Given data:
The given expression is 4x+y=-1.
The given expression can be written as,
y=-4x-1.
Here, slope is -4, and y-intercept is -1.
Thus, the slope intercept form is y=-4x-1.
the answer answer is red give the step by step by how u get the answer
In order to simplify the following expressions you use the one of the square root properties:
√a√b = √(ab)
5)
√(5n^3)√(20n) = √((5n^3)(20n)) = √(100n^4) = 10n^2
6)
√(8p)√(5p^3) = √((8p)(5p^3)) = √(40p^4) √(4*10p^4) = 2p^2√10
7)
3√(15n^2)√(5n^2) = 3√((15n^2)(5n^2)) = 3√(75n^4) = 3√(25*3n^4) = 15n^2√3
8)
√(3p^3)√(3p) = √((3p^3)(3p)) = √9p^4 = 3p^2
3) There are about 1.61 kilometers in 1 mile. Let x represent a distance measured in kilometers and y represent the same distance measured in miles. Write two equations that relate a distance measured in kilometers and the same distance measured in miles. (From Unit 2 Lesson 5)
Okay, here we have this:
Considering that there are about 1.61 kilometers in 1 mile. Let x represent a distance measured in kilometers and y represent the same distance measured in miles.
So, we obtain the following equations:
x=y/1.61
y=
whats is the standard deviation for the Binomial distribution with the mean being 35 the variance is 10 .5
Given the mean and standard deviation below
[tex]\begin{gathered} \sigma\text{ is standard deviation} \\ \mu\text{ is the mean } \end{gathered}[/tex]The formula for standard deviation is
[tex]\sigma=\sqrt[]{Variance}[/tex]Given that
[tex]\text{Variance}=10.5[/tex]Substitute for Variance into the formula for standard deviation
[tex]\begin{gathered} \sigma=\sqrt[]{10.5} \\ \sigma=3.24\text{ (two decimal places)} \end{gathered}[/tex]Hence, the standard deviation, σ is 3.24 (two decimal places)
1) Put these numbers in order from greatest to lea 7/8 0.89 5/8
Solve the fractions to convert it into decimal numbers
[tex]\frac{7}{8}=0.875[/tex][tex]\frac{5}{8}=0.625[/tex]Now, we can order these numbers from greatest to least:
0.89
0.875
0.625
It means the correct order is: 0.89, 7/8, 5/8.
What is the value of x in the circle below?80°2°.120°40°80°100°120°
Let us start by sketching out the image
To solve fo x, we are going to solve for y first using the Intersecting chord theorem.
[tex]y^0=\frac{1}{2}(AB+CD)[/tex]Given that,
[tex]\begin{gathered} AB=80^0 \\ CD=120^0 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} y^0=\frac{1}{2}(80^0+120^0) \\ y^0=\frac{1}{2}(200^0)=100^0 \\ y^0=100^0 \end{gathered}[/tex]Solving for x,
[tex]x^0+y^0=180^0(sumofanglesonastraightlineis180^o)[/tex][tex]\begin{gathered} x^0+100^0=180^0 \\ x^0=180^0-100^0 \\ x^0=80^0 \end{gathered}[/tex]Hence, x° = 80°.
The correct option is option 2.
Which equation is equivalent to7x – 2y = 8
7x =2(y+4)
7x-2y-8 and y= 7/2x -4
1) An equivalent number equation is an equation that has the same result on the right side.
In algebra, we can have equivalent equations by algebraic manipulation.
So for that:
7x-2y=8
We can say that, for example
7x =2(y+4) Factoring out 2y and 4
7x-2y-8=0 Placing the 8 on the left side of the equation
and
y= 7/2x -4 Writing that on the Standard linear equation form, dividing by 2
are Equivalent equations.
Which equation expresses the relationship between the pairs of values of X and why shown in the table below
We are given a table that relates values of "x" and values of "y". To determine which equation expresses the relationship we need to substitute the values of "x" and we should get the values of "y". We will begin with x = 1. For the first equation we have:
[tex]y=3x-2[/tex]Substituting x = 1 we get:
[tex]\begin{gathered} y=3(1)-2 \\ y=3-2 \\ y=1 \end{gathered}[/tex]Therefore, this is a possible solution. Now for the second equation, we get:
[tex]y=2x[/tex]Substituting the value we get:
[tex]\begin{gathered} y=2(1) \\ y=2 \end{gathered}[/tex]We got 2 instead of 1 as shown in the table, therefore, we can discard this equation as a possible solution.
