Mathematics High School
Answers
Answer 1
The missing parts of proof are:
∠JKM≅∠LKMMK≅MKAAS Congruence PostulateCorresponding parts of congruent triangle are equalDefinition of equidistant
Explain property of angles
In geometry, a line that divides an angle into two equal angles is referred to as an angle bisector. By definition, a bisector is something that divides an object or a shape into two equal parts. A ray is said to be an angle bisector if it divides an angle into two equal portions of the same measure.
Angle Bisector's Qualities:
All of the angle bisector's points are equally spaced from both of the angle's arms.Any angle, including acute, obtuse, and right angles, can have an angle bisector drawn to it.The ratio by which the angle bisector splits the opposite side of a triangle is the same as the ratio by which the other two sides are divided.
Given,
KM is the bisector of ∠JKL
1. As per the definition of bisector, ∠JKM≅∠LKM
Given,
∠KXM and ∠KYM are right angles
∠KXM≅∠KYM because all right angles are congruent
2. Because of Reflexive Property of congruence, MK≅MK
3. Given △KXM≅△KYM, AAS congruence postulate
4. Given MX≅MY, this is according to CPCTE property
5. Given, Point M is equidistant from the sides of ∠JKL, as per the definition of equidistant
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Related Questions
suppose that g(x) = f(x) -7 which statement best compares the graph of g(x) with the graph of f(x)
Answers
It implies that when F(x) shifts 7 units to the left, we get the value equal to G. (x). As a result, the graph of G(x) is the graph of F(x) with 7 units added to the left.
How is the graph of G related to the graph of f?
The graph of g is the reflection of the graph of f. If g(x) = f(-x), then the graph of g is obtained from the graph of f by reflecting about the y-axis.
For instance, the result of multiplying f(x) and g(x) is h(x) = fg (x), or h(x)=f(x)g (x). if f is the function denoted by f(x) = x2 and g is the function denoted by g(x) = x + 3.
Therefore,
The Correct answer is : The two functions G(x) and F are provided to us (x).
We must determine which assertion most accurately contrasts the graphs of G(x) and F(x).
Suppose
F(x) = x [/ tex]
G(x) = x-7
When x = 1 is substituted
So, F(x) = 1
G(x) = 1-7 = -6
It implies that we obtain the value equal to the value of G when F(x) shifts 7 units to the left (x).
The graph of G(x) is therefore the graph of F(x) with 7 units added to the left.
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Absolute value can never be negative,
true or false?
Answers
Answer:
Yes, an absolute value can never be false. So, the answer is true.
help meeeeeeeeeeeeeee pleaseeeeeee
Answers
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]
Find the slope and y-intercept of the line below
Answers
slope: 1/2
y-intercept: 2
y= 1/2x + 2
Use the long division method to find the result when 6x4 +423-7x²+3x-7 is
divided by 2x2 + 2x-3. If there is a remainder, express the result in the form
q(x) +5(2).
Answers
Answer:−6x4−3x3−2x2−4x−7x2+3=−6x2−3x+16+5x−55x2+3.
Step-by-step explanation: −6x4−3x3−2x2−4x−7x2+3. The Long Division method: −6x2−3x+16
three friends go grocery shopping together and each buys the same kind of oranges. lamar buys 2 pounds and pays $3.00 enrico buys 5 pounds and pays $7.50 anna buys 3 pounds and pays $4.50
Answers
The cost of 1 pound of orange will be $1.5. The total payment was $15. The total weight of orange was 10 pounds.
What is unitary method?
The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. A single or distinct unit is referred to by the word unitary. Therefore, the goal of this method is to establish values in relation to a single unit. The unitary method, for instance, can be used to calculate how many kilometers a car will travel on one litre of gas if it travels 44 km on two litres of fuel. The unitary method involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units.
Here,
cost of 2 pound of orange=$3
cost of 5 pound of orange=$7.50
cost of 3 pound of orange=$4.50
Therefore,
The cost of 1 pound of orange is $1.5
The total payment made=$7.50+$4.50+$3
=$15
The total weight of oranges=2+3+5
=10 pounds
One pound of oranges will cost $1.5. $15 was paid in total. Orange weighed ten pounds in total.
