a)The x co-ordinates of P and Q satisfy the equation x² + 4x - 5 = 0.
b)The co-ordinates of P and Q are (-5, -1) and Q = (1, 5).
What is defined as the equation of the circle?(x-h)² + (y-k)² = r² is the equation for a circle with (h, k) center and r radius. This is the equation's standard form. Thereby, if we recognise the coordinates of the circle's center and radius, we can usually find its equation.The given equation of the circle is;
x² + y² = 26.
Th circle satisfies the line y = x + 4.
Thus, Put the value of y in the main equation.
x² + (x + 4)² = 26.
Simplify the equation;
x² + x² + 16 + 8x = 26
2x² + 8x - 10 = 0
Divide the equation by 2.
x² + 4x - 5 = 0
Part a: This shows that x co-ordinates of P and Q satisfy the equation x² + 4x - 5 = 0.
Part b: Now, do the factorization of x² + 4x - 5 = 0.
(x + 5)(x - 1) = 0
x = -5 and 1.
For x = -5; y = -1
Point P = (-5, -1)
For x = 1; y = 5
Point Q = (1, 5)
Thus, the requires points P and Q are obtained.
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Solve 4∣x+5∣=24
A.x = –11 and x = –1
B.x = 11 and x = –1
C.x = –11 and x = 1
D.x = 11 and x = –11
Step-by-step explanation:
You first need to get the absolute vaule of x+5 by its self. So you need to divide 4 on yet sides
[tex] |x + 5| = 6[/tex]
Then set up two equations a negative and a postive on
[tex] |x + 5| = 6[/tex]
x=1
[tex] |x + 5| = - 6[/tex]
x=-11
Hope that helped!
Feel free to ask questions!
4. Technology required. Priya starts with $50 in her bank account. She then deposits $20
each week for 12 weeks.
a. Write an equation that represents the relationship between the dollar amount
in her bank account and the number of weeks of saving.
d=50+20w
b. Graph your equation using graphing technology. Mark the point on the graph
that represents the amount after 3 weeks.
The equation [tex]d=50+20w[/tex] represents the relationship between dollar amount in her bank account and the number of weeks of savings.
The definition of an equation is a formula that states that two formulas are equal. For example, 3x + 5 = 14 is an equation where 3x + 5 and 14 are two terms separated by an equal sign. The most basic and simple algebraic equations consist of one or more variables in mathematics. In mathematics, a graph can be defined as a graphical representation or chart that systematically represents data or values. A point on a graph often represents a relationship between two or more things.
(a) It is given that amount in bank account is $50 , amount deposited by Priya is $20 and time period is 12 weeks .
Let " d " be the dollar and " w " be the weeks
Multiply the number of weeks w by 20 to get the total savings and add up how much money she had in the account initially.
Money deposit by Priya in 1 week = $20
Money deposit by Priya in 1 week = [tex]20\times w[/tex]
Therefore , the equation will be [tex]d=50+20w[/tex]
(b) Graph of given equation is given below :
Let " w " represents the x - axis and " d " represents the y - axis
For 1 week , amount will be [tex]d=50+20=60[/tex]
For 2 week , amount will be [tex]d=50+20(2)=90[/tex]
For 3 week , amount will be [tex]d=50+20(3) = 110[/tex]
And so on..
From the graph ,the point which represents the amount after 3 weeks is
(3 , 110 )
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Math question on how to evaluate f(5)
The value of f(5) in the function are - 9 . Option B
What is function?A function can be defined as an expression, rule or law that shows the relationship between a dependent variable or independent variable.
Given the functions;
f(x) = 3x - 1 (1)f(x) = 1 - 2x (2)To determine the value f(5), substitute the value of x as 5
x > 1 , so we use equation 2
From function (2)
f(5) = 1 - 2x
f(5) = 1 - 2(5)
f(5) = 1 - 10
f(5) = - 9
Thus, the value of f(5) in the function are - 9 . Option B
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A walking tour of Washington, D.C., costs $20 per person. Show that the relationship between the number of people in a tour group and the total cost is a proportional relationship. Write an equation for the relationship.
