The equation of line passing through two points (x_1,y_1) and (x_2,y_2) is,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Substitute the points in the equation to obtain the equation of line.
[tex]\begin{gathered} y-3=\frac{-7-3}{3-(-3)}(x-(-3)) \\ y-3=\frac{-10}{6}(x+6) \\ 3(y-3)=-5(x+6) \\ 3y-9+5x+30=0 \\ 3y+5x+21=0 \end{gathered}[/tex]So equation of line is 3y+5x+21=0.
0=9 means no solution one solution or infinite solution?
Answer:
no solution
Step-by-step explanation:
If you end up with a false equality, then the initial statement is false, meaning that there are no solutions.
I really need help with number 9 find the value of x that makes abcd a parallelogram.
Given:
The adjacent angles of a parallelogram are 78 and x+10.
To find:
The value of x.
Explanation:
We know that,
The sum of the adjacent angles in a parallelogram is supplementary.
So, we can write,
[tex]\begin{gathered} 78+x+10=180 \\ x+88=180 \\ x=180-88 \\ x=92 \end{gathered}[/tex]Thus, the value of x is 92.
Final answer:
The value of x is 92.
Solve the equation3 x² - 12x +1 =0 by completing the
square.
By completing squares, we wll get that the solutions of the quadratic equation are:
x = 6 ± √35
How to complete squares?Here we have the quadratic equation:
x² - 12x + 1 = 0
We can rewrite this as:
x² - 2*6x + 1 = 0
So we can add and subtract 6² to get:
x² - 2*6x + 1 + 6² - 6² = 0
Now we rearrange the terms:
(x² - 2*6x + 6²) + 1 - 6² = 0
Now we can complete squares.
(x - 6)² + 1 - 36 = 0
(x - 6)² = 35
Now we solve for x:
x = 6 ± √35
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For the function f(x) = x² + 2x - 24 solve the following.
f(x) = 0
For the function, f(x) =0, we have x = -6 and x =4
The given function is f(x) = x² + 2x - 24
For f(x) = 0
f(x) = x² + 2x - 24 =0
x² + 2x - 24 =0
Middle Term Splitting is a method to solve quadratic equations of the form ax² + bx +c, In middle-term splitting, we split the middle term into the factors of the constant terms, then we take common multiples from the terms and then convert the equation into factors, we equate each factor to zero and we get the desired results.
By splitting the middle term, we have:
x² + 6x -4x - 24 =0
x( x + 6) -4(x+6) =0
( x + 6 ) ( x - 4 ) = 0
( x + 6 ) = 0 and ( x - 4 ) = 0
x = -6 and x = 4
Hence, for f(x) =0, we have x = -6 and x =4
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Find the length and width of a rectangle with the following information belowArea = 2x^2 + 3x Perimeter = 6x + 6
Length: L
Width: W
The area of a rectangle is:
[tex]A=L\cdot W[/tex]The perimeter of a rectangle is:
[tex]P=2W+2L[/tex]Given information:
[tex]\begin{gathered} A=2x^2+3x \\ \\ P=6x+6 \end{gathered}[/tex][tex]\begin{gathered} L\cdot W=2x^2+3x \\ 2W+2L=6x+6 \end{gathered}[/tex]Solve L in the second equation (Perimeter):
[tex]undefined[/tex]Can I have help with this problem? I don't really understand how to graph this
Step 1:
The graph of y = -2 is a horizontal line passing through -2.
Step 2
Frank will choose 7 colors to use for an art project. If there are 10 colors to choose from, how many different color combinations are possible?
120
Explanation:
total colours = 10
number of colours to be chosen = 7
We apply combination
The different color combinations possible:
[tex]^{10}C_7=\frac{10!}{(10-7)!7!}[/tex][tex]\begin{gathered} =\frac{10!}{3!7!}=\frac{10\times9\times8\times7!}{3\times2\times1\times7!} \\ =\frac{720}{6} \\ \text{= 120} \end{gathered}[/tex]The different color combinations possible is 120
we need to seat 200 people. A table holds 8 people How Many tables do we need ?