Now, we use the third equation:
[tex]y=2x+1[/tex]Substituting the value we get:
[tex]\begin{gathered} y=2(1)+1 \\ y=2+1 \\ y=3 \end{gathered}[/tex]We got 3 instead of 1, therefore, we can discard this equation as a possible solution.
Now the fourth equation:
[tex]y=x[/tex]Substituting the value we get:
[tex]y=1[/tex]Therefore, this is also a possible solution.
Now we use the value x = 2, we will substitute in the first and fourth equations which are the ones we haven't discarded yet. For the first equation we get:
[tex]\begin{gathered} y=3(2)-2 \\ y=6-2 \\ y=4 \end{gathered}[/tex]Therefore, this is a possible solution. Now for the fourth equation:
[tex]y=2[/tex]We got 2 instead of 4, therefore, this is not a solution, therefore, the right equation must be the first equation. To be sure we can replace the remaining values of "x" and we should get the corresponding values of "y".
Solve a quadratic equation by the square root method and write the solution in radical form simplify the solutions
The quadratic equation is given to be:
[tex]3x^2=36[/tex]Divide both sides by 3:
[tex]\begin{gathered} x^2=\frac{36}{3} \\ x^2=12 \end{gathered}[/tex]Recall the rule:
[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]Therefore, we have that:
[tex]x=\pm\sqrt{12}[/tex]Simplifying the radical, we have:
[tex]\sqrt{12}=\sqrt{4\cdot3}=2\sqrt{3}[/tex]Therefore, the solution is:
[tex]x=2\sqrt{3}\text{ or }-2\sqrt{3}[/tex]write a linear equation with the coordinates of (-4,4) and (4,-2)
The line equation is typically represented as
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-2-4}{4+4}=\frac{-6}{8}=-\frac{3}{4} \end{gathered}[/tex]Let find b
[tex]\begin{gathered} y=mx+b \\ 4=-\frac{3}{4}(-4)+b \\ b=1 \end{gathered}[/tex]The linear equation is
[tex]y=-\frac{3}{4}x+1[/tex]A mom took her daughter shopping with her allowance. Together, they spent $20. The mom spent 8 more than 4 times the amount of the daughter. Find the amount they each spent. x is the daughter's spending and y is the mother's spending
Given that, they spent a total of 20 dollars.
Therefore, the first equation becomes,
[tex]x+y=20[/tex]Also, mom spent 8 more than 4 times the amount of daughter.
Therefore, the second equation becomes,
[tex]y=4x+8[/tex]Substitute 4x+8 for y in the equation x+y=20 implies,
[tex]\begin{gathered} x+4x+8=20 \\ 5x=12 \\ x=2.4 \end{gathered}[/tex]Use the equation x+y=20 to find the value of y.
[tex]\begin{gathered} y=20-x \\ y=20-2.4 \\ y=17.6 \end{gathered}[/tex]Therefore, daughter's spending is 2.4 dollars and mom's spending is 17.6 dollars
two point four divided by eighty
Given:
[tex]\frac{2.4}{8}[/tex]Solution:
[tex]\begin{gathered} =\frac{2.4}{8} \\ =\frac{24}{80} \\ =0.3 \end{gathered}[/tex]value of 2.4 divided by 8 is 0.3.
-3/4 ÷ 2/9=I've missed days of school and am super. lost
Given square ABCD, find the following measures.АBEraDGiven thin the diOm AED=hij in blankmZACD= fill in blankhis...뿔g=45dl.
The angles of the four corners of the square are right angles, which means that they have a measure of 90º.
Each diagonal bisects the corner angles, this means that the diagonals divide the 90º angles into two equal angles:
[tex]\frac{90}{2}=45º[/tex]Each resulting angle measures 45º
The diagonals bisect each other so that they form 4 isosceles triangles.
The diagonals of the square are perpendicular, this means that the angles formed when they intersect each other are right angles. So the 4 central angles are right angles.
So you can conclude that the angles have the following measures:
∠AED= 90º
∠ACD= 45º
Create the required linear function an use it to answer the question.Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on thatexam. Persons taking a 70-hour review course average a score of 795. Based on these two data points, create alinear equation for the function that describes how score varies as a function of time. Use this function topredict an average score for persons taking a 54-hour review course. Round your answer to the tenths place.
Given:
For a 30-hour review course, the average score is 620.
For a 70-hour review course, the average score is 795.
To find: The linear equation and the average score for 54 hours review course.
