Answer:
Step-by-step explanation:
Use the Distributive Property to multiply.
3(2x + 7) = (3 x 2x) + (3 x 7)
(3 x 2x) + (3 x 7)
Solve.
3 x 2x = 6x
3 x 7 = 21
6x + 21
You cannot simplify this.
So the answer is 6x + 21.
I'm sorry if I misunderstood.
Good luck mate! :)
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Which function describes this table of values?
Answer:
[tex]y=\frac{4}{5}x[/tex]
Step-by-step explanation:
Equations in the given options are linear, so the table given represent a linear function.
Let the equation of the linear function is,
y = mx + b
Since this equation passes through (0, 0),
0 = m(0) + b
b = 0
Therefore, equation of the line will be,
y = mx
Slope of the line passing through (10, 8) and (5, 4),
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{8-4}{10-5}[/tex]
= [tex]\frac{4}{5}[/tex]
Therefore, equation of the line will be,
[tex]y=\frac{4}{5}x[/tex]
Option (2) will be the answer.
90 POINTS PLEASE HELP Describe the three main trigonometry functions, their ratios and reciprocal functions.
Answer and Step-by-step explanation:
There are three reciprocal trigonometric functions
making a total of six including cosine, sine, and tangent.
→The reciprocal cosine function is secant: sec(Ф)=1/cos(Ф).
→The reciprocal sine function is cosecant, csc(Ф)=1/sin(Ф).
→The reciprocal tangent function is cotangent, expressed two ways: cot(Ф)=1/tan(Ф) or cot(Ф)=cos(Ф)/sin(Ф).
We've already learned the basic trig ratios:
sin(A) = a/c
cos(B) = b/c
tan(C) = a/b
But there are three more ratios to think about:
→Instead of a/c, we can consider c/a
→Instead of b/c, we can consider c/b
→Instead of a/b, we can consider b/a
These new ratios are the reciprocal trigonometric ratios, and we’re about to learn their names.
The cosecant (csc)
The cosecant is the reciprocal of the sine. It is the ratio of the hypotenuse to the side opposite a given angle in a right triangle.
sin(A) = opp / hyp = a/c
csc(A) = hyp / opp = c/a
The secant (sec)
The secant is the reciprocal of the cosine. It is the ratio of the hypotenuse to the side adjacent to a given angle in a right triangle.
cos(A) = adj/hyp = b/c
sec(A) = hyp/adj = c/b
The cotangent (cot)
The cotangent is the reciprocal of the tangent. It is the ratio of the adjacent side to the opposite side in a right triangle.
tan(A) = opp/adj = a/b
cot(A) =adj/opp = b/c
7)
(4y2 - y) - (5y – 2y2) = - (12 – 3y) + 6y? Solve.
Answer:
y=-12/137
Step-by-step explanation:
Does anyone know this ???
Answer:
m<PKN = 270 - m<JKN
Step-by-step explanation:
The measures of the three right angles JKM, MKL, and LKN add to 270 deg.
The measures of the angles JKP and PKN add to 270 deg.
m<PKN = 270 - m<JKN
After heating up in a teapot, a cup of hot water is poured at a temperature of 210°F. The cup sits to cool in a room at a temperature of 70° F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between the temperature of the water and the temperature of the room, as given by the formula below: T = T. + (To - Tale To = the temperature surrounding the object To = the initial temperature of the object t = the time in minutes T= the temperature of the object after t minutes k = decay constant The cup of water reaches the temperature of 197°F after 1.5 minutes. Using this information, find the value of k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 4 minutes. Enter only the final temperature into the input box.
Newton's Law of Cooling:
[tex]T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}[/tex]
[tex]T(t) =[/tex] Temperature given at a time
[tex]t =[/tex] Time
[tex]T_{s} =[/tex] Surrounding temperature
[tex]T_{o}=[/tex] Initial temperature
[tex]e =[/tex] Constant (Euler's number) ≈ 2.72
[tex]k =[/tex] Constant
Using this information, find the value of [tex]k[/tex], to the nearest thousandth, then use the resulting equation to determine the temperature of the water cup after 4 minutes.
