The slope of the line that passes through the points (4, -2) and (4, 10) is 0. The slope of a line is 0 if it is horizontal. This function is constant.
What is slope?The ratio of the "vertical change" to the "horizontal change" between (any) two unique points on a line is used to compute slope. The ratio can also be written as a quotient ("rise over run"), which produces the same number for every two distinct points on the same line. A declining line has a negative "rise." The line might be useful, as determined by a road surveyor, or it might appear in a diagram that represents a road or a roof as a description or a design.
The slope's absolute value serves as a gauge for a line's steepness, incline, or grade. A steeper line is indicated by a slope with a higher absolute value. A line can be drawn with one of four directions: upward, downward, horizontal, or vertical.
If a line rises from left to right, it is said to be growing. The slope is upward, or m>0.
If a line slopes downward from left to right, it is diminishing. The slope, m0, is negative.
The slope of a line is 0 if it is horizontal. This function is constant.
A line's slope is ambiguous if it is vertical.
In other terms, the rise is (y2 y1) = y. The rise of a road between two points is the difference in the altitude of the road at those two sites, say y1 and y2. The run, or (x2 x1) = x, is the difference in distance from a given point measured along a level, horizontal line for relatively small distances where the Earth's curvature may be disregarded. Here, the ratio of the altitude change to the horizontal distance between any two places on the line is used to define the slope of the road between the two points.
In mathematical language, slope m of the line is
slope = [tex]\frac{x-x1}{y-y1} =\frac{4-4}{-2+10} = 0[/tex]
To know more about slope visit: https://brainly.com/question/3605446
#SPJ9
For what values of m does the graph of y = 3x² + 7x + m have two x-intercepts?
0 m> 25
O
Om<25
3
49
Om 12
49
m> 12
The graph of y = 3x² + 7x + m will have two x-intercepts if m < 49/12.
The given function is,
y = 3x² + 7x + m
Having two x-intercepts means that the value of y should be 0.
So, we can write,
3x² + 7x + m = 0
Now, this has become a quadratic equation and it will have two zeroes according to the question,
As we know, the condition of quadratic to have two different values of x is,
0 < √(b²-4ac)
Where,
a = 3
b = 7
c =m
Putting all the values,
√(7²-4(3)(m)) > 0
Squaring both sides,
7²-4(3)(m) > 0
49-12m > 0
49/12 > m.
So, the graph will have two intercepts if m < 49/12.
To know more about Quadratic equation, visit,
https://brainly.com/question/28038123
#SPJ9
A circle has a diameter of 24 centimeters. Central angle FOG is drawn, determining an arc FG. The radian measure of angle FOG is 3/4 What is the length of arc FG in centimeters?16 cm9 cm32 cm18 cm
Answer:
9 cm
Explanation:
We are given the following information:
Diameter = 24 cm
Angle FOG = 3/4 rad
The formula for calculating arc length is written below:
[tex]\begin{gathered} L=\theta\times r \\ where\colon \\ \theta=central\text{ angle of }arc,\text{ in }rad \\ r=radius \\ r=\frac{\text{Diameter}}{2}=\frac{24}{2}=12cm \\ \theta=\frac{3}{4}rad \\ \text{Substitute these into the formula, we have:} \\ L=\frac{3}{4}\times12 \\ L=\frac{3\times12}{4} \\ L=9cm \\ \\ \therefore L=9cm \end{gathered}[/tex]Therefore, the arc length is 9 cm
Graph the following function.
f(x)=2(x-2)²-4
The graph of the given expression f(x)=2(x-2)²-4 is shown (refer to the graph attached below.)
What is a graph?In mathematics, a graph is a visual representation or diagram that shows data or values in an ordered way. The relationships between two or more things are frequently represented by the points on a graph. Charts and graphs come in a variety of styles.Line graphs, bar graphs and histograms, pie charts, and Cartesian graphs are likely the four most popular types. A graph's function representation can be determined using the vertical line test. All points with a certain x value are included in a vertical line. Output for a given input x value is represented by the y value of the point on a graph where a vertical line intersects it.So, f(x)=2(x-2)²-4:
Now, graph the function f(x)=2(x-2)²-4 as follows.(Refer to the graph attached below)Therefore, the graph of the given expression f(x)=2(x-2)²-4 is shown (refer to the graph attached below.)
Know more about graphs here:
https://brainly.com/question/19040584
#SPJ13
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that
each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 18 couples.
Find the expected number of girls in groups of 18 births
Answer:
since the method is deemed to have no effect
which means probability of having a girl child is same as having a boy child which is 0.5
Total births = 18
Therefore, expected number of girls in groups should be equal to = 0.5 × 18 = 9
I hope this is helpful
Solve for brainliest and 20 points
Answer:
x = 50
Step-by-step explanation:
50 x 3 - 15 = 135
an octagon has 8 sides & 8 angles. 135 x 8 = 1,080 which is the amount of degrees an octagon equals.
Answer:
50
Step-by-step explanation:
Total angles in an octagon is 1080
Because there are 8 sides you must divide 1080/8 to find the angle of one side ... 1080/8 = 135
3x-15=135
1) 135+15 = 150
2)150/3=50
Hope this helps, have a great day!
What value of x makes this equation true?x+7------7A. 6B. 8C. 35 D. 42
We have
[tex]\begin{gathered} \frac{x+7}{7}=6 \\ x+7=6\times7 \\ x+7=42 \\ x=42-7 \\ x=35 \end{gathered}[/tex]Option C
[tex] 4 ^{ \frac{1}{3} } \times 4 ^{ \frac{1}{5} } = [/tex]pls answer this
The given Expression is :
[tex]4^{\frac{1}{3}}\cdot4^{\frac{1}{5}}[/tex]From the property of exponents
If the base value of the exponents are same then during the process of multiplication powers will add up.
Since in the given expression 4 is the base value on both base of the exponents
Thus, base value are equal
The powers will add up:
[tex]\begin{gathered} 4^{\frac{1}{3}}\cdot4^{\frac{1}{5}} \\ 4^{\frac{1}{3}+\frac{1}{5}} \end{gathered}[/tex]Simplify the farction of the exponents :
[tex]\begin{gathered} \frac{1}{3}+\frac{1}{5} \\ \text{Taking LCM of the 3 \& 5} \\ \frac{1}{3}+\frac{1}{5}=\frac{5+3}{15} \\ \frac{1}{3}+\frac{1}{5}=\frac{8}{15} \end{gathered}[/tex]So, the value of the given expression will be :
[tex]\begin{gathered} 4^{\frac{1}{3}}\cdot4^{\frac{1}{5}}=4^{\frac{1}{3}+\frac{1}{5}} \\ 4^{\frac{1}{3}}\cdot4^{\frac{1}{5}}=4^{\frac{8}{15}} \end{gathered}[/tex]Answer : 4 ^8/15
You are trying to memorize a speech for your public speaking class. After 1 day, you memorized 200 words. Each of the following days, you memorized an additional 30 words.
Use the given information to write a linear equation in point-slope form. Then use the equation to find the number of words will you have memorized after 8 days.
__words
can someone help me find the formule pls
The linear equation in point-slope form of the given condition is y = 30x + 170. The number of words after 8 days will be 410.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
Let's represent the number of days by x and the number of words by y.
At day 1 (x = 1) ⇒ Number of words (y = 200)
At day 1 (x = 2) ⇒ Number of words (y = 230)
The point-slope form of a linear equation is given as,
y = mx + c
Where m is the slope, while c is the y-intercept.
