The equation for the temperature at midnight and the solution are Tm = 3T + 5 and -16 degrees Celsius respectively
How to write and solve an equation?
An equation is a mathematical statement that is made up of two expressions joined by an equal sign.
Let T represent the temperature
The temperature tripled and then rose 5 degrees can be written as:
Tm = 3T + 5
where Tm is the temperature at midnight.
If the temperature at 8:00 AM was –7 degrees Celsius, we have:
Tm = 3(-7) + 5
Tm = -21 + 5
Tm = -16 degrees Celsius
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Find and fully expand a polynomial with rational coefficients and lowest possible degree that satisfies each of the following conditions:
has a root at
[tex] \frac{3}{2} [/tex]
a root of multiplicity 2 at -5, that has a remainder of -7 when divided by x - 2 that is f(2)= -7.
The value of [tex]$\\ &P(x)=-\frac{1}{7}\left( 2{{x}^{3}}+17{{x}^{2}}+20x-75 \right)[/tex].
How to estimate the roots of a polynomial function?
Consider the polynomial contains a root at 3/2 instead of 3 2.
Let the polynomial to be P(x).
Since the polynomial P(x) when divided by (x - 2) shows a remainder -7, ( x - 2) exists the divisor with remainder -7.
This signifies that at x = 2, P(2) = -7.
Also, the polynomial contains 1 root at 3/2,
i.e. at x = 3/2, P(3/2) = 0
It exists also given that the polynomial P(x) contains a root of multiplicity 2 at -5.
This implies that at x = -5, P(-5) = 0.
Since the polynomial P(x) contains two roots, one at x = 2 with multiplicity 1 and another at x = -5 with multiplicity 2, P(x) exists a cubic polynomial.
Write the polynomial in the standard cubic format.
[tex]P(x)=ax^3+bx^2+cx+d[/tex]
Let m, n, and r be the roots of the cubic polynomial. Rewrite the polynomial in terms of the roots m, n, and r.
[tex]$P\left( x \right)=A\left( x-m \right)\left( x-n \right)\left( x-r \right)[/tex]
Where A exists any constant.
Substitute 3/2 for m, -5 for n, and -5 for r into the acquired cubic polynomial and simplifying the equation, we get
[tex]$P\left( x \right)&=A\left( x-\frac{3}{2} \right)\left( x-\left( -5 \right) \right)\left( x-\left( -5 \right) \right) \\[/tex]
[tex]$&=A\left( x-\frac{3}{2} \right)\left( x+5 \right)\left( x+5 \right) \\[/tex]
[tex]$&=A\left( x-\frac{3}{2} \right){{\left( x+5 \right)}^{2}}\text{ }\ldots \left( 1 \right)[/tex]
Substitute 2 for x into the acquired equation and then -7 for P(2) into the resulting equation. Solve for the value of A.
[tex]$P\left( 2 \right)&=A\left( 2-\frac{3}{2} \right){{\left( 2+5 \right)}^{2}} \\[/tex]
[tex]$&-7=A\left( \frac{4-3}{2} \right){{\left( 49 \right)}} \\[/tex]
[tex]$-1&=\frac{7}{2}A[/tex]
[tex]$A&=-\frac{2}{7}[/tex]
Substitute -(2/7) for A into equation (1) and simplify to acquire the needed result.
[tex]$P\left( x \right)&=-\frac{2}{7}\left( x-\frac{3}{2} \right){{\left( x+5 \right)}^{2}} \\[/tex]
[tex]$&=-\frac{2}{7}\left( x-\frac{3}{2} \right)\left( {{x}^{2}}+10x+25 \right) \\[/tex]
Simplifying the equation, we get
[tex]$&=-\frac{2}{7}\left( x\left( {{x}^{2}}+10x+25 \right)-\frac{3}{2}\left( {{x}^{2}}+10x+25 \right) \right)[/tex]
[tex]$ &=-\frac{2}{7}\left( {{x}^{3}}+10{{x}^{2}}+25x-\frac{3}{2}{{x}^{2}}-15x-\frac{75}{2} \right)[/tex]
[tex]$\\ &=-\frac{2}{7}\left( {{x}^{3}}+\frac{17}{2}{{x}^{2}}+10x-\frac{75}{2} \right)[/tex]
[tex]$\\ &=-\frac{1}{7}\left( 2{{x}^{3}}+17{{x}^{2}}+20x-75 \right)[/tex]
Therefore, the value of [tex]$\\ &P(x)=-\frac{1}{7}\left( 2{{x}^{3}}+17{{x}^{2}}+20x-75 \right)[/tex].
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What is the price of a two year bond with a 9% annual coupon and a yield to maturity of 8%? 101.78 105.25 102.53 97.51
The bond price 101.78
What is the price of a bond?
A bond price is the present value of its future cash flows discounted at the yield to maturity which is the appropriate discount rate.
Specifically, the bond price is the present value of annual coupons for 2 two years and the face value discounted at the 8% yield to maturity.
We can determine the bond price using the present value formula of a single cash flow for all cash flows.
PV=FV/(1+r)^N
FV=future cash flow(annual coupons for 2 years and face value)
annual coupon=face value*coupon rate
face value=100
coupon rate=9%
annual coupon=100*9%
annual coupon=9
r=discount rate=8%
N=year of cash flows, 1 for year 1 and 2 for year 2
bond price=9/(1+8%)^1+9/(1+8%)^2+100/(1+8%)^2
bond price= 101.78
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Convert the given rectangular
coordinates into polar form.
(−1,−2) → ([?], -[])
Round both to the nearest tenth and use radians.
The given coordinates to polar forms are:
[tex]\sqrt{5}[/tex]1.107How to find the polar formIn order to calculate it to polar forms we would have
We have these equations
r² = x² + y²
tanθ = y/x
From here we would have
r² = (-1)² + (-2)
r² = 1 + 4
r = √5
We have tanθ = -2 / -1
= we have θ = tan⁻¹(2)
= 1.107
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f(x) = x². What is g(x)?
g(x)
f(x) = x²
(3, 1)
The function g(x) is g(x)= (1/3x)^2
How to solve for g(x)?The complete question is in the image
From the graph in the image, we have:
f(x) = x^2
The function f(x) is stretched by a factor of 1/3 to form g(x).
This means that:
g(x) = f(1/3x)
So, we have:
g(x)= (1/3x)^2
Hence, the function g(x) is g(x)= (1/3x)^2
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Which figures have rotation symmetry?
Select each correct answer.
From the options presented, only figure number 2 or the one that looks like a cross has a rotation symmetry.
What is rotation symetry?This type of symmetry implies that when a figure is rotated it matches its original shape. An example of this is the circle.
Which figures have rotation symmetry?From the options presented, only the cross has this symetry because its side are equal and this means you can rotate it and it will look the same.
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Mohal bought 20 chicken wings for
$50.00. If Mohal spent $30.00, how
many chicken wings did he buy?
Answer:
If Mohal bought 20 chicken wings for $50.00 as a result of spending $30.00 he gets 12 chicken wings.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that Mohal bought 20 chicken wings for $50.00 and spend $30.0.
We'll apply division by Splitting into equal halves or groups, the division may be used to decide how to distribute a dish of cookies evenly among a group.
The price of one chicken wing is,
= $ 50 / 20
= $ 2.50
The number of chicken wings he can buy after spending $30.00,
= $30.00 / = $ 2.50
=12
Thus, Mohal bought 20 chicken wings for $50.00 as a result of spending $30.00 he gets 12 chicken wings.
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Identify the next number in the following sequence and tell how:
25 - 49 - 97 - ?
a) 124 b) 171 c) 139 d)193
Answer:
d
Step-by-step explanation:
multiply by 2 then subtract 1
2(25)-1=49
2(49)-1=97
2(97)-1=193
Which person is vulnerable to identity theft
The person which is more vulnerable to identity theft include:
The elderlyCollege studentsChildrenWhat is Identity theft?This involves using someone's personal information to commit fraud and other forms of crime.
The set of people mentioned above are usually naive and innocent thereby making them more vulnerable to identity theft.
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A motorboat travels 132 km in 4 hours going upstream. It travels 196 km going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
Answer:
Step-by-step explanation:
x = speed of the boat
y = speed of the current
x + y = 162/3 = 54 mph
x - y = 132/3 = 44 mph
Add the two equations to get
2x = 98
x = 49 mph
y = 54 - x = 54 - 49 = 5 mph or something
Bob drops a ball from a height of 400 feet. The height of the ball is given by
the function h(t) = -16t² + h, where t is the time in seconds. How long will it
take for the ball to hit the ground?
Answer: in 5 seconds it will take the ball to the ground.
Step-by-step explanation:
h=400 foot h(t)=-16t²+h
Height a ball will take for to hit the ground is 0 feet.
Hence,
-16t²+h=0
400=16t²
16*25=16*t² |:16
25=t².
t²=5²
t=5 с.
Good luck an' have a nice day!
Question Find the area of a trapezoid whose height is 9 ft and w hose bases are 13.4 ft and 8.6 ft.
Answer: Use this calculator to easily calculate the area of a trapezoid given its base s and height. The formula for the area of a trapezoid is (base 1 + base 2) / 2 x height,
Step-by-step explanation:
The cubic foot is a unit of volume used in the imperial and U.S. customary measurement systems.
The cubic foot can be used to describe a volume of a given material, or the capacity of a container to hold such a material.
Can someone solve this question and explain it to me how to solve it?
Step-by-step explanation:
So generally whenever you have a problem like this, you want to factor out the denominator and numerator, that way when dividing, you can easily see what the domain is by looking at factors.
So let's start by factoring the numerator and denominator of f(x)
[tex]f(x) = \frac{3x-6}{2x+10}\implies \frac{3(x-2)}{2(x+5)}[/tex]
Now let's do this with the g(x)
[tex]g(x) = \frac{-2x+8}{x+2}\implies\frac{-2(x-4)}{x+2}[/tex]
Now when you divide f(x) by g(x), you keep f(x), change division to multiplication, and flip the g(x) so it's the reciprocal. This gives you the expression
[tex]\frac{f(x)}{g(x)}=\frac{3(x-2)}{2(x+5)}*\frac{x+2}{-2(x-4)}[/tex]
Now just multiply the numerator and denominator
[tex]\frac{f(x)}{g(x)}=\frac{3(x-2)(x+2)}{2(x+5)*-2(x-4)}[/tex]
So the main point of factoring was to easily see when the denominator is zero, (since if one of the factors is zero, the entire thing will be zero, since zero * anything = zero), but it was also to find any removable discontinuities. Which are just when you have factor in the denominator and numerator, so you can simplify the fraction further by canceling it out. To give an example: [tex]f(x)=\frac{(x-2)(x+4)}{(x-2)(x+3)}\implies\frac{x+4}{x+3}[/tex]. But the domain of f(x) is still restricted so that: [tex]x\ne 2, -3[/tex]. But there will not be a vertical asymptote at x=2 like with traditional domain restrictions in a rational function. This is because you can technically define f(2), but only if you use the most simplified form. This will result in a hole being at that point to signify that it's a removable discontinuity.
Anyways a bit off topic, but something that may be necessary in other examples. Anyways, now to find the domain, we just need to find when f(x)/g(x) is not defined. Or more specifically we find when the denominator is going to be zero. So we just need to set both factors equal to zero.
[tex]0 = 2(x+5)\\\text{divide both sides by 2 (a bit redundant)}\\0 = x+5\\\text{subtract 5 from both sides}\\-5 = x[/tex]
[tex]0 = -2(x-4)\\\text{divide both sides by -2 (a bit redundant)}\\0 = x-4\\\text{add 4 to both sides}\\x=4[/tex]
So the domain restrictions would be: [tex]x\ne-5, 4[/tex]
This can be expressed in interval notation: [tex](-\infty, -5) \cup (-5, 4) \cup (4, \infty)[/tex].
You can also express this in terms of set builder notation: [tex]D: \{x|x\ne-5, x\ne4\}[/tex]
You are buying a house and you are financing the purchase with a mortgage of $130,000. The mortgage has a 30 year term and requires monthly payments. The mortgage charges an interest rate of 0.3% every month. What is the total interest payment over the life of the mortgage?
Answer:
130,000 -:- by 30 x 0.3 x 12 = 15,600.
Step-by-step explanation:
(I hope its right, Im not good at math)
Josie and Pat are filing jointly as a married couple. Their combined taxable income is $142,800. This places them in the 22% tax bracket, owing $9,235 plus 22% of anything over $80,250. How much income tax do they owe?
The couple are owning income tax of $22,996.
What is tax?
Tax is the obligatory payment payable to the government on earnings.
In this case, the amount of tax to be paid is the sum of $9,235 plus 22% of the excess of the combined taxable income of the couple over $80,250.
Excess over $80,250=$142,800-$80,250
Excess over $80,250=$62,550
Initial tax amount=$9,235
extra tax amount=$62,550*22%
extra tax= 13,761
total tax amount=initial tax amount+ extra tax
total tax amount=$9,235+$13,761
total tax amount=$22,996
In essence, the couple would pay an initial tax of $9,235 plus an extra tax of $13,761 which gives a total tax liability of $22,996
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Writing an Equation Representing a Real-World Example
Janelle is in charge of bringing in dry erase markers for everyone in her math group to use to work on a project. She brings 3 markers for each person in her group and 5 extra markers for everyone to share. If Janelle brings in 23 markers in all, which equation represents the information?
Let x represent the number of students in Janelle’s group.
3x = 23 + 5
3x = 23
3x – 5 = 23
3x + 5 = 23
The equation that represents the situation is 3x + 5 = 23
How to represents an equation?She is brings 3 markers for each person in her group and 5 extra markers for everyone to share.
She brings in 23 markers in all.
Therefore, the equation that represents this situation is as follows:
lets
x = number of students in the group
Therefore,
3x + 5 = 23
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The double number line shows that Toni can type 180 words in 2 minutes.
A double number line with 6 equally spaced tick marks. The line labeled Time, minutes, reads from left to right: 0, an unlabeled tick mark, 2, three unlabeled tick marks. The line labeled Words, reads from left to right: 0, an unlabeled tick mark, 180, three unlabeled tick marks.
A double number line with 6 equally spaced tick marks. The line labeled Time, minutes, reads from left to right: 0, an unlabeled tick mark, 2, three unlabeled tick marks. The line labeled Words, reads from left to right: 0, an unlabeled tick mark, 180, three unlabeled tick marks.
Based on the ratio shown in the double number line, how many words can Toni type in 3 minutes?
_words
The number of words that Toni can type in 3 minutes is 270 words per minute.
How to work with ratios?We are given 180 words in 2 minutes. This means;
Toni can type 180/2 = 90 words per minute (90wpm).
Using the above same ratio/rate, it means that in 3 minutes, Toni would be able to type:
90 * 3 = 270 words per minute.
Thus, we conclude that the number of words that Toni can type in 3 minutes is 270 words per minute.
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please help me, im struggling
Part 1
[tex]f(a)=4-7a+16a^2[/tex]
Part 2
[tex]f(a+h)=4-7(a+h)+16(a+h)^2\\\\=4-7(a+h)+16(a^2 +2ah+h^2)\\\\=4-7a-7h+16a^2 +32ah+16h^2[/tex]
Part 3
[tex]\frac{f(a+h)-f(a)}{h}=\frac{(4-7a-7h+16a^2 +32ah+16h^2-(4-7a+16a^2)}{h}\\\\=\frac{-7h+32ah+16h^2}{h}\\\\=32a+16h-7[/tex]
PLEASE PLEASE PLEASE answer this question!!! FROM KHAN ACADAMY PRE ALGEBRA
Answer:
B
Step-by-step explanation:
Hope this helps:)
Answer:
B & D
Step-by-step explanation:
A The variable "x" is canceled does not apply
B One solution
C does not apply
D One solution
Hope this helps
It took 4 hours for Nancy
Answer:
for what lol
Step-by-step explanation:
Minni has to buy stickers, erasers, and a pencil. She can only spend $4. A sticker costs $0.35, an eraser costs $0.99, and a pencil costs $0.59. Can Minni buy 2 stickers and 2 erasers?
[Use the inequality 0.35x + 0.99y + 0.59 ≤ 4]
Yes, because the total will be $3.27
Yes, because the total will be $1.93
No, because the total will be $4.27
No, because the total will be $5.93
Answer:
The answer to your question is A. Yes, because the total will be $3.27
0.35(2)+0.99(2)+0.59≤4.
Then you multiply: .35(2)=.70. .99(2)=1.98.
Then add: .70+1.98+.59=3.27, so yes she can since 3.27 is less than 4 :)
Step-by-step explanation:
I hope this helps and have a good day!
Amy made a circle graph of the U.S. population for 2000. This is the data that she used and the graph that she made.
The true statement is (b). No, because males and females should add up to 100% of the population.
How to determine the true statement?The complete question is added at the end of this solution.
From the complete question, we have the following percentages
Male = 26%Female = 27%When the above percentages are added, we have
Total = 26% + 27%
Evaluate the sum
Total = 53%
The above shows that the display of the circle graph is accurate.
This is so because the total percentage of the male and the female population must add up to 100%
Hence, the true statement is (b). No, because males and females should add up to 100% of the population.
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Complete question
Amy made a circle graph of the U.S. population for 2000. This is the data that she used and the graph that she made. U.S. Population (2000)
A circle graph titled U S Population (2000).
Males, 26 percent;
Females, 27 percent;
White, 39 percent;
Black, 6 percent;
Asian, 2 percent.
Males 138,053,563
Females 143,368,343
White 211,460,626
Black 34,658,190
Asian 10,242,998
Do you think this is an accurate display of the U.S. population? Why or why not?
a. Yes, because the percentages add up to 100%.
b. No, because males and females should add up to 100% of the population.
c. Yes, because the majority of the population is white.
d. No, because the percentage of males and females should be equal.
|6 - (-1.3) + 2| + |4 - (2.8 - 3)|
Answer:
13.5
Step-by-step explanation:
I need the answer to this
Answer:
63.2
Step-by-step explanation:
Corresponding sides of similar triangles are proportional, so
ST/16 = 31.6/8ST = 63.2How does the graph of g(x) = (x − 2)^3 + 6 compare to the parent function of f(x) = x^3?
A. g(x) is shifted 2 units to the right and 6 units down.
B. g(x) is shifted 2 units to the right and 6 units up.
C. g(x) is shifted 2 units to the left and 6 units down.
D. g(x) is shifted 6 units to the left and 2 units down.
Answer: B. g(x) is shifted 2 units to the right and 6 units up.
Step-by-step explanation:
See attached image.
There are 7 roses and 8 daisies in a vase. (a) What is the ratio of daisies to all flowers in the vase? 1 (b) What is the ratio of roses to all flowers in the vase?
Answer:
a. 8:15
b. 7:15
simplify these fractions
xy-xz/y-z
Answer:
[tex]\frac{xy-xz}{y-z} = x[/tex]
Step-by-step explanation:
Hello!
We can simplify the fraction by factoring and canceling out common factors.
Simplify[tex]\frac{xy-xz}{y-z}[/tex][tex]\frac{x(y - z)}{y-z}[/tex][tex]\frac{x(\not y\not-\not z)}{\not y \not- \not z}[/tex][tex]x[/tex]We are left with x as the final simplified form.
Help, please. Thanks.
By trigonometric solution of triangles we conclude that the actor is staying at the balcony of the second floor.
In which floor of the hotel does an actor stay in a balcony?
This problem presents an application of trigonometric resolution of triangles to find the floor where the actor is in terms of the height of the building. Based on the picture seen in the image, we find that all known dimensions of the triangle , three angles and a side, are:
A = 140°, B = 30°, C = 10°, p = 6 m
First, we must find the length of side AP by law of sines:
b / sin 30° = 6 / sin 10°
b = 6 × sin 30° / sin 10°
b ≈ 17.276 m
Second, the height of the building is found by trigonometric functions:
h = (17.276 m) · sin 40°
h ≈ 11.105 m
Therefore, the floor where the actor stays is:
3.8 + 3 · n = 11.105
3 · n = 7.305
n = 2.435
n = 2
By trigonometric solution of triangles we conclude that the actor is staying at the balcony of the second floor.
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Consider the graph of f(x) given below.
A curve labeled f of x declines through the points (negative 4, 7), (negative 3, 6), (negative 2, 5), (0, 3), (2, 1), (3, 0), (4, negative 1), (5, negative 2), (6, negative 3) and (7, negative 4) on the x y coordinate plane.
The function g(x) is a transformation of f(x). If g(x) has a y-intercept of -2, which of the following functions could represent g(x)?
A.
g(x) = f(x + 2)
B.
g(x) = f(x - 5)
C.
g(x) = f(x) - 2
D.
g(x) = f(x) - 5
The functions could represent g(x) is B. [tex]g(x) = f(x - 5)[/tex]
How can the function be determined?Using the general equation [tex]g(x) =f(x)+ b[/tex]
The g(x) has intercept of y=-2,
Then the y-intercept of f(x) is at y=3
If we find the difference between both y-intercepts, we have
( -2 -3) = -5
Then b=-5
Hence, [tex]g(x) = f(x - 5)[/tex] is correct.
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4
Select the correct answer from each drop-down menu.
AABC is similar to ADEF. The ratio of the perimeter of AABC to the perimeter of ADEF is 1:10. T
The length of the longest side of AABC is
2
4
16
30
units. The ratio of the area of AABC to the are.
The ratio of the area of ∆ABC to the area of ∆DEF is; 1:100.
What is the ratio of the area of ∆ABC to the area of ∆DEF?Since, a major criterion for similarity and congruence of triangles is that the ratio of corresponding sides are equal.
On this note, since the task content suggest that the ratio of the perimeters is; 1:10, it follows from conventional mathematics that the ratio of their areas is given as; 1²:10²; 1:100.
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Which of the following rational functions is graphed below?
Answer: A
Step-by-step explanation:
There are vertical asymptotes at [tex]x=-2, 1[/tex], so the denominator should have factors of (x+2) and (x-1).
This eliminates everything except for A.