Irrational numbers just means that it isn’t rational so this means that A is true. If you look up a chart with irrational,rational,real, and integer it will show that all whole numbers are integers so this means B is true. C is false. Same thing about B proves that D is true. SHORT ANSWER: C is false. I hope this helps.
In the given statement D is false.
What is Rational number ?
In mathematics, a rational number is any number that can be written as a fraction, in which the numerator (the top number) and the denominator (the bottom number) are both integers, and in which the numerator is not equal to zero. In other words which can be written in p/q form.
It is rational to consider integers as rational numbers, not as irrational, because all integers, whether positive or negative, or zero can be written as p/q, for example, 2, 3 and 5 are rational because they can be written as 2/1, 3/1 and 5/1 respectively.
Due to the fact that the rational numbers as well as the irrational numbers can be added together, we can derive real numbers. This means that all real numbers are not rational numbers, since they contain irrational numbers as well.
Hence, the given statement D is false.
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A community is building a square garden with a walkway around the perimeter with the design shown at the right. Find the side length of the inner square that would make the area of the inner square equal to 75% of the total area of the garden. Round to the nearest tenth of a foot. 1. What is an expression for the area of the inner square? 2. What is the area of the entire garden? 3. What is 75% of the area of the entire garden? 4. Write an equation for the area of the inner square using the expressions from Steps 1 and 3. 5. Solve the quadratic equation. Round to the nearest tenth of a foot. 6. Which solution to the quadratic equation best describes the side length of the inner square? Explain.
Answer:
Part 1) An expression for the area of the inner square is [tex]x^{2}=0.75(20)^{2}[/tex]
Part 2) The area of the entire garden is [tex]400\ ft^{2}[/tex]
Part 3) 75% of the area of the entire garden is [tex]300\ ft^{2}[/tex]
Part 4) The equation is [tex]x^{2}=300[/tex]
Part 5) The solutions of the quadratic equation are [tex]x=(+/-)17.3\ ft[/tex]
Part 6) The solution that best describes the side length of the inner square is [tex]x=17.3\ ft[/tex]
Step-by-step explanation:
Part 1) What is an expression for the area of the inner square?
we know that
The area of the inner square is equal to
[tex]A=x^{2}[/tex]
[tex]A=0.75(20)^{2}[/tex]
so
[tex]x^{2}=0.75(20)^{2}[/tex]
Part 2) What is the area of the entire garden?
The area of the entire garden is
[tex](20)^{2}=400\ ft^{2}[/tex]
Part 3) What is 75% of the area of the entire garden?
we know that
[tex]75\%=75/100=0.75[/tex]
so
[tex]0.75*(400)=300\ ft^{2}[/tex]
Part 4) Write an equation for the area of the inner square using the expressions from Steps 1 and 3
[tex]x^{2}=0.75(20)^{2}[/tex]
[tex]x^{2}=300[/tex]
Part 5) Solve the quadratic equation. Round to the nearest tenth of a foot
we have
[tex]x^{2}=300[/tex]
square root both sides
[tex]x=(+/-)\sqrt{300}[/tex]
[tex]x=(+/-)17.3\ ft[/tex]
Part 6) Which solution to the quadratic equation best describes the side length of the inner square?
[tex]x=(+/-)17.3\ ft[/tex]
so
The solution that best describes the side length of the inner square is
[tex]x=17.3\ ft[/tex]
because
The side length can not be a negative number
WILL BE MARK BRAIN 2(2x+32)+2/5(4x+4)
28/5x + 328/5 is the answer. I did it and checked. Hope this helped
Which best represents the units of the average rate of change for the boiling point based on the amounts of ethylene glycol in the 100ml solutions?
a. 1/(mililiters*degrees Fahrenheit)
b. degrees Fahrenheit/(mililiters)
c. (mililiters)/degrees Fahrenheit
d. (mililiters*degrees Fahrenheit)/1
Answer:
Option b. degrees Fahrenheit/(mililiters)
Step-by-step explanation:
we know that
The formula to calculate the average rate of change between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have that
the units of the y-axis are [tex]{\°F}[/tex]
the units of the x-axis are [tex]{ml}[/tex]
therefore
the units of the the average rate of change are
[tex]m=\frac{\°F}{ml}[/tex]
which linear expression is a factor of the polynomoal function f(x)=x^3+2x^2
Answer:
x + 3
Step-by-step explanation:
Factor out the greatest common factor from f(x), which is x²
We get f(x) = x²(x + 3)
The (x + 3) factor is a linear component
Lines are in the form of y = mx + b, here we have y = x + 3
33) Find the volume of the triangular pyramid to the nearest whole number.
