Answer:
[tex]\Large \boxed{\sf 17 \ and \ 18}[/tex]
Step-by-step explanation:
The product means multiplication.
There are two positive consecutive integers.
Let the first positive consecutive integer be x.
Let the second positive consecutive integer be x+1.
[tex](x) \times (x+1) =306[/tex]
Solve for x.
Expand brackets.
[tex]x^2 +x =306[/tex]
Subtract 306 from both sides.
[tex]x^2 +x -306=306-306[/tex]
[tex]x^2 +x -306=0[/tex]
Factor left side of the equation.
[tex](x-17)(x+18)=0[/tex]
Set factors equal to 0.
[tex]x-17=0[/tex]
[tex]x=17[/tex]
[tex]x+18=0[/tex]
[tex]x=-18[/tex]
The value of x cannot be negative.
Substitute x=17 for the second consecutive positive integer.
[tex](17)+1[/tex]
[tex]18[/tex]
The two integers are 17 and 18.
The product of two consecutive positive integers is 306.
We need to find the integers
solution : Let two consecutive numbers are x and (x + 1)
A/C to question,
product of x and (x + 1) = 306
⇒x(x + 1) = 306
⇒x² + x - 306 = 0
⇒ x² + 18x - 17x - 306 = 0
⇒x(x + 18) - 17(x + 18) = 0
⇒(x + 18)(x - 17) = 0⇒ x = 17 and -18
so x = 17 and (x +1) = 18
Therefore the numbers are 17 and 18.
Hope it helped u if yes mark me BRAINLIEST
TYSM!
Which equation represents a line with slope į and y-intercept -6?
2x +3y=-6
3x - 2y= 6
2x - 3y= 18
3x - 2y= 12
Answer:
Answer:y=-2/9+3
Step-by-step explanation:
I need someone to answer this question for me correctly please?
Answer:
[tex]\boxed{x \leq -4}[/tex]
Step-by-step explanation:
Hey there!
Well to solve for x in,
16x - 7 ≤ -71
We need to single out x.
16x - 7 ≤ -71
+7 to both sides
16x ≤ -64
Divide both sides by 16
x ≤ -4
Hope this helps :)
Answer:
x ≤ -4
I hope this helps!
helpppppppppppppppppppppppppppp give bralienst
Answer:
Brainliest! Hope I helped!
Step-by-step explanation:
you know its greater than 1cm and less than 2cm,
1 and 7hundreths cm is = 1.07 cm
thats not right because you know it is greater than that for sure!
so the only answer left is 1.7 cm
You answer is 1.7 cm
another way...
read the ruler and see the answer
Answer:
1.7 cm.
Step-by-step explanation:
The midpoint of 1 - 2 is 5 so count the lines after 5 and you get .7 to add to one cm.
Hope this helps, have a good day :)
A major traffic problem in the Greater Cincinnati area involves traffic attempting to cross the Ohio River from Cincinnati to Kentucky using Interstate 75. Let us assume that the probability of no traffic delay in one period, given no traffic delay in the preceding period, is 0.9 and that the probability of finding a traffic delay in one period, given a delay in the preceding period, is 0.6. Traffic is classified as having either a delay or a no-delay state, and the period considered is 30 minutes.Required:a. Assume that you are a motorist entering the traffic system and receive a radio report of a traffic delay. What is the probability that for the next 60 minutes (two time periods) the system will be in the delay state?b. What is the probability that in the long run the traffic will not be in the delay state?c. An important assumption of the Markov process model presented here has been the constant or stationary transition probabilities as the system operates in the future. Do you believe this assumption should be questioned for this traffic problem? Explain.
Answer:
a) 0.36
b) 0.3
c) Yes
Step-by-step explanation:
Given:
Probability of no traffic delay in one period, given no traffic delay in the preceding period = P(No_Delay) = 0.9
Probability of finding a traffic delay in one period, given a delay in the preceding period = P(Delay) = 0.6
Period considered = 30 minutes
a)
Let A be the probability that for the next 60 minutes (two time periods) the system will be in the delay state:
As the Probability of finding a traffic delay in one period, given a delay in the preceding period is 0.6 and one period is considered as 30 minutes.
So probability that for the next two time periods i.e. 30*2 = 60 minutes, the system in Delay is
P(A) = P(Delay) * P(Delay) = 0.6 * 0.6 = 0.36
b)
Let B be the probability that in the long run the traffic will not be in the delay state.
