Option b) square root 19 + 7 over 2 will be an irrational sum because it includes the square root of a non-perfect square (19), which is an irrational number, added to a rational number (7/2).
The question asks which sum will be irrational. To determine this, we must look at each of the options:
a) 3+2 is the sum of two integers, which is also an integer, and thus a rational number.
b) square root 19 + 7 over 2 involves the square root of 19, which is an irrational number because 19 is not a perfect square. The sum of an irrational number and a rational number (7/2) is irrational.
c) 18 over 3 + 11 over 10,000 is the sum of two rational numbers, as both fractions can be simplified to a common form with integer numerators and denominators.
d) -6+(-3.251) is the sum of two rational numbers, since 3.251 can be expressed as a fraction.
The sum in option b will be irrational because it involves the sum of an irrational number, square root 19, and a rational number, 7/2. All the other sums are of rational numbers and will, therefore, also be rational.
100 increased by 3.1%
Answer:
103,1
Step-by-step explanation:
Use this formula: 100*(1+3.1%)
Which expression is equivalent to (x3 · x2)5? x10
Step-by-step explanation:
The given expression is
[tex]x^3.x^2[/tex]
To write the given expression is equivalent = ?
The given expression is
[tex]x^3.x^2[/tex]
We know that,
The exponential identity,
[tex]a^{m}.a^{n}=a^{m+n}[/tex]
= [tex]x^{3+2}[/tex]
= [tex]x^{5}[/tex]
∴ The given expression is equivalent = [tex]x^{5}[/tex]
Thus, the given expression is equivalent to [tex]x^{5}[/tex].
You can also see:
https://brainly.com/question/4456975
Answer:
The answer to (x3*x2)5 is x25
Step-by-step explanation:
PLEASE HELP ME ASAP IT"S VERY URGENT WILL MARK THE BRAINLEST
The interior angles formed by the sides of a quadrilateral have measures that sum to 360°.
What is the value of x?
Enter your answer in the box.
x =
Answer:
Step-by-step explanation:
3x - 6 + 2x + 108 + 88 = 360 Gather like terms
5x + 108 + 88 - 6 = 360
5x = 190 Divide by 5
x = 190/5
x = 38
how do you add and subtract
GL Stats: lviixea conrldence Intervals Practice
On each problem, verify that the conditions for a confidence interval are met!
(1) Suppose the height of senior girls at Anytown High School is known to be normally distributed. A sample of
leights in inches of 23 randomly selected senior girls were: 63, 68, 60, 59, 68, 65, 67, 64, 69, 69, 61, 67, 61, 60,
66, 67, 68, 66, 70, 79, 76, 75, 65. Construct and interpret a 99% confidence interval for the true mean height
Answer:
99% Confidence interval: (63.65,69.65
Step-by-step explanation:
We are given the following data:
63, 68, 60, 59, 68, 65, 67, 64, 69, 69, 61, 67, 61, 60, 66, 67, 68, 66, 70, 79, 76, 75, 65
Formula:
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{1533}{23} = 66.65[/tex]
Sum of squares of differences = 575.217
[tex]S.D = \sqrt{\dfrac{575.217}{22}} = 5.11[/tex]
99% Confidence interval:
[tex]\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}[/tex]
Putting the values, we get,
[tex]t_{critical}\text{ at degree of freedom 22 and}~\alpha_{0.01} = \pm 2.818[/tex]
[tex]66.65 \pm 2.818(\dfrac{5.11}{\sqrt{23}} ) = 66.65 \pm 3.002 = (63.65,69.65)[/tex]
Rewrite the following as a mix numbers 17/3
answer is 5 2/3.............
Answer:
5 2/3
Step-by-step explanation:
30 divided by 18 into improper fraction
Answer:
5/3
Step-by-step explanation:
30/18
you can easily simplify a large improper fraction by finding a common number.
in this case the number is 6.
