The solution of x² + 5x - 5 = 0 is :
x = 0.854 and -5.854 .
Solution:
Here given equation,
x2 + 5x - 5 = 0
To solve the given equation use quadratic formula,
Using the quadratic formula,
x = [-b ± [tex]\sqrt{b2 - 4ac}[/tex] ] /2a
Here,
a = 1, b = 5 and c = -5
By substituting,
x = [-5 ± [tex]\sqrt{52 - 4(1)(-5)}[/tex] ] /2(1)
= [-5 ± √[tex]\sqrt{25 + 20}[/tex]] /2
= [-5 ± √45] /2
= [-5 ± 6.708] /2
So,
x = (-5 - 6.708)/2
= -11.708/2
= -5.854
= (-5 + 6.708)/2
= 1.708/2
= 0.854
∴ the solutions of equation is : 0.854 and -5.854.
To learn more about quadratic equation refer to :
https://brainly.com/question/1214333
#SPJ13
Any equation that can be rearranged in standard form as follows, where x stands for, is referred to be a quadratic equation in algebra.
What constitutes the x2 + 5x - 5 = 0 solution set?
We must figure out the equation's answer. The answers to the problem are thus 0.854 and -5.854. x^2 + 5x - 5 = 0
It is impossible to factor a quadratic equation like this one. It can be resolved either by completing the square or by applying the quadratic formula.
x = (-b +-sqrt(b2 - 4ac))/2a is the quadratic formula, where an is the coefficient of the x2, b is the coefficient of the x, and c is the constant.
a = 1, b = 5, c = -5
x = (-5 +- sqrt(25+20))/2
x = (-5 +- sqrt(45))/2
x = (-5 + - 3 sqt 5))/2
x = (-5 + 3sqrt5)/2 as well as x = (-5 - 3sqrt5)/2.
To learn more about Quadratic equation refer to :
https://brainly.com/question/1214333
#SPJ13
determine the solution,if it exists,for each system of linear equation. Verify your solution on the coordinate plane. x + 3 = y 3x + 4y = 7
then
[tex]\begin{gathered} 3\mleft(y-3\mright)+4y=7 \\ 3y-9+4y=7 \\ 7y-9=7 \\ 7y-9+9=7+9 \\ 7y=16 \\ \frac{7y}{7}=\frac{16}{7} \\ y=\frac{16}{7} \end{gathered}[/tex]replacing in x
[tex]undefined[/tex]12. A teacher weighed 148 lbs. in 1999 and weighs 190 lbs. In 2020. What was the rate ofchange in weight?
Given,
The weight of the teacher in 1999 is 148 lbs.
The weight of the teacher in 2020 is 190 lbs.
The rate of change in weight is,
[tex]\begin{gathered} \text{Rate of change=}\frac{190-148}{2020-1999} \\ =\frac{42}{21} \\ =2 \end{gathered}[/tex]The teacher gained 2 pounds per year.
Hence, option A is correct.
K
Determine whether the statement is true or false, and explain why.
The derivative value f'(a) equals the slope of the tangent line to the graph of y=f(x) at x = a.
Choose the correct answer below.
OA. The statement is true because f'(x) is a function of x.
B. The statement is false because f(a) gives the instantaneous rate of change of f' at x = a.
OC. The statement is true because f'(a) gives the instantaneous rate of change of fat x = a.
OD. The statement is false because f'(a) gives the average rate of change of f from a to x.
Answer: C. The statement is true because f'(a) gives the instantaneous rate of change of fat x = a.
what is the sum of 141.2-79.83
Given:
141.2 - 79.83
Here, we are to subtract 79.83 from 141.2
Let's evaluate the given expression.
We have:
[tex]\begin{gathered} 141.20 \\ -79.83 \\ _{\text{ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}} \\ \text{ 61.37} \end{gathered}[/tex]ANSWER:
61.37
Evaluate the expression (4x^3y^-2)(3x^-2y^4) for x = –2 and y = –1.
Answer:
3x−2y)(4x+3y)
It can be written as =3x(4x+3y)−2y(4x+3y)
By further calculation =12x
2
+9xy−8xy−6y
2
So we get =12x
2
+xy−6y
2
Two functions are shown. f(x) = 29(0.5)* g(x) = 18x + 14 What is the value of f(2) + g(4)?
Answer:
93.25
Explanation:
Given the below functions;
[tex]\begin{gathered} f(x)=29(0.5)^x \\ g(x)=18x+14 \end{gathered}[/tex]To be able to find the value of f(2) + g(4), we have to 1st determine the value of f(2) and f(4) as shown below;
[tex]\begin{gathered} f(2)=29(0.5)^2=29\ast0.25=7.25 \\ g(4)=18(4)+14=72+14=86 \end{gathered}[/tex]Let's go ahead and find the value of f(2) + g(4);
[tex]f(2)+g(4)=7.25+86=93.25[/tex]Whichatest initial value?Use the drop-down menus to show your answer.Function AX026y0515Function Choose...has the greatest initial value.Choose...Functionhas the greatest rate of change.410Function By = 3x - 165432-Function C1 2 3 4 5 6X
Given:
Function A:
Function- B
[tex]y=3x-1[/tex]Function C
Find-:
The function has the greatest initial value
The function has the greatest rate of change
Explanation-:
(A)
The function has the greatest initial value
Check the value at x=0
Value of y is:
For functi
[tex]undefined[/tex]
Write an equation for the graph below in point-slope form and then solve rewrite in slope-intercept form.
We are given the graph of a line and we are asked to determine its equation in point-slope form.
The general form in slope point form of a line is:
[tex]y-y_0=m(x-x_0)[/tex]Where:
[tex]\begin{gathered} m=\text{ slope} \\ (x_0,y_0)\text{ is apoint in the line} \end{gathered}[/tex]to determine the slope we will use the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where:
[tex](x_1,y_1);(x_2,y_2)=\text{ points on the line}[/tex]We will choose two points on the line from the graph:
[tex]\begin{gathered} (x_1,y_1)=(0,1) \\ (x_2,y_2)=(2,2) \end{gathered}[/tex]Now, we plug in the values in the formula for the slope:
[tex]m=\frac{2-1}{2-0}=\frac{1}{2}[/tex]Now, we substitute the value of the slope in the equation of the line:
[tex]y-y_0=\frac{1}{2}(x-x_0)[/tex]Now, we plug in the first point we choose for the line:
[tex]\begin{gathered} y-1=\frac{1}{2}(x-0) \\ \\ y-1=\frac{1}{2}x \end{gathered}[/tex]And thus we have determined the equation of the line in point-slope form.
The slope-intercept form is the following:
[tex]y=mx+b[/tex]To convert this equation to slope-intercept form, we will take the previous equations and we will add 1 to both sides:
[tex]y=\frac{1}{2}x+1[/tex]And thus we have determined the slope-intercept form of the equations of the line.
Can you Help me with this i cannot do ir
To translate f(x) 4 units down we subtract 4 from f(x):
[tex]f(x)-4.[/tex]Now, to reflect f(x)-4 over the x-axis we multiply by -1:
[tex]-1(f(x)-4)=-f(x)+4.[/tex]Answer:
[tex]g(x)=-\sqrt[3]{x-2}+4.[/tex]What transaction occurs when an investor decides to liquidate assets?
A. buy
B. hold
C. sell
D. speculate
Answer:
What transaction occurs when an investor decides to liquidate assets?
A. buy
B. hold
(C. sell)
D. speculate
Step-by-step explanation:
I got a 5/5 on the test and i got the answer from a quizlet (:
Sell is the answer
The correct option is (C).
Given,
In the question:
What transaction occurs when an investor decides to liquidate assets?
Now, According to the question:
when an investor decides to liquidate assets.
when an investor decides to liquidate assets means he or she want to sell the property in the open market, in other words liquidate assets means
converting non- liquid assets into liquid assets.
In investing, liquidation occurs when an investor closes their position in an asset. Liquidating an asset is usually carried out when an investor or portfolio manager needs cash to re-allocate funds or rebalance a portfolio. An asset that is not performing well may also be partially or fully liquidated.
According to the statement
Therefore, Sell is the answer
The correct option is (C).
Learn more about Investor at:
https://brainly.com/question/14283683
#SPJ1
a coyote can run a hundred one in 5.3 seconds a jack-rabbit can run 75 m in 4.7 seconds compared their unit speeds to determine which animal is faster round to the nearest whole unit Blank#1 Coyote speedBlank#2 Jack Rabbit speedBlank#3 Which one is faster
Answer
Coyote's speed = 19 m/s
Jack Rabbit's speed = 16 m/s
The Coyote is faster since 19 > 16.
Explanation
To answer this, we need to note that the relationship between speed, distance and time is given as
Speed = (Distance/Time)
For the Coyote,
Distance = 101 m
Time = 5.3 seconds
Speed = (Distance/Time)
Coyote's speed = (101/5.3) = 19 m/s
For the Jack Rabbit,
Distance = 75 m
Time = 4.7 seconds
Speed = (Distance/Time)
Jack Rabbit's speed = (75/4.7) = 16 m/s
Since 19 m/s is evidently greater than 16 m/s, we can conclude that the Coyote is faster than the Jack Rabbit.
Hope this Helps!!!
Solve the inequality for x and identify the graph of its solution.|x+ 2] < 2Choose the answer that gives both the correct solution and the correct graph.
| x + 2 | < 2
-2 < x + 2 < 2
-2 - 2 < x + 2 < 2 - 2
-4 < x < 0 This is the inequality
Letter B is the right choice.
Calculate the average rate of change for the function f(x) = 3x4 − 2x3 − 5x2 + x + 5, from x = −1 to x = 1.
a
−5
b
−1
c
1
d
5
Average rate of change for the function f(x) = 3x⁴ -2x³ -5x² +x +5 from
x =-1 to x=1 is equal to -1.
As given in the question,
Given function :
f(x) = 3x⁴ -2x³ -5x² +x +5
Formula for average rate of change for (a, f(a)) and (b, f(b))
[f(b) -f(a)] / (b-a)
Substitute the value of a=-1 and b=1
f(-1)=3(-1)⁴ -2(-1)³-5(-1)² +(-1) +5
= 3+2-5-1+5
=4
f(1)=3(1)⁴ -2(1)³-5(1)² +(1) +5
= 3-2-5+1+5
= 2
Average rate of change = (2-4)/(1-(-1))
= -2/2
=-1
Therefore, average rate of change for the function f(x) = 3x⁴ -2x³ -5x² +x +5 from x =-1 to x=1 is equal to -1.
Learn more about function here
brainly.com/question/28744270
#SPJ1
A friend plans to purchase a 72-inch tv at a particular store for a cost of $1500. The store is offering 25% off any one item. He also has an internet coupon for an additional 10% off any discounted price. How much will your friend save (a) in dollar amount and (b) in percent?
the The Solution.
The marked price of the 72-inch TV = $1500
25% discount makes the actual discount to be:
[tex]\begin{gathered} \text{Actual Discount = 25 \% of 1500} \\ \text{ = }\frac{25}{100}\times1500=\text{ \$375} \end{gathered}[/tex]So, the discounted price will now be
Discounted price = 1500 - 375 = $1125
He has an additional 10% internet coupon discount on already dicounted price ($1125) .
