The sum of three consecutive, positive, odd integers such that two times the product of the first and middle integers minus 12 times the third integer is 42 is 27.
Let's assume the three consecutive odd integers to be x, x + 2, and x + 4.
So, their sum can be found by:x + x + 2 + x + 4 = 3x + 6
To find the product of the first and middle integers, we multiply x and x + 2.
So, the product becomes:x(x + 2)
To find two times the product of the first and middle integers, we multiply it by 2. So, it becomes:2x(x + 2)
Now, let's move to the second part of the given question:i.e. "two times the product of the first and middle integers minus 12 times the third integer is 42".
It can be written as:2x(x + 2) - 12(x + 4) = 42
On solving this equation, we get:x = 7
So, the three consecutive odd integers can be written as 7, 9, and 11.
Their sum will be:7 + 9 + 11 = 27
Therefore, the sum of three consecutive, positive, odd integers such that two times the product of the first and middle integers minus 12 times the third integer is 42 is 27.
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What is the solution to the system of equations? (7, 4) (7, startfraction 13 over 3 endfraction) (8, startfraction 14 over 3 endfraction) (9, 7)
The points are (7, 13/3).
Lets simplify the equation,
The equation of first line: y = 1/3 x + 2
the equation of second line: y= 4/3x - 5
Solve the system of equations by elimination,
Multiply equation A by -4 both sides
-4y = -4(1/3x +2)
-4y = -4/3x-8
After eliminating the equation we get,
y = 13/3
So now have to find x
13/3 = 1/3x + 2
Lets multiply above by 3
x = 13-6
x = 7.
Hence the points are (7, 13/3)
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Answer:
B
Step-by-step explanation:
What is the solution to the system of equations?
(7, 4)
(7, StartFraction 13 over 3 EndFraction)
(8, StartFraction 14 over 3 EndFraction)
(9, 7)
Ed wants to buy a new video game system which costs $250. he has
saved $135. ed charges $9 for each lawn he mows. which equation could
be used to find the number of lawns, x, ed must mow to have more than
the amount he needs to buy the video game system?
The required equation is 135 + 9x > 250.
The number of lawns Ed must mow is assumed to be x.
The amount Ed charges for each lawn he mows is $9.
Thus, the total amount Ed earns by mowing x lawns = $9x.
The savings which Ed has is $135.
Thus, the total amount Ed will have to spend can be written as the expression, $(135 + 9x).
The cost of the video game is given to be $250.
We are asked to write an equation, that can be used to find the number of lawns Ed mow, that is x so that the amount Ed has will be more than the amount he needs to buy the video game.
This can be shown as the equation:
Total amount Ed has > Cost of the video game,
or, 135 + 9x > 250.
Thus, the required equation is 135 + 9x > 250.
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The constant of 2/3 cupcakes per minute means that in a minute, 2/3 of a cupcake is made.
Given the graph of w(x), w(2) = ?
(the graph is below)
Based on the graph of the cupcakes done, we find that w(2) = 5.
How many cupcakes are made by the cooker?
Herein we have an application of linear equations to the production of cupcakes. In accordance with the graph, the horizontal axis is for the preparation time (x) and the vertical axis is for the quantity of cupcakes done (w). Based on the graph, we find that w(2) = 5.
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If three different orders are selected, find the probability that they are all from Restaurant B
If three different orders are selected, find the probability that they are all from Restaurant B is; 0.026
How to find the probability?Total orders both accurate and not accurate = 1131
Total orders from restaurant B (both accurate and not accurate) = 337
Probability of first order from B = 337/1131
Probability of second order from B = 336/1130
Probability of third order from B = 335/1129
Probability of the first three orders from B = 337/1131 × 336/1130 × 335/1129
Probability of the first three orders from B = 0.026
Complete question is;
Use the data in the following table , which lists drive - thru order accuracy at popular fast food chains Assume that orders are randomly selected from those included in the table Drive thru Restaurant A B C D Order Accurate 312 277 250 144 Order Not Accurate 32 60 37 19 If three different orders are selected , find the probability that they are all from restaurant A
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A rectangular corral is to be built using 70m of fencing. If the fencing has to enclose
all four sides of the corral, what would be the dimensions to produce the maximum
possible area and what would the area of the corral be? Include a complete solution
Answer:
306 square meters
Step-by-step explanation:
The maximum area is when the length and width are the closest together.
70/2=35 we divide because there are 2 lengths and 2 widths in a rectangle
35/2=17.5, find the 2 closest integers, they are 17 and 18
17*18=306
The triangles are similar. Find the value of the variable.
What is the polar form of -2√3-6i ?
Any complex number [tex]z[/tex] can be written in polar/exponential form as
[tex]z = |z| e^{i\arg(z)} = |z| (\cos(\arg(z)) + i \sin(\arg(z)))[/tex]
In the complex plane, the given complex number belongs to the third quadrant since both its real and imaginary parts are negative. This means the argument must be between π and 3π/2, so the first two options are eliminated.
The difference between the remaining two options is the coefficient [tex]|z|[/tex]. We have
[tex]z = -2\sqrt3 - 6i \implies |z| = \sqrt{(-2\sqrt3)^2 + (-6)^2} = 4\sqrt3[/tex]
so (D) (the last option) is the correct choice.
which function is greater at the given value y=3^x or y=x^3 at x=2
Answer:
[tex] {3}^{x} [/tex]
Step-by-step explanation:
[tex] {x}^{3} = 8[/tex]
[tex] {3}^{x} = 9[/tex]
PLS HELP WITH THIS AND SHOW WORK SHOW WORK
Answer:
option 3
Step-by-step explanation:
6x + 3x² - 4x ← collect like terms
= 6x - 4x + 3x²
= x(6 - 4) + 3x²
= x(2) + 3x²
= 2x + 3x²
Answer:
Option 3: [tex]2x+3x^{2}[/tex]
Step-by-step explanation:
Combine like terms: [tex]6x-4x=2x[/tex]
Put the equation together: [tex]2x+3x^{2}[/tex]
The correct answer option is Option 3: [tex]2x+3x^{2}[/tex].
4. Based on the triangle sum theorem, solve for x.
Answer:
x = 10
Step-by-step explanation:
180 = 90 + 40 + (4x + 10)
180 = 130 + (4x + 10)
4x + 10 = 180 - 130
4x + 10 = 50
4x = 50 - 10
4x = 40
x = 40/4
x = 10
Answer:
x = 10
Step-by-step explanation:
An euclidean triangle is defined to have sum of all 3 interior angles equal to 180°.
In the given triangle, we know three measurement:
4x+1040°90°You may be wondering, where does 90° come from. The answer is you can find it by looking if a triangle has a little square symbol or not. If it does, the measurement will always be 90°.
Now since we know that sum of 3 interior angles must equal to 180° in euclidean triangle. Therefore, sum up three of measurement then set to 180°.
[tex]\displaystyle{90 + 4x+10 + 40= 180}[/tex]
Evaluate and solve for the x-variable:
[tex]\displaystyle{90 + 4x+10 + 40= 180}\\\\\displaystyle{4x+140 = 180}\\\\\displaystyle{4x=180-140}\\\\\displaystyle{4x=40}\\\\\displaystyle{x=10}[/tex]
Therefore, the value of x is 10
Margo spends a quarter of her paycheck on a new dress, one-eighthof her paycheck on shoes, and $24 on a birthday present. if she spent $60 altogether, how much was margo’s paycheck?
Solving a linear equation, we conclude that Margo's paycheck is of 96 dollars.
How much was Margo's paycheck?
We know that she spends one quarter on a dress, one eight on shoes, and $24 on a birthday present.
We also know that she spent a total of $60.
If we define P as Margo's paycheck, then we know that:
(1/4)*P + (1/8)*P + $24 = $60
Now we just need to solve that linear equation for P, we will get:
(2/8)*P + (1/8)*P = $60 - $24 = $36
(3/8)*P = $36
P = (8/3)*$36 = $96
In this way, we conclude that Margo's paycheck is of 96 dollars.
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The measures of the angles of a triangle
are shown in the figure below. Solve for x.
33°
(3x-12)°
Answer:22
Step-by-step explanation:22
In the following diagram, BC is parallel to DE.
What is x?
Answer:
21
Step-by-step explanation:
Using alternate interior angles, we can conclude that angle C is equal to X (the 3rd, unmarked angle in the center triangle)
To find that 3rd angle, we can do 180 - 105 - 54. This is because all angles in a triangle must equal 180. Using this, we find that angle C is equal to 21. By the law, X must also equal 21.
Answer:
x is 21
Step-by-step explanation:
add 54 and 105, then subtract it by 180 and you get 21.
What is the volume, in cubic centimeters, of a cube whose side measures 4 centimeters ?
Fill in the blank by entering only a number as your answer.
The formula for the volume of a cube is-side length^3.
For your problem, side length=4, so the answer is 4^3=64
ANSWER: 64 CUBIC CENTIMETERS hope this helped you
(T-Tb)
help!!!!!!!!!!!! >>>>>Which number set contains all rational
numbers?
The only set that only has rational numbers is the first one:
{1/3, -3.45, √9}
Which of the given sets contains only rational numbers?
A rational number is a number that can be written as the quotient of two integers.
If we look at the first set, the elements are:
1/3 which is a rational number.-3.45 = -345/100 which is a rational number√9 = 3 = 3/1 which is a rational number.In the other sets we can see elements like:
√37, √44, or √2 which are all irrational numbers, then the only correct option is the first one.
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2. Which of the following expressions is equivalent to 322?
01
08.1/1
032.2
08-2
Answer:
C. (32/4)*2
Step-by-step explanation:
C is the correct answer because when we divide 4/2 it equals 2.
Hope this helps!
Answer:
D
Step-by-step explanation:
Given expression:
[tex] \dfrac{32}{4} \times \dfrac{4}{2} \times 2 [/tex]
Evaluation of the given expression:
[tex] = 8 \times 2 \times 2 [/tex]
[tex] = 32 [/tex]
A. [tex] \dfrac{32}{\frac{16}{4}} = \dfrac{32}{4} = 8 [/tex]
B. [tex] 8 \times \dfrac{4}{2} = 8 \times 2 = 16 [/tex]
C. [tex] \dfrac{32}{4} \times 2 = 8 \times 2 = 16 [/tex]
D. [tex]8 \times \dfrac{4}{2} \times 2 = 8 \times 2 \times 2 = 32[/tex]
Only expression D evaluates to the same value as the given expression.
Answer: D
Label the midpoint of PQ as point S, the midpoint of QR as point T, and the midpoint of RP as point U. Next, draw PT, QU, and RS. Which statements are true
The statements that are true based on the midpoint given in the question include:
m∠P + m∠Q + m∠R = 180°PT, QU, and RS intersect at the same point.What is midpoint?In geometry, the midpoint simply means the middle point of a line segment. The midpoint is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
Also, it should be noted that the midpoint bisects the segment.
In this case, m∠P + m∠Q + m∠R = 180°. This is because the sum of the angles in a triangle will be equal to 180°. Also, PT, QU, and RS intersect at the same point.
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Complete question:
Label the midpoint of PQ as point S, the midpoint of QR as point T, and the midpoint of RP as point U.
Next, draw PT, QU, and RS.
Which statements are true?
m∠Q = m∠R
The length of QU is half the length of RP.
m∠P + m∠Q + m∠R = 180°
QU ≅ RS
PT, QU, and RS intersect at the same point.
The sum of the lengths of QU and RS is equal to the length of PT.
It is estimated that the average person in the US uses 123 gallons of water per day. Some environmentalists believe this figure is too high and conducted a survey of 40 randomly selected Americans. They find a mean of 113.03 gallons and a standard deviation of 25.99 gallons. Calculate the appropriate test statistic to test the hypotheses.
The value of test statistic is Z = -2.42.
According to the statement
we have given that the person in the US uses 123 gallons of water per day.
And conducted a survey of 40 randomly selected Americans and get a mean value is 113.03 gallons and a standard deviation of 25.99 gallons.
And we have to test the hypotheses with test statistic.
So,
Here we use the the z- test for one population =
Z = (sample mean - Claimed hypothesis mean)/ (standard deviation/(sample size)^1/2.)
Here the sample mean = 113.03
And claimed hypothesis mean = 123
Standard deviation = 25.99
Sample size = 40
Now put the values in the above written formula is
Z = (sample mean - Claimed hypothesis mean)/ (standard deviation/(sample size)^1/2.)
Z = 113.03 - 123 / (25.99/(40)^1/2)
Z = -9.97 / (25.99 / 6.32)
Z = -9.97 / 4.11
Z = -2.42
So, The value of test statistic is Z = -2.42.
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HELP !! Which of the following points lies on the graph of this equation? y =2x -2
Answer:
A.
Step-by-step explanation:
i'm 99% sure!
Answer:
B
Step-by-step explanation:
Plug in the coordinates.
Evaluate if a = - 3 and c = 5
- Зас
7
Answer:
315
Step-by-step explanation:
-3ac7
-3x-3=9x5=45x7=315
❄ Hi there,
evaluate this expression by using substitution:
If
a=-3c=5then
-3ac= (see below)[tex]\sf{-3(-3)(5)}[/tex]
[tex]\sf{9\times5}[/tex]
[tex]\triangleright \ \sf{45}[/tex]
That's it!
❄
please help me it is an easy question
Answer:
200 yd²
Step-by-step explanation:
A = 17 yd
B = 15 yd
C = 2 yd
D = 8 yd
b) Area of rectangle = length * width
[tex]\sf Area \ of \ 2 \ triangle = 2* \dfrac{1}{2}* base * height = base* height\\\\[/tex]
Area of right triangular prism = Areas of two triangle + area of the upper rectangle + area of middle rectangle + area of below rectangle
= 8 * 15 + 17 * 2 + 15 *2 + 8*2
= 120 + 34 + 30 + 16
= 200 yd²
Please help me! Giving brainliest!
Identify the surface area
A. S=2332 m²
B. S=2283 m²
C. S=2234 m²
D. S=1919 m²
Using it's formula, the surface area of the figure is:
A. S=2332 m²
What is the surface area of a rectangular prism?The surface area of a rectangular prism of dimensions l, w and h is given by:
S = 2(lw + lh + wh)
In this problem, the dimensions are:
35m, 9m, 16m
Hence the surface area of the rectangular prism is:
S = 2(35 x 9 + 35 x 16 + 16 x 9) = 2038 m².
What is the surface area of a cube?The surface area of a cube of side length l is given by:
S = 6l².
In this problem, we have that l = 7 m, hence the surface area is:
S = 6 x 7² = 294 m².
What is the total surface area?
The total surface area is the sum of the surface areas, hence:
T = 2038 m² + 294 m² = 2332 m².
Which means that option A is correct.
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8. A spinner is divided into 6 equal sections o
numbered 1 through 6. What is the probability
that the arrow will land on a multiple of 3?
(A) =
(B)
116113-1
(C) 1/12
(D) 1
8 (0)
81(0)
Cla
brosse und Ato mondo Fran
S(A)
(80)
Answer:
1/3
Step-by-step explanation:
The numbers are 1, 2, 3, 4, 5, and 6.
Both 3 and 6 are multiples of 3.
So, 2/6 is the probability since there is an equal change that the arrow will land on each section.
This simplifies to 1/3.
Brainliest, please :)
Answer:
P (multiple of 3) = [tex]\bf \frac{1}{3}[/tex]
Step-by-step explanation:
Numbers on the spinner, ξ = {1, 2, 3, 4, 5, 6} (6 elements)
Multiples of 3 = {3, 6} (2 elements)
P (multiple of 3) = no. of multiples of 3 / total no. of numbers on spinner
= [tex]\frac{2}{6}[/tex]
= [tex]\bf \frac{1}{3}[/tex]
Question 6 (1 point)
Find m/RST.
(4x-24)
U
S/(3x)*
O a m/RST = 72°
Ob
mZRST 108⁰
Oc
mZRST = 156°
Od mZRST = 24°
Answer:
72°
Step-by-step explanation:
3x = 4x - 24 (alternate exterior angles theorem)
x = 24
So, angle RST measures 72°.
determine the slope of the line
Answer: -1/2
Step-by-step explanation:
The slope of a line tells you how steep the line is, and what direction it is going in. We can calculate the slope by seeing how much the line moves horizontally and vertically.
We can calculate the slope using [tex]\frac{rise}{run}[/tex], which is how much a point rises (goes up or down) and runs (goes left or right) to go to the next point.
Let's take two points on the graph: (-2, 0) and (0, -4). The rise will be the difference of the y-values, and the run will be the difference of the x-values.
[tex]\frac{-2-0}{0-(-4)}=\frac{-2}{4}=\frac{-1}{2}[/tex]
Hence, the slope of this line is [tex]\frac{-1}{2}[/tex]
Could someone please draw the triangle based off of this description
The altitudes of equal length, BE and CF gives AB = AC, from which we have;
∆ABC is an isosceles triangleHow can the RHS rule be used to indicate an isosceles triangle?From the given description, we have;
BE = CF
<CFB = <BEC = 90° All right angles are congruent
BC = BC by reflexive property of congruency
BC = The hypotenuse side of triangles ∆BFC and ∆CEB
Therefore;
∆BFC is congruent to ∆CEB by Right angle Hypotenuse Side, RHS, rule of congruency.
Therefore;
BF = CE by Corresponding Parts of Congruent Triangles are Congruent, CPCTC
Similarly, we have;
∆AEB is congruent to ∆AFC, by Side-Angle-Angle, SAA, rule of congruency
Which gives;
FA = AE by CPCTC
BF + FA = CE + AE, by substitution property of equality
BF + FA = AB
CE + AE = AC
Therefore;
AB = ACTherefore;
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Will’s meal of grilled chicken strips and carrots contained a total of 333 calories. The bag of grilled chicken strips contained x servings of 110 calories each. The bag of carrots contained y servings of 29 calories each. Which equation written in standard form represents the number of servings of chicken strips and carrots that Will may have eaten?
110y = –29x + 333
29x + 110y = 333
29y = –110x + 333
110x + 29y = 333
Answer:
correct answer is 110x + 29y = 333
Step-by-step explanation:
‼️‼️PLEASE HELP I WILL MARK BRAINLIEST ‼️‼️Dilate the figure by the scale factor. Then enter
the new coordinates.
C(-2,1)
A(1,4)
B(2,2)
K = 6
A' ([?], [])
B' ([ ], [ ])
C' ([ ], [ ])
Answer:After dialation
A'=6,24
B'=12,12
C'=-12,6
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Bill and his classmates completed 14 activities in 4 hours. what is the unit rate at which they ocompleted the activities
Step-by-step explanation:
we first divide fourteen by four
14/4= 3.5
then we change 0.5 to hours by multiplying by 60
0.5 * 60 = 30
so in conclusion it would take 3hrs 30mins to finish each activity
Island A is 160 miles from island B. A ship captain travels 170 miles
from island A and then finds that he is off course and 200 miles from
island B. What bearing should he turn to, SO he is heading straight
towards island B?
The ship captain should be turned 129.49 so it's heading straight for Island B.
Given Island A is 160 miles from Island B and the captain of a ship travels 170 miles from Island A and then discovers that he is off course and 200 miles from island B.
So we gave it
a = 200 feet
b = 170 feet
c = 160 feet
We need to find angle C which goes directly to island B.
We apply the "cosine law":
[tex]\begin{aligned}\cos C&=\frac{a^2+b^2-c^2}{2ab}\\ &=\frac{(200)^2+(170)^2-(160)^2}{2\times 200\times 170}\\ &=\frac{40000+28900-25600}{68000}\\ &=\frac{43300}{68000}\\ &=0.636\end[/tex]
Now we multiply both sides by cos⁻¹, we get
cos⁻¹(cos C)= cos⁻¹(0.636)
C = 50.51
The interior angle is 50.51°
We need to find the outer angle to find the bearing the captain needs to turn
Applying the additional angle ruler:
The outside angle = 180 - 50.51 = 129.49°
Therefore, he must turn so as to head directly for Island B, where Island A is 160 miles from Island B and the captain is sailing 170 miles.
from Island A and then discovers that it is off-road and 200 miles away
Island B is 129.49.
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