Answers
Answer:
The answer is -5
Step-by-step explanation:
Each number moves down 5 as it moves to the right 1. Right is positive, and down is negative. -5 divided by 1 is -5.
Related Questions
Making an Informed Decision Using the Quantitative Reasoning Process
Step 1: Understand the Problem
Keep the Old Car or Buy a Used Car
Manny is an online student who currently owns an older car that is fully paid for. He drives, on average, 190 miles per week to commute to work. With gas prices currently at $
2.9 per gallon, he is considering buying a more fuel-efficient car, and wants to know if it would be a good financial decision.
The old car Manny owns currently gets 18 miles per gallon for average fuel efficiency. It has been a great vehicle, but with its age, it needs repairs and maintenance that average $
770 per year (as long as nothing serious goes wrong).
The newer, more fuel-efficient car that he is looking at to purchase will cost a total of $
6,500 over a three-year loan process. This car gets 32 miles per gallon and would only require an average of $
10 per month for general maintenance. To help make a decision, Manny wants to calculate the total cost for each scenario over three years. He decides to use the quantitative reasoning process to do this.
Step 2: Identify variables and assumptions
Manny has identified some key variables for his situation. Select the two variables that should be removed from his list because they do not apply to the current situation.
Manny’s graduation date from elementary school.
The cost of repairs on the old car.
The cost of gas.
The number of miles Manny drives each week.
Manny’s wages.
The loan cost of the used car.
The year Manny was born.
The cost of the used car.
Manny has also made a list of key assumptions he will be using to make his decision. Check the boxes for the three assumptions from his list that are not useful in this scenario.
Manny assumes that nothing will go seriously wrong with either car during this three year period.
Manny assumes the loan period will be 3 years.
Manny assumes gas costs will remain about the same over the three years.
Manny assumes he will continue to go running in the mornings every weekday for the next three years.
Manny assumes there are 52 weeks in a year.
Manny assumes his lunches will continue to cost about the same for the next three years.
Manny assumes he will continue to drive about the same number of miles each week over this three year period.
Manny assumes he will still like spinach at the end of three years no matter which choice he makes.
Step 3: Apply Quantitative Tools
Use computational and algebraic tools to quantify the total costs (gas, maintenance/repairs, purchase price) for each scenario over the three years.
Round your answers to the nearest dollar.
Scenario
Total Cost for Three Years
Keep the old car
$
Number
Buy the fuel-efficient used car
$
Number
Step 4: Make an Informed Decision
Based on the information presented what do think Manny should decide?
Option #1: Keep the old car
Option #2: Buy the fuel-efficient used car
Option #
1
Step 5: Evaluate Your Reasoning
Manny plans to start looking at cars and will evaluate his reasoning before he makes a purchase.
( need help on the assignment)
Answers
The type-1 error (false positive) for a carbon monoxide detector installed in your house is 0.05 and its type-2
error (false negative) is 0.03. The probability that a gas heater malfunctions and releases carbon monoxide is
very low, only 0.000007.
What is the probability that the carbon monoxide detector will not go off?
O 0.9998642
O 0.9499936
O 0.0500064
O 0.0001358
Answers
The probability that the carbon monoxide detector will not go off is approximately 0.9998642 (rounded to 7 decimal places),
Option A is the correct answer.
We have,
The probability of the carbon monoxide detector not going off can occur in two ways: either there is no carbon monoxide present, or there is carbon monoxide present but the detector fails to detect it.
The probability of the detector failing to detect carbon monoxide when it is present (type-2 error) is 0.03, and the probability of the gas heater malfunctioning and releasing carbon monoxide is 0.000007.
So the probability of the detector failing to detect carbon monoxide when it is present is:
0.03 x 0.000007
= 0.00000021
The probability of there being no carbon monoxide present is 1 minus the probability that the gas heater malfunctions and releases carbon monoxide, which is:
1 - 0.000007
= 0.999993
Now,
So the overall probability of the detector not going off is the sum of the probabilities of these two events:
0.999993 + 0.00000021
= 0.99999321
Therefore,
The probability that the carbon monoxide detector will not go off is approximately 0.9998642 (rounded to 7 decimal places), which is option A.
