The solution of the system of equation is (3, 5) and (–4, 12) [option A]
The given system of equations is:
x + y = 8
y = x² – 4
To solve for x and y, we can substitute the second equation into the first equation for y:
x + (x² - 4) = 8
Simplifying, we get:
x² + x - 12 = 0
Now we can use the quadratic formula to solve for x:
x = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = 1, and c = -12
x = (-1 ± √(1² - 4(1)(-12))) / 2(1)
x = (-1 ± √(1 + 48)) / 2
x = (-1 ± 7) / 2
Solving for x gives us two possible values: x = 3 or x = -4.
To find the corresponding values of y for each value of x, we can substitute them into either of the original equations. Using y = x² - 4:
When x = 3, y = 3² - 4 = 5
When x = -4, y = (-4)² - 4 = 12
Therefore, the solution to the system of equations is (3, 5) and (-4, 12), which is answer choice (a).
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Which expression does not have the same value as −2+3×6/5
a (2 * 9 + 14) / 10
b (5 * 8 - 8) / 10
c (5 * 4 + 12) / 10
d is 5 * 8 / 10 - 8
What is the value of the first term in the
sequence below?
Rule:
Start at ?
Add 3 then divide by 2 each time
5
3.5-
4 -3.5
The first term in the given sequence is 5
How to determine the first term in the sequenceFrom the question, we have the following parameters that can be used in our computation:
Rule:
Start at 5Add 3 then divide by 2 each timeThe sequence starting at 5 and following the given rule is:
5(5+3)/2 = 4, (4+3)/2 = 3.5, (3.5+3)/2 = 3.25, (3.25+3)/2 = 3.125, ...The first term in the sequence is simply the starting number, which is 5.
Hence, the value of the first term in the sequence is 5.
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Sleight #1 and Sleigh #2 headed in the opposite directions. If sleight #1 traveled at a speed of 20 mph and sleight #2 traveled at a speed of 45 mph, how many hours was it before they were 390 miles apart?
it takes 6 hοurs fοr the sleighs tο be 390 miles apart.
What are Distance and velοcity ?velοcity is a unit οf measurement fοr the Distance an οbject travels in a
the predetermined periοd οf time. Here is a wοrd equatiοn that illustrates the cοnnectiοn between space, speed, and time: velοcity is calculated by
dividing the tοtal Distance traveled by the jοurney time.
Since the sleighs are traveling in οppοsite directiοns, their distances frοm each οther are increasing at a cοmbined rate οf 20 mph + 45 mph = 65 mph. We can use the fοrmula:
distance = rate x time
Let's call the time it takes fοr the sleighs tο be 390 miles apart "t". Then we can write:
390 = 65t
Sοlving fοr "t", we can divide bοth sides by 65:
t = 6
Therefοre, it takes 6 hοurs fοr the sleighs tο be 390 miles apart.
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Which statements must be true? Check all that apply.
A'A = C'C
C'Q = QC
Line P T⊥ A'A
C'C ⊥ B'B
A'A || B'B
m∠TRB = 90°
The true statements based on the shape in the given image are:
C'Q = QCLine P T⊥ A'AA'A || B'Bm∠TRB = 90°What is the Reflection of Triangles?The result of flipping a triangle on a coordinate system based on a line of reflection is a figure known as a triangle reflection.
Let's say we wish to mirror the triangle A B C over the -axis or the line. The image that results from reflecting the triangle, if A B C is the pre-image, is A ′ B ′ C ′. When using triangle reflections, the final image will keep the triangle's shape.
With this explanation in mind and from the image provided, C'Q = QC because they are parallel to each other.
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Write a system of equations to represent the number of each type of basket Jake scored. Explain your thinking.
The system of equations that represents the number of each type of basket Jake scored is given by:
x + y = 13
2x + 3y = 28
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Number of 2-point shots.
Variable y: Number of 3-point shots.
Jake scored 28 points in his basketball game by shooting only 2-point and 3-point shots, hence:
2x + 3y = 28.
He scored a total of 13 baskets, hence:
x + y = 13.
