The width of a rectangular slab of concrete is 7 m less than the length. The area is 98 m squared. Find the dimensions
Answers
Answer:
Length = 14 m, Width = 7 m
Step-by-step explanation:
Let the length is l and width is b.
Width, b = l-7
Area of the rectangle, A = 98 m²
We know that, the area of a rectangle is as follow :
\(A=lb\)
So,
\(98=l(l-7)\\\\98=l^2-7l\\\\l^2-7l-98=0\\\\l^2+7l-14l-98=0\\\\l(l+7)-14(l+7)=0\\\\l=14,-7\)
Length can't be negative. So,
Width, b = 14-7 = 7 m
So, the dimensions of the rectangle are 14 m and 7 m respectively.
Related Questions
A sequence can be generated by using an= 3an-1, where a1 = 10 and n is a whole number greater than 1.
What are the first 3 terms in the sequence?
A. 3, 13, 23
B. 10, 30, 90
C. 10, 13, 16
D. 3, 30, 300
Answers
Answer:
B
Step-by-step explanation:
using the recursive rule \(a_{n}\) = 3\(a_{n-1}\) and a₁ = 10, then
a₁ = 10
a₂ = 3a₁ = 3 × 10 = 30
a₃ = 3a₂ = 3 × 30 = 90
the first 3 terms are 10 , 30 , 90
Indicate the method you would use to prove the two 's . If no method applies, enter "none".
SSS
ASA
SAS
AAS
None
Answers
The method you would use to prove the two triangles are congruent include the following: B. ASA.
What are the properties of similar triangles?In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Additionally, the lengths of corresponding sides are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.
In Mathematics and Geometry, ASA is an abbreviation for Angle-Side- Angle and it states that when two (2) angles and their included side in two (2) triangles are congruent, then the triangles are said to be congruent.
Read more on triangle here: brainly.com/question/22891315
#SPJ1
Missing information:
The question is incomplete and the complete question is shown in the attached picture.
you did not provide enough information to answer the question
marking as brainlist pls help
Answers
Explanation:
For this problem, we can use the law of cosines to find the length C. We rearrange the formula for C and solve:
c^2 = a^2 + b^2 - 2ab cos(C)
c = sqrt(a^2 + b^2 - 2ab cos(C))
So for the values, use the following from our image:
a = 61
b = 63
C = 142 degrees
c = sqrt( 61^2 + 63^2 - 2(61)(63)cos(142))
c = sqrt( 3721 + 3969 - (-6056.65))
c = sqrt( 13746.65 )
c = 117.246
So, we have found the value of c to be 117.246.
To round to the nearest tenth, we will have 117.2
Cheers.
) A watershed experiences a rainfall of 8 inches. What is the runoff volume when the curve number is 80
Answers
Answer:
5.625 inches
Step-by-step explanation:
Given that:
Total Rainfall in inches (P) = 8 inches
The runoff volume (in inches) Q = ???
The curve number CN = 80
Recall that: The runoff volume can be calculated by using the formula:
\(Q = \dfrac{(P-0.2S)^2}{(P+0.8S)}\) for P > 0.2S
Q = 0 for P < 0.2S
\(S = \dfrac{1000}{CN}-10\)
where:
curve number CN = 80
\(S = \dfrac{1000}{80}-10\)
S = 2.5 inches
Since the rainfall (P) is greater than 0.25
Then:
\(Q = \dfrac{(P-0.2S)^2}{(P+0.8S)}\)
\(Q = \dfrac{(8-0.2(2.5))^2}{(8+0.8(2.5))}\)
\(Q = \dfrac{(8-0.5)^2}{(8+2)}\)
\(Q = \dfrac{(7.5)^2}{(10)}\)
\(Q = \dfrac{(56.25)}{(10)}\)
Q = 5.625 inches
Thus, the runoff volume = 5.625 inches
is - 5/1 a integer?
Answers
blake bike east at 5m/s. five seconds later he speeds up to 9 m/s.
what is his change in velocity? what is his acceleration?
Answers
Answer:
The answer is down below
Step-by-step explanation:
v-u=◇velocity
\( = 9 - 5\)
◇velocity =4ms‐¹
acceleration =◇velocity/time
\(a = \frac{4}{5} \)
\(a = 0.8m {s}^{ - 2} \)
Change in velocity:
\( \sf \:final \: velocity - initial \: velocity = change \: in \: velocity\)
\( \therefore \tt \delta \: v = 9 - 5 \\ \tt = 4m {s}^{ - 1} \)
To find acceleration:
\( \rm \: a = \frac{ \triangle \: v}{\triangle \: t} \)
\( \rm \: a = \frac{ 4}{5 - 0} = \frac{4}{5} = 0.8m {s}^{ - 1} \)
4.) Which equations below have no solution? Select all that apply, and justify your response with work. a.) x - 9 = 2(x - 3) + 12 b.) 5(-2x + 7) + 3 = -10x + 38 1 c.) (6x - 4) = 3(x - 2) 1 d.) 0.01x + 0.001 = (x + 10) 100 e.) 3(x + 2) + 1 = x + 2(4 + x)
Answers
Answer: Equations (b) and (e) do not have solutions
Step-by-step explanation: b) The x cancels out (-10x + 35) = -10x + 318; 35 = 318???? NO. e) 3(x + 2) + 1 = x + 2(4 + x); 3x + 7 = 3x + 8. The x cancels out again.
The other s can be solved for x.
Hi! I'm happy to help!
To solve this, we need to simplify all of the equations. There are 3 ways equations like this can go, infinitely many solutions, 1 solution, or no solution. Infinitely many is something like 6=6, that could mean infinite solutions because 6 always equal 6, and would apply in infinitely many ways. (in the equation) One solution refers to something like x=6. This tells your exactly what x is, and that is your only solution. (for the equation) And no solution is something like 5=6, 5 will never equal 6, so that is no solution. (to the equation)
Now, let's start out with our first equation. To find if our equations have solutions or not, we need to simplify them. We do this by singling out x to see what the solution is (if there is one).
x-9=2(x-3)+12
We can multiply 2, by x and -3 inside of the parenthesis, to simplify:
x-9=2x-6+12
Since we have at least one x on both sides, we can subtract it to isolate it:
x-9=2x-6+12
-x -x
-9=x-6+12
Combine -6 and twelve:
-9=x-6+12
-9=x+6
Now, we subtract 6 to fully isolate x:
-9=x+6
-6 -6
-15=x
We see we have 1 solution, so you should not pick option 1.
Second equation:
5(-2x + 7) + 3 = -10x + 38
We should first multiply the parenthesis:
-10x+35+3=-10x+38
Since we want to simplify, let's add 10x on both sides
-10x+35+3=-10x+38
+10 +10x
35+3=38
Add 35 and 3:
38=38
Since 38 will always equal 38, there are infinite solutions, and you should not pick option 2.
Third equation:
(6x - 4) = 3(x - 2)
Since there is nothing outside of the parenthesis (right side), we don't need them:
6x-4=3(x-2)
From here, multiply the parenthesis:
6x-4=3x-6
Subtract 3x from both sides:
6x-4=3x-6
-3x -3x
3x-4=-6
Add 4 to both sides to isolate x:
3x=-2
Divide both sides by 3, to fully isolate x:
x=-\(\frac{2}{3}\)
Since there is only 1 solution, you should not pick option 3.
Fourth equation: (not sure if the 100 is supposed to be there)
0.01x + 0.001 = (x + 10)
First, let's subtract 0.01x from both sides:
0.001=9.99x+10
Then, we subtract 10 from both sides to start isolating x:
-9.999=9.99x
Then, we divide both sides by 9.99:
______
1.000900900=x
Kind of a weird number, but regardless, you should not pick option 4, because it has 1 solution.
Fifth equation:
3(x + 2) + 1 = x + 2(4 + x)
First, let's multiply the parenthesis on both sides:
3x+6+1=x+8+2x
Combine like terms:
3x+7=3x+8
Subtract 3x from both sides:
7=8
7 will never equal 8, there will be no solution, and you should pick option 5.
You should pick option e, because it has no solution.
I hope this was helpful, keep learning! :D
Simplify the expression
Answers
Hello User!
Answer:
\(a^{9}/8\)
Last one is your answer
the kappa iota sigma fraternity polled its members on the weekend party theme. the vote was as follows: six for toga, four for hayride, eight for beer bash, and two for masquerade. display the vote count in a pareto chart.
Answers
Pareto chart is a type of bar graph which often displays the data in descending order of frequency.
It is made up of vertical bars, with the height of each bar representing the frequency of occurrence for each category. The chart is named after Vilfredo Pareto, who used it to analyze economic data in the late 19th century.
For the given data, we calculate the cumulative frequency of the data by adding the frequencies of each category.
Toga: 6
Hayride: 6 + 4 = 10
Beer Bash: 10 + 8 = 18
Masquerade: 18 + 2 = 20
The Pareto chart is created by plotting the cumulative frequency against the categories. The chart is plotted with the categories on the x-axis and the cumulative frequency on the y-axis.
Toga: 6 (30%)
Hayride: 10 (50%)
Beer Bash: 18 (90%)
Masquerade: 20 (100%)
Hence, the Pareto chart for the given data is as follows:
Toga: 30%
Hayride: 20%
Beer Bash: 40%
Masquerade: 10%
Learn more about Pareto chart here:
https://brainly.com/question/17840218
#SPJ4
Write the equation of the line that has a rate of change of 5 and passes through the point
(4, -1)
Answers
We are given that the rate of change (slope) is 5 and that the line passes through the point (4, -1).
Substituting the values into the point-slope form, we get:
y - (-1) = 5(x - 4)
Simplifying the equation, we get:
y + 1 = 5x - 20
y = 5x - 21
Therefore, the equation of the line that has a rate of change of 5 and passes through the point (4, -1) is y = 5x - 21.
Hello
Answer:
\(\Large \boxed{\sf y=5x-21}\)
Step-by-step explanation:
The slope-intercept form of a line equation is \(\sf y=mx+b\) where m is the rate of change (or the slope) and b is the y-intercept.
We know that the rate of change is 5 so : \(\boxed{\sf m=5}\)
\(\sf y=5x+b\)
Let's find the value of b !
Moreover, we know that the line passes through the point (4,-1).
Let's replace x and y with 4 and -1 in the equation and solve for b:
\(\sf -1=4\times5+b\)
\(\sf\iff -1=20+b\)
Let's substract 20 from both sides :
\(\sf -1-20=20-20+b\)
\(\boxed {\sf b=-21}\)
The equation of the line is : \(\boxed{\sf y=5x-21}\)
Have a nice day ;)
Find an angle in each quadrant with a common reference angle with 165°, from 0°≤θ<360°
Answers
Answer:
Here are the angles in each quadrant with a common reference angle of 165°:
First quadrant: angle is 15° (subtract 165° from 180°)
Second quadrant: angle is 195° (subtract 165° from 180° and add the result to 180°)
Third quadrant: angle is 195° (subtract 165° from 180° and then subtract the result from 180°)
Fourth quadrant: angle is 195° (subtract 165° from 360°)
please help with this question (d+2)(-7)
Answers
Answer:
-7d-14
Step-by-step explanation:
First, let's distribute -7 to (d+2)
-7xd
-7x2
We will get -7d-14
Skylar went shopping for a new video game. To find the total plus tax, she multiplied the price of the video game by 1.0775. What percent tax did she pay?
Answers
Answer:A topic sentence is used to bring
to a paragraph.
Step-by-step explanation:
A topic sentence is used to bring
to a paragraph.
Circle A has center of (4,6) and a radius of 5, and circle B has a center of (1,0) and a radius of 15. What steps will help show that circle A is similar to circle B? Dilate circle Dilate circle A by a scale factor of 3. translate Circle A using the rule (x - 3, y + 6). Rotate circle A 180° about the center. reflect circle A over the y-axis.
Answers
The answer is A. Dilate circle A by a scale factor of 3
I took the test :)
Set up and solve an equation for the value of x. Use the value of x and a relevant angle relationship in the diagram.
(please also show an step by step process of getting EAF!)
Answers
Answer:
x = 27 , ∠ EAF = 27°
Step-by-step explanation:
∠ GAF = 90° , then
∠ GAC + ∠ CAF = ∠ GAF , that is
x + 63 = 90 ( subtract 63 from both sides )
x = 27
∠ DAE = 90°
since CD is a straight angle of 180° , then
∠ CAE = 90° , so
∠ CAF + ∠ EAF = ∠ CAE , that is
63° + ∠ EAF = 90° ( subtract 63° from both sides )
∠ EAF = 27°
Hellppppp........ pleasee
Answers
Answer:
Step-by-step explanation:
The set of points in the 2nd row does not represent a function, because the x-coordinate 2 is associated with more than one y-coordinate.
Functions are one-to-one: For each x value there is one y value associated.
please write the answer in minutes.
Thank you.
My life depends on you
Answers
Note that the estimated time it will take to cause hearing loss at 106 decibels is 0.0625 hours or 3 minutes, 75 seconds.
How did we arrive at this conclusion?The formula used is:
Exposure Time = 8/ 2^((dBA-85)/3)
Since the decibel (dBA) given is 106
Exposure Time = 8/ 2^((106-85)/3)
= 8/2^1
= 8/ 128
= 0.0625 hours or 3 minutes, 75 seconds.
Learn more about hearing loss;
https://brainly.com/question/18548045
#SPJ1
Mia had $22. Then she started to receive $4 a week as an allowance. She plans to save all of her money for a bicycle and draws
a graph of her planned savings. Mia lets x represent the number of weeks she has received her allowance, and y represent her
total amount of money. Which of the following ordered pairs is on Mia's graph?
Answers
It should be noted that the equation to illustrate the information regarding Mia will be y = 22 + 4x.
How to illustrate the information?It should be noted that from the information, Mia had $22 and then she started to receive $4 a week as an allowance and plans to save all of her money for a bicycle.
Let lets x represent the number of weeks she has received her allowance.
Let y represent her total amount of money.
The equation to illustrate the information will be:
y = 22 + 4(x)
y = 22 + 4x
Note that the options were not given and the appropriate equation that fits rte scenario was illustrated.
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
Factor completely 2x^3 + 10x^2 + 14x + 70(2x^2 + 14)(x + 5)(x^2 + 7)(2x + 10)2(x^3 + 5x^2 + 7x + 35)2[(x^2 + 7)(x + 5)]
Answers
ANSWER
\(2x^3+\text{ 10x}^2\text{ +14x + 70 = 2\lbrack\lparen x}^2\text{ + 7\rparen\lparen x + 5\rparen\rbrack}\)EXPLANATION
Given polynomial function
\(2x^3\text{ + 10x}^2\text{ + 14x + 70}\)To factor the given polynomial function, follow the steps below
Step 1: Divide the expression through by 2 in order to make sure that the coefficient of x^3 is 1
\(\begin{gathered} 2x^3\text{ + 10x}^2\text{ + 14x + 70} \\ \frac{2x^3}{2}\text{ + }\frac{10x^2}{2}+\text{ }\frac{14x}{2}\text{ + }\frac{70}{2} \\ x^3\text{ + 5x}^2\text{ + 7x + 35} \end{gathered}\)Step 2: Factor the simplified expression in step 1
\(\begin{gathered} \text{ x}^3\text{ + 5x}^2\text{ + 7x + 35} \\ \text{ Factor}^\text{ x}^2\text{ out in the expression} \\ x^2(x\text{ + 5\rparen + 7\lparen x + 5\rparen} \\ \text{ \lparen x}^2\text{ + 7\rparen \lparen x + 5\rparen} \\ 2[(x^2\text{ +7\rparen\lparen x + 5\rparen\rbrack} \end{gathered}\)Hence, the correct answer is option D
Hey : please help no fake anwsers : I’ll mark you brainliest :3
Answers
Answer:
320units²
Step-by-step explanation:
one half triangle
area =1/2bh
area of the triangle= 1/2*5*8
= 20units²
area of the octagon= 16*20
=320units²
16 semi triangle will make up the octagon full
I hope it work for you
help me fast rapidly is of khan academy:
Answers
Answer:
0 hundreds
0 tens
7 ones
.
4 tenths
0 hundredths
8 thousandths
Standard form=7.408
Step-by-step explanation:
Lets first solve (7x1)+(4x1/10)+(8x1/1000)
7+0.4+0.008
Simplify:
7.408
PLEASE MARK AS BRAINLIESTA fire department's response time measures the time from when the alarm is sounded at the firehouse to the time the first fire engine leaves the station. The histograms below display the response times for fire departments in two small towns: Hilltown and Crestview.
Which of the following correctly compares the variability in response times for the two towns?
-Hilltown and Crestview show similar variability in their response times.
-The variability in Hilltown‘s response times is less than that of Crestview.
-The median response time in Crestview is greater than that of Hilltown.
-The variability in Hilltown‘s response times is greater than that of Crestview.
Answers
Answer:
B. The variability in Hilltown's response times is less than that of Crestview.
Step-by-step explanation:
This one makes most sense of all.
Tell me if I'm wrong :)
The interval that contains the median response time is; 50 - 60 seconds
What is the median of the histogram?The median of a histogram is defined as the middle element of the histogram.
Here, we have,
Now, in this histogram given, we see that the y-axis is for the relative frequency, while the x-axis is the Response time (in seconds).
Observing this histogram closely, it is clear that the response times are all symmetrical around the interval 50 - 60 seconds as it is also the middle element of the histogram.
Thus, we can conclude that the interval that contains the median response time is; 50 - 60 seconds
Read more about Histogram Median at;
brainly.com/question/26046231
#SPJ2
The function y = f(x) is graphed below. Plot a line segment connecting the points
on f where a = 2 and = 3. Use the line segment to determine the average rate of
change of the function f(x) on the interval 2 ≤ x ≤ 3.
Plot a line segment by clicking in two locations. Click a segment to delete it.
-10
-6
4
20
16
y
12
2
4
6
8
10
Answers
The average rate of change of the function over the interval is -4
Finding the average rate of changeFrom the question, we have the following parameters that can be used in our computation:
The graph
The interval is given as
From x = 2 to x = 3
The function is a polynomial function
This means that it does not have a constant average rate of change
So, we have
f(2) = 4
f(3) = 0
Next, we have
Rate = (4 - 0)/(2 - 3)
Evaluate
Rate = -4
Hence, the rate is -4
Read more about average rate of change at
brainly.com/question/17131025
#SPJ1
Explore
Drag the digits 0 to 9 to the boxes to create an original
rectangle and a scaled copy.
2
9
0
8
Answers
Answer:
I don’t understand this
Step-by-step explanation:
is 3π less than 3√3 or greater than
Answers
Answer:
3π is greater than 3√3.
Step-by-step explanation:
The square root of 3 is about 1.7, multiplying that by 3 equals 5.1.
We know that pi starts with 3.14 and etc. though let's round that to 3.1, so 3 x 3.1 is 9.3.
Acellus
Find the measure of an
interior angle of a regular
hexagon (6-sided polygon).
х
X = [?]°
Hint: Sum = (n-2)180
Answers
Answer:
120°
Step-by-step explanation:
Sum of angles = (n-2)180°, where n is the number of sides.
This is a hexagon, so n=6.
Sum of angles = (6-2)180° = 720°
Each interior angle = 720°/6 = 120°
40 subtracted from five times a number is 8 more than the number write the equation
Answers
Answer (let x be the number):
5x - 40 = x + 8
I hope this helps!
The number in the equation 5n - 40 + 8 = n is 8.
What is a numerical expression ?A numerical expression is formed by numbers and their operation.A numerical expression can also be constructed from given statements.
We can also construct numerical expression form real life scenarios.
According to to the question statement 40 subtracted from five times a number is 8 more than the number and we have to form an numerical expression.
Let the number be 'n'.
∴ 5n - 40 + 8 = n
5n - n = 40 - 8.
4n = 32.
n = 32/4.
n = 8.
learn more about numerical expression here :
https://brainly.com/question/14642484
#SPJ2
b) In a certain weight lifting machine, a weight of 1 kN is lifted by an effort of 25 N. While the weight moves up by 100 mm, the point of application of effort moves by 8 m. Find mechanical advantage, velocity ratio and efficiency of the machine
Answers
The mechanical advantage of the given machine is 40, Velocity ratio is 80 and efficiency is 0.5.
The given question is concerned with finding the mechanical advantage, velocity ratio and efficiency of a weight lifting machine.
