6}[/tex]
Rewrite as:
[tex]f^{-1}(x) = \sqrt{x - 6}[/tex]
Hence, the inverse function of f(x) is [tex]f^{-1}(x) = \sqrt{x - 6}[/tex] and the domain is x > 6
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Geoffrey is evaluating the expression
(-3)³(26) (2)
(-3) 5 (2²) (-3)*
C
-99
What are the values of a, b, c, and d?
O a=4, b=2, c= 16, d=9
O a=4, b= -2, c=16, d=9
O a=8, b= 8, c= 256, d=6,561
O a=8, b=8, c= 256, d=-6,561
(-3)³ (26)
(-3) (2²)
as shown below.
Answer: The values are a = 4, b = 2, c = 16, d = 9
simplified further
c = 16
d = 9
Hello, i am having a hard time solving this. If anyone can please explain how to solve it in order for me to solve future questions of the same type?
f(x) = 5x3 – 2x and g(x) = 3x3
perform the following :
f(g(x))
g(f(x))
----- Thank you for your help
Answer:
Step-by-step explanation:
PLEASE HELP
Which is the simplified form of the expression
The simplified form of the expression ( (2⁻²)(3⁴) )⁻³ × ( (2⁻³)(3²) )² is [tex]\frac{1}{3^8}[/tex].
Hence, option B is the correct answer.
What is the simplified form of the expression?Given the expression;
( (2⁻²)(3⁴) )⁻³ × ( (2⁻³)(3²) )²
First, we use the properties of exponents.
( 2⁻²ˣ⁻³ × 3⁴ˣ⁻³ ) × ( 2⁻³ˣ² × 3²ˣ² )
( 2⁶ × 3⁻¹² ) × ( 2⁻⁶ × 3⁴ )
We take out the parentheses, such that;
2⁶ × 2⁻⁶ × 3⁻¹² × 3⁴
Note that: 2⁶ × 2⁻⁶ = 1, as [tex]2^6*2^{-6}=2^{6+(-6)}=2^0=1[/tex]
Hence, we have
1 × 3⁻¹² × 3⁴
3⁻¹²⁺4
3⁻⁸
Next, we express with positive exponent
[tex]\frac{1}{3^8}[/tex]
The simplified form of the expression ( (2⁻²)(3⁴) )⁻³ × ( (2⁻³)(3²) )² is [tex]\frac{1}{3^8}[/tex].
Hence, option B is the correct answer.
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Solve for x : log(3x) + log(x + 4) = log(15).
Please explain it to me.
Answer:
x = 1
Explanation:
[tex]\sf \rightarrow log(3x) + log(x + 4) = log(15)[/tex]
Rule: log(a) + log(b) = log(ab)
[tex]\sf \rightarrow log(3x(x + 4)) = log(15)[/tex]
cancel out log on both sides
[tex]\sf \rightarrow 3x(x + 4) = 15[/tex]
relocate constant variable
[tex]\sf \rightarrow 3x^2 + 12x -15 = 0[/tex]
take 3 as a common factor
[tex]\sf \rightarrow 3(x^2 + 4x -5) = 0[/tex]
divide both sides by 3
[tex]\sf \rightarrow x^2 + 4x -5 = 0[/tex]
middle term split
[tex]\sf \rightarrow x^2 + 5x -x-5 = 0[/tex]
factor common terms
[tex]\sf \rightarrow x(x + 5) -1(x+5)= 0[/tex]
collect into groups
[tex]\sf \rightarrow (x-1)(x+5)= 0[/tex]
set to zero
[tex]\sf \rightarrow x-1 = 0 , \ x+5= 0[/tex]
relocate variables
[tex]\sf \rightarrow x = 1, \ x = -5[/tex]
There must be a positive solution for log, so the solution is only x = 1
Answer:
[tex]x=1[/tex]
Step-by-step explanation:
Given:
[tex]\log (3x)+\log(x+4)=\log (15)[/tex]
As the logs have no base, assume that the base is 10.