This statement means that the traffic will not be in Delay state but be in No_Delay state in long run.
Let C be the probability of one period in Delay state given that preceding period in No-delay state :
P(C) = 1 - P(No_Delay)
= 1 - 0.9
P(C) = 0.1
Now using P(C) and P(Delay) we can compute P(B) as:
P(B) = 1 - (P(Delay) + P(C))
= 1 - ( 0.6 + 0.10 )
= 1 - 0.7
P(B) = 0.3
c)
Yes this assumption should be questioned for this traffic problem because it implies that traffic will be in Delay state for the 30 minutes and just after 30 minutes, it will be in No_Delay state. However, traffic does not work like this in general and it makes this scenario unrealistic. Markov process model can be improved if probabilities are modeled as a function of time instead of being presented as constant (for 30 mins).
which terms are like terms in the following expression ? 6x + 8xy - 3x + 9y + 4x^2
Answer:
[tex]\Large \boxed{{6x \ \mathrm{and} \ -3x}}[/tex]
Step-by-step explanation:
Like terms have identical variables and exponents, the coefficients don’t have to be the same.
The like terms from the expression are 6x and -3x.
Step-by-step explanation:
Hey, there!!
6x and -3x are like terms.
Like terms in algebraic terms are those terms which has same variable or exponents. In This expression "6x+8xy-3x+9y4x^2"
6x and -3x has "x" common in them so, The answer is 6x and -3x.
Hope it helps..
Can someone do this assuming that it is infinite and as well as assuming it's not infinite? Thanks!
Answer:
see below
Step-by-step explanation:
4,7,12,19
We are adding 3,5,7,9..... each time
The sequence is not arithmetic because we are not adding a constant. It is not geometric since we are not multiplying by a constant term each time
There is no common difference or common ratio.
The explicit formula is
an =n^2 +3
The recursive formula is
(n+1)^2 +3 - (n^2 +3)
n^2 +2n+1+3 - ( n^2+3)
2n+1
a sub(n+1) = a sub( n) + 2n+1
The 10th term
an = n^2 +3
Let n=10
an = 10^2+3
= 100+3
= 103
summation
see image
since the numbers are increasing and greater than 1 the sum does not exist
plz help i'm having a really hard time with this
Answer:
Domain all reals
Range all reals
Step-by-step explanation:
The domain is the values that x can take, or the values of the input
x can be any real number
The range is the values that y can take, or the values of the output
y can be any real number
Answer:
C)
Step-by-step explanation:
it's fully continous, linear function thus all values are possible for both, x and y
Two tablespoons of peanut butter contain 190 calories. Two tablespoons of grape jelly contain 122 calories. Which contains more calories, two tablespoons of peanut butter or two tablespoons of grape jelly?
Explain how to solve the inequality (x + 1)(x – 2) ∙ (x – 3) > 0. Explain in your own words, each step necessary to solve the inequality, making sure to follow the proper order of operations. Is this inequality accurate? Explain why or why not.
Answer:
[tex]x > -1[/tex] or
[tex]x > 2[/tex] or
[tex]x > 3[/tex]
Step-by-step explanation:
Given
[tex](x + 1)(x - 2) (x - 3) > 0[/tex]
Required
Solve; with steps
[tex](x + 1)(x - 2) (x - 3) > 0[/tex]
Start by splitting the inequality as follows
[tex]x + 1 > 0[/tex] or [tex]x - 2 > 0[/tex] or [tex]x - 3 > 0[/tex]
Solve the inequalities one after the other
Solving: [tex]x + 1 > 0[/tex]
Subtract 1 from both sides
[tex]x + 1 - 1 > 0 - 1[/tex]
[tex]x > -1[/tex]
Solving: [tex]x - 2 > 0[/tex]
Add 2 to both sides
[tex]x - 2 +2 > 0 +2[/tex]
[tex]x > 2[/tex]
Solving: [tex]x - 3 > 0[/tex]
Add 3 to both sides
[tex]x - 3 +3> 0+3[/tex]
[tex]x > 3[/tex]
Hence, the solution to the inequality is
[tex]x > -1[/tex] or
[tex]x > 2[/tex] or
[tex]x > 3[/tex]
If SSR is 2592 and SSE is 608, then A. the standard error would be large. B. the coefficient of determination is .23. C. the slope is likely to be insignificant. D. the coefficient of determination is .81.
