Answer:
7
Step-by-step explanation:
You were correct in setting the equation equal to 0 because the problem is asking for when the rock hits the ground and in this problem, you may assume that the ground is y=0, unless the problem says otherwise.
Ok so where you went wrong is that when you factored out and got
(x-7)(x+2), which is correct, you forgot to set these equal to zero (because your actual equation is set to zero). So you should have
x-7 = 0
and
x+2 = 0
and this gives the actual answers +7 and -2. And since time cant be negative its 7 seconds.
This was a silly mistake and happens a lot more often than you think, so I wouldn't worry too much but make sure you practice more, better to lose points on harder questions than easy ones.
Good luck with your exam !
Answer:
7 seconds
Step-by-step explanation:
Given function:
[tex]y=-2x^2+10x+28[/tex]
where:
y = height above the ground (in feet)x = time (in seconds)To find the time when the rock hits the ground, set the equation to zero and solve for x.
First, simplify by factoring out the common term -2:
[tex]\implies -2(x^2-5x-14)=0[/tex]
Divide both sides by -2:
[tex]\implies x^2-5x-14=0[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b.
[tex]\implies ac=1 \cdot -14=-14[/tex]
[tex]\implies b=-5[/tex]
Therefore, the two numbers that multiply to -14 and sum to -5 are: -7 and 2
Rewrite b as the sum of these two numbers:
[tex]\implies x^2-7x+2x-14=0[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies x(x-7)+2(x-7)=0[/tex]
Factor out the common term (x - 7):
[tex]\implies (x+2)(x-7)=0[/tex]
Therefore:
[tex]\implies x+2=0 \implies x=-2[/tex]
[tex]\implies x-7=0 \implies x=7[/tex]
As time cannot be negative, the rock hits the ground in 7 seconds.
Write logb(x/y) as two logs
Answer:
[tex] log_{b}(x) - log_{b}(y) [/tex]
In the figure below, j || m. Find the values of x and y.
X and 73 are same-side interior angles, which are supplementary (they add up to 180).
x + 73 = 180
x = 107
X and (6y - 79) are vertical angles, which are congruent (have the same measure/value.
x = 6y - 79
107 = 6y - 79
6y = 186
y = 31
Hope this helps!
Preform the indicated operation.
(2x+y)(3 x² + y)
Answer:
[tex]6x^3+3x^2y+2xy+y^2[/tex]
Step-by-step explanations:
[tex](2x+y)(3x^2+y)\\2x*3x^2+2xy+3x^2y+y*y - Distribute\\6x^3+3x^2y+2xy+y^2 - Simplify[/tex]
Answer:
6x^3 + 2xy + 3x^ 2y + y^2
Step-by-step explanation:
Apply the distributive property of multiplication. First multiply (3x^2 + y) by 2, obtaining 6x^3 + 2xy, and then multiply (3x^2 + y) by y, obtaining
3x^2y + y^2. Finally, combine like terms (if any) in these two results:
6x^3 + 2xy + 3x^ 2y + y^2
Which of the following rational functions is graphed below?
Answer:
D
Step-by-step explanation:
I looked at the vertical asymptotes. -1 and 2. from the knowledge I have the answer with x=-1, 2 is D.
A 210-N mass is suspended from a horizontal beam by two cables that make angles of 29 degrees and 53 degrees with the beam. Find, using vectors, the tension in the cables.
The tension in both cables are calculated as; T₁ = 127.63 N and T₂ = 185.48 N
Resolving forces in the y direction gives us;
T₁ sin 29° + T₂ sin 53° = 210 ------(eq 1)
Resolving forces in the horizontal direction gives;
T₁ cos 29° = T₂ cos 53° ----(eq 2)
T₁ = T₂ cos 53°/cos 29°
Thus;
(T₂ cos 53°/cos 29°)sin 29° + T₂ sin 53° = 210
0.3336T₂ + 0.7986T₂ = 210
T₂ = 210/1.1322
T₂ = 185.48 N
Thus;
T₁ = 185.48 cos 53°/cos 29°
T₁ = 127.63 N
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+
A week after the incident at school, Charlotte received an envelope in the mail from Lisa's
mother. The envelope contained two $20 bills, and a note saying that she was sorry that Lisa had
hurt Charlotte and to please take the money to buy a new pair of jeans. Charlotte's new jeans cost
$25.99. Does she have enough to also buy a hoodie sweatshirt that cost $12.99? How much will
her new outfit cost?
