Answer:
1 3/20
Step-by-step explanation:
Find an equation for the plane that contains the line and is perpendicular to the plane
For the line and the plane to be perpendicular, they have to meet at right angles
The equation for the plane is x + 2y + 3z= 26
How to determine the equation?From the complete question, we have:
Point = (5,0,7)
Plane perpendicular to ⟨1,2,3⟩
The general equation is:
a * x+b * y+c * z = d
So, we have:
d = 5 * 1 + 2 * 0 + 7 * 3
Evaluate
d = 26
Recall that:
d = 5 * 1 + 2 * 0 + 7 * 3
Replace the points with x, y and z.
So, we have:
d = x * 1 + 2 * y + 3 * z
Evaluate
d = x + 2y + 3z
So, we have:
d = x + 2y + 3z and d = 26
Equate both equations
x + 2y + 3z= 26
Hence the equation for the plane is x + 2y + 3z= 26
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Don recently received his first credit card, a MasterCard with a credit line of $500. In the first month he had it, he ran up charges of $425. How much of that must he pay if he wants to charge a discount airline ticket, which costs $200, on his card without going over his credit limit
The amount Don must pay on his card without going over the credit limit is $125.
How much must Don pay?
Don's credit limit is $500. If Don does not want to go over the limit, he must not exceed the $500 limit. In order to determine the amount he should pay, add the sum of the charges and subtract it from the credit limit.
Amount to be paid = (425 + 200) - 500 = $125
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To determine the number of rams in a conservation area, a researcher catches and marks 103 rams. Then the researcher releases them. Later, 89 rams are caught and it is found that 21 of them are tagged. About how many rams are in the conservation area?
There are about rams in the conservation area.
(Round your answer to the nearest whole number as needed.)
Answer:
19 the explanation is 19 46
Agnes has $1,000 and she wants to have $1,100 accrued after 5 years. what rate does she need to have to meet her goal?
Answer:
the formula to use is R = 100I/ PT
Step-by-step explanation:
R = rate, I = interest = $1100, P = $ 1000, T= 5years
I needdddd helllppppppppp
1.1 2.4 3.3 right
Step-by-step explanation:
no have
The speed of the jet Alyssa flew on from Boston to London was 480 mph. on her return flight, the speed of the jet was 600mph with a tail wind. What was Alyssa's average speed on the round trip?
Based on the speed Alyssa used to get to London and the speed back to Boston, the average speed was 540 mph.
What is the average speed?The average speed that Alyssa was going can be found by the formula:
= (Initial speed + Final speed) / 2
Solving gives:
= (480 + 600) / 2
= 1,080 / 2
= 540 mph
In conclusion, Alyssa's average speed was 540 mph.
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Consider the equation - 3x2 + 27x - 63 = 0.
What is the discriminant of the equation?
Answer:
answer is 19/9.
Step-by-step explanation:
give me brielient.
The ratio of the measures of the three angles in a triangle is 15:8:13. Find the measure of the three angles.
Answer: 75, 40, 65
Step-by-step explanation:
Let the angles measure 15x, 8x, and 13x.
Since the sum of the angles of a triangle is 180 degrees,
15x+8x+13x=180, meaning that x=5.
So, the angles are 15(5)=75 degrees, 8(5)=40 degrees, and 13(5)=65 degrees.
A construction crew has just built a new road. They built the road at a rate of 3 kilometers per week. They built 18.75 kilometers of road. How many weeks did
it take them?
Answer:
6.25 weeks
Step-by-step explanation:
Take 18.75 and divide it by 3, since the crew is finishing 3 km per week. You get 6.25, so it took the crew 6.25 weeks to finish the road.
Hopefully this helps- let me know if you have any questions!
Help what's the correct question
23.-28. In a manner similar to Example 1, (a) identify input and
output consistent with the general proportional model; (b) write
an equation for the model; (c) determine a numerical value for the
constant k; and (d) solve the problem.
23. The maximum distance that you can see from the top of a tall
building is (directly) proportional to the square root of the
height of the building. You can see approximately 41 mi from
the Canadian National Tower lookout level, which is 1,135 ft
tall. How far can you see from the top of the Sears Tower in
Chicago (now the Willis Tower), which is 1,454 ft tall?
23. How far can you see from the top of the sears tower in Chicago, which is 1,454 ft tall?
The distance I can see from the top of the sears tower in Chicago is 46.41 mi.
How far can you see the from the top of the Sears Tower?The equation for direct proportionality = y = b√x
where:
y = dependent variable = distance you can seeb = constantx = independent variable = square root of the height of the building.b = y /√x
41 / √1135
b = 1.217
y = 1.217√1454
y = 46.41 mi
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Arsenic-74 is used to locate brain tumors. It has a half-life of 17.5 days. 90 mg were
used in a procedure. Write an equation that can be used to determine how much of
the isotope is left after x number of half-lives.
How much would be left after 70 days?
After x half-lifes, the amount of the isotope is:
A(x*T) = 90mg*e{-x*ln(2)}
And after 70 days, there are 5.628 mg
What is the half-life?
We define the half-life as the time such that the inital amount of a given substance reduces to half of it.
If the half-life is T, the amount of the substance can be written as:
A(t) = a*e^{-λ*t}
Where λ = ln(2)/T.
and a is the initial amount.
In this case, T = 17.5 days, then:
λ = ln(2)/17.5 days = 0.0396 / day
And we also have a = 90mg
Then the exponential equation is:
A(t) = 90mg*e^{-t*0.0396 / day}
After x half-lifes, the amount of the isotope left is:
A(x*T) = 90mg*e^{-x*T*ln(2)/T} = 90mg*e^{-x*ln(2)}
And after 70 days the amount is:
A(70 days) = 90mg*e^{-70 days*0.0396 / day} = 5.628 mg
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Answer:
Y=90mg(0.5)^5
1.86 after 70 days
Step-by-step explanation:
Which function has a constant additive rate of change of –1/4?.
2) Jessica is selling girl scout cookies and recorded how many she
sold in one afternoon. She sold Thin Mints, Trefoils, and Samoas.
a) She sold 54 boxes of Thin Mints, which was 60% of the total
number she sold. How many total boxes did she sell?
Answer: 90.
Step-by-step explanation: According to the question above, 54 Thin Mints cookies were 60% of the total amount of cookies she sold in one afternoon and the remaining 40% is still missing. 54 / 3 is 18, which is part of our answer, because if 54 is 60%, then 18 is 20%. 18 x 2 is 36, and 36 is 40%. Now that we've found the remaining 40%, the rest is adding 54 and 36, which gives you an answer of 90.
The equation 4x – 45 = y is used to find your profit, y, in dollars from buying $45 of supplies and washing cars for $4 each. What does the x stand for?
Can someone please help me with this? I need to turn it in tomorrow and I don't understand what to do.
Answer:
Step-by-step explanation:
Slope intercept form
y + 7 = 3(x + 4) Change all the double minuses to pluses.
y + 7 = 3x + 12 Remove the brackets.
y + 7 - 7 = 3x + 12-7 Subtract 7 from both sides
y = 3x + 5
Slope
Whatever number is in front of the x is the slope Answer: 3
y intercept
Whatever comes after the plus sign (or minus sign) is the y intercept. It is a single number. Answer: 5
x intercept.
This occurs when y = 0
0 = 3x + 5 Subtract 5 from both sides
-5 = 3x + 5 -5
-5 = 3x Divide by 3
-5/3 = 3x / 3
-5/3 = x
Answer: x_intercept = -5/3
a boy agreed to work one year for 1200 and a horse at the end of six months he quit and received 400 plus the horse what was the value of the horse
The cost of the horse given the amount received at the end of 6 months is 600
How to find the value of the horse?let
h = value of the horse6/12 × 1200 + 6h/12 = 400 + h
700 + 6h / 12 = 400 + h
700 - 400 = h - 6h/12
300 = 12h - 6h / 12
300 = 6h/12
cross product300 × 12 = 6h
3600 = 6h
h = 3600 / 6
h = 600
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Is -4,6 a solution to y=-9
Answer:
No, (-4, 6) is not a solution to y = -9.
Step-by-step explanation:
y= -9 has a horizontal line graph. Every point on this line has -9 as its y-coordinate. (-4, 6) does not lie on that line and is therefore not a solution to y = -9.
please help me ( if you get it right i will rate you 5/5)
Answer:
D.
Step-by-step explanation:
Okay, so 8:15 to 12:00 is 225 minutes, or 3.75 hours
12:45 to 17:30 is 285 minutes, or 4.75 hours
3.75 + 4.75 = 8.5 hours (total)
She earns 14.50 dollars per hour
8.5 * 14.5 = 123.25 dollars
D.
Answer:
The answers is D: 8.5 hours x $14.50 = $123.25
Step-by-step explanation:
This employee worked a total of 8.5 hours on Monday (3.75 hours in the morning and 4.75 hours in the afternoon).
Then, you have to multiply the total amount of hours worked by the number of dollars paid per hour.
8.5 hours x $14.50 = $123.25
PYTHAG THEOREM!
Aubrey is building a slide for her kids. If the ladder is 6 feet tall and she wants the bottom of the slide to be 5 feet from the ladder, how long does the slide need to be? If necessary, round to the nearest tenth.
Answer:
sqrt(11)
Step-by-step explanation:
a^2+b^2 = c^2
a = 5
c = 6
b = ?
25 - b^2 = 36
36 - 25 = b^2
b = sqrt(11)
The ladder should be 7.81 feet long.
What is Pythagoras theorem?Pythagoras theorem tell us the relation between the sides of a right-angled triangle, it states, the sum of the squares of the base and perpendicular is equal to the square of the hypotenuse.
Given that, Aubrey is building a slide for her kids. If the ladder is 6 feet tall, and she wants the bottom of the slide to be 5 feet from the ladder,
This slide is in the form of a right triangle, therefore applying the Pythagoras theorem, we have,
a²+b² = c² (refer to the figure attached)
5²+6² = c²
c² = 25+36
c² = 61
c = √61
c ≈ 7.81
Hence, the length of the slide should be 7.81 feet.
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my braincells are disappearing help me
Answer:
Last option
Step-by-step explanation:
In order to manipulate a, you have to divide by 3 on both sides.
20. Joseph has a shadow that is 7 feet long. If the
angle of elevation of the sun is 48°, how tall is
Joseph?
Answer:
7.8 feet
Step-by-step explanation:
Use the formula of tan to find his height.
tan Θ = [tex]\frac{opposite}{adjacent}[/tex]
tan 48 = [tex]\frac{x}{7}[/tex]
x = tan 48 × 7
x = 7.8 ft
what is the genaral term of this number pattern ? 45,41,37,33,29
Answer:
-4n + 49
Step-by-step explanation:
it is going down by 4 each step, hence, -4 and 45 -- 4 = 45 + 4 = 49.
Answer:
aₙ = -4n + 49Step-by-step explanation:
45, 41, 37, 33, 29, ....
a₁ = 45
a₂ = 45 - 4 = 41
a₃ = 41 - 4 = 37
a₄ = 37 - 4 = 33
a₅ = 33 - 4 = 29
...
It's an arithmetic sequence.
a₁ = 45, d = -4
A general term of an arithmetic sequence:
aₙ = a₁ + (n - 1)d
Substitute:
aₙ = 45 + (n - 1) · (-4) = 45 - 4n + 4 = -4n + 49
The scores at a golf course recorded last year followed a normal distribution with mean 78 and
standard deviation 11. you choose an srs of 15 scores and calculate xbar = mean score. which of
the following are the mean and standard deviation of the sampling distribution of x bar?
Using the Central Limit Theorem, it is found that the mean of the sampling distribution is of 78 and the standard deviation is of 2.84.
What does the Central Limit Theorem state?It states that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this problem, for the population, we have that [tex]\mu = 78, \sigma = 11[/tex].
Then, considering samples of n = 15, we have that the standard deviation is given by:
[tex]s = \frac{11}{\sqrt{15}} = 2.84[/tex].
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1. D=7.4 calculate the area of the circle
2. R=2.2 yd
Calculate the circumference of the circle
3. D=5 cm
Calculate the circumference of the circle
4. D=6 cm
Calculate the circumference of the circle
5. R=2.1 m
Calculate the area of the circle
6. R= 1.3 mm
Calculate the circumference of the circle
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
We need to know two formulas before we start ~
Area of circle = [tex]\sf \pi r² [/tex]Radius (r) = diameter (d) ÷ 2 Circumference = [tex]\sf 2\pi r \:\: or \;\;\pi d [/tex]Taking value of pi as 3.14
Let's solve ~
problem 1[tex]\qquad \sf \dashrightarrow \:d = 7.4[/tex]
[tex]\qquad \sf \dashrightarrow \:r = d \div 2[/tex]
[tex]\qquad \sf \dashrightarrow \:r = 7.4 \div 2[/tex]
[tex]\qquad \sf \dashrightarrow \:r = 3.7 \: \: units[/tex]
now,[tex]\qquad \sf \dashrightarrow \:area = 3.14 \times (3.7) {}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:a = 42.9866 \approx43 \: \: unit {}^{2} [/tex]
problem 2[tex]\qquad \sf \dashrightarrow \:r = 2.2 \: yd[/tex]
[tex]\qquad \sf \dashrightarrow \: circumference = 2 \times 3.14 \times 2.2[/tex]
[tex]\qquad \sf \dashrightarrow \: c =13.816 \: yd[/tex]
problem 3[tex]\qquad \sf \dashrightarrow \:d = 5 \: cm[/tex]
[tex]\qquad \sf \dashrightarrow \:circumference = 3.14 \times 5[/tex]
[tex]\qquad \sf \dashrightarrow \:c = 15.7 \: \: cm[/tex]
problem 4[tex]\qquad \sf \dashrightarrow \:d = 6 \: cm[/tex]
[tex]\qquad \sf \dashrightarrow \:circumference = 3.14 \times 6[/tex]
[tex]\qquad \sf \dashrightarrow \:c =18 .84 \: \: cm[/tex]
problem 5[tex]\qquad \sf \dashrightarrow \:r = 2.1 \: m[/tex]
[tex]\qquad \sf \dashrightarrow \:area = 3.14 \times (2.1) {}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:a = 3.14 \times 4.41[/tex]
[tex]\qquad \sf \dashrightarrow \:a \approx13.85 \: \: m {}^{2} [/tex]
problem 6[tex]\qquad \sf \dashrightarrow \:r = 1.3 \: mm[/tex]
[tex]\qquad \sf \dashrightarrow \:c = 2 \times 3.14 \times 1.3[/tex]
[tex]\qquad \sf \dashrightarrow \:c = 8.16 \: \: mm[/tex]
Here are clues for a puzzle involving two numbers.
Seven times the first number plus six times the second number equals 31.
Three times the first number minus ten times the second number is 29.
PART A
What are the two numbers?
Answer:
the first number is 5 1/2the second number is -1 1/8Step-by-step explanation:
The relations describing the two numbers can be written as equations. First, we need to assign variables: let x and y represent the first and second numbers, respectively.
The given relations are then ...
7x +6y = 31
3x -10y = 29
__
Such a system of equations can be solved many ways. One that is usually convenient is to use a graphing calculator. It tells us ...
the first number is 5 1/2the second number is -1 1/8Kaylee was out at a restaurant for dinner when the bill came. her dinner came to $24. after adding in a tip, before tax, she paid $28.08. find the percent tip.
Answer:
17%
Step-by-step explanation:
subtract/originial*100=lercent change
4.08/24=0.17*100=17
The answer is 17%
The ratio of the number of boys to the number of girls in choir is 6 to 7. There are 70 girls in choir. How many boys are in choir?
Answer:
48
Step-by-step explanation:
Instructions: Find the missing side. Round your answer to the nearest tenth.
Answer:
14.4
Step-by-step explanation:
We have hypotenuse so cannot use tangent. We have adjacent so we can't use sine, therefore, we have to use cosine.
x = cos(59) x 28
x = 14.4
Line of reflection
just the graph
rectangle GHIJ with vertices G(2,-1) H(7,-1) I(7,-4) J(2,-4)
Rectangle GHIJ with the vertices G(2,-1) H(7,-1) I(7,-4) J(2,-4) is reflected across the line y= -5 to give G'(2, 3) H'(7, 3) I'(7, -3) J'(2, -3)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Rectangle GHIJ with the vertices G(2,-1) H(7,-1) I(7,-4) J(2,-4) is reflected across the line y= -5 to give G'(2, 3) H'(7, 3) I'(7, -3) J'(2, -3)
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