P= $975, r=5.5%, t=60 days
What is 15x7 for the real answer?
The hypotenuse of a right triangle has endpoints A(4, 1) and B(–1, –2).
At which points could the vertex of the right angle in the triangle be located? Check all that apply.
(–1, 1)
(4, –2)
(1, 1)
(2, –2)
(4, –1)
(–1, 4)
Answer:
(–1, 1)
(4, –2)
Step-by-step explanation:
Let
(x,y) ----> the coordinates of point C
Applying the Pythagoras Theorem
[tex](-1-4)^2+(-2-1)^2=(x-4)^2+(y-1)^2+(x+1)^2+(y+2)^2[/tex]
step 1
Find the possibles values of x
[tex](-1-4)^2=(x-4)^2+(x+1)^2\\\\25=x^{2}-8x+16+x^{2}+2x+1\\\\2x^{2}-6x-8=0[/tex]
Simplify
[tex]x^{2}-3x-4=0[/tex]
Solve the quadratic equation
[tex]x^{2}-3x-4=(x+1)(x-4)[/tex]
The values of x are
x=-1 and x=4
step 2
Find the possibles values of y
[tex](-2-1)^2=((y-1)^2+(y+2)^2\\\\9=y^{2}-2y+1+y^{2}+4y+4\\\\2y^{2}+2y-4=0[/tex]
Simplify
[tex]y^{2}+y-2=0[/tex]
Solve the quadratic equation
[tex]y^{2}+y-2=(y+2)(y-1)[/tex]
The values of y are
y=-2, y=1
therefore
The possibles coordinates of point C are
(-1,1),(4,-2)
Answer:
(–1, 1)
(4, –2)
Step-by-step explanation:
Given that the hypotenuse of a right triangle has endpoints A(4, 1) and B(–1, –2), then two triangles can be formed (see figure attached).
The vertex of the right angle in each triangle are on points (-1, 1) and (4, -2), as can be seen in the figure.
The tables represent two linear functions in a system.
What is the solution to this system?
(1, 0)
(1, 6)
(8, 26)
(8, –22)
One angle has 10 degrees more than another angle. The sum of the angles us 90 degrees . How many degrees are in each angle? Please Explain.
The smaller angle is 40 degrees and the larger angle is 50 degrees.
Explanation:Let's represent the smaller angle by x degrees. According to the problem, the larger angle is 10 degrees more than the smaller angle, so it can be represented by x + 10 degrees. The sum of these two angles is 90 degrees, so we can set up the equation:
x + (x + 10) = 90
Simplifying the equation, we get:
2x + 10 = 90
Subtracting 10 from both sides, we have:
2x = 80
Finally, dividing both sides by 2, we find:
x = 40
So, the smaller angle is 40 degrees and the larger angle is 40 + 10 = 50 degrees.
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what are the coordinates of the x and y intercepts of the equation 3x+2y=12
The perimeter of an equilateral triangle is 27 centimeters. Find the altitude of the triangle
The altitude of the equilateral triangle is [tex]\( \frac{9\sqrt{3}}{2} \)[/tex] centimeters.
In an equilateral triangle, all three sides are equal in length. Let's denote the length of each side of the equilateral triangle as s centimeters.
The perimeter of an equilateral triangle is given as the sum of the lengths of all three sides:
Perimeter = 3s
Given that the perimeter is 27 centimeters, we can set up the equation:
27 = 3s
Now, we can solve for the length of each side s:
[tex]\[ s = \frac{27}{3} = 9 \][/tex]
So, each side of the equilateral triangle is 9 centimeters long.
Now, to find the altitude of the equilateral triangle, we can use the formula for the altitude of an equilateral triangle, which is:
[tex]\[ \text{Altitude} = \frac{\sqrt{3}}{2} \times \text{Length of a side} \][/tex]
Substituting the length of a side s = 9 into the formula, we get:
[tex]\[ \text{Altitude} = \frac{\sqrt{3}}{2} \times 9 \\\[ \text{Altitude} = \frac{9\sqrt{3}}{2} \][/tex]
So, the altitude of the equilateral triangle is [tex]\( \frac{9\sqrt{3}}{2} \)[/tex] centimeters.
write 42.5% as a fraction in simplest form
The fraction of 42.5% in its simplest form is 17/40.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
42.5%
= 42.5/100
= 425/1000
= 85/200
= 17/40
Thus,
The fraction is 17/40.
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42.5% can be expressed as the fraction 17/40 in simplest form.
To express 42.5% as a fraction in the simplest form, we need to convert the percentage to a fraction with the numerator and denominator in their simplest form. Here's the step-by-step process:
Recognize that a percentage is a fraction out of 100. In this case, 42.5% can be written as 42.5/100.
Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor. In this case, the greatest common divisor of 42.5 and 100 is 2. Dividing both the numerator and denominator by 2 gives us 21.25/50.
Continue simplifying the fraction by dividing both the numerator and denominator by any common factors. In this case, we can divide both by 25: 21.25/50 = 0.85/2.
Finally, express the fraction in simplest form by dividing both the numerator and denominator by their greatest common divisor, which is 5 in this case: 0.85/2 = 17/40.
Therefore, 42.5% can be expressed as the fraction 17/40 in simplest form.
This means that 42.5% is equivalent to 17 parts out of 40 parts.
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0.87 written as a fraction is _____.
The decimal 0.87 can be written as the fraction 87/100, which cannot be simplified further.
Explanation:The decimal 0.87 can be written as a fraction by placing the decimal over 100 and then simplifying the fraction if possible. In this case, 0.87 can be written as 87/100. However, this fraction can be simplified further. Both 87 and 100 can be divided by 1, making the simplified fraction 87/100.
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If $7,000 is placed in an account with an annual interest rate of 5.5%, how long will it take the amount to triple if the interest is compounded annually? Round your answer to two decimal places.
...?
Find the key number to the equation, the intervals into which the key numbers divide the number line, and the sign of y over each of these intervals. y=x+1/(x-1)^2
what I'll are the coordinates of point J (-5, -3) if point k (1,2) is the midpoint of JL
a) 4, 1
b) 7, 7
c) 8, 2
d) 6, 5
What is the sum of the arithmetic sequence 151, 137, 123,..if there are 26 terms?
A. -676
B.-650
C.-624
D.-598
Answer:
option C -624
Step-by-step explanation:
You drop a rock off a bridge. The rock’s height, h (in feet above the water), after t seconds is modeled by h = -16t2 + 541. What is the height of the rock after 2 seconds?
Which is longer 1/4 foot or 1/4 yard?
Final answer:
1/4 yard is longer than 1/4 foot because 1/4 yard is equivalent to 3/4 foot, and 3/4 is greater than 1/4.
Explanation:
The question is asking to compare the lengths of 1/4 foot and 1/4 yard. To make this comparison, it is crucial to understand the relationship between feet and yards. From the reference information, we know that 1 yard is equal to 3 feet. Thus, to find how long 1/4 yard is in feet, we use the conversion ratio:
1/4 yd = (1/4) × 3 ft = 3/4 ft.
Now, we compare 1/4 foot with 3/4 foot. Since 3/4 is greater than 1/4, it is clear that 1/4 yard is longer than 1/4 foot.
Divide the complex number: 7i/8+i
(i= imaginary #)
show step-by-step solution
A hummingbird beats its wings about 75 times in one second. Based on this rate, what is the number of times a hummingbird beats its wings one minute?
what is the difference between all real numbers and no solution how do you know when these situations occur
The difference between 'all real numbers' and 'no solution' is that the former means any real number satisfies the equation while the latter means no real number satisfies it. These concepts are essential in understanding and solving mathematical problems, which is a skill developed through practice.
Explanation:The difference between 'all real numbers' and 'no solution' in mathematical equations is significant. When an equation has all real numbers as its solution, it means that any real number can be substituted for the variable and the equation would still hold true. This situation typically occurs when both sides of the equation are identical after simplification. For example, if we simplify an equation and end up with a statement like 5 = 5, it implies that all real numbers are solutions since the statement is always true, regardless of the value of the variable.
On the other hand, 'no solution' means that there are no real numbers that satisfy the equation, often arising when a statement is made that is logically false after simplification, such as 0 = 5. Identifying knowns and unknowns and checking if an answer is reasonable are part of the problem-solving process, where we also look for unreasonable results that might suggest 'no solution'.
The occurrence of these situations during problem solving reflects the complexity of real-world problems, where we must determine which information is relevant and sort out the possible from the impossible. This discernment can be developed through consistent practice in evaluating and solving various types of problems. In some cases, particularly in systems of equations, if the number of unknowns is larger than the number of equations, it may indicate that there could be infinite solutions or no unique solution.
which ordered pairs are a solution to the equation? y=3x Select all that apply (-1,3) (2,5) (1,3) (-2,-6)
Find the equation of a line with the gradient 5 passing through the point (2,-5)
The difference of two numbers is more than 12,and one of the numbers is 3
Inequality for the other number x > 15.
What is inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The most frequent application is to size-compare two numbers on a number line.
Given,
Difference of two numbers is greater than 12
One number is 3
Let the other number be x
Then, inequality becomes
x - 3 > 12
Adding 3 on both sides
x > 12 + 3
x > 15
Hence, x>15 represents the other number so that difference of two numbers is greater than 12.
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The typical exponential function, y = ax, has asymptote ________ and y-intercept ________.
A)y = 0; (0,a)
B)y = 0; (0,1)
C)y = a; (0,a)
D)y = a; (0,1) ...?
Answer: B) The typical exponential function, y = ax, has asymptote the x-axis and y-intercept x = 0.
Step-by-step explanation:
For the funcion [tex]y = a^x[/tex], the asymptote is the value that the function would never assum, but gets really close. In this case, there is no value for y = 0, because[tex]y = a^x\\0 = a^x \\ln(0) = x.lna\\ln(0)[/tex]is not defined! This way, asymptote is x-axis (y=0).
y-intercept ⇒ x=0, so
[tex]y=a^x\\y=a^0=1[/tex]
This, way, the point (0,1)
alternative b
The typical exponential function y = ax has a horizontal asymptote y = 0 and a y-intercept at the point (0,1), which makes Option B the correct answer.
In this context, the function will approach an asymptote, which is a line that the graph gets infinitely close to without touching. Specifically, for an exponential function, the horizontal asymptote is y = 0 regardless of the value of a, provided that a is nonzero. As the value of x gets very large or very negative, the value of y will get very close to 0 but will never actually reach it.
Additionally, the y-intercept of the function is the point at which it crosses the y-axis. This occurs when x is 0. Substituting 0 for x in the function, we get y = a0, which simplifies to y = 1 because any nonzero number to the power of 0 is 1. Therefore, the y-intercept of the function is (0,1).
So, for the question asking about the asymptote and y-intercept of the typical exponential function y = ax, the correct answer is Option B: asymptote y = 0; y-intercept (0,1).
you randomly draw a marble from a bag of marbles that contains 7 blue marbles, 2 green marbles, and 1 red marble. what is the probability not draw a blue marble
Answer:
0.3
Step-by-step explanation:
It is given that,
Number of blue marbles = 7
Number of green marbles = 2
Number of red marbles = 1
Total number of marbles = 7+2+1=10
We need to find the probability that we do not draw a blue marble.
[tex]P=\dfrac{\text{Number of non-blue marbles}}{\text{Total number of marbles}}[/tex]
[tex]P=\dfrac{2+1}{10}[/tex]
[tex]P=\dfrac{3}{10}[/tex]
[tex]P=0.3[/tex]
Therefore, the required probability is 0.3.
what is the slope of 3x + 4Y = 24
The slope of the line 3x + 4y = 24 is -3/4.
The slope of a line is determined by the coefficient of x in the equation of a line written in the form y = mx + b, where m represents the slope.
In the equation 3x + 4y = 24, rearranging it to the slope-intercept form y = mx + b gives 4y = -3x + 24, and then y = -3/4x + 6. Thus, the slope is -3/4.
Four of 12 people choose milk what fractional part of the group chose other drinks
If four out of 12 people chose milk, then 8 did not choose milk, resulting in a fractional part of 2/3 representing those who chose other drinks.
Explanation:If four of 12 people chose milk, we can calculate the fractional part of the group that chose other drinks. We subtract the number of people who chose milk from the total number of people surveyed:
12 (total people) - 4 (people who chose milk) = 8 (people who chose other drinks).
The fractional part of the group that chose other drinks is therefore the number of people who chose other drinks divided by the total number of people:
8 (people who chose other drinks) / 12 (total people) = 2/3.
Two-thirds of the group chose drinks other than milk.
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A tortoise is walking in the desert. It walks for 4 minutes at a speed of 10.24 meters per minute. For how many meters does it walk?
Final answer:
To find the total distance a tortoise walked in the desert, use the formula distance = speed x time. In this case, the tortoise walked 40.96 meters by walking for 4 minutes at a speed of 10.24 meters per minute.
Explanation:
A tortoise is moving laboriously-khwanya-khwanya-khwanya! To calculate the total distance the tortoise walked, we use the formula: distance = speed x time. Given the tortoise walks for 4 minutes at a speed of 10.24 meters per minute, the calculation is 10.24 m/min x 4 min = 40.96 meters. Therefore, the tortoise walked a distance of 40.96 meters.
Prove triangle dih is congruent to triangle egh
Peaches are being sold for $2 per pound if X represents the number of pounds of peaches bought and Y represents the total cost for the peaches which best describes the value of X and Y
Answer:
Y = 2X is the expression which describes the value of X and Y.
Step-by-step explanation:
Peaches are being sold at the rate = $2 per pound
If X represents the number of pounds of peaches purchased then the total cost of the peaches = 2X
Total cost of the peaches is represented by Y, then the expression will be
Y = 2X
Therefore, expression which shows the relation between X and Y is
Y = 2X
One side of a triangle is 15 inches, and the area of the triangle is 90 sq. inches. Find the area of a similar triangle in which the corresponding side is 9 inches.
It took morry 2 and 5/6 hours to drive to the beach. it took jason twice as long. about how long did it take jason to drive to the beach?