Answer:
Rule is (x, y+k)
New point is (-3,9)
Step-by-step explanation:
A point translated vertically k units up means the x coordinate remains the same in the translation but the y coordinate is increased by k units
This can be represented mathematically as;
Let;s assume the point to be A with coordinates (x,y) then to get the image of the point under a vertical translation k units up you add k to the y coordinate value.
Given ;
[tex]A=(\frac{x}{y} )\\\\T=(0,k)\\\\A'=(\frac{x}{y} )+(\frac{0}{k} )=(\frac{0+x}{y+k} )\\\\A'=\frac{x}{y+k} =(x,y+k)[/tex]
where T is the translation
In the question
Given (-3,-6) and T is (0,5) the new coordinate will be
[tex]=(\frac{-3}{4}) +(\frac{0}{5} )=\frac{-3}{9} =(-3,9)[/tex]
Write this trinomial in factored form. 3b^2+b-14
Answer:
(b - 2)(3b + 7)
Step-by-step explanation:
Consider the factors of the product of the coefficient of the b² term and the constant term which sum to give the coefficient of the b- term
product = 3 × - 14 = - 42 and sum = + 1
The factors are - 6 and + 7
Use these factors to split the b- term
3b² - 6b + 7b - 14 ( factor the first/second and third/fourth terms )
= 3b(b - 2) + 7(b - 2) ← factor out (b - 2) from each term
= (b - 2)(3b + 7) ← in factored form
know factors and roots? please help me!!!!\
Answer: b) (2m³ - 4p⁵)(2m³ + 4p⁵)
Step-by-step explanation:
Use the difference of a square formula: a² - b² = (a - b)(a + b)
[tex]4m^6 - 16p^{10}\\\bullet a) \sqrt{4m^6}=2m^3\\\bullet b)\sqrt{16p^{10}}=4p^5[/tex]
(2m³)² - (4p⁵)² = (2m³ - 4p⁵)(2m³ + 4p⁵)
Use the figure above to identify a pair of similar triangles, then find the scale factor. The image is not drawn to scale.
A. HEF ~EGH with a scale factor of root 3.2.
B. HEG-GEF with a scale factor of 2:1.
C. HEF -EGF with a scale factor of root 3.1.
D. HEF -GEF with a scale factor of 3.1.
Answer:
Option C.
Step-by-step explanation:
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem triangles HEF and EGE are similar
because
[tex]EF/GF=HF/EF[/tex]
substitute the values
[tex]\frac{\sqrt{3}}{1}=\frac{3}{\sqrt{3}}\\ \\3=3[/tex]
Is true
The sides are proportional
and
∠HFE=∠GFE
∠EHF=∠GEF
∠HEF=∠EGF
The angles are congruent
The scale factor is equal to
[tex]EF/GF[/tex]
[tex]\frac{\sqrt{3}}{1}[/tex]
Answer:
Option C
Step-by-step explanation:
Two triangles are similar if they have at least 2 equal angles
Note that the HEF triangle has angles of 90 °, 60 ° and 30 °
Note that the EGF triangle has angles of 90 ° and 30 ° so the third angle must be 60 °
Then HEF and EGF are similar triangles.
By definition for similar triangles it is satisfied that if they have sides of length a, b, c and a ', b' c' then
[tex]\frac{a}{a'}=\frac{b}{b'}=\frac{c}{c'}=k[/tex]
Where the constant k is known as "scale factor"
In this case
[tex]\frac{HF}{EF}=\frac{HE}{EG}=\frac{FE}{GF}=k[/tex]
[tex]k=\frac{3}{\sqrt{3}}=\frac{2\sqrt{3}}{2}=\frac{\sqrt{3}}{1}=\sqrt{3}[/tex]
[tex]\frac{FE}{GF}=\frac{\sqrt{3}}{1}[/tex]
or
[tex]\sqrt{3}:1[/tex]
The answer is Option C
At a store, the probability that a customer buys socks is 0.15. The probability
that a customer buys socks given that the customer buys shoes is 0.20.
Which statement is true?
