Given the expression:
[tex]-3y+10=4x[/tex]Let's check if (x,y) = (-2,6) is a solution by substituting each value on the equation:
[tex]\begin{gathered} x=-2 \\ y=6 \\ -3y+10=4x \\ \Rightarrow-3(6)+10=4(-2) \\ \Rightarrow-18+10=-8 \\ \Rightarrow-8=-8 \end{gathered}[/tex]since we got on both sides -8, we can see that (-2,6) is a solution of -3y+10=4x
I have a question on area of a triangle an area of a circle. See picture of my problem
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
equilateral triangle:
side = 7x
circle:
radius = 4r
Step 02:
area:
a = circle area - triangle area
triagle area:
triagle area = (b * h) / 2
b = 7x
h:
[tex]\begin{gathered} (7x)^2=h^2+(\frac{7x}{2})^2 \\ 49x^2=h^2+\frac{49x^2}{4} \\ h^2=49x^2-\frac{49x^2}{4}=\frac{147x^2}{4} \\ h\text{ = }\sqrt[]{\frac{147x^2}{4}\text{ }}=6.06x=6.1x \end{gathered}[/tex]h = 6.1x
[tex]\text{triangle area = }\frac{7x\cdot6.1x}{2}=\frac{42.7x^2}{2}=21.35x^2[/tex]circle area:
circle area (r) = π r² = π (4r)² = 16 π r²
a = circle area - triangle area
a = 16 π r² - 21.35x²
The answer is:
a = 16 π r² - 21.35x²
Finding the Midpoint of a line SegmentUse this formula to find the Midpoint (mean) of the line segment (-5, -3) and (9,3)
The formula for determining the midpoint of a line is expressed as
[tex]\begin{gathered} \text{Midpoint = }\lbrack\frac{(x1\text{ + x2)}}{2},\text{ }\frac{(y1\text{ + y2)}}{2}\rbrack \\ \text{From the information given,} \\ x1\text{ = - 5, x2 = 9} \\ y1\text{ = - 3, y2 = 3} \\ \text{Midpoint = }\lbrack\frac{(-\text{ 5 + 9)}}{2},\text{ }\frac{(-\text{ 3 + 3)}}{2}\rbrack \\ \text{Midpoint = (- 2, 0)} \end{gathered}[/tex]4
Ellie goes to tutoring every 4 days for math
and every 12 days for Science. If Ellie
attended tutoring for both Math and Science
today, when is the next time she will attend
both sessions on the same day?
Answer:
gcm conditions
1. all numbers are entered (in the picture, enter numbers 2 and 3)
2. if there are the same number, take the number that has the largest power
ahe Will attend both sessions 12 days after today
Slope What is the slope of the line through (-4, 2) and (3,-3)?
We have the next formula in order to obtain the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where
(-4, 2)=(x1,y1)
(3,-3)=(x2,y2)
we substitute the values
[tex]m=\frac{-3-2}{3+4}=\frac{-5}{7}=-\frac{5}{7}[/tex]the slope is -5/7
2. For each of the next dot plots, guess the approximate location of the mean by thinking aboutwhere the balance point for the data would be. Then check how close your guess was bycalculating the mean.0 1 2 3 4 5 6 7 8 9 1001235 6 7 89 10012569 10
ANSWER
1) The plot looks like the fulcrum would balance at point 4
After calculation, the mean is 4.
2) The plot looks like the fulcrum would balance at point 3;
After calculation, the mean is 3.8.
3) The plot looks like the fulcrum would balance at point 8;
After calculation, the mean is 7.2
EXPLANATION
From the given data;
1) The plot looks like the fulcrum would balance at point 4.
the mean
[tex]\begin{gathered} mean(x)=\frac{(2+2+2)+(7+7)}{5} \\ =\frac{20}{5} \\ =4 \end{gathered}[/tex]2) The plot looks like the fulcrum would balance at point 2;
The mean;
[tex]\begin{gathered} x=\frac{0+1+1+2+2+2+3+3+4+10}{10} \\ =\frac{38}{10} \\ =3.8 \end{gathered}[/tex]3) The plot looks like the fulcrum would balance at point 8;
[tex]\begin{gathered} x=\frac{0+6+7+7+8+8+8+9+9+10}{10} \\ =\frac{72}{10} \\ =7.2 \end{gathered}[/tex]A translation 5 units right and 6 units down maps A onto A'. Write thetranslation as a vector.
