Answer:
d = sqrt( a^2 + b^2)
Step-by-step explanation:
Formula
d = sqrt( (x2 - x1)^2 + (y2 - y1)^2 )
Givens
x1 = a
x2 = 0
y1 = 0
y2 = b
Solution
d = sqrt( (0 - a)^2 + (b - 0)^2 )
d = sqrt( a^2 + b^2)
which is another way of writing the Pythagorean theorem.
To find the distance between points (a, 0) and (0, b), use the distance formula which results in √(a² + b²). This involves calculating the square root of the sum of the squares of the coordinates.
Therefore, the final distance is √(a² + b²).
Finding the Distance Between Two Points
To find the distance between two points (a, 0) and (0, b), we use the distance formula:
Distance formula: d = √((x2 - x1)² + (y2 - y1)²)
Let's denote the points as:
Point 1: (a, 0)
Point 2: (0, b)
Applying the coordinates to the distance formula, we get:
d = √((0 - a)² + (b - 0)²)
Simplifying inside the square root:
d = √(a² + b²)
So, the distance between the points (a, 0) and (0, b) is √(a²+ b²).
what is (68x95)+90÷10=
Hey!
--------------------------------------------
Solution:
Remember to follow PEMDAS.
= (68 * 95) + 90 / 10
= (6,460) + 90 / 10
= 6,460 + 9
= 6,469
--------------------------------------------
Answer:
6,469
--------------------------------------------
Hope This Helped! Good Luck!
In order to find the answer to the question you will have to use PEMDAS and then solve.
[tex](68\times95)+90\div10[/tex]
Using PEMDAS:
[tex]68\times95=6460[/tex]
[tex]6460+90\div10[/tex]
[tex]90\div10=9[/tex]
[tex]6460+9[/tex]
[tex]6460+9=6469[/tex]
[tex]=6469[/tex]
Therefore your answer is "6469."
Hope this helps.
Beau earns $26.50 per hour for regular hours worked and double
time for any overtime (over 40) he works. He is paid weekly. If he
worked 56.5 hours last week, how much can Beau expect that his
gross pay will be?
Answer:
$1694.5
Step-by-step explanation:
Hourly rate for Beau = $26.50
Weekly hours = 40 Hours
Basic earning = 26.50 × 40 = $820
Total number of hours Beau worked in week = 56.5 Hours
Overtime = 56.5 - 40 = 16.5 Hours
Overtime rate = 2 × Hourly rate = 2 × 26.50 = $53
Overtime earning = 53×16.5 = $874.5
Total earning for the week = 820 + 874.5 = $1694.5
Find the value of x ( please explainn)
Answer:
The value of x is 62°.
Step-by-step explanation:
It's 62° because it's a right angle (from the small box) . So you would do the given measurement (28°) and subtract that from 90°.
Which of the following pollygons cannot be used to form a regular tessellation
Answer:
B and C
Step-by-step explanation:
it is not like the other 3look at the angle sumthe angle sum of the interior angles of the regular polygons at a point add up to 360 degrees.looking at what I wrote in 3 we can see clearly why those polygons cannot tessellate .the sums of the interior angles are either greater than or less than 360 degrees .4.6(x - 3) = -0.4x + 16.2
Hey!
-----------------------------------------------
Steps To Solve:
4.6(x - 3) = -0.4x + 16.2
~Distributive property
4.6x - 13.8 = -0.4x + 16.2
~Add 0.4 to both sides
4.6x - 13.8 + 0.4= -0.4x + 16.2 + 0.4
~Simplify
5x - 13.8 = 16.2
~Add 13.8 to both sides
5x - 13.8 + 13.8 = 16.2 + 13.8
~Simplify
5x = 30
Divide 5 to both sides
5x/5 = 30/5
~Simplify
x = 6
-----------------------------------------------
Answer:
[tex]\large\boxed{x~=~6}[/tex]
-----------------------------------------------
Hope This Helped! Good Luck!
0.282828 to nearest tenth
Answer:
0.3
Step-by-step explanation:
7 is greater than 5 therefore round the tenths value up to 3
You used an app to hire a repair worker to do a series of small repairs around your office. The worker charges $54 for the first hour, and $15.50 for each additional 15 minutes. If the worker charged you $162.50, how long did the repairs take?
The repair took:
2 hours and 45 minutes.
Step-by-step explanation:The worker charges $54 for the first hour, and $15.50 for each additional 15 minutes.
