SOLUTION
The equation of a line written in slope-intercept form is
\(y=mx+b\)Where
\(\begin{gathered} m=\text{slope } \\ b=y-\text{intercept } \end{gathered}\)The y-intercept is the point where the line cuts the y-axis.
From the graph given, the line cut the y-axis at y= -2
the y-intercept is
\((0,-2)\)Hence, we have
\(\begin{gathered} \text{ Since b is the y-intercept, } \\ b=-2 \end{gathered}\)Therefore
Answer ; b = -2
The second option
What is the value of x?
Answer:
Step-by-step explanation:
45
Answer:
x=44°
Step-by-step explanation:
It's an Isosceles triangle, it has two equal sides (DC=CE) so also its two equal angles of 44 degrees
Hope this helps
what does new thousand mean?
We see here that new thousand is actually liken to be the result in thousand that is gotten after carrying out an operation.
What is a thousand?A thousand is a number that denotes the sum of 1,000 units or ten hundreds.
The word "thousand" is frequently used in daily speech to denote a significant but limited amount, such as a thousand money, a thousand individuals, or a thousand pages. Alternatively, it can be used as a round number to denote an approximation, as in "a thousand times" or "a thousand and one nights."
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Please help, thanks!
Calculate the third angle of a triangle in which two of the angles are as follows. 47° and 65° b 24° and 77 c 56° and 18⁰ d 39° and 21° e each 58°
The third angles in the given cases are:a) 68°b) 79°c) 106°d) 120°e) 64°.
To calculate the third angle of a triangle in which two of the angles are given, we need to use the fact that the sum of all the angles of a triangle is always 180°. Let's use this fact to solve each case given:a) Two angles are given as 47° and 65°. To find the third angle, we subtract the sum of the given angles from 180°.
That is, third angle = 180° - (47° + 65°) = 68°.b) Two angles are given as 24° and 77°. Similar to the previous case, the third angle = 180° - (24° + 77°) = 79°.c) Two angles are given as 56° and 18°. The third angle = 180° - (56° + 18°) = 106°.
d) Two angles are given as 39° and 21°. The third angle = 180° - (39° + 21°) = 120°.e) Each of the two angles is given as 58°. To find the third angle, we subtract twice the value of one of the given angles from 180°. That is, third angle = 180° - (2 × 58°) = 64°.
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A building has 6 homes per floor and 3 floors. On the first floor, there are 4 penguins per home. On the second and third floor, there are 3 penguins per home.
Which equation can we use the total number of penguins living in the building?
The equation that represent the number of penguins is (6 × 4) + (3 × 6) + (3 × 6) = p.
How to find the equation to represent a situation?A building has 6 homes per floor and 3 floors. On the first floor, there are 4 penguins per home. On the second and third floor, there are 3 penguins per home.
Therefore, the equation that can be used to find the total number of penguins living in the building is as follows:
Hence,
(6 × 4) + (3 × 6) + (3 × 6) = p
where
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You take Rocky to the Del Mar fair. His mom gives him $30 to spend. It costs $13 to get in and the $2 for every ride. How many rides can he ride?
Answe r with the system of equations. Please help me.
Answer:
8 rides
Step-by-step explanation:
$30-$13
=$17
1 ride= $2
x ride =$17
x= 17/2
= 8.5
= 8 rides
You take Rocky to the Del Mar Fair. His mom gives him $30 to spend.
It costs $13 to get in and $2 for every ride. he can ride 8 rides.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
You take Rocky to the Del Mar Fair. His mom gives him $30 to spend.
It costs $13 to get in and $2 for every ride.
$30 - $13
= $17
Let x be the ride he can rides.
1 ride = $2
x ride = $17
x = 17/2
= 8.5
= 8 rides
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A rectangle has a length that is 8 inches more than its width, w. The area of the rectangle is 65 square inches.
so i have to find the length. I need help ;-;
Answer:
13in
Step-by-step explanation:
Let the width be w
The length will be 8+w
(8+w)(w)=65
8w+w^2=65
w^2+8w-65
Use quadratic equation formula.
You will get two answers
w=5 or w= -13
Pick the answer that is more sensible.
It cannot be a negative number; hence use 5in
5in+8in= 13in
Answer:13 and 5 are the lengths
Step-by-step explanation: if its 8 inches more on one side than the other then it goes like this 9x1 is 9. 10x2 is 20. 11x3 is 33. 12x4 is 48. 13x5 is 65. 13x5 is the rectangle.
I need helpppppppp plssssssssss
3 6 9 12 15 18 21 24 27 30 is odd or even numbers?
Answer: Half of them are even and half of them are odd.
Step-by-step explanation:
The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.
The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.
Therefore, out of the given numbers, half of them are even and half of them are odd.
________________________________________________________
What is the product of -8z and -4z?
Answer:
the answer is 32z
Step-by-step explanation:
Wei wants to prove that the segment joining midpoints of two sides of a
triangle is parallel to the third side.
Select the appropriate rephrased statement for Wei's proof.
Now we know PR∥QX , according to construction with transversal line TX.
∠PTS=∠QXS (Alternate angle)
In △PTS and △QSX
∠PTS=∠QXS (Alternate angle)
∠PST=∠QSX(vertically opposite angles)
PS=SQ(S is mid point of PQ)
△PTS≅△QSX(AAS rule)
So, TP=QX(CPCT)
As we know, TP=TR (T is midpoint)
Hence, TR=QX
Now, in quadrilateral TSQR
TS∥QR
Hence proved.
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The present value of a perpetuity paying 1 every two years with first payment due immediately is 7.21 at an annual effective rate of i. Another perpetuity paying R every three years with the first payment due at the beginning of year two has the same present value at an annual effective rate of i + 0.01.
Calculate R.
(A) 1.23
(B) 1.56
(C) 1.60
(D) 1.74
(E) 1.94
Answer:
Step-by-step explanation:
image attached (representing first perpetuity on number line)
Present value is 7.21
\(7.21=\frac{1}{1-u^2} \\\\1-\frac{1}{7.21} =u^2\\\\\frac{6.21}{7.21} =(1+i)^{-2}\\\\(1+i)^2=\frac{7.21}{6.21} \\\\(i+1)=\sqrt{\frac{7.21}{6.21} }\\\\ i=\sqrt{\frac{7.21}{6.21} } -1\\\\=0.77511297\)
image attached (representing second perpetuity on number line)
we have ,
\(7.21=\frac{Ru}{1-u^3}\)
Here,
\(V=\frac{1}{1+i}\)i
i = 0.077511297 + 0.01
\(\therefore V =\frac{1}{1.087511295} =(1.087511297)^-^1\\\\7.21=\frac{R(1.087511297)^-^1}{1-(1.087511297)^-^3} \\\\7.21=4.132664645R\\\\R=\frac{7.21}{4.132664645} \\\\R= 1.7446370\approx1.74\)
Therefore, value of R is 1.74
Determine the amount of money you need to invest to accumulate $7,000 dollars in 4 years if you invest it at 2.5% annual interest, compounded quarterly.
An initial investment of $5,951.71 is needed to accumulate $7,000 in 4 years with 2.5% annual interest compounded quarterly.
To determine the amount of money needed to accumulate $7,000 in 4 years with 2.5% annual interest compounded quarterly, we need to use the formula for compound interest.
The formula is A = P(1+r/n)^(nt), where A is the final amount, P is the initial investment, r is the interest rate, n is the number of times compounded per year, and t is the number of years.
Using the given information, we can plug in the values and solve for P. A = $7,000, r = 0.025, n = 4, and t = 4.
A = P(1+r/n)^(nt)
A = P(1+0.025)^4
$7,000 = P(1+0.025/4)^(4*4)
$7,000 = P(1.00625)^16
P = $5,951.71
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Would like some help on this question please ?
Answer:
Position 1 slide b
Step-by-step explanation:
If you lay down you have more force. you would have more speed because flatter surface means you will not get as much speed
Use the following rectangle to solve for the values of X.
