x+3y=6 ----------------------------(1)
2x+4y=12---------------------------(2)
Using elimination method to solve;
we will eliminate x variable
To do that, we must make sure the coefficient of x in the two equation are the same.
This can be achieved by multiplying equation (1) by 2 and equation (2) by 1
That is;
2x + 6y = 12 ----------------------(3)
2x + 4y = 12 -----------------------(4)
subtract equation (4) from equation (3)
2y = 0
Divide both-side of the equation by 2
y=0
substitute y = 0 into equation (1)
x + 3(0) = 6
x = 6
Customers can pick their own blueberries at Blueberry Hill. They pay $5 toenter the patch and $4 per pound for the blueberries they pick. Write anequation to model the total cost, y, for x pounds of blueberries.
SOLUTION
Step1; Write out the parameters
[tex]\begin{gathered} \text{entry fe}e=\text{ \$5} \\ \cos t\text{ of blueberries per pound=\$4} \end{gathered}[/tex]Step2: Write out the variables
[tex]\text{let y=total cost and x=number of bluerries}[/tex]Step3: write out the model
[tex]\begin{gathered} \text{The total cost=number of blueberries}\times\text{\$}4+\text{ the entry fe}e \\ y=4x+5 \end{gathered}[/tex]There
Convert the Fahrenheit temperature to the equivalent Celsius temperature round to 1 decimal Places if necessary
Given
[tex]19^0F[/tex]To convert the given to Celsius
Solution
The formula connecting Fahrenheit and degree Celsius is given as
[tex]\begin{gathered} =\frac{5(F-32)^{}}{9} \\ =\frac{5(19-32)}{9} \\ =\frac{5(-13)}{9}=-7.222^0C \end{gathered}[/tex]Hence
19⁰F = -7.2⁰C
Given the definitions of f(x) and g(x) below, find the value of g(f(-2)). f(x) = 5x + 4 g(x) = x^2 - 6x - 13
f(-2) = 5(-2) + 4
= -10 + 4
= -6
g(f(-2))
= -6^2 -6*-6 -13
= 36 + 36 - 13
= 59
210000The first five multiples for the numbers 4 and 6 are shown below.Multiples of 4: 4, 8, 12, 16, 20, ...Multiples of 6: 6, 12, 18, 24, 30,...What is the least common multiple of 4 and 6?222122423 24 25Mark this and returnSave and ExitNext
Answer: 12
Explanation
The least common multiple can be calculated by getting the factor of each number. As we are told, the multiples of 4 are 4, 8, 12, 16, 20, ..., and the multiples of 6 are 6, 12, 18, 24, 30, ....
Thus, the lowest factor that they share is 12.
If you receive 360 promotional emails per month and only 2.5% percent of those emails are of interest to you, what is the expected number of promotional emails that will be of interest to you each month?
Total email 360
percentage email of interest 2.5%
Solution[tex]\begin{gathered} \frac{2.5}{100}\times360=9 \\ \end{gathered}[/tex]The final answer9 promotional emails that will be of interest to you each monthgraph the quadrilateral with the given vertices in a coordinate plane. then show the quadrilateral in a a parallelogram
First, let's graph the polygon:
Now, let's prove it's a parallelogram by showing that the segments NP and RQ are parallel, and NR and PQ are parallel as well.
Let's prove that the angular coefficient is the same for NR and PQ
[tex]\begin{gathered} m_{NR}=\frac{0-(-4)}{-5-(-3)}=-\frac{4}{3} \\ \\ m_{PQ}=\frac{5-0}{0-3}=-\frac{4}{3} \end{gathered}[/tex]Then they're parallel, just to confirm, let's do the same for NP and RQ
[tex]\begin{gathered} m_{NP}=\frac{4-0}{0-(-5)}=\frac{4}{5} \\ \\ m_{RQ}=\frac{-4-0}{-2-(3)}=\frac{4}{5} \end{gathered}[/tex]Then it's parallel as well.
Use the Distributive Property
solve the equation.
- 6(x + 3) = 30
Using the Distributive Property of multiplication, the equation - 6(x + 3) = 30 is solved as x = -8.
What is the distributive property of multiplication?The distributive property of multiplication shows that a mathematical expression in the form of a(b + c) is also equal to ab + ac.
The distributive property applies to either addition or subtraction in multiplication.
