Answer:
The correct options are;
A. 1·2 = 2
B. 1·1 = 1
E. 1 + 1 = 2
Step-by-step explanation:
Given that the equations 1.2 = 2 and 1.1 = 1 are correctly written as 1·2 = 2 and 1·1 = 2, we have;
The product of any number and one is equal the same number, that is a × 1 = a
Whereby we have the expression 1·2 which is 1 × 2, we therefore have;
1 × 2 = 1 · 2= 2
B. Similarly we have;
1 · 1 = 1 × 1 = 1
Also, 1 + 1 = 2 is correct as the sum of two numbers is equal to the sum of the count of the numbers, therefore;
E. 1 + 1 = 2 is correct.
represent 8/5 on number line
Answer:
Step-by-step explanation:
--------|--------|---------|------||----|--------|---------|--------------------->
-1 0 1 5/8 2 3 4 ∞
steps to solve x/8-5=-1
Answer: x = 32
Step-by-step explanation:
x/8 - 5 = -1
Add 5 both sides : x/8 = 4
Multiply both sides by four: x=4 times 8
Which of the following illustrates the truth value of the given conditional statement?
If dogs have five legs, then cats have three tails.
A.) F F → T
B.) T T → T
C.) T F → F
D.) F T → T
Correct Answer: A) F F → T
I did the assignment and got it right, trust me.
There are (32)4 ⋅ 30 bacteria in a petri dish. What is the total number of bacteria in the dish?
The total number of bacteria in the dish is 31457280
How to determine the total number?The expression is given as:
Total = (32)^4 * 30
Start by evaluating the exponent
Total = 1048576 * 30
Next, evaluate the product
Total = 31457280
Hence, the total number of bacteria in the dish is 31457280
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Answer:
A (3^8)
Step-by-step explanation:
I have this question on my test. I'm just assuming the person didn't put ^.
(3^2)^4 times 3^0
Enter the equation of the circle in standard form with center and radius given.\\\\\\\\\\\Center (8,0), radius = sqrt 3///////////
Answer:
(x - 8)^2 + y^2 = 3.
Step-by-step explanation:
(x - h)^2 + (y - k)^2 = r^2
Here h = 8, k = 0 and r^2 = (√3)^2 = 3
The answer is (x - 8)^2 + (y - 0)^2 = 3
or (x - 8)^2 + y^2 = 3.
Find the value of the variable. if Y is between X and Z.
segment XY = 4a and segment YZ = 9a and segment XZ = 6a+24
Answer:
[tex]\bold{a = \dfrac{24}{7}}[/tex]
Step-by-step explanation:
Kindly refer to the attached for the values labelled to the line XZ.
The point Y is in between XZ.
It can be clearly observed that XZ is made up of sum of two lines XY and YZ.
So, we can write:
XZ = XY + YZ ....... (1)
We are given the values of line segments:
XY = 4a
YZ = 9a and
XZ = 6a+24
To find: Value of variable 'a'.
Solution:
Putting all the values in equation (1):
[tex]6a+24 = 4a + 9a\\\Rightarrow 6a+24=13a\\\Rightarrow 7a=24\\\Rightarrow \bold{a = \dfrac{24}{7}}[/tex]
So, value of variable is
[tex]\bold{a = \dfrac{24}{7}}[/tex]
PLEASE help me. I am stuck on this question for a long time. This is a graph problem
Answer:
plot 2
Step-by-step explanation:
put number in order from least to highest:
1 ,3,4,5,8,8,9,11,11,11,14,15,15,18,19,19,19,21,22,23,
from 1 to 5 4 terms
5 to 10 3 terms
from 10 to 15 4 terms (since you can put the 15 in either 10 to 15 or 15to 20)
from 15 to 20 6 terms
from 20 to 25 3
A triangle has side lengths of (8.1t-6.1)(8.1t−6.1) centimeters, (8.1t+7.1)(8.1t+7.1) centimeters, and (3.4u+1.9)(3.4u+1.9) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
Answer:
(16.2t+3.4u+2.9)cm
Step-by-step explanation:
A triangle is a plane shape that has three sides. The perimeter of a triangle is gotten by taking the sum of all the lengths of the three sides. Let the length of the three sides by s1, s2 and s3, the perimeter of the triangle will be expressed as;
P = s1+s2+s3
Given the side lengths
s1 = (8.1t-6.1)cm
s2 = (8.1t+7.1)cm
s3 = (3.4u+1.9)cm
Perimeter of the triangle = 8.1t-6.1+8.1t+7.1+3.4u+1.9
collect the like terms
P = 8.1t+8.1t+3.4u-6.1+7.1+1.9
P = 16.2t+3.4u+2.9
Hence the expression that represents the perimeter, in centimeters, of the triangle is (16.2t+3.4u+2.9)cm
A woodworker made 60 decorative shelves to sell at a fair. 30% of the
shelves were made out of maple wood. How many maple shelves does he
have to sell?
