Answer:
The given lines are perpendicular.
Step-by-step explanation:
In the question, two lines are given as line 1 passes through (1,7) and (5,5). Whereas, line 2 passes through (-1,-3) and (1,1).
It is required to find the slope of given lines and figure out whether they are perpendicular, parallel or neither.
To solve this question, first find the slope of both lines. Check if their product is equal to -1, then they are perpendicular. If the slopes are equal the lines are parallel.
Step 1 of 2
Find the slope of first line.
[tex]$$\begin{aligned}m_{1} &=\frac{5-7}{5-1} \\m_{1} &=\frac{-2}{4} \\m_{1} &=-\frac{1}{2}\end{aligned}$$[/tex]
Step 2 of 2
Find the slope of first line.
[tex]$$\begin{aligned}&m_{2}=\frac{1-(-3)}{1-(-1)} \\&m_{2}=\frac{4}{2} \\&m_{2}=2\end{aligned}$$[/tex]
And
[tex]$$\begin{aligned}&m_{1} m_{2}=-\frac{1}{2}(2) \\&m_{1} m_{2}=-1\end{aligned}$$[/tex]
Since, both slopes are reciprocal of each other.
Therefore, the lines are perpendicular.
calculate the values of 2. f * x ^ 2 + y ^ 2 = 5/8 * and * 4/3 * xy = 1/4 (a) (x + y) (b) (x-y) (c) (x^2-y^2)
Answer:
(a) 1
(b) 1/2
(c) 1/2
Step-by-step explanation:
[tex]x^2 + y^2 = 5/8 (1)\\\frac{4}{3}xy = \frac{1}{4} (2)\\\\\textrm {From (2) by multiplying both sides by 3/4 we get}\\\\xy = \frac{3}{16} (3)\\\textrm{We know that } (x + y)^2 = x^2 + 2xy + y^2 \\\textrm{Adding 2xy to the LHS and RHS of equation 1 gisues us }\\x^2 + y^2 + 2xy = \frac{5}{8} + 2 * \frac{3}{16} = \frac{5}{8} + \frac{3}{8} = \frac{8}{8} = 1[/tex]
[tex](x + y)^2 = 1 == > x+y = \sqrt{1} = 1\\\\(x - y)^2 = x^2 -2xy + y^2\\\\\textrm{Subtracting 2xy from both sides of Equation 1}\\x^2 + y^2 - 2xy = \frac{5}{8} - 2*\frac{3}{16} = \frac{5}{8} - \frac{3}{8} = \frac{2}{8} = \frac{1}{4} \\x-y = \sqrt{\frac{1}{4}} = \frac{1}{2}\\\\x^2 - y^2 = (x+y)(x-y) = 1 . \frac{1}{2} = \frac{1}{2}[/tex]
A right triangle is plotted in an x y plane. The vertices of the triangle are as follows: (0, 0); (x sub 1, y sub 1) in the second quadrant; and (x sub 2, y sub 2) in the first quadrant. Right angle is at the origin.
What is the area of the triangle in the diagram?
A.
B.
C.
D.
Based on the calculations, the area of this triangle is equal to: A. Area = 1/2 × [√(x₂² + y₂²) × √(x₁² + x₁²)].
How to calculate the area of a triangle?Mathematically, the area of a triangle can be calculated by using this formula:
Area = 1/2 × b × h
Where:
b is the base area.h is the height.Next, we would find the distance between points A and B:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
AB = √[(x₂ - 0)² + (y₂ - 0)²]
AB = √(x₂² + y₂²)
Also, we would find the distance between points A and C:
Distance = √[(x₁ - x₂)² + (y₁ - y₂)²]
AC = √[(x₁ - 0)² + (y₁ - y0)²]
AC = √(x₁² + x₁²).
