Long Multiplication
1. Arrange the numbers one on top of the other and line up the place values in columns. The number with the most digits is usually placed on top as the multiplicand.
This will be written as follows:
467
x 48
---------------
2. Starting with the ones digit of the bottom number, the multiplier, multiply it by the last digit in the top number.
This product is 8*7 = 56
3. If that answer is greater than nine, write the ones place as the answer and carry the tens digit.
We should write 6 and carry 5:
467
x 48
---------------
6 (carry 5)
4. Proceed right to left. Multiply the ones digit of the bottom number to the next digit to the left in the top number. If you carried a digit, add it to the result and write the answer below the equals line. If you need to carry again, do so.
The next product is 8*6 = 48. Adding the carry: 48+5=53, Write 3, carry 5:
467
x 48
---------------
36 (carry 5)
Multiply 8*4 = 32. Add the carry 5: 32+5 = 37. Write the full number because it's the last of the products of this step:
467
x 48
---------------
3736
5. When you've multiplied the ones digit by every digit in the top number, move to the tens digit in the bottom number.
Multiply as above, but this time write your answers in a new row, shifted one digit place to the left.
Multiply 4*7 = 28. Write 8, carry 2.
467
x 48
---------------
3736
8 (carry 2)
Multiply 4*6=24. Add 2: 24+2=26. Write 6, carry 2:
467
x 48
---------------
3736
68 (carry 2)
Multiply 4*4=16. Add 2: 16+2=18. Write the full number:
467
x 48
---------------
3736
1868
6. When you finish multiplying, draw another answer line below your last row of answer numbers.
467
x 48
---------------
3736
1868
----------------
7. Use long addition to add your number columns from right to left, carrying as you normally do for long addition.
467
x 48
---------------
3736
1868
----------------
22416
Question 94 ptsONLY write your answer as a number. You do not needto write the unit measurement.Round you answer to the nearest tenth.15. A fireman leaned a 42-foot ladder against a building. If he placed the ladder 8.5 feetfrom the base of the building, what angle is formed between the ladder and the ground
The length of ladder is L = 42 foot.
The distance between base of building and ladder is b = 8.5.
Determine the measure of angle by using the trigonometry.
[tex]\begin{gathered} \cos \theta=\frac{8.5}{42} \\ \theta=\cos ^{-1}(0.20238) \\ =78.323 \\ \approx78.3 \end{gathered}[/tex]So measure of angle is 78.3 degree.
Enter the ratio as a fraction in lowest terms6 ft to 78 in.
To answer this question, we need to remember that a ratio is a comparison of two or more units. We can also need to have into account that these units must be in the same units.
We have one of the quantities is 6ft, the other is equal to 78 inches. We can convert 6ft to its equivalent in inches, or 78 inches into its equivalent in feet. Then, we have:
[tex]6ft\cdot\frac{12in}{1ft}=72in[/tex]Then, we can conclude that the ratio of 6feet (72 inches) to 78 inches is equivalent to:
[tex]\text{Ratio}=\frac{72in}{78in}=\frac{12}{13}\Rightarrow Ratio=\frac{12}{13}[/tex]The hypotenuse of a right triangle is four times the length of one of the legs. The length of the other leg is sqrt(240) feet. Find the lengths of the leg and hypotenuse
ANSWER
Hypotenuse: 16 ft
Leg: 4 ft
EXPLANATION
Given:
A right angle triangle with only one leg = sqrt(240) feet
Desired Outcomes:
Lengths of the leg and hypotenuse
Declaration of variables
Let x represent the length of leg
Hypotenuse = 4 times the length of leg = 4x
Apply Pythagorean theorem
[tex]\begin{gathered} Hyp^2=Opp^2+Adj^2 \\ (4x)^2=x^2+(\sqrt{240})^2 \\ 16x^2\text{ = }x^2\text{ + 240} \\ 16x^2-x^2\text{ = 240} \\ 15x^2\text{ = 240} \\ x^2\text{ = }\frac{240}{15} \\ x\text{ =}\sqrt{16} \\ x\text{ = 4 ft} \end{gathered}[/tex]Hypotenuse = 4x = 4 (4) = 16 ft
Hence, the Lengths of the leg and hypotenuse are 4 ft and 16 ft respectively.