Explanation:
Let us take two points
[tex](30,620)\text{ and }(70,795)[/tex]Using the two-point formula,
[tex]\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}[/tex]On substitution we get,
[tex]\begin{gathered} \frac{y-620}{795-620}=\frac{x-30}{70-30} \\ \frac{y-620}{175}=\frac{x-30}{40} \\ 40y-24800=175x-5250 \\ 40y=175x-5250+24800 \\ 40y=175x+19550 \\ y=\frac{35}{8}x+\frac{1955}{4} \end{gathered}[/tex]Thus, the linear equation is,
[tex]y=\frac{35}{8}x+\frac{1955}{4}[/tex]Therefore, for a 54-hour review course
The average score is,
[tex]\begin{gathered} y=\frac{35}{8}(54)+\frac{1955}{4} \\ y=725 \end{gathered}[/tex]Thus, the average score for a 54-hour review course is 725.
n sync On average, a person's heart beats about 4.2 x 10^7 times per year. There are about 7,600,000,000 people in the world. Use this data to approximate the number of heartbeats for all the people in the world per year. Expressing your answer in scientific notation in the form a x 10^b what are the values of a and b?
First, notice that if there are 4.2*10^7 hearbeats per year per person and there are 7,600,000,000 people in the world, then the total number of heartbeats in the world per year is equal to:
[tex](4.2\cdot10^7)(7,600,000,000)[/tex]Rewrite the number 7,600,000,000 using scientific notation. Moving the decimal point 9 places to the left:
[tex]7,600,000,000=7.6\cdot10^9[/tex]Therefore, the number of heartbeats per year can be expressed as:
[tex](4.2\cdot10^7)\cdot(7.6\cdot10^9)[/tex]Use the commutative property of multiplication to rewrite the product:
[tex]4.2\cdot7.6\cdot10^7\cdot10^9[/tex]Multiply 4.2 times 7.6:
[tex]31.92\cdot10^7\cdot10^9[/tex]Use the properties of the exponents to rewrite (10^7)(10^9):
[tex]31.92\cdot10^{7+9}=31.92\cdot10^{16}[/tex]Move the decimal point one place to the left by increasing by 1 the exponent of the power of 10:
[tex]3.192\cdot10^{17}[/tex]Comparing this number with the expression a x 10^b:
[tex]\begin{gathered} a=3.192 \\ b=17 \end{gathered}[/tex]Therefore, there is a total of 3.192 x 10^17 human heartbeats per year.
How are the numbers 0.444 and 0.4 the same How are they different?
We have the periodic number:
There is an infinite number of decimals, and all of them are 4. If we round this number to the 3 decimal places, this is:
So, to 3 decimal places, this is equal to 0.444, but the exact number is different because there are infinite decimals, not only 3.
points Write the equation in point slope form using the pair of points (-6, 4) and (-1,0)
Answer
y - 4 = (-4/5) (x + 6)
We can then simplify further by multiplying through by 5
5y - 20 = -4 (x + 6)
5y - 20 + 20 = -4x - 24 + 20
5y = -4x - 4
Explanation
The general form of the equation in point-slope form is
y - y₁ = m (x - x₁)
where
y = y-coordinate of a point on the line.
y₁ = This refers to the y-coordinate of a given point on the line
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
x₁ = x-coordinate of the given point on the line
Now, we need to calculate the slope
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For this question,
(x₁, y₁) and (x₂, y₂) are (-6, 4) and (-1, 0)
x₁ = -6
y₁ = 4
x₂ = -1
y₂ = 0
[tex]\text{Slope = }\frac{0-4}{-1-(-6)}=\frac{-4}{-1+6}=\frac{-4}{5}[/tex]Slope = m = (-4/5)
We can then use any of the points given as the point in the equation
(x₁, y₁) = (-6, 4)
x₁ = -6, y₁ = 4
y - y₁ = m (x - x₁)
y - 4 = (-4/5) (x - (-6))
y - 4 = (-4/5) (x + 6)
We can then simplify further by multiplying through by 5
5y - 20 = -4 (x + 6)
5y - 20 + 20 = -4x - 24 + 20
5y = -4x - 4
Hope this Helps!!!