Now, we can find the area of this triangle:
Area = 1/2 × b × h
Area = 1/2 × AB × AC
Area = 1/2 × [√(x₂² + y₂²) × √(x₁² + x₁²)]
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Answer: B. 1/2√(x2^2 - x1^2) ( y2^2 - y1^2
Step-by-step explanation: Edmentum
4) Fred, Bob and Gladys took a maths test. The test was out of 200. Fred scored 50%, Bob scored 25% and Gladys scored 10%. How much did each person score?
if you can please answer
Answer:
Fred scored 100
Bob scored 50
Gladys scored 20
Step-by-step explanation:
Fred = 50% * 200
= 50/100 * 200
= 0.5 * 200
= 100
Bob = 25% * 200
= 25/100 * 200
= 0.25 * 200
= 50
Gladys = 10% * 200
= 10/100 * 200
= 0.1 * 200
= 20
Cindy works at Jurassic Park and has been tasked to design a container in the shape of a rectangular prism for the incoming baby dinosaurs. The scaled model of the container has dimensions 2m by 4m by 6m. Cindy has decided to increase each dimension of the scaled model by the same amount in order to produce a container with a volume of 84 times the volume of the scale model. By what amount should Cindy increase each dimension of the scaled model?
The amount Cindy should increase in each dimension of the scaled model is 12 m.
What is a rectangular prism?It is defined as the six-faced shape, a type of hexahedron in geometry.
It is a three-dimensional shape. It is also called a cuboid.
We have:
The scaled model of the container has dimensions 2m by 4m by 6m.
Volume of the scaled model = 2×4×6 = 48 cubic m
Let x be the amount by which each dimension is increased.
(2 + x)(4 + x)(6 + x) = 84(48)
[tex]\rm 48+44x+12x^2+x^3=4032[/tex]
[tex]\rm x^3+12x^2+44x-3984=0[/tex]
[tex]\rm x-12=0\quad \mathrm{or}\quad \:x^2+24x+332=0[/tex]
The quadratic equation has no real solution so,
x = 12 m
Thus, the amount Cindy should increase in each dimension of the scaled model is 12 m.
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A book can travel 462 miles on 42 gallons of gasoline how much gasoline will it need to go 275 miles
Find the measure of side c if a is 5 cm and b is 9 cm in a right triangle
The measure of side c if a is 5 cm and b is 9 cm in a right triangle is √106 cms.
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.
The measure of side c if a is 5 cm and b is 9 cm in a right triangle will be,
c² = 5² + 9²
c = √106 cms
Hence, the measure of side c if a is 5 cm and b is 9 cm in a right triangle is √106 cms.
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A place kicker in pro football has a 77% probability of making a field goal over 40 yards, and each attempted field goal is independent. If the kicker made his first two but missed his third attempt and is now trying for his fourth field goal of the game to win in overtime, what is the probability that his team will win the game
The probability that the team will win the sport is 77%.
Given that an area kicker in pro football incorporates a 77% probability of creating a field goal over 40 yards and every attempt field goal is independent.
Probability is how something is likely to happen. The probability of a happening is calculated by the probability formula by simply dividing the favorable number of outcomes by the overall number of possible outcomes.
So, his team will win the sport if he makes a goal otherwise loses.
Therefore, the Probability that his team will win the sport P[E] =P[making a field goal]
P[E]=77%
Hence, the probability that the team will win the sport when making a field goal is 77%.
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I need help!!!
There are 3 times as many females as males on the maths course at university. What fraction of the course are male?
Give your answer in its simplest form.
The fraction of the course that are male is 1/4
How to determine the fraction?The given parameter is:
Female = 3 * Male
As a fraction, we have:
Female + Male = 1
Substitute Female = 3 * Male in the above equation
3 * Male + Male = 1
This gives
4 * Male = 1
Divide by 4
Male = 1/4
Hence, the fraction of the course that are male is 1/4
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a company sold it's bond to interested members of the public and paid them an interest rate of 15percent per annum. how much will Mr Rogers receive if he bought a bond worth k 200 000.00
The amount that Mr Rogers would receive per annum is K 30,000.
