The given quadratic equation is expressed as
5x^2 + 12x + 8 = 0
The standard form of a quadratic equation is expressed as
ax^2 + bx + c = 0
By comparing both equations, we have
a = 5, b = 12, c = 8
We would solve for x by applying the general formula for solving quadratic equations which is expressed as
[tex]\begin{gathered} x\text{ = }\frac{-\text{ b }\pm\sqrt[]{b^2-4ac}}{2a} \\ By\text{ substituting the values, we have} \\ x\text{ = }\frac{-\text{ 12}\pm\sqrt[]{12^2-4(5\times8)}}{2\times5}\text{ } \\ x\text{ = }\frac{-\text{ 12 }\pm\sqrt[]{144\text{ - 160}}}{10}\text{ = }\frac{-\text{ 12}\pm\sqrt[]{-\text{ 16}}}{10} \\ x\text{ = }\frac{-\text{ 12}\pm4i}{10} \\ x\text{ = }\frac{-\text{ 12 + 4i}}{10}\text{ or x = }\frac{-\text{ 12 - 4i}}{10} \\ x\text{ = }\frac{-\text{ 12}}{10}\text{ + }\frac{4i}{10}\text{ or x = }\frac{-\text{ 12}}{10}\text{ - }\frac{4i}{10} \\ x\text{ = }\frac{-\text{ 6}}{5}+\text{ }\frac{2i}{5}\text{ or x = }\frac{-6}{5}-\text{ }\frac{2i}{5} \end{gathered}[/tex]If.A = (e, x, a, m) and U = {a, b, c, d, e, f, g, h, I, J. K, 1. m. n. o. p. q. r, S, t. u, v. w.x.y.z} find A.
Given that the set A contains the letters e, x, a and m, the complement A' will be the set that does not include these letters, thus, A' can be written as:
[tex]A^{\prime}=\mleft\lbrace b,c,d,f,g,h,i,j,k,l,n,o,p,q,r,s,t,u,v,w,y,z\mright\rbrace[/tex]A catapult is malfunctioning and not throwing objects in the intended manner. The builders have modeled the path of the objects thrown by using thefollowing parametric equations. Rewrite the parametric equations by eliminating the parameter.
Solution
Given
[tex]\begin{gathered} x(t)=2t-1 \\ \\ y(t)=\sqrt{t}\Rightarrow y^2=t \\ \\ \Rightarrow x=2y^2-1 \end{gathered}[/tex]Hence, the correct option is D
The graph of a function g is shown below.Find g (0) and find one value of x for which g(x) = 4,
From the graph provided,
a) For g(0), on the graph,
[tex]g(0)=-2[/tex]b) One value of x for which g(x) = 4 is given below as,
[tex]\begin{gathered} g(x)=4 \\ x=3\text{ where g(x) = 4} \end{gathered}[/tex]Hence, g(0) = -2 and one of the value of x for which g(x) = 4 is 3
please help this math seem hard 50 points anyone
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The equivalent expression is
[tex]x^{3/2}y^{19/2}[/tex]
Option C is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
√(xy³) x ([tex]x^{1/2} y^4[/tex])²
This can be written as,
[ √ means 1/2, √a = [tex]a^{1/2}[/tex]]
√(xy³) = [tex]x^{1/2}y^{3/2}[/tex]
([tex]x^{1/2} y^4[/tex])² = x[tex]y^8[/tex]
Now,
√(xy³) x ([tex]x^{1/2} y^4[/tex])²
= [tex]x^{(1/2 + 1)}y^{(3/2 + 8)}[/tex]
= [tex]x^{3/2}y^{19/2}[/tex]
Thus,
The equivalent expression is
[tex]x^{3/2}y^{19/2}[/tex]
Option C is the correct answer.
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A bowl has 4 green marbles 3 red marbles and 2yellow marbles what is the probability that you are going to select a red marble and a yellow marble. You replace the marble before another marble is selected
ANSWER
2/27
EXPLANATION
There are a total of 9 marbles in the bowl. The probability of drawing a red marble is,
[tex]P(red)=\frac{\#red.marbles}{\#total.marbles}=\frac{3}{9}=\frac{1}{3}[/tex]Then you draw another marble, but you put the first back in the bowl, so the total number of marbles is the same. The probability of drawing a yellow marble is,
[tex]P(yellow)=\frac{\#yellow.marbles}{\#total.marbles}=\frac{2}{9}[/tex]The probability of drawing a red marble and a yellow marble is,
[tex]P(red.and.yellow)=P(red)\cdot P(yellow)=\frac{1}{3}\cdot\frac{2}{9}=\frac{2}{27}[/tex]Functions > 1.02 Function families and transformations How do we shift the graph of y = f(x) to get the graph of y = f(x) + 2?
y = f(x)
to
y = f(x) + 2
Move up the graph by 2 units along the y- axis. (vertical translation)
Assume that (a,b) is a point on the graph of f. What is the corresponding point on the graph of the following function?f(x-25)What is the point on the graph of f(x-25) that corresponds to the point (a,b) on the graph of f?
Given
There exist a point (a, b) on the original function f(x).
Two points are corresponding if they appear in the same place in two similar situations.
The new function f(x-25) is a function shifted right by 25 units.
Hence, the point on the graph of f(x-25) that corresponds to the point (a, b) on the graph of f is:
[tex](a+25,\text{ b)}[/tex]
I’m just starting writing these and I don’t understand it much
In geometry, formal definitions are formed using other defined words or terms. There are, however, three words in geometry that are not formally defined. These words are point, line, and plane, and are referred to as the "three undefined terms of geometry".
a. Defined terms can be combined with each other and with undefined terms to define still more terms. An angle, for example, is a combination of two different rays or line segments that share a single endpoint. Similarly, a triangle is composed of three noncollinear points and the line segments that lie between them.
b. Undefined terms can be combined to define other terms. Noncollinear points, for example, are points that do not lie on the same line. A line segment is the portion of a line that includes two particular points and all points that lie between them, while a ray is the portion of a line that includes a particular point, called the endpoint, and all points extending infinitely to one side of the endpoint.
determine the degree of the polynomial -56a^2y^3+23a^2y-29a+17
The degree a polynomial is determine by the highest highest power of variable in the equation.
However, for a multivariable polynomial, the degree is the highest sum of powers of different variables in any of the terms in the expression.
For this polynomial,
[tex]-56a^2y^3+23a^2y\text{ - 29a + 17}[/tex]The degree of polynomial is 5 at the term -56^2y^3 which has 2 and 3 exponent at variable a and y respectively.
If ABCD is dilated by a factor of 3, thecoordinate of D' would be:4C3B21-5 -4 -3-2 -1 012345DA-1-2D-3D' = ([?],[ ]
Answer:
(6, -6)
Explanation:
The coordinate of D is the figure = (2, -2)
If ABCD is dilated by a factor of 3, then:
[tex]\begin{gathered} D(2,-2)\to D^{\prime}(2\times3,-2\times3) \\ =(6,-6) \end{gathered}[/tex]The coordinate of D' would be (6, -6).
Lin family has completed 70% of a trip. They have traveled 35 miles. How far is the trip?A. 24.5 milesB. 50 milesC. 59.5 milesD. 200 miles
The given information is:
The family have traveled 35 miles and it represents the 70% of the trip.
To find how far is the trip we need to divide the 35 miles by the percentage that it represents:
[tex]35\text{miles}\cdot\frac{100\%}{75\%}=50miles[/tex]Thus, the trip is 50 miles.
Answer: B.
Directions: Drag each tile to the correct box.Put the recursive formulas below in order from least to greatest according to the value of their 10th terms.For all of the formulas, let n be equal to the whole numbers greater than or equal to one.
Solving for the 10th term for each of the recursive sequence
First sequence
[tex]\begin{gathered} a_1=32 \\ a_{n+1}=-5+a_n \\ \\ \text{This can be converted to} \\ a_n=a_1+(n-1)(-5) \\ \\ \text{Substitute }n=10 \\ a_{10}=32+(10-1)(-5) \\ a_{10}=32+(9)(-5) \\ a_{10}=32-45 \\ a_{10}=-13 \end{gathered}[/tex]Second sequence
[tex]\begin{gathered} a_1=2048 \\ a_{n+1}=-\frac{1}{2}a_n \\ \\ \text{This can be converted to} \\ a_n=a_1\cdot\Big(-\frac{1}{2}\Big)^{n-1} \\ \\ \text{Substitute }n=10 \\ a_{10}=2048\cdot\Big(-\frac{1}{2}\Big)^{10-1} \\ a_{10}=2048\cdot\Big(-\frac{1}{2}\Big)^9 \\ a_{10}=-4 \end{gathered}[/tex]Third sequence
[tex]\begin{gathered} a_1=0.125 \\ a_{n+1}=2a_n \\ \\ \text{This can be converted to} \\ a_n=a_1\cdot2^{n-1} \\ \\ \text{Substitute }n=10 \\ a_{10}=0.125\cdot2^{10-1} \\ a_{10}=0.125\cdot2^9 \\ a_{10}=64 \end{gathered}[/tex]Fourth sequence
[tex]\begin{gathered} a_1=-7\frac{2}{3} \\ a_{n+1}=a_n+1\frac{2}{3} \\ \\ \text{This can be converted to} \\ a_n=a_1+(n-1)\Big(1\frac{2}{3}\Big) \\ \\ \text{Substitute }n=10 \\ a_{10}=-7\frac{2}{3}+(10-1)\Big(1\frac{2}{3}\Big) \\ a_{10}=\frac{-23}{3}+(9)\Big(\frac{5}{3}\Big) \\ a_{10}=-\frac{23}{3}+\frac{45}{3} \\ a_{10}=\frac{22}{3} \\ a_{10}=7\frac{1}{3} \end{gathered}[/tex]Arranging the formulas from least to greatest according to their 10th terms, we have the following:
First Sequence → Second Sequence → Fourth Sequence → Third Sequence
The length of two sides of a triangle are 5 inches and 8 inches. Which of the following lengths could be the length of the third side of the triangle?
there are 2 possible triangles that can arranged one being the 8 the longest side, and another one being the 5 and 8 the sides of the triangle
use the pythagorean theorem to solve.
for the black triangle.
[tex]\begin{gathered} a^2+b^2=c^2 \\ (8^2+5^2)=c^2 \\ (89)=c^2 \\ \sqrt[]{89}=c \\ c=9.43 \end{gathered}[/tex]for the green triangle.
[tex]\begin{gathered} a^2+b^2=c^2 \\ 5^2+b^2=8^2 \\ b^2=(8^2-5^2) \\ b^2=39 \\ b=\sqrt[]{39} \\ b=6.25 \end{gathered}[/tex]what is 7^3? Describe the strategy you used and explain why you used that approach
Given expression is
[tex]7^3[/tex]We can expand the given expression as follows.
[tex]7^3=7\times7\times7[/tex]Multiplying 7 and 7, we get
[tex]=49\times7[/tex]Multiplying 49 and 7, we get
[tex]=343[/tex]Hence 7^3 is 343.
We multiply the number twice by itself to find the cube of 7.
This strategy is easy and basic to find the cube of the number.
Which of the following expressions is equivalent to the one shown below?71377OA. 791OB. 720O C. 76O D. 75
Given
[tex]\frac{7^{13}}{7^7}[/tex]Find
Equivalent expression
Explanation
Here , we use laws of exponents
[tex]\frac{a^m}{a^n}=a^{m-n}[/tex]so ,
[tex]\begin{gathered} =\frac{7^{13}}{7^7} \\ \\ =7^{13-7} \\ \\ =7^6 \end{gathered}[/tex]Final Answer
Therefore , the correct option is C
A parabola has a vertex at (2, -1) and a y- intercept at (0,3). Is this enough information to sketch a graph? Explain your answer. Henny Yoffe . 11:20 AM
It is given that the parabola has the vertex at (2,-1)and y intercept of 3,
Consider the general equation of the parabola with vertex (p,q),
[tex]y=a(x-p)^2+q[/tex]Sbstitute 2 for 'p' and -1 for 'q',
[tex]y=a(x-2)^2-1[/tex]Given that the y-intercept is 3, it means that the curve passess through (0,3),
So it must satisfy the equation,
[tex]3=a(0-2)^2-1\Rightarrow4a=4\Rightarrow a=1[/tex]Substitute the value of 'a', 'p', and 'q' in the standard equation,
[tex]y=1(x-2)^2-1\Rightarrow y=(x-2)^2-1[/tex]Thus, the equation of the parabola can be obtained using the given conditions.
1. An input-output table has constant differences. When the input is 3, the output is 10. When the input is 7, the output is 24. a. Find the constant difference. b. Find the output when the input is 0. C. Find the linear function that fits the table.
a)7,17
b)-25
c)
[tex]y=3.5x-25[/tex]Explanation
table
a) differences
10-3=7
24-7=17
Step 1
find the slope
[tex]\begin{gathered} \text{slope}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}[/tex]Let
P1(3,10)
p2(7,24)
replace,
[tex]\begin{gathered} \text{slope}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{24-10}{7-3}=\frac{14}{4}=\frac{7}{2} \\ \text{slope}=\frac{7}{2} \end{gathered}[/tex]Step 2
find the equation
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-10=\frac{7}{2}(x-10) \\ y-10=\frac{7}{2}x-\frac{70}{2} \\ y=\frac{7}{2}x-\frac{70}{2}+10 \\ y=3.5x-25 \end{gathered}[/tex]Step 3
when x=0
[tex]\begin{gathered} y=3.5x-25 \\ y=3.5\cdot0-25 \\ y=-25 \end{gathered}[/tex]I hope this helps you
slope = 2/5; y-intercept = -7
We want to find the equation of the line with given slope and y-intercept.
