GIVEN:
We are given two points on a line and these are;
[tex]A=(5,6),\text{ }B=(-5,-1)[/tex]Required;
We are required to determine the slope of the line passing through these points.
Step-by-step solution;
The slope of a line is given by the formula;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]The variables are;
[tex]\begin{gathered} (x_1,y_1)=(5,6) \\ \\ (x_2,y_2)=(-5,-1) \end{gathered}[/tex]We can now substitute these into the formula and then simplify;
[tex]\begin{gathered} m=\frac{-1-6}{-5-5} \\ \\ m=\frac{-7}{-10} \\ \\ m=\frac{7}{10} \end{gathered}[/tex]ANSWER:
The slope of the line passing through the given points is;
[tex]m=\frac{7}{10}[/tex]Use the transformations of the graph of f(x) = x^2 to determine the graph of the function. h(x) = -(x+2)^2
Answer:
Step-by-step explanation:
The graph f(x) = x^2 is shifted along the OX axis to the left by 2 and reflected relative to this axis:
She earns $12 per hour working at a store.
She earns $30 per lawn mowed working for a landscaper.
Her goal is to earn $1,800 to pay her monthly expenses.
The situation can be modeled by the formula below, where represents the hours Tina works in the grocery store and represents the number of lawns mowed.
Answer:
Change Mixed fraction to improper fraction 2/9
A number c is no less than -1.5 and less than 5.3
Step-by-step explanation/answer:
A number c is no less than -1.5 and less than 5.3.
So -1.5<= c < 5.3
You would label your number line and have a filled in closed circle at -1.5 and an open circle at 5.3 to signify that 5.3 is not a possible value of c.
Explain how to simplify ( (a*)") using the properties of exponents.
Simplifying ((a*)"),
In this type of expression, we apply the properties of exponents under Power Rules.
Under the power rule property of exponents,
[tex]((A^x)^y)=A^{x\text{ }\cdot\text{ y}}[/tex]This says that to raise a power to a power you need to multiply the exponents.
Let's apply this rule to simplify the given expression,
((a*)") = a*"
what fraction of a day is 45 minutes
To be able to determine what fraction of a day is 45 minutes, let's first determine how many minutes are there in a day.
1 day
8. 500 Vanessa is in charge of organizing volunteers to make sandwiches to feed the homeless during the Memorial Day weekend. She needs to have 500 sandwiches made so she will want to get the help of as many volunteers as possible to assist her and the 3 other paid staff who will also be making the sandwiches. Use the function s(v) = to determine s(v), the number of sandwiches each person will have to make based on v, the number of volunteers working.
ANSWER
EXPLANATION
In this problem, we have to complete the table by replacing v with each value from 0 to 6 in the table, and compute the corresponding value of s(v) based on the equation,
[tex]s(v)=\frac{500}{v+4}[/tex]Find the values for the table,
[tex]v=0;s(0)=\frac{500}{0+4}=\frac{500}{4}=125[/tex][tex]v=1;s(1)=\frac{500}{1+4}=\frac{500}{5}=100[/tex][tex]v=2;s(2)=\frac{500}{2+4}=\frac{500}{6}\approx83.3[/tex][tex]v=3;s(3)=\frac{500}{3+4}=\frac{500}{7}\approx71.4[/tex][tex]v=4;s(4)=\frac{500}{4+4}=\frac{500}{8}=62.5[/tex][tex]v=5;s(5)=\frac{500}{5+4}=\frac{500}{9}\approx55.6[/tex][tex]v=6;s(6)=\frac{500}{6+4}=\frac{500}{10}=50[/tex]need to know the steps and how to work it out to get the correct anwser
Given equation:
[tex]\text{y = -x + 1}[/tex]For two lines to be parallel, the slope of one will be the same as the slope of the second line
[tex]\begin{gathered} u\sin g\text{ equation of line:} \\ y\text{ = mx + b} \\ m\text{ = slope, b = y-intercept} \end{gathered}[/tex]comparing the given equation with the equation of line:
[tex]\begin{gathered} y\text{ = y} \\ mx\text{ = -x = -1(x)} \\ m\text{ = -1} \\ b\text{ = 1} \end{gathered}[/tex]This means the slope of the 1st line is -1. The slope of the second line will also be -1 since they are parallel
To get the y-intercept of the second line, we would insert the slope and the point given:
point given: (-7, 3) = (x, y)
[tex]\begin{gathered} y\text{ = mx + b} \\ 3\text{ = -1(-7) + b} \\ 3\text{ = 7 + b} \\ 3\text{ - 7 = b} \\ b\text{ = -4} \\ y-\text{intercept of 2nd line = -4} \end{gathered}[/tex]The second equation is the equation of line that is parallel to the line y = -x + 1 and passes through (-7, 3)
Second equation:
[tex]\begin{gathered} y\text{ = mx + b} \\ y\text{ = -1(x) + (-4)} \\ y\text{ = -x - 4} \end{gathered}[/tex][tex]\begin{gathered} In\text{ slope intercept form:} \\ y\text{ = -x - 4} \end{gathered}[/tex]Need helpQuick answer is okay. I will attach the other photos.
