Answer:
y=3x-10
Step-by-step explanation:
Slope: (y2-y1)/(x2-x1)
(2-8)/(4-6)
slope= -6/-2 = 3
Point: (6,8)
Slope-intercept: y-y1=m(x-x1)
y-8=3(x-6)
y-8=3x-18
y=3x-10
Geometry: Solve for x
Answer:
[tex]4\sqrt{3}[/tex]
Step-by-step explanation:
Since <PDA is right, the vertical angle, <BDC is right as well. Using sum of angles in a triangle, the angles in triangle BDC sum to 180, and for solving for <DCB, you get 30 degrees.
The line connecting the intersection of the tangents to the radius bisects the angle formed by the tangents; therefore, m<PCA is also 30 degrees.
A radius drawn to the point of tangency is perpendicular to the tangent, so <PAC is a right triangle. We can use sum of angles in a triangle for triangle PAC. Since <PCA is 30 and <PAC is right, <DPA is 60 degrees.
Now, we can look at triangle DPA, using sum of angles in a triangle, we can conclude triangle DPA is a 30-60-90 special right triangle. The leg opposite the 60 degree angle is √3 times the leg opposite the thirty degree angle. Since <DPA is 60 degrees and <PAD is 30:
[tex]DP\sqrt{3} = 6\\DP = \frac{6}{\sqrt{3} } \\DP = \frac{6}{\sqrt{3} } \times \frac{\sqrt{3} }{\sqrt{3} } \\DP = \frac{6\sqrt{3} }{3} \\DP = 2\sqrt{3}[/tex]
Also, in a 30-60-90, the hypotenuse is twice the leg opposite the 30 degree angle, so x is 2 * 2√3. or [tex]4\sqrt{3}[/tex].
A cyclist cycles a distance of 36 miles in a time of 3 hours.
What is her average speed?
Answer:
12mph
Explanation:
Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? Check all that apply.
For any value of x, g(x) will always be greater than h(x).
For any value of x, h(x) will always be greater than g(x).
g(x) > h(x) for x = -1.
g(x) < h(x) for x = 3.
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).
Using translation concepts, it is found that the correct statements are given as follows:
g(x) > h(x) for x = -1.For positive values of x, g(x) > h(x).For negative values of x, g(x) > h(x).What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the functions are:
g(x) = x².h(x) = -x².h(x) = -x² = -g(x), which means that h(x) is a reflection of g(x) over the x-axis. Since [tex]g(x) \geq 0[/tex] for all values of x, [tex]h(x) \leq 0[/tex] for all values of x, which means that they are equal at the origin and g is greater for other values of x, hence the correct statements are:
g(x) > h(x) for x = -1.For positive values of x, g(x) > h(x).For negative values of x, g(x) > h(x).More can be learned about translation concepts at https://brainly.com/question/4521517
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x/4+3y/5=1 into gradient interception form
Answer:
Write in slope-intercept form,
y
=
m
x
+
b
.
y
=
5
3
x
−
20
3
Step-by-step explanation:
Answer:
Step-by-step explanation:
y=-5/12x+5/3
Which statement is true about the net and the solid it can form?
The length of side a will be 5 m.
The length of side b will be 2 m.
The length of side c will be 7 m.
The length of side c will be 2 m.
Which line is parallel to the line that passes through the points (1, 7) and (-3, 4)?
A. y= -3/4x-5
B. y= 3/4x+1
C. y=4/3x-8
D. y= 11/4x+3
Answer:
B
Step-by-step explanation:
The slope of the line that passes through the given points is (4-7)/(-3-1) = 3/4.
Since parallel lines have equivalent slopes, the answer is B.
Find the median and mean of the data set below:
11,48,6,25,31
Answer:
mean 24.2
median 25
Step-by-step explanation:
6 11 25 31 48
Use the law of cosines to solve for the measure of the largest angle in triangle abc.