A) 72 units3
B) 96 units3
C) 144 units3
D) 288 units3
Answer:
its b because i took a test
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
plz help
math question
Answer: 0, I think?
Step-by-step explanation: In order to do this equation, we want to get the variable on one side. In order to do this, we add 7 to both sides to cancel out the -7's. Now, we divide 9 on both sides, giving us 0.
What is the answer to this?
Answer:
C. 97.6 in³Step-by-step explanation:
The formula of a volume of a cylinder:
[tex]V=\pi r^2H[/tex]
r - radius
H - height
We have
[tex]2r=4\ in\to r=2\ in\\\\H=8\ in[/tex]
Substitute:
[tex]V_1=\pi(2^2)(8)=\pi(4)(8)=32\pi\ in^3[/tex]
The formula of a volume of a cone:
[tex]V=\dfrac{1}{3}\pi r^2H[/tex]
We have
[tex]r=2\ in\\\\H=0.7\ in[/tex]
Substitute:
[tex]V_2=\dfrac{1}{3}\pi(2^2)(0.7)=\dfrac{1}{3}\pi(4)(0.7)=\dfrac{1}{3}\pi(2.8)=\dfrac{2.8\pi}{3}=\dfrac{28\pi}{30}=\dfrac{14\pi}{15}\ in^3[/tex]
The volume of the plastic object:
[tex]V=V_1-V_2[/tex]
[tex]V=32\pi-\dfrac{14\pi}{15}=\dfrac{480\pi}{15}-\dfrac{14\pi}{15}=\dfrac{466\pi}{15}\\\\\pi\approx3.141\\\\V\approx\dfrac{466}{15}\cdot3.141\approx97.6[/tex]
Which is a rational function??
Answer:
Number C is the rational function
Help and what does a = with a line through it mean ?
Answer:
see explanation
Step-by-step explanation:
given
[tex]\frac{x8x^2-8}{4x+4}[/tex] , x ≠ - 1
The x ≠ - 1 means that x cannot take the value of - 1 as this would make the denominator equal to zero which would make the fraction undefined.
Factor the numerator/ denominator
8x² - 8 = 8(x² - 1) ← factor out 8 from both terms
x² - 1 ← is a difference of squares, hence
8x² - 8 = 8(x - 1)(x + 1)
4x + 4 = 4(x + 1) ← factor out 4 from both terms
Thus the fraction now simplifies to
[tex]\frac{8(x-1)(x+1)}{4(x+1)}[/tex]
Cancel the 8 and 4 by 4 and cancel the factor (x + 1), leaving
= 2(x - 1) = 2x - 2 ← in the form ax + b
Sarah Drew a parallelogram that is not a rectangle what is the greatest number of right angles Sarah's parallelogram can have
Final answer:
A parallelogram is a quadrilateral with parallel and equal sides, but it does not necessarily have any right angles. The greatest number of right angles a parallelogram can have is two, which occurs when the parallelogram is a rectangle.
Explanation:
A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. In a parallelogram, the opposite angles are also equal. However, a parallelogram is not required to have any right angles, and in fact, most parallelograms do not have any right angles.
The greatest number of right angles a parallelogram can have is two. This would occur when the parallelogram is a rectangle, which is a special type of parallelogram. A rectangle has opposite sides that are parallel and equal in length, and all four angles are right angles, measuring 90 degrees each.
Therefore, the answer to Sarah's question is that the greatest number of right angles her parallelogram can have is two.
