Angle ACD is congruent to angle ADC by transitive equality if angles 1 and 2 are both ACD because angle ACB is congruent to angle ADE in the step above. Therefore, angle 1 equals angle 2, as you can see.
What is isosceles triangle?An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.
Here,
Given that segments AB and AE are congruent, the triangle ABE is required to be isosceles by definition.
As a result, angle ABC must be similar to angle AED, again in accordance with the definition of an isosceles triangle.
Consequently, triangle ABC must be congruent to triangle AED by SAS as you have been informed that segments BC and DE are congruent. Right now, it's unclear to you whether angle 1 is ACB or ACD.
Assuming it is ACB, CPCT shows that ACB is congruent to ADE. Angle 1 equals angle 2, so there you have it. Since angle ACB is supplementary to angle ACD and angle ADE is supplementary to angle ADC.
Since angle ACB is congruent to angle ADE from the step above, angle ACD is congruent to angle ADC by transitive equality if angle 1 and angle 2 are both ACD. Angle 1 equals angle 2, so there you have it.
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help help help help help help help help help help help help help help help help help help help help help hel
1. Which equation represents a line that has a slope of 2 and passes through the origin?
A y=2x
B. y=x+2
C. y x
D. y=-x
A regular jeepney ride costs $12.00 for the first 4 km, and each additional km adds P1.50 to the fare
2. Which of the following can be used to compute a regular fare (F), in pesos, for a 6-km nde?
A. F = 12(7)
B. F=12(7)+1.50
C.=12(150)+7
D.=12+2(1.50)
A regular jeepney ride costs P12.00 for the first 4 km, and each additional km adds P1.50 to the fare
3. How much is the regular fare for a 6-km ride?
A. P15
B. P13.50
C. P14.50
D. P16
4.Which equation represents a vertical line?
A. y =2x
B. x = 2
C. y = 3
D. y = -x
1. Which equation represents a line that has a slope of 2 and passes through the origin?
A y=2x
B. y=x+2
C. y x
D. y=-x
2. A regular jeepney ride costs $12.00 for the first 4 km, and each additional km adds P1.50 to the fare. Which of the following can be used to compute a regular fare (F), in pesos, for a 6-km nde?
A. F = 12(7)
B. F=12(7)+1.50
C.=12(150)+7
D.=12+2(1.50)
3. A regular jeepney ride costs P12.00 for the first 4 km, and each additional km adds P1.50 to the fare. How much is the regular fare for a 6-km ride?
A. P15
B. P13.50
C. P14.50
D. P16
4.Which equation represents a vertical line?
A. y =2x
B. x = 2
C. y = 3
D. y = -x
Solve the following problems
The values of x and y for fig. 1) is 5/4 and 4/7, for fig. 2) x = 15, y = 4 and for fig. 3) x = 3 and y = 2
What is Thales theorem?Thales's Theorem or Basic Proportionality Theorem states that if a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.
Given are three figures of triangles,
Figure 1)
5/x+5 = 8/10
50 = 40+8x
x = 5/4
y = 7/7+y = 8/10
70 = 56 +8y
y = 4/7
Figure 2)
12/12+y = 18/18+6
12/12+y = 18/24
48 = 36 +3y
y = 4
12/4 = x/5
x = 15
Figure 3)
y/4 = 1.5/3
y = 2
x/6 = 1.5/3
x = 3
Hence, the values of x and y for fig. 1) is 5/4 and 4/7, for fig. 2) x = 15, y = 4 and for fig. 3) x = 3 and y = 2
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What is the slope of the line that passes through the points (-8, -1) and
(-8, -11)? Write your answer in simplest form.
Answer:
Step-by-step explanation:
The slope of a line is defined as the change in y-coordinate divided by the change in x-coordinate between two points on the line. In this case, the change in y-coordinate between the two points is -11 - (-1) = -10, and the change in x-coordinate is 0 since both points have the same x-coordinate. Therefore, the slope of the line that passes through the points (-8, -1) and (-8, -11) is -10/0, which is undefined.
Mr. Tull bought 6 videotapes and 5 audio tapes. What is the ratio of videotapes to the total number of tapes?
