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Given the table;
Since the function is linear. The general equation is given as;
[tex]\begin{gathered} y=mx+c \\ \text{Where;} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ (-8,-2),(-4,0) \\ x_1=-8,y_1=-2,x_2=-4,y_2=0 \end{gathered}[/tex][tex]\begin{gathered} m=\frac{0-(-2)}{-4-(-8)} \\ m=\frac{2}{4} \\ m=\frac{1}{2} \end{gathered}[/tex]Now, let's use the third point to get the intercept c of the line. We have;
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Related Questions
Evaluate the logarithmic expression. Do not round the expression until the final answer. When necessary round the nearest hundredth
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Given:
[tex]\log_2(32)[/tex]First, we will write the expression in the following form:
[tex]\log_a(a^b)[/tex]We can rewrite 32 as:
[tex]32=2^5[/tex]With this, we now have:
[tex]\begin{gathered} \operatorname{\log}_2(32)=\operatorname{\log}_2(2^5) \\ \operatorname{\log}_a(a^b)=b \\ \Rightarrow\operatorname{\log}_2(2^5)=5 \end{gathered}[/tex]Therefore, the answer would be 5
Page 112 question 7 part c which equation matches the following graphA f(x)=2^xBf(x)=-2^xCf(x)=3x2^xDf(x)=-3x2^x
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Given:
We get the point (0,3) which is lie on the graph from the graph.
Aim:
We need to find the equation of the given graph.
Explanation:
The graph of the equation is growing upward.
The given graph is an exponential growth function.
Consider the eqaution of the exponential growth function.
[tex]f(x)=a\times2^x[/tex]Substitute x=0 and f(3)=3 in the equation.
[tex]3=a\times2^0[/tex][tex]a=3[/tex]Substitute a=3 in the equation.
[tex]f(x)=3\times2^x[/tex]Final answer:
[tex]f(x)=3\times2^x[/tex]Find the slope then write an equation for the line that passes through each pair of points (5, 6), (-10, – 15)
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The given points are,
x1, y1 = 5, 6
x2, y2 = -10, -15
The general line equation is,
y = mx +b
Here, m is the slope and b is the y intercept.
The slope m can be calculated as,
[tex]m=\frac{y2-y1}{x2-x1}=\frac{-15-6}{-10-5}=\frac{21}{15}[/tex]Now, b can be calculated by taking a point and susbtituting the values in the line equation.
Let us here take, th points (5,6). Therefore we have,
[tex]\begin{gathered} 6=\frac{21}{15}\times5+b \\ 6=7+b \\ b=-1 \end{gathered}[/tex]Thus, the equation is,
[tex]y=\frac{21}{15}x-1[/tex]Can u explain how to do these and help give the answer
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First it is necessary to know the logic symbols
⇒ material implication
¬ negation
Then if it is a cow, then it is an animal.
Answer: Letter D
What is the answer to the equation 1/4x + 3 = 4
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EXPLANATION :
From the problem, we have the equation :
[tex]\frac{1}{4}x+3=4[/tex]Solving for the value of x :
[tex]\begin{gathered} \text{ Subtract 3 from both sides :} \\ \frac{1}{4}x+3-3=4-3 \\ \\ \frac{1}{4}x=1 \\ \\ \text{ Multiply both sides by 4 :} \\ \\ 4(\frac{1}{4}x)=4(1) \\ \\ x=4 \end{gathered}[/tex]ANSWER :
The answer is x = 4
-3 -3
1/4x = 1
1/4 1/4
x = 0.25
A Normal Distribution has a mean of 96 and a standard Deviation of 10. find the probability that that a value selected at random is in the following interval at most 116
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Let's start by computing the z score at 116. The mean of the normal distribution and its standard deviation is already provided on the problem. The z-score can be computed using the equation
[tex]z=\frac{x-\mu}{\sigma}[/tex]where μ is the mean of the normal distribution while σ is the standard deviation of the normal distribution. The value of x for this problem is 116. Hence, the z score is
[tex]z_{116}=\frac{116-96}{10}=2[/tex]We want to take a look at the probability of picking a random sample with the upper ceiling equal to 116. No lower limit is considered hence we are considering the lowest random sample here. The normal distribution can be shown as
where the shaded curve is the probability where a random sample can be selected. The value 47.7% is retrieved using the empirical rule of normal distribution wherein if you have a z score that is equal to 2, the probability of getting the random sample at the right-hand side will be 47.7%. No lower limit is given in the problem, hence, we are sure that there is a 50% chance that we can get a sample on the left-hand side of the normal distribution. The total probability that we can get a random sample at most 116 is equal to 50% + 47.7% = 97.7%.
