Area of a triangle ABC with the given vertices is 3 square units.
Given that, the vertices of a triangle ABC, A(3,-6), B(5,-6), and C(7,–9).
What is the area of triangle formula in coordinate geometry?In Geometry, a triangle is a three-sided polygon that has three edges and three vertices. The area of the triangle is the space covered by the triangle in a two-dimensional plane.
Area of a triangle = [tex]\frac{1}{2} ( |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|)[/tex]
Here, (x1, y1) = A(3,-6), (x2, y2) = B(5,-6), and (x3, y3) = C(7,–9)
Now, the area of a triangle = 1/2 (|3(-6+9)+5(-9+6)+7(-6+6)|)
= 1/2 (|3(3)+5(-3)+7(0)|)
= 1/2 (|(9-15)|)
= 1/2 × 6
= 3 square units
Therefore, area of a triangle ABC with the given vertices is 3 square units.
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Write the following sentence using mathematical symbols:
n is greater than or equal to 0.
The sentence using mathematical symbols would form an inequality as; n ≥ 0.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions. If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solutions to that equation or inequality. The Set of such values is; called the solution set to the considered equation or inequality.
We need to write a sentence using mathematical symbols:
Given that "n is greater than or equal to 0"
The inequality form as;
n ≥ 0
Therefore, the sentence using mathematical symbols would form an inequality as; n ≥ 0.
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razy GolfmathsdivThe current value of a baseball card is 60 times its original value v (in dollars). The baseball card is worth$15. Write and solve an equation to find the original value of the baseball card.Equation:= 15Original value: $
Answer:
Equation: 60v = 15
Original value: $0.25.
Step-by-step explanation:
Current value: $15
Original value: v
The current value is 60 times the original value.
So, the equation is:
Equation: 60v = 15
Now we solve the equation to find the original value.
60v = 15
v = 15/60
v = 0.25
Original value: $0.25.
A shopper pushes a grocery cart with a force F of 50 N downward and to the right, as shown in the figure below. The anglethe handle makes with the horizontal is 37°, and the cart is moved 14 m. Find the work W done, in joules (1).Ed
Solution
For this case we can create the following plot:
We want to find the work so we can use this formula:
[tex]W=Fd\cos \theta[/tex]Replacing we got:
[tex]W=50\cdot14m\cdot\cos 37=559.04J[/tex]HELP ASAP
Solve z3 = 27.
z = 9
z = −9
z = 3
z = ±3
Answer:
the answer is 3
Step-by-step explanation:
Ms.Macncheese has 7 plates of fish sticks if she ate 4 how many dose she have left?
A. 3
B. 2
C.1
D.11
Answer:
3
Step-by-step explanation:
7 - 4 is 3
The difference of seven times a number and five is one hundred find the number
Let the number be x
seven times the number = 7x
The difference of seven times a number and five is one hundred. It means that
7x - 5 = 100
7x = 100 + 5
7x = 105
x = 105/7
x = 15
The number is 15
How do you do this step by step?
-7 + 9 + (-8)
Step-by-step explanation:
-7 + 9 + (-8)
2 + (-8)
-6
Hope this helps! :)
Step-by-step explanation: Remove parenthesis. If there is a "+" in front of an expression in parenthesis, the expression remains the same.
-7+9-8. Calculate the sum or difference. You should get -6.
Use the sketch tool to mark the picture with the given information. Then choose what postulate proves the triangles congruent.
We choose ASA Postulate to prove this triangle congruent.
In the given question given that
[tex]\overline{AC}[/tex] bisects [tex]\angle BAD[/tex].
[tex]\overline{AC}[/tex] bisects [tex]\angle BCD[/tex].
Since, [tex]\overline{AC}[/tex] bisects [tex]\angle BAD[/tex].
So [tex]m\angle BAC\cong m\angle DAC[/tex]
Since, [tex]\overline{AC}[/tex] bisects [tex]\angle BCD[/tex].
So [tex]m\angle BCA\cong m\angle DCA[/tex]
Then [tex]AC\cong AC[/tex]
Then [tex]\triangle BAC\cong \triangle DAC[/tex]
There given postulate are AAS, ASA, SSS, SAS.
