Triangle ABC is shown below.
What is the length of line segment AC?
7
9
14
18
Answers
Answer:
Option C. AC = 14 units
Step-by-step explanation:
In the given triangle ABC shown in the figure ∠ABC = ∠ACB
Since angles are equal so opposite sides of equal angles will be equal.
Now mAB = mAC
By putting values in terms of x
2x = 3x - 7
x = 7
Now mAC = 3x - 7
By putting value of x = 7
mAC = 3×7 - 7 = 21 - 7 = 14
Therefore length of line segment AC is 14 units.
Related Questions
in 2003, a gallon of gas cost $1.75. In 2013 a gallon of gas cost $3.25. Write an equation to model this situation.
Answers
To model the situation of the gas prices in 2003 and 2013, we can use a linear equation. The equation to model this situation is y = $0.15x - $298.70.
Explanation:To model the situation of the gas prices in 2003 and 2013, we can use the equation of a linear relationship between the year (x) and the cost of gas (y). We can use the formula y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope (m):
The change in cost of gas is $3.25 - $1.75 = $1.50The change in years is 2013 - 2003 = 10Therefore, the slope (m) is $1.50 / 10 = $0.15.
Next, let's find the y-intercept (b):
Using the point (2003, $1.75), we can substitute the values into the equation and solve for b:$1.75 = $0.15(2003) + b
b = $1.75 - $0.15(2003)
b = $1.75 - $300.45
b = -$298.70
Therefore, the equation to model this situation is y = $0.15x - $298.70, where x is the year and y is the cost of gas.
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A map has a scale of 1 cm : 11.5 km. Two cities are 5.5 cm apart on the map. To the nearest tenth of a kilometer, what is the actual distance corresponding to the map distance?
Answers
multiply 5.5 cm by 11.5 km
5.5 * 11.5 = 63.25
rounded to nearest tenth = 63.3 km
A boat makes a 120-mile trip downstream in 3 hours but makes the return trip in 4 hours. What is the rate of the current?
3 mph
4 mph
5 mph
Answers
Against the current 30 miles per hour
bv means boat velocity with NO current
cv means current velocity
A) bv + cv = 40 mph
B) bv - cv = 30 mph
Adding both equations:
2bv = 70
boat velocity with NO CURRENT = 35 miles per hour
Using equationA
bv + cv = 40
35 + cv = 40
current velocity = 5 miles per hour
Answer:
Speed of current = 5 mph
Step-by-step explanation:
Let u be the speed of boat and v be the speed of current.
A boat makes a 120-mile trip downstream in 3 hours.
120 = 3(u+v)
u + v = 40
It makes the return trip in 4 hours.
120 = 4(u-v)
u - v= 30
Adding both equations
u + v + u - v = 40+30
2u = 70
u = 35 mph
35 + v = 40
v = 5 mph
Speed of current = 5 mph
a store manager orders t-shirts so that 15 out of every 35 are medium. how many medium t-shirts would you expect to find when there are 105 t-shirts on the rack. explain how to get
Answers
What is the average of 5.24,6.875,3.298,5.7,4.98? Round the answer to 2 decimal points
Answers
Um cone reto tem 24cm de altura e o raio da base é igual a 18cm. Calcule
A) a medida de sua geratriz
B) a área total lateral (aproximadamente)
C) a área total (aproximadamente)
+volume
Answers
A geratriz pode ser encontrada através dum teorema de Pitágoras. Tendo a altura e o raio, podemos chegar à medida da geratriz. Soma-se o quadrado da altura com o quadrado do raio para se obter o quadrado da geratriz. depois basta fazer a raíz quadrada do quadrado da geratriz para encontrar a medida da geratriz.
[tex]\sqrt{24^{2}+ 18^{2} } = g [/tex] ⇔ 30 = g
A medida da geratriz é 30cm
B)
A área total lateral é obtida multiplicando o raio pela geratriz e pelo π.
