Answer:
WITDTH=7
Step-by-step explanation:
width = w
length = w + 2.
w(w + 2) = 63 (area)
quadratic equation in w:
w2 + 2w = 63
w2 + 2w - 63 = 0
FACTOR:
(w + 9)(w - 7) = 0
9-7=2
9x(-7) = -63
Two possible solutions:
w + 9 = 0 (solution w = -9) or
w - 7 = 0 (solution w = 7)
The width must be positive, the answer is 7 units.
length = w+2
length = 9
Solve by factorisation
2x2 + 3x - 20 = 0
The sum of thrice a number and 5 is greater than or equal to the sum of twice a number and 1. Write down the inequality and solve it..
Answer:
May be helpful.
thx.......
The formula D = 401t + 5940 can be used to approximate the total average credit card debt in a U.S. household (in dollars) t years after 1995. Use this formula to predict what the total average credit card debt will be in the year 2028. In the year 2028, the total average credit card debt for a U.S. household will be $
Step-by-step explanation:
The formula D = 401t + 5940 can be used to approximate the total average credit card debt in a U.S. household (in dollars) t years after 1995. Use this formula to predict what the total average credit card debt will be in the year 2028.
2028 - 1995 = 33 years, so t = 33
D = 401t + 5940
D = 401(33) + 5940
D = 13,233 + 5940
D = 19,173
Answer: In the year 2028, the total average credit card debt for a U.S. household will be $19,173
marjore needs to earn a C in her class. her current test scores are 67,78,75,78 and .her final exam is worth 6 test scores. In order to earn a C marjorties average must lie between 70 and 79 inclusive. What range of scores can marjorie's receive on the final exam to earn a C in the course?
The range of scores that Marjorie's can receive in the final exam to earn a C in the course is 67 to 82 .
in the question ,
it is given that
the Marjorie's score in the tests are 67 , 78 , 75 , 78 .
let the score in the final exam be "x"
it is given that the final exam score is worth 6 test scores , which means
the score in final exam is = 6x
and the total number of tests = 6+4 = 10
given that to get the grade C minimum average is = 70
that is (67 + 78 + 75 + 78 + 6x)/10 = 70
67 + 78 + 75 + 78 + 6x = 700
298 + 6x = 700
6x = 700 - 298
6x = 402
x = 402/6
x = 67
given that to get the grade C maximum average is = 79
that is (67 + 78 + 75 + 78 + 6x)/10 = 79
67 + 78 + 75 + 78 + 6x = 790
298 + 6x = 790
6x = 790 - 298
6x = 492
x = 492/6
x = 82
the range of scores is 67 to 82 .
Therefore , The range of scores that Marjorie's receive in the final exam to earn a C in the course is 67 to 82 .
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Mrs. Robinson made the table below showing the number of cells in a biology experiment after a number of days. Which type of function best models Mrs. Robinson’s data?
Days / Number of Cells
2 / 4
3 / 8
4 / 16
5 / 32
6 / 64
7 / 128
a) an exponential function
b) a quadratic function
c) an absolute value function
d) a linear function
The type of function best models Mrs. Robinson’s data is A. exponential function.
What is an exponential function?The formula f(x) = a^x defines an exponential function, where x is the input variable as an exponent. The exponential curve is determined by the exponential function and the value of x. Where an is greater than zero and less than one. x can be any actual number.
Mrs. Robinson created the table, which shows the number of cells in a biology experiment after a certain number of days. The independent variable, or x-value, in an exponential function is the exponent, while the base is a constant.
In this case, we can see that:
2 days = 2² = 4
3 days = 2³ = 8
4 days = 2⁴ = 16
This is an exponential function.
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how to solve/fhfhfhfhfhfhf
Answer:
b
Step-by-step explanation:
the right side base angle and 80° are vertically opposite angles and are congruent, both 80°
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
123° is an exterior angle of the triangle , then
x + 80 = 123 ( subtract 80 from both sides )
x = 43
Please Help Me!
