To solve the given equation, we first apply the distributive property of multiplication and reduce like terms:
[tex]\begin{gathered} 4(2-3t)+6t=-6t+8, \\ 8-12t+6t=-6t+8, \\ 8-6t=-6t+8. \end{gathered}[/tex]Now, we notice that the left and the right side of the equation are equal for any choice of t.
Answer: Identity.
Triangle A'B'C' is apparently - у А A' B C С B' O A clockwise 90 degree rotation of Triangle ABC O A reflection across the y-axis of Triangle ABC O A translation of Triangle ABC right 7 units O A clockwise 270 degree rotation of Triangle ABC
Since all coordinates of the transformated triangle are changed like this:
[tex](x,y)\rightarrow(y,-x)[/tex]Triangle A'B'C' is a clockwise 270 degree rotation of triangle ABC
A counterclockwise rotation of 90º is the same that a clockwise rotation of 270º
how do u knwo which way to face the inequality sign in the answer of these questions like 1>x<3 how do u know which way to face them. i put some examples os u cna use them to explain
Using the graph identify the intervals:
a) Function being less than or equal to 0: In which x interval is the graph under the x-axis (the functions are less than 0 when they are under x-axis)
As the ineqaulity sing is less than or equal to 0, the interval includes those x-values for which the function is 0:
Solution: Interval from x=1 to x=3
[tex]\begin{gathered} x^2-4x+3\leq0 \\ 1\leq x\leq3 \\ \lbrack1,3\rbrack \end{gathered}[/tex]b) Function being greater than or equal to 0: In which x interval is the graph over the x-axis.
As the ineqaulity sing is greater than or equal to 0, the interval includes those x-values for which the function is 0:
Solution: Interval from - infinite to 1 and from 3 to infinite
[tex]\begin{gathered} x^2-4x+3\ge0 \\ 1\ge x\ge3 \\ (-\infty,1\rbrack\cup\lbrack3,\infty) \end{gathered}[/tex]c) Function being greater than 0: In which x interval is the graph over the x-axis.
As the ineqaulity sing is greater than to 0, the interval does not include those x-values for which the function is 0.
[tex]\begin{gathered} x^2-4x+3>0 \\ 1>x>3 \\ (-\infty,1)\cup(3,\infty) \end{gathered}[/tex]d) Function being less than 0: In which x interval is the graph under the x-axis.
As the ineqaulity sing is less than 0, the interval does not include those x-values for which the function is 0:
[tex]\begin{gathered} x^2-4x+3<0 \\ 1A box contains different colored paper clips. The probability of drawing two red paper clips from the box without replacement is 1/7, and the probability of drawing one red paper clip is 2/5.What is the probability of drawing a second red paper clip, given that the first paper clip is red?1/65/142/32/35
SOLUTION
The probability of two red paper clips without replacement means
The probability of drawing the first and the probability of drawing the second one. This is represented as
[tex]P(R_{1st}\cap R_{2nd})[/tex]And this was given as
[tex]\frac{1}{7}[/tex]So
[tex]P(R_{1st}\cap R_{2nd})=\frac{1}{7}[/tex]Probalilty of drawing one red paper clip is
[tex]P(R_{1st})=\frac{2}{5}[/tex]Now the probability of drawing a second red paper clip, given that the first paper clip is red becomes
[tex]\begin{gathered} P(R_{1st}/R_{2nd})=\frac{P(R_{1st}\cap R_{2nd})}{P(R_{1st})} \\ \\ P(R_{1st}/R_{2nd})=\frac{\frac{1}{7}}{\frac{2}{5}} \\ \\ =\frac{5}{14} \end{gathered}[/tex]Solve the system of equations.y = x2 - 2y = -2x + 1A. (-3,7) and (-1,3)B. (-3,7) and (1, -1)C. (1.-1) and (3,-5)D. (-1,3) and (3, -5)
Answer
Option B is correct.
the solutions to the system of equations include
(-3, 7) and (1, -1)
Step-by-step Explanation
The question is to solve the system of equations
y = x² - 2 ..... equation 1
y = -2x + 1 ..... equation 2
To solve this, we can just equate the expression given for y in equation 1 to the expression given for y in equation 2.
