The smallest positive integer Joelle could have multiplied 756 by
15876
This is further explained below.
What is a perfect square?Generally, A perfect square number is a number in mathematics that, when its square root is calculated, yields a natural number.
To solve this problem we can do:
[tex]\sqrt{756}[/tex]
By properties of roots
[tex]\begin{aligned}&\sqrt{756}=\sqrt{6\cdot126} \\&=\sqrt{6 * 6 * 21} \\\\ =\sqrt{6^2 * 21} \\&=6 \sqrt{21}\end{aligned}[/tex]
So, so that the multiplication of 756 by an integer becomes a perfect square, you have to multiply it by 21 to make $21^2$ and thus "eliminate" the root.
756 * 21=15876
In conclusion, You can verify that 15876is a perfect square since root (15876)=132 and 132 is a natural number
Read more about perfect square
https://brainly.com/question/385286
#SPJ1
Calculate the perimeter and area of the triangle formed by the coordinates K (-4,-1), L (-2,2), and M (3,-1). Round your answer to two decimal places.
PERIMETER:
You can calculate the perimeter of a triangle knowing the coordinates, by calculating the distance between every point, as follows:
[tex]\bar{KL}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where x1=-4, y1=-1, x2=-2 and y2=2, replace these values:
[tex]\begin{gathered} \bar{KL}=\sqrt[]{((-2)-(-4))^2+(2-(-1))^2} \\ \bar{KL}=\sqrt[]{(2)^2+(3)^2} \\ \bar{KL}=\sqrt[]{4+9}=\sqrt[]{13}=3.61 \end{gathered}[/tex]Now, you have to do the same for the other segments, let's continue with LM:
[tex]\begin{gathered} \bar{LM}=\sqrt[]{(x_3-x_2)^2+(y_3-y_2)^2} \\ x_3=3\text{ and }y_3=-1\text{ by replacing:} \\ \bar{LM}=\sqrt[]{(3_{}-(-2))^2+((-1)-2)^2} \\ \bar{LM}=\sqrt[]{(5)^2+(-3)^2} \\ \bar{LM}=\sqrt[]{25+9}=\sqrt[]{34}=5.83 \end{gathered}[/tex]Same for segment KM:
[tex]\begin{gathered} \bar{KM}=\sqrt[]{(x_3-x_1)^2+(y_3-y_1)^2} \\ \bar{KM}=\sqrt[]{(3-(-4))^2+((-1)-(-1))^2} \\ \bar{KM}=\sqrt[]{(7)^2+(0)^2} \\ \bar{KM}=\sqrt[]{49+0^{}}=\sqrt[]{49}=7 \end{gathered}[/tex]The perimeter can be calculated as KL+LM+KM:
[tex]\begin{gathered} P=\bar{KL}+\bar{LM}+\bar{KM}=3.61+5.83+7 \\ P=16.44 \end{gathered}[/tex]AREA:
The area can be calculated by using the next formula:
[tex]A=\frac{1}{2}\mleft\lbrace\lbrack(x_1\cdot y_2)+(x_2\cdot y_3)+(x_3\cdot y_1)\mright]-\lbrack(x_1\cdot y_3)+(x_3\cdot y_2)+(x_2\cdot y_1)\rbrack\}[/tex]Then, you have to replace the values to find the area:
[tex]\begin{gathered} A=\frac{1}{2}\lbrace\lbrack((-4)_{}\cdot2)+((-2)\cdot(-1))+(3\cdot(-1))\rbrack-\lbrack((-4)\cdot(-1))+(3\cdot2)+((-2)\cdot(-1))\rbrack\} \\ A=\frac{1}{2}\lbrace\lbrack(-8)+(2)+(-3)\rbrack-\lbrack(4)+(6)+(2)\rbrack\} \\ A=\frac{1}{2}\lbrace\lbrack-9\rbrack-\lbrack12\rbrack\} \\ A=\frac{1}{2}\mleft\lbrace\lvert-21\rvert\mright\rbrace \\ A=\frac{21}{2}=10.50 \end{gathered}[/tex]Sam reads 30 pages of a book in 40 minutes. Which statement identifies a person with the same reading rate as Sam.
Answer:
The correct option is B
Leroy reads 22.5 pages in 30 minutes
At the rate of 3 pages in 4 minutes
Explanation:
Given that Sam reads 30 pages of books in 40 minutes, he reads at the rate of 3 pages in 4 minutes (3/4 = 0.75).