[tex]\textsf{Apply log Product law}: \quad \log_ax + \log_ay=\log_axy[/tex]
[tex]\implies \log_{10} (3x)+\log_{10}(x+4)=\log_{10} (15)[/tex]
[tex]\implies \log_{10} \left(3x(x+4)\right)=\log_{10} (15)[/tex]
Expand the brackets:
[tex]\implies \log_{10} \left(3x^2+12x\right)=\log_{10} (15)[/tex]
[tex]\textsf{Apply the log Equality law}: \quad \textsf{if }\: \log_ax=\log_ay\:\textsf{ then }\:x=y[/tex]
[tex]\implies 3x^2+12x=15[/tex]
Subtract 15 from both sides:
[tex]\implies 3x^2+12x-15=0[/tex]
Factor out the common term 3:
[tex]\implies 3(x^2+4x-5)=0[/tex]
Divide both sides by 3:
[tex]\implies x^2+4x-5=0[/tex]
Split the middle term:
[tex]\implies x^2+5x-x-5=0[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies x(x+5)-1(x+5)=0[/tex]
Factor out the common term (x + 5):
[tex]\implies (x-1)(x+5)=0[/tex]
Therefore:
[tex]x-1=0 \implies x=1[/tex]
[tex]x+5=0 \implies x=-5[/tex]
As logs cannot be taken of negative numbers, [tex]x=-5[/tex] is an extraneous solution. Therefore, the only valid solution is: [tex]x=1[/tex]
Which of the following is not a true bi-conditional statement?
A. A quadrilateral is a square if and only if it has 4 congruent sides and 4 right angles.
B. Jane goes to the beach if and only if it is a sunny day.
C It is the weekend if and only if today is Saturday or Sunday.
D A number is even if and only if it is divisible by two.
Jane goes to the beach if and only if it is a sunny day.
========================================================
Reason:
A regular conditional statement is in the form "If P, then Q" where P and Q are placeholders for other statements.
For example, we can replace "P" with "it rains" and replace "Q" with "the grass gets wet". This means "If P, then Q" becomes "If it rains, then the grass gets wet".
It's hopefully clear that the example above is a one way street. It points in only one direction. The act of raining leads directly to the grass being wet. However, we cannot go in reverse. If we see the grass is wet, it doesn't mean it rained. Perhaps someone turned on a hose or sprinkler system. P leads to Q, but Q does not lead to P.
In short, all of what is mentioned so far is considered a regular conditional statement. So far we haven't addressed bi-conditional statements.
----------------
Bi-conditional statements are conditionals that work in reverse.
An example would be "If a figure is a square, then it has 4 congruent sides and 4 right angles". That conditional statement works in reverse. Therefore "If a figure has 4 congruent sides and 4 right angles, then the figure is a square" is also true simply by what it means to be a square.
So the format "If P, then Q" can be reversed to "If Q, then P" to have an equivalently true statement. The common practice is to use "if and only if" to help shorten things.
We would have the template "P if and only if Q" which is the same as "Q if and only if P". The order doesn't matter since we can reverse things just fine.
Often you'll find bi-conditional statements when it comes to definitions. The term "weekend" literally means the day is either Saturday or Sunday, which is why choice C is another bi-conditional. A very similar situation applies to choice D as well.
--------------------
We've found that choices A, C and D are bi-conditional statements. They can be ruled out. We're left with choice B.
This is not a bi-conditional. Why not? It's assumed that Jane would go to the beach on a sunny day, but perhaps she enjoys the beach just fine on cloudy days. There's also the fact she could be doing other things on sunny days. The presence of the sun doesn't automatically mean the beach. If you said "It gets warm if and only if it's a sunny day", then I think this is more in line with a bi-conditional.
This is why choice B is the final answer.
HELP HELP HELP HELP
HELP HELP HELP
Answer: The base should be 4.
Step-by-step explanation:
1. We draw a triangle shape like the image.
(The steps was showed in the image).