- 6(x + 3) = 30
-6x - 18 = 30
-6x = 48
x = -8
Thus, x = -8 is the solution to the equation - 6(x + 3) = 30.
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Which relation represents a function sample A or sample B
Sample A is a function because we don't have 2 values of x that are the same
Sample B is not a function, because it fails the vertical line test (x = 4 and y =1 also x=4 and y = 10) (4, 1) and (4, 10)
Hence the correct option is ; sample A
A survey of a random sample of voters showsthat 56% plan to vote Yes to the newproposition and 44% plan to vote No. Thesurvey has a margin of error of +4%. What isthe range for the percentage of voters whoplan to vote Yes?
Answer:
G 52% to 60%
Explanation:
The percentage of voters that plan to vote Yes = 56%
The survey's margin of error = +/-4%
Therefore, the range for the percentage of voters who plan to vote Yes is:
[tex]\begin{gathered} 56\%\pm4\% \\ =56\%-4\%\text{ to }56\%+4\% \\ =52\%\text{ to }60\% \end{gathered}[/tex]The correct choice is G.
Find the difference. (10m+ 3) - (4m-2) O A. 14m-1 OB. 6m+ 5 O C. 6m-1 D. 14m + 5
(10m + 3) - (4m -2)
Firstly, use the negative sign to open the parenthesis
(10m + 3) -1 x 4m -1 x (-2)
minus x minus = plus
(10m + 3) -4m + 2
10m + 3 - 4m + 2
Collect the like terms
10m - 4m + 3 + 2
m(10-4) + 5
m(6) + 5
6m + 5
The answer is OPTION B
A resident is to receive 2 ounces of liquid . You know 30 ccs equals one ounce . How many ccs of the liquid will you give to ensure the resident receives 2 ounces
From the statement of the question, we know that 1 ounce and 30ccs are equivalent, we represent that with the following equation:
[tex]1\text{ounce}=30\text{ccs.}[/tex]Now, 2 ounces is double of 1 ounce, because 1 ounce is 30 ccs, 2 ounces must be 60ccs, the double of 30ccs.
[tex]2\text{ounces}=2\cdot1\text{ounce}=2\cdot30\text{ccs}=60\text{ccs.}[/tex]So if we want to ensure that the resident will receive 2 ounces of liquid, we must give him 60ccs.
Answer: we must give him 60ccs of liquid.
Need help with this exercise. It’s from a review the real test is next week need more explanation so I already know what to do on the test.
ANSWER
Options 1 and 4
EXPLANATION
First, let us find the length of the third side of the right triangle. To do this apply the Pythagoras theorem.
Let the length of the third side of the triangle be x.
It implies that:
[tex]\begin{gathered} x^2+8^2=17^2 \\ x^2=17^2-8^2 \\ x^2=289-64=225 \\ x=\sqrt[]{225} \\ x=15 \end{gathered}[/tex]Now, we can find the value of sinA, tanA, and sinC.
According to trigonometric ratios, SOHCAHTOA, we have that:
[tex]\begin{gathered} \sin A=\frac{\text{opposite}}{\text{hypotenuse}} \\ \tan A=\frac{\text{opposite}}{\text{adjacent}} \\ \sin C=\frac{\text{opposite}}{\text{hypotenuse}} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} \sin A=\frac{15}{17} \\ \tan A=\frac{15}{8} \\ \sin C=\frac{8}{17} \end{gathered}[/tex]Hence, the correct options are options 1 and 4.
In order to pass a science lab, you have to measure a beaker (container) of water with 5% error or less. The beaker has 12 ounces of water in it. You measure 13.2 ounces of water. Did you pass the lab? Why or why not?
Data:
Error: 5%
Volume of water in the Beaker: 12oz
Your measure: 13.2oz
As the error is 5% it means that the measure can be actually 5% more or 5% less.
Then, you calculate the 5% of the measure you have to measure: 12oz
[tex]12\cdot\frac{5}{100}=0.6oz[/tex]Then, the measure you need to take to pass the lab is between: 11.4oz and 12.6oz
[tex]12oz\pm0.6oz[/tex][tex]\begin{gathered} 12oz+0.6oz=12.6oz \\ 12oz-0.6oz=11.4oz \end{gathered}[/tex]Then, your measure of 13.2oz is not between the 5% of error. You didn't pass the lab.
Write a quadratic inequality represented by the graph.