6x5=30 & 6x3=18
therefore, if you divide each number by 6 you get 5/3
decimal: 1.66667 or 1.67 or 1.7
improper fraction: 5/3
proper fraction 1 2/3
Final answer:
30 divided by 18 as an improper fraction is ⅓, or 5/3, obtained by converting the division result into a mixed number and then back into an improper fraction.
Explanation:
To convert 30 divided by 18 into an improper fraction, you first divide 30 by 18 to get the decimal form, which is approximately 1.666. To express this as an improper fraction, we recognize that 1.666 is 1 and 2/3 in mixed number form.
Since 2/3 is already a fraction, we can convert the mixed number back into an improper fraction by multiplying the whole number 1 by the denominator 3 and then adding the numerator 2. This gives us 3 + 2 = 5, so the improper fraction is 5/3.
In circle L, arc NOP is 90° and the radius is 5 units. Which statement best describes the length of arc NOP?
Answer:
[tex]\frac{1}{4}[/tex] of circumference of the circle
Step-by-step explanation:
We are given that
Arc NOP=Central angle=[tex]\theta=90^{\circ}[/tex]
Radius of circle=5 units
We have to find the statement which describes best the length of arc NOP.
Arc length=[tex]\frac{central\;angle}{360}\times 2\pi r[/tex]
Using the formula
Arc length=[tex]\frac{90}{360}\times circumference\;of\;circle[/tex]
Where Circumference of circle=[tex]2\pi r[/tex]
Arc length NOP=[tex]\frac{1}{4}[/tex]circumference of circle
Hence, the arc length NOP=[tex]\frac{1}{4}[/tex] of circumference of the circle
Answer:
1/4 the circumference of circle L
Step-by-step explanation:
An Investment of $2,000 is earning interest at the rate of 6.2% compounded quarterly over 5 years. Approximately how much
interest is earned on the investment?
Answer: $720.37
Step-by-step explanation:
interest = 2000(1.0155)^20 - 2000
= 720.37
Hope this helps!!! Good luck!!! :)
Give each trig ratio as a fraction in simplest form.
1 point
Sin A=
Sin A=
Your answer
[tex]\boxed{sinA=\frac{a}{c}} \\ \\ \boxed{cosA=\frac{b}{c}}[/tex]
Explanation:The trigonometric functions are very important in math and physics. Sound, light and electricity all involve oscillations and are modeled by sine and cosine functions. So, we can provide a trig ratio for the sine and cosine function by taking a right triangle as shown in the figure below. So the relationships are as follows:
[tex]sinA=\frac{Opposite \ side}{Hypotenuse} \\ \\ cosA=\frac{Adjacent \ side}{Hypotenuse} \\ \\ \\ For \ the \ figure: \\ \\ a:Opposite \ side \\ \\ b:Adjacent \ side \\ \\ c:Hypotenuse[/tex]
So we can write:
[tex]\boxed{sinA=\frac{a}{c}} \\ \\ \\ \boxed{cosA=\frac{b}{c}}[/tex]
Learn more:Classification of triangles: https://brainly.com/question/10379190
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4. Which of the following points are solutions to the system of inequalities 2x - 3y > 9 and -x -
4y > 8?
• (-1,-3)
(1,3)
(-1,3)
(1,-3)
Answer:
(1, -3)
Step-by-step explanation:
Match the following items by evaluating the expression for x = -2.
x-2
x-1
x0
x1
x2
By substituting x = -2 in each expression, we find that x-2 equals -4, x-1 equals -3, x₀ equals 1, x₁ equals -2, and x₂ equals 4.
Explanation:To solve this, we need to substitute x = -2 into each expression. Here are the results:
For x-2, substituting -2 would give us -2 - 2 which is -4.In the expression x-1, substituting -2 would provide us with -2 - 1, which equals -3.For x₀, any non-zero number to the power of zero is 1.When we put -2 into x₁, we simply get -2.Finally, for x₂, -2 squared equals to 4.Learn more about Evaluating expressions here:https://brainly.com/question/21469837
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What do you know about two different integers that are opposites?
Only if they are each the same distance away from zero, but on opposite sides of the number line.
