Simplify the expression by multipliaction of terms.
[tex]\begin{gathered} k(k-9)=k\cdot k-9\cdot k \\ =k^2-9k \end{gathered}[/tex]So answer is
[tex]k^2-9k[/tex]If f(x) = x2 + x, find f(-3).-123O6
To find f(-3) we have to substitute x = -3 in the equation.
[tex]\begin{gathered} f(-3)=(-3)^2+(-3) \\ f(-3)=9-3 \\ f(-3)=6 \end{gathered}[/tex]solve: 10+7-4y=-5+6y+22 and decide whether it has infinite solutions or no solutions or one solution
answer is one solution
DIoll Solve the equation x³ + 2x² - 5x-6=0 given that 2 is a zero of f(x)= x³ + 2x² - 5x-6.The solution set is(Use a comma to separate answers as needed.)
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
f(x) = x³ + 2x² - 5x - 6
zero:
x = 2
Step 02:
roots:
solution set:
2 | 1 2 -5 -6
| 2 8 6
________________
1 4 3 0
x² + 4x + 3 = 0
(x + 3)(x + 1) = 0
x = - 3
x = - 1
The answer is:
solution set:
{-3 , -1 , 2}
Write the probability of getting 2 heads when flipping a coin 2 times. (Write as a reduced fraction)
we have that
The probability of getting 1 head when flipping a coin one time is
P=1/2
so
the probability of getting 2 heads when flipping a coin 2 times is
P=(1/2)*(1/2)=1/4
therefore
the answer is
P=1/4Find the area of the triangle with the given measurements. Round the solution to thenearest hundredth if necessary.B = 74º, a = 14 cm, c = 20 cm (5 points)
Let's begin by listing out the given information:
[tex]\begin{gathered} \angle B=74^{\circ} \\ a=14\operatorname{cm} \\ c=20\operatorname{cm} \end{gathered}[/tex]We will calculate the area as shown below:
[tex]\begin{gathered} \text{We will obtain the third side using the Cosine Rule:} \\ b^2=a^2+c^2-2ac\cdot cosB \\ b=\sqrt[]{a^2+c^2-2ac\cdot cosB} \\ b=\sqrt[]{14^2+20^2-2(14)(20)\cdot cos74^{\circ}} \\ b=21.02cm \end{gathered}[/tex]The formula for area is given by Heron's formula:
[tex]\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ s=\frac{a+b+c}{2}=\frac{14+21.02+20}{2}=\frac{55.02}{2}=27.51 \\ s=27.51 \\ \Rightarrow A=\sqrt[]{27.51(27.51-14)(27.51-21.02)(27.51-20)} \\ A=134.58cm^2 \end{gathered}[/tex]Therefore, the area f
The price of televisions has dropped dramatically over the last three years. Three years ago, a 32 inch television was $500. This year the tv was on sale for $199. What is the percent change?
it is due today!!! 7th honers
The percent change in the price of television from initial price $500 to final price $199 is 60.2.
What are Percentages?
The term 'per cent' means 'out of a hundred'.
Percentage is a way to define parts of a whole.
To convert fraction to a percentage, first convert fraction to decimal,
then multiply decimal value with 100, with '%' sign.
So, Percentage change = [tex]\frac{initial-final}{initial}[/tex]×100%
Percentage change = { ( $500 - $199 ) / $500 } × 100%
= { $301 / $500 } × 100%
= .602 × 100%
= 60.2%
Hence, the percentage change in tv price is 60.2%.
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The taxes on a house assessed at 90,000 are $3420 a year. If the assessment is raised to 119,000 and the tax rate did not change, how much would the taxes be now?
The amount of tax to be paid on the assessment of the house is $4522.
How to calculate the tax?Given that the taxes on a house assessed at 90,000 are $3420 a year, the tax rate will be:
= Tax / Total value.
= 3420 / 90000
= 3.8%
Therefore, when the assessment is raised to 119,000 and the tax rate did not change, the value of the tax will be:
= Tax percentage × New assessment
= 3.8% × 119000
= $4522
The tax is $4522.
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if R200 is musted at 6% simple interests per year detemine the interest if earch after 4years
The interest calculated after 4 years for a principal amount of 200 at 6% rate of interest , is 48 and the total amount is 248.
Given,
P = 200
rate of interest (r) = 6%
time (t) = 4 years.
we know the simple interest formula as:
S.I = P×r×t/100
substitute the above values.
Interest = 200 × 4 × 0.06/100
= 800 × 0.06/100
= 8 × 0.06
= 0.48 × 100
= 48
Total amount = 200+48
= 248
Hence we get the total amount as 248 at the end of 4 years.
