We are given the following two equations
\(\begin{gathered} y=(x+4)^2-1\qquad eq.1_{} \\ y=-3x-13\qquad eq.2 \end{gathered}\)Since both equations are equal to y then we can equate them as
\((x+4)^2-1=-3x-13\)Now let us simplify the equation
\(\begin{gathered} (x+4)^2-1=-3x-13 \\ x^2+2(x)(4)+4^2-1=-3x-13 \\ x^2+8x+16-1=-3x-13 \\ x^2+8x+3x+16-1+13=0 \\ x^2+11x+28=0 \end{gathered}\)As you can see, we are left with a quadratic equation.
The standard form of a quadratic equation is given by
\(ax^2+bx+c=0\)Comparing the equation with the standard form, the coefficients are
a = 1
b = 11
c = 28
Now recall that the quadratic formula is given by
\(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)Substitute the values into the above quadratic formula
\(x=\frac{-11\pm\sqrt[]{(11)^2-4(1)(28)}}{2(1)}=\frac{-11\pm\sqrt[]{121^{}-112}}{2}=\frac{-11\pm\sqrt[]{9}}{2}=\frac{-11\pm3}{2}\)So the two possible solutions are
\(\begin{gathered} x_1=\frac{-11+3}{2},\: x_2=\frac{-11-3}{2} \\ x_1=\frac{-8}{2},\: x_2=\frac{-14}{2} \\ x_1=-4,\: x_2=-7 \end{gathered}\)Therefore, the solutions of the equations are
x = -4 and x = -7
The Variance Inflationary Factor (VIF) measures the: a. correlation of the X variables with the Y variable. b. correlation of the X variables with each other. c. standard deviation of the slope. d. contribution of each X variable with the Y variable after all other X variables are included in the model. e. both a and b.
The X variables have an overall correlation of 0. VIF, or Variance Inflationary Factor, measures the
How much of an inflation variance factor is there?Regression analysis's level of multicollinearity is gauged by a variance inflation factor, or VIF. When several independent variables in some kind of a model with multiple regression correlate with one another, this is known as multicollinearity. The regression findings may be significantly impacted by this.
How high of a VIF is that?Greater correlation between the variable and other variables is indicated by a higher value. With values of Ten or more being considered very high, values greater than 4 or 5 are occasionally considered to be moderate to high.
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fill in the mission numbers to make the fractions equivalent. 1/2 and /8= 4/12 and /60= 2/3 and /12= 4/4 and /8=
To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:
1/2 and __/8
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:
1/2 and 4/8
Now, the fractions are equivalent.
---
4/12 and __/60
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:
4/12 and 20/60
Now, the fractions are equivalent.
---
2/3 and __/12
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:
2/3 and 8/12
Now, the fractions are equivalent.
---
4/4 and __/8
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:
4/4 and 8/8
Now, the fractions are equivalent.
2.75 round to the nearest hundreth
Answer:
Its already rounded. Rounded to tenths place would be 2.8
Step-by-step explanation:
5 or higher makes you round up. if its a 4 or lower it would stay the same.
How do you rotate a triangle 90 clockwise around the origin?
To rotate a triangle 90 clockwise around the origin we negate the x coordinate, and then swap it with the y coordinate
How do you rotate a triangle 90 clockwise around the origin?Represent the coordinate of the triangle with
Triangle = (x, y)
The rule of 90 degrees clockwise rotation around the origin is
(x, y) = (y, -x)
This means that we negate the x coordinate, and then swap it with the y coordinate
Hence, to rotate a triangle 90 clockwise around the origin we negate the x coordinate, and then swap it with the y coordinate
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At a baseball game a vendor sold a combined total of 136 sodas and hotdogs. the number of soda sold was three times the number of the hotdogs sold. find the number of sodas in the number of hotdogs sold
Answer:
Step-by-step explanation:
Let's call the number of hotdogs sold "x". According to the problem, the number of sodas sold is three times the number of hotdogs sold, or 3x.
We know that the total number of sodas and hotdogs sold is 136. So we can set up an equation:
x + 3x = 136
Simplifying this equation, we get:
4x = 136
Dividing both sides by 4, we get:
x = 34
This means that 34 hotdogs were sold. To find the number of sodas sold, we can multiply the number of hotdogs sold by 3:
3x = 3(34) = 102
So, 102 sodas were sold.
Point a is located at (2,6) and D is located at (-4, 10)
the volume of a rectangular prism is 10 cubic feet. what could the dimensions of the prism be
Answer: 2x5x1, 1x10x1 (in any order) and any 3 multiples that make 10
Step-by-step explanation:
Answer:
There are multiple possible sets of dimensions for a rectangular prism with a volume of 10 cubic feet. Here are some possible solutions:
A rectangular prism with dimensions of 1 ft x 2 ft x 5 ft (length x width x height) would have a volume of 10 cubic feet, since 1 x 2 x 5 = 10.
A rectangular prism with dimensions of 2 ft x 1 ft x 5 ft (length x width x height) would also have a volume of 10 cubic feet, since 2 x 1 x 5 = 10.
A rectangular prism with dimensions of 0.5 ft x 1 ft x 20 ft (length x width x height) would also have a volume of 10 cubic feet, since 0.5 x 1 x 20 = 10.
A rectangular prism with dimensions of 5 ft x 1 ft x 2 ft (length x width x height) would have a volume of 10 cubic feet, since 5 x 1 x 2 = 10.
There are infinitely many other possible sets of dimensions for a rectangular prism with a volume of 10 cubic feet.
2cosθ−2=0
please type here and not put in a file
Answer:
Step-by-step explanation:
You want the value of theta, I take it. Add 2 to both sides
2cos(theta) = 2 Divide by 2
2cos(theta)/2 = 2/2
cos(theta) = 1
So theta = 0 degrees.
So 0,360 .... n*360 is the general solution.
What is 3 1/2 miles - 3,520 yards ( And put your answer in miles)?
Answer:
1.5 miles
Step-by-step explanation:
There are 1760 yards in 1 mile, take 1760*3.5 to get the total yards in 3.5 miles. It’s =6,160. Take 6,160-3,520 and you get 2,640. Take 2,650/1760 to get 1.5 miles remaining.
1.5 miles is the value of \(3\frac{1}{2}\) miles - 3,520 yards.
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
We know that 1 yard=0.000568 miles.
We need to convert 3520 yards to miles
3250 yards=3250(0.000568)miles
=1.846miles=2 miles
\(3\frac{1}{2}\) miles - 3,520 yards
Convert \(3\frac{1}{2}\) to improper fraction
7/2 miles-2 miles
3.5 miles - 2 miles
1.5 miles
Hence, 1.5 miles is the value of \(3\frac{1}{2}\) miles - 3,520 yards.
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Write the equation of the line that is perpendicular to the line 5x + 6y= 18 and passes through the point (10, 7).
The equation of the line that is perpendicular to the line 5x + 6y= 18 and passes through the point (10, 7) is
According to the question,
We have the following information:
The equation of the line: 5x+6y = 18
Point through which line is passing = (10,7)
Now, we will convert the given equation of the line into slope-intercept form:
y = mx+b where m is the slope
6y = -5x+18
y = -5x/6+3
Now, the slope of this line is -5/6.
So, the slope of the perpendicular line:
-1/m
6/5
Now, following formula is used to find the equation:
(y-y') = m(x-x')
We have x' = 10 and y' = 7.
(y-7) = 6/5(x-10)
y-7 = 6x/5-12
Moving 7 from the left hand side to the right hand side:
y = 6x/5-12+7
y = 6x/5-5
Hence, the equation of the line that is perpendicular to the line 5x + 6y= 18 and passes through the point (10, 7) is y = 6x/5-5.
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The graph of the function f(x) = –(x + 6)(x + 2) is shown below.
On a coordinate plane, a parabola opens down. It goes through (negative 6, 0), has a vertex at (negative 4, 4), and goes through (negative 2, 0).
Which statement about the function is true?
The function is increasing for all real values of x where
x < –4.
The function is increasing for all real values of x where
–6 < x < –2.
The function is decreasing for all real values of x where
x < –6 and where x > –2.
The function is decreasing for all real values of x where
x < –4.
The statement about the function is: "The function is decreasing for all real values of x where x < -4." D.
The given information tells us that the graph represents a downward-opening parabola.
The vertex of the parabola is located at (-4, 4) indicates that this point is the highest point on the graph.
As we move to the left of the vertex, the function values decrease, indicating a decreasing trend.
Moreover, the graph passes through the point (-6, 0), which lies to the left of the vertex.
This confirms that the function is decreasing for all real values of x less than -4, including x < -6.
On the other hand, the graph also passes through the point (-2, 0), which lies to the right of the vertex.
This does not impact the conclusion that the function is decreasing for x < -4, as the graph's behavior to the right of the vertex is not relevant to this particular statement.
Based on the given information and the properties of the downward-opening parabola, we can conclude that the function is decreasing for all real values of x where x < -4.
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Help find anwser please
Answer:
D.92
Step-by-step explanation:
A triangle adds up to 180
1 Step.
180-148 = 32
this is the missing angle
2 Step.
to find h
180-(32+56)= 92
In order to increase customer service, a muffler repair shop claims its mechanics can replace a muffler in 13 minutes. A time management specialist selected six repair jobs and found their mean time to be 12.3 minutes. The standard deviation of the sample was 2.3 minutes. At α=0.05, is there enough evidence to conclude that the mean time in changing a muffler is less than 13 minutes?
There is not enough evidence to conclude that the mean time in changing a muffler is less than 13 minutes.
To determine whether there is enough evidence to conclude that the mean time in changing a muffler is less than 13 minutes, we can conduct a one-sample t-test with the following hypotheses:
Null hypothesis: The true mean time in changing a muffler is equal to 13 minutes.
Alternative hypothesis: The true mean time in changing a muffler is less than 13 minutes.
Use the formula to calculate the test statistic,
\(t = \dfrac{(x - \mu)} { \dfrac{s} { \sqrt{n}}}\)
where x is the sample mean, μ is the hypothesized population mean (13 minutes), s is the sample standard deviation, and n is the sample size (6).
Plugging in the numbers, we get:
t = (12.3 - 13) / (2.3 / √6) = -0.72
Using a t-distribution table with 5 degrees of freedom (n - 1), we find that the critical value for a one-tailed test with α = 0.05 is -2.571. Since our calculated t-value (-0.72) is greater than the critical value, we fail to reject the null hypothesis.
Therefore, there is not enough evidence to conclude that the mean time in changing a muffler is less than 13 minutes.
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9 weeks 2 days = ?
days?
Answer:
9weeks 2days = (9 × 7) + 2 = 63 +2=65 days
Step-by-step explanation:
Answer:
65 days
Step-by-step explanation: 7 days in a week so times that by 9 because its 9 weeks and that is 63 and add 2 more days
-2n = -6
thanks for helping
☁️ Answer ☁️
n = 3
Hope it helps.
Have a nice day noona/hyung  ̄▽ ̄
Answer:
n=3
Step-by-step explanation:
-2n=-6
-2n/-2= -6/-2
n=-3
I need help please, i dont understand
9514 1404 393
Answer:
(a) none of the above
Step-by-step explanation:
The largest exponent in the function shown is 2. That makes it a 2nd-degree function, also called a quadratic function. The graph of such a function is a parabola -- a U-shaped curve.
The coefficient of the highest-degree term is the "leading coefficient." In this case, that is the coefficient of the x² term, which is 1. When the leading coefficient of an even-degree function is positive, the U curve has its open end at the top of the graph. We say it "opens upward." (When the leading coefficient is negative, the curve opens downward.)
This means the bottom of the U is the minimum value the function has. For a quadratic in the form ax²+bx+c, the horizontal location of the minimum on the graph is at x=-b/(2a). This extreme point on the curve is called the "vertex."
This function has a=1, b=1, and c=3. The minimum of the function is where ...
x = -b/(2·a) = -1/(2·1) = -1/2
This value is not listed among the answer choices, so the correct choice for this function is ...
none of the above
__
The attached graph of the function confirms that the minimum is located at x=-1/2
_____
Additional comment
When you're studying quadratic functions, there are few formulas that you might want to keep handy. The formula for the location of the vertex is one of them.
Is 7-¹ a negative number? Explain.
Answer:
No
Step-by-step explanation:
\(7^{-1}\) is a fraction
using the rule of exponents
• \(a^{-m}\) = \(\frac{1}{a^{m} }\)
then
\(7^{-1}\) = \(\frac{1}{7^{1} }\) = \(\frac{1}{7}\) ← that is a fraction
Which type of video was rented most often! Use the graph to answer the question.
A. Children’s
B. Comedy
C. Action
D. Drama
Answer:
B
Step-by-step explanation:
the biggest portion of the pie graph is labeled comedy, so that would be your answer.
How many faces does a triangular pyramid have?
A. 3
B. 6
C. 4
D. 5
\(\huge{\textbf{\textsf{{\color{navy}{An}}{\purple{sw}}{\pink{er}} {\color{pink}{:}}}}}\)
C. 4.
thanks hope it helpsConvert f ( x ) = 48 ( 1.02 ) x to the form f ( x ) = a e k x . Round k to 4 decimal places.
The exponential function can be rewritten as:
f(x) = 48*e^(0.0198*x)
How to transform the function?Here we start with the exponential function:
f(x) = 48*(1.02)^x
And we want to write this in the general form:
f(x) =a*e^(kx)
Notice that we can write the second form as:
f(x) = a*[e^k]^x
So, comparing this with the given exponential, we will get:
a = 48
e^k = 1.02
Apply the natural logarithm in both sides:
ln(e^k) = ln(1.02)
k*ln(e) = ln(1.02)
k = ln(1.02) = 0.0198
Then the exponential function is:
f(x) = 48*e^(0.0198*x)
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Find the slope of each line part 2
Answer:
7. -3
8. 7/3
Step-by-step explanation:
________________
A box contains 7 blue socks, 13 yellow socks and 5 green socks. What is the probability of choosing a green sock at random? Question 5 options: 5/20 1/7 5/21 1/5
Answer:
1/5
Step-by-step explanation:
5 out of 25 reduces to 1 out of 5
Si una mosca real tiene una longitud de 9mm y su maqueta mide 18cm.cual a q escala se realizo la maqueta
The scale factor used is:
1 centimeter equals half millimiter.
How to find the scale factor?The scale factor tells us how many units in the sculpture represent a real unit.
We know that:
Real length = 9mm
Length in the sculpture = 18cm
Then we have the relation between the lengths:
18cm = 9mm
Dividing both sides by 18 we will get:
1cm = 9mm/18
1cm = 0.5mm
So the scale is 1 centimeter equals half millimiter.
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PLEASEEEEEEEEEEEEE HELPPPP
The total area of the regions between the curves is 4.5 square units
The graph is attached
Calculating the total area of the regions between the curvesFrom the question, we have the following parameters that can be used in our computation:
y = x² - 6x + 9 and y = x - 1
With the use of graphs, the curves intersect at
x = 2 and x = 5
So, the area of the regions between the curves is
Area = ∫x² - 6x + 9 - x + 1
This gives
Area = ∫x² - 7x + 10
Integrate
Area = x³/3 - 7x²/2 + 10x
Recall that x = 2 and x = 5
So, we have
Area = [2³/3 - 7(2)²/2 + 10(2)] - [5³/3 - 7(5)²/2 + 10(5)]
Evaluate
Area = 4.5
Hence, the total area of the regions between the curves is 4.5 square units
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54-90.27-90.22-90.87-90
Answer: -307.36 I think
Step-by-step explanation:
Write a function using function notation to describe each situation. Find a reasonably domain and range for each function. A newspaper charges $3 per line for the first 4 lines plus a $20 fee to advertize.
Answer:
The answer is below
Step-by-step explanation:
The domain of a function is the set of all independent variables for the function while the range of a function is the set of all possible dependent variables.