The displacement function of a rock thrown straight up in the air is given by f(t)= -2t^2 + 15.7t meters, where t is measured in seconds find the total distance traveled by the rock when it reaches the ground a. 30.81 mb. 31.40 mc. 61.62 md. 92.43 m
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As the rick is thrown straight up in the air and the function of its displacement is quadratic it means that the rock traveled a distance up to its maximum and then down to the ground. Then, the function value in the maximum is half the distance traveled by the rock.
[tex]f(t)=-2t^2+15.7t[/tex]Use the next formula to find the time (t) in the maximum point of quadratic function:
[tex]\begin{gathered} f(x)=ax^2+bx+c \\ \\ x_{max}=-\frac{b}{2a} \end{gathered}[/tex][tex]t_{max}=-\frac{15.7}{2(-2)}=-\frac{15.7}{-4}=3.925[/tex]Evaluate the function for t=3.925 to find the maximum value:
[tex]\begin{gathered} f(3.925)=-2(3.925)^2+15.7(3.925) \\ f(3.925)\approx-2(15.4056)+61.6225 \\ f(3.925)\approx-30.8112+61.6225 \\ f(3.925)\approx30.8113 \end{gathered}[/tex]Multiply the maximum value by 2 to get the total distance traveled by the rock:
[tex]30.8113*2\approx61.62[/tex]Then, the total distance traveled by the rock when it reaches the ground is 61.62metersAnswer: Cevaluate the expression when m=2 and n= 416/n -m
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Hello!
To solve this exercise, we have to replace where's m and n by its values, look:
[tex]\frac{16}{n}-m[/tex]Replacing:
• m, = 2
,• n, = 4
[tex]\begin{gathered} \frac{16}{4}-2=4-2=2 \\ \end{gathered}[/tex]So, the value of this expression when m=2 and n=4 is 2.
0 Find the perimeter of the shaded region above, Question Heln
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Define the perimeter of a shape
The perimeter of any shape is the distance around the edge of a shape. That is the total length of the outline of the shape
Draw the shape given with the appropriate dimension
The shape is shaded and the perimeter is the total length of the outline
Noted that line DE is equal to BC
[tex]DE=BC=8[/tex]Therefore, the perimeter is
[tex]AB+BC+CD+DE+EA[/tex][tex]P=6+8+7+8+6[/tex][tex]P=35\text{units}[/tex]simplify: 1x10^3/4x10^5
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The expression we have to simplify is:
[tex]\frac{1\times10^3}{4\times10^5}[/tex]To divide expression such as the one we have, we use the following law of exponents:
[tex]\frac{a^m}{a^n}=a^{m-n}^{}[/tex]This tells us that when we have the same term in the numerator and denominator, to divide we subtract the exponents.
In this case, we will have:
[tex]\frac{1\times10^3}{4\times10^5}=\frac{1}{4}\times10^{3-5}[/tex]since 3-5=-2, we have:
[tex]\frac{1\times10^3}{4\times10^5}=\frac{1}{4}\times10^{-2}[/tex]We simplify 1/4 to its decimal value 0.25:
[tex]\frac{1\times10^3}{4\times10^5}=0.25\times10^{-2}[/tex]The negative exponent on the number 10, indicates the number of times we have to move the decimal point to the left.