How much would Mr Rogers receive per annum?
The amount of money that Mr Rogers would receive per annum is a function of the worth of the bond bought and the interest rate.
Interest= bond value x interest rate
0.15 x 200,000 = $30,000
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Please answer both
1 and 2
1. 80 sheep when increase in the ratio 5:4 becomes 100 sheep.
2. The perimeter of the shape is : 26cm
What is Perimeter?Perimeter is the outside boundary of a shape.
It is usually calculated by summing up all the length of the sides of that shape.
Analysis:
1. if the sheep is increased in the ratio 5:4
then new number of sheep becomes 5/4 x 80 = 400/4 = 100 sheep
2. The perimeter of the shape is the sum of all the sides of the shape = 7 + 4 + 10 +5 = 26cm
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Suppose the correlation coefficient between a baby’s weight and the price of a smartphone is 0.87. Which statement must be true?
The true statement that explains the correlation coefficient is: C. As the baby gains weight, the prices of smartphone tend to increase.
What is Correlation Coefficient?The value of the correlation coefficient shows a relationship between two variables. A positive value suggests a positive relationship, meaning as one variable increases, the other also increases.
A correlation coefficient of 0.87 suggests a positive relationship between baby's weight and the price of smartphone, therefore, the true statement is:
C. As the baby gains weight, the prices of smartphone tend to increase.
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I NEED HELP ASAP 15 POINTS!
1) ray
2) line
3) line segment
4) adjacent angles
5) vertical angles
Answer:
1) RAY
2) LINE
3) LINE SEGMENT
4) VERTICAL ANGLES
5) VERTICAL ANGLES
At the carnival, we found a bean bag toss booth. There's a 0.64 probability of throwing the bean bag into the outer ring, a 0.11 probability of throwing it into the middle ring, and the remaining probability throwing it into the center of the target. Tickets are awarded depending on which ring the bean bag lands in. We get 1 ticket for the outer ring, 2 tickets for the middle ring, and 3 tickets for the center. What is the expected value (number of tickets) we will get if we play the game 10 times
The expected value after 10 game at a carnival is 16.1 tickets.
Given the probabilities that bag lands into the outer ring, middle ring, center are 0.64, 0.11 and remaining. 1 ticket awarded for the outer, 2 for middle and 3 for middle.
We have to find the expected value we will get if we play the game 10 times.
Probability is the chance of happening an event among all the events possible. Value of probability lies between 0 and 1. The formula of probability is as under:
Probability=number of items/ total items in consideration.
Probability that bag lands in center is 1-0.64-0.11=0.25.
Expected value when game is played 1 time=1*0.64+2*0.11+3*0.25
=0.64+0.22+0.75
=1.61
Expected value when the game is played 10 times=10*1.61
=16.1 tickets.
Hence the expected value when game is played 10 times is 16.1 tickets.
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Find the missing side of the triangle.
Answer:
1
Step-by-step explanation:
1 is ans p²=h²-b²
solved
Please help.
The function of t(n) has an input variable of n and an output variable of t. t(n) = 8·n+3/2. What is the equation for the inverse function n(t)?
A. n(t) = 4t+12
B. n(t)= t/4-3
C. n(t)= 8t-24
D. n(t)= 2t-3/8
I know the answer is B, I just don't know how to get to that answer. Please explain how to solve an inverse like this.
The equation of the inverse function is given as n(t) = (t+3)/4
Inverse of a functionGiven the function that is represented as;
[tex]t(n)=8\cdot\frac{n+3}{2}[/tex]
This is further simplified to have:
t(n) = 4(n + 3)
Replace t with t(n)
t = 4n - 3
Make n the subject of the formula
4n = t+3
n = (t+3)/4
Hence the equation of the inverse function is given as n(t) = (t+3)/4
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the perimeters of a square and rectangle are equal. one side of a rectangle is 11cm and the area of the square is 4cm^2 more than the area of the rectangle. find the side of the square.
