Prove that a line parallel to one side of a triangle divides the other two sides proportionally. Be sure to create and name the appropriate geometric figures.
Answers
A line parallel to one side of a triangle divides the other two sides proportionally.
What is triangle?
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
Let ΔADE and ΔABC are two triangles.
Given: DE∥BC
To prove: DB/AD = EC/AE
ΔADE and ΔAC share ∠A
∠A ≅∠A reflexive property
DE∥BC is given
∠ADE ≅ ∠B because they are corresponding angles when transversal
AB cuts parallel lines DE and BC
ΔADE ∽ ΔABC a pair of angles in each are congruent.
AB / AD = AC / AE
because corresponding sides of similar triangle's are proportional.
Now subtract 1 from each side
AB / AD - 1 = AC / AE - 1
Combining fractions,
(AB - AD) / AD = (AC - AE) / AE
⇒ DB / AD = EC / AE
Hence, a line parallel to one side of a triangle divides the other two sides proportionally.
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Geometric figure:
Related Questions
Help with this plsss !!!
Answers
Answer:
:))
Step-by-step explanation:
The maximum value is 22 as the last small line (end of the "whisker") is marked at 22. Hope this helps!! Pls mark as brainliest and lots of points, help ya girl out!!!
how many tens are in 7x30 or 30x7
Answers
There are 3 tens in 7x30 or 30x7.
What is an equation?
A mathematical statement is referred to as an equation when two expressions are connected by the equal sign. A mathematical equation serves as the connection between two expressions on each side of the sign. Usually, there is only one variable and an equal sign.
Equations can be categorized as identities or conditional equations. An identity holds true regardless of the value given to the variables. A conditional equation's variables can only have specific values that produce the truth.
An equation is created by joining two expressions with an equal sign. The solution to an equation is a number that may be used as the variable to generate a true number statement.
Here, we have
7x30 = 7 x 10 x 10 x 10
The value of 7x30 = 210
Hence, there are 3 tens in 7x30 or 30x7.
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The graph of g(x) is a transformation of the graph of f(x) = 2².
Enter the equation for g(x) in the box. g(x) =
Answers
3=k
G(x)=2^ˣ-k
Solution
G(x)=2ˣ - 3
Solve the following equation. Answer as a reduced, mixed number.
9(x − 6) = 8(x + 6)
Answers
The value of x in the equation 9(x − 6) = 8(x + 6) is 102.
How to calculate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
It should be noted that from the information given, the equation is illustrated as:
9(x − 6) = 8(x + 6)
9x - 54 = 8x + 48
Collect the like terms
9x - 8x = 48 + 54
x = 102
The value of x is 102.
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A 224-inch is cut into two pieces. One piece is three times the length of the other. Find the length of the shorter piece.
Answers
A 60-inch piece is the shorter one. 180 inches long is the longer piece.
Step-by-step explanation:
Let's use the variables L and S to symbolise the longer and shorter pieces of pipe, respectively.Since the pipe will be the sum of L and S, we can create the following equation:L + S = 240
Additionally, we are aware that the longer piece is tri-times the shorter piece, which means:L = 3 S
Replace the first equation with the second equation:L + S = 240 ( 3 S ) + S = 240 \s 4 S = 240 \s S = 60
A 60-inch piece is the shorter one.Replace the following with the lengthier piece's length:L = 3 S L = 3 ( 60 )
L =180
180 inches long is the lengthier piece.Let's give the shorter piece a value.The length is "X." The other piece is three times as big, or three times.When you add them up, you get 4X.To learn more about the lengths of the pieces refer to:
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Solve.
