Final answer:
By inserting parentheses to create the expression (6 + 10) x 2, we change the order of operations and get the desired result, which is 32.
Explanation:
The question involves inserting parentheses in the expression 6 + 10 x 2 so that the result of the expression equals 32. According to the order of operations, we typically perform multiplication before addition, so if we compute the expression as it stands, we would get 6 + (10 x 2) = 6 + 20 = 26, which is not the result we want. To achieve the desired result, we need to adjust this order. By adding parentheses, we can change the order in which the operations are performed. Thus, the correct placement of parentheses would be (6 + 10) x 2, which gives us (16) x 2 = 32.
An angle whose measure is 405 is in standard position. In what quadrant does the terminal side of the angle fall?
Answer:
The angle is in quadrant one because one rotation is 360° and it’s just 45° more than 360°.
Q1
Which of the following is the equation of a parabola with focus (0,2) and directrix y = -2?
Answer:
Alright well find the parabola with focus (0,2) and directrix y = - 2 So the Answer to the question is
x^2 = 8y Hope this helps have a nice day :)
Step-by-step explanation:
Answer:
the answer is (B) y = 1/8 x^2.
Step-by-step explanation:
How many solutions does the system of equations have ? Y= 6x +2 and 3y-18x=12
Answer:
0 solutions
Step-by-step explanation:
same slope, different y intercepts so they never intersect
Answer:
As both slopes are equal, and the values of b are different it means that the two lines are parallel and the system of equations does not have any solution. (Please see the picture below)
Step-by-step explanation:
1. First write the system of equations:
[tex]y=6x+2[/tex]
[tex]3y-18x=12[/tex]
2. Solve y for the second equation:
[tex]3y-18x=12[/tex]
[tex]3y=18x+12[/tex]
[tex]y=\frac{18x+12}{3}[/tex]
[tex]y=6x+4[/tex]
3. Re write both equations in the form y=mx+b, where m is the slope and b is the value of y when x=0 :
[tex]y=6x+2[/tex]
[tex]y=6x+4[/tex]
As both slopes are equal, and the values of b are different it means that the two lines are parallel and the system of equations does not have any solution.
HELPP PLEASE I WILL CROWN YOU!!!!!
(Solve for X)
Please make sure it correct
Thank you
Answer:
x=9
Step-by-step explanation:
These two angles are equal because they are corresponding angles and the two lines are parallel.
13x-7 = 11x+11
Subtract 11x from each side
13x-11x -7 = 11x-11x+11
2x-7 = 11
Add 7 to each side
2x-7+7 = 11+7
2x = 18
Divide each side by 2
2x/2 = 18/2
x =9
The cheese club members bought 6 tickets to a tournament for $15 how much would they have paid if all 9 members wanted to go
First you have to find out the cost of the ticket. To do so you have to Divide 15 and 6. Which equals $2.50. So each ticket is $2.50 dollars. Now you have to multiple 2.50 times 9. which equals 22.5. So your total answer is $22.50 dollars
find tge slope and the y-Intercept 7x-9y=1
Solve: -6x-1+5x^2=8x^2
Answer:
[tex]x_{1} = -1 - \sqrt{\frac{2}{3}} ; x_{2} = -1 +\sqrt{\frac{2}{3}}[/tex]
Step-by-step explanation:
-6x -1 + 5x² = 8x² Move all terms to the right-hand side
0 = 8x² - 5x² + 6x +1 Combine like terms
3x² + 6x + 1 = 0
Apply the quadratic formula
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
a = 3; b = 6; y = 1
[tex]x = \frac{-6\pm\sqrt{6^2 - 4\times 3 \times1}}{2\times 3}[/tex]
[tex]x = \frac{-6\pm\sqrt{36-12}}{6}[/tex]
[tex]x = \frac{-6\pm\sqrt{24}}{6}[/tex]
[tex]x = \frac{-6\pm \sqrt{4\times6}}{6}[/tex]
[tex]x = \frac{-6\pm 2\sqrt{2}}{6}[/tex]
[tex]x = -1 \pm \sqrt{\frac{2}{3}}[/tex]
[tex]x_{1} = -1 +\sqrt{\frac{{2}}{3}}; x_{2} = 1 -\sqrt{\frac{{2}}{3}}[/tex]
The graph below shows the roots at x₁ =-1.816 and x₂ = -0.184.
A loan given to people who are purchasing real estate is called a a______. amortization loan B. real estate loan C. house loan D. mortgage
Answer:
Option D. mortgage
Step-by-step explanation:
A loan given to people who are purchasing real estate is called mortgage.
Answer:
D. mortgage
Step-by-step explanation:
-Amortization loan is a loan in which the payments are applied to the principal and the interests.
-Real estate loan is a loan that people use to buy real estate.
-House loan refers to a loan people use to buy a home.
-Mortgage is a type of loan that financial institutions provide for people to buy a property.
According to this, the answer is mortgage.
how many tenths are in 3.6
Answer:
Step-by-step explanation:
3.6/10=3.3/5
получется 3 целых 6 десятых сокращаем и получается 3 целых 3 пятых
A 5 pound bag of potatoes cost $3.40 what is the cost per pound
It would be $0.68.
To find it, divide the cost by the weight. So, the equation would be 3.40/5 or 3.40 divided by 5.
The cost per pound of potato would be $0.68.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
We are given that 5 pound bag of potatoes cost $3.40
Then the cost per pound of potato .
We have to divide the cost by the weight.
So, the equation would be;
3.40 divided by 5.
3.40/5 = 0.68
The cost per pound of potato would be $0.68.
Learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
#SPJ2
pleaseeee helppp i keep getting the wrong so can somebody give me the correct answer
Answer: 39.25 miles per gallon.
Step-by-step explanation: To find miles per gallon, divide 314 miles by 8 gallons =
39.25 miles per gallon.
The answer is 39.25
note: if your teacher wants a fraction instead of a decimal, then it would be 157/4
=============================
Explanation:
Divide 314 over 8 to get 314/8 = 157/4 = 39.25
----
You can think of it as the ratio
314 miles: 8 gallons
(314/8) miles: (8/8) gallons <--- divide both parts by 8
(157/4) miles: 1 gallon
39.25 miles: 1 gallon
Meaning you can drive 39.25 miles on one gallon of gas
Kate and did a hike at an elevation of 400 m above sea level she had started at an elevation 02 150 m below sea level which integer represents Kates change in elevation
Answer:
2550 m
Step-by-step explanation:
Change in elevation = 400 – (-2150)
Change in elevation = 400 + 2150
Change in elevation = 2550 m
how long is the flight from baltimore to miami
Answer:
The flight from Baltimore to Miami
has a duration around 2 hours and 50 minutes
Step-by-Step Explanation:
2hr 50min duration with at least 12+ flights per day
i am completely lost... Is this a direct variation or an inverse variation? Explain.
You get 5x=y. The larger the x, the larger the y. So, this is a direct variation.
if the discount is 30% and the sale price is $206.50 what is the original price
To determine the original price before a 30% discount resulted in a sale price of $206.50, we calculate the sale price as 70% of the original price, leading to the original price being $295.00.
Explanation:If the discount is 30% and the sale price is $206.50, we need to determine the original price before the discount. To do this, we first understand that the sale price represents 70% of the original price, because a 30% discount has been applied. Thus, to find the original price, we can set up the following equation where original price × 70% = $206.50.
Converting 70% to decimal form, we get 0.70. The equation then becomes original price × 0.70 = $206.50. To find the original price, we divide both sides of the equation by 0.70:
Original price = $206.50 / 0.70
Original price = $295.00
Therefore, the original price of the item before the 30% discount was applied is $295.00.
prove that sin3a-cos3a/sina+cosa=2sin2a-1
Answer:
[tex]\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1[/tex]
Step-by-step explanation:
we are given
[tex]\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1[/tex]
we can simplify left side and make it equal to right side
we can use trig identity
[tex]sin(3a)=3sin(a)-4sin^3(a)[/tex]
[tex]cos(3a)=4cos^3(a)-3cos(a)[/tex]
now, we can plug values
[tex]\frac{(3sin(a)-4sin^3(a))-(4cos^3(a)-3cos(a))}{sin(a)+cos(a)} [/tex]
now, we can simplify
[tex]\frac{3sin(a)-4sin^3(a)-4cos^3(a)+3cos(a)}{sin(a)+cos(a)} [/tex]
[tex]\frac{3sin(a)+3cos(a)-4sin^3(a)-4cos^3(a)}{sin(a)+cos(a)} [/tex]
[tex]\frac{3(sin(a)+cos(a))-4(sin^3(a)+cos^3(a))}{sin(a)+cos(a)} [/tex]
now, we can factor it
[tex]\frac{3(sin(a)+cos(a))-4(sin(a)+cos(a))(sin^2(a)+cos^2(a)-sin(a)cos(a)}{sin(a)+cos(a)} [/tex]
[tex]\frac{(sin(a)+cos(a))[3-4(sin^2(a)+cos^2(a)-sin(a)cos(a)]}{sin(a)+cos(a)} [/tex]
we can use trig identity
[tex]sin^2(a)+cos^2(a)=1[/tex]
[tex]\frac{(sin(a)+cos(a))[3-4(1-sin(a)cos(a)]}{sin(a)+cos(a)} [/tex]
we can cancel terms
[tex]=3-4(1-sin(a)cos(a))[/tex]
now, we can simplify it further
[tex]=3-4+4sin(a)cos(a))[/tex]
[tex]=-1+4sin(a)cos(a))[/tex]
[tex]=4sin(a)cos(a)-1[/tex]
[tex]=2\times 2sin(a)cos(a)-1[/tex]
now, we can use trig identity
[tex]2sin(a)cos(a)=sin(2a)[/tex]
we can replace it
[tex]=2sin(2a)-1[/tex]
so,
[tex]\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1[/tex]
Answer:
To prove : sin(3a)-cos(3a)/sin(a)+cos(a) = 2sin(2a)-1
Step-by-step explanation:
\frac{\sin3a-\cos3a}{\sin a+\cos a}=2\sin 2a-1\\\cos3a=4\cos^{3}a-3\cos a\\\sin 3a=3\sin a-4\sin ^{3}a\\substituting the value, we get\\L.H.S= \frac{3\sin a-4\sin ^{3}a-[4\cos ^{3}a-3\cos a]}{\sin a+\cos a}\\\frac{3(\sin a+\cos a)-4(\sin ^{3}a+4\cos ^{3}a)}{\sin a+\cos a}\\\frac{3(\sin a+\cos a)-4[(\cos a+\sin a)(\cos ^{2}a+\sin ^{2}a-\sin a\cos a)]}{\sin a+\cos a}\\\frac{3(\sin a+\cos a)-4[(\cos a+\sin a)(1-\sin a\cos a)]}{\sin a+\cos a}\\\frac{(\sin a+\cos a)[3-4(1-\sin a\cos a)]}{\sin a+\cos a}\\\frac{(\sin a+\cos a)[3-4+4\sin a\cos a]}{\sin a+\cos a}\\\frac{(\sin a+\cos a)(-1+4\sin a\cos a)}{\sin a+\cos a}\\-1+4\sin a\cos a\\-1+2\sin 2a\\2\sin 2a-1=R.H.S
Since, sin(2a)= 2sin(a)cos(a)
2sin(2a)= 4sin(a)cos(a)
Is 3x+12-2x equivalent to x +12? Use two properties of operations to justify your answer.
Answer:
Yes, x + 12
Step-by-step explanation:
Simplify the following:
3 x - 2 x + 12
Grouping like terms, 3 x - 2 x + 12 = (3 x - 2 x) + 12:
(3 x - 2 x) + 12
3 x - 2 x = x:
Answer: x + 12
Answer:
Yes, it is.
Step-by-step explanation:
3x + 12 - 2x =
Use the commutative property of addition to change the order of the addition.
= 12 + 3x - 2x
Use the distributive property of addition over multiplication in reverse (which is factoring).
= 12 + x(3 - 2)
Do the operation: 3 - 2 = 1
= 12 + x * 1
Simplify x * 1 to just x.
= 12 + x
Use the commutative property of addition.
= x + 12
There you have x + 12 from 3x + 12 - 2x by using properties and operations.
PLEASE HELP
Write a ratio for the situation in three ways, comparing the first quantity to the second quantity. A zoo has 17 monkeys and 12 chimpanzees. (1 point) 12 to 17, 12:17, twelve over seventeen17 to 12, 17:12, 17 over 1217 to 22, 17:22, 17 over 1217 to 12, 12:17, 17 over 12
2. Write a ratio for the situation in three ways, comparing the first quantity to the second quantity. In Largo City, about one in every nine homes contains four televisions. (1 point)
1 to 9, 1:9, 1/91 to 4, 1:4, 1/44 to 9, 4:9, 4/99 to 13, 9:13, 9/13
3. Write three ratios equal to 7 over 35. (1 point) 1 over 7, 2 over 14, 3 over 21five sevenths, 10 over 7, 15 over 77 over 35, seven over forty, seven over forty fiveone fifth, two tenths, three over fifteen
4. Jake sold 28 tickets to the school fair, and Jeanne sold 21 tickets. What is the ratio, in simplest form, of the number of tickets Jeanne sold to the number of tickets Jak
Final answer:
The ratio of monkeys to chimpanzees is 17 to 12. For the televisions in Largo City homes, the ratio is 1 to 9. Three ratios equal to 7 over 35 are 1 over 5, 2 over 10, and 3 over 15. Lastly, the simplest form of the tickets ratio is 3 to 4.
Explanation:
To write a ratio for the situation in three ways, comparing the first quantity to the second quantity for a zoo that has 17 monkeys and 12 chimpanzees, you would use the following ratios:
17 to 12, 17:12, 17 over 12For the scenario where one in every nine homes contains four televisions in Largo City:
1 to 9, 1:9, 1 over 9Writing three ratios equal to 7 over 35:
1 over 5, 2 over 10, 3 over 15To find the ratio in the simplest form of the number of tickets Jeanne sold to the number of tickets Jake sold when Jake sold 28 tickets and Jeanne sold 21 tickets:
The ratio would be 21 to 28 which simplifies to 3 to 4, 3:4, 3 over 4.3(x−0.50)=5.97
what does x equal?
Answer:
x=2.49
Step-by-step explanation:
3(x−0.50)=5.97
Distribute the 3
3x - 3*.5 = 5.97
3x -1.5 = 5.97
Add 1.5 to each side
3x -1.5+1.5 = 5.97+1.5
3x = 7.47
Divide each side by 3
3x/3 = 7.47/3
x=2.49
The stem and lead plot below displays the ages of 30 attorneys at a small firm
Stems | Attorneys
2 | 99
3 | 00112589
4| 1234458
5| 1233458
6 | 0137
7 | 12
What is the age of the oldest attorney? What is the age of the youngest attorney?
HELP PLEASE!!!!!!!!!!!!
Karen is using an indirect method to prove that segment DE is not parallel to segment BC in the triangle ABC shown below:
She starts with the assumption that segment DE is parallel to segment BC. Which inequality will she use to contradict the assumption?
A. 6:7 ≠ 2:7
B. 6:8 ≠ 7:10
C. 6:2 ≠ 7:10
D. 6:2 ≠ 3:2
Answer:
Option B
Step-by-step explanation:
In order to prove that segment DE is not parallel to segment BC, Karen takes an indirect way, that is she assumes that DE is parallel to BC, then by using the basic proportionality theorem,
[tex]\frac{AD}{AB}=\frac{AE}{AC}[/tex]
Now, AD=6, AB=AD+DB=8, AE=7 and AC=10
therefore, [tex]\frac{6}{8}=\frac{7}{10}[/tex] according to basic proportionality theorem, but in actual, [tex]\frac{6}{8}{\neq}\frac{7}{10}[/tex].
Thus, DE is not parallel to BC, therefore Option B is correct.
Answer:
B, 6:8 ≠ 7:10.
Step-by-step explanation:
the body building club has an annual fee of $350. You plan to visit 10 times each month. how much is your cost per visit?
Answer:
≈ $2.92 per visit
Step-by-step explanation:
10 times each month
so 12 months = 12 x 10 = 120
an annual fee of $350
$350 / 120 ≈ $2.92
T(p) is a function that models the average yearly temperature based on the degree latitude(p) of the location on earth. The lines of latitude run from East to West, but they are measured in terms of North and South, extending from −90° to +90°. Which domain is appropriate for this function?
Answer:
All the real numbers between [tex]\pm 90^\circ[/tex] including [tex]\pm 90^\circ[/tex].
Step-by-step explanation:
T(p) models the average yearly temperature based on degree latitude of the location.
Since the lines of latitude runs from East to West and extending from [tex]-90^\circ[/tex] to [tex]+90^\circ[/tex], they can be included in the domain.
Also, the degrees of latitude can be fractional units, positive units, or negative units. Therefore, the domain appropriate for this function is All the real numbers between [tex]\pm 90^\circ[/tex] including [tex]\pm 90^\circ[/tex].
Answer:
D = all real numbers between ± 90, inclusive
Step-by-step explanation:
Degrees of latitude can be fractional units, positive units, or negative units.
**If you are on USA Test prep, the correct answer choice should be Dwhat value of p makes the equation true? 3/4p + 1/6 = 37/60
Question
what value of p makes the equation true? 3/4p + 1/6 = 37/60
Answer:
yes, p makes the equation true and it's value is 3/5 or 0.6Step-by-step explanation:
3/4p + 1/6 = 37/60
3/4p = 37/60 - 1/6
3/4p = 9/20
p = 9/20 : 3/4
p = 9/30 * 4/3
p = 3/5
-------------------
check
3/4 * 3/5 + 1/6 = 37/60
37/60 = 37/60
the answer is good
It takes 24 feet of fence to surround a square piece of land in Sam's backyard. Sam wants to plant flowers everywhere but on the diagonal sidewalk (shaded in the diagram attached). Note that there is 1 foot of sidewalk along two sides of the square as indicated in the diagram attached. What is the area of the sidewalk?
Answer:
Option B. 5.5 ft²
Step-by-step explanation:
Perimeter of the square piece of land = length of fence required
4(length of a side of the square) = 24 ft
Length of a side = 6 ft
Area of the square land = (Side)²
= 6²
= 36 square ft
Area of the side walk = Area of the square - [Area of two triangles separated by the sidewalk]
= 36 - [[tex]\frac{1}{2}(\text{Area of the square})+\frac{1}{2}(\text{Base})\tmes (\text{height})[/tex]]
= 36 - [[tex]\frac{36}{2}+\frac{1}{2}(6-1)(6-1)[/tex]]
= 36 - (18 + 12.5)
= 36 - 30.5
= 5.5 ft²
Therefore, Option B. is the correct answer.
Using synthetic division, what is the quotient (3x^3 + 4x − 32) ÷ (x − 2)?
Answer:
q1 = 3x^2 + 6x + 16
Step-by-step explanation:
2 || 3 0 4 - 32
6 12 32
========================
3 6 16 0
q(x) + r(x)/(x - 2)
r(x) = 0
q(x) = 3x^2 + 6x + 16
This does not factor down any further unless you have take complex number. The only real root isw
x = 2
Just in case you have done complex numbers
x2 = -1 + 2.0817i
x3 = -1 - 2.0817i
Plz Help I do not understand this
Cain is about to start a new job and his opponent employer has offered him two different options to get paid. Option A gives Cain $20 to start plus an additional $10 an hour option b gives Kane $40 to start plus an additional $5 an hour. Define your variables then create a system of equations.
Define Variables:
x =______
y =______
Equations
Option A: ______
Option B: ______
Hello,
So Y variable is what you would start with.
20 <= he'll start off with for a
40 <= what he'll start off with for b
And X variables would be the # of hours you're working.
10 <= meaning every hour worked is worth 10 dollars
5 <= meaning every hour worked will be paid 5 dollars
So let's just say for option a he works two hours
(Option A)
10 (2) + 20
20 + 20
= 40
(Option B)
5 (2) + 40
10 + 40
50
As for your equations
Y = 10x + 40
Y= 5x + 40
An ice sculpture is melting because of heat. Assuming its height changes bynegative 5 over 32m every hour, what will be the change in height after 4 hours? negative 20 over 8 meters 5 over 8 meter negative 5 over 32 meter negative 5 over 8 meter
Answer:
[tex]-\frac{-5}{32} *4=- \frac{5}{8}[/tex]
Step-by-step explanation:
Answer:
- 5/8
Step-by-step explanation:
To solve you would do - 5/32 times 4/1 to get 20/32, then you would simplify to get 10/16, then you would simplify that to get - 5/8.
what other information must be given in order to be able to prove the two triangles congruent by AAS
Define perpendicular lines.
A.
Lines that cut across two or more lines.
B.
Two coplanar lines that intersect at a 90 degree angle.
C.
Two coplanar lines that do not intersect.
D.
Two non–coplanar lines that do not intersect
Perpendicular lines are two coplanar lines that intersect at a 90-degree angle, option B in the question.
Perpendicular lines are defined as two coplanar lines that intersect at a 90 degree angle. This means that the correct answer to the given question is B. It's important to understand that when lines are perpendicular, they create four right angles at the point where they intersect. Various geometrical theorems relate to the properties of perpendicular lines, for example:
Theorem 15 states that if two planes are perpendicular, a line drawn in one perpendicular to their intersection is perpendicular to the other plane.
Theorem 14 explains that if a line is perpendicular to two intersecting lines at their intersection, it is perpendicular to all lines on their plane that pass through this point.
Theorem 11 describes that if two equal lines in a plane are erected perpendicular to a given line, the line joining their extremities will make equal angles with them.
In advanced contexts, such as the geometry of spacetime, perpendicularity can be defined differently, often using the concept of the dot product being zero to identify perpendicular vectors.