Substitute,(1,200) in y = mx + c
200 = m(1) + c
Now slope m = (230 - 200)/(2 - 1) = 30
200 = 30(1) + c
c = 170
Therefore, the equation become,
y = 30x + 170
The number of words after 8 days will be,
y = 30(8) + 170 = 410
Hence "The linear equation in point-slope form of the given condition is y = 30x + 170. The number of words after 8 days will be 410".
For more about the linear function,
brainly.com/question/21107621
#SPJ1
- The Freedom Tower in New York City is 1776 feet
tall. The equation f(t) = -16t² + 1776 models the
height f(t) (in feet) of an object t seconds after it is
dropped from the top of the tower.
a. After how many seconds will the object hit the
ground? Round your answer to the nearest
hundredth of a second.
b. What is the height of the object 3 seconds after
it has been dropped from the top of the tower?
A golf ball is hit from the ground, and its height
can be modeled by the equation h(t) ==16t² + 128t,
where h(t) represents the height (in feet) of the ball
t seconds after contact. What will the maximum
height of the ball be?
WILL GIVE BRAINLIEST PLSSS
Part a: time when object hit the ground is 10.5 sec.
Part b: The height of the object 3 seconds is 1632 ft.
What is termed as the equation of motion?A mathematical formula which describes this same position, velocity, as well as acceleration of a body in relation to a specific frame of reference is known as an equation of motion. The equation of motion is second law, that also states that the force that acts on an object is equivalent to the mass m of a body multiplied by the acceleration an of its center of mass.For the given question;
The equation that models the height f(t) (in feet) of an object t seconds after it is when dropped from the top of the tower is,
f(t) = -16t² + 1776
Part a: time when object hit the ground.
When the object hit the ground, height will be zero.
Put f(t) = 0.
0 = -16t² + 1776
-16t² = -1776
t² = 111
t = 10.5 sec.
The, time after which the object will hit the ground is 10.5 sec.
Part b: The height of the object 3 seconds;
Put t = 3 in the equation.
f(3) = -16(3)² + 1776
f(3) = 1632 ft
The height of the object after 3 sec will be 1632 ft.
Thus, the values for the object hitting the ground are found.
To know more about the equation of motion, here
https://brainly.com/question/28500560
#SPJ13
If you roll a die, find the probability that you: (Enter your answers in exact form or round to 3 decimalplaces.)(a) roll at least 4 or an odd number,Answer:(b) roll an even number or a number at most 5.Answer:
A.
The question asks us to find the probability of getting at least 4 or an odd number after throwing a die.
This is easily gotten using the OR probability of two events which states:
[tex]\begin{gathered} P(A\text{ OR B) = P(A) + P(B) - P(A AND B)} \\ \text{if A = rolling at least 4} \\ B\text{ = rolling odd number,} \\ \\ P(\text{rolling at least 4 OR rolling odd number) = } \\ P(\text{at least 4) + P(odd number) - P(at least 4 AND odd number)} \end{gathered}[/tex]To get at least 4, it means the possible values we can have are: 4, 5, 6.
To get an odd number, it means the possible values we can have are: 1, 3, 5.
From both set of possibilities, 5 is common. We need to subtract the probability of getting a 5 in both situations to prevent duplication.
Thus, we can compute each probability:
[tex]\begin{gathered} P(any\text{ number)= }\frac{1}{6} \\ \\ P(at\text{ least 4)= P(4) OR P(5) OR P(6) = P(4) + P(5) +P(6)} \\ \therefore P(at\text{ least 4)= }\frac{1}{6}+\frac{1}{6}+\frac{1}{6}=\frac{3}{6} \\ \\ P(\text{odd number) = P(1) OR P(3) OR P(5) = P(1)+P(3)+P(5)} \\ \therefore P(\text{odd number)= }\frac{1}{6}+\frac{1}{6}+\frac{1}{6}=\frac{3}{6} \\ \\ P(\text{at least 4 AND odd number) = }\frac{1}{6} \\ \\ \\ \therefore P(\text{at least 4 or odd number)=}\frac{3}{6}+\frac{3}{6}-\frac{1}{6}=\frac{5}{6} \end{gathered}[/tex]Therefore, the probability of getting at least 4 or an odd number is 5/6
B:
This part of the question asks us to find the probability of rolling an even number or a number at most 5.
We, once again, take a look at the possibilities to solve this question.
Possibilities of getting an even number are: 2, 4, or 6
Possibilities of getting at most 5 are: 1, 2 , 3, 4, 5.
Therefore, we can compute the probabilities as:
[tex]undefined[/tex]Arc Length S. Central Angle 0 82 miles. 135°Find the radius and radians r of a circle with an arc length s and a central angle 0.
Central angle of 135 degrees = 135 (Pi/180) = (3/4)Pi = 2.356 radians
First answer:
Central angle = 2.356 radians
Arc lenght = 2 Pi r (angle/360), in this case:
82 = 2 Pi r (135/360) = 2 Pi r (3/8) = (3/4) Pi r
82 = (3/4) Pi r
r = 82/(3/4)Pi = 82/2.35619449
r = 34.80188089
Second answer:
Radius = 34.8 miles
12+212+25,432*5,000+
Answer:
127160224
or use a calculator
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
h(x) = x−1⁄3 (x − 12)
The critical value of the given function is = -11/2
The x values for which f'(x) = 0 are the crucial values of a function f(x).
The function in this quandary is:
h(x) = x−1⁄3 (x − 12)
The derivative is discovered using the quotient rule as follows:
[tex]h(x) = \frac{x - 1}{3(x - 12)} \\\\h'(x) = \frac{ (x-1) (3x - 36)' - (x - 1)'(3x - 36)}{(3x - 36)^{2} }\\\\h'(x) = \frac{ (x-1) (3) - (-1)(3x - 36)}{(3x - 36)^{2} }\\\\On equating it to 0\\\\\frac{ (x-1) (3) + 1(3x - 36)}{(3x - 36)^{2} } = 0\\\\3x - 3 + 3x + 36 = 0\\\\6x + 33 = 0\\\\x = \frac{-11}{2}[/tex]
To learn more about critical numbers from given link
https://brainly.com/question/12958088
#SPJ9
please answer this anybody
Answer:
5 is a vertical angle. 1 is a vertical angle. 3 is a corresponding angle.
Step-by-step explanation:
Let me know if i got anything wrong!
need help with these parts. both parts use the same table
Given:
[tex]f(x)=h(2x)[/tex]And the values in the table.
Required:
The equation of a normal line to f at x=3.
Explanation:
The equation of the line that passes through from point (x,y) and has slope m
is given by the formula
[tex]y-y_1=m(x-x_1)[/tex]From the table at x=3, f(x)=h(2x)
that is f(3)= h(6)=9
And the slope from the table at x=3 is 1/2.
Now the equation of the line is:
[tex]\begin{gathered} y-9=\frac{1}{2}(x-3) \\ 2(y-9)=(x-3) \\ 2y-18=x-3 \\ x-2y=-15 \end{gathered}[/tex]Final answer:
Thus the equation of the normal line is
[tex]x-2y+15=0[/tex]QUESTION IN ATTACHMENTS
Answer:
C.
Step-by-step explanation:
Since you are missing a side, use the Pythagorean Theorem:
[tex]a^{2}+b^{2}=c^{2}\\ 5^{2}+8^{2}=c^{2}\\ 25+64=c^{2}\\ 89=c^{2}\\ \sqrt{89}=c Answer[/tex]
Answer:
the answer is C.
[tex] \sqrt{89} [/tex]
Solve for X. 70 degreeright angle 6solve
ANSWER:
The value of x is 16.49
STEP-BY-STEP EXPLANATION:
We can calculate the value of x by means of the tangent trignometric function, which is the following
[tex]\begin{gathered} \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \\ \theta=70\text{\degree} \\ \text{opposite = x} \\ \text{adjacent = 6} \end{gathered}[/tex]Replacing and solving for x:
[tex]\begin{gathered} \tan 70=\frac{x}{6} \\ x=6\cdot\tan 70 \\ x=16.49 \end{gathered}[/tex]what is the correct order of operations for the expression below
Given:
[tex](7-4)\div(5-2)[/tex]Required:
To choose the correct order of operations for the given expression.
Explanation:
Consider the given exprsesion
[tex](7-4)\div(5-2)[/tex]Here subtract 4 from 7, subtract 2 from 5, and divide the first difference by the second.
Final Answer:
Subtract 4 from 7, subtract 2 from 5, and divide the first difference by the second.
Thad needs to buy dirt for his children's playground. The dirt costs $15 per ton, and there is a delivery cost of $12 with each order. What types of numbers are possible in the domain? -All positive rational numbers -All rational numbers greater than 15 -All positive rational numbers less than 12 -All rational numbers
The domain is the set input values, it means the number of tons that can be deliver.
The type of numbers that are possible are the positive rational numbers. This is because you can order 1, 2, 2.5, 1/3 tons but you can not order -6, -4.4 or -0.3 tons.
It means that the type of numbers that are possible for the domain are the possitive rational numbers.
it says determine how to rewrite one of the two equations above in the form ax + by=c. where a B and C are consistent so that the sum of the new equation in the unchanged equation from the original system results in an equation of one variable
Solution
-3x +4y = 24 (1)
6x +2y =-18 (2)
We can multiply equation (1) by 2 and we got:
-6x + 12y = 48
6x +2y =-18
_____________
14 y= 30
y = 30/14= 15/7
And the value of x would be:
x= 4y-24/3
x= (60/7 -24)/3
Assume the annual day care cost per child is normally distributed with a mean of $8000 and a standard deviation of $1500. In a random sample of 300 familles, how many pay morethan $6440 annually for day care per child?Of the 300 families, approximately pay more than 56440 annually for day care per child(Round to the nearest whole number as needed.)
Let's begin by listing out the information given to us:
Mean = $8,000, SD = $1,500
In a sample of 300, how many pay more than $6440?
what is this answer i need it asap!
Answer:
The answer is 3.375
Step-by-step explanation:
You just multiply 1.5 by itself 3 times
Which equation has a constant of proportionality equal to 1? Choose 1 answer: A y 10 1 11 B y 7 8 3 y = 15 D y = 2
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx
where
k is the constan of proportionality
therefore
in this problem
the answer is the option Dy=x
because, the value of k =1
Evaluate the expression below using the properties of operations. -36 ÷ 1/4 • (-1/8) • (-3) ÷ 6
Answer:
-9
Step-by-step explanation:
We are working with multiplications and divisions, which have no precedence over each other. So we can do the operations in order. It is important to remind that in these operations, if two numbers have different signals, the result of the operation is negative, otherwise, positive.
-36 ÷ 1/4
Different signals, so the result will be negative
[tex]\frac{-36}{\frac{1}{4}}=-36\ast\frac{4}{1}=-36\ast4=-144[/tex]-36 ÷ 1/4 • (-1/8) = -144 * (-1/8)
Same signal, so positive
[tex]-144\ast(-\frac{1}{8})=\frac{144}{8}=18[/tex]-36 ÷ 1/4 • (-1/8) • (-3) = 18 * (-3) = -54
-36 ÷ 1/4 • (-1/8) • (-3) ÷ 6 = -54 ÷ 6 = -9
Which expression is equivalent to (sin 2θ)(sec2θ)? 2sin θ sin θ tan θ 2tan θ
Answer:
Explanation:
Here, we want to get the expression that is equivalent to the given expression
We have this as follows:
[tex]\begin{gathered} \text{ sec 2}\theta=\text{ }\frac{\sec^2\theta}{2-\sec^2\theta} \\ \\ \sin 2\theta\text{ = 2sin}\theta\cos \theta \end{gathered}[/tex]Now, we can rewrite the overall expression as:
[tex]undefined[/tex]Consider the rectangle with width 20 in and length 26 in, write a ratio of the width to length
The ratio of the width of the rectangle to the length of the rectangle is 10/13
We are provided with the rectangle. The dimensions of the rectangle are mentioned below;
Width of rectangle = 20
Length of rectangle = 26
We were asked to calculate the ratio of width of the rectangle to the length of the rectangle. So, to calculate the ratio of width of the rectangle to the length of the rectangle we need to divide the width of rectangle to the length of the rectangle as mentioned below;
( Width of rectangle/Length of rectangle ) = 20 / 26
( Width of rectangle/Length of rectangle ) = 10/13
So, we can finally conclude that the ratio of width of the rectangle to the length of the rectangle is 10/13 .
To know more about Problems related to Ratio refer to the link:
https://brainly.com/question/26460724
#SPJ1
4. A student asks, “If the average income of 10 people is $10,000 and one person gets a raise of $10,000, is the median or the mean changed and, if so, by how much?
Since we don't know the specific income of each person in the sample, we don't know for sure if the median will change. Nevertheless, the mean will surely raise.
Since the current average income is $10,000, if one of them gets a raise of $10,000, then the sum of all incomes would be $100,000+$10,000=$110,000. And the new average income will be:
[tex]\frac{110,000}{10}=11,000[/tex]Then, the mean increases by $1,000, and we can't say anything about the median.
Find
d93 /dx93 *(cos x)
by taking the first few derivatives and observing the pattern that occurs.
d93 /dx93 *(cos x) = - sin x
Now,
d/dx (cos x ) = -Sin x
d2/dx2 (cos x) = - cos x
d3/dx3 (cos x) = sin x
d4/dx4 (cos x) = cos x
d5/dx5 (cos x) = - sin x
d6/dx6 (cos x) = -cos x
The same pattern will repeat for every 6th derivative so ,
Now,
93 = (4 x 23) + 1
Therefore,
d93 /dx93 *(cos x) = - sin x
To know more about Derivative
Refer this link:
https://brainly.com/question/23819325
#SPJ1
Put in simplest radical form: -√3 + 4√3
Answer:
3√3
Step-by-step explanation:
You want the simplest radical form of -√3 + 4√3.
Like termsWe can consider these "like terms" in the sense that each is an integer multiple of √3. As such, they can be combined by combining coefficients.
-√3 + 4√3 = (-1 +4)√3 = 3√3
In the diagram below, the circle has a radius of 25 inches. the area of the unshaded is 500pi in^2Determine and state the degree measure of angle Q, the central angle of the shaded sect
1) In this question, we are going to make use of the formula for the area of that sector, to find the central angle.
2) So, let's write it out an expression involving the area of a circle, the unshaded area, and the shaded one and then plug into that the given data:
[tex]\begin{gathered} A=\frac{\alpha}{360^{\circ}}\times\pi r^2 \\ A_{Unshaded}+A_{shaded}=A_{Circle} \\ 500\pi+\frac{\alpha}{360}\times\pi r^2=\pi r^2 \\ \\ 500\pi+\frac{α}{360}\pi25^2=25^2\pi \\ \\ 500\pi+\frac{125\piα}{72}=625\pi \\ \\ 500\pi +\frac{125\pi α}{72}-500\pi =625\pi -500\pi \\ \\ \frac{125\pi α}{72}=125\pi \\ \\ \frac{72\times \:125\pi α}{72}=72\times \:125\pi \\ \\ \frac{125\pi α}{125\pi }=\frac{9000\pi }{125\pi } \\ \\ α=72^{\circ} \\ \\ \end{gathered}[/tex]Thus, the centra angle of that shaded area is 72º