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Which of the following statements about transportation in the United States is NOT true?
A. Most Americans commute to work in a personally owned vehicle.
B. Most Americans who commute to work in car's drive alone.
C. Americans spend more income on transportation than anything else except
housing.
D. The cost of gasoline is higher in the U.S. than anywhere else in the world.
Answers
Answer: D
Step-by-step explanation:
The answer is D. The cost of gasoline is higher in the U.S. than anywhere else in the world.
According to the U.S. Energy Information Administration, the average price of a gallon of regular unleaded gasoline in the United States was $3.53 on March 8, 2023. This is higher than the average price of gasoline in many other countries, including Canada ($1.56), Mexico ($1.97), and the United Kingdom ($1.73). However, the cost of gasoline in the United States is lower than the average price in some countries, such as Norway ($6.62), Sweden ($5.62), and Denmark ($5.51).
Here are the facts about the other statements:
A. Most Americans commute to work in a personally owned vehicle. According to the U.S. Census Bureau, in 2019, 77.4% of workers commuted to work by driving alone.
B. Most Americans who commute to work in car's drive alone. According to the U.S. Census Bureau, in 2019, 77.4% of workers who commuted to work by driving did so alone.
C. Americans spend more income on transportation than anything else except housing. According to the U.S. Bureau of Labor Statistics, in 2020, Americans spent an average of $10,564 on transportation, more than any other category except housing ($16,916).
Can someone help me in here please
Answers
The addition of the two matrix is [34 -12 -36 -18 58]
[-42 -8 16 30 8 ]
[ 24 34 4 34 23]
[-12 -32 -12 -42 -52]
What is the matrix addition?The addition of the matrix is calculated as follows;
The result to 4 multiplied by G is calculated as;
4[G] = [32 -20 -32 -8 40]
[-24 -28 4 36 8 ]
[ 16 24 12 28 20]
[-16 -12 0 -40 -36]
2[F] = [2 8 -4 -10 18]
[-18 20 12 -6 0 ]
[ 8 10 -8 6 3 ]
[4 -20 -12 -2 -16]
The addition of the two matrix is calculated as follows;
4[G] + 2[F] = [34 -12 -36 -18 58]
[-42 -8 16 30 8 ]
[ 24 34 4 34 23]
[-12 -32 -12 -42 -52]
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Triangle GFH has vertices G(2, –3), F(4, –1), and H(1, 1). The triangle is rotated 270° clockwise using the origin as the center of rotation. Which graph shows the rotated image?
On a coordinate plane, triangle G prime H prime F prime has points (negative 3, negative 2), (1, negative 1), (negative 1, negative 4).
On a coordinate plane, triangle G prime H prime F prime has points (3, 2), (negative 1, 1), (1, 4).
On a coordinate plane, triangle G prime H prime F prime has points (2, negative 3), (1, 1), (4, negative 1).
On a coordinate plane, triangle G prime H prime F prime has points (2, 3), (4, 1), (1, negative 1).
Answers
Check the picture below.
Answer:
b
Step-by-step explanation:
edge 2023
In IXL I need help im bad :(
Answers
Answer:
Wilma will pay $23.44 total.
Step-by-step explanation:
Cost of sweater = (+) $24.49
Discount = (-) $5
Shipping cost = (+) $3.95
Solve:
24.49 - 5 = 19.49
19.49 + 3.95 = 23.44
Wilma will pay $23.44 total.
what is the value for 43.7 x 0.25
Answers
Answer:
43.7 x 0.25 is 10.925
Step-by-step explanation:
To multiply decimals, we can use the following steps:
1. Multiply the numbers as if they were whole numbers, ignoring the decimal points.
2. Count the total number of decimal places in the factors being multiplied. This will be the number of decimal places in the product.
3. Place the decimal point in the product so that it has the same number of decimal places as the total counted in step 2.