[tex]\begin{gathered} \text{Additional discount = 10\% of 1125} \\ \text{ =}\frac{10}{100}\times1125=\text{ \$112.50} \end{gathered}[/tex]a. The friend will save
[tex]\begin{gathered} 375+112.50 \\ =\text{ \$487.50} \end{gathered}[/tex]b. in percentage, he saved
[tex]\frac{487.5}{1500}\times100=32.5\text{ \%}[/tex]Therefore, the correct answers are:
a. $487.50
b. 32.5%
Katie opened a savings account and deposited 1,000.00 as principal the account earns 4% interest compounded quarterly what is the balance after 6 years
P = $1000
r = 4% = 4/100 = 0.04
t = 6 years
Therefore,
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=1000(1+\frac{0.04}{4})^{4\times6} \\ A=1000\times1.26973464853 \\ A=1269.73464853 \\ A=\text{ \$1269.73} \end{gathered}[/tex]6-Find the measure of ∠AEB.A. 122°B. 132°C. 142°D. 152°7-Find the measure of ∠BEC.A. 58 °B. 48°C. 38°D. 28°8-Find the measure of ∠CED.A. 52 °B. 48 °C. 42 °D. 32°9-Find the measure of ∠FEB.A. 142°B. 180°C. 90°D. 0°10-Find the measure of ∠FED.A. 0°B. 180°C. 45°D. 90°
The answer for 6 is C. 142°
Explanation
∠AEB = 180 - ∠AEF (Sum of angle on a straight line)
∠AEB = 180 - 38 = 142°
.Find the area of the sector with radius 4 and central angle, ∅= 45°
Remember that the formula for the area of a sector is:
[tex]A=\frac{\pi\cdot r^2\cdot\theta}{360}[/tex]Where:
• r, is the radius
,• Theta ,is the central angle (in degrees)
Using this formula and the data given,
[tex]\begin{gathered} A=\frac{\pi\cdot4^2\cdot45}{360} \\ \rightarrow A=2\pi \end{gathered}[/tex]what is the area of a triangle with the legth of 8in,12in,6in
Area is
[tex]A=\frac{1}{2}bh=\frac{1}{2}\times6\times8=\frac{48}{2}=24[/tex]answer: 24 sq in
Susanna has played the piano for s years. Patrick has played the piano for 4 more than twice the number of years that susanna has been playing the piano. which expression correctly shows the number of years that Patrick has been playing the piano.2s + 44s + 22 (s + 4)(s - 4) ÷ 3none of the above
Given data:
The expression for Patrick paly Piano is,
[tex]P=2s+4[/tex]Thus, the first option is correct.
Solve the problem. Use 3.14 as the approximate value of pie
The volume of a cylinder is calculated using the formula:
[tex]V=\pi r^2h[/tex]where r is the radius of the cylinder and h is the height.
From the question, we have the following parameters:
[tex]\begin{gathered} diameter=4.8 \\ \therefore \\ r=\frac{4.8}{2}=2.4 \\ and \\ h=6.66 \end{gathered}[/tex]Therefore, we c n calculae tehe volume of a cylinder to be:
[tex]\begin{gathered} V=3.14\times2.4^2\times6.66 \\ V=120.455424 \end{gathered}[/tex]For four cylinders, the combined volume will be:
[tex]\begin{gathered} V=120.455424\times4 \\ V=481.821696 \end{gathered}[/tex]The volume i 481 .82 cubic inches.
Find the length of AC and the measures of a and 0
ANSWER:
AC = 3√ 17
α = 75.96°
Θ = 14.04°
STEP-BY-STEP EXPLANATION:
We can calculate the length of side AC by means of the Pythagorean theorem, just like this:
[tex]\begin{gathered} c^2=a^2+b^2 \\ \text{ in this case:} \\ (AC)^2=3^2+12^2 \\ (AC)^2=9+144 \\ AC=\sqrt[]{153} \\ AC=3\sqrt[]{17} \end{gathered}[/tex]We can calculate the angles by applying the following trigonometric ratios:
[tex]\begin{gathered} \sin \alpha=\frac{12}{3\sqrt[]{17}} \\ \alpha=\arcsin \mleft(\frac{12}{3\sqrt{17}}\mright) \\ \alpha=75.96 \\ \\ \sin \theta=\frac{3}{3\sqrt[]{17}} \\ \theta=\arcsin \mleft(\frac{3}{3\sqrt{17}}\mright) \\ \theta=14.04 \end{gathered}[/tex]I’m struggling on this math question and could use some help on it
Let's determine the values of f(-4) and g(6).
