Answer:
the smallest prime factor of 52 is 2
Step-by-step explanation:
What is the smallest prime that is a factor of 52?
52 = 4*13, or 52 = 2*2*13. So the smallest prime factor of 52 is 2.
A designer enlarged both the length and the width of a rectangular carpet by 60 percent. The new carpet was too large so the designer was asked to reduce its length and its width by 25 percent. By what percent was the area of the final item greater than the area of the original?
Answer:
300%
Step-by-step explanation:
Let the length of the carpet be L.
Let the width of the carpet be W.
The original area of the carpet is:
A = L * W = LW
The length and width are enlarged by 60%.
The new length is:
L + (L * 60/100) = L + 0.6L = 1.6L
The new width is:
W + (W * 60/100) = W + 0.6W = 1.6W
The length and width are then reduced by 25%.
The new length is:
1.6L + (1.6L * 25/100) = 1.6L + 0.4L = 2L
The new width is:
1.6W + (1.6W * 25/100) = 1.6W + 0.4W = 2W
The new area will be:
A = 2L * 2W = 4LW
To find the percentage increase in the area, we subtract the original area from the new area and divide by the original area:
4LW - LW = 3LW
% increase is:
[tex]\frac{3LW}{LW} * 100[/tex] = 300%
The area of the final item is 300% greater than the original item.
Answer:
44%
Step-by-step explanation:
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A virus is spreading around Summerfield. At the moment, 800 people are infected. If the virus is spreading at a rate of 15% each day, how many people in all will have caught the virus in 12 days? Write an equation to
represent the situation. *
A y=800(0.85)^12
B y=800(0.15)^12
C y=800(1.15)^12
D y=0.85(800)^12
E y=0.15(800)^12
F y=1.15(800)^12
G y=(0.85•800)^12
H y=(0.15•800)^12
I y=(1.15•800)^12
Answer:
C y=800(1.15)^12
Step-by-step explanation:
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Answer:
smaller r = ( 6.5 , 0)
larger r = ( 21.5 , 0)
vertex = ( 14, -56.25)
Step-by-step explanation:
f(r) = (r -14)² -56.25 square (r-14)
f(r) = r² -28r +196 -56.25 simplify
f(r) = r² -28r + 139.75
use quadratic formula
x=−b±√(b²−4ac)/ 2a
a = 1, b =-28, c = 139.75
x=−(−28)±√(−28)2−4(1)(139.75)2(1)
x=(28±√225)/2
x=43/2 or x=13/2
or 21.5 and 6.5
This parabola is given in vertex form f (r) = a(r - h)² + k, where (h, k) is the vertex of the parabola so just write the given numbers ( 14, -56.25)
please help me with math
Answer:
6. composite figure
7. 60+432=492
M + 3 / 5 is equal to 7 / 5
Answer:
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Which is the graph of f(x) = + (4)?
Answer:
Step-by-step explanation:
The graph of f(x) = + (4) is the same as that of g(x) = 4; it's a constant function defined for all x values but its range is just one number: 4.
What is the value of this expression when a = 7 and b = -4? | 2a | - b/3 A.) -6 B.) -3 1/3 C.) 3 1/3 D.) 6
The answer to the question what is the value of this expression when a = 7 and b = -4? | 2a | - b/3 it is D.) 6
The value of this expression (|2a| - b)/3 when a = 7 and b = -4 is 6. So, option D is correct.
What is the modulus function?The absolute value of a number or variable is returned by a modulus function. It is defined as
|x| = x, x > 0
= -x, x < 0
= 0, x = 0
How to solve this problem?The given expression is (|2a| - b)/3. Here, we have to put a = 7 and b = -4 to get the value.
Now, (|2a| - b)/3 = (|2×7| - (-4))/3 = (|14| + 4)/3 = (14 + 4)/3 [Since 14 is a positive integer]
i.e. (|2a| - b)/3 = 18/3 = 6
Therefore, the value of this expression (|2a| - b)/3 when a = 7 and b = -4 is 6. So, option D is correct.