O
A. Buying socks and buying shoes are dependent events.
O
B. The probability that a customer buys socks and shoes is 0.05.
C. Every customer who buys shoes also buys socks.
D. Buying socks and buying shoes are independent events.
Answer:
A. Buying socks and buying shoes are dependent events.
Step-by-step explanation:
We are given that
The probability that a customer buys socks ,P(A)=0.15
The probability that a customer socks given that the customer buys shoes P(A\B)=0.20
The probability that a customer buys shoes,P(B)=1-0.15=0.85
By using formula P(E')=1-P(E)
Where P(E)= Probability of an event that is happened
P(E')=Probability of an event that is not happened
We have to find [tex]P(A\capB)[/tex] for two events
[tex]P(A)\cdot P(B)[/tex]
[tex]=0.85\times 0.15=0.1275[/tex]
We know that conditional probability of an event when given that the probability of an event B is given
[tex]P(\frac{A}{B})=\frac{P(A\cap B)}{P(B)}[/tex]
[tex] 0.20=\frac{P(A\cap B)}{0.85}[/tex]
[tex]P(A\cap B)=0.20\times 0.85=0.17[/tex]
[tex]P(A\cap B)\neq P(A)\cdot P(B)[/tex].
Therefore, the two events are dependent .Hence, Buying socks and buying shoes are dependent events.
Therefore, option A is true.
Answer: A. Buying socks and buying shoes are dependent events.
Step-by-step explanation:
Solve the inequality.
x – 1 ≤ – 9
Answer:
[tex]X\leq -8[/tex]
This solution provides a step-by-step explanation to solve the inequality x – 1 ≤ -9, which results in the solution x ≤ -8. This solution indicates that all numbers x that are less than or equal to -8 will satisfy this inequality.
Explanation:To solve the given inequality x – 1 ≤ – 9, you should first isolate the variable on one side of the inequality:
Add 1 to both sides. This will cancel out the -1 on the left side of the inequality, and therefore, the inequality becomes: x ≤ -9 + 1.Then, simplify the right side by combining the constants, which results in: x ≤ -8.So, the solution to the inequality is x ≤ -8, which means all numbers x that are less than or equal to -8 will satisfy this inequality.
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Pablo wants to save $800 to buy a TV. He saves $19 each week. The amount, A (in dollars), that he still needs after
weeks is given by the following function.
A(w) = 800-19 w
Answer the following questions.
(a) How much money does Pablo still need after 6 weeks?
si )3
(b) If Pablo still needs $477, how many weeks has he been saving?
I weeks
Answer:
a) $686
b) 17 weeks
Step-by-step explanation:
a) Set [tex]w=6[/tex], as Pablo has already saved for 6 weeks. Plug in the value and solve for [tex]A(6)[/tex].
[tex]A(w)=800-19w[/tex]
[tex]A(6)=800-19(6)[/tex]
[tex]A(6)=800-114[/tex]
[tex]A(6)=686[/tex]
Pablo still needs $686.
b) Set [tex]A(w)=477[/tex], as it is the "final amount" for that week. Solve for [tex]w[/tex].
[tex]A(w)=800-19w[/tex]
[tex]477=800-19w[/tex]
[tex]-323=-19w[/tex]
[tex]w=17[/tex]
Pablo has been saving for 17 weeks if he still needs $477.
Answer:
Pablo wants to save $800 to buy a TV.
He saves $19 each week.
The amount, A (in dollars), that he still needs after weeks is given by the following function.
[tex]A(w)= 800-19w[/tex]
(a) How much money does Pablo still need after 6 weeks?
Putting w = 6 in the equation;
[tex]A(6)= 800-19(6)[/tex]
= $686
(b) If Pablo still needs $477, how many weeks has he been saving?
This means Pablo has already saved [tex]800-477=323[/tex] dollars
Means he has saved for [tex]\frac{323}{19}=17[/tex] weeks.