Let he does a job of additional 15 minutes for: x times.
This means that:
Cost for additional minutes will be: $ 15.50x
Hence, his total cost will be equal to: 54+15.50x
i.e.
54+15.50x=162.50
i.e.
15.50x=162.50-54
i.e.
15.50x=108.50
i.e.
x=108.50/15.50
x=7
Hence, the work took a total of:
60+15×7=165 minutes
which is: 2 hours and 45 minutes.
What happens to the graph f(x) = |x/, when f(x) is replaced by 0.3 f(x) +9
Answer:
Step-by-step explanation:
First, the graph is flattened, and secondly, the whole resulting graph is translated upward by 9 units.
can you guys solve 2 through 4? thanks, worth 40 points
Answer:
7, B, 24
Step-by-step explanation:
2 . x+12 = 19
So what added to twelve equals 19? Well, 7 added to 12 is nineteen so that means x is equal to 7.
3. Inverse means opposite, so then number three would be B.
4. Finding the inverse means the opposite so subtracting the inverse of 24 is just 24 because those are opposites.
"Round 2 significant figures
5,239"
what does it want me to do here?
Answer:
5,200
Step-by-step explanation:
Significant figure = digit number
they want you to change 5239 to 2 s.f
thus,5200 <--2 digit number
To round the number 5,239 to two significant figures, we determine that the digit following the second significant figure is less than 5, so the number rounds down to 5,200.
The student is asking about rounding the number 5,239 to two significant figures. To round a number correctly to a certain number of significant figures, you start counting from the leftmost non-zero digit and keep the number of digits required. For the number 5,239:
Determine the second significant figure: The second digit after the leading 5 is 2, so that is where we will round the number.
Look at the digit following the last significant digit: In this case, it's a 3, which is less than 5.
Apply the rounding rules: Since the digit after the second significant figure is less than 5, we do not increase the second figure, and the rest of the digits become zeros.
Therefore, 5,239 rounded to two significant figures is 5,200.
The height of this iron rod is estimated to be 100 centimeters. What is the possible error of measurement?
A. 10 cm
B. 5 cm
C. 2.5 cm
D. 1 cm
Hey!
-------------------------------------------------
[tex]\large\boxed{C.~2.5~cm.}[/tex]
-------------------------------------------------
Explanation:
On the centimeter it's measures in increments of 5. The iron passes the 95 mark, so we can automatically take out option A and B. The iron rod looks like its half way between the 100 and 95 mark. So we can say that the possible error of measurement is 2.5cm. 1cm. seems to small.
-------------------------------------------------
Hope This Helped! Good Luck!
Answer:
[tex]2,5\: cm[/tex]
Step-by-step explanation:
It is impossible to calculate half-measurements in his case, so we can say so about this measurement.
I am joyous to assist you anytime.
A bag contains 7 red marbles, 5 yellow marbles, 6 blue marbles, 4 green marbles, and 3 orange marbles. What is the probability of randomly selecting a yellow marble out of the bag?
A . 1/5
B . 1/2
C . 3/5
D . 3/4
Answer:
A. 1/5
Step-by-step explanation:
Add all the numbers up, you get 25. There is 5 yellow marbles, so that's a 5/25 chance of picking a yellow one, now you just have to simplify, you then get 1/5, because 5 ÷ 5 is 1, and 25 ÷ 5 is 5.
If t = -3, then 3t2 +5t+6 equals
If ( t = -3 ), then [tex]\( 3t^2 + 5t + 6 \)[/tex] equals 0.
To find the value of [tex]\( 3t^2 + 5t + 6 \)[/tex] when ( t = -3 ), substitute (-3) for ( t ) in the expression:
[tex]\[ 3(-3)^2 + 5(-3) + 6 \][/tex]
= 3(9) - 15 + 6
= 27 - 15 + 6
= 12 - 15
= -3
Therefore, when ( t = -3 ), \[tex]( 3t^2 + 5t + 6 \)[/tex] evaluates to (-3).
Understanding how to substitute values into algebraic expressions is fundamental in algebra. In this case, replacing ( t ) with (-3) allows us to find the specific value of the expression for that given input.