To know which of the options has the same rate as Sam's, we need to find which rate is equal to his'
A. Francine reads 40 pages in 55 minutes
Rate = 40/55 = 8/11
B. Leroy reads 22.5 pages in 30 minutes
Rate = 22.5/30 = 0.75
C. Paul reads 150 pages in 3.25 hours. Since 3.25 hours = 195 minutes
Rate = 150/195 = 0.77
D. Bill reads 60 pages in 2 hours
Rate = 60/120 = 0.5
(-5, 3) slope -4 into slope intercept form
The equation using slope intercept form would be...
[tex]y=-4x-17[/tex]
Hope this helps!
Write the equation in vertex form for the parabola with vertex (0, 6) and focus (0, 3).
Answer:
Step-by-step explanation:
the axis of the parabola is x=0So the parabola is of the form (x−0)2=4a(y−6)Now the length of latus rectum =4a=4× the distance between focus and vertex =4×3=12Hence the parabola is x2=−12(y−
Use the Pareto chart to tell the percent of students that enrolled in a private 4 year college.
20%
1) Analyzing that Pareto Chart, we can tell that the percentage of students enrolled in a private-4 year college is indicated by the height of the bar and the corresponding value for its vertical axis
2) Therefore, the answer is 20%
Edgar drew a scale drawing of the town library. The scale of the drawing was 5
centimeters: 2 meters. The parking lot is 34 meters wide in real life. How wide
is the parking lot in the drawing?
Answer:
85 cmStep-by-step explanation:
The scale factor is:
5 cm ÷ 2 mFind the width of the parking lot in the drawing:
5 cm ÷ 2 mx cm ÷ 34 mCross multiply and find the value of x:
x = 5*34/2x = 85 cmJose made $143 for 11 hours of work.
At the same rate, how many hours would he have to work to make $117?
Answer:
9 hours
Step-by-step explanation:
Can someone please explain to me where I did my math wrong and correct me. The answer is supposed to be $1065.00
The problem says: Lonnie Flanagan's weekly gross pay is $1250. Each week she has $64.37 in deductions, plus state tax of 2% of her gross pay, social security taxes of 6.2%, and Medicare taxes of 1.45%. What is her net pay?
I did 1250 - 64.37 = 1185.63
1185.63 (2%) = $23.71 State income Tax
1185.63 (6.2%) = $73.51 Social Security Tax
1185.63 (1.45%) = $17.19 Medicare tax
Then I added the 3 together.
$23.71 + $73.51 + $17.19 = $114.41
Then I subtracted $113.41 from $1250.
1250 - 113.41 = $135.59 net pay.
What did I do wrong?
The net pay for Lonnie Flanagan is $1065.
How to calculate the net pay?From the information, Lonnie weekly gross pay is $1250 and each week she has $64.37 in deductions, plus state tax of 2% of her gross pay, social security taxes of 6.2%, and Medicare taxes of 1.45%.
Her net pay will be:
= Gross pay - Deduction - Tax - Social security - Medicare
= $1250 - $64.37 - (2% × $1250) - (6.2% × $1250) - (1.45% × $1250)
= $1250 - $64.37 - $25 - $$77.50 - $18.125
= $1065
Learn more about tax on:
brainly.com/question/26316390
#SPJ1
Given the equation 5X-10=50 which properties will be used to solve for XA. Adition and subtractionB. Subtraction and divisionC. Adition and division D. Subtraction and Multiplication
Let's solve for x and see what properties are used
First, add 10 to both sides of the equation
[tex]\begin{gathered} 5x-10=50 \\ 5x-10+10=50+10 \\ 5x=60 \end{gathered}[/tex]Now, divide by 5 on both sides of the equation
[tex]\begin{gathered} \frac{5x}{5}=\frac{60}{5} \\ x=12 \end{gathered}[/tex]Therefore, the correct answer is C. Adition and division
The graph of f(x) = x^3 is stretched vertically by a factor of 6. The graph
is then translated 9 units to the right and 3 units down. Write the equation of the transformed function.
Answer:
Transformed equation: 6(x-9)³ - 3
Step-by-step explanation:
Answer:
6(x - 9)^3 - 3
Step-by-step explanation:
1. Vertical Stretching : f(x) -> g(x): [tex]g(x) = 6x^{3}[/tex]
2. Horizontal Move: g(x) -> h(x): [tex]h(x) = 6{(x - 9)}^{3}[/tex]
3. Vertical Move: h(x) -> F(x): [tex]F(x) = 6{(x - 9)} ^{3} - 3[/tex]
5) 13% of score
On a blueprint of a house, the living room has dimensions of 3 inches by 5 inches. If the scale for the
blueprint is 1 inch for every 7 feet, then what is the area of the actual living room?
A. 15 ft²
C. 735 ft²
B.
D.
105 ft2
56 ft²
Based on the dimensions of the blueprint of the house, the area of the actual living room can be found to be 735 ft²
How to find the area?The first thing to do is to convert the dimensions on the blueprint to their actual figures.
If 1 inch on the blueprint is 7 feet, then the actual dimensions are:
= 3 inches x 7
= 21 feet
Dimension B:
= 5 inches x 7
= 35 feet
The area can then be found by:
= Dimension A x Dimension B
= 21 x 35
= 735 ft²
Find out more on area at https://brainly.com/question/27853213
#SPJ1
Given the definitions of f(x) and g(x) below, find the value of (gof)(9). f(x) = -x + 11 g(x) = 3x2 - x + 14
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
f(x) = -x + 11
g(x) = 3x² - x + 14
(gof)(9) = ?
Step 02:
(gof)(x) = 3(-x+11)² - (-x+11) + 14
= 3(x² + 2(-x)(11) + 121) + x - 11 + 14
= 3(x² - 22x + 121) + x - 11 + 14
= 3x² - 66x + 363 + x - 11 + 14
= 3x² - 65x + 366
(gof)(9) = 3(9)² - 65(9) + 366
= 3(81) - 585 + 366
= 243 - 585 + 366
= 24
The answer is:
(gof)(9) = 24
The factors of 6 are also the factors of which number? A 5 C 20 B 10 D 30
Solution:
Factors of a number are defined as numbers that divide another number evenly or exactly without giving any remainder.
Hence,
The factors of 6 are the numbers that can divide 6 without any remainder.
[tex]\text{Factors of 6 =1,2,3,6}[/tex][tex]\begin{gathered} \text{Factors of 5=1,5} \\ \text{Factors of 20=1,2,4,5,10,20} \\ \text{Factors of 10=1,2,5,10} \\ \text{Factors of 30=1,2,3,5,6,10,15,30} \end{gathered}[/tex]From the above, we can deduce that the factors of 6 are also the factors of 30.
The corr
Evaluate and simplify the expression
when a = 2 and b = 4.
4a - 2(a + b) + 1 = [?]
Answer:
-3
Step-by-step explanation:
4(a) - 2(a + b) + 1 = [?]
4(2) - 2(2+4) + 1
8 - 4 - 8 + 1
appilcation of bodmas
4 - 8 + 1
- 4 + 1
-
3
When a number is divided by 5, the result is 50 less than if the number had been divided by $6$. What is the number?
IT SAYS 50 LESS NOT GREATER
The number will be 1500
Given in the question:
A number is divided by 5, the result is 50 less than
and, if the number had been divided by $6$.
To find the number.
Now, According to the question:
Let the number be x
x is divided by 5 = x/5
also, The number is divided by 6 = x/6
Here, The expression will be:
x/5 - 50 = x/6
30(x/5 - 50) = 30(x/6)
6x - 1500 = 5x
1500 = x
Hence, The number will be 1500 .
Learn more about Number at:
https://brainly.com/question/17429689
#SPJ1
Garcia Co. owns equipment that cost $81,600, with accumulated depreciation of $43,200.
Record the sale of the equipment under the following three separate cases assuming Garcia sells the equipment for (1) $50,600 cash, (2) $38,400 cash, and (3) $33,300 cash.
(1) $50,600 cash implies that $50,600 - $38,400 = $12,200
Hence gets gain of $12,200.
(2) $38,400 cash implies that $38,400 - $38,400 = $0
Hence No profit no loss.
(3) $33,300 cash implies that $33,300 - $38,400 = - $5,100
Hence loss of $5,100.
Depreciation :-Depreciation is the gross reduction in the book value of an asset due to regular use or wear and tear.
A capital gain occurs when Garcia Co. receives an amount in excess of the book value of the equipment.
If Garcia Co. receives an amount equal to the book value of the equipment, no profit or loss will result from the disposal.
If Garcia Co. receives an amount below the book value of the equipment, it will experience a capital loss.
In the given question cost of equipment is $81,600 with accumulated depreciation of $43,200 so that the book value will be
$81,600 - $43,200 = $38,400.
Now (1) $50,600 cash implies that $50,600 - $38,400 = $12,200
Hence gets gain of $12,200.
For (2) $38,400 cash implies that $38,400 - $38,400 = $0
Hence No profit no loss.
For(3) $33,300 cash implies that $33,300 - $38,400 = - $5,100
Hence loss of $5,100.
For more details about profit and loss visit link below
https://brainly.com/question/26483369
#SPJ9
If the events have the same theoretical probability of happening, then they are called
Answer:7937
Step-by-step explanation:7596
Find the value of x that will make A||B5x + 20A-В.3x + 60x= [?]Enter
ANSWER:
The value of x is 20
STEP-BY-STEP EXPLANATION:
By properties of the angles we know that these angles are equal, since they are alternative external angles. Thanks to that we can do the following equality to calculate the value of x:
[tex]5x+20=3x+60[/tex]Solving for x:
[tex]\begin{gathered} 5x-3x=60-20 \\ 2x=40 \\ x=\frac{40}{2} \\ x=20 \end{gathered}[/tex]I need help can someone help me?
The sum [tex]S_4[/tex] = 80
How is the summation calculated?
[tex]S_4= \sum_{k=1}^{4} 2(3^{n-1}) \\\\= 2 \sum_{k=1}^{4} (3^{n-1})\\\\=2[3^{1-1}+3^{2-1}+3^{3-1}+3^{4-1}]\\\\=2[3^{0}+3^{1}+3^{2}+3^{3}]\\\\=2[1+3+9+27]\\\\=2 [40]\\\\=80[/tex]
What is summation?
When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total. Series are summations of infinite sequences. A succession of adds is the summation of an explicit sequence. A regular pattern defines a sequence's elements according to their positions within the sequence.If the summation has no summands, then the evaluated sum is zeroBecause zero is the identity for addition and this is known as the empty sum.To learn more about summation, refer:
https://brainly.com/question/23012711
#SPJ13
Artrigerator contains 5 cans of diet soda and 8 cans of regular soda. If three cans of soda are randomly selected without replacement, determine the probability that all can selected are diet soda. Use combinations to determine theprobabilityThe probability that all can selected are diet soda is(Type an integer or a simplified fraction)
The total number of cans in the refrigerator is 5 + 8 = 13
The number of diet soda cans is 5 while the number of regular soda cans is 8
If three cans are selected, the probability that the can is a diet soda can is
5/13
Since it was not replaced, the number of diet soda cans left would be 4 and the total number of cans left would be 12. The probability that the next selected can is a diet can is
4/12 = 1/3
Since it was not replaced, the number of diet soda cans left would be 3 and the total number of cans left would be 11. The probability that the next selected can is a diet can is
3/11
Thus, the probability that the three selected cans are diet soda cans is
5/13 * 1/3 * 3/11 = 5/143
= 0.035
the probability that the three selected cans are diet soda cans is 0.035
da can
r
Cuál es la probabilidad de obtener exactamente 5 caras en 10 lanzamientos de una moneda?
The probability of getting exactly 5 heads in 10 tosses of a coin 24.6%
What is Probability ?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Ten times are spent flipping coins.
Total number of results = 2¹⁰ = 1024
C(10, 5) = 252 is the total number of favorable outcomes.
Probability is
252/1024,
which equals :
=0.24, or
=24.6%.
Therefore, the chance of getting exactly 5 "heads" out of a possible 10 is 0.246, or 24.6%.
To learn more about Probability click on the link
https://brainly.com/question/24756209
#SPJ9
A rectangular prism has dimensions of 2 cm by 2 cm by 5 cm. What is its surface area? Explain or show your reasoning
If a rectangular prism has dimensions of 2cm by 2 cm by 5 cm, then the surface area of the rectangular prism is 48 centimeter square
The length of the rectangular prism = 2 cm
The width of the rectangular prism = 2 cm
The height of the rectangular prism = 5 cm
The surface area of the rectangular prism = 2(lw+lh+hw)
Where l is the length
w is the width
h is the height
Substitute the values in the equation
The surface area of the rectangular prism = 2(2×2+2×5+2×5)
= 2(4+10+10)
= 2×24
= 48 centimeter square
Hence, if a rectangular prism has dimensions of 2cm by 2 cm by 5 cm, then the surface area of the rectangular prism is 48 centimeter square
Learn more about surface area here
brainly.com/question/14987814
#SPJ1
Find the length of CD.express the awnser as a fraction times pie.
Given the figure of the circle B
the radius of the circle = r = BC = 9
the measure of the angle CBD = 40°
We will find the length of the arc CD
The length of the arc is given by the formula:
[tex]l=\theta\cdot r[/tex]where: θ is the central angle opposite to the arc measured in radians
so, we will convert the given angle from degree to radian
[tex]\theta=40\cdot\frac{\pi}{180}=\frac{2}{9}\pi[/tex]Substitute with the given values
so, the length of the arc =
[tex]l=\frac{2}{9}\pi\cdot9=2\pi[/tex]So, the answer will be:
The length of the arc CD = 2π
13 (6x – 5) – x = 13 – 2(x + 1) find x
Answer:
x = 76/79 or 0.962
Step-by-step explanation:
Which is the better buy: 18 oz. of rice for $6.30, 12 oz. of rice for $4.56, or 7 oz. of rice for $2.59?
Answer:
18oz for 6.30 is the cheapest
Step-by-step explanation:
0.35$ per oz
0.38$ per oz
0.37$ per oz
:]
Find the area of the following figure. Show your work.area of odd shapes.
To find the area of the complex figure, divide it into simpler figures and the areas of these. Then find the sum of these areas.
Now, find the area of each of the simpler figures, in these case, the rectangles:
[tex]\begin{gathered} A=b\cdot h \\ A_A=7\cdot3=21 \\ A_B=6\cdot2=12 \\ A_C=7\cdot2=14 \\ A_D=5\cdot3=15 \\ A_E=3\cdot1=3 \end{gathered}[/tex]Finally, find the sum of all these areas to find the area of the figure:
[tex]A_F=21+12+14+15+3=65[/tex]The area of the figure is 65.
O GRAPHS AND FUNCTIONSFinding values and intervals where the graph of a functioning is..
a.
From the graph we notice that when x=-1 the value of the function is zero; therefore:
[tex]f(-1)=0[/tex]and it is not negative.
b.
The function is positive when its graph is above the x-axis. We notice that this happens in two regions of the graph:
From -4 to -3
From -1 to 4
Therefore, the function is positive in:
[tex]\lbrack-4,-3)\cup(-1,4)[/tex]c.
The function is zero when the graph intersect the x-axis; from the graph we have that the function is zero for:
[tex]\begin{gathered} x=-3 \\ x=-1 \\ x=4 \end{gathered}[/tex]Bags A and B each contain counters.
Bag A
60 counters
Each counter is green, blue or yellow
P(green counter from A) = P(red counter from B)
Work out the number of green counters in A.
Bag B
12 counters
9 blue and 3 red
In probability, A is 8 out of 16 and C is 3 out of 15.
What is probability explain?
The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.Out of the 17 counters in the bag 3 are yellow , 6 are red and the rest i.e., 17–3–6 or 8 nos.are green.
When selected randomly once one counter the probability of selecting one is
A. green is 8 out of 17 or 8/17 ,
B. getting a red one is 6 out of 17 or 6/17.
C. getting a yellow is 3 out of 17.
This is when the counter is put back in the bag for selecting.
If the selected one is not put back remaing counters are less by one each time it's drawn and then the probability figure is one out of 16 in the second case and one out of 15 for the third draw ime., then A is 8 out of 16 and C is 3 out of 15.
Learn more about probability
brainly.com/question/11234923
#SPJ13
Hello! Please take a look at the picture to see the questions, thank you!
In the question, we are asked to find the degree and the leading coefficient of the polynomial below
[tex]f(x)=3x^4+2x^3+5x^2+7[/tex]Explanation
The degree of the polynomial is the highest of all the degrees that make up the polynomial. Since each term in the polynomial has a degree we will pick the largest one.
Also, the leading coefficient is the coefficient of the term with the largest degree. Using these concepts, we can derive our answer as.
Answer:
[tex]4,3[/tex]Option A
Omg guys can y’all please help i’m begging
The equation of the function g(x) is -√(x-7).
We are given a function f(x).The function f(x) equals √x.Our objective is to do some transformations on the graph of the function f(x) and reach the equation of the function g(x).We first need to reflect the function on the x-axis.We just take negative of the function f(x) to reflect it about the x-axis.f(x) = -√xWe now need to translate the function to the right by 7 units.We subtract 7 from the argument of the function to translate it to the right by 7 units.f(x-7) = -√(x-7)This is our required function.Thus, the equation of the function g(x) is -√(x-7).To learn more about functions, visit :
https://brainly.com/question/12431044
#SPJ1