SOLUTION
The graph of
[tex]f(x)=\frac{1}{4}(3)^x[/tex]is shown below
Comparing to the options, the answer is option D
Santino tried to find the median from the following table, which shows the number of internet users in 2012 20122012 for the highest using countries. However, he made a mistake. Country China United States Japan India Brazil Number of internet users (in millions) 568 568568 254 254254 101 101101 152 152152 100 100100 Here is Santino's work: "The numbers are 568 568568, 254 254254, 101 101101, 152 152152, and 100 100100. There are 5 55 values, so the middle value is the 3 rd 3 rd 3, start superscript, start text, r, d, end text, end superscript value, 101 101101. The median is 101 101101 million internet users." What mistake did Santino make?
The median of the data set is 152 . Santino made the mistake of not arranging the numbers in the set.
The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory.
It could be referred to as "the middle" value for a data set. The fundamental difference between the mean and the median when describing data is that the median is more representative of the "normal" value because it is not skewed by a tiny fraction of exceptionally big or small values. Due to the fact that income distribution can be very skewed, the median income, for instance, might be a better indicator of what is considered a "normal" income. Given that it is the most resilient statistic, the median is crucial to strong statistics.the numbers of the data when arranged are :
100 ,101 , 152 ,254 ,568
Here n =5
Median =(n+1)/2 th data
or , median = 3rd data
or, median =152
Therefore Santino did not arrange the data in ascending order to find the median. the correct median is 152.
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Answer:
Santino should have ordered the numbers from least to greatest before picking the middle number.
Step-by-step explanation:
solve for the unknown angle measure given that f || g
The measure of the unknown angle is 75°
What is an angle?
An angle is a shape in Euclidean space created by two rays, termed the ends of the angle, that share a common termination, called the vertex of the angle. Angles produced by two rays are located in the longitudinal plane the rays. Angles are also generated when two planes overlap. These are known as dihedral angles. An angle defined by two intersecting curves is the angle of the rays lying tangent to the respective curves at their point of junction. Angle can also refer to the measurement of an angle or of a rotation. In the case of a geometric angle, the arc is defined by the sides and is centered at the vertex.
From figure,
x+70+25 = 180 (angle sum property of a triangle)
x = 180 - 95 = 75°
Hence, the measure of the unknown angle is 75°
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y= 2000 cos π/14 (8-4)
Solve the equation
First step is to find cos (pi/14), then solve the product)
[tex]\begin{gathered} y=2000\cdot\cos (\frac{\pi}{14})\cdot(8-4) \\ y=2000\cdot0.9749\cdot(4) \\ y=7799.42 \end{gathered}[/tex]A customer wants to put in a concrete driveway that is 10″ thick. How much concrete would it take to pour a driveway that measures 18′ by 42′? Express your answer in cubic yards.
The volume of concrete it would it take to pour a driveway that measures 18′ by 42′ and 10″ thick is equal to 23.33 cubic yard.