Using these steps, we can find the product of 43.7 and 0.25 as follows:
1. 437 x 25 = 10925
2. There are two decimal places in 43.7 and two decimal places in 0.25, so there are a total of four decimal places in the factors being multiplied.
3. Place the decimal point in the product so that it has four decimal places: 10.925
Therefore, the value of 43.7 x 0.25 is 10.925.
= 437/40
= 10(whole number)37/40
= 10.925
Spelled result in words is four hundred thirty-seven fortieths (or ten and thirty-seven fortieths).
How do we solve fractions step by step?
1.) Conversion a decimal number to a fraction: 0.25 = 25/100 = 1/4
a) Write down the decimal 0.25 divided by 1: 0.25 = 0.25/1
b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
0.25/1
= 2.5/10
= 25/100
Note: 25/100 is called a decimal fraction.
c) Simplify and reduce the fraction
25/100
= 1 * 25/4 * 25
= 1 * 25/4 * 25
= 1/4
2.) Conversion a decimal number to a fraction: 43.7 = 437/10 = 437/10
a) Write down the decimal 43.7 divided by 1: 43.7 = 43.7/1
b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
43.7/1. = 437/10
Note: 437/10 is called a decimal fraction.
c) Simplify and reduce the fraction
437/10 = 437 * 1/10 * 1= 437 * 1/10 * 1
3.)Multiple: 0.25 * 43.7 = 1 · 437/4 · 10
= 437/40
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(437, 40) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - one quarter multiplied by four hundred thirty-seven tenths is four hundred thirty-seven fortieths.
Raman is watching the movie 4 times and he fislokw s the value wirh
Answers
Answer:learn how to spell :)
Step-by-step explanation:
Researchers are analyzing the total annual cost for the top ranked universities. They need to display the data in a way that is helpful
for relaying information regarding the data.
Identify the advantage of using a dotplot (choose one) :
A- Easily identify outliers
B- Easily determine the total number of data points for larger data sets
C- Cannot determine the minimum or maximum
D-Cannot identify the exact median
Answers
One advantage of using a dot plot is that it makes it easy to identify outliers. Option A is correct.
An outlier is a data point that is significantly different from the others in the data set, either in terms of its value or its position within the range of values. In a dot plot, outliers are represented by individual dots that are far away from the other dots, either above or below them.
By looking at the dot plot, researchers can quickly identify any outliers and investigate them further to determine why they are different and whether they should be included or excluded from the analysis.
Hence, A. is the correct option.
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Write an inequality that matches the number line model. Then write
a situation that the inequality could represent.
-2.75 is greater than or equal to x
Answers
Answer:
x<=-2.75
Step-by-step explanation:
Select the correct answer.
Which set of coordinates satisfies the equations x − 2y = -1 and 2x + 3y = 12?
A.
(1, 2)
B.
(3, 1)
C.
(3, 2)
D.
(-3, -2)
E.
(3, -2)
Answers
The set of coordinates that satisfy the equation are as follows:
(2, 3)
How to solve equation?The equation given is as follows:
x - 2y = -1
2x + 3y = 12
Therefore, let's find the set of coordinates that satisfies the equation. Hence,
x - 2y = -1
2x + 3y = 12
multiply equation(i) by 2
Hence,
2x - 4y = -2
2x + 3y = 12
Therefore, subtract the equations
7y = 14
divide both sides of the equation by 7
y = 14 / 7
y = 2
Let's find x as follows
x - 2y = -1
x = -1 + 2(2)
x = -1 + 4
x = 3
Therefore, the solution is (2, 3)
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- x²= +x +12=0 .....................................
Answers
Therefore, the solutions of the equation -x² + x + 12 = 0 are x = -3 and x = 6.
What is equation?In mathematics, an equation is a statement that shows the equality between two expressions, typically separated by an equal sign (=). An equation can contain one or more variables, which are symbols that represent unknown or varying values. The value of the variable(s) can be found by solving the equation.
Here,
The given equation is:
-x² + x + 12 = 0
To solve for x, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.
