We are given the following system of equations:
[tex]\begin{gathered} 3x+5y=11,(1) \\ 2x+5y=4,(2) \end{gathered}[/tex]We can solve this system of equations using the method of elimination. To do that we will multiply equation (2) by -1:
[tex]-2x-5y=-4,(3)[/tex]Now we add equations (1) and (3):
[tex]3x+5y-2x-5y=11-4[/tex]Adding like terms:
[tex]x=7[/tex]Now we replace the value of "x" is equation (1):
[tex]\begin{gathered} 3(7)+5y=11 \\ 21+5y=11 \end{gathered}[/tex]Now we subtract 21 to both sides:
[tex]\begin{gathered} 5y=11-21 \\ 5y=-10 \end{gathered}[/tex]Dividing both sides by 5:
[tex]\begin{gathered} y=-\frac{10}{5} \\ y=-2 \end{gathered}[/tex]Therefore, the solution of the system is:
[tex](x,y)=(7,-2)[/tex]For the second system of equations:
[tex]\begin{gathered} y=3x+7,(1) \\ y=3x+4,(2) \end{gathered}[/tex]These equations represent two lines with the same slope, and therefore, parallel lines. Since they are parallel lines this means that the system has no solutions.
In a game, 2 players each flip a coin. If both land on heads, player A gets 2points and player B loses 1 points. If both land on tails, player B gets 2 points andplayer A loses 1 point. Find the expected value of the game for each player.
The expected value for player A is:
[tex]\begin{gathered} (\frac{1}{2}\times\frac{1}{2}\times2)-(1\times\frac{1}{2}\times\frac{1}{2}) \\ =(\frac{1}{4}\times2)-(1\times\frac{1}{4}) \\ =(\frac{1}{2})-(\frac{1}{4}) \\ =\frac{1}{4} \end{gathered}[/tex]The expected value of player B is:
[tex]\begin{gathered} (\frac{1}{2}\times\frac{1}{2}\times2)-(1\times\frac{1}{2}\times\frac{1}{2}) \\ =(\frac{1}{4}\times2)-(1\times\frac{1}{4}) \\ =(\frac{1}{2})-(\frac{1}{4}) \\ =\frac{1}{4} \end{gathered}[/tex]Write an algebraic expression for each phrase.1.the product of r and seven7x3. two more than the product of y and four2. the sum of 8 and p4. the quotient of k and ten
2) The symbol used to repesent sum is '+'. Thus, the algebraic expression for the the sum of 8 and p is
8 + p
what is 13 divide by 113.1 in long division
The value of 13 divided by 113.1 is 0.1149425.
How to calculate the division?It should be noted that the steps to calculate the division will be:
Step 1: Take the first digit of the dividend from the left. ...
Step 2: Then divide it by the divisor and write the answer on top as the quotient.
Step 3: Subtract the result from the digit and write the difference below.
Step 4: Bring down the next digit of the dividend
Therefore, 13 divided by 113.1 will be:
= 13 ÷ 113.1
= 0.1149425
In conclusion, the value is 0.1149425.
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what is 3 1/6 + 5 2/3
The given expression is
[tex]3\frac{1}{6}+5\frac{2}{3}[/tex]First, we transform each mixed number into a fraction
[tex]\begin{gathered} 3\frac{1}{6}=\frac{3\cdot6+1}{6}=\frac{18+1}{6}=\frac{19}{6} \\ 5\frac{2}{3}=\frac{5\cdot3+2}{3}=\frac{15+2}{3}=\frac{17}{3} \end{gathered}[/tex]We use these fractions to make the sum
[tex]\frac{19}{6}+\frac{17}{3}[/tex]Now, we use the following property
[tex]\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d+b\cdot c}{b\cdot d}[/tex][tex]\frac{19\cdot3+17\cdot6}{6\cdot3}=\frac{57+102}{16}=\frac{159}{16}[/tex]Hence, the result is 159/16.When the clock first starts counting down time, there are more than 300 seconds before the start of the game. Write an inequality statement that best describes t, the time in seconds, when the clock first starts counting down time.
