BF=CE in a triangle ABC, E and F are mid points of equal sides AB and AC of triangle ABC.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given E and F are mid point of equal sides AB and AC of triangle ABC
In ΔABF and ΔACE
AB=AC (given )
∠A=∠A (common angle )
The side FA is equal to EA
If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent
∴ΔABF≅ΔACE (SAS rule)
∴BF=CF ( Corresponding parts of Congruent triangles.)
Hence, in a triangle ABC, E and F are mid points of equal sides AB and AC of triangle ABC then BF=CE.
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Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
The solution set for the inequality is,
''A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.''
What is Inequality?Any relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ 3 (8 - 4x) < 6 (x - 5)
Now, Simplify the inequality as,
⇒ 3 (8 - 4x) < 6 (x - 5)
⇒ 24 - 12x < 6x - 30
⇒ 24 + 30 < 6x + 12x
⇒ 54 < 18x
Divide by 18;
⇒ 54/18 < 18x/18
⇒ 3 < x
Hence, The solution of inequality on number line is,
⇒ A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
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give an example of a negative correlation curve
Plotting the relationship between the number of hours studied and exam results reveals a negative correlation curve, where the exam results get worse as the number of hours studied rises.
The point (10,70) would be plotted on the negative correlation curve, for instance, if a student spent 10 hours studying and received a 70 on their exam. A downward sloping negative correlation curve would result as study time increased and exam score decreased. A graph illustrating the relationship between two variables, where an increase in one variable is accompanied by a drop in the other, is called a negative correlation curve. Numerous various types of situations, such as the amount of hours studied and exam results, might demonstrate this type of link. Exam scores typically decline as the amount of study time increases.
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What is the constant of variation for the subscription cost based on the number of weeks?
$1.50
$7.50
$15.00
$30.00
The constant of variation for the subscription cost based on the number of weeks is $7.5.
What is Slope?
A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
The straight line passes through the point
(4, 30), (8, 60) and (12, 90)
so, slope of line passing through the points
m = (60- 30)/ (8-4)
m = 30/ 4
m = 7.5
Thus, the constant of variation is $7.5.
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lindsay lines the bottom of the first pan with aluminum foil. the area of the rectangular piece of foil is 12 1/3 square inches its length is 4 3/4 hat is the width of the foil
The width of the foil is 37//19 inches
How to determine the width of the foilFrom the question, we have the following parameters that can be used in our computation:
Area of the rectangular piece of foil = 12 1/3 square inches
Length = 4 3/4 inches
The width is calculated as
Width = Area/Length
Substitute the known values in the above equation, so, we have the following representation
Width = (12 1/3)/(4 3/4)
Evaluate
Width = 37//19
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Factor out the GCF of 18x^3y^4+24x^2y^5
What is 5^2 + 45 - 67 + 15x, when x is 7?
Answer:
108
Step-by-step explanation:
5^2 + 45 - 67 + 15x when x = 7
= 5^2 + 45 - 67 + 15(7)
= 25 + 45 - 67 + 105
= 70 - 67 + 105
= 3 + 105
= 108
So, the answer is 108
Mrs. Cook used six jars of jelly to make sandwiches for the neighborhood kids at the pool. If she used 1/10 jar of jelly on each sandwich, how many sandwiches did she make?
Mrs. Cook was able to make 60 sandwiches using 6 jars of jelly.
Determine number of sandwichMrs. Cook was able to make 60 sandwiches. To find the answer, we can use the following equation:
Total number of sandwiches = (Total amount of jelly) / (Amount of jelly used per sandwich)
In this case, the total amount of jelly is 6 jars, and the amount of jelly used per sandwich is 1/10 jar.
Plugging these values into the equation gives us: Total number of sandwiches = (6 jars) / (1/10 jar)
To solve this equation, we can multiply the numerator and denominator by 10 to get rid of the fraction:
Total number of sandwiches = (6 jars × 10) / (1/10 jar × 10)
Simplifying gives us: Total number of sandwiches = 60 jars / 1 jar
Finally, we can cancel out the "jars" units to get:
Total number of sandwiches = 60
Therefore, Mrs. Cook was able to make 60 sandwiches using 6 jars of jelly.
