Answer:
The answer would be 6.
Refer to the figure and match the theorem that supports the statement.
1. If chords are =, then arcs are =. If BC = DE, then Arc BC = Arc DE
2. If arcs are =, then chords are =. If AX is perpendicular to BC, then BX = XC
3. Diameters perpendicular to chords bisect the chord If Arc BC = Arc DE, then BC = DE
The principles of circle geometry dictate that: if chords are equal then their corresponding arcs are equal; if arcs are equal then their chords are equal; and diameters perpendicular to chords bisect the chord. However, some of the proposed arguments in the question are not matching these principles.
Explanation:The three statements highlighted in this question are the principles of circle geometry.
1. If chords are equal, then arcs are equal: This theorem states that if two chords in a circle are equal in length, then their corresponding arcs (the part of the circumference that the chord subtends) are also equal. If BC = DE as stated, then Arc BC = Arc DE.
2. If arcs are equal, then chords are equal: This is the converse of the first theorem. If two arcs of a circle are equal, then the chords subtending these arcs are equal. However, this principle is not relevant for the condition if AX is perpendicular to BC, then BX = XC.
3. Diameters perpendicular to chords bisect the chord: This theorem states that if a diameter of a circle is perpendicular to a chord, then it bisects the chord. Therefore the statement if Arc BC = Arc DE, then BC = DE is not relevant to this theorem.
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A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week.
Answer:
Step-by-step explanation:
Let 'c' be the number of child bikes c=20
and 'a' be the number of adult bikes. a=6
According to the problem
The restriction of building time for a week is 4c+6a≤120 hours.........(1)
and the restriction of testing time for a week is 4c+4a≤100 hours..........(2)
Lets check whether company can build c=20 and a=6 bikes in a week by putting these values in (1) and (2).
4c+6a≤120 hours.........(1)
4(20)+6(6)≤120
80+36≤120
116≤120 (true)
4c+4a≤100 hours..........(2)
4(20)+4(6)≤100
80+24≤100
104≤100 (true)
Hence, the company can build 20 child bikes and 6 adult bikes in the week....
Which graph shows the line y-2 = 2(x + 2)?
A/B/co
A. Graph A
B. Graph B
C. Graph D
D. Graph c
Answer:
The answer is Graph A.
Step-by-step explanation:
i got the answer from the teachers answer key
Graph A shows the line y-2 = 2(x + 2).
The answer is option A
What is a straight line graph?
The graph follows a straight line equation shows a straight line graph.
equation of a straight line is y=mx+cy represents vertical line y-axis.x represents the horizontal line x-axis. m is the slope of the lineslope(m)=tan∅=y axis/x axis.
c represents y-intercepts (it is the point at which the line cuts on the y-axis)Straight line graphs show a linear relationship between the x and y values.solving the equation:-
y-2 = 2(x + 2)
y=2x+4+2
Y=2x+6
y-intercepts = 6 (Graph A represents this).
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the following table shows the distance from school as a function time
time in minutes. distance in meters
x. f(x)
0 36
3 32
6 28
9 24
12 20
find and intercept the meaning of the x intercept in this scenario
36,0 the distance away from the school
27,0 the time it takes to reach the school
36,0 the time it takes to reach the school
27,0 the distance away from the school
Answer:
27,0 the distance away from the school
Step-by-step explanation:
Apply the formula for equation of a straight line;
y=mx+c where c is the y intercept , and m is the gradient
From the graph, the slope is negative where speed decreases with increase in time
Find the gradient by applying the formula;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Taking y₁=24, y₂=20, x₁=9, x₂=12
Then;
[tex]m=\frac{20-24}{12-9} =\frac{-4}{3}[/tex]
write the equation of the function as ;
y=mx+c, c=36( the y-intercept when x=0) hence the equation is;
[tex]y=mx+c\\\\y=\frac{-4}{3}x+36[/tex]
To get x-intercept, substitute value of y with 0
[tex]y=mx+c\\\\\\y=-\frac{4}{3} +36\\\\\\0=-\frac{4}{3} x+36\\\\\frac{4}{3}x =36\\\\\\4x=36*3\\\\\\x=108/4=27[/tex]
This means that the x-intercept is 27 ,and this means you will require 27 minutes to cover the whole distance to the school.
Answer:
A: 36,0 the distance away from the school
Step-by-step explanation:
At 0 it means you have spent 0 minutes going to school which means you haven't left the starting point yet.