In this case, we have:
a = -1, b = 1, and c = 12
Substituting these values into the quadratic formula, we get:
x= (-1 ± √(1² - 4(-1)(12))) / 2(-1)
x = (-1 ± √(1 + 48)) / (-2)
x = (-1 ± √(49)) / (-2)
x = (-1 ± 7) / (-2)
There are two solutions:
x = (-1 + 7) / (-2)
= -3
x = (-1 - 7) / (-2)
= 6
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Using the discriminant
Answers
Answer:
n = 20/3
Step-by-step explanation:
Theory about the discriminant, and how solutions are acquired via the quadratic formula
One variable quadratic equations in the form [tex]0=ax^2+bx+c[/tex] have exactly one solution when the discriminant [tex](b^2-4ac)=0[/tex].
This is because for quadratic equations of the original form, the two solutions are given by the quadratic formula:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
which is equivalent to [tex]x=\dfrac{-b}{2a}\pm \dfrac{\sqrt{b^2-4ac}}{2a}[/tex].
The [tex]x=\dfrac{-b}{2a}[/tex] is the axis of symmetry, and the [tex]\dfrac{\sqrt{b^2-4ac}}{2a}[/tex] part is how much the solutions deviate from the axis of symmetry. If the deviation is zero, then the two solutions are both ON the axis of symmetry, and are the same number, giving exactly one solution.
Addressing the given equation
Putting it into standard form
Given the given equation...
[tex](n-4)u^2+6=8u[/tex]
subtract 8u from both sides to obtain an equation that looks like the standard form equal to zero...
[tex](n-4)u^2-8u+6=0[/tex]
The variable here is "u" instead of "x", so the solutions to this equation would be [tex]u=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex], where [tex]a=n-4[/tex], [tex]b=-8[/tex], and [tex]c=6[/tex].
Identifying the discriminant
The discriminant then, with values of a, b, and c, substituted, becomes:
[tex]Discriminant=(-8)^2-4(6)(n-4)[/tex]
If we want the discriminant to equal zero (so that there is exactly one solution for "u"), substitute zero on the left side of the equation, and solve for n.
Solving for n
[tex]0=(-8)^2-4(6)(n-4)[/tex]
[tex]0=64-4(6)(n-4)[/tex]
[tex]0=64-24(n-4)[/tex]
Add -24(n-4) to both sides...
[tex]24(n-4)=64[/tex]
Divide both sides by 24...
[tex]n-4=\dfrac{64}{24}[/tex]
Reduce the right hand side...
[tex]n-4=\dfrac{8}{3}[/tex]
Add 4 to both sides...
[tex]n=\dfrac{8}{3}+4[/tex]
Find a common denominator...
[tex]n=\dfrac{8}{3}+\dfrac{12}{3}[/tex]
Find a common denominator...
[tex]n=\dfrac{20}{3}[/tex]
So, if [tex]n=\dfrac{20}{3}[/tex], then the equation [tex](n-4)u^2+6=8u[/tex] has exactly one solution. Furthermore, this is the only value of "n" for which the equation has exactly one solution, because it is the only value of "n" for which the discriminant is zero.
PLEASE HELP (1 point)
Let X be a continuous random variable with probability
distribution represented by the graph below.
Find P (X≤2).
f(x)
Answers
The probability P (X≤2). from the probability distribution is 1/3
Evaluating the probability from the probability distributionA continuous random variable is a type of random variable that can take on any value within a specific range, often an infinite range.
It has a probability distribution function that describes the probability of the variable taking on certain values within that range.
This means that
P (X≤2) = the f(x) value
From the graph, we have
P (X≤2) = 1/3
Hence, teh value is 1/3
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The volume of a rectangular prism is 5,890.625cm3 . if the height is 14.5 cm and the length is 25 cm, with is the value of the width ?
A. 16.25 cm B. 16.5 cm C. 16.75cm D. 16.97cm
Answers
Answer:
Step-by-step explanation:
The answer is A. 16.25cm.
Explanation:-
We know,
The Volume of Prism =height*width*length;
Here, In the question Height and length is given.