He has been saving for 17 weeks now.
if m^-3=64, then 8m=
Answer:
The value of 8m is 2
Step-by-step explanation:
step 1
Find the value of m
we know that
[tex]m^{-3} =64[/tex]
so
[tex]\frac{1}{m^{3}}=64\\ \\m^{3}=\frac{1}{64}\\ \\ m=\frac{1}{\sqrt[3]{64}}\\ \\m=\frac{1}{4}[/tex]
step 2
Find the value of 8m
[tex]8m=8(\frac{1}{4})=2[/tex]
The graph of f(x) = 2x + 3 shifts 10 units to the right when it is replaced with the graph of f(x) = 2x − k. What is the value of k?
ANSWER
[tex]k = 17[/tex]
EXPLANATION
The given function is
[tex]f(x) = 2x + 3[/tex]
The translation that shifts this function 10 units to the right is
[tex]f(x - 10)[/tex]
This implies that
[tex]f(x - 10) = 2(x - 10) + 3[/tex]
We expand the parenthesis to get:
[tex]f(x - 10) = 2x -20+ 3[/tex]
[tex]f(x - 10) = 2x - 17[/tex]
Comparing this equation with
[tex]f(x) = 2x - k[/tex]
we have
[tex]k = 17[/tex]
k=17
The new function would be f(x)=2x-17
In the previous function when u put x=0 you got 3.
Now when the function moves 10 units to the right you still have to get y=3 for x=10. So
2x-k=3 substitute 10 for x
20-k=3 solve for k
K=17.
Which function has a range of {yly < 5}?
f(x) = (x - 4)^2 +5
f(x) = -(x-4)^2 + 5
f(x) = (x - 5)^2 + 4
f(x) = -(x – 5)^2 + 4
Answer:
f(x) = -(x-4)^2 + 5
Step-by-step explanation:
The function [tex]f(x) = -(x-4)^2 + 5[/tex] is a quadratic function. Its graph looks like a parabola. The graph has a vertex of (4,5) and opens up downward.
Proving that [tex]f(x) = -(x-4)^2 + 5 \le 5[/tex] for all x:
[tex]x^2 \ge 0 \Rightarrow (x-4)^2 \ge 0 \Rightarrow -(x-4)^2 \le 0 \Rightarrow -(x-4)^2 + 5 \le 5.[/tex]
The function which has a range of {y | y < 5} is f(x) = -(x – 5)² + 4.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given a range of the function, {y | y < 5}.
We want to find the corresponding function.
The range of the function contains all the values less than 5.
For the first two functions, when we substitute x = 4,
The value of the function, f(x) = 5
So this is not possible.
For the third function also, when we substitute any integers other than 5, the value of function is greater than 5.
Hence the correct option is D.
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What are the domain and range of the function f(x)=-square root x+3-2?
For this case we have the following function:
[tex]f (x) = - \sqrt {x + 3} -2[/tex]
By definition, the domain is given by all the values for which the function is defined.
The given function is no longer defined if the argument of the root is negative. So:
[tex]x + 3 \geq0\\x \geq-3[/tex]
Thus, the domain of the function is given by all the values of x greater than or equal to -3.
Domain: [-3, ∞)
Substituting the values of the domain, we find the range.
[tex]f (-3) = - \sqrt {-3 + 3} -2 = -2[/tex]
The function evaluated in ∞ gives -∞. So the range is given by:
(-∞, 2]
Answer:
Domain: [-3, ∞)
Range: (-∞, 2]
The answer for this equation is C.
What is the surface area of the right cone below? Thanks!!
[tex]A=\pi r(r+l)\\r=4\\l=13\\\\A=\pi \cdot 4(4+13)=4\pi \cdot 17=68\pi[/tex]
The question appears to be about finding the surface area of a cone, but the provided information discusses a concave mirror instead, which is not relevant for the surface area calculation of a cone.
Explanation:The question asks for the surface area of a right cone. However, the information provided pertains to the cross-sectional area of a concave mirror that is a quarter-section of a cylinder and not a cone. To find the surface area of a cone, one would use the formula A = πrs + πr^2 where r is the radius of the base and s is the slant height of the cone. In the given text, the radius of the mirror is mentioned to be 80.0 cm, and the insolation is 900 W/m². This data seems to be mistakenly provided instead of the cone's dimensions and is irrelevant for calculating the surface area of a cone.
