The two side lengths are congruent, and their opposite angles are congruent, and the hypotenuse is the length of either leg times the square root of two, √2.
A 45° 45° 90° triangle is a special type of isosceles right triangle where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.
A 45°−45°−90° triangle is a commonly encountered right triangle whose sides are in the proportion 1:1:√2.
properties of 45°-45°-90°:
It's the only possible right triangle that is also an isosceles triangle, and it has the smallest ratio of the hypotenuse to the sum of the legs.It has the greatest ratio of the altitude from the hypotenuse to the sum of the legs.To know more about 45° 45° 90° triangle:
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What is a log 10 transformation?
A log 10 transformation is a mathematical operation that is used to change the scale of a variable in a data set. The log 10 transformation is applied to the variable by taking the base-10 logarithm of each value in the data set. The result of this operation is a new variable that is on a different scale than the original variable.
The log 10 transformation is commonly used in statistics and data analysis to normalize data that is on a large scale, such as data that spans several orders of magnitude. By applying the log 10 transformation, the data is transformed into a more manageable scale that is easier to work with and analyze.
The log 10 transformation can also be used to stabilize the variance of a variable, this is particularly useful when the data is positively skewed. The log 10 transformation can also be useful for data that has a multiplicative relationship, for example, population growth or stock prices.
It is important to note that the log 10 transformation can only be applied to data that is positive and greater than zero because the logarithm of zero or a negative number is not defined.
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Which expression is equivalent to 7(d - 4)?
Submit
7(-4+ d)
-4(d + 7)
(d + 7).-4
-28d + 7
The phrase that is identical to 7(d - 4) in option B is -4(d+ 7). A mathematical expression is a statement that contains a minimum of two numbers .
what is expression ?A mathematical expression is a phrase having a minimum of two numbers or variables and at least one mathematical operation. This mathematical operation may be addition, subtraction, multiplication, or division. An expression's basic components are as follows: Expression is (Number/Variable, Math Operator, Number/Variable). A mathematical expression is a statement that contains a minimum of two numbers or variables and at least one mathematical operation. Let's learn how to write expressions. A number is 6 more than half of another number, and that other number is called x. In a mathematical expression, this statement is represented as x/2 + 6.
given
The correct response is 4 less than 7, since 4 is less than 7.
Thus, 7-4=3 could be considered.
The first section of 7–4 appears to be answer B.
The phrase that is identical to 7(d - 4) in option B is -4(d+ 7).
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An item costs $320 before tax, and the sales tax is $16.
Find the sales tax rate. Write your answer as a percentage.
3. How many groups 1/2 of days are in 1 week?
groups
Trapezoid LMNO with bases LM and ON , and Median PQ
If PQ = t +6, LM = t +3 and ON = 3t – 7, find ON
The length of base ON of trapezoid LMNO is 17 units
We know that the median theorem of trapezoid, which states that the median of a trapezoid is parallel to each base. Also, the length of the median equals one-half the sum of the lengths of the two bases.
Consider the following diagram of trapezoid LMNO with bases LM and ON , and Median PQ.
Given that the equations for the bases and median of trapezoid LMNO .
PQ = t +6, LM = t +3 and ON = 3t – 7
From above theorem,
PQ = 1/2 (LM + ON)
t + 6 = 1/2 ( t + 3 + 3t - 7)
2(t + 6) = 4t + 3 - 7
2t + 12 = 4t - 4
4t - 2t = 12 + 4
2t = 16
t = 8 units
So, ON = 3t - 7
ON = 3(8) - 7
ON = 24 - 7
ON = 17 units
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SHOW YOUR WORK 256 divided by 6400
For this exponential function,
what is the output value (y)
when the input value (x) is 2?
y = 4.2x
(2, [?])
Enter
The final statement is: y=16
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here: The exponential function y=4×2ˣ
Therefore for x=2 we get
y=4×2²
y=16
Hence, The value of y at x equal to 2 is 16
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1.The income of man increase in the ratio 7 : 8 . If the increase in his income is rs 4500 per month find his new income.
2.The ages of two sister are in the ratio 7 : 5 if the age of elder sister is 15 years 9 months, what is the age of younger sister.
The new income is new income.
Rs. 36000 per month. 6 years and 6 months.What is the new income.?Generally, To find the new income of the man, we can use the formula: New Income = Original Income + Increase in Income
Since the ratio of increase in income is 7:8, we can assume the original income to be 7x and the new income to be 8x.
The increase in income is given as Rs. 4500 per month, so we can set up the equation as:
8x = 7x + 4500
By solving for x, we get that
x = 4500.
