The description below proves that the perpendicular drawn from the vertex angle to the base bisect the vertex angle and base.
How to prove an Isosceles Triangle?Let ABC be an isosceles triangle such that AB = AC.
Let AD be the bisector of ∠A.
We want to prove that BD=DC
In △ABD & △ACD
AB = AC(Thus, △ABC is an isosceles triangle)
∠BAD =∠CAD(Because AD is the bisector of ∠A)
AD = AD(Common sides)
By SAS Congruency, we have;
△ABD ≅ △ACD
By corresponding parts of congruent triangles, we can say that; BD=DC
Thus, this proves that the perpendicular drawn from the vertex angle to the base bisect the vertex angle and base.
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Peaches are being sold for $2 per pound.The customer created a model to represent the total cost of peaches bought. If x represents the number of pounds of peaches bought and y represents the total cost of the peaches, which best describes the values of x and y?
The values of both x and y can be any real number.
The values of both x and y will be real numbers greater than or equal to 0.
The value of x and y will always be zero
The value of x can be any real number greater than or equal to 0, but the value of y must be an integer greater than or equal to 0.
Mark this and return
The thing that best describes the values of x and y is option B; they will be real numbers greater than or equal to 0.
What is a Real Number?The real number refers to the union of both rational and irrational numbers that can have negative or positive values.
From the given information:
Peaches are being bought and sold for $2 per pound.
There is no negative value used here if x represents the number of pounds of peaches bought and y represents the total cost of the peaches.
Thus, a conclusion that can be reached as to the values of x and y is that they contain real numbers greater than or equal to 0.
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Answer:
im pretty sure its d
Step-by-step explanation:
----- ______------
Please help!!!!!!!!! in the similarity transformation of abc to def, abc was dilated by a scale factor of ?, reflected across the , and moved through the translation. i need help with the last portion of the question.
The complete similarity transformation is: triangle abc was dilated by a scale factor of [2], reflected across the [x-axis], and moved through the translation [0].
What is Similarity?When it comes to Euclidean geometry, two things are said to be comparable if they have the same shape or the same shape as each other's mirror image. More specifically, by uniformly scaling (enlarging or decreasing), maybe with additional translation, rotation, and reflection, one can be created from the other. This indicates that one object may be properly aligned with the other object by rescaling, moving, and reflecting it. When two things are comparable to one another, one is consistent with the outcome of a specific uniform scaling of the other.From the figure, we have:
AB = 2 units
DE = 4 units
So, the scale factor (k) is:
k = DE/AB
k = 4/2
k = 2
Also, both shapes are on either sides of the x-axis, and they are equidistant from the x-axis.
This means that the triangle is reflected across the x-axis with no translation.
Hence, the complete similarity transformation is: abc was dilated by a scale factor of [2], reflected across the [x-axis], and moved through the translation [0].
So, the scale factor is 2
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What is the slope of the line through (-1, 4) and (1, -2)?
-3 -2
3
-1
-2
-3
y
2
(1,-2)
3
4
9+10=21
Yes, my calculation says , it is possible.
But only in other number base.
Let me explain.
9 + 10 = 21
or, 19 = 21
Assume that , 19 is a decimal number.
and 21 is a n base number.
As 19 is equivalent to 21,
So 10 base 19 is equivalent to n base 21.
So with the help of math I can get that,
19 = 1 × 10^1 + 9× 10^0
21 = 2 ×n^1 + 1×n^0 = 2n + 1
So , 2n + 1 = 19
or, 2n = 18
or, n = 9
So finally, we can say that,
10 base 19 = 9 base 21
Thus 9+10=21 is possible
The reason why people sometimes assume that the calculation 9 + 10 = 21 is as explained below.
How to calculate in number bases?We want to find out the reason why people say that; 9 + 10 = 21
Now, the way you have explained it is one way to look at it by utilizing number bases to play around with the figures to arrive at 21.