Hope this help! :)
Answer:If you add a negative and a positive you do the the integers step by changing the add operation to a subtraction.
Step-by-step explanation:-4+3
integers property -4 - 3 = 1
negative plus a positive is a positive.
The expression 210,000\left(1.02\right)^x210,000(1.02)
x
models the estimated home value after x years. Which statement is the correct representation of the 1.02 in the expression?
The house has a starting value of 1.02.
The house is decreasing in value by 2% each year.
The house is increasing in value by 2% each year.
The value of the house is changing by 0.02% each year.
Answer:
The house is increasing in value by 2% each year.
Correct the increase is 1.02 per year the value of b>0 and the percentage of increase each year is:
[tex] \frac{1.02-1}{1} *100 = 2\%[/tex]
Step-by-step explanation:
For this case if we have this expression
[tex] 210000(1.02)^x[/tex]
We have the same functional forma like the exponential model given by:
[tex] y = a b^x[/tex]
Where a = 210000 represent the constant or initial value and b = 1.02 represent the base.
So let's analyze the possible options:
The house has a starting value of 1.02.
False the starting value for this case is 210000 since if x=0 then we see that the value is 210000
The house is decreasing in value by 2% each year.
False the increase is 1.02 each year so then in % we have
[tex] \frac{1.02-1}{1} *100 = 2\%[/tex]
We have an increase of 2% each year
The house is increasing in value by 2% each year.
Correct the increase is 1.02 per year the value of b>0 and the percentage of increase each year is:
[tex] \frac{1.02-1}{1} *100 = 2\%[/tex]
The value of the house is changing by 0.02% each year.
False the increase is 2% per year
What is the area of a triangle with A = 15°, B= 113', and b = 7?
a. 3.8 units
c. 5.4 units
b. 4.2 units
d. 4.4 units
Answer:
The answer is C, 5.4 units
Step-by-step explanation:
What is the slope of (0,1) and (5,4)
Answer:
3/5
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(4-1)/(5-0)
m=3/5
Homework answers plz
Answer: 10.5
Step-by-step explanation:
Hello the answer is 10.5 you just have to multiply 3 1/2 times 3 and there's your answer
Have a great day hope this helps!:):):
Answer:
10 1/2
Step-by-step explanation:
convert 3 1/2 into an improper fraction
3 1/2 = 7/2
if the flour is tripled that means
3 1/2 x 3
= 7/2 x 3
= (7x3) / 2
= 21/2 (convert to mixed fraction, by long division)
= 10 1/2
Passing through (-6, -1) and PARALLEL 2x + 3y = 3
Answer:5
Step-by-step explanation:
What is the answer to 13d+25=8d
13d + 25 = 8d
13d - 8d = -25
5d = -25
d = -5
so the answer is (-5)
Answer:
Step-by-step explanation:
13d + 25 = 8d
13d = 8d -25
13d - 8d = -25
5d = -25
d = -5
Jenny had $17 more than Susan, and together they had enough money to buy a game for $93 and to have a pizza for $6. How much money did Susan have?
Answer:
Susan had $41.
Step-by-step explanation:
The amount of money they have is enough for $99 spending. The answer can be found by testing two numbers and seeing whether the amounts need to be increased or decreased to make the distance between them 17, with a sum of 99.
40 and 57: distance of 17, but not enough for $99. $41 and $58 equal 99, with a distance of 17 between them. Jenny, with $17 more, has 58. Susan has 41.
A frame around a rectangular family portrait has a perimeter of 150 inches. The length is ten more than four times the width. Find the length and width of the frame.
