Answer:12
Step-by-step explanation:
Peter's age = x
John's age = y
y=2x
after 8 years = y+8=y+x+2
=(y-y)+8-2=x
=6=x
y=2(6)=12
The diagram shows a field, ABCD, on horizontal ground. (a) There is a vertical post at C. From B, the angle of elevation of the top of the post is 19º. Find the height of the post.
(1)
Determine the equation of the line passing through the point (0; -1) and
parallel to the -axis. Do you remember what the gradient of this line is?
(2)
Determine the equation of the line passing through the point(-1;0) and
parallel to the -axis. Do you remember what the gradient of this line is?
We know that,
slope = [tex] \rm{\frac{(y2 - y1)}{(x2 - x1)} }[/tex]
Let (0,1)=(x 1 ,y 1 ) and (1,2)=(x 2,y 2 )
So,
Slope of line = [tex] \frac{(2 - 1)}{(1 - 0)} = 1[/tex]
Now,
The required line equaqtion is given by,
==> y−y 1 = m(x-x1)
==> y−1=1(x−0)
==> y−1=x
==> y=x+1
A certain skincare company's profit in millions of dollars, P(t), can be modeled by the polynomial function P(t) = –2t3 + 8t2 + 2t, where t represents the number of skincare items produced, in thousands. Today, the company produces 4 thousand products for a profit of $8 million. According to the graph of the function, what other quantity of product would result in the same profit?
1 thousand
2 thousand
3 thousand
5 thousand
The quantity of product that would result in the same profit is 1 thousand. Option A
How to determine the function
Given the polynomial function as;
P(t) = –2t³ + 8t² + 2t
Where;
P(t) is the company's profit = $8 milliont is the number of skincare profitLet's equate the values
–2t³ + 8t² + 2t = 8
–2t³ + 8t² + 2t - 8 = 0
Factorize the expression
(-2t³ + 8t²) + ( 2t -8) = 0
- t² ( 2t - 8) + (2t -8) = 0
We take the similar factor
2t - 8 = 0
2t = 8
t = 8/2
t = 4
But we have that the company produced 4 thousand products for $8 million profit, so we have
= 4/ 4
= 1 thousand
Thus, the quantity of product that would result in the same profit is 1 thousand. Option A
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Is (1, -1) a solution of y=3x-4?
Answer:
Yes because putting value of x and y as 1 and -1 in equation :
y=3x-4
-1 = 3 * 1 - 4
-1 = -1 (True)
In a class there are 15 boys and 15 girls 5/6 of the children have brown hair if someone is chosen at random what is the probability that they will not have brown hair
Probability someone chosen at random will not have brown hair = 1/6
Probability of two variablesThe number of girls = 15
The number of boys = 15
The total number of children = 15 + 15 = 30
Probability that someone chosen at random will have a brown hair, P(Brown hair) = 5/6
P(Brown hair) + P(Not Brown hair) = 1
5/6 + P(Not brown hair) = 1
P(not brown hair) = 1 - 5/6
P(not brown hair) = 1/6
Therefore, if someone is chosen at random, probability that they will not have brown hair = 1/6
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f(x)=x^2+4x-6
a. f(x) can be written in the form (x+m)^2+n. Find the value of m and the value of n
My answer: m= 2; n=-10
b. Use your answer to part (a) to find the positive solution to x^2+4x-6=0
x=
Answer:
[tex]x \approx 1.16[/tex]
Step-by-step explanation:
a.
To find the values of m and n, we have to first expand [tex](x + m)^2 + n[/tex] :
[tex](x + m)^2 + n[/tex]
⇒ [tex]x^2 + 2mx + m^2 + n[/tex]
[tex]f(x) = x^2 + 4x - 6[/tex]
Now compare the coefficients of the x-terms:
• [tex]2mx = 4x[/tex]
⇒ [tex]\bf m = 2[/tex]
• [tex]m^2 + n = -6[/tex]
⇒ [tex]2^2 + n = -6[/tex]
⇒ [tex]n = -10[/tex]
b.
[tex]x^2 + 4x - 6 = 0[/tex]
∴ [tex](x + 2)^2 - 10 = 0[/tex]
⇒ [tex](x + 2)^2 = 10[/tex]
⇒ [tex]x + 2 = \sqrt{10}[/tex]
⇒ [tex]x = \sqrt{10} -2[/tex]
⇒ [tex]x \approx 1.16[/tex]
need help with this asap
The converse, inverse and contrapositive of each conditional statement include:
Converse: If two angles have a common side, then they are adjacent.Inverse: If two angles are not adjacent, then they do not have a common side.Contrapositive: If two angles do not have a common side, then they are not adjacent.What is a conditional statement?
A conditional statement can be defined as a type of statement that can be written to have both a hypothesis and conclusion. Thus, it typically has the form "if P then Q."
Where:
P and Q represent sentences.
In this scenario, we would write the converse, inverse and contrapositive of each conditional statement as follows:
Converse: If two angles have a common side, then they are adjacent.Inverse: If two angles are not adjacent, then they do not have a common side.Contrapositive: If two angles do not have a common side, then they are not adjacent.Read more on conditional statement here: brainly.com/question/16951916
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Find the sum of the geometric series given a1=−1, r=2, and n=7
A. -127
B. -116
C. 1
D. -118
Answer:
A
Step-by-step explanation:
the sum to n terms of a geometric series is
[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex] , then for n = 7
S₇ = [tex]\frac{-1(2^{7}-1) }{2-1}[/tex] = [tex]\frac{-1(128-1)}{1}[/tex] = - 1 (127) = - 127
For each of the following equivalence relations, describe the corre-
sponding partition. Your description of each partition should have no redundancy,
and should not refer to the name of the relation.
The description of the corresponding partition is given as follows:
The infinite classes can be defined as:
At equal distance of x from point [1,2]
Where x can vary from o to infinity.
What is a corresponding partition?The analogous partition, commonly known as "the set of equivalence classes," is the set A/R, the elements of which are the subsets of A satisfying the following:
For every a∈A there is some B∈A/R such that a∈B.
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find an angle measure of angle A and B
A (5y-3)
C (3y+27)
The measure of angle A and C will be 94.5° and 85.5°.
How to calculate the angle?(5y - 3) + (3y + 27) = 180
Collect like terms
5y + 3y - 3 + 27 = 180
8y = 180 - 27 + 3
8y = 156
y = 156/8 = 19.5
(5y - 3) = (5 × 19.5) - 3 = 94.5
(3y + 27) = (3 × 19.5) + 27 = 85.5
Therefore, the measure of angle A and C will be 94.5° and 85.5°.
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4. Kelly has a list of patient temperatures in Fahrenheit, but she needs them converted to Celsius. Help her convert the
temperatures using the formula(°F-32) x = °C. Note: temperatures are listed to the nearest tenth.
Method
Oral
Axillary
Rectal
Temperature °F
98.2 °F
96.6 °F
100.1 °F
Temperature C
°℃
°C
°℃
F
After conversion 98.2 °F=119.2°C
96.6 °F=116.3°C
100.1 °F==122.6°C
How can we convert temperature from Fahrenheit to Celsius?
We will convert using this formula
C= (F-32) *5/9
We will convert temperature from Fahrenheit to Celsius as shown below:
C= (F-32) *5/9
For Oral
Temperature=98.2°F
C= (98.2-32) *5/9
=119.16°C
Rounding to nearest tenth
=119.2°C
For Axillary
Temperature=96.6 °F
C= (96.6-32) *5/9
=116.28°C
Rounding to nearest tenth
=116.3°C
For Rectal
Temperature=100.1 °F
C= (100.1-32) *5/9
=122.58
Rounding to nearest tenth
=122.6°C
Hence, after conversion 98.2 °F=119.2°C
96.6 °F=116.3°C
100.1 °F=122.6°C
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Jan and Jo live 1,170 miles apart. At the same time, they start driving toward each other on the same road. Jo’s constant rate is 60 mph. Jan’s is 70 mph. How long will it take them to meet?
A. 8 hours
B. 9 hours
C. 16 hours
D. 19 hours
Answer: B. 9 hours
Step-by-step explanation:
Question analysis (Optional if you can understand the question)
Since they are 1170 miles apart, with their speed, the question is asking how long would it take them to travel 1170 miles together.
In other words, the distance that Jo and Jan together add up to 1170 miles.
Given information
Total distance = 1170 miles
Jo's rate = 60 mph
Jan's rate = 70 mph
Set variables
Let x be the time they took to meet each other
Set equation
60x + 70x = 1170
Solve equation
130x = 1170
Divide 130 on both sides
130x / 130 = 1170 / 130
[tex]\boxed{x=9 \: hrs}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
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Finding the inverse function of [tex]f(x) = 5\sqrt{x + 3} - 2[/tex], it is best described by graph B.
How to find the inverse of a function?Supposing we have a function y = f(x), to find the inverse, we exchange x and y, and isolate y.
In this problem, the function is:
[tex]f(x) = 5\sqrt{x + 3} - 2[/tex]
[tex]y = 5\sqrt{x + 3} - 2[/tex]
Exchanging x and y:
[tex]x = 5\sqrt{y + 3} - 2[/tex]
Working through the function to isolate y:
[tex]5\sqrt{y + 3} = x + 2[/tex]
[tex]\sqrt{y + 3} = \frac{x + 2}{5}[/tex]
[tex](\sqrt{y + 3})^2 = \left(\frac{x + 2}{5}\right)^2[/tex]
[tex]y + 3 = \frac{(x + 2)^2}{25}[/tex]
[tex]y = \frac{(x + 2)^2}{25} - 3[/tex]
[tex]f^{-1}(x) = \frac{(x + 2)^2}{25} - 3[/tex]
Which is best represented by graph B.
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There are 10 M&Ms of which 6 are green, in a bowl. You select 2 of them and eat each after it is selected. Is this a binomial experiment? Why or why not?
The experiment is not a binomial experiment.
What is a binomial experiment?
A binomial experiment is an experiment where there is a fixed number of trials, and the results are usually between two options- a yes or a no.
The conditions for a binomial experiment include:
1. Each trial should be classified either as a success or a failure.
2. There are a fixed number of observations
3. The trials are independent.
4. The number of trials are fixed.
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Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise unless otherwise indicated. Integrate c ln(x+y)dx-x^2 dy where C is the rectangle with vertices (1,1), (3,1), (1,4), and (3,4).
Using Green's Theorem to evaluate the given line integral with the given conditions and vertices gives us; -30
How to evaluate an Integral with Green's Theorem?
The line integral of a vector-valued function along the edges of a rectangle or any other closed curve can be found by converting the line integral into a double integral. We apply Green's theorem to do this. The resulting double integral is integrated over the two-dimensional region bounded by the same closed curve.
Green's Theorem can be applied as follows:
∮_c (P.dx + Q.dy) = ∫∫_R ((dQ/dx) - (dP/dy))dA
The vertices of the rectangle (1,1), (3,1), (1,4), and (3,4).
Applying Green's Theorem to the given function gives;
∮_c (ln x + y) dx - x² dy
= ∫14∫13 Dx(-x2) -Dy(ln(x) +y) dx dy
= ∫₁⁴∫₁³ (-2x - 1) dx dy
= -3·[x² +x]₁³
= -30
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How do you work this equation? x² + x - 30 = 0
Answer:
x = 5 , x = - 6
Step-by-step explanation:
First we factor using factorisation method :
We need 2 numbers that multiply to give +1 and add to give -30 :
To find these numbers we write out all the factors of 30 :
1, 30
2 , 15
3 , 10
5 , 6 ----> These must be the numbers as -5+6 = 1
Now we split +x into -5x and +6x :
x² -5x + 6x -30 = 0
Factor the first 2 terms together and the last two terms :
x(x-5) + 6(x-5) = 0
Keep 1 bracket and terms outside the brackets collect them into one:
(x-5)(x+6) = 0
We know that 1 of these brackets must be equal to zero as anything multiplied by zero = 0
Either x - 5 =0 OR x + 6 = 0
So x = 5 x = - 6
These are our final answers
Hope this helped and have a good day
Answer:
(x-5) (x+6)
x=5
X=-6
Step-by-step explanation:
x²+x-30=0
factorizing
x²-5x+6x-30=0
x(x-5)+6(x-5) =0
(x-5)(x+6)=0
now solve individually
x-5=0
send 5 to the other side
x=5
x+6=0
send 6 to the other side
x=-6
hope you understand the procedure
Given the functions f(x) = x3 + x2 – 3x + 4 and g(x) = 2^x– 4, (Consider domain, range, x-intercepts, and y-intercepts.)
The first function is a type of cubic function and the second function is a type of linear function. The key feature(s) do f(x) and g(x) have in common as they both have value of domain and range as (-∞, ∞).
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The function given in the problem is:
f(x) = x³ + x² – 3x + 4
The highest degree (power) of this function is 3. Thus, this function is a type of cubic function.
The second function given in the problem is:
g(x) = 2x – 4
The highest degree (power) of this function is 1. Thus, this function is a type of linear function.
Both the function has the value of domain and range from -∞ to ∞ (-∞,∞).
Thus, the first function is a type of cubic function and second function is a type of linear function. The key feature(s) do f(x) and g(x) have in common as they both have value of domain and range as (-∞, ∞).
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Sarah had three times as many quarters as nickels. She had $3.20 in all. How many quarters did she have?
A. 12
B. 15
C. 4
Answer:
A. 12
Step-by-step explanation:
If she had 12 quarters, then she would have to have 4 nickels according to the problem.
12 * .25 = $3 (money in quarters)
4 * .05 = $.2 ( money in nickels)
Adding those 2 together, we get $3.2.
She have 12 quarters
what is unitary method?It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
There are two situation in Unitary method:
There are 5 ice-creams. 5 ice-creams cost $125.
Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.
Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.
Given:
If she had 12 quarters, then
12 * .25 = $3 ( quarters)
4 * .05 = $.2 ( in nickels)
Hence, she have 12 quarters.
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The following table shows Jace's earnings based on the number of hours that he works.
Number of hours 111 222 333
Jace's Earnings \$20$20dollar sign, 20 \$30$30dollar sign, 30 \$40$40dollar sign, 40
Are Jace's earnings proportional to the number of hours that he works?
Answer:
no
Step-by-step explanation:
because no
A washer and a dryer cost $737 combined. The washer costs $37 more than the dryer. What is the cost of the dryer
Answer: $350
Step-by-step explanation:
$700 divided by 2 is 350
josh is looking to get a new car because he decided he was spending too much on gas. over the past year he found that he drove 7,700 miles. at current gas prices [ youll need to actually consider your current cost for gasoline ]. he was getting about 27 miles per gallon. if he bought a vehicle that realizes 33 miles per gallon. what might be a reasonable estimate of monthly gas costs?
Josh's monthly fuel expenses are $1,050.
PricesGiven that Josh is looking to get a new car because he decided he was spending too much on gas, and over the past year he found that he drove 7,700 miles, and at current gas prices of $4.5 he was getting about 27 miles per gallon, To determine, if he bought a vehicle that realizes 33 miles per gallon, what might be a reasonable estimate of monthly gas costs, the following calculation must be made:
27 = 10033 = X3300 / 27 = X122.22 = X122.22 = 100100 = X10000 / 122.22 = X81.81 = X(7700 / 33) x 4.5 = X233.33 x 4.5 = X1050 = XTherefore, Josh's monthly fuel expenses are $1,050.
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Answer:Josh's monthly fuel expenses are $1,050.
Step-by-step explanation:
Prove that $5^{3^n} + 1$ is divisible by $3^{n + 1}$ for all nonnegative integers $n.$
When [tex]n=0[/tex], we have
[tex]5^{3^0} + 1 = 5^1 + 1 = 6[/tex]
[tex]3^{0 + 1} = 3^1 = 3[/tex]
and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)
Suppose this is true for [tex]n=k[/tex], that
[tex]3^{k + 1} \mid 5^{3^k} + 1[/tex]
Now for [tex]n=k+1[/tex], we have
[tex]5^{3^{k+1}} + 1 = 5^{3^k \times 3} + 1 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k}\right)^3 + 1^3 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k} + 1\right) \left(\left(5^{3^k}\right)^2 - 5^{3^k} + 1\right)[/tex]
so we know the left side is at least divisible by [tex]3^{k+1}[/tex] by our assumption.
It remains to show that
[tex]3 \mid \left(5^{3^k}\right)^2 - 5^{3^k} + 1[/tex]
which is easily done with Fermat's little theorem. It says
[tex]a^p \equiv a \pmod p[/tex]
where [tex]p[/tex] is prime and [tex]a[/tex] is any integer. Then for any positive integer [tex]x[/tex],
[tex]5^3 \equiv 5 \pmod 3 \implies (5^3)^x \equiv 5^x \pmod 3[/tex]
Furthermore,
[tex]5^{3^k} \equiv 5^{3\times3^{k-1}} \equiv \left(5^{3^{k-1}}\right)^3 \equiv 5^{3^{k-1}} \pmod 3[/tex]
which goes all the way down to
[tex]5^{3^k} \equiv 5 \pmod 3[/tex]
So, we find that
[tex]\left(5^{3^k}\right)^2 - 5^{3^k} + 1 \equiv 5^2 - 5 + 1 \equiv 21 \equiv 0 \pmod3[/tex]
QED
What is the measure of
if Jill's age is 84 and johns age is 21 how many years ago was Jill 10 times older than john
Find the equation of an ellipse satisfying the given conditions.
Foci: (-4, 0) and (4, 0); length of major axis: 14?
The equation of the ellipse is [tex]\frac{x^2}{49} + \frac{y^2}{65} = 1[/tex]
How to determine the ellipse equation?The given parameters are:
Foci: (-4, 0) and (4, 0)Length of major axis = 14The above means that:
c = 4 and
The semi-major axis, a = 7 i.e 14/2
Calculate b using
[tex]b = \sqrt{c^2 + a^2[/tex]
So, we have:
[tex]b = \sqrt{4^2 + 7^2[/tex]
[tex]b = \sqrt{65[/tex]
Square both sides
[tex]b^2 = 65[/tex]
The standard form of the ellipse is represented as:
[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]
This gives
[tex]\frac{x^2}{7^2} + \frac{y^2}{65} = 1[/tex]
Evaluate
[tex]\frac{x^2}{49} + \frac{y^2}{65} = 1[/tex]
Hence, the equation of the ellipse is [tex]\frac{x^2}{49} + \frac{y^2}{65} = 1[/tex]
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Please help me with this i need big help in this
The value of the angle TSU is.97°. Therefore, none of the given options are correct.
How to calculate the angle?From the information given, the value of UZ will be:
= YZ - YU
= 63 - 26
= 37°
UZ = TZ = 37°
Therefore, the value of TSU will be:
= 23° + (37° × 2)
° 23° + 74°
= 97°
In conclusion, the correct option is E.
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Write the trig form of the complex number
18i
The trigonometric form of the complex number given in the task content is; 18(isin(π/2)).
What is the trigonometric form of the complex number?If follows from the task content that the complex number whose trigonometric representation is to be determined is; 18i.
Hence, It follows that the trigonometric form is;
= 18(cos(π/2) + isin(π/2)). where; cos(π/2) = 0.
Hence, we have;
= 18(isin(π/2)).
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cual es el valor de 10=z-6
Answer:
z=16
Step-by-step explanation:
10=z-6
10+6=z-6+6
16=z
Answer:
10=z-6
or, z= 10+6
or, z = 16
the vale of y is 16
Translate the following phrase into algebraic expression , the number of dollars Paul owes minus 32
Using a system of equations, the translated expression is:
P - 32.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variable is the number of dollars Paul owes, which is P. That amount minus 32 is represented by:
P - 32.
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what is the sum of .74+.19+3.09+1.98=
Answer:
6
Step-by-step explanation:
no calculator at hand ?
really ? you are using us a simple calculator ?
Answer:
6
Step-by-step explanation:
what is the sum of .74+.19+3.09+1.98=
0.74+
0.19+
3.09+
1.98=
-----------------
6