So We have to do a simple calculation to find,width=
(Vol of Prism)/Heigth*length;=> 5890.625/(14.5*25)
=>16.25 cm .
We don't need to worry about dimensions because all are in the same cm dimensions.
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Answer:
A. 16.25 cm
Step-by-step explanation:
To solve for the volume of a rectangular prism, we would use the formula V = l·w·h, where:
"l" is the base length
"w" is the base width
"h" is the height of the prism
In this problem, we are given the volume, height, and length of the rectangular prism. That means we need to find the value of w, the base width. To do this, we plug our known values into the equation and solve for w.
5,890.625 = (14.5)(25)w
To get w by itself, we first divide each side of the equation by 14.5. Remember that when you divide a number by itself, they cancel out.
(5,890.625)/(14.5) = (14.5)(25)w/(14.5)
406.25 = (25)w
Next, we can divide each side of the equation by 25 to get our answer.
406.25/25 = (25)w/25
w = 16.25 cm
9 belongs to the set N
Answers
Answer:
9 belongs to set N, natural, whole, integer, rational, and real number
Step-by-step explanation:
* Natural number: use for counting
* Whole number: includes natural number and zero
* Integer : are whole numbers and their opposite
*Rational number:come from fraction, and their results can be positive integer
*Real number: includes all numbers
The Question Is Inside Of The Picture
Answers
The percentage of sugar price per pound less than 64 cents is 50%
What percentage of sugar price per pound are less than 64 centsFrom the question, we have the following parameters that can be used in our computation:
Mean = 64
Standard deviation = 2
For sugar price per pound that are less than 64 cents, we have
z = (64 - 64)/2
z = 0
This is then represented as
Probability = (z < 0)
Using a graphing calculator, we have
Probability = 0.5
Express as percentage
Probability = 50%
Hence, the probability is 50%
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fill it in The value of a certain investment over time is given in the table below. Answer the questions below to determine what kind of function would best fit the data, linear or exponential.
Number of Years Since Investment Made, x
1
2
3
4
Value of Investment ($), f(x)
14,944.54
16,357.04
17,974.72
19,891.18
function would best fit the data because as x increases, the y values change
. The
of this function is approximately
.
Answers
An exponential function would be more appropriate than a linear function, as exponential growth
the best function for the dataTo determine which type of function best fits the data, we can analyze the difference in the y values (Value of Investment) as x increases.
Differences between consecutive y values:
16,357.04 - 14,944.54 = 1,412.50
17,974.72 - 16,357.04 = 1,617.68
19,891.18 - 17,974.72 = 1,916.46
The differences between consecutive y values are increasing as x increases. This suggests that an exponential function would be more appropriate than a linear function.
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Can someone help me please
here is the picture
Answers
The result of adding -4 (row 1) to row 3 is determined as (0 - 9 2)|12.
What is the result of the row multiplication?The resultant of the row multiplication in the Matrice is calculated by applying the following method;
row 1 in the given matrices = [1 2 1] | -5
To multiply row by -4, we will multiply each entity by 4 as shown below;
= -4(1 2 1) | -5
= (-4 -8 - 4) |20
To add the result to 3;
(-4 -8 - 4)|20 + (4 - 1 6) | -8
= (0 - 9 2)|12
Thus, the result of the row multiplication is determined by multiplying each entry in row 1, by - 4.
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Can yall help me with this pls
Answers
Answer:
x=6.4
Step-by-step explanation:
2/3.2 = 4/x
2x=4(3.2)
2x=12.8
x=6.4
if a clock shows it is 3 o'clock, how could you describe the smaller angle made my the two hands of the clock? solve this problem any way you choose
Answers
The smaller angle made by the two hands of the clock at 3 o'clock is 90 degrees.
What is an angle?A figure known as an angle is created by two rays or line segments that meet at a place known as the vertex of the angle. The sides or legs of the angle are other names for the rays or line segments.