3/4(2/3 + 4/3) - 9 / 1/2 x 1/3
a. -52 1/2
b. - 5 1/4
c. - 4 1/2
d. -4 7/9
Answer: a. -52 1/2
Step-by-step explanation:
Given:
3/4(2/3 + 4/3) - 9 / 1/2 x 1/3
[tex]\displaystyle \frac{3}{4}(\frac{2}{3} +\frac{4}{3} )-\frac{9}{\frac{1}{2} *\frac{1}{3} }[/tex]
Add and multiply:
[tex]\displaystyle \frac{3}{4}(\frac{6}{3} )-\frac{9}{\frac{1}{6} }[/tex]
Simplify and divide:
[tex]\displaystyle \frac{3}{4}(2 )-54[/tex]
Multiply:
[tex]\displaystyle 1.5-54[/tex]
Subtract:
a. -52 1/2
Question is in the picture, please help.
Answer:
1)The equation is 3^N, where N starts at 4 and goes down 1 each time
2) 1 would be the 5th term
Step-by-step explanation:
3^4=81
3^3=27
3^2=9
3^1=3
3^0=1
two cyclists leave towns 74 miles apart at the same time and travel towards each other. one cyclist travels 3 mi/h faster than the other. If they meet in 2 hours, what is the rate of each cyclist?
The rates of each cyclist are 17mi/h and 20mi/h
What is rate?
Rate is a ratio that compares two different quantities which have different units.
In this comparison, one unit is taken to be a standard unit in which the other is compared with.
Analysis:
Let the speeds of both cyclists be x, x+3
distance travelled by x cyclist = 2x
distance travelled by (x+3) cyclist = 2(x+3)
Total distance = 2x + 2(x+3) = 74 miles
2x +2x +6 = 74
4x + 6 = 74
4x = 74 - 6
4x = 68
x = 68/4 = 17mi/h
The other cyclist speed is x +3 = 17 +3 = 20mi/h
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Simplify the following expression
Answer:
-ab^2
Step-by-step explanation:
7b^2a - 5b^2a - 3ab^2
= 2b^2a - 3ab^2
= (2 × b^2 × a) - (3 × a × b^2)
= -ab^2
b^2a and ab^2 is the same thing. hope it helps!
What is the sum of the polynomials?
(6x+7+x²)+(2x²-3)
O-x²+6x+4
O3x²+6x+4
O9x + 4
O gx² +4
Answer:
3x² + 6x + 4
Step-by-step explanation:
6x + 7 + x² + 2x² - 3
→ Collect like terms
x² + 2x² + 6x + 7 - 3
→ Simplify
3x² + 6x + 4
Answer:
3x^2+6x+4
Step-by-step explanation:
We can find the sum of the polynomials by combining like terms.
(6x+7+x²)+(2x²-3)
x^2+2x^2+6x+7-3
3x^2+6x+4
24. A pizzeria sells a medium pizza for $5.99 plus $0.75 for each topping.
They also sell a large pizza for $6.99 plus an additional $0.50 per topping.
After how many toppings will the medium and large pizzas cost the same
amount?
The pizzas will cost the same at 4 toppings.
The pizzas will cost the same at 5 toppings.
The pizzas will cost the same at 6 toppings.
The pizzas will never cost the same amount.
Answer:
a.) The pizzas will cost the same at 4 toppings
Step-by-step explanation:
Medium Pizza:
$5.99 + $0.75x
Large Pizza:
$6.99 + $0.50x
Find x
$5.99 + $0.75x = $6.99 + $0.50x
0.25x = 1
x = 4
Complete the following chart below.
FIll in the missing blanks.
