x- coordinate of vertex = - 3
the vertex lies on the axis of symmetry , which is positioned at the midpoint of the zeros
find the zeros by setting y = 0
(x - 6)(x + 12) = 0 ( equate each factor to zero and solve for x )
x - 6 = 0 ⇒ x = 6
x + 12 = 0 ⇒ x = - 12
x coordinate of vertex = [tex]\frac{- 12+6}{2}[/tex] = [tex]\frac{-6}{2}[/tex] = - 3
The bottom and top of a box are rectangles twice as long as they are wide. Find the volume of the box if it is four feet high and has a total surface area of 220 feet squared.
Let x = the width
then
2x = the length
:
The box dimensions: 2x by x by 4
Given the surface area:
2(2x*x) + 2(2x*4) + 2(x*4) = 220
:
4x^2 + 16x + 8x = 220
A quadratic equation:
4x^2 + 24x - 220 = 0
simplify, divide by 4
x^2 + 6x - 55 = 0
Factor
(x+11)(x-5) = 0
The positive solution is what we want here:
x = 5 ft is the width
then
2(5) = 10 ft is the length
:
Find the volume
10 * 5 * 4 = 200 cu/ft is the volume
Final answer:
The volume of the box is 192 cubic feet, calculated using the dimensions provided in the question.
Explanation:
The volume of the box is 192 cubic feet.
To find the volume, we need to calculate the dimensions of the base rectangle. Since the base and top are twice as long as they are wide, the larger square will have sides of 8 feet. With a height of 4 feet, the volume can be calculated as V = length*width*height. Plugging in the values, we get V = 8*4*4 = 192 cubic feet.
Mary mixes 11/12 oz of red paint with 1 3/4 oz of white paint.
How many ounces of paint does Mary mix?
A. 123 oz
B .156 oz
C. 178 oz
D .223 oz
Im assuming that to be the case, so:-
11/12 + 1 3/4
= 11/12 + 7/4
= 11/2 + 21 / 12
= 32 / 12
= 2 2/3 OZ. (Choice D).
Mary mixed Quatities of 2 2/3 ounces of paint by adding 11/12 oz of red paint and 1 3/4 oz of white paint.
Explanation:To find out how many ounces of paint Mary mixed, we need to add the amounts of red and white paint.
First, let's add the red paint: 11/12 oz.
Next, let's add the white paint: 1 3/4 oz.
To add fractions, we need a common denominator. In this case, the common denominator is 12, so we can rewrite 1 3/4 as 7/4: 7/4 oz.
Now, let's add the two amounts: 11/12 + 7/4.
To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 12. Multiply the numerator and denominator of the first fraction by 1 (12/12) and the numerator and denominator of the second fraction by 3 (3/3).
So, 11/12 + 7/4 is equal to (11/12) + (21/12) = 32/12.
We can simplify 32/12 to 2 8/12, and further simplify it to 2 2/3 oz.
Therefore, Mary mixed 2 2/3 ounces of paint.
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Ten times a number decreased by seven equals 101 plus that number. Find the number
Final answer:
A student's math problem involving an algebraic equation to find a number has been solved by isolating and solving variables, resulting in the number 12.
Explanation:
To solve the equation where ten times a number decreased by seven equals 101 plus that same number, we would set up the following equation:
10x - 7 = 101 + x
Now, we solve for x:
First, subtract x from both sides of the equation to get all the x terms on one side:
9x - 7 = 101
Next, add 7 to both sides of the equation to isolate the term with x:
9x = 108
Finally, divide both sides by 9 to solve for x:
x = 12
Hence, the number we are looking for is 12.
A box contains 4 red and 3 blue poker chips. Three chips are pulled random. What is the probability that all are red with a replacement
No. If red balls = 4, Total no. Of balls = 7
Prob of getting first red = 4/7
Second red = 4/7
Third red = 4/7
As all balls are taken out with replacement ,therefore total no. Of red balls remain same
Probability of drawing all red = 4/7×4/7×4/7
=64/343
Evaluate.
6^2+(3⋅4)−2^4
Enter your answer in the box.
To evaluate the given expression, we follow the order of operations (PEMDAS) and calculate the exponentials first. Next, we perform the multiplication and addition/subtraction operations from left to right to find the final result. Following the order of operations (PEMDAS), the expression 6^2+(3⋅4)−2^4 simplifies to 32.
Explanation:To evaluate the given expression, we need to follow the order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
First, let's calculate the exponentials:
6^2 = 6 * 6 = 36
2^4 = 2 * 2 * 2 * 2 = 16
Next, let's perform the multiplication and addition/subtraction operations from left to right:
3 * 4 = 12
36 + 12 - 16 = 48 - 16 = 32
Therefore, the result of the given expression is 32.
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Box A contains 53 cubes and has a mass of 1760 grams. Box B contains 18 cubes and has a mass of 1620 grams. The mass of box A is the same as the mass of box B. Every cube has the same mass.
To find the mass of each cube, divide the total mass of the box by the number of cubes. The mass of each cube in Box A is 33.21 grams, while the mass of each cube in Box B is 90 grams.
Explanation:To determine the mass of each cube, we need to divide the total mass of the box by the number of cubes.
Mass of each cube in Box A = Total mass of Box A / Number of cubes in Box A = 1760 grams / 53 cubes = 33.21 grams per cube.
Mass of each cube in Box B = Total mass of Box B / Number of cubes in Box B = 1620 grams / 18 cubes = 90 grams per cube.
The equation x^2-9=0 has how many real solutions
So remember that the degree of the polynomial will indicate how many solutions there are, real or complex. Since the degree of the polynomial is 2, this means that there is a maximum of 2 real solutions in this equation.
Next, we are going to apply the difference of squares rule to this polynomial, which is [tex]x^2-y^2=(x+y)(x-y)[/tex] . In this case:
[tex]x^2-9=(x+3)(x-3)\\(x+3)(x-3)=0[/tex]
Now, we are going to apply the Zero Product Property, which states that if a × b = 0, this means that either a or b = 0 or a and b = 0. In this case, a = x + 3 and b = x - 3. Solve each as such:
[tex]x+3=0\\x=-3\\\\x-3=0\\x=3[/tex]
In short, there are 2 real solutions: x = 3 and x = -3.
The equation [tex]x^2-9=0[/tex] has two real solutions which are x=3 and x=-3. The solutions are obtained by applying the quadratic formula, which indicates that every equation containing an unknown squared will have two solutions.
Explanation:The equation[tex]x^2-9=0[/tex] is a quadratic equation. For any quadratic equation in the form ax²+bx+c = 0, the solutions or roots can be calculated using the quadratic formula: -b ± √(b² - 4ac) / 2a.
In this specific equation, [tex]x^2-9=0[/tex]can be rewritten as x²-9+9 = 9, which simplifies to x² = 9. The solutions can then be obtained using the principal square root or the negative square root, resulting in x = ± √9. Therefore, the two real solutions are x = 3 and x = -3.
It's important to note that every equation containing an unknown squared will have two solutions, which can be both meaningful or only one of them can be reasonable depending on the context of the problem.
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Why does dividing by 10 shift each digit one place to the right?
Answer:
Step-by-step explanation:
As we move up the list -- as we push the digits one place right -- the number has been divided by 10 because each place to the right is worth 10 times less. ... As we move down the list -- as we push the digits to the left through the decimal point -- each number has been multiplied by 10
Dividing by 10 shifts each digit one place to the right due to our base-ten counting system. Each time we divide by 10, the number is broken into 10 equal parts, thereby moving its digits one place to the right. The same principle applies when dealing with larger powers of 10 and is often employed in scientific notation.
Explanation:The reason why dividing by 10 shifts each digit one place to the right relates directly to the base-ten number system we use, which relies on powers of ten. Whenever we divide by 10, we are asking how many times the number can be broken into 10 equal parts, thus moving its digits one place to the right.
For instance, if we take the number 250 and divide it by 10, the result is 25. We've essentially shifted the digits one place right. Similar to this when we are dealing with decimal numbers, the shift occurs with the decimal point. If we had 25.0 and divided by 10, the result would be 2.5
The same principle applies to larger powers of 10. If you divide by 100 (which is 10^2), you shift each digit two places to the right, and so on.
Another way to consider it is using scientific notation, which often uses powers of 10 to simplify large or small numbers. A number like 1,230,000,000 is written as 1.23 × 10⁹ in scientific notation. When we divide this number by 10, the exponent decreases by 1 to become 1.23 × 10⁸, effectively shifting each digit one place to the right.
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Please anyone help fast
For 20 points
Simplify: 9(3 + 4)
simplify 9[3+4}
using bodmass
=9{7}
63
In the image, shape DEFG is similar to shape WXYZ . Find the measure of side YZ.
DDFG:
Length: 18
Width: 24
WXYZ:
Legnth: 30
Width: YZ (unknown)
It is 40 because 24/40= 0.6 and 18/30= 0.6 so yeah its 40
Answer:
40
Step-by-step explanation:
We know that DEFG is similar to WXYZ. This means we can set up a proportion to find the length of the unknown side (let x be the unknown side):
18/30 = 24/x
Cross multiplying,
18(x) = 30(24)
18x = 720
Divide both sides by 18:
18x/18 = 720/18
x = 40
What is (-6,1) when it is reflected over y=x
ANSWER
The image point is [tex](1,-6)[/tex].
EXPLANATION
For a reflection in then line [tex]y=x[/tex], we simply swap the x and y coordinates.
Thus, in general the mapping for the reflection in the line [tex]y=x[/tex], is
[tex]P(x,y)\rightarrow P'(y,x)[/tex].
Hence,
[tex]P(-6,1)\rightarrow P'(1,-6)[/tex].
See graph.
The reflection of the point (-6,1) over the line y=x results in the point (1,-6).
Explanation:In the context of coordinate geometry, reflection over a line, specifically y=x, requires that we swap the x and y coordinates of a given point. So, when we have the point (-6,1), it is reflected to become (1,-6) over the line y=x. Hence, "this operation fundamentally changes the position of the point".
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four times the sum of some number plus 1 is equal 12 times the difference of the number and 3. Find the number
4(x + 1) = 12(3 - x)
Distributive property on both sides.
4x + 4 = 36 - 12x
Add 12x to both sides.
16x + 4 = 36
Subtract both sides by 4.
16x = 32
Divide both sides by 16.
x = 2
Scotty and Tyler are training for a pizza-eating contest. They are trying to eat 6 pizzas in total. So far, Scotty has eaten 2 3/4 pizzas and Tyler has eaten 1 7/8 pizzas. How much more pizza do they have left to eat?
Answer:
They are left with [tex]1\frac{3}{8}[/tex] pizza to eat.
Step-by-step explanation:
Scotty and Tyler are trying to eat 6 pizzas in total.
Sotty has eaten = [tex]2\frac{3}{4}[/tex] Pizzas
Tyler has eaten = [tex]1\frac{7}{8}[/tex] Pizzas
Total pizza eaten by them = [tex]2\frac{3}{4}[/tex] Pizzas + [tex]1\frac{7}{8}[/tex] Pizzas
= [tex]\frac{11}{4}[/tex] + [tex]\frac{15}{8}[/tex]
= [tex]\frac{37}{8}[/tex]
Total pizza was eaten = [tex]4\frac{5}{8}[/tex]
Pizza have left to eat = 6 - [tex]4\frac{5}{8}[/tex]
= 6 - [tex]\frac{37}{8}[/tex]
= [tex]\frac{11}{8}[/tex]
= [tex]1\frac{3}{8}[/tex]
They are left with [tex]1\frac{3}{8}[/tex] pizza to eat.
Simplify. 3/5+(-1/4)÷7/10
Enter your answer, in simplest form, in the boxes.
Please help, look down below at the attachment cuz Im not sure I set the problem up right!
Answer:
1/10
Step-by-step explanation:
There are three simple fractions in this problem: 3/5, -1/4 and 7/10. Rules of order require that the division (-1/4) divided by 7/10 be carried out first; the correct product is -10/28, or -5/14. Then we have 3/5 + (-5/14).
Here the LCD is 70. Then 3/5 + (-5/14) becomes 42/70 - 35/70, which simplifies to 1/10.
Answer:
1/10
Step-by-step explanation:
if ∠2 and ∠3 are supplementary angles, then ∠2 and ∠3 form a linear pair true or false
Answer:
True ,if they are adjacent and share a vertex and one side
Wich term best describes a figure formed by three segments connecting three noncollinear points ?
A triangle is the answer.
Answer:
ok the answer is
Step-by-step explanation:
69 gooba, go watch it NOW
Bob is making mini fondant cakes for next bake sale each cake costs bob $1.80 to make if he sells the cakes for $3.00 each how many will he have to sell to make a profit of exactly $36.00 please help me answer
Answer:
he would have to sell 30 cakes
Step-by-step explanation:
if you take the amount it actually cost to make it and the amount he is selling them for you would first do
1.80 - 3.00 = 1.20$
after you get 1 dollar and 20 cents you would divide it by 36 dollars to get 30
to check your answer do 30 x 1.20 = 36.00
Question 12 please , thank you in advance.
I think It is C but not sure
Which of the following illustrates the Law of Syllogism?
The answer is letter A.
Answer:
A.If[tex](p\implies q)\;and \;(q\implies r)[/tex],then [tex]p\implies r[/tex].
Step-by-step explanation:
We have to find the which statement illustrate the law of syllogism.
Law of syllogism: Premise: if p then q
Premise:If q then r.
Conclusion:If p then r.
It is like transitive property of equality.
A.If[tex](p\implies q)\;and \;(q\implies r)[/tex],then [tex]p\implies r[/tex].
It is true by definition of law of syllogism.
B.If[tex](p\implies q)\;and \;(q\implies p)[/tex],then [tex]p\implies r[/tex].
It is not true by definition of syllogism.
C.If[tex](p\implies q)\;and \;(p\implies r)[/tex],then [tex]q\implies r[/tex]
It is not true by definition of syllogism.
D.If[tex]p\implies r)\;and \;(q\implies r)[/tex],then [tex]p\implies r[/tex].
It is not true by definition of law of syllogism.
Answer:A
The height of a baseball thrown from the catcher to first base is modeled by the function h(t) = –0.09t2 + 0.72t + 6, where h is the height of the ball measured in feet and t is the time since being thrown, measured in seconds. The ball is in the air for 10 seconds before being caught. What's the height of the ball at 10 seconds?
The height of a baseball thrown from the catcher to first base is modeled by the function [tex]h(t) = -0.09t^2 + 0.72t + 6[/tex], where h is the height of the ball measured in feet and t is the time since being thrown, measured in seconds
To find out height of the ball at 10 seconds, we plug in 10 for t
[tex]h(t) = -0.09t^2 + 0.72t + 6[/tex]
[tex]h(10) = -0.09(10)^2 + 0.72(10) + 6[/tex]
h(10)=4.2 feet
the height of the ball at 10 seconds= 4.2 feet
When a figure is translated, its orientation (blank) and the measures of its angles (blank).
Answer:
Its orientation may change and the measures of its angles stay the same.
Step-by-step explanation:
Answer:
When a figure is translated its orientation may change and the measures of its angles keeps the same measure.
Step-by-step explanation:
Whenever we translate a figure, we move a figure into some orientation given by this same vector. But the angles will remain the same since there is no distortion.
Just as the picture below
Which ordered pairs are solutions to the inequality 2x+y>−4?
Select each correct answer.
(5, −12)
(−3, 0)
(−1, −1)
(0, 1)
(4, −12)
I think it’s pretty annoying that I need help on this...[I should know this but I don’t :( ] Can anyone help me on this I would really appreciate it. Thanks
The first one would be 1 since you're dividing and whenever you divide exponents you're supposed to subtract them. And the second one is also the first one since it's basically the work shown for how you got your first answer.
whats the meadian
3 4 6 3 3 5 4 2 0 1 4 3 5 3 6 4 2 2 5 1
The median is the number that is halfway into the set. To find the median, the numbers should be arranged in order from least to greatest. After arranging these numbers find the middlemost number in the set which is th median.
3 Is the median.
The median in a series of numbers represents the middle value when the numbers are arranged in ascending order. If the number of observations is even, as in this case, the median is the average of the two middle numbers. Therefore, the median of the given set of numbers is 3.
Explanation:The question is about finding the median of a given set of numbers. The median is the middle value in a set of numbers when the numbers are arranged in ascending or descending order. If the set has an even number of observations, the median is the average of the two middle numbers.
1. Firstly, arrange the set of numbers in ascending order: 0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6.
2. Since we have an even number of observations (20), we need to find the average of the 10th and 11th numbers. Those numbers are 3 and 3.
3. Average of 3 and 3 is 3.
So, the median of the given set of numbers is 3.
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as part of his workout Jamal does two sets of 25 push-ups. if he does this 10 times each month, how many push ups does he do each month? write equation to show your work.
Answer:
Step-25×2=50
50×10=500by-step explanation:
Someone give me a short history summary of the summary 17th amendment (government)
The 17th Amendment came about during the Progressive Era. During this time in American history, reformers were pushing to clean up health standards, improve moral standards, elevate American education and fight corruption in state and local governments. The push for popular election of Senators became part of that campaign.
Leading the way for this reform was the populist William Jennings Bryan. Bryan, who would later become Secretary of State, served as a representative of the House of Representatives. Bryan also ran for president, although he lost to William McKinley. Bryan was highly critical of the Senate's perceived corruption and ineffectiveness. Consequently, he actively campaigned for the passing of the 17th Amendment.
In addition to Williams Jennings Bryan, the yellow journalist William Randolph Hearst published in Cosmopolitan magazine a series of articles criticizing the way in which the Senate conducted business. This helped gain popular support for the new constitutional amendment.
a company rents out 15 food. booths and 20 games booths at the county fair.the fee for a food booths is 100 plus 5 per day the. fee for game booths is 50 plus 7per day the fair lests for d day and all the booths are rented for the entire time write and simplify and expression for the amount in dollars that the company is paid
Answer:
2500 + 215d
Step-by-step explanation:
Total revenue from all booths is the sum of the revenue from the food booths and from the games booths. The food booth revenue for each booth is 100 + 5d, where d is the number of days the fair lasts. There are 15 food booths, so the total revenue from them is ...
... (food booth revenue) = 15(100 +5d)
The games booth revenue for each booth is 50 + 7d, where d is the number of days the fair lasts. There are 20 games booths, so the total revenue from them is ...
... (games booth revenue) = 20(50 +7d)
Then the total revenue is
... total revenue = (food booth revenue) + (games booth revenue)
... = 15(100 +5d) + 20(50 +7d) . . . . . . use the expression for revenue from each
... = 1500 +75d + 1000 +140d . . . . . . eliminate parentheses
... = 2500 + 215d . . . . . . . . . . . . . . . . collect terms
The Atlantic Ocean borders 14 of the 50 states in the United States . What present of the 50 staates border the Atlantic Ocean
I got 28%. I divided 14 by 50 to get 0.28. The problem can then be multiplied by 100 to get 28.
divide sh.6300 in the ratio 3:4. how much is each share?
3 : 4 = 2700 : 3600
sum the parts of the ratio : 3 + 4 = 7
divide 6300 by 7 to obtain 1 part
[tex]\frac{6300}{7}[/tex] = 900 ← 1 part
3 parts = 3 × 900 = 2700
4 parts = 4 × 900 = 3600
note that 2700 + 3600 = 6300
The function p is defined as p(x)=x2+4x-12
Part A
Write an expression that defines p(x-6)+5
Part B
Describe the transformations that map the graph of p(x) to p(x-6)+5. Justify your answer algebraically or by using key features of the graph.
Given the function [tex]p(x)=x^2+4x-12.[/tex]
Part A.
To write the expression that defines [tex]p(x-6)+5,[/tex] you have to substitute x-6 instead of x into the function expression and then add 5 to the function:
[tex]p(x-6)+5=((x-6)^2+4(x-6)+12)+5,\\\\p(x-6)+5=x^2-12x+36+4x-24+12+5,\\\\p(x-6)+5=x^2-8x+29.[/tex]
Part B.
1 transformation is translation 6 units to the right (p(x-6) determines this transfromation).
2 transformation is translation 5 units up (+5 determines this transformation).