Given: B is the midpoint of AC. Complete the statementIf AB = 28, Then BC =and AC =
Answers
If B is the midpoint of AC, this means that point B divides the line AC exactly into 2 equal parts AB and BC, therefore,
[tex]AB=BC[/tex]Answer A
Thus, if AB = 28, BC = 28 too.
Answer B: Therefore, AC = 56
Related Questions
polygon wxyz has vertices W( 1, 5 ), X( 6, 5), Y( 6, 10), and Z(1, 10)
If w' x' y' z' is a dilation of wxyz with scale factor 5, give the coordinates of w' x' y' z'
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The coordinates of W'X'Y'Z' are W'(5, 25), X'(30, 25), Y'(30, 60) and Z'(5, 10) respectively.
Given that, polygon WXYZ has vertices W( 1, 5 ), X( 6, 5), Y( 6, 10), and Z(1, 10).
What is a dilation?Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.
We know that, scale factor = Dimension of the new shape ÷ Dimension of the original shape
Dimension of the original shape W'= 5(1, 5) = (5, 25)
X' =5(6, 5) = (30, 25)
Y' =5(6, 10) = (30, 60)
Z' =5(1, 10) = (5, 10)
Therefore, the coordinates of W'X'Y'Z' are W'(5, 25), X'(30, 25), Y'(30, 60) and Z'(5, 10) respectively.
To learn more about the dilation visit:
https://brainly.com/question/13176891.
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7) The water park is a popular field trip destination. This year the senior class at High School A and thesenior class at High School B both planned trips there. The senior class at High School A rented andfilled 1 van and 14 buses with 309 students. High School B rented and filled 4 vans and 14 buseswith 354 students. Each van and each bus carried the same number of students. Find the number ofstudents in each van and in each bus.C) Van: 19 Bus: 29 D) Van: 15, Bus: 21
Answers
Given
The water park is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 1 van and 14 buses with 309 students. High School B rented and filled 4 vans and 14 buses with 354 students. Each van and each bus carried the same number of students.
Answer
Let students in Van be x
And students in bus be y
A/Q
x + 14y = 309 (1)
4x + 14y = 354 (2)
Subtracting (1) and (2)
3x = 45
x = 15
Put in eq (1)
15 + 14 y = 309
14y = 309 - 15
14 y = 294
y = 21
St
Given a polyhedron with 6 vertices and 12 edges, how many faces does it have?
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SOLUTION
GIVEN
A polyhedron has 6 vertices and 12 edges.
TO DETERMINE
The number of faces
CONCEPT TO BE IMPLEMENTED
Euler’s formula for Polyhedron :
For polyhedron F + V = E + 2
Where F stands for number of faces , V stands for number of vertices , E stands for number of edges .
EVALUATION
Here it is given that a polyhedron has 6 vertices and 12 edges
V = Number of vertices = 6
E = Number of edges = 12
F = Number of faces = ?
By Euler’s formula
F + V = E + 2
⇒ F + 6 = 12 + 2
⇒ F + 6 = 14
⇒ F = 8
FINAL ANSWER
The number of faces = 8
im confused on premtier
Answers
we have to calculate the perimeter of the semicircle which radius is 16 mm
[tex]P_{sc}=\frac{2\pi\cdot r}{2}=\pi\cdot r=16\pi\approx50.26\operatorname{mm}[/tex]Now we have to add the outter sides of the triangle
[tex]P=20+20+50.26=90.26\operatorname{mm}[/tex]find the value of X and y if l || m.
Answers
The Solution.
Step 1:
We shall find two equations from the given angles.
First, by vertically opposite angle property of angles between two lines, we have that:
[tex]\begin{gathered} 7y-23=23x-16 \\ \text{Collecting the like terms , we get} \\ 7y-23x=23-16 \\ 7y-23x=7\ldots.eqn(1) \end{gathered}[/tex]Similarly, by alternate property of angles between lines, we have that:
[tex]\begin{gathered} 23x-16+8x-21=180 \\ \text{Collecting like terms, we get} \\ 31x-37=180 \\ 31x=180+37 \\ 31x=217 \\ \text{Dividing both sides by 31, we get} \\ x=\frac{217}{31}=7 \end{gathered}[/tex]Step 2:
We shall find the values of y by substituting 7 for x in eqn(1), we get
[tex]\begin{gathered} 7y-23(7)=7 \\ 7y-161=7 \\ 7y=7+161 \\ 7y=168 \\ \text{Collecting the like terms, we get} \\ y=\frac{168}{7}=24 \end{gathered}[/tex]Step 3:
Presentation of the Answer.