The quadratic inequality represented by the graph is y > -x².
What is meant by quadratic inequality?Simply put, an equation of the type with the highest degree of two and no equal sign is known as a quadratic inequality. There is a technique for resolving quadratic inequalities called the wavy curve approach. It is the same to solve quadratic equations as it is solving quadratic inequalities. When plotted, quadratic inequalities show a parabola, much like quadratic equations do. Quadratic inequalities can be solved to provide a variety of solutions. For instance, the quadratic equation x²+6x+5=0 has two solutions: x² + 6 x + 5 = 0 and x² + 6x + 5 = 0. A second-degree equation with a quadratic inequality substitutes an inequality sign for an equal sign. The quadratic inequalities x- 6x - 16 0, 2x² - 11x + 12 > 0, x² + 4> 0, and x² - 3x + 20 are some examples.
From the graph, we can see that it is a parabola with vertex points (0,-9)
Thus, y= -3² is the equation at the vertex and the equation of the parabola will be y= -x².
The graph is an increasing function, so the inequality will be
y > - x²
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Which of the following equations is equivalent to log(y)= 3.994
ANSWER:
[tex]y=10^{3.994}[/tex]STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]log\mleft(y\mright)=3.994[/tex]Applying property of logarithms we have:
[tex]\begin{gathered} \log _a(b)=c\rightarrow b=a^c \\ \text{ in this case:} \\ log(y)=3.994\rightarrow y=10^{3.994} \end{gathered}[/tex]For a winter-themed Valentine's Day party, Mr. Rivera made 12 cups of hot chocolate. Does he have enough hot chocolate to give 26 kids 1/2 of a cup each?
Multiply the number of kids by the number of cups for each kid. This is 26 times 1/2.
[tex]26\cdot\frac{1}{2}=\frac{26}{2}=13[/tex]It means 13 cups are needed to give each of the 26 kids 1/2 of a cup of chocolate.
Mr. Rivera does not have enough hot chocolate to give 26 kids 1/2 of a cup of chocolate.
Which of the following equations is equivalent to the given equation?
Answer:
[tex]\begin{equation*} 5(7a+5)-80=4(3a+15) \end{equation*}[/tex]Explanation:
Given the equation:
[tex]\frac{7a+5}{8}-2=\frac{3a+15}{10}[/tex]First, find the lowest common multiple of the denominators 8 and 10.
• The LCM of 8 and 10 = 40
Then, multiply all through by 40:
[tex]\begin{gathered} \frac{40(7a+5)}{8}-2(40)=\frac{40(3a+15)}{10} \\ \implies5(7a+5)-80=4(3a+15) \end{gathered}[/tex]The third option is equivalent.
Answer:
5(7a + 5) - 80 = 4(3a + 15)
Step-by-step explanation:
what is the shape of a cross section that is parallel to the bases
The cross-section that is parallel to the base will have a
RECTANGULAR Shape
It's just like cutting through the shape horizontally
Team A, B, and C are competing in a basketball tournament. The probability of team A winning is 0.2, the probability of team B winning is 0.45, and the probability of team C winning is 0.35. Anna can join either team A or team B. Elina can join either team B or team C. Nancy can join either team A or team C. Who is most likely to win?AnnaNancyElenaAll have an equal probability to win.
Solution
We are given that
[tex]\begin{gathered} p(A)=0.2 \\ p(B)=0.45 \\ p(C)=0.35 \end{gathered}[/tex]Note 1: Probability Formula To use
[tex]p(A\cup B)=p(A)+p(B)-p(A\cap B)[/tex]Note 2: Team A, B and C are Mutually Exclusive
[tex]\begin{gathered} p(A)+p(B)+p(C)=0.2+0.45+0.35=1 \\ Th\text{ey are mutually exclusive} \\ A\cap B=B\cap C=A\cap C=\varnothing \\ p(A\cap B)=p(B\cap C)=p(A\cap C)=0 \end{gathered}[/tex]Therefore, the formula to use now is
[tex]p(A\cup B)=p(A)+p(B)[/tex]For Anna
Anna can join either team A or team B.
We calculate the probability
[tex]\begin{gathered} p(A\cup B)=p(A)+p(B) \\ p(A\cup B)=0.2+0.45 \\ p(A\cup B)=0.65 \end{gathered}[/tex]For Elina
Elina can join either team B or team C.
