a certain linear function can be described by the equation below
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We are given the information that the equation of the line is of the form:
y = a x + b
where a is a negative number and b is a positive number.
And we are asked to select among a number of options that represent the situation.
SInce b is a positive number (being "b" what is understood as the y-intercept) the line DOESN'T pass through the origing of coordinates. So the first option is discarded.
SInce "a"is a negative number (this is the so called "slope' of the line) the line must be slanted, and dropping from left to right Therefore option b is also discarded because that represents a line going up from left to right.
Option c is also discarded, because a is a negative number (not a zero) and lines parallel to the x axis have slope zero.
The last option is the correct one, since the intercept oo the y-axis is at a positive value for y, the line must be going down due to the negative slope, and therefore going across the II, I and IV quadrant as shown below: (give me a few minutes to draw a line with this characteristics)
Then, please mark the last option (d) as the correct answer.
Related Questions
find perimeter and area of each triangle round to nearest hundredth
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Given is a right angled triangle. Consider the figure,
Using the trignoetric funcyion tan, we have,
[tex]\begin{gathered} \tan 18=\frac{a}{12} \\ a=12\times\tan 18=3.89 \end{gathered}[/tex]Now, as we have base, a = 3.89 and height c = 12, the perimeter can be calcualted as,
[tex]\begin{gathered} P=a+c+\sqrt[]{a^2+c^2} \\ \text{ =3.89+12+}\sqrt[]{3.89^2+12^2}=28.5=29 \end{gathered}[/tex]Now, the area can be calculated as,
[tex]\begin{gathered} A=\frac{1}{2}ac \\ \text{ =1/2}\times3.89\times12=23.34=23 \end{gathered}[/tex]What property is being used here?
4x-3
x=2
4(2)-3
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THE PROPERTY OF SUBSTITUTION IS USED. IF x=2 IT MEANS IN THE PLACE OF X IN THE EXPRESSION 4X-3 YOU WILL PLUG IN THE VALUE 2 AND SIMPLIFY.
[tex] = 4(2) - 3 \\ = 8 - 3 \\ = 5[/tex]
JUST AS I HAVE DONE ABOVE.
HOPE THIS HELPS
Please help with this math problems! This is due in a few hours!
Answers
(i) The vertex's x-coordinate is 25.
(ii) The maximum height of the cannonball is 12.48 meters.
(iii) Total horizontal distance that a cannon ball can travel is 50 meters.
(iv) Total horizontal distance that a cannon ball can travel with decreased angle is 22.5 meters.
(v) Distance the cannonball traveled before reaching the maximum height is 25 meters.
What is coordinate?
A pair of values is used to specify a point's placement on a coordinate plane using both horizontal and vertical distinctions from the two separate axes. usually represented by a pair of x-values and y-values (x,y).
(i) They are both at y = 4 and separated by (40-10) = 30
The symmetry line is halfway between 40 and 10
Consequently, the vertex's x-coordinate is 25.
(ii) y = -0.01x2 + 0.5x,
a = -0.01,
b = 0.5,
-b/2(a) = -0.5/(2X-0.01) = 0.5/0.02, and so on.
y=-0.01*2+0.5(25) =12.48 meters
The maximum height of the cannonball is 12.48 meters.
(iii) Total horizontal distance that cannon ball can travel is (0,0)-(50,0)= 50 meters.
(iv)Total horizontal distance that cannon ball can travel with decreased angle is (0,0)-(22.5,0) =22.5 metres
(v) Distance cannon ball travelled before reaching the maximum height is [(0,0)-(50,0)]/2 =25 meters
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How to make 9/2=x/24 a equation
Answers
Answer:
I wasn't too sure of your question, but this is what made sense to me.
Step-by-step explanation:
cross multiplication seems to be the best fit for this.
Like this:
[tex]\frac{9}{2}=\frac{x}{24}\\ 2(x)=9(24)\\ 2x=216\\x= \frac{216}{2}\\ x=108[/tex]
Hope this helped in any way.
please help me ASAP!!