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Chau is saving money to buy a game. The game cost $20, and so far he has saved four-fifths of this cost. How much money has Chau saved?
Answer:
16
Step-by-step explanation:
You need to multiply 4/5 * $20 = $16
what is the slope of the line shown below?
Answer:
it is 2
Step-by-step explanation:
Hello There!
The slope of this line would be 3.
The slope is gradually increasing so starting from the Y intercept value, its consistently going up 3 on the Y axis and going over 1 on the X axis
which of the following steps were applied to ABCD to obtain A’B’C’D’?
a- shifted 2 units right and 3units up.
b- shifted 2 units right and 4 units up.
c- shifted 3 units right and 4 units up.
d- shifted 3units right and 2 units up.
Answer:
c- shifted 3 units right and 4 units up
Step-by-step explanation:
In this problem, we have a quadrilateral named as ABCD. Recall that a quadrilateral is a two-dimensional shape having four sides. So, we need to identify what transformation has been performed to get A'B'C'D', which is the same quadrilateral shifted certain units right and up. So take one point, say, B, so how do we need to do to obtain point B'? well, we need to move that point 3 units right and 4 units up, but how can we know this? just count the number of squares you need to move from B to B' horizontally and vertically, which is in fact 3 units right and 4 units up.
Answer: The correct option is
(c) shifted 3 units right and 4 units up
Step-by-step explanation: We are given to select the correct steps that were applied o ABCD to obtain A'B'C'D' as shown in the figure.
From the graph, we note that
the co-ordinates of the vertices of quadrilateral ABCD are A(2, 3), B(4, 8), C(6, 8) and D(8, 3).
And, the co-ordinates of the vertices of quadrilateral A'B'C'D' are A'(5, 7), B'(7, 12), C'(9, 12) and D'(11, 7).
So, the transformations from the vertices of ABCD to the vertices of A'B'C'D' are as follows :
A(2, 3) ⇒ A'(5, 7) = (2+3, 3+4),
B(4, 8) ⇒ B'(7, 12) = (4+3, 8+4),
C(6, 8) ⇒ C'(9, 12) = (6+3, 8+4),
D(8, 3) ⇒ D'(11, 7) = (8+3, 3+4).
Therefore, the required rule of translation from ABCD to A'B'C'D' is
(x, y) ⇒ (x+3, y+4). That is, 3 units right and 4 units up.
Thus, the required steps applied to ABCD to obtain A'B'C'D' are
Shifted 3 units right and 4 units up.
Option (c) is CORRECT.
The sequence 3, 5, 7, 9, ... has the explicit rule f(n)= 2n +1.
What is the third term in the sequence?
Answer:7
Step-by-step explanation:since it has the rule f(n) =2n+1
Third term is when n=3
Therefore 2(3) +1=7
What is the slope of the line through (–4, 3) and (5, 3)?
Question 16 options:
a)
0
b)
undefined
c)
1
d)
9
Answer:
slope = 0
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 4, 3) and (x₂, y₂ ) = (5, 3)
m = [tex]\frac{3-3}{5+4}[/tex] = [tex]\frac{0}{9}[/tex] = 0
The population of a small town is 2,200
and is increasing at a rate of 3% per year;
10 years. Round to the nearest whole
number.
Answer:
2957
Step-by-step explanation:
Instead of just giving you a formula.. I want to show you how to understand the formula
So 2200 is the initial population
After 1st year, we are going to have an increase of 3% so 1st yr gives us 2200(1.03)=2266
After 2nd year, we are going to have increase of 3% from previous year so we could do 2266(1.03) or realize this is the same as 2200(1.03)^2 .
so you are going to keep multiplying factors of 1.03 to that per year.
So at 10 years we have 2200(1.03)^10
The formula I mentioned was really this initial population times (1.03)^(number of yrs)
So answer is 2956.616
To the nearest whole number is 2957
a quadrilateral has 2 right angles. the measure of the third angle is 73, what is the measure of the forth angle?
