Answer:
The correct answer is A).
Step-by-step explanation:
He have the quadratic functions f(x) = 16x²-240x+896. The first step should be to check if the coefficients 240 and 896 are divisible by 16, which is true. Then, extracting 16 as common factor we have
f(x) = 16(x²-15x+56).
Now we can use directly the formula to find the roots of a quadratic equation, or a more efficient way in terms of calculations. We must find to numbers such that their product is +56 and their addition or subtraction is -15. It is not difficult to check that -7 and -8 fulfill those conditions. Hence,
f(x) = 16(x²-15x+56)= 16(x-7)(x-8).
Therefore, the solutions are x=8 and x=7.
the volume of a rectangle gift box is 98 cubic inches. the height is 4 inches and the width is 3 1/2 inches.what is the length of the gift box
find the measure of angle x in each of the following diagrams
The length of a rectangle is 3 inches more that its width. The perimeter of the rectangle is at least 30 inches. Which inequality shows the possible range of widths of the rectangle?
A. w ≥ 16.5 inches
B. w ≥ 13.5 inches
C. w ≥ 9 inches
D. w ≥ 6 inches
An old-fashioned method of saving money is to stuff it in your mattress or hide it in a cookie jar on the top shelf of your closet. But most financial consultants will argue against this method of saving your money. Why? Give an example of a better solution to saving money that might be advised by a financial consultant.
Financial consultants argue against keeping cash at home and suggest opening a savings account or investing in a certificate of deposit (CD) for safer and more effective saving methods.
Explanation:Financial consultants argue against the old-fashioned method of saving money by stuffing it in a mattress or hiding it in a cookie jar because it is not a safe or effective way to save. Keeping cash in your home puts it at risk of theft or loss, and it does not provide any potential for growth or earning interest. Instead, a financial consultant may suggest opening a savings account at a bank or credit union. This allows your money to be securely stored and can also earn interest over time. Another option they may recommend is investing in a certificate of deposit (CD), which offers a higher interest rate but requires depositing the money for a specific period of time.
Estimate the circumference of a circle that has a diameter of 13 yards. yards
Answer:
a little bit more than 37.70 yards
Step-by-step explanation:
Need Help ASAP!!
Find the area of this parallelogram. Be sure to include the correct unit in your answer.
x^2 + 18x + 50 = 9
Solve by completing the square
Can someone please help me with this (its percent of change word problems)
I need help ASAP ?!?!?!?!?!
Why is the library not adding any more fairy tales
Final answer:
The library may not be adding more fairy tales due to decreased demand, a desire to offer a diverse collection, and a strategic choice to provide a balanced collection.
Explanation:
It is possible that the library is not adding any more fairy tales due to a variety of reasons. One reason could be that the demand for fairy tales has decreased among library patrons. Another reason could be that the library wants to diversify its collection and offer a wider range of books to its readers.
Additionally, the library may be focusing on acquiring books from different genres or themes to cater to the interests of its diverse audience.
It is important to note that libraries regularly make decisions about which books to add to their collection based on factors such as popularity, relevance, and availability. The decision to not add any more fairy tales could simply be a strategic choice made by the library to provide a more balanced and comprehensive collection for its readers.