First, plug in the given values in the equation and solve for [tex]k[/tex]:
[tex]T(t) =[/tex] 197°, [tex]t =[/tex] 1.5 minutes, [tex]T_{s} =[/tex] 70° and [tex]T_{o}=[/tex] 210°
[tex]T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}\\197=70+(210-70)e^{-1.5k} \\197 -70 = (140)e^{-1.5k} \\127 =(140)e^{-1.5k}\\\frac{127}{140}=e^{-1.5k} \\ln(\frac{127}{140})=-1.5k\\-0.097=-1.5k\\0.0649 = k[/tex]
[tex]k[/tex] ≈ [tex]0.065[/tex]
Let the temperature of the water cup after [tex]t = 4[/tex] minutes be [tex]T(t) = x[/tex]
Now, let's plug the new time and [tex]k[/tex] constant in the equation and solve for [tex]x[/tex]:
[tex]T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}\\\\\x=70+(210-70})e^{-0.065*4}\\\\x=70+(140})e^{-0.26}, -0.26=-\frac{26}{100}=-\frac{13}{50} \\[/tex]
[tex]x=70+(140})e^{-\frac{13}{50}}\\\\[/tex]
[tex]x=70+(140})e^{\frac{1}{\frac{13}{50}}\\\\\\[/tex]
[tex]x=70+e^{\frac{140}{\frac{13}{50}}\\\\\\[/tex]
[tex]x=70+{\frac{140}{\sqrt[50]{e^{13}}}\\[/tex]
[tex]x = 70 +\frac{140}{1.3} \\x=70+107.947\\[/tex]
[tex]x=177.95[/tex] ≈ [tex]178[/tex]
Temperature of water after 4 minutes is 178°
sorry if there's any misspelling or wrong step but I hope my answer is correct ':3
What are the roots of the equation 9x^2 + 54x +82 = 0 in simplest a + bi form?
Answer:
The roots are
[tex]x = - 3 + \frac{1}{3} i \: \: \: or \: \: \: x = - 3 - \frac{1}{3} i \\ [/tex]Step-by-step explanation:
9x² + 54x + 82 = 0
Using the quadratic formula
That's
[tex]x = \frac{ - b\pm \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]From the question
a = 9 , b = 54 , c = 82
Substitute the values into the above formula and solve
That's
[tex]x = \frac{ - 54\pm \sqrt{ {54}^{2} - 4(9)(82)} }{2(9)} \\ x = \frac{ - 54\pm \sqrt{2916 - 2952} }{18} \\ x = \frac{ - 54\pm \sqrt{ - 36} }{18} \\ x = \frac{ - 54\pm 6i}{18} [/tex]Separate the real and imaginary parts
That's
[tex]x = - \frac{54}{18} \pm \frac{6}{18} \: i \\ x = - 3\pm \frac{1}{3} i[/tex]We have the final answer as
[tex]x = - 3 + \frac{1}{3} i \: \: \: or \: \: \: x = - 3 - \frac{1}{3} i \\ [/tex]Hope this helps you
what digit is in the hundredths place 132.054
Answer:
5
Step-by-step explanation:
0 is 10ths 5 is 100ths
Can a translation, a reflection, or a rotation of a figure ever result in an image with
a different size or shape? Explain.
Answer:
no, it will always be the same size and image just in a different placement.
Step-by-step explanation:
No, a translation, a reflection, or a rotation of a figure never results in an image with a different size or shape.
What is a translation?Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.
Each point in a figure is transformed into a rotation by rotating it a specific amount of degrees around another point.
Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point.
Hence, a translation, a reflection, or a rotation of a figure never results in an image with a different size or shape.
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A map has a scale of 6 in. = 8 mi. If you measured the distance between two cities to be 25 in. On the map, how many miles would it actually be?
Answer:
33 2/6 miles
Step-by-step explanation:
So we know that every 6 inches equals 8 miles. To find one mile, we would divide both sides by 8, so every 6/8 of an inch is 1 mile. if the two cities are 25 in apart on a map, that means that we can first do 6*4:8*4 for the ease of it to get 24 inches and 32 miles. So so far it's already 32 miles. Then we have to calculate the leftover one inch. To find out how many miles one inch is, we can divide both sides by 6, so one inch=8/6 of a mile.
So then we add 32+8/6=33 2/6
Tell me if that works for you
4 solutions for z<-6
Answer:
-7, -8, -9, -10
Step-by-step explanation:
Is this actually the whole problem? If so, the answer is anything less than -6. z < -6 includes all the numbers less than -6, so that would include -7, -8, -1000, -6.000001, etc.; you get what I mean. This would NOT include -6, though, because z is less than, not equal to, -6.
You can visualize it on a number line. If every value that could possibly equal z had a dot on it, you would see an infinite number of dots starting from -6 and going left to infinity. Like: <-------------o, if o was -6.
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Geometry and I need help
Answer:
y = 11
Step-by-step explanation:
We use the definition of Supplementary Angles and Adjacent Angles.
Step 1: Set up equation 1 (Definition of Supplementary Angles)
5x - 4 +7x - 8 = 180
Step 2: Solve for x
12x - 4 - 8 = 180
12x - 12 = 180
12x = 192
x = 16
Step 3: Plug in x
5(16) - 4
80 - 4
76°
Step 4: Set up equation 2 (Definition of Supplementary Angles)
76 + 9y + 5 = 180
Step 5: Solve for y
9y + 81 = 180
9y = 99
y = 11
For what value of a is a(2x+3)=9x+15+x an identity?
Answer:
Expand the left side, group like terms on both sides, and get
(2a)x + 3a = 10x + 15
To be true for all x, equate like terms from both sides and get
2a = 10
3a = 15
Solution: a = 5
You can test the answer.
Step-by-step explanation:
Expand the left side, group like terms on both sides, and get
(2a)x + 3a = 10x + 15
To be true for all x, equate like terms from both sides and get
2a = 10
3a = 15
Solution: a = 5
You can test the answer.
2n = 16 What does "n" equal?
1. 0
2. 16
3. 8
4. 32
5. 36
1-1 Relations and Functions The following list details the numbers of tickets sold for a talent show: grade 9: 22; grade 10: 32; grade 11: 41; and grade 12: 30. What are the domain and range of this relation? A. domain: {22, 32, 41, 30}; range: {9, 10, 11, 12} B. domain: {9, 22, 10, 32}; range: {11, 41, 12, 30} C. domain: {9, 10, 11, 12}; range: {22, 32, 41, 30} D. domain: {11, 41, 12, 30}; range: {9, 22, 10, 32}
Answer:
[tex]Domain = \{9, 10, 11, 12\}[/tex]
[tex]Range = \{22, 32, 41, 30\}[/tex]
Step-by-step explanation:
Given
Grade 9: 22
Grade 10: 32
Grade 11: 41
Grade 12: 30
Required
Determine the domain and the range
The domain and range of a function is represented as thus (x,y)
From the given parameters;
[tex](x,y) = (Grade\ 9, 22), (Grade\ 10, 32) (Grade\ 11, 41), (Grade\ 12, 30)[/tex]
Remove "Grade" to represent as only digits
[tex](x,y) = (9, 22), (10, 32), (11, 41), (12, 30)[/tex]
Split to x and y values:
Where x = domain and y = range
[tex]Domain = \{9, 10, 11, 12\}[/tex]
[tex]Range = \{22, 32, 41, 30\}[/tex]
So, from the list of given options; option C answers the question.
Mr. Adams drove his delivery truck 151.2 miles during 2.4 days. He drove the same number of miles each day. How many miles did he drive in one day? *
Answer:
He drove 63 miles in one day
Step-by-step explanation:
151.2/2.4=63
Please answer this question for me please!!! Today I got headaching questions from other subjects and my mind has stopped!☠️ Question number 7, 13, and 16 please!!! It's worth 20 points!!!
Answer:
7a) 5/8 cup
7b) 4 3/8 cup
Step-by-step explanation:
a) Divide 1 1/4 by 2:
Do this by putting the 1 into the fraction and then convert to 8th
1 1/4 = 5/4 = 10/8
(10/8)/2 = 5/8
b) 3 1/2 * 1 1/4 = 7/2 * 5/4 = 7*5/(2*4) = 35/8 = 4 3/8
solve the given equation: 2 x ( x + 3 ) − 6 ( x + 3 ) = 0 2 x ( x + 3 ) - 6 ( x + 3 ) = 0
Answer:
x = 3 or x = -3
Step-by-step explanation:
Solve for x over the real numbers:
2 x (x + 3) - 6 (x + 3) = 0
Expand out terms of the left hand side:
2 x^2 - 18 = 0
2 x^2 - 18 = 2 (x^2 - 9):
2 (x^2 - 9) = 0
Divide both sides by 2:
x^2 - 9 = 0
x = (0 ± sqrt(0^2 - 4 (-9)))/2 = ( ± sqrt(36))/2:
x = sqrt(36)/2 or x = (-sqrt(36))/2
sqrt(36) = sqrt(4×9) = sqrt(2^2×3^2) = 2×3 = 6:
x = 6/2 or x = (-6)/2
6/2 = 3:
x = 3 or x = (-6)/2
(-6)/2 = -3:
Answer: x = 3 or x = -3
Solve the equation for u.
Uw + uq=r
Answer:
u = [tex]\frac{r}{w+q}[/tex]
Step-by-step explanation:
Given
uw + uq = r ← factor out u from each term on the left side
u(w + q) = r ← divide both sides by (w + q)
u = [tex]\frac{r}{w+q}[/tex]
The equation uw + uq = r is solved for u will be written as u = r / (w + q).
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The equation is given below.
uw + uq = r
Simplify the equation for u, then the equation will be written as,
uw + uq = r
u(w + q) = r
u = r / (w + q)
The equation uw + uq = r is solved for u will be written as u = r / (w + q).
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in the adjoining figure, ABC is a right-angled triangle, where
B = 90°, AB = 3 cm and AC
3V2 cm, find the size of ®.
Answer:
the value of theta i 45°
help me with this please! I haven’t found the solution since 11:30 am
Answer:
PT = 22
Step-by-step explanation:
Given that T is the midpoint of PQ, then
PT = TQ , substitute values
5x + 2 = 7x - 6 ( subtract 5x from both sides )
2 = 2x - 6 ( add 6 to both sides )
8 = 2x ( divide both sides by 2 )
4 = x
Thus
PT = 5x + 2 = 5(4) + 2 = 20 + 2 = 22
Which expression represents the measure of segment RS? A.7x – 3 B.7x + 5 C.x + 5 D.x – 3
Answer:
D) x-3
Step-by-step explanation:
(4x+1)-(3x-4)=
4x-3x+1-4=
x-3
At a school carnival, 57 out of 95 tickets sold were early-admission tickets. What percentage
of the tickets were early-admission tickets?
Write your answer using a percent sign (%).
Answer:
60%
Step-by-step explanation:
57/95×100
hope this helps :)
Answer:
60%
Step-by-step explanation:
There is a total of 95 tickets, and 57 of them were early-admission tickets.
To find the percentage, we divide early-admission tickets by the total number of tickets, which is 57/95.
We can then simplify 57/95, getting 3/5, or 0.6, which is 60%.
1/4x -18=-22 please include step by step i already know the answer i just need step by step. will award brainliest.
Answer:
Hope this helps
Step-by-step explanation:
1/4x = -22 + 18
1/4x = -4
4(1/4x) = 4(-4)
x = -16
Find the sum of (4x^3+2x) + (8x^3+4)
Write the numbers in decreasing order.
- 13. – 1.73, - 265,2.18,
Choose the correct answer below.
A.
2.18. - 13. - 1.73, -275
B. 2.18,
- 1.73, -275, -13
c. - 13, - 245, -1.73, 12
4: 2.18
D. -275, - 13, 2.18,
- 1.73
Answer the two please 1. A monopoly playing board is in the shape of a square.The sides measure 19 inches. What is the area of the monopoly board? Use the golf scores below to answer quest 2 72,75,82 75,72,74 2. What is the median golf score? A.74.5 B.74 C.75.5 D.75
Question 6 (1 point)
90 degrees clockwise is the same as?
Answer:
270 degrees counter clockwise
Step-by-step explanation:
360-90=270
How to graph the function (4,32) on a graph that only goes up to 8?
Answer:
Well make sure your answer is correct. If it’s correct extend your graph.
Step-by-step explanation:
100 milk cartons were put out for breakfast, After breakfast, there were 40 milk cartons left. What is the ratio of milk cartons drunk to total milk cartons put out?
Answer:
The ratio of milk cartons drunk to total milk cartons put out= 3 : 5
Step-by-step explanation:
Total milk cartons put out for breakfast=100
Milk cartons left after breakfast=40
Total milk cartons drunk during breakfast = Total milk cartons put out for breakfast - Milk cartons left after breakfast
=100 - 40
=60
Total milk cartons drunk during breakfast = 60
What is the ratio of milk cartons drunk to total milk cartons put out?
Total milk cartons drunk during breakfast : Total milk cartons put out for breakfast
= 60 : 100
=3 : 5
The ratio of milk cartons drunk to total milk cartons put out= 3 : 5
solve the equation (2^2x +2) (2^3x -7)= 2^25
Answer:
[tex]\Huge \boxed{x=6}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
[tex](2^{2x +2}) (2^{3x -7})= 2^{25}[/tex]
When multiplying same bases, add the exponents.
[tex](2^{2x +2+3x -7})= 2^{25}[/tex]
[tex](2^{5x -5})= 2^{25}[/tex]
Cancelling the same bases from both sides.
[tex]5x-5=25[/tex]
Adding 5 to both sides.
[tex]5x=30[/tex]
Dividing both sides by 5.
[tex]x=6[/tex]
[tex]\rule[225]{225}{2}[/tex]