The probability of meeting a random person who has the same birthday as you is365• whichis approximately 0.27%. What is the probability that the 25th person you meet is the firstperson who has the same birthday as you?00.27%00.14%00.25%00.03%
Given:
The same birthday probability is
[tex]\begin{gathered} =\frac{1}{365} \\ \\ =0.27\% \end{gathered}[/tex]Find:-
Person who has the same birthday
Explanation-:
The probability of meeting a random person who has the same birthday is:
[tex]=\frac{1}{365}[/tex]Probability of meeting a random person who does not has same birthday as you
[tex]\begin{gathered} =1-\frac{1}{365} \\ \\ =\frac{365-1}{365} \\ \\ =\frac{364}{365} \end{gathered}[/tex]The required probability that the 25th person you meet is the first person who has the same birthday as
[tex]\begin{gathered} =\text{ Probability that the first 24 persons we meet did not have same birthday \rparen}\times(\text{ probability that the first 25 person we meet has same birthday\rparen} \\ \end{gathered}[/tex]Therefor,
[tex]\begin{gathered} P=(\frac{364}{365})^{24}\times\frac{1}{365} \\ \\ =(0.9972)^{24}\times0.27 \\ \\ =0.9362\times0.27 \\ \\ =0.25\% \end{gathered}[/tex]I have no idea how this is worked out but the question is find the quotient and remainder of x^3-x^2-3 / x+1
We want to solve the following division:
[tex]\frac{x^3-x^2-3}{x+1}[/tex]Using the following division we want to locate the polynomials as shown in the next figure:
We have that the polynomial of the red square is:
[tex]x^3-x^2-3[/tex]we have that its coefficients (the number behind each terms) are:
for x³: 1
for x²: -1
for x: 0
for numbers: -3
Then:
for the polynomial of the purple square (x - z) = (x + 1), we have that
x + 1 = x - (-1), then
x - (-1) = x - z
Then z = -1:
The numbers of the answer section are going to be the addition of each column, and they will be multiplied by z = -1, as the following figure shows:
In the answer section we will have the coefficients of the quotient, and the last number is the remainder:
Now, we have the answer
Answer - the quotient is:
x² -2x + 2
and the remainder is: -5
Find the area of the shaded region under the standard distribution curve.
We have a standard distribution curve, and we need to find the area of the shaded region, which is given by:
[tex]P(-0.90This can be rewritten as the expression:[tex]\begin{gathered} P(-0.90In a standard normal table, we find the following values:[tex]\begin{gathered} P(z<1.60)=0.9452 \\ P(z<0.90)=0.8159 \\ 1-P(z<0.90)=1-0.8159=0.1841 \end{gathered}[/tex]If we replace these values into the expression we obtain:
[tex]P(-0.90The area of the shaded region is 0.7611In Sally's state, the weekly unemploymentcompensation is 60% of the 26-week averagefor the two highest-salaried quarters. Aquarter is three consecutive monthly. For July,August, and September, she earned a total of$8,050. In October, November and December,she earned a total of $8,120. Determine Sally'sunemployment compensation.
Can you guys please help me on this question ?
If one tail of the distribution is longer than the other, showing any kind of symmetry, it is said to be skewed, otherwise, if a distribution is said to be symmetric if one half of the distribution is a mirror image of the other half.
AnswerIn this case, the distribution representing the class sizes at Northview HS is symmetric and the distribution representing the sizes at Southdale HS is skewed negativily, it is a negative skewness because it has a long left tail (long tail in the negative direction on the number line)
SummaryOption A is the correct answer, Northview HS is symmetric and Southdale HS is negatively skewed.
The base of a rectangle measures 8 feet and the altitude measures 6 feet. find to the nearest degree, the measure of the angle that the diagonal makes with the base.
The rectangle can be drawn as follows:
The angle we are to find is labelled θ.
Considering ΔDBC, we can use the Tangent Trigonometric Ratio to get the angle:
[tex]\tan \theta=\frac{BC}{DC}[/tex]Therefore, we can substitute as follows:
[tex]\begin{gathered} \tan \theta=\frac{6}{8} \\ \tan \theta=0.75 \\ \theta=\tan ^{-1}0.75 \\ \theta=36.9\approx37^{\circ} \end{gathered}[/tex]Therefore, the angle is 37°
A manufacturing company performs a quality control analysis on the ceramic tile it produces. Suppose a batch of 22 tiles has 6 defective tiles. If 5 tiles are sampled at random, what isthe probability that exactly 1 of the sampled tiles is defective?How many ways can 5 tiles be selected from 22 tiles?ways(Type a whole number)Help Me Solve ThisView an ExampleGet More HelpClear AllCheck Answer
ANSWER:
The probability is 0.4147
26334 ways
STEP-BY-STEP EXPLANATION:
The first thing is to calculate numbers of ways of choosing 5 out of 22 (without replacement), just like this:
[tex]\begin{gathered} \text{nCr}=\frac{n!}{r!\cdot(n-r)!} \\ \text{ replacing} \\ 22C5=\frac{22!}{5!\cdot(22-5)!}=26334 \end{gathered}[/tex]Out of 22 tiles, 6 are defective and remaining 16 are not defective.
Let a = number of defective among randomly selected 5 tiles.
Here a follows hypergeometric distribution with parameters N = 22, k = 6, n = 5.