Answer: 107 degrees.
Step-by-step explanation:
A quadrilateral is defined as a 2-dimensional closed shape which has four sides and four vertices.
By definition the interior angles of a quadrilateral add up 360 degrees.
We know that this quadrilateral has 2 right angles (which are angles that measure 90 degrees) and we know that the measure of the third angle is 73 degrees.
Let be "x" the measure of the fourth angle.
Then you can write this expression:
[tex]360\°=90\°+90\°+73\°+x[/tex]
And finally solve for "x":
[tex]360\°=253\°+x[/tex]
[tex]360\°-253\°=x[/tex]
[tex]x=107\°[/tex]
If f(x) = 5х + 40, what is f(x) when x=-5?
Answer:
15
Step-by-step explanation:
Substitute x = - 5 into f(x)
f(- 5) = 5(- 5) + 40 = - 25 + 40 = 15
cos x = sin 34°
What is the value of x?
Enter your answer in the box.
[tex]\bf \textit{Cofunction Identities} \\\\ sin\left(90^o-\theta\right)=cos(\theta) \qquad cos\left(90^o-\theta\right)=sin(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ cos(x)=\stackrel{90-56}{sin(\stackrel{\downarrow }{34^o})}\implies cos(\stackrel{\downarrow }{x})=sin(90^o-\stackrel{\downarrow }{56^o})\implies cos(56^o)[/tex]
There are 2 way to find value of x
cos x = sin 34°
First
Co-function identities
sin(90° -∅ ) =cos(∅) cos(90 -∅) =sin(∅)
90-56 ↓
cos(x)=sin(34°)⇒ cos (x) =sin(90°-56)⇒ cos(56°)
∴ value of x = 56°⇒ 0.5592
Second way to find value x
x = cos-1(0.5592)
This is much simpler,
cos (90 - x)= sin x
So,
90 - 34 = 56
∴ x = 56
cos(56) = 0.5592
sin(34) = 0.5592.
What is Trigonometry ?A branch of mathematics that studies relationships between side lengths and angles of triangles.
What is the exact value of sin 34?Sin 34 degrees is the value of the sine trigonometric function for an angle equal to 34 degrees. The value of sin 34° is 0.5592
The value of cos 34
= 0.829
The value of cos 34° is equal to the x-coordinate (0.829).
∴ cos 34° = 0.829.
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How much is the sales tax on $29.50 worth of goods if the tax rate is 7%?
$0.21
$0.42
$2.07
$4.21
Answer:
Third Option: $2.07
Step-by-step explanation:
Sales tax is the tax that is applied on the sales of goods by the government paid by the public. Here,
Given
Amount = $29.50
And
Sales tax rate = 7%
The formula for calculation of tax is:
Sales tax = Amount * tax rate
= 29.50 * 7/100
= 29.50*0.07
= 2.065
Rounding off will give
$2.07
So third option is correct ..
Answer:
$2.07
Step-by-step explanation:
If I purchase this product for 79.99 and two accessories for 9.99 and 7.00 how much would I owe after the 8.75 tax is applied
77.99+7.00+9.99=96.98
96.98 times 8.75% or 0.0875=8.48575 or 8.49 8.49+96.98=$105.47
Help please!
Find x
Answer:
6√2
Step-by-step explanation:
A 45 45 90 right triangle, so ratio of leg : leg: hypotenuse = a: a : a√2 (a = value of leg)
Given: leg = 6
So the ratio of leg : leg: hypotenuse = 6 : 6 : 6 √2
Answer:
x = 6√2
Answer:
B
Step-by-step explanation:
Since the triangle is right use the sine ratio to solve for x
and the exact value for sin45° = [tex]\frac{1}{\sqrt{2} }[/tex], then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{6}{x}[/tex]
Multiply both sides by x
x × sin45° = 6 ( divide both sides by sin45° )
x = [tex]\frac{6}{sin45}[/tex] = [tex]\frac{6}{\frac{1}{\sqrt{2} } }[/tex] = 6[tex]\sqrt{2}[/tex]
What is the common ratio of the sequence?