Kyah, this is the solution to the exercise:
People = 200
Capacity of each table = 8 people
In consequence, we need:
Number of tables = People/Capacity of each table
Replacing by the values we know:
Number of tables = 200/8
Number of tables = 25
Find the equation of the axis of symmetry of the following parabola using graphingtechnology.y = x^2 – 8x + 32
Explanation:
If we graph this parabola we can see the vertex at point (4, 16)
The axis of simmetry is a vertical line that passes through the vertex of the parabola.
Any vertical line's equation is:
[tex]x=a[/tex]'a' is any value of x.
Answer:
The equation of the axis of simmetry is x = 4
The Wong family and the Nguyen family each used their sprinklers last summer. The water output rate for the Wong familys sprinkler was 35 L per hour. The water output for the Nguyen familys sprinkler was 20 L per hour. The families used their spirit for a combined total of 75 hours, resulting in a total water output of 2100 L. How long was each sprinkler used?
Let W be the time of the wong family and N the time of the Nguyen family. We are told that the output rate of the Wong family is 35 L/h and the output for the Nguyen family is 20 L/h, if the total water output is 2100 L, then we can write this mathematically as:
[tex]35W+20N=2100,(1)[/tex]Where "35W" is the total water output of the wong family and "20N" is the total water output of the Nguyen family. The two outputs combined must be 2100. We are also told that the total time is 75 hours, therefore we have:
[tex]W+N=75,(2)[/tex]We get a system of two equations and two variables. We can solve for "W" in equation (2), by subtracting "N" from both sides:
[tex]W=75-N[/tex]Now we can replace this value in equation (1):
[tex]35(75-N)+20N=2100[/tex]Now we apply the distributive property:
[tex]2625-35N+20N=2100[/tex]Now we add like terms;
[tex]2625-15N=2100[/tex]Now we subtract 2625 from both sides:
[tex]\begin{gathered} -15N=2100-2625 \\ -15N=-525 \end{gathered}[/tex]Now we divide both sides by 15:
[tex]N=-\frac{525}{-15}=35[/tex]Now we replace this value in equation (2) where we already solved for W:
[tex]\begin{gathered} W=75-35 \\ W=40 \end{gathered}[/tex]Therefore, the time for the Wong family is 40 hours and the Nguyen family is 35 hours.
14 POINTS!!!!! BRAINLY!!!!A lamp produced a shadow of a man standing in the middle of a stage.How long is the shadow.A 9.60B 11.38C 20.98D 22.51
Given the graph:
The length of the shadow = y - x.
• To find x:
[tex]\begin{gathered} tan21\text{\degree}=\frac{opposite}{adjacent} \\ \\ tan21\text{\degree}=\frac{x}{25} \\ \\ x=25\times tan21\text{\degree = 9.6m} \end{gathered}[/tex]• To find y:
[tex]\begin{gathered} tan40\text{\degree}=\frac{y}{25} \\ \\ y=25\times tan40\text{\degree}=21m \end{gathered}[/tex]Length of the shadow:
[tex]\begin{gathered} length=21-9.6 \\ \text{ }=\text{ 11.4 m} \end{gathered}[/tex]ANSWER
Length of the shadow = 11.4 m
Can you help me with this problem? I will send a screenshot of the problem and the answer choices.
Given:
Distance of her beagle = 25/4 meters to the right
Distance of her labrador = 51/20 meters directly to her left.
Let's determine the expression which represents how far apart the two dogs are.
We have the following:
Since the beagle is to the right, the distance is = 25/4 meters
Since the labrador is to the left, the distance is = -51/20 meters.
Now, to find how far apart the two dogs are, let's use the absolute value expression:
[tex]\lvert\frac{25}{4}-(-\frac{51}{20})|[/tex]Therefore, the expression which represents how far the two dogs are is:
[tex]\lvert\frac{25}{4}-(-\frac{51}{20})\rvert[/tex]ANSWER:
[tex]\lvert\frac{25}{4}-(-\frac{51}{20})\rvert[/tex]A biologist just discovered a new strain of bacteria that helps defend the human body against the flu virus. To know the dosage that should be given to someone, the doctor must first know if the bacteria can multiply fast enough to combat the virus. To find the rate at which the bacteria multiplies, she puts 10 cells in a petri dish. In an hour, she comes back to find that there are now 12 cells in the dish.