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7a) The roots of the equation 4x^2 - 7x - 1 = 0 are G and H. Evaluate G^2+ H^2B) Write the equation of a quadratic with integer coefficients whose solutions are G^2 and H^2.Pls see the pic for more detail.
Given:
[tex]4x^2-7x-1=0[/tex]Solve:
Quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Where,
[tex]ax^2+bx+c=0[/tex]Compaire the equation then:
[tex]\begin{gathered} ax^2+bx+c=0 \\ 4x^2-7x-1=0 \\ a=4,b=-7,c=-1 \end{gathered}[/tex]So roots of equation is:
[tex]\begin{gathered} x=\frac{-(-7)\pm\sqrt[]{(-7)^2-4(4)(-1)}}{2(4)} \\ x=\frac{7\pm\sqrt[]{49+16}}{8} \\ x=\frac{7\pm\sqrt[]{65}}{8} \end{gathered}[/tex]So value of G and H is:
[tex]\begin{gathered} G=\frac{7+\sqrt[]{65}}{8};H=\frac{7-\sqrt[]{65}}{8} \\ G=\frac{7}{8}+\frac{\sqrt[]{65}}{8};H=\frac{7}{8}-\frac{\sqrt[]{65}}{8} \end{gathered}[/tex]So:
[tex]\begin{gathered} =G^2+H^2 \\ =(\frac{7}{8}+\frac{\sqrt[]{65}}{8})^2+(\frac{7}{8}-\frac{\sqrt[]{65}}{8})^2 \\ =(\frac{7}{8})^2+(\frac{\sqrt[]{65}}{8})^2+2(\frac{7}{8})(\frac{\sqrt[]{65}}{8})+(\frac{7}{8})^2+(\frac{\sqrt[]{65}}{8})^2-2(\frac{7}{8})(\frac{\sqrt[]{65}}{8}) \\ =2(\frac{49}{64}+\frac{65}{64}) \\ =2(\frac{114}{64}) \\ =\frac{114}{32} \\ =3.5625 \end{gathered}[/tex](B)
If roots is a and b the equation is:
[tex]x^2-(a+b)x+ab=0[/tex]Then equation is:
[tex]G^2+H^2=3.5625[/tex][tex]\begin{gathered} G^2H^2=(\frac{7}{8}+\frac{\sqrt[]{65}}{8})^2(\frac{7}{8}-\frac{\sqrt[]{65}}{8})^2 \\ =(0.875+1.00778)^2(0.875-1.00778)^2 \\ =(3.54486)(0.01763) \\ =0.0624 \end{gathered}[/tex]So equation is:
[tex]x^2-3.5625x+0.0624[/tex]2. Select ALL coordinate pairs that are solutions to the inequality 5x + 9y<45. *
From the problem we have the inequality 5x + 9y < 45
Substitute the options and check if it satisfies the inequality.
(0, 0)
5(0) + 9(0) < 45
0 + 0 < 45
0 < 45
TRUE!
(5, 0)
5(5) + 9(0) < 45
25 < 45
TRUE!
(9, 0)
5(9) + 9(0) < 45
45 < 45
FALSE!
(0, 5)
5(0) + 9(5) < 45
45 < 45
FALSE!
(0, 9)
5(0) + 9(9) < 45
81 < 45
FALSE!
(-5, -9)
5(-5) + 9(-9) < 45
-25 - 81 < 45
-106 < 45
TRUE!
ANSWERS :
(0, 0), (5, 0) and (-5, -9)
hello this is a plane trigonometry question hopefully you can help I did every thing else it's just the last one I can't get the reference angle for five in this question
rs + 2r210rs5s2Find the binomial factors
Rs+2r^2-10rs-5s^2
Combine like terms
2r^2-9rs-5s^2
The table represents the cost to eat at a buffet-style restaurant.Number ofPeople (p)2Cost (C)(including tax)27.5441.3155.0868.85345682.62Which equation could be used to calculate the cost. C, for any number of people, p, to eat at the restaurant?
We need to take the values of the table and check which of the options fit with the results.
In the first line of the table we have p=2 and C=27.54.
Using the equation in option A, for p=2 we would get:
[tex]\begin{gathered} C=p+27.54 \\ C=2+27.54 \\ C=29.54 \end{gathered}[/tex]Which is not value for C in the table. Thus we discard option A.
Using the equation for option B, for the value of p=2, we would get:
[tex]\begin{gathered} C=13.77p \\ C=13.77(2) \\ C=27.54 \end{gathered}[/tex]Which is indeed the value of the table.