9^(3x+1) = 27^2x
Answers
Answer: the equations has no solution
Step-by-step explanation:
[tex]9^{3x+1}=27^{2x}\\\\(3^2)^{3x+1}=(3^3)^{2x}\\\\3^{2(3x+1)}=3^{3(2x)}\\\\3^{6x+2}=3^{6x}\\\\Hence,\\\\6x+2=6x\\\\6x+2-6x=6x-6x\\\\2\neq 0\\\\Thus,\ the\ equations\ has\ no\ solution[/tex]
Determine how many digits are to the right of the decimal point in the answer from multiplying: 0.3568 x 0.042
Responses
A. 5
B. 9
C. 7
D. 3
Answers
The number of the digits after the decimal point is 7. The correct option is C.
What is a number system?A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols. In several numeral systems, the same set of symbols may represent various numbers.
Given that the numbers are 0.3568 and 0.042. The multiplication of the two numbers will be done as,
P = 0.3568 x 0.042
P = 0.0149856
The number of the digits after the decimal is 7.
Therefore, the number of the digits after the decimal point is 7. The correct option is C.
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In how many ways can a person order one ice cream cone with 3 different
flavors of ice cream if there are 14 flavors to choose from and it matters to
the person how the 3 flavors are stacked on the one cone? That is, which
flavor is on the top, middle, and bottom.
Answers
Answer:
2184
Step-by-step explanation:
You want to know the possible number of ways 3 flavors can be chosen from 14 when order matters.
PermutationsThe number of permutations of 14 flavors taken 3 at a time is ...
14 × 13 × 12 = 2184
There are 14 ways to choose the bottom flavor, then 13 ways to choose a different middle flavor, and finally 12 ways to choose a different top flavor. Each flavor can go with any combination of the others, so the total number is the product of 14·13·12, or 2184.
The formula for the number of n things taken k at a time is ...
P(n, k) + n!/(n-k)!
For n=14, k=3, this is the product shown above.
Suppose Colleen works two jobs. At job A, Colleen’s monthly earnings can be described by the distribution N(2100, 200) and at job B, her monthly earnings can be described by the distribution N(550, 70). Assuming that her earnings are independent,
1) What is the mean and standard deviation of the TOTAL amount of money she earns in a month? (this will use knowledge from prior units)
2) What is the probability that she earns more than $2750 in a given month?
Answers
1) The mean and the standard deviation of the total amount of money that she earns in a month are of:
Mean: 2650.Standard deviation: 211.9.2) The probability that she earns more than $2750 in a given month is of: 0.3192 = 31.92%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.When two variables are added, the mean is given by the sum of the means, hence:
[tex]\mu = 2100 + 550 = 2650[/tex]
The standard deviation is given by the square root of the sum of the variances, hence:
[tex]\sigma = \sqrt{200^2 + 70^2} = 211.9[/tex]
The probability that she earns more than $2750 in a given month is one subtracted by the p-value of Z = 2750, hence:
Z = (2750 - 2650)/211.9
Z = 0.47
Z = 0.47 has a p-value of 0.6808.
1 - 0.6808 = 0.3192 = 31.92%.
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how do i find x? please help me, I tried everything :(
Answers
We are given an isosceles triangle because two sides are marked congruent, and therefore, the base angles opposite those sides are congruent. First we need to calculate the angles of the triangle using the Isosceles Triangle Theorem.
We are given a 110° angle with a ray that forms a straight line. Straight lines measure 180° by definition. So, we can calculate the vertex angle in the triangle by creating this equation:
110+x=180
110 degrees plus x creates a 180 degree line. Now, solve for x:
x=70
We have our first angle in the triangle, and we know a triangle must sum up to 180°. We also know the triangle is isosceles, and so the two base angles are congruent. We can create another equation to find all angles in the triangle:
70+2x=180
Remember, we have one angle and because the two base angles are congruent, we can denote them with the same variable and multiply by 2 because the angles will add to each other twice. Solve for x:
2x=110
x=55
So, we now have all there angles and can solve for “x.” Like we did before, a straight line forms one of the rays of the angle. So, we can create the equation:
55+x=180
55° plus x° sums up to 180. Now, solve for “x:”
x=125
Question 10
What is the equation of the line shown?
