Answers
The solution to the inputs of the given function are:
a) f(0) = 13
b) f(2) = -1
c) f(-2) = 27
d) f(1) + f(-1) = 26
How to solve Function Inputs?The set of input values of a function is referred to as the domain of the function. Then, the set of output values of the function is referred to as the range of the function. Thus, if we possess a set of ordered pairs, we can find the domain by listing all of the input values, which are the x-coordinates.
We are given the function:
f(x) = (-x)³ - x² - x + 13
a) f(0) = (-0)³ - (0)² - 0 + 13
f(0) = 13
b) f(2) = (-2)³ - (2)² - 2 + 13
f(2) = -1
c) f(-2) = (2)³ - (-2)² + 2 + 13
f(-2) = 27
d) f(1) = (-1)³ - (1)² - 1 + 13
f(1) = 10
f(-1) = (1)³ - (-1)² + 1 + 13
f(-1) = 16
f(1) + f(-1) = 10 + 16 = 26
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Related Questions
If 86
is added to a number, the result is 44
less than three times the number. Find the number.
Answers
Answer:
x = 65
Step-by-step explanation:
let the number be 'x'.
If 86 is added to a number, the result is 44 less than three times the number. Therefore the equation will be,
=> 86 + x = 3x - 44
Rearranging,
=> x - 3x = -44 - 86
=> -2x = -130
=> x = 130/2
=> x = 65
14 A national standardized test is given in May that generates a mean score of 350 with a standard
deviation of 18. What is the probability that a randomly selected test score will fall in the
interval 360 to 380?
(1) 0.56
(2) 0.013
(3) 0.24
(4) 0.76
Answers
The probability that a randomly selected test score will fall in the interval 360 to 380 is the option (3), 0.24.
How to solveTo calculate the probability that a test score falls between 360 and 380, we need to standardize these values by subtracting the mean and dividing by the standard deviation.
This gives us:
z(360) = (360-350)/18 = 0.56
z(380) = (380-350)/18 = 1.67
We can then use a standard normal distribution table or a calculator to find the area under the curve between these two z-scores.
The probability is approximately 0.24.
Therefore, the answer is option (3), 0.24.
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which expresion shows 7+21 written as a product of two factors
Answers
As we used the distributive property of multiplication to rewrite 7+21 as a product of 7 x (1+3) or 7 x 4.
However, you are asked to express this sum as a product of two factors. A factor is a number that is multiplied by another number to produce a product. Therefore, to express 7+21 as a product of two factors, we need to find two numbers that, when multiplied together, give us the sum of 7+21.
One way to approach this problem is to use the distributive property of multiplication, which states that a(b+c) = ab + ac. We can apply this property by rewriting 7+21 as 7+3*7, since 21 is equal to 3 times 7. Then, we can factor out the common factor of 7 from the expression to get:
7+37 = 7(1+3)
Now, we have expressed 7+21 as a product of two factors: 7 and (1+3), or simply 7 and 4. Therefore, the expression that shows 7+21 written as a product of two factors is:
7 x (1+3) or 7 x 4
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-(4-8) + (-3-7)−(−1+6) + (−2+5) =
Step by step
Answers
Answer:
Step-by-step explanation:
-4+8-3-7+1-6-2+5
4-10-5+3
-6-2
-8
Step-by-step explanation:
the negative sign changes to a positive sign so
( -12)+ (-10) -(-7)+(-7)
= -22
You are trying to determine if a router you’re thinking of purchasing will give off a strong enough wifi signal to cover the area in your house. The router you have selected will cover an area of 850 ft^2.
Answers
According to the information, the router cannot cover the kitchen area.
Does the router cover the kitchen area?To calculate if the router covers the kitchen area, we must identify the area that the router can cover. In this case, the router covers an area of 850 square feet. However, we must take into account that this area is counted around the router. So, we have to calculate the square root of 850 ft^2.
[tex]\sqrt{850}[/tex] = 29.129.1 / 2 = 14.5From the above, we can infer that the router has signal coverage of 14 meters around it, so it would only cover the living room area.