Answer:
The side of the square can be 13 or 9
Step-by-step explanation:
Let x equal the unknown side of the rectangle and y equal the side of the square. The given information is that the area of the square is 4cm^2 larger than that of the rectangle. Mathematically this can be represented as
[tex]11x+4=y^2[/tex]
The second known is that their perimeters are equal so,
[tex]22+2x=4y[/tex]
Solve the first equation in terms of x and substitute it into the second and you get the quadratic
[tex]y^2-22y+117=0[/tex]
[tex](y-13)(y-9)=0[/tex]
Therefore your side length for the square can be either of those.
PLEASE HELP, ASAP (PLEASE, I MEAN THAT AS NICE AS POSSIBLE) GEOMTRY BTW
The value of angle x is 127 degrees.
How to find angles?The angle x can be found as follows:
Angle on a straight line is 180 degrees.
Therefore, the sum of 53 degrees and x degrees is 180 degrees.
Therefore,
53 + x = 180°(sum of angles on a straight line)
subtract 53 from both sides of the equation
53 - 53 + x = 180 - 53
x = 127°
Therefore, the angle of x is 127 degrees.
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Manda converted the following repeating decimal a fraction. Her work is shown below.
In analyzing Manda’s work, she made a mistake instep 3, she did not subtract one x from the left side.
What is the fraction about?Fractions are known to be the parts of a complete or whole numbers of objects. It is known to have a numerator and a denominator and when solving for it, the rule of BODMAS must be obeyed.
In step 3 we see that (image attached) she did not subtract one x from the left side. The right thing to do is to use x to cancel out on the both side and that will make the answer to be correct but she did not.
So her error is seen in step 3 and as such, option C is correct.
See full question in the image attached.
Options are
Analyze Manda’s work. Is she correct? If not, what was her mistake?
A. Yes, she is correct.
B. In step 2, she needed to multiply both sides by 10.
C. In step 3, she did not subtract one x from the left side.
D. In step 4, she did not simplify her fraction.
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Can someone help me with this
The measure of angle B = 31 degrees, measure of angle C = 121 degrees, and b = 9. Then a =
nearest tenth.
to the
Answer: 8.2
Step-by-step explanation:
As angles in a triangle add to 180 degrees,
[tex]\angle A=180^{\circ}-121^{\circ}-31^{\circ}=28^{\circ}[/tex]
So, by the Law of Sines,
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}\\\\a=\frac{b \sin A}{\sin B}\\\\a=\frac{9 \sin 28^{\circ}}{\sin 31^{\circ}}\\\\a \approx \boxed{8.2}[/tex]
A characteristic of a simple random sample is that all samples of the same _______ have an equal chance to be selected.
A characteristic of a simple random sample is that all samples of the same population have an equal chance to be selected.
What is a simple random sampling?A subset of a statistical population called a simple random sample is one in which each member has the same chance of being picked or selected.
A subset of participants is chosen at random by the researcher using this sampling approach from a population.
To make sure that the sample represents the population, simple random sampling is often performed and this technique helps to sample bigger populations more frequently than smaller subpopulations.
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Given the following set of data: 3, 4, 5, 6, 8, 9, 9, which measures below have a value of 6? (Check all that apply.)
(1) mode
(2) range
(3) high value
(4) median
Answer:
Range and median
Step-by-step explanation:
Range = 9 - 3 = 6
Median = 6
Mode = 9
Given u = 3i - 8j and v = -4i + 8j, what is u v?
The sum of the vectors given is -i
Sum of vectorsVectors consists of y and x axis. They are plotted on an xy plane known as the argand diagram.
Given the following vectors
u = 3i - 8j
v = -4i + 8j
Take the sum of the vectors
u + v = (3i - 8j) + (-4i + 8j)
Take the sum to have
u + v = (3i-4i)+(-8j+8j)
u + v = -I
Hence the sum of the vectors given is -i
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Geometry question I’m confused with this help
Answer:
<PQR is 130 degrees
Step-by-step explanation:
When it says the line bisects the angle, that means the two smaller angles are equal to each other.
