Answer
To multiply integers, simply multiply the unsigned numbers and place the sign on the product by repeating the above rules.
To divide unsigned integers, we divide the unsigned numeric values and put a minus sign on the result.
Statement 1: If √12 - √8 = a, then √12 + √8 is equal to 4/a.
Statement 2: a + √b is called the rationalizing factor of c + √d if their product is 1.
• Statement 1 is true; Statement 2 is true; Statement 2 is the correct explanation of Statement 1.
• Statement 1 is true; Statement 2 is true; 2 is not the correct explanation of Statement 1.
• Statement 1 is true; Statement 2 is false.
• Statement 1 is false; Statement 2 is true.
It is an assertion-reasoning question. Please help me to solve this. Need step-by-step explanation as well. Thank you.
Answer:
Statement 1 is true; Statement 2 is false.
Step-by-step explanation:
Statement 1:
√12 - √8 = a
Let's use the given value of √12 + √8 ,that is, 4/ a.
If we multiply both the expressions such that their Left Hand Sides get multiplies together and Right Hand Sides together:
=> (√12- √8)(√12 + √8) = a × 4/a
On the LHS,
identity used:
(a-b)(a+b) = a²-b²
On the RHS:
a gets canceled due to its presence in both the numerator as well as the denominator.
=> 12 - 8 = 4
=> 4 = 4
That's it!
We got LHS = RHS, that approves the existence of the given statement.
___________________
Statement 2:
"a + √b is called the rationalizing factor of c + √d if their product is 1"
That's not entirely right!
The correct statement would be:
" a + √b is called the rationalizing factor of c + √d if their product is a rational number ."
Since, rationalizing has got nothing to do with 1, (1 is just another rational number), even if we get 2 by their multiplication, it will be called rationalizing as long as we're getting a rational number.
___________________
Answer:
Hence, I'd say:
Statement 1 is correct but Statement 2 isn't.
That's the third option.
Under his cell phone plan, Nathaniel pays a flat cost of $41 per month and $4 per gigabyte. He wants to keep his bill at $45.80 per month. Write and solve an equation which can be used to determine 2, the number of gigabytes of data Nathaniel can use while staying within his budget.
Answer:
equation: 41+4x=45.80
answer: x=1.20
Step-by-step explanation:
The equation is $45.80 = $41 + ($4 × x) which can be used to determine the number of gigabytes of data Nathaniel can use while staying within his budget. And Nathaniel can use up to 1.2 gigabytes of data while staying within his budget of $45.80 per month.
Let's denote the number of gigabytes of data Nathaniel can use as x.
Then the equation representing his cell phone bill can be set up as:
Total cost = Flat cost + (Cost per gigabyte × Number of gigabytes)
$45.80 = $41 + ($4 × x)
Now, we can solve for x:
$4 × x = $45.80 - $41
$4 × x = $4.80
x = $4.80 / $4
x = 1.2
So, Nathaniel can use up to 1.2 gigabytes of data while staying within his budget of $45.80 per month.
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What is the value of x
Answer:
x = 5
Step-by-step explanation:
Δ EAB and Δ EDC are similar by the AA postulate , so the ratio of corresponding sides are in proportion , that is
[tex]\frac{AB}{DC}[/tex] = [tex]\frac{EA}{ED}[/tex] , substitute values
[tex]\frac{10}{4}[/tex] = [tex]\frac{2x+10}{x+3}[/tex] ( cross- multiply )
10(x + 3) = 4(2x + 10 ) ← distribute parenthesis on both sides
10x + 30 = 8x + 40 ( subtract 8x from both sides )
2x + 30 = 40 ( subtract 30 from both sides )
2x = 10 ( divide both sides by 2 )
x = 5
write the equation of the line in fully simplified slope-intercept form
Answer:
y = 3x - 7
Step-by-step explanation:
Slope - Intercept Form : [tex]y = mx+b[/tex]
[tex]m[/tex] = slope
[tex]b[/tex] = y - intercept
Slope = [tex]\frac{rise}{run}[/tex]
= [tex]\frac3{1}[/tex]
= [tex]3[/tex]
So far: [tex]y = 3x + b[/tex]
Plug in a point from the graph, ex. (3,2)
[tex]2 = 3(3) + b\\\\2 = 9 + b\\\\b = -7[/tex]
Equation : [tex]y = 3x - 7[/tex]
-Chetan K
A basketball player only scores two-point and three point goals during a game. The basketball player score a total of 25 points with a total of 11 goals during the game
Answer:
3 three pointers and 8 two pointers
Step-by-step explanation:
hope this helps
plsssssssss help
joey decided to start a lawn care business. He charges customers $25 per hour, plus a $75 service fee for each visit, which can be represented by the function f(x)=25x+75. In the equation, what is represented by the "x" variable?