We calculate the probability
[tex]\begin{gathered} p(B\cup C)=p(B)+p(C) \\ p(B\cup C)=0.45+0.35 \\ p(B\cup C)=0.8 \end{gathered}[/tex]For Nancy
Nancy can join either team A or team C.
We calculate the probability
[tex]\begin{gathered} p(A\cup C)=p(A)+p(C) \\ p(A\cup C)=0.2+0.35 \\ p(A\cup C)=0.55 \end{gathered}[/tex]The one with the highest probability is most likely to win and that is
ELINA
Correct answer is Elina
-7.9 cm 26.2 cm 6.2 cm 19.1 cm 2.8 cm The perimeter of the figure is (Type a whole number or a decal.) .
ANSWER
The perimeter is 81.5 cm
EXPLANATION
The perimeter of any polygon is the sum of the length of its sides. The perimeter of this figure is:
[tex]P=7.9+26.2+6.2+22.8+18.4=81.5\operatorname{cm}[/tex]Allen is choosing a 2 letter password from the letters ABCD. the password cannot be the same letter repeated in it .how many such passwords are possible?
Since we can choose 2 letters and they can not be the same, we have the following possibilities:
[tex]{}\lbrace AB,AC,AD,BC,BD,BA,CB,CA,CD,DA,DB,DC\rbrace[/tex]As we can note, there are 12 possible combinations of 2 different letters. So, How many such passwords are possible? The answer is 12 passwrods
A seven digit telephone number is of theform ABC-DEFG. In one particular state,the digit ‘A’ is restricted to any numberbetween 1 and 9. The digits B and Carerestricted to any number between 2 and9. The digits D,E,F, and G have norestriction. How many seven digit phonenumbers are possible with theserestrictions?
9 x 8 x 8 x 10 x 10 x 10 x 10 = 5760000 possible phone numbers
I need help with this questionthe question to this question is below is a graph of a logarithmic function, identify it key characteristics. match accordingly
The answers to the problem :
[tex]\begin{gathered} 1.\text{ Domain : x >-6} \\ 2\text{ Range : -}\infty\text{ to +}\infty \\ 3.\text{ Aymptote : x = -6} \\ 4\text{. Transformation : left 6, down 1} \\ 5.\text{ End behaviour : As x approaches }\infty,\text{ f(x) approaches }\infty.\text{ As x approaches -6, f(x) approaches -}\infty \\ 6.\text{ x-intercept : (-4,0)} \end{gathered}[/tex]nQuestion 6Mutiple Choice Worth 1 points)(06.04 MC)The length of a rectangle is represented by the function L(x)= 2x. The width of that same rectangle is represented by the function W(x)=8x²-4x+1. Which of the following shows the area of the rectangle interms of x?(L+ W)(x)=8x²-2x+1(L + W)(x)=8x² - 6x +1(L• W)(x)=16x-4x+1(L • W)(x)=16x³-8x²+2x
Answer:
[tex]D\text{ :}(L\text{ }\circ\text{ W\rparen\lparen x\rparen= 16x}^3-8x^2+2x[/tex]Explanation:
Here, we want to select the option that best represents the area of the rectangle in terms of x
Mathematically, the area can be calculated by:
[tex]A(x)\text{ = L\lparen x\rparen }\times\text{ W\lparen x\rparen}[/tex]We have that as:
[tex]\begin{gathered} 2x\text{ }\times\text{ 8x}^2-4x+1 \\ =\text{ 2x\lparen8x}^2-4x+1) \\ =\text{ 16x}^3-8x^2+2x \end{gathered}[/tex]how do you do this why does it make me put so many words
Part 5
we have the points
(0,4) and (4,8)
Find the slope
m=(8-4)/(4-0)
m=4/4
m=1
Find the equation in slope intercept form
y=mx+b
we have
m=1
b=4
so
y=x+4Part 6
we have the points
(0,8) and (2,4)
m=(4-8)/(2-0)
m=-4/2
m=-2
y=mx+b
we have
m=-2
b=8
so
y=-2x+8Solving a trigonometric equation involving an angle multiplied by a constant
In these questions, we need to follow the steps:
1 - solve for the trigonometric function
2 - Use the unit circle or a calculator to find which angles between 0 and 2π gives that results.
3 - Complete these angles with the complete round repetition, by adding
[tex]2k\pi,k\in\Z[/tex]4 - these solutions are equal to the part inside the trigonometric function, so equalize the part inside with the expression and solve for x to get the solutions.
1 - To solve, we just use algebraic operations:
[tex]\begin{gathered} \sqrt[]{3}\tan (3x)+1=0 \\ \sqrt[]{3}\tan (3x)=-1 \\ \tan (3x)=-\frac{1}{\sqrt[]{3}} \\ \tan (3x)=-\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]2 - From the unit circle, we can see that we will have one solution from the 2nd quadrant and one from the 4th quadrant:
The value for the angle that give positive
[tex]+\frac{\sqrt[]{3}}{3}[/tex]is known to be 30°, which is the same as π/6, so by symmetry, we can see that the angles that have a tangent of
[tex]-\frac{\sqrt[]{3}}{3}[/tex]Are:
[tex]\begin{gathered} \theta_1=\pi-\frac{\pi}{6}=\frac{5\pi}{6} \\ \theta_2=2\pi-\frac{\pi}{6}=\frac{11\pi}{6} \end{gathered}[/tex]3 - to consider all the solutions, we need to consider the possibility of more turn around the unit circle, so:
[tex]\begin{gathered} \theta=\frac{5\pi}{6}+2k\pi,k\in\Z \\ or \\ \theta=\frac{11\pi}{6}+2k\pi,k\in\Z \end{gathered}[/tex]Since 5π/6 and 11π/6 are π radians apart, we can put them together into one expression:
[tex]\theta=\frac{5\pi}{6}+k\pi,k\in\Z[/tex]4 - Now, we need to solve for x, because these solutions are for all the interior of the tangent function, so:
[tex]\begin{gathered} 3x=\theta \\ 3x=\frac{5\pi}{6}+k\pi,k\in\Z \\ x=\frac{5\pi}{18}+\frac{k\pi}{3},k\in\Z \end{gathered}[/tex]So, the solutions are:
[tex]x=\frac{5\pi}{18}+\frac{k\pi}{3},k\in\Z[/tex]10 Students share 1 hour to give their science reports
Answer:
1/10
Explanation:
If 10 students share 1 hour, we need to divide 1 hour into 10 students. So, the fraction is
[tex]\frac{1\text{ hour}}{10\text{ students}}=\frac{1}{10}[/tex]It means that each student has 1/10 hour to give the science report.
Given `lim_(x -> 2) 2x - 3 = 1`, use the formal definition of a limit to find the value of δ that corresponds to ε = 0.3.
A. 0.05
B. 0.15
C. 0.30
D. 0.50
Answer: B. 0.15
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a rectangle has the perimeter of 116 cm and its length is 1cm more than twice its width. I got 39L and 19w but I'm having problems setting up the problems
To answer this question, we can proceed as follows:
1. We have that the perimeter of the rectangle is equal to 116cm, then, we have:
[tex]w+l+w+l=116\Rightarrow2w+2l=116[/tex]We know that a rectangle is a parallelogram. Then, its opposite sides are congruent.
2. We have that the length of the rectangle is 1 cm more than twice its width. We can translate this, algebraically, as follows:
[tex]l=2w+1[/tex]Now, to find the measures of the length and the width of the rectangle, we can substitute this last formula into the first one, as follows:
[tex]2w+2(2w+1)=116[/tex]We need to apply the distributive property to find w:
[tex]2w+4w+2=116[/tex]Adding like terms:
[tex]6w+2=116[/tex]Subtracting 2 to both sides of the equation, and then dividing by 6:
[tex]6w+2-2=116-2\Rightarrow6w=114\Rightarrow\frac{6w}{6}=\frac{114}{6}\Rightarrow w=19[/tex]Then, the width of the rectangle is equal to 19cm. The measure of the length can be calculated using either equation above. Let us use the first equation:
[tex]2w+2l=116\Rightarrow2\cdot19+2l=116\Rightarrow38+2l=116[/tex]Then, using similar properties as before, we have:
[tex]38-38+2l=116-38\Rightarrow2l=78\Rightarrow\frac{2l}{2}=\frac{78}{2}\Rightarrow l=39[/tex]In summary, we have that the measures of the length and width of this rectangle are:
• Width, ,(w) =, 19cm
,• Legth (l) = ,39cm
Hello am I correct, if not can you help me understand?
total kilometer of journey = 353miles
she stopped at mile 36