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The computer lab at school has a new computer system. The system had a total cost of $1895. There is a special printer that can be added to the system. The printer can be purchased separately for $649. Write an equation and solve to determine the cost of the system with the printer.
Answer:
meaning the computer is $1246
Step-by-step explanation:
$1895-$649=$1246
solve x+8=3x wefsdf eferc4frtvtgervgbeg4t
Answer:
x = 4
Step-by-step explanation:
x + 8 = 3x
8 = 2x
x = 4
So, the answer is x = 4
Five friends went to an amusement park. The group wanted to calculate the total cost, so Kathie wrote the expression 5x + 70. Each of her friends wrote expressions, too.
Determine which friends' expressions are equivalent to Kathie's. Show or explain your reasoning.
Kathie: 5x+70
Stephanie: 3(x+30)+2x−20
Jon: 3x+30+2x−20
Mary: 5(x+14)
Nicole: 3(x+30−20)+2x
Answer:
Stephanie Mary and Nicole
Step-by-step explanation:
Which drawing shows two rays whit the same endpoint?
Two rays with the same endpoint would form an angle, where the common endpoint is the vertex of the angle.
A ray is a part of a line that has a fixed starting point, called the endpoint, and extends infinitely in one direction. Thus, a ray can be thought of as a half-line. If two rays have the same endpoint, they will form an angle. The common endpoint is the vertex of the angle, and the two rays extend outward from the vertex in opposite directions, forming a straight line on one side of the vertex. In mathematical notation, the angle formed by two rays with the same endpoint A can be denoted as ∠BAC, where B and C are the points where the rays extend outwards. Note that the order in which the rays are written matters; ∠BAC and ∠CAB represent different angles.
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Please Help me
QUESTION 9
x
0246
8
10
12
24
14
*****
y
9
9
10
11
11
12
13
13
I
[1.5 darks] Given the (x, y)-data as shown in Table below
Find the best line model for the data
and find the correlation coefficient r.
Solution. Please write your
detailed solution here, You can
also put some needed information
in the Table above:
Answer:
To find the best line model for the data, we will use linear regression analysis.
First, we need to calculate the mean of x and y:
mean of x = (0 + 2 + 4 + 6 + 8 + 10 + 12 + 24 + 14) / 9 = 8
mean of y = (9 + 9 + 10 + 11 + 11 + 12 + 13 + 13 + 14) / 9 = 11
Next, we need to calculate the deviations of x and y from their respective means:
deviation of x = x - mean of x
deviation of y = y - mean of y
x y deviation of x deviation of y (deviation of x)^2 deviation of x * deviation of y
0 9 -8 -2 64 16
2 9 -6 -2 36 12
4 10 -4 -1 16 4
6 11 -2 0 4 0
8 11 0 0 0 0
10 12 2 1 4 2
12 13 4 2 16 8
24 13 16 2 256 32
14 14 6 3 36 18
Then, we can calculate the slope (b) of the best-fit line using the formula:
b = sum of (deviation of x * deviation of y) / sum of (deviation of x)^2
b = (16 + 12 + 4 + 0 + 0 + 2 + 8 + 32 + 18) / (64 + 36 + 16 + 4 + 0 + 4 + 16 + 256 + 36) = 0.190
Next, we can calculate the y-intercept (a) of the best-fit line using the formula:
a = mean of y - b * mean of x
a = 11 - 0.190 * 8 = 7.48
Therefore, the equation of the best-fit line is:
y = 0.190x + 7.48
Finally, we can calculate the correlation coefficient (r) using the formula:
r = sum of (deviation of x * deviation of y) / (sqrt(sum of (deviation of x)^2) * sqrt(sum of (deviation of y)^2))
r = (16 + 12 + 4 + 0 + 0 + 2 + 8 + 32 + 18) / (sqrt(64 + 36 + 16 + 4 + 0 + 4 + 16 + 256 + 36) * sqrt(16 + 16 + 1 + 0 + 0 + 1 + 4 + 4 + 1)) = 0.905
Therefore, the best-fit line for the given data is y = 0.190x + 7.48, and the correlation coefficient is r = 0.905.
Step-by-step explanation:
Shen does a weekly exercise program consisting of cardiovascular work and weight training. Each week, he exercises for at least 12 hours. He spends at most 9 hours on weight training. He spends at most 6 hours doing cardiovascular work. Let x denote the time (in hours) that Shen spends doing cardiovascular work. Let y denote the time (in hours) he spends on weight training. Shade the region corresponding to all values of x and y that satisfy these requirements.
PLEASE!!!!! GRAPH AND NUMBERS TOO!!!
The solution to the system of inequalities is the region enclosed in the triangle
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.
Let x denote the time (in hours) that Shen spends doing cardiovascular work. Let y denote the time (in hours) he spends on weight training.
Each week, he exercises for at least 12 hours, hence:
x + y ≥ 12 (1)
He spends at most 9 hours on weight training. Therefore:
x ≤ 6 (3)
He spends at most 6 hours doing cardiovascular work. Hence:
y ≤ 9 (3)
The solution to the system of inequalities is the darker region shown in the graph.
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There are 5 cities in a country and any 2 are connected with 1 road that goes straight between them
Using functions we can find that there would be nine roadways for six cities. This is due to the fact that each city must be connected to every other city, and since there are 5 pairs of connected cities, there must be 5 highways.
What is a function?A function is a statement, concept, or rule that establishes an association between two variables.
Functions in mathematics are required for the development of meaningful relationships. If there are more than one dependent values for a particular independent value, then we are aware of this.
In that situation, the relation is not a function. Nevertheless, if there are multiple dependent values for a given independent value.
The relationship is then a function.
Now as per the question,
The remaining 4 cities must then be connected, which requires building an additional 4 roads, for a total of 9.
There would be 12 roadways for 7 cities.
This is due to the fact that each city must be connected to every other city, and since there are 6 pairs of connected cities, there must be 6 highways.
Then, the final five cities must be connected, which requires five more roads, for a total of twelve.
The number of highways for N cities would be N(N-1)/2.
This is because there are N(N-1)/2 pairs of cities that need to be connected, and each city must be connected to every other city.
For instance, if N = 10, 90 highways or 10× 9 = 90 pairs of cities must be connected.
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The complete question is:
There are five cities in a country, and two are connected with one road that goes straight between them. How many roads would be in this country if there were 6 cities? 7 cities? And N cities?
the cube root of 125 is 5. how much larger is the cube root of 126.2? estimate using the linear approximation.
The cube root of 126.2 is approximately 0.016 larger than the cube root of 125.
Linear approximation is a strategy for approximating the values of complicated functions. When a graph is relatively straight, this approximation is quite effective. A linear approximation for a function is a straight line that represents a close approximation of the original function.
The formula to be used is given by
df/dx = (f(x+dx)-f(x))/dx
The first derivative of the cube root of x can be computed as follows:
f(x) = x^(1/3)
df/dx = (1/3)*x^(-2/3)
Using this formula, we can calculate the linear approximation of the cube root of 126.2. This can be done as follows:
f(x + dx) ≈ f(x) + df/dx * dx
In the given case, the f(x) = ∛125 ⇒ 5
Let dx = 126.2 - 125 ⇒ 1.2
Then the linear approximation of the cube root of 126.2 is given by
f(126.2) ≈ f(125) + df/dx * dx
⇒ f(126.2) ≈ 5 + (1/3)*125^(-2/3) * 1.2
⇒ f(126.2) ≈ 5 + 0.016
⇒ f(126.2) ≈ 5.016
Therefore, the cube root of 126.2 is roughly 0.016 greater than the cube root of 125.
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7 i - 15= 16 with the way
Answer:
31/7
Step-by-step explanation:
7 i - 15 = 16
1. add 15 to both sides you will get
7i = 31
2. dividing both sides gives us 31/7
3. i = 31/7
Calculate the perimeter of the following.
19 to the -3rd power times 19×19 to the -4th power times nine to the third power using only positive exponents
The simplified expression with only positive exponents is 729 / 19^7.
We can simplify the expression as follows, using the exponent rules:
19 to the -3rd power = 1 / (19^3)
19×19 to the -4th power = (19^2)^-2 = 1 / (19^2)^2 = 1 / (19^4)
nine to the third power = 9^3
Therefore, the expression can be written as:
(1 / (19^3)) × (1 / (19^4)) × (9^3)
To simplify further, we can combine the two terms with powers of 19 into a single term:
(1 / (19^3 × 19^4)) × (9^3) = (1 / 19^7) × (9^3)
Finally, we can evaluate 9^3 to get the final answer:
(1 / 19^7) × (9^3) = (1 / 19^7) × 729 = 729 / 19^7
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The given question is incomplete, the complete question is:
19 to the -3rd power times 19×19 to the -4th power times nine to the third power. Simplify the expression using only positive exponents
SOMEBODY HELP ME OUT
Answer:
Below
Step-by-step explanation:
Area of a triangle = 1/2 base * height
this triangle has base = 4 ( 3 in) = 12 in and height = 3 (3 in) = 9 in
area = 1/2 * 12 * 9 = 54 in^2
54 in^2 * $ 2.75 /in^2 = $ 148.50
If the window is scaled down by .5 then the dimensions would be
base = 6 in height = 4.5 in
area = 1/2 * 6 * 4.5 = 13.5 in^2
cost would be 13.5 in^2 * $ 2.75/in^2 =~ $37.13
20 POINTS
Given: CD is an altitude of ΔABC
Prove:
[edAsset type="image" caption="" figure="false" alt="" class="block-center img-responsive " /edAsset]In an Image of a Triangle ACB with b is the length between AC, a is the length between CB and c is the base length between AB. D is a point between AB at the Right angle forming DCB
Proof:
Statements Reasons
1. CD is an altitude of ΔABC. Given
2. ∠ADC and ∠BDC are right angles. Definition of altitude
3. ΔADC and ΔBCD are right triangles. Definition of right triangles
4.
Definition of sine
5. ? Multiplication property of equality
6. b sin(A) = a sin(b) Substitution property of equality
7.
Division property of equality
Which statement completes this proof?
A.
CD = b sin(B) and CD = a sin(A)
B.
b = CD sin(A) and a = CD sin(B)
C.
CD = b sin(A) and CD = a sin(B)
D.
b = CD sin(B) and a = CD sin(A)
In the triangle , the cοrrect οptiοn is B) b = CD sin(A) and a = CD sin(B).
What is triangle?A triangle is a fοrm οf pοlygοn with three sides; the intersectiοn οf the twο lοngest sides is knοwn as the triangle's vertex. There is an angle created between twο sides. One οf the crucial elements οf geοmetry is this.
Certain fundamental ideas, including the Pythagοrean theοrem and trigοnοmetry, rely οn the characteristics οf triangles. The angles and sides οf a triangle determine its kind.
Here the given triangle CD is altitude.
According to the given statement table , in 4th statement we have definition of sine , Then
=> Sin(A) = [tex]\frac{CD}{b}[/tex] and Sin(B) = [tex]\frac{CD}{a}[/tex]
Here simplifying this sine equation for a and b then,
=> b = CD sin(A) and a = CD sin(B).
Hence the correct option is B) b = CD sin(A) and a = CD sin(B).
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Find the area of this triangle
7cm and 3cm as the base,5cm as the side. No height
The area of the triangle is approximately 6.4936 square centimeters.
We can use Heron's formula to find the area of a triangle given the lengths of its sides. Heron's formula states that the area (A) of a triangle with sides a, b, and c is:
A = √[s(s-a)(s-b)(s-c)]
where s is the semi-perimeter of the triangle, defined as:
s = (a + b + c) / 2
Using the values given in the problem, we have:
a = 7 cm, b = 3 cm, c = 5 cm
The semi-perimeter is:
s = (a + b + c) / 2 = (7 + 3 + 5) / 2 = 7.5 cm
Substituting these values into Heron's formula, we get:
A = √[s(s-a)(s-b)(s-c)]
= √[7.5(7.5-7)(7.5-3)(7.5-5)]
= √[7.5(0.5)(4.5)(2.5)]
= √[42.1875]
= 6.4936 cm² (rounded to 4 decimal places)
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Find x.
Please help, and thank you!
Answer: 42
Step-by-step explanation:
We start by looking at the 49 degree angle. A common method of solving geometric problems is to bring things together. To follow this concept, we can say that the 49 degree angle has a vertical angle inside the triangle, which means that angle is 49 degrees. We now work with the 91 degree angle. We can see the 91 degree angle falls on a line, so the other side of the angle equals 180-91=89. All angles in a triangle add up to 180 degrees, so x + 49 + 89 = 180, so x=180 - 138 = 42.
First, find the length of each edge of the cube one side is 3
fill the area for each of the composite shapes below
Step-by-step explanation:
1) 12×5=60
8×4=32
32÷2=16
60+16=82
2) 12×14=168
10×2=20
20÷2= 10
168+10+10=188
3) 4×4= 16
4×11=44
4×5=20
16+44+20=80
4) 8×4=32
3×3= 9
9÷2= 4.5
32+4.5=36.5
The Scale Used in a Map is 2 : 10,000. Two cities are 1450 km apart what will be the distance between these cities on the map? (Hint)= 2 : 10,000 means that 2cn on map corresponds with 10,000 cm of actual distance.
Answer:
3.44827586
Step-by-step explanation:
1450:10,000::x:2
=10,000x=2900
x= 10,000
----------
2900
x=3.44827586 km
Manny walked around a basketball court the court is 27 m long and 17 m wide what is the perimeter A. G, O. N, S. A. Grade 4 pls help
A basketball court takes the shape of a rectangle and the perimeter of a rectangle is =88m
The area encircling a two-dimensional figure is known as its perimeter. Whether it is a triangle, square, rectangle, or circle, it specifies the length of the shape. The two primary characteristics of a 2D shape are area and perimeter.
Each form has a different perimeter depending on its measurements. The perimeter is only ever stated as the circle's diameter when referring to a circle. So we must add all of the sides of each polygon to determine its perimeter, which is the same for all polygons.
A basketball court takes the shape of a rectangle and the perimeter of a rectangle is calculated by the formula:
= Length + Length + Width + Width
Slotting the figures in will give:
= 27 + 27 + 17 + 17
= 88 m
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Two marathon training procedures are tried for comparison purposes. Their efficacy is to be determined in a marathon race. Assume race times are given in minutes. The following results were observed: The data is given below. Procedure-1 Procedure-2
149 166
131 160
159 166
139 181
131 165
160 160
151 149
153 140
157 175
136 167
138 187
152 152
153 188
155 188
145 176
145
174
171
163
189
178
185 157
183
166
178 (a) Do the populations appear to be normal? Hint: use a probability plot to decide and an α
=
0.05
A. Yes, Both procedure A and procedure B appear to be normal
B. Yes, procedure B appears to be normal but procedure A does not appear to be normal
C. No, Both procedure A and procedure B appear to be normal
D. Yes, Both procedure A and procedure B appear to be non-normal
E. No, neither procedure A appears to be normal nor procedure B appears to be normal
F. Yes, procedure A appears to be normal but procedure B does not appear to be normal
(b) Using technology available to you, test to see if the variances are equal or not?
A. There appears to be more variation in the 2nd procedure than in the 1st.
B. They appear to be equal.
C. There appears to be more variation in the 1st procedure than in the 2nd.
D. There appears to be an unequal amount of variation in the 2nd procedure than in the 1st.
(c) Report the p-value of the test you ran in (b)(this is from Levene's te
a) E
b) C
c) p-value 0.03 significant difference in two procedures
A. No, neither procedure A appears to be normal nor procedure B appears to be normal
B. There appears to be more variation in the 1st procedure than in the 2nd.
C. The p-value of the test is 0.03, which indicates that there is a statistically significant difference in the variances of the two procedures.
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Stats and probability find E
If VAR[-4X+5]=13 and E[X]=2.5, find E[(X-3)^2]
(a) 1.06
(b) -3.00
(c) -1.75
(d) 3.06
If VAR[-4X+5]=13 and E[X]=2.5, so E[(X-3)²] will be 1.06. The correct answer is A
We have VAR[-4X+5] = 13, which means VAR[-4X] = 13 since VAR[c] = 0 for any constant c, and VAR[aX] = a² VAR[X] for any constant a.
So we have:
VAR[-4X] = (-4)² VAR[X] = 16 VAR[X] = 13
Solving for VAR[X], we get:
VAR[X] = 13/16
Now, we want to find E[(X-3)^2]:
E[(X-3)²] = E[X² - 6X + 9]
= E[X²] - 6E[X] + 9 (by linearity of expectation)
We can use the formula VAR[X] = E[X²] - (E[X])² to solve for E[X²]:
VAR[X] = E[X²] - (E[X])²
13/16 = E[X²] - (2.5)²
E[X²] = 13/16 + 6.25
E[X²] = 7.31
Therefore, we have:
E[(X-3)²] = E[X²] - 6E[X] + 9
= 7.31 - 6(2.5) + 9
= 1.06
So the answer is (a) 1.06.
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rohan had 36 pens . he gave 15 of them to mike and 11 of them to karan . what fraction of his original 36 pens does rohan have left ? write two equivalent fractions for that amount ?
Answer: 10/36 or 5/8
Step-by-step explanation:
Let’s start by solving how many pens Rohan has left. 36-11-15=36-26=10. Rohan has 10 pens left. Now to solve the fraction of pens Rohan has left, we divide our 10 by 36, or 10/36. Another fraction of this could be 5/18, because both the denominator and numerator have 2 as a factor.
help please I really appreciate it
Answer:
Quadratic Function, Second Difference
Rani and her friends are raking leaves as a part of a school service project. The regular price
of the supplies they need is $60, but the store manager is giving them a 20% discount. Rani
wants to know the sale price of the supplies.
What percent represents the regular price of
the supplies
Answer:
Sale Price-$48 What Percent Represents the reg. Price?-%100
Step-by-step explanation:
20% of 60 is 12, so if supplies are 20% off, they are $12 off, so 60 - 12 =48.
And if the regular price is $60, then $60 is the whole price, a.k.a. 100% of the price. So, the percent that represents the regular price of supplies is 100%.
Eimy and Enerlyn are selling pies for a school fundraiser. Customers can buy apple pies and lemon meringue pies. Eimy sold 6 apple pies and 8 lemon meringue pies for a total of $208. Enerlyn sold 6 apple pies and 2 lemon meringue pies for a total of $88. Find the cost each of one apple pie and one lemon meringue pie
The cοst each οf οne apple pie is $8 and οne lemοn meringue pie is $20.
What is apple pie?Apples serve as the primary filling in fruit pies, which are knοwn as apple pies. Apple pies are cοmmοnly served with whipped cream, cheddar cheese, custard, ice cream, οr custard. The upper crust οften has pastry abοve and belοw the filling and may be sοlid οr latticed. The bοttοm crust can be baked separately tο prevent it frοm becοming sοggy. Deep dish apple pies typically just feature the tοp crust. The tarte tatin's crust is baked οn tοp, even thοugh it is placed οn the bοttοm when it is served.
Suppοse the cοst οf each apple pie is x and οne lemοn meringue pie is y.
Eimy sοld 6 apple pies and 8 lemοn meringue pies fοr a tοtal οf $208.
Then, 6x+8y= 208
Or, 6x=208-8y…………(1)
Enerlyn sοld 6 apple pies and 2 lemοn meringue pies fοr a tοtal οf $88.
Then, 6x+2y=88……………(2)
Putting the value οf 6x in equatiοn nο 2
208-8y+2y=88
Or, -6y=88-208
Or,y=120/6=20
Putting the value οf y in equatiοn 1
6x= 208-8*20
Or, x= 48/6
Or, x= 8
Hence the cοst each οf οne apple pie is $8 and οne lemοn meringue pie is $20.
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