Given:
The eqution is given as, x^2 + 4x + 1 = 0.
The objective is to solve the equation by compleing the square.
Consider the middle of the equation.
[tex]2\cdot a\cdot b=4x[/tex]Here, the value of a is x. Then, the value of b can be calculated as,
[tex]\begin{gathered} 2(x)\cdot b=4x \\ b=\frac{4x}{2x} \\ b=2 \end{gathered}[/tex]To complete the equation add +b^2 and -b^2 to the equation.
[tex]\begin{gathered} x^2+4x+2^2-2^2+1=0 \\ x^2+4x+2^2-4+1=0 \\ x^2+4x+2^2-3=0 \\ (x+2)^2-3=0 \\ (x+2)^2=3 \end{gathered}[/tex]Take square root on both sides, to solve the value of x,
[tex]\begin{gathered} \sqrt[]{(x+2)^2}=\sqrt[]{3} \\ x+2=\pm\sqrt[]{3} \\ x=\pm\sqrt[]{3}-2 \\ x=+\sqrt[]{3}-2\text{ and -}\sqrt[]{3}-2 \end{gathered}[/tex]Hence, the value of x are +√3-2 and -√3-2.
When 8 is subtracted from a number and that difference is doubled, the result is 10. What is the number?
A) 6
B) 5
C) 18
D) 13
Answer:
n = 13
Step-by-step explanation:
Find the number
8 is subtracted from a number
(n-8)
that difference is doubled
2(n-8)
the result is 10
2(n-8) = 10
Solve the equation by dividing each side by 2
2(n-8)/2 = 10/2
n-8 = 5
Add 8 to each side
n-8+8 = 5+8
n = 13
round 6.991 to two decimal places
Since 6.99 < 6.991 < 7.00, and the number 6.991 is nearer to 6.99 than to 7.00, then 6.991 rounded to two decimal places, is:
[tex]6.99[/tex]A football team is losing by 14 points near the end of a game. The team scores two touchdowns (worth 6 points each) before the end of the game. After each touchdown, the coach must decide whether to go for 1 point with a kick (which is successful 99% of the time) or 2 points with a run or pass (which is successful 45% of the time). If the team goes for 1 point after each touchdown, what is the probability that the coach’s team wins? loses? ties? If the team goes for 2 points after each touchdown, what is the probability that the coach’s team wins? loses? ties? Can you develop a strategy so that the coach’s team has a probability of winning the game that is greater than the probability of losing
His football team is losing 14 points near the end of the game. The team scores two touchdowns with each worth 6 points (total = 12 points).
After each touchdown, the coach must decide whether to go for 1 point with each kick(99% successful) or 2 points with a run or pass(45% successful).
Note
Two touchdown = 12 points
So, it remaining 2 point to level up and more than 2 points to win the game
a.
If the team goes for 1 point after each touchdown, the probability that the coach's team loses? wins? ties? can be computed below
[tex]undefined[/tex]What is the value of 32 / (-4)?- 128 8- 828
The expression given is,
[tex]\frac{32}{(-4)}[/tex]Let us now evaluate the expression
[tex]\frac{32}{(-4)}=\frac{32}{-4}=-8[/tex]Hence, the answer is -8.
Teresa has a bookcase with 8 shelves. There are n books on each shelf. Using n, write an expression for the total number of books.
Answer:
8*n
Step-by-step explanation:
You solve this question by multiplying the number of shelves by the number of books to find the total number of books on the shelves.
Reece increases the amount of money he pays into his savings account by 4% each year. This year, he paid £3000 into his account. To the nearest penny, how much did Reece pay into his account a) 1 year ago? b) 10 years ago?
The money deposited 1 year ago is $2884.61 and the money deposited 10 years ago is $2142.85.
Given that, Reece increases the amount of money he pays into his savings account by 4% each year.
What is savings account?A savings account is a bank account at a retail bank. Common features include a limited number of withdrawals, a lack of cheque and linked debit card facilities, limited transfer options and the inability to be overdrawn.
We know that, simple interest = (P×R×T)/100
a) P=$x, R=4% and T=1 year
SI=3000-x
⇒ 3000-x = (x×4×1)/100
⇒ 3000-x=0.04x
⇒ 1.04x=3000
⇒ x=3000/1.04
⇒ x=$2884.61
Money deposited 1 year ago is $2884.61.
b) P=$y, R=4% and T=10 year
SI=3000-y
⇒ 3000-y = (y×4×10)/100
⇒ 3000-y = 0.4y
⇒ 1.4y = 3000
⇒ y=3000/1.4
⇒ y=$2142.85
Therefore, the money deposited 1 year ago is $2884.61 and the money deposited 10 years ago is $2142.85.