1. For T (-1,2),(7,8): 10
For E (3,-4), (-2,5): 10.3
For A (-7,0), (-4,12): 12.4
For N (1,-5), (-9,-9): 10.8
2. For S (2,6), (3,10): (2.5, 8)
For F (15,-1),(9,-5): (12, -3)
For T (7,-2), (-10,-8): (-1.5, -5)
For E (-3,0), (-11,9): (-7, 4.5)
Here are the distances and midpoints, calculated step by step:
Distances:
T: (-1, 2), (7, 8)
Difference in x-coordinates: 7 - (-1) = 8
Difference in y-coordinates: 8 - 2 = 6
Distance using the Pythagorean theorem: √(8² + 6²) = √100 = 10
E: (3, -4), (-2, 5)
Difference in x-coordinates: -2 - 3 = -5
Difference in y-coordinates: 5 - (-4) = 9
Distance: √((-5)² + 9²) = √106 ≈ 10.3
A: (-7, 0), (-4, 12)
Difference in x-coordinates: -4 - (-7) = 3
Difference in y-coordinates: 12 - 0 = 12
Distance: √(3² + 12²) = √153 ≈ 12.4
N: (1, -5), (-9, -9)
Difference in x-coordinates: -9 - 1 = -10
Difference in y-coordinates: -9 - (-5) = -4
Distance: √((-10)² + (-4)²) = √116 ≈ 10.8
Midpoints:
S: (2, 6), (3, 10)
Midpoint: ((2 + 3)/2, (6 + 10)/2) = (2.5, 8)
F: (15, -1), (9, -5)
Midpoint: ((15 + 9)/2, (-1 - 5)/2) = (12, -3)
T: (7, -2), (-10, -8)
Midpoint: ((7 - 10)/2, (-2 - 8)/2) = (-1.5, -5)
E: (-3, 0), (-11, 9)
Midpoint: ((-3 - 11)/2, (0 + 9)/2) = (-7, 4.5)
Complete question:
Write the exercise letter in the box above the answer at the bottom of the page. Find the distance between the two given points. If necessary, round to the nearest tenth.
T (-1,2),(7,8)
E (3,-4), (-2,5)
A (-7,0), (-4,12)
N (1,-5), (-9,-9)
Find the midpoint between the two given points.
S (2,6), (3,10)
F (15,-1),(9,-5)
T (7,-2), (-10,-8)
E (-3,0), (-11,9)
find the missing dimension. base: 27 cm and area: 256.5 cm sq
The train to Sun City travels 150 miles per hour. How long will a trip take if Sun City is 525 miles away?
A. 4 hours
B. 3 hours 30 minutes
C. 3 hours 15 minutes
D. 3 hours
Speed of train is 3 hours 30 minutes
Given that;Speed of train = 150 miles per hour
Distance of Sun city = 525 miles
Find:Speed of train
Computation:Speed of train = Distance of Sun city / Speed of train
Speed of train = 525 / 150
Speed of train = 3.5
Speed of train = 3 hours 30 minutes
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Given a circle with measures of (C, d, and r) and a circle with measures of (C', d', and r'), what is r if C C' = 5 and d' = 20?
Answer:
r = 50Step-by-step explanation:
We know that:
[tex]\frac{C}{C'}=5[/tex][tex]d'=20[/tex]So, the ratio between the circumferences is 4 and the diameter of the second circle is 20. In this case, we have to use the ratio between those two circumferences, because that's what is our given data.
[tex]\frac{C}{C'}=\frac{d}{d'}\\5=\frac{d}{20}\\ 100=d[/tex]
From this proportion, we deduct that the diameter of the initial circle is 100. Now, we know that the radius in a circumference is have the diameter. Therefore, the radius is:
[tex]r=\frac{d}{2}=\frac{100}{2}=50[/tex]
Your class is conducting an experiment to study geometric sequences. The class forms a line . The first person takes a whole pizza and divides it in half ,keeps half and hands the other half to the next person in line . The next people in line do the same with there slices of pizza . Which portion of the whole pizza does the 7th person in line get ? Please help !!!
The 7th person in line get 1/64th part of pizza.
What is Geometric sequence?
An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.
Given that;
The first person takes a whole pizza and divides it in half ,keeps half and hands the other half to the next person in line .
And, The next people in line do the same with there slices of pizza .
Now,
Since, The first person takes a whole pizza and divides it in half ,keeps half and hands the other half to the next person in line . The next people in line do the same with there slices of pizza .
Hence, We get the sequence as;
⇒ 1, 1/2, 1/4, 1/8,....
Clearly, The sequence is geometric sequence.
⇒ T (7) = 1 × (1/2)⁶
= 1/64
Thus, The 7th person in line get 1/64th part of pizza.
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Multiply. (3x+1)(x−1) Express the answer in standard form.
Answer:
3x2−2x−1
Step-by-step explanation:
y = 2x + 5
y= -x - 1
Dilate (9, 6) using a scale factor of 1/3
To dilate the point (9, 6) using a scale factor of 1/3, multiply the x-coordinate and y-coordinate by the scale factor to find the new coordinates which are (3, 2).
Explanation:To dilate the point (9, 6) using a scale factor of 1/3, we can multiply the x-coordinate and y-coordinate of the point by the scale factor to find the new coordinates.
For the x-coordinate, we have (9) * (1/3) = 3.
For the y-coordinate, we have (6) * (1/3) = 2.
So the dilated point is (3, 2).
A study found that 9% of dog owners brush their dogs teeth. Of 578 dog owners, about how many would be expected to brush their dogs teeth? Explain. Please help I am confused
Final answer:
About 52 dog owners would be expected to brush their dog's teeth.
Explanation:
The question is asking to estimate the number of dog owners who brush their dogs' teeth based on the given percentage from a study. To calculate this, you would take the total number of dog owners and multiply it by the percentage that brush their dogs' teeth. In this case, there are 578 dog owners and 9% of them are expected to brush their dogs' teeth.
Here is the calculation:
Number of dog owners who brush their dogs' teeth = Total number of dog owners × Percentage of owners who brush teethNumber of dog owners who brush their dogs' teeth = 578 × 0.09Number of dog owners who brush their dogs' teeth ≈ 52Therefore, about 52 dog owners out of 578 are expected to brush their dogs' teeth.
suppose the side length of a square A is 10 inches and the area of square C is 162 inches squared what is the area of square B if the squares form a right triangle ?
Answer:
62
Step-by-step explanation:
My teacher told me
What is circumference of a circle if the diameter is 7 ft
WILL MARK BRAINLIEST! PLEASE HELP MEH!Use the relationship between the angles in the figure to answer the question. Which equation can be used to find the value of x? Drag and drop the equation into the box.
A) x=180−31+40
B)x=90−40
C)x=180−(31+40)
D)x=90−(31+40)
Answer:
C. [tex]x=180^o-(31^o+40^o)[/tex]
Step-by-step explanation:
We have been given a figure of angles formed on a straight line.
Since we know that the angles on a straight line add up-to 180 degrees. Upon using this property we can set an equation as:
[tex]31^o+x^o+40^o=180^o[/tex]
Let us subtract 40 and 31 degrees from both sides of our equation to solve to x.
[tex]31^o-31^o+x^o+40^o-40^o=180^o-31^o-40^o[/tex]
[tex]x=180^o-31^o-40^o[/tex]
Upon factoring negative sign from right side of our equation we will get,
[tex]x=180^o-(31^o+40^o)[/tex]
Therefore, the equation [tex]x=180^o-(31^o+40^o)[/tex] can be used to find the value of x and option C is the correct choice.
what is this expression 2(5x-1)+14
I really need help with these questions.. Even if you can only answer one anything helps! Will give points and mark for smartest
1. Evaluate the determinant for the following matrix:
Below is all in one Bracket
-4 -4 -3
3 3 -5
-5 2 -5
Answer Choices
A. –152
B. –203
C. 75
D. –263
2.
Complete the multiplication: AB.
All sets of numbers are within a bracket.
A = 3 0 B= 2 8
2 -1 6 3
A. 6 0
1.2 -3
B. 6 24
3.4 5
C. 22 -8
7.8 -3
D. 6 24
3.4 13
3. Is in the 1st Picture
4.Use Gauss-Jordan elimination to solve the following linear system:
–3x + 4y = –6
5x – y = 10
A. (–6,2)
B. (2,–5)
C. (2,2)
D. (2,0)
5. If you were to use Gauss-Jordan elimination on the following linear system, what would the augmented matrix be? [ you can refer to second picture for 4 multiple choice answers ]
3w − x = 2y + z − 4
9x − y + z = 10
4w + 3y − z = 7
12x + 17 = 2y − z + 6
6. Refer to 3rd photo
triangle ABC undergoes a series of transformations to result in Triangle DF is triangle DEF congruent to triangle ABC
Since, translation and rotation both are rigid transformations which maps only congruent images. They do not change the size and shape of pre-image.
Thus, here ΔABC is congruent to ΔDEF.
Triangle ABC is reflected over x axis ,and then translated 6 units down to form triangle DEF.Since, translation and reflection both are rigid transformations which maps only congruent images. They do not change the size and shape of pre-image.
Thus, here ΔABC is congruent to ΔDEF.
Triangle ABC is rotated 180°, and then dilated by a scale factor of 3 to form triangle DEF.Here rotation is a rigid transformation which maps only congruent images but dilation is not a rigid transformation because it produces similar images for scale factor other than 1 (with scale factor 1 it also produce congruent images) .
Thus, here ΔABC is not congruent to ΔDEF.
The determination of congruency between Triangle DEF and Triangle ABC depends on the nature of the transformations applied to Triangle ABC. If these transformations are rigid motions, then Triangle DEF will be congruent to Triangle ABC.
Explanation:The question concerns whether Triangle DEF is congruent to Triangle ABC after undergoing a series of transformations. Congruent triangles are those that are identical in terms of size and shape, meaning their corresponding sides and angles are equal.
According to the given information, to determine congruency, we must consider the properties of the transformations involved. If the transformations applied to Triangle ABC are rigid motions (such as rotation, reflection, or translation), which do not alter the shape or size of figures, then Triangle DEF will be congruent to Triangle ABC. If however, the transformations include dilation or other non-rigid transformations that change the size but not the shape, Triangle DEF would not be congruent, although it could be similar to Triangle ABC.
Since the question provided involves linear transformations that transform lines into lines and take parallel lines to parallel lines, it is likely referring to rigid motions. Therefore, it suggests that Triangle DEF should be congruent to Triangle ABC, assuming that the series of transformations includes only those that preserve lengths and angles.
Factor the expression. d^2-14d+49
the college textbook this year was 197. the following year it was 222. what is the percent change in the price of the book HEEEEELLLLPPPPPP
what is 3 groups of 1/8
Use multiplication to find 2 equivalent fraction for 3/4 and 4/5
To find two equivalent fractions for 3/4 and 4/5 using multiplication, multiply both the numerator and denominator of each fraction by the same number.
Explanation:To find two equivalent fractions for 3/4 and 4/5 using multiplication, we can multiply both the numerator and denominator of each fraction by the same number. Let's choose 2 as the multiplying factor.
For 3/4, multiplying both numerator and denominator by 2 gives us: 6/8.
For 4/5, multiplying both numerator and denominator by 2 gives us: 8/10.
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PLEASE HURRY WILL MARK BRAINLIEST WOULD GIVE MORE POINTS IF I HAD MORE Model each scenario with an equation and a sketch. Solve for the missing value and u. Use complete sentences to interpret the solution. In your final answer, include your equation, sketch, interpretation, and all calculations necessary for the solution. To get home from school, Bob walks four blocks north and three blocks east. What is the straight line distance between Bob’s house and his school? One of the requirements of your summer window-washing job is to provide yourself with all of the necessary supplies, including a fourteen foot ladder. When you arrive at your first job, you place your ladder on the ground six feet from the base of the house and lean it towards a second story window, only to realize that the ladder doesn’t reach the window. Given the length of the ladder and its current position, what is one possible height of the second story window? (Hint: There is more than one correct answer.) In a softball diamond, each of the bases, including home plate, are equidistant from each other. Although the name implies differently, a softball diamond is in the shape of a square. Given that the distance between the bases is unknown, determine an expression for the straight line distance between first and third bases. A sailboat drifts 600 meters west, makes a turn and sails 800 meters south. How far is the sailboat from its original position?
Answer:
First question: 5. Second question:
You can do any really high number instead of doing the math.
a^2 + b^2 = c^2. A being side one, B being side 2, and C being side 3. Pythagorean theorem
1000 meters
Step-by-step explanation:
For the first question, we can use the Pythagoras theorem. make a square that is a 4 by 3. Then cut the square in half diagonally. Now to 4^2 + 3^2 which is 25. The square root of 25 is 5 so in a straight line, it'll be 5.
You can do any high number instead of calculating the minimum height.
Same as first with different inputs.
Same as first with different inputs.
What is the median of the data set?
{20, 25, 36, 41, 87, 91, 92, 95, 99}
Enter your answer in the box.
The median number means the middle number so the number in the middle would be the answer
Answer:
87
hope o helped
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