36 is the distance left (in meters) from your current position and school. This means that the school is 36 meters away from the starting point.
What is the seventh term of the geometric sequence where a1=128 and a3=8
[tex]\bf \begin{array}{lll} term&value\\ \cline{1-2} a_1&128\\ a_2&128r\\ a_3&128rr\\ &128r^2 \end{array}~\hspace{5em}\stackrel{a_3}{128r^2}=\stackrel{a_3}{8}\implies r^2=\cfrac{8}{128}\implies r^2=\cfrac{1}{16} \\\\\\ r=\sqrt{\cfrac{1}{16}}\implies r=\cfrac{\sqrt{1}}{\sqrt{16}}\implies r=\cfrac{1}{4}\qquad \leftarrow \textit{common ratio} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} n=7\\ a_1=128\\ r=\frac{1}{4} \end{cases}\implies a_7=128\left( \frac{1}{4} \right)^{7-1} \\\\\\ a_7=128\left( \frac{1}{4} \right)^6\implies a_7=128\cdot \cfrac{1}{4096}\implies a_7=\cfrac{128}{4096}\implies a_7=\cfrac{1}{32}[/tex]
Find the distance from the Theater to the Library. Leave your answer in simplest radical form if necessary.
12
√12
74
√74
Answer:
See explanation
Step-by-step explanation:
Some important information is missing in the question, however I will try to help.
Let us assume the theater is located at (-5,6) and the library is located at (4,1), then we can use the distance formula to find the distance from the Theater to the Library.
The distance formula is given by:
[tex]d = \sqrt{(x_2-x_1) ^{2} +(y_2-y_1) ^{2} } [/tex]
We plug in the values to get:
[tex]d = \sqrt{ {(4 - - 5)}^{2} + {(6 - 1)}^{2} } [/tex]
[tex]d = \sqrt{81 + 25} [/tex]
[tex]d = \sqrt{144} = 12[/tex]
You can plug in the points you have to get the required answer
Answer:
D, √74
Step-by-step explanation:
got it right on odyssey ware
riangle XYZ is translated 4 units up and 3 units left to yield ΔX'Y'Z'. What is the distance between any two corresponding points on ΔXYZ and ΔX'Y'Z′?
Answer:
5 units
Step-by-step explanation:
According to the given statement Δ XYZ is translated 4 units up and 3 units left to yield ΔX'Y'Z' which means that each point in ΔXYZ is moved 4 units up and moved 3 units left.
To find the distance of each corresponding point we will use the Pythagorean theorem which states that the square of the length of the Pythagorean of a right triangle is equal to the sum of the squares of the length of other legs
The square of the required distance = 4^2+3^2 = 16+9 =25
By taking root of 25 we get:
√25 = 5
Thus, we can conclude that the the distance between any two corresponding points on ΔXYZ and ΔX′Y′Z′ is 5 units. ..
which of the following recursive formulas represent the same arithmetic sequence as the explicit formula an=5+(n-1)2
a. a1=5
an=an-1+2
b. a1=5
an=(an-1+2)5
c. a1=2
an=an-1+5
d. a1=2
an=an-1*5
Answer:
Choice A:
[tex]a_1=5[/tex]
[tex]a_{n}=a_{n-1}+2[/tex]
Step-by-step explanation:
[tex]a_n=5+(n-1)2[/tex]
means we looking for first term 5 and the sequence is going up by 2.
In general,
[tex]a_n=a_1+(n-1)d[/tex]
means you have first term [tex]a_1[/tex] and the sequence has a common difference of d.
So it is between the first two choices.
The explicit form of an arithmetic sequence is: [tex]a_n=a_1+(n-1)d[/tex]
An equivalent recursive form is [tex]a_n=a_{n-1}+d \text{ where } a_1 \text{ is the first term}[/tex]
So d again here is 2.
So choice a is correct.
[tex]a_1=5[/tex]
[tex]a_{n}=a_{n-1}+2[/tex]
Answer: Option a
[tex]\left \{ {{a_1=5} \atop {a_n=a_{(n-1)}+2}} \right.[/tex]
Step-by-step explanation:
The arithmetic sequences have the following explicit formula
[tex]a_n=a_1 +(n-1)*d[/tex]
Where d is the common difference between the consecutive terms and [tex]a_1[/tex] is the first term of the sequence:
The recursive formula for an arithmetic sequence is as follows
[tex]\left \{ {{a_1} \atop {a_n=a_{(n-1)}+d}} \right.[/tex]
Where d is the common difference between the consecutive terms and [tex]a_1[/tex] is the first term of the sequence:
In this case we have the explicit formula [tex]a_n=5+(n-1)*2[/tex]
Notice that in this case
[tex]a_1 = 5\\d = 2[/tex]
Then the recursive formula is:
[tex]\left \{ {{a_1=5} \atop {a_n=a_{(n-1)}+2}} \right.[/tex]
The answer is the option a.