Learn more about the modulus function here -
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Answer:
256
Step-by-step explanation:
<1=<8 -->alt exterior angles
<4=<1 --> vertical angles
= <1=<4=<8(128)
256
If mike reads 50 pages an hour how long would it take him to read 1225 pages
What is the exact value of sin(5π/12)?
(please give steps)
Answer:
0.966053748
Step-by-step explanation:
[tex] \sin \bigg( \frac{5\pi}{12} \bigg) \\ = \sin \bigg( \frac{5 \times 180 \degree}{12} \bigg) \\ = \sin ( 5 \times 15 \degree) \\ = \sin ( 75 \degree) \\ = \sin ( 45 \degree + 30 \degree) \\ = \sin 45 \degree \times \cos 30 \degree + \cos 45 \degree \times \sin 30 \degree \\ \\ = \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2} + \frac{1}{ \sqrt{2} } \times \frac{1}{2} \\ \\ = \frac{ \sqrt{3} }{2 \sqrt{2} } + \frac{1}{2 \sqrt{2} } \\ \\ = \frac{ \sqrt{3} + 1}{2 \sqrt{2} } \\ \\ = \frac{1.732 + 1}{2 \times 1.414} \\ \\ = \frac{2.732}{2.828} \\ \\ = 0.966053748[/tex]
Please help! Correct answer only, please! Find the following product if possible. Explain if it is not possible. A. B. C. D.
Answer:
Option (B)
Step-by-step explanation:
If A = [tex]\begin{bmatrix}1 & 3\\ -2 & 5\end{bmatrix}[/tex] and B = [tex]\begin{bmatrix}-2 & 1\\ 3 & 4\end{bmatrix}[/tex]
Multiplication of these matrices,
A.B = [tex]\begin{bmatrix}1 & 3\\ -2 & 5\end{bmatrix}\times \begin{bmatrix}-2 & 1\\ 3 & 4\end{bmatrix}[/tex]
= [tex]\begin{bmatrix}(1(-2)+3(3) & 1(1)+3(4)\\ (-2)(-2)+5(3) & 1(-2)+5(4)\end{bmatrix}[/tex]
= [tex]\begin{bmatrix}7 & 13\\ 19 & 18\end{bmatrix}[/tex]
Therefore, Option (B) will be the answer.
What is the volume of this cylinder?
Use a ~ 3.14 and round your answer to the nearest hundredth.
10 mm
7 mm
Answer:
[tex]1538.6mm^{3}[/tex]
Step-by-step explanation:
[tex]V=\pi r^{2} h[/tex]
[tex]V=3.14*7^{2} *10[/tex]
[tex]V=31.4*49=1538.6[/tex]
The graph shown here is the graph of which of the following rational functions
Answer:
The answer is 100% B
Step-by-step explanation:
The graph of the polynomial rational function is f ( x ) = x / ( x + 2 ) ( x - 5 )
What is Equation of Graph of Polynomials?Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.
Identify the even and odd multiplicities of the polynomial functions' zeros.
Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.
The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities
Given data ,
Let the polynomial function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = x / ( x + 2 ) ( x - 5 )
The rational function is of the form P ( x ) / Q ( x ) , where Q ( x ) ≠ 0
So , the value of P ( x ) = x
And , the value of Q ( x ) = ( x + 2 ) ( x - 5 )
Therefore , the graph of the rational function is plotted
Hence , the graph of the polynomial is f ( x ) = x / ( x + 2 ) ( x - 5 )
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Solve the exponential equation. 4x = 0.5 -2 -1 -1/2
Answer:
[tex]x=-1/2[/tex]
Step-by-step explanation:
[tex]4^x=1/2[/tex]
Make the bases 2 on both sides of the equation.
[tex]2^{2^x}=2^{-1}[/tex]
Multiply the exponents.
[tex]2^{2x}=2^{-1}[/tex]
Cancel the bases.
[tex]2x=-1[/tex]
Divide 2 into both sides of the equation.
[tex]x=-1/2[/tex]
A house valued at £210,000 correct to 2 significant figures. A) What is the lowest value of the house? B) What is the highest value of the house?
