The given line is,
[tex]y=4x+6[/tex]Here, the slope is, 4 and y intecept is 6.
For x = 4, we have,
[tex]y=4\times4+6=16+6=22[/tex]Therefore, the two points on the graph is, (0, 6) and (4, 22).
Now, for y = 1, we have,
[tex]\begin{gathered} 1=4x+6 \\ 4x=-5 \\ x=-\frac{5}{4} \end{gathered}[/tex]Preform the indicated Operation g(n)=2n^2-4nh(n)=n-1find g(h(1-b))
GIven:
The expressions are given as,
[tex]\begin{gathered} g(n)=-2n^2-4n \\ h(n)=n-1 \end{gathered}[/tex]The objective is to find g(h(-1-b)).
Explanation:
To find h(-1-b):
The value of h(-1-b) can be calculated by replacing the n with (-1-b) in the expression of h(n).
[tex]\begin{gathered} h(n)=n-1 \\ h(-1-b)=-1-b-1 \\ h(-1-b)=-2-b\text{ . . . . . . (1)} \end{gathered}[/tex]To find g(h(-1-b)):
The value of g(h(-1-b)) can be calculated by replacing the n with h(-1-b) in the expression g(n).
[tex]\begin{gathered} g(n)=-2n^2-4n \\ g(h(-1-b))=-2(-2-b)^2-4(-2-b)\text{ . . . . (2)} \end{gathered}[/tex]On further solving the equation (2),
[tex]undefined[/tex]How many possible triangles can be created if measure of angle B equals pi over 6 comma a = 20, and b = 10?
First, we have to find the height using the following equation:
[tex]h\text{ = }b\sin (B)[/tex][tex]h\text{ = 10}\times\sin (\frac{\pi}{6})=5[/tex]We have found the height. If h < b < a, we can have only one triangle. That is the case. So the answer will be 1 triangle.
Graph each line given the slope and y-intercept.Label each one
A)
Equation:
[tex]y=\frac{1}{3}x-3[/tex]B)
Equation:
[tex]y=0.5x+1.5[/tex]C)
Equation:
[tex]y=-2x-5[/tex]D)
Equation:
[tex]y=\frac{3}{2}x+2[/tex]Every rational number is also an integer.TrueorFalse
Every rational number is also an integer.
we have that
The rational numbers include all the integers
so
the answer is trueList the values at which X has a local Minimum or no minimum. What is the local minima, if one exist?
Looking at the graph
we have that
The local minimum is at
x=-4 and x=1The values of the local minimum are
For x=-4 ------> y=-1
For x=1 -----> y=-1
The values of the local minimum are equal to -1determine the type and key parts of the graph of the second equation
ANSWER
[tex]\begin{gathered} \left(h,\:k\right)=\left(0,\:0\right),\:a=3,\:b=6 \\ major\text{ axis;vertical} \\ minoraxis;horizontal \end{gathered}[/tex]EXPLANATION
The second equation;
[tex]\frac{x^2}{9}+\frac{y^2}{36}=1[/tex]It is an Elipse.
Ellipse standard equation;
[tex]\frac{\left(x-h\right)^2}{a^2}+\frac{\left(y-k\right)^2}{b^2}=1[/tex]Rewrite the given equation in the form of the standard equation;
Hence, we have;
[tex]\frac{\left(x-0\right)^2}{3^2}+\frac{\left(y-0\right)^2}{6^2}=1[/tex]Therefore the ellipse properties are;
[tex]\left(h,\:k\right)=\left(0,\:0\right),\:a=3,\:b=6[/tex]Major axis is;
[tex]\begin{gathered} 2a \\ =2\times6=12 \end{gathered}[/tex]Minor axis is;
[tex]\begin{gathered} 2b \\ =2\times3=6 \end{gathered}[/tex]What is the yintercept of O A. (0,0) O B. (0,1) O C. (1,0) OD (9)
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
y-intercept = ?
f(x) = (1/2) ^ x
Step 02:
y-intercept :
x = 0
[tex]\begin{gathered} y\text{ = (}\frac{1}{2})^0=1 \\ \end{gathered}[/tex]The answer is:
y-intercept
(0 , 1)
Find the reference angle for a rotation of 129º.