However, another way is to use algebra trick pattern which is;
9 can be expressed as 3 * 3
Also, 10 can be expressed as 5 * 2. Thus, we now have;
(3 * 3) + (5 * 2)
The applying properties of algebra to cross multiply gives;
(3 * 2) + (5 * 3)
= 6 + 15
= 21
Now, though your explanation arrived at 21 and mine also 21, but those are not correct mathematical methods as 9 + 10 must be equal to 19 and not 21.
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The total cost of 2 novels and 4 fiction books is $84. Each novel costs $6 more than each fiction book. What is the total cost of a novel and a fiction book?
Answer:
$30
Step-by-step explanation:
Let,
x - fiction book
x + $6 - novel
EQUATION:
4(x) + 2(x + $6) = $84
6x + $12 = $84
6x = $84 - $12
6x = $72
x = $12
SUBSTITUTE:
novel = $12
fiction = $18
TOTAL COST OF NOVEL AND FICTION
$18 + $12 = $30
The table shows certain values of a cubic function
Use the table to complete the statements.
The function has a relative maximum when x is near... -1, 3,-3, 7, or -7
As x approaches positive infinity, the value of the function approaches... negative infinity, positive infinity or zero.
Considering the given table, we have that:
The function has a relative maximum when x is near 3.As x approaches positive infinity, the value of the function approaches negative infinity.When a function has a relative maximum?A function has a relative maximum when it changes from increasing to decreasing.
Looking at the given table, it happens when x is near 3.
Also, looking at the table, for x > 3 the function is decreasing, hence as x approaches positive infinity, the value of the function approaches negative infinity.
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prove the diagonals of a square are perpendicular
Answer:
Given :- ABCD is a square.
To proof :- AC = BD and AC ⊥ BD
Proof :- In △ ADB and △ BCA
AD = BC [ Sides of a square are equal ]
∠BAD = ∠ABC [ 90° each ]
AB = BA [ Common side ]
△ADB ≅ △BCA [ SAS congruency rule ]
⇒ AC = BD [ Corresponding parts of congruent triangles are equal ]
In △AOB and △AOD
OB = OD [ Square is also a parallelogram therefore, diagonal of parallelogram bisect each other ]
AB = AD [ Sides of a square are equal ]
AO = AO [ Common side ]
△AOB ≅ △ AOD [ SSS congruency rule ]
⇒ ∠AOB = ∠AOD [ Corresponding parts of congruent triangles are equal]
∠AOB + ∠AOD = 180° [ Linear pair ]
∠ AOB = ∠AOD = 90°
⇒ AO ⊥ BD
⇒ AC ⊥ BD
Hence proved, AC = BD and AC ⊥BD
If the machine can produce 280 inches of ribbon in 30 minutes, approximately
how many feet can it produce in an 8 hour work day?
O 328 feet
O 358 feet
O 373 feet
O 309 feet
Answer:
373 feet
Step-by-step explanation:
Since the rate of the machine producing ribbon is proportional to time, we can determine the number of inches of ribbon in 8 hours by some quick operations.
There are 16 1/2 hours in 8 hours, so we can multiply 280 by 16.
[tex]280 *16=4480[/tex]
Now, we have the number of inches it can produce in an 8-hour work day. However, we must convert to feet since that is the form of measurement the question is asking for. We can do so by dividing by 12.
[tex]4480/12=373.33[/tex]
Therefore, the number of feet the machine can produce in an 8-hour work day is 373.
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Step-by-step explanation:
the other answer is correct.
a few add-ons :
1 ft = 12 in
30 minutes = 1/2 hour (as every hour has 60 minutes)
every hour has therefore 2 half hours.
1 hour = 2 × 1/2 hour
8 hours = 8 × 2 × 1/2 hours = 16 × 1/2 hour
so, in 16 times the amount of time (8 hours) the machine can produce 16 times the amount of ribbon (16 × 280 in).
16 × 280 = 4480 in
and because every 12 in is 1 ft, this is then
4480/12 = 373.3333333... ft
therefore, 373 is the right answer (rounded).