To confirm, we try now with the next value of p, p=3, and check if we get the same result with equation B as with the table:
[tex]\begin{gathered} C=13.77p \\ C=13.77(3) \\ C=41.31 \end{gathered}[/tex]Which is also the value for C in the table.
Thus we confirm that option B is the correct equation
I need help describing the sequence of transformations for 12 and 13.
12. For the first part we rotate 90° and reflect on the y-axis
Then we reflect on the x-axis
13. First we reflect on the y-axis, then we rotate 90° and finally we reflect on the x-axis
i need help trying to write a system of linear equations for the graph below
We need to find the equation in slope-intersect form
[tex]y=mx+b[/tex]of the given lines.
For the horizontal line, we can see that it passes through points
[tex]\begin{gathered} (x_1,\text{y}_1)=(0,7) \\ (x_1,y_2)=(4,6) \end{gathered}[/tex]the its slope (m) is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-7}{4-0}=\frac{-1}{4}=-\frac{1}{4}[/tex]Then, the line equation has the form
[tex]y=-\frac{1}{4}x+b[/tex]where b is the y-intercept. From the picture, we can see that the line crosses the y-axis at y=7, therefore, b=7. Then, the line equation for the horizontal line is
[tex]y=-\frac{1}{4}x+7[/tex]Similarly, we can apply the same procedure for the other line. We can see that it passes through points
[tex]\begin{gathered} (x_1,\text{y}_1)=(0,-2) \\ (x_2,\text{y}_2)=(4,6) \end{gathered}[/tex]Then, the slope (m) of this line is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-(-2)}{4-0}=\frac{6+2}{4}=\frac{8}{4}=2[/tex]Then, the line equation has the form
[tex]y=2x+b[/tex]Since this line crosses y-axis at y=-2 then b=-2. Hence, the equation is
[tex]y=2x-2[/tex]In summary, the system of linear equations is:
[tex]\begin{gathered} y=-\frac{1}{4}x+7 \\ y=2x-2 \end{gathered}[/tex]Daig 20. Sample Problem using Daum Equation Editor 4 - [3 :) and B - [: 6 51 Determine -3A + 2B Show all work using the Daum Equation Editor. Insert your image here:
The question is given as : -3A +2 B
[2 5] + { 6 5 }
[7 0 } { 1 1 }
For the first matrix , multiply by -3 and the second matrix multiply by 2
To multiply a matrix, every value in the bracket is multiplied by the scalar.
For -3A multiply the values in the bracket with -3 as;
[tex]\begin{bmatrix}{2} & {5} & \\ {7} & {0} & {} \\ {} & {} & \end{bmatrix}\times-3\text{ = }\begin{bmatrix}{-6} & {-15} & \\ {-21} & {0} & {} \\ {} & {} & {}\end{bmatrix}=-3A[/tex]For 2B
[tex]\begin{bmatrix}{6} & {5} & {} \\ {1} & {1} & {} \\ {} & {} & {}\end{bmatrix}\times2=\begin{bmatrix}{12} & {10} & \\ {2} & {2} & {} \\ {} & {} & {}\end{bmatrix}=2B[/tex]Now perform the addition as; -3A + 2B
[tex]\begin{bmatrix}{-6} & {-15} & \\ {-21} & {0} & {} \\ {} & {} & {}\end{bmatrix}+\begin{bmatrix}{12} & {10} & \\ {2} & {2} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{-6+12} & {-15+10} & \\ {-21+2} & {0+2} & {} \\ {} & {} & {}\end{bmatrix}[/tex]This will give the following;
[tex]\begin{bmatrix}{6} & {-5} & {} \\ {-19} & {2} & {} \\ {} & {} & {}\end{bmatrix}[/tex]Please help will mark Brainly
Answer:
Below
Step-by-step explanation:
A yes all values of y
B yes slope is undefined for a vertical line
C no there is no y axis intercept for this line
D yes the line intercepts the x-axis at x = -2
E no the domain is only x = -2
A sociology teacher asked her students to complete a survey at the beginning of the year. One survey question asked, "How responsible are you?" Another question asked, "How many siblings do you have?" Irresponsible Responsible O siblings 6 3 1 sibling 4 5 What is the probability that a randomly selected student has 0 siblings and is irresponsible? Simplify any fractions.