A translation 5 units right and 6 units down maps A onto A'. Write the
translation as a vector.
we have that
the rule for the translation is
A(x,y) -------> A'(x+5, y-6)I need help with this. can you help me find the answer please?
ANSWER
15 degrees Celcius
STEP-BY-STEP EXPLANATION:
From the graph provided in the question tab, you will see that the outdoor temperature is plotted against the number of chips made per 25 seconds by the cricket.
On the x-axis, one box represents 10 units, on the y-axis, one box represents 4 units
At 33 cricket chirps in 25 seconds on the x-axis, we can trace the point to the y-axis, and this will give us 15 degrees Celcius.
Hence, the predicted outdoor temperature is 15 degrees Celcius
у = 3х – 7у = 3х + 1Are these equations, parallel, perpendicular or neither
A line equation can be written in slope-intercept form, which is
[tex]y=mx+b[/tex]Where m represents the slope and b represents the y-intercept.
If the slopes of two lines are equal they are parallel, if one slope is minus the inverse of the other they are perpendicular, otherwise they are neither.
Comparing our lines to the slope-intercept form, we can find their slopes.
[tex]\begin{gathered} y=3x-7\Rightarrow m=3 \\ y=3x+1\Rightarrow m=3 \end{gathered}[/tex]Since their slopes are equal, those lines are parallel to each other.
The owner of a small store buys coats for 40.00 each. She sells the coats for 72.00 each. What percent of the purchase price is the sales price?
In order to calculathe the percent, we just need to divide the sales price by the purchase price.
So we have:
[tex]\frac{72}{40}=\frac{36}{20}=\frac{18}{10}=1.8=180\text{\%}[/tex]Therefore the sales price represents 180% of the purchase price.
A cyclist pedals at a rate of 300 m min(exponent of -1) for 20 minutes. Then she slows down to 150 m min (exponent of -1) for 16 minutes, then races at 400 m min (exponent -1) for four minutes. find the distance traveled after20 minutes36 minutes40 minutesWrite a piecewise linear function for the distance of D(t) in terms of time (T) in minutes. find the distance traveled after 30 minutes38 minutesbonus - when has the cyclist traveled? 8km9 km
Given:
A cyclist pedals at a rate of 300 m min(exponent of -1) for 20 minutes. Then she slows down to 150 m min (exponent of -1) for 16 minutes, then races at 400 m min (exponent -1) for four minutes.
We will draw the diagram between the rate (speed of the cyclist) and the time (t) in minutes, the graph will be as follows:
For the first 20 minutes, the rate increased from 0 to 300 m/min
Then the next 16 minutes, the rate decreased to 150 m/min
And in the last 4 minutes, the rate increased to 400 m/min.
To find the distance traveled, we will find the area under the lines according to a specific time.
So, first, we will find the distance traveled after 20 minutes
It will be as follows = d(20)
[tex]d(20)=\frac{1}{2}*300*20=3000\text{ }m=3\text{ }km[/tex]And the distance traveled from 20 min to 36 min is the area of a trapezoid with a height = 16 min. and the parallel base are 150 and 300
So, the area will be =
[tex]\frac{1}{2}(300+150)*16=3600\text{ }m=3.6\text{ }km[/tex]So, the distance traveled after 36 minutes = 3 + 3.6 = 6.6 km
And the distance traveled from 36 min to 40 min is the area of a trapezoid with a height = 4 min. and the parallel bases are 150 and 400
So, the area =
[tex]\frac{1}{2}(150+400)*4=1100\text{ }m=1.1\text{ }km[/tex]So, the total distance after 40 minutes = 6.6 + 1.1 = 7.7 km.
=========================================================
To find the piecewise linear function for the distance of D(t) in terms of time (T) in minutes.
First, we will write the function v(t) that represents the rate from the graph.
[tex]v(t)=\begin{cases}{15t\rightarrow0\leq t\leq20} \\ -9.375t+487.5\rightarrow20\leq t\leq36 \\ {62.5t-2100\rightarrow t\ge36}\end{cases}[/tex]To find the function of the distance integrate each function with respect to the time t:
[tex]D(t)=\begin{cases}{7.5t^2}\rightarrow0\leq t\leq20 \\ {-4.6875t^2+487.5t-4875\rightarrow20\leq t\leq36} \\ {31.25t^2-2100t+41700\rightarrow t\ge36}\end{cases}[/tex]A Distance Run (km) B Distance Run (km) 0 1 1 1 | 2 | 4 | 7 7 088 9 1 1|224 5 5 8 1 2 3 2 3 3 6 8 9 2 3 5 5 6 7 8 9 2 1 1 3 6 | 7 3 03 4 4 15 310 What is the DIFFERENCE in the ranges of the 2 sets of data?Type your answer without a label.
The range of a data set is said to be the difference between the highest value and the lowest value in the given set of data.
To find the difference in the ranges of the 2 sets of data, find the range of data set A, find the range of data set B, then subtract the range of A from B.
Thus, we have:
For data A:
Minimun data value = 08
Maximum data value = 35
Range of data set A = 35 - 08 = 27
For data set B:
Minimum data value = 01
Maximum data value = 30
Range of data set B = 30 - 01 = 29
Difference in the ranges = Range of set B - Range of set A = 29 - 27 = 2
Therefore, the difference in the ranges of the sets of data is 2
ANSWER:
2
How do you determine the domain and range of a relation• when the relation is presented as a set of ordered pairs?• when the relation is presented in a mapping diagram?• when the relation is presented as a graph?B./UType your response here.
First item:
When a relation is presented as a set of ordered pairs (a,b) its domain is given by all the different values that appear in the first coordinate of the pairs. Analogously its range is given by all the different values that appear in the second coordinate. For example, if we have the following relation:
[tex]\mleft\lbrace(1,2\mright),(2,3),(2,4)\}[/tex]There are only two different values in the first coordinate of the pairs: 1 and 2. Then its domain is {1,2}.
There are three different values in the second coordinate of the pairs: 2, 3 and 4. Then its range is {2,3,4}.
Second item:
When the relation is presented in a mapping diagram we have something like this:
Each ellipse represents a set. The set from which the arrows come from is the domain and that at which the arrows arrive is the range. So for the relation shown in the picture its domain is {a,b,c,d} and its range is {x,y,z}
Third item:
When the relation is presented as a graph in a grid the domain will be given for all the values in the horizontal axis for which there's a corresponding value in the graph. If you draw a vertical line that passes through a value A in the horizontal axis you can find two cases:
- The line meets the graph at least once. Then A is part of the domain.
- The line never meets the graph. Then A is not part of the domain.
Something very similar happens with the range. The values that are part of the range are values in the vertical axis for which there's at least one corresponding value in the graph. If you draw a horizontal line that passes through a value B in the vertical axis you have:
- The line meets the graph at least once. Then B is part of the range.
- The line never meets the graph. Then B is not part of the range.
how does h (x) =-0.1x-5 change over the interval from x=2 to x=4
The given expression is,
[tex]h(x)==0.1x-5[/tex]Let us first consider, x = 2. We have,
[tex]h(2)=0.1\times2-5=-4.98[/tex]Now, let us take x = 4, we have,
[tex]h(4)=0.1\times4-5=-4.6[/tex]So the range is, -4.98 to -4.6. So, h (x) decreases by 0.3
Write the 12.4% as simplified fractions. ANS. ___________ .
The Solution
The given percentage is
[tex]12.4\text{ \% =}\frac{12.4}{100}=\frac{\frac{124}{10}}{100}[/tex][tex]12.4\text{ \% =}\frac{124}{10}\times\frac{1}{100}=\frac{124}{1000}=\frac{31}{250}[/tex]Hence, the correct answer is 31/250
Solve the equation 2(8+4c)=32
c = 2
Explanation:
2(8+4c)=32
we open the bracket:
2×8 + 2×4c = 32
16 + 8c = 32
collect like terms:
8c = 32 - 16
8c = 16
Divide through by 8:
8c/8 = 16/8
c = 2
The length of a rectangle is 2ft more than twice the width. The area is 144 ft squared. Find the length and width of the rectangle.
