Answer:
See proof below
Step-by-step explanation:
If B is the midpoint of AC, then AB = BC
If C is the midpoint of BD then BC = CD
Using the transitive property of equality, if a = b and b = c then a =c
We apply this to the above line segments and get
If AB = BC and BC = CD then AB=CD
For two line segments to be congruent they must have the same length
So AB is congruent to CD
how can you apply the Laws of Exponents to evaluate expressions that include integer exponents?
Exponent rules are those laws that are applied to exponent-based expressions to make them simpler. The principles of exponents make it simple and rapid to execute numerous arithmetic operations like addition, subtraction, multiplication, and division. These guidelines are also useful for reducing the complexity of numbers that have complex powers incorporating fractions, decimals, and roots.
Exponent rules, commonly referred to as the "laws of exponents" or "properties of exponents," facilitate the task of simplifying exponent-based statements. These guidelines are useful for reducing the complexity of expressions whose exponents are decimals, fractions, irrational numbers, or negative integers.
When an exponent is a negative number, we apply the negative law of exponents. This rule states, "The reciprocal should be taken to convert any negative exponent into a positive exponent." The change in sign of the exponent values moves the expression from the numerator to the denominator.
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the measure of an angle is 26.5 what is the measure of its complementary angle
Answer: 63.5
Step-by-step explanation:
90 - 26.5 = 63.5
how do I determine whether each linear relationship is a direct variation and if so how do I state the constant of proportionality.
Pictures, x 3
Profit, y 24
By using the given pair of values we can see that the constant of proportionality is 8, and the proportional relation is:
y = 8*x
How to determine the proportional relation?A proportional relation is a linear relation with an y-intercept of 0, so these are written as:
y = a*x
Where a is the constant of proportionality.
By knowing a pair of values x and y, we can find the value of a. In this case we can see that when x = 3, y = 24, replacing that in the general equation we get:
24 = a*3
24/3 = a = 8
Then the constant of proportionality is 8, and the proportional relation is:
y = 8*x
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What is the answer for 10x=4x + 5
I don't see why my answer got deleted from last time as nothing was wrong with it, but your answer is: x = 5/6.
--------------------------------------------------------
Hope this helps!
Have a great day and God bless! :)
Please help me asap!!!!
Answer:
Option 1
Step-by-step explanation:
Perpendicular lines form right angles
Eliminate Options 3 and 4.Parallel lines never intersect.
Eliminate Option 2.Solve please? I'm struggling haha
Answer:
Hello,
Answer d
Step-by-step explanation:
Since x=y then 3v-1=2v+6 ==> v=7
Answer d
juan rolls a fair regular octahedral die marked with the numbers $1$ through $8$. then amal rolls a fair six-sided die. what is the probability that the product of the two rolls is a multiple of $3$?
The probability that the product of the two rolls is a multiple of 3 is 1/2.
Probability:
Probability mean the fraction of the possibility of the required event.
The formula for the probability is
P(E) = n(E)/n(S)
Where
P(E) = Probability of the event
n(E) = number of required event
n(S) = Total number of event
Given,
Juan rolls a fair regular octahedral die marked with the numbers 1 through 8.
Then Amal rolls a fair six-sided die.
Here we need to find the probability that the product of the two rolls is a multiple of 3.
We know that,
On both dice, only the faces with the numbers 3,6 are divisible by 3.
Let
P(a) = 2/8
P(a) = 1/4
it is the probability that Juan rolls a 3 or a 6,
and Similarly,
P(b) = 2/6
P(b) = 1/3
Is the probability of Amal does.
By the Principle of Inclusion-Exclusion,
[tex]\[P(a \cup b) = P(a) + P(b) - P(a \cap b) = \frac{1}{4} + \frac{1}{3} - \frac{1}{4} \cdot \frac{1}{3} = \frac{1}{2} \Rightarrow \mathrm{(C)}\][/tex]
Thus the total probability is 1/2.
