The width of the rectangle is 4 cm, found by dividing the area of the square (36 cm^2) by the length of the rectangle (9 cm).
Explanation:To solve the problem we need to first understand two main concepts; the area of a square and the area of a rectangle. The area of a square can be found by squaring the length of one of its sides, which can be described with the formula A = a^2 where a is the side length of the square. Since the perimeter of the square is 24 cm, each side is 24 cm / 4 = 6 cm. Therefore, the area of the square is 6 cm * 6 cm = 36 cm^2.
The area of a rectangle is calculated by the formula A = length * width. We are given that the length is 9 cm and that the area of the rectangle is equal to that of the square, which we found to be 36 cm^2. To find the width, we divide the area by the length: 36 cm^2 / 9 cm = 4 cm. Thus, the width of the rectangle is 4 cm.
Which of the following piecewise functions is graphed above?
The answer is:
The piecewise function that represents the graph, is the option A (first option):
f(x) (piecewise function):
[tex]8; x\leq -1\\\\x^{2} -4x+1;-1<x<5\\\\-x+1\geq 5[/tex]
Why?To find the correct option, we need to look for the piecewise function that contains the following functioncs existing in the determined domains (inputs).
From the graph, we know that we need the following functions:
- A horizontal line, which exists from -∞ to -1, givind as input 8.
The function will be:
[tex]y=8[/tex]
Then, the piecewise function it will be:
[tex]8; x\leq -1[/tex]
- A quadratic function (convex parabola) which y-intercept is equal to 1, exists from -1 to 5, and it vertex (lowest point for this case) is located at (2,-3)
The function will be:
[tex]y=x^{2}-4x+1[/tex]
Finding the y-intercept, we have:
[tex]y=0^{2}-4*80)+1[/tex]
[tex]y=1[/tex]
Finding the vertex of the parabola, we have:
[tex]x_{vertex}=\frac{-b}{2}\\\\x_{vertex}=\frac{-(-4)}{2}=\frac{4}{2}=2[/tex]
[tex]y_{vertex}=x_{vertex}^{2}-4x_{vertex}+1[/tex]
[tex]y_{vertex}=2^{2}-4*2+1=4-8+1=-3[/tex]
The vertex of the parabola is located at the point (2,-3).
Then, for the piecewise function it will be:
[tex]x^{2} -4x+1;-1<x<5[/tex]
- A negative slope function, which evaluated at x equal to 5 (input), gives as output -4.
The function will be:
[tex]y=-x+1[/tex]
Proving that it's the correct equation by evaluating "x" equal to 5, we have:
[tex]y=-5+1[/tex]
[tex]y=-4[/tex]
It proves that the equation is correct.
Then, for the piecewise function it will be:
[tex]-x+1\geq 5[/tex]
Hence, we have that the piecewise function that represents the graph, is the option A (first option):
f(x) (piecewise function):
[tex]8; x\leq -1\\\\x^{2} -4x+1;-1<x<5\\\\-x+1\geq 5[/tex]
Have a nice day!
Determine whether f(x) = -5x2 - 10x + 6 has a maximum or a minimum
value. Find that value and explain how you know.
Answer:
The function has a maximum
The maximum value of the function is
[tex]f (-1) = 11[/tex]
Step-by-step explanation:
For a quadratic function of the form:
[tex]ax ^ 2 + bx + c[/tex] where a, b and c are the coefficients of the function, then:
If [tex]a <0[/tex] the function has a maximum
If [tex]a> 0[/tex] the function has a minimum value
The minimum or maximum value will always be at the point:
[tex]x=-\frac{b}{2a}\\\y=f(-\frac{b}{2a})[/tex]
In this case the function is: [tex]f(x) = -5x^2 - 10x + 6[/tex]
Note that
[tex]a = -5,\ a <0[/tex]
The function has a maximum
The maximum is at the point:
[tex]x=-\frac{-10}{2(-5)}[/tex]
[tex]x=-1[/tex]
[tex]y=f(-1)[/tex]
[tex]y= -5(-1)^2 - 10(-1) + 6[/tex]
[tex]y= 11[/tex]
The maximum value of the function is
[tex]f (-1) = 11[/tex]
The function [tex]f(x) = -5x^2 - 10x + 6[/tex] has a maximum value at the vertex of its parabola. The maximum value is f(x) = 11 when x = -1.
To determine whether the quadratic function [tex]f(x) = -5x^2 - 10x + 6[/tex] has a maximum or a minimum value, we need to examine the coefficient of the [tex]x^2[/tex]term. The general form of a quadratic function is [tex]f(x) = ax^2 + bx + c.[/tex] If 'a' is negative, the parabola opens downwards, and the function has a maximum value at its vertex. In this case, 'a' is -5, which is negative, so the function has a maximum value.
To find the vertex of the parabola, we use the formula for the x-coordinate of the vertex, which is given by -b/(2a). Here, a = -5 and b = -10. Plugging these values into the formula gives us:
x = -(-10) / (2 * (-5))
x = 10 / -10
x = -1
Now that we have the x-coordinate of the vertex, we can find the y-coordinate (the maximum value) by substituting x = -1 into the original function:
[tex]f(-1) = -5(-1)^2 - 10(-1) + 6[/tex]
f(-1) = -5(1) + 10 + 6
f(-1) = -5 + 10 + 6
f(-1) = 5 + 6
f(-1) = 11
Therefore, the maximum value of the function [tex]f(x) = -5x^2 - 10x + 6[/tex] is 11 when x = -1. This is the value at the vertex of the parabola, confirming that it is the maximum value since the parabola opens downwards.
If 1 dish of craft paint covers an area of 720 square centimeters, how many dishes of paint are required to paint the top surface and the lateral faces of the table shown in the diagram? Ignore the bottom of the tabletop and the legs.
(540 + 540 + 900 + 900) + (2160) = (Surface area of Lateral faces) + (Top) = 5040 sq cm.
5040 / 720 = dishes of craft paint = 7 dishes
Answer:
7 dishes
Step-by-step explanation:
Which is the better buy?
A. 3-yard piece of cotton cloth for $4.41
B. 3-foot piece of cotton cloth for $1.05
Answer:
Step-by-step explanation:
It’s is a because if you divide 4.41 divide by 3 you will get 1.47
Step-by-step explanation:
1 yard = 3 feet
So 3 yards = 9 feet
$4.41 / 9 feet = $0.49 per foot
$1.05 / 3 feet = $0.35 per foot
The second one is cheaper, so that's the better buy.
is 3-6x=y proportional
Answer:
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
The equation of a proportional relation is of the form
y = kx,
where k is a number.
Here you have
3 - 6x = y,
which can be rewritten as
y = -6x + 3
Because of the +3, your equation is not for the form y = kx, and it is not a proportional relation.
623 + 433 + 56 = ? show your work
Answer:
1112
Step-by-step explanation:
(1.1•10^-5)(3 •10^-2)
A. 4.1 • 10 ^-7
B. 4.1 • 10^10
C. 3.3 • 10^-7
D. 3.3 • 10^10
Answer:
C. 3.3 • 10^-7
Step-by-step explanation:
(1.1•10^-5)(3 •10^-2)
Multiply the numbers out front of the powers of ten, then add the exponents on the powers of 10
1.1 * 3 * 10 ^(-5+-2)
3.3 ^ (-7)
Answer:
C
Step-by-step explanation:
Find the perimeter of an isosceles triangle ABC. Side AB=4, and the base BC=3. Angles B & C are both 70 degrees.
Answer:
11 units
Step-by-step explanation:
Since ∆ABC is isosceles, it means that at least two sides are congruent/equal in length.
Sides CA and AB are congruent, since BC is the base. So, CA = 4.
That means the perimeter is 4 + 4 + 3 = 11 un
Four expressions are shown below:
4(8x + 2)
4(7x + 3)
32x + 8
28x + 12
Which two expressions are equivalent to 4(7x + 2 + x)?
It’s the first one and the third one
Answer: A and C
Step-by-step explanation:
Find the Exact value of each equation between [tex]0\leq theta\leq2\pi[/tex]
15) [tex]cos(-\frac{13\pi }{3} )[/tex]
16)[tex]csc(\frac{23\pi }{4}[/tex])
17)[tex]sec-(\frac{7\pi }{2}[/tex])
18)[tex]cot(-\frac{29\pi }{6}[/tex])
Use the fact that the co/sine functions are [tex]2\pi[/tex]-periodic and that the tangent function is [tex]\pi[/tex]-periodic. Also, recall that [tex]\cos x[/tex] is even (so that [tex]\cos(-x)=\cos x[/tex]) and [tex]\sin x[/tex] is odd (so that [tex]\sin(-x)=-\sin x[/tex].
15.
[tex]\cos\left(-\dfrac{13\pi}3\right)=\cos\dfrac{13\pi}3=\cos\left(\dfrac\pi3+4\pi\right)=\cos\dfrac\pi3=\boxed{\dfrac12}[/tex]
16.
[tex]\sin\dfrac{23\pi}4=\sin\left(\dfrac{3\pi}4+5\pi\right)=\sin\left(\dfrac{3\pi}4+\pi\right)=\sin\dfrac{7\pi}4=-\dfrac1{\sqrt2}[/tex]
[tex]\implies\csc\dfrac{23\pi}4=\boxed{-\sqrt2}[/tex]
17.
[tex]\cos\left(-\dfrac{7\pi}2\right)=\cos\dfrac{7\pi}2=\cos\left(\dfrac\pi2+3\pi\right)=\cos\left(\dfrac\pi2+\pi\right)=\cos\dfrac{3\pi}2=0[/tex]
[tex]\implies\sec\left(-\dfrac{7\pi}2\right)=\boxed{\text{undefined}}[/tex]
18.
[tex]\tan\left(-\dfrac{29\pi}6\right)=\dfrac{\sin\left(-\frac{29\pi}6\right)}{\cos\left(-\frac{29\pi}6\right)}=-\dfrac{\sin\frac{29\pi}6}{\cos\frac{29\pi}6}[/tex]
[tex]\sin\dfrac{29\pi}6=\sin\left(\dfrac{5\pi}6+4\pi\right)=\sin\dfrac{5\pi}6=-\dfrac12[/tex]
[tex]\cos\dfrac{29\pi}6=\cos\dfrac{5\pi}6=\dfrac{\sqrt3}2[/tex]
[tex]\implies\tan\left(-\dfrac{29\pi}6\right)=-\dfrac{-\frac12}{\frac{\sqrt3}2}=\dfrac1{\sqrt3}[/tex]
[tex]\implies\cot\left(-\dfrac{29\pi}6\right)=\boxed{\sqrt3}[/tex]
A survey find that 61% of people are married. They ask the same group of people and 75% of them have at least one kid. If 48% are married and have one kid what is probability that a person in a survey is married or has a child?
Answer:
22/25
Step-by-step explanation:
The overlap between the 61% and the 75% is the 48%, which means that 13% of the people are married and have no kids (61-48=13)
The 75% includes the people who have one or more kids, and the people who have one or more kids and are married.
Now all we have to do is 13% + 75% = 88% = 22/25
Using Venn probabilities, it is found that there is a 0.88 = 88% probability that a person in a survey is married or has a child.
What is a Venn probability?In a Venn probability, two non-independent events are related with each other, as are their probabilities.
The "or probability" is given by:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
In this question, the events are:
Event A: Person is married.Event B: Person has a child.The probabilities are given by:
[tex]P(A) = 0.61, P(B) = 0.75, P(A \cap B) = 0.48[/tex]
Hence:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
[tex]P(A \cup B) = 0.61 + 0.75 - 0.48[/tex]
[tex]P(A \cup B) = 0.88[/tex]
0.88 = 88% probability that a person in a survey is married or has a child.
More can be learned about Venn probabilities at https://brainly.com/question/25698611
In triangle ABC AB =BC and m
the length of DE is 9/2 units and m<CAB is 45
The measurements of DE and angle CAB in the given triangle ABC are 4.5 units and 45° respectively.