We have proved using the ASA postulate.
Now describing the ASA postulate.
ASA means Angle-Side-Angle Postulate.
According to ASA Postulate, two triangles are congruent if two angles and the included side of one triangle are congruent with two angles and the included side of another triangle.
Hence, we choose ASA Postulate to prove this triangle congruent.
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write down in terms of n, an expression for the nth term of the following sequences
-7,-12,-17,-22,-27
The expression for the nth term of the sequence -7, -12, -17, -22, -27... is -5n-2
The sequence is -7, -12, -17, -22, -27...
The first term = -7
The common difference = The second term - The first term
= -12 - (-7)
= -12+7
= -5
The nth term of the sequence = a+(n-1)d
Where a is the first term
d is the common difference
n is the n terms
Substitute the values in the equation
The nth term of the sequence = -7+(n-1)-5
= -7-5n+5
= -5n-2
Hence, the expression for the nth term of the sequence -7, -12, -17, -22, -27... is -5n-2
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Don buys a shirt for $24.85. His friend Daryl spends $3.15 more for his shirt. Sean paid the same price as Daryl for his shirt but bought 2. How much did Sean spend for his 2 shirts?
Solution
- Don buys a shirt for $24.85.
- Daryl spends $3.15 more for his shirt. This means that Daryl spends
[tex]\$24.85+\$3.15=\$28[/tex]- Thus, Daryl spends $28 on his shirt.
- Sean paid the same price as Daryl, that is, he paid $28 for each shirt.
- Sean bought two shirts, thus, Sean spends:
[tex]\$28+\$28=\$56[/tex]Final Answer
Sean spends $56 on his 2 shirts
Jose invests $8,216 in a savings account with a fixed annual interest rate of 7% compounded 12 times per year. What will the account balance be after 11 years?
After 11 years, the account balance is $17,704.987. (approx.)
Compound interest is defined.The principle of the first loan is multiplied by the annual interest rate multiplied by the number of compound periods minus one to calculate compound interest.
The principal of the loan plus compound interest will then be what is left.
Given,
P = $8,216 for the principal value.
Interest rate, r = 7% or 0.07.
Period, with t = 11.
Interest applied n times every time period, or 12 times.
As far as we are aware, A = P(1 + r/n) n*t
where A is the whole sum.
Fill out the formula with the values,
=> A = 8216(1 + 0.07/12) ^ 11*12
= 8216((12 + 0.07)/12) ^ 132
Upon calculation, we obtain,
≅ $17,704.987
As a result, after 11 years, the account will have a balance of $17,704.987 (about).
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solve the equations and verify the answer
Answer:
See below
Step-by-step explanation:
I THINK what you wrote is:
2(x-2) - 3(x-3) = (5x-5) - 4(x-8)
2x -4 -3x+9 = 5x-5 -4x+ 32
2x-3x-5x+4x = 4 -9 -5 +32
-2x = 22 *** EDITED ***
x = - 11
(04.01 LC)The graph shows a system of equations:y = x + 433y = -2x + 2-3-4-5What is the solution to the system of equations?0 1-2, 2)(2, 2)(2,-2)O(-2,-2)
Explanation:
We have two equation of line. Both lines intersect at a point.
The point of intersection of two graphs, is the solution of the graph.
At this point, both will have same x and y values
Tracing the graph:
The point of intersection occurs at x = -2, y = 2
Hence, the solution is at (-2, 2)
Please solve for x using steps 1/3x= 1/3+6/x
You have the following algebraic equation:
1/3x = 1/3 + 6/x
In order to solve the previous equation you first multiply both sides of the equation by x, thus, you can quit x denominators in the equation. Proceed as follow:
1/3x = 1/3 + 6/x multiply by x both sides
1/3 = x/3 + 6 multiply by 3 both sides
1 = x + 18 subtract 18 both sides
1 - 18 = x + 18 - 18
-17 = x
-17 = x is the same as x = -17. The solution to the given equation is x = -17.
