7x-(x-3)=4x-2
We need to solve first the brackets
7x-x+3=4x-2
Next, we need to put all the terms with x on one side and all the terms without x on the other side, remember is you change the side of a term the sign will be the opposite that's why 4x change to -4x on the other side
7x-x-4x=-2-5
then we sum of the term
2x=-7
the term with x the 2 is multiplying x so on the other side change to divide the seven
x=-7/2
Solving systems y=2-2x. x=y-5
we get that:
[tex]x=2-2x-5\rightarrow x+2x=-3\rightarrow3x=-3\rightarrow x=-1[/tex]so we get
[tex]y=2-2\cdot-1=2+2=4[/tex]Find the zeros by using the quadratic formula and tell whether the solutions are real or imaginary. F(x)=2x^2+6x–16
Where
a = 2
b = 6
c = -16
Using quadratic formula, we solve for x:
[tex]undefined[/tex]Mai works a total of 31 hours per week at two jobs. The number of hours she works at a coffee stand is 5 less than 2 times the number of hours she works at the animal shelter. How many hours does Mai work at the animal shelter?
Show the equation you use and your work solving the equation.
Answer:
12
Step-by-step explanation:
Let x = number of hours at the shelter
"The number of hours she works at a coffee stand is 5 less than 2 times the number of hours she works at the animal shelter."
The number of hours at the coffee stand is
2x - 5
The total number of hours is 31, so x added to 2x - 5 must equal 31.
2x - 5 + x = 31
3x - 5 = 31
3x = 36
x = 12
She works 12 hours at the shelter.
Find the value of x. Round to thenearest tenth.1.47 2.1ft2xx = [? ]ft=Enter
To find the value of x:
Consider the right angle triangle,
The opposite side is 1.4 ft
The adjacent side is x
The hypotenuse side is 2.1ft
Using Pythagoras theorem,
[tex]\begin{gathered} \text{Hyp}^2=\text{Opp}^2+\text{Adj}^2 \\ (2.1)^2=(1.4)^2+x^2 \\ 4.41=1.96+x^2 \\ x^2=4.41-1.96 \\ x^2=2.45 \\ x=1.5652 \\ x\approx1.57ft \end{gathered}[/tex]Hence, the value of x is 1.57 ft.
Tyler’s monthly allowance is $42 dollars and Jeremiah’s allowance is $63. How many times Jeremiah’s monthly allowance is Tyler’s monthly allowance?
Convert the following point from polar to Cartesian coordinates. Write the exact answer as an ordered pair. Do not round.(s. - 2)5.2.3
Answer::
[tex](-2.5,-2.5\sqrt{3})[/tex]Explanation:
Given the point in polar coordinate:
[tex]\left(5,-\frac{2\pi}{3}\right)[/tex]To convert to Cartesian coordinates, use the formula below:
[tex](x,y)=(r\cos\theta,r\sin\theta)[/tex]Thus:
[tex]\begin{gathered} (x,y)=\left(5\cos\left(-\frac{2\pi}{3}\right),5\sin\left(-\frac{2\pi}{3}\right)\right) \\ =\left(5\times-\frac{1}{2},5\times-\frac{\sqrt{3}}{2}\right) \\ =(-2.5,-2.5\sqrt{3}) \end{gathered}[/tex]The Cartesian coordinates are:
[tex](-2.5,-2.5\sqrt{3})[/tex]Define an exponential function, h(x), which passes through the points (1,16) and(5, 1296). Enter your answer in the form a*b^xh(x) =
We want the answer in exponential form:
[tex]h(x)=a\cdot b^x[/tex]where a and b are the constants to be determined. We can find a and b by substituting the given points and construct a system of equatons, that is, by replacing point (1,16) we have
[tex]\begin{gathered} 16=a\cdot b^1 \\ so \\ 16=a\cdot b \end{gathered}[/tex]and by substituting point (5,1296), we get
[tex]1296=a\cdot b^5[/tex]Then, we have 2 equations in 2 unknonws:
[tex]\begin{gathered} a\mathrm{}b=16 \\ a\mathrm{}b^5=1296 \end{gathered}[/tex]By isolating a from the first equation and substituting this result into the second one, we get