The law used for determining the measure of unknown sides and angles of a triangle. The measure of the largest angle in triangle abc is 98.25 degrees
Law of cosinesThe law used for determining the measure of unknown sides and angles of a triangle. It is expressed as:
c² = a² + b² - 2abcosC
Given the following
c = 16
a = 12
b = 9
Substitute
16² = 12² + 9² - 2(9)(12)cosC
256 = 144 + 81 - 216cosC
31 = -216cosC
cosC = -31/216
C = 98.25 degrees
Hence the measure of the largest angle in triangle abc is 98.25 degrees
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Please answer quickly!!
Answer:
B is true
C is false
D is false
Step-by-step explanation:
- B is true because two negative numbers are added together, the outcome is negative hence always less than 0
- C is false due to needing a negative number add to -1.5 to be less, a positive only makes the number greater
- D is false since you are adding 0.9 (9/10), anything less than this will m ake the sum be greater than 0
example: - 0.5 + 0.9 = 0.4 or - 0.8 + 0.9 = 0.1
4951 to the nearest 1000
Answer:
5000
makes the best sense
Type the correct answer in each box. Round the vector's magnitude to the nearest tenth.
Vector u has its initial point at (14,-6) and its terminal point at (-4, 7). Write the component form of u and find its magnitude.
Component form of u is (-18,13) and The magnitude of u is 22.2
What is a vector?A vector is a two-dimensional entity with both magnitude and direction. A vector can be visualized geometrically as a directed line segment.
The component form of a vector is an ordered pair that describes the change in x and y values
This is mathematically expressed as (Δx, Δy) where Δx=x₂-x₁ and Δy=y₂-y₁
Given ;
Initial points of the vector as (14,-6)
The terminal point of the vector is (-4,7)
Here x₁=14,x₂=-4, y₁=-6,y₂=7
The component form of the vector u is (-4-14,7--6) =(-18,13)
Finding the Magnitude of the vector
u=√(x₂-x₁)²+(y₂-y₁)²
u=√-18²+13²
u=√324+169
u=√493
u=22.2
Therefore the Component form of u is (-18,13) and The magnitude of u is 22.2
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73 in = 0ft 0qt
ixl question help please
Answer:
6 ft 1 in
Step-by-step explanation:
if you divide 73in by 12 you get 6ft 1in
What is the solution to the system of equations graphed below?
(0, 4)
(3, 1)
(1, 3)
(4, 0)
Answer:
(c) (1, 3)
Step-by-step explanation:
The solution to the system of equations shown on the graph is the point where the lines intersect.
__
The coordinates of the point of where the lines cross are (1, 3).
The solution to the system of equations is (x, y) = (1, 3).
Match each function formula with the corresponding transformation of the parent function Y equals( X -1)^2
Step-by-step explanation:
1. translated down by 3 units.
2. reflected over the x-axis
3. translated left by 4 units : (x-1 + 4)
4. translated right by one unit : (x-1 - 1)
5. reflected over the y-axis (but it is really a translation to the left by 2 units : x-1 + 2).
6. translated up by 1 unit
Bella can rake the leaves in 3 hours and Jordan can complete the same task in 4 hours. If they work together, how long will it take Bella and Jordan to rake the leaves? Round your answer to the nearest hundredth of an hour.
Using the together rate, it is found that it will take 1.71 hours for Bella and Jordan to rake the leaves.
What is the together rate?It is the sum of each separate rate.
In this problem, the rates are given as follows:
Together: 1/x.Bella's: 1/3.Jordan's: 1/4.Hence:
[tex]\frac{1}{x} = \frac{1}{3} + \frac{1}{4}[/tex]
[tex]\frac{1}{x} = \frac{4 + 3}{12}[/tex]
[tex]x = \frac{12}{7}[/tex]
x = 1.71.
It will take 1.71 hours for Bella and Jordan to rake the leaves.
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A recent survey of people who eat salad suggest that 78% like tomatoes on their salad, 49% like cheese on their salad, and 36% like both tomatoes and cheese on their salad. suppose a person who eats salad is selected at random, and find they like cheese on their salad. what is the probability that the person also likes tomatoes on their salad? 0.29 0.46 0.49 0.73
By definition of conditional probability, the probability that the person also likes tomatoes on their salad is 0.73 or 73% (last option).
Definition of probabilityProbability is the greater or lesser possibility that a certain event will occur.
In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.
