Given the equations:
[tex]\begin{gathered} f(x)=3x^2+5 \\ \\ g(x)=4x+4 \end{gathered}[/tex]Let's find the point where both equations intersect.
To find the point let's first find the value of x by equation both expression:
[tex]3x^2+5=4x+4[/tex]Now, equate to zero:
[tex]\begin{gathered} 3x^2+5-4x-4=0 \\ \\ 3x^2-4x+5-4=0 \\ \\ 3x^2-4x+1=0 \end{gathered}[/tex]Now let's factor by grouping
[tex]\begin{gathered} 3x^2-1x-3x+1=0 \\ (3x^2-1x)(-3x+1)=0 \\ \\ x(3x-1)-1(3x-1)=0 \\ \\ \text{ Now, we have the factors:} \\ (x-1)(3x-1)=0 \end{gathered}[/tex]Solve each factor for x:
[tex]\begin{gathered} x-1=0 \\ Add\text{ 1 to both sides:} \\ x-1+1=0+1 \\ x=1 \\ \\ \\ \\ 3x-1=0 \\ \text{ Add 1 to both sides:} \\ 3x-1+1=0+1 \\ 3x=1 \\ Divide\text{ both sides by 3:} \\ \frac{3x}{3}=\frac{1}{3} \\ x=\frac{1}{3} \end{gathered}[/tex]We can see from the given options, we have a point where the x-coordinate is 1 and the y-coordinate is 8.
Since we have a solution of x = 1.
Let's plug in 1 in both function and check if the result with be 8.
[tex]\begin{gathered} f(1)=3(1)^2+5=8 \\ \\ g(1)=4(1)+4=8 \end{gathered}[/tex]We can see the results are the same.
Therefore, the point where the two equations meet is:
(1, 8)
ANSWER:
B. (1, 8)
What is the equation in slope-intercept form of the line that passes through the point (1,5) and is parallel to the line represented by 3x-y=4?
Answer:
[tex]3x - 14[/tex]
Step-by-step explanation:
-y= -3x+4
-1 because de y no have a number in front
-1y÷-1= -3x÷-1 4÷-1
I need help figuring out how to write out this problem correctly.
Answer
[tex]\frac{\sqrt{10}}{11}[/tex]Step-by-step explanation
Given the expression:
[tex]\sqrt{\frac{10}{121}}[/tex]Distributing the square root over the division and evaluating the square root at the denominator:
[tex]\begin{gathered} \frac{\sqrt{10}}{\sqrt{121}} \\ \frac{\sqrt{10}}{11} \end{gathered}[/tex]Finding the final amount in a word problem on continuous exponential growth or decay
Given:
The mass of radioactive follows an exponential decay model
The initial mass = 418 kg
Decreases at a rate = r = 4% per day
So, the general formula for the mass will be:
[tex]m=418\cdot(1-0.04)^d[/tex]where: (m) is the mass after (d) days
So, to find the mass after 2 days, we will substitute with d = 2
so,
[tex]m=418\cdot(1-0.04)^2=418\cdot0.96^2=385.2288[/tex]rounding to the nearest tenth
so, the answer will be mass after 2 days = 385.2 kg
Let v be the vector from initial point P1=(−4,−9) to terminal point P2=(6,2). Write v in terms of i and j.
Step 1;
P1 = ( - 4 , -9 )
P2 = ( 6 , 2 )
Step 2:
[tex]\begin{gathered} \text{Let P}_1=(x_1,y_1)_{} \\ P_2=(x_2,y_2\text{ ) } \end{gathered}[/tex]Step 3:
[tex]\text{v = (x}_2-x_1)i+_{}(y_2-y_1\text{ ) j}[/tex]Step 4:
[tex]\begin{gathered} \text{v = (x}_2-x_1)i+_{}(y_2-y_1\text{ ) j} \\ \text{v = (6}-(-4))i+_{}(2-(-9)\text{) j} \\ v\text{ = (6+4)i + (2 + 9)j} \\ v\text{ = 10i + 11 j} \end{gathered}[/tex]I really need help please
The surface area of the given figure is the sum of the area of the six faces.
Two of them have an area A1:
A1 = 2.5 x 4 ft² = 10 ft²
Other two have an area A2:
A2 = 1.25 x 2.5 ft² = 3.125 ft²
and the other two have an area A3:
A3 = 1.25 x 4 ft² = 5 ft²
Then, the total surface area is:
AT = 2(A1) + 2(A2) + 2(A3)
AT = 2(10 ft²) + 2(3.125 ft²) + 2(5 ft²)
AT = 36.25 ft²
Hence, the total surface area of the given figure is 36.25 ft²
I need an quadratic equation with -3 and 6 for this assignment
If a quadratic equation has solutions
[tex]x=a,x=b[/tex]Then
[tex]x-a=0\text{ and x-b=0}[/tex]Furthermore, the quadratic can be written as
[tex]\begin{gathered} y=(x-a)(x-b) \\ where,y=0 \end{gathered}[/tex]Therefore,
[tex](x-a)(x-b)=0[/tex]Given:
[tex]a=-3,b=6[/tex]Hence,
[tex]\begin{gathered} (x--3)(x-6)=0 \\ (x+3)(x-6)=0 \end{gathered}[/tex]Simplify
[tex]\begin{gathered} x(x-6)+3(x-6)=0 \\ x^2-6x+3x-18=0 \\ x^2-3x-18=0 \end{gathered}[/tex]Hence, the quadratic equation is
[tex]x^{2}-3x-18=0[/tex]Solve the following compound inequality:0< x+7< 9
you need to subtract 7 in each section of the inequality is
-7< x<2
-7< x and x<2
A sample of 25 measurements at breaking strength of cotton thread gave a mean of 7.4 and a standard deviation of 1.2 gms. Find 95% confidence limits for the mean breaking strength of cotton thread.
Answer:
(6.9296, 7.8704)
Explanation:
Given:
• Sample Mean = 7.4
,• Sample Standard Deviation = 1.2
,• n = 25
First, determine the standard error.
[tex]S.E.=\frac{\sigma}{\sqrt{n}}=\frac{1.2}{\sqrt{25}}=\frac{1.2}{5}=0.24[/tex]At 95% confidence limits, Z=1.96.
Using the formula below:
[tex]\bar{x}-Z_{\frac{\alpha}{2}}(S.E)<\mu<\bar{x}+Z_{\frac{\alpha}{2}}(S.E)[/tex]The limits is calculated below:
[tex]\begin{gathered} 7.4-(1.96\times0.24)<\mu<7.4+(1.96\times0.24) \\ 7.4-0.4704<\mu<7.4+0.4704 \\ 6.9296<\mu<7.8704 \end{gathered}[/tex]At 95%, the confidence limits for the mean breaking strength of cotton thread is (6.9296, 7.8704).
2.3 I can apply the Pythagorean Theorem and Triangle Inequality.Which of the following could be lengths for a triangle?Show your work on a separate piece of paper.(Select all that apply.)5, 6, 9D 4,8, 127, 8, 17Are any of the selected triangles above right triangles?How do you know?Suami
For the triangle with sides 5, 6 and 9, you have:
5 + 6 > 9
5 + 9 > 6
9 + 6 > 9
9² ≠ 5² + 6²
≠ 25 + 36
≠ 61
Then, it is not a right triangle
For the triangle with sides 4, 8 and 12:
4 + 8 ≥ 12
in this case the triangle inequality is not present
12² ≠ 4² + 8²
Then, it is not a right triangle
For the triangle with sides 7, 8 and 17:
7 + 8 < 17
in this case the triangle inequality is not present
17² ≠ 8² + 7²
Then, it is not a right triangle
What is the coordinate point location of the y-intercept of the graph below?
The y-intercept is located at the coordinate (0, 4) as shown below. Y-intercept is the point where a line or a graph crosses the y-axis.
Write this ratio as a fraction in simplest form without any units.75 minutes to 1 hourYou can use the table below to help convert the units.1 minute = 60 seconds1 hour = 60 minutes-1 day = 24 hours1 week = 7 days0
To get an unitless ratio, both of our quantities have to be in the same units. Let's convert that hour into minutes:
[tex]1h\rightarrow60\min [/tex]Thereby, our ratio would be:
[tex]\frac{75\min }{60\min }\rightarrow\frac{5}{4}[/tex]The graph of y=(x + 2)^2 – 1 is reflected across the x axis and then translated up 3 units and right 4 units. What is the equation for the transformed graph?
ANSWER
[tex]y=-(x-2)^2\text{ + 4}[/tex]EXPLANATION
We have that the graph of y is:
[tex]y=(x+2)^2\text{ - 1}[/tex]It is first reflected about the x axis.
A reflection about the x axis is represented as:
y = -f(x)
which means that we find the negative of the function:
[tex]\begin{gathered} \Rightarrow y=-\lbrack(x+2)^2\text{ - 1\rbrack} \\ y=-(x+2)^2\text{ + 1} \end{gathered}[/tex]Then, it is translated 3 units up (vertical shift) and 4 units right (horizontal shift).