[tex]\begin{gathered} (\frac{16}{b})b^5=1296 \\ \end{gathered}[/tex]which gives
[tex]\begin{gathered} 16b^4=1296 \\ b^4=\frac{1296}{16} \\ b^4=81 \\ b=\sqrt[4]{81} \\ b=3 \end{gathered}[/tex]Then, by substituting this result into the first equation of our system, we obtain
[tex]\begin{gathered} a\cdot3=16 \\ \text{then} \\ a=\frac{16}{3} \end{gathered}[/tex]Therefore, the answer is
[tex]h(x)=\frac{16}{3}\cdot(3)^x[/tex]Usqqe format HTH to mean that the first toss is heads, the second is tails and the third is heads more than one element in the set, separate them with commas
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: State the number of outcomes possible for three tossing of a coin
Since a coin has two possible outcomes and is tossed three times, the total outcomes will be:
[tex]\begin{gathered} 2^3=8 \\ 8\text{ outcomes} \end{gathered}[/tex]STEP 2: Find the number of sample spaces for the three tosses
STEP 3: Get the outcomes of the events for which the second toss is tails
Hence, the answers are given as:
Sample Space:
[tex]\lbrace HHH,HHT,HTH,HTT,THH,THT,TTH,TTT\rbrace[/tex]The event that the second toss is tails:
[tex]\lbrace HTH,HTT,TTH,TTT\rbrace[/tex]what is the greatest common factor of 18 and 24 with 18/24 in the simplest form i do not understand how to do this
Answer:
Greatest common factor: 6
The simplest form of 18/24 = 3/4
Explanation:
First, we need to identify the factors of 18 and 24. The factors are the numbers that divide 18 and 24.
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
Then, the common factors are: 1, 2, 3, and 6
Finally, the greatest common factor is 6.
On the other hand, if we want to write 18/24 in the simplest form, we need to divide both numbers by the greatest common factor, so:
[tex]\frac{18\div6}{24\div6}=\frac{3}{4}[/tex]So, 18/24 in the simplest form is 3/4
g+3 1/2=10 answer to g
Answer:
Exact form: G = 12/2
decimal form: G = 6.5
3.5.3 Test (CST): Functions Does this graph show a function? Explain how you know. 66 PE -2 E C N 6 8 A. No; there are y-values that have more than one x-value. B. Yes; the graph passes the vertical line test. C. Yes; there are no y-values that have more than one x-value. D. No; the graph fails the vertical line test. here is the answer for the people who need it
Find the value for k given the line through (-1, k) and (-7, -2) is parallel to the line y = x + 1.
The value of k is 4 , the line through (-1,k) and (-7, -2).
Given,
The line through (-1, k) and (-7, -2) is parallel to the line y = x + 1.
To find the value of k
Now, According to the question is:
For Parallel lines, We know that
It has same slope as y = x + 1
Also, We know y = x +1 has slope of 1.
Using the formula for the slope :
m = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
Now, For value k
We have, 1 = (-2-k)/(-7-1)
=> 1 = (-2-k)/(-6)
=> -6 = -2 -k
=> -6+2 = -k
=> k = 4
Hence, The value of k is 4.
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The sum o{ the squares of two
consecutive positive even integers
is one hundred. Find the two integers.
For the curve, estimate the instantaneous rate of change at x=5 without the use of derivatives
Answer: -0.733
Step-by-step explanation:
To estimate the instantaneous rate of change, we can take the slope of the secant through two points on the curve that are close to x=5.
In this case, we will consider [tex](4.9, f(4.9))[/tex] and [tex](5.1, f(5.1))[/tex].
