Answer:
Vertex (2,2)
y- Intercept is 10
On problems like this, use Desmos Graphing. It helps a lot.
Answer:
Step-by-step explanation:
the base of the vertex is going to be on 2,2, with a y intercept of 10
According to the Rational Root Theorem, which number is a potential root of f(x) = 9x8 + 9x6 – 12x + 7?
Answer:
\(\pm 1, \pm\dfrac{1}{3},\pm\dfrac{1}{9},\pm 7, \pm\dfrac{7}{3},\pm\dfrac{7}{9}\).
Step-by-step explanation:
According to the Rational Root Theorem, the potential roots of a polynomial are
\(x=\pm\dfrac{p}{q}\)
where, p is a factor of constant and q is a factor of leading term.
The given polynomial is
\(f(x)=9x^8+9x^6-12x+7\)
Here, 9 is the leading term and 7 is constant.
Factors of 9 are ±1, ±3, ±9.
Factors of 7 are ±1, ±7.
Using rational root theorem, the rational or potential roots are
\(x=\pm 1, \pm\dfrac{1}{3},\pm\dfrac{1}{9},\pm 7, \pm\dfrac{7}{3},\pm\dfrac{7}{9}\)
Therefore, the potential root of f(x) are \(\pm 1, \pm\dfrac{1}{3},\pm\dfrac{1}{9},\pm 7, \pm\dfrac{7}{3},\pm\dfrac{7}{9}\).
Answer:
its D, 3/7.
Step-by-step explanation:
just did it egen2020
Help!! Stuff about triangles
Answer:
3
Step-by-step explanation:
Since \(\angle A \cong \angle A\) by the reflexive property and \(\angle ABC \cong \angle ADE\) since they are both right angles, \(\triangle ABC \sim \triangle ADE\) by AA.
It follows that:
\(\frac{x}{9}=\frac{5}{9+6} \implies x=3\)
Find the area of the sector. Round the answer to the nearest tenth.
Answer:
63.4
Step-by-step explanation:
Area of arc is (pi*(11)^2*(60/360))=63.4
the regression equation is determined by minimizing _____________.
The regression equation is determined by minimizing the residuals.
The regression equation is an essential statistical formula that predicts a relationship between two variables. It can be in two ways: simple regression and multiple regressions. The equation is an estimator that predicts one variable from another variable that's called the predictor or independent variable. Also, it is referred to as the regression line equation.The equation is determined by minimizing the residuals.
The residuals are the differences between the observed and predicted values of the dependent variable. The regression line or equation passes through the point of the average x-value and y-value. The equation of the regression line is represented as y = a + bx, where "y" is the dependent variable, "x" is the independent variable, "b" is the slope, and "a" is the y-intercept.
The process of minimizing residuals is known as the ordinary least squares method. It is a technique that's used to estimate unknown parameters in the linear regression model. The objective of the OLS method is to find the regression line that has the smallest sum of the squared residuals. The least-squares method works by minimizing the difference between the predicted values and the actual values of the dependent variable by adjusting the slope and intercept of the regression line.
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6.1 Colby bought a laptop worth Rx for his university studies. The value of the laptop decreased at r% per annum using the reducing balance method. After 4 years, the value of the laptop was worth 31 of its original price. Calculate r, the rate of depreciation.
6.2 On 1 February 2014 , Ncominkosi took a loan from a bank to buy a car. His first payment for the loan was due on 31 July 2014 . Once he started paying the loan, it took him 6 years to fully pay the loan at an interest rate of 9,5% p.a. compounded monthly. In total, he paid the bank R596 458,10.
6.2.1 How much was his monthly instalment?
6.2.2 How much money did he borrow from the bank? Write down your answer to the nearest rand.
6.1). the rate of depreciation, r, is approximately 10.77%.
6.2.1). Ncominkosi's monthly installment amount was approximately R 10,505.29.
6.2.2). Ncominkosi borrowed approximately R 377,510.83 from the bank.
6.1) Let's assume the original price of the laptop is P. According to the reducing balance method, the value of the laptop after 4 years can be calculated as P * (1 - r/100)^4. We are given that this value is 31% of the original price, so we can write the equation as P * (1 - r/100)^4 = 0.31P.
Simplifying the equation, we get (1 - r/100)^4 = 0.31. Taking the fourth root on both sides, we have 1 - r/100 = ∛0.31.
Solving for r, we find r/100 = 1 - ∛0.31. Multiplying both sides by 100, we get r = 100 - 100∛0.31.
Therefore, the rate of depreciation, r, is approximately 10.77%.
6.2.1) To determine the monthly installment amount, we can use the formula for calculating the monthly payment on a loan with compound interest. The formula is as follows:
\(P = \frac{r(PV)}{1-(1+r)^{-n}}\)
Where:
P = Monthly payment
PV = Loan principal amount
r = Monthly interest rate
n = Total number of monthly payments
Let's calculate the monthly installment amount for Ncominkosi's loan:
Loan amount = Total amount paid to the bank - Interest
Loan amount = R 596,458.10 - R 0 (No interest is deducted from the total paid amount since it is the total amount paid)
Monthly interest rate = Annual interest rate / 12
Monthly interest rate = 9.5% / 12 = 0.0079167 (rounded to 7 decimal places)
Number of monthly payments = 6 years * 12 months/year = 72 months
Using the formula mentioned above:
\(P = \frac{0.0079167(Loan Amount}{1-(1+0.0079167)^{-72}}\)
Substituting the values:
\(P = \frac{0.0079167(596458.10}{1-(1+0.0079167)^{-72}}\)
Calculating the value:
P≈R10,505.29
Therefore, Ncominkosi's monthly installment amount was approximately R 10,505.29.
6.2.2) To determine the amount of money Ncominkosi borrowed from the bank, we can subtract the interest from the total amount he paid to the bank.
Total amount paid to the bank: R 596,458.10
Since the total amount paid includes both the loan principal and the interest, and we need to find the loan principal amount, we can subtract the interest from the total amount.
Since the interest rate is compounded monthly, we can use the compound interest formula to calculate the interest:
\(A=P(1+r/n)(n*t)\)
Where:
A = Total amount paid
P = Loan principal amount
r = Annual interest rate
n = Number of compounding periods per year
t = Number of years
We can rearrange the formula to solve for the loan principal:
\(P=\frac{A}{(1+r/n)(n*t)}\)
Substituting the values:
Loan principal (P) = \(\frac{596458.10}{(1+0.095/12)(12*6)}\)
Calculating the value:
Loan principal (P) ≈ R 377,510.83
Therefore, Ncominkosi borrowed approximately R 377,510.83 from the bank.
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For which of these variables would you be interested in finding the biserial correlation coefficient rather than the point-biserial correlation coefficient?
Answer:
The formula for the point biserial correlation coefficient is:
point biserial correlation formula
M1 = mean (for the entire test) of the group that received the positive binary variable (i.e. the “1”).
M0 = mean (for the entire test) of the group that received the negative binary variable (i.e. the “0”).
Sn = standard deviation for the entire test.
p = Proportion of cases in the “0” group.
q = Proportion of cases in the “1” group.
Most people won’t work this formula by hand as most statistical software packages can calculate the coefficient for you.
Find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line. Parallel to the line x=10; containing the point (5,6)
The equation for the line is given by either the general form or the slope-intercept form of the equation of a line. Slope-intercept form of the equation of a line is y = mx + b where m is the slope of the line and b is the y-intercept of the line. General form of the equation of a line is Ax + By = C where A, B, and C are constants. The equation of the line is x = 5.
Given that a line is parallel to the line x=10 and containing the point (5, 6). Given the line is parallel to the line x = 10.Since the given line is vertical, the slope of the given line is undefined. Therefore, the slope of the parallel line is undefined. So, the equation of the line is x = c where c is a constant. Now, we have to determine the value of c. As the line passes through the point (5, 6), so we have 5 = c. So, the equation of the line is x = 5.
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Omar has a new debit card. He earns 1{,}8001,8001, comma, 800 reward points for spending 300300300 dollars.
At this rate, if Omar earned 600600600 reward points, how much money did he spend?
The reward of 600 points will be earned by spending the amount of $300.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that, Omar earns 800 reward points for spending 300 dollars.