18 shelves he needs to sell
What is the next step when solving the following equation?
8x + 8-6 = 60 - 24x - 20
8x + 2 = 40 - 24x
8x + 24x + 2 = 40 - 24x + 24x
32x + 2 = 40
Answer:
8x + 2 = 40 - 24x
Step-by-step explanation:
8x + 8-6 = 60 - 24x - 20
Next step is simplification and is:
8x + 2 = 40 - 24xThe following steps:
8x + 24 x + 2 = 4032x + 2= 4032x = 40 - 232x = 38x = 38/32x = 19/16Are the fractions 1/4 and 3/12 common denominators?
Answer:
No
Step-by-step explanation:
Common denominators are the same number. Since 1/4 has a denominator of 4 and 3/12 has a denominator of 12 they are not the same, and therefore are not common denominators.
Answer:
no
Step-by-step explanation:
How would you solve this?
Answer:
The area of the black square is equal to the sum of the areas of the gray squares.
Answer:
The area of the black square is equal to the sum of the areas of the gray squares.
Given x=-3, y=6, and z=-4 xz/-2y
Answer:
-1
Step-by-step explanation:
sub in the values of x, y and z into the equation
you get:
(-3)(-4)/(-2)(6)
= 12/-12
= -1
Answer: -1
Step-by-step explanation:
xz/-2y, given x=-3, y=6, and z=-4
------------
xz/-2y
=(-3)(-4)/-2(6) ⇔ substitute x y and z value
=12/-12 ⇔ calculate it
=-1 ⇔ simplify fraction
Hope this helps!! :)
Please let me know if you have any question
Solve the following by opening the parenthesis and then applying MDAS. 52−{32+[9−(4−3)]}
Answer:
40
Step-by-step explanation:
4-3=1
9-1=8
32+8=40
52-40=12
12 is your final answer
Complete the statements about the associative property and equivalent expressions.
The associative property allows us to change the grouping of the factors that are multiplied together to create ________
1. equibalent expression
2. operations
3. parentheses
4. variables
When changing the grouping, the order of the factors stays the same; only the change position.
The expression______ is an equivalent expression to w(xy)z.
1. w+x+y+z
2. w+xy+z
3. (wx)yz
4. wx + yz
The expression ________ is also an equivalent expression to w(xy)z.
1. 2wx(2yz)
2. wx(yz)
3. wx + yz
4. z+y+x+w
Answer:
1,3,3,2
Step-by-step explanation:
hope this helps :)
The required solutions are,
1. operations.
2. w(xy)z.
3. w(xy)z
The associative property is a mathematical principle that states that the grouping of operations or factors does not affect the final result of a calculation, as long as the order of the terms remains the same.
Here,
The associative property allows us to change the grouping of the factors that are multiplied together to create 2. operations.
When changing the grouping, the order of the factors stays the same; only the position changes.
The expression 3. (wx)yz is an equivalent expression to w(xy)z.
The expression 2. wx(yz) is also an equivalent expression to w(xy)z.
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Prove that a positive integer $n \geq 2$ is prime if and only if there is no positive integer greater than $1$ and less than or equal to $\sqrt{n}$ that divides $n$
Answer:
Proof given by contradiction.
Step-by-step explanation:
Given that:
[tex]n \geq 2[/tex]
To prove:
[tex]n[/tex] is prime if and only if no positive integer > 1 and [tex]\leq[/tex] [tex]\sqrt n[/tex] divides [tex]n[/tex].
Solution:
First of all, let [tex]n[/tex] is a composite number i.e. not a prime number such that:
[tex]n =a\times b[/tex]
and [tex]a[/tex] and [tex]b[/tex] are prime and [tex]a[/tex] divides [tex]n[/tex] and [tex]b[/tex] also divides [tex]n[/tex].
Let [tex]\sqrt n = p[/tex]
or [tex]n = p\times p[/tex]
1. [tex]\underline{a < p}[/tex]:
[tex]a[/tex] is prime and is a divisor of [tex]n[/tex].