How much grain can a farmer hold in this silo? Use π = 3.14.A. 2,093.3 ft³B. 11,513.3 ft³C. 9,420 ft³D. 12,560.2 ft³
To find out how much grain the farmer can hold we need to find the volume of the silo. The silo is made from a circular cylinder and half a sphere.
The volume of the cylinder is given by:
[tex]V=\pi r^2h[/tex]In this case r=10 and h=30, plugging this values in the equation above we have that the volume of the cylinder is:
[tex]\begin{gathered} V=(3.14)(10)^2(30) \\ V=9420 \end{gathered}[/tex]Hence the volume of the cylinder is 9420 cubic feet.
Now we need to find the volume ot half the sphere, the volume og an sphere is given by:
[tex]V=\frac{4}{3}\pi r^3[/tex]Plugging the radius we have that:
[tex]\begin{gathered} V=\frac{4}{3}(3.14)(10)^3 \\ V=4186.6 \end{gathered}[/tex]Now, we only need half this volume then the volume of the top of the silo is:
[tex]V=2093.3[/tex]Finally we add the volume of the cylinder and half the sphere, therefore the volume of the sylo is:
[tex]11513.3[/tex]and the answer is B.
How much hectares is 61,230 km²
Answer:
6 hecters in the khlathmandu
Trevor's bonus last year with $6720 and this was 12% of his base salary. what is his base salary?
Answer:
$56,000.
Explanation:
Let his base salary = s
12% of his base salary = $6720
Thus, we have:
[tex]12\%\text{ of s=6720}[/tex]Next, solve for s:
[tex]\begin{gathered} \frac{12}{100}\times s=6720 \\ 12s=6720\times100 \\ s=\frac{6720\times100}{12} \\ s=56,000 \end{gathered}[/tex]His base salary is $56,000.
HELP PLSSSSSSSSSSSSSS
Answer: 64
Step-by-step explanation:
Length x width x higth= volume
4 x 8 x 2 = 64
Answer:
4 cm
Step-by-step explanation:
First, find the volume of the rectangular prism.
4*8*2=32*2=64 cm^-3
Now, the formula for the volume of the cube is:
Volume = side ^ 3
We know the volume is 64 cm^3, so plug it in to the equation:
64 = side ^ 3
take the cube root of both sides
4 = side
Write the equation for the graph below.Tomato Prices108Price (In dollars)01 2 3 4 5 6 7 8 9 10Weight(in pounds)
The form of the linear equation is
y = m x + b
m is the slope of the line
b is the y-intercept
The rule of the slope is
[tex]m=\frac{y2-y1}{x2-x1}[/tex](x1, y1) and (x2, y2) are two points on the line
Since (0,0) and (10, 12) are two points on the line
x1 = 0 and y1 = 0
x2 = 10 and y2 = 12
Now substitute them in the rule to find m
[tex]m=\frac{12-0}{10-0}=\frac{12}{10}=1.2[/tex]The slope of the line is 1.2
Substitute it in the form of the equation
y = 1.2 x + b
b is the y-intercept which means value y at x = 0
Since at x = 0, y = 0
Then b = 0
The equation of the line is
y = 1.2 x
a cylinder had a radius of 3 and height of 2 need answer quick
To find the volume of a cylinder with radius 3 and height 3
we will use the formular below:
[tex]V=\pi r^2h[/tex]where r is the radius and h is the height
From the question, r=3 and h = 2
substitute the value into the formula
[tex]V=\pi(3)^2\times2[/tex][tex]V=18\pi[/tex]If we substitute the value of pie = 22/7
Then,
[tex]V=18\times\frac{22}{7}[/tex][tex]V\approx56.57\text{ cubic unit}[/tex]a1 = 1; d = 3a1 = 1; d = −3a1 = 17; d = 3a1 = 17; d = −3
Given:
A graph is given and the points on the graph are as:
(1, 17), (2, 14), (3, 11), (4, 8), (5, 5), (6, 2)
Required:
To determine the value of
[tex]a_1[/tex]and d for the given sequence.
Explanation:
We can observe from the graph that the given sequence is an arithmetic sequence.
Here
[tex]a_1[/tex]represent the first value and d represent the common ratio.