The correct answers are; x = 7 , and y = 24
Select all the true statements about this graph A. The graph is nonlinearB. The function increases at the same rateC. The rate decreases after x = 2.D. The graph is a functionE. The graph is increasing in two intervals.SELECT ALL ANSWER CHOICES THATS RIGHT
Answers
In the graph the points are connected by the straight lines, so graph is linear graph. In nonlinear graph the points are connected by the curve. So option A is incorrect.
The slope of the line changes after x=2. The inclination of line with positive x axis is different before and after x=2. So the function not increases at same rate. Then option B is incorrect.
The rate is given by the slope of line. The inclination of line with positive x axis increase after x=2, so rate increases not decreases. Then option C is incorrect.
The graph of a straight line is function or not a function can be inspected by vertical line test.
If we draw a vertical line, then the vertical line intersect the line only once, so the graph is function. Option D is correct.
The value of y increases with increase in value of x but increase in value of y with x is different for two lines. So graph is increasing in two intervals. Option E is also correct.
Thus option D and E is only true for given graph.
which property justifies the following statement if 3x=9,then x=3.
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Answer:
Multiplication Property
Division Property
This can be justified using multiplication property and division property:
Multiplication property:
If both sides of equation:
3x = 9
are multiplied by 1/3, we have:
x = 3
Division property
Divide both sides of the equation:
3x = 9 by 3, we have:
x = 3
A certain marine engine has cylinders that are 5.25 cm in diameter and 5.64 cm deep.Find the total volume of 4 cylinders (to the nearest hundredth). Use 3.14 as the approximate value of
Answers
Given:
A cylinder is given with 5.64 cm deep and 5.25 cm diameter.
Required:
Total volume of 4 cylinders.
Explanation:
Diameter of cylinder d = 5.25 cm
Height of cylinder or deepness of cylinder h = 5.64 cm
Radius r of cylinder is
[tex]r=\frac{d}{2}=\frac{5.25}{2}=2.625\text{ cm}[/tex]volume of cylinder is
[tex]v=\pi r^2h=3.14*2.625^2*5.64=122.03\text{ cm}^3[/tex]here we need volume of 4 cylinder
for this we just multiply v with 4
[tex]V=4v=4*122.03=488.121\text{ cm}^3[/tex]Final Answer:
The volume of 4 cylinder is 488.121 cube cm
use the graph to complete the ordered pair solution (0,_) for f.
Answers
we must look the value of the graph when x=0
the graph trought x=0 when y=-1 so, the point is
[tex](0,-1)[/tex]If there are 78 questions on a test , how many do you have to get correctly to get an 84 % or better on the exam ?
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To answer this question, we have to multiply the number of questions times 0.84 (which is 84% written as a decimal):
[tex]78\cdot0.84=65.52\approx66[/tex]Yo have to get 66 questions correctly to get an 84% or better on the exam.
What is the equation in slope-intercept form of the line that passes through the points (-4,8) and (12,4)?
Answers
ANSWER
y = -0.25 + 7
EXPLANATION
The line passes through the points (-4, 8) and (12, 4).
The slope-intercept form of a linear equation is written as:
y = mx + c
where m = slope
c = y intercept
First, we have to find the slope of the line.
We do that with formula:
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \text{where (x}_1,y_1)\text{ = (-4, 8) } \\ (x_2,y_2)\text{ = (12, 4)} \end{gathered}[/tex]Therefore, the slope is:
[tex]\begin{gathered} m\text{ = }\frac{4\text{ - 8}}{12\text{ - (-4)}}\text{ = }\frac{-4}{12\text{ + 4}}\text{ = }\frac{-4}{16}\text{ = }\frac{-1}{4} \\ m\text{ = -0.25} \end{gathered}[/tex]Now, we use the point-slope method to find the equation:
[tex]\begin{gathered} y-y_{1\text{ }}=m(x-x_1) \\ \Rightarrow\text{ y - 8 = -0.25(x - (-4))} \\ y\text{ - 8 = -0.25(x + 4)} \\ y\text{ - 8 = -0.25x - 1} \\ y\text{ = -0.25x - 1 + 8} \\ y\text{ = -0.25x + 7} \end{gathered}[/tex]That is the equation of the line. It is not among the options.
hi I need on this. $6000 invested at 5.5% interest, compounded annually. how how would i have in 6years?