The amount of money spent to earn 600 reward points will be calculated as,
800 reward points = $300 spending
1 reward point = $300 / 800 spending
600 reward point = ($300 x 600) / 800
600 reward points = $225
Therefore, the reward of 600 points will be earned by spending the amount of $300.
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for a randomly selected policy, what is the probability that the wife will have between $50,000 and $100,000 of insurance and the husband will have between $0 and $50,000 of insurance? round your answer to three decimal places, if necessary.
0.833
The probability that the wife will have between $50,000 and $100,000 of insurance and the husband will have between $0 and $50,000 of insurance for a randomly selected policy is 0.833.
This answer is rounded to three decimal places if necessary.
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Find the inverse function. f (x) = 1/x+2
Answer:
f^-1(x)= 1/(x-2)
Step-by-step explanation:
interchange the variables and solve for y.
Draw the image of ABC under a translation by 2 units down.
I need help please !!!
Answer:
Please find attached drawing created with Microsoft word, that shows the image of of the triangle ΔABC. with coordinates of the vertices as, A(2, -4), B(0, -5), and C(6, 2), translated down 2 units to give the triangle ΔA prime B prime C prime , with coordinates of the vertices as A prime (2, -6), B prime (0, -7), and C prime (6, 0)
Step-by-step explanation:
Answer:
Here u go
Step-by-step explanation:
Because yeah
What is the constant in this expression? 3x+9y+12
A. 3
B. 9
C. 12
D. 3x
Answer:
The answer is 9
Step-by-step explanation:
the constant in a expression is the number with no variable
diagram shows the position of a ship (s) and a marine base (b) the scale of the diagram is 1cm represents 20km
a) work out the real distance between the ship and the base
b)measuring the bearing of B from S
c) a fishing boat (f) is 20km from s on a bearing of 95 degrees
The real distance between the ship and the base is 35 km and the measure of the bearing of B from S would be; 70 degrees.
How to find the scale factor?Scale factor is the factor which is used to enlarge or smaller the original figure. Scale factor is the ratio of representation measurement of the figure to the original figures.
The figure represent the position of the ship(S) and the marine base(B).
a) Real distance between the ship and the base is;
When the distance from ship and the base is measured by rules. It comes out 3.5 cm.
The scale of the diagram is 1 cm, represents 10 km. Thus,
BS = 10/ 1 x 3.5
BS = 35 km
b) Measure the bearing of B from S
With the help of compass, the bearing angle of B from S is measured as the given;
Angle BSN = 70 degree
Thus, the real distance between the ship and the base is 35 km and the measure of the bearing of B from S would be; 70 degrees.
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Hannah is making cakes for the bake sale at her school. Each cake requires 1 1/2 cups of sugar. How many complete cakes can Hanna make if she has 6 3/4 cups of sugar?
Help please ? :)
Answer:
4
Step-by-step explanation:
Divide 6 3/4 by 1 1/2
Convert into improper fractions, 27/4 and 3/2
\(\frac{27}{4} / \frac{3}{2}\)
\(\frac{27}{4} * \frac{2}{3}\)
\(\frac{9}{2} = 4.5\)
The question asks for the number of whole cakes, so the answer would be 4.
Answer : 4
Step - by - step explanation :
In - order to find out how many cakes Hannah can make we need to find out how many 1 1/2 cups of sugar she has . . .
what is 6 3/4 divided by 1 1/2 --> 6 3/4 divided by 1 2/4 ? 4 1/2
SO ! Hannah can make 4 complete cakes
2xy + 13 mn- 9x + 3
How many terms are in the polynomial
Answer:
4
Step-by-step explanation:
im pretty sure the answer is 4 i learned about this last year
What is the value of the expression 2 + 2 x 42 - (5 - 3) 2?
Answer:
82Step-by-step explanation:
The value of the expression
2 + 2×42 - (5 - 3)² =2 + 84 - 2² =86 - 4 =82Answer:
\(82\)
Step-by-step explanation:
1. simplify 5 - 3 to 2.
\(2 + 2 \times 42 - 2 \times 2\)
2. Simplify 2 × 42 to 84.
\(2 + 84 - 2 \times 2\)
3. simplify 2 × 2 to 4.
\(2 + 84 - 4\)
4. Simplify 2 + 84 to 86.
\(86 - 4\)
5. Simplify.
\(82\)
Therefor, the answer is 82.