[tex]y=2(x+1)^2+6[/tex]
The vertex (−1,6)
Equation of axis of symmetry is x = -1
minimum at (-1,6)
[tex]y=\frac{-(x-1)}{2} ^2-4[/tex]
The vertex (1,-4)
Equation of axis of symmetry is x = 1
maximum at (1,-4)
What is graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
[tex]y=2(x+1)^2+6[/tex]
The vertex (−1,6)
Equation of axis of symmetry is x = -1
minimum at (-1,6)
[tex]y=\frac{-(x-1)}{2} ^2-4[/tex]
The vertex (1,-4)
Equation of axis of symmetry is x = 1
maximum at (1,-4)
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A group of marketing students at a large university wants to determine the proportion of first year students who use certain types of social media. The students want their estimate to be within 0.03 of the true proportion with a 95% level of confidence. Two years ago, a similar study determined the proportion to be 0.796. How large of a sample is required
The required sample size is 694.
Given a student wants to make a guess within 0.03 of the true ratio with a 95% confidence level.
Margin of Error, E = 0.03
significance level α=0.05 {95% confidence}
A given estimate of the percentage of population p is p = 0.79.
The critical value for the significance level α = 0.05 is Zc = 1.96. This can be determined using either Excel or a normal probability table.
Use the following formula to calculate the minimum sample size required to estimate the percentage of population p within the required margin of error.
n≥p(1-p)(Zc÷E)²
n=0.796×(1-0.796)(1.96÷0.03)²
n=693.1016
Therefore, the resample sizequired to meet the condition is n ≥ 693.1016 and must be an integer. From this, we conclude that the minimum sample size required is n = 694.
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alison, beatrice and chole each had some books. alison gave beatrice and chole some books that doubled the number of books they had, lastly chole gave alison and beatrice some books that doubled the number of books they had. each of them had 32 books at the end. how many books did each of them have at first?
alison, beatrice and chole each of them have at first 56, 8, 32 books.
alison, beatrice and chole each had some books. alison gave beatrice and chole some books that doubled the number of books they had, lastly chole gave alison and beatrice some books that doubled the number of books they had. each of them had 32 books at the end.
What is Working backward?Working backward is process in which calculation done in reverse direction.
let alison, beatrice and chole has x,y and z books initially,
alison gave beatrice and chole some books that doubled the number of books they had
alison, beatrice and chole has (96-2y-2z), (2y) , (2z)
chole gave alison and beatrice some books that doubled the number of books they had. each of them had 32 books at the end.
alison, beatrice and chole has 2(96-2y-2z), 2(2y) , (96-2(96-2y-2z)-4y)
at the end,
beatrice = 32
4y=32
y = 8
chole =32
96-2(96-2y-2z)-4y)=32
z=32
alison = 96-y-z
x=96-8-32
x=56
Thus the required alison, beatrice and chole each of them have at first 56, 8, 32 books.
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What value of k makes the statement true?
x² (2x³ + 7x²yª) = 2xªyª + 7x³y8?
By apply the distributive property of multiplication, the value of k which makes the statement true is 1.
What is the distribution property?Mathematically, the distributive property of multiplication is given by tis expression:
x(y + z) = xy + xz.
Next, we would apply the distributive property of multiplication to the given equation by distributing to the left-hand side using xy⁴:
k(2x⁴y⁴ + 7x³y⁸) = 2x⁴y⁴ + 7x³y⁸
Dividing both sides by the common factor, we have:
k = (2x⁴y⁴ + 7x³y⁸)/(2x⁴y⁴ + 7x³y⁸)
k = 1.
In conclusion, the value of k which makes the statement true is 1.
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Complete Question:
What value of k makes the statement true?
[tex]x^k[/tex]y⁴(2x³ + 7x²y⁴) = 2x⁴y⁴ + 7x³y⁸
Which statements are correct? Check all that apply.
One-halfQP = UT
One-halfTS = RQ
SU = PR
SU ∥ RP
UT ⊥ RP
By applying the triangle midpoint theorem to the two triangles (see attachment), the correct statements are:
A. One-halfQP = UT
D. SU ∥ RP
What is triangle midpoint theorem?Triangle midpoint theorem states that the line segment which connects the midpoints of two (2) sides of a triangle must be parallel to the third side, and it's congruent to one-half of the third side.