Answer:
D. the coefficient of determination is .81.
Step-by-step explanation:
SST = SSE + SSR
where
SST is the summation of square total
SSE is the summation of squared error estimate = 608
SSR is the summation of square of residual = 2593
with these in mind we put the values into the formula
= 2592 + 608
=3200
Coefficient of determination = SSR/SST
= 2592/3200
= 0.81
Therefore option D is the correct answer to the question.
120 meals to 52 meals what is the percentage change?
Answer: The percentage change is 56.67%.
Step-by-step explanation:
From 120 meals to 52 meals, change in meals = ( 120- 52) meals
= 68 meals
The percentage change = [tex]\dfrac{\text{change in meals}}{\text{Original quantity of meals}}\times100[/tex]
[tex]=\dfrac{68}{120}\times100\\\\=56.67\%[/tex]
Hence, the percentage change is 56.67%.
Suppose a vine maple grows in height linearly. Four weeks after it is planted it stands 10.67 inches, and after seven weeks it is 15.67 inches tall. Write an equation that models the growth, in inches, of the vine maple as a function of time, in weeks. 1. What is the slope of the function? 2. How tall was the tree when it was first planted? 3. Write the function 4. How tall will the vine maple be after 16 weeks?
Answer:
Height (z)= 4+(5/3)(z)
Where z is the number of weeks
1). Slope = 4
2). Height= 5.67 inches
3).Height (z)= 4+(5/3)(z)
4).Height= 30.67 inches
Step-by-step explanation:
At week four
10.67= x+4y
Week 7
15.67= x+7y
Solving both equation simultaneously
3y= 5
Y= 5/3
15.67= x+7y
15.67= x+7(5/3)
15.67-35/3= x
15.67-11.67= x
4= x
The modeled equation is
Height (z)= 4+5/3(z)
Where z is the number of weeks
Slope of the function as compared to y= mx+c is 4
The first week of it's plantation
Height (z)= 4+5/3(z)
Height (1)= 4+5/3(1)
Height= 5.67 inches
After 16 weeks
Height (z)= 4+(5/3)(z)
Height (16)= 4+(5/3)(16)
Height= 30.67 inches
Hi people, Please if someone can give me a hand, l already have done the first part of the exercise, but l cant make Angle CAB= X^0 c) calculate the lower bound for the value of tan X^0 there is the answer 1.02 (2dp) but l have no clue how to get it thanks i used Toa (Tan = Opp/ adj) but l couldnt find it thanks
Answer:
(c) 1.02
Step-by-step explanation:
(c) The tangent is the ratio of Opposite to Adjacent. Its lowest value will be found where Opposite is lowest, and Adjacent is highest:
min tan(A) = (min BC)/(max AB) = 75/73.5 ≈ 1.020408...(42-digit repeat)
Find the value of x.
Answer:
[tex]here \: the \: two \: sides \: are \: equal \: so \: \\ the \: triangle \: is \: issosceles \\ then \: x = 40 \\ thank \: you[/tex]
Identify the equivalent expressions of 4(2x + x-3) - 3x + 3 by substituting x = 2 and x = 3.
9x - 9
9x - 1
9x + X-9
9(x - 1)
4(3x - 3) + 3 - 3x
Answer:
9x -9
9(x - 1)
4(3x-3) - 3x + 3
Step-by-step explanation:
4(2x + x-3) - 3x + 3
Combine like terms
4(3x-3) - 3x + 3
Distribute
12x -12 -3x+3
Combine like terms
9x -9
Factor out 9
9(x-1)
Answer:
9
18
Step-by-step explanation:
x = 2:
4(4 + 2 - 3) - 6 + 3 = 12 - 6 + 3 = 9
x = 3:
4(6 + 3 - 3) - 9 + 3 = 24 - 9 + 3 = 18
solve the following equations
x-1=6/x
Answer:
or,x2-x=6
or,x2-x-6=0
or,x2-3x+2x-6=0
or,x(x-3)+2(x-3)=0
or,(x-3)(x+2)=0
so either x=3
or x=-2
What is 22 x 2 + 6 = x
Answer:
x=50
Step-by-step explanation:
22•2=44
44+6=50
Answer:
50
Step-by-step explanation:
22×2=44+6=50.