Therefore, the new income of the man is
8x = 8 * 4500
= Rs. 36000 per month.
b)
The ages of the two sisters are in the ratio 7:5. If the elder sister is 15 years 9 months old, we can assume her age in months to be
15*12 + 9 = 189 months.
Let's assume x be the age of younger sister in months.
So, according to the ratio 7:5, we can set up the equation as:
x = (5/12)*189
By solving this equation we get
x= 78.75 months, which is roughly 6 years and 6 months.
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Please answer #6a and 6b
The possible values of x for the given triangle ABC are 0.75<x<8.
What is the triangle inequality theorem?The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.
Given that, m∠A < m∠B < m∠C.
a) From triangle ABC,
BC<AC<AB
2x+3<6x<5x+8
Now, 2x+3<6x
Subtract 2x on both the sides of an inequality, we get
3<4x
Divide 4 on both the sides of an inequality, we get
0.75<x
Here, 6x<5x+8
Subtract 5x on both the sides of an inequality, we get
x<8
So, possible values of x are 0.75<x<8
b) From triangle ABC,
BC<AC<AB
3x+1<4x+8<7x+2
Now, 3x+1<4x+8
Subtract 3x on both the sides of an inequality, we get
1<x+8
Subtract 8 on both the sides of an inequality, we get
-7<x
Here, 4x+8<7x+2
Subtract 4x on both the sides of an inequality, we get
8<3x+2
Subtract 2 on both the sides of an inequality, we get
6<3x
Divide 3 on both the sides of an inequality, we get
2<x
So, possible values of x are -7<x<2
Therefore, the possible values of x for the given triangle ABC are 0.75<x<8.
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For what value of a the system of equations Ax Y 2 and 6x 2y 3 has a unique solution?
The value of 'a' for which the system of equations has a unique solution is a = 4/3.
The given system of equations can be written as:
Ax = 2
6x – 2y = 3
To find the value of 'a' for which the system has a unique solution, we can solve the equations for 'x' and 'y' and equate them.
Solving for 'x' in the first equation, we get:
x = 2/a
Solving for 'y' in the second equation, we get:
y = (3 + 6x)/2
Substituting the value of 'x' in the above equation, we get:
y = (3 + 6(2/a))/2
Equating the two equations, we get:
2/a = (3 + 6(2/a))/2
Multiplying both sides of the equation by 'a', we get:
2 = 3a + 6
Subtracting 2 from both sides of the equation, we get:
3a = 4
Dividing both sides of the equation by 3, we get:
a = 4/3
Therefore, the value of 'a' for which the system of equations has a unique solution is a = 4/3.
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Boxes A and B contain some counters.
6y + 2
counters
Box A
Clip A19b
4y + 6
counters
Box B
The number of counters in each box is the same.
Work out the value of y
Find a Clip
106
Please give me the answer it’s really hard no one will help
By simple algebra, The number of counters in each box is 2.
What is Algebra?Algebra is the study of mathematical symbols and the methods for incorporating them into formulas.
Why is algebra so difficult?Since algebra is the first math subject most students take where they must deal with variables, complex concepts, and problem-solving abilities, many find it scary.
Given,
counter in Box A = 6y+2
counter in Box b=4y+6
Since there are the same amount of counters in both boxes.
hence
6y+2=4y+6
6y-4y=6-2
2y=4
y=2
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Find the volume of the composite solid. Round your answer to the nearest tenth.
The volume of the composite solid round to the nearest tenth is 83.7 inches³.
What is Volume?Volume of a three dimensional shape is the space occupied by the shape.
There are 2 hemispheres and a cylinder in the given composite solid.
Volume of hemisphere = [tex]\frac{2}{3}[/tex] π r³, where r is the radius.
Volume of the cylinder = π r² h, where r is the radius and h is the height.
Here r = 2 inches and
h = 8 - 4 = 4 inches
Volume of hemisphere = [tex]\frac{2}{3}[/tex] π × 2³
= [tex]\frac{16}{3}[/tex] π
There are two hemispheres.
Volume of two hemispheres = 2 × [tex]\frac{16}{3}[/tex] π = [tex]\frac{32}{3}[/tex] π
Volume of the cylinder = π r² h
= π × 2² × 4
= 16 π
Volume of the composite Solid = [tex]\frac{32}{3}[/tex] π + 16 π
= [tex]\frac{80}{3}[/tex] π
= 83.7 inches³
Hence the volume of the composite solid is 83.7 inches³.
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Due to delay, a company had to extend a project from 108 day to 137 day. What wa the percentage increae in time to complete the project, round you anwer to the nearet tenth
The percentage increase in project completion time is 26.85%.
What is percent?Percentage is a relative number that represents the hundredth part of any quantity. One percent (symbolized 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount. percentage. Mathematics percentile is a related topic. A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100.
Here,
=(137-108)/108*100
=26.85%
The percentage increase in time to complete the project is 26.85%.
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Which statement correctly describes this picture?
The length of an object in feet is equal to 3 times it's length in yards. The length of the boat is 36 feet. Write and solve a multiplication equation to find the length of the boat in yards
In linear equation ,The length of waterslide is 12 yards.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Given that,
The length of an object object in feet is equal to 3 times it’s length in yards
The length of wall water side slide is 36 feet
Let "y" be the length of object in yards
From given,
Length in feet = 3 times length in yards
36 = 3 * y
3y = 36
y = 36/3
y = 12
Thus length of waterslide is 12 yards.
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A rectangle has an area of 16x + 24. What could the length and width of the rectangle be
The length and width of the rectangle will be 2 and 8x + 12
Area of rectangle = 16x + 24.
A rectangle is a four-sided geometric shape having opposite sides that are equal in length and four right angles. The length and width of the rectangle are its opposing sides.
A rectangle's area is found by multiplying its length and width together, so:
Area = length x width
Calculating the length and width of the rectangle -
Factoring out 2 from the equation -
Therefore -
2 (8x+12)
Since, the area is the length times width, thus -
2 x (8x+12)
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The sum of an integer and seven times next consecutive odd integers -26 find the value of the lesser integer
Answer:
-5
Step-by-step explanation:
Let n = an integer
Let (n+2) = the next consecutive odd integer
n + 7( n + 2) = -26 Distribute the 7
n + 7n + 7(2) = -26
n + 7n + 14 = -26 Combine like terms
8n +14 = -26 Subtract 14 from both sides
8n + 14 - 14 = -26 -14
8n = -40 Divide both sides by 8
n = -5
The next consecutive odd integer would be -3
Consecutive just means the next number.
Need answer quick 65 points and brainlyest
Graph using this picture
y+4=25(x−3)
The linear function y = 25x - 79 is plotted on a graph with x - intercept at 3.16
What is Graph of Linear FunctionA graph of a linear function is a line that goes through the origin (0, 0). The line can be described by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of the line can be positive, negative, zero, or undefined.
In this problem, the linear function given y + 4 = 25(x - 3) can be written in slope - intercept form and then plotted in a graph using a graphical calculator.
y + 4 = 25(x - 3), the linear function can written;
y + 4 = 25(x - 3) = y + 4 = 25x - 75 ;
This becomes y = 25x - 75 - 4;
Collecting like terms
y = 25x - 79
Plotting this on a graph;
The line passes through the x - axis at 3.16 which is the x - intercept
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A carpenter bought a piece of wood that was 0.42 meters long. Then she sawed 0.3 meters off the end. How long is the piece of wood now?
The length of piece of wood now will be;
⇒ 0.72 meters
What is Addition?
A process of combining or adding two or more numbers is called addition.
Given that;
A carpenter bought a piece of wood that was 0.42 meters long.
And, She sawed 0.3 meters off the end.
Here,
A carpenter bought a piece of wood that was 0.42 meters long.
And, She sawed 0.3 meters off the end.
Hence, The length of piece of wood now = 0.42 + 0.3 meter
= 0.72 meters
Thus, The length of piece of wood now = 0.72 meters
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What is the best explanation of irrational numbers?
The best explanation of Irrational Numbers is that , the numbers that cannot be expressed as a ratio of integers are called as Irrational Numbers .
What are Irrational Numbers ?
The Irrational numbers are the real numbers that cannot be represented in the form of a ratio ([tex]\frac{p}{q}[/tex]) . In other words, the real numbers that are not rational numbers are called as irrational numbers.
For Example : [tex]\pi[/tex] is an irrational number as [tex]\pi =3.1415925...[/tex] The decimal value in the expansion never stops at any point.
Some Property of Irrational Numbers are :
(i) The Irrational numbers consist of only non-terminating and non-recurring decimals.
(ii) The Irrational Numbers are real numbers only.
(iii) The Addition, subtraction, multiplication, and division of any two irrational numbers may or may not be a rational number.
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Given this equation in slope y - intercept form y=2x+5, the slope, and the y-intercept are represented as ______.
Answer:
slope is 2 ,, y intercept is 5
Step-by-step explanation:
y=mx+c
m represents slope
c represents y intercept
How do you find the 3rd side of a triangle?
The third side of a triangle, the following formula can be used c² = a² + b² - 2abcos(C)
To calculate the third side of a triangle, first find the lengths of the other two sides and the angle opposite the third side. Then plug these values into the formula above and solve for c.
Where c is the third side of the triangle, a and b are the other two sides, and C is the angle between them.