According to question:To determine the smaller angle made by the two hands of a clock when it is 3 o'clock, we can use the following formula:
angle = |(11/2) * m - 30h|
where:
m is the number of minutes past the hour (in this case, since it is 3 o'clock, m = 0)
h is the hour (in this case, h = 3)
By using this formula, we get:
angle = |(11/2) * 0 - 30(3)| = |0 - 90| = 90
Therefore, the smaller angle made by the two hands of the clock at 3 o'clock is 90 degrees.
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(PLEASE ANSWER BOTH)
1. What is the value of Angle X?
2. How do you know (What type of angle pairs are they)?
Answers
Answer:
angle x is 160
Step-by-step explanation:
180 - 20
Let S be a collection of subset of {2000, 2001, 2002, …, 2020} such that intersection of any two sets in S is nonempty. What is the maximum cardinality of S?
Answers
The maximum cardinality of S is 20.
How to find the maximum cardinality ?To increase the number of subsets within S, our goal must be to find as many non-empty subset intersections as possible. This is achieved by constructing subsets that possess only one shared element. In this particular case, any two sets contained in the collection will include the element 2000 in their intersection causing it to become a valid subset.
Now, we shall investigate whether an additional subset can be added to S. If an extension exists without including 2000, its intersection with the previous 20 subsets would negligibly have no common elements and would hence not be regarded as a valid subset for addition into S.
As a result, a total of 20 subsets represent maximum cardinality for set S per these conditions.
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Help please
Condense to a single logarithm is possible
In(6x^9)-In(x^2)
Answers
The logarithm expression can be simplified to:
In(6x^9)-In(x^2) =7·ln(6x)
How to write this as a single logarithm?There are some logarithm properties we can use here.
log(a) - log(b) = log(a/b)
log(a^n) = n*log(a)
(these obviously also apply to the natural logarithm)
Now let's look at our expression, it says that:
In(6x^9)-In(x^2)
Using the first rule, we can rewrite this as.
In(6x^9)-In(x^2) = ln(6x^9/x^2)
Now solving the quotient in the argument:
ln(6x^9/x^2) = ln(6x^7) = 7·ln(6x)
That is the expresison simplified.
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The sales of a certain product after an initial release can be found by the equation s=12 sqrt (4t) + 10 , where s represents the total sales (in thousands) and t represents the time in weeks after release. Make a table of values, graph the function and use the graph to estimate the sales 12 weeks after release.
about $586,000
about $586
about $93
about $93,000
Answers
The sales 12 weeks after release is $586,000 . Option A is the correct answer.
To create a table of values, we can plug in different values of t and find the corresponding values of s:
t s
0 10
1 19.882
2 26.248
3 31.177
4 35.064
5 38.185
6 40.731
7 42.837
8 44.6
9 46.095
10 47.384
11 48.508
12 49.498
To graph the function, we can plot the values from the table on a coordinate plane. The horizontal axis represents time in weeks, and the vertical axis represents sales in thousands of units. The resulting graph is a curve that starts at (0,10) and increases as t increases.
To estimate the sales 12 weeks after release, we can look at the graph and see that the corresponding value of s is around 49.5 thousand units. Therefore, the answer is about $586,000 (49.5 x 1000 x 12). Option A is the correct answer.
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Which of the points plotted is farther away from (−7, 8), and what is the distance?
A: Point (5, 8), and it is 11 units away
B: Point (5, 8), and it is 13 units away
C: Point (−7, −5), and it is 12 units away
D: Point (−7, −5), and it is 13 units away
Answers
The distance between point (−7, 8) and point (5, 8) is 12 units (since they are on the same horizontal line). The distance between point (−7, 8) and point (−7, −5) is 13 units (using the Pythagorean theorem). Therefore, the point that is farther away is option D: Point (−7, −5), and it is 13 units away.
Triangle AABC, right angled at C, is given. Height and the median from point C form an angle y.
The measure of larger acute angle of AABC is:
A 45°-
B
C
D
60° +
90°
24
92
2
92
4
Answers
The measure of the larger acute angle of ΔABC is: α = 45° + φ/2. Option A.