For f(-4),
[tex]\text{ f\lparen x\rparen= -2x}^3\text{ - 5}[/tex][tex]\text{ f\lparen-4\rparen= -2\lparen-4\rparen}^3-5\text{ = -2\lparen-64\rparen- 5}[/tex][tex]\text{ f\lparen-4\rparen = 128 - 5}[/tex][tex]\text{ f\lparen-4\rparen = 123}[/tex]Therefore, f(-4) = 123
For g(6),
[tex]\text{ g\lparen x\rparen = -3x - 3}[/tex][tex]\text{ g\lparen6\rparen = -3\lparen6\rparen - 3 = -18 - 3}[/tex][tex]\text{ g\lparen6\rparen = -21}[/tex]Therefore, g(6) = -21
The function f(t) = 2(2.25)^t models the growth of bacteria cells, where f(t) is the number of bacteria cells and t is time in days. After 10 days, approximately how many bacteria cells are there?
Step 1
write out the function
[tex]\begin{gathered} f(t)=2(2.25)^t \\ \end{gathered}[/tex]Step 2
for every input, an input produce unique output
t = 10days is the input
Step 3
substitute t = 10 in the function
[tex]\begin{gathered} f(t)=2(2.25)^{10} \\ =\text{ 2 }\times2.25^{10} \\ =\text{ 2 x 3325.25673} \\ =\text{ 6650.51} \\ =\text{ 6651} \end{gathered}[/tex]An object is dropped from 27 feet below the tip of the pinnacle atop a 1471-ft tall building. The height h of the object after t seconds is giveh= - 16t^2 + 1444. Find how many seconds pass before the object reaches the ground.How many seconds pass before the object reaches the ground
The Solution:
Given:
[tex]h=-16t^2+1444.[/tex]We are required to find t when h = 0.
[tex]\begin{gathered} -16t^2+1444=0 \\ \\ -16t^2=-1444 \end{gathered}[/tex]Divide both sides by -16.
[tex]t^2=\frac{-1444}{-16}=90.25[/tex][tex]\begin{gathered} t=\sqrt{90.25} \\ \\ t=9.5\text{ or }t=-9.5 \end{gathered}[/tex]Thus, the correct answer is 9.5 seconds.
Which of the following tables represents a function?
Answer:
Table A represents a function
Step-by-step explanation:
Table A represents function because it is the only table that doesn't repeat an output or input number.
1. Consider the graph f(x) = 34. Describe how to graph thetransformation f(x – 3) + 2.
If the graph shows a constant function, the value of f(x) will always be the same no matter which value does x take. It means: to graph the transformation of this function do an horizontal translation right 3 units (which would show the same graph, basically) and then do a vertical translation up 2 units
Sue would like to join a gym. Gym A has a $56 joining fee with $3 per visit. Gym B has a $30 joining fee with a $5 per visit. Let x represent the number of visits. After how many visits would the cost of the two gyms be the same?
Let x represent the number of visits it will take for the cost of the two gyms to be the same.
Gym A has a $56 joining fee with $3 per visit. This means that the cost of x visits of gym A would be
3 * x + 56
= 3x + 56
Gym B has a $30 joining fee with a $5 per visit. This means that the cost of x visits of gym B would be
5 * x + 30
= 5x + 30
For both costs to be the same, it means that
3x + 56 = 5x + 30
5x - 3x = 56 - 30
2x = 26
x = 26/2
x = 13
After 13 visits, the cost of the two gyms would be the same
15% of $764.69rounded to the nearest cent.
Percentage is expressed in terms of 100. To find 15% of 764.69, we would multiply ratio of 15% to 100% by 764.69. Thus, we have
15/100 * 764.69
= 114.7035
How to draw the graphs of the following non-linear functions?y=x^2 + 1y=3^x + 1
The first step is to substitute values of x into each equation.