It's worth noting that this expression equals 0 for ( t = -3 ). This is an interesting mathematical result, indicating that the expression [tex]\( 3t^2 + 5t + 6 \) factors as \( (t + 3)(3t + 2) \),[/tex] making it equal to 0 when either \[tex]( t = -3 \) or \( t = -\frac{2}{3} \).[/tex] This connection between factors and roots is a crucial concept in algebra.
What is the sum of 308, 622 and 381.
Answer:
755
Step-by-step explanation:
The sum of 308+622+381=755
The sum of the numbers 308,622, and 381 is 755.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the numbers are 308, 622 and 381. The sum of the numbers will be calculated by adding all the numbers as below,
Sum = 308+622+381
Sum = 755
Hence, the sum of the numbers will be 755.
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What was built in Lowell, Massachusetts that helped change the lives of Americans?
A. Grain mills
B. Steel mills
C. Corn mills
D. Textile mills
Answer:
The Correct Answer is D
Textile mills
Step-by-step explanation:
Lowell's influence on industrialization in the United States was huge as his techniques were quickly replicated in different industries beyond the nation.By 1839, the facilities in Lowell hired at some measures more than 7,000 textile laborers, generally known as mill ladies or industry ladies. The Lowell mills were the primary reflection of the industrial revolution to happen in the United States, and with their achievement got two separate aspects of the facilities.I need help with geometry
A linear pair is supplementary.
It always helps to draw out a diagram with the information you have - it makes the solving process more visual and sometimes easier. I have attached a diagram of this linear pair.
So, since a linear pair is supplementary, we know these two angles add to equal 180°. Let's write this in an equation.
(5n + 15) + (4n + 21) = 180
Solve for n.
(5n + 15) + (4n + 21) = 180
5n + 15 + 4n + 21 = 180
9n + 36 = 180
9n = 144
n = 16
We're not done yet - now we have to plug this in for n to find the angle measures.
5n + 15
5(16) + 15
80 + 15
95
4n + 21
4(16) + 21
64 + 21
85
Lastly, check your work by adding the angle measures.
95 + 85 = 180
Answer:m∠EFG = 95°
m∠GFH = 85°
(8a to the 3rd power -3b to the 2nd power) -(-a to the third power +b to the 2nd power)
Simplify
Answer:
7a³-2b²
Step-by-step explanation:
[tex]8a^3-3b^2-(-a)^3+b^2=(8-1)a^3+(-3+1)b^2=7a^3-2b^2[/tex]
_____
Math symbols were invented so that expressions could be written unambiguously. You might find you are more likely to get the answers you need if you use them.
what is the image of the point (-8,3) after a rotation of 270 counterclockwise
Answer:
[3, 8]
Step-by-step explanation:
Now, a 90°-clockwise rotation is the exact same as a 270°-counterclockwise rotation, and according to the 270°-counterclockwise rotation [90°-clockwise rotation] rule, you take the y-coordinate, bring it over to your new x-coordinate, and take the OPPOSITE of the x-coordinate and set it as your new y-coordinate:
Extended Rotation Rules
270°-clockwise rotation [90°-counterclockwise rotation] >> (x, y) → (-y, x) 270°-counterclockwise rotation [90°-clockwise rotation] >> (x, y) → (y, -x)180°-rotation >> (x, y) → (-x, -y)So, perform your rotation:
270°-counterclockwise rotation [90°-clockwise rotation] → [-8, 3] moves to [3, 8]
I am joyous to assist you anytime.
The image of the point (-8,3) after a rotation of 270 degrees counterclockwise is (3,8).
The image of the point (-8,3) after a rotation of 270 degrees counterclockwise can be determined by using the concept of rotation of vectors in a coordinate plane. A rotation of 270 degrees counterclockwise is equivalent to a 90 degrees clockwise rotation. To rotate a point, you can use the rotation matrix:
For a 90 degrees clockwise rotation, the rotation matrix is:
[0 1]
[-1 0]
Applying this matrix to point (-8,3) gives us:
[0 1] [-8]
[-1 0] [3]
Which results in:
[3]
[8]
Therefore, the new coordinates after rotation will be (3,8).
Complete the sentence to make true statements 5 is 100 times
Complete statement is;
⇒ 5 is 100 times of 0.05.
Here,
We have to make true statements of ''5 is 100 times _____''
What is Fraction?
A fraction represent how many part of a whole.
Now,
Since, 5/100 is equal to 0.05,
Hence, we can say that 5 is the result of multiplying 0.05 by 100.
As, 0.05 x 100 = 5
So, 5 is 100 times of 0.05.