How do you solve for the larger acute angle of ΔABC ?Let's denote the angles of triangle ΔABC as follows:
∠A = x
∠B = y
∠C = 90° (right-angled triangle)
Let D be the midpoint of AB, so CD is the median. Let E be the point on AB such that CE is the height from point C.
Since CD is the median, we know that angle ∠ECD = φ.
In right-angled triangle ΔCEB, we have:
∠CEB = 90° - y
Now, let's examine triangle ΔCED. We know that the sum of the angles in a triangle is 180°. Therefore:
∠CED + ∠CEB + ∠ECD = 180°
Substitute the known values:
∠CED + (90° - β) + φ = 180°
Since ∠CED and ∠A are supplementary angles, we can also write:
∠CED = 180° - x
Now substitute this value into the previous equation:
(180° - x) + (90° - y) + φ = 180°
Simplify the equation:
270° - x - y + φ = 180°
Subtract 90° from both sides:
180° - x - y + φ = 90°
From this equation, we get:
x + y = 90°
Substitute this value back into the equation involving φ:
180° - (90°) + φ = 90°
Simplify:
90° + φ = 90°
Therefore, the measure of the larger acute angle of ΔABC is:
x = 45° + φ/2 (option a)
the above answer is in response to the full question below;
Triangle ΔABC, right angled at C, is given. Height and the median from point C form an angle φ. The measure of larger acute angle of Δ ABC is:
a. 45⁰ + φ/2
b. 60⁰ + φ/2
c. 90⁰ - φ/2
d. 2φ
find more exercise on finding acute angle of ΔABC;
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[tex]y=2cos^{2}(x) , y=2e^{-x}+2x-2[/tex]
(a) Write an equation whose solutions are the points of intersection of the graphs.
(b) Use the intersect feature of the graphing utility to find the points of intersection (to four decimal places). (Enter the point of intersection whose x-coordinate is within the interval [0, 2). If there is no solution, enter NO SOLUTION.)
Answers
a. The equation whose solutions are the points of intersection of the graphs is y = -0.14x + 0.80.
b. The points of intersection are (-0.827, 0.918) and (0.951, 0.675).
The solution has been obtained using the slope - intercept form.
What is the slope - intercept form?
When you are aware of the slope of the line being investigated and the given point is also the y intercept, use the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is represented by the symbol b in the equation.
a. From the graph, we have two points of intersection.
Using this, we get the slope as;
m = -0.14
Now, using the slope intercept form, we get the intercept as
b = 0.80
So, the equation comes out to be
y = -0.14x + 0.80
b. The graph of the equations have been attached below.
From the graph, we get the points of intersection as (-0.827, 0.918) and (0.951, 0.675). Both the points have their x-coordinate within the interval [0, 2).
Hence, the required solutions have been obtained.
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The expression 5(2) gives the number of leaves on a plant as a function
of the number of weeks since it was planted.
What does 2 represent in this expression?
Choose 1 answer:
B
The plant was planted 2 weeks ago.
There were initially 2 leaves on the plant.
The number of leaves is multiplied by 2 each week.
Answers
C: the number of leaves is multiplied by 2 each week
Step-by-step explanation
The proper expression ought to be 5(2) ^ t =5(2)^{t}
where t speak to the number weeks after it planted.
On the off chance that we put to the time(t) we are going know how numerous clears out at first are. The calculation will be:
5(2)^{t}= 5(2)^{0} =5
This appear that coefficient 5 decide how much the takes off at first are.
Let see how the number going for distinctive esteem of t. On the off chance that its 1 week after plant, the leaf will ended up:
5(2)^{t}= 5(2)^{1} = 10
At that point the number of takes off 2 weeks after planted will be:
5(2)^{t}= 5(2)^{2}= 20
The number keeps twofold each week since coefficient 2 speaks to the proportion of the development of the work and the proportion decides how much takes off duplicated each week.
So, the reply will be C.
Given the circle below with secants GHI and KJI. If JI = 4, KJ = 10 and
HI = 5, find the length of GH. Round to the nearest tenth if necessary.
Answers
Answer:
GH = 6.2
Step-by-step explanation:
