The slope of the line that passes through the points (-2, 2) and (-4, -1) is 3/2 i.e. 1.5 .
How can we define the slope for a given line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. Therefore, the relationship between the change in the y-coordinate and the change in the x-coordinate is provided by the formula m = change in y/change in x = Δy/Δx, where "m" is the slope of a line.
Mathematically, slope of a line = m = (y₂ - y₁)/(x₂ - x₁)
Given, the line passes through the points (-2, 2) and (-4, -1)
Now, using the formula established in the literature, we get:
slope = m = (y₂ - y₁)/(x₂ - x₁) = (-1 - 2)/(-4 - (-2)) = -3/-2 = 3/2 = 1.5
Therefore, the slope of the line that passes through the points (-2, 2) and (-4, -1) is 3/2 i.e. 1.5 .
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what is the arithmetic mean of all of the positive two-digit integers with the property that the integer is equal to the sum of its first digit plus its second digit plus the product of its two digits?
The arithmetic mean is 59.
What is arithmetic mean?
It is the sum of collection of numbers divided by the count of the numbers.
Conider AB is the nuber satisfying the condition. Hence,
[tex]10A+B=A+B+A\times B\\9A=A\times B\\[/tex]
Since AB is a two digit number hence, [tex]A\neq 0\\[/tex]. Hence, divide both sides by [tex]A[/tex].
[tex]9=B[/tex]
Hence, B is 9 and A can take any value from 1 to 9.
Hence, numbers are 19, 29, 39, 49, 59, 69, 79, 89,99.
Now, calculate arithmetic mean as follows:
[tex]AM=\frac{Sum \ of \ numbes}{Count \ of \ numbers}\\=\frac{19+29+39+49+59+69+79+89+99}{9}\\=59[/tex]
Hence, arithmetic mean of numbers is 59.
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In the figure below, N lies between M and P.
Find the location of N so that the ratio of MN to NP is 7 to 2.
M
- 27
Location of N
N
?
X
→→
Ś
P
-9
The position of N on the line segment is at the -14 mark
What are coordinates?A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
How to determine the location of N?The complete question is added as an attachment
From the attachment, we have
The ratio is given as:
MN : NP = 7 : 2
Also, we have
Location of M = -27
Location of P = -9
The location of N is then calculated as
N = MN/(MN + NP) * (M - P)
Substitute the known values
N = 7/(7 + 2) * (-27 + 9)
Evaluate the sum
N = 7/9 * -18
Evaluate the product
N = -14
Hence, the location of point N is -14
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Kayla gave 13 of a pan of brownies to Ella and 16 of the pan to Eli. Which choice is the MOST reasonable for the part of the pan of brownies Kayla gave away?
The reasonable fraction for the part of the pan of brownies Kayla gave away is 1/2.
How to illustrate the information?Kayla gave 1/3 of a pan of brownies to Ella and 1/6 of the pan to Eli.
Therefore, the part given away will be the addition of the fractions. This will be:
= 1/3 + 1/6
= 2/6 + 1/6
= 3/6
= 1/2
Therefore, 1/2 of the brownies were given away.
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What is the number sentence for "4 and N together make9"?
Given:
The number sentence for 4 and n
Required:
We have to find the given sentence
Explanation:
4 and N, simply means you mixed them up, you sum them up
your result is 9, 4+N=9
Required solution :
4+N=9
I need help with my mathWrite the slope-intercept form of the equation of each line
Answer:
y = -1
Explanation:
The slope-intercept form of the equation of a line has the form:
y = mx + b
Where m is the slope and b is the y-intercept.
The slope can be calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x1, y1) and (x2, y2) are the coordinates of two points in the line.
So, replacing (x1, y1) by (1, -1) and (x2, y2) by (2, -1), we get:
[tex]m=\frac{-1-(-1)}{2-1}=\frac{-1+1}{1}=\frac{0}{1}=0[/tex]On the other hand, the y-intercept is the point where the line crosses the y-axis. So, the y-intercept is -1.
Finally, the equation of the line in the slope-intercept form is:
y = 0x - 1
y = -1
So, the answer is y = -1
Use the associate property to write an expression equivalent to (w+9)+3
W+(9+3) is the equivalent expression of (w+9)+3 by using associate property
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is (w+9)+3
The operator in given expression is plus and variable is W.
The associative property of addition states that Changing the grouping of addends does not change the sum.
(x+y)+z=x+(y+z)
Similarly (W+9)+3=W+(9+3)
W+(9+3) is the equivalent expression of (w+9)+3 by using associate property
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Water flows through a pipe at a rate of 7 liters every 9.5 hours. Express this rate of
flow in pints per week. Round your answer to the nearest whole number.
The rate of water flow per week is 124 liters.
What is the of water flow?
Running water naturally travels along the slope in a direction determined by gravity. This is referred to as a water flow.
Given is, the water flows through a pipe at a rate of 7 liters every 9.5 hours.
So,
water flows per hour = [tex]\frac{7}{9.5}[/tex]
Hours in a week = 7 x 24 = 168 hours
Water flow per week = hours in a week x water flow per hour.
[tex]= 168 x \frac{7}{9.5} \\= 123.7894[/tex]
Water flow per week = 124 liters.
Therefore, the water flow per week is 124 liters.
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PLEASE HELP ASAP!!!!!!!!!!!!! WITH STEPS PLEASEEEEEE!!!!!!!!!!!!!
Given f(x) = x2 + 4x − 1, describe the new function g(x) = f(x + 4)
If function f(x) = [tex]x^2[/tex] + 4x -1, then the value of g(x)= f(x+4) = [tex]x^2[/tex] + 12x +31
The function is
f(x) = [tex]x^2[/tex] + 4x -1
The function is the expression that represents the relationship between one variable and another variable. If one variable is dependent variable then the another variable is independent variable.
The value of g(x) = f(x+4)
First we have to find the value of f(x+4)
Substitute the values in the function
f(x) = [tex]x^2[/tex] + 4x -1
f(x+4) = [tex](x+4)^2[/tex] + 4(x+4) - 1
= [tex]x^2[/tex] + 8x +16 + 4x+16 - 1
Rearrange the terms and combine the like terms
= [tex]x^2[/tex] + 8x+4x + 16+16-1
= [tex]x^2[/tex] + 12x +31
Hence, if function f(x) = [tex]x^2[/tex] + 4x -1, then the value of g(x)= f(x+4) = [tex]x^2[/tex] + 12x +31
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ABCD is a rectangle. Find angles a and b to the nearest degree
Solution
Given, ABCD is a rectangle AC is diagonal
Then AD=BC and AB=CD
And ∠ABC=∠BCA=∠CDA=∠DAB=90
0
In ΔABC and ΔADC
∠ABC=∠ADC (Angle of rectangle)
AB=DC (Opposite side of rectangle )
AC=AC (Common side)
∴ΔABC≅ΔADC
∴∠ACD=∠ACB
∵∠ACD+∠ACB=90
0
..........[Angle ACB is the angle of rectangle]
∴2∠ACD=90
0
⇒∠ACD=45
0
The dial on a combination lock contains markings which represent the numbers from 0 to 39. How many 3- number combinations are possible if the first and the second must be different odd numbers, while the third number must not be an odd number?.
There are 64000 distinct combinations .
The dial for the standard combination lock is fastened to a spindle. The spindle travels through many wheels and a drive cam inside the lock. Every number has one wheel, hence the number of wheels in a wheel pack depends on how many numbers are in the combination.
The lock uses the numbers 0 to 39 and has 64,000 distinct combinations.
How many possible three-number combinations are there?
You have 10 options for the first digit, 9 options for the second digit, and 8 options for the third digit, giving you 10x9x8 = 720 if you want all three possible numbers with no duplication of the digits.
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The marked price of an article is Rs.2080. After allowing d% discount and levying(d-2)% VAT,the cost of the article becomes Rs 1997.84. find the discount amount and VAT amount
The discount rate is 15% and the VAT rate is 13%
What is the value of the discount?The following can be deduced:
MP = 2080
Discount = d%
VAT = (d-2)%
Cost = 1997.84
Apply discount:
2080 - d% = 2080*(1 - 0.01d)
Add VAT:
2080*(1 - 0.01d) + (d - 2)%
2080*(1 - 0.01d) * (1 + (d -2)/100)
2080*(1 - 0.01d) * (0.98 + 0.01d)
= 1997.84
(1 - 0.01d)(0.98 + 0.01d) = 1997.84/2080
0.98 + 0.01d - 0.0098d - 0.0001d²
= 0.9605
- 0.0001d² + 0.0002d + 0.98- 0.9605 = 0
0.0001d²- 0.0002d - 0.0195 = 0
d² - 2d + 195 = 0
Solving the quadratic equation we get:
d = 15
Therefore discount is 15%
VAT rate = d - 2 = 15% - 2% = 13%
The concept shown above is the calculation for the discount and the amount of the value added tax.
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One fourth the sum of r and ten is identical to r minus 4.
⇒Mathematically this means
[tex]\frac{1}{4} (r+10)= r-4\\\frac{r}{4} +\frac{10}{4} =r-4\\\frac{r}{4}(4) +\frac{10}{4} (4)=r(4)-4(4)\\r+10=4r-16\\r-4r=-16-10\\-3r=-26\\\frac{-3r}{-3} =\frac{-26}{-3} \\r=\frac{26}{3}[/tex]
Attached is the solution.
The table shows the inputs and outputs for the function f (x) = -7x-5.Input-10-5O5Output65?-5-40What is the output value of the function when the input is –5?403050
Answer:
30
Explanation:
To know the output value of the function, we need to replace x by -5 and calculated f(x). So:
[tex]\begin{gathered} f(x)=-7x-5 \\ f(-5)=-7(-5)-5 \\ f(-5)=35-5 \\ f(-5)=30 \end{gathered}[/tex]Therefore, if the input x is -5, the output f(x) is 30
So, the answer is 30.
Help da brother out.
Answer:
top: y=f(x)=-2x+5
middle: y=4x
last: y=(9/2)x-3
allison drove home at 58 mph, but her brother austin, who left at the same time, could drive at only 46 mph. when allison arrived, austin still had 24 miles to go. how far did allison drive?
When Allison arrived, Austin still had 24 miles to go. Allison drive 116 miles per hour.
What is distance?
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.
As given, Allison drove home at 58 mph, but her brother Austin, who left at the same time, could drive at only 46 mph. Allison arrived, Austin still had 24 miles to go.
Let t be the time they drove.
Then you have this "distance" equation
58t = 46t + 24
saying that both parts of the equation represent the same distance. Then
58t - 46t = 24
12t = 24
t = 2 hours.
Hence the distance is, 2 x 58 = 116 mph.
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find the area of this shape. 100pts
Answer:
A = 540 m²
Step-by-step explanation:
consider the shape split into 3 rectangles
the length is divided into 3 congruent sections
single dash = 30 m ÷ 3 = 10 m
the width is divided into 3 congruent sections
double dash = 27 m ÷ 3 = 9 m
then area (A) is the total of the 3 rectangular areas
A of left rectangle = 10 × 9 = 90 m²
A of middle rectangle = 10 × (9 + 9) = 10 × 18 = 180 m²
A of right rectangle = 10 × 27 = 270 m²
total area = 90 + 180 + 270 = 540 m²
Solve. (−7x−14)−(x−5)
Step-by-step explanation:
-7x(x-5)-(-14)(x-5)
-7x²+35+14x-70
-7x²-14x-35
Hope this is correct
Have a good day
Write an equation of the line through (-3,- 6) having slope17/16Give the answer in standard form.The equation of the line is
The equation of a line in Standard form is:
[tex]Ax+By=C[/tex]Where "A", "B" and "C" are Integers ("A" is positive).
The Slope-Intercept form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
In this case you know that:
[tex]m=\frac{17}{16}[/tex]And knowing that the line passes through the point
[tex]\mleft(-3,-6\mright)[/tex]You can substitute values and solve for "b":
[tex]\begin{gathered} y=mx+b \\ -6=(\frac{17}{16})(-3)+b \\ \\ \\ -6=-\frac{51}{16}+b \\ \\ -6=-\frac{51}{16}+b \\ \\ -6+\frac{51}{16}=b \\ \\ b=-\frac{45}{16} \end{gathered}[/tex]Then, the equation of this line in Slope-Intercept form is:
[tex]y=\frac{17}{16}x-\frac{45}{16}[/tex]Now that you have this equation, you can write it in Standard form as following:
[tex]\begin{gathered} y+\frac{45}{16}=\frac{17}{16}x \\ \\ \frac{45}{16}=\frac{17}{16}x-y \\ \\ \frac{17}{16}x-y=\frac{45}{16} \end{gathered}[/tex]The answer is:
[tex]\frac{17}{16}x-y=\frac{45}{16}[/tex]Simplify14. (5-2)(4 + 31)20 - 81 - 612b. 26 + 7i20 + 4i
At first, we multiply 5 by 4
[tex]5\times4=20[/tex]Then multiply 5 by 3i
[tex]5\times3i=15i[/tex]Then multiply -2i by 4
[tex]-2i\times4=-8i[/tex]Then multiply -2i by 3i
[tex]-2i\times3i=-6i^2[/tex]Since i^2 = -1, then we will multiply -6 by -1
[tex]-2i\times3i=-6i^2=-6\times-1=6[/tex]Now, we will add the terms
[tex]20+15i-8i+6[/tex]Then we will add the like terms
[tex]20+15i-8i+6=(20+6)+(15i-8i)=26+7i[/tex]So the answer is b
the average number of miles driven on a full tank of gas for a hyundai veracruz before its low fuel light comes on is 320. assume this mileage follows the normal distribution with a standard deviation of 30 miles. what is the probability that, before the low fuel light comes on, the car will travel
The probability that, before the low fuel light comes on the car will travel is 0.2576
Given,
The average number of miles driven on a full tank of gas before its low fuel light comes on is ( μ )= 320
It follows the standard deviation of ( δ ) = 30
For the normal distribution,
P(X < x) = P( Z < x - μ / δ)
a)
P( X < 330) = P( Z < 330 - 320 / 30)
= P( Z < 0.3333)
= 0.6306
b)
P( X > 308) = P( Z > 308 - 320 / 30)
= P( Z > -0.4)
= P( Z < 0.4)
= 0.6554
c)
P( 305 < X < 325) = P( X < 325) - P( X < 305)
= P( Z < 325 - 320 / 30) - P( Z < 305 - 320 / 30)
= P( Z < 0.1667) - P( Z < -0.5)
= 0.5662 - ( 1 - 0.6915)
= 0.2576
d) P(X = 340) = 0
Since X is a continuous random variable (For normal distribution).
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describe the transformation of f represented by G then graph each function
Transfomation 1: the function will undergo vertical shrinking( by a factor of 0.
5)
Transformation 2: the function is shifted 2 units up
Explanation
[tex]f(x)=x^4[/tex]Step 1
the first transformation is the function multiplied by a constant ( 1/2)
If the function is multiplied by a value less than one, all the values of the equation will decrease, leading to a “shrunken” appearance in the vertical direction
so
[tex]\begin{gathered} f(x)=x^4\Rightarrow\frac{1}{2}x^4 \\ \frac{1}{2}is\text{ smaller than 1, so} \end{gathered}[/tex]Transfomation 1: the function will undergo vertical shrinking( by a factor of 0.
5)
Step 2
the second transformation is add 5
[tex]f(x)=x^4\Rightarrow\frac{1}{2}x^4\Rightarrow g(x)=\frac{1}{2}x^4+5[/tex]If a positive number is added, the function shifts up the y-axis by the amount added.
so,
Transformation 2: the function is shifted 2 units up
I hope this helps you
Solve the following system of equations by graphing. If this system is inconsis
identify the type of constraint.
y = 4x + 4
-12x + 3y = 3
Answer:
Inconsistent: parallel lines.
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y=4x+4\\-12x+3y=3\end{cases}[/tex]
Use arithmetic operations to isolate y in the second equation:
[tex]\implies -12x+3y+12x=3+12x[/tex]
[tex]\implies 3y=12x+3[/tex]
[tex]\implies\dfrac{3y}{3}=\dfrac{12x}{3}+\dfrac{3}{3}[/tex]
[tex]\implies y=4x+1[/tex]
Therefore, we can see that both equations have the same slope and so the graphs of these equations are parallel.
The solution to a system of linear equations is the point of intersection.
As parallel lines never intersect, there are no solutions to this system and the system is said to be inconsistent.
A Ford F-150 truck is considered a half-ton truck because that is how much it can haul. How many pounds can the truck haul?
The truck can haul 1102 pounds.
According to the question,
We have the following information:
A Ford F-150 truck is considered a half-ton truck because that is how much it can haul.
(More to know: ton, pounds and kilograms are the most commonly used units for measuring weight.)
Now, we already have the knowledge that 1 ton is equal to 1000 kilograms.
So, half ton will make 500 kg.