Answers
does it want the answer in a specific form?
slope intercept form; y = mx + b
slope = 2
b = -1
plug the values in
y = 2x -1 or y = 2/1x -1
The replacement set for an equation is {10, 24, 25, 36}.
The equation is represented by the sentence, "5/6 of a number is 30."
What is the solution set of the equation?
options:
Responses
{10}
{24}
{25}
{36}
ill give brainleist
Answers
{25} is the solution set of the equation {10, 24, 25, 36}.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given set of equation is {10, 24, 25, 36}
Since, The equation is represented by the sentence that is 5/6 of a number is 30.
So the required solution,
5/6 of the number 30 = 25
The solution set of the equation is {25}.
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is 2/5 equivalent to 25
Answers
Answer:
2/5 ≠ 25
Step-by-step explanation:
Given question,
→ Is 2/5 equivalent to 25?
Let's check the problem,
→ 2/5 = 25
→ 0.4 ≠ 25
The equivalent fractions of 2/5 are,
→ 2/5 = 4/10
→ 2/5 = 6/15
→ 2/5 = 8/20
→ 2/5 = 10/25
Hence, 2/5 is not equivalent to 25.
please help ASP WIIL GIVE Brilliance
Answers
Answer:
2. Definition of Midpoint
3. Vertical Angles Theorem
Step-by-step explanation:
Definition of Midpoint is the middle point of a line segment
Vertical Angles Theorem is proving angles that are opposite each other and formed by two intersecting straight lines, are congruent.
Need answer will mark Brainliest
Answers
Answer:
see explanation
Step-by-step explanation:
from the table we can obtain that
f(x ) = 6x³ + 8x - 12 ( 6 0 8 - 12 , being the coefficients of the polynomial )
f(x) is divided by (x + 7) , since evaluated at - 7
the quotient is
6x² - 42x + 302 ( 6 - 42 302, are the coefficients of the quotient )
with remainder - 2126
pls help immediately
Answers
The simplified form of [tex]\sqrt{(2 - \sqrt5)^2} + \sqrt{(2 + \sqrt{5})^2}[/tex] is [tex]\sqrt{9 - 4\sqrt{5}} + \sqrt{9 + 4\sqrt{5}[/tex].
What are surds and indices?We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,
The other type of radicals are indices where a number is raised to such power that is greater than one.
Given, [tex]\sqrt{(2 - \sqrt5)^2} + \sqrt{(2 + \sqrt{5})^2}[/tex].
= [tex]\sqrt{4 - 4\sqrt{5} + 5}+ \sqrt{4 + 4\sqrt{5} + 5}[/tex].
= [tex]\sqrt{9 - 4\sqrt{5}} + \sqrt{9 + 4\sqrt{5}[/tex].
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A substance grows exponentially, and its weight doubles every 3 hours. Suppose it weighs 2 pounds at noon. After how many hours will it weigh 9 pounds? (Do not simplify result)
Answers
The substance will weigh 9 pounds after 4.5123 hours.
Here it is given that every 3 hours the weight of the substance doubles.
At 12 noon it weighed 2 pounds. Hence we will consider the initial weight to be 2.
Let the weight after x hours be w(x)
Here it doubles in 3 hours, hence the growth rate is 100%
Since the growth rate is given, the equation for the growth rate will be
w(x) = w₀.eˣ
where x = no. of 3-hour spans.
Here
w₀ = 2
and w(x) is given 9
Hence,
2eˣ = 9
or, e²ˣ = 9/2
Taking log on both sides we get
loge²ˣ = ln(9/2)
or, 2xloge = ln(9/2)
Since loge = 1 we get
2x = log(9/2)
or, x = 1.5041
Hence they will become 9 pounds after
3 X 1.5041 hours
= 4.5123 hours
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If a polynomial function has integer coefficients, then every rational zero of the function has the form p/q, where p is a factor of the ? and q is a factor of the ?