In order to find a reference angle, we need to find the smallest possible angle formed between the x-axis and the terminal line of the given angle, going either clockwise or counterclockwise.
Since the given angle is 129°, and 90<129<180, it will look something like this:
As we can see, the reference angle will be
[tex]180-129=51[/tex]so it will be 51°.
z divided by 13=28 i need the answers this is hard for me
Answer:
364
Step-by-step explanation:
z/13 = 28
z = 13 x 28
z = 364
Graph the linear function g(x) = -4+7xGraph the linear function G (x equals negative 4 + 7x
Given a function,
[tex]g(x)=-4+7x[/tex]At x = 0,
[tex]g(0)\text{ = -4}[/tex]At g(x) = 0,
[tex]\begin{gathered} -4+7x=0 \\ x=\frac{4}{7} \end{gathered}[/tex]At x= 1,
[tex]g(1)\text{ = 3}[/tex]Therefore, the required graph is,
If there are three black, four white, two blue, and four gray socks in a drawer, what would be the probability of picking a blue sock? Round your answer to the nearest tenth.15.4%25%22%15.38%
The formula for determining probability is expressed as
Probability = number of favorable outcomes/number of total outcomes
number of favorable outcomes = number of blue socks = 2
number of total outcomes = number of all socks = 3 + 4 + 2 + 4 = 13
Thus, the probability of picking a blue sock is
2/13 = 0.1538
Converting to percentage, we would multiply by 100. We have
0.1538 x 100
= 15.38%
A linear function contains the following points.
X
y
What are the slope and y-intercept of this function?
A. The slope is 4.
The y-intercept is (0, -1).
5
B. The slope is.
The y-intercept is (0, -1).
C. The slope is.
The y-intercept is (-1,0).
D. The slope is.
0
-1
The y-intercept is (0, -1).
5
3
The slope will be 4/5.
And, The y - intercept will be (0, - 1)
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The points are,
(0, - 1) and (5, 3)
Now,
Since, The slope of the line passing through the points (x₁ , y₁) and (x₂, y₂) is;
m = (y₂ - y₁) / (x₂ - x₁)
So, The slope of the line passing through the points (0, - 1) and (5, 3) is;
m = (y₂ - y₁) / (x₂ - x₁)
m = (3 - (-1)) / (5 - 0)
m = (3 + 1) / 5
m = 4/5
And, The y - intercept is at x = 0
Thus, The slope will be 4/5.
And, The y - intercept will be (0, - 1)
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Determine the smallest integer value of x in the solution of the following inequality.3x + 4> -18
We have the following inequality:
3x + 4 > -18
Subtracting 4 from both sides we got:
3x > -22
Dividing both sides by 3 we got:
x > -22/3
Since -22/3 is between -7 and -8 and x must be equal or greater than -22/3, the smallest integer value in the solution of the inequality is -7 (note that -8 isn't part of the solution)
what does 1,580÷25=I know the answer, I need to show how I got it.
19.) A.) use the idea of walking and turning around a shape to determine the sum of the exterior angles of the quadrilateral and figured 10.93. In other words, determine e + f + g + h. Measure with a protractor m to check that your formula is correct for this quadrilateral. B.) Will there be a similar formula for the sum of the exterior angles of Pentagon ‘s, hexagons, heptagon ‘s, octagons, and so on? Explain.C.) using your for your formula for the sum of the exterior angles of a quadrilateral, reduce the sum of the interior angles of the quadrilateral.in other words, find a+b+c+d, as pictured in figure 10.93. Explain your reasoning. Measure with a protractor to verify that your formula is correct for this quadrilateral.D.) based on your work, what formula would you expect to be true for the sum of the interior angles of a pentagon? what about for a hexagon? What about for a polygon with 10 sides? Explain briefly
A) To find the external angles of the quadrilateral we will walk around the shape measuring every turn we take. We will start on the A point, rotate clock-wise and move in the direction of point "B", when we get there we will rotate clock-wise again and walk to the direction of point "C". When we do get to the point C we will notice that we rotated 180 degrees in relation to the initial position we had in point A. Moving forwars we will now rotate clockwise and go to the poind D, rotate clock-wise again when we get there, performing all the rotations needed. We will notice that we have the same orientation from the beginning, this means that we rotated 360 degrees. In other words the sum of the external angles of the quadrilateral is 360 degrees.
B) Yes, any regular polygon will have the sum of its external angles equal to 360 degrees.
C) The internal and external angles are suplementary. This means that the sum of these angles must be equal to 180 degrees, therefore:
[tex]\begin{gathered} external\text{ = 180-internal} \\ e+f+g+h=360 \\ (180-a)+(180-b)+(180-c)+(180-d)=360 \\ a+b+c+d=180+180+180+180-360 \\ a+b+c+d=4\cdot180-2\cdot180 \\ a+b+c+d=(4-2)\cdot180 \\ a+b+c+d=2\cdot180=360 \end{gathered}[/tex]Since each external angle is the same as "180 degrees" minus the internal angle that is close to it we can represent the sum of the external angles as 360 degrees and use the mentioned relation to convert them into internal angles. If we isolate them as a sum we will find the value of the sum of the internal angles.
D) If we look at the fith line from the solution above we will notice that the sum of internal angles is represented by "(4-2)*180", the polygon had "4" sides. This means that for one that is 5 sides we should expect that it would be "(5-2)*180" and so on. So the formula is:
[tex]\text{internal = (n-2)}\cdot180[/tex]Where "n" is the number of sides of the polygon.
How to find the inverse of the matrix Question number 19
Okay, here we have this:
We need to find the inverse of the matrix, let's do it:
[tex]\begin{bmatrix}{2} & {4} & {1} \\ {-1} & {1} & {-1} \\ {1} & {4} & {0}\end{bmatrix}[/tex]For that we are going to make the augmented form with the identity matrix and convert the original matrix into the identity:
[tex]\begin{gathered} \begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ -1 & 1 & -1 & | & 0 & 1 & 0 \\ 1 & 4 & 0 & | & 0 & 0 & 1\end{pmatrix} \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & -\frac{1}{2} & | & \frac{1}{2} & 1 & 0 \\ 1 & 4 & 0 & | & 0 & 0 & 1\end{pmatrix}\text{ }R_2\leftarrow R_2+\frac{1}{2}R_1 \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & -\frac{1}{2} & | & \frac{1}{2} & 1 & 0 \\ 0 & 2 & -\frac{1}{2} & | & -\frac{1}{2} & 0 & 1\end{pmatrix}\text{ }R_3\leftarrow R_3-\frac{1}{2}R_1 \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & -\frac{1}{2} & | & \frac{1}{2} & 1 & 0 \\ 0 & 0 & -\frac{1}{6} & | & -\frac{5}{6} & -\frac{2}{3} & 1\end{pmatrix}R_3\leftarrow R_3-2/3R_2 \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & -\frac{1}{2} & | & \frac{1}{2} & 1 & 0 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_3\leftarrow-6R_3 \\ =\begin{pmatrix}2 & 4 & 1 & | & 1 & 0 & 0 \\ 0 & 3 & 0 & | & 3 & 3 & -3 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_2\leftarrow R_2+\frac{1}{2}R_3 \\ =\begin{pmatrix}2 & 4 & 0 & | & -4 & -4 & 6 \\ 0 & 3 & 0 & | & 3 & 3 & -3 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_1\leftarrow R_1-R_3 \\ =\begin{pmatrix}2 & 4 & 0 & | & -4 & -4 & 6 \\ 0 & 1 & 0 & | & 1 & 1 & -1 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_2\leftarrow\frac{1}{3}R_2 \\ =\begin{pmatrix}2 & 0 & 0 & | & -8 & -8 & 10 \\ 0 & 1 & 0 & | & 1 & 1 & -1 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_1\leftarrow R_1-4R_2 \\ =\begin{pmatrix}1 & 0 & 0 & | & -4 & -4 & 5 \\ 0 & 1 & 0 & | & 1 & 1 & -1 \\ 0 & 0 & 1 & | & 5 & 4 & -6\end{pmatrix}R_1\leftarrow\frac{1}{2}R_1 \end{gathered}[/tex]Finally the inverse is on the right side of the augmented matrix:
[tex]=\begin{pmatrix}-4 & -4 & 5 \\ 1 & 1 & -1 \\ 5 & 4 & -6\end{pmatrix}[/tex]what is 1 plus 1?help me
Answer:
it's 2
Step-by-step explanation:
don't forget to follow rate like
hXL for School: Practice & Problem Solving 5.2.PS-19 Question Help Equivalent ratios can be found by extending pairs of rows or columns in a multiplication table. Write 3 3 ratios equivalent to using the multiplication table. 5 Click the icon to view the multiplication table. 3 Find three ratios that are equivalent to 5 12 6 4 IA. B. OC. 20 10 6 15 15 9 OD OE. F. 9 30 15 Click to select your answer(s) and then click Check Answer. All parts showing Clear All Check Answer Review progress Question 7 of 12 Back Next >
To find equivalent ratios to 3/5, we just have to multiply each part by 4, 2, and 3.
[tex]\begin{gathered} \frac{3\cdot4}{5\cdot4}=\frac{12}{20} \\ \frac{3\cdot2}{5\cdot2}=\frac{6}{10} \\ \frac{3\cdot3}{5\cdot3}=\frac{9}{15} \end{gathered}[/tex]Hence, the right answers are A, B, and F.What is the answer
(3t/t^5)^-5
The resultant answer of the given expression (3t/t⁵)⁻⁵ is t²⁰/243.
What exactly are expressions?A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.To evaluate an algebraic expression, you must substitute a number for each variable and perform the arithmetic operations.The previous example's variable x is equivalent to 6 because 6 plus 6 = 12.If we know the values of our variables, we can replace the original variables with those values before evaluating the expression.So, solve the expression as follows: (3t/t^5)^-5
Apply exponent rule:
(3t/t^5)^-51/((3t/t^5)^5)Simplify as shown:
(3t/t^5)^5: 243/t²⁰1/243/t²⁰Apply function rule:
t²⁰/243Therefore, the resultant answer of the given expression (3t/t⁵)⁻⁵ is t²⁰/243.
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In the image below ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯∥⎯⎯⎯⎯⎯⎯⎯⎯⎯LM¯∥OP¯. Given the lines are parallel, ∠≅∠∠LMN≅∠PON because and that ∠≅∠∠LNM≅∠ONP by the , you can conclude the triangles are similar by the AA Similarity Theorem. If NP = 20, MN = x+ 6, NO = 15, and LN = 2x - 3 then x = .
Given:
Required:
We need to answer the questions
Explanation:
Angle LMN and angle PON are the congruent because both are alternate angles
Now angle LNM and angle ONP are also congruent because those two triamgles are similar and both are internal angles
Now to find the value of x
[tex]\begin{gathered} \frac{NP}{MN}=\frac{NO}{LN} \\ \\ \frac{20}{x+6}=\frac{15}{2x-3} \\ \\ 40x-60=15x+90 \\ 25x=150 \\ x=6 \end{gathered}[/tex]Final answer:
x=6
The graph shows a relationship between two quantities.ДУ200018001600140012001000800600400200ХOd-8 -6 4-2 0 2 4Which equation best represents the relationship between the variables?
First let't find the slope
Pick any two point and locate its coordinate
(0, 1500) and (2, 1800)
x₁ = 0 y₁=1500 x₂=2 y₂=1800
substitute the values into the formula below to find the slope
[tex]\text{slope(m)}=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]=\frac{1800-1500}{2-0}[/tex][tex]=\frac{300}{2}=150[/tex]The y-intercept(b) of the graph is b=1500
Substitute the values of the slope and intercept into y=mx +b
This gives the equation of the graph.
That is:
[tex]y=150x\text{ + 1500}[/tex]How do you figure out what the order pairs are in this equation? 2x-2=y
Equations express relationships between variables and constants. The solutions to two-variable equations consist of two values, known as ordered pairs, and written as (a, b) where "a" and "b" are real-number constants. An equation can have an infinite number of ordered pairs that make the original equation true.
Here, the given equation is,
[tex]2x-2=y[/tex]Rewriting this equation in terms of x, we have,
[tex]\begin{gathered} 2x-2=y \\ 2x=y+2 \\ x=\frac{y+2}{2} \end{gathered}[/tex]So, now creating a table, with the values, we get the ordered pair. For example, let us take x as 1, then ,
[tex]\begin{gathered} 1=\frac{y+2}{2} \\ 2=y+2 \\ y=0 \end{gathered}[/tex]So, (1,0) is an ordered pair in this equation.
If x =0,
[tex]y=0-2=-2[/tex]So the pair is, (0,-2).
1) The expression 5p represents the total price of buying 5 movie tickets. • What do the parts of the expression 5p represent? ) The variable p represents the ticket price The number 5 represents the number of tickets Today there is a discount of $10 off a purchase of 5 or more movie tickets. Which expression can you use to find the total price of 5 movie tickets after the discount? 10p + 5 5p - 10 10p - 5 5p + 10
Solution
The expression 5p represents the total price of buying 5 movie tickets. • What do the parts of the expression 5p represent?
The variable p represents the ticket price The number 5 represents the number of tickets
For this case the correct answer would be:
5p -10
The coefficient 5 represents the price of 1 ticket
for the next part the answer would be:
7 +3x
And the last part
2/3 y -6
Tools - Question 4 The coordinate planle below shows the location of segment QR. 109Y 5 Q1-4,3) 70-9-8-7-6-5-4-3-3 2 3 4 5 6 7 8 9 TU R(8,-6) What is the unit distance between the two endpoints of the segment? Illuminate Education TM, Inc.
Apply the distance between 2 points formula:
[tex]D=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]We have the points:
(x1,y1) = (-4,3)
(x2,y2) = (8,-6)
[tex]D=\sqrt[]{(8-(-4))^2+(-6-3)^2}=\sqrt[]{(8+4)^2+(-9)^2}=\sqrt[]{144+81}=\sqrt[]{225}=15[/tex]Distance = 15
Write down the expansion of (2x+y)^4
Use the following formula:
[tex](a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4[/tex]Let:
[tex]\begin{gathered} a=2x \\ b=y \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} (2x+y)^4=(2x)^4+4(2x)^3y+6(2x)^2y^2+4(2x)y^3+y^4 \\ (2x+y)^4=16x^4+32x^3y+24x^2y^2+8xy^3+y^4 \end{gathered}[/tex]What is the approximate percentage of huskies that weigh less than Jason's dog
step 1
Find the z-score
z=(49-52)/7
z=-0.43
using the tables
P=33.36%
therefore
answer is 33%Put the following equation of a line into slope-intercept form, simplifying all
fractions.
12y-2x = 108
Answer: y= x/6+9
Step-by-step explanation:
need to show 1,242 ÷ 23 = and 732 x 268 = show answers on graph
1,242 ÷ 23 = 54
and
732 x 268 = 196, 176
Which quadrant includes every points with a negative x-coordinate and a negative y-coordinateA) Quadrant IVB) Quadrant IC) Quadrant IID) Quadrant III
Hello!
Let's analyze the points from each quadrant:
Quadrant I:
x > 0 and y > 0
Quadrant II:
x < 0 and y > 0
Quadrant III:
x < 0 and y < 0
Quadrant IV:
x > 0 and y < 0
So, the answer is:
Alternative D) Quadrant III.
between 1993 and 1996 there where 6545 injured horses find the ratio of injuries per year
First, we have to know the total number of years between 1993 and 1996. If we subtract, we find the there are 3 years in between.
Now, we divide the total number of injured horses by the total numbers of years.
[tex]r=\frac{6545}{3}=2,181.7[/tex]However, we can't round to 2,182 because horses are not incomplete.
Therefore, the total number of injured horses per year is 2,181.