PMF is given: P(a = k), in this case:
[tex]P(a=1)=\frac{(\text{choose 1 of 6 defective)}\cdot(\text{choose 4 of 16 not defective) }}{(\text{select 5 from 22 total)}}[/tex]replacing:
[tex]P(a=1)=\frac{\frac{6!}{1!\cdot(6-1)!}\cdot\frac{16!}{4!\cdot(16-4)!}}{\frac{22!}{5!\cdot(22-5)!}}=\frac{6\cdot1820}{26334}=0.4147[/tex]if 24 compact car represent 12% of the cars made this week. What was the total number of cars made this week?
Given Data:
Total number of compact cars made is: n=24
The persentage of cars made this week is: 12%
The 12% of 24 will be the total number of cars made this week.
Let 'x' be the total number of cars made this week.
[tex]x=n\times\frac{12}{100}[/tex]Substitute valeus in the above expression.
[tex]\begin{gathered} x=24\times\frac{12}{100} \\ =24\times0.12 \\ =2.88 \\ \approx3\text{ cars} \end{gathered}[/tex]Thus, approximately 3 cars are made in a week.
If x = 37.5, solve for z using geometric mean. Round your answer to the nearest tenth if necessary.
ANSWER
z = 22.5
EXPLANATION
We want to use the geometric mean theorem to find the value of z.
The geometric mean theorem for similar triangles states that:
[tex]\frac{z}{x}\text{ = }\frac{x\text{ - 24}}{z}[/tex]This is gotten by equating the ratio of corresponding sides of similar triangles.
This implies that:
[tex]\begin{gathered} \text{Cross}-mu\text{ltiplying:} \\ z\cdot\text{ z = x(x - 24)} \\ \Rightarrow z^2\text{ = 37.5(37.5 - 24)} \\ z^2\text{ = 37.5 }\cdot\text{ }13.5\text{ = }506.25 \\ z\text{ = }\sqrt[]{506.25} \\ z\text{ = }22.5\text{ } \end{gathered}[/tex]That is the value of z.
What is the slope of the line that passes through the points (-3,5) and (21,5)?
The slope of the line passing through the points (-3,5) and (21,5) is 0
Explanation:The slope of a line passing through the points (x₁, y₁) and (x₂, y₂) is calculated as:
[tex]\begin{gathered} \text{Slope = }\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex]For the line passimng through the points (-3,5) and (21,5):
Substitute x₁ = -3, y₁ = 5, x₂ = 21, y₂ = 5 into the slope formula above
[tex]\begin{gathered} \text{Slope = }\frac{5-5}{21-(-3)} \\ \text{Slope = 0} \end{gathered}[/tex]Therefore, the slope of the line passing through the points (-3,5) and (21,5) is 0
Use the center of rotation point C and rotatepoint P clockwise around it 90°. Label the image P'. With point C as a center of rotation also rotate point P 180°. Label this image P".P':__; P'':__
Solution
We have a point P=(a=7,b=6) and we need to rotate around C=(x= 4,y=1)
And we can use the following formula:
We can change the origin and the new coordinates are now:
C (0,0), P= (3 ,5)
Then the rotated point is:
Px' = (5, -3)
And the real value would be:
P' = (5+4, -3+1)= (9,-2)
For the second case the new coordinate is:
Px'' = (-5, -3)
And with the transformation we have:
P'' =(-5+4, -3+1)= (-1, -2)
the graph of linear function f passes through the point (1, -8) and has a slope of 2. what is the zero of f ?A) -2B) 5 C) 2D) -5
Goven,
The function is passes through point (1, -8).
The slope of the function is 2.
The standard equation of function is,
[tex](y-y_1)=m(x-x_1)[/tex]Substituting the values then,
[tex]\begin{gathered} (y-(-8))=2(x-1_{}) \\ y+8=2x-2 \\ y=2x-10 \end{gathered}[/tex]To get the zeroes of the function take y = 0 then,
[tex]\begin{gathered} 0=2x-10 \\ x=5 \end{gathered}[/tex]Hence, the zeroes of the function is 5.
how do I find the the two numbers that lie between the squareroot of 74?
Given the expression;
[tex]\begin{gathered} \sqrt[]{74} \\ \end{gathered}[/tex]First is to simplify the expression
[tex]\sqrt[]{74}=8.6[/tex]we can see that the approximate value of the square root of 74 is 8.6 and this values only lies between 8.5 and 9. Hence the squaroot of 74 can be expressed as;
[tex]8.5<\sqrt[]{74}<9.0[/tex]Hence option B is correct among the options