Área total lateral = r×g×π ⇔ Atl = 18cm×30cm×π ⇔ Atl ≈ 1696,5cm²
C)
A área total é calculada somando a área da base e a área lateral. A área da base é calculada multiplicando o quadrado do raio pelo π.
Área total ≈ 1696,5cm²+(18²cm×π) ≈ 1696,5cm²+1017,9cm² ≈ 2714,4cm²
O volume do cone é dado pela área da base vezes a altura a dividir por três.
Volume do cone = (área da base×altura do cone)÷3 ≈ (1017,9cm²×24cm)÷3 ≈ 24429,6cm³÷3 ≈ 8143,2cm³
What is the surface area of a cylinder whose radius is 3 inches and whose height is 10 inches? Round to the nearest tenth.
SA = 2π r2 + 2π rh
A. 226.1 square inches
B. 241.8 square inches
C. 244.9 square inches
D. 543.3 square inches
Answers
Which transformation is not isometric?
Answers
On average, how many times must a 6-sided die be rolled until a 6 turns up twice in a row?
Answers
Chance of two 6s: (1/6)² = 1/36
The chance of rolling a 6 on 2 dice is 1/6 x 1/6.
1/6 x 1/6 = 1/36.
The average number of times for the first 6 would be 6
I'm not sure how to explain this part
But the average number of times for the second one would be 7.
To get the consecutive number of times, multiply them together:
6 x 7 = 42.
It would take an average of 42 times.
Hope This Helps You!
Good Luck :)
- Hannah ❤
Deidre is 5 feet 4 inches tall and her weight is 135 pounds. her bmi is closest to _____ kg/m2.
Answers
1. Multiply the weight by .45:
135 X .45 = 60.75kg
2. Multiply the height in INCHES by .025
Convert 5feet 4inches to only inches (5*12+4) = 64 inches
Now multiply 64 X .025 = 1.6 m
3. Square the answer from the above step.
1.6 X 1.6 = 2.56m
4. Divide the answer from the first step by the answer from the third step.
60.75kg/2.56m = 23.73.
Deidre bmi is 23.73.
Write the next two terms in the pattern. 3, 10, 17, 24, . . .
Answers
So next values would be 31 and 38
10-3 =7
each term increases by 7
so 24 +7 = 31
31+7 = 38
next 2 terms are 31 & 38
Find the volume of the composite solid. Round your answer to the nearest hundredth.
A.239.24cm^3
B.246.08cm^3
C.294.03cm^3
D.308.78cm^3
Answers
We can find the total vol. by adding the two together: Vol (v)total = vol (pyra) + vol (box)
vol (tot) = (1/3×base×height) + (l×w×h)
In order to find the height (h) of the triangle, we imagine a string dropped straight down from the apex (tip), which falls perfectly to center of the base of pyramid. Now the distance from the bottom of that string to edge is 1/2×6.7 = 3.35. Use Pythagorean Theorem to determine the pyramid height:
[tex] {5.8}^{2} = {h}^{2} + {3.35}^{2} \\ {h}^{2} = {5.8}^{2} - {3.35}^{2} \\ h \: = \sqrt{({5.8}^{2} - {3.35}^{2})} \\ h = \sqrt{(33.64 - 11.22)} \\ h = \sqrt{22.42} = 4.73 \: cm[/tex]
Now we can solve our volume, so the base of pyra = l×w = 6.2×6.7 = 41.54
vol (tot) = (1/3×base×height) + (l×w×h)
vol = (1/3×41.54×4.73) + (6.7×6.2×5.5)
vol = (65.49) + (228.47) = 293.96
[tex]vol = 294 \: {cm}^{3} > > \: answer \: (c)[/tex]
Help with math please.
Select the correct rate of change and y -intercept for the linear function that contains the points (4, 6) and (5, 3).
Question 1 options:
The rate of change is –3, and the y -intercept is 18.
The rate of change is 3, and the y -intercept is –6.
The rate of change is 1/3, and the y intercept is 4 2/3
The rate of change is -1/3, and the y intercept is 7 1/3
Answers
The rate of change is the slope (rise/run, y/x). To find that, we use the equation (y2-y1) over (x2-x1). It means take the second "y" and subtract it from the first "y" and the same to "x". If I plug in the numbers, it would be (3-6) over (5-4), and after you subtract, the answer simplifies to: -3/ 1 which is -3. Yay! We got the slope (rate of change) done.
Now let's find the y-intercept by using the formula of point-slope form,
y-y1= m (slope) (x-x1). This is saying you "y" is subtracted from the first
"y" of the points which equals the slope (m) times the quantity of "x" subtracted by the first "x" of the points.
Let's plug the numbers in: y-6 = -3 (x-4). Let's distribute -3 to the parenthesis, and after that it should simplify to: y-6 = -3x + 12. To get "y" by itself, add 6 to both sides: y = -3x +18. We have finally found the slope-intercept equation for those two points (4,6) and (5,3). To then find the y-intercept in this equation, it would be the 18, because -3 is the slope, so that makes 18 the y-intercept.
In conclusion, the rate of change is -3 and the y-intercept is 18.
I hope this helps!
May
Bill Payne visits his local bank to see how long it will take for $1,000 to amount to $1,900 at a simple interest rate of 12 ½%. Provide Bill with the solution to his problem in years. A. 6.5 years B. 7.2 years C. 12.5 years D. 10.2 years
Answers
with an initial starting balance of $1,000.00Balance after 6 years with annual interest of 12.05% $1,979.12
7 years- 2,217.60$
12 years- 3,916.90
Complete the square: x2 – 6x + ____ = –13 + ____
Help Please!!!
Answers
x^2-6x+9=-13+9
(x-3)^2=-4
This quadratic equation have unreal solutions
The complete expression for the given equation is x^2 - 6x + 9= -13 +9
Complete the squareGiven the quadratic expression x^2 - 6x = -13
In order to complete the square, we will follow the steps
Coefficient of x is -6
Half of the coefficient. = (-6/2) = -3
Square of the result = (-3)^2 = 9
Add 9 to both sides of the equation
x^2 - 6x + 9= -13 +9
Hence the complete expression for the given equation is x^2 - 6x + 9= -13 +9
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2.What is the correct equation of the line shown below ?
Answers
Since the line enters the y-axis at (0,3) the y-intercept of the equation would be 3 (as according to the y=mx+b format where b is the y-intercept and m is the slope). The slope would be 3/2 since when you find two perfect points (I used (0,3) and (2,6)) and you use the rise over run method (move up 3 from (0,3) and 2 to the right to get to (2,6)), your slope is 3/2.
The equation of the line shown is y = (3/2)x + 3.
What is the equation of line?The general equation of a straight line is
y = mx + c,
where m is the gradient or slope, and
y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
Now given points from the line passes are (0,3) and (-4,-3)
Therefore we have,
x₁ = 0
y₁ = 3
x₂ = -4
y₂ = -3
Now since the slope of the line is given as,
m = (y₂ - y₁)/(x₂ - x₁)
⇒ m = (-3 - 3)/ (-4-0)
⇒ m = -6/(-4)
⇒ m = 6/4
or, ⇒ m = 3/2
Now, for intercept c we can put any of points in the equation of line.
So, put (0,3)in the equation of line
3 = m(0) + c
3 = 0 + c
⇒ c = 3
Hence the required equation of line is given as,
y = mx + c
put the values of m and c,
y = (3/2)x + 3
which is the required equation of the line shown
Hence,the equation of the line shown is y = (3/2)x + 3.