Definition of conditional probabilityThe conditional probability P(A|B) is the probability that an event A occurs, knowing that another event B also occurs. That is, it is the probability that event A occurs if event B has occurred. Is defined as:
P(A|B) = P(A∩B)÷ P(B)
Probability that the person also likes tomatoes on their saladIn this case, you know:
Event A: Person likes tomatoes on their salad.Event B: Person likes cheese on their salad.Being the event A∩B (A intersection B) when A and B occur simultaneously, then:
P(A)= 78%=0.78P(B)= 49%= 0.49P(A∩B)= 36%=0.36Suppose a person who eats salad is randomly selected and likes cheese on his salad, the probability that the person also likes tomatoes on their salad is:
P(B|A) = P(A∩B)÷ P(B)
Then:
P(A|B) = 0.36÷0.49
P(B|A) = 0.73= 73%
Finally, the probability that the person also likes tomatoes on their salad is 0.73 or 73% (last option).
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geometry please help me !
Answer:
64
Step-by-step explanation:
This is a kite. Kite's diagonals are perpendicular. Since they are perpendicular, they form a 90° at where the two diagonals intersect.
The sum of all degrees for a triangle is 180. 180 - 90 - 26 = 64
(giving 100 points) What is the equation of the line of best fit for the following data? Round the slope and y-intercept of the line to three decimal places.
x y
4 3
6 4
8 9
11 12
13 17
A: y = 1.560x - 4.105
B: y = -4.105x + 1.560
C: y = 4.105x - 1.560
D: y = -1.560x + 4.105
please hurry
Answer:
Slope-intercept form of a linear equation: [tex]y=mx+b[/tex]
where:
[tex]m[/tex] is the slope[tex]b[/tex] is the y-interceptTo determine the equation of the line of best fit from the given answer options, examine the relationship between the x and y values.
From inspection of the data, we can see that as x increases, y increases. Therefore, the slope of the equation will be positive.
(If the y-values decrease as the x-values increase, then the slope would be negative).
Therefore, we can immediately discount answer options B and D as they have negative slopes.
The x and y values are not very far away from each other. The options given for the slope are either 1.560 or 4.105. If the slope was 4.105, we would expect to see values of y that were further away from the x-values.
Therefore, the line of best fit is:
A: y = 1.560x - 4.105
To prove this, plot the 5 points on a graph and draw a line of best fit (see attached).
Choose 2 points on the line of best fit: (4, 2) and (11, 13)
Use the slope formula with these points to calculate the approximate slope:
[tex]\implies \sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}\approx\dfrac{13-2}{11-4}=\dfrac{11}{7}=1.57[/tex]
Thus proving that y = 1.560x - 4.105 is an appropriate option for the equation of the line of best fit.
Drag each tile to the correct box.
Match each equation with its solution.
Equation
Solution
arrowRight
arrowRight
arrowRight
arrowRight
The correct match of each tile of the equation with its solution is:
n - 13 = - 12 →→→ 1n/5 = -1/5 →→→ -1n + 15 = - 10 →→→ -25How do we match each tile to the correct box?To match each tile to the correct box, we have to solve the arithmetic operations in the box, then drag the correct tile that matches our answer into the box.
From the image attached below;
1.
n - 13 = - 12
Let us add (+13) to both sides to eliminate (-13), i.e.
n - 13 + 13 = - 12 + 13
n = 1
2.
n/5 = -1/5
multiply both side by 5
n/5 × (5) = -1/5 × (5)
n = -1
3.
n + 15 = - 10
n +15 - 15 = - 10 - 15
n = -25
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NEED HELP ASAP!!!!
A flavored drink is made using a mixture of a powder drink mix and water, with ratio of powder to water that is 3:2 based on weight. If 20 g of the powdered mix is needed for a certain amount of the flavored drink, how much water will be needed?
