Answer:
B. (3, -6)
Step-by-step explanation:
Given line
y= 1/4x + 3
given line is in form of y = mx + c
where m is slope of line and c is y intercept
thus, in line y= 1/4x + 3 m is 1/4 is slope
we know product of slope of two perpendicular line is -1
m1 * m2 = -1
let the line perpendicular to y= 1/4x + 3 be
y = mx + c
thus
m * 1/4 = -1
m = -4
Thus, in y = mx + c , m is -4
updated equation until now by putting value of m as -4
y = -4x + c
this, line passes through point (0,6)
putting x as 0 and y as 6 in y = -4x + c
we have
6 = -4*0 + c
=> c = 6
Thus, equation of perpendicular line is
y = -4x + 6
_______________________________________________
we have to find which point from the option lies on y = -4x + 6
lets plug in value of x from given points and see if value of y calculated is as given in option . if the value is different then point does not lie on perpendicular line
(4, -2)
y = -4*4 + 6
y = -16 + 6 = -10
-10 is not equal to -2 as given in option, thus point (4,-2 ) does not lie on
y = -4x + 6
(3,-6)
y = -4*3 + 6
y = -12 + 6 = -6
-6 is equal to -6 as given in option, thus point (3,-6 ) does lie on
y = -4x + 6
(0, -6)
y = -4*0 + 6
y = 0 + 6 = 6
6 is not equal to -6 as given in option, thus point (0,-6 ) does not lie on
y = -4x + 6
(-2,2)
y = -4*-2 + 6
y = 8 + 6 = 14
14 is not equal to 2 as given in option, thus point (-2,2 ) does not lie on
y = -4x + 6
Thus, option B. (3, -6) is the correct choice.
What is the volume, in terms of π, for a cylindrical
container with a radius of 3.25 centimeters and a
height of 10 centimeters? (use the formula V
= I1r2 h)
Answer:
[tex]105.625\pi cm^3[/tex]
Step-by-step explanation:
[tex]V=\pi r^2h=\pi *3.25^2*10=331.83072\\=331.83[/tex]
Answer in terms of [tex]\pi[/tex]
[tex]105.625\pi cm^3[/tex]
15 POINTS!!!
Solve 3(−3−3x)+4=−5.
The solution is x=___
Mike wants to buy a 20 oz bottle of water for $4.00.
Mary isn't as thirsty and only wants an 8 ounce bottle of water for $1.75.
Mike says "its cheaper PER OUNCE to buy the 20 oz bottle of water." Mary disagrees.
Who is correct and why?
Answer: Mary is cheaper than mike
Step-by-step explanation:
Hopes this Helps
Declaring war and coining money are considered
states' rights.
implied powers.
national rights.
expressed powers.
Answer: Expressed powers
Step-by-step
The shorter leg of a right triangle is 21 feet less than the other leg. Find the length of the two legs if the hypotenuse is 39 feet.
Answer:
leg 1= 36 feet
leg2 = 15 feet
Step-by-step explanation:
Hi, we have to apply the Pythagorean Theorem:
c^2 = a^2 + b^2
Where c is the hypotenuse of the triangle (in this case the distance between Doreen’s house and the tower) and a and b are the other legs.
leg1 = x
leg2 = x-21 (21 feet less than the other leg)
Replacing with the values given:
39^2 = x^2 + (x-21)^2
1,521 = x^2 + x^2 -42x +441
0 = 2x^2 -42x +441-1,521
0= 2x^2 -42x -1,080
For: ax2+ bx + c
x =[ -b ± √b²-4ac] /2a (quadratic formula)
Replacing with the values given:
x=-(-42)± √(-42)²-4(2)-1080] /2(2)
x= 42± √10,404] /4
x = 42± 102 /4
Positive:
x = 42+102 /4 = 36
leg 1= 36
leg2 = 36-21 =15
Feel free to ask for more if needed or if you did not understand something.
The length of shorter leg is 15 feet and other leg is 36 feet.
Pythagoras theorem:Let us consider that, length of shorter leg is x feet.
So that, length of other leg is [tex](x+21)[/tex] feet.
It is given that, the hypotenuse is 39 feet.
Apply Pythagoras theorem,
[tex]x^{2} +(x+21)^{2} =(39)^{2}\\ \\x^{2} +x^{2} +441+42x=1521\\\\2x^{2} +42x-1080=0\\\\x=15 ,-36[/tex]
Since, side can not be negative.
So that, we have to consider x=15 feet.
Length of other leg[tex]=x+21=15+21=36feet[/tex]
Learn more about the Pythagoras theorem here:
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In the diagram shown,
ABCE is a trapezium,
AD is parallel to BC,
DE = 4cm,
Area of ABCE = 60cm^2,
Area of ABCD = 48cm^2,
Work out the values of f and g.
You must show all your working.