The formula for the area of a rectangle (A) is given as
[tex]A=\text{length}\times breadth[/tex]Given that
The length of a rectangle is 2ft more than twice the width,
Therefore,
length = 2 + 2width
where,
[tex]\begin{gathered} w=\text{width} \\ l=2+2w \\ A=144ft^2 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} 144=(2+2w)\times w \\ 144=2w+2w^2 \\ 144=2(w+w^2) \\ \frac{144}{2}=\frac{2(w+w^2)}{2} \\ 72=w+w^2 \\ w^2+w-72=0 \end{gathered}[/tex]Factorizing the equation above
[tex]\begin{gathered} w^2+9w-8w-72=0 \\ w(w+9)-8(w+9)=0 \\ (w-8)(w+9)=0 \\ w-8=0\text{ or }w+9=0 \\ w=8\text{ or w=-9} \\ \therefore w=8or-9 \end{gathered}[/tex]Note that the width can never be negative, therefore the width of the rectangle is 8.
Recall that:
[tex]\begin{gathered} l=2_{}+2w=2+2(8)=2+16=18 \\ l=18 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} \text{length = 18ft} \\ \text{width = 8ft} \end{gathered}[/tex]
Let s be an Integer. Alonso claims that -s must always be less than zero. Iliana claims that -s is only sometimes less than zero. Whose statement is correct? Explain, support your reasoning with an example
Answer:
Iliana's claim is correct
Explanation:
If s is an integer.
Integers are positive or negative whole numbers.
• Illiana's claim is correct.
This is as a result of the fact that when s is negative: e,g s=-5
[tex]\begin{gathered} s=-5 \\ -s=-(-5)=5 \\ 5\text{ is greater than 0} \end{gathered}[/tex]However, when s is a positive integer:
[tex]\begin{gathered} s=5 \\ -s=-5 \\ -5\text{ is less than 0} \end{gathered}[/tex]Therefore, for an integer s, -s is only sometimes less than zero.
Illiana's claim is correct.
Find the next number 7.14.28.56, ?*
Answer: 112
Explanation:
The sequence we have is:
[tex]7,14,28,56[/tex]We can see that the numbers are all multiples of 7:
[tex]\begin{gathered} 7\times1=7 \\ 7\times2=14 \\ 7\times4=28 \\ 7\times8=56 \end{gathered}[/tex]In each step, the number we multiply 7 by, doubles.
So the next number must be 7 multiplied by double of 8 which is 16:
[tex]7\times16=112[/tex]Another way to see this sequence is that each number is twice the previous number:
14 is twice 7
28 is twice 14
56 is twice 28
So the next number must be twice 56:
[tex]56\times2=112[/tex]In any case, the next number is 112
I NEED HELPPP Which expression is equivalent to 34.3-97
-62.7
1) Solving that expression we'll find an equivalent number or expression.
34.3 -97=
2) Rewriting 97 as 97.0 to proceed with the subtraction:
Since -97 is the number whose absolute value is greater than 34.3 than the result is : -62.7
You invest $275 to start a sandwich stand and decide to charge $5.15 per sandwich.Set up a Linear Model that determines your profit or loss based on the number of sandwiches.How much money will you make if you sell 75 sandwiches?How many sandwiches must you sell to make a $100 profit?
Let the number of sandwichs sold be "x"
If you charge $5.15 per sandwich then the total sales of the sandwich will be 5.15x
Cost price = $275
The Linear Model that determines your profit or loss based on the number of sandwiches will be expressed as:
[tex]\text{Profit}=\text{Selling price - Cost price}[/tex]Substitute the given parameters;
[tex]\begin{gathered} \text{Profit/Loss}=5.15x\pm275 \\ p(x)=5.15x\pm275 \end{gathered}[/tex]If 75 sandwiches were sold, the amount of money made will be expressed as:
[tex]\begin{gathered} p(75)=5.15(75)-275 \\ p(75)=386.25-275 \\ p(75)=\$111.25 \end{gathered}[/tex]Hence the amount of money made if you sell 75 sandwiches is $111.25
To make $100 profit, the amount of sandwiches must you sell is given as:
[tex]\begin{gathered} 100=5.15x-275 \\ 5.15x=100+275 \\ 5.15x=375 \\ x=\frac{375}{5.15} \\ x\approx72\text{sandwiches} \end{gathered}[/tex]Hence 72 sandwiches must be sold to make a profit of $100
You have two spinners each with three sections of equal size, one labeled with the numbers 1,2,3 and the others 2,4,6. You spin both and observe the numbers. Let X be the sum of the two numbers. In the game you are playing, you win if you get a sum of at least a 600 in 100 spins. If not you lose, should I play?
From the table
[tex]\text{Total possible outcomes = 9}[/tex]we are to find the probability of getting a sum of at least 600 in 100 spins
This means, we need to get a sum of at least 6 in 1 spin
Hence
[tex]\begin{gathered} P(\text{getting a sum of at least }6\text{ in one spin)} \\ =\text{ }\frac{number\text{ of possible outcome}}{total\text{ possible outcome}} \end{gathered}[/tex]From the table
number of the possible outcome of getting a sum of at least 6 = 5
Therefore
[tex]\begin{gathered} P(\text{getting sum of at least 6 in one spin)} \\ =\text{ }\frac{5}{9} \\ \cong\text{ 0.56} \end{gathered}[/tex]Since the probability is more than 0.5 then
I can play the game
4. Principal Sanders wants to know if wearing school uniforms will help students improve theirmath test scores. She decides to conduct an experiment to find out She chooses two groups ofstudents to test One group will wear uniforms, the other will not.Part A. Define the variables and treatment for the experiment. (3 points)I1 What is the control variable? Why?
Note that:
The control variable is the variable that does not change (that is, constant ) in an experiment. It does not take part in the experiment
The response variable is the dependent variable that determines the outcome of the experiment.
The treatment of an experiment is the independent variable, and it determines the outcome of the experiment.
From the illustration given in this exercise, the control variable, the response variable, and the treatments are identified below with reasons.
1) The control variable = The mathematical abilities of the students
Reason: The students chosen for the experiment must have the same mathematical abilities to prevent bias in the results of the experiment.
2) The response variable = Math test scores
Reason: The maths test scores of the two groups of students are the outcomes of the experiment, hence the response variable.
3) The treatment for the experiment = Wearing of school uniforms
Reason: Wearing of school uniforms is the treatment that the two groups of students were subjected to in order to confirm if their will be any effects on their Maths test scores.
it says, "or use prime factorization" #1-3, and 5 pls!!
The LCM (lowest common multiple) of the following;
(1) 5 and 7
5 = 1 x 5
7 = 1 x 7
LCM = 1 x 5 x 7
LCM = 35
(2) 4, 5 and 10
4 = 2 x 2
5 = 1 x 5
10 = 2 x 5
LCM = 2 x 2 x 5
LCM = 20
(3) 6, 9 and 12
6 = 2 x 3
9 = 3 x 3
12 = 2 x 2 x 3
LCM = 2 x 2 x 3 x 3
LCM = 36
Find the LCD (lowest common denominator) of the fractions,
[tex]\begin{gathered} \frac{3}{8},\frac{3}{5} \\ We\text{ take the LCM of the denominators, that is 8 and 5} \\ \text{The LCM is,} \\ 5=1\times5 \\ 8=2\times2\times2 \\ \text{LCM}=2\times2\times2\times5 \\ \text{LCM}=40 \\ \text{The fractions can now be re-written as } \\ \frac{15}{40}\text{ and }\frac{24}{40} \end{gathered}[/tex]Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin.Horizontal axis and passes through the point (9, −4)
Answer:
[tex]x=\frac{9}{16}y^2[/tex]Step-by-step explanation:
Since the vertex of the parabola at the origin (h,k) is (0,0). The standard form of the parabola is represented as:
[tex]\begin{gathered} x=a(y-k)^2+h \\ \end{gathered}[/tex]If the parabola passes through the point (9,-4), we can substitute for (x,y) and (h,k) and solve for ''a.'' and determine the equation:
[tex]\begin{gathered} 9=a(-4-0)^2+0 \\ 9=a(16)+0 \\ a=\frac{9}{16} \\ \end{gathered}[/tex]Then, the equation of the parabola in standard form would be:
[tex]x=\frac{9}{16}y^2[/tex]use the spinner shown find the probability the pointer lands on purple. A. 1/3 B. 3/8C. 30/180D. 1/6
The answer is B. 3/8
In right triangle ABC, angle c is a right angle and sin A= sin B. What is m
which
In plane trigonometry, the sine theorem or also known as the law of sines is a ratio between the lengths of the sides of a triangle and the sines of their corresponding opposite angles.