Answer:
Range could be 205000 to 214999. Any number in this range, when rounded to two signnificant digits will yield 210000.
Which of the following options have the same value as %70, percent of 80?
Answer:
A, C and E.
Step-by-step explanation:
[tex]70 \% \times 80[/tex]
[tex]70/100 \times 80[/tex]
[tex]560/10[/tex]
[tex]=56[/tex]
[tex]0.7 \times 80[/tex]
[tex]=56[/tex]
[tex]7/10 \times 80[/tex]
[tex]=56[/tex]
x | f(x)
2.0 | 2.8
2.5 | 1.1
3.0 | –0.8
3.5 | –1.2
4.0 | –0.3
4.5 | 0.7
For the given table of values for a polynomial function, where must the zeros of the function lie?
A. between 2.0 and 2.5 and between 4.0 and 4.5
B. between 2.5 and 3.0 and between 4.0 and 4.5
C. between 2.0 and 2.5 and between 3.5 and 4.0
D. between 2.5 and 3.0 and between 3.5 and 4.0
Answer:
Option B.
Step-by-step explanation:
If the value of function is 0 at x=c, then c is a root or zero of the function. It means the graph of function intersect x-axis at its zeroes.
From the given table it is clear that the value of function are
x | f(x) | Sign
2.0 | 2.8 | Positive
2.5 | 1.1 | Positive
3.0 | –0.8 | Negative
3.5 | –1.2 | Negative
4.0 | –0.3 | Negative
4.5 | 0.7 | Positive
The sign of values of function changes in interval 2.5-3.0 and 4.0-4.5.
It means, the graph of function must intersect x-axis in interval 2.5-3.0 and 4.0-4.5. So, the zeros of the function lie between 2.5 and 3.0 and between 4.0 and 4.5.
Therefore, the correct option is B.
Answer:
between 2.5 and 3.0 and between 4.0 and 4.5
Step-by-step explanation:
B on my computer but always double check!
Find all solutions for a triangle with C = 130°, c = 17, and b = 5. Round to the nearest tenth.
a.A= 37.0°, B = 15.0°, a = 15.2
c.A = 37.0°, B = 13.0°, a = 13.4
b. A= 35.0°, B = 13.0°; a = 15.4
d no solutions
Answer:
C
Step-by-step explanation:
Use sine rule
17/sin130=5/sinB
(5×sin130)÷17=sinB
sinB=0.2253017892
B=sin^-1ans above
=13.4
A=(130+13) subtracted from 180=37°
a/sin37=17/sin130
=13.4
A bookstore manager marks down the price of older hardcover books, which originally sell for b dollars, by 42%. Part 1 out of 4 Enter an expression for the markdown using a decimal. The markdown is ..... (Answer this question piece)
Answer:
0.42
Step-by-step explanation:
The original price of the old hardcover books was sold for b dollars. But the manager markdown the hardcover books by 42%.
The expression of the markdown using a decimal can be represented below.
Recall the markdown is 42 %. If you want to convert from percentage to a decimal, you have to move the decimal point two places to the left . The percentage sign is removed at this stage and the value is represent in decimal. Or you can just divide the percentage value by 100.
In our case the percentage value can be solved as 42/100 = 0.42 in decimal or by just simply moving the decimal points two places to the left which is 0.42.
Solve
1. x2 + x - 6 = 0
Answer:
x = -3 x=2
Step-by-step explanation:
x^2 + x - 6 = 0
Factor
What two numbers multiply to -6 and add to 1
3*-2 =-6
3+-2 =1
(x+3) (x-2) = 0
Using the zero product property
x+3 = 0 x-2 = 0
x = -3 x=2
Shama’s age is three times the age of her son Ankit. 10 years ago Shama
was 5 times the age of Ankit. Find the present age of Shama.
Answer:
Step-by-step explanation:
Let sharma age be S and Ankit age be A
S = 3a
(s-10) = 5(a-10)
substitute 1 in 2
3a-10 = 5a -50
40 = 2a
a = 20
s = 3 * 20 = 60
Find the area of the shape.