What is a triangle?A triangle is a polygon with three angles and sides.
Given that, a right triangle ABC, right-angled at B,
Here D and E are midpoints of AB and BC, and also AB = AC, CB = 9 units.
We need to find the measurements of DE and angle CAB in the given triangle ABC,
Since, the two sides are equal in the triangle then it is a right-isosceles triangle,
In a right-isosceles triangle, the two acutes angles are measured 45°
Therefore, ∠ CAB = ∠ ACB = 45°
Hence, ∠ CAB = 45°
Now, using the midpoint theorem, we will get. CB = 2DE
Therefore,
9 = 2DE
DE = 4.5 units
Hence, the measurements of DE and angle CAB in the given triangle ABC are 4.5 units and 45° respectively.
Learn more about triangles, click;
https://brainly.com/question/2773823
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what is this simplified?
Answer: -8 square root of 3 (choice a)
Step-by-step explanation:
You have to find 2 numbers that multiply to 48 and in the same time, 1 of these numbers is a perfect square. In this case, the numbers are 16 and 3. So -2√16*3
Then since 16 is. A perfect square, and the square root is 4, you take out the 4 and multiply it by -2 so that is -8 and now you are left with -8√3. Hopefully that helped.
ANSWER
[tex] - 8 \sqrt{3} [/tex]
EXPLANATION
We want to simplify:
[tex] - 2 \sqrt{48} [/tex]
Remove the perfect square under the radical sign.
[tex] - 2 \sqrt{16 \times 3} [/tex]
Split the radical sign for the factors under it.
[tex] - 2 \sqrt{16} \times \sqrt{3} [/tex]
Simplify:
[tex] - 2 \times 4\times \sqrt{3} [/tex]
This finally gives us:
[tex] - 8 \sqrt{3} [/tex]
The first choice is correct.
Find the area of the trapezoid !!!!
A. 70 in^2
B. 77.2 in^2
C. 75 in^2
D. 80 in^2
Answer:
The answer is A. 70 in^2
Step-by-step explanation:
trust me it is right :) hope this helps! I JUST TOOK THE TEST
ANSWER
A. 70 in^2
EXPLANATION
The area of a tra-pezoid is
[tex] = \frac{1}{2} (sum \: of \: parallel \: sides) \times height[/tex]
Substitute the side lengths into the formula to obtain,
[tex] = \frac{1}{2} (8 + 14) \times 7[/tex]
Simplify the parenthesis
[tex] = \frac{1}{2} (20) \times 7[/tex]
Cancel out the common factors,
=10×7
Simplify
[tex] = 70 {in}^{2} [/tex]
The correct answer is A
5(x+y)-3(y/x) plz help me
Answer:
[tex]\large\boxed{5(x+y)-3\left(\dfrac{y}{x}\right)=5x+5y-\dfrac{3y}{x}}[/tex]
Step-by-step explanation:
[tex]5(x+y)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=5x+5x\\\\3\left(\dfrac{y}{x}\right)=\dfrac{3y}{x}\\\\5(x+y)-3\left(\dfrac{y}{x}\right)=5x+5y-\dfrac{3y}{x}[/tex]
A printer can print at a rate of 48 copies per minute. Find the time taken for the printer to
print 656 copies. Give your answer in minutes and seconds.
Answer:
13 min 40 sec
Step-by-step explanation:
656 copies *(1 min/48 copies)= 656 /48 min = 13 32/48 min = 13 2/3 min
2/3 min = 2/3 min * 60 sec/1 min = 40 sec
13 2/3 min = 13 min 40 sec
Ivan is putting books in his bookcase. He has
already put 74 books in the bookcase but he has
225 books. How many more books does he have to
put in the bookcase?
Answer:
151
Step-by-step explanation:
because 225-74 =151
151 books
There are 225 books, and 74 have already been placed on the shelf. Subtract 225 minus 74 to find that Ivan needs to place 151 more books on the shelf.
How many degrees are there in angle C?