Answer: 6:11
Step-by-step explanation:
Find the total by 6 + 5 =11
He bought 6 videotapes so ratio is 6:11
An equiangular triangle has one side of length six inches. What is the height of the triangle, drawn from that side, to the nearest tenth of an inch?
height = ------------- in.
Answer:
5.2
Step-by-step explanation:
Construct an altitude. Using the Pythagorean theorem, the height is [tex]\sqrt{6^2-3^2} \approx 5.2[/tex]
Luis solves the following system of equations by elimination. {5s+3t=30 2s+3t=-3
The Elimination equations: 3s = 33, s = 11.
What is Equation?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including linear, quadratic, cubic, etc
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.
According to our question-
5s+3t=30
-1(2s+3t=-3)
which will eventually
5s+3t=30
-2s-3t=3
which then becomes
3s = 33, s=11
Hence, The Elimination equations: 3s = 33, s = 11.
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2 1/2 + 3 1/5 x 5 5/8
The solution to the expression 2 1/2 + 3 1/5 x 5 5/8 is 223/2
What is Fraction?fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
2 1/2 + 3 1/5 x 5 5/8 can be solved by converting all the mixed fraction to improper fraction
2 1/2 = 5/2
3 1/5 = 16/5
5 5/8 = 45/8
which reduces it to
5/2 + 45/8 x 16/5
using BODMAS we taking care of the multiplication section first
45/8 x 16/5 = 18
5/2 + 18
18 can be writen as a fraction which is 36/2
5/2 + 36/2 = 41/2
in conclusion the simplified form of the expression is 41/2
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A textbook store sold a combined total of 447 biology and sociology textbooks in a week. The number of sociology textbooks sold was 63 less than the number of biology textbooks sold. How many textbooks of each type were sold?
255 biology and 192 sociology textbooks were sold in a week.
What is linear equation?Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
While the graph of a linear equation with two variables, x and y, creates a straight line, the graph of a linear equation with just one variable, x, forms a vertical line that is parallel to the y-axis.
Step 1:
Let x be the number of biology textbooks and y be number of sociology textbooks.
x + y = 447 ------(1)
x - y = 63 ------(2)
Step 2:
Adding (1) and (2), we get
2x = 510
x = 255
Step 3:
Subtracting (1) from (2), we get
2y = 384
y = 192
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Please help with these two questions!
The inverse of the function g(x) = ∛(2x + 4) is equal to: D. g(x)⁻¹ = 1/2(x³) - 2.
The domain of the function shown in the graph is: B. [-2, 1].
What is an inverse function?In Mathematics, an inverse function can be defined as a type of function that is obtained by reversing (undoing) the operation of a given function (f(x)).
In order to determine the inverse of the given function, we would interchange input value (x) and the output value (y) as follows:
g(x) = ∛(2x + 4)
x = ∛(2y + 4)
Next, we would take the cube root of both sides of the function;
x³ = 2y + 4
2y = x³ - 4
y = (x³ - 4)/2
y = x³/2 - 2
g(x)⁻¹ = 1/2(x³) - 2
How to identify the domain any graph?In Mathematics, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right as follows;
Domain = [-2, 1].
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6am air traffic controller i tracking two plane to tart plane A wa at an altitude of 1500 meter and plane B wa at an altitude of 1115 meter plane A i going altitude at 19 meter per econd and plan B wa gaining altitude at 26 meter per econd let x be the number of econd that have pae
At 55 seconds , both the plane A and plane B will have same altitude.
According to the question,
The altitude of plane A = 1500m
The altitude of plane B = 1115m
Altitude plane A gained = 19m/s
Altitude plane B gained = 26m/s
Let "x" be the number of second
Let the equation of plan A and plane B is
a(x) = m₁ x + 1500
b(x) = m₂ x + 1115
We know how fast they are gaining altitude. The are the m values
m₁ = 19
m₂ = 26
So, now we have
a(x) = 19 x + 1500
b(x) = 26 x + 1115
So , to have same altitude ,
a(x) = b(x)
=> 19 x + 1500 = 26 x + 1115
Solving for x,
=> 26x-19x = 1500 - 1115
=> 17x = 385
=> x = 55 seconds
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An art museum gift shop sells prints of a famous painting. The original
painting is 120 cm wide and 85 cm tall. If the print is 50 cm wide, how tall
is the print?
SOLUTION
The print is 35.41 cm tall.