The values of f and g are;
f = 6
f = 6g = 8
We are given the trapezium ABCE where;
AD is parallel to BC
DE = 4 cm
Area of ABCE = 60 cm²
Area of ABCD = 48 cm²
f and g are sides of the rectangle ABCD. Thus;
fg = 48 - - - (eq 1)
Also,for the trapezium ABCE;
½(g + g + 4)f = 60
(2g + 4)f = 120 - - - (eq 2)
From eq 1, f = 48/g
Thus;
(2g + 4) × (48/g) = 120
96 + 192/g = 120
192/g = 120 - 96
192/g = 24
g = 192/24
g = 8
Thus;
8f = 48
f = 48/8
f = 6
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Easy way to get points: What is 1+2+3+4+5+6+7+8+9+10?
Answer:55
Step-by-step explanation:addition
Martha types a 4−digit code into a keypad to unlock her car doors. The code uses the numbers 1 and 0. If the digits are selected at random, what is the probability of getting a code with exactly two 1's? Enter your answer as a simplified fraction.
The probability of getting two 1's is_________.
Answer:
3/8
Step-by-step explanation:
1. We list all codes that start with 0 and have 0 as second digit:
2. We list all codes that start with 0 and have 1 as second digit:
3. We list all codes that start with 1 and have 0 as second digit:
4. We list all codes that start with 1 and have 1 as second digit:
5. We find the number of codes which have exactly 2 zeros: 6 codes
6. The total number of outcomes is: 16 codes
7. We find the probability that the number of codes has exactly 2 zeros: 6/16 3/8
Answer:
The probability of getting two 1's is 3/8
Step-by-step explanation:
Martha types a 4−digit code into a keypad to unlock her car doors.
The code uses the numbers 1 and 0
So the sample space of all the possible combinations is given by
1. 0 0 0 0
2. 0 0 0 1
3. 0 0 1 0
4. 0 0 1 1
5. 0 1 0 0
6. 0 1 0 1
7. 0 1 1 0
8. 0 1 1 1
9. 1 0 0 0
10. 1 0 0 1
11. 1 0 1 0
12. 1 0 1 1
13. 1 1 0 0
14. 1 1 0 1
15. 1 1 1 0
16. 1 1 1 1
So there are total 16 possible outcomes.
Now count the number of combinations that has exactly two 1's
4. 0 0 1 1
6. 0 1 0 1
7. 0 1 1 0
10. 1 0 0 1
11. 1 0 1 0
13. 1 1 0 0
So there are 6 possible outcomes with exactly two 1's
The required probability is
P(two 1's) = Number of outcomes with two 1's/Total number of outcomes
P(two 1's) = 6/16
P(two 1's) = 3/8
Therefore, the probability of getting two 1's is 3/8
The hypotenuse of a right triangle is 55 inches long. One leg is 2 inch(es) longer than the other. Find the
lengths of the legs of the triangle. Round your answers to the nearest tenth of an inch. Answer: The lengths are
Answer:
Step-by-step explanation:
Angles: 45°: 45°: 90°
Ratio of sides: 1:1:√2
Given c= 55
a =c/√2
a=55/√2 = 38.9
b=a+2 = 38.9+2 =41.9
The length of the legs of the triangle is 41.9
What is the right triangle?A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.
Angles are: 45°: 45°: 90°
The ratio of sides: 1:1:√2
Given c = 55
a = c/√2
a = 55/√2
a = 38.9
b = a+2
b = 38.9+2
b =41.9
Thus, the length of the legs of the triangle is 41.9
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What is the factored from of y2+6y-16
Answer:
(y + 8)(y - 2)
Step-by-step explanation:
Given
y² + 6y - 16
Consider the factors of the constant term (- 16) which sum to give the coefficient of the y- term (+ 6)
The factors are + 8 and - 2, since
8 × - 2 = - 16 and 8 - 2 = 6, thus
y² + 6y - 16 = (y + 8)(y - 2)
Determine whether the two triangles can be proven congruent using the AAS congruence method. If they can, select the congruence statement. answers: A) ΔABC ≅ ΔEDC B) ΔCBA ≅ ΔCED C) The triangles aren't congruent using AAS. D) ΔCAB ≅ ΔEDC
Answer:
A) ΔABC ≅ ΔEDC
Step-by-step explanation:
To prove triangles congruent with the AAS method, you need two angles and the non-included side of one triangle to be congruent to the corresponding parts of another triangle.
Let's see what we have in these two triangles.
Side AB is congruent to side ED. This is one pair of sides.
Angle A is congruent to angle E. This is one pair of sides.
Now we need a second pair of angles, that will make the two sides not-included in the angles.
By the congruence of vertical angles, we see that angles ACB and ECD are congruent. This is another pair of congruent angles.
We have two angles and a non-included side of one triangle congruent to two angles and a non-included side of another triangle. The triangles are congruent by AAS.