A step function h(x) is represented by y = -2[x]. Which phrase best describes the range of the function h(x)
O all real numbers
O all rational numbers
O all negative integers
all even integers
Mark this and return
Save and Exit
lext
Subm
The range of the step function is all negative integers, thus, the correct option is A.
What are domain and range of a function ?Domain is the set of values for which the given function is defined.
Range is the set of all values which the given function can output.
For the given function h(x)=-2|x|, any value of x will return a negative value, therefore, the range of the function is all negative numbers. This can be observed in the graph given below.
Hence, the range of the step function is all negative integers, thus, the correct option is A.
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Please help ill give whoever answers the best the brainliest answer :)
Answer:
The 3rd graph from the top.
Step-by-step explanation:
Just Like the story, the third graph goes up slowly and plateaus for the duration of a school day, then goes back down quicker than it went up.
Volume = in2
Help me please
What is the volume
Answer: 1344
Step-by-step explanation:
Using the Pythagorean theorem, if we consider the unknown leg of the base, we get that it has a length of 12.
So, the area of the base is 96.
Multiplying this by the height, we get the volume is 1344 cubic inches.
In construction, the precision used to build a structure directly influences the strength of the structure. In the Rocky Mountains, many houses’ roofs are built using trusses, which are strong enough to support the heavy load from snow, but light enough to build in a stockyard and transport to the construction site. Chris works in the stockyard. He has been told he needs to build a series of trusses for a new house using the pattern below. He has also been told the pattern may be inaccurate—so he needs to check and make sure the following features are all parallel, and adjust the pattern before starting.
On this discussion board, post your answers to these questions:
1) What method(s) can Chris use to make sure the segments in the pattern are all parallel and that his new trusses are built precisely and strongly?
2) What method(s) can Chris’s boss use to verify the precision of the trusses Chris builds?
3)Identify any alternate interior angles, corresponding angles, and/or alternate exterior angles.
The method that Chris can use to make sure the segments in the pattern are all parallel is to treat AI as a single line that acts as a transversal for the lines that need to be parallel.
How to illustrate the information?Within the set of lines which need to be parallel, the acute angles must be congruent.
Both angles CDE and EDF need to be 180° minus twice the measure of one of the congruent acute angles.
The pair of the acute angles previously within each of the two sets of parallel lines are corresponding.
The fact that the transversals go through endpoints, there are no alternate angles, interior or exterior because alternate angles are on opposite sides of the transversal.
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Help please I will mark brainliest
(a) Using Fermat's little theorem, show that 999 999 is divisible by 7.
(b) A number has digits that are all 9 and is divisible by 13. Show that
it is also divisible by 1001.
(a) Fermat's little theorem states that for any prime [tex]p[/tex], we have
[tex]a^{p-1} \equiv 1 \pmod p[/tex]
for any integer [tex]a[/tex]. Then
[tex]999,999 \equiv 1,000,000 - 1 \equiv 10^6 - 1 \equiv 1 - 1 \equiv 0 \pmod 7[/tex]
so 7 does indeed divide 999,999.
(b) Generalizing, we have
[tex]10^{12n} - 1 \equiv \underbrace{999\ldots999}_{12n \text{ nines}} \equiv (10^n)^{12} - 1 \equiv 0 \pmod {13}[/tex]
for positive integer [tex]n[/tex]. Now, since 1 = 1001 - 1000 and [tex]-1\equiv1000\pmod{1001}[/tex], it follows that [tex]10^3[/tex] is its own inverse modulo 1001, i.e.
[tex]10^3 x \equiv 1\pmod{1001} \implies x = 10^3[/tex]
This means
[tex]10^{12n} \equiv (10^3\times10^3)^{2n} \equiv 1^{2n} \equiv 1\pmod{1001} \\\\ \implies 10^{12n} - 1 \equiv 0 \pmod{1001}[/tex]
which is what we wanted to show.