Answers
We have to solve:
[tex]\begin{gathered} 2^x-3=(x-6)^2-4_{} \\ 2^x-3+4=(x-6)^2 \\ 2^x+1=(x-6)^2 \end{gathered}[/tex]We can not write a explicit expression to find the value of x, but we can test each option to see which one is correct:
[tex]\begin{gathered} x=5 \\ 2^5+1=(5-6)^2 \\ 33=(-1)^2\longrightarrow\text{Not true} \end{gathered}[/tex][tex]\begin{gathered} x=3 \\ 2^3+1=(3-6)^2 \\ 8+1=(-3)^2 \\ 9=9\longrightarrow\text{True} \end{gathered}[/tex][tex]\begin{gathered} x=4 \\ 2^4+1=(4-6)^2 \\ 17=(-2)^2\longrightarrow\text{Not true} \end{gathered}[/tex][tex]\begin{gathered} x=-2 \\ 2^{-2}+1=(-2-6)^2 \\ \frac{1}{4}+1=(-8)^2\longrightarrow\text{Not true} \end{gathered}[/tex]Answer: x=3
Human hair grows at a rate of about 6.849×10-4 cm per hour to 2.329×10−2 cm per hour. The rate depends on gender, genetics, age, and health. Find the difference between the high end and the low end of the range. Express your answer in scientific notation rounding to 2 decimal places.
Answers
Answer:
2.×10^-2 cm/h . . . . rounded to 2 dp
2.26×10^-2 cm/h . . . . rounded to 3 sf
Step-by-step explanation:
You want the difference in growth rates between 6.849×10^-4 cm per hour and 2.329×10^-2 cm per hour.
DifferenceThe difference of two numbers written in scientific notation requires that they have the same power-of-ten multiplier.
2.329×10^-2 - 6.849×10^-4
= 2.329×10^-2 - 0.06849×10^-2 = 2.26051×10^-2 = 0.0226051
RoundingThe question asks for the answer rounded to 2 decimal places and expressed in scientific notation.
0.0226051 ≈ 0.02 = 2×10^-2 . . . . cm per hour
It makes more sense to round the mantissa to 2 decimal places, meaning the value is rounded to 3 significant figures.
2.26051×10^-2 ≈ 2.26×10^-2 . . . . cm per hour
NO LINKS!! Please help me with this probability question
Answers
===========================================================
Explanation:
Define these two events
A = father born in Michigan
B = mother born in Michigan
The notation ~A and ~B represent the opposite of each defined event above.
According to the table
P(A) = 0.48
P(B) = 0.73
If A and B were independent, then P(A and B) = P(A)*P(B) = 0.48*0.73 = 0.3504 = 35.04% but this contradicts the 29% in the "father born in Michigan" column and "mother born in Michigan" row. The table states that P(A and B) = 0.29 should be the case instead of 0.3504.
Because of this contradiction, this means P(A and B) = P(A)*P(B) is false and therefore A and B are NOT independent
--------------------------------------
Another way to look at it:
P(A) = 0.48
P(A given B) = P(A and B)/P(B)
P(A given B) = 0.29/0.73
P(A given B) = 0.39726 approximately
If A and B were independent, then P(A) and P(A given B) would be the same value. However, they are not. This is another way to see why the events are NOT independent
Through similar calculations, P(B given A) = P(A and B)/P(A) = 0.29/0.48 = 0.6042 approximately which doesn't match with P(B) = 0.73; if A and B were independent then P(B) needs to be equal to P(B given A).
MATH HELP PLEASEEEE 35 POINTS
Answers
Answer:
Step-by-step explanation:
3.75 is a2 x (b-c)
4.85 gose with the b + c -a
3.3 gose to the a - b + c
you should now know the last one
Answer:
1. A² × ( B - C ) = 3.75
2. B + C - A = 3.65
3. A - B + C = 4.85
4. B × ( A - C ) = 3.3
Step-by-step explanation:
1. (5 × 5) × (4.4 - 4.25)
25 × .15 = 3.75
2. (4.4 + 4.25) - 5
8.65 - 5 = 3.65
3. (5 - 4.4) + 4.25
.6 + 4.25 = 4.85
4. 4.4 × ( 5 - 4.25 )
4.4 × .75 = 3.3
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Answers
The number of red balloons is 5.
The number of blue balloons is 7.
The number of yellow balloons is 12.
ExplanationTo find the probability of randomly selected a yellow balloon
[tex]P=\frac{number\text{ of red balloons}}{total\text{ number of balloons}}[/tex][tex]\begin{gathered} P=\frac{12}{5+7+12} \\ P=\frac{12}{24} \\ P=\frac{1}{2} \end{gathered}[/tex]AnswerHence the correct option is C that is 1/2.
The graph shows a coordinate plane that goes from negative 8 to 8 in each direction. The graph also shows two lines that intersect at ( 2 , 3 ). That point is labeled "solution." That's right. When you have two or more linear equations, it is called a "system of linear equations". The solution to a system of linear equations consists of the - and -value that make BOTH equations true. Graphically, this appears as the point where the lines intersect. In this case, the solution is the ordered pair , as shown on the graph. If you are trying to decide whether a system of equations has a solution, would you rather have the equations or the graphs? Why?
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To visualize the solution of a system of equations, a graph is ideal, as we can see whether the functions intersect or not.
What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the context of the problem. The pair/tuple/... containing these values is called the solution of the system.
The equations that construct a system are functions, and the solution of a system is at the point of intersection of these functions. The intersection of two points is easier to visualize graphically then calculating, hence a graph is ideal, as we can see whether the functions intersect or not, while for the function we would have to calculate.
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3х2 + 14х — 49 = 0solve for x
Answers
The given expression 3x^2 +14x-49=0
we will de factorization tos solve for x
[tex]\begin{gathered} 3x^2+14x-49=0 \\ 3x^2-7x+21x-49=0 \\ (3x^2-7x)+(21x-49)=0 \\ \text{Taking x common from (}3x^2-7x)=x(3x-7) \\ \text{Taking 7 common from }(21x-49)=7(3x-7) \\ (3x^2-7x)+(21x-49)=0 \\ x(3x-7)+7(3x-7)=0 \\ \text{Taking (3x-7) common} \\ (3x-7)(x+7)=0 \\ \text{ Thus, for} \\ \text{(3x-7)=0} \\ 3x=7 \\ x=\frac{7}{3} \\ \text{and for (x+7)=0} \\ x+7=0 \\ x=-7 \end{gathered}[/tex]The value of x is -7 and 7/3
Answer : x = -7 and x = 7/3
Estimate sqrt(37) to the nearest tenth. Then locate sqrt(37) on a number line.137 =(Round to the nearest tenth as needed.)
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The given number is
[tex]\sqrt{37}[/tex]Which is equal to 6,0827625302982196889996842452021...
However, rounded to the nearest tenth is
[tex]\sqrt{37}\approx6.1[/tex]The image below shows the number graphed on a number line.
what is the answer to 389+_=2,897
Answers
Answer:
the answer is 2508
Margaret can fit 17 pencils in a small box and 50 pencils in a large box. She has 10 small boxes of pencils and would like to reorganize the pencils into large boxes. How many large boxes could she fill?
Answers
Answer:
She can fill five boxes with 20 pencils left over.
Step-by-step explanation:
17x10=170
170/50=3.4
50x3=150
170-150=20
give the answer, which of the following are composite numbers? 4 9 15 3 5
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Given
we are given numbers 4, 9, 15, 3, 5
Required
we need to find which of the above numbers are composite.
Explanation
Here
[tex]\begin{gathered} 4=2\times2 \\ 9=3\times3 \\ 15=3\times5 \\ 3=3\times1 \\ 5=5\times1 \end{gathered}[/tex]clearly 4, 9, 15 have factors other than 1 and itself.
so 4, 9 and 15 are composite numbers
What is the solution and working?
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The value of the length AB xcm = -3½ which is derived using the completing the square method, and satisfies the expression 2x² - 5x - 42 = 0.
Completing the square methodTo solve for the unknown value of a quadratic equation; say ax² + bx + c = 0:
First make the coefficient of x² one by dividing through by "a"Move the constant "c" to the right hand side of the equationDivide the coefficient of "x" by 2, square the result and add to both sides of the equation.The left hand side of the equation would have a complete square which will then be easier to solve for the value "x".From the derived quadratic equation, applying the method of completing the square as follows;
2x² - 5x - 42 = 0
divide through by 2
x² - (5/2)x - 21 = 0
add 21 to both sides
x² - (5/2)x = 21
divide the coefficient of x, square the result and add it to both sides
x² - (5/2)x + (5/4)(5/4) = 21 + (5/4)(5/4)
factor the left hand side of the equation
(x - 5/4)² = 21 + (25/16)
simplify the right hand side
(x - 5/4)² = 361/16
take the square root of both sides
x - 5/4 = (+ or -)(19/4)
then;
x = 5/4 + 19/4 or 5/4 - 19/4
x = 3 or x = -3½
The quadratic equation 2x² - 5x - 42 = 0 is true for the value of x = -3½.
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Please see photo I think it is the first answer but I wanted to confirm
Answers
Hello
The sample which she has to study is 200
The answer to this question is option A
A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third
side is 13 feet more than the length of the shortest side. Find the dimensions if the perimeter is 157 feet.
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Answer:
The triangle has sides of 36 feet, 72 feet, and 49 feet.
=====================================================
x = shortest side
2x = second side
x+13 = third side
The three sides add up to the perimeter of 157
(x)+(2x)+(x+13) = 157
4x+13 = 157
4x = 157-13
4x = 144
x = 144/4
x = 36
The shortest side is 36 feet.
The second side is 2x = 2*36 = 72 feet.
The third side is x+13 = 36+13 = 49 feet.
Check:
side1+side2+side3 = 36+72+49 = 157
The answers are confirmed.
write 1.09 × 10^-4 in standard notation
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1.09 × 10^-4 in standard form is
[tex]\text{ 1.09 x 10}^{-4}[/tex]Part A and B answer snd explaintion please
Answers
Answer:
Step-by-step explanation:
63 and 117
I need help with this worksheet that’s due tomorrow for algebra 1 it’s about Characteristics of Quadratic Functions
Answers
We have the following quadratic Function in a graph:
Now, we solve one aspect at a time:
Zeros
Let's remember that the zeros or roots of the quadratic function are those values of x for which the expression is 0. Graphically, the roots correspond to the abscissae of the points where the parabola intersects the x-axis.
By looking at the graph we can identify these, which in this case it is:
[tex](-2,0)[/tex]Axis of symmetry
Recall that the graph of a quadratic function is a parabola. The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola.
By looking at the graph we can identify this, which in this case it is:
[tex]x=-2[/tex]Max or min
In mathematical analysis, the maxima and minima of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range or on the entire domain.
By looking at the graph we can identify this, which in this case it is:
[tex]y=0[/tex]Vertex
Remember that the vertex of a quadratic equation or parabola is the highest or lowest point of the graph corresponding to that function. The vertex lies in the plane of symmetry of the parabola; whatever happens to the left of this point will be an exact reflection of what happens to the right.
By looking at the graph we can identify this, which in this case it is:
[tex](-2,0)[/tex]HELP ME ASAPPP
Mr. Anderson worked with the following number of students each year.
42 in 2023-2024
256 in 2022-2023
195 in 2021-2022
228 in 2020-2021
174 in 2019-2020
136 in 2018-2019
216 in 2017-2018
204 in 2016-2017
151 in 2015-2016
What would we call 42 in this situation?
A.
Mean Absolute Deviation
B.
Mode
C.
Outlier
D.
Range
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Notice how 42 is a much smaller number than 256,195,174, etc? the number that is much bigger or smaller from the other numbers is called an outlier.
Find anequation for the perpendicular bisector of the line segment whose endpoints are(-8, 4) and (-4,-8).
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to solve this question, we need to difine our variables
we have values for end points as
x1 = -8
y1 = 4
x2 = -4
y2 = -8
next we can find the slope of the equation
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{-8-4}{-4-(-8)} \\ \text{slope}=\frac{-12}{4} \\ \text{slope}=-3 \end{gathered}[/tex]step 2
let's find the mid-point using mid-point formula
[tex]\begin{gathered} md=\frac{x_1+x_2}{2},\frac{y_2+y_1}{2} \\ md=\frac{-8+(-4)}{2},\frac{-8+4}{2} \\ md=-6,-2 \end{gathered}[/tex]mid-point = (-6, -2)
now we know the perpendicular line travels (-6 , -2) and has a slope of -3
equation of a straight line => y = mx + c
we can solve for c to find the equation.
[tex]\begin{gathered} y=mx+c \\ -2=(-3)(-6)+c \\ -2=18+c \\ c=-2-18 \\ c=-20 \end{gathered}[/tex]note: m = slope
c = intercept
the equation of the perpendicular bisector can be written as
y = -3x - 20
[tex]y=-3x-20[/tex]In triangle ABC, the segments drawn from the vertices intersect at point G. Segment FG measures 6 cm, and segment FC measures 18 cm. Which best explains whether point G can be the centroid? (are the answers given here right? cos I'm not quite sure)
Answers
A centroid divides each median in a ratio 2:1, in this case, the segment FC is the sum of the segments FG and GC:
[tex]FC=FG+GC[/tex]By solving for GC, we get:
[tex]GC=FC-FG=18-6=12[/tex]Then, the part of the median that goes from C to G has a length of 12 and the part that goes from the centroid to F has a length of 6, then we can express their ratio as 12:6, which is equivalent to 2:1.
Then the answer is:
Point G can be the centroid because 12:6 equals 2:1
The earth's average distance from the sun is 92,960,000 miles. Venus’s distance from the sun is an average of 67,230,000 miles. The Earth is how much farther from the sun than Venus? Express the answer in scientific notation.
Answers
Answer:
[tex]2.573 \times 10^7[/tex]
Step-by-step explanation:
[tex]92960000-67230000=25730000=2.573 \times 10^7[/tex]
a) Rotation, then reflectionb) Reflection, then rotation c) Reflection, then translationd) Rotation, then translation
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The first transformation applied to the pre image is a reflection.
The second transformation applied is a 270° rotation.
It means the right answer is Reflection, then rotation.
Graph the linear function f(x)=4x+1 by plotting points.
To plot points, click on a point on the graph and drag it to the desired location.
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A graph of the linear function (f(x) = 4x + 1) is shown in the image attached below.
What is a graph?A graph is a type of chart that's commonly used for the graphical representation of data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
Generally speaking, the graph of any proportional relationship such as a linear function is characterized by a straight line with the points passing through the origin (0, 0) because as the values on the x-axis increases or decreases, the values on the y-axis increases or decreases simultaneously as shown in the image attached below.
In conclusion, a graph which represents the given linear function shows a proportional relationship between the value of x and y.
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can you please list 1-6 if they are rational irrational integer whole and natural
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1. -14/2 = -7 Integer, Rational
2. √64 = 8 Natural, Whole, Integer, Rational
3. 0 Whole, Integer, Rational
4. π Irrational
5.
[tex]0.\bar{45}[/tex]can be expressed as a fraction, then it's rational
6. 3/8 Rational
What is the answer to this?
Answers
Answer: 4/7
Step-by-step explanation:
There are 7 students with brothers, 4 of which have sisters.
So, the probability is 4/7.
The area of the desert is 25,000 square miles a scale drawing of the desert has a scale drawing 10 square inches. What is the scale of the map?
Answers
The scale of the map is 1 square inches = [tex]10^{13}[/tex] square inches.
Given that:-
Area of the desert = 25,000 square miles
Area of the desert in the map = 10 square inches
We have to find the scale of the map.
We know that,
1 mile = 63360 inches
Hence, conversion of square miles to square inches:-
1 mile * 1 mile = 63360 inches *63360 inches
1 square mile = 4,01,44,89,600 square inches
25,000 square miles = 40144893600*25000 = 10,03,62,24,00,00,000 square inches =[tex]10.036224 *10^{13}[/tex] ≈ [tex]10*10^{13}[/tex] square inches.
Now, we can say that [tex]10*10^{13}[/tex] square inches is scaled to 10 square inches.
Hence, the scale of the map is :-
1 square inches = [tex]10^{13}[/tex] square inches.
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