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1 - Dada a função f(x)= -Ix²-5x+4I, determine o valor de função para x = -1. * 1 ponto a) -10 b) 10 c) 9 d) -9 e) -8
Option a) -10
[tex] f(x)=-|x^2-5x+4|[/tex]
put $x=-1$
$f(-1)=-|(-1)^2-5(-1)+4|$
$\implies f(-1)=-|1+5+4|=-|10|=10$
Answer:
option a
Step-by-step explanation:
Option a) -10
put $x=-1$
$f(-1)=-|(-1)^2-5(-1)+4|$
$\implies f(-1)=-|1+5+4|=-|10|=10$
find the equation of the sides of an isosceles right angled triangle whose vertex is (-2,-3) and the base is on the line x=0
Answer:
AC:y=x-1 CB:y=-x-5 AB:x=0
Step-by-step explanation:
Consider the triangle. The base AB is on the line x=0, the vertex C is (-2,-3)
The side AC is equal to BC. The angle ACB is 90 degrees. If the base is on the line x=o, it is on the axis Y.Explore the distance from the point C to the AB
c(-2,-3), the distance to the axis Y is equal to the modul of the coordinate x (-2), it is 2. The coordinates of point projected by the point C to the axis Y is N(0,-3). The modul of the height is 2, the height of the isosceles triangle to the base is the bisectrix, so the angle BCA is 90/2=45degrees, CBA is 180-90-45=45 degrees too
the heigt CN is equal to side NB, NB=2
Suppose B is (0,y) (x=0 because the base is on this line)
THe modul of the vector NB is equal to sqrt ((0-0)^2+(y+3)^2)= 2
modul (y+3)= 2
y=-1 or y=-5
(0,-1), (0,-5) - two points, one of them (suppose B) is (0,-5) when A is (0,-1) (A is remote from the point N on the same distance with B, because AB is the median too)
Find CB and AC
Use the equation for AC
(x-0)/(-2-0)= (y+1)/(-3+1)
x/-2= (y+1)/-2
x=y+1
y=x-1
For CB
(x-0)/ (-2-0)= (y+5)/ (-3-(-5))
x/-2= (y+5)/2
-x=y+5
y=-x-5
Which cross-sectional shapes do you find the most surprising? Which shapes do you find the least surprising? Explain why.
Answer:
I was surprised that a plane parallel to the vertical axis creates a rectangular cross-section. I guess I was expecting to always see a circle or a circular shape in the cross-section, not purely straight edges as seen in a rectangle.
Step-by-step explanation:
edmentum answer
Answer:
The circles were the least surprising because the base of the cone is a circle. The curves that look like bent rods were the most surprising because I have not seen geometric figures like those before.
Step-by-step explanation:
c program to generate prime numbers from 1 to 100.Also count prime numbers.
Answer:
Step-by-step explanation:
#include <stdio.h>
int main()
{
int num1, num2, flag_var, i, j;
/* Ask user to input the from/to range
* like 1 to 100, 10 to 1000 etc.
*/
printf("Enter two range(input integer numbers only):");
//Store the range in variables using scanf
scanf("%d %d", &num1, &num2);
//Display prime numbers for input range
printf("Prime numbers from %d and %d are:\n", num1, num2);
for(i=num1+1; i<num2; ++i)
{
flag_var=0;
for(j=2; j<=i/2; ++j)
{
if(i%j==0)
{
flag_var=1;
break;
}
}
if(flag_var==0)
printf("%d\n",i);
}
return 0;
}
Which is a factor of: 2x2+10x+8 ?
Answer:
2 ( x+4) ( x+1)
Step-by-step explanation:
2x^2+10x+8
Factor out 2
2 ( x^2 +5x+4)
What two numbers multiply to 4 and add to 5
4*1 = 4
4+1 = 5
2 ( x+4) ( x+1)
[tex] \large{ \underline{ \underline{ \bf{ \pink{To \: factorise}}}}}[/tex]
2x² + 10x + 8Factorisation:By middle term factorisation,
⇛ 2x² + 2x + 8x + 8
⇛ 2x(x + 1) + 8(x + 1)
⇛ (2x + 8)(x + 1)
⇛ 2(x + 4)(x + 1)
☃️ Now you can break it down and check which are the factors of the polynomial according to options.
