Let x be the
width of the frame.
Area of the picture is 5*7 = 35 sq in
Area of the frame given as the same, frame = 35 sq in also
Therefore the total area (picture & frame) will be 70 sq in
A simple equation would be made and it will look like this: (7+2x) * (5+2x) =
70
Using the FOIL
method
35 + 14x + 10x + 4x^2 = 70
4x^2 + 24x + 35 - 70 = 0; subtract 70 from both sides:
4x^2 + 24x - 35 = 0
unluckily this will not factor easily, so we should use the quadratic equation:
where: a = 4; b = 24; c = -35
x = -b sqrt b^2 – 4*a*c divided by 2 * a
x
= -24 ±
sqrt 24^2 -4*4*(-35) divided by 2*4
x = -24 ±sqrt 576 -
-(560) divided by 8
x = -24 ± sqrt 576 + 560 divided by 8
x = -24 ± sqrt1136
divided by 8
x = -24 + 33.7046 divided by 8
x = 9.7046 divided by 8
x =1.213 inches is the answer
Which of the following represents side lengths that form a Pythagorean triple?
A. 7, 8, 9
B. 1, 2, 3
C. 4, 5, 6
D. 3, 4, 5
Answer:
D. 3, 4, 5
Step-by-step explanation:
Pythagorean theorem : [tex]Hypotenuse^2 = Perpendicular^2+Base^2[/tex]
If the given options satisfy the theorem .So, they form a Pythagorean triple.
Hypotenuse is the longest Side
A)7, 8, 9
Hypotenuse = 9
[tex]Hypotenuse^2 = Perpendicular^2+Base^2[/tex]
[tex]9^2 = 7^2+8^2[/tex]
[tex]81 = 49+64[/tex]
[tex]81 \neq 113[/tex]
Hence not a Pythagorean triple.
B)1,2,3
Hypotenuse = 3
[tex]Hypotenuse^2 = Perpendicular^2+Base^2[/tex]
[tex]3^2 = 2^2+1^2[/tex]
[tex]9 = 4+1[/tex]
[tex]9 \neq 5[/tex]
Hence not a Pythagorean triple.
C) 4,5,6
Hypotenuse = 6
[tex]Hypotenuse^2 = Perpendicular^2+Base^2[/tex]
[tex]6^2 = 3^2+4^2[/tex]
[tex]36 = 9+16[/tex]
[tex]36 \neq 25[/tex]
Hence not a Pythagorean triple.
D)3,4,5
Hypotenuse = 5
[tex]Hypotenuse^2 = Perpendicular^2+Base^2[/tex]
[tex]5^2 = 3^2+4^2[/tex]
[tex]25 = 9+16[/tex]
[tex]25 = 25[/tex]
Hence a Pythagorean triple.
Hence Option D represents side lengths that form a Pythagorean triple
Answer:
it is D 3,4,5
"Eventually the things in life that gave you pause mean nothing. Time... becomes your friend." (math 1 help plz)
What is the value of the expression?
5/6−(1/8÷3/4)
Enter your answer, as a fraction in simplest form, in the box
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
We are given that an expression
[tex]\frac{5}{6}-(\frac{1}{8}\div\frac{3}{4})[/tex]
We have to find the value of expression.
[tex]\frac{5}{6}-(\frac{1}{8}\div\frac{3}{4})[/tex]
When we change divide into multiply then the term will be reciprocal.
By using this property
[tex]\frac{5}{6}-(\frac{1}{8}\times \frac{4}{3})[/tex]
[tex]\frac{5}{6}-\frac{1}{6}[/tex]
By simplification
[tex]\frac{5-1}{6}[/tex]
By simplification
[tex]\frac{4}{6}[/tex]
By using subtraction property of integers
[tex]\frac{2}{3}[/tex]
Hence, the value of given expression =[tex]\frac{2}{3}[/tex]
Tours of the art museum are offered every 1/3 hour starting at 10 A.M. The museum closes at 4:00 P.M. How many tours are offered each day?
And
Small juice bottles come in packages of 6. yogurt treats come in packages of 10. paula qanta to have the exact same number of each item. what is the least number of bottles of juice and individual yogurt treats she will have? how many packages of each will she need?