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Solve the equation for x -4X+3=11
Answers
Answer:
x = -2
Step-by-step explanation:
-4x + 3 = 11
Subtract 3 from both sides:
-4x = 8
Divide both sides by -4:
x = -2
According to Bureau of Labor Statistics26.0% of the total part-time workforce in the USwas between the ages of 25 and 34 during a recent monthA random sample of 90 part-time employees was selected during this quarter. Using the normal approximation to the binomial distribution, what is the probability that fewer than 18 people from this sample were between the ages of 25 and 342 (round standard deviation to 4 decimal places)
Answers
The probability that fewer than 18 people from this sample were between the ages of 25 and 34 is 0.1089 (or 10.89%).
Using the normal approximation to the binomial distribution, the mean (μ) of the sample is:
μ = np = 90 x 0.26 = 23.4
The standard deviation (σ) of the sample is:
σ = √(np(1-p)) = √(90 x 0.26 x 0.74) = 4.37 (rounded to 4 decimal places)
To find the probability that fewer than 18 people from this sample were between the ages of 25 and 34, we need to calculate the z-score:
z = (x - μ) ÷ σ = (18 - 23.4) ÷ 4.37 = -1.24
Using a standard normal table or calculator, we find that the probability of a z-score less than -1.24 is 0.1089.
0.1089 = 10.89%
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need help with this geometry problem
Answers
The shaded area of the circle is around 65.44 square meters in size.
How to find area?To find the area of the shaded region, subtract the area of sector FGH from the area of sector FEGH.
The area of sector FEGH is:
A1 = (1/2) r² θ₁
where r = radius of the larger circle and θ₁ = angle subtended by the arc EH.
Since EH = 30 m and the radius of the larger circle = 18 m (half of 10 + 8):
θ₁ = (EH arc length) / r = 30/18π radians
So,
A₁ = (1/2) (18)² (30/18π) = 270/π m²
The area of sector FGH is:
A₂ = (1/2) r² θ₂
where θ₂ = angle subtended by the arc GH.
Since GH is 8 m and the radius of the larger circle is 18 m:
θ2 = (GH arc length) / r = 8/18π radians
So,
A₂ = (1/2) (18)² (8/18π) = 64/π m²
Therefore, the area of the shaded region is:
A = A₁ - A₂ = (270/π) - (64/π) = 206/π ≈ 65.44 m²
Hence, the area of the shaded region is approximately 65.44 square meters.
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Julie was testing how far two new electric cars—model A and model B—could drive on a full charge. She obtained a sample of 5 55 new cars of each model, charged them fully, and drove them as far as she could along a controlled route. Here is a summary of the distances: Distance Model A Model B Mean 168 km 168 km168, start text, space, k, m, end text 172 km 172 km172, start text, space, k, m, end text Standard deviation 5.4 km 5.4 km5, point, 4, start text, space, k, m, end text 7.5 km 7.5 km7, point, 5, start text, space, k, m, end text Number of cars 5 55 5 55 Julie wants to use these results to test H 0 : μ A − μ B = 0 H 0 : μ A −μ B =0start text, H, end text, start subscript, 0, end subscript, start text, colon, space, end text, mu, start subscript, start text, A, end text, end subscript, minus, mu, start subscript, start text, B, end text, end subscript, equals, 0 versus H a : μ A − μ B ≠ 0 H a : μ A −μ B =0start text, H, end text, start subscript, start text, a, end text, end subscript, start text, colon, space, end text, mu, start subscript, start text, A, end text, end subscript, minus, mu, start subscript, start text, B, end text, end subscript, does not equal, 0. Assume that these are representative samples and all other conditions have been met. What is the P-value associated with these sample results? Choose 1 answer: Choose 1 answer: (Choice A) P -value < 0.01 P-value<0.01P, start text, negative, v, a, l, u, e, end text, is less than, 0, point, 01 A P -value < 0.01 P-value<0.01P, start text, negative, v, a, l, u, e, end text, is less than, 0, point, 01 (Choice B) 0.01 ≤ P -value < 0.05 0.01≤P-value<0.050, point, 01, is less than or equal to, P, start text, negative, v, a, l, u, e, end text, is less than, 0, point, 05 B 0.01 ≤ P -value < 0.05 0.01≤P-value<0.050, point, 01, is less than or equal to, P, start text, negative, v, a, l, u, e, end text, is less than, 0, point, 05 (Choice C) 0.05 ≤ P -value < 0.10 0.05≤P-value<0.100, point, 05, is le
Answers
The p value based on the information will be E. P - value ≥ 0.20
How to compute the valueOpen Minitab 17. Select 'Stat' -> 'Basic Statistics' -> '2 - Sample t... Select 'Summarized data' from the dropdown menu.