it is
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}[/tex]According to the question Sin A=Sin B, so
[tex]a=b[/tex]wich means that this right traingle has two equal sides
if the two sides of a right triangle have the same length, then, they form the same angle with the hypotenuse
also, the question says that C=90 °
we know the sum of the internal angles on a triangle must be 180 °,then
[tex]\begin{gathered} A+B+C=180 \\ A=B \\ 2A+C=180 \\ A=\frac{180-C}{2} \\ A=\frac{90}{2} \\ A=45\text{ \degree} \\ B=45\text{\degree} \end{gathered}[/tex]so the answer is B)45 °
Each vertex of a quadrilateral is dilated by a factor of 1/2 about the point P (-3,7). What will be the effect on the perimeter of the resulting figure.
Note that the perimeter of any quadrilateral is the sum of its sides.
[tex]P=\sum ^n_{i\mathop=1}a_i[/tex]So it is always proportional to the length of any side,
[tex]P\propto a_i[/tex]Note that the dilation either stretches of compresses the sides.
For the factor 1/2, each side of the quadrilateral will get multiplied by 1/2, which simply means that the sides will get halved.
So the new perimeter is given by,
[tex]P^{\prime}=\sum ^n_{i=1}(\frac{1}{2}a_i)=\frac{1}{2}\sum ^n_{i=1}(a_i)=\frac{1}{2}P[/tex]Thus, the perimeter will also get halved due to the dilation.
Therefore, option A is the correct choice.
A road crew Musri pave a road that is 7/8 miles long they can repave 1/56 miles each hour how long will it take the crew to repave the road
Given data :
[tex]1\text{ hour = }\frac{1}{56}miles[/tex]distance required to cover =
[tex]\frac{7}{8}[/tex]thus, the time taken is,
[tex]\begin{gathered} =\frac{\frac{7}{8}}{\frac{1}{56}} \\ =\frac{7}{8}\times56 \\ =\frac{7}{1}\times7 \\ =7\times7 \\ =49 \end{gathered}[/tex]thus the time taken is 49 hours.
How do you turn 2x+3y=12 into slope intercept form?
Answer:
y = -2x/3 + 4
Explanation:
The equation of a line in slope-intercept form is expressed as y = mx+c
Given the equation 2x+3y=12, you will have to make y the subject of the formula as shown:
Given
2x+3y=12
3y = 12 - 2x
3y = -2x + 12
Divide through by 3
3y/3 = -2x/3 + 12/3
y = -2x/3 + 4
Hence the expression in slope intercept form is y = -2x/3 + 4
Help me please so i can see if i’m on the rights track. if csc (θ) = 13/12 and 0° < θ < 90°, what is cos (θ)? write the answer in simplified, rationalized form.
Given in the question is:
[tex]\csc (\theta)=\frac{13}{12}[/tex]Recall the trigonometric identity:
[tex]\csc (\theta)=\frac{1}{\sin (\theta)}[/tex]Therefore, we have that
[tex]\sin (\theta)=\frac{12}{13}[/tex]Recall the trigonometric ratio:
[tex]\begin{gathered} \sin (\theta)=\frac{\text{opp}}{\text{hyp}} \\ \cos (\theta)=\frac{\text{adj}}{\text{hyp}} \end{gathered}[/tex]and, using the Pythagorean Theorem:
[tex]hyp^2=opp^2+adj^2[/tex]From the sin value, we have:
[tex]\begin{gathered} opp=12 \\ hyp=13 \\ \therefore \\ 13^2=12^2+adj^2 \\ 169=144+adj^2 \\ adj^2=169-144=25 \\ adj=\sqrt[]{25} \\ adj=5 \end{gathered}[/tex]Therefore, the value of cos(θ) is:
[tex]\sin (\theta)=\frac{5}{13}[/tex]