[tex]\frac{f(5.1)-f(4.9)}{5.1-4.9} \approx -0.733[/tex]
Which expression simplifies to 5? 7 points A. 27/3 -- 14 B. 27/3 + 4 C. --27/3 -- 4 D. --27/3 + 4
The expression simplifies to 5 is -27/3 +14 .
The option D is correct.
What is Simplification?
Simplification is the process of replacing a mathematical expression by an equivalent one, that is simpler, usually shorter.
Given,
Which expression simplifies to 5?
Here, Options are
A. 27/3 - 14
= 9 - 14 = -5
B. 27/3 + 4
= 9 + 4 = 13
C. --27/3 - 4
= -9 - 4 = -13
D. -27/3 +14
= -9 + 14 = 5
Hence, The expression simplifies to 5 is -27/3 +14 .
The option D is correct.
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what is -4 7/22 wrriten as a decimal
Answer:
-4.31818 or 2.13636
Step-by-step explanation:
I can't really tell how its written if it's -4 and 7/22 it would be -95/22 or -4.31818. if it is -47/22 it would be 2.13636. I did this by dividing the numerator by the denominator
Answer:
-4.31818 or -2.13636
Step-by-step explanation:
if its -4 and 7/22 then the first one and if its -47/22 then the second one
The Rodriguez family has a fixed incomeof $4,000 a month. Their fixed expensesare $1,800 a month. They save at leastone fourth of the remaining income eachmonth. What is the minimum amountsaved by the Rodriguez family in a year?
we know that
The Rodriguez family has a fixed income of $4,000 a month.
Their fixed expenses are $1,800 a month
so
The remaining amount in a month is
4,000-1,800=$2,200
The one fourth of the remaining income is
(1/4)(2,200)=$550
To find out the minimum amount in a year, multiply $550 by 12
550*(12)=$6,600
therefore
the answer is$6,600State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.A No; it is a ratioBYes; degree 1CNo; x is a negative termDYes; degree 4
Given:
The function is,
[tex]\frac{8-x^4}{9}[/tex]It can be written as,
[tex]\frac{8}{9}-\frac{x^4}{9}[/tex]Polynomial is a combination of terms seperated using + and - sign which does not contain,
1) Variable in demominator
2) Variables under radical
3) special features like trigonometric function, absolute values etc.
So, it shows that the given function is polynomial with degree 4.
Answer: option D)
What is the slope of the line that contains the points (9,-4) and (1,-5)?O A. -B. 1C. -1D. /718
Answer: D. 1/8
Explanation
The slope of the line can be calculated with:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x₁, y₁) and (x₂, y₂) are the two points given. Then:
• x₁ = 9
,• y₁ = –4
,• x₂ = 1
,• y₂ = –5
Thus, replacing the values and simplifying:
[tex]m=\frac{-5-(-4)}{1-9}[/tex][tex]m=\frac{-5+4}{-8}[/tex][tex]m=\frac{1}{8}[/tex]You draw one card from a 52-card deck. Then the card is replaced in the deck and the deck is shuffled, and you draw again. Find the probability of drawing a nine the first time and a heart the second time
SOLUTION:
Step 1:
In this question, we are given the following:
You draw one card from a 52-card deck.
Then the card is replaced in the deck and the deck is shuffled, and you draw again.
Find the probability of drawing a nine the first time and a heart the second time
Step 2:
From the question, we can see that the probability of drawing a nine the first time and a heart the second time is:
[tex]\frac{4}{52\text{ }}\text{ x }\frac{13}{52}=\text{ }\frac{52}{52\text{ x 52}}=\frac{1}{52}[/tex]CONCLUSION:
The probability of drawing a nine the first time and a heart the second time is:
[tex]\frac{1}{52}[/tex]
How many units can be obtained from f(x) =|x+7|−6 if the graph has been shifted down and left?
The translation we need to get f(x) is a translation of 7 units to the left and 6 units down.