By applying the triangle midpoint theorem to the two triangles (see attachment), we can infer and logically deduce that one-half of side QP is equal to side UT and side SU is parallel to side RP (SU ∥ RP).
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Complete Question:
Points S, U, and T are the midpoints of the sides of ΔPQR. ΔSUT is inside of ΔPQR. Points S, U, and T are the midpoints of ΔPQR. Which statements are correct? Check all that apply.
A. One-half QP = UT
B. One-half TS = RQ
C. SU = PR
D. SU ∥ RP
E. UT ⊥ RP
Answer: a and d
Step-by-step explanation:
write the equations after translating the graph of y = | 1/2 x -2 | + 3 one unit to the right
Using translation concepts, the equation of the graph is:
y = |0.5x - 2.5| + 3.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The function is:
y = |0.5x - 2| + 3.
When it is shifted one unit to the right, we have that x -> x - 1, hence:
y = |0.5(x - 1) - 2| + 3
y = |0.5x - 2.5| + 3.
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One evening 1500 concert tickets were sold for the fair mount jazz festival. tickets cost 20 for covered pavilion seats and $10 for lawn seats total receipts were 23,000 how many tickets of each were sold
A total of 800 tickets for the covered pavilion and 700 tickets for lawn seats were sold, solved using a system of equations.
We assume the number of covered pavilion tickets sold to be x and the number of lawn seat tickets sold to be y.
As a total of 1500 tickets were sold, we can form an equation:
x + y = 1500 ... (i),
as we had only those two types of tickets.
The cost of each covered pavilion ticket = $20.
Hence, the total revenue from covered pavilion tickets = $20x.
The cost of each lawn seat ticket = $10.
Hence, the total revenue from lawn seat tickets = $10y.
The total receipts were said to be $23,000.
Thus, we can represent this as an equation:
20x + 10y = 23000 ...(ii).
Combining (i) and (ii), we get a system of equations:
x + y = 1500 ... (i).
20x + 10y = 23000 ... (ii).
Dividing equation (ii) by 10, we get:
2x + y = 2300 ... (iii).
Subtracting (i) from (iii), we get:
2x + y = 2300.
x + y = 1500.
(-) (-) (-)
____________
x = 800.
Substituting x = 800 in (i), we get:
x + y = 1500,
or, 800 + y = 1500,
or, y = 1500 - 800,
or, y = 700.
Thus, a total of 800 tickets for the covered pavilion and 700 tickets for lawn seats were sold, solved using a system of equations.
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What is the LCM of 24 ,40,30
Answer:
LCM(24,30,40)=120.The Least common multiple for three numbers 24,30 and 40 is 120
Step-by-step explanation:
Categorize the graph as linear increasing, linear decreasing, exponential
growth, or exponential decay.
A. Exponential decay
B. Linear increasing
C. Linear decreasing
D. Exponential growth
Answer:
B. Linear increasing
Step-by-step explanation:
decay means decreasing
exponential graph would have a curve
4 cm
A
C
If BX = 2 cm, XA = 3 cm, and BY = 3, find the value of YC.
O 5.5 cm
5 cm
B
O 45 cm
Y
4
Answer:
Step-by-step explanation:
Comment and answer
ABC is similar to XBY The triangles are similar because
B is a common angle to both<A = <BXY AB is a transversal cutting 2 parallel lines<C = <BYX BC is a transversal cutting 2 parallel linesBX = 2 Given
XA = 3 Given
BY = 3 Given
YC = x Object of question
BX/(BX + XA) = BY / (BY + YC) Parts of two similar triangles
2/(2 + 3) = 3/(3+ x) Combine the left
2/5 = 3/(3 + x) Cross Multiply
2*(3 + x) = 3*5 Remove the brackets
6 + 2x = 15 Subtract 6 from both sides
6-6+2x = 15 - 6 Combine
2x = 9 Divide by 2
2x/2 = 9/2
x = 4.5
Answer
x = 4.5 or D