Answer:
[tex]13.\overline 3[/tex]
Step-by-step explanation:
We can use proportions to find the amount of water needed
Let [tex]x[/tex] be the amount of water needed
[tex]\frac{3}{2} = \frac{20}{x}[/tex] (with the ratio being 3 powder to 2 water)
Now we can cross multiply and solve for [tex]x[/tex]
[tex]3(x) = 20(2)\\3x = 40\\x = \frac{40}{3}\\ x = \boxed{13.\overline3}[/tex]
You will need [tex]13.\overline3[/tex] grams of water to make the flavored drink.
fractions and decimals
(just the simplest fractions, but if i did anything wrong on the greatest common factor, correct that please & thank you)
Answer:
All the GCFs look good! Here's the simplified fractions:
Step-by-step explanation:
1. 2/3
2. 3/4
3. 3/7
4. 3/16
5. 27/29
6. 4/11
7. 2/11
Simply divide the numerator by the GCF to find the simplified numerator, and the denominator by that same GCF to find the simplified denominator!
Find the missing base of the triangle when the area is 94.5cm2
Answer:
this is your answer
hope it will help you
The volume of this cone is 3,183.96 cubic meters. What is the height of this cone?
Use ≈ 3.14 and round your answer to the nearest hundredth.
Answer:
height = 18m
Step-by-step explanation:
cone volume = 3183.96 m³
1/3 πr²h = 3183.96
1/3×3.14×13×13×h = 3183.96
h = 3183.96×3/13×13×3.14
h = 9551.88/530.66
h = 18
lolllll helppppp it’s probably simple buttttt
Solve 5ax + 6 ax = 7ax+ 8 for x. Assume a # 0. O A. x = = B. x = 2a ( C. 2 = D. x = a n
5ax+6ax=7ax+8
5ax+6ax-7ax=8
4ax=8
x= 8/4a
x=2a
Which graph represents the inequality y − 2x ≤ 1?
graph A
graph B
graph C
graph D
four graphs related to the answer options
The graph (A) in the picture represents the solution to the inequality, option (A) is correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
The options are missing.
The graph is in the picture, please refer to the picture.
We have an inequality:
y − 2x ≤ 1
The above inequality represents a straight line with a positive slope.
The right side region of the line is representing the solution to the inequality.
Graph (A) represents the inequality.
Thus, the graph (A) in the picture represents the solution to the inequality, option (A) is correct.
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What is the value of d in the equation?
1 and three-fourths d = 14
Answer:
hope you can understand
For ten school days, the numbers of bikes parked at a school bike rack are 10, 12, 8, 11, 13, 9, 2, 1, 9, and 12.
a. What is the mean number of bikes per day? [already answered]
b. Identify two outliers for the data. Describe how the outliers affect the mean.
"the numbers, Mason, what do they mean??"
The mean number is 8.7 and the outliers 1 and 2 reduce the mean value
How to determine the mean number?The dataset is given as:
10, 12, 8, 11, 13, 9, 2, 1, 9, and 12.
The mean number is calculated using:
Mean = Sum/Count
So, we have:
Mean = (10+ 12+ 8+ 11+ 13+ 9+ 2+ 1+ 9+12)/10
Evaluate
Mean = 8.7
Hence, the mean number is 8.7
The outlier and how it affects the meanOutliers are relatively far from other data elements of the dataset
In the given dataset, 1 and 2 are far from other data element.
So, the outliers are 1 and 2
Because 1 and 2 smaller than other data elements, they affect the mean by reducing the mean value
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Answer:87/10 is the answer because there are no tens
Step-by-step explanation:
grades are do today please help
Answer:
length of PR is [tex]4\sqrt{5}[/tex]
Is an isosceles triangle
because PQ is congruent to QR
Step-by-step explanation:
Calculate length of P(-6,0) R(2,4)
=> apply distance formula
[tex]\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
[tex]\sqrt{\left(2-\left(-6\right)\right)^2+\left(4-0\right)^2}[/tex]
[tex]4\sqrt{5}[/tex]
Calculate length of P(-6,0) Q(-3,4)
[tex]\sqrt{\left(-3-\left(-6\right)\right)^2+\left(4-0\right)^2}[/tex]
= 5
5(PQ) = 5(QR)
The ratio of legs to dogs in the cat shelter was 4 to 1. If there were 8 cats , then how many cats were there?
Answer:
if there were 8 cats then theres 8 cats, or 32 dogs
Step-by-step explanation: