The equation of a line between two points is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]plugging the values given we have:
[tex]\begin{gathered} y-(-17)=\frac{-19-(-17)}{6-2}(x-2) \\ y+17=\frac{-19+17}{6-2}(x-2) \\ y+17=-\frac{2}{4}(x-2) \\ y+17=-\frac{1}{2}(x-2) \\ y+17=-\frac{1}{2}x+1 \\ y=-\frac{1}{2}x+1-17 \\ y=-\frac{1}{2}x-16 \end{gathered}[/tex]Therefore the equation of the line is:
[tex]y=-\frac{1}{2}x-16[/tex]Victoria and Rachael both leave the restaurant at the same time, but in opposite directions. If Rachael travels 9 mph faster than Victoria and after 9 hours they are 189 miles apart, how fast is each traveling?
The both left in opposite direction.
Therefotre we say, let Victoria's speed be represented by a mph
Then Racheal who travel in opposite direction with 9 hours faster is - ( a + 9 ) mph = ( - a - 9 ) mph
( please note that the above is negative because the directions are opposite and the 9 is included because it is 9 mph faster )
Next, we were told that the distance between them is 189 miles. We therefore need to subtract the distance covered by both of them and make it equal to 189 miles.
Since, distance = speed x time. And the time is 9 hours
The distance covered by Victoria therefore is ( a x 9 ) mph = 9a miles
The distance covered by Rachael therefore is 9 ( - a - 9 ) = - 9a - 81 miles
The distance between them therefore is ( -9a - 81 ) - 9a = 189
-9a - 9a - 81 = 189
-18a - 81 = 189
-18a = 189 + 81
-18a = 270
a = 270 / -18a ( divided both sides by 18a )
a = - 15
Therefore it is clear that victoria traveled with a speed of -15 mph
and Rachael who is - a - 9 = - ( -15 ) - 9 = 15 - 9 = 6 mph
Finally, we say Victoria travels at 15 mph and travels at 6 mph in the opposite direction.
29 23/200 as a decimal
To transform 29 23/200 as a decimal, you have to divide 23 by 200
Then, 23/200 = 0.115 and 29 23/200 = 29.115
True or False.To graph the line y = -4/5 x + 6, you would plot the y-intercept of 6 on they-axis and then move 4 units down and 5 units right from the y-interceptto plot the second point.
Given the instructions on the problem, we have the following:
which is the graph of the equation y = -4/5 x+ 6. Also, we have that the second point is (5,2)
In 1990, approximately 1,820,000 violent crimes were reported in the U.S. By 2019, this number had fallen to approximately 1,200,000.(a) Write a linear model to describe the number of violent crimes in the U.S. from 1990 onward.Pt =(b) Using this linear model, predict the number of violent crimes in 2032. Round your answer to the nearest whole number.violent crimes(c) When do you expect the number of violent crimes to reach 800,000? Give your answer as a calendar year (ex: 2020).During the year
Data:
• A,( 0, 1,820,000)
,• B,( 29, 1,200,000)
,• Year 2 - year 1 = 2019 - 1990 = 29
a)
Based on the point A and B, the linear model is as follows:
• Slope ( ,m ,)
[tex]m=\frac{1,200,000-1,820,000}{29\text{ -}0}=-\frac{620,000}{29}[/tex]• Parameter b
[tex]\begin{gathered} P(t)=mt+b \\ 1,200,000=-\frac{620,000}{29}\cdot29+b \\ 1,200,000=-620,000+b \\ b=1,200,000+620,000=1,820,000 \end{gathered}[/tex]Answer a) (linear model):
[tex]P(t)=-\frac{620,000}{29}t+1,820,000[/tex]b)
2032-1990 = 42
[tex]\begin{gathered} P(42)=-\frac{620,000}{29}\cdot42+1,820,000 \\ P(42)=922068.97 \end{gathered}[/tex]Answer of the number of violent crimes in 2032:
[tex]P(42)=922068.97[/tex]c)
[tex]\begin{gathered} 800,000=-\frac{620,000}{29}\cdot t+1,820,000 \\ 800,000-1,820,000=-\frac{620,000}{29}\cdot t \\ -1,020,000=-\frac{620,000}{29}\cdot t \\ t=\frac{-1,020,000}{-\frac{620,000}{29}}=47.71 \\ 1990+47.71=2037.71 \end{gathered}[/tex]Answer of c: 2037
What us the solution for (3×5)+(6×5)=(16×5)-(-×5)
We have the above equation and we must solve, the only unknown is "x", we must solve the mathematical operations and then clear "x"
[tex]\begin{gathered} 15+30=80-5x \\ 5x=80-45 \\ x=\frac{35}{5} \\ x=7 \end{gathered}[/tex]The answer is x=7
Eliminate the x in the following system of equations. What is the result when you add the two equations?Şx+y=2(3x – 4y = 270 -7y = 210 -7y = -257y = 25O 7y = -21
Given the system of equations:
x + y = 2
3x - 4y = 27
Let's eliminate x in the system and find the result when the two equations are added.