For y = x^2 + 1,
if x = - 2, y = (- 2)^2 + 1 = 4 + 1 = 5
if x = - 1, y = (- 1)^2 + 1 = 1 + 1 = 2
if x = 0, y = (0)^2 + 1 = 0 + 1 = 1
if x = 1, y = (1)^2 + 1 = 1 + 1 = 2
if x = 2, y = (2)^2 + 1 = 4 + 1 = 5
We would plot the corresponding values of x and y on the graph as shown below
For y = 3^(x + 1),
if x = - 2, y = 3^(-2 + 1) = 3^-1 = 0.33
if x = - 1, y = 3^(-1 + 1) = 3^0 = 1
if x = 0, y = 3^(0 + 1) = 3^1 = 3
if x = 1, y = 3^(1 + 1) = 3^2 = 9
if x = 2, y = 3^(2 + 1) = 3^3 = 27
We would plot the corresponding values of x and y on the graph as shown below
10) 4 4.5 5 5 5.5 6 Y | 0.5 0.6 0.8 LE 0.9 1.2 Which is most likely the equation of the line of best fit for the data given in the table? DELLE А y=034X=09 B y = 0.25x -0.7 с y =0.45x = 1 y=0.50 x -0.6
y = 0.34x - 0.9 (Option A)
We are given the data and we want to find the line of best fit.
The line of best fit is a line that goes through the data points and it gives the best representation of the spread of the data.
The equation of a line is given as:
y = mx + c
y represents y-values
x represents x-values
m is the slope of the line
c is the y-intercept of the line or where the line crosses the y-axis.
To get this equation for this question, we need to find both m and c.
In order to do this, the formulas are given below:
[tex]\begin{gathered} M=\frac{\sum(x_i-\bar{\bar{X})(y_i-\bar{Y)}}}{\sum(x_i-\bar{X)^2}} \\ \text{where M is slope} \\ x_i=\text{ individual data points of x} \\ X=\operatorname{mean}\text{ of x values} \\ Y=\text{ mean of y values} \end{gathered}[/tex]While for c or the y-intercept, we have:
[tex]\begin{gathered} c=\bar{Y}-m\bar{X} \\ \text{where Y and X retain their same meaning from before} \end{gathered}[/tex]Before we can calculate m and c, we need to calculate the means of both x and y values give to us.
This is done below:
[tex]\begin{gathered} \operatorname{mean}=\frac{\sum x_i}{n} \\ \\ \bar{Y}=\frac{0.5+0.6+0.8+0.9+1.2}{5}=0.8 \\ \bar{X}=\frac{4+4.5+5+5.5+6}{5}=5 \end{gathered}[/tex]Now we can proceed to get the slope m of our line.
In order to be tidy, we shall use a table to solve. This table is shown in the image below:
Thus, we can now calculate our slope m:
[tex]\begin{gathered} M=\frac{\sum(x_i-\bar{\bar{X})(y_i-\bar{Y)}}}{\sum(x_i-\bar{X)^2}} \\ \\ M=\frac{(-1)(-0.3)+(-0.5)(-0.2)+0(0)+(0.5)(0.1)+(1)(0.4)}{1+0.25+0+0.25+1} \\ \\ M=\frac{0.3+0.1+0+0.05+0.4}{2.5}=0.34 \end{gathered}[/tex]Therefore the slope (m) = 0.34
Now to calculate intercept (c)
[tex]\begin{gathered} c=\bar{Y}-m\bar{X} \\ \bar{Y}=0.8\text{ (from previous calculation above)} \\ \bar{X}=5\text{ (from previous calculation above)} \\ \\ c=0.8-0.34\times5 \\ c=0.8-1.7=-0.9 \end{gathered}[/tex]Therefore, the intercept (c) = - 0.9
Bringing it all together, we can write the equation of the line as:
y = 0.34x - 0.9
Therefore the answer is: y = 0.34x - 0.9 (Option A)