Answers
If a polynomial function has integer coefficients, the every rational zero of the function has the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
The rational zero theorem says that if a polynomial has integer coefficients then any rational zeros must be of the form p/q where p is the factor of the constant term and q is the factor pf the leading coefficients.
The rational zero theorem is used to determine the rational roots of a polynomial function.
Rational Zero Theorem statement:-
The rational zero theorem states that each rational zero(s) of a polynomial wit integer coefficients
f(x) = anxⁿ + an-1xⁿ⁻¹ + ... + a₂x² + a₁x + a₀ is of the form p/q where,
p is a factor of the constant a₀,
q is a factor of the leading coefficient an,
and p and q are relatively prime.
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3) Juakali used Kingo's computer to type a report document which had 123 pages, and
each page occupied by 70 lines. 36 of 70 lines had 14 words while the remaining lines
had 18 words each. He wanted to take the document with him, and he had only a flash
disk with 256 KB as free space. Can he successfully save the document on the device?
Why?
Answers
To determine whether Juakali can successfully save the document on the flash disk, you can calculate the total number of words in the document and compare it to the amount of free space on the flash disk.
First, calculate the total number of lines in the document by multiplying the number of pages by the number of lines per page:
Total number of lines = 123 pages * 70 lines/page
= 8610 lines
Next, calculate the number of lines with 14 words by multiplying the total number of lines by the proportion of lines with 14 words:
Number of lines with 14 words = 8610 lines * 36/70
= 4380 lines
Calculate the total number of words in the lines with 14 words by multiplying the number of lines by the number of words per line:
Total number of words in lines with 14 words = 4380 lines * 14 words/line
= 61320 words
Calculate the number of lines with 18 words by subtracting the number of lines with 14 words from the total number of lines:
Number of lines with 18 words = 8610 lines - 4380 lines
= 4230 lines
Calculate the total number of words in the lines with 18 words by multiplying the number of lines by the number of words per line:
Total number of words in lines with 18 words = 4230 lines * 18 words/line
= 76140 words
Finally, add the total number of words in the lines with 14 words and the total number of words in the lines with 18 words to find the total number of words in the document:
Total number of words = 61320 words + 76140 words
= 137,460 words
To determine whether Juakali can successfully save the document on the flash disk, you can compare the total number of words in the document to the amount of free space on the flash disk. Since the flash disk has 256 KB of free space and there are 137,460 words in the document, Juakali will not be able to save the document on the flash disk. This is because the document is larger than the amount of free space available on the flash disk.
It is important to note that the capacity of a storage device is usually measured in bytes, and 1 KB is equal to 1024 bytes.
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raphael drives to his office which is 75km away from his house what is his speed if it takes him 1 hour and 15 minutes to get to his office
Answers
Answer:
1km\h
Step-by-step explanation:
like in physics, the calculation of speed is total distance divided by total time, you should do the same in math, and so you do 1 hour (60 minutes) + 15 minutes which gives you 75 minutes, and then you divide 75 km by the time so it should look something like this:
[tex]\frac{75 km}{75 minutes}[/tex] which gives you 1
so raphael is going 1 km\h
Answer:
[tex]\huge\boxed{\sf v = 60\ km/hr}[/tex]
Step-by-step explanation:
Given:Distance = S = 75 km
Time = t = 1.25 hours
Required:Speed = v = ?
Formula:v = S/t
Solution:v = 75/1.25
v = 60 km/hr
[tex]\rule[225]{225}{2}[/tex]
If both dimensions are doubled then which of the following statements about it’s perimeter will be true
Refer to this rectangle
4mm
9mm
The new perimeter will be 3 times larger then the old perimeter
The new perimeter will be 2 times larger then the old perimeter
The new perimeter will be 1/3 times larger then the old perimeter
The new perimeter will be 4. Times larger then the old perimeter
Answers
The new perimeter will be 2 times larger then the old perimeter, if both dimensions of rectangle are doubled.