To eliminate the x variable, let's multiply each equation by the value that makes the coefficients of x opposite.
Let's multiply equation 1 by -3:
(-3x) + (-3y) = -3(2)
3x - 4y = 27
---------------------------------------
-3x - 3y = -6
3x - 4y = 27
Add both equations:
-3x - 3y = -6
+ 3x - 4y = 27
________________
- 7y = 21
Therefore, after eliminating the x variable, the result is:
-7
2Select the correct answer from each drop-down menu.The equation of a line is fx +žy=it.The x-intercept of the line isand its y-intercept is
SOLUTION
The equation of the line is given as
[tex]\begin{gathered} \frac{3}{5}x\text{ + }\frac{1}{3}y\text{ = }\frac{1}{15} \\ To\text{ find the x intercept, we put y = 0 } \end{gathered}[/tex][tex]\begin{gathered} \frac{3}{5}x\text{ + }\frac{1}{3}(0)\text{ = }\frac{1}{15} \\ \\ \frac{3x}{5}\text{ + 0 = }\frac{1}{15} \\ \\ \frac{3x}{5}\text{ = }\frac{1}{15} \\ 3x\text{ }\times15\text{ = 5 x 1} \\ \\ \frac{3x\text{ }\times15}{3\times15}\text{ = }\frac{5}{3\text{ }\times15} \\ \\ x\text{ = }\frac{1}{9} \\ \text{x intercept of the line is ( }\frac{1}{9},\text{ 0)} \end{gathered}[/tex]To find the y intercept, we put x = 0
[tex]\begin{gathered} \text{From }\frac{3}{5}x\text{ + }\frac{1}{3}y\text{ = }\frac{1}{15} \\ \\ \frac{3}{5}(0)\text{ + }\frac{1}{3}y\text{ = }\frac{1}{15} \\ \\ 0\text{ + }\frac{y}{3}\text{ = }\frac{1}{15} \\ \\ \frac{y}{3}\text{ = }\frac{1}{15} \\ 15y\text{ = 3} \\ \\ y=\text{ }\frac{3}{15}\text{ = }\frac{1}{5} \\ \\ y\text{ intercept of the line is (0, }\frac{1}{5}) \end{gathered}[/tex]What is the minimum additional information needed to prove that the triangle pair shown is congruent using the ASA Theorem?
Sertengie, thiis is the solution:
Let's recall that ASA Theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
As you can see, we have a right angle in both triangles and Sides PQ and MN are congruent, therefore, we need to know the measures of a pair of angles, either:
• Angles Q and N
,• Angles O and L
That is the minimum additional information needed to prove that the triangle pair shown is congruent using the ASA Theorem
May I please get help with this for I am confused and have tried many times to figure out how to rotate the figure 90° clockwise to find the original point on the final part
A rotaion of a point 90° clockwise is given by:
[tex](x,y)\rightarrow(y,-x)[/tex]The coordinates of the original point are (1,-3), applying the rule to this point we have:
[tex](1,-3)\rightarrow(-3,-1)[/tex]Therefore:
Point in the original figrue (1,-3)
Point in the final figure (-3,-1)
using the matrix solver on your calculator, find the solution to the system of equations shown below.5x+5y=202x+2y=8
Given: The system of equations is shown below.