In two or more complete sentences, compare the number of x-intercepts in the graph of f(t) = t2 to the number of x-intercepts in the graph of g(t) = (t – 8)2. Be sure to include the transformations that occurred between the parent function f(t) and its image g(t).
Answer
Both graphs have the same number of x-intercepts. The graph of the function f(t) = t² has one x-intercept, which is the value of t for which f(t) = t² = 0, and that is t = 0. The graph of the function g(t) = (t - 8)² has also one x-intercept, which is the value of t for which g(t) = 0 and that is t = 8.
The function f(t) = t² is the most simple form of a parabola, so it is considered the parent function. The function g(t) = (t - 8)² is a daughter function of f(t); then, the graph of g(t) is a horizontal translation of the graph of f(t), 8 units to the right, so the number of x-intercepts (the points where the x-axis is crossed or touched by the graph) does not change, it is just their position what changes.
Explanation:
The x-intercepts are the points where the graph of the function touches or crosses the x-axis. They are found by doing the function equal to zero. In this case f(t) = 0 and g(t) = 0.
You can solve easily f(t) = t², as, just by simple inspection, the soluton is t = 0.
Then, when you realize that the function g(t) = (t - 8)² is a horizontal translation (8 units to the right) of the parent function f(t), you can conclude quickly that the number of x-intercepts of both graphs is the same. Thus, uisng the transformation of the parent function, 8 units to the right, you conclude that both the graph of f(t) and the graph of g(t) have the same number of x-intercepts: one.
f rests at (0/0) and grows upwards, so there is only a single x-intercept. g is f moved 3 to the left, so it also only has one intercept but at (-3,0).
What is the solution of 4.5x-100>125
Answer:
x > 50Step-by-step explanation:
[tex]4.5x-100>125\qquad\text{add 100 to both sides}\\\\4.5x-100+100>125+100\\\\4.5x>225\qquad\text{divide both sides by 4.5}\\\\\dfrac{4.5x}{4.5}>\dfrac{225}{4.5}\\\\x>50[/tex]
The solution to the inequality 4.5x - 100 > 125 is x > 50.
The given inequality is 4.5x - 100 > 125.
To solve it, first, add 100 to both sides to get 4.5x > 225. Then, divide by 4.5 to find x > 50. Therefore, the solution to the inequality is x > 50.
Steps for solving 3x + 18 = 54 are shown.
Explain how Step 1 helps solve the equation.
3x+18 = 54
3x + 18-18 = 54 -18
3x = 36
3x_36
33
X = 12
Original equation
Step 1
Step 2
Step 3
Step 4
) A. Adding 18 to both sides undoes the subtraction.
O
B. Adding 18 to both sides combines like terms.
O
C. Subtracting 18 from both sides isolates the variable term.
O
D. Subtracting 18 from both sides isolates the variable.
C
By subtracting 18 to both sides you are separating the 3x because you are not ready to isolate the variable (x) in step 1
Answer:
WELP i got little different answers and for me it was A
A.
Adding 18 to both sides isolates the variable term.
B.
Adding 18 to both sides isolates the variable.
C.
Subtracting 18 from both sides undoes the subtraction.
D.
Subtracting 18 from both sides combines like terms.
(x)=3log(x+5)+2 what is the x intercept
Answer:
[tex]\large\boxed{x-intercept=-2+\sqrt[3]{0.01}}[/tex]
Step-by-step explanation:
[tex]f(x)=3\log(x+5)+2\to y=3\log(x+5)+2\\\\\text{Domain:}\ x+5>0\to x>-5\\\\\text{x-intercept is for }\ y=0:\\\\3\log(x+5)+2=0\qquad\text{subtract 2 from both sides}\\\\3\log(x+5)=-2\qquad\text{divide both sides by 3}\\\\\log(x+5)=-\dfrac{2}{3}\qquad\text{use the de}\text{finition of logarithm}\\\\(\log_ab=c\iff b^c=a),\ \log x=\log_{10}x\\\\\log(x+2)=-\dfrac{2}{3}\\\\\log_{10}(x+2)=-\dfrac{2}{3}\iff x+2=10^{-\frac{2}{3}}\qquad\text{use}\ a^{-n}=\left(\dfrac{1}{a}\right)^n[/tex]
[tex]x+2=\left(\dfrac{1}{10}\right)^\frac{2}{3}\qquad\text{use}\ \sqrt[n]{a^m}=a^\frac{m}{n}\\\\x+2=\sqrt[3]{0.1^2}\qquad\text{subtract 2 from both sides}\\\\x=-2+\sqrt[3]{0.01}\in D[/tex]
Nolan buys baseball bats to sell in his store. Each bat costs him $19.99 and he is using a mark up rate of 85%. At what selling price will Nolan sell each bat?