** multiple choice question
There are 50 degrees in angle c
Answer: A. 50°
Step-by-step explanation:
Since the measure angles of a triangle add up to 180° and the right triangle=90°, therefore when you subtract 180-90-40, you get 90-40, which then equals to 50°.
before school began mrs. weeks bought a total of 86 balls us the information below to help you write a numerical expression
For this case we have that the total of the balls is 86. We know there are 8 footballs then:
Basketball: Two more than twice the number of footballs are basketballs, that is:
[tex]2 + 2 (8) = 2 + 16 = 18[/tex]
There are 18 Basketballs.
Baseballs: Four less than 5 times the number of footballs are baseballs, that is:
[tex]5 (8) -4 = 40-4 = 36[/tex]
There are 36 Baseballs.
Softballs: Six more than half of baseballs are softballs. That is to say:
[tex]6+ \frac {36} {2} = 6 + 18 = 24[/tex]
There are 24 Softballs
If we add we must get 86.
[tex]8 + 18 + 36 + 24 = 86[/tex]
ANswer:
There are 8 Footballs
There are 18 Basketballs.
There are 36 Baseballs.
There are 24 Softballs
Elijah spends 5 hours each week working out in a pool. This is twice the
amount of time he spends working out in the weight room. How much time
does he spend in the weight room each week?
Answer: he spends 2.5 hours in the weight room each week.
Step-by-step explanation: 2.5 multiplied by 2 (which is the twice amount of time spent working out in the pool) is 5.
So the answer is 2.5
find the measure of an angle between 0 and 360 coterminal coterminal with the given angle 495 degrees
Answer:
135 degrees
Step-by-step explanation:
Coterminal means it ends at the same spot around the circle.
To calculate the resulting angle we need to reduce/increase the started value to arrive to a value between 0 and 359 degrees.
If the starting angle is greater or equal to 360, we subtract 360 until we get below 360.
If the starting angle is below 0, we add 360 until we get equal or greater than 0.
So, starting with 495, we subtract 360 a first time....
A = 495 - 360 = 135
We're already in the desired range (0-359)... so we have our answer.
What is the value of m in the equation 1/2m-3/4n=16, when n = 8?
A. 20
B. 32
C. 44
D. 48
Answer:
44
Step-by-step explanation:
0.5 m - 0.75 n = 16
Substitute n = 8 into the equation
0.5 m - ( 0.75 × 8 ) = 16
0.5 m - 6 = 16
( Add 6 to both sides )
0.5 m = 26
( Divide by 0.5 )
m = 52
2. What percent of rolling a 2
3 probability of getting HH
Answer:
2. The correct answer option is 25%.
3. The experimental probability is 3% greater than the theoretical probability.
Step-by-step explanation:
2. We are given that a number cube is rolled 20 times out of which 5 times it lands on the number 2.
We are to find the experimental probability of getting the number 2.
P (2) = [tex]\frac{5}{20} \times 100 =\frac{1}{4} \times 100[/tex] = 25%
3. The theoretical Outcomes are: HH HT TH TT
So theoretical probability of getting HH = [tex]\frac{1}{4} \times 100[/tex] = 25%
Total number of outcomes = [tex]28+22+34+16[/tex] = 100
So experimental probability of getting HH = [tex]\frac{28}{100} \times 100[/tex] = 28%
Therefore, the experimental probability is 3% greater than the theoretical probability.
write the comparison below as a ratio in it's simplest form using a fraction, a colon and the word to. _____ 15 dollars to 27 dollars
Answer:
Step-by-step explanation:
15/27 - 5/9
5:9
5 to 9 ratio
In a marathon 90% runner were managed to complete it and 30% were men if 270 men completed it how many total runner began the marathon
Answer:
1000 runners
Step-by-step explanation:
Take total number of runners to be -----------x
90% of x managed to complete the marathon= 90/100 × x =0.9x
30% of those who completed the marathon were men= 30% × 0.9x
=0.3×0.9x= 0.27x
=270 men completed the marathon; this means
0.27x=270--------------------------------find x by dividing both sides by 0.27
x= 270/0.27
x=1000 runners
Answer:
1000
Step-by-step explanation:
Given : In a marathon 90% runner were managed to complete it and 30% were men.
To Find: If 270 men completed it how many total runner began the marathon.
Solution:
Let x be the number of total runners
Now we are given that 90% runner were managed to complete it
So, number of runners managed to complete = [tex]90\% \times x =\frac{90}{100}x=0.9x[/tex]
Now we are given that out of 90% , 30% were men
So, Numbers of men runners = [tex]30\% \times 0.9x=\frac{30}{100} \times 0.9x =0.27x[/tex]
Now we are given that 270 men completed it
So, [tex]0.27x=270[/tex]
[tex]x=\frac{270}{0.27}[/tex]
[tex]x=1000/tex]
Hence 1000 runners began the marathon.
In the diagram, what is the measure, of
For this case we have that by definition, a flat angle is the space included in an intersection between two straight lines whose opening measures 180 degrees.
Now, according to the figure we have that from V to S there are 180 degrees, like this:
[tex]5x + 25x + 30 = 180[/tex]
We add similar terms:
[tex]30x + 30 = 180[/tex]
Subtracting 30 from both sides of the equation:
[tex]30x = 150[/tex]
Divide by 30 on both sides of the equation:
[tex]x = \frac {150} {30}\\x = 5[/tex]
Answer:
[tex]x = 5[/tex]
(40pts) Mr. Green had 200 dollars and Mrs.Green had 180 dollars. After they each bought the same t-shirt, the ratio of the number of dollars that Mr. Green had remaining to number of dollars that Mrs. Green had remaining was 3:2. How much money was the t-shirt?
Answer:
The t-shirt cost $23.33.
Step-by-step explanation:
Answer:
$140
Step-by-step explanation:
If x was the amount of money Mr. Green had remaining, and y was the amount of money Mrs. Green had remaining, then:
x / y = 3 / 2
And, since they spent the same amount of money:
200 - x = 180 - y
We can solve this system of equations through substitution.
x = 3/2 y
200 - 3/2 y = 180 - y
20 = 1/2 y
y = 40
So Mrs. Green had $40 remaining. Since she started with $180, she must have spent $140. So that was the cost of the shirt. Let's check our answer by seeing how much Mr. Green had remaining and how it compares.
$200 - $140 = $60
$60 / $40 = 3 / 2
Yep, it checks out.
Can the three segments below form a triangle
Answer:
Step-by-step explanation:
The sum of the two shorter sides must be greater than the longest side.
5 + 8 = 13
13 is not greater than 14, so the three segments cannot form a triangle.
Answer: No
Step-by-step explanation:
A triangle can be formed only if the sum of 2 sides of the triangle is bigger than the length of the third side of this triangle.
In this case we have AB = 5, BC = 8 and AC = 14.
AB + AC > BC → 5 + 14 > 8 →1 9 > 8 ok!
AB + BC > AC → 5 + 8 > 14 → 13 > 14 false!
BC + AC > AB → 8 + 14 > 5 → 22 > 8 ok!
As we have that AB + BC > AC FALSE, this segments cannot form a triangle.
Kane is saving money. He starts with $14. The next day he has $21 and the third day he has $28. Assuming this pattern continues, what is the equation for the nth term of the arithmetic sequence?
Answer:
x+7
Step-by-step explanation:
let x= the amount of money he got that day
he gains $7/day
x+7
Find k and the roots if
3x^2+kx+4=0 and the sum of the roots is 3
Answer:
k = -9roots: (9±√33)/6Step-by-step explanation:
In the form ...
ax^2 +bx +c = 0
the sum of the roots is -b/a. Here, that is -k/3. You want that value to be 3, so we have ...
-k/3 = 3
k = -9
__
The solution can be found by completing the square. We choose to start by making the leading coefficient be 1.
x^2 -3x +4/3 = 0
(x^2 -3x +9/4) + (4/3 -9/4) = 0 . . . . . . . add and subtract (3/2)^2
(x -3/2)^2 = 11/12 . . . . . . . . . . . . . . . . . . add 11/12, write as square
x = 3/2 ± √(11/12) = (9±√33)/6 . . . . . . . .simplify