[tex]\begin{gathered} 5x+5y=20 \\ 2x+2y=8 \end{gathered}[/tex]Required: To find the solution of given equations.
Explanation: The given equations represent co-incident lines. Co-incident lines have infinitely many solutions. This can be checked as follows:
[tex]\frac{a1}{a2}=\frac{b1}{b2}=\frac{c1}{c2}=\frac{5}{2}[/tex]Final answer: The correct option is c. more than one solution.
Create a third equation that could be added to the system so that this solution does not change the graph line on the coordinate plane above (PART C)
Given that the solution of the initial system of equations is (1,4), we need to find a third line such that it goes through (1,4); then,
[tex]\begin{gathered} y=ax+b \\ and \\ (1,4) \\ \Rightarrow4=a+b \end{gathered}[/tex]We can set any value for a; for example, a=1; thus,
[tex]\begin{gathered} a=1 \\ \Rightarrow4=1+b \\ \Rightarrow b=3 \end{gathered}[/tex]Therefore, one possible third line is
[tex]y=x+3[/tex]The green line is the one you need to graph, the others have already been plotted.
Find x. Give your answer inthe simplest form.450 у845X = [?]ХEnter the number that belongs inthe green box
As you can see in the picture, the triangle is a Right triangle, because it has an angle that measures 90 degrees (also known as "Right angle").
Then, you can use the following Trigonometric function:
[tex]\tan \alpha=\frac{opposite}{adjacent}[/tex]In this case:
[tex]undefined[/tex]i need a little help. please use evidence and steps leading to answer. I asks to find the error in one or more of the steps and explain why its wrong
To identify the error in the procedure shown in the picture, it is important to remember the following:
[tex]\begin{gathered} (a+b)^2=a^2+2ab+b^2 \\ (a-b)^2=a^2-2ab+b^2 \end{gathered}[/tex]Keeping this on mind, you can solve the given equation as following:
1. Given:
[tex]\sqrt[]{5x}=x+2[/tex]2. Square both sides of the equation:
[tex]\begin{gathered} (\sqrt[]{5x})^2=(x+2)^2 \\ 5x=x^2+2(x)(2)+2^2 \\ 5x=x^2+4x+4 \end{gathered}[/tex]3. Move the the term on the left side to the right side and add like terms:
[tex]0=x^2-x+4[/tex]4. Apply the Quadratic formula to find "x":
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \\ x=\frac{-(-1)\pm\sqrt[]{(-1)^2-4(1)(4)}}{2(1)} \\ \\ x_1=\frac{1}{2}(i-\sqrt[]{15)} \\ \\ x_2=\frac{1}{2}(i+\sqrt[]{15)}_{} \end{gathered}[/tex]Therefore, you can identify that the error is in Step C, because:
[tex](x+2)^2=x^2+4x+4[/tex]7. The boxplot represents concert tickets sold on random days for a local venue. Identify the firstand third quartiles.245297323369388
The Solution:
Given the boxplot below:
Thus:
The first quartile = 297
The third quartile = 369
Therefore, the correct answer is [option 4]
18 pt to quarts ? qt
This is a conversion problem
we need to convert 18 Pints to Quarts
since 1 pt = 0.5 qt , then:
[tex]18\cdot0.5=9[/tex]In summary
18 pt = 9 qt
$4000 deposit at an apr of 4% with daily compounding for 8 years
EXPLANATION
Let's see the facts:
Investment = Principal = P = 4,000
Interest rate = r = 4% = 0.04 (decimal form)
n= number of times the interest rate is compounding per unit of t = 365
t= time = 8
The compounding interest formula is:
[tex]I\text{ = P(1+}\frac{r}{n})^{nt}[/tex]Replacing terms:
[tex]I=4,000(1+\frac{0.04}{365})^{365\cdot8}[/tex]Adding numbers:
[tex]I=4,000(1.000109589)^{2,920}[/tex]Solving the power:
[tex]I=4,000\cdot1.377[/tex]Multiplying numbers:
[tex]I=5,508[/tex]The answer is $5,508
this isint really a question but i would like to study because i have a test in a few days can someone help me practice please in learing percent increase and decrease.