Answer:
\(x = 8.64^o\)
Step-by-step explanation:
Given
The attached rectangle
Required
Find x
To do this, we make use of:
\(11x - 5 = 90\) ---- angle at diagonal
Collect like terms
\(11x = 5 + 90\)
\(11x = 95\)
Solve for x
\(x = \frac{95}{11}\)
\(x = 8.64^o\) --- approximated
A package of 4 pairs of insulated costs $24.76. What is the unit price of the pairs of ?
Make r the subject of the formula t=r/r-3
Answer:
I think the answer is
t=r/r-3
r=t(r-3)
r=tr-t3
View, please help! Thank you.
Answer:
- 6
Step-by-step explanation:
Rate of change over the interval 1 ≤ x ≤3 is given by
\(\dfrac{f(3) - f(1)}{3-1} \\\\= \dfrac{66- 78}{2}\\ \\= \dfrac{-12}{2}\\\\= -6\)
We can see from the table that the function value drops by 6 for every 1 unit increase in x
The population of a city was 10,000 in 2010. The population increase at an annual rate of 2.5% per year. Is the growth model function that represents the population of the city linear?
Answer:
The growth model that represents the population of this city is not linear--it is exponential:
\(f(t) = 10000( {1.025}^{t} )\)
\(t = 0 \: represents \: 2010\)
Identify the solution(s) of z^2-4=0
answer
(z+2)(z-2)
steps
its a rule
a²-b²= (a+b) (a-b)
vedantu
What is 2.02 times 4.2?
Answer:
8.484
Step-by-step explanation:
Answer:
8.484
Step-by-step explanation:
Find the distance between the two points rounding to the nearest tenth
(-4, 2) and (3, 5)
Answer:
-8.66666666666666666666666666666666666
-9
Step-by-step explanation:
How can I factor the following expression by grouping:
a) 4x^3 - 2x^2 + 8x - 4
The factored expression of 4x³ - 2x² + 8x - 4 is (2x² + 4)(2x - 1) by grouping
How to factor the expression by groupingFrom the question, we have the following parameters that can be used in our computation:
4x³ - 2x² + 8x - 4
Group the expression in 2's
So, we have
(4x³ - 2x²) + (8x - 4)
Factorize each group
2x²(2x - 1) + 4(2x - 1)
So, we have
(2x² + 4)(2x - 1)
Hence, the factored expression is (2x² + 4)(2x - 1)
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2
Let g(x) = x + 4x-7.
What is g(x) in graphing form?
(x + 2) - 7 = 4
O g(x) = (x + 2)²-7
Onone of the answer choices
x² + 4x-7=0
O g(x) = (x + 2)² - 11
The graphing form of the function g(x) is: C) none of the answer choices.
The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.
Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:
a = 1 (coefficient of x^2)
b = 4 (coefficient of x)
c = -7 (constant term)
Therefore, the graphing form of the function g(x) is:
C) none of the answer choices
None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.
In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.
The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C
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Record Examination) are normally distributed with a mean of 555 and a standard
deviation of 110. Use the 68-95-99.7 Rule to find the percentage of people taking the test who score below 335.
The percentage of people taking the test who score below 335 is
Answer:
2.5%
Step-by-step explanation:
You want the percentage below 335 if the distribution is normal with a mean of 555 and a standard deviation of 110, using the empirical rule.
Z scoreThe z-score of 335 is ...
Z = (X -µ)/σ
Z = (335 -555)/110 = -220/110 = -2
DistributionThe empirical rule tells you that 95% of the distribution is between Z = -2 and Z = 2. That is, 5% of the distribution is evenly split between the tails Z < -2 and Z > 2. Half that value is in each tail.
P(X < 335) = 5%/2 = 2.5%
The percentage of people taking the test who score below 335 is 2.5%.
<95141404393>
Please help me I need help?!!!
Answer:
B
Step-by-step explanation:
use what you know about inverse functions to determine the derivative of the inverse function beginning with f ( f -1(x)).
The inverse function of f (x) = 1/3x - 2 is f⁻¹(x) = 3(x + 2), the value of a is 3, and the value of x-intercept is x = -2.