w 10 159
Math Level 6-Lesson 13
Answer:
outfit costs 81 dollars
Step-by-step explanation:
Answer: Yes, she received $40 and the total cost of the outfit would be $38.98.
On a coordinate plane, solid circles appear at the following points: (negative 2, negative 5), (negative 1, 3), (1, negative 2), (3, 0), (4, negative 2), (4, 4).
Which explains why the graph is not a function?
make a 2 column proof
please make it simple like JK is parallel to NM(given)
i will also give brainliest
Answer:
Given: L is the midpoint of [tex]\overline{JM}[/tex] (given)
[tex]\overline{JL} =\overline{LM}[/tex] (definition of a midpoint)
Given: [tex]\overline{JK} \parallel \overline{NM}[/tex] (given)
[tex]\angle KJL \cong \angle NML[/tex] (alternate interior angles theorem)
[tex]\angle JKL \cong \angle MNL[/tex] (alternate interior angles theorem)
[tex]\triangle JKL \cong \triangle MNL[/tex] (SAA postulate)
(I have also created it in table form and attached a screenshot)
What are the solutions of the equation (x 2)2 – 2(x 2) – 15 = 0? use u substitution to solve.
The solution of the equation is x=3 or x=-5.
Given that the equation is (x+2)²-2(x-+2)-15=0 and use u substitution method to solve.
Let's assume that the (x+2)=u.
The given equation is rewritten as u²-2u-15=0.
Factorize the quadratic equation by adding or subtracting two number that gives the sum of -2u and product 15u² as
u²-5u+3u-15=0
u(u-5)+3(u-5)=0
Taking out (u-5) as common and get
(u-5)(u+3)=0
Compare each equation with 0 and get
u-5=0 or u+3=0
u=5 or u=-3
Performing back substitution by substituting the values of u in x+2
when u=5 then x is
x+2=5
x=3
And when u=-3 then x is
x+2=-3
x=-5
Hence, the solutions of the (x+2)²-2(x-+2)-15=0 is x=3 and x=-5.
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Answer:X=-5 and X=3
Step-by-step explanation:
If a hotel decreases the price of its rooms from $80 to $40. As a result, the total quantity demanded of its service increased from 2000 to 4000. Which type of price elasticity of demand does the hotel room have?
a.
Elastic
b.
Inelastic
c.
Perfectly inelastic
d.
Unitary
The angle of depression from the hot-air
balloon to the car is 32°
How high is the hot-air balloon flying?
Give your answer to 2 s.f.
6600 feet
Not drawn accurately
Answer:
3497.47 feet
I think it's the answer because when you look where I've drawn...that's where the angle of depression is and 6600 is the hypotenuse, so you use the sine method where you have opposite over hypotenuse
[tex] \sin(32 = opposite \6600) [/tex]
and you'll get your answer as 3497.47
Peter's father told Peter to buy four-tenths of a pound of chili powder. Each package is marked with its weight. What package should Peter buy?
Peter should buy 0.4 pound weight package
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct," "pct," and occasionally "pc" are also used, the percent sign, " percent ", is frequently used to signify it. A % is a number without dimensions and without a measurement system.
Given Peter's father told Peter to buy four-tenths of a pound of chili powder and Each package is marked with its weight.
We have to find which weight package should Peter buy
The four-tenths of a pound will be 40 % of one pound which is 0.4 pound. So peter should buy 0.4 pound weight package.
