Answers
This is a 45-45-90 triangle; 45-45-90 triangles' sides are in the ratio 1:1:[tex] \sqrt{2} [/tex].
Since the legs measure 7 units, the hypotenuse (x) measures [tex]7 \sqrt{2} [/tex].
Answer:
[tex]7 \sqrt{2} [/tex]
Related Questions
Nicholas buys 3/8 pound of cheese. He puts the same amount of cheese on 3 sandwiches. How much cheese does Nicholas put on each sandwich?
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[tex]\bf \cfrac{3}{8}\div 3\implies \cfrac{3}{8}\div \cfrac{3}{1}\implies \cfrac{\underline{3}}{8}\cdot \cfrac{1}{\underline{3}}\implies \cfrac{1}{8}[/tex]
how many times does 5 go in to 47
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9*5=45
47/5= 9 2/5
Find the common ratio of the sequence
-125,-25,-5,-1.....
1/5
5
-100
100
Answers
Answer:
Step-by-step explanation:
common ratio of a Geometric series can be found by dividing the second term by first term of the series .
we are given that first term a1= -125 and second term a2 =-25
so the common ratio must be
[tex]r=\frac{a2}{a1}[/tex]
[tex]r=\frac{-25}{-125}[/tex]
[tex]r= \frac{1}{5}[/tex]
Hence the common ratio is 1/5.
The contour plot of is shown below. determine if the given quantity in each part is positive, negative, or zero.
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Jack and Jill are 20m apart. Jack sees the top of the building at 30 degrees and Jill sees the top of the building at 40 degrees. What is the height of the building
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The height of the building seen by both Jack and Jill is 37m to the nearest whole metre.
Let the distance of Jill from the base of the building be represented with x while the height of the building be y so that by observation we get two right triangles with same opposite sides to the angles formed by Jack and Jill. We can solve for x and y using tangent of the angles as follows:
tan 40 = y/x {opposite/adjacent}
y = xtan40 {cross multiplication}
tan 30 = y/(20 + x)
y = tan30(20 + x)
Thus;
xtan40 = tan30(20 + x)
xtan40 = 20tan30 + xtan30
xtan40 - xtan30 = 20tan30 {collect like terms}
x(tan40 - tan30) = 20tan30
x = 20tan30/(tan40 - tan30)
x = 44.1230m
Putting the 44.1230m for x in y = xtan40 we have;
y = 44.1230m × tan40
y = 37.0236m.
Therefore, the height of the building approximately to the nearest whole metre is 37.
Given two vectors a⃗ = 4.60 i^+ 7.20 j^ and b⃗ = 5.10 i^− 2.70 j^ , find the scalar product of the two vectors a⃗ and b⃗ .
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b=<5.10,2.70>
The scalar product, or the inner product, or the dot-product, is by summing the products of the respective directions,
a.b=4.6*5.1+7.2*2.7
=23.46+19.44
=42.9
In this exercise we have to use the knowledge of vectors to find the dot product between them, in this way we can say that:
[tex]|a|*|b|=42.9[/tex]
Knowing that it was stated by the text that the vectors have the value of :
[tex]a=<4.60,7.20>\\ b=<5.10,2.70> [/tex]
The scalar product, or the inner product, or the dot-product, is by summing the products of the respective directions, will be:
[tex]|a|*|b|=4.6*5.1+7.2*2.7\\ =23.46+19.44\\ =42.9 [/tex]
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Let be the linear transformation that first reflects points through the -axis and then then reflects points through the line . find the standard matrix for
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In the case above, the standard matrix A for T:
T= [0 1]
[-1 0]
What is linear transformation about?A linear transformation is known to be a kind of a function that exist from one vector point to another and it is one that often respects the linear) structure of all of vector space.