Moving the decimal point two places to the left we get rid of the 10^-2, and the result is:
[tex]\frac{1\times10^3}{4\times10^5}=0.0025[/tex]Answer: 0.0025
Multiply: (5j + 3k) (5j - 3k)Multiply: (5j + 3k) (5j - 3k)
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Answer:
25j^2 - 9k^2
Explanation:
WHAT IS THE MEDIAN OF THE DATA BELOW: 7,7,4,6,7,4,7,6,2THE ANSWER I GOT WAS 6?
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Given:
7,7,4,6,7,4,7,6, and 2.
Required:
We need to find the median of the given data set.
Explanation:
Recall that the median is the value in the middle of a data set.
The number of data in the given set is 9.
Arrange the data points in increasing order.
2,4,4,6,6,7,7,7,7.
The 5th term is the middle term of the given data set.
[tex]Median=6[/tex]Final answer:
[tex]Median=6[/tex]A midwestern music competition awarded 32 ribbons. The number of blue ribbons awarded was 1 less than the number of white ribbons. The number of red ribbonswas 3 more than the number of white ribbons. How many white ribbons were awarded?
Answers
Let b be the number of blue ribbons and r be the number of red ribbon and w be the number of white ribbons
b= w - 1
r = w + 3
But,
b + w + r = 32
substitute b= w- 1 and r = w+ 3 into the equation
w- 1 + w + w+ 3 = 32
Re-arrange
w + w + w - 1 + 3 = 32
3w + 2 = 32
Subtract 2 from both-side of the equation
3w = 32 - 2
3w = 30
Divide both-side of the equation by 3
w = 10
Hence, there are 10 numbers of white ribbons
Ariana has created a paper airplane for her physics class, the physics teacher is requiring her paper airplane to swoop down at a single point to graze the ground before it rises back into the air. Her initial attempt is modeled by the function below where h is height in feet and X is time in seconds. In how many seconds will the paper airplane crash into the ground?
Answers
Given:
[tex]h(x)=x^2-12x+35[/tex]The given function h(x) represents the height in feet and (x) is time in seconds.
We will find the time the paper airplane will crash into the ground.
When the paper airplane crashes into the ground, h(x) = 0
So, substitute h = 0
[tex]x^2-12x+35=0[/tex]Solve the equation to find (x), we will factor the equation as follows:
[tex]\begin{gathered} (x-5)(x-7)=0 \\ x-5=0\rightarrow x=5 \\ x-7=0\rightarrow x=7 \end{gathered}[/tex]So, the answer will be the time = 5 seconds and 7 seconds
Geometry midpoint If E is the midpoint of segment DF, DE = 2x + 4 and EF = 3x - 1, thenx=DE=EF=DF=
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ANSWERS
x = 5
DE = 14
EF = 14
DF = 28
EXPLANATION
We have that E is the midpoint of DF.
This means that DE is the same as EF.
We have that:
DE = 2x + 4
EF = 3x - 1
=> 2x + 4 = 3x - 1
Collect like terms and solve:
3x - 2x = 4 + 1
x = 5
=> DE = 2(5) + 4 = 10 + 4
DE = 14
=> EF = 3(5) - 1 = 15 - 1
EF = 14
Since DE and EF lie on DF, we have that:
DE + EF = DF
=> DF = 14 + 14
DF = 28
X*d multiply by x*18
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The point here is to remember the additive property of exponents. In general, it says that
[tex]x^b\cdot x^c=x^{b+c}[/tex]In our case, it becomes
[tex]x^d\cdot x^{18}=x^{d+18}[/tex]
if x, y, z are the sides of a triangle and s is the semi perimeter, then calculate the area of the triangle
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the area can be calculated with the next formula
[tex]A=\sqrt[]{s(s-x)(s-y)(s-z)}[/tex]The area of a triangle can also be calculated from its semiperimeter and side lengths x,y,z sing Heron's formula
Part "c" is the only part I need assistance with. Is anyone available to help with this question?
