Answer:
When the initial velocity is 6m/s and acceleration is 3m/s², the final velocity after a distance of 29m is √210m/s.
Step-by-step explanation:
Concept: In the problem it is given that u = 6m/s, a = 3m/s² and s = 29m. We need to find the v. In such kinematical problems, we have an equation v² = u² + 2as. From this relation we can find v.
v² = 6² + 2×3×29
v² = 36 + 174
v² = 210
v = √210 m/s
So, the final velocity is the under-root of 210 or √210 m/s.
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Find the missing term.
(x12)5 x (x-2)⁹ X ____=
(140)5
Answer:
x12×x5x×x-2×9) ____=((140)5
60x × (x-18)x _______=(140)5
60x×x-10x _______=(140)5
60x-18x______=140×5
42x_______=700
42x-42x ____=700-42x
658x
Find the reflection of point (50, 25) across the x-axis.
The reflection of any point across the x-axis:
⇒ means that x-coordinate remains the same
⇒ but the y-coordinate is multiplied by '-1'
In this case:
⇒ (50,25) becomes (50,-25)
Answer: (50,-25)
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Answer:
(50, -25)
Step-by-step explanation:
When we reflect a point across the x-axis, only the sign of the y-value the changes. In this case, the y-value is 25, so after the reflection it becomes -25. The x-value stays the same. So your resulting point is (50, -25)
Which is the graph of g(x) = 2x-1+3?
O
-12
-8
-4
8-
4
-8
-12+
8
X
Answer:
See below
Step-by-step explanation:
The question is garbled. I don't see a graph nor can I interpret the list of numbers.
g(x) = 2x-1+3 can be simplified to:
g(x) = 2x+2
This line is shown in the attached graph. It has a slope of 2 and a y-intercept of 2.
Evaluate:
20
Σ 4(8/9)^n-1 = [?]
1
Round to the nearest hundredth.
Answer:
32.59 (nearest hundredth)
Step-by-step explanation:
Geometric sequence
General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]
(where a is the first term and r is the common ratio)
Given:
[tex]\displaystyle \sum^{20}_{n=1} 4 \left(\dfrac{8}{9}\right)^{n-1}[/tex]
Therefore:
a = 4r = 8/9Sum of the first n terms of a geometric series:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
To find the sum of the first 20 terms, substitute the found values of a and r, together with n = 20, into the formula:
[tex]\implies S_{20}=\dfrac{4\left(1-\left(\frac{8}{9}\right)^{20}\right)}{1-\left(\frac{8}{9}\right)}[/tex]
[tex]\implies S_{20}=32.58609013...[/tex]
[tex]\implies S_{20}=32.59\:\: \sf (nearest\:hundredth)[/tex]
General form of geometric progression
ar^n-1On comparing to the summation
a=4r=8/9Apply Sum formula
[tex]\boxed{\sf S_n=\dfrac{a(1-r^n)}{1-r}}[/tex]
[tex]\\ \implies \sf S_{20}=\dfrac{4\left(1-\left(\frac{8}{9}\right)^{20}\right)}{1-\left(\frac{8}{9}\right)}[/tex]
[tex]\\ \implies\sf S_{20}=32.586[/tex]
[tex]\\ \sf\mplies S_{20}=32.59[/tex]
11. Work backwards to write a quadratic equation that will have solutions of x = 12 and x = 2.
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{x}^2\textsf{ - 14x + 24}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{x = 12 and x = 2}[/tex]
Find: [tex]\textsf{Determine the quadratic equation}[/tex]
Solution: In order to determine the quadratic equation we need to move the integers onto the side where x is and then distribute.
Move the integers
Solution #1[tex]\textsf{x - 12 = 12 - 12}[/tex][tex]\textsf{x - 12 = 0}[/tex]Solution #2[tex]\textsf{x - 2 = 2 - 2}[/tex][tex]\textsf{x - 2 = 0}[/tex]Create and expression and distribute
[tex]\textsf{(x - 12)(x - 2) = 0}[/tex][tex]\textsf{(x * x) + (x * -2) + (-12 * x) + (-12 * -2) = 0}[/tex][tex]\textsf{x}^2\textsf{ - 2x - 12x + 24 = 0}[/tex][tex]\textsf{x}^2\textsf{ - 14x + 24 = 0}[/tex]Therefore, after completing the steps we were able to determine that the quadratic equation that will have solutions of x = 12 and x = 2 is x^2 - 14x + 24.
Graph the image of this figure after a dilation with a scale factor of centered at the origin.
Use the polygon tool to graph the dilated figure.