Find the value of x
Answer: 65°
Step-by-step explanation:
You can determine the total degree within a shape by using the formula 180°(n-2), where n is the number of sides of the shape. Thus, the total degree within the parallelogram is 360°.
Angles sum up to the total degree, meaning we need to add up all the angles we see and set them equal to the total degree. We have two (2x-15) and two x's.
2(2x-15) + 2x = 360
Distribute the 2 to (2x-15), you will get 4x - 30.
4x - 30 + 2x = 360
Add like terms, 4x + 2x to get 6x.
6x - 30 = 360
Add both sides by 30 to isolate the 6x, because we are trying to determine the value of x, we need to isolate the term.
6x = 390
Divide both sides by 6, and you are left with the value of x being 65°
For a ride on a rental scooter, Tom paid a 5 fee to start the scooter plus 9 cents per minute of the ride. The total bill for Tom's ride was 21.38 . For how many minutes did Tom ride the scooter?
Answer:
182 minutes
Step-by-step explanation:
0.09x+5=21.38
-5. -5
0.09x=16.38
/0.09. /0.09
X=182
182 minutes
Hopes this helps please mark brainliest
A dam has a floodgate. When it is open, it lets out 10,000 gallons of water per minute.
How many gallons of water will it let out in 10 minutes?
A. 1,000
B. 10,000
C. 100,000
D. 1,000,000
Answer: C. 100,000 gallons
Step-by-step explanation:
10,000 gallons a minute.
10 minutes.
10,000 x 10 = 100,000.
Gallons: 10,000 20,000 30,000 40,000 50,000 60,000
Minutes: 1 2 3 4 5 6
... 70,000 80,000 90,000 100,000
... 7 8 9 10
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A rectangle that maximize the enclosed area has a length 800 yards and width is 800 yards. The maximum area is 640,000 square yards.
In the given question we have to find the maximum area of the rectangular area.
Liana has 3200 yards of fencing to enclose a rectangle.
So we know that the perimeter of rectangle is
P= 2(l+b)
Let length of the rectangle is x yards and width is y yards.
So the equation should be
2(x+y) = 3200
Divide by 2 on both side we get
x+y = 1600................(1)
As we know the area of rectangle is
A = xy
From the equation the value of y is 1600-x.
Now putting the value of y
A = x(1600-x)
A = 1600x-x^2
On differentiating
dA/dx = 1600-2x
Putting dA/dx=0
1600-2x=0
Subtract 1600 on both side we get
-2x= -1600
Divide by -2 on both side we get
x = 800 yards
Now putting the value of x in the y=1600-x
y=1600-800
y=800 yards
So the maximum area is
A= 800*800
A= 640,000 square yards
Hence, a rectangle that maximize the enclosed area has a length 800 yards and width is 800 yards. The maximum area is 640,000 square yards.
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22. A train travels 3 hours at 20km per
hour. How long will it take another
train to travel the same distance at
10km per hour?
(a) 6²/³ hours
(b) 6¹/2hours
(c) 6 hours
(d) 3 hours
(e) 2 hours
ans
6 hours will it take another train to travel the same distance .
What is speed?
Speed indicates the rate of movement of something or someone. If you know the distance traveled and the time it took, you may calculate an object's average speed. Speed is calculated as distance times speed.Average speed = Total distance/Total time
A train travels 3 hours at 20km per hour.
train travels 20 km in 1 hours.
then in 3 hours train travels = 3 * 20 = 60 km
total speed = 10 km/hr
t = distance/speed
= 60/10 = 6 hours
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What is an equation of the line that passes through the points (-7, 3) and (5, 3)?
the equation of the line passing through the given points is y = 3
What is an equation of the line?
An expression which is satisfied by every point on the line is known as equation of the line. generally it is given in y = mx + c form where m is the slope and c is the y-intercept
We are given two point (-7,3) and (5,3)
We first find the slope of the lines passing through the given points
Slope = [tex]\frac{3-3}{5+7}[/tex]
Slope = 0
Substituting the value in the equation we get
y = c
Now the value of y in both the cases is 3
Substituting that we get c = 3
Hence y = 3 is the required equation of the line
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R is inversely proportional to A.
R = 12 when A = 1.5
a) Work out the value of R when A = 5.
b) Work out the value of A when R = 9
The value of R when A equal 5 is 3.6 and the value of A when R equal 9 is 2 as R is varies inversely to A.
What is the value of R when A equal 5 and value of A when R equal 9?Proportional relationships are relationships between two variables where their ratios are equivalent.
If R is inversely proportional to A.
R ∝ 1/A, then
R = k/A
Where k is the proportionality constant.
Given that;
R = 12 A = 1.5Proportionality constant k = ?First, we determine the proportionality constant.
R = k/A
Plug in R = 12 and A = 1.5 and solve for k
k = R × A
k = 12 × 1.5
k = 18
a) The value of R when A = 5 will be;
R = k/A
R = 18 / 5
R = 3.6
b) The value of A when R = 9
R = k/A
R × A = k
A = k/R
A = 18 / 9
A = 2
Therefore, the value of A when R equal 9 is 2.
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Simplify.
ab2−−−√+39ab2−−−−√−34ab2−−−−√
Assume all variables are nonnegative.
Answer:In this item, I take it that we are to get the cube root of the given expression, -64x6y9. First, we look into the numerical coefficient, this is the product when -4 is multiplied to itself three times as shown below.
-64 = (-4)(-4)(-4)
Then,
x6 = x2 (x2) (x2)
and,
y9 = (y3)(y3)(y3)
If we take the cube root, we consider only one item per product. Thus, the answer is,
-4x²y³
Step-by-step explanation:
Find the slope and reduce.
P=(-8, 3) Q=(-6, 2)
Slope
=
Answer:
2-3/-6-(-8)
= -1/2
i need to find the diameter and the area of this equation[tex]A=\pi \frac{d}{2} x^{2}[/tex]
Answer:
Step-by-step explanation:
during the course of the basketball season, shawna made 67 out of 100 free throws. when we say that her probability of making a free throw during the playoffs is 0.67, what type of probability are we starting?
The type of probability are we starting will be relative frequency probability or the empirical probability,
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
Given that, Shawna made 67 out of 100 free throw attempts during the course of the basketball season. When we state that she has a 0.67 chance of making a free shot during the postseason,
The ratio of the number of times an event occurs to the total number of outcomes that occurred is known as relative frequency.
Thus, the type of probability are we starting will be relative frequency probability or the empirical probability,
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Simplify each expression.
1) 7w + 2w - 6w
2) 9x - 3x + 2x 3) 8p + 3p - p
4) 6b-3b+5b
The simplified expressions for the questions will be, 1) 3w, 2) 8x, 3) 10p, 4) 8b.
The simplification of an algebraic expression generally means breaking the equation into a smaller form for easier calculation with the help of formulas or using the rule of BODMAS.
Here, all the questions can be solved by using the BODMAS rule.
1) 7w + 2w - 6w
= (7w + 2w) - 6w
= 9w - 6w
= 3w.
2) 9x - 3x + 2x
= (9x + 2x) -3x
= 11x - 3x
= 8x.
3) 8p + 3p - p
= (8p + 3p) - p
= 11p - p
= 10p.
4) 6b - 3b + 5b
= (6b +5b) - 3b
= 11b -3b
= 8b.
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Step-by-step explanation:
[tex]7w + 2w - 6w \\ 9w - 6w \\ = 3w[/tex]
[tex]9x - 3x + 2x \\ 6x + 2x \\ = 8x[/tex]
[tex]8p + 3p - p \\ 11p - p \\ = 10p[/tex]
[tex]6b - 3b + 5b \\ 3b + 5b \\ = 8b[/tex]
a random variable is normally distributed with a mean of 25 and a standard deviation of 5. if an observation is randomly selected from the distribution, what value will 15% of the observations be below?
the 2 values X(19.8,30.2) is value will 15% of the observations be below .
by hypothesis .
What is hypothesis ?
A hypothesis is an assertion, a notion put up for the purpose of debating and then examined to discover if it might be true. Prior to conducting any relevant research, other than a brief background review, the hypothesis is developed using the scientific method.Here, Mean(\mu) and Standard Deviation (\sigma)= 5. You need to find the 2 values of which the smallest has 15% of the values below it i.e (Z<x)= 0.15 and the largest has 15% of the values above it i.e(Z>y)= 0.15.
Now we need to refer to the Z tables and see which value of x corresponds to 0.15, and we see that -1.04 is = 0.149 \sim 0.15
Now we know that the Z value is given by Z = X - μ/σ
Substituting we get
-1.04= (X-25)/5
therefore -5.2= X-25 or X= 19.8
Now let us get the value of X for (Z>y)=0.15`. Since Z tables give values for Z<a only, hence we can write that
Z>y=0.15 is the same as Z<y= 1-0.15= 0.85. We now check the Z tables and see which value of Z corresponds to 0.85, and we get 0.850 = +1.04
Again, substituting Z in the equation Z = X - μ/σ
we get
+1.04= (X-25)/5
Therefore 5.2= X-25, therefore X= 30.2
From the 2 values X(19.8,30.2)
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Let's find 1/10 + 1/2
First write the addition so the fractions have denominator 10. Then add
Answer:
3/5
Step-by-step explanation:
Given problem,
→ (1/10) + (1/2)
Let's solve the problem,
→ (1/10) + (1/2)
→ (1/10) + (5/10)
→ 6/10
→ 3/5 {simplest form}
Thus, answer is 3/5.
in how many ways can you put 8 distinguishable balls into 3 distinguishable boxes such that each box has at least one ball?
We can put 8 distinguishable balls into 3 distinguishable boxes such that each box has at least one ball in 21 ways.
Given, that there are 3 boxes and we have to put 8 balls in them such that no box is empty.
Let, a + b + c = 8, where a , b , c represent three different boxes.
The equation be reduced by allotting 1 ball to each box so that no box remains empty.
Hence, a + b + c = 5
Now, using the formula of "no. of ways in which 'n' objects can be grouped into 'r' groups" i.e. C(n+r-1 , r-1)
So, the required number of ways = C(5+3-1 , 3-1) = C(7 , 2)
Calculating, C(7 , 2) = (7×6)/2 = 21
Hence, we can put 8 distinguishable balls into 3 distinguishable boxes such that each box has at least one ball in 21 ways.
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Marie has $180 in a savings account in week 1. She plans to deposit $12 each following week. Assuming that she does not withdraw any money from her account, what will her balance be in week 20?
The balance in Marie saving account in week 20 will be $408 .
In the question ,
it is given that
the amount in Marie's saving account in week 1 is $180 .
amount of money deposited every week is = $12 .
to find the balance in week 20 means , she deposited money for 19 weeks .
the amount deposited in 19 weeks = 19 × 12 = $228
the equation to represent the balance after w weeks = 180 + 12*w
putting w = 19 in the equation , we get
the balance in saving account in week 20 = 180 + 12*19
the balance in week 20 = 180 + 228
= $408
Therefore , The balance in Marie saving account in week 20 will be $408 .
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Can somebody help me on this please
Since it is labeled that this triangle has two equal sides, it is isosceles. Isosceles triangles' acute angles are always congruent, so we can infer that there are two angles with a measurement of 29 degrees. Knowing that all of the angles in a triangle add up to 180 degrees, we can set up this equation:
2*29 + 11x - 65 = 180
58 + 11x - 65 = 180
-7 + 11x = 180
11x = 187
x = 17
Knowing that "x = 17" we can find the measurement of the obtuse angle:
11*17 - 65
= 187 - 65
= 122
Solve the system of equations using substitution.
3x + 2y = 7
x = 3y + 6
The solution of the system of equation by substitution is x = 3 and y = -1.
How to solve system of equation by substitution?System of equation can be solved using different techniques such as substitution method, elimination method and graphical method.
Let's solve the system of equation by substitution method
Therefore,
3x + 2y = 7
x = 3y + 6
Substitute equation(ii) in equation(i)
3(3y + 6) + 2y = 7
9y + 18 + 2y = 7
9y + 2y + 18 = 7
11y = 7 - 18
11y = -11
y = -11 / 11
y = -1
Hence, let's find x
x = 3(-1) + 6
x = -3 + 6
x = 3
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At a real estate agency, an agent sold a house for $307,000. The commission rate is 5.5% for the real estate agency and the commission rate for the agent is 25% of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?
The commission that thereal estate agency gets is $16885.
The commission that the agent gets is $76750
How to calculate the commission?The selling price for a house = $ 307,000
The commission rate for real estate agency = 5.5 %
The commission rate for the agent = 25 %
So, the commission which real estate agency gets:
= 5.5 % of $307,000
= 0.055 × $ 307,000
= $16885
The commission which agent get:
= 25% of $ 382,000
= 0.25 × $ 307,000
= $76750
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Can anyone write the equation this graph?
The equation of the graph given in the diagram which represents an absolute value function is: y = |x - 3| + 5.
What is the Equation of the Graph of an Absolute Value Function?The equation, in vertex form, of a absolute value function is expressed as y = a|x – h| + k, where:
(h, k) = vertex of the graph a = this value determines if the graph opens up or opens down.h = horizontal translation factork = vertical translation factorFrom the graph, we know that:
Vertex (h, k) = (3, 5)
Substitute h = 3 and k = 5 into the equation, y = a|x – h| + k:
y = a|x - 3| + 5
A point on the graph is (5, 7). To find the value of a, substitute x = 5 and y = 7 into the equation y = a|x - 3| + 5:
7 = a|5 - 3| + 5
7 = 2a + 5
7 - 5 = 2a + 5 - 5 [subtraction property of equality]
2 = 2a
Divide both sides by 2
2/2 = 2a/2 [division property of equality]
Substitute a = 1 into y = a|x - 3| + 5:
y = |x - 3| + 5 [equation of the absolute value function]
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A plumber has a 36-inch pipe that he has to cut into two
pieces so that one piece is 8 in. longer than the other. Find
the length of each piece.
A plumber has a 36-inch pipe that he needs to cut into two pieces, one 8 inches longer than the other. Each piece's length is x = 14, while the other piece's length is 22.
What is meant by length?The measurement or extent of something from end to end is defined as length. In other words, it is the larger of the two or the highest of three geometrical shapes or objects' dimensions. A rectangle, for example, has length and breadth dimensions.Centimeters, meters, kilometers, inches, feet, yards, and other standard units of length measurement are some examples.A segment's length or the dimensions of a room are examples of length measurements. Distance is the distance between two objects, such as two cities or two points. There will never be a negative value for length or distance.Therefore,
let x = the first piece and x+14 is the second.
2x + 8 = 36
2x = 28
x = 14, the other piece is 22
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he types at a rate of 30 words per minute is this stament a function or not a function
Lol help quick pleaseeeeeeeeee
The answer to be entered in the boxes for the area model is 17, 0 and 17
How to find the division problem the area model represents?
An area model is a rectangular diagram or model used for solving multiplication and division problems, in which the quotient and divisor define the length and width of the rectangle
Given:
....60.....1.............
36|2160 | 36 | 17
2160 ÷ 36 = 60 R 0
36 ÷ 36 = 1 R 0
17 ÷ 36 = 0 R 17
Note: (0 x 36) + 17 = 17
Therefore, the answer to be entered in the boxes is 17, 0 and 17 respectively
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Find an equation, in slope-intercept form, that passes through point (-2, 2) with slope -2.
[A] y = -2x-2 [B] y = 2x-2
[C] y = 2x-4 [D] y = -2x-4
The equation of a line on a point (-2,2) is y = -2x-2. That option A is correct.
Here we have to find the equation of a line.
The given data:
Point = ( -2, 2)
Slope(m) = -2
Equation of a line:
y = mx + c
Now putting the values as
y = 2
x = -2
m = -2
We will get the y-intercept.
So we have:
2 = -2 × -2 + c
c = 2 - 4
= -2
So, y = -2x -2
Therefore we get the equation of line as y = -2x -2.
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