Note that in the linear transformation;
T: R² R²
T= (x, y), (-x, y)
Since:
(x,y) - (x,-y) - (y,-x)
A= [-1 0]
[0 1]
A= [-1 0] = A= [-x]
[0 1] [y]
Then [tex]T_{b}[/tex] is the reflection of (x- y); Since;
B = [0 1]
[1 0]
Then [tex]T_{B} (T_{a}(x) )[/tex] = [0 1] = A= [-x]
[0 1] [y]
= [-x]
[y]
Then: T: = [0 1] [x]
[0 1] [y]
Therefore, In the case above, the standard matrix A for T:
T= [0 1]
[-1 0]
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Huey works 175 hours each month and earns $14.25 per hour after taxes. His monthly budget is shown. How much money is left over in his budget for unplanned expenses?
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y = 14.25x
Where,
x: number of hours
y: total salary
For x = 175 we have:
y = 14.25 * (175)
y = 2493.75
The amount of money for unexpected expenses is:
unplanned expenses = 2493.75 - 1250 - 200 - 350 - 400 - 225 - 300
unplanned expenses = -231.25 <0
We note that there is no money left for unexpected expenses
Answer:
there is nothing left over
Answer:
Nothing will be left over.
Step-by-step explanation:
You need to multiply the 175 by 14.25 to get his total income each month.
Then you add all of the expenses of 1250, 200, 350, 400, 225, 300.
Huey earns 2,493.75 every month, and his expenses are 2,725.
2,493.75 - 2725 = a negative rational number
I ain't gonna do it, because he ain't got no money in his wallet.
(I don't talk like that above, I'm just pretending to be an official Texan.)
If he has negative money left over, I don't think he would spend some more tbh, so the answer would be nothing would be left over.
Hope this helps someone in the future!
Identify all the real roots of 4x^4+31x^3-4x^2-89x+22=0
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4 x^4 + 31 x^3 - 4 x^2 - 89 x + 22 = 0
The left hand side factors into a product with three terms:
(x + 2) (4 x - 1) (x^2 + 6 x - 11) = 0
Split into three equations:
x + 2 = 0 or 4 x - 1 = 0 or x^2 + 6 x - 11 = 0
Subtract 2 from both sides:
x = -2 or 4 x - 1 = 0 or x^2 + 6 x - 11 = 0
Add 1 to both sides:
x = -2 or 4 x = 1 or x^2 + 6 x - 11 = 0
Divide both sides by 4:
x = -2 or x = 1/4 or x^2 + 6 x - 11 = 0
Add 11 to both sides:
x = -2 or x = 1/4 or x^2 + 6 x = 11
Add 9 to both sides:
x = -2 or x = 1/4 or x^2 + 6 x + 9 = 20
Write the left hand side as a square:
x = -2 or x = 1/4 or (x + 3)^2 = 20
Take the square root of both sides:
x = -2 or x = 1/4 or x + 3 = 2 sqrt(5) or x + 3 = -2 sqrt(5)
Subtract 3 from both sides:
x = -2 or x = 1/4 or x = 2 sqrt(5) - 3 or x + 3 = -2 sqrt(5)
Subtract 3 from both sides:
Answer: x = -2 or x = 1/4 or x = 2 sqrt(5) - 3 or x = -3 - 2 sqrt(5)
The real roots of a function are the rational and the irrational roots of the function
The real roots are: [tex]\mathbf{x = -2}[/tex], [tex]\mathbf{x = \frac 14}[/tex], [tex]\mathbf{x = -3 - 2\sqrt{5}}[/tex] and [tex]\mathbf{x = -3 + 2\sqrt{5}}[/tex]
The equation is given as:
[tex]\mathbf{ 4x^4+31x^3-4x^2-89x+22=0}[/tex]
Factorize
[tex]\mathbf{(x + 2) (4 x - 1) (x^2 + 6 x - 11) = 0}[/tex]
Split
[tex]\mathbf{x + 2 = 0\ or\ 4 x - 1 = 0 \ or\ x^2 + 6 x - 11 = 0}[/tex]
Solve for x
[tex]\mathbf{x = -2\ or\ x = \frac 14 \ or\ x^2 + 6 x - 11 = 0}[/tex]
Solve
[tex]\mathbf{x^2 + 6 x - 11 = 0}[/tex] using the following quadratic formula:
[tex]\mathbf{x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]
So, we have:
[tex]\mathbf{x = \frac{-6 \pm \sqrt{6^2 - 4 \times 1 \times -11}}{2 \times 1}}[/tex]
[tex]\mathbf{x = \frac{-6 \pm \sqrt{80}}{2}}[/tex]
[tex]\mathbf{x = \frac{-6 \pm 4\sqrt{5}}{2}}[/tex]
[tex]\mathbf{x = -3 \pm 2\sqrt{5}}[/tex]
Hence, the real roots are:
[tex]\mathbf{x = -2}[/tex], [tex]\mathbf{x = \frac 14}[/tex], [tex]\mathbf{x = -3 - 2\sqrt{5}}[/tex] and [tex]\mathbf{x = -3 + 2\sqrt{5}}[/tex]
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solving radical equations
check for extraneous solutions
[tex] \sqrt{2x + 30} = x + 3[/tex]
Answers
I don't see an extraneous value there, -7 checks out well if you plug it in the original equation, and so does 3.
The level of nitrogen oxides (nox) in the exhaust after 50,000 miles or fewer of driving of cars of a particular model varies normally with mean 0.03 g/mi and standard deviation 0.01 g/mi. a company has 64 cars of this model in its fleet. what is the level l such that the probability that the average nox level x for the fleet is greater than l is only 0.01? (hint: this requires a backward normal calculation. round your answer to three decimal places.)
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We can use the z-score formula with the known z-score corresponding to a probability of 0.01 to calculate the exhaust NOx emission level. This gives us approximately 0.001 g/mi.
Explanation:In this scenario, we're dealing with a normal distribution problem wherein we use the formula for z-score to answer it. The z-score formula is =(−)/(/√), where x is the data point, μ is the population mean, n is the size of the data set, and σ is the standard deviation.
In this case, we want to find x, or the NOx emission level, such that the probability of finding an automobile with a level greater than x is 0.01. So, we need to find the z-score that corresponds to a probability of 0.01 and then use it in our formula to solve for x.
Using standard z-score tables or an online z-score calculator, we find that a probability of 0.01 corresponds to a z-score of approximately -2.33 (p and z have opposite signs). We then substitute this z-score, along with the given mean μ=0.03 and standard deviation σ=0.01 into the z-score formula, solving for x. The value of n is 64 (number of vehicles in the fleet).
Inserting these values into the formula gives us = + z/√ =0.03 + (-2.33)*(0.01/√64), which simplifies to =0.03 - (2.33/80) = 0.03 - 0.029125= 0.000875 g/mi. Therefore, the NOx emission level, such that the probability of finding an automobile with a level greater than it, is 0.01 for this fleet is approximately 0.001 g/mi when rounded to three decimal places.
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To find the level l such that the probability that the average NOx level x for the fleet is greater than l is only 0.01, we can use the z-score formula and the properties of the normal distribution. The z-score formula allows us to convert a probability into a corresponding value on the distribution. Rearranging the z-score formula, we can find the value of l.
Explanation:To find the level l such that the probability that the average NOx level x for the fleet is greater than l is only 0.01, we can use the z-score formula and the properties of the normal distribution. The z-score formula is z = (x - µ) / (σ / √n), where x is the average NOx level, µ is the mean, σ is the standard deviation, and n is the sample size. We want to find the value of l such that the area to the right of l under the normal curve is 0.01.
First, we need to find the z-score corresponding to a right-tail probability of 0.01. This can be done using a z-table or a calculator. In this case, the z-score is approximately 2.326. Now we can use the z-score formula to find the value of l. Rearranging the formula, we have l = µ + (z * σ / √n). Substituting the given values, l = 0.03 + (2.326 * 0.01 / √64). Calculating this, we get l ≈ 0.031.
Therefore, the level l such that the probability that the average NOx level x for the fleet is greater than l is only 0.01 is approximately 0.031 g/mi.
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At 6 1/2¢ per pound of string beans, how much does 7 pounds cost?
Answers
6.50 cents lb of string beans............................1 lb
? cents..............................................................7 lb
(6.50*7)/1=45.50 cents for 7 lb of beans
A 500500-gallon tank initially contains 200200 gallons of brine containing 100100 pounds of dissolved salt. brine containing 11 pounds of salt per gallon flows into the tank at the rate of 44 gallons per minute, and the well-stirred mixture flows out of the tank at the rate of 11 gallon per minute. set up a differential equation for the amount of salt a(t)a(t) in the tank at time tt. how much salt is in the tank when it is full? (round your answer to the 2 decimal places).
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The rate at which salt flows in and out of the tank is given by the relation
[tex]\dfrac{\mathrm dA}{\mathrm dt}=\underbrace{\dfrac{11\text{ lb}}{1\text{ gal}}\times\dfrac{44\text{ gal}}{1\text{ min}}}_{\text{rate in}}-\underbrace{\dfrac{A(t)}{200+(44-11)t}\times\dfrac{11\text{ gal}}{1\text{ min}}}_{\text{rate out}}[/tex]
[tex]\implies A'(t)+\dfrac{11}{200+33t}A(t)=484[/tex]
Find the integrating factor:
[tex]\mu(t)=\exp\left(\displaystyle\int\frac{11}{200+33t}\,\mathrm dt\right)=(200+33t)^{1/3}[/tex]
Distribute [tex]\mu(t)[/tex] along both sides of the ODE:
[tex](200+33t)^{1/3}A'(t)+11(200+33t)^{-2/3}A(t)=484(200+33t)^{-1/3}[/tex]
[tex]\bigg((200+33t)^{1/3}A(t)\bigg)'=484(200+33t)^{-1/3}[/tex]
[tex]A(t)=484\displaystyle\int(200+33t)^{-1/3}\,\mathrm dt[/tex]
[tex]A(t)=22(200+33t)^{2/3}+C[/tex]
Since [tex]A(0)=100[/tex], we get
[tex]100=22(200)^{2/3}+C\implies C\approx-652.39[/tex]
so that the particular solution for [tex]A(t)[/tex] is
[tex]A(t)=22(200+33t)^{2/3}-652.39[/tex]
The tank becomes full when the volume of solution in the tank at time [tex]t[/tex] is the same as the total volume of the tank:
[tex]200+(44-11)t=500\implies 33t=300\implies t\approx9.09[/tex]
at which point the amount of salt in the solution would be
[tex]A(9.09)\approx733.47\text{ lb}[/tex]
factor 64a^2b^36-1
1. (8ab6 + 1)(8ab6 – 1)
2. (8ab18 – 1)
3. (8ab18 + 1)(8ab18 – 1)
4. (8ab6 – 1)
Answers
[tex]= (8ab^{18})^{2} - (1)^2 [/tex]
[tex]=(8ab^{18} - 1)(8ab^{18} + 1)[/tex]
----------------------------------------------------------
Answer: (8ab¹⁸ - 1)(8ab¹⁸ + 1) (Answer 3)
----------------------------------------------------------
Two people taking the test are chosen at random. what is the probability that at least one of them scores more than 500 points?
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Vicki started jogging. The first time she ran she ran 3/16 mile. The second time, she ran 3/8 Mile, and the third time, she ran 9/16 mile. If she continue this pattern, when was the first time she ran more than one mile explain
Answers
Answer:
In seventh time she ran more than one mile from first time she ran.
Step-by-step explanation:
Given Vicki started jogging. The first time she ran she ran 3/16 mile. The second time, she ran 3/8 Mile, and the third time, she ran 9/16 mile.
We have to find when was the first time she ran more than one mile.
The sequence followed is
[tex]\frac{3}{16}, \frac{6}{16}, \frac{9}{16}, \frac{12}{16}, \frac{15}{16}, \frac{18}{16}, \frac{21}{16}....[/tex]
First time she ran more than 1 mile is [tex]\frac{3}{16}+1=\frac{19}{16}[/tex]
In the seventh time she ran [tex]\frac{21}{16}[/tex] miles which is more than one mile from the first time.
Hence, in seventh time she ran more than one mile from first time she ran.
Please help me with the question 15 POINTS
Answers
If you want random people that meet certain criteria (have phones, shop in eyeglasses stores, use specific venues), then these protocols will deliver.
What is the sum of (–2.1x + 3.7) and (5 + 4.9x)?
-7.0x + 8.7
-2.8x + 8.7
2.8x + 8.7
7.0x + 8.7
Answers
Hope this helps?
Answer
C.
2.8x + 8.7
2.4.5 journal: graphs of exponential functions
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What is the measurement at x? m
(1/3+9) x ( 8-3) tell me the steps help
Answers
(Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction)
Solve parenthesis first
(1/3+9) x ( 8-3)
28/3 x 5
Use Multiplication
28/3 x 5 ≈ 4.7
After rounding 4.7 should be your answer
67 ,73 ,77,82,86,,86,91,98 find the median
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The median of a set that has an even number of numbers is the average of the middle two after they are sorted into order.
.. (82 +86)/2 = 84
Your median is 84.
Brent tosses a quarter 4 times and 3 times it comes up heads. the probability of heads is:
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Mr Thomas shoveled 12 1/2 yards of sand in 2 1/2 hours . At that rate how many yards did he shovel in one hour ?
Answers
1 hr + 1 hr = 10 yards
1/2 hr= 2.5 yards
Express in exponential form. log100.001 = -3
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Answer:
I believe you meant to put " log10 (0.001)= -3
10^-3=0.001
The expression log100.001 = -3 in exponential form is 10^-3 = 0.001. This demonstrates that 10 raised to the power of -3 equals 0.001, showing the inverse relationship between logarithms and exponents.
To express log100.001 = -3 in exponential form, recall that the logarithm is the exponent to which the base, in this case, 10, must be raised to produce the given number. The equation log10(0.001) = -3 tells us that the base 10 raised to the power of -3 equals 0.001.
In exponential form, this can be written as 10-3 = 0.001.The concept of converting a decimal to a negative power of 10 involves moving the decimal point to make the number into a whole number, and the negative exponent indicates how many places the decimal point needs to move to the left. In our case, 10-3 means we move the decimal three places to the left: 1 becomes 0.001.
When filled, a particular round balloon has a diameter of 14 inches. What is the approximate volume of air needed to fill this balloon?
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Hope this helps! Study on!
Answer:
the answer is 1,437
Step-by-step explanation:
Jill sold half of her comic books and then bought sixteen more. she now has 43. how many comic books did she begin with?
Answers
27 x 2 = 54
she had 54
Answer: 54
Step-by-step explanation: 43-16=27 times 2 =54
write a doubles fact that can help you solve 6+5=11
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<5 and <6 are complementary angles m<5=13 what is the measure of <6
Answers
90-13 = 77
Chin woo brought a home for $160,000. He put down 20%. The mortgage is at 8 1/2% for 30 years his monthly payment is.
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List 3 values that would make this inequality true 43 < y -30
Answers
add 30 to both sides
73 < y
y can be anything that is greater than 73
so it could be...
101, 74, 90, 75, 980767, 5674, etc.
Hope this helps!
Final answer:
To make the inequality 43 < y - 30 true, add 30 to both sides to get 73 < y. Any number greater than 73, such as 74, 80, or 90, will satisfy the inequality.
Explanation:
To find values that make the inequality 43 < y - 30 true, you simply need to add 30 to both sides of the inequality. This gives you:
73 < y
This means that any value greater than 73 will make the inequality true. Here are three examples:
y = 74 (since 74 is greater than 73)y = 80 (since 80 is greater than 73)y = 90 (since 90 is greater than 73)You can choose any three numbers greater than 73, and they will satisfy the inequality 43 < y - 30.