"When the clock first starts counting down time, there are more than 300 seconds before the start of the game", that means the variable t we will use to represent when the clock first starts counting down time is greater than 300, so we can represent this sentence with the following inequality:
[tex]t>300[/tex]So the inequality statement that best describes t is t > 300.
Timothy mows his neighbor lawn for $6.50 per week. He continues to do this for 37 weeks until winter. In winter he shovels snow off their lawn for $10.25 per week for 25 weeks. How much money did Timothy earn in total?
ANSWER
$496.75
EXPLANATION
Timothy mows his neighbor's lawn for $6.50 per week for 37 weeks until winter.
This means that the amount of money he made mowing is the product of the amount per weeks and the number of weeks.
That is:
[tex]\begin{gathered} 6.50\cdot37 \\ =\text{ \$}240.50 \end{gathered}[/tex]He shovels the snow for $10.25 per week for 25 weeks.
The amount of money he made shoveling is therefore:
[tex]\begin{gathered} 10.25\cdot25 \\ =\text{ \$256.25} \end{gathered}[/tex]The total amount of money that he made in total is the sum of money he made mowing and shoveling:gg
[tex]\begin{gathered} 240.50+256.25 \\ =\text{ \$496.75} \end{gathered}[/tex]That is the answer.
This parabola opens to the left. P. O A. True O B. False
Answer:
True.
Explanation:
We take the analogy from the graph of y = ax^2
When y = x^2, the parabola opens upward (towards the positive y-axis). However, when the parabola is y = -x^2, it opens downward (towards the negative y-axis).
In a similar way, when we have x = ay^2, the parabola opens towards the positive x-axis ( towards the right). However, if we have x = -ay^2, then the parabola opens towards the negative x-axis ( towards the left).
Therefore, by comparison, x = - 1/8 y^2, opens to the left, and the correct option to choose is 'True'.
solve each system of equations below by graphing, please use my graphy = 2xy = -x + 3
Given:
y= 2x ; y=-x+3
Substitute the value of x as -2,-1,0,1,2
y=2x
[tex]\text{When x=-2, y=-4}[/tex][tex]\text{When x=-1, y=-}2[/tex][tex]\text{When x=0, y=}0[/tex][tex]\text{When x=1, y=}2[/tex][tex]\text{When x=2, y=}4[/tex]y= -x+3
[tex]\text{When x=-2, y=}5[/tex][tex]\text{When x=-1, y=}4[/tex][tex]\text{When x=0, y=}3[/tex][tex]\text{When x=1, y=}2[/tex][tex]\text{When x=2, y=}1[/tex]Therefore, the solution is (1,2) .
D.) what is the probability of selling 25 cheesecakes ?E.) what is the probability of selling at most 10 cheesecakes ?F.) give the expected number of cheesecakes sold on any given day using the discrete probability distribution
D)
To find the probability of selling 25 cheesecakes:
It is impossible to find the probability of selling 25 cheesecakes.
So,
P(x=25)=0
The probability of selling 25 cheesecakes is 0.
E)
To find the probability of selling at most 10 cheesecakes:
That is,
[tex]\begin{gathered} P(x\leq10)=P(x=0)+P(x=5)+P(x=10) \\ =0.1+0.23+0.04 \\ =0.37 \end{gathered}[/tex]Therefore, the probability of selling at most 10 cheesecakes is 0.37.
F)
To find the expected number of cheesecakes sold on any given day using the discrete probability distribution:
[tex]\begin{gathered} \sum ^5_{i\mathop=1}x_ip_i=x_1p_1+x_2p_2+x_3p_3+x_4p_4+x_5p_5 \\ =0(0.1)+5(0.23)+10(0.04)+15(0.46)+20(0.17)_{}_{}_{} \\ =0+1.15+0.4+6.9+3.4 \\ =11.85 \end{gathered}[/tex]Hence, the expected number of cheesecakes sold on any given day using the discrete probability distribution is 11.85.
Solve the inequality and graph your answerx + 19 < 16
Solution
For this case we have this inequality:
x+19 <16
We can subtract 16 in both sides and we got:
x +19-19 < 16-19
x < -3
For the second part we have:
[tex]\frac{x}{5}\ge-2[/tex]We can multiply both sides by 5 and we got.