y = x² - 2
y = -2x + 1
Since
y = y
x² - 2 = -2x + 1
x² + 2x - 2 - 1 = 0
x² + 2x - 3 = 0
This gives a quadratic equation which we will now solve
x² + 2x - 3 = 0
x² + 3x - x - 3 = 0
x (x + 3) - 1 (x + 3) = 0
(x - 1) (x + 3) = 0
So,
x - 1 = 0 or x + 3 = 0
x = 1 or x = -3
If x = 1,
y = x² - 2
= 1² - 2
= 1 - 2
= -1
x = 1, y = -1
If x = -3
y = x² - 2
= (-3)² - 2
= 9 - 2
= 7
x = -3, y = 7
So, the solutions to the system of equations include
x = -3, y = 7, that is, (-3, 7)
And
x = 1, y = -1, that is, (1, -1)
Hope this Helps!!!
A. Step 1B. Step 2C. Priya did not make a mistake
We will have the following:
[tex]\frac{f}{0.25}=16\Rightarrow f=16\cdot0.25[/tex][tex]\Rightarrow f=4[/tex]From this we can see that there was no mistaky on Priya's side. [Option 3]
Consider functions f and g.1 + 12f(1) = 12 + 4. – 12for * # 2 and 7 -64.2 – 16. + 1641 +48for a # -12 Which expression is equal to f(x) · g(t)?OA.41 - 81 + 61OB.SIKIAOC.21 + 6I + 2D.6
Given the following functions below,
[tex]\begin{gathered} f(x)=\frac{x+12}{x^2+4x-12}\text{ and} \\ g(x)=\frac{4x^2-16x+16}{4x+48} \end{gathered}[/tex]Factorising the denominators of both functions,
Factorising the denominator of f(x),
[tex]\begin{gathered} f(x)=\frac{x+12}{x^2+4x-12}=\frac{x+12}{x^2+6x-2x-12}=\frac{x+12}{x(x+6)-2(x+6)}=\frac{x+12}{(x-2)(x+6)} \\ f(x)=\frac{x+12}{(x-2)(x+6)} \end{gathered}[/tex]Factorising the denominator of g(x),
[tex]\begin{gathered} g(x)=\frac{4x^2-16x+16}{4x+48}=\frac{4(x^2-4x+4)}{4(x+12)} \\ \text{Cancel out 4 from both numerator and denominator} \\ g(x)=\frac{x^2-4x+4}{x+12}=\frac{x^2-2x-2x+4}{x+12}=\frac{x(x-2)-2(x-2)}{x+12}=\frac{(x-2)^2}{x+12} \\ g(x)=\frac{(x-2)^2}{x+12} \end{gathered}[/tex]Multiplying both functions,
[tex]undefined[/tex]Given that: 100 = 2^2 * 5^2, how is 400 written as a product of its prime factors?
Answer:
400 written as a product of it's prime factors is 2^4 * 5²
Step-by-step explanation:
We have to factore the number, dividing by prime factors(2, 3, 5, 7, ...)
400|2
200|2
100
We already have the factorization of 100. So
400 = 2²*100 = 2²*2²*5² = 2^4 * 5²
400 written as a product of it's prime factors is 2^4 * 5²
l A golf ball is hit in the air. The table shown describes y, the height of the ball, in feet, given the time elapsed, x, in seconds, since the time the ball was hit.Based on the information in the table, which statements are true? Select each correct statement.
Given:
y is the height of the ball in feet
x is the time in seconds
In the given table you can identify the next maximum:
x=3
y=30
The ball has height 0 when it is in the earth so it is hit at second 0 and will be back in the earth at second 6
Then, from the given statements the next are true:
The maximum height of the ball was 30 feetThe ball was in the air for only 6 secondsDraw the image of the figure under thegiven transformation.6.reflection across the x-axis7. (X,y) - (x - 4, y + 1)8. reflection across the y-axis
6.
While transformation with the reflection across the x-axis, the absicssa (x-coordinate) remains the same but ordinate (y-coordinate) changes its sign.