Can someone help me PLZ! I keep posting the same question and no ones helping me :(((((((((((( its dues in 20 mins!!
Solve the system of equations below. Write your answer as an ordered pair. Start by multiplying the first equation by 2.
2x + 2y = 12
5x + 4y = 28
Answer:
x=4
y=2
Step-by-step explanation:
2*4+2*2=12
8+4=12
5*4+4*2=28
20+8=28
Have a good day ;-),
and can I please have brainliest? Thanks!
The Answer is 4,2
x=4 y=2
8th grade math pls help
Answer:
6/4 = 3/2
just count the rise/run
Step-by-step explanation:
Answer:
The slope is 3/2
Step-by-step explanation:
We'll call the bottom point (-3,-2) and the top point (1,4). We could rise/run the rise would be 6 units and the run would be 4 units. And we can simplify 6/4 to 3/2.
How do you draw an acute angled isosceles triangle?
Answer:
To draw an isosceles acute triangle, the first step is to draw a line segment horizontally which will be the base of the triangle.
Step-by-step explanation:
Now, draw two angles of equal measurements (each should be less than 90 degrees) on both the ends of the line segment. Join the arms of the angles. In this way, we will get an acute isosceles triangle.
Factor the polynomial completely
10³ -25r² - 12r + 30
Evaluate 11.5x + 10.9y when x = 6 and y =7
The value of the algebraic expression 11.5x + 10.9y at x = 6 and y = 7 is 145.3
What is an algebraic expression?
Algebraic expression consists of variables and numbers connected with addition, subtraction, multiplication and division
The given algebraic expression is 11.5x + 10.9y
We have to find the value of the algebraic expression at x = 6 and y = 7
Putting x = 6 and y = 7 in the algebraic expression,
\(11.5 \times 6 + 10.9 \times 7\)
69 + 76.3
145.3
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Instructions: Write the equation for the following
function. Do not use any spaces in your answer.
X
0
1
2
-1
y
0
-2
-4
-12
Y=
The function of the given data would be F(x) = y = 4x.
What is a function?The function is a type of relation, or rule, that maps one input to specific single output.
Given;
X(input) Y ( output)
0 0
1 4
2 8
3 12
We can see that
When the input is zero the output is also zero.
And when the input is some real number the output gives the multiple of 4.
Thus, The function could be
f(x) = 4x
The given function is represented by x as the independent variable.
Therefore, The function of the given data would be F(x) = y = 4x.
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Solve |4n−15|=|n|.
The solutions are n=
and n=
.
Answer:
n=3 n=5
Step-by-step explanation:
|4n−15|=|n|
Positive
4n−15=n
Subtract 4n from each side
-15 = -3n
Divide by -3
-15/-3 = n
5 = n
negative
4n -15 = -n
Subtract 4n from each side
-15 = -5n
Divide by -5
-15/-5 = n
3 = n
Answer:
n=3 and n=5
Step-by-step explanation:
|4n−15|=|n|
we know either
4n-15=-n or 4n=15=n
4n+n=15 4n-n=15
5n=15 3n=15
n=15/5=3 n=15/3=5
I complete ⅔ of my project last month and ¼ of it this week. What fraction of my project is not completed?
Answer:
1/12
Step-by-step explanation:
Add the fraction that is complete
2/3 + 1/4
Get a common denominator or 12
2/3 * 4/4 + 1/4 * 3/3
8/12 + 3/12
11/12
11/12 is complete
Subtract this from 1 to find what is not complete
1 -11/12
Get a common denominator
12/12 -11/12
1/12
1 /12 is not complete
Answer: 1/12
Step-by-step explanation:
Convert to like fractions
2/3= 8/12; 1/4= 3/12
8/12+3/12= 11/12, 1/12 of project is not completed.
OR
percengtages
2/3= 66.6%
1/4= 25%
66.6+25= 91.6% not completed
11/12= 91.6%
Two friends, Francisco and Zoe, had just bought their first cars. Zoe uses 14 gallons of gas to drive 390.6 miles in her car. The graph below represents the number of miles, y, that Francisco can drive his car for every x gallon of gas.