Hence Peter should buy 0.4 pound weight package
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When the expression 3(x²+6-3x) - (2x²-8) + 3(x² + 4x) is simplified, the coefficient
of x is
A. 7
B. 4
C. 3
D. 2
The correct answer is option C which is 3.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
The given expression will be solved as follows:-
E = 3( x² +6 -3x)- ( 2x² - 8 ) +3(x² + 4x )
E = 3x²+18-9x-2x²+8+3x²+12x
E= 4x² +3x+8
We can see the coefficient of x is 3.
Therefore the correct answer is option C which is 3.
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what are simultaneous equations
Answer:
Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. Each of these equations on their own could have infinite possible solutions.
Part of the proceeds from a garage sale was $540 worth of $5 and $20 bills If there were 3 more bills $5 bills than $20 bills, find the number of each denomination.
An equation is formed when two equal expressions. There are 21 $20 bills and 24 $5 bills.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the number of $5 bills be x, while the number of $20 bills be y.
Given there were 3 more $5 bills than $20 bills. Therefore, this can be represented as
x = y + 3
Also, The total worth of the dominations is $540. Therefore, we can write,
5x + 20y = 540
Substitute the value of x form the first equation,
5x + 20y = 540
5(y+3) + 20y = 540
5y + 15 + 20y = 540
25y = 525
y = 21
Substitute the value of y in the first equation,
x = 21 + 3
x = 24
Hence, there are 21 $20 bills, and 24 $5 bills.
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Ali had 3 times as many marbles as cho does. After cho gives 4 marbles to Ali, Ali has 18 more marbles than cho does. How many more marbles does cho have in the beginning
a. 5
b. 9
c. 10
d. 15
Answer:
d. 15
Step-by-step explanation:
Let A and C be the initial number of marbles Ali and Cho have, respectively.
We are told that:
A = 3C [Ali had 3 times as many marbles as cho does]
We then discover that
C-4 = A-18 [After cho gives 4 marbles to Ali, Ali has 18 more marbles than cho does]
How many more marbles does cho have in the beginning?
We have 2 equations and 2 unknowns (A and C). That means we can likely rearrange one of the equations and isolate one unknown on the left, and then use that in the second equation.
The first equation already has one of the unknowns isolated (A) so I'll use that in equation 2.
Eq. 1: A = 3C
Eq. 2: C-4 = A-18
Use the definition of A from Eq. 1 (=3C) to replace A in Eq. 2:
Eq. 2: C-4 = A-18
C-4 = (3C)-18 [Replace A with 3C, as promised in E1q. 1]
-2C = -14
C=7
If C = 7, then from Eq. 1, A = 21
In the beginning, Ali has 21 marbles and Cho has 7.
Cho has 15 more marbles than Ali in the beginning.
a. 5
b. 9
c. 10
d. 15
a−(−3.75)=6.11
What is a?
Answer:
a = 2.36
Step-by-step explanation:
a-(-3.75)=6.11
The negative 3.75 is being subtracted from the 'a'. A negative number being subtracted from another number makes it positive. So, 3.75 is actually being added to 'a' which is equal to 6.11
I re-wrote the question as:
a + 3.75 = 6.11
Subtract 3.75 from both sides to leave 'a' by itself
a + 3.75 = 6.11
-3.75 -3.75
a = 2.36
What is the research hypothesis when using anova procedures?
When using ANOVA procedures, the research hypothesis is: there is no significance difference within the mean values of the groups.
What is a Research Hypothesis in ANOVA Procedure?ANOVA procedure compares the mean values of different groups that are administered with treatments. The research hypothesis, such as the null hypothesis would be stated as: no significance difference in the mean values within the groups.
Thus, we can conclude that the research hypothesis when using the ANOVA procedures can be stated as a null hypothesis, which states that: there is no significance difference within the mean values of the groups.