Answer: A) ΔABC ≅ ΔEDC
1. Which number is greater: 35% or 3.5?
Answer:
3.5
Step-by-step explanation:
35% is only 0.35
Answer:
3.5
Step-by-step explanation:
Select the correct product.
(y+ z)3
y 3+3y2z+ 3yz 2 + z 3
y 3 y+ 3 z
y 3 z 3
y 3 + z 3
Answer:
Step-by-step explanation:
Points A B C and D lie on a line consecutively so that AB = BC = CD = 6in. Find the distance between the midpoints of segments AB and CD.
Answer:
Distance of segments AB and CD = 12
Step-by-step explanation:
AB+BC + CD = 6+6+6 = 18inch
midpoint AB = 6/2 = 3
midpoint CD =6/2 = 3
Midpoint AB+Midpoint CD = 3+3 = 6
To solve we just 18-6 = 12
Distance of segments AB and CD = 12
Answer:
its 12
Step-by-step explanation:
Distance of segments AB and CD = 12
Solve.
6x2 + 7x – 20 = 0
Answer:
(3x + 4)(2x - 5)
[tex]6x^{2}+7x-20=0[/tex] = (3x + 4)(2x - 5)
Hope this helped! Have a great day!
Solve this inequality.
-5x + 7 > 42
A. x> 245
B. x < -175
C. x > 7
D. x < -7
Answer:
x < -7
Step-by-step explanation:
-5x + 7 > 42
Subtract 7 from each side
-5x + 7-7 > 42-7
-5x > 35
Divide each side by -5, remembering to flip the inequality
-5x/-5 <35/-5
x < -7
Which ordered pair maximizes the objective function P = 3x + 8y?
оооо
(0, 0)
(2, 7)
(5, 6)
о(8, 1)
Answer:
(5,6)
Step-by-step explanation:
I think you are asking whats the biggest sum you can get out of the ordered pairs. If you are I'm pretty sure (5,6) is correct. If you are not asking that, I am sorry.
Which statements are true regarding the quadratic statement?
Answer:
E
Step-by-step explanation:
I hope am right coz it seems most appropriate
Which algebraic expression is a polynomial with a degree of 5?
8 - n = -4 what does N equal
Answer:
Make N alone
There is an 8 so we subtract 8 from both sides so the equation is still equal
-4 - 8 = -12
Because we are subtracting N it is positive
N = 12
8 - 12 = -4
Hope this helps
Step-by-step explanation:
F(x) = x^2, g(x) = 2/3 x^2 comparison
Answer:
g(x) is a vertical compression of f(x)
Step-by-step explanation:
Equation of graph 1 :[tex]f(x)=x^2[/tex]
Equation of graph 2 :[tex]g(x)=\frac{2}{3}x^2[/tex]
f(x)→a f(x)
Its is case of vertical stretch or compression
Vertical stretch if |a|>1
Vertical compression if 0<|a|<1
f(x)→a f(x)
So, [tex]x^2[/tex] →[tex]\frac{2}{3}x^2[/tex]
So, [tex]a= \frac{2}{3}=0.67[/tex]
So,0<|a|<1
So,It is a case of vertical compression
So, g(x) is a vertical compression of f(x)
The following graphs have no scales assigned to them. Which of them could
not possibly be density curves for a continuous random variable if they were
provided with the right scale?
Check all that apply
A. Graph A
B. Graph B
C. Graph
D. Graph D
E.Graph E
Graph A, and graph C could not possibly be density curves for a continuous random variable if they were provided with the right scale.
Given four graphs of different nature as options.
We are required to find a graph that is not a continuous variable.
What is continuity?In mathematics, a continuous function is a function such that a continuous variation of the argument induces a continuous variation of the value of the function.
Continuous lines are those lines that when decreased, decrease with continuity and when increased, increase with continuity.
When we observe graph A, graph C. In these graphs, the value of the function keeps increasing and decreasing a lot and is not in continuity.
Hence, graph A, and graph C could not possibly be density curves for a continuous random variable if they were provided with the right scale.
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Answer: Graph B and Graph C
Step-by-step explanation:
15 pts!!! will mark BRAINLIEST Sharon found a couch for $1,770.00. The sales person said it was on sale for 25% off. How much did Sharon pay for the couch if she also had to pay 6% sales tax on the total?
Answer:
$1407.15
Step-by-step explanation:
$1,770.00*0.25= $442.5
$1.770-$442.50 = $1327.5
$1327.5*0.06 = $79.65
$1327.50+$79.65 = $1407.15
The value of 32 cos 85 ° is ____ a0. Round your answer to the nearest tenth of the number.
Answer:
2.8
Step-by-step explanation:
32cos 85≈2.8
Were you surprised by the shape of your scatter plot? Explain.
