Answer:
Jack is 31
Lacy is 10
Step-by-step explanation:
x - 9 = 22
since jack is 3 times as old as lacy,
the formula is
3x - 9 = 22
3x = 31
x = 10.3
So Jack is 31
And Lacy is 10
To prove this, subract 9 (years) from both ages
It will give you an approximate sum of 22 years for both their ages, as the question states
Since Lacy is a little over 10 years old, Jack is 31 instead of 30
The formula was taken from someone elses answer so sorry if it`s wrong
how many one third cup servings are in 16 cups
A rare species of insect was discovered in the rain forest. In order to protect the species,
environmentalists declare the insect endangered and transplant the insects into a protected area.
The population of the insect t months after being transplanted is given by P(t).
P(t) =
60(1+0.4)
0.01t+3
a. How many insects were discovered? In other words, what was the population when t = 0?
b. What will the population be after 5 years? Round to the nearest whole insect.
Using the given function, it is found that:
a) 20 insects were discovered.
b) The population after 5 years will be of 417 insects.
What is the function for the number of insects after t months?As stated in the exercise, it is given by:
[tex]P(t) = \frac{60(1 + 0.4t)}{0.01t + 3}[/tex]
Item a:
[tex]P(0) = \frac{60[1 + 0.4(0)]}{0.01(0) + 3} = \frac{60}{3} = 20[/tex]
20 insects were discovered.
Item b:
5 years = 60 months, hence:
[tex]P(60) = \frac{60[1 + 0.4(60)]}{0.01(60) + 3} \approx 417[/tex]
The population after 5 years will be of 417 insects.
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Part A: Given sine of theta is equal to radical 3 over 2 comma determine three possible angles θ on the domain [0,∞).
Part B: Given θ = 675°, convert the value of θ to radians and find sec θ.
(Picture below is equation stated in Part A)
Answer:
A. {60°, 120°, 420°}
B. θ = 15π/4; sec(θ) = √2
Step-by-step explanation:
A.The sine function is periodic with period 360°, and it is symmetrical about the line θ = 90°. The reference angle for the given value of sin(θ) is ...
θ = arcsin(√3/2) = 60°
The next larger angle with the same sine is (2×90°) -60° = 120°. Any multiple of 360° added to either one of these angles will give an angle with the same sine. A possible set of 3 angles is ...
{60°, 120°, 420°}
__
B.One degree is π/180 radians, so the given angle in radians is ...
θ = 675° = 675(π/180) radians = 15π/4 radians
This angle has the same trig function values as 7π4, a 4th-quadrant angle with a reference angle of π/4, or 45° The secant of that angle is
sec(45°) = √2
The 4th-quadrant angle has the same sign, so ...
sec(675°) = sec(15π/4) = √2
Please help 300 points
Answer:
4x + 9 ≥ 0
Step-by-step explanation:
The inside of the square root, the radicand, cannot be negative.
It can only be zero or positive.
Zero or positive is also described as being greater than or equal to 0.
Set the radicand to be greater than or equal to zero.
4x + 9 ≥ 0
Answer:
4x+9>=0
Step-by-step explanation:
The domain of a square root is that it can’t be less than 0. So we have the equation 4x+9>=0.
Determine the value of y, if x is -1. y= | x |-4
can someone solve what is n/n^3
Answer:
Alex = No B.
Step-by-step explanation:
1) Use Quotient Rule: [tex]\frac{x^{a} }{x^{b} } =x^{a-b}[/tex]
[tex]n^{1-3}[/tex]
2) Simplify 1 - 3 = 2
[tex]n^{-2}[/tex]
3) Use Negative Power Rule: [tex]x^{-a} =\frac{1}{x^{a} }[/tex]
[tex]\frac{1}{n^{2} }[/tex]
The graph of f(x) = 8 - x and line l which is tangent to f at x =1 is
shown in the figure to the right. The equation for line l is y =-3x +10.
Region R is the shaded region between line l, the graph off and the
y-axis while S is the shaded region between line l, the graph off and
the x-axis.
(a) Find the area of the shaded region R.
By taking the integral of the difference between the two given lines, we will see that R = 0.75.
How to find the area of the region R?Notice that the area will be given by the integral of the difference between the line L and our function on the interval [0, 1]
Then we just need to compute:
[tex]R = \int\limits^1_0 {-3x + 10 - (8 - x^3)} \, dx[/tex]
Solving that we will get:
[tex]R = \int\limits^1_0 {-3x + 10 - (8 - x^3)} \, dx = \int\limits^1_0 ({-3x + 10 - 8 + x^3} )dx\\\\\R = \int\limits^1_0 ({-3x + 2 + x^3} )dx\\\\\\[/tex]
[tex]R = \int\limits^1_0 ({-3x + 2 + x^3} )dx\\\\R = \frac{-3}{2}*(1)^2 + 2*1 + \frac{1^4}{4} = 0.75[/tex]
So the area of region R is 0.75 square units.
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convert 5'5 into meters
It will be around 1.6metres
hope it helps
Answer:
1.65 meters
Step-by-step explanation:
1 ft = 0.3048 meters
just multiply
SOMEONE PLSSSSSS HELP ME SOLVE THIS FAST
I WILL MARK BRAINLIEST
Answer:
D
Step-by-step explanation:
I calculated the area for 54 feet and then for 0.5 feet using the equation [tex]A=\sqrt{\frac{3}{4} }a^{2}[/tex] , where a is the size and then divided first area by second area
ΔQRS is a right triangle.
Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle.
Select the correct similarity statement.
Answer:
∆QRS is a right triangle
Step-by-step explanation:
correct similarity statement is RST
Answer:
I think its B
Step-by-step explanation:
Edge 2022
Liam is a tyre fitter. it takes him 124 minuets to fit 4 tyre's to a lorry. how long would t take him to fit 6 tyre's to a lorry?
if he works for 93 minuets how many tyre's will he fit?
168 minutes or 2 hours 48 minutes
Step-by-step explanation:
Since 12 tyres is 3 times 4 tyres, it will take 3 times as long as 56 minutes.
3 * 56 minutes = 168 minutes
We can convert the answer to hours and minutes.
60 minutes = 1 hour
120 minutes = 2 hours
168 minutes – 120 minutes = 48 minutes
168 minutes = 2 hours 48 minutes
Answer: 168 minutes or 2 hours 48 minute
Carrie uses her phone primarily to take a lot of selfies. The storage space on her phone is limited, so Carrie needs to keep track of how many selfies she takes.
There is a proportional relationship between the number of selfies Carrie takes, x, and the amount of storage (in megabytes) she uses taking selfies, y.
x (selfies) y (megabytes)
10 20
12 24
21 42
22 44
Write an equation for the relationship between x and y. Simplify any fractions.
y=
Explanation:
A direct proportion is of the form y = kx
To find k, pick any row to divide the y over x value
k = y/x = 20/10 = 2k = y/x = 24/12 = 2k = y/x = 42/21 = 2k = y/x = 44/22 = 2No matter which row you go for, the constant of proportionality is 2. Meaning that we double the x value to get to y.
Therefore, we go from y = kx to y = 2x
(7 point)
13. Amir posts on social media frequently, while Naomi posts rarely. Their number of posts over
the last six days are given in the table below. Compare the spreads of the data sets using both
range and IQR
Amir Naomi
15
2
12
4
14
10
16
2
15
3
19
0
The number of social media post of Noami has a greater spread when compared to that of Amir.
What is the range and intequartile range of the social media posts?Range is the difference between the highest and lowest values of a set of observations
Range = highest value - lowest value
The range of Amir's social media posts = 19 - 15 = 4 The range of Noami's social media posts = 10 - 0 = 10The inter quartile range is the difference between the third quartile and the first quartile of a data set.
IQR = Q3 - Q1
The IQR of Amir's social media posts: 7
The IQR of Naomi's social media posts = 10
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Answer:
Naomi"s data set has more spread since her range is 10 and her IQR is 3.
Step-by-step explanation:
Range IQR
12,14,15,15,16,19 16-14=2
0,2,2,4,5,10 5-2=3
19-12=7 10-0=10
I will give brainliest if you answer these 10 questions :) 1.Jill has to go to the post office before she drops her 3 children off at the elementary school. She is going straight home after dropping them off. How long is Jill traveling roundtrip?
A. 9 miles
B. 12 miles
C. 18 miles
D. 27 miles
2.Jill leaves her house and goes to pick up a friend from the airport, drops the friend at City Hall. What is the shortest distance Jill travels?
A. 16 miles
B. 25 miles
C. 48 miles
D. 54 miles
3.Jill leaves work from the High School, but has to pick up her friend at the airport before going back home. What is the shortest distance she can travel?
A. 27 miles
B. 21 miles
C. 56 miles
D. 84 miles
4.Mary works at the Elementary School, but has to go to the airport to pick up her father. Her father works at City Hall. She drops her father at City Hall and then returns to the Elementary School. How far did Mary travel if she took the shortest route?
A. 32 miles
B. 36 miles
C. 64 miles
D. 96 miles
5.What is the shortest distance Jill can travel is she leaves her house, goes to City Hall, to the Post Office, and then returns home?
A. 9 miles
B. 16 miles
C. 38 miles
D. 48 miles
6.Mary works at the Middle School, but has to go to the airport to pick up her father. Her father works at City Hall. She drops her father at City Hall and then returns to the Middle School. How far did Mary travel if she took the shortest route?
A. 32 miles
B. 36 miles
C. 64 miles
D. 96 miles
7.Jill works at the High School. If she travels from her house and does not make any stops, what is the shortest distance that she travels roundtrip?
A. 11 miles
B. 12 miles
C. 22 miles
D. 33 miles
8.Jill has to go to the post office before she drops her 3 children off at the elementary school. She is going straight home after dropping them off. How long is Jill traveling before going back home?
A. 9 miles
B. 12 miles
C. 18 miles
D. 27 miles
9.Jill works at the High School. If she travels from her house and does not make any stops, what is the shortest distance that she travels one way to get to work?
A. 11 miles
B. 12 miles
C. 22 miles
D. 33 miles
10.What is the shortest distance Jill can travel if she leaves her house, goes to the post office, to the grocery store, and then returns home?
A. 15 miles
B. 28 miles
C. 45 miles
D. 60 miles
What is the factorization of the trinomial below?
x^3 - 12x^2 + 35x
A. (x - 7)(x + 5)
B. x(x - 7)(x - 5)
C. (x^2 - 7)(x + 5)
D. x(x - 7)(x + 5)
How many sides does a regular polygon have if each interior angle measures 150°?
Answer:
12
Step-by-step explanation:
Its interior angle has measure 150∘. Therefore, the exterior angle has measure 180∘−150∘=30∘. Therefore, the number of sides of the regular polygon with interior angle 150∘ is 12.
Evan walked 2 1/8 miles to his aunts house. He has already walked 6/8 mile. How much farther does Evan have to go?
Rewrite 2 1/8 as 17/8
Now subtract:
17/8 - 6/8 = 11/8 = 1 3/8
answer : 1 3/8 miles left
need help with the questions below. screenshots are provided. need help asap
Answer:
Step-by-step explanation:
12g - 17 ≥ 17
12g ≥ 34
g ≥ [tex]\frac{34}{12}[/tex]
g ≥ [tex]\frac{17}{6}[/tex]
A number w minus 3 is less than or equals to 10
Answer:
Step-by-step explanation:
A number w minus 3 (w - 3) is less than or equal (≤) to 10
w - 3 ≤ 10
+ 3 + 3
w ≤ 13
Hope this helps!
A farmer ploughts his lands in 12 days if he use 5 tractors ow long will it if he uses 3 tractors?
Answer:
Step-by-step explanation:
By proportion it will be (5/3) * 12
= 60/3
= 20 days.
Solve for x. Round all answers to the nearest tenth.
11
11.7
10.2
11.9
11.9 - last one
Step-by-step explanation:
Adjacent + hypotenuse = Cos / Cah
Cos32 = x/14
x14
11.87... = x
So, 11.9 to nearest tenth
Hope this helps!
Round to the nearest tenth, I will give brainlyest PLEASE
1. cos B= a/x
x= 11/cos 37°
x= 13.77
2. tan A= a/x
x= 4/tan 41°
x= 4.60
3. sin B = x/c
x= sin 37° × 10.3
x= 6.20
4. tan A= a/b
tan A= 4/13
A= tan-1(0.31)
A= 17°6'10"
5. cos A= b/c
cos A= 12/13
A= cos -¹(0.92)
A= 22°37'12"
6. tan B= a/b
tan B= 3/3
tan B= 1
B= tan‐¹(1)
B= 45°
Help me out please, should be easy
Answer:
I'm pretty sure the points are plotted at (-1,-2) but I'm not exactly sure. Correct me if I'm wrong! :D
Rewrite the following without an exponent. (9/5)^-1
Answer:
5/9
Step-by-step explanation:
What we have here is the reciprocal of (9/5). Inverting (9/5) results in (5/9), which is the desired result.
LOTS OF POINTS + BRAINLIEST
Suppose p and q are both prime numbers with p > q. Prove that p-q and p+q cannot both be positive perfect squares.
FULL PROOF REQUIRED.
Answer:
The list od prime number is a quadratic sequence, each time going up by n + 2. for example, 1, 4, 9, 16, 25. they are going up by 3, then + 2 and add 2 every step. The sequence is always going up by an odd number. a negative number take away a negative number always gives you a positive number, likewise, adding does too. Therefore, you can not get both of them to fit into the sequence of increasing odd numbers.
Find the distance between the two points (1, -4) and (5, 3). Give an exact answer in
terms of a square root.
Answer:
A lovely answer of : [tex]\sqrt{17}[/tex]
For those of you who use a dark theme : square root of (17)
And a short Explanation:
Use the Pythagorean theorem to find the result
Below is the graph of a polynomial function with real coet
of the function are shown in the graph.
m
27
Use the graph to answer the following questions.
(a) Over which intervals is the function increasing? Choose all that apply.
o(-00,-5) o (-5, -2) 0 (-2,2) 0 (2,6) o(-2,6) o (6,00)
(b) At which x-values does the function have local maxima? If there is more than
one value, separate them with commas.
(c) What is the sign of the function's leading coefficient?
(Choose one)
(d) Which of the following is a possibility for the degree of the function? Choose all
that apply.
5
06
08 09
04
07
This question is about Polynomial Functions. The reading below is done using the attached graph.
a) Over which intervals is the function increasing?The function is increasing over the following intervals:
(2,6) Option D; and (-2,6) Option E.b) Yes, the points on the x-axis that has local maxima are:
Point -2, and Point 6.
c) The leading coefficient is negative. The sign is given as:
f(x) → -∞
as x → + ∞
d) The possible degree of the function is:
06- (Option B).
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Use the open number line to find the difference.
423 – 160 = ____
An open number line is shown. A hop to the left of negative 100 begins at 423. A second hop to the left of negative 50 begins where the first hop ends. A third hop to the left of negative 10 begins where the second hop ends.
A.
363
B.
360
C.
263
D.
260
Please help me with this!!
Answer:
A, B, D, F
Step-by-step explanation:
Given expression: [tex]8^{\frac23}[/tex]
Apply exponent rule [tex]a^{bc}=(a^b)^c[/tex]
[tex]\implies 8^{\frac23}=(8^2)^{\frac13}[/tex]
Apply exponent rule [tex]a^{\frac{1}{n}}=\sqrt[n]{a}[/tex]
[tex]\implies (8^2)^{\frac13}=\sqrt[3]{8^2}[/tex]
Therefore, option A
Apply exponent rule [tex]a^{bc}=(a^b)^c[/tex]
[tex]\implies 8^{\frac23}=(8^{\frac13})^2[/tex]
Apply exponent rule [tex]a^{\frac{1}{n}}=\sqrt[n]{a}[/tex]
[tex]\implies (8^{\frac13})^2=(\sqrt[3]{8})^2[/tex]
Therefore, option B
Apply exponent rule [tex]a^{bc}=(a^b)^c[/tex]
[tex]\implies 8^{\frac23}=(8^{\frac13})^2[/tex]
As [tex]8^{\frac13}=2[/tex]
[tex]\implies (8^{\frac13})^2=2^2[/tex]
Therefore, option D
Apply exponent rule [tex]a^{bc}=(a^b)^c[/tex]
[tex]\implies 8^{\frac23}=(8^{\frac13})^2[/tex]
As [tex]8^{\frac13}=2[/tex]
[tex]\implies (8^{\frac13})^2=2^2[/tex]
[tex]\implies 2^2=4[/tex]
Therefore, option F
What is the Area of this shape?
14 * 12 = 168
(12*8) / 2 = 48
216 cm ^2
Answer:
1,344 cm counting the side shape or 168 cm counting only the rectangle.
Step-by-step explanation:
14 cm x 12 cm = 168cm
168 x 8 = 1,344 cm