Enter 5 in both Sample size of sample 1 and sample 2, 168 and 172 in Sample mean of Sample 1 and Sample 2. 5.4 and 7.5 in Standard deviation of Sample 1 and Sample 2.
Click on 'Options' and Enter 'Confidence level' 95.0(or the given Cofidence level) , 'Hypothesized difference' 0.0 , 'Alternative hypothesis' 'Difference \\neq Hypothesized difference'. Also the box 'Assume equal variance' can be ticked as requirement.
Click on 'Ok' -> 'Ok'.
Output: -
P - value = 0.361 i.e., P - value ≥ 0.20
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Bree is replacing the wire on her farm paddock fences. She has measured a couple of the sides and drawn a sketch of the paddock shape. (pic below)
a. Find the two missing sides and calculate the perimeter of the paddocks
Perimeter?
b. The cost of fencing wire is $5 per meter. How much will the wire cost
Cost?
Answers
a. The perimeter of the paddock is 120 meters
b. The cost of the wire will be $600
a. To find the missing sides and calculate the perimeter of the paddock, let's analyze the given sketch.
The length of the missing side on the left can be determined by subtracting the known length of 10m from the total height of 20m. Therefore, the left side has a length:
20m - 10m = 10m.
The missing side on the right is equal in length to the known side of 40m.
Now we can calculate the perimeter by adding up all the side lengths:
Perimeter = 10m + 40m + 20m + 10m + 40m
= 120m.
b. To calculate the cost of the wire, we need to multiply the perimeter of the paddock by the cost per meter of fencing wire, which is $5/m.
Wire Cost = Perimeter × Cost per meter
= 120m × $5/m
= $600.
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A net of a rectangular prism is shown.
A net of a rectangular prism with dimensions 7 centimeters by 3 and three-fifths centimeters by 2 and two-fifths centimeters.
What is the surface area of the prism?
Answers
Answer:
The surface area of a rectangular prism is calculated by adding the areas of all six faces. The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is the length, w is the width and h is the height.
In this case, the length is 7 cm, the width is 3 and three-fifths cm (or 3.6 cm), and the height is 2 and two-fifths cm (or 2.4 cm). Plugging these values into the formula gives us a surface area of 2(7) (3.6) + 2(7) (2.4) + 2(3.6) (2.4), which simplifies to 50.4 + 33.6 + 17.28, or 101.28 square centimeters.
So, the surface area of this rectangular prism is 101.28 square centimeters.
Received message. The surface area of a rectangular prism is calculated by adding the areas of all six faces. The formula for the surface area of a rectangular prism is `2lw + 2lh + 2wh`, where `l` is the length, `w` is the width and `h` is the height. In this case, the length is 7 cm, the width is 3 and three-fifths cm (or 3.6 cm), and the height is 2 and two-fifths cm (or 2.4 cm). Plugging these values into the formula gives us a surface area of `2(7)(3.6) + 2(7)(2.4) + 2(3.6)(2.4)`, which simplifies to `50.4 + 33.6 + 17.28`, or **101.28 square centimeters**. So, the surface area of this rectangular prism is **101.28 square centimeters**.
Step-by-step explanation:
what is 45 x 6 i need help
Answers
Answer:
270
Step-by-step explanation:
I am showing my mental math, hope this helps you:
45 x 6 is the same as 4 x 6 = 10s place value and 5 x 6 = 1s place value:
4 x 6 = 24
5 x 6 = 30
Therefore, the answer is:
2 (4 + 3) 0
270
The value of the expression 45 x 6 is 270.
We have,
To calculate the product of 45 multiplied by 6, you can follow these steps:
- Start by multiplying the units digits of the two numbers: 5 x 6 = 30.
- Write down the units digit of the result, which is 0, and carry over the tens digit, which is 3.
- Multiply the tens digit of the first number by the second number: 4 x 6 = 24.
- Add the carried-over value from step 2 to this result: 24 + 3 = 27.
- Write down the tens digit of the result, which is 7, and carry over the hundreds digit, which is 2.
- Multiply the hundred digit of the first number by the second number: 4 x 6 = 24.
- Add the carried-over value from step 5 to this result: 24 + 2 = 26.
- Write down the hundred digit of the result, which is 6.
- Combine the hundreds, tens, and units digits together: 6, 7, 0.
- The final product of 45 multiplied by 6 is 270.
So, 45 x 6 = 270.
Thus,
The value of the expression 45 x 6 is 270.
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Someone please help!! (20 POINTS!)
Answers
Answer: C
Step-by-step explanation: Rise/run so 1/1=1 but it's going down so it negative. -1
A supermarket sells fruit snacks by the box. AEach box holds x pachages of strawberry snacks and y packages of cherry snacks. Nina bought 6 boxes.
Write two expressions for home many more strawberry packages than cherry packages nina bought. Then write what the few expressions being equivalent mean in terms of the situation
Answers
The two equivalent expressions are 6(x − y) and 6x − 6y.
What are the equivalent expressions?These expressions look different but their simplified forms are same expressions are called equivalent expressions.
The 1st expression shows subtracting the number of packages of cherry snacks from the number of packages of strawberry snacks in each box.
When we multiplying the difference by the number of boxes then, it will be: 6(x-y)
Now, total number of cherry snacks and subtracting it from the total number of strawberry snacks will be 6x - 6y. So, equivalent expressions means in terms of situation are 6(x − y) and 6x − 6y.
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A motorist travelled from Town A to Town B. After travelling for 1 1/2 hours , he passed
a cyclist travelling at an average speed of 45 Km/h in the opposite direction.
when the motorist reached Town B 2 h later, the cyclist was 30 km away from Town A.
a) Find the average speed of the motorist.
b) Find the distance between Town A and Town B.
Answers
Answer:
the formula: Speed = Distance / Time.
Let's break down the problem into two parts:
a) Find the average speed of the motorist.
Let's assume the average speed of the motorist is "v" km/h.
The distance the motorist traveled in 1 1/2 hours is given by: Distance = Speed × Time = v × (3/2) km.
The distance the cyclist traveled in 1 1/2 hours (opposite direction) is given by: Distance = Speed × Time = 45 × (3/2) km.
Since they passed each other, the sum of their distances should be equal to the distance between Town A and Town B.
So, we can set up the equation: v × (3/2) + 45 × (3/2) = Distance between Town A and Town B.
b) Find the distance between Town A and Town B.
When the motorist reached Town B 2 hours later, the cyclist was 30 km away from Town A.
We can set up the equation: Distance between Town A and Town B = v × 2 + 30.
Now, let's solve the equations:
v × (3/2) + 45 × (3/2) = v × 2 + 30.
Simplifying the equation, we have: (3v + 135)/2 = 2v + 30.
Multiplying both sides of the equation by 2 to eliminate the fraction, we get: 3v + 135 = 4v + 60.
Subtracting 3v from both sides of the equation, we have: v = 75.
Therefore, the average speed of the motorist is 75 km/h.
To find the distance between Town A and Town B, we substitute the value of v into the equation:
Distance between Town A and Town B = v × 2 + 30 = 75 × 2 + 30 = 150 + 30 = 180 km.
Therefore, the distance between Town A and Town B is 180 km.
Un elevador de taller mecánico tiene pistones de entrada y salida de 5 cm y de 60 cm de radio respectivamente. Con este dispositivo se mantiene levantado un auto de 2000 kg. ¿Cuál es la fuerza aplicada al pistón de entrada?
Answers
The force applied to the input piston is 136.25 N.
How to find the force applied to the intake piston?This problem can be solved using the principle of hydraulic systems, which states that pressure in a confined fluid is transmitted equally in all directions.
