You originally draw a design for an art contest on a 4 in. x 5 in. card. The second phase of the contest requires the drawing to be transferred to an 8.5 in x 11 in. standard sheet of paper and utilize as much of the space on the paper as possible. You determine that the largest size one of the dimensions of your drawing can be is 10.5 in. What is the length of the other dimension if the two drawings are similar? Type your exact answer in the blank without the units, and round to the nearest tenths.
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Answer:
x = 8.4
Explanation:
Related Questions
Which is the solution to the equation 2.6a + 18.4 = 28.8 round the nearest tenth if necessary. 1.4, 4, 18.2, 27
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Answer:
Your answer is B=4
Step-by-step explanation:
hope it helps once again
A guidance counselor has 2 3/6 hours to meet with students. If she meets with each student for 1/6 hour how many students can she see
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let's convert the mixed fraction to "improper", and divide then.
[tex]\bf \stackrel{mixed}{2\frac{3}{6}}\implies \cfrac{2\cdot 6+3}{6}\implies \stackrel{improper}{\cfrac{15}{6}}\\\\ -------------------------------\\\\ \cfrac{\quad \frac{15}{6}\quad }{\frac{1}{6}}\implies \cfrac{15}{6}\cdot \cfrac{6}{1}\implies \cfrac{15}{1}\implies \stackrel{students}{15}[/tex]
15/6 / 1/6 = 15 * 6 / 6 = 15 answer
Suppose 5 days before the day after tomorrow is Monday. What day of the week was yesterday?
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Let c be the curve of intersection of the parabolic cylinder x2 = 2y, and the surface 3z = xy. find the exact length of c from the origin to the point 2, 2, 4 3 . step 1
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The length of [tex]C[/tex] is given by the line integral
[tex]\displaystyle\int_C\mathrm dS=\int_{t=0}^{t=2}\|\mathbf r'(t)\|\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2\left\|\left\langle1,t,\dfrac{t^2}2\right\rangle\right\|\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2\sqrt{1+t^2+\dfrac{t^4}4}\,\mathrm dt[/tex]
[tex]=\displaystyle\frac12\int_0^2\sqrt{4+4t^2+t^4}\,\mathrm dt[/tex]
[tex]=\displaystyle\frac12\int_0^2\sqrt{(t^2+2)^2}\,\mathrm dt[/tex]
[tex]=\displaystyle\frac12\int_0^2(t^2+2)\,\mathrm dt[/tex]
[tex]=\dfrac12\left(\dfrac{t^3}3+2t\right)\bigg|_{t=0}^{t=2}[/tex]
[tex]=\dfrac12\left(\dfrac83+4\right)[/tex]
[tex]=\dfrac{10}3[/tex]
The heights of a group of 5 people are measured. Four of the people have the following heights: 64 inches, 67 inches, 72 inches, and 65 inches. If the average height of the group is 66 inches, how tall is the fifth person?
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Write an explicit formula for the sequence (3,7,11,15,19,23,27,...)
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The explicit formula for the given sequence is a_n = 3 + 4(n-1).
Explanation:The given sequence is (3, 7, 11, 15, 19, 23, 27, ...).
To find the explicit formula for this sequence, we can observe that each term is obtained by adding 4 to the previous term. So, the formula can be written as:
an = 3 + 4(n-1)
where n represents the position of the term in the sequence.
On a town map, each unit of the coordinate plane represents 1 mile. Three branches of a bank are located at A(−3, 1), B(4, 3), and C(2, −1). A bank employee drives from Branch A to Branch B and then drives halfway to Branch C before getting stuck in traffic. What is the minimum total distance the employee may have driven before getting stuck in traffic? Round to the nearest tenth of a mile if necessary.
Answers
(-3,1)...x1 = -3 and y1 = 1
(4,3)...x2 = 4 and y2 = 3
now we sub
d = sqrt ((4 - (-3)^2 + (3 - 1)^2)
d = sqrt ((4 + 3)^2 + (2^2))
d = sqrt (7^2 + 2^2)
d = sqrt (49 + 4)
d = sqrt 53
d = 7.28 ...so its 7.28 miles from A to B
d = sqrt ((x2 - x1)^2 + (y2 - y1)^2)
(4,3)...x1 = 4 and y1 = 3
(2,-1)...x2 = 2 and y2 = -1
now we sub
d = sqrt ((2 - 4)^2 + (-1 - 3)^2)
d = sqrt (-2^2) + (-4^2)
d = sqrt (4 + 16)
d = sqrt 20
d = 4.47....but the employee only drives halfway....so this trip was 4.47/2 = 2.235
so the minimum total distance is : 7.28 + 2.235 = 9.515 rounds to 9.5 miles
Assume that the distance from Earth to the moon is exactly 238,855 miles and that it took astronauts 75 hours to reach the moon in 1969. How far did the astronauts travel each hour, on average, during their trip to the moon? 3,004.73 miles mc026-1.jpg miles 3,317.4305 miles mc026-2.jpg miles
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On average during their trip, their speed was 3184.8 miles/hr.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
We know Distance = Speed×Time.
∴ Speed = Distance/Time.
Given, The distance from Earth to the moon is exactly 238,855 miles and it took astronauts 75 hours.
So, the average speed is (238855/75) miles/hr.
= 3184.8 miles/hr.
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which is the smallest number? 3/4,1/5,10/23,2/31
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H O P E T H I S H E L P S!
The radius r of a circle is increasing at a rate of 8 centimeters per minute. find the rate of change of the area when r = 39 centimeters
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dA/dt = ?
but A= πr²
so dA/dr =2πr
but recall
dA/dt = dA/dr • dr/dt
dA/dt = 2πr • 8cmM-¹
dA/dt = 2×π×39 ×8 = 624cm²M-1
The rate of change of the area of the circle when the radius is 39 centimeters is 1976π cm²/min. This uses the concept of related rates in calculus and the area formula A = πr².
Explanation:The problem deals with the concept of related rates in calculus. In this problem, we're looking at how the rate of change of the radius of a circle impacts the rate of change of the area of the circle. The formula for the area of a circle is A = πr².
Differentiating both sides with respect to time(t) gives dA/dt = 2πr(dr/dt). In this case, dr/dt (the rate of change of the radius) is given as 8 cm/min. To find dA/dt (the rate of change of the area) when r = 39 cm, we substitute these values into the differentiated equation: dA/dt = 2π(39cm)(8 cm/min) = 1976π cm²/min
So, the rate of change of the area when r = 39 centimeters is 1976π cm²/min. As the radius increases, the area of the circle increases at a rate directly proportional to the radius.
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A scanner scanned 56 photos in 7 minutes. If it scans photos at a constant rate, it can scan _____ photos in 27 minutes. Numerical Answers Expected! PLEASE HELP
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56 photos x
-------------- = ------------
7 min 27 min
x is found as follows: (56 photos)(27 minutes) = (7 min)(x)
Divide both sides by (7 min) to get the answer, x, which is measured in "photos."
Approximate, to the nearest 0.1°, all angles θ in the interval [0°, 360°) that satisfy the equation. (Enter your answers as a comma-separated list.)
(a) sin θ = 0.9263 θ = °
(b) cos θ = −0.6909 θ = °
(c) tan θ = −1.5416 θ = °
(d) cot θ = 1.3952 θ = °
(e) sec θ = 1.4293 θ = °
(f) csc θ = −2.3174
Answers
a) [tex]\[ \theta = 67.9^\circ, 112.1^\circ \][/tex], b) [tex]\[ \theta = 133.7^\circ, 226.3^\circ \][/tex], c) [tex]\[ \theta = 122.7^\circ, 302.7^\circ \][/tex], d) [tex]\[ \theta = 35.8^\circ, 215.8^\circ \][/tex], e) [tex]\[ \theta = 45.5^\circ, 314.5^\circ \][/tex] and f) [tex]\[ \theta = 154.4^\circ, 334.4^\circ[/tex].
