Answer:
[tex]11, 13, 15[/tex]
B) 6x + 16 = 82
Note: I just kept my wrong approach.
Step-by-step explanation:
Let first define an odd integer.
Considering [tex]x\in\mathbb{Z}: 2k+1[/tex], [tex]x[/tex] is an odd integer.
Now, three consecutive odd integers are [tex]a_1 = 2k+1[/tex] , [tex]a_2 = 2k+3[/tex] and [tex]a_3 = 2k+5[/tex]
The sum of the first, two times the second and three times the third can be written as
[tex]a_1 + 2a_2 + 3a_3 = 2k+1 + 2(2k+3)+3(2k+5)[/tex]
Expanding and simplifying
[tex]2k+1 + 2(2k+3)+3(2k+5) = 2k+1 +4k+6+6k+15 = 12k+22[/tex]
This is what I have done initially, but considering [tex]x[/tex] to be an odd integer, three consecutive integers can be written as
[tex]x, x+2, x+4[/tex] such that [tex]x\in\mathbb{Z}: 2k+1[/tex]
Therefore,
[tex]x+2(x+2)+3(x+4)=82 \implies x+2x+4+3x+12 = 82 \implies 6x+16 = 82[/tex]
and [tex]6x+16 = 82 \implies 6x = 66 \implies x = 11[/tex]
The three consecutive odd integers such that the sum of the first, two times the second and three times the third is 82 are [tex]11, 13, 15[/tex]
Brandie lives on the twelfth floor of her apartment building. She walks down 2 flights to visit a friend, then up 3 flights to deliver a message to a neighbor. Which integer best represents the number of flights Brandie must walk to get back to her starting point?
Answer:
1
Step-by-step explanation:
12 - 2 + 3 = 13
13 - 12 = 1
Answer:
-1
Step-by-step explanation:
she must walk down 1 flight of stairs
PLS HELP ASAP, THANK YOU
PS. WILL MARK BRAINLIEST
i am so sorry me dont know
Answer:
Answer: Composite figure: 360 ft3
Explanation:
The volume of the triangular prism:
The base area of the prism = 1/2 x 4 x 6 = 12 ft2
Height = 6 ft
The volume of the triangular prism = 12 x 6 = 72 ft3
The volume of the rectangular prism:
The base area of the prism = 4 x 6 = 24 ft2
Height = 12 ft
The volume of the triangular prism = 12 x 24 = 288 ft3
Volume of the composite figure = (288 + 72)ft3 = 360 ft3
Step-by-step explanation:
The pressure resulting from a force of 50 N exerted over an area of 5 m2 is (2
marks)
Answer:
[tex]pressure = \frac{force}{area} \\ = \frac{50}{5} \\ = 10 \: N {m}^{ - 2} [/tex]
Solve the inequality. k - 3 < 5
Answer and Step-by-step explanation:
To solve the inequality, we have to get k by itself.
Add 3 to both sides of the inequality.
k < 8 is the answer.
#teamtrees #PAW (Plant And Water)
Look at the cone above. If r = 4 cm and h = 4 cm, what is the volume of the cone? (Assume = 3.14) A. 64 cm3 B. 66.99 cm3 C. 64 cm2 D. 100.53 cm3
Answer:
66.99 cm³
Step-by-step explanation:
the volume = ⅓× 3.14 × 4²× 4 = 3.14 × 64/ 3
= 66.99 cm³
Suppose we want to write 2/3 as an equivalent fraction with a denominator of 15. What number must we multiply both the numerator and the denominator by?
Answer:
5
Step-by-step explanation:
US
Find the circumference of this circle
using 3 for 7
C [?]
1
C = 27
Answer:
[tex]6.283185307[/tex]
Step-by-step explanation:
[tex]Formula - C = 2\pi r[/tex]
[tex]Formula = 2*\pi*1 = 6.283185307[/tex]
Answer:
C≈6
Step-by-step explanation:
remember circumference formula
[tex] \displaystyle C = 2\pi r[/tex]
given that,r=1 thus substitute:
[tex] \displaystyle C = 2\pi .1[/tex]
simplify mutilation:
[tex] \displaystyle C = 2\pi [/tex]
substitute the given value of π:
[tex] \displaystyle C = 2.3[/tex]
simplify multiplication:
[tex] \displaystyle C = 6[/tex]
and we are done!
What is the slope of a line perpendicular to the line y=2x+5 ?What is the slope of a line perpendicular to the line y=2x+5 ?
1/2
−2
2
−1/2
Answer:
[tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
Hi there!
In the given equation [tex]y=2x+5[/tex], the slope of the line is 2.