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ANSWER
[tex]\begin{equation*} \begin{bmatrix}{4} & {6} & {3} \\ {-5} & {-1} & 1 \\ {} & {} & {}\end{bmatrix} \end{equation*}[/tex]EXPLANATION
We want to translate triangle ABC by 2 units right and 4 units down.
To do this, we have to add 2 to the x-coordinates and subtract 4 from the y-coordinates of the vertices of the triangle.
In other words, add 2 to each value in the first row and subtract 4 from each value in the second row.
That is:
[tex]\begin{gathered} \begin{bmatrix}{2+2} & {4+2} & {1+2} \\ {-1-4} & {3-4} & {5-4} \\ {} & {} & {}\end{bmatrix} \\ \\ \begin{bmatrix}{4} & {6} & {3} \\ {-5} & {-1} & 1 \\ {} & {} & {}\end{bmatrix} \end{gathered}[/tex]That is the answer.
What is the midpoint of (2, 13) and (0, 11)? WHAT IS THE X VALUE? *
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Given the points (2 , 13) and (0 , 11)
Let the midpoint is (x , y)
so,
[tex]x=\frac{2+0}{2}=\frac{2}{2}=1[/tex][tex]y=\frac{13+11}{2}=\frac{24}{2}=12[/tex]so, the midpoint is ( 1 , 12 )
What is the solution to the equation below? 13 - 2% (4% 2
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Given:
[tex]\frac{\sqrt[]{3-2x}}{\sqrt[]{4x}}=2[/tex]To find: The value of x
Explanation:
Squaring on both sides, we get
[tex]\begin{gathered} (\frac{\sqrt[]{3-2x}}{\sqrt[]{4x}})^2=2^2 \\ \frac{3-2x}{4x}=4 \end{gathered}[/tex]Solving we get,
[tex]\begin{gathered} 3-2x=16x \\ 16x+2x=3 \\ 18x=3 \\ x=\frac{3}{18} \\ x=\frac{1}{6} \end{gathered}[/tex]Final answer: Option C
[tex]x=\frac{1}{6}[/tex]Sergio writes the rational number -4.8. What is its opposite and absolute value? A. Its opposite is 4.8 and its absolute is 4 8/10.B. Its opposite is 4 8/10 and its absolute is -4 8/10.C. Its opposite is 4 1/8 and its absolute is 4 1/8.D. Its opposite is 4.8 and its absolute is 4 1/8.
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The correct answer is:
A. Its opposite is 4.8 and its absolute value is 48/10
The lifting force, F, exerted on an airplane wing varies jointly as the area, A, of the wing's surface andthe square of the plane's velocity, v. The lift of a wing with an area of 290 square feet is 3000 poundswhen the plane is going 250 miles per hour. Find the lifting force on the wing if the plane slows downto 210 miles per hour. (Leave the variation constant in fraction form or round to at least 5 decimalplaces. Round off your final answer to the nearest pound.)
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Given that:
[tex]f\alpha av^2[/tex]Hence, the equation relating them is
[tex]f=kav^2[/tex]where,
f is the lifting force.
k is the constant of variation.
a is the area of the wing's surface.
v is the velocity of the plane.
Given
[tex]\begin{gathered} f=3000pounds \\ a=290ft^2 \\ v=250milesperhour \end{gathered}[/tex]Solving for k
[tex]k=\frac{f}{av^2}=\frac{3000}{290\times250^2}=\frac{3}{18125}[/tex]Now that you know k, you can solve the problem.
Let us now solve for f
Therefore,
[tex]\begin{gathered} a=290squarefeet \\ v=210milesperhour \\ \therefore f=\frac{3}{18125}\times290\times210^2=2116.80000pounds \end{gathered}[/tex]Hence, the answer is
[tex]f=\text{ }2117pounds[/tex]Findthefollowing:a) Whatis55%of262?b) Whatpercentof372is297.6?
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To find 55% of 262, we just have to multiply. (55% is equivalent to 0.55)
[tex]0.55\cdot262=144.1[/tex]Therefore, 144.1 represents 55% of 262.(b)In this case, we have to divide to find the percentage 297.6 represents of 372.
[tex]\frac{297.6}{372}=0.80[/tex]Then, we multiply by 100 to express in percentage.
[tex]0.80\cdot100=80[/tex]Therefore, 297.6 represents 80% of 372.Dairon needs to make 30 pieces of string 3/8 inch in length. He has already cut a 4 7/8 inch piece of stringinto pieces that are 3/8 of an inch long each. How many more pieces of string does he need?
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Answer:
He needs 17 more pieces;
[tex]17\text{ pieces}[/tex]Explanation:
Given that Dairon needs to make 30 pieces of string 3/8 inch in length.
[tex]\frac{3}{8}\text{ inch per piece}[/tex]And He has already cut a 4 7/8 inch piece of string;
[tex]4\frac{7}{8}=\frac{4(8)+7}{8}=\frac{32+7}{8}=\frac{39}{8}\text{ inch}[/tex]The number of pieces that can be cut from the 4 7/8 inch piece is;
[tex]\frac{39}{8}\div\frac{3}{8}=\frac{39}{8}\times\frac{8}{3}=\frac{39}{3}=13\text{ pieces}[/tex]The number of pieces he needs more is;
[tex]n=30-13=17\text{ pieces}[/tex]Therefore, he needs 17 more pieces;
[tex]17\text{ pieces}[/tex]Bruce walks 3/4 mile in 1/5 hour. What is his speed in Miles per hour? Show your work.
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To solve
Speed = distance / time
From the question
distance =3/4 mile time = 1/5 hour
substituting the above in the formula
Speed =
[tex]\text{speed =}\frac{\frac{3}{4}}{\frac{1}{5}}[/tex]speed = 3/4 x 5/1
[tex]\text{speed =}\frac{15}{4}\text{ miles per hour}[/tex]speed =3.75 miles per hour
Identify the part, whole, and percent in the following statement: Find 15% of 750. part = 750, whole = n, percent = 15part = 15, whole = 750. percent=ppart = n, whole = 750, percent = 15none of theseWrite a percent equation that can be used to solve the following problem: 820 is 20% of whatnumber?n=0.2 x 820820 = 0.2 xn0.2 = n < 820none of these
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For the first part we have that:
[tex](750)\cdot(0.15)=112.5[/tex]Now, 112.5 is the part of the percentage, the percent is 15% and the whole is 750.
For the second part, we have that if 820 is 20% of number n, then:
[tex]\begin{gathered} n=\frac{820}{0.2}=4100 \\ \Rightarrow0.2\cdot n=820 \end{gathered}[/tex]Therefore, we can use the equation 0.2xn = 820
The perfect square trinomial ax^2 + bx+c is equivalent to (1.2x -0.7)^2. Which of thefollowing is equivalent to a-b+c?A 0.95B 3.61С 0.25D-0.73
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(1.2x -0.7)²
Applying the square:
(1.2x)² + 2(1.2x)(-0.7) + (-0.7)²
1.44x² - 1.68x + 0.49
where:
a = 1.44
b = -1.68
c = 0.49
Then, a - b + c = 1.44 - (-1.68) + 0.49 = 1.44 + 1.68 + 0.49 = 3.61
Help me with number 6 please thanks just need answer no need explanation n
Answers
Given: A cone of the height of 15 meters and base diameter of 40 meters.
Required: To determine the volume of the cone.
Explanation: The volume of the cone is given by-
[tex]V=\frac{1}{3}\pi r^2h[/tex]Here,
[tex]\begin{gathered} h=15\text{ m} \\ r=\frac{40}{2}=20\text{ m} \end{gathered}[/tex]Hence, the volume of the cone is-
[tex]V=\frac{1}{3}\times3.14\times(20)^2\times15[/tex]Further solving as-
[tex]\begin{gathered} V=3.14\times400\times5 \\ =6280\text{ m}^3 \end{gathered}[/tex]Final Answer: Option B is correct.
Write the equation for the line through (-1/2, -7/2) and (2,14) in slope intercept form
Answers
SOLUTION
The slope-intercept form for the equation of a line is given by
[tex]\begin{gathered} y=mx+c \\ \text{where m=slope and c=intercept} \end{gathered}[/tex]Giving the point
[tex]\begin{gathered} (-\frac{1}{2},-\frac{7}{2}) \\ \text{and} \\ (2,14) \end{gathered}[/tex]Then
[tex]\begin{gathered} x_1=-\frac{1}{2},y_1=-\frac{7}{2} \\ \text{and } \\ x_2=2,y_2=14 \end{gathered}[/tex]We apply the two point-form for the equation of a line
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]Substituting the values into the formula, we obtain
[tex]\frac{y-(-\frac{7}{2})}{x-\frac{1}{2}}=\frac{14-(-\frac{7}{2})}{2-(-\frac{1}{2})}[/tex]Simplify the equation above
[tex]\begin{gathered} \frac{y+\frac{7}{2}}{x-\frac{1}{2}}=\frac{14+\frac{7}{2}}{2+\frac{1}{2}} \\ \\ \frac{y+\frac{7}{2}}{x-\frac{1}{2}}=\frac{28+7}{2}\frac{.}{\text{.}}\frac{4+1}{2} \end{gathered}[/tex]Then, change the division to multiplication and take the reciprocal of the last fraction
[tex]\begin{gathered} \frac{y+\frac{7}{2}}{x-\frac{1}{2}}=\frac{35}{2}\times\frac{2}{5} \\ \frac{y+\frac{7}{2}}{x-\frac{1}{2}}=7 \end{gathered}[/tex]Multiply both parts of the equation by the denominator (x-1/2), we obtain
[tex]\begin{gathered} y+\frac{7}{2}=7(x-\frac{1}{2}) \\ \text{expand the parenthesis} \\ y+\frac{7}{2}=7x-\frac{7}{2} \end{gathered}[/tex]Then, make y the subject of the formula
[tex]\begin{gathered} y+\frac{7}{2}=7x-\frac{7}{2} \\ \text{subtract 7/2 from both sides } \\ y=7x-\frac{7}{2}-\frac{7}{2} \\ y=7x-\frac{14}{2} \end{gathered}[/tex]Hence the equation of the line becomes
[tex]\begin{gathered} y=7x-7\ldots..\text{ in slope-intercept } \\ \text{slope}=7\text{ and intercept =-7} \end{gathered}[/tex]Therefore the equation of the line in slope-intercept is
y=7x-7
A test is made of H0 : μ = 47 versus H1 : μ > 47. A sample of size n=69 is drawn, and x=48. The population standard deviation is σ=27. Compute the value of the test statistic z.
Answers
EXPLANATION
Let's consider the facts:
u=47
H_1 --> u>47
n=69
The standard deviation is 27
The z-score is given by the equation:
[tex]z-\text{score}=\frac{x-\mu}{\sigma}[/tex]Now,the Test Statistic z is:
[tex]Z=\frac{\bar{X}-\mu}{\frac{\sigma}{\sqrt[]{n}}}[/tex]Substituting terms:
[tex]Z=\frac{48-47}{\frac{27}{\sqrt[]{69}}}=\frac{\sqrt[]{69}}{27}[/tex]=0.30765
So, the test statistic z is equal to 0.30765.
The answer is Z=0.30765