The coordinate of point A is (3,0), coordinate of point B is (1,4) and the coordinate of point C is (5,3).
After transformation the, coordinate with the image can be shown as,
Thus, the coordinates of the image after transformation is A'(3,0), B'(1,-4) and C'(5,-3).
a cellular phone company charges a base rate of $15.00 per month and $0.05 per minute,m, which equation could be used to find the total monthly charge in dollars,c?
Suppose you use "m" minutes in a month and each minute is $0.05, so your minute bill would be:
0.05 * m
Per month, there is a fixed rate of $15 , no matter how many minutes you use.
So, that's a fixed cost.
Total monthly charge would be:
15 + 0.05m
The cost, c, is:
[tex]c=0.05m+15[/tex]Correct Answer Choice is Option B
sec40+ sec20 tan2 0 - 2 tan4 0 =3 sec² 0 -2Sect0-210
Given:
[tex]sec^4\theta+sec^2\theta tan^2\theta-2tan^4\theta=3sec^2\theta-2[/tex]Required:
We need to prove the given equation.
Explanation:
Consider the left-hand side of the equation.
[tex]Add\text{ and subtract }3tan^4\theta.[/tex][tex]sec^4\theta+sec^2\theta tan^2\theta-2tan^4\theta=sec^4\theta+sec^2\theta tan^2\theta-2tan^4\theta+3tan^4\theta-3tan^4\theta[/tex][tex]=sec^4\theta+sec^2\theta tan^2\theta+tan^4\theta-3tan^4\theta[/tex][tex]Add\text{ and subtract -2}sec^2\theta tan^2\theta.[/tex][tex]=sec^4\theta+sec^2\theta tan^2\theta+tan^4\theta-3tan^4\theta-2sec^2\theta tan^2\theta+2sec^2\theta tan^2\theta[/tex][tex]=sec^4\theta-2sec^2\theta tan^2\theta+tan^4\theta-3tan^4\theta+sec^2\theta tan^2\theta+2sec^2\theta tan^2\theta[/tex][tex]=sec^4\theta-2sec^2\theta tan^2\theta+tan^4\theta-3tan^4\theta+3sec^2\theta tan^2\theta[/tex][tex]Use\text{ }sec^4\theta-2sec^2\theta tan^2\theta+tan^4\theta=(sec^2\theta-tan^2\theta)^2[/tex][tex]=(sec^2\theta-tan^2\theta)^2-3tan^4\theta+3sec^2\theta tan^2\theta[/tex][tex]=(sec^2\theta-tan^2\theta)^2+3tan^2\theta(sec^2\theta-tan^2\theta)[/tex][tex]Use\text{ }sec^2\theta-tan^2\theta=1.[/tex][tex]=1^2+3tan^2\theta(1)[/tex][tex]=1+3tan^2\theta[/tex][tex]Use\text{ }tan^2\theta=sec^2\theta-1.[/tex][tex]=1+3(sec^2\theta-1)[/tex][tex]=1+3sec^2\theta-3[/tex][tex]=3sec^2\theta-2[/tex]We get the right-hand side of the equation.
Final answer:
[tex]sec^4\theta+sec^2\theta tan^2\theta-2tan^4\theta=3sec^2\theta-2[/tex]Justin earned $600 last week fixing computers.Is it possible to determine how many hours Justin worked?explain
Since Justin earned $600 last week
If we want to find the number of hours that he worked, we must have how much he earned per hour
But we do not have how much did he earn per hour, so
It is impossible to find how many hours did he work from the given information
The answer is
No, it is impossible to find that
A hot air balloon is flying above Groveburg. To the left side of the balloon, the balloonist measure the angle of depressionto the Groveburg soccer fields to be 20° 15'. To the right side of the balloon, the balloonist measures the angle ofdepression to the high school football field to be 62° 30'. The distance between the two athletic complexes is 4 miles.What is the distance from the balloon to the football field?a.b.>3.6 miC.~6.2 mi>2.2midy1.4 miPlease select the best answer from the choices providedOAOBOCOD
The distance from the balloon to the football field will be 1.4 miles.
Angle of depression to the Grove burg soccer fields = 20° 15'.
Use 1' = 1 / 60° :
15' = 1 / 4 ° = 0.25 °
20° 15' = 20.25°
Angle of depression to the high school football field = 62° 30'.
30' = 0.5°
62° 30' = 62.5°
the distance from the balloon to the football field will be:
Let the distance be a
a / sin a = c / sin c
a / sin (20.25) = 4 / sin (97.5)
a = 4 sin (20.25) / sin (97.5)
a = 1.4 miles.
Therefore, we get that, the distance from the balloon to the football field will be 1.4 miles.
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A phone company charges for service according to the formula: C(n) = 19 + 0.08n , where n is the number of minutes talked , and C(n) is the monthly charge, in dollars .The rate of change in this equation is:The initial value in this equation is:
In a linear equation, the coefficient of the variable is the rate of change and the constant term is the initial value.
For example, a linear function with rate of change m and initial value b is:
[tex]f(x)=mx+b[/tex]In the given formula, the variable is n, its coefficient is 0.08 and the constant term is 19.
Since n is measured in minutes and C is measured in dollars (as well as the initial value), then, the coefficient 0.08 must have the units necessary for the minutes to cancel out, leaving dollars as the unit of 0.08n. Then, the units of the rate of change must be dollars per minute.
Since the constant term is 19, then the initial value is 19.
Therefore, the answers are:
The rate of change in the equation is 0.08 dollars per minute.
The initial value in the equation is 19 dollars.
Determine the height of the ball after 4 seconds *Height of Ball over Time160144128112Height (in feet)96NO643216O1 2 3 4 5 6Time (in seconds)
80 ft
1) In the graph, we can find out the height after 4 seconds simply locating the point when the x-axis at t=4
2) Hence, after 4 seconds the height of the ball is:
3) Hence, the answer is 80 ft (the blue dot) (4,80)
How to do 2 step equations Can you solve 2x + 5=21?
Given
The equation,
[tex]2x+5=21[/tex]To find the value of x or to solve for x.
Explanation:
It is given that,
The equation is,
[tex]2x+5=21[/tex]That implies,
[tex]\begin{gathered} 2x+5=21 \\ 2x=21-5 \\ 2x=16 \\ x=\frac{16}{2} \\ x=8 \end{gathered}[/tex]Hence, the value of x is 8.
If AABC = ADEC,ZB = 44º and ZE = 4xx= [?]
Solution
Given that Triangle, ABC is congruent to Triangle DEC
=> ∠A = ∠D; ∠B = ∠E; ∠C = ∠C
Given that ∠B = 44, ∠E = 4x
=> 44 = 4x
=>x = 44/4 = 11
Hence, x = 11
Hi, can you help me answer this question please, thank you!
Given that
[tex]\begin{gathered} \mu_1=sample\text{ of soda in the coke can} \\ \mu_2=sample\text{ of soda in the pepsi can} \end{gathered}[/tex]Therefore, in the first statement, we are to test how accurate the companies package these cans.
Mathematically it can be expressed as,
[tex]H_0\colon\mu_1\leq\mu_2[/tex]In the second statement, we wish to test the claim that the mean of the amount of liquid in coke cans is greater than the amount of liquid in pepsi cans. This can be expressed mathematically as,
[tex]H_a\colon\mu_1>\mu_2[/tex]Hence, the correct option is Option 1.
find the value of the term in the arithmetic sequence 1,6,11,16...(8th term)
We need to find the 8th term of the following arithmetic sequence:
[tex]1,6,11,16,...[/tex]The formula to find the n-th term an of aₙ arithmetic sequence is:
[tex]a_n=a_1+(n-1)d[/tex]where a₁ is the first term and d is the difference between two consecutive terms.
The first term of this sequence is a₁ = 1, and d is given by:
[tex]\begin{gathered} d=a_2-a_1 \\ \\ d=6-1 \\ \\ d=5 \end{gathered}[/tex]Then, for n = 8, we obtain:
[tex]\begin{gathered} a_8=1+(8-1)5 \\ \\ a_8=1+7(5) \\ \\ a_8=1+35 \\ \\ a_8=36 \end{gathered}[/tex]Answer:
The 8th term is 36.
Write the equation in slope-intercept form through the point (2, -1) and is perpendicular to the line y = -5x + 1 and graph.
First, we are going to calculate the perpendicular slope. The condition for perpendicular lines is the following:
[tex]m1m2=-1[/tex]First, m1 = -5
[tex]m2=\frac{-1}{m1}=\frac{-1}{-5}\rightarrow m2=\frac{1}{5}[/tex]Now, for b
[tex]b=y-m2x[/tex]For the point (2,-1)
[tex]b=-1-\frac{1}{5}\cdot(2)[/tex][tex]b=-\frac{5}{5}-\frac{2}{5}=\frac{-7}{5}[/tex][tex]y=\frac{1}{5}x-\frac{7}{5}[/tex]What is this expression in simplest form?
+2
4x² + 5x + 1
Ο Α.
О в.
O C.
O D.
4x + 1
²-4
(x + 1)(x − 2)
-
I
(z = 2)
1
4x + 1
(x + 1)(x-2)
ww
4x+1
#12
Answer:
[tex] \frac{x + 2}{4 {x}^{2} + 5x + 1 } . \frac{4x + 1}{ {x}^{2} + 4} \\ \frac{x + 2}{4 {x}^{2} + (4 + 1)x + 1 } . \frac{4x + 1}{ {(x + 2)}^{2} } \\ \frac{1}{4 {x}^{2} + 4x + x + 1}. \frac{4x + 1}{x + 2} \\ \frac{1}{x(4x + 1) + 1(4x + 1)} . \frac{4x + 1}{x + 2} \\ \frac{1}{(4x + 1)(x + 1)} . \frac{4x + 1}{x + 2} \\ \frac{1}{(x + 1)}. \frac{1}{(x + 2)} \\ \frac{1}{(x + 1)(x + 2)} [/tex]
A. is the answer!!
The value of 0.36 when converted to a fraction in the simplest form is 9/25.
What is fraction?A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.
here, we have,
to calculate fractions in simplest form:
Your information is incomplete. Therefore, an overview will be given. It should be noted that a fraction is in its simplest form when the numerator and denominator are prime.
From example, let's convert 0.36 to a fraction on its simplest form. This will be:
0.36 = 36/100 = 9/25
In conclusion, 0.36 is 9/25 in the simplest form.
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in a survey of 1300 people who owned a certain type of car 585 said they would buy the type of car again what percent of people surveyed were satisfied with the car
In order to find the percentage of people that were satisfied with the car, we just need to divide this amount of people by the total amount of people surveyed.
So we have:
[tex]\frac{585}{1300}=0.45=45\text{\%}[/tex]So 45% of the surveyed people were satisfied with the car.
Determine the probability of being dealt 4 Aecs of cards, from a deck of 52 playing cards, with a replacement.
Given:
4 Aces of cards from a deck of 5 playing cards.
[tex]\begin{gathered} \text{Probability of drawing 4 Aces }=\frac{4}{52}\times\frac{4}{52}\times\frac{4}{52}\times\frac{4}{52}\times4! \\ \text{Probability of drawing 4 Aces }=\frac{1}{13}\times\frac{1}{13}\times\frac{1}{13}\times\frac{1}{13}\times24 \\ \text{Probability of drawing 4 Aces }=\frac{24}{28561} \end{gathered}[/tex]Find the general solution to dy/dx = 2y passing through the point (5, 1)
We will have the following:
[tex]\frac{\partial y}{\partial x}=2y\Rightarrow\frac{1}{2y}\partial y=\partial x[/tex][tex]\Rightarrow\int (\frac{1}{2y})\partial y=\int \partial x\Rightarrow\frac{\log (y)}{2}=x+c[/tex]Then we find "c":
[tex]\frac{\log(1)}{2}=5+c\Rightarrow c=-5[/tex]Thus, the general solution passing through (5, 1) is:
[tex]\frac{\log(y)}{2}=x-5[/tex]Write the expression and simplifyThe difference of -10 and the product of p and q
We start with a subtraction, where we want to subtract the second term from - 10. The second term consists in a multiplication between p and q. Writing this as a mathematical expression we have
[tex]-10-pq[/tex]This expression is already on simplest form.