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What is the value of n? 9.6x10^9=(2x10^5)(4.8x10^n)
[tex]9.6\times 10^9~~ = ~~(2\times 10^5)(4.8\times 10^n)\implies \cfrac{9.6\times 10^9}{2\times 10^5}~~ = ~~4.8\times 10^n \\\\\\ \cfrac{9.6}{2}\times \cfrac{10^9}{10^5}~~ = ~~4.8\times 10^n\implies 4.8\times 10^{9-5}~~ = ~~4.8\times 10^n \\\\\\ 4.8\times 10^4~~ = ~~4.8\times 10^n\implies \cfrac{4.8\times 10^4}{4.8}=10^n\implies \cfrac{4.8}{4.8}\times 10^4=10^n \\\\\\ 1\times 10^4=10^n\implies 10^4=10^n\implies 4 = n[/tex]
Factor
completely 3x^4 30x^3 + 75x^2
PLS HELP!
The factors of the expression is 3x²(x+5)(x+5) .
Factors of a number are defined as the numbers which divide the given number completely.
For an algebraic expression the factors of the expression are smaller polynomials which divide the given expression completely.
Factors of algebraic expression can be calculated by the following methods:
Middle-term factorizationcompletion of squareUsing factor theoremThe given polynomial is of the form:
3x⁴ + 30x³ + 75x²
Taking 3x² common from all the terms we get:
3x² (x² + 10x + 25)
Now we use middle- term factorization method to factor (x² + 10x + 25)
3x² (x² + 5x + 5x + 25)
or, ( 3x² ){x ( x + 5 ) + 5 ( x + 5 )}
or, 3x² (x + 5) (x + 5)
or, 3x² (x + 5)²
Hence the factors of the expressions are: 3x² (x + 5)²
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Factor completely: 3x⁴ + 30x³ + 75x²
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for a given non-zero vector v in r 3 there is a unique unit vector parallel to it. is it true or false? explain your answer.
The given statement is true that for a given non-zero vector v in r³ there is a unique unit vector parallel to it.
A vector is defined by its length and direction. If two vectors have the same direction, they are parallel. The length is irrelevant.If the length of a vector is one, it is a unit vector. The direction is irrelevant.So, in order to locate a unit vector parallel to another vector, it must point in the same direction and be of length 1.For a given non-zero vector, there are an infinite number of parallel vectors to it but with different magnitudes. There is only one vector which is not only parallel to the given non-zero vector but also has a magnitude of 1, i.e., the unit vector parallel to it.Thus, it is true that for a given non-zero vector v in r³ there is a unique unit vector parallel to it.To learn more about vectors, visit :
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Mrs. Banks wants to make 44 qt of jelly with 70 lb of fruit. If each gallon of jelly needs 6
6
12
1
2
lb of fruit, will she have enough fruit? How much leftover fruit does she have, or how much more fruit is needed? Use the conversion factor 1 gallon4 quarts
1
gallon
4
quarts
Answer:
6
12
1
2
Step-by-step explanation:
In 1, is 4. Okay, this a good answer.
$. Compare the costs of Spa Treatment A ($210) to Spa Treatment B ($250) in both absolute
and relative terms.
(a) Absolute Difference = $40; Relative Difference = 16%
(b) Absolute Difference = $40; Relative Difference = 19%
(c) Absolute Difference = -$40; Relative Difference = -16%
The Absolute Difference and the Relative Difference is mathematically given as
Absolute Difference = $40;
Relative Difference = 19%. Option B
This is further explained below.
What is Relative Difference?Generally, Divide the difference in values by the value that was used initially, and you will get the relative difference between the two values: difference original value
Perform the conversion to get a percentage out of this amount. If there was a rise in value, we would say there was an increase of x %.
We state there was an x % decline in the value if there was a decrease in the value. x represents the number that was arrived at by us.