Polygon
+Move
10
9
8
7
6
5
3
2
y
Undo
Redo x Reset Graph the image of this figure after a dilation with a scale factor of 1/3 centered at the origin
A picture of the dilated figure with its points at (-2, 10), (2, 6), and (-8, 4) is provided.
What exactly is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
The complete question is;
"Graph the image of this figure after a dilation with a scale factor of 2 centered at (2, 2) .
Use the polygon tool to graph the dilated figure."
The center of dilation and figure are first translated, making the origin the center of dilation.
We map every point because the point (2, 2), which is our center of dilatation, must be translated left 2 and down 2 to become the origin.
(x, y)→(x-2, y-2)
Each point will be multiplied by two when the scale factor is two, giving us the rule.
(x, y)→(2x-4, 2y-4)
In order to return the figure to its original location, we must translate it right 2 and up 2; this gives us the rule.
(x,y)→(2x-4+2, 2y-4+2) = (2x-2, 2y-2)
At the top of the original figure, the first point is (0, 6). When we use the transformation, we get
(0, 6)→(2*0-2, 2*6-2) = (0-2, 12-2) = (-2, 10)
The pre-rightmost image's point is (2, 4). The results of using the transformation rule are;
(2, 4)→(2*2-2, 2*4-2) = (4-2, 8-2) = (2, 6)
The pre-leftmost image's point is at (-3, 3). The transformation rule being applied, w
(-3, 3)→(-3*2-2, 3*2-2) = (-6-2, 6-2) = (-8, 4)
Hence,an picture of the dilated figure with its points at (-2, 10), (2, 6), and (-8, 4) is provided.
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Claire and jane did an examination together. jane scored 9 more marks than claire and her marks were 60% of the sum of their scores. what are the scores of each student?
The score of Jane is 27 and the score of Claire is 18.
A linear equation is an equation where highest degree of variables is 1.
Let the score of Jane's mark is x
Given, that score Jane is 9 more than the score of Claire.
So, the score of Claire= x-9
Given, the score of Jane is 60% of the sum of their scores.
the sum of their scores is = x+x-9= 2x-9
from the above it is clear that
the linear equation will be
x=60%(2x-9)
⇒x=0.6(2x-9)
⇒x= 1.2x -5.4
⇒1.2x-x= 5.4
⇒0.2x= 5.4
⇒x= 5.4/0.2
⇒x= 27
So the score of Jane is 27.
As score Jane is 9 more than the score of Claire.
the score of Claire is = x-9= 27-9=18
Therefore the score of Jane is 27 and the score of Claire is 18.
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What is the 17th term in the arithmetic sequence an=77+(n-1)(-5)
Answer:
a₁₇ = - 3
Step-by-step explanation:
substitute n = 17 into the nth term rule
a₁₇ = 77 + 16 × - 5 = 77 - 80 = - 3
Which method is better to solve the following equation?
²-25=0
Your answer:
O Quadratic Formula
O Square Rooting
Clear answer
Next
Please solve it. It will help me for my exam preparation.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{ y{ }^{2} }{(p - y) {}^{y} }[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{ {p}^{2} }{(p - y) {}^{y} } + \cfrac{ - 2p}{(p - y) {}^{y - 1} } + \cfrac{1}{(p - y) {}^{y - 2} } [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{ {p}^{2} + ( - 2p)(p - y) + 1(p - y) { }^{2} }{(p - y) {}^{y} } [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{ {p}^{2}- 2p {}^{2} + 2py + p {}^{2} + y{ }^{2} - 2py}{(p - y) {}^{y} } [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{ {p}^{2} + {p}^{2} - 2p {}^{2} + 2py - 2py + y{ }^{2} }{(p - y) {}^{y} }[/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{ y{ }^{2} }{(p - y) {}^{y} }[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Passengers under the age of 8 and whose height is less than 57 inches must be in the _________ seat of a vehicle.
Passengers under the age of 8 and whose height is less than 57 inches must be in the back seat of a vehicle.
When you journey in the backseat of a automobile, you take a seat within the row of seats behind the motive force. Kids once in a while combat over the front seat, not wanting to take a seat within the backseat. you may tour within the backseat of a car except you're the driver or are using a two-seat sports activities vehicle.
The cushion in which the driving force or passenger sits is either known as a horizontal cushion or seat cushion. The back of the automobile seat is called the seat again however it could additionally be called a backrest.
An infant protection seat every so often referred to as an toddler protection seat, infant restraint device, baby seat, child seat, car seat, or booster seat is a seat designed particularly to shield youngsters from injury or death throughout automobile collisions.