A translation is represented as:
y = f(x - a) + b
where a = horizontal shift; b = vertical shift
So, we have to find:
y = f(x - 4) + 3
That is:
[tex]\begin{gathered} y\text{ = }-\lbrack(x-4)+2\rbrack^2\text{ + 1 + 3} \\ y=-(x-4+2)^2\text{ + 4} \\ y=-(x-2)^2\text{ + 4} \end{gathered}[/tex]Therefore, that is the equation of the transformed graph.
rewrite 2x+5y=10 in slope intercept form then graph them
The slope intercept of a line is:
[tex]y=mx+b[/tex]We re-write the equation given:
[tex]\begin{gathered} 2x+5y=10 \\ 5y=-2x+10 \\ y=\frac{-2x+10}{5} \\ y=\frac{-2x}{5}+\frac{10}{5} \\ y=-\frac{2}{5}x+2 \end{gathered}[/tex]The graph of this line is shown below:
Finding Slope
Help mee
Answer:
-5 over 30
Step-by-step explanation:
Can you please help me solve this question. Thank you
Answer:
0.4384 < p < 0.5049
Explanation:
The confidence interval for the population proportion can be calculated as:
[tex]p^{\prime}-z_{\frac{\alpha}{2}}\sqrt[]{\frac{p^{\prime}(1-p^{\prime})}{n}}Where p' is the sample proportion, z is the z-score related to the 95% level of confidence, n is the size of the sample and p is the population proportion.
Now, we can calculate p' as the division of the number of voters of favor approval by the total number of voters.
[tex]p^{\prime}=\frac{408}{865}=0.4717[/tex]Additionally, n = 865 and z = 1.96 for a 95% level of confidence. So, replacing the values, we get:
[tex]\begin{gathered} 0.4717-1.96\sqrt[]{\frac{0.4717(1-0.4717)_{}}{865}}Therefore, the confidence interval for the true proportion is:
0.4384 < p < 0.5049
The linear regressionequation andcorrelation coefficientfrom the above datawas calculated to be:Predicted y = 16.2+2.45(x) with r = 0.98What is the coefficientof determination?Answer Choices:A. Coefficient of determination = 0.98B. Coefficient of determination = 0.96C. Coefficient of determination = 0.99D. Coefficient of determination cannot be determined with only the given information.
Given:
[tex]\text{ coefficient of correlation \lparen r\rparen = 0.98}[/tex]To find:
Coefficient of determination
Explanation:
The coefficient of determination is also known as the R squared value, which is the output of the regression analysis method.
If the value of R square is zero, the dependent variable cannot be predicted from the independent variable.
So, here the required coefficient of determination is:
[tex]r^2=(0.98)^2=0.9604\approx0.96[/tex]Final answer:
Hence, the required coefficient of determination is (B) 0.96.
Round 13.134 to the nearest tenth.
Answer: 13.1
13.1
Rounded to the nearest 0.1 or
the Tenths Place.
Explanation:
13.134
You rounded to the nearest tenths place. The 1 in the tenths place rounds down to 1, or stays the same, because the digit to the right in the hundredths place is 3.
13.1
When the digit to the right is less than 5 we round toward 0.
13.134 was rounded down toward zero to 13.1
Finding a time to reach the limit in a word problem on exponential growth or decay
We are told that each year the value of the laptop is 75% of the value of the value of the previous year. This means that every year the current value of the laptop is multiplied by 0.75. Then if v is the original value of the laptop its value after t years is given by:
[tex]V(t)=v0.75^t[/tex]We need to find after which year V(t) is equal to 500 or less then we have V(t)≤500 and since the original value of the laptop was 4200 we have v=4200:
[tex]4200*0.75^t\leq500[/tex]We divide both sides by 4200:
[tex]\begin{gathered} \frac{4200\times0.75^t}{4200}\leqslant\frac{500}{4200} \\ 0.75^t\leq\frac{5}{42} \end{gathered}[/tex]Then we apply the logarithm to both sides:
[tex]\log_{10}(0.75^t)\leqslant\log_{10}(\frac{5}{42})[/tex]Then we use the property of logarithm regarding exponents:
[tex]\begin{gathered} \operatorname{\log}_{10}(0.75^{t})\leqslant\operatorname{\log}_{10}(\frac{5}{42}) \\ t\log_{10}(0.75)\leq\operatorname{\log}_{10}(\frac{5}{42}) \end{gathered}[/tex]And we divide both sides by the logarithm of 0.75 (we change the inequality symbol because log(0.75) is negative):
[tex]\begin{gathered} \frac{t\operatorname{\log}_{10}(0.75)}{\operatorname{\log}_{10}(0.75)}\ge\frac{\log_{10}(\frac{5}{42})}{\operatorname{\log}_{10}(0.75)} \\ t\ge\frac{\log_{10}(\frac{5}{42})}{\operatorname{\log}_{10}(0.75)} \end{gathered}[/tex]Then we get:
[tex]t\ge7.398[/tex]So the laptop's value is less than $500 after 7.398 years.