So the values are as:
[tex]\begin{gathered} a_1=1 \\ d=14-17=\text{ -3} \end{gathered}[/tex]Final Answer:
[tex]a_{1=1},\text{ d = -3}[/tex]The second option is the correct answer.
A= hlba)10. The volume of a large can of tuna fish can be calculated using the formula V = ar?h.Write an equation to find the radius, r, in terms of V and h. Determine the diameter, tothe nearest inch, of a large can of tuna fish that has a volume of 66 cubic inches and aheight of 3.3 inches.
Given the formula for volume:
[tex]V\text{ = }\pi r^2h[/tex]Let's rewrite the formula in terms r, V and h.
i) Rewriting for r in terms of V and h :
[tex]\begin{gathered} V\text{ = }\pi r^2h \\ \frac{V}{h}=\pi r^2 \\ \\ \sqrt[]{\frac{V}{\pi h}}=r \\ \\ r\text{ = }\sqrt[]{\frac{V}{\pi h}} \end{gathered}[/tex]2) Given:
Volume, V = 66 cubic inches
height, h = 3.3 inches
We know that diameter is radius multiplied by 2.
To find the diameter, first find the radius.
Therefore, we have:
[tex]\begin{gathered} r\text{ = }\sqrt[]{\frac{V}{\pi h}} \\ \\ r\text{ = }\sqrt[]{\frac{66}{3.3\pi}} \\ \\ r\text{ = }2.52\text{ inches} \end{gathered}[/tex]Since the radius is 2.52 inches, the dia,eter will be:
D = r x 2 = 2.52 x 2 = 5.04 inches
To the nearest inch = 5 inches
ANSWER:
diameter = 5 inches
Your friend has a coln that is not fair. It comes up heads 70% of the time and talls 30% of the time. You flip it twice. Let Xbe the number of heads that come up. Find the probability distribution for X
Let X be the number of heads that come up
[tex]\begin{gathered} \text{Probability of head = 70\% = }\frac{70}{100} \\ \text{Probability of tail = 30\% = }\frac{30}{100} \end{gathered}[/tex]Step 1: Write out the formula for the binomial probability distribution
[tex]P_x=^nC_xp^xq^{n-x}[/tex][tex]undefined[/tex]The data represents the number of cars that the sales staff at Templeton Motors sold this week.
4, 7, 6, 8, 3, 5, 4, 3, 4, 5, 2, 3
Which line plot correctly displays the data?
OA.
Formula Sheet
3.
Number of Cars Sold
X X
X X X
X X X X X X
+++
AHH
+
0 1 2 3 4 5 6 7 8 9 10
X
Number of Cars Sold
X X X X X X X
H
0 1 2 3 4 5 6 7 8 9 10
OC.
OD.
←
Number of Cars Sold
X X
X X X
X X X X X X X
++
0 1 2 3 4 5 6 7 8 9 10
X X
Number of Cars Sold
X X
X X X
H11
0 1 2 3 4 5 6 7 8 9 10
The line plot that correctly displays the data set, 4, 7, 6, 8, 3, 5, 4, 3, 4, 5, 2, 3, is: A.
How to Represent a Data on a Line Plot?A line plot is a graphical representation of a data whereby the frequency of each data point is represented by a dot on the line plot.
The dots on each data point on the line plot corresponds to the frequency of a data point in a data distribution.
Given the data set, 4, 7, 6, 8, 3, 5, 4, 3, 4, 5, 2, 3, the frequency for each data point is:
2 - 1 dot
3 - 3 dots
4 - 3 dots
5 - 2 dots
6 - 1 dot
7 - 1 dot
8 - 1 dots
Thus, the line plot that correctly represents these data points alongside their frequencies is: A.
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If Y (-7, -4) and Z (5, 2), find the slope of a line perpendicular to YZ
Answer:
slope of perpendicular line = - 2
Step-by-step explanation:
calculate the slope of YZ using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = Y (- 7, - 4 ) and (x₂, y₂ ) = Z (5, 2 )
[tex]m_{YZ}[/tex] = [tex]\frac{2-(-4)}{5-(-7)}[/tex] = [tex]\frac{2+4}{5+7}[/tex] = [tex]\frac{6}{12}[/tex] = [tex]\frac{1}{2}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2
The variables x and y vary directly. Write an equation that relates the variable. Then find x when y=16.
7) We know that x = 5 and y = 2
We can write an equation that relates this values as a proportion.
Let's say there is a number r such as:
x*r=y
That's a equation that relates x and y. Let's solve for the values given.
[tex]5\cdot r=2[/tex]Now solve for r:
[tex]r=\frac{2}{5}[/tex]The relation we found is:
[tex]x\cdot\frac{2}{5}=y[/tex]Now to find the value of x when y = -6, we replace it in the equation:
[tex]\begin{gathered} x\cdot\frac{2}{5}=-6 \\ x=-6\cdot\frac{5}{2}=-15 \end{gathered}[/tex]Then with this relation, x = -15 when y = -6
HELP ASAP WILL GIVE BRAINLEST
How many times larger is (1.064 x 10^1) than (7 x 10^−1)?
0.152
15.2
6.58
7.448
1.064 x 10¹ is 15.2 times larger than the 7 x 10⁻¹. It is obtaining the taking ratio of the given number. Option B is correct.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
We'll apply division by splitting into equal halves or groups, the division may be used to decide how to distribute a dish of cookies evenly among a group.
Let 7 x 10⁻¹ be x times the number 1.064 x 10¹.
The value of x is obtained by taking the ratio of 1.064 x 10¹ and 7 x 10⁻¹.
x = 1.064 x 10¹ / 7 x 10⁻¹
x = 15.2
Thus,1.064 x 10¹ is 15.2 times larger than the 7 x 10⁻¹. It is obtaining the taking ratio of the given number. Option B is correct.
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X Consider lines L and M on the graph below. Which of the following BEST describes the slope of these two lines? y L М. 10 9 8 7 6 5 3 2 1 X 0 1 2 3 4 5 6 7 8 9 10 L has a greater slope than M. Land M have the same slope. M has a greater slope than L.
since they are parellel lines, we conclude that they have the same slope, the second option is the correct one.
Which graph represents the solution set of the system of inequalities-2x+y<_4 y>x+2
The graph of the solution set of the system of inequalities y > x + 2 and
- 2x + y ≤ 4 is shown in figure.
What is mean by Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequalities is,
⇒ y > x + 2
And, - 2x + y ≤ 4
Now,
The inequality is,
⇒ - 2x + y ≤ 4
Add 2x both side, we get;
⇒ - 2x + y + 2x ≤ 4 + 2x
⇒ y ≤ 2x + 4
And, The second inequality is;
⇒ y > x + 2
So, Plot the graph of the inequalities y ≤ 2x + 4 and y > x + 2.
We get the solution set of the system of inequalities.
Which is shown in figure.
Thus, The graph of the solution set of the system of inequalities y > x + 2 and - 2x + y ≤ 4 is shown in figure.
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The country of Latveria has a population of 11.2 million at the start of 1988, which grows at 4.4% per year.A) Write a recursive equation for the population of Latveria.B) Write an explicit equation for the population of Latveria.C) To the nearest tenth of a million, what is the population of Latveria at the start of 1994.
A) The recursive formula takes into account the previous term. For each term, the next term is expressed in respect to it
Looking at the given scenario, the popularion is increasing by 4.4%. This means that the common ratio is
1 + 4.4/100 = 1.044
Given that the initial population is 11200000, the recaursive formula or equation would be
[tex]\begin{gathered} f_n=\text{ 1.044}f_{n\text{ - 1}} \\ \text{where f}_1=\text{ 11200000} \end{gathered}[/tex]B) For the explicit formula, the general formula for a geometric sequence is
an = a1 * r^(n - 1)
a1 = first term = 11200000
r = common ratio = 1.044
The explicit equation would be
an = 11200000 * 1.044^(n - 1)
C) At the start of 1994, the number of terms, n = 7
We would find a7 by substituting n = 7 into the explicit equation. We have
a7 = 11200000 * 1.044^(7 - 1)
a7 = 11200000 * 1.044^6 = 14501770