We can show that x² + 5x = 3 given the dimensions of the rectangle that has an area of 9 cm² as explained below.
How to Find the Area of a Rectangle?To find the area of a rectangle, use the formula given below:
Area of a rectangle = (length)(width).
Given the parameters:
Area of rectangle ABCD = 9 cm²Length of the rectangle = BC = (x + 3) cmWidth of the rectangle = AB = (x + 2) cmTo show that x² + 5x = 3, plug in the values into the formula for the area of a rectangle:
(x + 3)(x + 2) = 9
Apply the distributive property of equality
x(x + 2) + 3(x + 2) = 9
x² + 2x + 3x + 6 = 9
Combine like terms:
x² + 5x + 6 = 9
Add -6 to both sides of the equation
x² + 5x + 6 - 6 = 9 - 6 [subtraction property of equality]
x² + 5x = 3
Thus, if the area of the rectangle with the given dimensions is 9 cm², then we can show that, x² + 5x = 3 as explained above.
Learn more about the area of rectangle on:
https://brainly.com/question/25292087
#SPJ1
Trigonometry please help!
Answer:
the first one
Step-by-step explanation:
y( x+a ) m solve for the variable x.
Answer:
x=y/m-a
Step-by-step explanation:
y=(x+a)m
Divide m on both sides
y/m=x+a
Subtract a on both sides
y/m-a=x
I need this answered please
Answer:
x=45
Step-by-step explanation:
20-.24=9.2
I need help with qeustion 36 please
Answer:
8 + 2(x + 3) = 2x + 14
Would be infinitely many solutions.
Step-by-step explanation:
8 + 2x + 6 = 2x + 14
2x + 14 = 2x + 14
0 = 0; True
All real numbers
mp Learning
A fair costs $28 for admission plus $3 for each roller coaster ride.
Given that x represents the number of roller coaster rides, choose the algebraic expression that models this situation.
A
B
D
E
28x + 3
31x
31
28 + 3x
You answer is: 28 + 3[tex]x[/tex]
Since $28 is a one-time fee and does not have to be paid again for each and every ride, it does not need a variable in front of.
But for every ride you want, you pay $3 so you need the variable "[tex]x[/tex]" which represents how many times you ride.
For example, if you ride the roller coaster once, your total amount, in dollars, will be:
T = 28 + 3 * (1)
T = $31
But if you ride the roller coaster 3 times, your cost, in dollars, will be:
T = 28 + 3 * (3)
T = 28 + 9
T = $37
The coordinates of point T are (0,5). The midpoint of ST is (5,-8). Find the coordinates of point S.
The other endpoint is
(Type an ordered pair.)
... HELP PLS!!!!
A cube is being compacted. Given that the volume decreases at a rate of 2 cubic meters per minute, find the rate of change of an edge of the cube when the volume is exactly 27 cubic meters.
The rate of change of an edge of the cube is 0.074 m/min.
What is the rate of change of volume of cube?The rate at which the volume of the cube changes is calculated as follows;
dv/dt = 2 m³/min
where;
v is the volume of the cubeThe length of edge of the cube will be denoted with a, and it is related to the volume of cube in the following equation.
v = a³
a = v^¹/₃
where;
a is the length of the edgeThe change in the edge with volume;
da/dv = 1/3 (1/v)^2/3
The change in edge of the cube with time is given as;
da/dt = da/dv . dv/dt
da/dt = 1/3 (1/v)^2/3 x 2 m³/min
da/dt = 1/3 (1/27)^2/3 /m² x 2 m³/min
da/dt = 1/27 x 2 m/min
da/dt = 2/27 m/min
da/dt = 0.074 m/min
Thus, the rate at which the edge of the cube changes with time is smaller compared to the volume.
Learn more about rate of change of volume here: https://brainly.com/question/22716418
#SPJ1
What's 4/9+9/18 please help with this thanks you
After solving the equation 4/9+9/18, we have to come to find the solution is 1.57.
