The Declaration of Independence was signed on July 4, 1776. The United States celebrated the bicentennial on July 4, 1976. How much time was that
translate this phrase into an algebraic expression
three more than the product of 17 and Vanessa height
use the variable v to represent Vanessa height
What are the solutions of the equation x^2 - 7x -8= 0? Complete the square.
the solutions to the equation [tex]\( x^2 - 7x - 8 = 0 \)[/tex] are ( x = 8 ) and ( x = -1 ).
To solve the quadratic equation[tex]\( x^2 - 7x - 8 = 0 \)[/tex]by completing the square, we follow these steps:
1. Move the constant term to the other side of the equation:
[tex]\[ x^2 - 7x = 8 \][/tex]
2. To complete the square, take half of the coefficient of ( x ) (which is -7), square it, and add it to both sides of the equation:
[tex]\[ x^2 - 7x + \left( \frac{-7}{2} \right)^2 = 8 + \left( \frac{-7}{2} \right)^2 \]\[ x^2 - 7x + \frac{49}{4} = 8 + \frac{49}{4} \][/tex]
3. Simplify the right side of the equation:
[tex]\[ x^2 - 7x + \frac{49}{4} = \frac{32}{4} + \frac{49}{4} \]\[ x^2 - 7x + \frac{49}{4} = \frac{81}{4} \][/tex]
4. Write the left side of the equation as a perfect square:
[tex]\[ \left( x - \frac{7}{2} \right)^2 = \frac{81}{4} \][/tex]
5. Take the square root of both sides to solve for ( x ):
[tex]\[ x - \frac{7}{2} = \pm \sqrt{\frac{81}{4}} \]\[ x - \frac{7}{2} = \pm \frac{9}{2} \][/tex]
6. Solve for ( x ) by adding [tex]\( \frac{7}{2} \)[/tex]to both sides:
[tex]\[ x = \frac{7}{2} \pm \frac{9}{2} \][/tex]
This gives us two solutions:
[tex]\[ x = \frac{7}{2} + \frac{9}{2} = \frac{16}{2} = 8 \]\[ x = \frac{7}{2} - \frac{9}{2} = \frac{-2}{2} = -1 \][/tex]
So, the solutions to the equation [tex]\( x^2 - 7x - 8 = 0 \)[/tex] are ( x = 8 ) and ( x = -1 ).
mr. martinez has 3 ice chests. he is placing 14 lunches in each ice chest. each lunch contains a sandwich, a bag of chips, and a drink. about 55% of these lunches contain a ham sandwich. which of the following is closest to the number of lunches that contain a ham sandwich?
The required number of lunch that contains 55% of ham sandwich is given as 23.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The total number of lunches is given as,
= 3 × 14
= 42 lunch in the 3 ice chests,
Now, 55% of the lunch consists the ham sandwich,
The number of lunch that contains the ham sandwich is given as,
= 0.55 × 42
= 23.1
≈ 23
Thus, the required number of the lunch that contains 55% of the ham sandwich is given as 23.
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Find the area of the triangle. (round to the nearest whole number)
D is 32 - g by the way
A line passes through the point (2, 3) and has a slope of -2. Which is the equation of the line in point-slope form?
The correct answer is option B: [tex]\( y = -2x + 7 \).[/tex] To write the equation of a line passing through the point (2, 3) with a slope of -2, we can use the point-slope form of a linear equation.
The point-slope form is given as:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Where [tex]\( (x_1, y_1) \)[/tex] is a point on the line and [tex]\( m \)[/tex] is the slope.
Given that the point is [tex]\( (2, 3) \)[/tex] and the slope is [tex]\( -2 \)[/tex], we can substitute these values into the point-slope form:
[tex]\[ y - 3 = -2(x - 2) \][/tex]
Now, we can simplify and rewrite the equation in various forms to match the options provided:
Option A: [tex]\( 2x + y = 7 \)[/tex]
To match this option, let's rearrange the equation:
[tex]\[ y - 3 = -2(x - 2) \][/tex]
[tex]\[ y - 3 = -2x + 4 \][/tex]
[tex]\[ 2x + y = 7 \][/tex]
So, option A is equivalent to the given equation.
Option B: [tex]\( y = -2x + 7 \)[/tex]
Let's solve the equation for [tex]\( y \):[/tex]
[tex]\[ y - 3 = -2(x - 2) \][/tex]
[tex]\[ y - 3 = -2x + 4 \][/tex]
[tex]\[ y = -2x + 7 \][/tex]
This matches option B.
Option C: [tex]\( y - 3 = -2(x - 2) \)[/tex]
This is already in point-slope form and matches the given equation.