Question 15 options:
the total cost for the lawn care visit
the number of hours Joey worked
the amount Joey charges per hour
the fixed fee for the service call
Answer:
X = The number of hours Joey worked (C)
Step-by-step explanation:
$25 is the fee per hour worked. x is the amount of hours worked. added onto this total is another flat $75 fee for the whole visit, making the equation $25 multiplied by the number of hours worked, plus 75.
i'm so confused pls somebody help me
Answer:
(6x-8)+(3x)+x=180 - the equation that would be used to find x
Step-by-step explanation:
(6x-8)+(3x)+x=180
I´m not sure what the answer of the equation is but this is the equation. im sorry :(
Answer:
see explanation
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
sum the 3 angles and equate to 180
3x + x + 6x - 8 = 180 , that is
10x - 8 = 180 ( add 8 to both sides )
10x = 188 ( divide both sides by 10 )
x = 18.8
3x = 3 × 18.8 = 56.4
6x - 8 = 6(18.8) - 8 = 112.8 - 8 = 104.8
Then the 3 angle measures are
18.8° , 56.4° , 104.8°
Meriel works in a lab and needs to measure 7.5 grams of a substance with a percent error of less than
5%. What is the smallest and largest amount they can measure to stay under this percent error?
Answer:
Step-by-step explanation:
A common way of measuring the mass of objects is to use balance scales. A balance scale works by placing the object you want to weigh on one side and adding gram masses to the other side until the scales are level. Masses for weighing usually come as 1 g, 5 g, 10 g, 20 g or more!
If you were to graph the function f(x)=−15x+4 on the semester test, you should first graph the y-intercept, then use the slope to graph a second point, and connect the points with a line.
Write the y-intercept of the function f(x)=−15x+4 in the first box. Just write the number, no y= or f(x) =.
Write the slope of the function f(x)=−15x+4 in the second box. Just write the number, no m= or slope=.
Answer:
4
-15
Step-by-step explanation:
Here's the Question ~
[tex] {2 - 1}^{2} [/tex]
Answer:
The answer is 1
Step-by-step explanation:
1² = 1×1
= 1
2 - 1² = 2 - 1
= 1
8x - 60 less than or equal to 2 (5 - 3x)
Answer:
x less than or equal to 5
i think thats what u wanted
jack makes 55$ for 6 hours of work. How much does he make per hour
Answer:
$9.16
Step-by-step explanation:
55/6=9.16
what is the cosine rule
Answer:
The sum of the squares of the lengths of the other sides minus twice the product of the other two sides multiplied by the cosine of angle contained between them equals the square of the length of any side of a given triangle.
Step-by-step explanation:
hope it helps
A piece of metal with a length of 2.83 cm was measured using four different devices. Which of the following measurements is the most accurate? O 2.812 cm O 2.837 cm O 2.805 cm 0 2.829 cm
Answer:
2.829
Step-by-step explanation:
ita the closest to 2.83
The most accurate measure is 2.829 cm.
What is rounding off a number?To change a number into an approximation having fewer significant digits.
Given that, A piece of metal with a length of 2.83 cm was measured using four different devices.
a) 2.812 =
Rounding off to the 10th place = 2.81 cm
b) 2.837 =
Rounding off to the 10th place = 2.84 cm
c) 2.805 =
Rounding off to the 10th place = 2.8 cm
d) 2.829 =
Rounding off to the 10th place = 2.83 cm
Hence, the correct answer is 2.829 cm
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need help on these 2 questions
Answer: y = -1 and x = 3
Step-by-step explanation:
x=-2y+6
3x-4y = 28
There are two ways to solve this: 1) solve directly with the equations, and 2) graph the line and look for the intersection.
---
Use the definition of x from the first equation and substitute it in the second:
3x-4y = 28
3(-2y+6)-4y = 28
-6y + 18 -4y = 28
-10y = 10
y = - 1
---
Graph the two lines and find the value of y at the point they intersect. See the attachment.
y = -1 at x= 8
=======================
For the second question:
y=3x-10
4x+5y=7
---
4x+5y=7
4x+5(3x-10)=7
4x+15x-50=7
19x = 57
x = 3
----
Verify whether:
p(x)= 3x+1 has x=-1/3 as a factor
Hey there!
p(x) = 3x + 1
y = 3x + 1
y = 3(-1/3) + 1
y = -1 + 1
y = 0
Therefore, your answer SHOULD be: y = 0
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
PLEASE HELP ME I BEG IMMA FAILLLLLLLLLLLLLLLL
On a sunny day, a 4-foot red kangaroo casts a shadow that is 5 feet long. The shadow of a nearby eucalyptus tree is 20 feet long. Write and solve a proportion to find the height of the tree.
Answer:
25 feet long
Step-by-step explanation:
this is because the ratio is 4:5
so if one side is 20 then the other side must be in proportion to 4:5
multiply both sides by 5 and u get 20:25
hope that helps
Construct a 60° angle
A cat gave birth to 3 kittens who each had a different mass between 147 and 159 g. Then the cat gave birth to a 4th kitten with the mass of 57 g. How will the birth of the 4th kitten affect the mean and median?