What is perimeter ?The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width.
The figure's length is essentially revealed by the perimeter. Assume that the perimeter of a square with equal sides will be four times that square's sides. The perimeter of a circle, which is determined by its radius, is known as its circumference.
The new dimensions of rectangle = 4mm and 9mm
The original dimension = 2mm and 4.5 mm
Perimeter of rectangle = P=2(l+w) = 2 (4.5 +2 ) = 13 mm
Perimeter of rectangle after doubled dimension = 2 (9 + 4) = 26
So, the new perimeter will be 2 times larger then the old perimeter
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Write the equation of the line which passes
through the point (2. −3) and has a slope of -2/5
A. 2x + 5y = 4
C. 2x+ 5y = −11
B. 2x+5y = −9
D. 2x-5y = −16
Show work for this question please & thank u
Answers
y = -2/5 x -11/5 is the equation of line with slope -2/5 that passes through the point (2, -3).
What is the equation of line?The slope of the line is the rise to run ratio, or the rise divided by the run. It expresses the slope of a line in the coordinate plane.
The standard form of an equation is y = mx+c.
Here given,
A line with a slope of -2/5 that passes through the point (2, -3).
Simplify y = mx+c with m=2/5 and (x, y)=(2, -3). That is to say,
-3 = -2/5 (2)+c
⇒ -3 = -4/5 +c
⇒ c = -3 + 4/5
⇒ c = (-15 + 4) / 5
=> c = -11/5
When m = -2/5 and c = -11 /5 are substituted in y = mx+c, we get
y = -2/5 x -11/5
As a result, an equation for a line with a slope of -2/5 that passes through the point (2,-3) is y = -2/5 x -11/5.
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Answer:
C. 2x+ 5y = −11
Step-by-step explanation:
You want the equation of the line with slope -2/5 through point (2, -3).
Point-slope equationThe equation of a line with slope m through point (h, k) can be written as ...
y -k = m(x -h)
Then the equation of the line with slope -2/5 through point (2, -3) will be ...
y +3 = -2/5(x -2)
Standard formWe can put this in standard form by ...
5(y +3) = -2(x -2) . . . . . multiply by 5
5y +15 = -2x +4 . . . . . . eliminate parentheses
2x +5y = -11 . . . . . . . . . add 2x-15 to both sides
The desired equation is 2x +5y = -11.
one number is six less than a second number. Four times the first is 2 more than 6 times the second. Finde the numbers
Answers
The numbers are -19 and -13 by the given conditions.
How to solve word problems?
It's actually fairly easy to solve word problems using a tried-and-true step-by-step approach. Aloud to yourself, read the issue.
Make a Drawing.Consider: "What am I trying to find?”List the items that have been provided.Locate the key phrases.Solve.Verify your work.Let the two numbers be x and y
One number is six less than a second number: x = y - 6 ⇒ i
Four times the first is 2 more than 6 times the second: 4x = 6y + 2 ⇒ ii
Substitute the value of x in (ii)
4(y-6) = 6y + 2
4y - 24 = 6y + 2
2y = -26
y = -13
Now substitute the value of y in (i);
x = -13 - 6
x = -19
Hence, the numbers are -19 and -13 by the given conditions.
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b) The price of a house increases exponentially over time. A house presently costs $400,000, and it future
value can be modeled by the equation: A = 400,000 (1.04)*, where A is the value of the home after x years.
i) What percent is the house's value going up each year?
ii) What is the value of the home in 15 years?
ii) Assuming the trend continues, when will the value of the home double?