Sarah got a $60 gift card to Walmart. She uses the gift card to buy orange juice for $4.50. She also wants to use the gift card to buy shirts. Each shirt costs $2.29. Write an inequality to describe this situation, where n is the number of shirts Sarah wants to buy?Please answer quick, will give 18 points
ANSWER
[tex]4.50+2.29n\le60[/tex]EXPLANATION
We have that Sarah got a $60 gift card to use in Walmart.
This means that everything she can buy cannot be worth more than $60 (i.e. less than or equal to $60).
She buys orange juice for $4.50 and she wants to buy shirts (which cost $2.29 each)
Let n be the number of shirts Sarah wants to buy.
This means that the cost of n shirts is $2.29n.
Recall that she can only spend less than or equal to $60. This means that the sum of the cost of the orange juice and n shirts is less than or equal to $60.
That is:
[tex]4.50+2.29n\le60[/tex]That is the inequality that represents the situation.
Maria is to weld a support for a 23-m conveyor so that it will operate at a 20 degree angle. What is the length of the support?
The length of the support when Maria is to weld a support for a 23-m conveyor is 7.87 m.
How to illustrate the information?From the information, Maria is to weld a support for a 23-m conveyor so that it will operate at a 20 degree angle.
Let AB = 23m
Let x = 20°
We can then use the sine rule to find the length. This will be illustrated thus:
Sin x = AC / AB
Sin 20° = AC / 23
AC = 23 × sin 20°
AC = 7.87
The length is 7.87m
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I need help with please!!!
Karl earned $188 last month doing chores after school. If 68% of the money he earned was from doing yard work, about how much did Karl earn doing yard work?
Determine algebraically ifthe function is even, odd, or neither.f(x)=3x-2
A function is even if
[tex]f(-x)=f(x)[/tex]A function is odd if
[tex]f(x)=-f(x)[/tex]For the given question, we will test for both even and odd conditions
Step 1: Test for an even condition
[tex]\begin{gathered} f(-x)=3(-x)-2 \\ f(-x)=-3x-2 \\ \sin ce \\ f(-x)\ne f(x) \\ it\text{ is not an even function} \end{gathered}[/tex]Step 2: Test for an odd function
[tex]undefined[/tex]Question 2 (4 points)y = x|d: {-8, -3, 4,7} {Blank 1:Blank 2:Blank 3:Blank 4
r: {8, 3, 4, 7}
Explanation:
y = |x|
domain = -8, -3, 4, 7
domain are the x values or input
r = range
Range are the y values or output
when x = -8
y = |-8| = 8
when x = -3
y = |-3| = 3
when x = 4
y = |4| = 4
when x = 7
y = |7| = 7
r: {8, 3, 4, 7}
blank 1 = 8
blank 2 = 3
blank 3 = 4
blank 4 = 7
Factor this polynomial. The image is attached here. Need help!
Answer:
[tex]4x^2+11xy-3y^2=(x+3y)(4x-y)[/tex]Step-by-step explanation:
To factor the following polynomial, break the expression into groups:
The grouping method can be used to factor polynomials whenever a common factor exists between the groupings. Just find families easier-to-factor groups that we can better approach the problem.
[tex]\begin{gathered} 4x^2+11xy-3y^2 \\ (4x^2-xy)+(12xy-3y^2) \end{gathered}[/tex]Then, factor it using factor by grouping:
[tex]\begin{gathered} x(4x-y)+3y(4x-y) \\ \text{ Since the two terms have (4x-y) as a common factor:} \\ (x+3y)(4x-y) \end{gathered}[/tex]The table below shows the number of house calls three different plumbers made on three different days.
Number of House Calls
Plumber A
Plumber B
Plumber C
Monday
2
8
8
Tuesday
4
7
10
Wednesday
3
9
9
The total amount of money earned by all three plumbers on Monday was $1,400. On Tuesday they earned a total of $1,660, and on Wednesday, they earned a total of $1,650. On Thursday, Plumber A made four house calls, Plumber B made six house calls, and Plumber C made three house calls. How much total money is earned on Thursday?
$250
$1,060
$1,090
$1,130
The total money that is earned on Thursday is $1090
How to determine the total money that is earned on Thursday?From the question, we have the following table of values
Monday Tuesday Wednesday
Plumber A 2 8 8
Plumber B 4 7 10
Plumber C 3 9 9
Using the given parameters in the question, we have the following system of equations
2a + 8b + 8c = 1400 --- (1)
4a + 7b + 10c = 1660--- (2)
3a + 9b + 9c = 1650 --- (3)
Subtract equation (2) from twice equation (1)
So, we have
(4a + 16b + 16c = 2,800) - (4a + 7b + 10c = 1,660)
This gives
9b + 6c = 1140 --- (4)
Subtract four times equation (3) from three times equation (2)
So, we have
12a+ 21b +30c = 4,980 -(12a + 36B + 36c = 6,600)
This gives
-15b - 6c = -1,620 --- (5)
Add equations (4) and (5)
(9b + 6c = 1140) + (-15b - 6c = -1620)
So, we have
-6B = -480
Divide by -6
b = 80
Substitute b = 80 in -15b - 6c = -1,620
-15 x 80 - 6c = -1,620
Evaluate
-1200 - 6c = -1,620
So, we have
-6c = -420
Divide
c = 70
In (2), we have
4a + 7b + 10c = 1660
This gives
4a + 7 * 80 + 10 * 70 = 1660
Evaluate
4a = 400
Divide
a = 100
On Thursday, we have
a = 4, b = 6 and c = 3
So, we have
Total = 4 * 100 + 6*80 + 3*70
Evaluate
Total = 1090
Hence, the total earnings is 1090
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The weight M of an object on the moon varies directly as its weight E on earth. A person who weighs 162.71lb on earth weighs 27.66lb on the moon. How much would a 220lb person weigh on the moon?
A 220lb person on earth would weigh 23.81lb on moon
Given
Weight of an object on moon varies same as that on the planet earth
This means the weights are directly proportional
Weight of person on earth = 162.7lb
Weight of person on moon = 27.66lb
Also,
Weight of person on earth = 220lb
We need to find weight of this person on moon.
Let weight of person on moon be x
According to the data equation can be formed as
27.66 x 220 = 162.71x
3885.2 = 162.71x
x= 23.81
Hence the weight of the person on moon is 23.lb
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Consider the function whose input value is time of day and whose corresponding output value is temperature at that time of day, rounded to the nearest degree. Is this a one-to-one function? Explain why or why not.
No, a function whose input value is time of day and whose corresponding output value is temperature at that time of day, rounded to the nearest degree is not a one-to-one function.
What is a one-to-one function?A one-to-one function is also referred to as an injective function and it can be defined as special type of function in which every element of the range is mapped to exactly a single element of its domain. This ultimately implies that, the output values (y-values) of a one-to-one function never repeat themselves.
Additionally, a one-to-one function maps distinct elements of its domain (y-values) to distinct elements of the range (x-values) and as such, it connotes the mapping of two (2) sets.
In this context, we can reasonably and logically deduce that this function is not a one-to-one function because it fails the horizontal line test as there could be the same temperature at different times of the day.
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Find the area of the figure.
Based on the given figure, the area of the figure can be found to be 126.50 cm²
How to find the area?The figure given is a mix of a triangle and a rectangle. The area of the figure can then be found by finding the area of the triangle and the rectangle individually, and then summing them up.
The area of a rectangle is:
= Length x Width
= 8 x 11
= 88 cm²
The area of the triangle is:
= 1/2 x base x height
= 1/2 x 11 x 7
= 38.5 cm²
The area of the figure is:
= 88 + 38.5
= 126.50 cm²
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15. Which of the following is true about the relationship in the table shown? Х 7 11 20 25 100 8.4 13.2 24 30 120 A. The table is non-proportional because it does not include the point (0,0). B. The table is non-proportional because the x-values do not increase at a constant interval. C. The table is proportional because all of the x and y-values are positive and increasing, D. The table is proportional because the ratio between y and x is constant.
Explanation:
To determine if the table is proportional or not, we need to find the ratio between x and y for each of the data. if it is constant, then it is proportional
Proportional relationship:
y = kx
k = constant of proportionality
k = y/x
for the x = 7, y = 8.4
k = 8.4/7 = 1.2
for x = 11, y = 13.2
k = 13.2/11 = 1.2
for x = 20, y = 24
k = 24/20 = 1.2
for x = 25, y = 30
k = 30/25
k = 1.2
when x = 100, y = 120
k = 120/100
k = 1.2
Since the ratio between y and x is the same for all, the table is proportional
The correct option:
The
or each ordered pair, determine whety=5x-315x-3y=9(2,7)(-1,– 8)(3,4)(0,-9)
Four friends use a spinner to decide the luckiest person. Who is more likely to be the luckiest person?
The luckiest person is Clinton because it is more likely.
Answer: Clinton
Which is true about investments and risk?
Answer:
Every investment carries some degree of risk, All investments carry some degree of risk. Stocks, bonds, mutual funds, and exchange-traded funds can lose value, even all their value, if market conditions sour. Even conservative, insured investments, such as certificates of deposit (CDs) issued by a bank or credit union, come with inflation risk. They may not earn enough over time to keep pace with the increasing cost of living.
Step-by-step explanation:
A wealthy businessman invests $10,000 and expects a 6.75% rate of return annually. How many years will it take the investment to reach $15,000 in value?Round your answer to the nearest number of years.
Answer
7 years
Explanation
Given:
Principal, P = $10,000
Rate, R = 6.75%
Amount, A = $15,000
What to find:
The years will it take the investment to reach $15,000 in value.
Step-by-step solution:
You need to first calculate the total interest on the investment using;
Interest, I = Amount, A - Principal, P
Interest, I = $15,000 - $10,000
Interest, I = $5,000
The final step is to find the years it takes the investment to reach $15,000 in value using simple interest formula.
[tex]\begin{gathered} S.I=\frac{T\times P\times R}{100} \\ \\ \Rightarrow T=\frac{S.I\times100}{P\times R} \end{gathered}[/tex]Putting the values of the parameters into the formula, we have;
[tex]\begin{gathered} T=\frac{5000\times100}{10000\times6.75}=\frac{500,000}{67,500}=7.407\text{ }years \\ \\ To\text{ }the\text{ }nearest\text{ }number\text{ }of\text{ }years, \\ \\ T=7\text{ }years \end{gathered}[/tex]Therefore, it will take 7 years for the investment to reach $15,000 in value.
Question A maritime flag is shown. What is the area of the shaded part of the flag
Answer:
There is no picture.
Step-by-step explanation:
If you ask a question, be mindful that people cannot read each other minds.
Graph the line with the given slope that passes through the given point.
(a) slope:
3
4
,
point:
(1, 5)
The linear equation can be written as:
y = (3/4)*x + 17/4
And the graph can be seen at the end.
How to graph the linear equation?
A general linear equation is of the form:
y = m*x + b
Where m is the slope and b is the y-intercept.
Here we have the slope m = 3/4, so we get:
y = (3/4)*x + b
And the line passes through (1, 5), replacing these values in the equation we get:
5 = (3/4)*1 + b
5 - 3/4 = b
20/4 - 3/4 = b
17/4 = b
So the linear equation is:
y = (3/4)*x + 17/4
To graph the line we need other point, if we use x = 0 we get:
y = (3/4)*0 + 17/4 = 17/4
Then we have the points (1, 5) and (0, 17/4).
To graph the line, we just need to find these two points and connect them with a line, the graph can be seen below.
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what function is represented in the table ?- y = 3 (4x )- y = 2 ( .25x )- y = 4 ( .25 ) x - y = 4 ( 3x )
1) To determine which is the function from the table we need to attentively look for a constant factor in the y-column.
2) As we can see from this table, the factor we can tell that goes from 64 to 16 and then 4 is 1/4. Or in decimal form 0.25. So, we can tell the factor "b" is going to be 1/4 considering this model:
[tex]\begin{gathered} y=a(b)^x \\ y=a(0.25)^x \end{gathered}[/tex]3) Let's pick one point (0,4) and plug it to find the other elements:
[tex]\begin{gathered} y=a(\frac{1}{4})^x,(0,4) \\ 4=a(\frac{1}{4})^0 \\ a=4 \end{gathered}[/tex]And finally, we can tell the function is:
[tex]undefined[/tex]If 2x+y=4 and 2x-y=8, then what does 3x-y equal?
THE TRICK IS TO FIND THE VALUE OF X AND Y FIRST.
I WILL USE SUBSTITUTION TO SOLVE THIS SYSTEM OF EQUATIONS.