2. [tex]\underline{a>p}[/tex]:
[tex]n = a\times b = p\times p[/tex]
We have assumed that [tex]a > p \Rightarrow b <p[/tex]
[tex]b[/tex] is a prime number and is a divisor of [tex]n[/tex].
But we are given that no prime number [tex]\leq \sqrt n[/tex] divides [tex]n[/tex] but we have proved that [tex]b < \sqrt n[/tex] divides [tex]n[/tex].
So, it is a contradiction to our assumption.
Therefore, our assumption is wrong that [tex]n[/tex] is a composite number.
Hence, proved that [tex]n[/tex] is a prime number.
Find the solutions to 8x^2-56x=0 check all that apply
Answer:
[tex]\boxed{ x = 0 \ \ OR \ \ x = 7}[/tex]
Step-by-step explanation:
[tex]8x^2 -56 = 0[/tex]
Greatest common factor = 8x
=> [tex]8x(x-7) = 0[/tex]
Setting results equal to 0
Either:
8x = 0 OR x-7 = 0
x = 0 OR x = 7
Answer:
x= 0 or 7
Step-by-step explanation:
if you factor out the equation by 8, you get 8x(x-7)=0, which if you simplify that, gets you 0 or 7.
A construction crew is lengthening a road. Let L be the total length of the road (in miles). Let D be the number of days the crew has worked. Suppose that L=3D+200 gives L as a function of D. The crew can work for at most 90 days. Identify the correct description of the values in both the domain and range of the function. Then, for each, find the most appropriate set of values. PLEASE PLEASE PLEASE HELP!!! I WILL GIVE BRAINLIEST!!!
Answer:
Step-by-step explanation A construction crew is lengthening a road. Let L be the total length of the road (in miles). Let D be the number of days the crew has worked. Suppose that =L+4D200 gives L as a function of D . The crew can work for at most 70 days. =L+4D200 is not clear, not an equation.on:
how do you solve
2/5x+10=0
Answer:
x = -25
Step-by-step explanation:
Step 1: Write out equation
2/5x + 10 = 0
Step 2: Subtract 10 on both sides
2/5x + 10 - 10 = 0 - 10
2/5x = -10
Step 3: Multiply both sides by 5/2
5/2(2/5x) = -10(5/2)
x = -50/2
x = -25
It takes 3 cats 3 minutes to catch 3 mice. How many cats are needed to catch 99 mice in 99 minutes?
Greetings,
I hope you and your family are staying safe and healthy!
So basically, we have 3 cats catching 3 mice in 3 minutes. That means 1 cat is catching 1 mouse, but it takes it 3 mn.
Now if we have 99 mice and we need to catch them in 99 minutes, we will need 99 cats.
99 cats will catch 99 mice in 99 minutes...meaning each cats will take 1 minute to catch their mice.
----------------
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The expression s² is used to calculate the area of a square, where s is the sidelength of the square. What does the expression (8x)² represent?A.The area of a square with a side length of 8b.The area of a square with a side length of 16c.The area of a square with a side length of 4xd.The area of a square witha side length of 8x
Answer:
Step-by-step explanation:
s^2 represents the area of a square whose side length is s.
(8x)^2 represents the area of a square whose side length is 8x.
Suppose a population consists of 50,000 people. Which of the following
numbers of members of the population being surveyed could result in a
sample statistic but not a parameter?
A. 500
B. Both 500 and 50,000
C. Neither 500 nor 50,000
D. 50,000
SUB
Answer:
500
Step-by-step explanation:
Parameter= whole population
Sample statistic= outcome of part of population surveyed
I’ll give you 30 points if you help
Answer:
2, -2
Step-by-step explanation:
f(x) = 2x + 1
g(x) = x - 3
To find g(f(x)), you need to put f(x) into g(x).
g(f(x)) = (2x + 1) - 3
g(f(x)) = 2x + 1 - 3
g(f(x)) = 2x - 2
Your answer will be 2 and -2.
Jana ran every day for 8 days.
•She ran a total of 50 miles
•She ran the same number of miles each day.
A. 4/25
B. 25/4
C. 8/25
D. 25/8
Answer:
B. 25/4
Step-by-step explanation:
to calculate how many miles Jana ran everyday, divide the total distance by number of days
50/8
simplify, 25/4
the answer is B
3x+1=43 but you have to regroup/ divide the number next to x
Answer:
x = 14
Step-by-step explanation:
3x+1=43
Subtract 1 from each side
3x+1-1=43-1
3x = 42
Divide by 3
3x/3 = 42/3
x =14
Answer:
x =14
Step-by-step explanation:
Find the volume and total surface area of the composite figure below.
Answer:
Volume = 6467.492mm³
Surface area = 1332.035mm²
Step-by-step explanation:
volume of a cone is [tex]\pi[/tex]r²h. V=[tex]\pi[/tex]10²(24)=7539.822mm³
volume of a sphere is 4/3[tex]\pi[/tex]r³. V=4/3[tex]\pi[/tex](8³)=2144.66mm³
Since it's a half of a sphere, it would be 1072mm.33³
7539.822-1072.33=6467.492mm³
Surface area of a cone is [tex]\pi[/tex]r(r+√h²+r²)=1130.97
area of a circle= [tex]\pi[/tex]r²=201.06
surface area of a sphere is 4[tex]\pi[/tex]r²=804.25
Since it's a half sphere, it would be 402.125
1130.97-201.06+402.125=1332.035mm²
i need help please!
Answer:
[tex]\Huge \boxed{y=3x+6}[/tex]
Step-by-step explanation:
y = mx + b
m = slope
b = y-intercept
The slope can be found from two points.
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
The two points from the graph are (1, 9) and (2, 12).
Plugging in the values and evaluating.
[tex]\displaystyle m=\frac{12-9}{2-1}[/tex]
[tex]\displaystyle m=\frac{3}{1}[/tex]
[tex]m=3[/tex]
The slope of the line is 3.
The y-intercept of the line is where the line cross the y-axis.
The line crosses the y-axis at (0, 6).
[tex]b=6[/tex]
The slope-intercept form of the line is:
[tex]y=3x+6[/tex]
How to do this question plz answer my question
Answer:
$121.82
Step-by-step explanation:
Okay, this is kind of complex, so let's go step by step.
First, we want to find the area of the rectangular lawn - we can do this by multiplying the length and width. The length is 100 and the width is 45 so [tex]45\cdot100=4500[/tex] m² is the area of the rectangle.
However, there are 3 ponds in which the grass seeds will not be going - so we need to find the area of all 3 of these circles and subtract it from 4500 (our rectangle area).
The area of a circle is represented by the formula [tex]\pi r^2[/tex]
The diameters are given here, which is double the radius, so to find the radius of each circle let's divide the diameters by 2.
First circle's radius: [tex]20\div2=10[/tex]
Second circle's radius: [tex]10\div2=5[/tex]
Third circle's radius: [tex]5\div2=2.5[/tex]
Now let's find the area of each circle.
First Circle: [tex]\pi \cdot10^2 = \pi\cdot100=3.14\cdot100=314[/tex]
Second Circle: [tex]\pi\cdot5^2 = \pi \cdot25 = 3.14\cdot25=78.5[/tex]
Third Circle: [tex]\pi \cdot 2.5^2 = \pi \cdot6.25 = 3.14\cdot6.25=19.625[/tex]
Adding all of these values gets us 412.125.
Now we can subtract from this from 4500 to get us 4087.875
If the grass seeds that cost £1.49 cover 50m² each, then we need [tex]4087.875\div50=81.7575[/tex] bags.
Each bag costs £1.49, so the total cost is [tex]81.7575\cdot1.49\approx121.82[/tex]
Hope this helped!!
Write a linear (y=mx+b), quadratic (y=ax2), or exponential (y=a(b)x) function that models the data. Y=?
Answer:
y = 8x - 6
Step-by-step explanation:
find the common difference (+ or -) / ratio (x or ÷)
34 - 26 = 8
42 - 34 = 8
50 - 42 = 8
58 - 50 = 8
the common difference is 8
y = 8x + b
plug in an (x, y) value to find b
(7, 500
50 = 8(7) + b
50 = 56 + b
b = -6
y = 8x - 6
Consider the difference of cubes identity: a3 − b3 = (a − b)(a2 + ab + b2). For the polynomial x3 − 64, a = and b =
Answer:
a= x, b= 4
Step-by-step explanation:
a³ − b³ = (a − b)(a² + ab + b²)x³ - 64Comparing polynomials:
a³= x³ ⇒ a = xb³= 64 ⇒ b³ = 4³ ⇒ b= 4Applying same formula:
x³ - 64 = (x- 4)(x² + 4x + 16)