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The african bush elephant weighs between 4.4 tons and 7.7 tons. What are its least and greatest wieghts rounded to the nearest ton
Answers
7.7=8 tons rounded
7.7 rounds to i
Let r1 and r2 be relations on a set a represented by the matrices mr1 = ⎡ ⎣ 0 1 0 1 1 1 1 0 0 ⎤ ⎦ and mr2 = ⎡ ⎣ 0 1 0 0 1 1 1 1 1 ⎤ ⎦. find the matrices that represent
a.r1 ∪ r2.
b.r1 ∩ r2.
c.r2 ◦r1.
d.r1 ◦r1.
e.r1 ⊕ r2.
Answers
[tex]r1 = \left[\begin{array}{ccc}0&1&0\\1&1&1\\1&0&0\end{array}\right] \,\, and \,\, r2= \left[\begin{array}{ccc}0&1&0\\0&1&1\\1&1&1\end{array}\right] [/tex]
Part a. r1 ∪ r2
This assembles matrix elements from either r1 and/or r2.
[tex]r1 \cup r2 = \left[\begin{array}{ccc}0&1&0\\1&1&1\\1&1&1\end{array}\right] [/tex]
Part b. r1 ∩ r2
This assembles matrix elements common to both r1 and r2.
[tex]r1 \cap r2 = \left[\begin{array}{ccc}0&1&0\\0&1&1\\1&0&0\end{array}\right] [/tex]
Part c. r2 . r1
[tex]r2 \circ r1 = \left[\begin{array}{ccc}0&1&0\\0&1&1\\1&1&1\end{array}\right] \left[\begin{array}{ccc}0&1&0\\1&1&1\\1&0&0\end{array}\right] = \left[\begin{array}{ccc}1&1&1\\2&1&1\\2&2&1\end{array}\right] [/tex]
Part d. r1 . r1
[tex]r1 \circ r1 = \left[\begin{array}{ccc}0&1&0\\1&1&1\\1&0&0\end{array}\right] \left[\begin{array}{ccc}0&1&0\\1&1&1\\1&0&0\end{array}\right] = \left[\begin{array}{ccc}1&1&1\\2&2&1\\0&1&0\end{array}\right] [/tex]
Part e. r1 ⊕ r2 (Direct sum)
[tex]r1 \oplus r2 = \begin{bmatrix} r1&0\\0&r2\end{bmatrix} = \begin{bmatrix} 0&1&0 &0&0&0\\ 1&1&1 &0&0&0\\ 1&0&0 &0&0&0\\ 0&0&0 &0&1&0\\0&0&0 &0&1&1\\ 0&0&0 &1&1&1\end{bmatrix}[/tex]
The operation results on the matrices representing relations r1 and r2 are beautiful illustrations of how relations are manipulated in set theory. Given the limitations imposed by the data available, only three of the five stipulated operations can be carried out.
Explanation:In the given question, the student needs to perform different operations on the matrices that represent relations r1 and r2. Here is the solution:
r1 ∪ r2 (Union of r1 and r2): It's obtained by taking the union of the corresponding elements in the two matrices. If either or both of the matrices have a 1 in a position, then put a 1, else 0. So the matrix for r1 ∪ r2 is ⎡ ⎣ 0 1 0 1 1 1 1 1 1 ⎤ ⎦ r1 ∩ r2 (Intersection of r1 and r2): It's obtained by taking the intersection of the corresponding elements in the two matrices. If both of the matrices have a 1 in a position, then put a 1, else 0. So the matrix for r1 ∩ r2 is ⎡ ⎣ 0 1 0 0 1 1 1 0 0 ⎤ ⎦ r2 ◦r1 (Composition of r2 and r1): If there exists an element in the set such that (a, b) is in r1 and (b, c) is in r2, then put a 1 in A[ac] else put a 0. Due to this, the matrix comprehension is studied in higher mathematics, and it can't be calculated from the given matrices. r1 ◦r1 (Composition of r1 and r1): Same as the previous operation but with both relations being r1. It also requires the full set of elements to calculate and can't be derived from the given matrices. r1 ⊕ r2 (Symmetric difference of r1 and r2): It is obtained by taking the XOR of each element in the matrices. So if the two elements are the same, put a 0, else put a 1. So the matrix for r1 ⊕ r2 is ⎡ ⎣ 0 0 0 1 0 0 0 1 1 ⎤ ⎦ Learn more about Matrix Operations here:
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The relative frequency of a car travelling through a road junction having exactly two occupants is 0.26.If 5,000 cars are observed passing through the junction, how many of the cars could be expected to have only two occupants?
Answers
5000 x 0.26 = ??
PLEASE HELP
Solve for x.
−32>−5+9x
Enter your answer, as an inequality, in the box.
Answers
-32 + 5 < 9x
-27 < 9x
-3 < x
x > -3
hope that helps, God bless!
Inequality is a statement of an ordered relationship
The value of x as inequality is less than -3.
x < -3 is our answer.
What is inequality?It is a statement of an ordered relationship
- greater than,
- greater than or equal to,
- less than,
- less than or equal to between two numbers or algebraic expressions.
Example:
x > 3
y < 5
x ≤ 6
y ≥ 2
We have,
-32 > -5 + 9x
Add 5 on both sides.
-32 + 5 > -5 + 9x + 5
[ -32 + 5 = -27 ]
-27 > 9x
Divide both sides by 9.
-27/9 > 9x/9
-9 x 3 / 9 > 9x / 9
-3 > x
This can be written as:
x < -3
Thus,
The value of x as inequality is less than -3.
i.e x < -3
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14-3x=4x solve and explain
Answers
Flip
4x = 14 - 3x
Add both sides by 3x
7x = 14
Divide both sides by 7
x = 2
Have an awesome day! :)
Find the quotient. Show all work for full credit. 4+2i/6-i
Answers
(4 + 2i)(6 + i) 24 + 16i - 2 22 + 16i
----------------- = ---------------- = -----------
(6 - i)(6 + i) 36 - (-1) 37
The quotient of 4+2i/6-i is (11/4-4i)/*1/5.
What is quotient?Quotient is a result obtained by dividing one quantity by another.
explanation;
(4-2i)/(6-i)
Multiply and divide by the denominator = (6+i)
=>(4-2i)/(6-i)/(6+i)(6+i)
=> (4*6 + 4i - 12i - 2i^2)/[6^2 - (2i)^2]
=> (24 - 8i -2)/ [36 + 4] [since i^2 = -1]
=> (22-8i) /40
=> 22/40 - 8i/40
=> 11/20 - i/5
Hence, the quotient of 4+2i/6-i is (11/4-4i)/*1/5.
A ratio is an ordered pair of numbers a and b, written a / b in which b does no longer identical zero. A proportion is an equation wherein ratios are set equal to each other. The share components is used to depict if two ratios or fractions are same. we can find the lacking fee by dividing the given values. the proportion formula can be given as a: b::c : d = a/b = c/d wherein a and d are the acute terms and b and c are the mean phrases.
The quantitative relation among two quantities showing the number of times one cost consists of or is contained inside the other. The indicated quotient of two mathematical expressions. b : the connection in quantity, quantity, or size among or more matters.
A ratio can be defined as the connection or assessment among two numbers of the same unit to check how larger is one variety than the alternative one. as an instance, if the quantity of marks scored in a take a look at is 2 out of 5, then the ratio of marks received to the total range of marks is written as 2:5.
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The domain for f(x) and g(x) is the set of all real numbers. Let f(x) = 2x2 + x − 3 and g(x) = x − 1. Find f(x) • g(x).
A. 2x3 − x2 + 4x − 3
B. x2 − 4x + 3
C. 2x3 − x2 − 4x + 3
D. 2x3 − 4x2 + 3
Answers
so the answer should be C
Six students measure the acceleration (in meters per second per second) of an object in free fall. The measured values are: 10.56, 9.52, 9.73, 9.80, 9.78, 10.91.The students want to state that the absolute deviation of each measured value xfrom the mean is at most
d. Find the value of
d.