Answer: The length is 62 inches and the width is 13 inches
Step-by-step explanation: The perimeter of the rectangular portrait has been given as 150 inches. We also know that the perimeter of a rectangle is given as
Perimeter= 2(L + W)
However we don't have the measurements for the length and width. What we do have are descriptions of both. The length is given as W, while the length is ten more than four times the width. That is, the length equals
10 + 4W
Therefore we have the length and the width as
L = 4W + 10 and
W = W
If the perimeter is 150, and
Perimeter = 2(L + W) then,
150 = 2(4W + 10 + W)
150 = 2(5W + 10)
150 = 10W + 20
Subtract 20 from both sides of the equation
130 = 10W
Divide both sides of the equation by 10
13 = W
With that in mind we can now calculate the length as
L = 4W + 10
Substitute for the value of W
L = 4(13) + 10
L = 52 + 10
L = 62
Therefore, the length is 62 inches and the width is 13 inches
Answer:
Length = 62 inches, Width = 13 inches
Step-by-step explanation:
Let L represent the length of the frame, W, the width and P, the perimeter
Perimeter of a rectangle, P = 2 (L + W) .....eq 1
Also, P = 150 inches
and
L = 10 + 4W .....eq 2
Slotting in the respective values of P and L in eq 1
150 = 2 {(10 + 4W) + W}
Expanding the bracket
150 + 2 (10 + 5W)
150 = 20 + 10W
Subtracting 20 from both sides of the equation
150 - 20 = 20 - 20 + 10W
130 = 10W
Dividing both sides by the coefficient of W which is 10
13 = W
Therefore, W = 13 inches
Slotting in the value of W in eq 2
L = 10 + 4 (13)
L = 10 + 52
L = 62 inches
Lets ensure that the values of L and W are correct
P = 2 (L + W)
150 = 2 (13 + 62)
150 = 2(75)
150 = 150
Hence, L = 62 inches, W = 13 inches
Someone help me please
Answer:
A because it is increasing
Step-by-step explanation:
Answer:
I would say c
Step-by-step explanation:
you think if you go down a hill what happen is you speed up so you would need to be go down or heading in a negative direction.
Suppose Ellie starts making a lamb stew using a 6.5-quart pot. She decides to make a bigger stew. She pours everything into a pot that is 40 percent bigger. How big is the bigger pot?
Answer:
The bigger pot is a 9.1-quart pot
Step-by-step explanation:
Initial pot size = 6.5-quart
New pot is 40% bigger than the initial pot size
Bigger pot size = 6.5-quart + (0.4 × 6.5-quart) = 6.5-quart + 2.6-quart = 9.1-quart
question for class 4
What’s the slope for Y=8x+2
what is 6(5−8v)+12=−54
Answer:
v = 2
Step-by-step explanation:
+5x+3.
What are the factors of the polynomial?
(2x+3)(x+1)
(2x-3)(x-1)
(3x+2)(x+1)
(3x-2)(x-1)
2x^2 + 5x + 3
What are the factors of the polynomial?
(2x+3)(x+1)
(2x-3)(x-1)
(3x+2)(x+1)
(3x-2)(x-1)
Answer:Option A
The factors are:
[tex]2x^2+5x+3 = (2x+3)(x+1)[/tex]
Solution:Given that, the quadratic equation is:
[tex]2x^2 + 5x + 3[/tex]
We have to find the factors of polynomial
Find the factors:[tex]2x^2+5x+3[/tex]
Split 5x as 2x and 3x
[tex]2x^2+5x+3 = 2x^2 +2x + 3x + 3[/tex]
[tex]\mathrm{Break\:the\:expression\:into\:groups}[/tex]
[tex]2x^2+5x+3=\left(2x^2+2x\right)+\left(3x+3\right)[/tex]
[tex]\mathrm{Factor\:out\:}2x\mathrm{\:from\:}2x^2+2x\mathrm{:\quad }2x\left(x+1\right)[/tex]
Thus we get,
[tex]2x^2+5x+3 = 2x(x+1) + (3x+3)[/tex]
[tex]\mathrm{Factor\:out\:}3\mathrm{\:from\:}3x+3\mathrm{:\quad }3\left(x+1\right)[/tex]
Thus we get,
[tex]2x^2+5x+3 = 2x(x+1) + 3(x+1)[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}x+1[/tex]
Thus we get,
[tex]2x^2+5x+3 = (2x+3)(x+1)[/tex]
Thus the factors are found for given polynomial
Final answer:
The correct factors of the polynomial +5x+3 are (2x+3)(x+1), as they multiply to give the original polynomial. None of the other provided options yield the correct polynomial upon multiplication.
Explanation:
The question asks to identify the factors of the polynomial +5x+3. Factors are expressions that, when evaluated, produce the value of the polynomial. Let's examine the provided options to find which pair of binomials gives us the correct polynomial upon multiplication:
(2x+3)(x+1) = 2x² + 2x + 3x + 3 = 2x² + 5x + 3, which matches the original polynomial.
(2x-3)(x-1) = 2x² - 2x - 3x + 3 = 2x² - 5x + 3, which does not match the original polynomial.
(3x+2)(x+1) = 3x² + 3x + 2x + 2 = 3x² + 5x + 2, which does not match the original polynomial.
(3x-2)(x-1) = 3x² - 3x - 2x + 2 = 3x² - 5x + 2, which does not match the original polynomial.
Therefore, the correct factors of the polynomial +5x+3 are (2x+3)(x+1).
x + 6y = -7
2x + 12y = -14
ALL OF THESE WILL BE SOLVE FOR X AND Y!!!
Problem 1 Solve For x: x=−6y−7
Show work: Add -6y to both sides.
x+6y+−6y=−7+−6y
x=−6y−7
Problem 1 Solve For y: y = -1/6x + -7/6
Show work: Add -x to both sides.
x+6y+−x=−7+−x
6y=−x−7
Step 2: Divide both sides by 6.
6y/6 = -x -7/6
Problem 2 Solve For x: x=−6y−7
Show work: Add -12y to both sides.
2x+12y+−12y=−14+−12y
2x=−12y−14
Step 2: Divide both sides by 2.
2x/2 = -12y - 14/2
Problem 2 Sovle For y: y=-1/6x + -7/6
Show work: Add -2x to both sides.
2x+12y+−2x=−14+−2x
12y=−2x−14
Step 2: Divide both sides by 12.
12y/12 = -2x-14/12
lines AD and BE intersect at point C, as shown. create an expression that represents the measure of the angle DCE in terms if X
part 2 of question: using your expression, solve for the missing value of X if DCE was 120 degrees.
Answer:
Please, find the image with the diagram of the lines corresponding to this question:
The answers are:
Equation: m ∠ DCE = 180º - x
Value of x = 60º
Explanation:
First question:
You must use the fact that the angles DCE and BCD are adjacent angles, because they share the vertex (C) and have a common side (CD).
Thus, as a first fact, the measure of the angle BCE is equal to the sum of the measures of the angles BCD and DCE.
On the other hand, BE is a straight line, thus the measure of angle BCE is 180º.
Hence, you can write:
m ∠ DCE + m ∠ DCB = 180ºm ∠ DCE + x = 180ºm ∠ DCE = 180º - xSecond question:
Solve for x:
Given: m ∠ DCE = 180º - xAdd x to both sides: m ∠ DCE + x = 180º Subtract m ∠ DCE from both sides: x = 180º - m ∠DCESubstitute m ∠DCE with 120º:
x = 180º - 120º = 60ºHence, for m ∠DCE = 120º, x = 60º.
17. WEATHER Heavy rain in Brieanne's town caused the river to rise. The river rose three
inches the first day, and each day after rose twice as much as the previous day. How
much did the river rise in five days?
Answer:
30
Step-by-step explanation:
It states that it rained twice as much in 5 days all you do is multiply the 2 times 3 which is 6 so then u multiply 6 times 5 which is 30.
The river rose a total of 93 inches over five days.
The question asks how much a river rises in five days given a certain pattern of increase. To find the solution, we use a geometric sequence because the river rises by a constant multiple each day. On the first day, the river rises three inches. Since on each subsequent day the river rises by twice the amount it did the previous day, the sequence of increases over five days is: 3 inches, 6 inches, 12 inches, 24 inches, and 48 inches.
The total rise of the river is the sum of these increases:
3 + 6 + 12 + 24 + 48 = 93 inches.
Therefore, the river rose a total of 93 inches over the span of five days.