Thus, we can equate the pressure on the input piston to the pressure on the output piston, and solve for the force on the input piston. That is:
P₁ = P₂
F₁/A₁ = F₂/A₂ (Pressure = Force/Area)
F₂ = 2000 * 9.81 = 19620 N (F = mg)
A₁ = π * r₁² = π * 5² = 25π cm²
A₂ = π * r₂ ² = π * 60² = 3600π cm²
F₁ = F₂/A₂ * A₁
F₁ = (19620/3600π) * 25π
F₁ = 136.25 N
Therefore, the force applied to the input piston is 136.25 N.
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Question in English
A machine shop lift has input and output pistons of 5 cm and 60 cm radius respectively. With this device, a 2000 kg car is kept lifted. What is the force applied to the intake piston?
does a number being squared with x and being negative make it so it has to be multiplied by 2 like the first number in the third part of the question? I'm unsure where it came from
Answers
Squaring a number implies increasing it by itself. In case the number being squared is negative, the result will continuously be positive. Increasing a number by 2 implies multiplying it, which is not linked to squaring a number.
What is the number about?To square a number, one must raise it to the power of two, that is different from carrying out its multiplication with itself. One way of squaring a value is shown by taking the number 3 and raising it to the power of 2.
3² = 3 x 3 = 9
By the same way , if we raise -2 to the power of 2, the result will be a positive value of four.
Raising numbers to the power of two is a frequent mathematical procedure use in numerous academic fields such as algebra, geometry, physics, and statistics.
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If tanθ=-5/2 and sinθ>0, find the exact values of sinθ,cosθ,secθ,cscθ,cotθ.
Answers
The exact values are;
sinθ = -5/√29
cosθ = 2/√29
secθ =√29/2
cscθ = -√29/5
cotθ = -2/5
We are given that
tanθ=-5/2 and sinθ>0
First quadrant: I, 0°<θ<90°
We can find the first quadrant between 0° and 90° , the values from 0 to the positive numbers for the x-axis and the y-axis, the functions sine, cosine and tangent will always have positive values.
sinθ = -5/√29
cosθ = 2/√29
secθ =√29/2
cscθ = -√29/5
cotθ = -2/5
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what’s the numbers that correspond to the corret number of solutions
Answers
The number of solutions for the given system of linear equations is: Infinitely many solutions.
Calculating the number of solutionsTo determine the number of solutions for the given system of linear equations:
3x - y = 4
6x - 2y = 8
We can use the algebraic method of solving the system of equations by substitution or elimination.
Let's use the algebraic method to determine the number of solutions:
3x - y = 4 (1)
6x - 2y = 8 (2)
We can simplify equation (2) by dividing both sides by 2:
3x - y = 4 (1)
3x - y = 4 (2')
Equations (1) and (2') are equivalent, which means that they represent the same line.
Therefore, the two equations represent the same line, and we have infinitely many solutions.
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Complete question
What’s the numbers that correspond to the corret number of solutions
0 solution, 1 solution, Many solutions
3x - y = 4
6x - 2y = 8
Write an equation in standard form
Answers
The equation of the quadratic with a directrix of x = 2 and vertex of (0 , 0) is: y² = -8x
The equation of the quadratic with a directrix of y = 4 and vertex of (1, 3) is: (x - 1)² = -4 (y - 3)
How to write the equation of parabola with directrix of x = 2 and vertex of (0, 0)Quadratic equation when the directrix is at x direction is of the form:
(y - k)² = 4P (x - h)
OR
standard vertex form, x = a(y - k)² + h where a = 1/4p
The vertex
v (h, k) = (0, 0)
P in this problem, is the distance between the vertex and the directrix
P = 0 - 2 = -2
substitution of the values into the equation gives
(y - k)² = 4P (x - h)
(y - 0)² = 4 x -2 (x - 0)
y² = -8x
Quadratic equation when the directrix is at y direction is of the form:
(x - h)² = 4P (y - k)
OR
standard vertex form, y = a(x - h)² + k where a = 1/4p
The vertex
v (h, k) = (1, 3)
P in this problem, is the distance between the vertex and the directrix
P = 3 - 4 = -1
substitution of the values into the equation gives
(x - h)² = 4P (y - k)
(x - 1)² = 4 * -1 (y - 3)
(x - 1)² = -4 (y - 3)
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find the measure of angle PRT
Answers
measure of Angle PRT = 90 degrees
Step-by-step explanation:A circle with center T exists -- Given
Point R is on the the circle. -- THIS IS AN ASSUMPTION BASED ON THE PICTURE (if you have more information that makes this not true, the rest of this logic fails).