Part 3
An exponential growth function has the general form:
[tex]f(t)=a\cdot(1+r)^t[/tex]where r is the rate of growth, t is the time, and a is a constant. Notice that if calculate f(t) for t = 0, we have (1 + r)º = 1 (any number with exponent 0 equals 1). So, we obtain:
[tex]f(0)=a(1+r)^0=a\cdot1=a[/tex]Thus, the constant a is the initial value of the function.
Now, the rate at which a bacteria grows is exponential. So, the function C(h) is given by:
[tex]C(h)=C(0)\cdot(1+r)^h[/tex]Notice that we represented the time by the letter h instead of t.
Since C(0) = 10 and C(1) = 12, we can replace h by 1 to find:
[tex]\begin{gathered} C(1)=10\cdot(1+r)^1 \\ \\ 12=10+10r \\ \\ 12-10=10r \\ \\ 10r=2 \\ \\ r=0.2 \end{gathered}[/tex]Thus, the number of cells C(h) is given by:
[tex]C(h)=10\cdot(1.2)^h[/tex]Notice that this is valid for C(15) = 154:
[tex]C(15)=10\cdot(1.2)^{15}\cong154.07\cong154_{}[/tex]Part 1
Then, using this formula, we find:
[tex]\begin{gathered} C(2)=10(1.2)^2\cong14 \\ \\ C(3)=10(1.2)^3\cong17.3\cong17 \\ \\ C(4)=10(1.2)^4\cong20.7\cong21 \\ \\ C(5)=10(1.2)^5\cong24.9\cong25 \\ \\ C(6)=10(1.2)^6\cong29.9\cong30 \\ \\ C(7)=10(1.2)^7\cong35.8\cong36 \\ \\ C(8)=10(1.2)^8\cong43 \\ \\ C(9)=10(1.2)^9\cong51.6\cong52 \\ \\ C(10)=10(1.2)^{10}\cong61.9\cong62 \\ \\ C(11)=10(1.2)^{11}\cong74.3\cong74 \\ \\ C(12)=10(1.2)^{12}\cong89.2\cong89 \\ \\ C(13)=10(1.2)^{13}\cong107 \\ \\ C(14)=10(1.2)^{14}\cong128.4\cong128 \end{gathered}[/tex]Part 2
Now, plotting the points, rounded to the nearest whole cell, on the graph, we obtain:
Part 4
Using a calculator, we obtain the following graph of the function C(h):
Comparing the graph to the plot of the data, we see that they match.
Part 5
After a full day, it has passed 24 hours. So, we need to use h = 24 in the function C(h):
[tex]C(24)=10(1.2)^{24}\cong795[/tex]Therefore, the answer is 795 cells.
which point lies on the line with the slope of m=7 that passes through the point (2,3)
Answer:
B. Monkey Man
Step-by-step explanation:
M+o+n+k+e+y
give two-sided of a triangle, find a range of a possible side length of the third side 24 and 52
For a triangle to be possible with 3 given lengths, the largest side must be lower than the sum of the two remaining sides.
Let L be the length of the third side. There are two cases:
If L is the largest side, then:
[tex]\begin{gathered} L<24+52 \\ \Rightarrow L<76 \end{gathered}[/tex]If L is not the largest side, then the largest side has a measure of 52 and:
[tex]\begin{gathered} 52<24+L \\ \Rightarrow52-24Since both conditions should meet for a triangle to be formed, then:[tex]28Therefore, the range of possible values for L is:[tex]undefined[/tex]If the image of point J under a 180* rotation about the origin is (7, -3), what are the coordinates of point J?
Answer:
4,3 is the right answer
Step-by-step explanation:
The function table below is intended to represent the relationship y=-2x-5. However, one of the entries for y does not correctly fit the relationship with x.
x = 1 , f(x) = -2•1 - 5 = -7
Then it doesnt corresponds to f(1) = 6
Answer is OPTION E)
the sum of the angle measures of a polygon with n sides is given find n1440
Given in the question:
a.) The sum of all angles of a polygon is 1,440 degrees.
To be able to determine what polygon has a total sum of angles of 1,440 degrees, we will be using the following formula:
[tex]\text{ }\Theta=(n-2)x180^{\circ}[/tex]We get,
[tex]\text{ 1},440^{\circ}=(n-2)x180^{\circ}[/tex][tex]\text{ 1},440^{\circ}=180n-360^{\circ}[/tex][tex]180n=1,440^{\circ}\text{ + 360}^{\circ}[/tex][tex]180n=1,800^{\circ}[/tex][tex]\frac{180n}{180}=\frac{1,800^{\circ}}{180}[/tex][tex]n\text{ = 10}[/tex]Therefore, that polygon is a decagon or a polygon with 10 sides.
the diameter of the bagels 4.2 in what is the biggest circumference in inches
Diammeter = 4.2 inch
Radius = diammeter/2 = 4.2/2 =2.1 inch
[tex]\text{Circumference =2}\times\text{ }\pi\times r[/tex][tex]\begin{gathered} \pi\text{ = 3.14} \\ \text{Circumference = 2 }\times3.14\times2.1\text{ =13.188 inches} \end{gathered}[/tex]give a reason that justifies each statement for questions 4-9.
4.
The angles ∠6 and ∠8 are congruent because they are alternate interior angles.
5.
The angles ∠4 and ∠5 added are equal to 180° because they are supplementary angles.
6.
If ∠1 is equal ∠7, then they are alternate exterior angles, therefore the lines p and q need to be parallel.
7.
The angles ∠1 and ∠2 are congruent because they are vertically opposite angles.
8.
If ∠2 and ∠6 are supplementary, they are consecutive interior angles, therefore the lines p and q need to be parallel.
9.
The angles ∠6 and ∠9 are congruent because they are corresponding angles.
pls help no need for no need for long explanations just a summary
As shown in the figure:
There are two parallel lines of the triangle
Using the ratio and proportional to find the value of x
So,
[tex]\begin{gathered} \frac{x}{6}=\frac{9}{2} \\ \\ x=6\cdot\frac{9}{2}=\frac{54}{2} \\ \\ x=27 \end{gathered}[/tex]So, the answer is: x = 27
which table of ordered pairs represents a line that has a slope that is the same as the slope of the line represented by the equation y=2x + 1?
Answer:
From the above options, the only table that have the same slope as the given line in the equation (m=2) is Table C.
[tex]\begin{gathered} m=\frac{3-\mleft(-7\mright)}{4-(-1)} \\ m=\frac{10}{5} \\ m=2 \end{gathered}[/tex]Explanation:
Given the equation;
[tex]y=2x+1[/tex]The slope of the above line is;
[tex]m=2[/tex]From the given options, let us find the table that has the same slope as the above equation;
A.
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-8-7}{3-(-2)} \\ m=\frac{-15}{5} \\ m=-3 \end{gathered}[/tex]B.
[tex]\begin{gathered} m=\frac{4-2}{2-(-2)} \\ m=\frac{2}{4} \\ m=\frac{1}{2} \end{gathered}[/tex]C.
[tex]\begin{gathered} m=\frac{3-\mleft(-7\mright)}{4-(-1)} \\ m=\frac{10}{5} \\ m=2 \end{gathered}[/tex]D.
[tex]\begin{gathered} m=\frac{-1-2}{4-(-2)} \\ m=\frac{-3}{6} \\ m=-\frac{1}{2} \end{gathered}[/tex]From the above options, the only table that have the same slope as the given line (m=2) is Table C.
[tex]\begin{gathered} m=\frac{3-\mleft(-7\mright)}{4-(-1)} \\ m=\frac{10}{5} \\ m=2 \end{gathered}[/tex]7. Principal = $39,300, Rate = 4.5%, Time = 6 months. What will that total principal + interest payment be rounded to the nearest dollar? o Lidhe total amount of
Given :
Principal = $39,300,
Rate = 4.5% = 0.045
Time = 6 months = 6/12 year = 0.5 year
Assume simple interest
So,
interest = Principal * rate * time = 39,300 * 0.045 * 0.5 = 884.25
So, the total = Principal + interest = 39,300 + 884.25 = 40,184.25
Rounding the answer to the nearest dollar
So, the total = $40,184
involving two rolls of a dieESEAn ordinary (falr) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a dle is rolled twice in successionand that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.Compute the probability of each of the following events.Event A: The sum is greater than 8.Event B: The sum is an odd number.Write your answers as fractions.Ola(a) P(A) = 1х5?(b) P(B) = 0
Answer:
[tex]\begin{gathered} a)\text{ }\frac{5}{18} \\ \\ b)\text{ }\frac{1}{2} \end{gathered}[/tex]Explanation:
Here, we want to compute some probabilities
The first thing to do is to get the count of results in our sample space
In the sample space, the total possible results is 36
Now, let us get the probabilities
a) The event that the sum is greater than 8
We have to count possible results greater than 8 here
3, 6 (3 on the first die, 6 on the second)
6,3 (6 on the first die, 3 on the second)
6,4 (6 on the first die, 4 on the second)
4,6
4,5
5,4
5,5
5,6
6,5
6,6
The number of possible results greater than 8 is 10
Thus, we have the probability as the count of this divided by the total number of possible results
Mathematically, we have that as:
[tex]\frac{10}{36}\text{ = }\frac{5}{18}[/tex]b) The sum is an odd number
For the sum to be an odd number, we know that if we add a table of 6 rows for all the sums, the even sum on each line is 3
The total even sum is 6 * 3 = 18
The probability is thus:
[tex]\frac{18}{36}\text{ = }\frac{1}{2}[/tex]What is the seventy-seven is forty-six more than r
Answer: 77 = 46 + r, r = 31
Step-by-step explanation:
We will write an equation to represent this situation. Then, we will solve for r by isolating the variable.
Seventy-seven is forty-six more than r.
77 is forty-six more than r.
77 = forty-six more than r.
77 = 46 more than r.
77 = 46 + r
77 = 46 + r
(77) - 46 = (46 + r) - 46
31 = r
r = 31
vertical anges are always equal to each other
Given the statement:
Vertical angles are always equal to each other
The answer is: True
Because they are inclosed by the same lines
Find the percent of change from 120 bananas to 40 bananas.
Answer:
67% decrease
Explanation:
From the given problem:
Initial number of bananas = 120
Final number of bananas = 40
[tex]\begin{gathered} \text{Percent Change=}\frac{Final\text{ Value-Initial Value}}{\text{Initial Value}}\times100 \\ =\frac{40-120}{120}\times100 \\ =-\frac{80}{120}\times100 \\ =-0.667\times100 \\ =-66.7\% \\ \approx-67\% \end{gathered}[/tex]Since we have a negative value, we have a 67% decrease.
write an expression for the perimeter of this pentagon. if the perimeter is 157 united find x
The perimeter of the pentagon = the sum of the lengths of the sides
There are two sides of the length (4x-1) and three sides of the length (3x+2)
so,
The perimeter =
[tex]2\cdot(4x-1)+3\cdot(3x+2)[/tex]Given the perimeter = 157
So,
[tex]2\cdot(4x-1)+3\cdot(3x+2)=157[/tex]Solve the equation to find the value of x
[tex]\begin{gathered} 2\cdot(4x-1)+3\cdot(3x+2)=157 \\ 8x-2+9x+6=157 \\ 17x+4=157 \\ 17x=157-4 \\ 17x=153 \\ \\ x=\frac{153}{17}=9 \end{gathered}[/tex]So, the value of x = 9
College students are offered a 6% discount on a textbook that sells for
$32.50. If the sales tax is 6%, find the cost of the textbook including the sales
tax.
32.383 is the cost of the textbook including the sales tax.
How does sales tax work?
Government-imposed consumption taxes on the purchase of goods and services are known as sales taxes. A typical sales tax is imposed at the moment of sale, paid for by the shop, and then given to the government.The original price of the textbook = $32.50
Also, the discount percentage = 6%
Thus, the price of the textbook after discount = 32.50 - 6 % of 32.50
= 32.50 - 6 * 3250/100
= 32.50 - 1.95
= 30.55
Now, the sales tax = 6 %
Hence, the cost of the textbook including sales tax
= 30.55 + 6 % of 30.55
= 30.55 + 6 * 30.55/100
= 30.55 + 1.833
= 32.383
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Translate this phrase into an algebraic expression.Six less than the product of 13 and Mai's heightUse the variable m to represent Mai's height.
If m is the Mai's height you can write for the given description:
13m - 6
The previous expression means six less than the product of 13 and Mai's height.