Give the name and degree of the polynomial 2x-4
The given polynomial 2x-4 is of degree 1 and is typically referred to as a linear polynomial because its highest power of the variable is 1.
Explanation:The polynomial in question is 2x-4. It's important to note that the degree of a polynomial is the highest power of the variable that appears in the polynomial. In this case, the highest power of the variable 'x' is 1. Therefore, the polynomial 2x-4 is of degree 1. It is referred to as a linear polynomial because linear polynomials always have a degree of 1.
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The polynomial 2x-4 is a first-degree polynomial, also known as a linear polynomial.
Explanation:The given expression, 2x-4, is a polynomial. A polynomial is a mathematical expression composed of variables and coefficients. In this case, the variable is 'x' and the coefficients are '2' and '-4'. This specific polynomial is of first degree, because the highest power of the variable 'x' is 1. Therefore, the given expression is a linear polynomial.
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Draw a picture to show the product of 4:7 x 3. Then write the product
Answer:
¹²/₇
Step-by-step explanation:
Model ⁴/₇ × 3
Assume that you have three pies, each dived into seven slices.
There are only four slices remaining in each pie, that is, there is ⁴/₇ pie in each pie plate
The picture represents ⁴/₇ × 3.
Model the product
Now, transfer slices to get as many filled pie plates as possible.
Count the total slices.
You have 12 slices, and each slice represents ⅐ of a pie.
You have ¹²/₇ pie.
∴ ⁴/₇ × 3 = ¹²/₇
$800 is deposited in an account that pays 9% annual interest compounded annually. Find the balance after four years
Answer:
$1,129.27Step-by-step explanation:
Compounded interest formula is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where [tex]A[/tex] is the final amount, [tex]P[/tex] is the principal, [tex]r[/tex] is the anual interest in decimal, [tex]n[/tex] is the numer of compounded periods in one year and [tex]t[/tex] is the time in years.
[tex]P=\$800\\r=0.09\\n=1\\t=4[/tex]
Notice that [tex]n=1[/tex], because the interest is compounded anually, if the interest is compounded, then [tex]n=12[/tex], because there would be 12 compound periods in one year.
Then, we replace all these vaules in the formula
[tex]A=P(1+\frac{r}{n})^{nt}\\A=800(1+\frac{0.09}{1})^{1(4)}=800(1.09)^{4}\\ A=1,129.26[/tex]
Therefore, after 4 years, the amount would be $1,129.27.
kristen bought a pack of 12 pencils for $1.35 how much was each pencil
Answer: 8.8pi
Step-by-step explanation:you have to divide 12 by 1.35 then you get your answer.
Please help asap, 50 points and I'll give brainliest! :)
Answer:
1. 50
2. They are congruent
3. They are equidistant
4. No, a chord has endpoints on the edges of a circle while a radius has endpoints on the center of the circle and an edge.
5. Since the chords are not congruent, the lines cannot be congruent.
Step-by-step explanation:
Using Theorem 84, we can find that since CA = BD, the corresponding arcs are congruent. Using this theorem, we can find the answers to the rest of the questions.
If f(x) = –2x + 7 and g(x) = x2 – 2, what is [f o g](3)?
Answer:
[tex](f\circ g)(3)=-7[/tex]
Step-by-step explanation:
The given functions are;
[tex]f(x)=-2x+7[/tex]
and
[tex]g(x)=x^2-2[/tex]
We need to first of all find [tex](f\circ g)(x)[/tex]
[tex](f\circ g)(x)=f(g(x))[/tex]
[tex](f\circ g)(x)=f(x^2-2)[/tex]
[tex](f\circ g)(x)=-2(x^2-2)+7[/tex]
[tex](f\circ g)(x)=-2x^2+4+7[/tex]
[tex](f\circ g)(x)=-2x^2+11[/tex]
We now plug in x=3
[tex](f\circ g)(3)=-2(3)^2+11[/tex]
[tex](f\circ g)(3)=-18+11[/tex]
[tex](f\circ g)(3)=-7[/tex]
The answer is A. -7 on edge :)
Solve the following system. x2 + y 2= 25 2x + y = 10 The solution set
Answer: {(5,0), (3,4)}
Step-by-step explanation:
You can apply the Substitution method:
- Solve for y from the second equation.
- Substitute into the first equation and solve for x.
Then:
[tex]y=10-2x[/tex]
[tex]x^2+y^2=25\\x^2+(10-2x)^2=25\\[/tex]
(Remember that: [tex](a\±b)^2=a^2\±2ab+b^2[/tex])
[tex]x^2+(10^2-2(10)(2x)+(2x)^2)=25\\x^2+100-40x+4x^2=25\\5x^2-40x+75=0\\x^2-8x+15=0\\(x-5)(x-3)=0\\\\x=5\\x=3[/tex]
Substitute the values obtained into one of the original equation and solve for y:
[tex]2(5)+y=10\\10+y=10\\y=0\\\\2(3)+y=10\\6+y=10\\y=4[/tex]
The solution set is: {(5,0), (3,4)}
if m ACB =(11x-32),find the value of x
Answer: x= acb/11 + 32/11
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Calculation to finding the value of x:
Given:
[tex]m\ ACB =(11x-32) [/tex]
To find:
x=?
Solution:
[tex]m\ ACB =(11x-32) [/tex]
Given that ABCD is a square,
[tex] \angle ACB = 45[/tex]
Putting the given value in the question:
[tex]\to 45 = 11x-32\\\\ \to 45 + 32= 11x\\\\ \to 77 = 11x\\\\ \to 11x= 77\\\\ \to x=\frac{77}{11}\\\\ \to x=7 [/tex]
Therefore, the final answer is "7".
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Find the unit rate. A 6oz jar of jalapeños cost $2.34
Answer:
1oz cost $0.39 which will be the unite rate
Step-by-step explanation:
Answer:
$0.39 per oz
Step-by-step explanation:
[tex]\frac{6}{2.34} =\frac{1}{x} \\\\6x=2.34\\\\x=\frac{2.34}{6} \\\\x=0.39[/tex]
What is the area of the original rectangle?
A.8cm sq
B.20cm sq
C.25cm sq
D.40cm sq
Answer:
A. 8 cm sq
Step-by-step explanation:
Find the scale factor
new width/original width
8/1.6=5
calculate length of original rectangle
new length/scale factor
25/5=5cm
Find area of original rectangle
A=l×w
A=1.6×5=8cm²
A is the answer
You find the scale factor by doing 8÷1.6 which = 5
Then you do 25÷5=5
And then times 5 and 1.6 together to get 8cm sq
Can someone help me on number 22, Thanks!!!
Answer:
About 19 feet
Step-by-step explanation:
You divide 5280 by 275.5 to get feet per rotation.
The bus that takes you to school always seems to be late one month you decide to determine just how often the bus really is late for four weeks 20 school days you record of the buses later not according to the table what is the probability that the bus will be late A.0.27 B.0.5 C.0.6 D 0.75
Answer:
Step-by-step explanation:
Answer: D. 0.75
Step-by-step explanation: The bus was late 15 out of 20 times. Therefore, the experimental probability that the bus will be late is 0.75.
What is the least common multiple of 6, 18, and 8?
Answer:
6 = 2 • 3
8 = 23
18 = 2 • 32
Answer:
72
Step-by-step explanation:
Consider the least common multiple of 6 and 8
The multiples of 6 are : 6, 12, 18, 24, 30, 36, ......
The multiples of 8 are : 8, 16, 24, 32, 40, ......
The common multiple is 24 or 48 or 72
The multiples of 18 are : 18, 36, 54, 72, 90, ....
Since 72 is a common multiple of 8 and 6 and also a multiple of 72
Then the least common multiple of 6, 18 and 8 is 72
Describe the difference between vertical angles and linear pairs of angels
Answer: Vertical angles and linear pairs of angles
Step-by-step explanation:
1) Vertical angles are angles that are opposite each other when two straight lines intersect
2) A linear pair of angles is formed when two lines intersect. They are linear if they are adjacent angles formed by two intercepting lines. Linear pairs of angles add up to 180 degrees.
Tom walked around his yard. His property is rectangular with a length of 20 yards and a width of 31 yards. How much fence will he need to buy to completely surround his property?
Answer:
20 x 31= 620 ft of fence
Step-by-step explanation:
triangle STV has sides with lengths of 7, 11, and 14 units. Determine whether this is a right triangle.
Final answer:
By applying the Pythagorean theorem, we find that the sum of the squares of the two shorter sides of triangle STV (7 and 11) is not equal to the square of the longest side (14). Therefore, triangle STV is not a right triangle.
Explanation:
To determine if triangle STV with sides of 7, 11, and 14 is a right triangle, we can apply the Pythagorean theorem, a² + b² = c², where c is the hypotenuse (the longest side of the triangle) and a and b are the other two sides. For triangle STV, assume that the side with a length of 14 units is the hypotenuse, and the sides with lengths of 7 and 11 units are the other two sides.
Now, let's calculate:
a² = 7² = 49
b² = 11² = 121
a² + b² = 49 + 121 = 170
c² = 14² = 196
Since 170 does not equal 196, the sums of the squares of the sides do not equal the square of the hypotenuse. Therefore, triangle STV is not a right triangle.
a recipe calls for 2 2/4 cups of raisins,but Julie only has a 1/4 measuring cup. how many 1/4 cups does Julie need to measure out 2 and 2/4 cups of raisins
Answer:
10
Step-by-step explanation:
Divide 2 2/4 cups of raisins by 1/4 cup:
10 cups
-------------
4
=============
1 cup
--------
4
Invert the divisor and then multiply:
10 cups 4
------------- · ---------- = 10
4 1 cup
Julie must measure out 10 of these 1/4-cup measures (of raisins).
which equation has no solutions
|4x-2|=-6 because an absolute value can’t be equal to a negative
please help 15 points only help if you know the answer please.
1. 6 movies
2. 10 movies
3. The students
4. 10 - 6 = 4
5. For teachers: 9 - 4 =5
For students: 13 - 6 = 7
i need the work asap
Answer:
Step-by-step explanation:
Seven
I imagine that 7 is the one giving you the problem. There are 29 steps between where A is and where B is. The problem is in the directions. If you follow the first direction, there are 29 squares separating them meaning that B and starts on square 31 and A starts on one. If, however, you read on, your find out that B actually starts on 29. Which is it? If you follow the first direction, you get the both land on 13. Here's how.
A's motion is 3 up 1 back. His net motion is that he moves 2 forward.
B's motion is 5 down and 2 up. His not motion is - 3 each time
A B
1 31
3 28
5 25
7 22
9 19
11 16
13 13
=============================
Let's do it again starting with the second direction
A B
1 29
3 26
5 23
7 20
9 17
11 14
13 11 and they miss but keep going. You might have to go another round
15 8
17 5
19 2 Now if you try going forward you can't so B uses As rule.
21 4
23 6
25 8 And these two will never meet on this round.
I think you should follow the first rule.
27 10
28 12
25 14
22 16
19 18 another miss.
Well you can carry it on. I would ask your teacher about this one.
Eight
I can give you an answer, but I don't know how you would find it on your own. The smallest number I found was 301
You can see that 2 and 5 do leave a remainder of 1.
You can also see the 301 / 3 leaves a remainder of 1
What about 4? 301 / 4 = 75 with a remainder of 1.
301 / 6 = 50 with a remainder of 1.
301/7 = 43 with no remainder.
What a strange question.
All of these from 2 to 6 divide into 300 evenly. 301 gives a remainder of 1.
But 301 = 7 * 43
Nine
Let the smaller to the 2 angles = x
Therefore the larger one is 3x + 2
The third angle = 90 degrees.
3x + 2 + x + 90 = 180 Combine like terms on the left.
4x + 92 = 180 Subtract 92 from both sides.
4x = 180 - 92
4x = 88 Divide by 4
x = 88/4
x = 22
So the three angles are
22
66 + 2 = 68
90
This problem seems much easier than the other 2.