Let's solve each part:
(a) [tex]\(\sin \theta = 0.9263\)[/tex]
1. Find the reference angle using [tex]\(\theta = \sin^{-1}(0.9263)\)[/tex]:
[tex]\[ \theta \approx 67.9^\circ \][/tex]
2. Since [tex]\(\sin \theta\)[/tex] is positive, the angles are in the first and second quadrants:
[tex]\[ \theta_1 \approx 67.9^\circ \][/tex]
[tex]\[ \theta_2 \approx 180^\circ - 67.9^\circ = 112.1^\circ \][/tex]
So, the solutions are:
[tex]\[ \theta = 67.9^\circ, 112.1^\circ \][/tex]
(b) [tex]\(\cos \theta = -0.6909\)[/tex]
1. Find the reference angle using [tex]\(\theta = \cos^{-1}(-0.6909)\)[/tex]:
[tex]\[ \theta \approx 133.7^\circ \][/tex]
2. Since [tex]\(\cos \theta\)[/tex] is negative, the angles are in the second and third quadrants:
[tex]\[ \theta_1 \approx 133.7^\circ \][/tex]
[tex]\[ \theta_2 \approx 360^\circ - 133.7^\circ = 226.3^\circ \][/tex]
So, the solutions are:
[tex]\[ \theta = 133.7^\circ, 226.3^\circ \][/tex]
(c) [tex]\(\tan \theta = -1.5416\)[/tex]
1. Find the reference angle using [tex]\(\theta = \tan^{-1}(-1.5416)\)[/tex]:
[tex]\[ \theta \approx -57.3^\circ \][/tex]
2. Adjust the reference angle to fall within the interval [tex]\([0^\circ, 360^\circ)\)[/tex]:
[tex]\[ \theta_1 = 360^\circ - 57.3^\circ = 302.7^\circ \][/tex]
3. Since [tex]\(\tan \theta\)[/tex] is negative, the angles are in the second and fourth quadrants:
[tex]\[ \theta_2 = 180^\circ + (-57.3^\circ) = 122.7^\circ \][/tex]
So, the solutions are:
[tex]\[ \theta = 122.7^\circ, 302.7^\circ \][/tex]
(d) [tex]\(\cot \theta = 1.3952\)[/tex]
1. Find the reference angle using [tex]\(\theta = \cot^{-1}(1.3952)\)[/tex]:
[tex]\[ \theta \approx 35.8^\circ \][/tex]
2. Since [tex]\(\cot \theta\)[/tex] is positive, the angles are in the first and third quadrants:
[tex]\[ \theta_1 \approx 35.8^\circ \][/tex]
[tex]\[ \theta_2 \approx 180^\circ + 35.8^\circ = 215.8^\circ \][/tex]
So, the solutions are:
[tex]\[ \theta = 35.8^\circ, 215.8^\circ \][/tex]
(e) [tex]\(\sec \theta = 1.4293\)[/tex]
1. Convert to [tex]\(\cos \theta\)[/tex]:
[tex]\[ \cos \theta = \frac{1}{1.4293} \approx 0.6996 \][/tex]
2. Find the reference angle using [tex]\(\theta = \cos^{-1}(0.6996)\)[/tex]:
[tex]\[ \theta \approx 45.5^\circ \][/tex]
3. Since [tex]\(\cos \theta\)[/tex] is positive, the angles are in the first and fourth quadrants:
[tex]\[ \theta_1 \approx 45.5^\circ \][/tex]
[tex]\[ \theta_2 \approx 360^\circ - 45.5^\circ = 314.5^\circ \][/tex]
So, the solutions are:
[tex]\[ \theta = 45.5^\circ, 314.5^\circ \][/tex]
(f) [tex]\(\csc \theta = -2.3174\)[/tex]
1. Convert to [tex]\(\sin \theta\)[/tex]:
[tex]\[ \sin \theta = \frac{1}{-2.3174} \approx -0.4316 \][/tex]
2. Find the reference angle using [tex]\(\theta = \sin^{-1}(-0.4316)\)[/tex]:
[tex]\[ \theta \approx -25.6^\circ \][/tex]
3. Adjust the reference angle to fall within the interval [tex]\([0^\circ, 360^\circ)\)[/tex]:
[tex]\[ \theta_1 = 360^\circ - 25.6^\circ = 334.4^\circ \][/tex]
4. Since [tex]\(\sin \theta\)[/tex] is negative, the angles are in the third and fourth quadrants:
[tex]\[ \theta_2 = 180^\circ + (-25.6^\circ) = 154.4^\circ \][/tex]
So, the solutions are:
[tex]\[ \theta = 154.4^\circ, 334.4^\circ[/tex]
The complete question is:
Approximate, to the nearest 0.1°, all angles θ in the interval [0°, 360°) that satisfy the equation. (Enter your answers as a comma-separated list.)
(a) sin θ = 0.9263
θ = °
(b) cos θ = −0.6909
θ = °
(c) tan θ = −1.5416
θ = °
(d) cot θ = 1.3952
θ = °
(e) sec θ = 1.4293
θ = °
(f) csc θ = −2.3174
θ = °
If the circumference of a circle is 201 centimeters what is the radius of the circle (to the nearest whole number)? Use 3.14 for pi
A) 32 centimeters
B) 128 centimeters
C) none
D) 16 centimeters
E) 64 centimeters
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Final answer:
The radius of a circle with a circumference of 201 centimeters is approximately 32 centimeters, found by dividing the circumference by 2 times pi (π), using 3.14 as the value of pi. The correct answer is A) 32 centimeters.
Explanation:
The question asks us to find the radius of a circle when its circumference is given to be 201 centimeters. We use the circumference formula of a circle, which is C = 2πr, where C stands for circumference, π (pi) is a constant approximately equal to 3.14, and r represents the radius of the circle.
To find the radius, we rearrange this formula to solve for r:
Divide both sides of the equation by 2π to isolate r.
Plug in the given circumference value, C = 201 cm, and the approximate value of pi, π = 3.14, into the rearranged formula.
So the calculation would be r = C / (2π) = 201 / (2 * 3.14) = 201 / 6.28. When we compute this, we get r ≈ 32 centimeters to the nearest whole number.
Therefore, the correct answer is A) 32 centimeters.
Kevin and randy Muise have a jar containing 41 coins all of which are either quarters or nickels . The total value of coins in the jar is 7.45 how many of each type of coin do they have
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To find the number of quarters and nickels, we can set up a system of equations using the total number of coins and the total value of the coins. Solving this system of equations, we find that Kevin and Randy have 27 quarters and 14 nickels.
Explanation:To solve this problem, we can set up a system of equations. Let's use the variables q (number of quarters) and n (number of nickels). We know that there are a total of 41 coins, so we can write the equation q + n = 41. We also know that the total value of the coins is $7.45, so we can write the equation 0.25q + 0.05n = 7.45.
Now we can solve this system of equations using substitution:
Isolate one variable in one of the equations. Let's isolate q in the first equation: q = 41 - n.Substitute this expression for q in the second equation: 0.25(41 - n) + 0.05n = 7.45.Simplify and solve for n: 10.25 - 0.25n + 0.05n = 7.45. Simplifying further, we get 0.20n = 2.80. Dividing by 0.20, we find that n = 14.Substitute this value of n back into the first equation to find q: q = 41 - 14 = 27.Therefore, Kevin and Randy have 27 quarters and 14 nickels in their jar.
how does a model help me multiply decimals
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please help me with this problem
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71.4725 * .06 = 4.28835
71.4725 + 4.28835 = $75.76
Answer = $75.76
-3 1/2 * 0.5 help please
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Result is -7/4 (answer)
Let 0.5 = 1/2.
(-7/2)(1/2) = -7/4
Done.
which of the following shows a strategy to use to find 4x275 (4x300)+(4x25)
(4x300)-(4x25) (4x275)-100 (4x200)+75
Answers
The correct strategy is (4x275) - 100. So option (3) is correct.
To find 4 multiplied by 275 using the given strategies, let's go through each one:
1. (4x300) + (4x25):
First, calculate (4x300) = 1200. Then, calculate (4x25) = 100. Finally, add these results together: 1200 + 100 = 1300.
2. (4x300) - (4x25):
Calculate (4x300) = 1200. Then, calculate (4x25) = 100. Now, subtract the second result from the first: 1200 - 100 = 1100.
3. (4x275) - 100:
Simply multiply 4 by 275 to get 1100. Then, subtract 100: 1100 - 100 = 1000.
4. (4x200) + 75:
Calculate (4x200) = 800. Then, add 75: 800 + 75 = 875.
The correct strategy is the third one: (4x275) - 100.
Detailed Calculation:
1. [tex]\(4 \times 275 = 1100\)[/tex]
2. [tex]\(1100 - 100 = 1000\)[/tex]
So, using the strategy of (4x275) - 100, the result is 1000.
There are 10 apples in the fridge and 2 of them are bad. if you grab 3 apples, what is the expected number of bad apples
Answers
The expected number of bad apples is [tex]\( \frac{2}{10} \times 3 = 0.6 \) bad apples.[/tex]
The expected number of bad apples when grabbing 3 apples from a pool of 10, of which 2 are bad, can be calculated using probability.
To calculate this, follow these steps:
1. Calculate the probability of picking a bad apple:
The probability of picking a bad apple is the ratio of the number of bad apples to the total number of apples. In this case, it's [tex]\( \frac{2}{10} = 0.2 \) or 20%.[/tex]
2. Multiply the probability by the number of apples picked:
Multiply the probability of picking a bad apple by the number of apples you're picking.
[tex]\( 0.2 \times 3 = 0.6 \)[/tex]
When you pick 3 apples randomly from a pool of 10, you're essentially conducting a sampling experiment. The probability of picking a bad apple on any given pick is[tex]\( \frac{2}{10} \),[/tex] which simplifies to 0.2 or 20%.
Since you're picking 3 apples, you multiply the probability of picking a bad apple by 3 to find the expected number of bad apples. This is because in expectation, you would expect that proportion of bad apples in your sample. So, [tex]\( 0.2 \times 3 = 0.6 \)[/tex], which means you would expect to pick approximately 0.6 bad apples when picking 3 from the pool of 10, assuming the picking is random.
So, the final answer is that you would expect about 0.6 bad apples when picking 3 apples from a pool of 10, of which 2 are bad.
complete question
There are 10 apples in the fridge and 2 of them are bad. if you grab 3 apples, what is the expected number of bad apples
And 1. if a person bought 1 share of google stock within the last year, what is the probability that the stock on that day closed at less than the mean for that year? hint: you do not want to calculate the mean to answer this one. the probability would be the same for any normal distribution.
Answers
The graph would be bell shaped. So the odds are 50/50
The probability that the stock closed at less than the mean for that year is approximately 0.5, assuming a normal distribution.
1. In a normal distribution, the mean divides the distribution into two equal halves, with 50% of the data falling below the mean and 50% above it.
2. Therefore, the probability that a randomly chosen data point (in this case, the closing price of stock) is below the mean is 0.5 or 50%.
Now, let's dive into the step-by-step calculation to illustrate this:
1. Identify the Mean and Standard Deviation: While you mentioned not to calculate the mean, it's important to understand that for a normal distribution, the mean is at the center and separates the distribution into equal probabilities on either side. However, we do need to know the standard deviation, which measures the spread of data points around the mean. Let's assume the mean closing price for stock over the past year is $X, and the standard deviation is $Y.
2. Use the Standard Normal Distribution: Since we're dealing with a normal distribution, we can use the standard normal distribution to find probabilities. This distribution has a mean of 0 and a standard deviation of 1.
3. Standardize the Data: To work with the standard normal distribution, we need to standardize the data point we're interested in. Let's denote the closing price of stock on the chosen day as $Z. We standardize this value using the formula:
[tex]\[ Z = \frac{{Z - X}}{{Y}} \][/tex]
Here, ( Z ) is the standardized value.
4. Find the Probability: Once we have the standardized value ( Z ), we can look it up in a standard normal distribution table or use software/tools to find the probability that a randomly chosen value from a standard normal distribution is less than ( Z ). This probability will be the same as the probability that the stock closed at less than the mean for that year.
5. Conclusion: Based on the properties of a normal distribution, the probability that a randomly chosen data point (stock closing price) is below the mean is always 0.5 or 50%. This holds true regardless of the specific mean or standard deviation values for stock.
complete question
And 1. if a person bought 1 share of stock within the last year, what is the probability that the stock on that day closed at less than the mean for that year? hint: you do not want to calculate the mean to answer this one. the probability would be the same for any normal distribution.
Devin brought his snails collection to school. He has 10 snails. How could he put them into 2 tanks so two classes could see them?
Write equation for all the possible ways.
One of the ways is given.
Explain how you know you have found all the ways.
Answers
Standard 6 sided die is weighted so that the probabilities of rolling 2,3,4,5 or 6 are equal and the probability of rolling 1 is three times the probability of rolling a 2. if the die is thrown twice, what is the probability that the sum of the numbers thrown will be 4
Answers
There are 6 sides of the die, let us say that side 1 is S1, side 2 is S2 and so on.
Assigning a value of 3 to S1, so the probabilities are:
Probability
S1 = 3 3/8
S2 = 1 1/8
S3 = 1 1/8
S4 = 1 1/8
S5 = 1 1/8
S6 = 1 1/8
total = 8
The combinations that the sum of the two rolls will be 4 are:
S1 and S3
S3 and S1
S2 and S2
So the total probability is:
P = (3/8) * (1/8) + (1/8) * (3/8) + (1/8) * (1/8)
P = 0.1094 = 10.94%
So there is about 0.1094 or 10.94% probability that the sum will be 4.
Answer: [tex]\frac{1}{4}[/tex]
Step-by-step explanation: If this is from a quiz from Buzz (Acceleration Education) Then this is the answer.
Hope This Helps You!
jamal has a box with some toy cars in it. he puts 3 more toy cars into the box now there are 22 toy cars in the box how many toy cars were in the box before
Answers
Find the quotient 4/6÷4/12
Answers
First- 4/6 divided by 4/12
Next- Change the division sign to multiplecation 4/6 time 4/12
Then- Flip the second number 4/6 times 12/4
Now multiply
48/24 this simplifies down to 2
Which angle has a measure equal to the sum of the m∠SQR and the m∠QRS?
Answers
Proof:
Refer to the diagram shown below.
Let
x = m∠SQR
y = m∠QRS
z = m∠RSQ
w = the external angle (supplement) of m∠RSQ
Because the sum of angles in a triangle is 180°, therefore
x + y + z = 180°
x + y = 180° - z
That is,
m∠SQR + m∠QRS = 180° - z (1)
Because the sum of angles on one side of straight line is 180°, therefore
w + z = 180°
or
w = 180° - m∠RSQ (2)
Equate equations (1) and (2) to obtain
m∠SQR + m∠QRS = completes∠RSQ
This completes the proof.
The sum of the square of two consecutive whole number is 25. Find the numbers
Answers
The sum of the squares of two consecutive whole numbers is 25. Find the numbers. Let the first be represented by x and the second by x+1.
Then x^2+(x+1)^2=25. Expanding, x^2+x^2+2x+1=25.
Rewriting this as a quadratic equation in standard form,
2x^2+2x+1=25, or 2x^2+2x-24=0. Simplifying, x^2+x-12=0.
Factoring, (x-3)(x+4)=0. Solving for x: x-3=0, so x=3; x+4=0, so x=-4.
Choose the positive x value: x=3. Then the next consecutive number is 2+1=3+1=4.
Check: Does 3^2 + 4^2 = 5^2 = 25? Yes.
The numbers are 3 and 4.
a construction company charges $500 for the plans plus $600 per square foot to build a new home. Write an equation that shows this relationship
Answers
x = square feet
total cost = 500 + 600x
14.4% of what number is 10.44
Answers
Lucy deposits $7000 into an account that pays simple interest at a rate of 3% per year. How much interest will she be paid in the first 6 years?
Answers
Lucy will be paid $1260 in interest in the first 6 years.
Explanation:To calculate the interest Lucy will be paid in the first 6 years, we will use the simple interest formula:
Interest = Principal x Rate x Time
Given:
Principal (P) = $7000Rate (R) = 3% per yearTime (T) = 6 yearsPlugging in the values, we get:
Interest = $7000 x 0.03 x 6 = $1260
Therefore, Lucy will be paid $1260 in interest over the first 6 years.
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will award 40 points if you answer correctly
Bottles of water sell for 1.50$ each.
Graph the relationship between the number of bottles sold and the total cost.
Answers
see picture for the graph
equation: y = 1.50x
Answer:
Step-by-step explanation:
took the test (k12) and its halfway to 50 if you see in the picture