Perpendicular lines always have slopes that are negative reciprocals, like negative "flipped" fractions.
Example: The negative reciprocal of [tex]\frac{3}{1}[/tex] (which is the same as 3) is [tex]-\frac{1}{3}[/tex].
Example 2: The negative reciprocal of [tex]-\frac{4}{3}[/tex] is [tex]\frac{3}{4}[/tex].
Using this logic, the negative reciprocal of 2, or [tex]\frac{2}{1}[/tex], is [tex]-\frac{1}{2}[/tex]. Therefore, the slope of a line perpendicular to the line [tex]y=2x+5[/tex] is [tex]-\frac{1}{2}[/tex].
I hope this helps!
If f(x) = 8x and g(x) = 2x +1 find (f o g) (x)
Answer:
(fog) (x) = 8*(2x+1)=16x+8
Step-by-step explanation:
FAST HELP PLEASE
A Square weighs 7 grams and a Triangle weighs 8 grams. How much does a Circle weight
Answer:
69420
Step-by-step explanation:
6
Give the values of A, B, and C needed to write the equation's general form.
(5 + x)(5 - x) = 7
1. A = 1; B = 0; C = -18
2. A= -1; B = 0; C = 25
3. A = 25; B = 0; C = -1
Given:
The equation is:
[tex](5+x)(5-x)=7[/tex]
To find:
The value of A, B and C for the equation's general form.
Solution:
We have,
[tex](5+x)(5-x)=7[/tex]
Using distribution property, we get
[tex](5)(5)+(5)(-x)+(x)(5)+(x)(-x)=7[/tex]
[tex]25-5x+5x-x^2=7[/tex]
[tex]25-x^2=7[/tex]
Taking all terms on one side, we get
[tex]25-x^2-7=0[/tex]
[tex]-x^2+18=0[/tex]
[tex]-(x^2-18)=0[/tex]
[tex]x^2-18=0[/tex]
On comparing this equation with the general form of a quadratic equation [tex]Ax^2+Bx+C=0[/tex], we get
[tex]A=1[/tex]
[tex]B=0[/tex]
[tex]C=-18[/tex]
Therefore, the correct option is 1.
In the diagram below, m_MON = 1249, m _ MOP = 2x + 1, and m2 NOP = 2x
+1. What are the exact measures of the angles?
N
A. m2 MOP= 62
m2 NOP = 62
B. m2 MOP = 61
m 2 NOP = 61
C. m MOP = 48
m2 NOP = 72
D. m2 MOP = 122
m 2 NOP = 122
Answer:
The answer is below
Step-by-step explanation:
The Angle Addition Postulate states that the measure of an angle formed by two or more angles which are placed side by side is the sum of the measures of the two angles.
Therefore:
∠MON = ∠MOP + ∠NOP (angle addition postulate)
Substituting values gives:
124 = (2x + 1) + (2x + 1)
124 = 2x + 2x + 1 + 1
124 = 4x + 2
subtracting 2 from both sides of the equation:
124 - 2 = 4x + 2 - 2
4x = 122
Dividing through by 4:
4x / 4 = 122 / 4
x = 30.5
Therefore ∠MOP = 2x + 1 = 2(30.5) + 1 = 62°, ∠NOP = 2x + 1 = 2(30.5) + 1 = 62°
∠MOP = 62°, ∠NOP = 62°
359
110"
350
Triangle A
Triangle B
Given the triangles above, what is the measure, in degrees, of angle x?
i think the answer is 35° because the triangles are congruent to each other
Find the average of -8, -1, and 3
Im doing a test pls help quick!
Answer:
-2
Step-by-step explanation:
To find the mean, add all of the values together. With that sum, divide it by the amount of addends/values. In this case 3.
-8 + -1 + 3 = -6
-6/3= -2
hope this helps :D
Mrs. Banks was just given 2mL of morphine solution. How many milligrams of morphine did she receive
Answer:
2000 milligrams
Step-by-step explanation:
You do conversion and it make sense.
A sample of 26 elements from a normally distributed population is selected. The sample mean is 10 with a standard deviation of 4. The 95% confidence interval for μ is _____. a. 6.000 to 14.000 b. 8.384 to 11.616 c. 8.462 to 11.538 d. 9.846 to 10.154
Answer:
B. 8.384 to 11.616
Step-by-step explanation:
We have
mean = 10
s = 4
n = 26
the degrees of freedom = n-1
= 26 - 1 = 25
α = 1-95%
= 1 - 0.95
= 0.05
α/2 = 0.05/2 = 0.025
using the t table
t0.025, 25 = 2.06
we find the margin of error
t * s/√n
= 2.06 * 4/√26
= 1.616
10-1.616 < μ < 10+1.616
= 8.384<μ<11.616
therefore option b is the right solution
A train leaves at 15:43 and arrives at 17:13. It travelled at an average speed of 75 km/h.
How far did it travel? Give your answer in km to 1DP.
Can anyone answer this
Answer:
Distance cover by train = 112.5 km
Step-by-step explanation:
Given;
Speed of train = 75 km/h
Time started = 15:43 min
Time ended = 17:13 min
Find:
Distance cover by train
Computation:
Time started = 15:43 min = 15.716 hour
Time ended = 17:13 min = 17.216 hour
Total time taken = 17.216 - 15.716
Total time taken = 1.5 hour
Distance cover by train = Total time taken x Speed of train
Distance cover by train = 75 x 1.5
Distance cover by train = 112.5 km
Enter the value that belongs in the green box
Answer:
0,83
Step-by-step explanation:
tan(40)=0,83
0.8390996312tep-by-step explanation:
Helppppp ASAPPPPPP TST FULL CREDIT
Answer:
24.
[tex] log_{2}(9) \\ = log_{2}(3) {}^{2} \\ = 3 log_{2}(3) \\ = \frac{3 log(3) }{ log(2) } \\ = 4.75[/tex]
25.
[tex]5. {9}^{x} = 12.48 \\ {9}^{x} = 2.496 \\ x log(9) = log(2.496) \\ x = \frac{ log(2.496) }{ log(9) } \\ x = 0.42[/tex]
26.
[tex]4 + 9. ln(x) = 15.8 \\ ln(x) = \frac{15.8 - 4}{9} \\ ln(x) = 1.311 \\ x = e {}^{1.311} \\ x = 3.71[/tex]
5. The volume of a rectangular prism is 2058 cm3. The length is three times
the width. The height is twice the width. Find the width, length and height of the prism.
a. L- 18 cm, W-6 cm, H- 12 cm
c. L-20 cm, W-6 cm, H-12 cm
b. L- 21 cm, W- 7 cm, H- 14 cm
d. L- 22 cm, W-8 cm, H- 15 cm
Answer:
c
Step-by-step explanation:
The greatest common factor (GCF) of x^3, x^7, x^9 is ?
Please help
Answer:
[tex]x^3[/tex]
Step-by-step explanation:
Let the greatest common factor of [tex]a,b,c[/tex] such that [tex]a,b,c \in\mathbb{Z}[/tex] and they are not all equal to zero, [tex]d[/tex] is the common divisor of [tex]a[/tex] and [tex]b[/tex]. Therefore, [tex]d \mid a[/tex] and [tex]d \mid b[/tex]
You can write
[tex]D(a) = \{d \in\mathbb{Z} : d \mid a\}[/tex]
[tex]D(b) = \{d \in\mathbb{Z} : d \mid b\}[/tex]
The greatest common factor of [tex]a,b[/tex] is given as
[tex]D(a,b) = \{d \in\mathbb{Z} : d \mid a \text{ and } d \mid b\}[/tex]
and
[tex]D(a, b) = D(a) \cap D(b)[/tex]
This happens because [tex]D(a,b)[/tex] is upper bounded because if [tex]a\neq 0[/tex] then [tex]d \leq |a|[/tex]
for all [tex]d\in D(a, b)[/tex]. Therefore, the set [tex]D(a, b)[/tex] has the greatest elements.
Taking [tex]x^3, x^7, x^9[/tex] such that [tex]x>0[/tex]
You can note that [tex]x^7 = x^3 \cdot x^4[/tex] and [tex]x^9 = x^3 \cdot x^6 = x^3 \cdot x^3 \cdot x^3[/tex]
Therefore, the greatest common factor is [tex]x^3[/tex]
Note: [tex]x^3 \cap x^7 \cap x^9 = x^3[/tex]
Select the correct answer.
Using synthetic division, what is the factored form of this polynomial?
x^4+ 6x^3 + 33x^2 + 150x + 200
Answer:
(x + 2) (x +4) (x^2 + 25)
Step-by-step explanation:
Just did this problem
( + 2 ) ( ^3 + 4 ^2 + 2 5 + 1 0 0 )
( + 2 ) ( + 4 ) ( ^2 + 2 5 )
A factor is a number that completely divides another number. The factored form of the polynomial is (x² + 25 )(x + 2 )(x + 4 ).
What are factors?A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.
The given expression can be factorized using the steps as shown below. Therefore, we can write the steps as,
Rewrite for factoring : ([tex]x^{2}[/tex] + 33[tex]x^{2}[/tex] + 200) + 6[tex]x^{3}[/tex] + 150[tex]x^{}[/tex]
Rewrite the term: x⁴ + 8x² + 25x² + 200 + 6x³+ 150x
Regroup terms into two proportional parts: (x⁴ + 8x²) + (25x² + 200) + 6x³ 150x
Factor Greatest Common Factors out: x²(x² + 8 ) + 25(x² + 8) + 6x³ +150x
Factor Greatest Common Factors out:
(x² + 8 )(x² +25 ) + (6x³ + 150 )
Rewrite the term: (x² +25 )(x² + 2x + 4x + 8)
Regroup terms into two proportional parts: (x² + 25 ){(x + 2x ) + (4x +8)}
Factor Greatest Common Factors out: ( x² + 25 ){(x(x + 2) + 4(x + 2)}
Factor Greatest Common Factors out: (x² + 25 )(x + 2)(x + 4)
Learn more about Factors here:
https://brainly.com/question/24182713
#SPJ2
PLEASE HELP I WILL AWARD BRAINLY
Eight pipes were turned on to fill the pool in 36 hours. Then, after 12 hours some of the pipes were turned off, and the rest of the pool was filled in 32 hours. How many pipes were turned off?
Answer:
2 pipes
Step-by-step explanation:
So.. I'm not too sure either, but I'll try to solve it.
Equation: 4x=8 when x=number of pipes turned off after 12 hours
Since there were initially 8 pipes and there are 4 hours between 36 planned hours to fill the whole pool and 32 actual hours passed to fill the rest of the pool, you multiply them.
An experiment has three steps with three outcomes possible for the first step, two outcomes possible for the second step, and five outcomes possible for the third step. How many experimental outcomes exist for the entire experiment
Answer:
30 experimental outcomes exist for the entire experiment.
Step-by-step explanation:
Fundamental counting principle:
States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.
In this question:
Three outcomes possible for the first step.
Two for the second step.
Five for the third step.
How many experimental outcomes exist for the entire experiment?
Steps are independent, so, by the fundamental counting principle:
3*2*5 = 6*5 = 30
30 experimental outcomes exist for the entire experiment.
Does anyone know how to solve this equation?
9514 1404 393
Answer:
$80
Step-by-step explanation:
You are given the formula ...
P = I/(rt)
and the values I = 20, r = 0.05, t = 5.
Put the numbers in place of the corresponding variables and do the arithmetic.
P = 20/(0.05·5) = 20/0.25 = 80
The amount $80 will generate $20 in interest over 5 years at 5% per year.
Please help also due in morning THE WHOLE PAGE. 50 points for right now
What options are available to the decision maker if the probabilities of the states of nature are unknown?
Answer:
The states of nature refer to future events, not under the control of the decision maker, which may occur. States of nature should be defined so that they are mutually exclusive and collectively exhaustive.
help me pelaseeeeeeeee
Answer: 1. x=18
2. x=21
Step-by-step explanation:
1.Q 114=7x-12
7x=126
x=18
2.Q 4x-2=3x+19
4x-3x=19+2
x=21
Answer:
Step-by-step explanation:
if im right but i think
7x-12=144 opposite sides are congruent
7x/7=156/7
X= 22.285
What is the perimeter of ABC?
Perimeter = ___ units.
Answer:
12 units
Step-by-step explanation:
From the given figure,
AB=4 units & BC=3 units
By Pythagoras Theorem, [tex]AC^{2} = AB^{2} + BC^{2}[/tex]
Here, [tex]AC^{2} = 4^{2} + 3^{2}[/tex]
Thus, AC=5 units
Now, perimeter of triangle is equal to the sum of all sides.
Perimeter = AB + BC + AC = 4 + 3 + 5 = 12 units
PART A. A fruit juice recipe uses three ingredients. Two of the ingredients use a ratio of 2 ounces of pineapple juice to 5 ounces of fruit punch.Graph a line on the coordinate plane to represent this relationship.
PART B. Create an equation to represent this relationship let X represent ounces of pineapple juice. Let Y represent ounces of fruit punch. the picture is apart of Part A
Answer:
(B) The equation of line is 5 X = 2 Y.
Step-by-step explanation:
2 ounces of pineapple juice
5 ounces of fruit punch
Other is 4 ounces pineapple juice and 10 ounces fruit punch
(A) Graph is shown below:
(B) Let X is the pineapple juice and Y is the fruit punch
(2, 5) and (4, 10)
So, the equation of line is
[tex]Y - 5 = \frac{10-5}{4-2}\times (x -2)\\\\Y-5=2.5 (X-2)\\\\Y - 5 = 2.5 X - 5 \\\\2.5 X = Y\\\\ 5 X = 2 Y[/tex]