In conclusion, since we are comparing A from be we have
Absolute Difference = 250-210
Absolute Difference = $40;
and
Relative Difference = (Original-ref)/ref
Therefore
Relative Difference 250-210/210
Relative Difference=19%
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find point G on AB such that the ratio of AG to GB is 3:2
The point G on AB such that the ratio of AG to GB is 3:2 is; G(4.2, 2)
How to partition a Line segment?
The formula to partition a line segment in the ratio a:b is;
(x, y) = [(bx1 + ax2)/(a + b)], [(by1 + ay2)/(a + b)]
We want to find point G on AB such that the ratio of AG to GB is 3:2.
From the graph, the coordinates of the points A and B are;
A(3, 5) and B(5, 0)
Thus, coordinates of point G that divides the line AB in the ratio of 3:2 is;
G(x, y) = [(2 * 3 + 3 * 5)/(2 + 3)], [(2 * 5 + 3 * 0)/(2 + 3)]
G(x, y) = (21/5, 10/5)
G(x, y) = (4.2, 2)
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pls solve this question step by step solution.
Answer:
42, 12)
Step-by-step explanation:
Let the present ages of the father and son be x years and y years respectively.
According to the question,
Condition I,
Three years ago the sum of the ages of the father and his son was 48 years.
or,(x−3)+(y−3)=48
or,x−3+y−3=48
or,x−6=48−y
or,x=54−y - (i)
Condition II,
Three years hence the father's age will be three times the son's age,
or,(x+3)=3(y+3)
or,x+3=3y+9 - (ii)
Put value of x from equation (i) in equation (ii), we get,
or,(54−y)+3=3y+9
or,54−y=3y+9−3
or,54−6=3y+y
or,48=4y
or,y=484
∴y=12
Put the value of y in equation (i), we get,
or,x=54−12
∴x=42
So, (x,y) = (42, 12)
Therefore, the required present ages of the father and the son are 42 years and 12 years respectively.
Use the picture below to solve for the missing information, given PQ = 2x + 8, QR = x + 11, and PR = 5x - 3.
Someone please help, BE SPECIFIC on the answers & how you got them, with a explanation. (please fill in all the blanks, thank you)
NO TROLLING. please.
(For geometry class by the way, we're learning about segments).
Given that Q is a point between P and R, the numerical values of x, segment PQ, QR and PR are 11, 30, 22 and 52 respectively.
What are the numerical values of x, segment PQ, QR and PR?Given the data in the question;
Q is a point between P and RSegment PR = 5x - 3Segment PQ = 2x + 8Segment QR = x + 11Numerical value of x, segment PQ, QR and PR = ?Since Q is a point between P and R.
PR = PQ + QR
Plug in the given values and solve for x.
5x - 3 = ( 2x + 8 ) + ( x + 11 )
5x - 3 = 2x + 8 + x + 11
5x - 3 = 3x + 19
5x - 3x = 19 + 3
2x = 22
x = 22/2
x = 11
Numerical value of segment PQ when x = 11 will be;
PQ = 2x + 8 = 2(11) + 8 = 30
Numerical value of segment QR when x = 11 will be;
QR = x + 11 = (11) + 11 = 22
Numerical value of segment PR when x = 11 will be;
PR = 5x - 3 = 5(11) - 3 = 52
Given that Q is a point between P and R, the numerical values of x, segment PQ, QR and PR are 11, 30, 22 and 52 respectively.
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Find the equation of the linear function represented below in the slope intercept form.
to get the equation of any straight line, we simply need two points off of it, let's use those two points off the table in the picture below.
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{18})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-22}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-22}-\stackrel{y1}{18}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-4)}}} \implies \cfrac{-40}{6 +4} \implies \cfrac{ -40 }{ 10 }\implies -4[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{18}=\stackrel{m}{-4}(x-\stackrel{x_1}{(-4)})\implies y-18=-4(x+4) \\\\\\ y-18=-4x-16\implies y=-4x+2[/tex]
Write the equation of the line in slope-intercept form that passes through the points (5,3) and (1,−5).