Do you think there might be other factors that influence the association between the variables?
If you switched which axis each variable is graphed on, would your scatter plot look different? Describe and interpret the association between the variables.
Answer:
Answers are below
Step-by-step explanation:
Yes I was surprised by the scatter plot because I didn't know there would be the most rain at 77 degrees F on the red line.
If you switched which axis each variable is graphed on, your graph would look different because the graph could be sideways on the left or the right.
The graph has a trend of increasing temperature and amount of rain as you get up to the 7th column. After the 7th column, the trend shows decreasing rain and temperature.
M is directly proportional to r3
When r = 4, M = 160
a) Work out the value of M when r = 2.
Answer:
M = 20
Step-by-step explanation:
Given that M is directly proportional to r³ then the equation relating them is
M = kr³ ← k is the constant of proportion
To find k use the condition when r = 4, M = 160, that is
160 = k × 4³ = 64k (divide both sides by 64 )
2.5 = k
M = 2.5r³ ← equation of proportion
When r = 2, then
M = 2.5 × 2³ = 2.5 × 8 = 20
Answer:
M<varies>r³
M=kr³(k= constant)
when M=160,r=4
160=k(4)³
160=64k
k=2.5
therefore,M=2.5r³
when r=2
M=2.5r³
M=2.5(2)³
M=2.5(8)
M=20
HELP! WILL GIVE BRAINLIEST!
Answer: The answer is A
Step-by-step explanation: There are different ways to solve this type of problem. One way I would do it is to use a piece of wax paper to trace the shape then rotate the paper to get the answer.
Which angles are acute?
А в
H
Check all that apply.
Answer:
The answer is A and D.
Step-by-step explanation:
Acute angles are angles that are less than 90°.
0° < θ < 90°.
So by looking at the diagram, any angles that are smaller than a L-shaped(90°) are all acute angle.
Help! Look at the picture
Answer:
171 square ft
Step-by-step explanation:
Area of side walk of the pool = Are of outer square - Area of inner square
[tex] = {30}^{2} - {27}^{2} \\ = (30 + 27)(30 - 27) \\ = 57 \times 3 \\ = 171 \: {ft}^{2} [/tex]
Alison, the owner of a regional chain of pizza stores, is trying to decide whether to add calzones to the menu. She conducts a survey of 700 people in the region and asks whether they would order calzones if they were on the menu. 46 people responded “yes.” Create a 90% confidence interval for the proportion of people in the region who would order calzones if they were on the menu.Round your answer to four decimal places.
Answer:
Step-by-step explanation:
Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
p = x/n
Where
n represents the number of samples
x represents the number of success
From the information given,
n = 700
x = 46
p = 46/700 = 0.066
q = 1 - 0.066 = 0.934
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.05 = 0.95
The z score corresponding to the area on the z table is 1.645. Thus, the z score for a confidence level of 90% is 1.645
Therefore, the 90% confidence interval is
0.066 ± 1.645√(0.066)(0.934)/700
= 0.066 ± 0.0094
The lower limit of the confidence interval is
0.066 - 0.0094 = 0.0566
The upper limit of the confidence interval is
0.066 + 0.0094 = 0.0754
Answer:
(0.0503, 0.0811).
Step-by-step explanation:
The confidence interval for the unknown population proportion p is (p^−z⋆p^(1−p^)n−−−−−−−−√,p^−z⋆p^(1−p^)n−−−−−−−−√). The confidence interval can be calculated using Excel.
1. Identify α. Click on cell A1 and enter =1−0.90 and press ENTER.
2. Thus, α=0.1. Enter the number of successes, x=46, and sample size, n=700, in the Excel sheet in cells A2 and A3. To find the proportion of successes, p^, click on cell A4 and enter =A2/A3 and press ENTER.
3. Thus, p^≈0.0657. Use the NORM.S.INV function in Excel to find z⋆. Click on cell A5, enter =NORM.S.INV(1−A1/2), and press ENTER.
4. The answer for z⋆, rounded to two decimal places, is z⋆≈1.64. To calculate the standard error, p^(1−p^)n−−−−−−−−√, click on cell A6 and enter =SQRT(A4∗(1−A4)/A3) and press ENTER.
5. The answer for the standard error, rounded to four decimal places, is p^(1−p^)n−−−−−−−−√≈0.0094. To calculate the margin of error, z⋆p^(1−p^)n−−−−−−−−√, click on cell A7 and enter =A5*A6 and press ENTER.
6. The answer for the margin of error, rounded to four decimal places, is z⋆p^(1−p^)n−−−−−−−−√≈0.0154. The confidence interval for the population proportion has a lower limit of A4−A7=0.0503 and an upper limit of A4+A7=0.0811. Thus, the 90% confidence interval for the population proportion of people in the region who would order calzones if they were on the menu, based on this sample, is approximately (0.0503, 0.0811).