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
principal = $6000
rate (interest) = 5.5%
time = 6 years
Step 02:
compound interest:
n = annually
n = 1
r = 5.5 % = 5.5 / 100 = 0.055
A = amount
[tex]A\text{ = P \lparen1 + r/n\rparen}^{nt}[/tex][tex]A\text{ = 6000 * \lparen1 + }\frac{0.055}{1})\placeholder{⬚}^{1*6}[/tex][tex]A\text{ = 6000 * \lparen1.3877\rparen = 8273.06}[/tex]The answer is:
$8273.06
you started this year with $141 saved and you continue to save $27 per month. Write an equation to model this situation (use m for months and s for savings)
Answers
The money we would have at any time can be modeled as
M = 27k + 141
Why?
you started with $141, so that is the base amount,
every month you add 27 dollars,
in one month you add 27 dollars,
in two months you 27 again making 54 dollars,
so , in x months, you have added 27x dollars to the 141 dollars,
thus our equation is
M = 27k + 141
Try This question out and I’ll give you brainliest no links or I will report you
Answers
Answer: ∠ABD = 19°
Step-by-step explanation:
The angle formed by ABC is a complementary angle. This means the sum of both angles adds up to 90 degrees.
Since angle DBC is 71 degrees, 90 - 71 equals ∠ABD
90 - 71 = 19
Therefore ∠ABD = 19°
Answer:
m∠ABD = 19°
Step-by-step explanation:
Hello!
Recall that all angles of a rectangle are 90° in measure.
Angle B is 90°, and is made up of angles ABD and DBC.
We know the measure of angle DBC, it's given as 71°. We can find the measure of ABD by subtracting 71° from 90°.
Find ABDABC = ABD + DBC90 = ABD + 7119 = ABDSo the measure of angle ABD is 19°.
Which system of linear equations could be used to determine the price of each book
Answers
Answer:
Let the price of the maths book be m and price of the novel book be n
Given that,
Total cost of the books is $54
The price of math book is $8 more than 3 times the price of novel book.
we get,
The system of equation as,
[tex]\begin{gathered} m+n=54 \\ m=8+3n \end{gathered}[/tex]Hence the system of equation to determine the price of the maths and novel book is,
[tex]\begin{gathered} m+n=54 \\ m=8+3n \end{gathered}[/tex]Find an equation of the line.Write the equation in the standard form.Through (8,4); parallel to 7x-y= 2.
Answers
Answer:
7x-y=53
Explanation:
Given the line
[tex]7x-y=2[/tex]Making y the subject of the equation, we have:
y = 7x-2
Therefore, the slope of the line, m=7
• If two lines are parallel, their slopes are equal.
Therefore, the slope of the parallel line = 7
The equation of the parallel line through (8,4) will then be:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-4=7(x-8) \\ y-4=7x-57 \\ 7x-y=-4+57 \\ 7x-y=53 \end{gathered}[/tex]In the diagram shown, ray CD is perpendicular to ray CE. If the measure of DCF is 115then what is the measure of ECF?
Answers
m∠FCE =25º
1) Since the measure of ∠DCF = 115º and ∠DCE = 90º then by the Angle Addition postulate we can state that
∠DCF = ∠DCE +∠FCE Plugging into that the given values
115º = 90º + ∠FCE Subtracting 90º from both sides
115-90=∠FCE
25º =∠FCE
2) Then the measure of ∠FCE is 25º
A circular plot of land has a diameter of 16 yards. What is the area of theland? Use 3.14 for it.O A. 803.84 yd2O B. 50.24 yd2O C. 200.96 yd2O D. 25.12 yd2
Answers
The area of the circle can be calculated with the following formula
[tex]A=\pi\cdot r^2[/tex]First let's find the radius
[tex]\begin{gathered} r=\frac{16}{2}\text{yds} \\ r=8\text{yds} \end{gathered}[/tex][tex]\begin{gathered} A=\pi\cdot8^2 \\ A=3.14\cdot64 \\ A=200.96\text{ yd2} \end{gathered}[/tex]The answer would be 200.96 square yards
Bell Ringer -- Find the distance of each side of the triangle: A(-10, 6) B(-6, 9) C(-6, 6)
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Answer:
It is c) (-6, 6)
For the polynomial below, 1 is a zero.h(x) = x² – 3x? - 2x + 4Express h(x) as a product of linear factors.
Answers
Step 1
Given the zero, 1, we can use synthetic division to acquire the other factors
Using synthetic division we will write out all coefficients of the terms of h(x) and proceed thus
1 | 1 -3 -2 +4
1 -2 -4
-----------------------
1 -2 -4 0
Hence the quadratic equation we will need to split into linear factors is given as
[tex]x^2-2x-4[/tex]Since the remainder is 0
Step 2
Factorize the quadratic equation above completely
[tex]\begin{gathered} x^2-2x-4=0 \\ we\text{ will use} \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]Where
a= 1
b= -2
c= -4
[tex]\begin{gathered} x=\frac{-(-2)\pm\sqrt[]{(-2)^2-4\times1\times-4}}{2\times1} \\ x=\frac{2\pm\sqrt[]{4+16}}{2} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{2\pm\sqrt[]{20}}{2} \\ x=\frac{2}{2}+\frac{\sqrt[]{20}}{2}=1+\frac{2\sqrt[]{5}}{2}=1+\sqrt[]{5} \\ Or \\ x=\frac{2}{2}-\frac{\sqrt[]{20}}{2}=1-\frac{2\sqrt[]{5}}{2}=1-\sqrt[]{5} \end{gathered}[/tex]Hence the product of linear factor will be
[tex](x-1)(1+\sqrt[]{5})(1-\sqrt[]{5})[/tex]
I need to find the length x of KL
Answers
Answer:
3.6Step-by-step explanation:
We're going to use length DC and ML, along with DA and MJ
[tex]\frac{DC}{ML} = \frac{5}{6}[/tex] which is 0.833333333
now for
[tex]\frac{DA}{MJ} =\frac{7}{8.4}[/tex] which is 0.833333333 (again)
as you can see since the shapes ABCD and JKLM are similar, they have a relationship which in this case is 0.833333333
and we can use this 0.833333333 to help us find the length of KL
knowing that any length for ABCD divided by JKLM is 0.833333333
we can do
[tex]\frac{CB}{LK}=0.833333333[/tex]
since we don't know what KL is, we can switch the spots and enlongate it, to become:
[tex]\frac{CB}{0.833333333} =LK[/tex]
put in the value for CB
[tex]\frac{3}{0.833333333} =LK[/tex]
and we get 3.6
The length of x of KL is...
3.6HELPPPPPP PLEASEEEEEEEEEEEEEE
Answers
Answer:
Option C, [tex]f(x)=-3x^2-6xh-3h^2+2x+2h+1[/tex]
Step-by-step explanation:
Oooo the ol canvas quiz yeesh.
Anyway, for this sort of problem, anywhere in your second equation that you see an x, sub for (x+h).
[tex]f(x)=-3x^{2} +2x+1[/tex]
[tex]f(x)=-3(x+h)^{2} +2(x+h)+1\\[/tex]
You must foil the first part
[tex]f(x)=-3(x^2+h^2+2xh)+2(x+h)+1\\[/tex]
Now distribute to eliminate the parentheses
[tex]f(x)=-3x^2-3h^2-6xh+2x+2h+1[/tex]
As your answer choice has it:
[tex]f(x)=-3x^2-6xh-3h^2+2x+2h+1[/tex]
Quadrilateral ABCD with vertices A(0,7) B(1,3), C(-1,-4), and D(-5,1): <7,-3>
Answers
We will have the following:
2)
A(0, 7) : <7, -3>
[tex]A^{\prime}(7,4)[/tex]B(1, 3) : <7, -3>
[tex]B^{\prime}(8,0)[/tex]C(-1, -4) : <7, -3>
[tex]C^{\prime}(6,-7)[/tex]D(-5, 1) : <7, -3>
[tex]D^{\prime}(2,-2)[/tex]3)
From the graph we will have the following:
a.
[tex](x,y)\to(x+7,y+5)[/tex]b.
[tex]\langle7,5\rangle[/tex]***Explanation***
For point 2, we will simply apply the vector to the corresponding coordinates, that is:
We have the coordinates:
[tex]A(a,b)[/tex]and the vector:
[tex]\langle c,d\rangle[/tex]So, in order to determine the final image we will have to follow the transformation rule:
[tex]A^{\prime}(a+c,b+d)[/tex]*For point 3, we will simply count the number of units the image has moved to the left or rigth and that will be our transformation rule for the x-axis, and the number of units the image has moved up or down and that will be our transformation rule for the y-axis.
In the case of the problem, the images moved 7 units to the rigth (+7) and then moved 5 units up (+5), so the transformation rule in coordinate notation is given by:
[tex](x,y)\to(x+7,y+5)[/tex]And in order to write it in vector notation, we simply write the units the images move:
[tex]\langle7,5\rangle[/tex]A line has slope 3. Through which two points could this line pass? a. (24. 19), (8, 10) b. (10, 8). (16, 0) C. (28, 10). (22, 2) d. (4, 20). (0, 17) Please select the best answer from the choices provided D
Answers
Step 1: Concept
You are going to apply the slope formula to find the slope of the line through each coordinate.
Step 2: Slope formula
[tex]\text{Slope = }\frac{y_2-y_1}{x_2-x_1}[/tex]Find the variance for the set of data: 22, 26, 17, 20, 20.The variance is
Answers
The variance of a given data set with size N is given by the formula:
[tex]\begin{gathered} \sigma=\sqrt{\frac{1}{N}\sum_{i=1}^N(x_i-\mu)^2} \\ Var(X)=\sigma^2 \end{gathered}[/tex]Then, for the data set {22, 26, 17, 20, 20} and N = 5, we have:
[tex]\begin{gathered} \mu=\frac{22+26+17+20+20}{5}=21 \\ \sigma=\sqrt{\frac{1^2+5^2+(-4)^2+(-1)^2+(-1)^2}{5}}=\sqrt{\frac{44}{5}}=2\sqrt{\frac{11}{5}} \\ \therefore Var(X)=\frac{44}{5}=8.8 \end{gathered}[/tex]Tran is in charge of the school's Awards Dinner. She set up the multi-purpose room with a stage in front and round tables for parents, students, and family members to sit around for dinner. Below is the floorplan that she drew for the eventStageHow many people can be seated as the tables are arranged right now? (In the box below, type your answer as a number only
Answers
Tran has made a plan with 12 tables for 8 people each of them. Then, we have 12 tables * 8 ( amount of chairs each of them) = 96. So 96 people can be seated.
V256 rational or irrational
Answers
First, in order to get to know if 256 it is a rational or irrational number we have to begin with the definition of what is rational and irrational number.
Rational numbers are all the number that can be represented as fractions, while the irrational numbers are all the numbers that can not be expressed as fractions.
In this case, then we can confirm that the number 256 can be considered as a rational number because it can be expressed as the quotient of the two integers: for example 256/1.
Reduce the rational expression to lowest terms. If it is already in lowest terms, enter the expression in the answer box. Also, specify any restrictions on the variable.y²-3y - 18/y²-9y + 18Rational expression in lowest terms:Variable restrictions for the original expression: y
Answers
Given: The expression below
[tex]\frac{y^2-3y-18}{y^2-9y+18}[/tex]To Determine: The lowest term of the given rational fraction
Solution
Let simplify both the numerator and the denominator
[tex]\begin{gathered} Numerator:y^2-3y-18 \\ y^2-3y-18=y^2-6y+3y-18 \\ y^2-3y-18=y(y-6)+3(y-6) \\ y^2-3y-18=(y-6)(y+3) \end{gathered}[/tex][tex]\begin{gathered} Denominator:y^2-9y+18 \\ y^2-9y+18=y^2-3y-6y+18 \\ y^2-9y+18=y(y-3)-6(y-3) \\ y^2-9y+18=(y-3)(y-6) \end{gathered}[/tex]Therefore
[tex]\begin{gathered} \frac{y^2-3y-18}{y^2-9y+18}=\frac{(y-6)(y+3)}{(y-3)(y-6)} \\ y-6-is\text{ common} \\ \frac{y^{2}-3y-18}{y^{2}-9y+18}=\frac{(y-6)(y+3)}{(y-3)(y-6)} \\ \frac{y^{2}-3y-18}{y^{2}-9y+18}=\frac{y+3}{y-3} \end{gathered}[/tex]Hence, the rational expression in its lowest term is
[tex]\frac{y+3}{y-3}[/tex]The variable for the original expression is as given as
[tex]\begin{gathered} \frac{y^{2}-3y-18}{y^{2}-9y+18}=\frac{(y-6)(y+3)}{(y-3)(y-6)} \\ y\ne3,y\ne6 \end{gathered}[/tex]Two train leave stations 210 miles apart at the same time and travel toward each other. One train travels at 80 miles per hour while the other traves a 70miles per hout. How long will it take for the two trains to meet?___ hours Do not do any rounding
Answers
SOLUTION
At the same time t,
Train 1 would have covered a distance of 80t, since distance = average speed x time.
Train 2 would have covered a distance of 70t.
Now both added should give 210 miles
That is 80t + 70t = 210
150t = 210
t = 210/150
t = 1.4 hours
Evaluate the expression.If x=12, y=8, and z=3x3 + y + z3
Answers
We need to find the value of
[tex]x^3+y+z^3[/tex]Where x = 12, y = 8, and z = 3
Substitute these values in the expression above
[tex](12)^3+8+(3)^3[/tex]12^3 = 1728
3^3 = 27
Then
[tex]1728\text{ + 8 + 27 = 1763}[/tex]The value of the given expression is 1763