Now, in order to convert this into pounds, we will multiply 500 kg by 2.205 because we know that 1 kg makes 2.205 pounds.
1 kg = 2.205 pounds
500 kg = (500*2.205) pounds
500 kg = 1102.5 pounds
Hence, the truck can haul 1102.5 pounds.
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if p || , m<7 = 131°, and m<16 = 88°, find the measure of the missing angle m<4= ?
According to the theorem, the corresponding angles, formed by a transversal on a pair of parallel sides, are always equal.
Also, the sum of angles on a straight line is 180 degree.
The angles 5 and 7 constitute a pair of corresponding angles, formed by the transversal 'r' on the pair of parallel sides 'p' and 'q'. So they must be equal,
[tex]\begin{gathered} \angle5=\angle7 \\ \angle5=131^{\circ} \end{gathered}[/tex]The angles 4 and 5 constitute a straight line, so they must add up to be 180 degrees,
[tex]\begin{gathered} \angle4+\angle5=180^{\circ} \\ \angle4+131^{\circ}=180^{\circ} \\ \angle4=180^{\circ}-131^{\circ} \\ \angle4=49^{\circ} \end{gathered}[/tex]Thus, the angle 4 measures 49 degrees.
If α and β are the roots of the equation ax2+bx+c=0,αβ=4ax2+bx+c=0,αβ=4 and a,b,,c are in A. P then α+β=
Considering the sum and the product of the roots of the quadratic equation, it is found that the numeric value of the expression is given as follows:
[tex]\alpha + \beta = -2.5[/tex]
What are the sum and the product of the roots of a quadratic equation?A quadratic equation is defined as follows:
[tex]y = ax^2 + bx + c, a \neq 0[/tex]
The roots of the equation are given as follows:
[tex]\alpha, \beta[/tex]
The sum of the roots is given as follows:
[tex]\alpha + \beta = -\frac{b}{a}[/tex]
The product of the roots is given as follows:
[tex]\alpha\beta = \frac{c}{a}[/tex]
In the context of this problem, the product is of 4, as [tex]\alpha\beta = 4[/tex] hence:
c/a = 4
c = 4a.
The coefficients are in an arithmetic progression, hence:
b = a + d. (d is the common difference of the sequence).c = a + 2d.We have that c = 4a, hence:
4a = a + 2d
2d = 3a
d = 1.5a.
Hence coefficient b is calculated as follows:
b = a + d = a + 1.5a = 2.5a.
Then the sum of the roots is given as follows:
[tex]\alpha + \beta = -\frac{b}{a} = -\frac{2.5a}{a} = -2.5[/tex]
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Explain if the triangles below are congruent or not and explain why you think that.
In this picture, we have the triangles with two common sides and one common angle. However, they are not congruent, as they do not follow any of the congruence theorems. The congruence theorem with two sides and an angle is the SAS(Side-Angle-Side). However, the angle has to be the angle between the two sides, which does not happen in this case.
How do you write out the sum of 2 consecutive even intergers
Let's call x to an unknown even integer. The next (consecutive) even integer will be x + 2. For instance, if x = 6, then the next even integer will be 6 + 2 = 8.
In consequence, the sum of two consecutive even integers is:
x + (x + 2)
1. In polynomial x - 12; 12 is a ______
Answer :- Constant term
In p(x) = x - 12, 1 is the coefficient of x and -12 is the constant term.
solve the system by graphing; y= -5/3x + 3 y= 1/3x - 3
Answer:
The solution to the given system is:
x = 3
y = -3
Explanation:
Given the following system of equation:
[tex]\begin{gathered} y=-\frac{5}{3}x+3 \\ \\ y=\frac{1}{3}x-3 \end{gathered}[/tex]The solution to these is the point where the lines intersect.
The graph is shown below:
The solution is x = 3, y = -3
Find the midpoint of CD
C=(1,9) and D=(7,-7)
Answer:
(4, 1 )
Step-by-step explanation:
given endpoints (x₁, y₁ ) and (x₂, y₂ ) , then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
here (x₁, y₁ ) = C (1, 9 ) and (x₂, y₂ ) = D (7, - 7 ) , then
midpoint = ( [tex]\frac{1+7}{2}[/tex] , [tex]\frac{9-7}{2}[/tex] ) = ( [tex]\frac{8}{2}[/tex] , [tex]\frac{2}{2}[/tex] ) = (4, 1 )