Answer:
y = −2x + 8
Step-by-step explanation:
y = −2x + 8, the answer is this because, in order to find the slope, you must use the formula y2-y1/x2-x1, and the y-intercept is found by using the formula y=mx+b, in which b is the y-intercept which leads to the awnser, y = −2x + 8.
Hi! Your answer is y = −2x + 8
Step-by-step explanation:
In order to find the slope, you have to use y2-y1/x2-x1 for the formula. The y-intercept can be found by using the formula y=mx+b. This means b is the y-intercept which makes the answer: y = −2x + 8.
Hope this helps! Have a good day :)
Simplify:(4x^2 - 2x) - (-5x^2 - 8x)
aye could yall help a brother out?
Answer: 9x^2+6x
Step-by-step explanation:
(4x^2 - 2x) - (-5x^2 - 8x)=
4x^2 - 2x +5x^2 + 8x=
4x^2+5x^2 - 2x + 8x=9x^2+6x
the angle of elevation to the top of a very tall building is found to be 11° from the ground at a distance of 1 mi from the base of the building. using this information, find the height of the building. (round your answer to the nearest foot.)
The height of the building = 1026.328ft
Given the angle of elevation = 11°
The angle of elevation is the angle formed between the horizontal distance to the base of the building and the line of sight to the top of the building.
We know that tan x = opposite side/adjacent side.
Here the opposite side gives the height of the building and the adjacent side is the distance to the base of the building on the ground.
Distance to the base of the building on the ground = 1 mile = 5280 ft.
So tan 11° = h/5280
⇒ h= tan 11° x 5280 = 0.194 x 5280 = 1026.328 ft
So the height of the building = 1026.328 ft
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¿Cuál de las siguientes expresiones es equivalente a 6 x (4+5)
Answer:
es equivalente al es 54x
i need help with this question asap
Answer:
x² + y² = z²
Step-by-step explanation:
(a)
Using the right triangle altitude theorem,
x/z = p/x
x² = pz
(b)
y/z = q/y
y² = qz
(c)
x² + y² = pz + qz
x² + y² = z(p + q)
z = p + q
x² + y² = z × z
x² + y² = z²
[tex]x {}^{2} + 2x + 6 = 0[/tex]
please give me answer.....
Answer:
[tex]\sf x = -1 + \sqrt{5}\:i,\: -1 - \sqrt{5}\:i[/tex]
Explanation:
[tex]\sf \rightarrow x^2 + 2x +6 = 0[/tex]
[tex]\sf use\:quadratic\:formula: x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad when \: \: ax^2 + bx + c = 0[/tex]
comparing identify:
a = 1, b = 2, c = 6Substitute inside the formula:
[tex]\rightarrow \sf x = \dfrac{ -2 \pm \sqrt{2^2 - 4(1)(6)}}{2(1)}[/tex]
evaluate:
[tex]\rightarrow \sf x = \dfrac{ -2 \pm \sqrt{4 - 24}}{2}[/tex]
[tex]\rightarrow \sf x = \dfrac{ -2 \pm \sqrt{- 20}}{2}[/tex]
[tex]\rightarrow \sf x = \dfrac{ -2 \pm 2\sqrt{5}\:i}{2}[/tex]
[tex]\rightarrow \sf x =-1 \pm \sqrt{5}\:i[/tex]
[tex]\rightarrow \sf x = -1 + \sqrt{5}\:i,\: -1 - \sqrt{5}\:i[/tex]
what are the two major advantages of experimental research over correlational studies? multiple select question. experiments are more efficient. causal relationships can be inferred. random assignment is possible. sample size is always greater in experiments.
The experimental research has two key advantages over correlational studies.
1. The possibility of random assignment
2. Causal connections can be assumed.
What benefit does experimental research have over correlational research?Correlational studies merely examine the data that already exists, whereas experimental studies give the researcher the opportunity to influence the study's factors. Researchers can make inferences about how changes in one variable affect changes in another through the use of experimental investigations.