[tex]x\ge-10[/tex]the minimum point on the graph of the equation y = f(x) is (-1,-3). what is the minimum point on the graph of the equation y=f(x)+5?
the minimum point on the graph of the equation y = f(x) is (-1,-3). what is the minimum point on the graph of the equation y=f(x)+5?
we have that
the rule of this transformation is equal to
(x,y) ------> (x, y+5)
so
(-1,3) -----> (-1,3+5)
(-1,8) is the minimum pointWrite 1.75 % as decimal AND simplified fraction. ANS. As decimal __________. As simplified fraction. ________.
The given percentage is 1.75%.
To find the decimal expression of this percentage, we just have to divide it by 100. It's important to know that when we divide a number by 100, we just have to move the decimal point two spots to the left, as follows
[tex]\frac{1.75}{100}=0.0175[/tex]Therefore, as a decimal is 0.0175.
Now, to find the simplified fraction, we divide the number by 10000, as follows
[tex]\frac{175}{10000}[/tex]The reason for dividing by 10000 is that we need to have a whole number in the numerator, so the extra two zeros allow us to get rid of the two of the number. Now, we simplify the fraction dividing each part by 5
[tex]\frac{175\colon5}{10000\colon5}=\frac{35}{2000}=\frac{7}{400}[/tex]Once we get the simplest fraction, we can finish.
Therefore, as a simplified fraction is 7/400.
The drink booth at the school fair had these 5 types of drinks: ice tea, root beer, apple cider, lemonade, and orange juice. The 12 students from Mr. Yu's class were asked which drink they ordered. Here are the results: apple cider, orange juice, lemonade, root beer, orange juice, orange juice, lemonade, orange juice, ice tea, root beer, orange juice, orange juice Draw the bar graph for these data. Frequency 24 Explanation root beer Check apple cider lemonade orange juice Type of drink X ? 2022 McGraw H LLC. All Rights Reserved. Terms of
The first step is to find the frequency of each type of drink. It is shown below
apple cider = 1
Orange juice = 6
Lemonade = 2
root beer = 2
ice tea = 1
The bar graph is shown below
. Find an ordered pair that represents a solution to the equation x + 2y = 20
we have
x + 2y = 20
The linear equation represent the equation of a line
If a ordered pair is a solution of the equation, that means that the ordered pair lies on the line
so
Find a ordered pair that represents a solution
Assume the value of x
so
For x=1
substitute in the equation
(1)+2y=20
solve for y
2y=20-1
2y=19
y=19/2
y=9.5
therefore
The ordered pair (1,9.5) represents a solutionFind the slope of the line passing through thepoints (-5,4) and (7,8).
We have two points and we have to calculate the slope of the line pasing through this points.
We can calculate the slope as the ratio of the difference between the y-coordinates and the difference between the x-coordinates.
This can be written as:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{8-4}{7-(-5)}=\frac{4}{7+5}=\frac{4}{12}=\frac{1}{3}[/tex]The slope of the line is 1/3.
find (8.4x10^11)/(5.25x10^2)(8.0x10^3), expressed in a scientific notation
The simplified form of the expression, (8.4 x 10^11)/(5.25 x 10^2)(8.0 x 10^3), in scientific notation is 2.0 × 10⁵
Evaluating an expression in scientific notationFrom he question, we are to evaluate the given expression in scientific notation.
The given expression is
(8.4 x 10^11)/(5.25 x 10^2)(8.0 x 10^3)
First, we will write this expression properly
The expression written properly is
(8.4 x 10¹¹)/(5.25 x 10²)(8.0 x 10³)
Evaluating
(8.4 x 10¹¹)/(5.25 x 8.0)(10² x 10³)
(8.4 x 10¹¹)/(5.25 x 8.0)(10² ⁺ ³)
(8.4 x 10¹¹)/(42.0)(10⁵)
(8.4 x 10¹¹)/(42.0 × 10⁵)
(8.4/42.0) × (10¹¹ / 10⁵)
(0.20) × (10¹¹ ⁻ ⁵)
(0.20) × (10⁶)
= 0.20 × 10⁶
= 2.0 × 10⁵
Hence, the expression is 2.0 × 10⁵
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3SpointsWhich is the image of vertex C after the triangle is rotated 180 degrees about the origin?