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(Scale Factor LC)
Figure 1 and figure 2 are right triangles.
two right triangles labeled figure 1 and figure 2, where the legs of figure 1 are 3 units long and the legs of figure 2 are 5 units long
What scale factor was used to produce Figure 2 from Figure 1?
3 over 5
5 over 3
3
5
The scale factor that was used to produce Figure 2 from Figure 1 include the following: B. 5 over 3.
What is scale factor?In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)
Substituting the given parameters into the scale factor formula, we have the following;
Scale factor = 5/3
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Sally is 12 years old and Uncle Mike is three times as old. How many years must pass before her Uncle Mike is only twice as old as Sally? How many years ago was Uncle Mike 7 times as old?
Answer:
Uncle Mike was 7 times as old as Sally 17 years ago.
Step-by-step explanation:
Let's call Uncle Mike's current age "x."
Sally is 12 years old, so x = 12 * 3 = 36 years old.
We are looking for years that must pass before Uncle Mike is only twice as old as Sally. So we need to find the age when x = 2 * (12 + n), where n is the number of years that have passed. Solving for n:
36 = 2 * (12 + n)
36 = 24 + 2n
12 = 2n
n = 6
So, six years must pass before Uncle Mike is only twice as old as Sally.
To find out how many years ago Uncle Mike was 7 times as old as Sally, we need to find the age when x = 7 * (12 - m), where m is the number of years ago. Solving for m:
36 = 7 * (12 - m)
36 = 84 - 7m
120 = 7m
m = 17
So, Uncle Mike was seven times as old as Sally 17 years ago.
Refer to the circle graph below. Suppose there are 300 students at York Middle School. Determine the number of students that have veggies as a snack. No Snack 12% Fruit. 23% Chips · 18% Cheese 15% Veggies 17% L Cookies 15%
The number of students that have veggies as a snack is equal to 51 students.
What is a circle graph?In Mathematics, a circle graph is sometimes referred to as a pie chart and it can be defined as a type of graph that is used for the graphical representation of the proportional relationship between each part to a whole, especially by dividing a circle into various sectors or sections.
Since there are 300 students at York Middle School, the number of students that have veggies as a snack can be calculated as follows;
Number of students that had veggies = 17/100 × 300
Number of students that had veggies = 0.17 × 300
Number of students that had veggies = 51 students.
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What is 14 oz to ml?
We know that :1 oz. to ml = 29.57353 ml, 2 oz. to ml = 59.14706 ml and so on. Therefore, based on the above information:
14 oz. to ml. = 414.0294156 milliliter.
Milliliter:
A milliliter (ml) equals 1/1000 of a liter or 0.001 liter. The liter (Commonwealth English spelling liter, US English spelling liter) is a unit of volume. There are two official symbols. The Latin letter el is l and L in both cases. The liter is not an SI unit but can be used with SI. The SI unit of volume is the cubic meter (m³).
Fluid Ounce:
A fluid ounce is actually a fairly simple unit of measurement. In the Imperial system, one ounce of liquid is 28.41306 ml, whereas in the US it is 29.57353 ml.
These measures are important to know if you want to convert fluid ounces to ml. This is a very old dimension and many have decided it is worth using. I need to find the difference between British fluid ounces and US fluid ounces. A British fluid ounce is 1/160 of an imperial gallon and a US fluid ounce is based on a gallon of wine which is 231 cu. inch.
We know that:
1 milliliter = 0.0351951 oz.
Therefore,
milliliter (mL) = Ounce Value × 29.5735296
⇒ mL = 14 × 29.5735296
⇒ mL = 414.029
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Como convertir un decimal con entero a fracción
Answer: Para convertir un decimal a una fracción, coloque el número decimal sobre su valor posicional. Por ejemplo, en 0.6, el seis está en el lugar de las décimas, entonces colocamos 6 sobre 10 para crear la fracción equivalente, 6/10. Si es necesario, simplifica la fracción.
Step-by-step explanation:
cuanto es 2 + 2 +2 +3 +2+ +++2++ +2
The equivalent sum of the given expression is 15.