The slope-intercept form of a line is:
[tex]y=mx+b[/tex]Where
m is the slope
b is the y-intercept (y-axis cutting point)
We are given the slope and y-intercept, so we simply substitute it. Steps are shown below:
[tex]\begin{gathered} y=mx+b \\ y=\frac{2}{5}x+(-7) \\ y=\frac{2}{5}x-7 \end{gathered}[/tex]The equation of the line is:
[tex]y=\frac{2}{5}x-7[/tex]Sailor SheftalSimilar Figures / Proportion (Level 1)Aug 02, 10:17:02 AM?Triangle EFG is similar to triangle HIJ. Find the measure of side HI. Round youranswer to the nearest tenth if necessary.G94425Submit AnswerAnswer:attempt 1 out of 2
If we have two similar triangles, that ratio of the corresponding sides are all the same. This means that:
[tex]\frac{GF}{JI}=\frac{EF}{HI}[/tex]Substituting the lengths, we get:
[tex]\begin{gathered} \frac{44}{9}=\frac{25}{HI} \\ HI=25\cdot\frac{9}{44}=5.1136\ldots\approx5.1 \end{gathered}[/tex]John wishes to build a square fence with an area of 121 square yards. What is the perimeter of the fence in yards.
Solution:
Given that John wishes to build a square fence with an area of 121 square yards, as shown below:
The area of a square is expressed as
[tex]\begin{gathered} Area\text{ of square = L}^2 \\ where \\ L\Rightarrow length\text{ of a side of the square} \end{gathered}[/tex]Given that the area of the square fence is 121 square yards, this implies that
[tex]\begin{gathered} 121=L^2 \\ take\text{ the square root of both sides,} \\ \sqrt{121\text{ }}\text{ =}\sqrt{L^2} \\ \sqrt{11\times11}\text{ =}\sqrt{L\times L} \\ \Rightarrow L=11\text{ yards} \end{gathered}[/tex]The perimeter of a square is expressed as
[tex]\begin{gathered} Perimeter\text{ of square = 4}\times L \\ where \\ L\Rightarrow length\text{ of a side of the square} \end{gathered}[/tex]Thus, the perimeter of the fence is evaluated by substituting the value of 11 for L into the perimeter formula.
[tex]\begin{gathered} Perimeter\text{ of fence = 4}\times11 \\ \Rightarrow Perimeter\text{ of fence = 44 yards} \end{gathered}[/tex]Hence, the perimeter of the fence is 44 yards.
Please see attached photo for question
For the function g(x), the graph is shown and the domain of that function is set of all integer numbers.
Domain of a function is all possible input values for that function.
Here, the domain of g(x) is set of all integers numbers
The x intercept of g(x)
The x intercept is when the value of y is zero, analysing the graph the x intercept can be interpreted as -5 and 1
The y intercept is when the value of x is zero, analysing the graph the y intercept can be interpreted as 1
From the graph,
g(4) is 1
Therefore, For the function g(x), the graph is shown and the domain of that function is set of all integer numbers.
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The length of a rectangle is 5 times its width if the perimeter is at most 96 cm what is the greatest possible value for the width
The value of the width in the rectangle is 8cm.
How to calculate the width?Based on the information, let the width be represented as w.
Let the width be represented as 5 × w = 5w
Perimeter = 96cm
Perimeter of a rectangle = 2(length + width)
Perimeter = 2(5w + w)
96 = 12w
Divide
w = 96/12
w = 8
The value of the width is 8cm.