Answer: Probability is 1/3
Step by step explanation:
The probability (P) of an event is:
[tex]P=\frac{\text{Number of ways it can happen}}{\text{Total number of outcomes}}[/tex]The probability that a randomly selected student has 0 siblings and is iiresponsible is:
[tex]P=\frac{6}{6+3+4+5}=\frac{6}{18}=\frac{1}{3}[/tex]Which coordinate plane contains the points (4 1/2,1) and (–2 1/2, –2)?
option C
Explanation:
To determine the graph with the coordinates given, let's check and state some of the coordinates of each graph in the option:
[tex]\begin{gathered} \text{Given coordinates:} \\ (4\frac{1}{2},1)\text{ : x = 4}\frac{1}{2},\text{ y = 1} \\ (-2\text{ }\frac{1}{2},\text{ -2) : x = }-2\text{ }\frac{1}{2},\text{ y = -2} \end{gathered}[/tex]a) Coordinates: (-2, -3), (4, 4)
There is no point at -4 1/2 or -2 1/2 on this graph
b) coordinates: (-2, -3), (3, 1/2)
Tere is no x value at -4 1/2 or -2 1/2 on this graph
c) when x = -2 1/2, y = -2
when x = 4 1/2, y = 1
d) There is no x value at 4 1/2 on this graph. There is also no x value at -2 1/2 on this graph
Hence, the coordinate plane that contains points (4 1/2, 1) and (-2 1/2, -2) is option C
How wide is the space betweeneach number on this clock?
Solution:
Given:
We have the angle between each hands of the clock to be
[tex][/tex]How many ounces of water must be added to 85oz of a 40% salt solution to make a solution that is 17% salt?
Okay, here we have this:
Considering the provided information, we are going to calculate the requested value, so we obtain the following:
Accordingly, since the amount of salt remains the same, then we have the following equality, where x represents the amount of water that must be added:
0.4(85)=0.17(x+85)
Let's solve for x:
34=0.17x+14.45
0.17x=34-14.45
0.17x=19.55
x=19.55/0.17
x=115
Finally we obtain that must be added 115 ounces of water to make a solution that is 17% salt.
determine the domain of each function y=2x^4-3x^4+7x^2-1
Given:
[tex]y=2x^4-3x^4+7x^2-1[/tex]Simplify the function,
[tex]\begin{gathered} y=2x^4-3x^4+7x^2-1 \\ y=-x^4+7x^2-1 \end{gathered}[/tex]Domain: The domain of the function is the set of all possible input values for which the function is real or defined.
So, the domain of the given function is,
[tex]-\inftyDetermine the domain and range Express your answer in interval notation
The domain of a function is the set of all values that the x-variable can take.
On the other hand, the range of the function is the set of all values that the function takes when it is evaluated at elements of the domain.
For the given expression:
[tex]p(x)=-\frac{1}{(x-1)^2}[/tex]The denominator is (x-1)^2. Since the denominator must be different from 0, then:
[tex]\begin{gathered} (x-1)^2\ne0 \\ \Rightarrow x-1\ne0 \\ \Rightarrow x\ne1 \end{gathered}[/tex]Then, the only restriction for the variable x is not to be equal to 1. Then, the domain of p(x) is the set of all real numbers except 1, which can be written using interval notation as:
[tex](-\infty,1)\cup(1,\infty)[/tex]Since the exponent of the denominator is 2, then the denominator is always positive. Since the coefficient of the term 1/(x-1)^2 is -1, then the whole expression must always be negative. Additionally, there is no way in which the expression can be equal to 0.
Then, the range of the function is the set of all negative numbers, which can be expressed using interval notation as:
[tex](-\infty,0)[/tex]Therefore, the answers are:
[tex]\begin{gathered} \text{ Domain: }(-\infty,1)\cup(1,\infty) \\ \\ \text{ Range: }(-\infty,0) \end{gathered}[/tex]Find the values of x and y in the parallelogram.A46x+2211 BO x= 11, y = 24O x = 24, y = 11Ox=-11, y = 46O x=46, Y =-11
Since the opposite sides of a parallelogram are congruents, we can write the following equations:
[tex]\begin{cases}DA=BC \\ AB=CD\end{cases}[/tex]From the first one, we have:
[tex]y=11[/tex]From the second one, we have:
[tex]\begin{gathered} x+22=46 \\ x=46-22 \\ x=24 \end{gathered}[/tex]So we have x = 24 and y = 11, therefore the correct option is the second one.
solve the quadratic equation by the square root method. show all steps.
We have to solve the equation with the square root method:
[tex]\begin{gathered} 2(x-4)^2-6=18 \\ 2(x-4)^2=18+6 \\ 2(x-4)^2=24 \\ (x-4)^2=\frac{24}{2} \\ (x-4)^2=12 \\ \sqrt[]{(x-4)^2}=\sqrt[]{12} \\ x-4=\pm\sqrt[]{12} \\ x=4\pm\sqrt[]{12} \\ x=4\pm2\sqrt[]{3} \end{gathered}[/tex]Answer: The solutions are:
[tex]\begin{gathered} x_1=4-2\sqrt[]{3} \\ x_2=4+2\sqrt[]{3} \end{gathered}[/tex]Ron bought two comic books on sale. Each comic book was discounted $1 off the regular price r. Write an expression to find what Ron paid before taxes. If each comic book was regularly $2.50, what was the total cost before taxes?
Step 1
Given;
[tex]\begin{gathered} A\text{ regular price of r for a comic book on sale} \\ A\text{ discount of \$1 before tax} \end{gathered}[/tex]Required; To
1) write an expression to find what was paid by Ron before taxes
2)Find the total cost before taxes of the comic books, if each one costs $2.50
Step 2
Write the expression of what Ron paid before taxes
[tex]\begin{gathered} \text{\$}2(r-1) \\ \text{Note; One book costs \$(r-1)} \\ \text{\$}(2r-2) \end{gathered}[/tex]Step 3
If each book was regularly $2.50, find the total cost before taxes
[tex]\begin{gathered} r=\text{\$}2.50 \\ \text{Total cost=\$(2(2.50)-2)} \\ \text{Total cost=\$(5-2)=\$}3 \end{gathered}[/tex]If the line joining the points (a,4) and (2,-5) is parallel to the line with given equation 2x-3y=12 find the value of a
Parallel lines have the same slope, thus, using the equation of the parallel line, we can find out the slope of the line that passes through the given points.
To find the slope of a line given its equation, we have to put the equation into the slope-intercept form, whcih we can do by solving the equation for y:
[tex]\begin{gathered} 2x-3y=12 \\ -3y=-2x+12 \\ y=\frac{-2}{-3}x+\frac{12}{-3} \\ y=\frac{2}{3}x-4 \end{gathered}[/tex]The slope of the line is the coefficient multiplying x, which is 2/3 in this case.
So, let's name the slope m:
[tex]m=\frac{2}{3}[/tex]Since the lines are parallel, both have the same slope m.
Also, if we want to find the slope given two numbers on the line, we can use the following equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, we have the points (a, 4) and (2, -5) and we have the slope m = 2/3. Substituting these, we have:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1}_{} \\ \frac{2}{3}=\frac{-5-4}{2-a} \\ \frac{2}{3}=\frac{-9}{2-a} \\ 2(2-a)=3\cdot(-9) \\ 4-2a=-27 \\ -2a=-27-4 \\ -2a=-31 \\ a=\frac{31}{2} \end{gathered}[/tex]Thus, the value of a is 31/2.
Find the solution of the system of equations. 3x + 3y = 6 9x - 5y = -24
3x + 3y = 6 (eq. 1)
9x - 5y = -24 (eq. 2)
Multiplying equation 1 by 3,
3(3x + 3y) = 3*6
3(3x) + 3(3y) = 18
9x + 9y = 18 (eq. 3)
Subtracting equation 2 to equation 3,
9x + 9y = 18
-
9x - 5y = -24
---------------------
14y = 42
y = 42/14
y = 3
Replacing this result into equation 1,
3x + 3(3) = 6
3x + 9 = 6
3x = 6 - 9
3x = -3
x = -3/3
x = -1
Solve the equation for c: 52 = 4(c + 5)
Given:
[tex]52\text{ = 4(c + 5)}[/tex]Solution
We are required to solve the equation for c.
First, we open the bracket:
[tex]52\text{ = 4c + 20}[/tex]Next, we make c the subject of formular:
[tex]\begin{gathered} 4c\text{ = 52 - 20} \\ 4c\text{ = 32} \\ \text{Divide both sides of the equation by 4} \\ c\text{ = 8} \end{gathered}[/tex]Answer: c = 8
A giant panda gave birth to her baby at a zoo. The baby panda weighed 100 grams. At its health exam 51 days later the baby weighed 2.17 kilograms. How much weight did the panda cub gain after 51 days?
Day 1 Weight of Baby Panda = 100 grams
Day 52 (after 51 days) Weight of Baby Panda = 2.17 kg
To determine the weight increase of our baby panda, we have to convert first the units from kg to grams.
[tex]1kg=1000grams[/tex]Please know that 1kg = 1000 grams. Therefore, 2.17 kg is equal to:
[tex]2.17kg\times1000grams=2170grams[/tex]So now, the weight of our baby panda after 51 days is 2170 grams. To determine weight increase, we will subtract 100 grams from 2170 grams.
[tex]2,170grams-100grams=2,070grams[/tex]Therefore, the panda cub gained 2,070 grams after 51 days or 2.07kg.