To calculate the percentage increase, we can follow the general rule:
[tex]\begin{gathered} \text{Increase=New Number - Original Number} \\ \text{then} \\ \text{ \%increase = Increase /(Original number }\cdot\text{ 100)} \end{gathered}[/tex]Notice that if the answer is a negative number, then this is a percentage decrease.
For example, if you work 35 hours one week and another you work 45.5, to find the percentage increase we do the following:
[tex]\begin{gathered} \text{Increase = New Number - Original Number} \\ \Rightarrow Increase=45.5-35=10.5 \end{gathered}[/tex]then:
[tex]\frac{10.5}{35\cdot100}=\frac{1050}{35}=30[/tex]therefore, the percentage increase is 30%
What is the answer ? A. B. C. or D?
By definition, a Right triangle is a triangle that has an angle that measures 90 degrees (which also called "Right angle").
For this case, you can identify that the triangle given in the exercise is a Right triangle.
To find the measure of the missing angle, you need to use Arccosine function, which is the inverse of the cosine function:
[tex]\alpha=\cos ^{-1}(\frac{a}{h})[/tex]Where "α (alpha)" is the angle you must find, "a" is the adjacent side and "h" is the hypotenuse.
You can set up that, for this case:
[tex]\begin{gathered} a=11 \\ h=23 \end{gathered}[/tex]Then, substituting values and evaluating, you get that the measure of the angle is:
[tex]\begin{gathered} \alpha=\cos ^{-1}(\frac{11}{23}) \\ \alpha=61.42\degree \end{gathered}[/tex]Rounding the answer to nearest whole degree, you get:
[tex]\alpha\approx61\degree[/tex]The answer is: Option C.
What are the terms in the expression,3 + 5 + 7b – 18a?
Given: An expression-
[tex]3+5+7b-18a[/tex]Required: To determine the terms in the expression.
Explanation: The terms in an expression are the variables, constants, or combination of variables and constants separated by a + or - operator.
Hence, the terms in the expression are-
[tex]3,5,7b,-18a[/tex]Final Answer: The terms are: 3, 5, 7b, and -18a.
There are 36 students in a class and 2/3 of them are female. how many students are female and male
Answer:
23 = Female
12 = Male
Step-by-step explanation:
To find what 1/3 of 36 is we can divide by 3...
36 / 3 = 12
So...
If females are 2/3...
12 x 2 = 24
If males are 1/3...
12 x 1 = 12
Hope this helps! :)
Find the measure of the arc or angle indicated. Assume that lines which appeartangent are tangent.130°TKM45°L
Question 1 of 102 PointsThe slope of the line below is – 3. Use the coordinates of the labeled point tofind a point-slope equation of the line.(5.-7)
The slope of a line m can be found by using
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]You can use any two points on the graph
Let us use points (0, -1), (4, 2)
[tex]\begin{gathered} x_1=0 \\ x_2=4 \\ y_1=-1 \\ y_2=2 \end{gathered}[/tex]Substitute them in the rule
[tex]\begin{gathered} m=\frac{2-(-1)}{4-0} \\ m=\frac{2+1}{4} \\ m=\frac{3}{4} \end{gathered}[/tex]The slope is 3/4
Answer A
How to write a two column proof for number 38
1.- We are given that:
[tex]\angle B\cong\angle ACB[/tex]therefore:
[tex]AB\cong AC.[/tex]2.- Recall that a condition that must be satisfied for three lengths to be the sides of a triangle is that the sum of any pair of lengths is greater than the other length, therefore:
[tex]AD+AC>CD.[/tex]3.- Substituting AC for AB, using the congruence statement in point number 2, we get:
[tex]AD+AB>CD.[/tex]In a recent poll 590 people were asked if they liked dogs, and 66% said they did. Find the margin of error of this poll at the 90% confidence level. Give your answer to three decimals
SOLUTION
We will use the formula
[tex]\begin{gathered} p\pm_Z\sqrt{\frac{p(1-p)}{n}} \\ where\text{ p = 66\% = 0.66} \\ n=590 \\ Z_{90\%}=1.645 \end{gathered}[/tex]Plugging in we have
[tex]\begin{gathered} 0.66\pm_1.645\sqrt{\frac{0.66(1-0.66)}{590}} \\ 0.66\pm\sqrt{\frac{0.66\times0.34}{590}} \\ 0.66\pm0.0195022 \\ 0.67950,0.6404978 \end{gathered}[/tex]Hence the answer is
(0.640, 0.680)
after eating dinner at a restaurant marcuse Bill's before the tax is 54.00 the sales taxs rate is 8% Marcuse decided to leave 25% tip for the waiter on the pre tax amount how much money will maurice pay total including tax and tip
Bill before tax = 54.00
tax amount = 8% of 54 = 8/100 x 54 = 0.08 x 54 = 4.32
tip given to waiter 25% of 54 = 0.25 x 54 = 13.5
Total money Maurice pay including tax and tip = 54.00 + 4.32 + 13.5 = 71.82
Using a table of values, determine the solution to the equation below to the nearest fourth of a unit.2x - 4 = 3-x + 1A. x=2.5B. x=1C. x=2D. x= 3.25
The equation is:
[tex]2x-4=3^{-x}+1[/tex]Now we can evaluate the posible values of x so:
for x=2.5
[tex]2(2.5)-4=3^{-2.5}+1[/tex]so now we operate:
[tex]\begin{gathered} 5-4=0.06+1 \\ 1=0.06+1 \\ 0\approx0.06 \end{gathered}[/tex]For x=1
[tex]2(1)-4=3^{-1}+1[/tex]Now we operate:
[tex]\begin{gathered} 2-4=0.33+1 \\ -2\ne1.33 \end{gathered}[/tex]for x=2
[tex]\begin{gathered} 2(2)-4=3^{-2}+1 \\ 4-4=0.11+1 \\ 0\ne1.11 \end{gathered}[/tex]and for x=3.25
[tex]\begin{gathered} 2(3.25)-4=3^{-3.25}+1 \\ 6.5-4=0.02+1 \\ 2.5\ne1.02 \end{gathered}[/tex]So the clousest one is the option A
i need help on this assignment an i was wondering if you can help me - number 2
Explanation:
Collinear points are the points that lie on the same straight line or in a single line. If two or more than two points lie on a line close to or far from each other, then they are said to be collinear, in Euclidean geometry.
From the question, we can see that X, W, and Z do not lie on the same line. Therefore
Answer: False
The time it takes duck eggs to hatch in a nursery is normally distributed with a meanof 42 days and a standard deviation of 3.8 days. What is the probability that arandomly selected duck egg takes between 34 and 43 days to hatch?
The time it takes duck eggs to hatch in a nursery is normally distributed with a mean
of 42 days and a standard deviation of 3.8 days. What is the probability that a
randomly selected duck egg takes between 34 and 43 days to hatch?
step 1
Find the z-scores
For x=34
z=(34-42)/3.8
z=--2.105
For x=43
z=(43-42)/3.8
z=0.263
step 2
using Standard Normal Distribution Table
we have
For z=-2.105 --------> P=0.4842
For z=0.263 -------> P=0.1026
therefore
the probability is
P=0.4842+0.1026=0.5868If Priya followed these instructions, what information is guaranteed to betrue about her construction? (Hint: you may want to follow themyourself.)
The quadilateral can be formed as,
As both the circle have same radius AB, hence the radius of the circle with center A have,
AC=AB=AD.....(1)
Also for circle with center B,
BD=BA=BC....(2)
From (1) and (2),
AB=BC=CD=DA.
Thus,all four sides of the quadilateral are equal.
But triangle ABC is an eqilateral triangle from equation (1) and (2), hence angle C will be 60 degrees.
A quadilateral with all four sides equal and one angle equals to 60 degrees must be rhombus.
Thus, option (a) is correct.
For #1 - 4, use the given diagrams and what you have learned about similar polygons. Hint: use the radius of the circles.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
diagram
Step 02:
scale factor:
We must analyze the polygons to find the solution.
1. Circle A ===> Circle B
Circle A:
ra = 5
Circle B:
rb = 3
scale factor (k):
ra * k = rb
5 * k = 3
k = 3 / 5
k = 0.6
The answer is:
scale factor of dilation = 0.6