━━━━━━━━━━━━━━━━━━━━
The circumference of a redwood tree trunk is 16π ft, and it is 100 ft tall. What is the approximate volume of the redwood tree trunk? 2,560π ft3 640π ft3 25,600π ft3 6,400π ft3
Answer:
volume of redwood tree is 6400 π ft^3(option 4)
Step-by-step explanation:
concept =
volume of cylinder = πr^2l
where r is the radius and l is the length of cylinder
circumference of cylinder = 2πr
_____________________________________
shape of redwood tree can be taken as cylindrical
given
circumference of a redwood tree trunk is 16π ft
2πr = 16π
=> r = 16π/2π = 8
Thus, radius is 8 feet
Therefore volume of redwood tree = πr^2l = π8^2*100 = π*64*100
volume of redwood tree =6400 π ft^3
Answer:
6,400π ft3
Step-by-step explanation:
took test and got it right
Y=-×+1 and y=2×+4 how many solutions when graphed
Answer:
One solution (-1,2)
Step-by-step explanation:
Since these two linear equations have different slopes, different y-intercepts, and are indeed linear, these equations will only have one crossing when graphed, and hence one solution.
To find that solution, we can simply set the equations equal to each other.
y = -x + 1
y = 2x + 4
-x + 1 = 2x + 4
-3 = 3x
-1 = x
Now plug that value back into one of the equations:
y = -x + 1
y = -(-1) + 1
y = 2
So now you know the crossing for these two equations occurs at (-1,2).
Cheers.
Pls help!!
An educator hypothesizes that the median of the number of students enrolled in cyber schools in school districts in southwestern Pennsylvania is 25. At a = 0.05, is there enough evidence to reject the educator’s claim? The data are shown here. What benefit would this information provide to the school board of a local school district? 12 41 26 14 4 38 27 27 9 11 17 11 66 5 14 8 35 16 25 17
Answer:
nbbhhghhhjjjjjjjjjkjjjjnnmmmmmmmmbv b b j
In the 30-60-90 triangle below, side s has a length of__and side q has a
length of
30°
g
8
90°
60"
S
O A. 16-3,5
OB. 1613, 16-3
O C. 4,8-13
O D. 8-5, 16
O E. 4, 4.5
O F. 4/2, 412
Answer:
Option E, 4, 4√3
Step-by-step explanation:
s = 4
q = 4√3
helppfind the value of x and y
I know tje answer
x+6kkkkkkkk
Answer:
X=75°;AND Y=30°
Step-by-step explanation:
Angle( x+75°)+(y)=180°
Angle(2x)+(y)=180°
[by subtracting both the equation we get;]
-1x=-75
x=75°
Now,value of y;
2x+y=180
2×75+y=180
150+y=180
y=180-150
y=30°
The function g is defined as follows for the domain given.
g(x) = 2x+1,
domain = (-5, -1, 2, 3)
Write the range of g using set notation. Then graph g
Answer:
g(x): 2(-5)+1= -10+1=-9
2(-1)+1= -2+1=-1
2(2)+1= 4+1=5
2(3)+1=6+1= 7
Hence, the range of [tex]g[/tex] using the set notation is [tex](-9,-1,5,7)[/tex].
What is the function?
Functions are often defined by a formula that describes a combination of arithmetic operations and previously defined functions; such a formula allows computing the value of the function from the value of any element of the domain.
Here given that,
The function g is defined as follows for the domain given.
[tex]g(x) = 2x+1,[/tex] and domain [tex]= (-5, -1, 2, 3)[/tex]
So,
[tex]x=-5\\2(-5)+1\\= -10+1\\=-9\\\\x=-1\\2(-1)+1\\= -2+1\\=-1\\\\x=2\\2(2)+1\\= 4+1\\=5\\\\x=3\\2(3)+1\\=6+1\\= 7[/tex]
Hence, the range of [tex]g[/tex] using the set notation is [tex](-9,-1,5,7)[/tex].
To know more about the function
https://brainly.com/question/10500042
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Malek sets out for a hike at 8.00 am and returns at 17:15.
How long was Malek hiking for?
hours and
minutes
Answer:
9 hours and 15 mins
Step-by-step explanation:
17 - 8 (time calculation)
ASAP
Which of the following factors determine a plane? A. line and a point on the line B. two lines C. a straight line D. a line and a point not on that line
Answer:
D. a line and a point not on that line
Step-by-step explanation:
That is how you determine a plane.
The factors which determine a plane are a line and a point not on that line.
What is plane ?
In geometry, a plane is a flat surface that extends into infinity.
In a three dimensional space, a plane can be defined by three points it contains, as long as those points are not on the same line.
Therefore, the factors which determine a plane are a line and a point not on that line.
Hence, option D is correct.
Learn more about plane here:
https://brainly.com/question/17458011
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