What is a conversion factor?In Mathematics, a conversion factor simply refers to a number that is typically used to convert a number in one (1) set of units to another, either by multiplying or dividing.
Additionally, an appropriate conversion factor to an equal unit of value must be chosen and used when it is necessary to perform any mathematical conversion.
Note: The double quotation mark " is a notation that represent inches while the apostrophe mark ' represents foot.
Next, we would convert the unit in inches to feet:
1 inch = 0.0833333 feet.
10 inches = 10 × 0.0833333 = 0.833333 feet.
For the volume of concrete required, we have:
Volume of concrete = Length × Width × Thickness
Volume of concrete = 18 × 42 × 0.833333
Volume of concrete = 629.999748 cubic feet.
Also, we would convert cubic feet to cubic yard:
1 cubic feet = 0.037037 cubic yard
629.999748 cubic feet = x cubic yard
Cross-multiplying, we have:
Volume of concrete = 629.999748 × 0.037037
Volume of concrete = 23.33 cubic yard.
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Alana has 12.5 cups of flour with which she is baking four loaves of raisin bread and one large pretzel. The pretzel requires 2.5 cups of flour to make. How much flour is in each loaf of raisin bread? Explain the steps to follow to get the answer.
Martina is driving on a highway. She uses one gallon of gas every 30 miles she drives. The distance, D (in miles), she travels on g gallons of gas is given
by the following function.
D (g) = 30g
How far does Martina drive if she uses 3 gallons of gas?
Answer:
90 miles
Step-by-step explanation:
First the formula is solving for distance in miles. and is says distance = 30 x gallons. So if it's asking for how far she drives with 3 gallons, it's asking for her distance driven when using 3 gallons of gas. So the formula would be D = 30g. D = 30 x 3 is the formula, we have to put in 3 for g. When we do 30 x 3 we would get our answer as 90. Therefore our final answer is 90 miles.
Andre and Elena are reading the same book over the 1 summer. Andre says he has read 1/5 of the book. Elena ! says she has read 20 more pages than Andre. If Elena is on page 55, how many pages are in the book? Lin has drawn a diagram to solve this question. Find her error..
Answer:
The book has 175 pages
Explanation:
Andre says that he has read 1/5 of the book, so the correct diagram should have each rectangle label as a (the number of pages that Andre has read)
because 5 times 1/5 of the book makes the complete book.
On the other side, Elena has read 20 more pages than Andre, so we should have the second rectangle divided and one part should be label as 20 and the sum of a and 20 is equal to 55.
So, the correct diagram is:
Therefore, we can calculate the number of pages that Andre has read as:
a = 55 - 20 = 35
Then, the number of pages of the book is 5 times a, so:
5 x a = 5 x 35 = 175
Therefore, the answer is the book has 175 pages
Use synthetic division to divide.
(-4x3 - 22x2 - 12x - 10) ÷ (x + 5)
Answer:
-4x² - 2x - 2
Step-by-step explanation:
(-4x3 - 22x2 - 12x - 10) ÷ (x + 5)
-5 | -4 -22 -12 -10
↓ 20 10 10
-----------------------------------
-4 -2 -2 0
-4x² - 2x - 2
I hope this helps!