Answer:
The selling price of each bat is $36.98
Step-by-step explanation:
* Lets explain how to solve the problem
- Nolan buys baseball bats to sell in his store
- Each bat costs him $19.99
- He is using a mark up rate of 85%
- The selling price = cost price + markup
* Lets solve the problem
∵ The cost price of each bat is $19.99
∵ The markup is 85%
- To find the markup multiply its percent by the cost price
∴ The markup = 19.99 × 85/100 = $16.9915
∵ The selling price = the cost price + the markup
∴ The selling price = 19.99 + 16.9915 = 36.9815
* The selling price of each bat is $36.98
If (x + 2) is a factor of x3 − 6x2 + kx + 10, k =
Answer:
The value of k is -11
Step-by-step explanation:
If (x+2) is a factor of x3 − 6x2 + kx + 10:
Then,
f(x)=x3 − 6x2 + kx + 10
f(-2)=0
f(-2)=(-2)³-6(-2)²+k(-2)+10=0
f(-2)= -8-6(4)-2k+10=0
f(-2)= -8-24-2k+10=0
Solve the like terms:
f(-2)=-2k-22=0
f(-2)=-2k=0+22
-2k=22
k=22/-2
k=-11
Hence the value of k is -11....
What is the missing side length in this right triangle? A. 15 B. 21 C. 225 D. 441
9,12?
Answer:
A. 15.
Step-by-step explanation:
9^2 + 12^2
= 81 + 144
= 225.
Taking the square root: we get 15.
The Pythagorean theorem is a basic relationship between the three sides of a right triangle in Euclidean geometry. The missing side length in the given right-angled triangle is 15. Thus, the correct option is A.
What is Pythagoras theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.
Given the two sides of the triangle, therefore, using the Pythagorean theorem, the third side of the triangle can be written as,
x² = 12² + 9²
x² = 144 + 81
x² = 225
x = 15
Hence, the missing side length in the given right-angled triangle is 15. Thus, the correct option is A.
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Kevin’s car requires 5 liters of diesel to cover 25 kilometers. How many liters of diesel will Kevin need if he has to cover 125 kilometers?
Answer: 25 litres
Step-by-step explanation: If it takes 5 litres of diesel to cover 25km, it means it will take more litres to cover 125km. So you have to divide 125km by 25km then you will get 5 which you will then multiply by 5 litres to get 25 litres of diesel.
for the function f(x)=3(x-1)^2+2 identify the vertex, domain, and range.
Answer:
The vertex of the function is (1 , 2)
The domain is (-∞ , ∞) OR {x : x ∈ R}
The range is [2 , ∞) OR {y : y ≥ 2}
Step-by-step explanation:
* Lets revise the standard form of the quadratic function
- The standard form of the quadratic function is
f(x) = a(x - h)² + k , where (h , k) is the vertex point
- The domain is the values of x which make the function defined
- The domain of the quadratic function is x ∈ R , where R is the set
of real numbers
- The range is the set of values that corresponding with the domain
- The range of the quadratic function is y ≥ k if the parabola upward
and y ≤ k is the parabola is down ward
* Lets solve the problem
∵ f(x) = 3(x - 1)² + 2
∵ f(x) = a(x - h)² + k
∴ a = 3 , h = 1 , k = 2
∵ The vertex of the function is (h , k)
∴ The vertex of the function is (1 , 2)
- The domain is all the real number
∵ The domain of the quadratic function is x ∈ R
∴ The domain is (-∞ , ∞) OR {x : x ∈ R}
- The leading coefficient of the function is a
∵ a = 3 ⇒ positive value
∴ The parabola is opens upward
∴ The range of the function is y ≥ k
∵ The value of k is 2
∴ The range is [2 , ∞) OR {y : y ≥ 2}
What is the distance between the points (4,3) and (1,-1) on the coordinate plane?