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
The original painting is 120 cm wide and 85 cm tall.
and, the print is 50 cm wide.
let the print is x cm tall
So, x/ 50 = 85 / 120
120x = 4250
x= 35.41 cm
Hence, the print is 35.41 cm tall.
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Easy i just want confirmation What is 3 to the power of three halves equal to?
- cube root of 9
- square root of 9
- cube root of 27
- square root of 27
The 3 to the power of three halves equal to square root of 27 sqrt(27).
What is the square root?
A square root of a number x is a number y such that y² = x; in other words, a number y whose square is x. For example, 4 and −4 are square roots of 16, because 4² = ² = 16.
A square root is a number that can be multiplied by itself to give the original number.
3 to the power of 3/2 is equal to the square root of 3 to the power of 3, which is equal to the square root of 27. The square root of 27 is approximately 3.872983346207417.
To calculate this value, you can use a calculator or you can use the following formula:
3^(3/2) = sqrt(3^3) = sqrt(27) = 3.872983346207417
Hence, the 3 to the power of three halves equal to square root of 27 sqrt(27).
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Molly works at an electronics store. Her last customer purchased a DVD player for $63.48 and five DVDs for $52.02, including taxes. If the customer paid her with two $100 bills, how much change should she give him?
Answer:
$84.50
Step-by-step explanation:
Add the amounts:
$63.48 + $52.02 = $115.50
Two $100 bills add to $200.
To find the change, subtract the total cost from the amount of money handed over.
$200 - $115.50 = $84.50
Molly should give him $84.50. Thus option B is the correct answer.
The change given must be equal to the balance left after deducting the price of the goods from the total money received.
In this case,
Price of goods = Price of DVD player + Price of five DVDs
= $63.48 + $52.02
=$115.50
Total Money Received = 2 x $100 = $200
Therefore, Change = Total Money Received - Price of goods
= $200 - $115.50
= $84.50
solve
2(2.1z+4.5)<21.6
The solution to the given inequality 2(2.1z + 4.5) < 21.6 to solve for the unknown value of z is z < 3
How to solve inequality?Inequality refers to a statement that is of two quantities in which one is specifically less than (or greater than) another.
The symbols of inequality includes;
Greater than >Less than <Equal to =Greater than or equal to ≥Less than or equal to ≤2(2.1z + 4.5) < 21.6
open parenthesis
4.2z + 9 < 21.6
substract 9 from both sides
4.2z < 21.6 - 9
4.2z < 12.6
divide both sides by 4.2
z < 12.6 / 4.2
z < 3
Hence, z < 3 satisfies the value of z in the inequality 2(2.1z + 4.5) < 21.6
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Hello please solve this with steps
List the possible rational zeros of
f(x)= x^3-6x^2+6x-18 using the rational zero theorem
Answer:
±{1, 2, 3, 6, 9, 18}
Step-by-step explanation:
You want the possible rational zeros of f(x)= x^3-6x^2+6x-18.
Rational root theoremThe rational root theorem tells you the possible rational zeros are of the form ...
±{divisors of the constant term} / {divisors of the leading coefficient}
Here, the leading coefficient is 1, so its only divisor is 1.
The constant term is 18, and its divisors are 1, 2, 3, 6, 9, 18.
The possible rational roots are ±{1, 2, 3, 6, 9, 18}.
__
Additional comment
A graph shows the only real root is between 5 and 6, so none of the roots are rational.
dory orders three soft tacos and three double Deckers for 11.25. Nemo pays 10.00 for four soft tacos and two double Deckers. write a system of equations that represent the lunch orders for dory and Nemo. Use x to represent soft tacos and y to represent double Deckers.
Answer:
Soft tacos are $1.25 each, while double deckers are $2.5 each.
(I didn't have time for a step by step explanation at the moment)
Sorry
PLEASE HELP ASAP! (35 POINTS)
Ummi sees an advertisement for her favorite cereal. Then she writes these quotients.
2.90/10 = 0.29/1 3.48/12 = 0.29.1 4.48/16 = 0.28.1
Part A: What do Ummi's quotients represent in this situation?
Part B: If you were to graph the (weight, cost) pairs for each box, would you be able to draw a straight line through the points? EXPLAIN.
ANSWER ALL PARTS.
Ummi's quotients in this situation represent the unit rates of the advertisement
You will not be able to draw a straight line through the points
Part A: What do the quotients represent?From the question, we have the following quotients parameters that can be used in our computation:
2.90/10 = 0.29/1 3.48/12 = 0.29.1 4.48/16 = 0.28.1
These can be rewritten as
2.90/10 = 0.29/1
3.48/12 = 0.29/1
4.48/16 = 0.28/1
The quotients mean that
Unit rate = Total amount spent/Number of adverts
So, the quotient expressions represent the unit rate
Part B: Would you be able to draw a straight line through the points?Recall that
2.90/10 = 0.29/1
3.48/12 = 0.29/1
4.48/16 = 0.28/1
The values of the quotients are not equal
This means that it is not possible to draw a straight line through the points
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Because m < n m = n am < bn am = bn this is where the function is undefined
Answer: This is where the answer is undefined
Step-by-step explanation:
Edge 2022 :)
Answer: 5th option
Step-by-step explanation:
edge 2023
PLEASE HELP ITS GEOMETRY ASAP HELP ME
What is the approximate percentage of women with platelet counts between 3 and 4.1?
The approximate percentage of women with platelet count between 3 and 4.1 is 350
How to solve for approximate percentage?We should know that platelet deals the cells that are found in our body which assemble together when they discover bad blood in the cells.
The range of women is given as 3-4.1
The average of the women is [tex]\frac{3+4.1}{2}=\frac{7.1}{2}[/tex]
Simplifying the expression we have
= 3.5
The appromimate percentage is 3.1*100=350 women
In conclusion the approximate percentage of women with blood platelet is 350 women
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HELP. ITS AN EMERGENCY. ANSWER WITHIN 20MINS FOR 100 CREDITS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
12: This one if fairy simple: all you need is a line that is not parallel to the line provided, and combined with it, it will provide a solution that's on that line. For example:
y = 2x
x - y = 10
13: Just find two lines that cross (6, -4).
You can use point-slope form:
y - y1 = m(x-x1)
y + 4 = m(x - 6)
then choose two equations with different m's
y = 2(x-6) - 4
y = 3(x-6) - 4
14:
Line one has a slope of two and an intercept at y=0 so it is y = 2x
Line two has a slope of one and an intercept at y=-1 so it is y = x - 1
To find the solution of the system, substitute y:
2x = x - 1
x = -1
Then plug back in:
y = 2 * -1 = -2
So the solution is: (-1, -2)
This morning, Russell took a history test. He got 25 out of 50 problems right. What percentage did Russell get right?
Answer: 40%
Step-by-step explanation:
i tried the cosine rule and the sine rule but i dont get why the answer is wrong.
Answer:
93.2° (nearest tenth)
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Sine Rule} \\\\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]
From inspection of the given triangle:
B = 38°b = 9 cmc = 11 cmSubstitute the values into the sine rule to find the measure of angle C:
[tex]\implies \dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
[tex]\implies \dfrac{\sin 38^{\circ}}{9}=\dfrac{\sin C}{11}[/tex]
[tex]\implies \sin C=\dfrac{11\sin 38^{\circ}}{9}[/tex]
[tex]\implies C=\sin ^{-1} \left(\dfrac{11\sin 38^{\circ}}{9}\right)[/tex]
[tex]\implies C=48.80523914...^{\circ}[/tex]
Interior angles of a triangle sum to 180°.
[tex]\implies A+B+C=180^{\circ}[/tex]
[tex]\implies A+38^{\circ}+48.80523914...^{\circ}=180^{\circ}[/tex]
[tex]\implies A=93.19476086...^{\circ}[/tex]
Therefore, the size of angle A is 93.2° (nearest tenth).
Write the equation of the line that goes through the point (4, -7) and is perpendicular to the line
y +6=-2/5(x-1). Use the table to show your work, if needed, to determine each form, and then give each form.
Point-Slope Form
Slope-Intercept Form
Show your work.
The point-slope form with a slope of 5/2 and a point of (4,-7) is 5x-2y=34.
What is line equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10. Linear equations are classified into three types: point-slope, standard, and slope-intercept.
Here,
The slope of line perpendicular to the line y +6=-2/5(x-1)
m1=5/2
point=(4,-7)
y-y1=m(x-x1)
y+7=5/2(x-4)
2y+14=5x-20
5x-2y=34
The point-slope form for slope given as 5/2 and point as (4,-7) will be 5x-2y=34.