Answers
x = [10.56, 9.52, 9.73, 9.80, 9.78, 10.91]
There are 6 measurements.
Calculate the mean.
m = (10.56+9.52+9.73+9.80+9.78+10.91)/6 = 10.05
Calculate deviations from the mean.
y = |x - m|
= [0.51, 0.53, 0.32, 0.25, 0.27, 0.86]
The greatest deviation from the mean is d = 0.86.
Calculate the average absolute deviation.
(0.51+0.53+0.32+0.25+0.27+0.86)/6 = 0.4567
Answer:
d = 0.86
Help me i hate word problems
Answers
so the question would be: how many times does fit into 3.5?
if you want to divide by a fraction, you need to multiply by the reverse of it.
so the answer is: 10 servings of lemonade ( and a little bit will be left over for half a serving).
Hope this helps!
A new truck that sells for $25,000 depreciates (decreases in value) 11% each year. What will be the value of the truck in 2 years
Answers
Depreciation rate = 11%
Note that 1 - 0.11 = 0.89.
Value after 1 year = $25,000 (0.89) = $22,250
Value after 2 years = $22,250 (0.89) = $19,802.50
Answer: $19,802.50
Answer:
Price of Truck after 2 year = $ 19802.50
Step-by-step explanation:
Given: Price of truck = $ 25,000
Price depreciate at rate of 11% in a year
To find: Price of truck after 2 years
If we let Price of truck to be P = $ 25000
And Rate of deprecation to be R = 11%
And time to be n = 2
now by using formula of deprecation, we get
[tex]A=P\times(1-\frac{R}{100})^n[/tex]
[tex]A=25000\times(1-\frac{11}{100})^2[/tex]
[tex]A=25000\times0.7921[/tex]
A = $ 19802.50
Therefore, Price of Truck after 2 year = $ 19802.50
8 less than one third of x is y
Answers
I think this is what you were looking for seeing that you cannot solve this problem without an 'x' or 'y'.
Sharon needs 64 credits to graduate from her community college. So far she has earned 24 credits. What percent of the required credits does she have?
Answers
A percentage is a number or ratio expressed as a fraction [tex]100[/tex]. Hence, Sharon has [tex]12.5[/tex]% of the credits required.
What is the percentage?
A percentage is a number or ratio expressed as a fraction [tex]100[/tex]. It is often denoted using the percent sign, "%".
Here given information:-
Sharon needs [tex]64[/tex] credits and he earned [tex]24[/tex] credits.
So,
[tex](\frac{24}{64})[/tex]×[tex]100[/tex][tex]=\frac{1}{8}[/tex]×[tex]100[/tex]
[tex]=0.125[/tex]×[tex]100[/tex]
[tex]=12.5[/tex]%
Hence, Sharon has [tex]12.5[/tex]% of the credits required.
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How is an emulsion different from a solution?
:The components are mixed unevenly instead of evenly within the emulsion.
:Insoluble instead of soluble particles are suspended within the emulsion.
:Two liquids that normally are not mixable are mixed in the emulsion.
:The components of an emulsion are single elements or compounds instead of a mixture of compounds.
Answers
Ronald walks from home to Taco Bell to eat everyday. It takes him 30 minutes to walk the 2 mile distance. A) write a function for Ronald’s wall. Let x be the number of minutes he walks.
B) what should the domain of the function be?
Answers
[tex]d=vt[/tex]
where d[tex]y= \frac{1}{15}x [/tex]= distance,
v = velocity,
t = time
In this case, d = 2 mi., t = 30 min. So we get
[tex]2=30v[/tex]
Dividing both sides by 30, we get
[tex]v= \frac{2}{30}= \frac{1}{15} [/tex]
Thus a function for his walk would be
[tex]y= \frac{1}{15} x[/tex]
where y = distance and x = number of minutes he walks.
b) Domain of a function is a set of x-values on which the function defined. In this case, the number of minutes is 30 at maximum. So the domain of the function is [0, 30].