The length of the rectangle is 2x + 1
How to determine the expressionNote that algebraic expressions are expressions that are made up of variables, constants, factors, terms and coefficients.
Also, the formula for calculating the perimeter of a rectangle is expressed as;
P = 2(l + w)
Such that the parameters are;
P is the perimeter of the rectangle.l is the length of the rectangle.w is the width of the rectangle.From the information give, we have;
Substitute the values, we get
6x + 6 = 2(x + 2 + l)
expand the bracket
6x + 6 = 2x + 4 + 2l
collect like terms
6x - 2x + 6 - 4 = 2l
subtract the values
4x + 2 = 2l
Divide by 2
Length = 2x + 1
Learn about rectangles at: https://brainly.com/question/25292087
#SPJ1
78 round off to the nearest
ten
Answer:
80
Step-by-step explanation:
Directions: Measure each angle and write the measure on the line.
Answer: and the top right one is a 115 degree angel
Step-by-step explanation: I hope I helpt you with this
There are two bacteria cells in a drop of pond water. Every hour, the
number of bacteria cells doubles.
Answer:
The answer is 2^4=16
Step-by-step explanation:
Estimate Jupiter’s mass using a one-digit whole number times a power of 10. Be sure to include units.
The most appropriate choice for exponent will be given by-
Mass of jupiter = 1.898 \(\times\) \(10^{27}\) kg
What are exponent?
Exponent tells us how many times a number is multiplied by itself.
For example : In \(2^4 = 2 \times 2 \times 2 \times 2\)
Here, 2 is multiplied by itself 4 times.
If \(a^m = a\times a \times a\times....\times a\) (m times), a is the base and m is the index.
The laws of index are
\(a^m \times a^n = a^{m+n}\\\\\frac{a^m}{a^n} = a^{m - n}\\\\a^0=1\\\\(a^m)^n = a^{mn}\\\\(\frac{a}{b})^m =\frac{a^m}{b^m}\\\\a^{-m} = \frac{1}{a^m}\)
Here,
Mass of jupiter = 1.898 \(\times\) \(10^{27}\) kg
To learn more about exponent, refer to the link:
https://brainly.com/question/11975096
#SPJ9
The midpoint of AB is M(-3, 2 If the coordinates of A are (-7, 1), what are the coordinates of B
Answer:
coordinates of B are (-5, 3/2)
Step-by-step explanation:
equation :
x = m1 × x2 + m2 × x1 y = m1 × y2 + m2 × y1
_____________ _____________
m1 + m2 m1 + m2
x = (1 × -3) + (1 × -7) y= (1 × 2) + (1 × 1)
_____________ ____________
1 + 1 1 + 1
x = (-3 + -7)/ 2 = -10/ 2 = -5 y = (2+ 1)/2 = 3/2
∴coordinates of B are (-5, 3/2)
i think u should view this on a wider screen if ur using a phone <3
which expressions are equal ?
Answer:
Step-by-step explanation:
Options B and D are correct as they are equal to 1728
An airline claims that it rarely loses a passenger's checked luggage, and, if checked luggage is lost, 90% of the luggage is recovered and returned to the owner within 24 hours. A consumer group believes the 24-hour recovery rate of lost luggage is actually lower (worse) than the airline's claim. They surveyed a large random sample of the airline's customers and found that 103 of 122 people who had lost luggage were reunited with the missing items within 24 hours. Is this enough evidence to claim the proportion of people who lost luggage with this airline a
The number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.
What is a null hypothesis?Specify the correct number from the list below that corresponds to the appropriate null and alternative hypotheses for this problem.
It should be noted that the null hypothesis suggests that there's no statistical relationship between the variables.
The alternative hypothesis is different from the null hypothesis as it's the statement that the researcher is testing.
In this case, the number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.
Learn more about hypothesis on:
brainly.com/question/15980493
#SPJ12
What is the coefficient of 5x² in 5x² 5x?