What is addition?Addition of a number to an existing number is a method of increasing the magnitude of the existing number.
We can explain addition as -
{a} + {b} = {c}
For example -
2 + 3 = 5
Given is to find the sum -
2 + 2 + 2 + 3 + 2+ 2 + 2
We can write the sum as -
2 + 2 + 2 + 3 + 2+ 2 + 2
4 + 5 + 4 + 2
9 + 4 + 2
15
Therefore, the equivalent sum of the given expression is 15.
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{Question in English -
What is 2 + 2 +2 +3 +2+ +++2++ +2?}
What are some conversion factors?
A conversion factor is a mathematical expression that is used to convert a quantity from one unit of measure to another. It is a ratio that expresses the relationship between two different units of measurement.
There are many conversion factors used to convert one unit of measure to another. Here are some common conversion factors that you may find useful:
1 inch = 2.54 centimeters
1 foot = 0.3048 meters
1 mile = 1.609 kilometers
1 pound = 0.4536 kilograms
1 ounce = 28.35 grams
1 gallon = 3.785 liters
1 liter = 1000 milliliters
1 meter = 100 centimeters
1 kilometer = 1000 meters
1 square meter = 10.764 square feet
1 cubic meter = 35.315 cubic feet
1 atmosphere = 101.3 kilopascals
These are just a few examples of the many conversion factors that are used in various fields of science, engineering, and everyday life. It's important to know and use the appropriate conversion factor when converting units of measure to ensure accurate and meaningful results.
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solve for y 3/2x + 12 = - y
Step-by-step explanation:
3/2x + 12 = -y
divide all sides by -1
-y/-1 = (3/2x)/-1 + 12/-1
y = -3/2x - 12
What is A∩B in math?
In maths, A∩B refers to the intersection of two sets, A and B. This means that it includes all the elements that are in both sets A and B. For example, if A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, then A∩B = {3, 4}, as these are the elements that are in both sets.
To find the intersection of two sets, you can list out all the elements in each set and then look for the ones that are in both. Alternatively, you can use a Venn diagram to visually represent the two sets and their intersection.
Here is an example using a Venn diagram:
A = {1, 2, 3, 4}
B = {3, 4, 5, 6}
As you can see, the intersection of A and B is the area where the two circles overlap, which includes the elements 3 and 4. Therefore, A∩B = {3, 4}.
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Standard Questions
Question Progress
10
Karim is 2.03 metres tall.
Lucas is 1.59 metres tall.
Carlo is taller than Lucas by half the difference between Karim's height and
Lucas's height.
How tall, in metres, is Carlo?
Answer:
.28
Step-by-step explanation:
you subtract Lucas's from karim's hight wich is .56 then devid in by 2 wich is .28
Check that the EAN-13 barcode of Mr. Chips Nacho Cheese Flavor (100 g) 4-800016-653094 is valid or invalid.
Final Answer:
(The final answer of your computation)
Therefore, the EAN-13 code is
The EAN-13 code of Mr. Chips Nacho Cheese Flavor (100 g) 4-800016-653094 is valid.
To check the validity of the EAN-13 barcode, we need to perform a computation based on the numbers in the code. The EAN-13 code consists of 13 digits, where the first digit represents the number system, the next five digits represent the manufacturer code, the following five digits represent the product code, and the last digit is the check digit.
The check digit is calculated based on the previous 12 digits using a specific algorithm.
For the given EAN-13 code 4-800016-653094, we can extract the previous 12 digits as 480001665309. To calculate the check digit, we need to multiply the first, third, fifth, etc. digits by 3, and the second, fourth, sixth, etc. digits by 1, and then sum these products. In this case, the calculation is as follows:
(4x3) + 8 + (0x3) + 0 + (0x3) + 1 + (6x3) + 6 + (5x3) + 3 + (0x3) + 9 = 74
The check digit is then the smallest number that, when added to the sum above, results in a multiple of 10. In this case, the check digit is 6, since 74 + 6 = 80, which is a multiple of 10.
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108 in the ratio 4 : 5
9x-3y=15 3x+3y=-3 What is the solution? ! Solve A (6,-7) B (2,1) C (1,-2) by elimination.