Solve the following system hood equations by the substitution method
Question:
Solution:
Consider the following system of linear equations:
Equation 1:
[tex]6x+7y=17[/tex]Equation 2:
[tex]x=22-5y[/tex]Replacing the above equation into equation 1, we get:
[tex]6(22-5y)+7y=17[/tex]Applying the distributive property, we get:
[tex]132-30y+7y=17[/tex]this is equivalent to:
[tex]-30y+7y=17-132[/tex]this is equivalent to:
[tex]-23y=\text{ -115}[/tex]or
[tex]23y=\text{ 115}[/tex]solving for y, we obtain:
[tex]y=\frac{115}{23}=5[/tex]Now, replacing this into Equation 2, we obtain:
[tex]x=22-5(5)=22-25=-3[/tex]So that, we can conclude that the correct answer is:
The solution is (-3, 5)
I need help with this Struggling It asks to answer (a) and (b) Put these separately ^ so I know which is which
We are given that:
[tex](3x^5-\frac{1}{9}y^3)^4[/tex]a) We know that binomial theorem in summation form
[tex](a+b)^n=\sum ^{r=n}_{r\mathop=0}\begin{bmatrix}{n} \\ {r}\end{bmatrix}a^{n-r}\cdot b^r[/tex]Using the formula and substitute
[tex]a=3x^5,b=-\frac{1}{9}y^3\text{ and n=4}[/tex]Therefore,
[tex](3x^5-\frac{1}{9}y^3)^4=\sum ^{r=4}_{r\mathop=0}\begin{bmatrix}{4} \\ {r}\end{bmatrix}(3x^5)^{4-r}\cdot(-\frac{1}{9}y^3)^r[/tex]Hence, the sum in summation notation that he uses to express the expansion is
[tex](3x^5-\frac{1}{9}y^3)^4=\sum ^{r=4}_{r\mathop{=}0}\begin{bmatrix}{4} \\ {r}\end{bmatrix}(3x^5)^{4-r}\cdot(-\frac{1}{9}y^3)^r[/tex]b) Let us now write the simplified terms of the expansion.
Therefore,
Using Combination formula to expand the expression above
The combination formula is,
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]Where,
[tex]n!\text{ = n(n-1)(n-2)}\ldots3.2.1[/tex]Hence,
[tex]\begin{gathered} =\frac{4!}{0!\left(4-0\right)!}\mleft(3x^5\mright)^4\mleft(-\frac{1}{9}y^3\mright)^0+\frac{4!}{1!\left(4-1\right)!}\mleft(3x^5\mright)^3\mleft(-\frac{1}{9}y^3\mright)^1+\frac{4!}{2!\left(4-2\right)!}\mleft(3x^5\mright)^2\mleft(-\frac{1}{9}y^3\mright)^2 \\ +\frac{4!}{3!\left(4-3\right)!}\mleft(3x^5\mright)^1\mleft(-\frac{1}{9}y^3\mright)^3+\frac{4!}{4!\left(4-4\right)!}\mleft(3x^5\mright)^0\mleft(-\frac{1}{9}y^3\mright)^4 \end{gathered}[/tex]Simplifying the above, we have
[tex]=81x^{20}-12x^{15}y^3+\frac{2x^{10}y^6}{3}-\frac{4x^5y^9}{243}+\frac{y^{12}}{6561}[/tex]Hence, the simplified terms of the expansion are
[tex]81x^{20}-12x^{15}y^3+\frac{2x^{10}y^6}{3}-\frac{4x^5y^9}{243}+\frac{y^{12}}{6561}[/tex]Enter the correct answer in the box.What are the solutions of this quadratic equation?1 2 = 161 – 65Substitute the values of a and b to complete the solutions.TIsin cos tan sin-costan-1α βhaE908 001vo yoΖΔfo?X• Dlot<λμ ρ>CSC seccot log logIn=x= a + bix=a-biResetNext
Given the equation
[tex]x^2=16x-65[/tex]To find a and b, you have to find the roots, following the steps below.
Step 01: Write the equation in the general quadratic form.
The general quadratic form is ax²+bx+c=0.
Then, add -16x + 65 to both sides of the equation.
[tex]\begin{gathered} x^2-16+65=16x-65-16x+65 \\ x^2-16+65=0 \end{gathered}[/tex]Step 2: Use the Bhaskara formula to find the roots.