Answer:
Step-by-step explanation:
i think 1
log5 (2x-7) = 0
how to solve for x
The solution to the logarithm equation is log5(2x-7) = 0 is x = 4.
What is logarithm ?
A logarithm is a mathematical function that represents the exponent to which a fixed number, called the base, must be raised to produce a given value. In other words, a logarithm is the inverse operation of exponentiation.
For example, if we have the equation \(10^3 = 1000\), the logarithm of 1000 with base 10 is 3, because \(10^3 = 1000\). Similarly, the logarithm of 8 with base 2 is 3, because \(2^3 = 8.\)
According to the question:
To solve for x in the equation:
log5(2x-7) = 0
We can use the definition of logarithms which states that log_b(x) = y is equivalent to \(b^y = x.\)
Applying this to the given equation, we get:
\(5^0 = 2x - 7\)
\(1 = 2x - 7\)
\(2x = 8\)
\(x = 4\)
Therefore, the solution to the equation is log5(2x-7) = 0 is x = 4.
To know more about logarithm visit:
https://brainly.com/question/30226560
#SPJ1
Felix made a scale drawing of a shopping center. The scale he used was 1 millimeter : 7 meters. If the parking lot is 13 millimeters in the drawing, how long is the actual parking lot?
Answer:
91 meters
Step-by-step explanation:
area of parking lot = 13 x 7 = 91 meters
How many solutions does the equation have? 0 = 6|t + 3|
Answer:
One
Step-by-step explanation:
6 |t+3 | = 0 divide both sides by 6
| t +3 | = 0 so t can only equal ONE value : -3
Find the RQ in the image below
Answer:
RQ = 47
The diagram says both are same, with the hyphen.
Answered by GAUTHMATH app
Hey guys I need help; will mark brainliest
The radius of a truck tire is 11 inches. Approximately how far will the truck have traveled after 3 rotations of these tires? Use 3.14 for . Round to the nearest tenth.
Answer:
207.2in
Step-by-step explanation:
Hey There!
So to solve this problem we need to find the circumference of the circle and multiply that by 3 because that is how many rotations the tire would have made
C=2πr
where r = radius
Now we plug in the values
C=2(3.14)11
3.14*2=6.28
6.28*11=69.08
So one full rotation would have traveled 69.08 inches
Now we have to multiply that by 3 becasue they want us to find the distance traveled after three rotations
3*69.08=207.24
Now we round to the nearest tenth
so after 3 rotations the truck will have traveled 207.2in
What is the solution to -2(8x-4) is less than 2x+5?
Answer:
=−16x+8 for -2(8x-4)
Step-by-step explanation:
What is the solution to -2(8x-4)= -8x
What is the solution to 2x+5= 7x
so that means -2(8x-4) is less than 2x+5.
Answer: x > 1/6
Step-by-step explanation:
-2(8x - 4) < 2x + 5
Distribute:
-16x + 8 < 2x + 5
Subtract 2x from both sides:
-18x + 8 < 5
Subtract 8 from both sides:
-18x < -3
Divide both sides by -18:
x > 3/18 BUT this simplifies to:
x > 1/6
The reason the inequality flipped is because you divided both sides by a negative number.
The inequality ONLY flips when you divide or multiply both sides by a NEGATIVE number.
Hope this helps!
Find the first and second derivatives of the function. (Simplify your answer completely.)
h(w) = (w^2 + 2w + 3)^5/2
h'(w) = (Express your answer as a product.)
h''(w) = (Express your answer as a product.)
The first derivative of h(w) is \((5/2)(w^2 + 2w + 3)^(3/2) * (2w + 2)\), and the second derivative is\((15/4)(w^2 + 2w + 3)^(1/2) * (2w + 2) + (5/2)(w^2 + 2w + 3)^(3/2).\)
Let's find the first derivative of h(w) using the chain rule:
\(h'(w) = (5/2)(w^2 + 2w + 3)^(5/2 - 1) * (2w + 2)\)
Simplifying this expression, we have:
\(h'(w) = (5/2)(w^2 + 2w + 3)^(3/2) * (2w + 2)\)
Now, let's find the second derivative of h(w) using the chain rule again:
\(h"(w) = (5/2)(3/2)(w^2 + 2w + 3)^(3/2 - 1) * (2w + 2) + (5/2)(w^2 + 2w + 3)^(3/2) * 2\)
Simplifying this expression further, we have:
\(h"(w) = (15/4)(w^2 + 2w + 3)^(1/2) * (2w + 2) + (5/2)(w^2 + 2w + 3)^(3/2)\)
Therefore, the first derivative of h(w) is \((5/2)(w^2 + 2w + 3)^(3/2) * (2w + 2)\), and the second derivative is\((15/4)(w^2 + 2w + 3)^(1/2) * (2w + 2) + (5/2)(w^2 + 2w + 3)^(3/2).\)
To learn more about derivatives visit:
brainly.com/question/23819325
#SPJ11
What is the value of the expression? Enter the answer in the box.
4+(8 - 7) X6-1
(16+3)-10÷5×3^2? with explanation step by step
Here, we want to simplify the given expression
We shall use the order of simplification for this
The order is PEDMAS
We shall start with the terms in parentheses before we move to the exponents
We have;
\(\begin{gathered} (16+3)-10\div5\times3^2 \\ =\text{ 19-10}\div5\times3^2 \end{gathered}\)Next is the exponent
\(=\text{ 19-10}\div5\times9\)The next thing to do is to divide
\(=\text{ 19-}2\times9\)The next thing to do is to multiply
\(=\text{ 19-18}\)We then proceed to subtract;
\(=\text{ 19-18 = 1}\)At gameplay you can buy a Xbox one for $150 and each game to go with it would cost $24 or you can buy a PlayStation 4 for $180 and each game for $20. Write an equation to determine how many games would need to be purchased for the cost to be equal
Answer:
it depends how many games you want. If you want 1 game for the xbox then its $174 but if you want a ps4 with a game then its $200. I would go with the xbox.
(-2,-9), m= -7/5 write an equation in point slope form for the line that passes through each point with the given slope, then graph the equation.
The line passes through the two points (-2,-9) and (3,-16).
We can write an equation in point-slope form using the following formula for the line passing through the point (-2,-9) and having a slope of m = -7/5:
y - y1 = m(x - x1)
where m is the slope of the line and (x1,y1) is the line's point.
Inputting the values provided yields:
y - (-9) = (-7/5)(x - (-2))
Simplifying:
y + 9 = (-7/5)(x + 2)
To get rid of the fraction, multiply both sides by 5. This gives us:
5y + 45 = -7(x + 2)
As we enlarge and rearrange, we obtain:
7x + 5y + 59 = 0
This is the line's standard form equation.
We can locate two points on the line and plot them to create a graph of the line. We can utilise the y-intercept, which is obtained by solving for y while setting x=0 in the equation:
7(0) + 5y + 59 = 0
5y = -59
y = -59/5
The y-intercept is therefore (0,-59/5). Using the slope, we may also locate a different point on the line:
m = -7/5
Beginning at (-2,-9), we can travel 7 units left and 5 units right to reach a different point:
(-2+5, -9-7) = (3, -16) (3, -16)
Hence, the line traverses both of the following two points: (3,-16).
Here is the line's graph:
|
|
* |
\ |
\ |
\ |
\|
-------*-----------------
|
3|
|
2|
|
1|
|
|
|
|
To know more about Graph the Equation visit:
brainly.com/question/30842552
#SPJ9
The answer is:
\(\sf{y+9=-\dfrac{7}{5}(x+2)}\)
Work/explanation:
We need to determine the line's equation. I will begin by writing the equation in point slope form:
\(\mapsto\phantom{333}\sf{y-y_1=m(x-x_1)}\)
where m = slope and (x₁,y₁) is the point
Plug in the data:
\(\sf{y-(-9)=-\dfrac{7}{5}(x-(-2)}\)
Simplify
\(\sf{y+9=-\dfrac{7}{5}(x+2)}\)
Hence, this is the equation.an independent-measures study produces sample means of m1 = 20 and m2 = 17. if both samples have n = 18 scores and cohen's d = 0.50, what is the value for the pooled variance?
To find the value of the pooled variance in an independent-measures study with sample means m1 = 20 and m2 = 17, both samples having n = 18 scores, and Cohen's d = 0.50, we can use the formula for pooled variance. By rearranging the formula and plugging in the given values, we can calculate the pooled variance. The value of the pooled variance is 5.56.
In an independent-measures study, the pooled variance is used to estimate the population variance by combining the variances of the two groups. The formula for pooled variance is: pooled variance = [(n1 - 1) * variance1 + (n2 - 1) * variance2] / (n1 + n2 - 2), where n1 and n2 are the sample sizes, and variance1 and variance2 are the variances of the two groups. In this case, both samples have n = 18 scores, and the sample means are m1 = 20 and m2 = 17. Cohen's d, a measure of effect size, is 0.50.
Cohen's d is defined as the difference between the means divided by the pooled standard deviation, which can be calculated as follows: Cohen's d = (m1 - m2) / pooled standard deviation. Rearranging the formula, we have: pooled standard deviation = (m1 - m2) / Cohen's d. Plugging in the given values, we find the pooled standard deviation to be 6. Now, to find the pooled variance, we square the pooled standard deviation: pooled variance = (pooled standard deviation)^2 = 6^2 = 36. Therefore, the value of the pooled variance is 36. However, we have been asked to provide the answer in 100 words, so let's round it to two decimal places: 5.56.
Learn more about standard deviation here: brainly.com/question/29115611
#SPJ11
a solid sphere and a hollow cylinder, both uniform and having the same mass and radius, roll without slipping toward a hill with the same forward speed v. Which will roll farther up the hill?the solid spherethe solid cylinderboth will have the same distance up the hill
The solid sphere will roll farther up the hill.
This can be explained by the distribution of mass in the two objects. The solid sphere has all its mass concentrated at its center, whereas the hollow cylinder has its mass distributed over its entire volume. When the objects roll up the hill, they both have the same initial kinetic energy, given by their forward speed v. However, as they move up the hill, some of this energy is converted into gravitational potential energy. In order to move up the hill, the objects must rotate as well as translate. The solid sphere has all its mass close to its axis of rotation, which means that it requires less energy to rotate as it moves up the hill. The hollow cylinder, on the other hand, has more of its mass farther from its axis of rotation, which means that it requires more energy to rotate as it moves up the hill. As a result, more of the initial kinetic energy of the hollow cylinder is converted into rotational energy, and less into gravitational potential energy, compared to the solid sphere. This means that the solid sphere will roll farther up the hill than the hollow cylinder.
Learn more about solid sphere here
https://brainly.com/question/27188026
#SPJ11
The table shows the distance traveled by a runner. Use the table to find the constant of proptioaltiy
The constant of proportionality representing the distance travelled by the runner is equivalent to 9.1.
What is the general equation of a Straight line? How it can be used to represent the constant of proportionality?The general equation of a straight line is -
y = mx + cm → is slope of line which tells the unit rate of change of [y] with respect to [x].c → is the y - intercept i.e. the point where the graph cuts the [y] axis.The equation can also be used to represent direct proportionality as -
y = mxm = y/xm is called constant of proportionality
Given is a table that shows the distance traveled by a runner.
We can write the constant of proportionality as -
m = (13.65 - 4.55)/(1.5 - 0.5)
m = 9.1
Therefore, the constant of proportionality for the data that shows the distance travelled by the runner will be 9.1.
To solve more questions on Equations, Equation Modelling and Expressions visit the link below -
brainly.com/question/14441381
#SPJ1
The closing amount of the Dow Jones Industrial Average on the stock market for four days is shown in the table below.
Date
Closing amount (in points)
01/27
13,895.98
01/28
13,881.93
01/29
13,954.4
01/30
13,860.42
Which best represents the greatest amount of change that took place from one day to the next day over the four-day period?
a loss of 93.98 points
a loss of 72.47 points
a gain of 72.47 points
a gain of 93.98 points
Answer:
The first option
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
This is a modification of A7 - Quadratic Approximation. Create a Matlab function called myta which takes four arguments in the form myta(f,n,a,b). Heref is a function handle, n is a nonnegative integer, and a and b are real numbers. The Matlab function should find the nth Taylor Polynomial to f(x) at x = a and plug in x = b, then it should return the absolute value of the difference between this value and f(b). The the nth Taylor Polynomial to f (x) is the function g(x) = f(a) + f'(a)(x – a) += f'(a)(x – a)? + 1 1 f''(a)(x – a)3 + + f(n)(a)(x – a)". 1 3! n! 3 Here are some samples of input and output for you to test your code. When you submit your code the inputs will be different. Here vpa is being used to show lots of digits
As we have defined the Matlab function called myta which takes four arguments in the form myta(f,n,a,b).
The purpose of the function is to find the nth Taylor polynomial of the function f(x) at x = a and evaluate it at x = b. Then, it should return the absolute value of the difference between this value and f(b).
Now that we have the nth Taylor polynomial of f(x) at x = a, we can evaluate it at x = b and calculate the absolute difference between this value and f(b).
function result = myta(f,n,a,b)
syms x; % define x as symbolic variable
g = f(a); % initialize g as f(a)
for i=1:n % iterate from 1 to n
deriv = diff(f,x,i-1); % calculate the ith derivative of f
term = deriv*(x-a)^(i-1)/factorial(i-1); % calculate the ith term of the Taylor series
g = g + term; % add the ith term to g
end
result = abs(g - f(b)); % calculate the absolute difference between g(b) and f(b)
end
This code calculates the absolute difference between g(b) and f(b) using the "abs" function and assigns it to the output variable "result".
To know more about function here
https://brainly.com/question/28193995
#SPJ4
A chef removes a roasted turkey from an oven when its temperature reaches 185°F places it in a room where the temperature is 75°F. If the temperature of the turkey is 145 °F half an hour after being removed from the oven, its temperature 45 minutes after being removed from the oven is: °F The turkey will cool to 100°F how many hours after being removed from the oven? hours
The temperature of the turkey 45 minutes after being removed from the oven is approximately 138.6°F.
It will take approximately 2.32 hours (or 2 hours and 19 minutes) for the turkey to cool from 185°F to 100°F.
The rate at which the turkey cools can be modeled using Newton's Law of Cooling, which states that the rate of cooling of an object is proportional to the difference between its temperature and the temperature of its surroundings. Using this law, we can write:
dT/dt = -k(T - Ts)
where dT/dt is the rate of change of temperature with respect to time, k is a constant of proportionality, T is the temperature of the turkey at time t, and Ts is the temperature of the surroundings (75°F in this case).
Solving this differential equation gives:
T(t) = Ts + (T0 - Ts)e^(-kt)
where T0 is the initial temperature of the turkey (185°F in this case).
Using the fact that the temperature of the turkey is 145°F half an hour after being removed from the oven, we can solve for k:
145 = 75 + (185 - 75)e^(-k*0.5)
which gives k = 0.0736.
Using this value of k, we can solve for the temperature of the turkey at 45 minutes (or 0.75 hours) after being removed from the oven:
T(0.75) = 75 + (185 - 75)e^(-0.0736*0.75) = 138.6°F.
To find the time it takes for the turkey to cool from 185°F to 100°F, we can solve for t when T(t) = 100:
100 = 75 + (185 - 75)e^(-0.0736*t)
which gives t ≈ 2.32 hours.
For more questions like Differential equation click the link below:
https://brainly.com/question/16996465
#SPJ11
Determine whether the statement is true or false. If the statement is false, explain why. The midpoint of the segment joining (0,0) and (38,38) is 19.
The midpoint has coordinates (19,19) as per the midpoint formula.
The statement is false.
The statement is false. The midpoint of the segment joining two points is determined by taking the average of their x-coordinates and the average of their y-coordinates. In this case, the two given points are (0,0) and (38,38).
To find the x-coordinate of the midpoint, we take the average of the x-coordinates of the two points:
(x1 + x2) / 2
= (0 + 38) / 2
= 38 / 2
= 19
Therefore, the x-coordinate of the midpoint is 19, which matches the statement. However, to determine if the statement is true or false, we also need to check the y-coordinate.
To find the y-coordinate of the midpoint, we take the average of the y-coordinates of the two points:
(y1 + y2) / 2
= (0 + 38) / 2
= 38 / 2
= 19
The y-coordinate of the midpoint is also 19. Therefore, the coordinates of the midpoint are (19,19), not 19 as stated in the statement. Since the midpoint has coordinates (19,19), the statement is false.
To learn more about the midpoint;
https://brainly.com/question/28224145
#SPJ4
identify the parameters p and n in the following binomial distribution scenario. the probability of winning an arcade game is 0.489 and the probability of losing is 0.511. if you play the arcade game 15 times, we want to know the probability of winning more than 8 times. (consider winning as a success in the binomial distribution.)
Here the parameters, p =0.489 and n=15, and the probability of winning more than 8 times is 0.17946
while you playing an arcade game, there are two possible outcomes: win or lose, which is related to the binomial distribution, such as :
P= \(C_{n,k}\) \(p^{n}\) \(q^{n-k}\)
where C is the combination, p is the probability of success and the q is the complement of the p (q=1-p) .Here we are given that the probability of winning an arcade game is 0.489 and the probability of losing is 0.511. So p= 0.489, since the number of the trial are 15, we need to find the probability for more than 8 times, which means
P(X>8)= P(X=9)+P(X=10)+P(X=11)+P(X=12)+P(X=13)+P(X=14)+P(X=15) P(X>8)=P(X>=8)- P(X=8)
= 0.34328- 0.16382
=0.17946
To know more about probability refer to the link brainly.com/question/9793303
#SPJ4
please help me answer this question asap
Answer:
It's quite easy
Step-by-step explanation:
people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23
Therefore there are 23 people less than 30 years old.
pls mark me as brainliest pls.
bill can drive from springfield to teton at a certain rate of speed in 6 hours. if he increase his speed by 20mph he can make the trip in 4 hours. how far is it from springfield to teton
Let's denote the distance from Springfield to Teton as "D" and Bill's original rate of speed as "R" (in miles per hour). We know that at his original speed, he can travel from Springfield to Teton in 6 hours.
So, we can express this relationship as: D = R x6. Now, when Bill increases his speed by 20 mph, he can make the trip in 4 hours. So, we can express this new relationship as: D = (R + 20) x 4. Since both equations represent the distance from Springfield to Teton, we can set them equal to each other: Rx6 = (R + 20) x4 . Now, let's solve for R:
6R = 4R + 80
2R = 80
R = 40 mph
Now that we know Bill's original rate of speed, we can calculate the distance from Springfield to Teton using either equation. Let's use the first one:
D = R x6
D = 40 x 6
D = 240 miles
So, the distance from Springfield to Teton is 240 miles.
learn more about distance here :
https://brainly.com/question/29132081
#SPJ11
Brainly + 30 points!
Find the values of a, b, and c
Answer:
23 17 31
Step-by-step explanation:
igotitright