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I’m not quite sure on why I’m not getting the correct solution. Please help!The questions are A) what is the initial value of Q, when t = 0? What is the continuous decay rate? B) Use the graph to estimate the value of t when Q = 2 C) Use logs to find the exact value of t when Q = 2
The given exponential function is
[tex]Q=11e^{-0.13t}[/tex]The form of the exponential continuous function is
[tex]y=ae^{rt}[/tex]a is the initial amount (value y at t = 0)
r is the rate of growth/decay in decimal
Compare the given function by the form
[tex]a=11[/tex][tex]\begin{gathered} r=0.13\rightarrow decay \\ r=0.13\times100\text{ \%} \\ r=13\text{ \%} \end{gathered}[/tex]a)
The value of Q at t = 0 is 11 and the decay rate is 13%
The initial value of Q is 11
The continuous decay rate is 13%
From the graph
To find the value of t when Q = 2
Look at the vertical axis Q and go to the scale of 2
Move horizontally from 2 until you cut the graph
Go down to read the value of t
The value of t is about 13
b)
At
Q = 2
t = 13
c)
Now, we will substitute Q in the function by 2
[tex]2=11e^{-0.13t}[/tex]Divide both sides by 11
[tex]\frac{2}{11}=e^{-0.13t}[/tex]Insert ln on both sides
[tex]ln(\frac{2}{11})=lne^{-0.13t}[/tex]Use the rule
[tex]lne^n=n[/tex][tex]lne^{-0.13t}=-0.13t[/tex]Substitute it in the equation
[tex]ln(\frac{2}{11})=-0.13t[/tex]Divide both sides by -0.13
[tex]\begin{gathered} \frac{ln(\frac{2}{11})}{-0.13}=t \\ \\ 13.11344686=t \end{gathered}[/tex]At
Q = 2
t = 13.11344686
You would like to make Chili, Tacos and Grilled Cheese this week. The grocery store prices and ingredients for the meals are listed above. One of each item will be enough to cover all recipes, except you will need two packages of cheese to make all three recipes. How much will you spend on groceries?
Answer:
i dont get it
Step-by-step explanation:
Rational Expression and EquationsClassify each equation as direct inverse or joint variation then state the constant of variation
2. Given:
[tex]y=7z[/tex]To classify the equation as direct, inverse or joint variation then state the constant of variation:
It is of the form,
[tex]y=kz,\text{ whe}re\text{ }k\text{ is the constant}[/tex]If y increases then z increases and if y decreases then z decreases.
Therefore, it is direct variation.
We know that the ratio between two variables in a direct variation is a constant of variation.
Thus, the constant of variation is k = 7.
Lisa is saving $50 that she received from her grandmother. She earns $6 each time she walks her neighbor's dog, which she also saves. Which function can be used to find f, the amount of money Lisa will have saved after walking the neighbor's dog d times?
Let
f ------> the amount of money Lisa will have saved
d -----> number of times that she walking the neighbor's dog
so
Remember that
The linear equation in slope intercet form is equal to
f=md+b
where
m is the unit rate or slope
b is the y-intercept or initial value
in this problem we have
m=6
b=50
therefore
substitute
f=6d+50
answer is last one option
Um Im in fith grade and i need help with some of my math questions if your able to help me with five or 10 questions that will be great
Solution
For this case we can do the following:
Then the solution would be:
21 6/24 = 21 1/4
For this case we can do the following for 21 1/4
[tex]21\cdot\frac{1}{4}=\frac{21\cdot4+1}{4}=\frac{85}{4}[/tex]For the second part we can do this:
[tex]\frac{1}{3}\cdot5=\frac{5}{3}[/tex]Then the answer is 5/3
An empty shipping box weighs 250 grams. The box is then filled with t-shirts. Each tshirts weighs 132.5 grams. The equation W = 250 + 132.5T represents the relationship between the quantities in this solution where W is the weight in grams of the filled box and T the number of shirts in the box. Consider this equation 2900 = 250 + 132.5T. What does the solution to this equation tell us?
Given the next equation
2900 = 250 + 132.5T
its solution is:
2900 - 250 = 132.5T
2650 = 132.5T
2650/132.5 = T
T = 20
Given that W is weigth and T is t-shirts, the solution tell us that a box with 20 t-shirts weights 2900 grams
Enter your searchrmFind the compound interest and future value. Do not round intermediate steps. Round your answers to the nearest cent.Principal Rate Compounded Time$895Annually11 years2%The future value is $, and the compound interest is $ХS
Given:
Principal, P = $895
Time, t = 11 years
Rate, r = 2% compounded annually.
Let's find the compound interest and the future value.
To find the future value apply the formula:
[tex]A=P(1+r)^t[/tex]Where:
A is the future amount.
P is the principal = 895
r is the rate = 2% = 0.02
t is the time in years = 11
Hence, we have:
[tex]\begin{gathered} A=895(1+0.02)^{11} \\ \\ A=895(1.02)^{11} \\ \\ A=895(1.2433743) \\ \\ A=1112.82 \end{gathered}[/tex]Therefore, the future value is $1112.82
To find the compound interest, substitute the principlal (P) from the future value (A).
Compound interest = $1112.82 - $895
= $217.82
The compound interest is $217.82
A
Help Please, I don’t understand and it’s really confusing me
We have this expression:
[tex]\frac{15}{y}[/tex]Let's substitute y = 1/4 into this expression.
[tex]\frac{15}{\frac{1}{4}}[/tex]Multiply the top and bottom by 4/1 in order to get rid of the double fractions.
[tex]15(\frac{4}{1})=60[/tex]The answer to this problem is C) 60.