The factors in a correlation study are out of the control of the researcher or research team. The researcher merely measures the information she discovers in the outside world. She can then determine whether changes in one are related to changes in the other, or if the two variables are correlated. In such a study, experimenters gather existing data and use statistical methods to examine it, such as economic statistics from governments. The findings of correlation studies can lead to hypotheses that can be verified through a more focused experimental one.
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On a number line, point A is at 5, and point B is at -10. Point C is on AB such that the ratio of AC to CB is 1: 3. Find D on BC such that the ratio of BD to DC is 3:5.
The location of point D on the number line is -5.15625
How to determine the location of point D?The given parameters are:
A = 5
B = -10
AC : CB = 1 : 3
This means that
C = AC/(AC + AB) * (A - B)
This gives
C = 1/4 * (5 + 10)
Evaluate
C = 3.75
Also, we have:
BD : DC = 3 : 5
So, we have:
D = BD/(BD + DC) * (B - C)
This gives
D = 3/8 * (-10 - 3.75)
Evaluate
D = -5.15625
Hence, the location of point D on the number line is -5.15625
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Please help me with this page
Answer:
a) A = 1, C = 0, and D > 0 --> Graph B
b) A = 1, C = 0, and D < 0 --> Graph C
c) A > 1, C > 0, and D > 0 --> Graph D
d) 0 < A < 1, C < 0, and D < 0 --> Graph A
( b ) = 2/3 Please help me solve this equation
Answer:
b=2/3
Step-by-step explanation:
Let's solve the equation step by step
( b ) = 2/3
Remove bracket
b=2/3
HELP ASAP
BX bisects
Answer: 124 degrees ==> Option 3
Step-by-step explanation:
ABC=ABX+XBC
ABX=XBC ==> bisected angles are equal since when an angle is bisected, it is divided into two equal angles. Hence:
ABC=XBC*2
ABC=62*2
ABC=124 degrees ==> Option 3
is y=x+8 a inverse variation
It should be noted that y=x+8 is not an inverse variation.
What is an inverse relation?The relationships between variables that are expressed in the form of y = k/x, where x and y are two variables and k is a constant number, are known as inverse variations. According to this statement, if the value of one item rises, the value of the other quantity falls.
Ab example is when a constant of variation is k = xy = 5(2) = 10 if y changes inversely as x and x = 5 when y = 2. Consequently, xy = 10 is the equation that describes this inverse variation.
Therefore, it should be noted that y=x+8 is not an inverse variation.
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find the intrest for Rs. 10,000 for 2 ½ yrs at 5% per annum compounded annually.
Answer:
Interest = Rs. 1297.26
Step-by-step explanation:
To calculate the final amount, we can use the following formula:
[tex]\boxed{A = P(1 + \frac{r}{100})^n}[/tex],
where:
A = final amount
P = principal (initial) amount
r = rate
n = time in years,
and then we can subtract the initial amount from the final amount to find the interest.
We have been told in the question that the principal, P = Rs. 10,000; and the time is [tex]2\frac{1}{2}[/tex] years, therefore n = 2.5. The rate is 5%, therefore r = 5.
Using this information, and the formula above, we can calculate the final amount:
[tex]A = 10000(1 + \frac{5}{100})^{2.5}[/tex]
⇒ [tex]A = 10000(1.05)^{2.5}[/tex]
⇒ [tex]A = \bf 11297.26[/tex]
Now that we know what the final amount was, we can calculate the interest by subtracting the initial amount from it:
Interest = 11297.26 - 10000
= 1297.26
Therefore the interest was Rs. 1297.26.
odeling with Mathematics
angle.
4
S
In Exercises 9-12, find the angle measure. Then classify
the angle. (See Example 2.)
9. mZAOC
11. m/COD
40 50 60 70 80 90 100 110 120 130
140 130 120 110 100 90 80 70 60 50
10 20
10 170 160 150 1
A
C
D
E
30 20 10
150 160 170 180
B
성향
10. m/BOD
12. mZEOD
Answer: Give me 11 min
Step-by-step explanation: