In geometry, when line s is perpendicular to line t, statements a, c, and g are true: Lines s and t have slopes that are opposite reciprocals, the product of the slopes of s and t equal -1, and the intersection of s and t forms a right angle.
Explanation:In geometry, if line s is perpendicular to line t, several facts about these two lines can be stated:
a. Lines s and t have slopes that are opposite reciprocals. This is true. If the slope of one line is m, the slope of the line perpendicular to it is -1/m.b. Lines s and t have the same slope. This is false as orthogonal lines have slopes that are negative reciprocals of each other.c. The product of the slopes of s and t is equal to -1. This is true. When two lines are perpendicular, the product of their slopes is -1.d. The lines have the same steepness. This is false because perpendicular lines have different slopes.e. The lines have different y intercepts. This assertion is not necessarily true. Perpendicular lines may or may not have different y-intercepts.f. The lines never intersect. This is false. Perpendicular lines intersect once, forming a 90 degrees angle.g. The intersection of s and t forms a right angle. This is true. The definition of perpendicular lines states that they intersect at a right angle.h. If the slope of s is 6, the slope of t is -6. This is false. If the slope of s is 6, the slope of t, being a negative reciprocal, would be -1/6, not -6.Learn more about Perpendicular Lines here:https://brainly.com/question/18271653
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A jet flies at a rate of 1.3 x 10^ 6 feet per hour. Written in scientific notation, which is the best estimate of how many feet the jet will travel in 2.8 x 10^ 3 hours?
1/4 is to 1 1/4 as 2 is to b
what is b equal to?
1 1/4 is 5 times larger than 1 /4
so b is 5 times larger than 2
5*2 =10
so 1/4 is to 1 1/4 as 2 is to 10
b=10
how to calculate the volume of a equilateral triangular prism
Answer:
I believe the answer would be "Multiply the area of the triangular base by the prism’s height." i'm not sure tho
Step-by-step explanation:
you can correct me if im wrong
Which coordinates will best represent point B'?
Three subtracted from x is less than or equal to -17
mary and jolene are both growing tomatoes in thier backyards to sell.jolene had 3 times as many as mary.but birds had eaten 6 before she picked them all.for the season they have a total of 54 tomotoes.how many did mary grow?
Mary grew 15 tomatoes. A simple algebraic equation was formulated and solved to determine the quantity: m + 3m - 6 = 54, where m represents the number of tomatoes grown by Mary.
Given that Jolene had 3 times as many tomatoes as Mary and birds ate 6 of Jolene's tomatoes, and together they have 54 tomatoes, we need to set up an equation to solve for the number of tomatoes Mary grew.
Let's denote the number of tomatoes Mary grew as m. Therefore, Jolene grew 3m tomatoes. Since birds ate 6 of Jolene's tomatoes, we have 3m - 6 for the number of tomatoes left with Jolene. The equation representing the total number of tomatoes then becomes m (Mary's tomatoes) + (3m - 6) (Jolene's remaining tomatoes) = 54. Simplifying this equation:
m + 3m - 6 = 54
4m - 6 = 54
4m = 60
m = 15
Therefore, Mary grew 15 tomatoes.
What is the solution to this system of linear equations?
x − 3y = −2
x + 3y = 16
Answer:
the correct answer is A 7,3
Step-by-step explanation:
hope this helps
The cost of a service call to fix a washing machine can be expressed by the linear function y = 45x + 35, where y represents the total cost and x represents the number of hours it takes to fix the machine. What does the slope represent?
the cost for each hour it takes to repair the machine
the cost for coming to look at the machine
the total cost for fixing the washing machine
the amount of time that it takes to arrive at the home to make the repairs
Answer:
A
Step-by-step explanation:
What is the value of theta , if tan theta = -1/squareroot3
Complete the multiplication: AB.
A.
B.
C.
D.
what is the value of y?
Answer:
The correct option is D) 60°
Step-by-step explanation:
Consider the provided triangle.
From the provided figure it is given that one angle is 60° and we need to find the value of y.
As we know the sum of all interior angle in a triangle is 180°.
y°+y°+60°=180°
Now solve the above equation to find the value of y.
2y°+60°=180°
2y°=180°-60°
2y°=120°
y°=120°÷2
y°=60°
Hence, the value of y is 60°.
Thus, the correct option is D) 60°
if a mixture of a 6% acid solution with an 11% acid solution is to be made, how much of each solution is needed to make 10 liters of an 8% acid solution
Use technology to approximate the solution(s) to the system of equations to the nearest tenth of a unit.
Select all that apply.
1 (0,0)
2 (9.2, 1.5)
3 (9.6, 3.5)
4 (5.3, 9.8)
5 (3.5, 9.6)
Final answer:
To approximate solutions for the system of equations, enter them into graphing technology, look for intersection points, and match them to the provided coordinates, rounding to the nearest tenth.
Explanation:
To approximate the solution(s) to the system of equations using technology, such as a graphing calculator or graphing software, you typically enter the equations into the device or program and view their intersection points. These intersection points represent the solutions to the system of equations. To get an accurate approximation to the nearest tenth of a unit, you may zoom in on the graph to clearly see where the lines intersect or use the device's built-in features to find the intersection.
You would then compare the given coordinates to the intersection points you found graphically and select the ones that match:
(0,0)
(9.2, 1.5)
(9.6, 3.5)
(5.3, 9.8)
(3.5, 9.6)
Remember to round your values to the nearest tenth as required and to quickly check if these values make sense in the context of the original problem.
The table below shows four systems of equations: System 1 System 2 System 3 System 4 4x − 5y = 2 3x − y = 8 4x − 5y = 2 10x − 7y = 18 4x − 5y = 2 3x − 8y = 4 4x − 5y = 2 10x + 3y = 15 Which pair of systems will have the same solution?
Answer:
System 1 and System 2 are equivalent.Step-by-step explanation:
The first and second system have the same solutions, the are equivalent systems of equations. Let's calculate solutions to demonstrate it:
System 1.[tex]\left \{ {{4x - 5y = 2} \atop { 3x - y = 8}} \right.[/tex]
If we multiply the second equations by -5, we can eliminate one variable and find the first solution:
[tex]\left \{ {{4x - 5y = 2} \atop { -15x +5y = -40}} \right.\\-11x=-38\\x=\frac{38}{11}[/tex]
Now, we use this value to find the other solution:
[tex]3x - y = 8\\3(\frac{38}{11})-y=8\\\frac{114}{11}-8=y\\ y=\frac{114-88}{11}=\frac{26}{11}[/tex]
The solution of the first system is [tex](\frac{38}{11} ;\frac{26}{11} )[/tex]
System 2.[tex]\left \{ {{4x - 5y = 2} \atop { 10x - 7y = 18}} \right.[/tex]
We do the same process than we did before, but this time we have to multiply by [tex]-\frac{5}{7}[/tex]:
[tex]\left \{ {{4x - 5y = 2} \atop { -\frac{50}{7}x + 5y = \frac{90}{7} }} \right.\\\frac{28x-50x}{7}=\frac{-90+14}{7}\\-22x=-76\\x=\frac{38}{11}[/tex]
Then,
[tex]4x - 5y = 2\\4(\frac{38}{11})-5y=2\\\frac{152}{11}-2=5y\\ 5y=\frac{152-22}{11}\\y=\frac{130}{5(11)}=\frac{26}{11}[/tex]
The solution of the second system is [tex](\frac{38}{11} ;\frac{26}{11} )[/tex]
Therefore, system 1 and system 2 are equivalent.
Given the function f (x) = 10x + 4, find each of the following. f(8), f(-4), f (0)
f(8)=?
f(-4)=?
f(0)=?
Please solve. best answer gets rewarded! show step by step.
What is the solution to the system of linear equations?
The point of intersection of lines represents the common solution of the system of linear equations. The solution of linear equations given in the graph is (0,2).
Linear equation represents a line on the graph. The system of linear equations represents couple/s of linear equations or lines.
The solution of system of linear equations means the common point satisfying the different linear equations.
Graphically, the point of intersection of two lines represents the common solution of these two lines or simply the solution of the system of linear equations.
So, the point of intersection from the given graph is (0,2).
Therefore, the solution of linear equations given in the graph is (0,2).
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A gutter at the edge of a roof drops 2 inches for every 30 feet of length. The measure of the angle to the nearest tenth of a degree that the gutter makes with the roof is ____ degrees. (Enter only the number.)
f={(x,y)| y=x+3} find f(3.6) & f(-0.2)
Solve the triangle. B=36 a=41 c=20
In the triangle with B = 36°, a = 41, c = 20, b ≈ 45.3, C ≈ 29.5, A ≈ 114.5.
To solve the triangle, we can use the Law of Sines and the fact that the sum of angles in a triangle is 180 degrees.
Given:
[tex]- Angle \( B = 36° \)[/tex]
[tex]- Side \( a = 41 \)[/tex]
[tex]- Side \( c = 20 \)[/tex]
First, we need to find angle [tex]\( A \)[/tex]. We can use the fact that the sum of angles in a triangle is 180 degrees:
[tex]\[ A = 180 - B - C \][/tex]
We can find angle [tex]\( C \)[/tex] using the Law of Sines:
[tex]\[ \frac{\sin C}{c} = \frac{\sin B}{b} \][/tex]
Solving for [tex]\( C \):[/tex]
[tex]\[ \sin C = \frac{c \times \sin B}{b} \][/tex]
[tex]\[ \sin C = \frac{20 \times \sin 36°}{b} \][/tex]
[tex]\[ \sin C = \frac{20 \times 0.5878}{b} \][/tex]
[tex]\[ \sin C = \frac{11.756}{b} \][/tex]
Now we can find angle [tex]\( C \)[/tex] using the inverse sine function:
[tex]\[ C = \sin^{-1}\left(\frac{11.756}{b}\right) \][/tex]
Now, we can substitute [tex]\( C \) i[/tex]nto the equation for [tex]\( A \)[/tex] and solve for [tex]\( b \):[/tex]
[tex]\[ A = 180 - B - C \][/tex]
[tex]\[ A = 180 - 36 - \sin^{-1}\left(\frac{11.756}{b}\right) \][/tex]
[tex]\[ A = 144 - \sin^{-1}\left(\frac{11.756}{b}\right) \][/tex]
Since we know all three angles of the triangle, we can find [tex]\( b \)[/tex] using the Law of Sines again:
[tex]\[ \frac{\sin A}{a} = \frac{\sin B}{b} \][/tex]
[tex]\[ \sin A = \frac{a \times \sin B}{b} \][/tex]
[tex]\[ \sin A = \frac{41 \times \sin 36}{b} \][/tex]
[tex]\[ \sin A = \frac{41 \times 0.5878}{b} \][/tex]
[tex]\[ \sin A = \frac{24.0678}{b} \][/tex]
Now, we can find [tex]\( b \)[/tex] using the inverse sine function:
[tex]\[ b = \frac{24.0678}{\sin A} \][/tex]
Finally, we'll use the given values and calculate the closest option:
[tex]\[ A \approx 144 - \sin^{-1}\left(\frac{11.756}{b}\right) \][/tex]
[tex]\[ b \approx \frac{24.0678}{\sin A} \][/tex]
[tex]\[ c \approx 20 \][/tex]
B = 36°
[tex]\[ a = 41 \][/tex]
After the calculation, the closest option is:
[tex]\[ b \approx 45.3, \ C \approx 29.5, \ A \approx 114.5 \][/tex]
Complete Question:
Solve the triangle.
B = 36°, a = 41, c = 20
choices:
b ≈ 27.5, C ≈ 115.5, A ≈ 28.5
b ≈ 45.3, C ≈ 25.5, A ≈ 118.5
b ≈ 45.3, C ≈ 29.5, A ≈ 114.5
b ≈ 27.5, C ≈ 25.5, A ≈ 118.5
What is the distance between -14 and 5
When combining functions, what operation requires that you restrict the domain of one or both functions?
simplify (2 (radical 5) - 4) (3 (radical 5) +2)
Find the missing term. If y = 1 + i, then y3 − 3y2 + (-3y) (-3y + 1) (3y) (3i ) − 1 = -i .
Answer:3y is the answer
Step-by-step explanation:
Pick the geometric term that matches the real-word object: a lip-gloss tube.
Answer: Cylinder.
Step-by-step explanation: Lip-gloss tubes may have different shapes, but the usual form of a lip-gloss tube is, as the name says, a tube.
This means that it has a circular base and a circular top, and a given height that connects the base and the top, the geometrical shape that has this shape is called a cylinder.
At a grocery store, an uncooked beef roast is on sale for $4.99/lb. At the same store, prepared roast beef is at the deli for $2.99/100g. How many times more expensive is the deli roast compared to the uncooked roast?
What is the area of the triangle given below?
Answer:
26 sq. units
Step-by-step explanation:
a-p-e-x
The area of the triangle is 26 sq.unit, the correct option is B.
What is a Triangle?A triangle is a polygon with three sides, angles and vertices.
The triangle is classified into various types on the basis of the angle and on the basis of the equality of the length of the sides, as obtuse , acute and right angled triangle and scalene, isosceles and equilateral triangle.
The triangle is shown in the figure has side 13 and height 4 units.
The area of the triangle whose base and height is given is calculated by using the formula:
Area = (1/2) * base * height
Substituting the value in the formula.
Area = (1/2) * 13 *4
Area = 13 * 2
Area = 26 sq.unit
To know more about Triangle
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The cost of a long-distance phone call is $0.46 for the first minute and $0.37 for each additional minute. if the total charge for a long-distance call is $6.75, how many minutes was the call?
1st minute = 0.46
additional minutes = 0.37
6.75 -0.46 = 6.29
6.29/0.37 =17
17 +1 = 18 total minutes
What is the approximate measure of acute ∠A when cosA=0.1045cosA=0.1045? Make sure your calculator is in degree mode. Round to the nearest degree.
To find the acute angle A when cosA=0.1045, use a calculator in degree mode to perform the inverse cosine operation and round the result to the nearest degree, which is approximately 84 degrees.
Explanation:To find the measure of acute ">∠A when cosA=0.1045, we use the inverse cosine function (also known as arccos or cos-1). Make sure your calculator is in degree mode. The approximate measure of acute ∠A can be calculated as follows:
Enter the value 0.1045 into the calculator.Press the inverse cosine button (often labeled as cos-1, acos, or similar) to find the angle whose cosine is 0.1045.Round the result to the nearest degree.Using a calculator set to degree mode, the result for cos-1(0.1045) should be approximately 84 degrees, when rounded to the nearest whole degree.
the answer to the triangle the hexagon and the Diamond