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A coordinate plane is labeled street on the x-axis and avenue on the y-axis. ping is at point (3, 6) and ari is at point (21, 18). a line is drawn from ping to ari. ping lives at the corner of 3rd street and 6th avenue. ari lives at the corner of 21st street and 18th avenue. there is a gym two-thirds the distance from ping's home to ari's home. x = (startfraction m over m n endfraction) (x 2 minus x 1) x 1 y = (startfraction m over m n endfraction) (y 2 minus y 1) y 1 where is the gym? 9th street and 10th avenue 12th street and 12th avenue 14th street and 12th avenue 15th street and 14th avenue
The gym location is (15th street, 14th Avenue). so the option D is correct.
What is graph ?A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
Given :
Ping's residence = (3rd street, 6th Avenue)
Ari's residence = (21st street, 18th Avenue)
Gym location is 2/3 the distance of Ping's residence to Ari's residence
So, distance between Ping's home to Ari's home will be
Distance = (21st street, 18th Avenue) - (3rd street, 6th Avenue)
Distance = (21 - 3) street, (18 - 6) avenue
Distance between ping and Ari will be
= (18th , 12th )
We know that
Gym distance = 2/3 × (18), 2/3 ×(12)
Gym distance = (12, 8)
Gym location = Ping's location + gym distance
Gym location = (3rd street, 6th Avenue) + (12th street, 8th Avenue)
Gym location = (15th street, 14th Avenue)
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Jack goes to a restaurant in a state with a 7.25% sales tax. He buys a
meal and tips 20% before tax. Select the meal cost that would allow his
total bill, including tip and tax, to have a total cost equal to $15.
The meal cost spent by Jack at the restaurant if he spent $15 including tip and bill is $11.79.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the meal cost, hence:
Total cost = x + 0.2x + 0.0725x
15 = 1.2725x
x = 11.79
The meal cost spent by Jack at the restaurant if he spent $15 including tip and bill is $11.79.
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Given the function, f(x)=√x-2 +3, choose the correct transformation.
right 2, up 3
Right2, down 3
left 2, up 3
left 2, down 3
Define the hypothesis and the conclusion of the following conditional statement.
Conditional Statement: All kids who wear braces will have straight teeth.
The hypothesis will be that "If a kid wears braces, then the kid will have a straight teeth".
What is hypothesis?It should be noted that a hypothesis means a proposed explanation based on reasoning and evidence.
In this case, the hypothesis will be that "If a kid wears braces, then the kid will have a straight teeth".
The conclusion is that kids who wear braces will have straight teeth.
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The courthouse is the tallest building in the city. If it is 71/2 6 inches tall in the model, how tall is the actual building?
The actual height of the building is 67 1/2 feet
Complete questionThe courthouse is the tallest building in the city. If it is 7 1/2 inches tall in the model, how tall is the actual building?
Scale factor: 1 inch = 9 feet
How to determine the actual height?The given parameters are:
Scale height = 7 1/2 inchesScale factor: 1 inch = 9 feetThis means that:
7 1/2 inches : Actual = 1 inch = 9 feet
So, we have:
Actual =7 1/2 * 9 feet
Evaluate the product
Actual = 67 1/2 feet
Hence, the actual height of the building is 67 1/2 feet
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Suppose y varies inversely as x², and y = 64 when x = 1/4. Find y when x = 7.
Finding the proportionality constant :
y = k/x²64 = k/(1/4)²k = 4Finding y when x = 7 :
y = 4/(7)²y = 4/49The value of y is 4/49 when x = 7.
[tex]y = \frac{k}{ {x}^{2} } \\ \\ 64 = \frac{k}{ { (\frac{1}{4}) }^{2} } \\ \\ 64 = \frac{k}{ \frac{1}{16} } \\ \\ 64 = 16k \\ \\ k = \frac{64}{16} \\ \\ k = 4.[/tex]
Finding 'y'
[tex]y = \frac{4}{ {7}^{2} } \\ \\ y = \frac{4}{49} .[/tex]
Find the distance between the point (3, 5) and a line with the equation 5 x - 3 y + 10 = 0
The distance between the point (3, 5) and a line with the equation 5x – 3y + 10 = 0 will be 10 / √(34) units.
What is the distance between a point and a line?Let (x₁, y₁) be the point and ax + by + c = 0 be the line.
Then the distance between a point and a line will be
[tex]\rm d = \dfrac{|ax_1 + by_1 + c|}{\sqrt{a^2 + b^2}}[/tex]
The point (3, 5) and a line with the equation 5x – 3y + 10 = 0.