For example, for a triangle with two sides of length 4 and 6, and an angle between them of 75 degrees, the formula would look like this:
c² = 42 + 62 - 2(4)(6)cos(75)
Solving for c yields a third side length of 8.4.
To solve for c, first square the two side lengths: 42 = 16 and 62 = 36. Then, multiply the two side lengths together and multiply by the cosine of the angle between them: 2(4)(6)cos(75) = 43.9. Finally, add the two squared values together and subtract the result of the multiplication: 16 + 36 - 43.9 = 8.1. Then, take the square root of this result to get the length of the third side: √8.1 = 8.4.
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3) Terri and her friends fly 2234 miles to Spain for college. It takes them 9 hours to get there.
How many miles did they travel per hour? Show your thinking.
Answer:
approximately 248 miles per hour if we are taking average speed
Step-by-step explanation:
In baseball, each time a player attempts to hit the ball, it is recorded. the ratio of hits compared to total attempts is their batting average. each player on the team wants to have the highest batting average to help their team the most. for the season so far, jana has hit the ball 8 times out of 10 attempts. tasha has hit the ball 9 times out of 12 attempts. which player has a ratio that means they have a better batting average? tasha, because she has the lowest ratio since 0.75 < 0.8 tasha, because she has the highest ratio since 48 over 60 is greater than 45 over 60 jana, because she has the lowest ratio since 0.75 < 0.8 jana, because she has the highest ratio since 48 over 60 is greater than 45 over 60
Answer: Jana
Step-by-step explanation: because she has the highest ratio 48 over 60 > 45 over 60
I did the test
45 PTS no need to explain.
Answer:
B. SAS-----------------------------------
The two triangles have 2 sides marked as congruent and the included angles are congruent as vertical angles:
AC ≅ EC,BC ≅ DC,∠ACB ≅ ∠ECDThis gives us SAS congruence postulate.
The matching choice is B.
A high school coach wants to buy new athletic shorts for the 15 members of the basketball team. The coach must spend less than $200 on the shares. Which inequality represents the maximum cost of each pair, s, the coach can buy
An office manager is planning to set up three computer workstations and a file cabinet in a space that is 27 feet wide. The file cabinet takes up 3 feet. What is the width of the space available for each computer station?
Answer:
The width of the space available for each computer station is 8 feet-------------------------------
The width of the space for computer stations is:
27 - 3 = 24 feetEach computer station has a space of:
24/3 = 8 feetExplain why the initial value of any function of the form
f(x) = a(b*) is equal to a.
The formula becomes a times 1, which is merely a, when you swap out 0 for the exponent x. This is so because 1 equals any number raised to the power of 0. The value of a will always be the initial value for any function with this form since the initial value is the function's value with an input of 0.
How do you determine F's starting value?By looking for an equation's constant, one can also locate initial values. Graph functions benefit from understanding the y-intercept.
Any number that is multiplied by 0 equals 1.
A number is equal to a number multiplied by 1.
The value of a multiplied by one will equal its starting value.
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The price of a notebook has risen to $3.80 today. Yesterday's price was $3.30 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
The percentage increase in the price of the notebook is 15%.
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100.
The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Finding the increase in the price of the notebook:
$3.80 - $3.30 = $0.50
Dividing the increase by the original amount:
0.50 / 3.30 = 0.1515
To change to a percent multiply by 100 and round off to significant numbers:
0.1515 *100 = 15.15% or, 15%.
Thus, the percentage increase in the price of the notebook is 15%.
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A marble is selected from a bag containing eight marbles numbered 1 to 8.
The number on the marble selected will be recorded as the outcome.
Consider the following events.
Event A: The marble selected has a number less than 4.
Event B: The marble selected has an odd number.
Give the outcomes for each of the following events.
If there is more than one element in the set, separate them with commas.
A
(a) Event "A and B": {
(b) Event "A or B":
(c) The complement of the event B: {}
0,0..
X
From set theory, A and B: {4, 6} A or B: {2, 3, 4, 5, 6, 8} B's complement is 1, 2, 7, and 8.
What are the types of set theory?Basic set theory describes these various kinds of sets as follows: Finite set: There are only a finite number of elements. A set with an infinite number of elements. A set that is empty has no elements. A singleton set consists of just one element.
The elements that appear in both A and B at the same time are referred to as A and B.
From 1 to 8, the even numbers are 2, 4, 6, and 8.
The numbers 3, 4, 5, and 6 are in that order.
Look for the components that are the same in both sets.
A and B: {4, 6}
The union of the two sets is either A or B.
Combine the components from both sets.
A or B: {2, 3, 4, 5, 6, 8}
All the components that are absent from B make up its complement.
Except for the event elements, write all of the sample space's components.
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