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Draw a graph of y=3x-2. Using a scale of 2cm to 5units on both axes for values from x -2 to +2
What is the x-intercept
What is the y- intercept
Find the value of x when y= 5
Find the value of y when x= 0.5
pls pls ASAP
Function: y = 3x - 2
To find x-intercept, set [y = 0]:
[tex]\rightarrow \sf 3x - 2 = 0[/tex]
[tex]\rightarrow \sf 3x = 2[/tex]
[tex]\rightarrow \sf x = \dfrac{2}{3}[/tex]
The x-intercept: (2/3, 0)
To find y-intercept, set [x = 0]
[tex]\rightarrow \sf y = 3(0) - 2[/tex]
[tex]\rightarrow \sf y = - 2[/tex]
The y-intercept: (0, -2)
When [y = 5], x is:
[tex]\rightarrow \sf 3x - 2 = 5[/tex]
[tex]\rightarrow \sf 3x = 5 + 2[/tex]
[tex]\rightarrow \sf 3x = 7[/tex]
[tex]\rightarrow \sf x = \dfrac{7}{3}[/tex]
[tex]\rightarrow \sf x = 2 \dfrac{1}{3}[/tex]
Value of x is 2.33...
When [x = 0.5], y is
[tex]\rightarrow \sf y =3(0.5) - 2[/tex]
[tex]\rightarrow \sf y =-0.5[/tex]
Value of y is -0.5
Graph shown:
Find the surface area of a hexagonal prism if the length of each side of the hexagonal base is 4 cm and the height is 7 cm.
The surface area of a hexagonal prism willl be 251.13844 cm².
What is the surface area?The total land area of all the faces of a three-dimensional object is its surface area. When we wish to wrap something in real life, we employ the notion of surface areas of distinct things.
A=6ah+3√3a²
A=6×4×7+3√3×4²
A≈251.13844
Hence the surface area of a hexagonal prism willl be 251.13844 cm².
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Which equation justifies why 93 - ?
=
(0³) 1_9(²+³)_9
93
(³)
93
³_9(²+³)=9
(0³) -
93
93
=9=9
_g(¹-³)_9
=9
=9
The equation that justifies [tex]9^{1/3}=\sqrt[3]{9}[/tex] is [tex](9^{1/3}) ^{3} = 9^{3/3} = 9[/tex]
How to find equation that justifies another?The expression given is [tex]9^{1/3}=\sqrt[3]{9}[/tex].
The equation that justifies [tex]9^{1/3}=\sqrt[3]{9}[/tex] is as follows:
Therefore, using indices law,
[tex]a^{x/y} =\sqrt[y]{a^{x} }[/tex]
Hence,
[tex]9^{1/3}=\sqrt[3]{9}[/tex]
Therefore, the equation that shows it is correct is as follows;
[tex](9^{1/3}) ^{3} = 9^{3/3} = 9[/tex]
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quadrilateral ABCD is similar to quadrilateral EFGH find the measure of side EF round your answer to the nearest tenth if necessary
Answer:
EF = 2.9
Step-by-step explanation:
The geometric figures are similar so we can use the similarity ratio to calculate the length of EF:
GF/ CB = EF/AB
5/29 = EF/17 cross multiply expressions
29EF = 85 divide both sides by 29
EF = 2.9 approximately
Expand . ( 3x –2 ) 2 please help me with this.
Answer:
6x-4
Step-by-step explanation:
3x•2= 6x
-2•2=-4
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{9x}^2\textsf{ - 12x + 4}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{(3x - 2)}^2[/tex]
Find: [tex]\textsf{Simplify the expression}[/tex]
Solution: It looks like 2 is at the end of the parenthesis where the power would be instead of distributing the number. If so the following steps would be followed.
Expand
[tex]\textsf{(3x - 2)}^2[/tex][tex]\textsf{(3x - 2)(3x - 2)}[/tex][tex]\textsf{(3x * 3x) + (3x * (-2)) + (3x * (-2)) + (-2 * (-2))}[/tex]Simplify
[tex]\textsf{9x}^2\textsf{ - 6x - 6x + 4}[/tex][tex]\textsf{9x}^2\textsf{ - 12x + 4}[/tex]Therefore, after following the provided information we are able to determine that the expanded form would be 9x^2 - 12x + 4.
128 (4 + 2) = (128 ÷ 4) + 2
A. True
B. False
Answer:
B. False
Step-by-step explanation:
Just like last time, solve it first to check.