Therefore 3x+5 = 2x+25
Now rearrange to get x.
3x-2x=25-5
x=20
Now plug the x back into both phrases and them together to get the final answer for <PQR.
20 * 3 + 5 = 65
20 * 2 + 25 = 65
65*2 = 130
Consider the following system of linear inequalities and corresponding graph:
y ≥ 2x - 4
x > -3
y < 5
Which of the following points is a solution to this system of linear inequalities?
a.)
(5,6)
b.)
(-4,5)
c.)
(-3,7)
d.)
(2,0)
How many grapes?
Help me please! Thanks
Using proportions, considering the given ratio, it is found that 9090 grapes were there.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The ratio of bananas to grapes of 3:101 means that out of 104 fruits, 3 are bananas and 101 are grapes. Hence the rule of three is given as follows:
3 bananas - 101 grapes
270 bananas - n grapes.
Applying cross multiplication:
3n = 101 x 270
n = 101 x 270/3
n = 9090.
9090 grapes were there.
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cos theta=8/17. Find tan theta
A. 15/8
B. 15/17
C. 17/15
D. 8/15
Answer:
A) [tex]\frac{15}{8}[/tex]
Step-by-step explanation:
remember Soh Cah Toa!!
[tex]sin=\frac{opposite}{hypotenuse}\\ cos=\frac{adjacent}{hypotenuse} \\tan=\frac{opposite}{adjacent} \\\\cos=\frac{8}{17}\\\\a^2+b^2=c^2\\8^2+b^2=17^2\\64+b^2=289\\b^2=225\\\sqrt{b^2} =\sqrt{225}\\b=15=opposite\\\\tan=\frac{15}{8}[/tex]
can anybody help me with order of operations
Answer:
The order of operations is Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction.
Step-by-step explanation:
The order of operations is PEMDAS.
P: Parenthesis
E: Exponents
M: Multiplication
D: Division
A: Addition
S: Subtraction
An easy way to remember PEMDAS is, please excuse my dear aunt sally.
Hope this helps!
If not, I am sorry.
HELP ME PLEADE I NEED THIS ( PLATOOOOOO)
Answer: f(x+3), f(x+2), f(x), f(x-1/2), f(x-4), f(x-7)
Step-by-step explanation:
For y=f(x-a), the vertex is shifted a units to the right.
So, to order from left to right, we need to order them so that the value of a increases from the least to the most.
Seriously help I’m about to submit this: A researcher wishes to estimate the percentage of adults who support abolishing the penny what size sample should be obtained if he wishes the estimate to be within three percentage points with a 95% confidence if he:
A: uses a previous estimate of 26%?
B: he does not use any prior estimates?
Using the z-distribution, the sample sizes are given as follows:
a) 822.
b) 1068.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
Item a:
The estimate is of [tex]\pi = 0.26[/tex], hence we solve for n when M = 0.03.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.26(0.74)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.26(0.74)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.26(0.74)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.26(0.74)}}{0.03}\right)^2[/tex]
n = 821.2
Rounding up, a sample of 822 is needed.
Item b:
No prior estimate, hence [tex]\pi = 0.5[/tex].
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.5(0.5)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.03}\right)^2[/tex]
n = 1067.11
Rounding up, a sample of 1068 is needed.
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Explain why the value of the sine ratio for an acute angle of a right triangle must always be a positive value less than 1
The sine is defined as the ratio of the length of the opposite leg and the hypotenuse. Since the hypotenuse is the longest side, the numerator will be less than the denominator, and thus the fraction will be less than 1.
Answer:
The sine is defined as the ratio of the length of the opposite leg and the hypotenuse. Since the hypotenuse is the longest side, the numerator will be less than the denominator, and thus the fraction will be less than 1.
Step-by-step explanation: