Answer:
When the slopes of lines a and b are multiplied, the product is −1.
Line a and line b intersect to form four right angles.
Step-by-step explanation:
Given
Perpendicular lines a and b
Required
Select the true statements
Represent the slope of line a with [tex]m_1[/tex] and the slope of b with [tex]m_2[/tex].
The condition for perpendicularity is:
[tex]m_1 * m_2 = -1[/tex]
Solving further:
[tex]m_1 = -\frac{1}{m_2}[/tex]
To solve further, we need to analyze each of the given options
(a) This is not true because the slope of perpendicular lines are not reciprocal
(b) This is also not true because perpendicular lines do not necessarily have to intersect at their midpoints
(c) This is true because of the condition stated above: [tex]m_1 * m_2 = -1[/tex]
(d) This is also true because perpendicular lines form right angles when they intersect
(e) This is not true because of the condition stated above: [tex]m_1 = -\frac{1}{m_2}[/tex]
(f) This is not true because of the condition stated above: [tex]m_1 = -\frac{1}{m_2}[/tex]
The product of the slope of the perpendicular lines is negative of one. Then the correct options are B and C.
What is the linear system?It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.
Lines a and b are perpendicular.
Then the product of the slope of the perpendicular lines is negative of one. That is given as
[tex]\rm m_1*m_2 = -1[/tex]
a. The slopes of lines a and b are reciprocals Line a and line b intersect at their midpoints. This is false.
b. When the slopes of lines a and b are multiplied, the product is −1. This is true.
c. Line a and line b intersect to form four right angles. This is true.
d. The slopes of lines a and b are equal. This is false.
e. The slopes of lines a and b are opposites. This is false.
More about the linear system link is given below.
https://brainly.com/question/20379472
Answer the question for 10 points
Answer:
(3x + 8) (3x - 8)
Step-by-step explanation:
Not sure if you need the steps
p(x)+p(x+3)=10x-7 find p(3)
Answer:
Simplify each term.
Px+px+3p=10x−7
Move all terms not containing P to the right side of the equation.
Px=10x−7−px−3p
Divide each term by x and simplify.
P=10−7/x−p−3p/x
Step-by-step explanation:
Evaluate the expression 3.2t when t is 1
Answer:
3.2
Step-by-step explanation:
3.2t when t=1
replace t with 1 so 3.2(1)
hence =3.2
Edwin goes to a restaurant with some friends.
Here are the meals they have
2 fish and chips at £9.25 each
1 chicken and chips at £9.50
1 roast lamb at £10.55
4 puddings at £4.55 each.
Edwin pays for the meals with three £20 notes.
How much change should Edwin get?
Answer:
£3.25
Step-by-step explanation:
£9.25×2+ £9.50+£10.55+£4×4.55
18.5+9.50+10.55+18.2
=£3.25
Answer:
£2.75
Step-by-step explanation:
2(9.25) + 1(9.50) + 1(10.55) + 4(4.55) = x
19.00 + 9.50 + 10.55 + 18.20 = x
28.50 + 28.75 = x
57.25
60 - 57.25 = 2.75
Tell whether each pair of angle measurements are complementary, supplementary or neither. 36°,24° 18°,72° 96°,84°
Given:
The pairs of angles are:
36°,24°
18°,72°
96°,84°
To find:
Whether each pair of angle measurements are complementary, supplementary or neither.
Solution:
Two angles are complementary if there sum is 90 degrees.
Two angles are supplementary if there sum is 180 degrees.
For 36° and 24°,
[tex]36^\circ+24^\circ =60^\circ[/tex]
So, this pair is neither complementary not supplementary.
For 18° and 72°,
[tex]18^\circ+72^\circ =90^\circ[/tex]
So, this pair is complementary.
For 96° and 84°,
[tex]96^\circ+84^\circ =180^\circ[/tex]
So, this pair is supplementary.
Amy’s dog weighs 14 pounds.
What is the dog’s weight in ounces?
30
64
210
224
Answer:
64
Step-by-step explanation:
thats all my answer...
Answer:
16 ounces in a pound
14 x 16= 224 ounces
I need help with all my 7 questions can someone help me with the first one ?