Then the distance between them will be
[tex]\rm d = \dfrac{|5 *3 - 3 *5 + 10|}{\sqrt{5^2 + (-3)^2}}\\d = \dfrac{10 }{\sqrt{34}} \ units[/tex]
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Margret divides a packet of 20 biscuits among her 8 friends. Find the number of biscuits each friend gets. Express the answer as a rational number
The number of biscuits each friend can get would be 2.5.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Margret divides a packet of 20 biscuits among her 8 friends.
In order to find the number of biscuits each friend gets.
20 / 8
= 2.5
Hence, the number of biscuits each friend can get would be 2.5.
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0.33632287 to 3sf please
Answer:
.
Step-by-step explanation:
I really could use help with this
Answer:
B. [tex]\mathsf {\frac{1}{13}(26x-169)=\frac{1}{12}(-156+24x) }[/tex]
Step-by-step explanation:
[tex]\mathsf {\frac{1}{13}(26x-169)=\frac{1}{12}(-156+24x) }[/tex]
2x - 13 = -13 + 2x
2x - 13 = 2x - 13
As both sides are equal, any value can be substituted for x, and hence it has infinitely many solutions.
Answer:
B. 1/13(26x - 169) = 1/12(-156 + 24x)
Step-by-step explanation:
When looking for an equation with infinetly many solutions, we are looking for an equation that is true when simplified
such as: 3c = 3c
or x - 10 = - 10 + x
this is because any value that we put in for x will simplify to a true equation (will be a solution)
so, let's examine the options:
A. if we combine like-terms on both sides, we will end up with 23 + 32x = 32x + 26
which is false, for any value that we put in for x
B. this statement is true--regardless of the value for x.
1/13 · 26 is the same as 1/12 · 24 (both equal 2; so both sides would distribute to 2x)
1/13th of -169 is -13; and 1/12th of -156 is -13
so, for all values of x, option B is true
(all values of x are a solution; and "x" could be any value)
C. by distributing the 2 (6 - 4x = -5x + 7), we find an equation that is not true for all values of x [we don't even have to find the solution, we just know that there will only be a/a few solution ]
D) because the variable, x, is only on one side (and when distributed, is not cancelled by any other x), we know that it cannot be true for infinetly many solutions
(the only true solution will be when the equation is simplified to 4/18 = 4/18)
hope this helps!!
Find the relationship between zeros and intercepts of the polynomial m2 + 5m + 4.
They are equal to zero
They are same
They are different
They are opposites
The zeros and intercepts of the polynomial m^2 + 5m + 4 will be different.
Intercepts and zero of a functionA quadratic function is a function that has a degree of 2.
Given the following equation
f(m) = m^2 + 5m + 4
The x-intercept occurs at the point where f(m) is zero and same is applicable to the zeros of the function.
This shows that the zeros and intercepts of the polynomial m^2 + 5m + 4 will be different.
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HEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEELP
Answer:
C.
Step-by-step explanation:
Adding 2 fractions results in a fraction.
Answer:
B: The sum is a non-terminating and a non-reapeating decimal
Step-by-step explanation:
-11/4 +5/g
There is 15 steps you have to do after (look in the picture)
but this is what you get:
[tex]-\frac{11g-20}{4g}[/tex]
PLS HELP!!
Find the zeros of y=x² - 6x-4 by completing the square.
O A. x= 3± √13
OB. x = 3± √5
O C. x = -3± √13
OD. x = ±3
Answer:
A
Step-by-step explanation:
y = x² - 6x - 4
(x - 3)² - 3² - 4 = 0
(x - 3)² - 13 = 0
(x - 3)² = 13
x - 3 = ±√13
x = 3 ± √13
Which point is on the graph of the inverse function h-¹(x)?
O (2,4)
0 (0)
O (0, 1)
O (-5, 1)
Answer: (0,1)
Step-by-step explanation:
If (x,y) lies on the graph of the original function, then (y,x) lies on the graph of the inverse.
Since (1,0) lies on the graph of h(x), (0,1) lies on the graph of its inverse.
(0, 1) point is on the graph of the inverse function h-¹(x).
What are inverse functions?Two functions f(x) and g(x) are inverses if their composition is equal to the identity.
Equation of line will be
y = -2x + 2 = h(x)
h⁻¹(x) will be calculated as:
x = -2y + 2
x - 2 = -2y
y = (2 - x)/2
So, y = h⁻¹(x) = (2 - x)/2
put x = 0 in the equation y = (2 - x)/2
y = 1
(0, 1) = (0, 1)
This, (0, 1) is the point on h⁻¹(x).
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Enter the correct answer in the box.
Consider this expression.
x² + x - 72
Replace the values of a and b to rewrite the given expression.