True or false the function f(x) = -3(x+10)^2 has a minimum
Notice that:
[tex]\begin{gathered} f^{\prime}(x)=-6(x+10), \\ f^{\prime\prime}(x)=-6. \end{gathered}[/tex]Since for all x, f''(x)<0, by the second derivative criteria we get that f(x) reaches a maximum.
Answer: False.
katie has 5.455 apples and sadie has 10.31 how many apples do they have in all
Katie has 5.455
Sadie has 10.31
To find how many apples they have in all add the two numbers
They have = 5.455 + 10.31
They have = 5.455 + 10.310
0 + 5 = 5
1+ 5 = 6
3 + 4 = 7
10 + 5 = 15
They have = 15.765 apples in all
Write the equation of the line that is perpendicular to the line given and through the given point. Do not use spaces in your equation. y=-2X+1 (0,5) *
Answer:
y = 0.5x + 5
Explanation:
The equation of a line can be calculated as:
[tex]y=m(x-x_1)+y_1[/tex]Where m is the slope and (x1, y1) is a point in the line.
To find the slope of our line, we need to identify the slope of the given line.
Since the equation of the given line is y = -2x + 1, the slope of this line is -2, because it is the number beside the x.
Then, two lines are perpendicular if the product of their slopes is equal to -1. So, we can write the following equation:
[tex]-2\cdot m=-1[/tex]Therefore, the slope m of our line will be:
[tex]m=\frac{-1}{-2}=0.5[/tex]Now, we can replace the value f m by 0.5 and the point (x1, y1) by (0, 5) and we get that the equation of the line is:
[tex]\begin{gathered} y=0.5(x-0)+5 \\ y=0.5(x)+5 \\ y=0.5x+5 \end{gathered}[/tex]Therefore, the answer is y = 0.5x + 5
The lengths of the diagonals of a rectangle are representedby 2x + 3 and 4x - 11. Find the value of x.
The problem says that there are formulas for the diagonals of a rectangle. they are both givan in terms of x
Now, recall that the diagonals of a rectangle should be equal to each other, therefore those two expressions must equal ech other
2 x + 3 = 4 x - 11
Now let's solve for x:
move all terms with "x" to one side of the equation, and all "numerical" terms to the other side:
start by subtracting 2x from both sides:
3 = 4 x - 2 x - 11
3 = 2 x - 11
Now add 11 to both sides:
11 + 3 = 2 x
14 = 2 x
then x is 7
The product of two whole numbers is 592 and their sum is 53. What are the two numbers?
To solve this problem, we have to build two equations with the given information. Using x and y to represent the two numbers:
• Equation 1
[tex]x\times y=592[/tex]• Equation 2
[tex]x+y=53[/tex]Now that we have to equations, we have to isolate one variable from one equation and replace it in the other.
[tex]x=53-y[/tex]Then, we will replace this value of x in Equation 1:
[tex](53-y)\cdot y=592[/tex]Solving for y we get:
[tex]53y-y^2=592[/tex][tex]-y^2+53y-592=0[/tex]As we got this expression, we will have to use the General Quadratic Formula. With the help of a calculator, we get both values:
[tex]y_1=16[/tex][tex]y_2=37[/tex]Finally, we have to replace these values in Equation 1 to evaluate which meets the condition:
[tex]x_1=\frac{592}{y_1}[/tex][tex]x_1=\frac{592}{16}=37[/tex][tex]x_2=\frac{592}{y_2}[/tex][tex]x_2=\frac{592}{37_{}}=16[/tex]We have to evaluate the values in each equation:
[tex]\begin{gathered} 37+16=53 \\ 53=53 \end{gathered}[/tex][tex]37\cdot16=592[/tex]The first numbers meet the condition.
Answer: 37 and 16