Answer:
x = 53
Step-by-step explanation:
x = 53 (Vertically Opposite Angles)
write the equation of a line that is parallel to 2x-5y=-20 and passes through the point (7,6)
Answer:
I guess the answer is 0.4x+3.2=y (0.4 equals to 2/5 ) .
trigonometry please help! work need to be shown
Given:
The figure of a right angle triangle.
To find:
The value of x to the nearest hundredth.
Solution:
In a right angle triangle,
[tex]\cos \theta=\dfrac{Base}{Hypotenuse}[/tex]
Using the above trigonometric ratio for the given triangle, we get
[tex]\cos 46^\circ=\dfrac{x}{8}[/tex]
[tex]0.6947=\dfrac{x}{8}[/tex]
[tex]0.6947\times 8=x[/tex]
[tex]5.5576=x[/tex]
Approximate the value to the nearest hundredth.
[tex]x\approx 5.56[/tex]
Therefore, the value of x is 5.56 units.
Calculate the missing measure in the triangle 35º and 85º
Answer:
60º
Step-by-step explanation:
180º-35º-85º=60º
Given the functions f(n) = 500 and g(n) = (nine tenths)n − 1, combine them to create a geometric sequence, an, and solve for the 11th term.
Answer:
[tex]A(n) = 500 * (\frac{9}{10})^{n-1[/tex]
[tex]A(11) = 174.34[/tex]
Step-by-step explanation:
Given
[tex]f(n) = 500[/tex]
[tex]g(n) = (\frac{9}{10})^{n-1[/tex]
Represent the combination of f(n) and g(n) with A(n)
So, we have:
[tex]A(n) = f(n) * g(n)[/tex]
This gives:
[tex]A(n) = 500 * (\frac{9}{10})^{n-1[/tex]
To calculate the 11th term, we make use of n = 11
[tex]A(11) = 500 * (\frac{9}{10})^{11-1[/tex]
[tex]A(11) = 500 * (\frac{9}{10})^{10[/tex]
This gives:
[tex]A(11) = 500 * (0.9)^{10}[/tex]
[tex]A(11) = 500 * 0.3486784401[/tex]
[tex]A(11) = 174.33922005[/tex]
Approximate to 2 dp
[tex]A(11) = 174.34[/tex]
Please help me find the volume :3
9514 1404 393
Answer:
(d) 539 mm³
Step-by-step explanation:
The total volume is the sum of the volumes of the parts. The volume of each part is the product of its dimensions.
volume of bottom part
V = LWH
V = (13 mm)(7 mm)(4 mm) = 364 mm³
volume of the top part
V = (5 mm)(7 mm)(5 mm) = 175 mm³
Then the total volume is ...
364 mm³ +175 mm³ = 539 mm³ . . . volume of the figure
Brenda bought 2 and one-half dozen donuts for 8.10. What was the cost per donut
Answer:
I came up with $3.20 each donut cost.
If you need to construct a dog run for your dog and the total perimeter needs to be 40 feet, and you only have enough room to make it 5 feet wide, how long can you make the dog run?
Answer:15 ft
Step-by-step explanation:
Given
The total perimeter needed is [tex]40\ ft[/tex]
The available width of the room is [tex]w=5\ ft[/tex]
Suppose l is the length of the room
So, the perimeter of a rectangle-shaped room is [tex]2(l+w)[/tex]
Putting values
[tex]\Rightarrow 40=2(l+5)\\\Rightarrow l+5=20\\\Rightarrow l=15\ ft[/tex]
Find the center and radius of x2+2x+y2+10y=15
Answer: (x + 7)^2 + (y + 5)^ =9
Step-by-step explanation:
From the parking lot at red hill shopping center the angle of the top of the hill is about 25 from the base of the hill the angle of elevation to the top of the hill is 55
Answer:
512 ft.
Step-by-step explanation:
From the parking lot at the Red Hill Shopping Center, the angle of sight (elevation) to the top of the hill is about 25. From the base of the hill you can also sight the top but at an angle of 55. The horizontal distance between sightings is 740 feet. How high is Red Hill? Show your subproblems.