Answer:
(1, - 2 )
Step-by-step explanation:
9x - 3y = 15 → (1)
3x + 3y = - 3 → (2)
add (1) and (2) term by term to eliminate y
(9x + 3x) + (- 3y + 3y) = 15 - 3
12x + 0 = 12
12x = 12 ( divide both sides by 12 )
x = 1
substitute x = 1 into either of the 2 equations and solve for y
substituting into (2)
3(1) + 3y = - 3
3 + 3y = - 3 ( subtract 3 from both sides )
3y = - 6 ( divide both sides by 3 )
y = - 2
solution is (1, - 2 )
how to find the coefficient of variance
Answer:
56
Step-by-step explanation:
Scott is trying to decide which amusement park to go to during vacation. Amusement park A costs $2.50 per ride with a $40 entry fee. Amusement park B costs $4.00 per ride with a $30 entry fee. Which inequality can be used to find x, the minimum number of rides Scott has to go on so that the total charge at amusement park A costs less than the total charge at amusement park B?
The minimum number of rides Scott has to go on is 7 or more rides.
What is inequality ?
An inequality is a mathematical statement that compares two quantities, expressing that one is greater than, less than, or equal to the other. Inequalities are often represented using inequality symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).
According to the question:
Let's start by finding an expression for the total cost of each amusement park in terms of the number of rides, x. For Amusement Park A, the total cost is:
Total cost for Amusement Park A = 40 + 2.5x
This is because there is a $40 entry fee plus $2.50 for each ride.
For Amusement Park B, the total cost is:
Total cost for Amusement Park B = 30 + 4x
This is because there is a $30 entry fee plus $4.00 for each ride.
To find the minimum number of rides Scott has to go on so that the total charge at amusement park A costs less than the total charge at amusement park B, we can set up an inequality comparing the total cost of the two amusement parks:
40 + 2.5x < 30 + 4x
This inequality is saying that the total cost for Amusement Park A is less than the total cost for Amusement Park B. We want to solve for x, which represents the minimum number of rides that Scott has to go on to make Amusement Park A cheaper than Amusement Park B.
To solve for x, we can simplify the inequality:
40 + 2.5x < 30 + 4x
10 < 1.5x
6.67 < x
So the minimum number of rides Scott has to go on to make Amusement Park A cheaper than Amusement Park B is 7 (rounded up from 6.67). Therefore, if Scott goes on 7 or more rides, Amusement Park A will be cheaper than Amusement Park B.
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what is unit circle table ?
A unit circle table is a table that lists the coordinates of points on a unit circle, which is a circle with a radius of 1.
The unit circle is often used in trigonometry to represent the relationships between angles and the values of the trigonometric functions sine, cosine, and tangent. The table typically lists the angle in radians or degrees in one column, and the corresponding values of sine, cosine, and tangent in other columns. The table may also include values for other trigonometric functions such as cosecant, secant, and cotangent, as well as their inverse functions such as arcsine, arccosine, and arctangent.
The unit circle table is a useful reference tool for solving trigonometric equations and for understanding the geometric properties of the trigonometric functions. Many mathematical and scientific applications use the unit circle, including engineering, physics, and astronomy.
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Amy Folsom had a small pickup truck that can carry
5
8
cord of firewood. Find the number of trips needed to deliver 40 cords of wood
Amy Folsom will need to make 64 trips to deliver 40 cords of wood with her small pickup truck.
Number of tripsTo find the number of trips needed to deliver 40 cords of wood, we can use the following formula:
Number of trips = Total amount of wood / Amount of wood per trip
In this case, the total amount of wood is 40 cords and the amount of wood per trip is 5/8 cord.
Plugging these values into the formula, we get:
Number of trips = 40 / (5/8)
Number of trips = 40 * (8/5)
Number of trips = 64
Therefore, Amy Folsom will need to make 64 trips to deliver 40 cords of wood with her small pickup truck.