Let x represent the number of newspaper lines and f(x) be the charges for advertisement. x is the independent variable and f(x) is the dependent variable.
Since the newspaper charges $3 per line for the first 4 lines plus a $20 fee to advertise, the function is given as:
f(x) = 3x + 20 for 0 < x < 4
But for more than four lines, the charges is given as:
f(x) = 12 + 20 = 32 4 < x < ∞
Therefore, the domain and range of the function is:
Domain = (0, ∞)
Range = (20, 32}
What should be included in a financial plan to protect assets?
a. how much money you will make
b. how much money you will have in savings
how much money you will invest
d. how much insurance you will carry
C.
Please select the best answer from the choices provided
A
B
Ο Ο Ο Ο
Answer:
d
Step-by-step explanation:
The financial plan to protect assets
how much insurance you will carry
What is Financial plan?A financial plan is a document containing a person’s current money situation and long-term monetary goals, as well as strategies to achieve those goals. A financial plan begins with a thorough evaluation of the person’s current financial state and future expectations and may be created independently or with the help of a certified financial planner.
Your assets: This may include a home and a car, some cash in the bank, money invested in a plan, and anything else of value that you own.Your liabilities: These may include credit card debt, student debt, an outstanding mortgage, and a car loan. In some cases, you may have access to a grace period or moratorium.According to the financial plan to protect your assets you have to
how much insurance you will carry.
Insurance is like the back up plan for assets.
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Two street lights change every 30 seconds and 50 seconds respectively. They last change together at 10:40 am. When will they change together again?
so umm I need help on this question haha
The time when they change again = 432seconds
m_ZBC =2x+8, m_ABC=21x-5,
and m ABZ=139° Find m ABC.
to
z
B
Answer:
163°
Step-by-step explanation:
Assuming that BZ is a ray inside angle ABC:
2x+8+139=21x-5
8+139+5=21x-2x
152=19x
8=x
m<ABC=21x-5=
21(8)-5=
168-5=
163
Bound
Figure 2.
Jenny would like to buy a new air conditioner for his home. As seen in Figure 2 above he has
3 types of brands that he can consider. The cash price for Daewoo is RM1,899, Daikin at a
price of RM1,699 and last choice is Mitsubishi at a price of RM1.999. He plans to make 18
monthly instalments, if he pays RM300 as a down payment for the air conditioner that he would
like to buy, find the interest charge for each brand if the interest rate is 4% based on originall
balance if he chooses to buy from Daikin, find the monthly instalment price and instalment
price that he needs to pay.
if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).
How to determine the monthly instalment price and instalment price that Daikin needs to pay.Calculating the loan amount for each brand by subtracting the down payment from the cash price:
Loan amount for Daewoo = RM1,899 - RM300 = RM1,599
Loan amount for Daikin = RM1,699 - RM300 = RM1,399
Loan amount for Mitsubishi = RM1,999 - RM300 = RM1,699
Calculating the interest charge for each brand:
Interest charge for Daewoo = Loan amount for Daewoo * Interest rate = RM1,599 * 0.04 = RM63.96
Interest charge for Daikin = Loan amount for Daikin * Interest rate = RM1,399 * 0.04 = RM55.96
Interest charge for Mitsubishi = Loan amount for Mitsubishi * Interest rate = RM1,699 * 0.04 = RM67.96
To find the monthly installment price, divide the total amount (cash price + interest charge) by the number of monthly installments:
Monthly installment price for Daewoo = (Cash price of Daewoo + Interest charge for Daewoo) / Number of monthly installments = (RM1,899 + RM63.96) / 18 ≈ RM107.22
Monthly installment price for Daikin = (Cash price of Daikin + Interest charge for Daikin) / Number of monthly installments = (RM1,699 + RM55.96) / 18 ≈ RM98.89
Monthly installment price for Mitsubishi = (Cash price of Mitsubishi + Interest charge for Mitsubishi) / Number of monthly installments = (RM1,999 + RM67.96) / 18 ≈ RM116.72
Therefore, if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).
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