(x+ a)(x+b)
The correct values of a and b to rewrite the expression as (x + a)(x + b) are:
a = 9
b = -8
So, (x + 9)(x - 8) is the correct form of the given expression.
Here, we have to rewrite the expression x² + x - 72 in the form (x + a)(x + b), we need to find two numbers a and b such that when multiplied,
it give us the constant term -72 and when added, it give us the coefficient of the x term, which is 1.
The expression x² + x - 72 can be factored as follows:
x² + x - 72
= x² + 9x - 8x - 72
=x(x+9) -8(x+9)
= (x + 9)(x - 8)
Therefore, the correct values of a and b to rewrite the expression as (x + a)(x + b) are:
a = 9
b = -8
So, (x + 9)(x - 8) is the correct form of the given expression.
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Kyle borrows $25000 at 6% p.a. simple interest for four years. Calculate the monthly repayment required to pay this loan off in 48 equal instalments.
Answer:
$587.13
Step-by-step explanation:
Monthly Payment Formula
[tex]\sf PMT=\dfrac{Pi(1+i)^n}{(1+i)^n-1}[/tex]
where:
PMT = monthly paymentP = loan amounti = interest rate per month (in decimal form)n = term of the loan (in months)Given:
P = $25,000i = 0.005n = 48To calculate i, divide the interest rate per annum by 12 and convert to decimal form:
[tex]\implies \sf i=\dfrac{6\%}{12}=\dfrac{0.06}{12}=0.005[/tex]
Substitute the given values into the formula and solve for PMT:
[tex]\implies \sf PMT=\dfrac{25000 \cdot 0.005(1+0.005)^{48}}{(1+0.005)^{48}-1}[/tex]
[tex]\implies \sf PMT=\dfrac{125(1.005)^{48}}{(1.005)^{48}-1}[/tex]
[tex]\implies \sf PMT=587.1257262...[/tex]
Therefore, the monthly repayment required to pay this loan off in 48 equal installments is $587.13 (nearest cent).
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The first three steps in writing f(x) = 40x + 5x2 in vertex form are shown.
Write the function in standard form.
f(x) = 5x2 + 40x
Factor a out of the first two terms.
1(x) = 5(x2 + 8x)
Form a perfect square trinomial.
(%) =16
1(x) = 5(x2 + 8x + 16) -5(16)
What is the function written in vertex form?
® f(x) = 5(x + 4) -80
® f(x) = 5(x + 8) - 80
O f(x) = 5(x + 4)2 - 80
• f(x) = 5(x + 8) - 80
Answer: Choice C [tex]f(x) = 5(x+4)^2 - 80[/tex]
======================================================
Reason:
The expression [tex]x^2+8x+16[/tex] factors to [tex](x+4)^2[/tex] using the perfect square trinomial formula [tex](a+b)^2 = a^2 + 2ab + b^2[/tex]. In this case, a = x and b = 4.
The -5(16) simplifies to -80
Therefore, [tex]5(x^2+8x+16) - 5(16)[/tex] turns into [tex]5(x+4)^2 - 80[/tex]
Compare this to [tex]a(x-h)^2 + k[/tex] to see that h = -4 and k = -80. The vertex is located at (h,k) = (-4, -80)
Answer:
c) 5(x+4)² - 80
Step-by-step explanation:
You have already gotten the third (second-last) step for finding the vertex as follows:
f(x) = 5(x² + 8x + 16) -5(16)
= 5(x+4)² - 80
Additional remarks: to find the vertex, you can just use find the value of x when x+4 = 0, meaning x = -4 and y = -80. Hence, the vertex is (-4, -80).
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The function y=3^x is called an_______ function because the exponent is a _______. Now, let’s look at how to graph the exponential function y=3^x
The function is called an exponential function became the exponent is a variable.
The function is called an exponential function became the exponent is a variable.
What is an exponential function?An exponential function is a Mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
So, here given a fill in the blank statement, we need to find the words to be filled in the blanks,
So, the whole statement is =
The function is called an exponential function became the exponent is a variable.
The function y = 3ˣ is an exponential function because it is having a power which is a variable.
The graph of the same is attached to the solution.
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What is the slope of the line segment?
Answer:
A
Step-by-step explanation:
Givens
y2 = 15
y1 = 0
x2 = 3
x1 = 0
Equation
slope = (y2 - y1) / (x2 - x1)
Solution
The question is a bit unfair. It looks like you should be answering one. It's not true. What makes it not so is that the axis (x and y) have different intervals.
Substitute the givens into the equation
slope = (15 - 0) / (3 - 0)
slope = 15 / 3
slope = 5
Answer Slope = 5 or A
Answer:
it's A
Step-by-step explanation:
that's what i put on that question