To find the inverse of the given function as it is not a one to one function (has the same value f(x) for more that one value of x) you restrict the domain to get a function one to one.
What is a function?
Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.
Given:
f (x) = 1/3x - 2
Find its inverse as shown below,
Add 2 to x and then divide by 1/3 as shown below,
f⁻¹(x) = (x + 2) / 1/3
f⁻¹(x) = 3(x + 2)
compare with f⁻¹(x) = a (x + 2)
a = 3
Calculate the x-intercept by putting f(x) = 0
0 = x + 2
x = -2
In a quadratic function as given use the vertex to restrict the domain; restrict the domain using coordinate x of the vertex.
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Jessica went shopping and bought a pair of jeans that were on sale for 25% off the original price of $23.98. A 6% tax was also added on to the sale price. Enter the total amount that Jessica spent on the jeans. Round your answer to the nearest cent, if necessary.
Applying Angle Relationships.
Please help me quick
Answer:
Step-by-step explanation:
1) a) 15x = 12x + 15 {Alternate interior angles}
b) 15x - 12x = 15 {Subtract 12x from both sides}
3x = 15
x = 15/3
x = 5
c) Alternate interior angles
2) a) 3x + 10 + 3x - 28 = 180 {co- interior angles are supplementary}
b) 6x - 18 = 180 { Combine like terms}
6x = 180 + 18
6x = 198
x = 198/6
x = 33
c) co- interior angles are supplementary
3) a) 7x + 9 + 5x +3 = 180
b) 12x + 12 = 180
12x = 180 - 12
12x = 168
x = 168/12
x = 14
c) linear pair
4) a) 12x - 18 = 8x + 10
b) 12x - 8x - 18 = 10
4x - 18 = 10
4x = 10 +18
4x = 28
x = 28/4
x = 7
c) Vertically opposite angles are equal.
17 The table below shows the distance a car has traveled.
50
20
f
40
Minutes
Distance
Traveled
(in miles)
What is the meaning of the slope of the linear model for the data?
60
100
a) The car travels 5 miles every minute.
b) The car travels 4 miles every minute.
c) The car travels 4 miles every 5 minutes.
d) The car travels 5 miles every 4 minutes.
125
80
100
Given statement solution is :- None of the given options (a, b, c, or d) match the meaning of the slope. The correct interpretation is that the car travels approximately 0.8 miles every minute.
To determine the meaning of the slope of the linear model for the given data, let's analyze the information provided. The table represents the distance traveled by a car at different time intervals.
Minutes | Distance Traveled (in miles)
50 | 20
20 | f
40 | 60
100 | a
125 | 80
100 | 100
To find the slope of the linear model, we need to calculate the change in distance divided by the change in time. Let's consider the intervals where the time changes by a fixed amount:
Between 50 minutes and 20 minutes: The distance changes from 20 miles to 'f' miles. We don't have the exact value of 'f', so we can't calculate the slope for this interval.
Between 20 minutes and 40 minutes: The distance changes from 'f' miles to 60 miles. Again, without knowing the value of 'f', we can't calculate the slope for this interval.
Between 40 minutes and 100 minutes: The distance changes from 60 miles to 'a' miles. We don't have the exact value of 'a', so we can't calculate the slope for this interval.
Between 100 minutes and 125 minutes: The distance changes from 'a' miles to 80 miles. Since we still don't have the exact value of 'a', we can't calculate the slope for this interval.
Between 125 minutes and 100 minutes: The distance changes from 80 miles to 100 miles. The time interval is 25 minutes, and the distance change is 100 - 80 = 20 miles.
Therefore, based on the given data, we can conclude that the car travels 20 miles in 25 minutes. To determine the meaning of the slope, we divide the distance change by the time change:
Slope = Distance Change / Time Change
= 20 miles / 25 minutes
= 0.8 miles per minute
So, none of the given options (a, b, c, or d) match the meaning of the slope. The correct interpretation is that the car travels approximately 0.8 miles every minute.
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