In ABC, side BC is extended to point E. When connected to vertex A, segment EA is parallel to segment BD. In this construction, you are given that BD bisects
Two triangles are said to be congruent if they have similar properties. Thus the required options to complete the paragraph proof are:
a. angle 1 is congruent to angle 2.
b. alternate angles are congruent if two parallel lines are cut by a transversal.
c. [tex]\frac{AD}{CD}[/tex] = [tex]\frac{AB}{CB}[/tex]
The similarity property of two or more shapes implies that the shapes are congruent. Thus they have the same properties.
From the given diagram in the question, it can be deduced that
ΔABC ≅ ΔABE (substitution property of equality)
Given that EA is parallel to BD, then:
i. <2 ≅ <3 (corresponding angle property)
ii. <1 ≅ < 4 (alternate angle property)
Thus, the required options to complete the paragraph proof are:
Angle 1 is congruent to angle 2.Alternate angles are congruent if two parallel lines are cut by a transversal.[tex]\frac{AD}{CD}[/tex] = [tex]\frac{AB}{CB}[/tex]For more clarifications on the properties of congruent triangles, visit: https://brainly.com/question/1619927
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By selling my car for sh 276000,the price was below the initial price. What is the initial price?
The initial price in this scenario is > sh 276000 and was therefore sold at a loss.
What is Loss?This is a situation in which the selling price of goods or services is lower than the cost price.
We were told that the selling price is sh 276000 which is less than the initial(cost) price hence he ran at a loss during the business transaction.
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Please help! Most Beagles have shoulder heights between 36 and 41 centimeters. The following compound inequality relates the estimated shoulder height (in centimeters) of a dog to the internal dimension of the skull D (in cubic centimeters):
36 ≤ 1.02D – 31.2 ≤ 41
Which compound inequality represents the range for the skull size of Beagles? Answer choices are rounded to the nearest tenth.
Answer: B
Step-by-step explanation:
Given:
36=<1.02D-31.2<=41
Solve the compound inequality for D:
36+31.2<=1.02D<=41+31.2
67.2<=1.02D<=72.2
65.9<=D<=70.8
Therefore, option (b) is correct answer
Two cards are chosen at random from a deck of 52 cards. What is the probability of
choosing a red jack at first and then choosing a red card without replacement?
We gujra weeeeeeee
We gujra weeeeeeee
We gujra weeeeeeee
We gujra weeeeeeee
f(x) = 3x+2
What is f(5)?
Answer:
f(5)=17
Step-by-step explanation:
if,f(x)=3x+2
Then,f(5)=3*5+2
f(5)=17
at first decreased by 60% now increased by 80%
Answer:
72Step-by-step explanation:
at first decreased by 60% now increased by 80%
100 - 60% = 40
40 + 80% =
40 + 40 :100 * 80 =
40 + 32 =
72
A flagpole casts a shadow 22 feet long. If a man 6 feet tall cast a shadow 4.3 feet long at the same time, how tall is the flagpole? Please explain your answer.
Answer:
30.70 ft
Step-by-step explanation:
For shadow problems, we make the assumption that an object's height and its shadow length are proportional.
SetupThe proportion for the two objects is ...
height/shadow = pole/(22 ft) = (6 ft)/(4.3 ft)
SolutionMultiplying by 22 ft, we find the pole height to be ...
pole = (22 ft)(6 ft)/4.3) ≈ 30.70 ft
The flagpole is about 30.70 feet tall.
For the following exercises, determine whether each of the following relations is a function.
2. {(2, 1), (3, 2), (−1, 1), (0, −2)}
Answer:
The relation {(2,1),(3,2),(-1,1),(0,-2)} is a function because the domain {2,3,-1,0} and range {1,2,1,-2} of the relation is paired exactly only once.
Step-by-step explanation:
The given relation is {(2,1),(3,2),(-1,1),(0,-2)}.
It is required to determine the relation is a function.