Using linear function to solve this problem, for every 1 gallon of gas, Francisco travelled 27.9 miles
Linear FunctionA linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2. A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. where m is slope of the line and b is the y - intercept
We can use the data given in writing out our equation
y = Number miles coveredx = number of gallon390.6 = 14x
If 14 gallons = 390.6 miles
1 gallon = x miles
x = 390.6 / 14
x = 27.9 miles
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write two statements of inequality please!
Answer:
a. A number c is less than 4. A number c is less than 4. c. < An inequality is c < 4.
b. A number k plus 5 is greater than or equal to 8. A number k plus 5 is greater than or equal to 8. k + 5. ≥ ...
Step-by-step explanation:
Evaluate the discriminant for each equation. Determine the number of real solutions. x²+4 x+5=0 .
The roots of the equation will be imaginary. Then the number of real solutions will be zero.
What is the discriminant of the quadratic equation?The discriminant represents the types of the root. And the discriminant (D) of the equation ax² + bx + c = 0 is given as
D = b² - 4ac
The type of roots will be given below.
D > 0, Real and Distinct rootsD = 0, Real and Equal rootsD < 0, Imaginary rootsThe equation is given below.
x² + 4x + 5 = 0
The discriminant of the given equation will be
D = 4² - 4 x 1 x 5
D = 16 - 20
D = - 4
D < 0
The roots of the equation will be imaginary. Then the number of real solutions will be zero.
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If y varies directly with x and y= 12 when x= 16, what is the value of x when y= 5?
Answer:
\(x = 6 \frac{2}{3} \)
Step-by-step explanation:
Since y varies directly with x,
y= kx, where k is a constant.
① Find the value of the constant k.
When y=12, x= 16,
12= k(16)
16k= 12
\(k = \frac{12}{16} \\ k = \frac{3}{4} \)
②Substitute the value of k back into the equation:
\(y = \frac{3}{4} x\)
③ Find value of x when y=5.
When y=5,
\(5 = \frac{3}{4} x \\ x = 5 \div \frac{3}{4} \\ x = 5 \times \frac{4}{3} \\ x = \frac{20}{3} \\ x = 6 \frac{2}{3}\)
whats the radius for the circle? x^2+2x+y^2+4y-6=0
Answer:
r = \(\sqrt{11}\)
Step-by-step explanation:
So we need to complete the square for both parts of the equation
First though we can add the 6 to the other side so we have x² + 2x + y² + 4y = 6
So first we can complete the square for x² + 2x
To do so we need to use \((\frac{b}{2} )^{2}\) to figure out the number we need to add to both sides
In this case our b is 2, so substituting this in we get \((\frac{2}{2} )^{2} =(1)^{2} =1\)
Here we add 1 to both sides and now we have x² + 2x + 1 + y² + 4y = 6 + 1
Now we can follow the same steps to complete the square for y² + 4y
Here our b is 4, so substituting this in we get \((\frac{4}{2} )^{2}=(2)^{2} =4\)
Now we add 4 to both sides and now we have x² + 2x + 1 + y² + 4y + 4 = 6 + 1 + 4
Now condensing everything we have (x + 1)² + (y + 2)² = 11
The formula for a circle is (x - h)² + (y - k)² = r²
In our equation we have r² = 11
To find the radius we need to take the square root of both sides \(\sqrt{r^{2}} =\sqrt{11}\) to get r = \(\sqrt{11}\)
Find the values of b such that the function has the given minimum value.
f(x) = x2 + bx − 21;
Minimum value:
−70
Answer: b = 14.
Step-by-step explanation:
We have the function:
f(x) = x^2 + b*x - 21
The minimum of a quadratic function will be at the vertex, and the vertex is at the value of x such that:
f'(x) = 2*x + b = 0
then the vertex is at:
x = -b/2
Then the minimum of the function f(x) will be:
f(-b/2) = (-b/2)^2 + b*(-b/2) - 21
and we know that the minimum value is -70, then:
f(-b/2) = -70 = (b^2)/4 - (b^2)/2 - 21
Now we need to solve this equation for b.
-70 = (b^2)/4 - (b^2)/2 - 21
-70 = -(b^2)/4 - 21
-70 + 21 = -(b^2)/4
49 = (b^2)/4
49*4 = b^2
196 = b^2
√196 = b = 14
The value of b is 14.