The problem has provided the following information:
Weight of the object, W = 1 kN = 1000 NEffort applied, E = 25 NHeight through which the object is lifted, h = 100 mm = 0.1 m Distance through which the effort is applied, d = 8 m
We know that, mechanical advantage = load/effort = W/E and velocity ratio = distance moved by effort/distance moved by the load.Mechanical advantage
The mechanical advantage of the given machine is given by; Mechanical advantage = load/effort = W/E= 1000/25= 40Velocity ratioThe velocity ratio of the given machine is given by;
Velocity ratio = distance moved by effort/distance moved by the load.= d/h = 8/0.1= 80EfficiencyThe efficiency of the given machine is given by;
Efficiency = (load × distance moved by load) / (effort × distance moved by effort)Efficiency = (W × h) / (E × d)= (1000 × 0.1) / (25 × 8)= 0.5
Therefore, the mechanical advantage of the given machine is 40, velocity ratio is 80 and efficiency is 0.5.
For more questions on Velocity .
https://brainly.com/question/25749514
#SPJ8
A commuter plane provides transportation from an international airport to surrounding cities. One commuter plane averaged 260 mph flying to a city and 140 mph returning to the international airport. The total flying time was 4 h. Find the distance between the two airports.
Answers
Answer:
364 miles
Step-by-step explanation:
Rate Time Distance
Flight #1 260 x 260x
Flight #2 140 4-x 140(4-x)
Because each flight was to or from the same airports the distance traveled by flight #1 and flight #2 must be the same. This means that you can set the two calculated distances equal to each other.
260x = 140(4-x)
260x = 560 - 140x
400x = 560
x = 1.4 hours This is the amount of time flight 1 spent in the air.
now we can use this and plug it into the distance formula (260x) to find the distance
260(1.4) = 364
so the distance between the two airports is 364 miles
Find the lateral surface area of the composite figure shown below that
consists of a right cone sitting atop a right circular cylinder. Use 3.14
for It.
I = 21 mm
r = 10 mm
H = 7mm
Answers
The surface area of the composite figure consisting of a right cone sitting atop a right cylinder is approximately 511.506 square centimeters.
To find the surface area of the composite figure consisting of a right cone atop a right cylinder, we need to calculate the surface areas of both the cone and the cylinder separately, and then sum them up.
Let's consider the dimensions of the cone and the cylinder:
Cone:
Radius of the base (r) = 5 cm
Height of the cone (h_cone) = 10 cm
Cylinder:
Radius of the base (r) = 5 cm
Height of the cylinder (h_cylinder) = 8 cm
Surface area of the cone:
The surface area of a cone can be calculated using the formula A_cone = πr(r + √(\(r^2 + h_cone^2\))). This formula takes into account the curved surface area of the cone and the base area.
Substituting the given values, we have:
A_cone = 3.14 × 5(5 + √(\(5^2 + 10^2\)))
A_cone = 3.14 × 5(5 + √(25 + 100))
A_cone = 3× 5(5 + √125)
A_cone = 3.14 × 5(5 + 11.18)
A_cone = 3.14 × 5(16.18)
A_cone = 3.14 × 80.9
A_cone ≈ 254.026 square cm (rounded to the nearest thousandth)
Surface area of the cylinder:
The surface area of a cylinder consists of the curved surface area and the areas of the two circular bases. The formula to calculate the surface area of a cylinder is A_cylinder = 2πrh_cylinder + 2πr^2.
Substituting the given values, we have:
A_cylinder = 2 ×3.14 × 5 × 8 + 2 × 3.14 × 5^2
A_cylinder = 100.48 + 157
A_cylinder = 257.48 square cm
Now, we can find the total surface area of the composite figure by summing up the surface areas of the cone and the cylinder:
Total Surface Area = A_cone + A_cylinder
Total Surface Area ≈ 254.026 + 257.48
Total Surface Area ≈ 511.506 square cm (rounded to the nearest thousandth)
Therefore, the surface area of the composite figure consisting of a right cone sitting atop a right cylinder is approximately 511.506 square centimeters.
for such more question on surface area
https://brainly.com/question/20771646
#SPJ11
Question
Find the surface area of the composite figure shown below that consists of a right cone sitting atop a right cylinder. Use 3.14 for π and give the answer in square centimeters.