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During a heavy rainstorm a city in Florida received 12 1/4 inches of rain in 25 1/2 hours.What is the approximate rainfall rate in inches per hour?
Data:
The city received 12 (1/4) inches of rain in 25 (1/2) hours.
Procedure:
Rewriting the numbers as decimals.
[tex]12\cdot\frac{1}{4}=12.25[/tex][tex]25\cdot\frac{1}{2}=25.5[/tex]To find the approximate rainfall rate in inches per hour, we have to do as follows:
[tex]\frac{12.25}{25.5}\approx0.48\frac{in}{h}[/tex]Rounding the result, we get...
[tex]0.48\approx0.5\approx\frac{1}{2}[/tex]Answer: D. about 1/2 inch per hour
The Consumer Price Index (CPI), which measures the cost of a typical package of consumer goods, was 202.9 in 2011 and 233.2 in 2016. Let x=11 correspond to the year 2011 and estimate the CPI in 2013 and 2014. Assume that the data can be modeled by a straight line and that the trend continues indefinitely. Use two data points to find such a line and then estimate the requested quantities. Let y represent the CPI. The linear equation that best models the CPI is____ (Simplify your answer. Use integers or decimals for any numbers in the equation. Round to the nearest hundredth as needed.)
The first thing we have to identify in our problem are the variables
[tex]\begin{gathered} x\to\text{time} \\ y\to\text{CPI} \end{gathered}[/tex]Now we see the points (x,y) that gives us the problem
[tex]\begin{gathered} 2011\to(11,202.9) \\ 2016\to(16,233.2) \end{gathered}[/tex]Since behavior can be modeled by a straight line, we use the general equation of the straight line
[tex]y=mx+b[/tex]Where m is the slope of the line and b is the y-intercept.
Taking this into account and with the 2 points that they give us, we proceed to calculate the equation of the line starting with the slope:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{233.2-202.9}{16-11} \\ m=\frac{30.3}{5} \\ m=6.06 \end{gathered}[/tex][tex]\begin{gathered} y=6.06x+b \\ 202.9=6.06(11)+b \\ b=202.9-66.66 \\ b=136.24 \end{gathered}[/tex]The equation that models the behavior of the CPI is
[tex]y=6.06x+136.24[/tex]Now we calculate the CPI values for the years 2013 and 2014
[tex]\begin{gathered} 2013\to x=13 \\ y=6.06(13)+136.24 \\ y=78.78+136.24 \\ y=215.02 \end{gathered}[/tex][tex]\begin{gathered} 2014\to x=14 \\ y=6.06(14)+136.24 \\ y=84.84+136.24 \\ y=221.08 \end{gathered}[/tex]the Anderson are going on a long sailing trip during the summer however one of the sails on their sailboat ripped and they have to replace it the sail is pictured below if the sailboat sails are sale for 2$ per square foot how much will the new sail cost?
Firs we need to calculate the area of a triangle
[tex]A=\frac{b\cdot h}{2}[/tex]b= base
h=heigth
in our case
b=8ft
h=12ft
[tex]A=\frac{8\cdot12}{2}=\frac{96}{2}=48ft^2[/tex]then we will calculate the total cost
1 square foot ----- $2
48 square feet ----- x
the total cost is 48*2=96
total cost is $96
Use the given instructions to answer question 17 to question 20.
Given
The boxplot.
And, the total number of students in the class is 60.
To find:
a) The percentage of students who received one or more moving violation.
b) The number of parking violations received by at least 50% of students.
c) How many students received two or more parking violation.
Explanation:
a) From the figure,
The percentage of students who received one or more moving violation is,
[tex]Percentage\text{ of students}=75\%[/tex]Because the number of students having minimum moving violation is 0, and the number of students having maximum moving violation is 4.
b) The number of parking violation received by at least 50% of students is,
[tex]\begin{gathered} Number\text{ }of\text{ }parking\text{ }violation\text{ received by at least 50}\%\text{ of students } \\ is\text{ }2\text{ }or\text{ }more. \end{gathered}[/tex]c) The number of students who received two or more parking violation is,
[tex]\begin{gathered} Number\text{ of students}=75\%\times60 \\ =\frac{75}{100}\times60 \\ =45 \end{gathered}[/tex]Hence, the number of students who received two or more parking violation is 45.
Find the length of the third side. If necessary, write in simplest radical form.
4
4√5
can u pls help me with this question and this is homework
the probability is:
[tex]\frac{15+5}{50}=\frac{20}{50}=\frac{2}{5}[/tex]so the answer is 2/5
The days high temperature in Detroit , Michigan was recorded as 41 degrees F . Use the formula C = 5/9 ( F- 32) to write 41 degrees F as degrees celsius
Step 1
Given;
Step 2
[tex]\begin{gathered} C=\frac{5}{9}(F-32) \\ F=41 \\ C=\frac{5}{9}(41-32) \\ C=\frac{5}{9}(9) \\ C=5^{\circ}C \end{gathered}[/tex]Answer;
[tex]5^{\circ}C[/tex]Consider the graph of the linear function shown.What is the approximate average rate of change of this function from = -2 to r = 2?lesleso3-Yes
The average rate of change of this function from x = -2 to x = 2 can be gotten by finding the slope of the line using both x coordintes;
From the graph, when x1 = -2, y1 = 2.5
Also when x2 = 2, y2 = 0.5
Using the formula for calculating slope expressed as;
m = y2-y1/x2-x1
Substitute the given values
m = 0.5-2.5/2-(-2)
m = -2.0/2+2
m = -2/4
m = -1/2
Hence average rate of change of this function from x = -2 to x = 2 is -1/2. Option C is correct.
I really am struggling with this, could I have some help?
We are to find f(x) - g(x):
We will subtract the expressions of g(x) from f(x)
[tex]\begin{gathered} f(x)-g(x)=x^2\text{ + 1 - (2x - 5)} \\ \end{gathered}[/tex]Expanding the parenthesis using distributive property:
[tex]\begin{gathered} f(x)-g(x)=x^2\text{ + 1 - (2x) -(-5)} \\ mu\text{ltiplication of same signs gives positive sign} \\ m\text{ ultiplication of opposite signs give negative sign} \\ \\ f(x)-g(x)=x^2\text{ + 1 -2x + 5} \end{gathered}[/tex]collect like terms:
[tex]\begin{gathered} f(x)-g(x)=x^2\text{ -2x + 5 }+\text{ 1} \\ f(x)-g(x)=x^2\text{ - 2x + 6} \end{gathered}[/tex]Using everyday knowledge, indicate whether the if-then statements are correct forward-only or both forward and reverse.
Statement 1: If Bob is Sally’s spouse, then Sally is Bob’s spouse.
Statement 2: If the light is red Northbound, then the traffic is stopped.
Subtract the expressions. (10y - 2) - (8y + 3)
SOLUTION
We want to solve the expression
[tex]\mleft(10y-2\mright)-(8y+3)[/tex]Now, use the minus sign to multiply the other part
That is
[tex]-(8y+3)[/tex]We have
[tex]\begin{gathered} (10y-2)-(8y+3) \\ 10y-2-8y-3 \\ \text{collecting like terms } \\ 10y-8y-2-3 \\ 2y-5 \end{gathered}[/tex]Hence the answer is 2y - 5
Jx+Ky< assume J<0
The equivalent inequality with x isolated in the left side is
The equivalent inequality with x isolated in the left side is x<(L-Ky)/J
What is equivalent inequality?A positive number divided by both sides of an inequality results in an equal inequality. And if the inequality symbol is reversed, division on both sides of an inequality with a negative value results in an analogous inequality.
Following step by step process-
Jx+Ky<L (Given)
Subtracting Ky on both the side
Jx<L-Ky
Now dividing by J both side
x<(L-Ky)/J
Therefore, equivalent inequality with x isolated in the left side is x<(L-Ky)/J.
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The complete question is:
"Jx+Ky<L assume J<0
The equivalent inequality with x isolated in the left side is"
Determine an algebraic model of a function that satisfies the following key features.
Solution:
Given the conditions;
[tex]As\text{ }x\rightarrow-\infty,y\rightarrow\infty\text{ and }x\rightarrow\infty,y\rightarrow\infty[/tex]When;
[tex]x\rightarrow-\infty,y\rightarrow\infty[/tex]Then, the degree of the polynomial is even.
Then, given three x-intercepts, it means one of the root could have been repeated.
Thus, the model function is;
[tex]f\lparen x)=\left(x+1\right)\left(x-3\right)\left(x^2\right)[/tex]Solve for the remaining angles and side of the one triangle that can be created. Round to the nearest hundredth:A = 100"a = 3.5, b = 3
Given:
• A = 100 degrees
,• a = 3.5
,• b = 3
Let's solve for the remaining angles and side of the triangle.
Here, we are given one angle and two sides.
To solve, apply the Law of Sines:
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]• To solve for measure of angle B, we have:
[tex]\begin{gathered} \frac{\sin A}{a}=\frac{\sin B}{b} \\ \\ \frac{\sin100}{3.5}=\frac{\sin B}{3} \\ \\ \sin B=\frac{3\sin 100}{3.5} \\ \\ \sin B=\frac{2.954}{3.5} \\ \\ \sin B=0.844 \end{gathered}[/tex]Take the sine inverse of both sides:
[tex]\begin{gathered} B=\sin ^{-1}(0.844) \\ \\ B=57.58^0 \end{gathered}[/tex]Therefore, the measue of angle B is = 57.58 degrees.
• To solve for angle C, apply the Triangle Angle Sum Theorem.
m∠A + m∠B + m∠C = 180
m∠C = 180 - m∠A - m∠B
m∠C = 180 - 100 - 57.68
m∠C = 22.32
The measure of angle C is 22.32 degrees.
• To find the length of c, apply the Law of Sines:
[tex]\begin{gathered} \frac{\sin A}{a}=\frac{\sin C}{c} \\ \\ \frac{\sin100}{3.5}=\frac{\sin 22.32}{c} \\ \\ c=\frac{3.5\sin 22.32}{\sin 100}\tan ^{-1}\tan ^{-1} \\ \\ c=\frac{1.329}{0.9848} \\ \\ c=1.35 \end{gathered}[/tex]The length of side c is 1.35 units.
ANSWER:
• B = 57.58,°
,• C = 22.32,°
,• c = 1.35
Jalisa needs to purchase a cover for her oval-shaped pool. The pool's length and width measurements, as marked by dotted lines, are 30 feet and 13 feet.If Jalisa wants the pool cover to extend one foot from the pool's edge, as shown in the drawing, what will be the area of therectangular pool cover?A. 390 square feetOB. 434 square feetOC 480 square feetD. 86 square feet
She wants to cover the pool with a rectangular pool cover that extends one foot from the pool edges in every direction.
The length of the pool is 30ft and the width is 13ft, if the pool cover must extend 1ft over the pool's edge, then you have to add 2ft to the length and 2ft to the width, as shown below:
So, the length of the pool cover will be equal to the length of the pool plus two feet:
[tex]length=30ft+2ft=32ft[/tex]And the width of the pool cover will be equal to the width of the pool plus two feet:
[tex]width=13ft+2ft=15ft[/tex]Once you determined the width and length of the rectangular pool cover, you can calculate its area:
[tex]\begin{gathered} A=wl \\ A=15*32 \\ A=480ft^2 \end{gathered}[/tex]The area of the rectangular pool cover is 480 square feet (option C)
Kyle has a container of flour in the shape of a cylinder.
Answer:
Part A:
The volume of a cylinder is given below as
[tex]\begin{gathered} V_{cylinder}=\pi\times r^2\times h \\ r=\frac{d}{2}=\frac{10in}{2}=5in \\ h=8in \end{gathered}[/tex]By substituting the values , we will have
[tex]\begin{gathered} V_{cyl\imaginaryI nder}=\pi r^2h \\ V_{cyl\mathrm{i}nder}=\pi\times5^2\times8 \\ V_{cyl\mathrm{i}nder}=\pi\times200 \\ V_{cyl\mathrm{i}nder}=628.3in^3 \end{gathered}[/tex]Hence,
The volume = 628.3in³
Part B:
To determine the weight of the flour in ounces, we will use the relation below
[tex]\begin{gathered} 0.13ounce=1in^3 \\ x=628.3in^3 \\ cross\text{ multiply, we will have} \\ x=0.13\times628.3 \\ x=81.679 \\ x\approx81.7ounces \end{gathered}[/tex]Hence,
The weight = 81.7 ounces
can someone please help me find the answer to the following?
We are given a tangent and a chord of a circle. The angle ABC form by the intersection of the tangent and the chord is half the arc they both intersect, therefore, we must find the major arc of the circle, we can do that with the fact that the total arc of the circle is 360, therefore:
[tex]\begin{gathered} \text{arcAB}=360-50 \\ \text{arcAB}=310 \end{gathered}[/tex]Therefore, the angle is:
[tex]\begin{gathered} \angle ABC=\frac{1}{2}\times310 \\ \angle ABC=155 \end{gathered}[/tex]Angle ABC is 155 degrees.
12) A row of roses is planted in a repeating pattern of "red, red, yellow, yellow, pink, pink
There is a total of 56 roses planted in the row. How many red roses are there?
Answer:
********
Answer:
22
Step-by-step explanation:
XXxxxxXXxxxxXXxxxxXXxxxxXXxxxxXXxxxxXXxxxxXXxxxxXXxxxxXX
Each of the capital X's are red roses, and there are 56 x's in total.
2+2 is what i need help???
We have the following problem given:
[tex]2+2=4[/tex]Then the final answer for this case would be 4
On number 9, you have to figure out the value of X. I attempted to solve the equation and got the answer of 46. Am I correct?
From the number line given, we have the miles increasing from x all the way to 184. Similarly, we have the hours increasing all the way from 4 to 16.
To find out the value of x, we need to set up an equation that uses the ratio of both miles and hours. This is shown below;
[tex]\frac{x}{4}=\frac{184}{16}[/tex]We now cross multiply and we have;
[tex]\begin{gathered} x=\frac{4\times184}{16} \\ x=\frac{184}{4} \\ x=46 \end{gathered}[/tex]ANSWER:
[tex]x=46[/tex]Tina designed an electric skateboard that has a speed of 4 miles per hour. She wants to write a function that represents the distance the skateboard will travel over a given amount of time.Which is the dependent variable in this scenario?the skateboardthe speedthe time traveledthe distance traveled
ANSWER
The distance traveled
EXPLANATION
We want to identify the dependent variable from the scenario.
The dependent variable in a function is the variable that changes as a result of a change in the independent variable. This implies that it depends on the independent variable for its value.
From the scenario, the distance that the skateboard travels is dependent on the amount of time spent traveling.
Therefore, the dependent variable is the distance traveled.
For the data shown in the scatter plot, which is the best estimate of r?The answer choices are .94 .-45 .-94 .45
Pearson's correlation coefficient, r, measures the linear relationship between two variables. The correlation coefficient can take a range of values from +1 to -1.
• A value of 0 indicates that there is no association between the two variables.
,• A value ,greater than 0, indicates a ,positive association., That is, as the value of one variable increases, so does the value of the other.
,• A value ,less than 0, indicates a ,negative association,; that is, as the value of one variable increases, the value of the other decreases.
Graphically,
In this case, you can see that as the value of a variable x increases, the value of the variable y other decreases. Then, the correlation coefficient of these two variables is negative.
Also, you can see that the values of the variables do not completely fit a line but are very close to one.
Therefore, the best estimate of r is -.94.
Can you help me resolve this using the quadratic formula?
a) Time taken to hit the ground = 1.674 seconds
b) Height at 1 second = 12 m
Explanation:The equation representing the height of the water balloon after t seconds is:
[tex]h(t)=-16t^2+25t+3[/tex]a) At the ground, h(t) = 0
[tex]\begin{gathered} 0=-16t^2+25t+3 \\ \\ 16t^2-25t-3=0 \\ \\ Using\text{ the quadratic formula} \\ t=\frac{-(-25)\pm\sqrt{(-25)^2-4(16)(-3)}}{2(16)} \\ \\ t=\frac{25\pm\sqrt{817}}{32} \\ \\ t=-0.111975,\text{ 1.67448} \end{gathered}[/tex]Since time cannot be negative:
Time taken to hit the ground = 1.674 seconds
b) Height at t = 1 second
[tex]\begin{gathered} H(t)=-16t^2+25t+3 \\ \\ H(1)=-16(1^2)+25(1)+3 \\ \\ H(1)=-16+25+3 \\ \\ H(1)=12\text{ m} \end{gathered}[/tex]Height at 1 second = 12 m
if the radius of the circle is 5 units, find the arc length of RQ
The radius of the circle is r = 5 units.
The formula for the arc length of RQ is,
[tex]RQ=2\pi r\times(\frac{\theta}{360})[/tex]Substitute the values in the formula to obatin the arc length RQ.
[tex]\begin{gathered} RQ=2\pi\cdot5\cdot(\frac{142}{360}) \\ =12.391 \\ \approx12.39 \end{gathered}[/tex]So arc length of RQ is 12.39 units.