What is an equation?An equation can be defined in a number of different ways. An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.
In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal." There are one or more variables in even the most fundamental and straightforward algebraic equations.
The value of the variable that makes the equation a true statement is the solution of the equation.
We have been asked to solve the equation 4/9 + 9/8
Lets solve
⇒ 4/9 + 9/8
⇒ (32+81)72 (finding the LCM of denominators and multiplying with
⇒ (32+81)72 numerators)
⇒ 113/72
⇒ [tex]1\frac{41}{72}[/tex]
⇒ 1.57
Learn more about equation
https://brainly.com/question/2972832
#SPJ13
a researcher is interested in the sleeping habits of students at the local state college. the average number of hours spent sleeping each night for the entire set of students enrolled at the college is an example of a .
One example of a parameter is the typical number of hours each night that the entire group of college-enrolled students sleeps.
What do we mean by a parameter?In mathematics, a parameter is a variable whose range of possible values identifies a number of unique cases in a problem. A parametric equation is any equation that is expressed in terms of parameters. To describe the entire population under study, a parameter is used. For instance, we are interested in learning the typical length of a butterfly. This information about the entire butterfly population makes it a parameter. The local state college's students' sleeping patterns are of interest to a researcher. One example of a parameter is the typical number of hours each night that the entire group of college-enrolled students sleeps.Therefore, one example of a parameter is the typical number of hours each night that the entire group of college-enrolled students sleeps.
Know more about a parameter here:
https://brainly.com/question/13281171
#SPJ9
The correct question is given below:
A researcher is interested in the sleeping habits of students at the local state college. The average number of hours spent sleeping each night for the entire set of students enrolled at the college is an example of a ____.
A family is taking a trip to a maill 45 miles away. They have seven gallons of gas in their car's fuel tank and the car gets 22 miles per gallion on this trip. Explain why it is okay to estimate the fuel supply for the trip.
Trip of 45miles with seven gallons of gas in a car and car gets 22 miles per gallon ,estimate fuel supply for trip is 2 gallons.
As given in the question,
Total distance covered in family trip is 45 miles
Total fuel in car is seven gallons
Average of the on trip=22 miles per gallon
Estimate fuel supply for trip =(45 miles )/(22 miles per gallon)
=2.04545gallons
≈2gallons(approximately)
As the fuel used in the trip is 2.04545.. gallons which is nearest to the 2 gallons, it is okay to estimate the fuel supply.
Therefore, trip of 45 miles with 7gallons of gas in a car with average 22 miles per gallon ,estimate fuel supply for trip is 2 gallons.
Learn more about estimate here
brainly.com/question/14347037
#SPJ1
Omar owns a sandwich shop, and his best selling sandwich is the BLT. When making BLT sandwiches, it takes
3
4
of a pound of bacon to make 4 sandwiches. He uses
1
1
20
pounds of bacon for every 2 tomatoes used and 5 tomatoes for every full head of lettuce used.
If Omar is making enough BLT sandwiches to use 2 full heads of lettuce, then he is going to use pounds of bacon and will make a total of BLT sandwiches.
Reset Next
by using multiplication, we get that 28 BLT sandwiches can be made by Omar.
We are given that:
For every full head of lettuce used,
Number of tomatoes used = 5
Now, we will use multiplication.
2 full heads of lettuce used = 5 × 2 = 10 tomatoes used
Now, we also have:
2 tomatoes used = 1 1/20 pounds of bacon used.
= 21/20 pounds of bacon used.
1 tomato = (21 / 20) × (1 / 2) = 21 / 40 pounds bacon
10 tomatoes = (21 / 40) × 10 = 21 / 4 pounds bacon
Also,
3 / 4 pounds of bacon = 4 sandwiches
1 pound of bacon = 16 / 3 sandwiches.
21 / 4 pounds of bacon = (16 / 3) × (21 / 4) = 28 sandwiches
Therefore, by using multiplication, we get that 28 BLT sandwiches can be made by Omar.
Learn more about multiplication here:
https://brainly.com/question/10873737
#SPJ1
The two lines at right represent the growing profits of Companies A and B. Homework Help ✎ Sketch this graph on your paper. If Company A started out with more profit than Company B, determine which line represents A and which represents B. Label the lines appropriately. In how many years will both companies have the same profit? Approximately what will that profit be? Which company’s profits are growing more quickly? How can you tell?
Using concepts of linear functions, it is found that:
They will have the same profit after 3 years.This profit will be of $65,000.Due to the higher slope, Company B profit is growing more quickly.What do the slope and the intercept of a linear function represent?The slope-intercept representation of a linear function is:
y = mx + b.
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).Two linear functions have the same value when they intersect each other, hence, from the graph given at the end of the answer, they intersect around point (3,65), meaning that they will have the same profit after 3 years, and this profit will be of $65,000.
From the Graph, as it assumes higher values as n goes to infinity, company B has the higher slope, hence it's profit is growing more quickly.
What is the missing information?The graph is missing, and is given by the image at the end of the answer.
A similar problem, also about linear function concepts, is given at https://brainly.com/question/24808124
#SPJ1
pleaseee help, question what is the sum of 4x^2 + 2x - 5 and 7x^2 - 5x + 2
Answer:
Add the expressions.
11x2−3x−3
Step-by-step explanation:
Simplification of polynomials.
Polynomials are mathematical expressions made up of many terms.To simplify a polynomial the most, you must collect all like terms and rearrange them from highest to lowest power.
4x² + 2x -5 + 7x² - 5x+24x² + 2x -3 + 7x² - 5x+211x² + 2x - 3 - 5x11x² - 3x - 3 ====> Option "A"a new test has been developed to determine whether a given student is overstressed. this test is 95% accurate if the student is not overstressed, but only 85% accurate if the student is in fact overstressed. it is known that 99.5% of all students are overstressed. given that a particular student tests negative for stress, what is the probability that the test results are correct, and that this student is not overstressed?
The probability that the test results are correct, and that this student is not overstressed is mathematically given as
3.08%
This is further explained below.
What is probability?Generally,
Let A: student is overstressed
B: The test is positive. Given
[tex]P(\bar{B} / \bar{A})=0.95, P(B / A)\\P(\bar{B} / \bar{A}) =0.85, P(A)\\P(\bar{B} / \bar{A})=0.995, \\[/tex]
[tex]P\left(\frac{\text { correctresult }}{\text { Test negative }})=P(\bar{A} / \bar{B}) \\\\ =\frac{P(\bar{A} \cap \bar{B})}{P(\bar{B})} \\\\ =\frac{P(\bar{A} \cap \bar{B})}{P(\bar{A} \cap \bar{B})+P(A \cap \bar{B})}\right.[/tex]
[tex]=\frac{P(\bar{B} / \bar{A}) P(\bar{A})}{P(\bar{B} / \bar{A}) P(\bar{A})+P(\bar{B} / \bar{A}) P(A)} \\\\=\frac{0.95 \times 0.005}{0.95 \times 0.005+0.15 \times 0.995} \\[/tex]
=0.0308
=3.08%
Read more about probability
https://brainly.com/question/11234923
#SPJ1
what is7.9 times 0.99
Answer:
7.821 or 7821/1000
Step-by-step explanation:
Answer:
7.821
Step-by-step explanation:
Can someone help. fill fill
Answer:
x = 13
calculations in the pic hope it helps
Answer is 13
Step by step
1.4 + x / 6 = 2.4
We want to get rid of the 6 first
It is a divide so we want to do the inverse, which is multiply both sides by 6
1.4 + x * 6/ *6 = 2.4 * 6
Combine (the 6/6 becomes 1)
1.4 + x = 14.4
Now we want to isolate the x
Subtract 1.4 from both sides to solve for x
1.4 - 1.4 + x = 14.4 - 1.4
Combine
x = 13
pleaseeee helpp nowwwwwwwww :/
.