Which shift do we have here?I assume we want to identify the transformation that we need to apply to the parent absolute value function |x| in order to get f(x).
Remember that a horizontal translation of N units and a vertical translation of M units is written as:
y = |x - N| + M
In this case we have:
f(x) = |x + 7| - 6
Comparing it with the formula above, we get:
N = -7
M = -6
This means that we have a translation of 7 units to the left, and 6 units down.
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help me please !!!
thank youuu
Answer:
Step-by-step explanation:
I am not entirely sure that this is correct, but I believe the interval notation of your point is (∞,-4). I hope this helps you!
A clock takes 12 seconds to strike 4. How long does it take to strike 12?
Answer If the answer is not 36 you have to look at the way the sentence is structured . Time is taken between hours not on them The answer should be 44. To go on 4 it takes four strikes on three spots that take a total of 12 secs and four per space
So the answer should be 44
help meeeeeeeeeeeeeeeeeeeeeee
thank you
The value of the function f(-5) is -6
How to evaluate the function?The given parameters are the graphs in the figure
From the question, we have the function definition to be f(-5)
When the graphs are analysed, we have the following highlights
The equation of the first graph is illustrated by the function f(x), while the second is illustrated by the function g(x)
Recall that the function definition is f(-5)
So, we use the function represented by f(x) i.e. the first graph
The function f(-5) means the value of x is -5
Looking at the values on the first graph, we have the following representation
f(-5) = -6
Hence, the function f(-5) has a value of -6
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A pancake recipe for Christ 3 1/3 cups of milk to 1 cup of flour. At 3 3/4 cups of milk is used, what quantity of flour will be needed, according to the recipe?
Given:
3 1/3 cups of milk to 1 cup of flour
3 3/4 cups of milk
So:
[tex]\frac{3\frac{1}{3}}{3\frac{3}{4}}=\frac{1}{x}[/tex]Simplify:
[tex]\begin{gathered} \frac{\frac{10}{3}}{\frac{15}{4}}=\frac{1}{x} \\ \frac{10\times4}{3\times15}=\frac{1}{x} \\ \frac{40}{45}=\frac{1}{x} \\ \frac{8}{9}=\frac{1}{x} \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} 8\cdot x=1\cdot9 \\ 8x=9 \\ \frac{8x}{8}=\frac{9}{8} \\ x=\frac{9}{8}=1\frac{1}{8} \end{gathered}[/tex]Answer:
[tex]1\frac{1}{8}[/tex]Which choice is equivalent to the fraction below? (Hint: Rationalize the denominator and simplify.)A.B.C.2D.
Given: A fraction
[tex]\frac{2-\sqrt{2}}{2+\sqrt{2}}[/tex]Required: To simplify the given fraction.
Explanation: The given fraction can be simplified by rationalizing the denominator of the fraction. The rationalizing factor is
[tex]2-\sqrt{2}[/tex]Hence,
[tex]\begin{gathered} \frac{(2-\sqrt{2})}{2+\sqrt{2}}\times\frac{(2-\sqrt{2})}{(2-\sqrt{2})} \\ \frac{(2-\sqrt{2})^2}{(2)^2-(\sqrt{2}^{)2}} \end{gathered}[/tex]Which gives
[tex]\begin{gathered} \frac{4+2-4\sqrt{2}}{4-2} \\ \frac{2(3-2\sqrt{2})}{2} \\ 3-2\sqrt{2} \end{gathered}[/tex]Final Answer: Option A is correct.
At an aquarium, researchers are preparing a mixture of salt water. The desired ratio is 90 grams of salt per liter of water.1 ounce= 28.35 grams1 gallon= 3.8 literswhat is the ratio in ounces per gallon
Based on the question, the ratio of the salt mixture is:
[tex]\frac{90grams}{1\text{liter}}[/tex]So, if we have 3.8 liters in 1 gallon, we would need 90grams x 3.8 = 342 grams of salt in 1 gallon.
[tex]\frac{90grams}{1\text{liter}}\times\frac{3.8liters}{1\text{gal}}=\frac{342grams\text{ }}{1gal}[/tex]The next step is to determine how many ounces are there in 342 grams. If 1 ounce = 28.35 grams, then 342 grams divide 28.35 grams = 12.06. Hence, in 342 grams, there are 12.06 ounces.
Thus, we can say that:
[tex]\frac{342\text{grams}}{1\text{gal}}=\frac{12.06\text{ounces}}{1\text{gal}}[/tex]The ratio of the salt mixture is 12.06 ounces per gallon.
Please help with math problem FAST
For a standard normal distribution, given:
P(z < c) = 0.9663
Find c.
The value of c for a standard normal distribution, P(z < c) = 0. 9663 is 0.47.
What is standard normal distribution?
The standard normal distribution table gives the probability of a regularly distributed random variable Z, whose mean is equivalent to 0 and difference equal to 1, is not exactly or equal to z. The normal distribution is a persistent probability distribution.
What is z score?
Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by
z = (x - μ)/σ
Where x is the raw score, μ is the mean and σ is the standard deviation.
Given that P(z < c) = 0. 9663; hence:
From the normal distribution table, c = 0.47
The value of c for a standard normal distribution, P(z < c) = 0. 9663 is 0.47.
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Please help and provide explanation I want to understand this!
We will have to find the equation that follows the form:
[tex]a+bx=y[/tex]That is:
*The value of a is:
[tex]a=547.4666667[/tex]*The value of b is:
[tex]b=29.91428571[/tex]So, the linear regression is:
[tex]y=29.91428571x+547.4666667[/tex]We can see it graphically as follows:
Here we can see the linear regression line and the points used.
***How to manually determine linear regressions***
We will start as follows:
We will have to use the following expressions in order to manually find the linear regression:
[tex]b=\frac{n(\sum^{}_{}xy)-(\sum^{}_{}x)(\sum^{}_{}y)}{n(\sum^{}_{}x^2)-(\sum^{}_{}x)^2}[/tex]And:
[tex]a=\frac{\sum ^{}_{}y-b(\sum ^{}_{}x)}{n}[/tex]Here we have that n is the number of values on the dataset. So, we solve for b as follows [Based on the problem given]:
*We will determine the values of n, the sum of x, the sum of y, xy, x^2 & y^2 as follows:
Sum of x:
[tex]\sum ^{}_{}x=1+2+3+4+5+6\Rightarrow\sum ^{}_{}x=21[/tex]Sum of y:
[tex]\sum ^{}_{}y=588+298+640+650+707+730\Rightarrow\sum ^{}_{}y=3913[/tex]Value of n: We have that the number of datasets given is 6 [6 pairs of values on the table].
[tex]n=6[/tex]*The sum of xy:
[tex]\sum ^{}_{}xy=(1)(588)+(2)(598)+(3)(640)+(4)(650)+(5)(707)+(6)(730)\Rightarrow\sum ^{}_{}xy=14219[/tex]*The sum of X^2:
[tex]\sum ^{}_{}x^2=1^2+2^2+3^2+4^2+5^2+6^2\Rightarrow\sum ^{}_{}x^2=91[/tex]*The square of the sum of x:
[tex](\sum ^{}_{}x)^2=21^2\Rightarrow(\sum ^{}_{}x)^2=441[/tex]Now that we have all the values, we replace in the first equation and solve for b:
[tex]b=\frac{(6)(14219)-(21)(3913)}{(6)(91)-(441)}\Rightarrow b=29.91428571[/tex]And we solve now for a:
[tex]a=\frac{(3913)-(29.91428571)(21)}{(6)}\Rightarrow a=548.4666667[/tex]And then we simply replace on the expression:
[tex]y=bx+a[/tex]And the expression after the replacement of a & b is the linear regression.