T' (3,0) A' (5,-1) and C' (2,-4)
1) Considering that the Pre-image coordinates are :T(-3,0), A (-5,1) C(-2,4)
and there was a rotation 180º about the origin, then
2) In the Rotation, the rules for 180º rotation Counterclockwise and clockwise is
Pre-image Image
(x,y) ---- (-x, -y)
3)
Thus,
T' (3,0) A' (5,-1) and C' (2,-4)
1. Gustava Valadez opened a new checking account by depositing her paycheck for$347.95. The check register shows her transactions since opening her account.What should her new balance be?
When he deposite the paycheck for $347.95. An amount of $347.95 will be creted to in his account.
Therfore, the new balance is $347.95
Translate to an equation and solve: 4 is the product of 8 and b. Simplify all fractions.Provide your answer below:b=
If 4 is the product of 8 and b, 4 is the result of the multiplication of 8 and b. Then,
4 = 8b
Which is the same as:
8b = 4
To find b, let's divide both sides by 8:
[tex]\begin{gathered} \frac{8b}{8}=\frac{4}{8} \\ b=\frac{4}{8} \end{gathered}[/tex]
Dividing the numerator and the denominator by 4:
[tex]\begin{gathered} b=\frac{\frac{4}{4}}{\frac{8}{4}} \\ b=\frac{1}{2} \end{gathered}[/tex]Answer:
[tex]b=\frac{1}{2}[/tex]create a trinomial with a constant of 4 and -1 coefficient of the x term. fast help!!!
A trinomial with a constant of 4 and -1 coefficient of the x term is x² - x + 4 = 0.
What is defined as the trinomial?A trinomial is a three-term algebraic expression. An algebraic expression is made up of one or more terms' variables and constants. A perfect square trinomial is an algebraic expression formed by squaring a binomial formation. It has the formula ax² + bx + c. Here, a, b, as well as c are all real numbers, and a ≠ 0.For the given question;
Trinomial have-
constant of 4 and -1 coefficient of the x termThe general equation of the trinomial is-
ax² + bx + c = 0
Where, a and b are the coefficients and c is the constant.
Thus,
Put b = -1 and c = 4
ax² - x + 4 = 0
Now, value of a can be any number but not zero.
Thus, suitable value of a is 1.
The trinomial becomes,
x² - x + 4 = 0
Thus, a trinomial with a constant of 4 and -1 coefficient of the x term is x² - x + 4 = 0.
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what is the equation of the line? O y=3/2x O y=2/3x O y=3x O y=2x
Explanation:
We would apply the slope formula:
slope = change in y/change in x
change in y = 4 - 0 = 4
change in x = 6 - 0 = 6
Also note on the graph, the change in y is represented by y. And the change in x is represented by x
[tex]\begin{gathered} slope=\frac{4}{6} \\ \text{slope =}\frac{y}{x} \end{gathered}[/tex]Equating both:
[tex]\begin{gathered} \frac{y}{x}=\frac{4}{6} \\ \frac{y}{x}=\frac{2}{3} \end{gathered}[/tex]Multiply both sides by x:
[tex]\begin{gathered} \frac{y}{x}\times x=\frac{2}{3}\text{ }\times\text{ x} \\ y\text{ = }\frac{2x}{3}\text{ (option B)} \end{gathered}[/tex]the probability that describe the related frequency of actual observation of an event is an experiment is which of the following
The relative frequency is an empirical probability. So, the answer is the first option
Is 49 prime or composite?
Can Mario organize his marbles into equal piles ?
You are dealt one card from a standard 52-card deck. Find the probability of being dealt a heart and a spade.The probability of being dealt a heart and a spade is __.(Type an integer or a simplified fraction.)
Okay, here we have this:
3x-8=2x+18Solve for x
x=26
Explanation
[tex]3x-8=2x+18[/tex]Step 1
subtract 2x in both sides
[tex]\begin{gathered} 3x-8=2x+18 \\ 3x-8-2x=2x+18-2x \\ x-8=18 \end{gathered}[/tex]Step 2
add 8 in both sides
[tex]\begin{gathered} x-8=18 \\ x-8+8=18+8 \\ x=26 \end{gathered}[/tex]I hope this helps you
Find the zeros by using the quadratic formula and tell whether the solutions are real or imaginary. F(x)=3x^2+4x+2
The quadratic formula states that the solutions x1 and x2 of a quadratic function in the form y = ax^2 + bx + c is equal to:
[tex]\begin{gathered} x_1=\frac{-b+\sqrt[]{b^2-4ac}}{2a} \\ x_2=\frac{-b-\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]So, using this formula with the values a = 3, b = 4 and c = 2, we have that:
[tex]\begin{gathered} x_1=\frac{-4+\sqrt[]{4^2-4\cdot3\cdot2}}{2\cdot3}=\frac{-4+\sqrt[]{16-24}}{6}=\frac{-4+\sqrt[]{-8}}{6} \\ x_1=\frac{-4+\sqrt[]{2^2\cdot(-2)}}{6}=\frac{-4+2\cdot\sqrt[]{-2}}{6}=\frac{-2+\sqrt[]{-2}}{3}=-\frac{2}{3}+i\cdot\frac{\sqrt[]{2}}{3} \\ x_2=\frac{-4-\sqrt[]{-8}}{6}=\frac{-2-\sqrt[]{-2}}{3}=-\frac{2}{3}-i\cdot\frac{\sqrt[]{2}}{3} \end{gathered}[/tex]Since the zeros have a complex part, the solutions are imaginary.
Sasha has $850 todeposit into twoaccounts.Sasha will deposit $450at First Oak Bank.She will deposit the restinto River Point Bank.Sasha will not make additionaldeposits or withdrawals.How much more money will bein her account at First Oak thanat River Point after 2 years?
Given
Sasha has $850 to deposit into two accounts.
Sasha will deposit $450 at First Oak Bank.
She will deposit the rest into River Point Bank.
Sasha will not make additional deposits or withdrawals.
To find how much more money will be in her account at First Oak than at River Point after 2 years.
Now,
It is given that,
In the first Oak bank the rate of interest is 6%.
Then, the amount in her account after 2 years is,
[tex]\begin{gathered} A=P+\frac{Pnr}{100} \\ A=450+\frac{450\times2\times6}{100} \\ A=450+54 \\ A=454 \end{gathered}[/tex]Hence, the amount in the First Oak bank is $454.
In the River point bank the rate of interest is 2% compounded annually.
Then, the amount in her account after 2 years is,
[tex]\begin{gathered} A=P(1+\frac{r}{100})^t \\ A=P(1+\frac{2}{100})^2 \end{gathered}[/tex]Since Sasha will deposit $450 at First Oak Bank and she will deposit the rest into River Point Bank.
Then, the amount deosited in the River point bank is,
[tex]\begin{gathered} P=850-450 \\ =400 \end{gathered}[/tex]Therefore,
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I think I got the two that I did but I’m not sure and really need help
b) You have the following expression:
[tex]x^3=\frac{27}{64}[/tex]Take into account that 27/64 can be written as follow:
[tex]\frac{27}{64}=\frac{3}{4}\cdot\frac{3}{4}\cdot\frac{3}{4}[/tex]Then, x = 3/4
c) For the following expression:
[tex]x^3=\frac{1}{8}[/tex]you can write it as follow:
[tex]\frac{1}{8}=\frac{1}{2}\cdot\frac{1}{2}\cdot\frac{1}{2}[/tex]Then, x = 1/2
what are 4 numbers that are divisible by both 4 and 6
We need 4 numbers that are divisible by 4 and 6 at the same time, so the first number will be the multiplication of them:
[tex]4\cdot6=24[/tex]Now wecan multiply this new number for 4 or for 6 to get other two numbers:
[tex]\begin{gathered} 24\cdot4=96 \\ 24\cdot6=144 \end{gathered}[/tex]and finally we can multiply 96 for 4 to get the last number:
[tex]96\cdot4=384[/tex]these four numbers works
Any answer?? I'm struggling to find the answer to this equation
The last option is the correct answer ( no solution)