Solution:
Let x be the distance from the base of the hill to the middle of the hill perpendicular to the height, let h be the height of the hill. Therefore:
tan 25 = h/(x + 740)
h = (x + 740)tan 25 (1)
tan 55 = h / x
h = x tan 55 (2)
Hence:
(x + 740)tan 25 = xtan 55
0.4663(x + 740) = 1.428x
0.4663x + 345.07 = 1.428x
0.9617x = 345.07
x = 359 ft.
h = xtan55 = 359 tan(55) = 512 ft.
Which situations illustrate that the sum of opposite numbers is zero? Which situations illustrate that the sum of opposite numbers is zero?A) Shelley finds $50 in an old purse and deposits it in her bank account.B) Sara deposits $500 in her checking account and withdraws $500 from the ATM.C) After 3 forward flips and 3 backward flips, Anna is back where she started.D) Evan wins 1,000 points on a video game and wins another 1,000 points on the next game.E) At daybreak, the temperature is 18 degrees below zero. The temperature at noon is zero
Answer:
Step-by-step explanation:
b
Answer:
B) C) and E) (i just took this in USA TestPrep
Step-by-step explanation:
What Is The Measure Of X?
Answer:
114°
Step-by-step explanation:
here's your solution
=> x° + 66° = 180°
=> x = 180° - 66°
=> x = 114°
hope it helps
Answer:
66°+x=180°[by linear pair]
x=180°- 66°
x=114°.
please help with my geometry
Answer: 9.90
Step-by-step explanation:
tan 48= 11/x
1.11=11/x
1.11x=11
x=9.90
Find the measure of angle h
Answer:
62 degrees
Step-by-step explanation:
Since we know 3 sides of the triangle, we can use law of cosines.
[tex] {gk}^{2} = {gh}^{2} + {kh}^{2} - 2(gh)(kh) \times \cos(h) [/tex]
[tex] {8}^{2} = {17}^{2} + {15}^{2} - 2(17(15) \times \cos(h) [/tex]
[tex]64 = 289 + 225 - 510 \times \cos(h) [/tex]
[tex]64 = 314 - 510 \times \cos(h) [/tex]
[tex] - 250 = - 510 \times \cos(h) [/tex]
[tex] \frac{250}{510} = \cos(h) [/tex]
[tex] \frac{25}{53} = \cos(h) [/tex]
Take the arcos or cosine inverse
[tex] \cos {}^{ - 1} = \frac{25}{53} [/tex]
Which is about 62 degrees.
pleaseee help im really confused
you are shopping for a Nintendo Switch and you have a choice to make. You can pay $420 and add 10% for shipping or pay $400 and add 20% for shipping. Which costs less?
Answer:
420 x .1 = 42
420 + 42 = 462
400 x .2 = 80
400 + 80 = 480
The first one is cheaper
Help me PLEASE I need HELP
Answer:
x=20
Step-by-step explanation:
180=2x+6x+20
180=8x+20
160=8x
20=x
Complete the table. Then identify the y intercept and the coordinate where x = 1. (Help please)
Need help ASAP plz. Right answer plz.
2y +3<11
What is the largest value of y could be?
Answer:
Step-by-step explanation:
2y + 3<11 Subtract 3 from both sides
2y < 11 - 3
2y < 8 Divide by 2
2y/2 <8/2
y < 4
The question is very hard to answer. That's because the answer is very close to 4, but it is not 4.
For example 3.8 is a possible answer. Try it
2*3.8 + 3 < 11
7.6 + 3 < 11
10.6 < 11
But is that the largest value possible? No.
For example
y could be 3.99999999 Well maybe that could be the answer. No it isn't. Because, though very close to 11, it still cannot be 11. It might round to 11, but it does not equal 11.
I don't exactly know what you are expected to answer. I can only say that y cannot be 4, but it can be as close to 4 as you care to make it. If the question means what is the largest integer that y could be, then the answer is 3.
PLS HELP ILL GIVE BRAINLIEST
Explain how symmetry can help you find a figure's perimeter on the coordinate plane.
Answer: Think of it this way, symmetry is basically a mirror and you can better find the perimeter because you'll know that the sides are the same length
Step-by-step explanation:
Well if you have two sides that are symmetrical or an entire shape is symmetrical you can find the perimeter easier. So let's say two lines are symmetrical and one has the length of 2 the other one can also be two. If we have a symmetrical shape, then is would be a complete reflection.