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A triangle has sides with lengths of 5x – 7,
3x -- 4, and 2x – 6. What is the simplified
expression for the perimeter of the triangle?
Answer:
10x - 17
Step-by-step explanation:
Perimeter is the sum of all sides
5x - 7 + (3x - 4) + (2x - 6)
10x - 7 - 4 - 6
10x - 17
3y + 1 - 2y = -3 - 3y
Answer:
Step-by-step explanation:
3y + 1 - 2y = -3 -3y
4y = -4
y = -1
Answer:
y=-1
Step-by-step explanation:
First you combine like terms.
1y+1=-3-3y
Then you add 3 on both sides so the -3 cancels out.
1y+4=-3y
Then you subtract 1y on both sides to cancel out y.
4=-4y
Then you divide both sides by -4 to get y by itself.
y=-1
let f(x) = x^2 - 2x + 2 and g(x) = x - 3. find f(x) times g(x)
Answer:
x³ - 5x² + 8x - 6
Step-by-step explanation:
(x² - 2x + 2)(x - 3) ← product is required
Each term in the second factor is multiplied by each term in the first factor , that is
x²(x - 3) - 2x(x - 3) + 2(x - 3) ← distribute all 3 parenthesis
= x³ - 3x² - 2x² + 6x + 2x - 6 ← collect like terms
= x³ - 5x² + 8x - 6 → (b)
Answer:
g( x)^2=x^2-6x+9=f(x)-4x+7, f(x)=g(x)^2-4g(x)-5=(g(x)-2)^2-9=(g(x)+7)×(g(x)-11)
f(x)=x^2-2x+2=g(×)^2+4x-7
3 The volume of a cube is 8 ft}. What is the length of each
edge of the cube?
Answer:
The correct answer is 4.
Step-by-step explanation:
Each grade level at Hooperville Schools has 298 students.
a. If there are 13 grade levels, how many students attend Hooperville Schools?
b. A nearby district, Willington, is much larger. They have 12 times as many students. How many students attend schools in Willington?
Answer:
(a) 3,874 students.
(b) 46,488 students.
Step-by-step explanation:
We have been given the each grade level at Hooperville Schools has 298 students.
(a) To find the number of students that attend Hooperville Schools, we will multiply the number of grades by 298.
[tex]\text{Students that attend Hooperville Schools}=13\times 298[/tex]
[tex]\text{Students that attend Hooperville Schools}=3,874[/tex]
Therefore, 3,874 students attend Hooperville Schools.
(b) We have been given that nearby district, Willington, is much larger. They have 12 times as many students.
To find the number of students that attend schools in Willington, we will multiply number of students at Hooperville schools by 12.
[tex]\text{Students that attend Willington Schools}=12\times 3,874[/tex]
[tex]\text{Students that attend Willington Schools}=46,488[/tex]
Therefore, 46,488 students attend schools in Willington.
11. During a thunderstorm, 143 out of 333
houses lost electrical power.
a. Write the decimal equivalent for
b. Use Structure What do you notice
about the digits in the decimal
equivalent?
Answer:
a).429 with all numbers repeating
b)They all repeat
The equivalent decimal value is 0.429429 and the number 429 is repeated after the decimal.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The question is incomplete.
The complete question is:
During a thunderstorm, 143 out of 333
houses lost electrical power.
a. Write the decimal equivalent for 143/333.
b. Use Structure What do you notice about the digits in the decimal equivalent?
As we know from the definition of the fraction, the number 143 is in the numerator and the number 333 is in the denominator.
= 143/333
After dividing:
= 0.429429....
The equivalent decimal value is 0.429429.
As we can see after dividing the number 429 is repeated after the decimal.
Thus, the equivalent decimal value is 0.429429 and the number 429 is repeated after the decimal.
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Order these numbers from Least to Greatest 4,209 2,438 4,703 3,026
2,438 3,026 4,209 4,703
Answer: 2,438 3,026 4,209 4,703
Step-by-step explanation:
I need help on number 2.
Greetings!
This is how your double number line should look:
(lbs) 0 1 2 3 4 5
↓-----↓-----↓-----↓-----↓-----↓
0 3.5 7 10.5 14 17.5 (dollars)
Hope this helps!
Find the area of the region that is NOT shaded .
146 ft^2
122 ft^2
90 ft^2
234 ft^2
Answer:
122 ft^2.