The Total cost for a tour group consisting of n number of people is 20n
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let T represent the total cost if a tour group consisting of n people
Since A walking tour of Washington, D.C., costs $20 per person. Hence, for n number of people:
Total cost = $20 per person * n persons = 20n
The Total cost for a tour group consisting of n number of people is 20n
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HELP PLS THIS MATH ADD AND SUBTRACT FRACTION I DING GET BC I FORGET EVERYTHING I LEARN FROM PAST YEARS
Answer: 1. 35 5/6 - 4 1/2
2. 1 5/8 - 2/3
3. 1 5/8 + 2/3
4. 35 5/6+4 1/2
Step-by-step explanation:
1. E=Eli. J=Jamison
E=J+4 1/2
35 5/6=J+4 1/2
J=35 5/6 - 4 1/2
2. s=cups of strawberries
b=cups of blueberries
m=more cups of b than s
m=b-s
m=1 5/8 - 2/3
3. o=original length of patio.
i=increase in length of patio
t=total length of patio after increase.
o+i=t
1 5/8 + 2/3=t
4. p=pine tree. a=palm tree. i=inches taller
p+i=a
35 5/6+4 1/2=a
According to Descartes's rule of sign, how many possible positive and negative roots are there for the equation 0=−8x10−2x7+8x4−4x2−1?
Drag the choices to the boxes to correctly complete the table.
According to Descartes' rule of sign,
a. We have 0 or 2 real positive roots for the equation and
b. We have 0 or 2 real negative roots for the equation.
What is Descartes'rule of sign?Descartes' rule of sign states that
The number of real positive zero of a polynomial f(x) is the number of sign changes of the coefficients of f(x) or an even number less than the number of sign changes of the coefficients of f(x)The number of real negative zero of a polynomial f(x) is the number of sign changes of the coefficients of f(-x) or an even number less than the number of sign changes of the coefficients of f(-x)How to find the number of possible positive and negative roots are there for the equation?Since we have the equation 0 = −8x¹⁰ − 2x⁷ + 8x⁴ − 4x² − 1, we now re-write it as a polynomial function. So, it is now f(x) = −8x¹⁰ − 2x⁷ + 8x⁴ − 4x² − 1
a. What are the number of positive rootsTo find the number of positive roots, we require the number of sign changes of the polynomial f(x).
Thus, f(x) = −8x¹⁰ − 2x⁷ + 8x⁴ − 4x² − 1
Thus, the coefficients of f(x) are -8, -2, + 8, -4, -1, and we see that there are two sign changes from -2 to + 8 and from + 8 to -4.
Thus, there are 2 or 2 - 2 = 0 real positive roots.
Thus, we have 0 or 2 real positive roots for the equation.
b. What are the number of negative rootsTo find the number of negative roots, we thus need to find the number of sign changes of the polynomial f(-x).
Thus, f(-x) = −8(-x)¹⁰ − 2(-x)⁷ + 8(-x)⁴ − 4(-x)² − 1
= −8x¹⁰ + 2x⁷ + 8x⁴ − 4x² − 1
Thus, the coefficients of f-(x) are -8, +2, + 8, -4, -1. We see that there are two sign changes from -8 to + 2 and from + 8 to -4.
Thus, there are 2 or 2 - 2 = 0 real negative roots.
Thus, there are 0 or 2 real negative roots for the equation.
Thus,
We have 0 or 2 real positive roots for the equation andWe have are 0 or 2 real negative roots for the equation.Learn more about Descartes' rule of sign here:
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Alessa had 50 in her account. she then received four $-25 charges to her account. what is the new balance of her account?
The width of a rectangle is the length minus 5 units. The area of the rectangle is 24
units. What is the length, in units, of the rectangle?
Answer:
L = 8
w = 3
Step-by-step explanation:
Givens
w = L - 5
L = x
Area = 24
Formula
Area = L * w
Solution
Area = (x) * (x - 5)
24 = x * (x - 5) Remove the brackets
24 = x^2 - 5x Subtract 24 from both sides
0 = x^2 - 5x - 24 This will factor
0 = (x - 8)(x + 3)
x + 3 is an extraneous root. You cannot have a length of -3 units no matter what the units are.
x - 8 = 0
x = 8
Answer
The length = 8
The width is = 8 - 5 = 3
call a set of integers spacy if it contains no more than one out of any three consecutive integers. how many subsets of , including the empty set, are spacy?
According to the given statement, there are 129 spacy subsets of, such as the empty set.
The correct option is E.
What is consecutive integers?Whole numbers that followed each other with no gaps are known as consecutive integers. For example, the numbers 15, 16, and 17 are all consecutive integers. If is an integer, then the following consecutive integers begin at:,, and so on.
According to the given data:A divider counting argument can be employed because each member of the subgroups must be at least two apart.
We select no more than four numbers first from set 1,2,3,4,5,6,7,8,9,10,11,12. Let's use balls to represent these numbers. There are least two dividers between each of the balls.
So for example, o | | o | | o | | o | | represents {1,4,7,10}.
There must be 2(k - 1) dividers between both the balls in subsets of size k, leaving 12 - k - 2(k - 1) = 12 - 3k + 2 dividers to be placed at k + 1 spots between the balls.
[tex]\left(\begin{array}{c}(12-3 k+2)+(k+1)-1 \\k\end{array}\right)=\left(\begin{array}{c}12-2 k+2 \\k\end{array}\right)[/tex]
As a result, the number of spacy subsets is reduced:
[tex]\left(\begin{array}{l}6 \\4\end{array}\right)+\left(\begin{array}{l}8 \\3\end{array}\right)+\left(\begin{array}{c}10 \\2\end{array}\right)+\left(\begin{array}{c}12 \\1\end{array}\right)+\left(\begin{array}{c}14 \\0\end{array}\right)[/tex] = 129
According to the given statement, there are 129 spacy subsets of, such as the empty set.
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I understand that the question you are looking for is:
Call a set of integers spacy if it contains no more than one out of any three consecutive integers. How many subsets of $\{1,2,3,\ldots,12\},$ including the empty set, are spacy?
(A).121
(B). 123
(C). 125
(D). 127
(E) 129
If n+ 2 is divisible by 2 then which statement is always True?
A- n is an even number
B - n is an odd number
C- n is a prime number
D- b is equal to n + 1.
Answer:
the right answer is A
Step-by-step explanation:
the even number can be always divided by 1,2 and themselves
In a rotation pairs of corresponding points are on parallel lines true or false
In a rotation, parallel lines connect pairs of corresponding spots. If the two lines are parallel, corresponding angles are congruent. Corresponding pairs are all angles that are positioned in relation to the parallel and transversal lines in the same way.
What do you mean by correlating angles?Any pair of angles that is both on the same side of the transversal and on one of the two lines that it cuts.
Congruent is what?When two figures or objects in geometry have the same shapes, sizes, or are mirror images of one another, they are said to be congruent.
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Evaluate v-w for the given values. v = -14; w = 7
Answer:
I believe the answer would be :
-14 - 7 = -21
Answer = -21
In order to calculate the market basket used for the cpi, what information is needed
Market pricing and the goods and services purchased by the average household must be taken into account in order to compute the market basket utilized for the cpi.
The cpi formula is Market Price in the current year / Base year x 100.
What is meant by price market?
The rate at which a product or service can potentially be bought or sold is known as the market price. The supply and demand forces determine the market price of a good or service; the price at which the quantity supplied and demanded are equal is the market price.Market price is the price that is in effect on a specific day or at a specific moment. It is the outcome of supply and demand in the market. The normal price, on the other hand, is the outcome of long-term supply and demand.To learn more about Market price, visit:
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Please help it would be very much helpul
x = 12.
Perpendicular lines are lines that intersect at a 90-degree angle. So, for example, line ST is perpendicular to line CD. So line ST is perpendicular to line CD.
Perpendicular lines always intersect each other, however, all intersecting lines are not always perpendicular to each other. The two main properties of perpendicular lines are: Perpendicular lines always meet or intersect each other. The angle between any two perpendicular lines is always equal to 90.
Given that
line m and n are perpendiculars
then angle ∠a = ∠b
then
5x + 20 = 7x -4
7x -5x = 20 + 4
2x = 24
x = 24/ 2
x = 12.
Hence the value of x = 12
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____ is the vertical distance between two or more lines or surfaces (part features) that are in horizontal planes.
Height is the vertical distance between two or more lines or surfaces (part features) that are in horizontal planes.
What are horizontal planes?Horizontal plane can as well be described as the plane or surface that can be seen as the one that is parallel to the surface of the earth, , it should be noted that this plane is usually at the at an angle of zero degree hence horizontal plane.
Therefore, the plane is perpendicular to the horizontal plane , hence Height is the vertical distance between two or more lines or surfaces (part features) that are in horizontal planes.
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G
H
OI and M
OJ and L
OH and N
OG and O
-6
-5
264
K
-3
1Which two points are 4 units from K?
L
-2
3
-1
N
0
For the following problem, match the name of the number property that was used to get to each step from the previous step.
37x2x(-5+1/2+5)
Answer:
74
Step-by-step explanation:
Multiplication
37×2=74
Brackets
Addition
1/2+5=6
Subtraction
6-5=1
The whole question will read as 74x1
The answer will be 74
Select the correct answer.
Consider figures 1 and 2 shown in the coordinate plane. Figure 1 has been transformed to produce figure 2.
-00
55-
N
2
N
ON
6
80
Which notation describes this transformation?
OA. (x,y) = (x,-)
OB. (x,y)=(x-4,y - 8)
OC. (x,y) = (x - 8,y - 8)
OD. (x,y)= (-2,-y)
9.
8.
Using translation concepts, the notation that describes this transformation is:
C. (x,y) -> (x - 8, y - 8).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
To generate figure 2 from figure 1, these following translations happened:
8 units left, hence x -> x - 8.8 units down, hence y -> y - 8.Thus the rule is given by:
C. (x,y) -> (x - 8, y - 8).
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Answer: (x',y') = (x - 4,y - 8)
Step-by-step explanation:
I’d really appreciate any kind of help :)
Answer: it is B
Step-by-step explanation: i would love to help
Need help on this problem
The given equation solved for z is z = s/(r - 6c⁴)
Solving linear equationsFrom the questions, we are to solve the given equation for the specified value
The given equation is
s = zr - 6zc⁴
The specified value is z.
Thus, we are to solve for z.
Solving for z
s = zr - 6zc⁴
First, factor out z
s = z(r - 6c⁴)
Now, divide both sides by r - 6c⁴
s/(r - 6c⁴) = z(r - 6c⁴)/r - 6c⁴
s/(r - 6c⁴) = z
∴ z = s/(r - 6c⁴)
Hence, the given equation solved for z is z = s/(r - 6c⁴)
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28. Use the properties of the mean and median to determine which
are the correct mean and median for the following histogram.
(i) Mean is 3.6; median is 4.8
(ii) Mean is 4.8; median is 3.6
(iii) Mean is 3.5; median is 3.1
(iv) Mean is 4.2; median is 4.1
The properties of the mean and median to determine which
are the correct mean and median for the following histogram. The answer is Mean is 3.5; median is 3.1.
Mean
[tex]\mu=& \varepsilon x \cdot P(x)[/tex]
= 0(0.04)+1(0.08)+2(0.125)+3(0.24) +4(0.15)+5(0.14)+6(0.12)+7(0.05)
= 0+0.08+0.25+0.72+0.6+0.7+0.72+0.35
= 3.42 [Approx: 3.5]
Mean =3.5 of median 3.1.
A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When a data collection is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data collection is called the mode.
The median is computed by sorting the scores into numerical order, dividing the total by 2, rounding the result up if the number of scores is odd to determine the median position, or by averaging the median position and the position after it, if the number of scores is even.
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PLS HELP Precalculus Unit 3 sample work for Connexus I got the rest of it figured out, it's these two that I'm having trouble with.
The asymptotes of the graph are vertical asymptotes as; x = 0 and x = -4
The end behavior of the second graph is that as x → ∞, f(x) → -∞ and x → -∞, f(x) → -∞
What is the Asymptote of the graph?An asymptote is defined as a line that a curve approaches, as it heads towards infinity. There are three types of Asymptotes namely horizontal, vertical and oblique.
It is called a Horizontal Asymptote when as x goes to positive or negative infinity the curve approaches some constant value.
It is called a Vertical Asymptote when as x approaches some constant value (from the left or right) then the curve goes towards positive or negative infinity
It is called an Oblique Asymptote when as x goes to positive or negative infinity, then the curve goes towards a line y = mx + b
Thus, the asymptotes of the graph are vertical asymptotes as;
x = 0 and x = -4
The end behavior of the second graph is that as x → ∞, f(x) → -∞ and x → -∞, f(x) → -∞
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Describe how you would graph the inequality x ≥−13
Pls help me
You are 5 feet 4 inches tall and cast a shadow 3 feet long. At the same time, a nearby water tower casts a shadow 74 feet 3 inches long.
a. Find the height of the water tower.
The height of the water tower is 132 feet
How to solve for the height of the towerWe have the height to be 5 feet 4 inches
then 1 feet = 12 inches
inch = 1 / 12 ft
Then 4 inches = 1 / 12 x 4
= 1 / 3 ft
Height = 5 1/3
= 16 / 3
height of the shadow cast = 3 feet
For the water tank
74 ft 3 inches
= 74 x 3 / 12
297 / 4
the height of the tower
[tex]\frac{height of person}{height of shadow} =\frac{height of tower}{height of person}[/tex]
= [tex]\frac{16/3}{3} =\frac{x}{297/4} \\\\\frac{16}{3*3} =\frac{4x}{297}[/tex]
Then x = 132
Therefore the height of the water tower is 132 feet
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what is -14/64 as a decimal ?
Hi ~
︵‿︵‿︵‿︵︵‿︵‿︵‿︵︵‿︵‿︵‿︵︵‿︵‿︵‿︵︵‿︵‿︵
-14/64
⚜ E x p l a n t i o n : -Divide the numbers: [tex]\bold{14}[/tex] ÷ [tex]\bold{64 = 0.21875}[/tex]
[tex]\bold{= -0.21875}[/tex]
Hope It Helps...
[tex]\textsc{A \: n \: s \: w \: e \: r:}[/tex]
TheAestheticGirl
n a triangle, the ratio of the measures of the sides is 2: 2: 3 and the perimeter is 392 inches. Find the length of the longest side of the triangle.
Answer:
168 inches
Step-by-step explanation:
what is the slope y intercept and equation?
Answer:
Below in bold.
Step-by-step explanation:
Slope = difference in y values / difference is x values
= (1 - (-3)) / (0 - (-1)
= 4 / 1
= 4.
The y-intercept is the y value when x = 0, so it is
= 1.
So, the equation is
y = 4x + 1.
what is the volume of this pyramid? 720 cm³ 720 cm³ 1080 cm³ 1080 cm³ 1440 cm³ 1440 cm³ 2160 cm³ 2160 cm³ a pyramid with a right triangular base. the right triangular base has leg lengths of 9 centimeters and 15 centimeters. the height of the pyramid is 32 centimeters.
Based on the calculations, the volume of this pyramid is equal to 1440 cm³.
Given the following data:
Length of right triangular base = 9 centimeters and 15 centimeters.
Height of right triangular base = 32 centimeters.
How to calculate the volume of a pyramid?Mathematically, the volume of a pyramid can be calculated by using this formula:
Volume = 1/3 × b × h
Where:
h is the height of a pyramid.
b is the base area of a pyramid.
Substituting the parameters into the formula, we have:
Volume = 1/3 × 9 × 15 × 32
Volume = 3 × 15 × 32
Volume of pyramid = 1440 cm³.
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-1/4 x-6 =2 what is x equal to
Answer:
x=−32Step-by-step explanation:
−1/4x−6=2
Add 6 to both sides:−1/4x−6+6=2+6
−1/4x=8
Multiply both sides by 4/(-1):(4−1)*(−14x)=(4−1)*(8)
x=−32
Answer: x=−32
−1/4x−6=2
Add 6 to both sides:
−1/4x−6+6=2+6
−1/4x=8
Multiply both sides by 4/(-1):
(4−1)*(−14x)=(4−1)*(8)
x=−32
Step-by-step explanation: hope this helps!!!
The image represents what geometric construction?
A Parallel Lines Construction
B Copy an Angle Construction
C Angle Bisector Construction
D Perpendicular Bisector Construction