A geometric object or form is symmetric when it can be broken up into two or more identical pieces and then placed in a systematic way.
what is symmetry ?The definition of symmetry is a proportionate and balanced similarity between two sides of an object, where one half is the mirror image of the other. For instance, certain geometric forms like, rectangle, and circle are symmetric along their respective axes of symmetry.
since the shape's two halves would perfectly match if you folded it along the line. The shape will also remain unchanged if a mirror were positioned along the line , a square has four lines of symmetry.
A geometric object or form is symmetric when it can be broken up into two or more identical pieces and then placed in a systematic way.
To know more about symmetry visit :-
brainly.com/question/15970176
#SPJ2
What do you want to be when you grow up? According to a nationwide survey of a random sample of 1000 kids under the age of 12 some kids want to be a ninja, a dragon keeper, a dancing unicom, and even an octopus. Fifty-five of the 1000 kids want to be a doctor. We would like to use this study to find a 98% confidence interval for the true proportion of kids who want to be a doctor.
a. Identify the parameter of interest.
b. Check if the conditions for constructing a confidence interval for p are met.
C. Find the critical value for a 98% confidence interval. Then calculate the interval
d. Interpret the interval in context
Using the z-distribution, we have that:
a) The parameter of interest is the proportion of kids who want to be a doctor.b) Since there are more than 10 successes and more than 10 failures in the sample, the conditions are met.c) The critical value is [tex]z = 2.327[/tex]. The interval is (0.0339, 0.066).d) We are 98% sure that the true proportion of kids who want to be a doctor is between 0.0339 and 0.066.Confidence interval of a proportionIn a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].Item a:
We are interested in the confidence interval for the true proportion of kids who want to be a doctor, hence the parameter of interest is the proportion of kids who want to be a doctor.
Item b:
Fifty-five of the 1000 kids want to be a doctor, hence, since there are more than 10 successes and more than 10 failures in the sample, the conditions are met.
Item c:
Fifty-five of the 1000 kids want to be a doctor, hence [tex]n = 1000, \pi = \frac{55}{1000} = 0.055[/tex].98% confidence level, hence[tex]\alpha = 0.98[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.98}{2} = 0.99[/tex], so the critical value is [tex]z = 2.327[/tex].The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.05 - 2.327\sqrt{\frac{0.05(0.95)}{1000}} = 0.0339[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.05 + 2.327\sqrt{\frac{0.05(0.95)}{1000}} = 0.066[/tex]
The interval is (0.0339, 0.066).
Item d:
We are 98% sure that the true proportion of kids who want to be a doctor is between 0.0339 and 0.066.
You can learn more about the use of the z-distribution to build a confidence interval at https://brainly.com/question/25649070
If an object is projected upward with an initial velocity of 64ft per second from ground level, then its height in feet t seconds after it is projected is a function defined by: h(t)= -16t^2 + 64t. how long after it is projected will it be 48 feet above the ground?
Answer:
not sure
Step-by-step explanation:
1 Factorise completely.
(a) 2a+4+ap+2p
(b) 162 – 8t^2
Answer:
Step-by-step explanation:
a) 2a + 4 + ap + 2p = 2*a + 2*2 + a *p + 2*p
= 2(a + 2) + p(a + 2)
= (a +2) (2 + p)
b) 162 - 8t² = 2*81 - 2*4t²
= 2 (81 - 4t²)
= 2( 9² - (2t)² ) {a² - b² = (a + b)(a -b)
= 2 ( 9 + 2t) (9 - 2t)
Step-by-step explanation:
a. 2a + 4 + ap + 2p
2a + ap + 4 + 2p
a (2 + p) + 2 (2 + p)
= ( a + 2) ( 2 + p)
b. 162 - 8t^2
2( -4t^2 + 81)
Rewrite in simplest terms: −10(5t+5)−10(10t+6)
Answer:-150t-110
Step-by-step explanation:
-10(5t+5)-10(10t+6)
-50t - 50 - 100t - 60
=
-150t-110