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Please ignore the triangles on the side
best answer gets brainliest
Answer:
103.98cm
Step-by-step explanation:
14 + 14 = 28
20 + 20 = 40
(14(3.14)) / 2+ 14 = 35.98cm
40 + 28 + 35.98 = 103.98cm
36. Rapid City is having its annual citywide celebration. The city wants to rent a bumper-car ride. The pieces used to make the floor are 4 foot-by-5 foot rectangles. The ride covers a rectangular space that is 40 feet by 120 feet. a. How many rectangular floor pieces are needed? b. The ride costs $20 per floor piece and $10 per bumper car. How much would it cost Rapid City to rent the floor and the bumper cars? (You will need to decide how many bumper cars will be appropriate.)
Answer:
a. 240pieces
b. 4800+ 10x
Step-by-step explanation:
a. 40÷4=10, 120÷5=24, 10×24=240
b. (240×20)+ (x×10)= 4800+ 10x ===> x is the number of cars
elimination method. please help
3x+4y=21
3x-2y=11
Answer:
(x, y) = (4 7/9, 1 2/3)
Step-by-step explanation:
You want to solve this system of equations using the elimination method.
3x +4y = 213x -2y = 11AnalysisFirst of all, take a look at the coefficients of the variables:
x: 3 and 3. Subtracting one from the other will eliminate x
y: 4 and -2. Adding twice the second to the first will eliminate y.
ExecutionThe easiest elimination is accomplished by subtracting the second equation from the first:
(3x +4y) -(3x -2y) = (21) -(11)
6y = 10 . . . . . . . . . . simplify
y = 10/6 = 5/3 = 1 2/3 . . . . divide by the coefficient of y
Finding xSubstitute for y to find x.
3x +4(5/3) = 21
x +20/9 = 7 . . . . . . divide by 3
x = 7 -(2 2/9) = 4 7/9
The solution is (x, y) = (4 7/9, 1 2/3).
__
Additional comment
A graphing calculator confirms this solution.
Gia is making chocolate truffles. Using the table, find the constant of proportionality
Using the table we find the constant of proportionality is 15/8
What is constant of proportionality?The ratio that establishes a proportionate link between any two given values is referred to as the constant of proportionality. There are also other names for the constant of proportionality, such as constant ratio, constant rate, unit rate, constant of variation, and even rate of change.
Here,
Since from the table we have to find the constant of proportionality
So, the values of ounces of milk(x) are
30,45
and the values of amount of truffle(y) are
16,24
So for finding the constant of proportionality We take 2 cases,
a)Taking first values of x & y
x/y=30/16
x/y=15/8
b)Taking secondary values of x & y
x/y=45/24
x/y=15/8
Therefore the constant of proportionality is 15/8
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Jacob distributed a survey to his fellow students asking them how many hours they'd spent playing sports in the past day. He also asked them to rate their mood on a scale from 0 00 to 10 1010, with 10 1010 being the happiest. A line was fit to the data to model the relationship.
The best estimate of the average change in mood rating linked with an additional hour spent playing sports is 1.5 points, according to the presented linear function.
Modeling a linear function involves:
y = mx + b
The slope, or m, measures how quickly y changes when x changes by one.
The value of y at x = 0 is represented by the y-intercept, or b.
In the given problem
The amount of time they invested in sports is x.
Their mood score is y.
The required equation is ,
y =1.5 + 5
Given that the slope is m = 1.5, the best estimate of the average change in mood rating resulting from an extra hour spent playing sports is 1.5 points.
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need help on this one
Answer:
19 units
Step-by-step explanation:
You have midline LM marked as 6x+1 and parallel baseline IJ marked as -6x+56 in triangle IJK. You want to know the length of LM.
MidlineThe midline of a triangle is half the length of the parallel base:
LM = 1/2(IJ)
6x +1 = 1/2(-6x +56) . . . . . substitute expressions
6x +1 = -3x +28 . . . . . . . simplify
9x = 27 . . . . . . . . . . . . sdd 3x-1
x = 3
Now, we can find LM:
6x +1 = 6(3) +1 = 19
The measure of LM is 19 units.