Option D: [tex]\( y = -\frac{1}{2} x + 5 \)[/tex]
Let's solve the equation for [tex]\( y \):[/tex]
[tex]\[ y - 3 = -2(x - 2) \][/tex]
[tex]\[ y - 3 = -2x + 4 \][/tex]
[tex]\[ y = -2x + 7 \][/tex]
This does not match option D.
Therefore, the correct answer is option B: [tex]\( y = -2x + 7 \).[/tex]
The complete question is:
A line passes through the point (2, 3) and has a slope of -2. Which is the equation of the line in point-slope form?
A) 2x + y = 7
B) y = -2x + 7
C) y - 3 = -2(x - 2)
D) y = - 1 2 x + 5.
Volume of a square based pyramid is 588 cubic inches the height of the pyramid is 9 inches what is the area of the base of this pyramid
What is the exact volume of a cylinder with a base height of 30, and a radius of 13
My good friends,for the second time in our history,a British prime minister has returned from Germany bringing peace with honor.i believe It is peace for our time... Go home and get a nice quiet sleep This statement reflects to the British belief that which of the following policies would prevent another war? A) containment B) imperialism C) appeasement
Please help it is important 8 points
There are two squares, and the ratio of their perimeters is 5:8 If the area of the
first square is 225 , then what is the area of the second one?
Evaluate the numerical expression.
3.8 − 4.8 ÷ 0.4 − 2.4
use distributive property to multiply 5(2a-7b-2) please show work?
Final answer:
To multiply 5 by the expression (2a-7b-2), each term inside the parentheses is multiplied by 5, resulting in the final expression 10a - 35b - 10.
Explanation:
To use the distributive property to multiply 5(2a-7b-2), multiply each term inside the parentheses by 5.
Multiply 5 by 2a which gives 10a.
Multiply 5 by -7b which gives -35b.
Multiply 5 by -2 which gives -10.
Now, combine these results to get the final expression: 10a - 35b - 10.
I need help with number 3 plzzz helpppppppppppppp
Determine the sum: (14abc2 + 12a2b + 16b2c) + (−3abc2 + 2b2c).
11abc2 + 12a2b + 18b2c
11a2b2c4 + 12a2b + 18b4c2
41a4b7c6
42a3b4c3 − ab3c3
what is the difference between the least number of minutes jumpes and the greatest minutes jumped?
How many inches in 17.5 feet
Bethanie recently used her cell phone to deposit a check. This is considered to be what type of electronic banking service?
Answer:
Transactional service - APEX
Step-by-step explanation:
Describe the type of angles formed when you divide a circle into 4 equal parts
When we divide a circle into 4 equal parts, the angles formed are the right angles.
When a circle is divided into 4 equal parts, we get 4 quarters of the circle.
What is a quarter of a circle?The area that is intercepted by two radii that are at 90° to each other and a quarter portion of the circumference of a circle is known as a quarter circle.
In a quarter of a circle, the angle between radii is 90 degrees.
So, When we divide a circle into 4 equal parts, the angles formed are the right angles.
Hence, When we divide a circle into 4 equal parts, the angles formed are the right angles.
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Help please........................
There are four red bicycle helmets in a bin. If a helmet is selected without looking, what is the probability that the helmet is red?
A 1/4
B 1/3
C 4/4
D 3/4
Given that all helmets in the bin are red, the probability of randomly selecting a red helmet is 1, which corresponds to answer C.
Explanation:The question is asking for the probability that a randomly selected helmet from a bin of four is red. Since all the helmets in the bin are red, no matter which one you pick, it will be red. In probability, this is represented as the total number of favorable outcomes divided by the total number of outcomes. In this scenario, both favorable outcomes (red helmets) and total outcomes (helmets in the bin) are four. Mathematically, 4/4 results in 1. So, the correct answer is C which symbolize the probability to be 1.
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if a right angle has a hypotenuse of 19 units and a leg with the length of 7 units, find the length of the other leg
which expression represents the area of the triangle drawn below?
The answer choices are in the photo.. PLEASE HELP!
Which expression represents the area of the triangle drawn below?
Base of the triangle=4x+2
Height of the triangle=2x+1
Area of triangle=[tex] \frac{1}{2} [/tex]*b*h
Area=[tex] \frac{1}{2} [/tex]*(4x+2)(2x+1)
Simplifying 4x+2 we get, 2(2x+1)
So, we have, Area=[tex] \frac{1}{2} [/tex]*2(2x+1)(2x+1)
Area=[tex] \frac{1}{1} [/tex]*1(2x+1)(2x+1)
=(2x+1)(2x+1)
FOILing the two we get, 2x*2x +2x*1 +1*2x+1*1
(2x+1)(2x+1)=4x²+2x+2x+1
Area=4x²+4x+1
So, Area of the triangle=4x²+4x+1
Answer:Option C
Answer:
It is C
Step-by-step explanation:
I just took the same quiz. I saw that this was the answer.