.
.
Find the value of m: −3(m − 4) = −6
m = −6
m = −2
m = 2
m = 6
The solution of the equation is m = 6.
How to find the variable of an equation?The variable to find is variable m.
The equation is as follows:
−3(m − 4) = − 6
Hence, let's open the bracket on the left side of the equation
−3(m − 4) = − 6
- 3m + 12 = -6
subtract 12 from both sides of the equation
- 3m + 12 = -6
- 3m + 12 - 12 = -6 - 12
- 3m = - 18
divide both sides of the equation by -3
- 3m / - 3 = - 18 / -3
Therefore,
m = 6
learn more on equation and variable here: https://brainly.com/question/23831632
#SPJ1
Answer:
m = 6Step-by-step explanation:
Find the value of m: −3(m − 4) = −6
m = −6
m = −2
m = 2
m = 6
-3(m - 4) = -6
-3m + 12 = -6
-3m = -6 - 12
- 3m = -18
m = -18 : (-3)
m = 6
-----------------------------
check-3(6 - 4) = -6
-18 + 12 = -6
-6 = -6
the answer is goodReflect point M across the axis
Answer:
coordinates (-4,6)
Answer:
C the answer is v
Step-by-step explanation:
if this wrong mark this as brainliest
A city is paving a bike path. The same length of path is paved each day. After 4 days, 15 miles of path remain to be paved. After 6 more days, 12 miles of path remain to be paved. Find the average rate of change.
15 km of walkway still need to be paved after 4 days. There are still 12 miles of trail to be paved after another 6 days. The average rate of the change is 24.
Given that,
The paving of a bike route by a city. Every day, the same amount of the path is paved. 15 km of walkway still need to be paved after 4 days. There are still 12 miles of trail to be paved after another 6 days.
We have to find the average change rate.
1st we find the slope with the points (4,15) and (6,12).
Slope =[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Slope=[tex]\frac{12-15}{6-2}[/tex]
Slope=-3/4
Now,
y=mx+b
15=-3/4(4)+b
b=15+3
b=18
We got the equation of line as y=-3/4x+18
Now take y=0
0=-3/4x+18
-3/4x=-18
x=(18×4)/3
x=72/3
x=24
Therefore, the average rate of the change is 24.
To learn more about average visit: https://brainly.com/question/12322912
#SPJ1
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
a
Solve.
4x +6 <−6
b
Solve.
−2/5 x −9 < 9/10
bbbbbbbbbbbbbbb bbbbbbbbbbbbbb
In a boxplot, if the median is to the left of the center of the box and the right whisker is substantially longer than the left whisker, the distribution is skewed.
The distribution is skewed to the right if the median is to the left of the center of the box and the right whisker is substantially longer the the left whisker
In a boxplot of distribution, the following are the scenarios:
When the median is at the middle of the box, and the whisker are about the same on both ends of the box, the distribution is symmetric.When the median is to the right of the box, the right whisker will be substantially longer than the left whisker and the distribution is skewed to the rightWhen the median is to the left of the box, the left whisker will be substantially longer than the right one, and the distribution will be negatively skewed or skewed to the leftLearn more about Boxplot distribution here:
https://brainly.com/question/28827323
#SPJ4
Last year, Ken bought a mountain bike for $400. It is now worth $320. What percent
did the value of Ken's bike depreciate over the past year, to the nearest whole
percent?
The percent by which the value of Ken's bike depreciated over the past year is 20%.
What is the percentage deprecation?
Depreciation is the decline in the value of an asset with the passage of time. Depreciation is as a result of wear and tear of an asset. The price of an item would decline when it depreciates.
Percentage is the fraction of an amount that is expressed as a number out of hundred. Percentage is used to measure the frequency of data. The sign that represents percentage is %. To convert a number to percentage, multiply the number by 100.
Percent depreciation = (value of the mountain bike today / value of the mountain bike last year) - 1
($320 / $400) - 1 = -0.20
0.20 x 100 = 20%
To learn more about percentages, please check: https://brainly.com/question/25764815
#SPJ1
11) Convert 3 miles to feet
Answer: 15840[tex]covert 3 miles to feet[/tex]
Step-by-step explanation:
3 miles equals 15840 feet
Answer: 15840
Step-by-step explanation:
3 miles have 15840 feet
If this helped you please consider marking this as the Brainliest Answer, if i make it to 10, I can be promoted to an expert. How? - Once you get more than 1 answer of a question. A message is shown above each answer that is "Mark as brainiest". Click on the option to mark it the best answer. Thank you!
Describe the slope of the line. (0, 3) (5,-1) m= The slope is negative Find the slope.
Answer:
Step-by-step explanation:
Slope formula: m=[tex]\frac{rise}{run}[/tex] so m= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]y_1[/tex]=3
[tex]y_2[/tex]=-1
[tex]x_1[/tex]=0
[tex]x_2[/tex]=5
So the formula is, [tex]\frac{(-1)-3}{5-0}[/tex] = [tex]\frac{-4}{5}[/tex]
Slope is negative.
Slope is -4/5
I need help with this question
he Solution:
iven:
The y-intercept of function 1 is:
[tex]y-\text{intercept}=5\text{ }[/tex]The y-intercept of function 2 is:
[tex]y=1[/tex](a) So, the farthest y-intercept from 0 is function 1.
he slope of function 1 is
[tex]\text{Slope}=\frac{2-5}{1-0}=-\frac{3}{1}=-3[/tex]The slope of function 2 is
[tex]\text{slope=}\frac{3-1}{1-0}=\frac{2}{1}=2[/tex]he solope of function 3 is -1
The slope of function 4 is 5
(b) hus, the steepest graph is the function with the highest slope.
So, the steepest graph is the graph of function 4 since it has the greatest slope.
(c)
Functions with y-intercept greater than -3 are:
unction 1, function 2, amnd function 4.
[tex]\text{ function 3 has y-intercept=-4}<-3[/tex]A scuba diver dove from the surface of the ocean to an elevation of −69 9/10
feet at a rate of −21.5 feet per minute. After spending 12.5 minutes at that elevation, the diver ascended to an elevation of −38 9/10
feet. The total time for the dive so far was 19 1/8
minutes. What was the rate of change in the diver's elevation during the ascent? Round your answer to the nearest hundredth.
The rate of change of the divers elevation = 19.274
Given,
The depth to which the Scuba dove = -69 [tex]\frac{9}{10}[/tex] feet
The rate at which he dove = -21.5 feet per min.
The time which he spent at the elevation = 12.5min.
The elevation the diver then ascended to -38 [tex]\frac{9}{10}[/tex] feet
Thee total time for the dove = 19 [tex]\frac{1}{8}[/tex] minutes.
Therefore, the time [tex]t_{d}[/tex] with which the scuba diver descended to -69 [tex]\frac{9}{10}[/tex] feet
is given as follows:
[tex]t_{d} = \frac{Distance}{speed}[/tex] = [tex]= \frac{-69\frac{9}{10} }{-21.5}= \frac{-681}{-21.5}[/tex] = 3.167 minutes
The time [tex]t_{e}[/tex], it took the scuba diver to elevate to -38 [tex]\frac{9}{10}[/tex] feet is given as follows:
[tex]t_{e}[/tex] = 19 [tex]\frac{1}{8}[/tex]minutes - (3.167 + 10.5) minutes = 5.458 minutes
The rate of change of the divers elevation = (Final elevation - Initial elevation)/(Time taken).
∴ The rate of change of the divers elevation
= (-38 [tex]\frac{9}{10}[/tex] - (-69 [tex]\frac{9}{10}[/tex] )) / 5.458 min
=(37.1 - (-68.1))/ 5.458 min
= 19.274 feet/minutes to the nearest hundredth.
Hence, The rate of change of the divers elevation = 19.274
Learn more about Elevation at:
https://brainly.com/question/20305317
#SPJ1
Could anybody help me? Math!!!!
The products of the fractions given are:
1. (-3/4)(7/8) → -21/32
2. (2/3)(-4)(9) → -24
3. (5/16)(-2)(-4)(-4/5) → -2
4. (2 3/5)(7/9) → 91/45
How to Multiply Fractions?To multiply two or more fractions, multiply the denominators of both fractions together, and their numerators together.
1. (-3/4)(7/8)
Multiply the denominators of the fractions together, and also multiply their numerators:
= (-3 × 7) / (4 × 8)
= (-21) / (32)
(-3/4)(7/8) → -21/32
2. (2/3)(-4)(9)
Multiply the denominators of the fractions together, and also multiply their numerators:
= (2 × -4 × 9) / (3)
= -72/3 = -24
(2/3)(-4)(9) → -24
3. (5/16)(-2)(-4)(-4/5)
= (5 × -2 × -4 × -4) / (16 × 5)
= -160/80 = -2
(5/16)(-2)(-4)(-4/5) → -2
4. (2 3/5)(7/9)
= (13/5)(7/9)
= (13 × 7)/(5 × 9) = 91/45
(2 3/5)(7/9) → 91/45
Learn more about fractions on:
https://brainly.com/question/6078120
#SPJ1
What is the right answer
No solution is the answer of inequality.
What is inequality
The relationship between two values in an imbalanced algebraic statement is represented by an inequality in mathematics. One of the two variables can be larger than, more than or equal to, smaller than, or equal to another value by using a sign of inequality. Make use of the following steps to solve an inequality: Step 1: Remove fractions by multiplying all terms by the fractions' lowest common denominator. Step 2 Combine like terms on both sides of the inequality to simplify. Step 3 Obtain the unknown on one side and the integers on the other by adding or subtracting quantities.
Given Data
[tex]\frac{4}{3}[/tex]g - 3< g + [tex]\frac{2}{3}[/tex] - [tex]\frac{1}{3}[/tex]g
([tex]\frac{4}{3}[/tex]g - g) + [tex]\frac{1}{3}[/tex]g <( [tex]\frac{2}{3}[/tex] + 3)
Taking LCM,
[tex]\frac{4e+3e+1e}{3}[/tex] < [tex]\frac{2+9}{3}[/tex]
8g < 11
g < [tex]\frac{11}{8}[/tex]
No solution is the answer of inequality.
To learn more about inequality, visit:
https://brainly.com/question/15064057
#SPJ13
Mai biked 6\frac{3}{4} miles today, and Noah biked 4\frac{1}{2} miles.
How many times the length of Noah’s bike ride was Mai’s bike ride?
Mai's bike ride was 1.5 times the length of Noah's bike ride
Fractions: A numerical value that designates a portion of a whole is used to represent fractions. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.
Distance travelled by Mai in miles = 6 3/4 miles
Distance of Mai in improper fraction = 27/4
Distance travelled by Noah in miles = 4 1/2
Distance of Noah in improper fraction = 9/2
Length of Noah's bike ride as compared to Mai's bike ride = (27/4)/(9/2)
= 27/4*2/9
= 3/2 or 1.5 times
Learn more about fractions:
https://brainly.com/question/1301963
#SPJ1
Exterior angle, theorem, and triangle sum theorem
Answer:
x = 4Step-by-step explanation:
It is assumed you are looking for the value of x.
According the diagram, we have:
∠JEF is exterior angle to triangle EFG and ∠F and ∠G are remote interior angles.Property of exterior angle - it is same as the sum of remote interior angles.
Set equation:
m∠F + m∠G = m∠JEF16x + 4 + 14x + 6 = 13030x + 10 = 13030x = 120x = 4It is easy to calculate the unknown angle measures if needed:
m∠F = 16*4 + 4 = 68m∠G = 14*4 + 6 = 62