Step-by-step explanation:
This area can be divided into 2 rectangles:
One of size 14 * 4 = 56 ft^2 and
another of size (15 - 4)* 6 = 66ft^2
Total 66 + 56 = 122 ft^2.
Answer:
Step-by-step explanation:
Let's start with the bigger portion of the non-shaded area.
It is 15*6 because it is showing us that the distance between the non-shded area and the shaded area is 6 feet, if we slide that over, it is exactly what we need. So...
15*6=90 feet
Now, the smaller part. BTW, we are pretending there is a line from the bottom left corner of the shaded, straight across to the real line at the 14.
That being said, we need to subtract 6 from 14 to get the dimension.
So...
14-6= 8 feet.
It tells us that the width is 4 feet.
8*4= 32.
Now we have to add. 32+90=122feet squared.
making the answer, B
Hope this helps!!!
Brady
Drag and drop the answers into the boxes to correctly complete the statement.
A sequence of transformations that maps △RST to △R′S′T′ is a _____ followed by a _____
A. reflection across the x-axis
B. Translation 1 unit down
C. Reflection across the y-axis
D. Rotation of 180 degrees about the origin
Answer:
A sequence of transformations that maps △RST to △R′S′T′ is a Reflection across the x-axis followed by a Translation 1 unit down
Step-by-step explanation:
step 1
Find out the reflection of △RST across the x-axis
we know that
The rule of the reflection of a point across the x-axis is
(x,y) -----> (x,-y)
we have
R(1,3),S(1,1),T(4,1)
Applying the rule of reflection across the x-axis
R(1,3) -----> R''(1,-3)
S(1,1) -----> S''(1,-1)
T(4,1) ----> T''(4,-1)
step 2
Find out the translation of △R''S''T'' 1 unit down
The rule of the translation is
(x,y) -----> (x,y-1)
Applying the rule of the translation
R''(1,-3)-----> R'(1,-3-1)
R''(1,-3)-----> R'(1,-4)
S''(1,-1)----> S'(1,-1-1)
S''(1,-1)----> S'(1,-2)
T''(4,-1) ----> T'(4,-1-1)
T''(4,-1) ----> T'(4,-2)
therefore
A sequence of transformations that maps △RST to △R′S′T′ is a Reflection across the x-axis followed by a Translation 1 unit down
1-5 Skills Practice
Descriptive Modeling and Accuracy
1. TEST SCORES A teacher compares the ratio of the number of questions answered correctly to the
total number of questions on a test as a metric. For a student to earn and A or B on a test, the ratio
must be greater than or equal to 0.8. The last test given by the teacher had a total of 40 questions.
Using this metric, what is the least number of questions a student can answer correctly and earn an
A or B on the test?
number of questions answered correclty
Ratio to earn an A or B - -
number of questions
Answer:
The least number of questions a student can answer correctly is 32
Step-by-step explanation:
Let
x -----> the number of questions answered correctly
y ----> the total number of questions on a test
[tex]ratio=\frac{x}{y}[/tex]
we know that
For a student to earn and A or B on a test, the ratio must be greater than or equal to 0.8
so
[tex]\frac{x}{y} \geq 0.8[/tex]
For y=40 questions
Find the value of x
substitute
[tex]\frac{x}{40} \geq 0.8[/tex]
solve for x
Multiply both sides by 40
[tex]x \geq 0.8(40)[/tex]
[tex]x \geq 32[/tex]
so
The least number of questions a student can answer correctly is 32
Verify the ratio
For x=32, y=40
[tex]\frac{32}{40}=0.8[/tex]
Compare
[tex]0.8 \geq 0.8[/tex] ----> is ok
Final answer:
This math question involves determining the minimum number of questions a student needs to answer correctly to earn an A or B grade based on a specific ratio criterion.
Explanation:
Mathematics: In this question, we are dealing with a scenario where a teacher evaluates students' test performance based on a specific ratio criterion to determine if they earn an A or B grade. The focus is on determining the minimum number of questions a student must answer correctly to achieve the desired grades.
Step-by-step explanation:
Given that the ratio of correct answers to the total questions must be greater than or equal to 0.8 to earn an A or B.
We know the total number of questions on the test is 40.
To find the least number of questions a student must answer correctly, we calculate 0.8 x 40 = 32.
Therefore, the student needs to answer at least 32 questions correctly to earn an A or B on the test.