Step 1 of 1
The given relation is {(2,1),(3,2),(-1,1),(0,-2)}.
This relation shows that the domain of the relation {2,3,-1,0} is paired with one element of the range {1,2,1,-2}.
Hence, the relation is a function.
Someone PLEASEEEEE HELP!! :(
The equation that represents the line that passes through the points is [tex]y-1 = \frac{5}{4}(x-1)[/tex]. The correct option is D. [tex]y-1 = \frac{5}{4}(x-1)[/tex]
Equation of a lineFrom the question, we are to determine the equation of the line that passes through the given points
Using the formula
[tex]\frac{y-y_{1} }{x-x_{1}} =\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
From the give information,
[tex]x_{1} = 1 \\y_{1} = 1\\{x_{2} =5[/tex]
[tex]y_{2} = 6\\[/tex]
Putting the parameters into the formula,
[tex]\frac{y-1 }{x-1} =\frac{6-1}{5-1}[/tex]
[tex]\frac{y-1 }{x-1} =\frac{5}{4}[/tex]
∴ [tex]y-1 = \frac{5}{4}(x-1)[/tex]
Hence, the equation that represents the line that passes through the points is [tex]y-1 = \frac{5}{4}(x-1)[/tex]. The correct option is D. [tex]y-1 = \frac{5}{4}(x-1)[/tex]
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Evaluate the expression if a = 3, b = 4, and c = 2. Simplify, if possible
a = 3, b = 4, and c = 2
a + b = c
3 + 4 = 2
3a + 4b = 2c
-4 -4
3a = -6c
3 3
a = -2
3a + 4b = 2c
-3 -3
4b = -1c
4 4
36. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.
36. x-intercept at (-2, 0) and y-intercept at (0, -3)
Answer:
The linear equation for the line with an x - intercept at (-2,0) and y-intercept at (0,-3) is found as [tex]$y=-\frac{3}{2} x-3$[/tex].
Step-by-step explanation:
A condition is given that a line has an x- intercept at (-2,0) and y - intercept at (0,-3).
It is asked to find a linear equation satisfying the given condition.
Step 1 of 2
Determine the slope of the line.
The points of the intercepts of the line are given as (-2,0) and (0,-3). Next, the formula for the slope is given as,
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
Substitute -3&0 for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and 0&-2 for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,
[tex]$$\begin{aligned}m &=\frac{-3-0}{0-(-2)} \\m &=\frac{-3}{2} \\m &=-\frac{3}{2}\end{aligned}$$[/tex]
Step 2 of 2
Write the equation in the slope-intercept form.
The slope-intercept form of a line is given as follows,
y=mx+b
The coordinates at the y- intercept is (0,-3). Now, as the y- coordinate is -3, so b=-3.
So, substitute -3 for b and [tex]$-\frac{3}{2}$[/tex] for m in the equation y=mx+b, and simplify to get the equation as follows,
[tex]$$\begin{aligned}&y=-\frac{3}{2} x+(-3) \\&y=-\frac{3}{2} x-3\end{aligned}$$[/tex]
This is the required linear equation.
At lincoln high school, the probability that a student takes both art and music is 9%. the probability that a student takes music is 12%. what is the probability that a student takes art, given that the student takes music?
The probability that a student takes art, given that the student takes music is 10.8%
In probability, we say two events are independent if knowing one event occurred doesn't change the probability of the other event.
For example, the probability that a fair coin shows "heads" after being flipped is 1/21/21, slash, 2. What if we knew the day was Tuesday? Does this change the probability of getting "heads?" Of course not. The probability of getting "heads," given that it's a Tuesday, is still 1/21/21, slash, 2. So the result of a coin flip and the day being Tuesday are independent events; knowing it was a Tuesday didn't change the probability of getting "heads."
Two events, A and B, are independent if
P(A ∣ B)=P(A)
P(A).P(B) = P(A ∩ B)
In the given question there are independent events.
Given:-
P(A) = Student takes both art and music = 0.9
P(B) = Student takes music = 0.12
P(A ∩ B) = student takes art, given that the student takes music
Thus by using the formula we get,
P(A ∩ B) = 0.9 x 0.12 = 0.108 = 10.8%
The probability that a student takes art, given that the student takes music is 10.8%
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Which ordered pair makes both inequalities true?
y > –2x + 3
y < x – 2
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 2) and (2, 0). Everything to the right of the line is shaded. The second dashed line has a negative slope and goes through (0, 3) and (1, 1). Everything to the right of the line is shaded.
(0,0)
(0,–1)
(1,1)
(3,0)
The ordered pair which makes both inequalities true is: D. (3, 0).
How to determine ordered pair?In Mathematics, an inequality can be used to show the relationship between two (2) or more integers and variables in an equation.
In order to determine ordered pair which makes both inequalities true, we would substitute the points into the inequalities as follows:
At (0, 0), we have:
y > -2x + 3
0 > -2(0) + 3
0 > 3 (false).
y < x – 2
0 < 0 - 2
0 < -2 (false)
At (0, -1), we have:
y > -2x + 3
-1 > -2(0) + 3
-1 > 3 (false).
y < x – 2
-1 < 0 - 2
-1 < -2 (false)
At (1, 1), we have:
y > -2x + 3
1 > -2(1) + 3
1 > -1 (true).
y < x – 2
1 < 1 - 2
1 < -1 (false)
At (3, 0), we have:
y > -2x + 3
0 > -2(3) + 3
0 > -3 (true).
y < x – 2
0 < 3 - 2
0 < 1 (true).
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During a basketball season, a player scored a total of 650 points in 31 basketball games. What is his scoring average for the season?
what is the solution to the system of equations: 4x-y=10 and x-4=y
Answer:
(2, - 2 )
Step-by-step explanation:
4x - y = 10 → (1)
x - 4 = y → (2)
substitute x - 4 = y into (1)
4x - (x - 4) = 10 ← distribute parenthesis on left side by - 1
4x - x + 4 = 10
3x + 4 = 10 ( subtract 4 from both sides )
3x = 6 ( divide both sides by 3 )
x = 2
substitute x = 2 into either of the 2 equations and solve for y
substituting into (2)
2 - 4 = y
- 2 = y
solution is (2, - 2 )
Answer:
x = 2 , y = -2
Step-by-step explanation:
I will use the elimination method :
4x-y = 10 - Equation Number 1
x-4 = y - Equation Number 2
For the second equation we add 4 to both sides and subtract y from both sides :
x = y + 4
x - y = 4 - Let's call this equation number 3 :
Now we can subtract the equation 1 with 3 to eliminate y :
3x = 6
x = 2
Now we substitute this value into equation 2 to solve for y :
(2)-4 = y
y = -2
Substitute these values into equation 1 to verify :
4(2) - (-2) = 10
8 + 2 = 10
10 = 10
So these values must be correct
Hope this helped and have a good day
Which table represents a linear functionWhich table represents a linear function
The table that has a constant average rate of change represents a linear function.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output of the function divided by the change in the input.
When this rate is constant, the function is said to be linear, hence the table that has a constant average rate of change represents a linear function.
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Answer:
C
Step-by-step explanation:
Five times a number decreased by nine is equal to twice the number increased by 23. which equation could be used to solve the problem? 5x – 9 = x 23 5x – 9 = 2x 23 5x 23 2x = 23 5x 23 = 2x 23
Answer:
Step-by-step explanation:
5x-9 = 2(x+23) or 5x-9 = 2x+46
Let' x be the "number."
"Five times a number decreased by nine" means: 5x - 9
"equal to twice the number increased by 23" means: = 2(x+23)
Put them together: 5x-9 = 2(x+23)
5x-9 = 2(x+23)
5x-9 = 2x+46
[The formatting of the possible answers does not include parentheses nor algebraic symbols, making selection of a correct answer difficult. ]