If (5^0)^x = 1, what are the possible values of x?
Answer:
x can be any value
Step-by-step explanation:
(5^0)^x = 1,
5^0 =1
1^x =1
X can be any value
For this case we have the following expression:
[tex](5^{ 0})^{x} = 1[/tex]
By definition of power properties we have to:
[tex](a ^ n) ^ m = a ^{n * m}[/tex]
Then, rewriting the expression:
[tex]5 ^ 0 = 1[/tex]
Thus, the variable "x" can take any value:
Answer:
The variable "x" can take any value
The set of ordered pairs in the graph below can be described as which of the following? A. a relation B. a function C. a relation and function D. neither a relation nor function
Answer:
a relation and function ⇒ answer C
Step-by-step explanation:
* Lets revise the relation and the function
- The relation is between the x-values and y-values of ordered pairs.
- The set of all values of x is called the domain, and the set of all values
of y is called the range
- The function is a special type of relation where every x has a unique y
- Every function is a relation but not every relation is a function
* Lets solve the problem
∵ The graph is a parabola
∵ The parabola is a function because every x-coordinates of the
points on the parabola has only one y-coordinate
- Ex: some ordered pairs are (-5 , -5) , (-2 , 5) , (0 , 7) , (2 , 5) , (5 , -5)
∵ Every x-coordinate has only one y-coordinate
∴ The graph represents a function
∵ Every function is a relation
∴ The set of ordered pairs in the graph below can be described as
a relation and function
If 20% of a = b, then b% of 20 is same as?
[tex]20\%\text{ of } a=b \Longleftrightarrow0.2a=b\\\\b\%\text{ of } 20 \Longleftrightarrow \dfrac{b}{100}\cdot20\\\\\dfrac{b}{100}\cdot20=\dfrac{b}{5}=\dfrac{0.2a}{5}=\boxed{\boxed{a}}[/tex]
The Retread Tire Company recaps tires. The fixed annual cost of the recapping operation is $65,000. The variable cost of recapping a tire is $7.5. The company charges$25 to recap a tire.
a. For an annual volume of 15, 000 tire, determine the total cost, total revenue, and profit. b. Determine the annual break-even volume for the Retread Tire Company operation.
Part a) Total Cost
Total Cost for recapping the tires is the sum of fixed cost and the variable cost. i.e.
The total cost is ( $65,000 fixed) + (15,000 x $7.5)
=$65,000+$112,500
=$177,500
Part b) Total Revenue
Revenue from 1 tire = $25
Total tires recapped = 15000
So, Total revenue = 15000 tires x $25/tire
Total Revenue =$375,000
Part c) Total Profit
Total Profit = Revenue - Cost
Using the above values, we get:
Profit = $375,000 - $177,500
Profit = $197,500
Part d) Break-even Point
Break-even point point occurs where the cost and the revenue of the company are equal. Let the break-even point occurs at x-tires. We can write:
For break-even point
Cost of recapping x tires = Revenue from x tires
65,000 + 7.5 x = 25x
65,000 = 17.5 x
x = 3714 tires
Thus, on recapping 3714 tires, the cost will be equal to the revenue generating 0 profit. This is the break-even point.
The graphs below have the same shape. What is the equation of the blue graph?
For this case we have that by definition of vertical translations of functions, it is fulfilled:
Assume [tex]k> 0[/tex]:
To graph [tex]y = f (x) + k[/tex], the graph k units is moved up.
To graph [tex]y = f (x) -k[/tex], the graph moves k units down.
In the figure it is observed that:
The original function is [tex]G (x) = x ^ 2[/tex], the function was moved 4 units down. So, the new function is:
[tex]F (x) = x ^ 2-4[/tex]
Answer:
Option B
Answer:
Option B is correct.
Step-by-step explanation:
G(x) = x^2
then f(x) = x^2-4
since the graph is shifted 4 units down because when something is subtracted from the function the graph is shifted down.
that's why f(x) = x^2-4.
Hence Option B is correct.
In a pet shop, there are 3 hamsters for every 2 guinea pigs, and there are 2 giant cloud rats for every 3 guinea pigs. If n is the total number of hamsters, guinea pigs, and giant cloud rats, and n>0, then what is the smallest possible value of n?
Answer:
n = 19.
Step-by-step explanation:
If there are x guinea pigs then there are 3/2 x and 2/3 x rats.
So n = x + 3/2 x + 2/3 x
n = 19x / 6
19x = 6n
Let x = 6 , then n = 19*6 / 6 = 19.
Now n and x must be whole numbers so x is 6 and n = 19 are the smallest possible values.
Answer:
n=19
Step-by-step explanation:
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Determine if the two figures are congruent and explain your answer.
To determine if two figures are congruent, we need to check if one can be obtained from the other through a combination of rigid transformations. The specific transformations that can be applied to one figure to make it coincide with the other need to be described to explain if the figures are congruent or not.
If two figures are congruent, we need to check if one can be obtained from the other through a combination of rigid transformations. Rigid transformations include translations, rotations, and reflections. If we can apply a series of these transformations to one figure to make it coincide exactly with the other, then the figures are congruent.
Without specific information about the figures, I can provide a general explanation of how you might approach this:
Translation (Slide): Check if one figure can be translated (slide) to coincide with the other. If you can move one figure to overlap with the other without rotating or reflecting it, they might be congruent.Rotation (Turn): Check if one figure can be rotated to match the orientation of the other. If a rotation can make the two figures coincide, they may be congruent.Reflection (Flip): Check if one figure can be reflected (flipped) to match the other. If a reflection can be applied to one figure to make it coincide with the other, they may be congruent.To explain your answer, describe the specific transformations (translations, rotations, reflections) that can be applied to one figure to make it coincide with the other. If you can perform a sequence of these transformations to superimpose one figure onto the other, then the figures are congruent. If not, they are not congruent.
the system of equations graphed below has how many solutions? y=-3/2x-3 y=-3/2x+5
Answer:
No solutions.
Step-by-step explanation:
The value of y cannot be equal to both -3/2x - 3 and -3/2x + 5.
what is the slope of the line that passes through the points (1, −3) and (3, −5)
Answer:
Slope = -1
Step-by-step explanation:
Use the following formula:
slope (m) = (y₂ - y₁)/(x₂ - x₁)
Let:
(x₁ , y₁) = (1 , -3)
(x₂ , y₂) = (3 , -5)
Plug in the corresponding numbers to the corresponding variables. Simplify:
m = (-5 - (-3))/(3 - 1)
m = (-5 + 3)/(3 - 1)
m = -2/2
m = -1
The slope of the line is -1.
~
For this case we have that by definition, the slope of a line is given by:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
We have as data the following points:
[tex](x_ {1}, y_ {1}) :( 1, -3)\\(x_ {2}, y_ {2}): (3, -5)[/tex]
Substituting the values:
[tex]m = \frac {-5 - (- 3)} {3-1}\\m = \frac {-5 + 3} {3-1}\\m = \frac {-2} {2}\\m = -1[/tex]
Thus, the slope is -1.
Answer:
The slope is -1
Question 12 Multiple Choice Worth 1 points)
(03.07 LC)
Choose the equation of the horizontal line that passes through the point (-8, -7).
Answer:
linear inqution
Step-by-step explanation:
relationship
ANSWER
[tex]y = - 7[/tex]
EXPLANATION
A horizontal line that passes through (a,b) has equation
[tex]y = b[/tex]
This is because a horizontal line is a constant function.
The y-values are the same for all x belonging to the real numbers.
The given line passes through (-8,-7).
In this case, we have b=-7.
Therefore the equation of the horizontal line that passes through the point (-8, -7) is
[tex]y = - 7[/tex]
An ant can run an inch per second. How long will it take the same ant to run a foot?
Answer:
12 seconds.
Step-by-step explanation:
There are 12 inches in a foot so the ant can run a foot in 1 *12 = 12 seconds.
Find the shortest distance from A to B in the diagram below.
Answer: 14 m
Step-by-step explanation:
8 m + 6 m = 14 m
Answer:
10 cm.
Step-by-step explanation:
We have been given a cuboid. We are asked to find the shortest distance from A to B is the given diagram.
We know that shortest distance from A to B will be equal to hypotenuse of right triangle with two legs 8 meters and 6 meters.
[tex]AB^2=8^2+6^2[/tex]
[tex]AB^2=64+36[/tex]
[tex]AB^2=100[/tex]
Now, we will take square root of both sides of our given equation as:
[tex]AB=\sqrt{100}[/tex]
[tex]AB=10[/tex]
Therefore, the shortest distance from A to B is 10 cm.