128(4+2)=(128/4)+2
Remember PEMDAS, parenthesis first.
128(6)=(32)+2
Now multiply the left side and add the right side.
128*6=768. The star sign is just another way to write a multiplication sign.
32+2=34
768≠34
This is a false statement. 768 does not equal 34.
Hope this helps!
If not, I am sorry.
Anne is visiting a friend who lives 18.5 km away. She travels 10 km by train, 1.5 km by bus, and walks the rest of the way. If she walks at a rate of 3.5 km per hour, for how long will Anne walk
Anne will walk a distance of 7 km, and she takes 2 hours to walk that distance.
For how long will Anne walk?
The total distance is 18.5 km.
She travels 10km by train and 1.5km by bus, for a total of 11.5km.
The distance that she walks is given by:
18.5km - 11.5km = 7km
So she walks for a distance of 7 km, at a speed of 3.5km per hour.
Remember the relation:
distance = time*speed
That can be rewritten to:
time = distance/speed.
Then the time that she walks is given by:
T = (7 km)/(3.5 km/hour) = 2 hours
She walks for 2 hours.
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Two-Variable Systems of Inequalities
On a piece of paper, graph this system of inequalities. Then determine which
region contains the solution to the system.
ysx-2
y24x-4
O A. Region D
B. Region B
C. Region C
D. Region A
10
6
6
A 4
10 B 84
D
999
B
C
XA¹
10
Inequalities help us to compare two unequal expressions. The correct option is B.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
The solution to two systems of inequalities in the region where the area of the two inequalities overlaps. As it can be observed in this case that the overlap area is B.
Hence, the correct option is B.
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Si en un autobús hay disponibles solo tres asientos y siete personas están de pie ¿De cuántas maneras distintas podrían ocupar esos asientos?
Usando la fórmula de combinación, se encuentra que hay 35 manerias distintas de ocupar esos asientos.
El orden en que se sientan las personas no es importante, por lo que se utiliza la fórmula de combinación para resolver este problema.
¿Cuál es la fórmula de combinación?[tex]C_{n,x}[/tex] es el número de combinaciones diferentes de x objetos de un conjunto de n elementos, dado por:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
3 personas son selecionadas de un conjunto de 7, por eso, el número de maneras es dado por:
[tex]C_{7,3} = \frac{7!}{3!4!} = 35[/tex]
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help … fr …. D: D: D: D:
Step-by-step explanation:
Let x be mixture x liters and y be mixture y liters.
We need a total of 4 liters so
[tex]x + y = 4[/tex]
Mixture x is 20% saline solution
Mixture Y is a 10% saline solution
4 liters of a 15% saline solution is 60% saline solution.
[tex].20x + .10y = 0.6[/tex]
So a is the system of equations,
Using Elimination, eliminate the variable x.
[tex] - 5(.20x + .10y) = 0.6[/tex]
[tex]( - x - .50y) = - 3[/tex]
Add to the first system.
[tex]0.50y = 1[/tex]
[tex]y = 2[/tex]
Plug this into the of system of equations, to find x
[tex]x + 2 = 4[/tex]
[tex]x = 2[/tex]
So our solution is (2,2) We would need 2 liters of Mixture X and 2 liters of Mixture Y
Hello hello :))) please help me with this problem
What are the domain and range of the function below?
A. Domain: (-4,0)
Range: [-2,∞)
B. Domain: (-3,0)
Range: [-2,∞)
C. Domain: (-∞,∞)
Range: [-2,∞)
D. Domain:
Range: (-∞,∞)
PS don't mind that dot on the graph, didn't mean to put it there.
The domain is (-∞,∞) and the range is [-2,∞)
How to determine the domain and the range?From the graph, we can see that the x values extend at both sides of the graph.
This means that the domain is the set of real values i.e. (-∞,∞)
However, the minimum y value is -2 and it increases from their
This means that the range is [-2,∞)
Hence, the domain is (-∞,∞) and the range is [-2,∞)
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