-2, 6, -18, 54,...
−3
−2
3
8
Answer:
-3
Step-by-step explanation:
Consider the geometric sequence:
[tex]b_1=-2\\ \\b_2=6\\ \\b_3=-18\\ \\b_4=54\\ \\....[/tex]
Note that
[tex]b_2=b_1\cdot q\\ \\b_3=b_2\cdot q\\ \\b_4=b_3\cdot q\\ \\...[/tex]
So,
[tex]6=-2q\\ \\-18=6q\\ \\54=-18q\\ \\...[/tex]
From all of these equalities we can state that
[tex]q=-3[/tex]
Answer:
r = - 3
Step-by-step explanation:
The sequence is geometric if a common ratio r exists between consecutive terms.
6 ÷ - 2 = - 3
- 18 ÷ 6 = - 3
54 ÷ - 18 = -3
The sequence is geometric with common ratio r = - 3
What is the sum of the geometric sequence 1, −6, 36, … if there are 6 terms?
Answer:
The sum of the geometric sequence is: -6665
Step-by-step explanation:
By looking at the geometric sequence, we can note that each term is multiplied by -6.
So, the fourth term is going to be: -216
The fifth term is going to be: 1296
The sixth term is going to be: -7776
The sum of the geometric sequence is: 1 - 6 + 36 - 216 + 1296 - 7776 = -6665
Please help....Alinakincsem Ace
Answer:
The correct answer option is E. [83 + 2(79) + 4(88)] × 1/7.
Step-by-step explanation:
We are given the quiz average, test average and final average for Sabra's grades for a class.
Given that her test average counts twice as much as her quiz average and final exam counts twice as much as her test average for her overall average:
[tex](83+79+79+88+88+88+88)[/tex] ÷ [tex]7[/tex]
This can also be written as:
[83 + 2(79) + 4(88)] × 1/7
What is the value of y in this linear system?
The calculated value of y in this linear system is 18
How to determine the value of y in this linear system?
From the question, we have the following parameters that can be used in our computation:
x + y + z = 62
x - y = 12
2x + y + z = 92
Subtracting the equations 1 and 2, we have
2x - x = 92 - 62
x = 30
In equation (2), we have
x - y = 12
This gives
y = x - 12
Substitute the known values into the equation
y = 30 - 12
Evaluate
y = 18
Hence, the value of y is 18
Use the function below to find f(3).
f(x) =1/3* 4*
Answer:
f(3) = 64/3
Step-by-step explanation:
f(x)=1/3•4^x
Let x = 3
f(3) = 1/3* 4^3
= 1/3 * 64
= 64/3
Answer:
64/3 (APEX)
Step-by-step explanation:
What is the value of (-7 + 31) – (2 - 6/)?
The arithmetic expression (-7 + 31) minus (2) equals 22 when you apply the order of operations, which requires us to calculate expressions within parentheses first.
Explanation:To solve this arithmetic problem, let's break down the expression into two parts, working within the parentheses first. The term inside the first set of parentheses is -7 + 31 which equals 24. The term inside the second set of parentheses appears to have missing or incorrect data.
If we ignore that, we have just (2). Now we subtract the second term (2) from the first term (24). Thus, the value of (-7 + 31) – (2) is 22.
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Can someone please help me ..I can’t get anymore questions wrong or else I will fail I need help
Answer:
maybe number 2
Step-by-step explanation:
because if 2+k=18 then there is no other k there and where did the additional 2 come from ?and 2k=18 then value of k is 9 + there is balance.I may be wrong correct me but i think it is no.2
Answer:
2k = 18
k = 9
Step-by-step explanation:
First we have to look at each side of the hanger.
There are 2 k's, which can be represented as "2 times the value of k" or 2k.
On the other side, we have the value of 18. The question states that the two sides are balanced. Therefore, the correct equation that represents the image is:
2k = 18.
To find the value of k that makes the equation true, we must isolate the variable k. To do this, we divide 2 from each side of the equation.
2k ÷ 2 = 18 ÷ 2
k = 9.
The value of k that makes the equation true is 9.