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These ordered pairs represent a proportional relationship. Use the interactive and the constant of proportionality to find the missing coordinates for the ordered pairs.
(3, 9), (A, 12), (5, 15), (6, B
Answers
Missing coordinates for the ordered pairs given are A= 4 and B= 18.
What are coordinates ?
An integer pair used to define a point's location on a coordinate plane using the horizontal and vertical separations from the two reference axes Coordinates are two numbers (Cartesian coordinates) or, less frequently, a letter and a number that identify a specific location on a grid, also known as a coordinate plane. They are frequently represented by the x-value and y-value pair (x,y). The x (horizontal) and y (vertical) axes are the two axes of a coordinate plane with four quadrants (vertical)
Calculation
12/A = 9 / 3
A = 4
Same as above
B/6 = 9/3
B = 18
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Problem 2: Solve the matrix equation for "x" and "y" 8 -X 2 13 4 1- [ 3 -9 10 -4y 5 6 [ 0 16
Answers
Solve the operation of the matrix
[tex]\begin{gathered} 2\begin{bmatrix}{8} & {-x} & {} \\ {5} & {6} & {} \\ & {} & {}\end{bmatrix}{}-\begin{bmatrix}{3} & {-9} & {} \\ {10} & {-4y} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{13} & {4} & {} \\ {0} & {16} & {} \\ {} & {} & {}\end{bmatrix} \\ \begin{bmatrix}{16} & {-2x} & {} \\ {10} & {12} & {} \\ {} & & {}\end{bmatrix}-\begin{bmatrix}{3} & {-9} & {} \\ {10} & {-4y} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{13} & {4} & {} \\ {0} & {16} & {} \\ {} & {} & {}\end{bmatrix} \\ \begin{bmatrix}{13} & {-2x+9} & {} \\ {0} & {12+4y} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{13} & {4} & {} \\ {0} & {16} & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}[/tex]
From this result we know that
[tex]\begin{gathered} -2x+9=4 \\ 12+4y=16 \end{gathered}[/tex]
Now clear x and y from the equations
[tex]\begin{gathered} -2x+9=4 \\ -2x=-5 \\ x=-\frac{5}{-2} \\ x=\frac{5}{2} \end{gathered}[/tex][tex]\begin{gathered} 12+4y=16 \\ 4y=4 \\ y=\frac{4}{4} \\ y=1 \end{gathered}[/tex]
x is 5/2 and y is 1
what would the new points be after the transformation:
g(x)=f(-5x+10)
Answers
Answer:
There's nothing that can be done with the given information
Step-by-step explanation:
The sum of two numbers is 38 and their product is 165. Find the larger number. PLEASE HELP
Answers
First set up the initial equation, x+y = 38
Second equation is x*y =165
x = 38-y
(38-y)y = 165
38y-y^2 =165
-y^2+38y-165
-38+or- square root (38^2-4(-1)(-165))/2(-1)
=5 so y =5 and x = 33
Answer:
The larger number is 33
Step-by-step explanation:
Writing and solving a system of equations
Let x and y be the numbers
sum of two numbers is 38
x+y = 38
their product is 165
xy = 165
x = 38-y
Substitute this into xy =165
(38-y) * y = 165
38y - y^2 = 165
-y^2 + 38y -165 = 0
Multiply by -1
y^2 - 38y + 165 =0
Factor
( y-33) ( y-5) = 0
Using the zero product property
y -33 =0 y-5 =0
y =33 y=5
Now we can find x for each solution
x = 38-33 =5 x = 38-5 = 33
The two numbers are 33 and 5
The larger number is 33
what do you think the answer is? No it’s not the 3rd option or not that I think I just clicked a random answer on accident.
Answers
Answer
Option C is correct.
Sandra will be paid 72.30 dollars for babysitting for 12 hours.
Explanation
We are told that Sandra earned 60.25 dollars babysitting 10 hours.
If she babysits at the same rate, we are asked to calculate the amount she would earn if she babysits for 12 hours.
Let the amount Sandra is paid for babysitting for 12 hours be x dollars
10 hours = 60.25 dollars
12 hours = x dollars
We can write a mathematical relationship by cross multiplying
10 × x = 12 × 60.25
10x = 723
Divide both sides by 10
(10x/10) = (723/10)
x = 72.3 dollars
Hope this Helps!!!
Can anyone help with this? Thanks
Answers
The surface area of the prism is 1440 mm²
Given,
Triangular prism
Height of the prism = 32 mm
Base of the prism = 24 mm
Length of the prism = 7 mm
We have to find the surface area of the prism;
Surface area, SA = bh + (b₁ + b₂ + b₃) l
Here,
Base, b = 24 mm
Height, h = 32 mm
Length, l = 7 mm
b₁ = 24 mm
b₂ = 32 mm
b₃ = [tex]\sqrt{b_{1} ^{2} + b_{2} ^{2} }[/tex] = [tex]\sqrt{24^{2}+ 32^{2} }[/tex] = [tex]\sqrt{576 + 1024}[/tex] = √1600 = 40 mm
Then,
Surface Area = bh + (b₁ + b₂ + b₃) l
SA = 24 x 32 + (24 + 32 + 40) 7
SA = 768 + 96 x 7
SA = 768 + 672
SA = 1440 mm²
That is,
The surface area of the prism is 1440 mm²
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Question 12(Multiple Choice Worth 1 points)(07.04 LC)Factor completely 36x² - 49.(3x + 7)(12x-7)(3x-7)(12x+7)(6x-7)(6x-7)(6x + 7)(6x-7)
Answers
The factor the binomial
[tex]a^2-b^2[/tex]
Find the square root of a and the square root of b, then put them as the product of the sum and difference of these square roots
[tex]\begin{gathered} \sqrt{a^2}=a \\ \sqrt{b^2}=b \\ a^2-b^2=(a+b)(a-b) \end{gathered}[/tex]
We will use this rule to factor in the given expression
[tex]36x^2-49[/tex]
Find the square root for each term
[tex]\begin{gathered} \sqrt{36x^2}=6x \\ \sqrt{49}=7 \end{gathered}[/tex]
Write the two factors
[tex]36x^2-49=(6x+7)(6x-7)[/tex]
The answer is the last choice (6x + 7)(6x - 7)
5. The circle graph shows the favorite music genre of radio listeners. Which of the following 2 categories combinedmake up the biggest percentage?Music PreferenceClassical 10%a. Alternative and classicalb. Country and rock15%AlternativeRock 35%C.Jazz and countryCountry25%Jazz 15%d. Rock and Classical
Answers
rock with 35% and country with 25% are the highest percentages, therefore the answer is: B
What is the equation of the line parallel to 3x + 5y = 11 that passes through the point (15, 4)?3x-29= 3x - 295y-y-x-21y--x+533y=-5* +13Mart this and returnSavond uit
Answers
Recall that two equations in standard form represent parallel lines if they are as follows:
[tex]\begin{gathered} Ax+By=C_1, \\ Ax+By=C_2, \end{gathered}[/tex]
Where A>0, and all the coefficients are integers.
Therefore the equation of a parallel line to the given line is as follows:
[tex]3x+5y=k[/tex]
Since the parallel line passes through (15,4) then:
[tex]3*15+5*4=k.[/tex]
Simplifying the above result we get:
[tex]\begin{gathered} 45+20=k, \\ k=65. \end{gathered}[/tex]
Therefore:
[tex]3x+5y=65.[/tex]
Solving the above equation for y we get:
[tex]\begin{gathered} 3x+5y-3x=65-3x, \\ 5y=-3x+65, \\ \frac{5y}{5}=-\frac{3x}{5}+\frac{65}{5}, \\ y=-\frac{3}{5}x+13. \end{gathered}[/tex]
Answer: Last option.
Answer:
D
Step-by-step explanation:
Theslopeof the the straight line equation3x+5y=11is(−35)Hence the slope of the line parallel is same to the given line i.e,(−35)We can write the equation in the following form slope intercept form i.e,y=mx+cHerec=−6andm=−35The answer isy=−35x−6⇒5y=−3x−30⇒3x+5y=−30Hope it helps...Thanks you...
Determine weather the statement is true or false. Justify your answer
Answers
[tex]\begin{gathered} \cos (-\frac{7\pi}{2})=\cos (\pi+\frac{\pi}{2}) \\ \cos (-\frac{7\pi}{2})=\cos (\frac{3\pi}{2}) \end{gathered}[/tex]
As we know:
[tex]\begin{gathered} \cos (x)=0 \\ for \\ x=\pi n-\frac{\pi}{2} \\ n\in Z \end{gathered}[/tex]
For:
[tex]\begin{gathered} n=2 \\ x=2\pi-\frac{\pi}{2}=\frac{3\pi}{2} \\ for \\ n=-3 \\ x=-3\pi-\frac{\pi}{2}=-\frac{7\pi}{2} \end{gathered}[/tex]
Therefore:
[tex]\begin{gathered} \cos (-\frac{7\pi}{2})=0 \\ and \\ \cos (\frac{3\pi}{2})=0 \\ so\colon \\ 0=0 \\ This_{\text{ }}is_{\text{ }}true \end{gathered}[/tex]
Therefore, the statement is true
A survey estimates the current average cost of college to be $34,179.
(a) If the average cost of college increased by 7.4% each year, what will be the average cost of college 15 years from now?
(b) If a savings plan offers a rate of 5.4% compounded continuously, how much should be put in the plan now to pay for 1 year of college 15 years from now?
(Round to the nearest cent as needed)
Answers
the answer to part a is 72,114 this is because 7.4% of 34,179 is 2529 so 2529 multipled by 15 would give you 37,935 so now you must add 37,935 + 34,179 which would give you 72,114
part b) final balance is 76,115.22 and the compounded intrest is 4,001.22
Find the measure of the angle indicated. pls help
Answers
Answer:
85
Step-by-step explanation:
There is a property of angle of triangles.
Exterior angle = Sum of opposite interior angles
7x + 8 = 3x - 9 + 61
7x + 8 = 3x + 52
7x - 3x = 52 - 8
4x = 44
x = 44/4
x = 11
m∠WHG = 7x + 8
= 7 ( 11 ) + 8
= 77 + 8
m∠WHG = 85
Answer:
Angle WHG is 85 degrees.
Step-by-step explanation:
X = 11.
7(11) + 8 = 85.
180 - 85 = 95 (Angle FHG.)
3(11) - 9 = 24 (Angle GFH.)
A triangle's angles always add up to 180 degrees.
24 + 95 + 61 = 180.
To double check, 180 - 95 = 85 degrees.
I hope this helped! And as for finding X, I kind of forgot how to get X, so I tried X being number 5-10 first, then tried 11, and it worked. Sorry for the late response.
3x^4+2x^3-12x-6solve for ;x=-2
Answers
The function f(x) = 3x⁴ + 2x³ - 12x - 6 is equal to 60 for x = -2.
What is a expression? What is a mathematical equation? What is Equation Modelling?
A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the following equation -
[tex]3x^4+2x^3-12x-6[/tex]
We have -
f(x) = 3x⁴ + 2x³ - 12x - 6
for x = - 2
f(- 2) = 3(-2)⁴ + 2(-2)³ - 12(-2) - 6
f(-2) = 48 - 16 + 24 - 6
f(- 2) = 48 + 8 - 6
f(- 2) = 60
Therefore, the function f(x) = 3x⁴ + 2x³ - 12x - 6 is equal to 60 for x = -2.
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For the number line shown which statement is not true?
|d| <|c|
Ic|c|>c
|d| = d
Answers
Answer:
The answer is C
Step-by-step explanation:
it's always the one in the lines at least that's what my math teacher told me he said it's really easy All you have to do is pick the ones with the lines there's more to it when you're doing homework but when there's just like a few questions it's way easier
Type the correct answer in the box. Rewrite the quadratic function in the form that best reveals the zeros of the function.
Answers
Answer:
f(x) = (2x + 3)(2x + 1)
Explanation:
The form that best reveals the zeros of the function is:
f(x) = (x - a)(x - b)
Where a and b are the zeros of the function.
So, we need to apply the distributive property as:
[tex]\begin{gathered} f(x)=2(2x^2+4x)+3 \\ f(x)=2\cdot2x^2+2\cdot4x+3 \\ f(x)=4x^2+8x+3 \end{gathered}[/tex]
Then, we can factorize the quadratic function as:
[tex]f(x)=(2x+3)(2x+1)[/tex]
So, now we can identify the zeros of the function if we solve the following equation:
[tex]\begin{gathered} f(x)=(2x+3)(2x+1)=0 \\ 2x+3=0\rightarrow x=-\frac{3}{2} \\ or \\ 2x+1=0\rightarrow x=-\frac{1}{2} \end{gathered}[/tex]
Therefore, the form that best reveals the zeros in the function is:
f(x) = (2x + 3)(2x + 1)
You decide to invest $10,000 in an account where the interest compounds annually. Create an exponential function to represent how much money you will have after 20 years if the money grows at a rate of 7.5 percent
Answers
Apply the compound interest formula:
• A= P (1 + r/n)^nt
Where:
A = future value
P = Principal investment = $10,000
r = interest rate in decimal form = 7.5 /100 = 0.075
n= number of compounding periods per unit t = 1 (anually)
t= years = 20
Replacing:
A = 10,000 ( 1+ 0.075 )^20
17.09+3.98 estimated
Answers
Answer:
21.07
Step-by-step explanation:
Page 5.26, Problem 3: A baseball team had 80 players show up last year and this year had 96 players show up for tryouts. Find increase in players from last year to this year. Your answer.
Answers
In order to determne the increse in the number of players, estimate the percentage increase. Proceed as follow:
First, calculate the difference in the number of player:
96 - 80 = 16
next, determine what is the associated percentage of such difference:
(16/80)(100) = 20%
Hence, the percentage increase was of 20%
B. A concrete tank has an external diameter of 10 m and an internal height of 3 m. If the walls and bottom of the tank are 30 cm thick, how many cubic meters of concrete are required to make the tank? 10 m 30 cm 3 m 30 cm
Answers
The concrete required to make the tank be 27.4122 m³.
Given, a concrete tank has an external diameter of 10 m and an internal height of 3 m. If the walls and bottom of the tank are 30 cm thick.
External diameter = 10 m
Height = 3 m
Thickness = 0.3 m
External radius = 5 m
Internal radius = 5 - 0.3 = 4.7 m
Volume = πh(e.r² - i.r²)
Volume = (3.14)(3)(5² - 4.7²)
Volume = 9.42(9.7)(0.3)
Volume = 27.4122 m³
Hence, the concrete required to make the tank be 27.4122 m³.
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i need help i suck at dividing decimal
Answers
34.02 divided by 6.3 answer: 5.4
453.6 divided by 8.1 answer: 56
264.684 divided by 4.2 answer: 15.004
Answer: 1. 0.185185185 keeps going
2. 56
3. 63.02
Step-by-step explanation:
Factor completely, then place the factors in the proper location on the grid.
b2 - 7b + 12
Answers
Answer:
(b - 4)(b - 3)
Step-by-step explanation:
b² - 7b + 12
consider the factors of the constant term (+ 12) which sum to give the coefficient of the b- term (- 7)
the factors are - 4 and - 3 , since
- 4 × - 3 = + 12 and - 4 - 3 = - 7 , then
b² - 7b + 12 = (b - 4)(b - 3)
Mcm de 2,5,10,25 grupo de valores
Answers
i don't know the answer
How do you graph y=4x at x=-4? What does it look like on a graph
Answers
We want to plot the graph of the equation;
[tex]y=4x[/tex]
we can do this by assuming to different values of x and deriving the corresponding values of y at those points.
for x= -4;
[tex]\begin{gathered} y=4(-4) \\ y=-16 \end{gathered}[/tex]
Also taking a second point.
at x = 0;
[tex]\begin{gathered} y=4(0) \\ y=0 \end{gathered}[/tex]
Since the equation is a linear equation, the graph will be a straight line graph;
the graph will be a straight lin passing through the two points derived.
[tex](-4,-16)\text{ and (0,0)}[/tex]
the graph of the given equation can be shown below;
Step 3: determine if point c represents a solution
Answers
Point C (7 , 52.5) represents a solution of the equation of line y =7.5x
A point is a solution of the equation if and only if it satisfy the line equation.
To check point C is solution o it should satisfy the equation of line y = 7.5x
In point C , x = 7 and y = 52.5
putting x in equation of line and solving for y ,
y = 7.5(7)
y = 52.5
which is true so ,
The coordinates (7 , 52.5) make the equation true
so , (7,52.5) is a solution of y = 7.5x
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