AnswerSince we are requested to write a whole number as the answer and the smallest whole number that is bigger than 7.398 is 8 we have that the answer is 8 years.
What is the solution to the system of equations shown below?3x+8y=-186x+16y=-54A.) The solution is (0, −18).B.) The solution is (−18, 0).C.) There are an infinite number of solutions.D.) There is no solution.
3x + 8y = -18 -----------------------(1)
6x + 16 y = - 54 ---------------------------(2)
Using elimination method,
multiply equation (1) by 6 and equation (2) by 3
18x + 48y = -108 -----------------(3)
18 x + 48y = 162 -------------------(4)
From this, we can deduce that there is no solution to the system of equations
(8x+6)=mL(blank)
8x+6) =
8x=
x=
the L is an angle
The value of the unknown angle is as follows;
∠ = 62 degreesHow to find the unknown angle?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.
Therefore, the angle 4 can be found as follows:
∠4 = 8x + 6 (alternate angles)
Hence,
8x + 6 + 118 = 180(sum of angles on a straight line)
8x = 180 - 118 - 6
8x = 56
divide both sides by 8
x = 56 / 8
x = 7
Therefore,
∠4 = 8(7) + 6 = 56 + 6 = 62 degrees
learn more on angle here: https://brainly.com/question/7153708
#SPJ1
Reginald wants to buy a new collar for each of his 3 cats. The collars come in a choice of 6 different colors. How many selections of collarsfor each of the 3 cats are possible if color repetitions are allowed
We will have the following:
Assuming that color repetitions can be made, then total number of selections for collars for the 3 cats will be:
[tex]6\ast6\ast6=216[/tex]So, there will be a total of 216 possible permutations of choices.
What is the most precise name for quadrilateral ABCD with vertices A(−5,7), B(6,−3), C(10,2), and D(−1,12)?A. rectangleB. parallelogramC. squareD. rhombus
Answer:
A. Rectangle
Step-by-step explanation:
Hunter has $300 in a savings account. The interest rate is 8%, compounded annually.To the nearest cent, how much will he have in 3 years?
EXPLANATION
If Hunter has $300 in savings and the interest rate is 8%, compounded annualy, we can apply the following equation:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where, P=Principal=300, r=rate (in decimal form) = 8/100 = 0.08, n=number of compounded times = 1 and t = time = 3
Substituting terms:
[tex]A=300\cdot(1+\frac{0.08}{1})^{1\cdot3}[/tex]Adding numbers:
[tex]A=300\cdot(1.08)^3[/tex]Computing the powers:
[tex]A=300\cdot1.26[/tex]Multiplying numbers:
[tex]A=378[/tex]In conclusion, there will be 378.00 in three years
Rectangle CARD has a length of 2x-5 and a width of 6x+10. Triangle BEST has a length of 10x+3 and a width of 4x-7. Find the difference between triangle CARD and triangle BEST. *
Given:
Rectangle CARD: {length = 2x-5 and width = 6x+10}
Triangle BEST: {length = 10x+3 and width = 4x-7}
To find the differnce, let's first the perimeter of both.
Perimeter of rectangle CARD: 2(length + width)
= 2(2x - 5 + 6x + 10)
= 2(2x + 6x - 5 + 10)
= 2(8x + 5)
= 16x + 10
Perimeter of triangle BEST: 2(length + width)
2(10x + 3 + 4x - 7)
= 2(10x + 4x + 3 - 7)
= 2(14x - 4)
= 28x - 8
Therfore, the difference between both of them is calculated below:
(28x - 8) - (16x + 10)
= 28x - 8 - 16x + 10
= 28x - 16x - 8 10
= 12x - 18
ANSWER:
12x -
Select the correct choice below and, if necessary, fill in the answer box within your choice
x² - 20x + 100
Find two numbers, such that its sum gives -20 and its product gives 100
If such numbers exist, this implies that the polynomial is NOT prime
The two numbers are: -10 and -10
Replace the coefficient of x with the two numbers
x² - 10x -10x + 100
x(x-10) - 10(x - 10)
(x-10)(x-10)
(x-10)²
Therefore, the correct option is A.
x² - 20x + 100 = (x-10)²
Date: t rates to determine the better buy? b. Stop and Shop: 6 packages of Oreos cost $15.00 Key Food: 5 packages of Oreos cost $13.25
To determine the better buy you have to calculate how much one package costs in each shop.
1) 6 packages cost $15.00
If you use cross multiplication you can determine how much 1 package costs:
6 packs ______$15.00
1 pack _______$x
[tex]\begin{gathered} \frac{15.00}{6}=\frac{x}{1} \\ x=\frac{15}{6}=\frac{5}{2}=2.5 \end{gathered}[/tex]Each package costs $2.5
2) 5 packages cost $13.25
5packs_____$13.25
1 pack______$x
[tex]\begin{gathered} \frac{13.25}{5}=\frac{x}{1} \\ x=\frac{13.25}{5}=2.65 \end{gathered}[/tex]Each package costs $2.65
For the second purchase each package cost $0.15 more than in the first purchase.
Is best to buy the 6 packages at $15.00
Ms.Lee has 7 boys and 13 girls in her class. If she selects a student at random, what is the probability that she will select a boy?
Answer: 35 percent chance
Step-by-step explanation: 7+13=20 20x5=100 7x5=35 13x5=65 65+35=100
Which of the following is a solution to the inequality below?
Answer:
q = -1
Step-by-step explanation:
We are given the inequality [tex]11-\frac{64}{q} > 60[/tex]
We want to find out which value of q is a solution to the inequality. In other words, which value of q makes the statement true?
We can substitute the values given for q into the inequality to see this.
Let's start with q=2.
Replace q with 2.
[tex]11-\frac{64}{2} > 60[/tex]
Divide 64 by 2.
64/2= 32
11 - 32 > 60
Subtract 32 from 60
11-32 = -21
-21 > 60
The inequality reads "-21 is greater than 60", which is false (negative numbers are less than positive ones).
This means q=2 is NOT an answer.
Next, let's try q=-2
[tex]11 - \frac{64}{-2 } > 60[/tex]
64/-2 = -32
11 - - 32 > 60
- - 32 means subtracting a negative, which is the same as adding 32 to 11.
11 + 32 > 60
43 > 60
This is also NOT true (it reads "43 is greater than 60").
So q=-2 is also NOT an answer.
Now, let's try q = -1
[tex]11-\frac{64}{q} > 60[/tex]
[tex]11-\frac{64}{-1} > 60[/tex]
64/-1=-64
11 - -64 > 60
11 + 64 > 60
75 > 60
This reads "75 is greater than 60".
This is a true statement, meaning q = -1 IS an answer.
We are technically done, but just to be sure, we can check q=1 as well.
[tex]11 - \frac{64}{q} > 60[/tex]
[tex]11 - \frac{64}{1} > 60[/tex]
11 - 64 > 60
-53 > 60
This reads "-53 is greater than 60", which is false.
So this confirms that q = -1 is the only option that is an answer.
Which sample size will produce the widest 95% confidence interval, given asample proportion of 0.5?A. 40B. 70C. 60D. 50
The confidence interval depends on the margin of error. When finding the margin of error, the z score corresponding to the 95% confidence level would be multiplied by the square root of the product of the estimated proportion of success and failure divided by the sample size. The greater the sample size, the smaller thie value that would be gotten from this operation. The smaller the sample size, the greater the value that would be gotten from this operation. A greater value would give a bigger margin of error. Thus, the confidence interval would be wider. Hence, the correct option for the sampe size is
A. 40
3. There are two city buses in Saratoga. Bus A completes its route in 25 minutes. Bus B completes its route in 40 minutes. Both of their routes end at the bus station. If both buses leave the bus station at the same time in the morning, how many minutes will pass before the two buses meet at the train station?
To find the answer, we have to find the LCM of 25 and 40.
To get LCM, we
Write each number as prime factors
take the prime factor that occurs greatest number of time
take the product of those
Thus,
25 = 5 * 5
40 = 2 * 2 * 2 * 5
2 occurs 3 times and 5 occurs 2 times (greatest).
hence,
LCM(25, 40) = 2 * 2 * 2 * 5 * 5 = 200
So,
200 mins will pass before the two buses meet