A one compartment vertical file is to be constructed by bending the long side of an 8 in 8 in. by 10 10 in. sheet of plastic along two lines to form a U shape. How tall should the file be to maximize the volume that it can hold?
In order to maximize the volume of the file, it should be 2 inches high. This is calculated using the optimization principle in calculus applied to the volume formula of a rectangular prism.
Explanation:This problem involves optimizing the volume of a vertically filed object, which is a common theme in calculus. The file is being formed from a rectangular sheet of plastic that is 8 inches by 10 inches by bending it to form a U-shape.
The volume of a rectangular prism (which is what the file will essentially be) is given by the formula length x width x height. In this case, the length will always be 10 inches because it's the undisturbed dimension. The 8-inch side will be divided into a height part and a width part once we bend it into a U shape. Since we don't know a priori what the height is yet, let's call it x. This means the width will then be 8 - 2x (since we lose x from each side to form the height).
Our volume function V becomes: V(x) = length x width x height = 10(8-2x)x. To maximize this volume, you want to take the derivative V'(x), set it to 0 and then solve for x. Taking the derivative will give you V'(x) = 10(8-4x), and setting it to 0 and solving gives you x = 2 inches. So, the file should be 2 inches high to maximize the volume it can hold.
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Of all rectangles with a fixed perimeter of p, which one has the maximum area? (give the dimensions in terms of p.)
For a rectangle with a fixed perimeter P, the one with maximum area has dimensions L = P/4 and W = P/4 obtained by optimizing the area expression.
To find the rectangle with the maximum area given a fixed perimeter P, we can use optimization techniques. Let L represent the length and W represent the width of the rectangle. The perimeter is given by P = 2L + 2W, and the area is given by A = LW.
Since P is fixed, we can express one of the variables in terms of the other using the perimeter equation. Solving for L, we get L = (P/2) - W. Substituting this expression into the area equation, we have A = ((P/2) - W)W.
To find the dimensions that maximize A, we take the derivative of A with respect to W, set it equal to zero to find critical points, and check for endpoints (since we are dealing with real-world dimensions).
(dA/dW) = (P/2) - 2W = 0.
Solving for W, we get W = P/4. Substituting this value back, we find L = P/4.
Therefore, the rectangle that maximizes the area for a fixed perimeter P has dimensions L = P/4 and W = P/4.
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The question probable may be:
What are the dimensions of the rectangle with the maximum area given a fixed perimeter P?
In a flock of black and white sheep, 2 out of 5 sheep are white. If there are 8 more black sheep than white sheep, how many sheep are in the flock?
To find the total number of sheep in the flock where 2 out of 5 are white and there are 8 more black than white sheep, we set up a ratio and solve for the number of white sheep (W), which is 16. We then determine the number of black sheep (B) to be 24, leading to a total of 40 sheep.
Explanation:The subject of the question is mathematics, and it appears to be at the middle school level. The task involves determining the total number of sheep given that 2 out of 5 are white and there are 8 more black sheep than white. Let's define the variables: W for white sheep and B for black sheep. From the statement, we have the ratios W/B = 2/3 because for every 2 white sheep, there are 3 black sheep which are proportionally 5 sheep in total (2+3=5), and we have the relationship B = W + 8 because there are 8 more black than white sheep. Using these equations, we can solve for W and B.
From the ratio W/B = 2/3, we can express B as B = 3/2 * W.Replace B in the second equation with 3/2 * W:Therefore, the total number of sheep in the flock is 40.
Marisol keeps track of her weekly quiz grades as shown in the table.
a. Complete the table
b. In which class did Marisol have the higher score?
c. Suppose Marisol scored a 96% on an english test. There were 50 questions on the test. How many did Marisol answer correctly?
Test / Number/Score/Total
Correct
____________________
Math/ 68 / /85
Science/ / 90% / 70
Marisol got 80% on her Math quiz by answering 68 out of 85 questions correctly, and 90% on her Science quiz by answering 63 out of 70 questions correctly. She scored higher in Science. For her English test, by scoring 96%, she got 48 out of 50 questions correct.
Explanation:To complete the table and find the number of questions Marisol got correct in Science, we use the percentage score and total number of questions. For the Math test, she got 68 questions correct out of a total of 85 questions. To find the corresponding percentage, we calculate (68/85) * 100%.
For the Science test, we use the given percentage score of 90% and the total of 70 questions to find the number of correct answers. The calculation is (90/100) * 70.
To find out in which class Marisol had the higher score, we compare the calculated percentage scores from the Math and Science classes.
Finally, to determine the number of questions Marisol answered correctly on the English test, where she scored 96% on a 50 question test, we use the calculation (96/100) * 50.
Express each product in the simplest form.
What is the measure of ∠DAE? 45° 46° 91° 146°
Answer:
The answer/measure is 45 degress.
Step-by-step explanation:
The measure of ∠DAE is 45°.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
In the given figure let's say angle FAE = x than
x = 180 - 134 = 46 degree
Now by line CAF angle ∠DAE = 180 - ( 89 + 46 ) = 45° hence it will be correct answer.
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the simplest form of the square root of 3,025 is
The function y = [x] is defined as follows: for any input x, the output is the smallest integer that is greater than or equal to x (“rounding up” any non-integer to the next integer).
Draw the graph of y = [x] for -2 ≤ x ≤ 2. Upload a handwritten copy of your graph as your final answer.
Answer:
Step-by-step explanation:
What is a classification for a triangle with angle measures of 20, 80, and 80 degrees,?
Answer:
its a icolaleas
Step-by-step explanation:
This is the process of predicting values for points which occur between those given in a set of bivariate data.
A triangle can have at most ____ right angle(s).
No
1
2
4
Answer:
The answer is 1
Wilma and Betty are playing a number game. Wilma tells Betty, "I'm thinking of a number between 1 and 10. If I take the number and add 4 to it and then multiply that by 3, I get 30." What number is Wilma thinking of?
Sylvia has 6 1/2 boxes of chocolate to share at a family picnic. if she gives eacah person 1/3 of a box, how many people can receive chocolate
Answer:
The correct Answer is 19
The number of people who will receive the chocolate will be equal to 19.
What is a fraction?In mathematics, a fraction is represented by a specific number that designates a portion of an entire. A fraction is a piece or section of a whole, whereby a can have been any number, a particular value, or an object.
As per the provided data in the question,
Total boxes of chocolate = 13/2
Chocolate received by each person = 1/3 of a box
Then, the number of people who receive the chocolate is,
13/2 ÷ 1/3 = 19.5 or,
A total of 19 people will receive the chocolate.
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In triangle ABC, < A = 38° and < B = < C. Find < B.
m< B =
A.) 26°
B.) 71°
C.) 142°
71 odyssey just had this
describe how you could estimate thw IQR of the data set from a histogram
Answer: Once you put the numbers in order and find the median do the same process that you did to find the median to the left and right side of the median. Once you find the " median " of the left and right sides ( which are called the 1st and 3rd Quartiles ) You will subtract the 1st quartile from the 3rd Quartile and that will give you the IQR.
Step-by-step explanation:
solve for n , S = (n - 2)180
When using the law of sines, why can the SSA case result in zero, one, or two triangles? Explain.
Answer: If you have SSA, then the third side determines the triangle. If it is too short to intersect the other side, then it does not form a triangle. The third side can also be just the right length to meet the other side, making one triangle. Finally, the third side might be long enough to intersect the other side at two different points, creating two triangles.
i just took the assignment
There are different rules in mathematics. The explanation is that when a person have SSA, the third side is often used to know the type of triangle and also;
When it too short to pass through the other side, it rather then not form a triangle. The third side can be the appropriate length to meet the other side, creating one triangle.
Furthermore, the third side can be able to pass through or intersect the other side at two key areas or points, forming two triangles.
Note that;
When the third side of the triangle is too little to intersect the other side, there is no triangles that is created.When the third side is said to be long enough to meet the other side at a certain point, only one triangle is created.When the third side is able and long enough to pass through the other side at two points, as a result, two triangles are created or made.Can The Law of Sines be used in SSA case?"SSA" is known to be when one knowns two sides and an angle that is said to be not or not part of the angle between the sides.
The Law of Sines is known to be used first to calculate one of the other two angles.
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The school is planning a field trip. There are 14670 students and 48 seats on each school bus. How many buses are needed to take the trip?
plz explain how you got your answer
Bonita is testing prototype model rocket engines. To be considered a successful launch, the rocket must reach a height of at least 24 ft and must go a horizontal distance of no more than 10 ft. The vertical height must be at least three times as high as the horizontal distance. No rocket should go higher than 33 ft.