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Half of the sum of two numbers is 12, while one-fourth of their products is 35. Find the numbers
Answer:
10 and 14
Step-by-step explanation:
let the 2 numbers be x and y , then
[tex]\frac{1}{2}[/tex] (x + y) = 12 ( multiply both sides by 2 to clear the fraction )
x + y = 24 ( subtract x from both sides )
y = 24 - x → (1)
and
[tex]\frac{1}{4}[/tex] xy = 35 ( multiply both sides by 4 )
xy = 140 → (2)
substitute y = 24 - x into (2)
x(24 - x) = 140
24x - x² = 140 ( subtract 140 from both sides )
24x - x² - 140 = 0 ( multiply through by - 1 and arrange in standard form )
x² - 24x + 140 = 0 ← in standard form
(x - 10)(x - 14) = 0 ← in factored form
equate each factor to zero and solve for x
x - 10 = 0 ⇒ x = 10
x - 14 = 0 ⇒ x = 14
corresponding values of y are by substituting values of x into (1)
x = 10 → y = 24 - 10 = 14
x = 14 → y = 24 - 14 = 10
then the numbers are 10 and 14
factorise using common factor method 2x-8
Answer:
2(x-4)
Step-by-step explanation:
2 is common and (x-4) is the leftover.. simple as that.
compare 2.2 and 14/4
we can conclude that 2.2 is less than 14/4.
what is fraction ?
A fraction is a mathematical representation of a part of a whole or a ratio between two quantities. It is typically represented as a top number (numerator) divided by a bottom number (denominator), separated by a horizontal line.
For example, the fraction 3/4 represents three parts out of four equal parts of a whole. The numerator (3) represents the number of parts, while the denominator (4) represents the total number of parts that make up the whole.
According to the question:
To compare 2.2 and 14/4, we can convert 14/4 to a decimal:
14/4 = 3.5
Now we can see that 2.2 is less than 3.5. Therefore, we can say that:
2.2 < 14/4
Another way to compare them is to convert both numbers to a common denominator. In this case, the common denominator of 2.2 and 14/4 is 10:
2.2 = 22/10
14/4 = 35/10
Now we can see that:
22/10 < 35/10
Therefore, we can conclude that 2.2 is less than 14/4.
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What does surface analysis chart show?
Answer:
Step-by-step explanation:
A surface analysis chart is a type of weather map that displays information about the current pressure and wind patterns over a particular region. The chart provides a snapshot of the weather conditions at a specific point in time and helps meteorologists to identify and track the location, movement, and development of high- and low-pressure systems, fronts, and other weather features.
The surface analysis chart typically shows a map of the Earth's surface with various meteorological symbols and information, including isobars (lines of equal pressure), fronts (boundaries between different air masses), and wind direction and speed. The chart may also include information about temperature, precipitation, and cloud cover.
Surface analysis charts are used in weather forecasting, air traffic control, and other applications where an understanding of current weather conditions is important. They provide important information for short-term weather forecasting, such as predicting the location of fronts and the development of thunderstorms, and for long-term weather planning, such as determining the most suitable routes for shipping or aviation.
What is the annual interest for a principal of $4200 at a simple annual interest rate of 3%?
Answer:
$126Step-by-step explanation:
At a simple annual interest rate of 3%, the following formula might be used to determine the annual interest for a $4200 principal:
Interest is calculated as follows: Principal * Rate * Time
Where,
Capital = $4200
Rate = 3% (expressed as a decimal by dividing by 100) (expressed as a decimal by dividing by 100)
t = one year
When we enter the values, we obtain:
Interest is equal to $4200 multiplied by 0.03 times one.
Therefore, $126 would be the annual interest for a $4200 principal at a basic annual interest rate of 3%.
Five children played a card game. At some point, each of them had to give a card to each of the other ones. Then, everybody had to discard the cards just received, and continue the game without them. How many cards in total were in the game before this exchange if after it only one half of the cards were played with?
Assuming that each of the five children had the same amount of cards before the exchange, the total number of cards in the game was twenty.
What is amount?Amount is the term used to describe a quantity or size of something it will stop to use to refer your numbers of object items are people with as well as measure of money time and distance.
The exchange between the children meant that each of them gave away four cards, for a total of twenty cards being given away. Thus, before the exchange there were forty cards in the game. After the exchange, each of the five children had ten cards, and only half of those cards were played with, meaning that the total number of cards in the game was twenty.
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