Line segment TR is the radius of the circle. -- Definition of radius
Line PR is tangent to the circle. -- PR touches at exactly one point: R
Angle PRT has a vertex as point R. -- definition of angle PRT
Since PR is tangent to the circle, TR is perpendicular to PR -- consequence of lines perpendicular to circles
Perpendicular lines form right angles. -- Consequence of two congruent angles that form a straight angle pair.
The measure of a right angle is 90 degrees. -- definition of right angle
Therefore, the measure of angle PRT is 90 degrees.
Please help! Daniel incorrectly solved the equations shown. Explain what he did wrong in each solution and then solve both equations correctly.
25x^2-16=9
√(25x^2 )-√16=√9
5x-4=±3
5x=±7
x=±7/5
z^3-2=6
z^3=8
∛(z^3 )=∛8
z=±2
Answers
Daniel incorrectly applied the square root to both terms on the left side of the equation and he forgot to take into account the possibility of multiple roots when solving for the cube root of z³.
Let's first look at the first equation that Daniel solved incorrectly:
25x²-16=9
Daniel's solution:
√(25x² )-√16=√9
5x-4=±3
5x=±7
x=±7/5
What Daniel did wrong here is that he incorrectly applied the square root to both terms on the left side of the equation.
Instead, he should have simplified the left side first, using the fact that √(a²) = |a|, before applying the square root. So the correct solution is:
25x²-16=9
25x²=25
x²=1
x=±1
Now let's look at the second equation that Daniel solved incorrectly:
z³-2=6
Daniel's solution:
z³=8
∛(z^3 )=∛8
z=±2
What Daniel did wrong here is that he forgot to take into account the possibility of multiple roots when solving for the cube root of z³.
In fact, z³ = 8 has three roots: z = 2, z = -1 + i√3, and z = -1 - i√3. So the correct solution is:
z³-2=6
z³=8
z=2
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Match the situation with its probability.
Answers
The given probabilities are as follows:
Spinner landing on at least one A = 7/16Spinner landing on C and D in any order = 1/8Spinner landing on two Bs = 1/16Spinner landing on C on the second spin = 1/4What are the probabilities?The probabilities are determined using the formula below:
Probability = number of expected outcome / number of total outcomesSpinner landing on at least one A:
number of at least one A = 7
Spinner landing on at least one A = 7/16
Spinner landing on C and D in any order:
number of landing on C and D in any order = 2
Spinner landing on C and D in any order = 2/16
Spinner landing on C and D in any order = 1/8
Spinner landing on two Bs:
number of landing on two Bs = 1
Spinner landing on two Bs = 1/16
Spinner landing on C on the second spin:
Number of landing on C on the second spin = 4
Spinner landing on C on the second spin = 1/4
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a 7 cm times 5 cm rectangle sits inside a circle with a radius of 6 cm
Answers
The shaded area of the portion as shown in the diagram is 78.04 cm².
What is area?Area is the region bounded by a plane shape.
To calculate the shaded area of the portion, we use the formula below
Formula:
A = πr²-lw.................. Equation 1Where:
A = Area of the shaded portionr = Radius of the circlel = Length of the rectanglew = Width of the rectangleFrom the question,
Given:
r = 6 cml = 7 cmw = 5 cmSubstitute these values into equation 1
A = 3.14×6²-(7×5)A = 113.04-35A = 78.04 cm²Learn more about area here: https://brainly.com/question/25292087
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Complete question: A 7 cm times 5 cm rectangle sits inside a circle with a radius of 6 cm. Calculate the area of the shaded portion.
Pls, HELP!!
Law of Cosines
Solve for c. Round your final answer to the nearest tenth
Answers
The length of c in the triangle is 4.2 units.
How to find the side of a triangle?The side of a triangle can be found using cosine law as follows:
Hence,
c² = a² + b² - 2ab cos C
where
a, b and c are the side lengthC is angle opposite to side cTherefore,
c² = 7² + 8² - 2(7)(8) cos 32°
c² = 49 + 64 - 112 cos 32°
c² = 113 - 112(0.84804809615)
c² = 113 - 94.9813867695
c² = 18.019
square root both sides of the equation
c = √18.019
c = 4.24487926801
c = 4.2 units
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what is the slope of the line below?
Answers
Answer:
B. Y= 5x - 2
Step-by-step explanation:
The Y is negative, you can see the number -5 below the point, if you go to the top, that is, to 0 and count down, the lines are two and the X is positive 5, you can see where the number 5 is and the point is above.
on the first day of training Zari runs 2 miles north, the 4 miles east and then back home via shortest route. Taye runs 2 miles west then 4 miles south, and then back home again via the shortest route. a. draw their routes on the coordinate plane above, use a straightedge for accuracy. b. create a proof that demonstrates that the two triangles formed by their routes are congruent. proof needs three pairs of congruent properties of the triangles followed by a triangle congruency statement. show if congruent by ASA, SAS, or SSS.
Answers
By ASA (Angle-Side-Angle) congruence, triangle ABC is congruent to triangle DEF.
Instructions to draw the routes:
Draw the x-axis and y-axis to create a coordinate plane.
Mark the starting point of Zari's run as (0,0) on the coordinate plane.
From (0,0), move 2 units north to reach (0,2).
From (0,2), move 4 units east to reach (4,2).
From (4,2), move directly back to the starting point (0,0) using the shortest route.
Mark the starting point of Taye's run as (0,0) on the coordinate plane.
From (0,0), move 2 units west to reach (-2,0).
From (-2,0), move 4 units south to reach (-2,-4).
From (-2,-4), move directly back to the starting point (0,0) using the shortest route.
Instructions to prove that the two triangles are congruent using ASA:
Label the vertices of Zari's triangle as A (0,0), B (4,2), and C (0,0).
Label the vertices of Taye's triangle as D (0,0), E (-2,-4), and F (0,0).
Show that angle A and angle D are congruent because they are both right angles (90 degrees).
Show that segment AB and segment DE are congruent because they both have a length of 4 units.
Show that segment AC and segment DF are congruent because they both have a length of 2 units.
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Where will X be after a rotation 90° clockwise about (-5,-1)?
Click on the grid to place the point.
Answers
The image point of the coordinate X after the rotation is (-1, 5).
Calculating the image point of the coordinate XWhen a point is rotated 90° clockwise around the origin, the new point will be formed by switching the x and y-coordinates and then negating the new x-coordinate.
So for point X (-5, -1), the new x-coordinate will be -1, and the new y-coordinate will be -(-5) = 5, giving the new point (-1, 5).
Therefore, after a rotation of 90° clockwise, point X (-5, -1) will be at the new location (-1, 5).
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Which of the following is a biconditional statement?
A) If x2 = 25, then x = 5 or x = –5
B) x = 5 if x2 = 25
C) x = 5 if and only if x + 5 = 10
D) If x ≠ 5 then x2 ≠ 25
Answers
Answer:
C) x = 5 if and only if x + 5 = 10
Step-by-step explanation:
You want to identify the biconditional statement among those that are given.
ConditionalA conditional statement is of the form ...
If P, then Q.
ConverseThe converse of the above conditional statement is ...
If Q, then P.
BiconditionalWhen both the statement and its converse are intended, the statement can be written as the biconditional ...
If and only if P then Q.
The given example of a biconditional statement is ...
x = 5 if and only if x +5 = 10.
__
Additional comment
This can be abbreviated ...
Iff P then Q
meaning "if P then Q, and if Q then P", or "if and only if P, then Q."
Consider the letters in the word SAMPLE. In how many ways can you arrange 5 of the letters?
Answers
Answer: 720
Step-by-step explanation: There are 6 choices for the first letter, 5 for the second, 4 for the third and so on. 6*5*4*3*2=720
Step-by-step explanation:
according to the law of combination
⁵C6 note 6 is a base numberCombining formula: 6!/(6-1)! 6!solving 6!/5! 6! :120ways