The graph shows the feasible region, where x represents the horizontal distance and y represents the vertical distance.
Which ordered pairs meet all the constraints for a successful launch and make sense in context of the situation?
Select each correct answer.
(0, 33)
(4, 36)
(4.8, 30.5)
(9, 26)
(2, 22)
How to find the angle measure of a triangle with x and x+4 and 9x?
Determine the x-intercepts of the function. Check all that apply. (–2, 0) (–1, –2) (0, 0) (1, 0) (2, 0)
it's (0, 0) and (-2, 0) so A & C
Answer: A, C
Step-by-step explanation:
Hope this helps!!
A particular shade of purple paint is made of a ratio of 2 pints of red paint to 1 pint of blue paint. List 4 other combinations of red and blue paint that would make the same shade of purple paint
find the area of a figure whose coordinates are A (-2,2) B (2,2) C (2,-2) D (-2,-2)
12 units.squared
16 units.squared
20 units.squared
24 units.squared
A triangle is isosceles. if one angle of the triangle measures 102°, what are the measures of the largest and smallest angles of the triangle?
In an isosceles triangle with one angle measuring 102°, the other two angles are both 39°. The sum of all angles in a triangle is 180°. Therefore, the largest angle is 102° and the smallest are both 39°.
If a triangle is isosceles and one angle measures 102°, we can determine the measures of the other two angles. Since it's an isosceles triangle, two angles are the same. According to the properties of triangles, we know that the sum of all three angles must be 180°. Therefore, we can subtract the known angle from 180° to determine the sum of the remaining two angles.
180° - 102° = 78°
Since the two remaining angles are equal, we divide 78° by 2 to find the measure of each angle.
78° ÷ 2 = 39° each
The measures of the largest and smallest angles in the isosceles triangle are 102° (the largest) and 39° (the smallest).
Vivian is going to do some yard work, but she needs to leave her house at 1:00 to go to a football game. She is going to mow the lawn for 1 hour and 10 minutes, trim some bushes for 30 minutes, and put down some mulch for 35 minutes. She will also need 20 minutes to shower and get dressed. What time should she start the work so she will be ready at 1:00?
Answer:
Vivian should start working by 10.25 am.
Step-by-step explanation:
Time taken to mow the lawn = 1 hour and 10 minutes
Time to trim bushes = 30 minutes
Time for putting down mulch = 35 minutes
Time to get dressed = 20 minutes.
Total time = 1 hour + (10+30+35+20) minutes
= 1 hour + 95 minutes
= 1 hour + (60+35) minutes
= 1 hour + 1 hour + 35 minutes
= 2 hours 35 minutes.
This means Vivian should start working 2 hours 35 minutes before 1:00 pm.
So, it becomes ; 10:25 am.
when a graph of a cubic polynomial function rises to the left, it falls to the right true or false
Final answer:
The statement about cubic polynomial functions rising to the left and falling to the right is false; the behavior of a cubic function's graph depends on the sign and magnitude of its coefficients, particularly the leading coefficient.
Explanation:
The statement that a graph of a cubic polynomial function that rises to the left must necessarily fall to the right is false. While this behavior is common for many cubic functions, it's not a definitive rule. Cubic functions are defined by the equation f(x) = [tex]ax^3 + bx^2[/tex] + cx + d, where a, b, c, and d are constants, and a ≠ 0. The sign and magnitude of these constants, especially the leading coefficient 'a', influence the end behavior of the function.
For example, if 'a' is positive, the right end of the cubic function's graph will rise, and depending on the signs and magnitudes of the other coefficients, the left end might also rise or fall. Similarly, if 'a' is negative, the right end will fall, and the left end's behavior can vary. Cubic graphs can also exhibit turning points where the function's direction changes, which is dictated by the local minima and maxima.
Therefore, while many cubic polynomials may display the behavior of rising to the left and falling to the right, others with different coefficients could have a completely different end behavior or shape, such as rising on both ends or falling on both ends. Two-dimensional (x-y) graphing tools and learning about graphing polynomials can provide visual understanding of these concepts.