This is a [tex]90^\circ[/tex] sector of a circle of radius 8, or one-fourth of the circle, so the area is [tex]\frac{\pi(8)^2}{4}=\boxed{16\pi}.[/tex]
Answer: 50.2656
Step-by-step explanation:
A total of 937 people attended the play admission was two dollars for adults and $.75 for students the total ticket sales amounted to $1109 how many students and adults attended the school play
Answer:
325 adults
Step-by-step explanation:
x=#adults
y=#children
x+y=937
2x+0.75y=1109
2x+2y=1874
-2x-0.75y=1109
1.25y=765
y=612
x=937-612
x=325
This table shows the time it took a group of students to complete a quiz
If a ray _______ an angle of a triangle, it divides the opposite side into segments proportional to the lengths of the other two sides. An angle bisector divides an angle into two _______ halves. A perpendicular bisector is the line perpendicular to a segment passing through the segment’s _______.
Answer:
bisects, equal, midpoint
Step-by-step explanation:
According to the "Angle Bisector" Theorem, an angle bisector of a triangle divides the opposite side into segments proportional to the lengths of the other two sides of the triangle.
If a ray bisects an angle of a triangle, it divides the opposite side into segments proportional to the lengths of the other two sides. An angle bisector divides an angle into two equal halves. A perpendicular bisector is the line perpendicular to a segment passing through the segment’s midpoint.
Solve the given system of equations.
Answer: x= -1/2 y=3/4
Step-by-step explanation:
Answer:
x = -4y + 5/2
Step-by-step explanation:
step 1: 2x +8y + -8y = 5 + -8y
2x = -8y+ 5
step 2: divide both sides by 2
2x /2 = -8y+5/2
x= -4 + 5/2
Target sells 24 bottles of water for $3.and 36 bottles of water for $4 Which is the better buy and by how much
24 bottles for $3 by 1.50 per bottle
B)
24 bottles for 53 by 700 per bottle
24 bottles for $3 by 75c per bottle
36 bottles for $4 by 1 46 per bottle
60
Answer:
The last answer choice is the correct answer
Step-by-step explanation:
im hoping this helped, if not im sorry.
The formula for converting a temperature,C, in degree Celsius ('C) to a temperature degree Fahrenheit ('F). F=(9C+160)/5 Q:) What temperature is same on both scale.
Answer:
-40
At -40, the value on both scales are the same.
-40 °C = -40 ° F
Step-by-step explanation:
Given that;
F = temperature in Fahrenheit
C = temperature in Celsius
And;
F=(9C+160)/5 .........1
For temperature to be the same on both scale;
Temperature in Fahrenheit mist be equal to the temperature in Celsius
F = C
Substituting F = C into the equation 1;
C = (9C +160)/5
Multiply both sides by 5
5C = (9C+160)
Collecting the like terms.
5C -9C = 160
-4C = 160
C = -160/4
C = -40
F = C = -40
At -40, the value on both scales are the same.
That means;
-40 °C = -40 ° F
Help appreciated please and thank you
Answer:
D. [tex] \frac{4 \sqrt{33} }{33} [/tex]
Step-by-step explanation:
[tex] \tan \alpha = \frac{4}{ \sqrt{33} } \\ = \frac{4}{ \sqrt{33} } \times \frac{ \sqrt{33} }{ \sqrt{33} } \\ \\ = \frac{4 \sqrt{33} }{ {( \sqrt{33)} }^{2} } \\ \\ \tan \alpha = \frac{4 \sqrt{33} }{33} [/tex]
Solve for m.
m − 10 + 6m = 10 + 2m
m =
Answer:
m = 4
Step-by-step explanation:
m−10+6m=10+2m
7m-10=10+2m
Subtract 2m from both sides
5m-10=10
Add 10 to both sides
5m=20
Divide both sides by 5
m=4
Answer:
m=4
Step-by-step explanation:
m − 10 + 6m = 10 + 2m
7m - 10 = 10 + 2m (subtract 2m from both sides)
7m - 10 - 2m = 10
5m - 10 = 10 (add 10 to both sides)
5m = 10 + 10
5m = 20 (divide both sides by 5)
m = 20/5
m = 4