+4
Answers
Answer: The percent that the house's value is going up each year is given by the factor 1.04 - 1, which is 0.04. This represents a 4% increase in the value of the house each year.
ii) To find the value of the home in 15 years, you can substitute x = 15 into the equation to get:
A = 400,000 (1.04)^15
= 400,000 (1.7589)
= 700,356
Therefore, the value of the home in 15 years is $700,356.
iii) To find when the value of the home will double, you can set the value of A equal to 2*400,000 and solve for x:
2*400,000 = 400,000 (1.04)^x
2 = (1.04)^x
x = log(2)/log(1.04)
= 10.67
Therefore, it will take approximately 10.67 years for the value of the home to double, assuming the trend continues.
The local weather forecast has been accurate for 25 of the past 37 days. Based on this fact, what is the relative frequency probability that the
forecast for tomorrow will be accurate?
Answers
The relative frequency probability that the forecast for tomorrow will be accurate = 16/33.
What is probability?
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means.P(A) = Number of accurate days/ Total number of days
Here, the number of accurate days is 25 and total number of days is 37.
Substitute the above values as follows:
P(A) = 25/37
Hence, the relative frequency probability that the forecast for tomorrow will be accurate = 16/33.
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help meeeeeeeeeee pleaseee
Answers
The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.
What is an expression?An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.
Calculation:It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as
f(x) = 0.48 ln(x+2) + 27
Here x is the distance in miles from the eye of the hurricane.
f(x) is the pressure of the mercury in a barometer in inches
So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is
(Here f(x) = 28)
f(x) = 0.48 ln(x+2) + 27
⇒ 28 = 0.48 ln(x+2) + 27
⇒ 0.48 ln(x+2) = 28 - 27
⇒ ln (x+2) = 1/0.48
⇒ ln(x+2) = 2.0833
Applying exponential base "e" on both sides, we get
(x+2) = [tex]e^{2.0833}[/tex]
⇒ x + 2 = 8.0309
⇒ x = 8.0309 - 2 = 6.0309
When the result is rounded to the nearest whole number, we get x = 6 miles.
Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.
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19. The amount of money in a savings account increases from $ 250 to $ 270 in one month. If the percent increase is the same for every month, how much money will be in the account at the end of the next month?
(A) $ 291.60
(B) $ 295
(C) $ 289.60
(D) $ 300
Answers
Answer:
the answer will be the options A
Mrs.Barrera learned that 21 of her 25 students ride the school bus every morning.What percent of her students ride the school bus every morning?
Answers
The percentage of her students that ride the school bus every morning would be = 84%
What is percentage expression?A percentage expression is an representation of a data set to a fraction of 100.
The total number of students = 25 students
The number of students that ride the school bus = 21
To calculate the percentage of the students that ride the bus the following is done;
= 21/25 × 100
= 2100/25
= 84%
Therefore, the percentage of her students that ride the school bus every morning is 84%
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Which type of information could best be displayed on a two-way frequency table? Select all that apply.
A the number of library books, by genre, borrowed by children and adults during the summer
B the amount of rainfall each week during a year
c the number of daylight hours each day for a month
D the number and type of meals students choose in a lunchroom
Answers
Answer: B C and D
Step-by-step explanation:
Find the inverse function to y=f(x)= 8-9x/5-4x
x=g(y)=
Answers
Therefore , the inverse function to y=f(x)= 8-9x/5-4x is 8-5x /-4x+9 .
A function is what?In mathematics, a function from a set X to a set Y assigns each item in X exactly one element in the other set. The sets X and Y represent the function's domain and codomain, respectively.
Here,
Given :
function :8-9x/5-4x
To find the inverse ,
Inverse of 8-9x. 8-5x 5 4x -4x+9
Steps Function Inverse definition A function g is the inverse of function F if for y=√(x), x=g(v)
y= 8-9x 5-4x
Replace x with y
x = 8-9y/ 5-4y
Solve for y,
x = 8-97/ 5-4y
=>8-5x /-4x+9
Therefore , the inverse function to y=f(x)= 8-9x/5-4x is 8-5x /-4x+9 .
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