The Bhaskara formula for a general equation is:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4\cdot a\cdot c}}{2\cdot a}[/tex]In this exercise,
a = 1
b = -16
c = 65
Then,
[tex]\begin{gathered} x=\frac{-(-16)\pm\sqrt[]{(-16)^2-4\cdot1\cdot65}}{2\cdot1} \\ x=\frac{+16\pm\sqrt[]{256-260}}{2} \\ x=\frac{+16\pm\sqrt[]{-4}}{2} \end{gathered}[/tex]√-4 can also be written as:
[tex]\sqrt[]{-4}=\sqrt[]{(4)\cdot(-1)}=\sqrt[]{4}\cdot\sqrt[]{-1}[/tex]Knowing that i = √-1:
[tex]\sqrt[]{-4}=\sqrt[]{4}\cdot i[/tex]Then:
[tex]\begin{gathered} x=\frac{+16\pm\sqrt[]{-4}}{2}=\frac{+16\pm\sqrt[]{4}\cdot i}{2} \\ x=\frac{16\pm2\cdot i}{2} \\ x=\frac{16}{2}\pm\frac{2}{2}\cdot i \\ x=8\pm i \end{gathered}[/tex]The roots are:
8 + 1i
8 - 1i
So, the Answer is:
a = 8
b = 1
The radius of a sphere is 4 inches. If the radius is doubled, how does that change the surface area of the sphere?aThe surface area is multiplied by fourbThe surface area is squaredcThe surface area is doubleddThe surface area is multiplied by eight
Solution:
Given the radius of the sphere is 4inches.
The surface area, A, of the sphere is;
[tex]\begin{gathered} A=4\pi r^2 \\ \\ A=4\pi(4^2) \\ \\ A=201.06in^2 \end{gathered}[/tex]But when the radius is doubled;
[tex]\begin{gathered} r=8in \\ \\ A=4\pi(8^2) \\ \\ A=804.25in^2 \end{gathered}[/tex]Hence, when the radius is doubled, the surface area is multiplied by four.
Kaitlyn wants to buy Nikes but only brought $156.50 with her to the store. If the Nikes cost $209, what percent discount would she need in order to be able to afford the Nikes? Round your answer to the nearest whole percent.
Kaitlyn's money =$156.50
Nike's cost = $209
We have to write an equation:
The cost of the Nikes (209) multiplied by the percentage(x) in decimal form (divided by 100) must be equal to the money available (209)
209 x = 156.50
x = 156.50/209
x= 0.75
0.75 x 100 =75%
1- 75 = 25%
Percent discount= 25%
what else would need to be congruent to show that triangle ABC=DEF
(AAS): If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent
Hugo averages 41 words per minute on a typing test with a standard deviation of 7.5 words per minute. Suppose Hugo's words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then, X∼N(41,7.5).
Suppose Hugo types 45 words per minute in a typing test on Wednesday. The z-score when x=45 is ________. This z-score tells you that x=45 is ________ standard deviations to the ________ (right/left) of the mean, ________.
Correctly fill in the blanks in the statement above.
At x = 30, the result is -1.57. According to this z score, x = 30 is 1.57 standard deviations away from the mean. 41 At x = 30, the result is -1.57. According to this z score, x = 30 is 1.57 standard deviations away from the mean.
What is the z score and standard deviation?
In essence, standard deviation represents the degree of variability present in a given data collection. To compute the standard deviation, first, get the distance between each data point and the mean. After that, the discrepancies are squared, added up, and averaged. The variance is caused by this. The variance's square root yields the standard deviation.The Z-score, in contrast, indicates how far a given data point deviates from the mean. The Z-score is adverse for data points that are below the mean. 99% of the values in most sizable data sets have a Z-score between -3 and 3, which denotes that they are within three standard deviations of the mean either above or below.Given, the Normal distribution with,
mu = 41
sigma = 7
The z-score formula is
z score = (X - mu) / sigma
So , z score at X = 30 is
z score = (X - mu) / sigma = (30 - 41) / 7 = -1.57
At x = 30, the result is -1.57. According to this z score, x = 30 is 1.57 standard deviations away from the mean. 41 At x = 30, the result is -1.57. According to this z score, x = 30 is 1.57 standard deviations away from the mean.
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Perform the indicated operation. 22 6/11 x 1 1/2
Answer:
[tex]1\frac{1}{2}[/tex] <2<2 [tex]\frac{6}{11}[/tex]
Step-by-step explanation:
[tex]1\frac{1}{2}[/tex] is less than 2 is less than 2 [tex]\frac{6}{11}[/tex]
[tex]\frac{33}{22} < \frac{44}{22} < \frac{56}{22}[/tex]
what does it mean to subtract 4 on both sides of 76 equals 7 and 2x
Use the connect line tool to draw your path so that it meets the requirements. Then drag water fountains to the map and place them along the path based on the requirements. Diagonal lines may not be used.