[tex]y = 4 - 2x......(3)equation[/tex]
[tex]2x - (4 - 2x) = 8 \\ 2x - 4 + 2x = 8 \\ 2x + 2x = 8 + 4 \\ 4x = 12 \\ \frac{4x}{4} = \frac{12}{4} \\ x = 3[/tex]
[tex]y = 4 - 2(3) \\ y = 4 - 6 \\ y = - 2[/tex]
THEN FOR 3X-Y PLUG IN THE VALUES YOU FOUND FOR X AND Y
[tex] = 3(3) - ( - 2) \\ = 9 + 2 \\ = 11 \\ 3x - y = 11[/tex]
ATTACHED IS THE SOLUTION
Vă rog,Am nevoie urgent
Mulțumesc
Step-by-step explanation:
The Answer
I hope you are doing well and I don't want to be a part of this the only reason why you would want this
can someone please help me with this angle puzzle?!
Answer:
See below
Step-by-step explanation:
If I did the math numbers correctly : ( a = 51° too)
URGENT HELP PLEASE SOLVE QUESTIONS FIVE AND SIX USING THE INSTRUCTIONS IN THE PIC VERY URGENT PLEASE HELP ME!!!!!!
Answer:
4.number 1
5.number 2
Step-by-step explanation:
4.Because the the expression tan can be written as sin divided by cos it will be beneficial to write the square of cos as cos multiplied by cos so that after canceling out we are left with cos multiplied by sin of the left hand side.
5.because transforming cos squared to 1-sin squared will allow us to to have a fraction where both the numerator and denominator are the same which equals one.
The measure of the angle 6 = _____
What is the actual distance between these two cities in kilometers?
1) Whenever we have problems that deal with the real distance and distance on the map, we can write out the following formula:
[tex]\begin{gathered} Scale=\frac{distance\: on\: the \: map}{real\: distance} \\ S=\frac{3.5}{R} \end{gathered}[/tex]So, let's call the Real distance "R". Note that in this question, 1 centimeter represents 20 kilometers
2) So, in order to plug that as the scale we need to convert kilometers to centimeters:
[tex]\begin{gathered} 1km--100000cm \\ 20km---x \\ x=2000000cm \end{gathered}[/tex]3) Finally, we can plug that into the formula and cross multiply the ratios this way:
[tex]\begin{gathered} \frac{3.5}{r}=\frac{1}{2000000} \\ r=2000000\times3.5 \\ r=7000000cm \end{gathered}[/tex]Converting it back to kilometers we can write:
[tex]\frac{7000000}{100000}=70km[/tex]Evaluate without a calculator.[tex] log_{4}(16) + log_{3}(27) [/tex]please show your work..!
Answer:
The value of the given expression is;
[tex]5[/tex]Explanation:
Given the logarithmic expression;
[tex]\log _416+\log _327[/tex]To solve, Recall the rules of logarithm;
[tex]\begin{gathered} \log _ax^y=y\times\log _ax\text{ ------1} \\ \log _aa=1\text{ -------2} \end{gathered}[/tex]Apply the above rules;
[tex]\begin{gathered} \log _416+\log _327 \\ \log _44^2+\log _33^3 \\ \text{Applying rule 1;} \\ 2\log _44+3\log _33 \end{gathered}[/tex]Aplplying rule 2;
[tex]\begin{gathered} 2\log _44+3\log _33 \\ =2(1)+3(1) \\ =2+3 \\ =5 \\ \log _416+\log _327=5 \end{gathered}[/tex][tex]\begin{gathered} \text{Note that from the rule 2;} \\ \log _aa=1 \\ so\text{ when a logarithm has the same number as the base it will equal to 1;} \\ \text{for example;} \\ \log _44=1 \\ \log _33=1 \\ \log _55=1 \end{gathered}[/tex]Therefore, the value of the given expression is;
[tex]5[/tex]Quadrilateral ABCD has coordinated a(-4,3) b(-3,6) c(0,8) d(-2,5). Prove that quadrilateral ABCD is a parallelogram and explain whether quadrilateral ABCD is a rectangle or not.
Quadrilateral ABCD has coordinate
A(-4, 3) , B(-3, 6) C(0,8) & D(-2,5)
so we will find the length of the sides
[tex]AB=\sqrt[]{(6-3)^2+(-3-(-4))}^2=\sqrt[]{9+1}=\sqrt[]{10}[/tex]for CD
[tex]CD=\sqrt[]{(5-8)^2+(-2-0)^2}=\sqrt[]{9+4}=\sqrt[]{13}[/tex]as we can see AB and CD is not equal to Quadrilateral is not equal.
now we compute the midpoint of the diagonals
midpoint of
[tex](x,y)=(\frac{-4-3}{2},\frac{3+6}{2})=(-\frac{7}{2},\frac{9}{2})[/tex]