Look at picture this is so hard pls help
Answer:
The answer is B
Step-by-step explanation:
BRAINLIEST
Please answer these
12.
Answer: 30.25π
11π = circumference
diameter * π = circumference
diameter = 11
radius = 5.5
Area = 5.5 * 5.5 * π
Area = 30.25π
13.
Answer: 52π
Area = radius * radius * pi
Area = 676π
Radius = 26
Diameter = 2 * radius
Diameter = 52
Circumference = 52π
14.
Answer: 38π
Area = radius * radius * pi
Area = 1134.11
Radius ≈ 19
Diameter = 38
Circumference = 38π
15.
Answer: 72.25π
Circumference = diameter * π
53.41 = diameter * π
Diameter ≈ 17
Radius = 8.5
Area = radius * radius * π
Area = 72.25π
Answer:
Step-by-step explanation:
(7*10 to the power of 5)*(3*10 to the power of 2)
Step-by-step explanation:
do you mean
7×10⁵ × 3×10²
as you can see, these are all multiplications. and we can do in a first step the multiplications that combine the factors with the same exponent base or simple constants :
7×3 × 10⁵×10² = 21 × 10⁷
in what format do you need the result ?
21 × 10⁷
2.1 × 10⁸ (standard format)
210,000,000
if you discovered a leaking faucet in your home , do you think it would be important to get it fixed why or why not ??
Answer:
b
Step-by-step explanation:
It is important to get a leaking faucet fixed as soon as possible to save water, money, and prevent potential problems in the future.
It is important to get a leaking faucet fixed because of the following reasons;
1. Water waste: A leaking faucet wastes a significant amount of water over time, which can contribute to higher utility bills and water shortages in drought-prone areas.
2. Cost-saving: Fixing a leaking faucet can save you money in the long run by reducing your water bill.
3. Preventing bigger issues: Ignoring a leaking faucet can lead to more serious plumbing problems down the line, which can be more expensive to fix.
4. Environmental impact: Wasting water unnecessarily has a negative impact on the environment and can contribute to water scarcity.
Overall, it is important to address a leaking faucet promptly to save water, money, and prevent potential problems in the future.
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After heating up in a teapot, a cup of hot water is poured at a temperature of 203°F.
The cup sits to cool in a room at a temperature of 72°F. Newton's Law of Cooling
explains that the temperature of the cup of water will decrease proportionally to the
difference between the temperature of the water and the temperature of the room, as
given by the formula below:
T = Ta +(T. -T.)e-kt
To = the temperature surrounding the object
To = the initial temperature of the object
t = the time in minutes
T = the temperature of the object after t minutes
k=decay constant
The
cup of water reaches the temperature of 183°F after 2.5 minutes. Using this
information, find the value of k, to the nearest thousandth. Use the resulting
equation to determine the Fahrenheit temperature of the cup of water, to the
nearest degree, after 5 minutes.
Answer:
asd
Step-by-step explanation:
A number written in expanded form is 700,000 + 5,000 + 200 + 80 + 7. What is this number written in word form?
1 seven hundred five thousand, two hundred eighty-seven
2 seventy-five thousand, two hundred eighty-seven
3 seven hundred eighty-two thousand, five hundred seventy
4 seven hundred eighty-two thousand, five hundred seven
What is the slope of a line perpendicular to the line y = 8x -5?
Answer:
-1/8
Step-by-step explanation:
the slope would be the opposite reciprocal of 8, which would be -1/8
Answer:
Y=-1/8x-5
Step-by-step explanation:
Perpendicular lines are negative reciprocals to each other
A car travels 270 kilometers in 6 hours. How far will it
travel in 9 hours at the same speed?
Pls pa help po
Answer:
405
Step-by-step explanation:
divide 270 by 6 the multiply what you got with 9
:)
pls answer quickly
This Histogram shows the heights in inches of members of a middle school volleyball team.
How many members are between 50 and 70 inches tall?
A. 12
B. 10
C. 6
D. 4
Answer:
B. 10
Step-by-step explanation:
Look at the chart.
Find how many members are 50-60 inches tall. (6)
Find how many members are 61-70 inches tall. (4)
Add each member count up. (10)
Algebra 2
What is the sum If x≠0?
Answer:
14x^4sqrt10
Step-by-step explanation:
Out of the two possible answers showing in the picture it seemed as is it was the only valid answer
Andrea runs a fruit store. She started Sunday with 20 cherries in stock. During
the day, she sold 17 cherries and got a shipment of fresh cherries. The
shipment contained 4 times as many cherries as she started the day with.
How many cherries does Andrea have in stock at the end of the day?
Answer:
Andrea has 83 cherries in stock at the end of the day.
Step-by-step explanation:
starts with 20 cherries
sold 17 cherries
3 cherries remain
get 4 times as many she starts with 20×4= 80
80 + the 3 that remained