1 mile is equivalent to 5280 feet which is equivalent to 5280/440 in = 12 in
Hence, a path of 2miles is equivalent to 24 in on the graph
The connect line is as shown in the image from the School to the Park and it is colored red and 24 in long.
The position of the water fountains are marked in pink on the graph,
The first is 1/3 of the way from the School which is 8 in from the school.
The second is 2/3 of the way from the School which is 16 in from the school.
I need help figuring out what angle these degrees are
1) Looking at the picture we can state that
m∠1 = 57º and m∠2 = 180-57
m∠2 = 123º
We can state that according to the Same side interior angles that states that those angles ∠1 , and ∠2 are supplementary since those angles belong to lines that have been crossed by a transversal line t.
The display shows the data set from a survey about time spent on social media in a day. Vertical box plot titled average time spent on social media in a day, with minutes labeled on the vertical axis. The minimum is at 5, and the maximum is at 80. The lower quartile is at 30, the median is at 50, and the upper quartile is at 60. Which of the following describes the data set? Categorical and bivariate Categorical and univariate Numerical and bivariate Numerical and univariate
The data-set in this problem is classified as follows:
Numerical and univariate.
What are the classification of variables?The variables can be classified as categorical or numerical as follows:
Categorical: The possible values assumed by the variable are labels, such as yes/no, good/bad, and so on...Numerical: The values assumed by the variable are numbers.In the context of this problem, the minimum, the maximum and the quartiles of the variable all assume numeric values, hence the variable is classified as numerical.
From the text, the variable under study is the time spent on social media in a day, as a function of minutes. Since the output of the study is a single variable, the study is called univariate.
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Answer:
Numerical and univariate.
Step-by-step explanation:
What is the value of 24 - 5²?Record your answer and fill in thebubbles on your answer document.Be sure to use the correct placevalue.
24 - 5²
24 - 25 (Raising 5 to the power of 2)
-1 (Subtracting)
The answer is -1.
-12- (-35)
If 6 times a number is decreased by 2, the principal square root of this difference is 3 less than the number. Find the number(s).
So first we have the expression "six times a number". Let's use x to designate the number, then this expression can be written as 6x. We are being told that this term is decresed by 2 which means that now we have 6x-2. Then we have a certain condition on the principal square root, this would be:
[tex]\sqrt[]{6x-2}[/tex]We are being told that this square root is equal to "3 less than the number". This last term can be written as x-3. Knowing that x-3 has to be equal to the square root I mentioned before we can build an equation for x:
[tex]\sqrt[]{6x-2}=x-3[/tex]Know let's find x. First I'm going to get rid of the square root by squaring both sides of the equation:
[tex]\begin{gathered} (\sqrt[]{6x-2})^2=6x-2=(x-3)^2 \\ 6x-2=(x-3)^2=x^2-6x+9 \\ 6x-2=x^2-6x+9 \end{gathered}[/tex]Know let's move all terms to the right side:
[tex]\begin{gathered} 6x-2=x^2-6x+9 \\ 0=x^2-6x+9-6x+2 \\ 0=x^2-12x+11 \end{gathered}[/tex]So we have a cuadratic function equalizing 0. This means that we can use the cuadratic formula:
Where a, b and c are the coefficients of the cuadratic equation.In this case a=1, b=-12 and c=11 so we have:
[tex]\begin{gathered} x=\frac{-(-12)\pm\sqrt[]{(-12)^2-4\cdot1\cdot11}}{2\cdot1}=\frac{12\pm\sqrt[]{144-44}}{2}=\frac{12\pm\sqrt[]{100}}{2} \\ x=\frac{12\pm10}{2}=6\pm5 \end{gathered}[/tex]So we have two possible values for x, 1 and 11. Then the solution set is {1,11}