Hope this helps!
Pyramid-shaped gift boxes have a square bases that measure 5 inches on each side. The slant height is 6.5 inches. How much cardboard is used to make each box?
The cardboard is used to make each box is 90 in²
What is surface area?The surface area of a solid object is a measure of the total area that the surface of the object occupies.
Given that, pyramid-shaped gift boxes have a square bases that measure 5 inches on each side, the slant height is 6.5 inches.
We need to find that how much cardboard is used to make each box,
For the same we will simply find the surface area of the box,
So,
SA = b² + 2bs
= 5²+2(5)(6.5)
= 25+65
= 90 in²
Hence, the cardboard is used to make each box is 90 in²
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a new parking lot is being built for a medical office. the expression representing the number of parking spots in the new lot is 15x/4-9 where x represents the number of parking lots in the first row. how many spots are in the parking lot if there are 32 parking spots in the first row?
Answer:
The number of spots in the parking lot if there are 32 parking spots in the first row =111.
Step-by-step explanation:
We are given that a new parking lot is being built for a medical office.
We are given that
The expression representing the number of parking spots in the new lot =[tex]\frac{15x}{4}-9[/tex]
Where x= The number of parking lots in the first row
We have to find number of spots in the parking lot when parking spots in the first row is 32.
The number of parking spots in the first row =x=32
Substitute the value of x in the given expression then we get
Number of spots in the parking lot =[tex]\frac{15\times 32}{4}-9[/tex]
Number of spots in the parking lot=[tex]\frac{480}{4}-9[/tex]
The number of spots in the parking lot=120-9
The number of spots in the parking lot=111.
Hence, the number of spots in the parking lot if there are 32 parking spots in the first row=111.
A cylindrical grain bin has a radius of 5 feet and a height of 29 feet. What is the surface area of the bin?
A. 1,067.6 ft2
B. 157 ft2
C. 910.6 ft2
D. 612.3 ft2
Hurry! pppplllleeeeeaaaasssseeeee!
1.Bill and Lisa are surveying their classmates about their summer reading. Their questions are given below:
Bill: How many books were recommended by the book reading club for summer?
Lisa: Which was your favorite book from the book reading club's recommendation?
Who wrote a statistical question and why?
Bill, because there will be variability in the responses collected
Lisa, because there can be only one answer to the question
Bill, because every student will give the same answer
Lisa, because there can be many answers to the question
2.Tammy did a survey to answer the following question:
What is the average reading score of grade 6 students?
The mean reading score was 4.5 points. If all the students scored the same, what would be the reading score of each student?
4.5 points
Less than 4.5 points
Greater than 4.5 points
Cannot be determined
WILL GIVE BRAINLIEST
1. The student that wrote a statistical question is Lisa. This is because there can be many answers to the question
2. The score of each student is: 4.5 points.
What is a Statistical Question?A statistical question is a question whose answer can be gotten by collecting data that has variability. That is, the answers to the question may be many.
1. The question that is more statistical in nature is Lisa's. This is because there can be many answers to the question
2. The average of a data is the mean, which is the sum of all data points divided by the number of data points.
Therefore, if all students had the same score and the mean score was 4.5, it means the score of each student is: 4.5 points.
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Piecewise function help!
solve for x please!!!!
11) Since the triangle has a pair of congruent base angles, it is an isosceles triangle which means that the two pairs of legs are congruent.
Make them equal to each other in an equation.
5x = x + 20
Subtract x from both sides.
4x = 20
Divide both sides by 4.
x = 5
12) The two legs are congruent so that means the base angles must be congruent. First find the measure of the base angles. Create an equation:
x + x + 50 = 180
Combine like terms.
2x + 50 = 180
Subtract 50 from both sides.
2x = 130
Divide both sides by 2.
x = 65
Now make the base angle plus x equal 180, because they form a straight line.
65 + x = 180
Subtract 65 from both sides.
x = 115
13) You know the vertex angle (top angle) is 90 degrees because it is supplementary to a right angle. The triangle is isosceles because the two legs are congruent, so make the base angles plus 90 add up to 180 in an equation.
x + x + 90 = 180
Combine like terms.
2x + 90 = 180
Subtract 90 from both sides.
2x = 90
Divide both sides by 2.
x = 45
colin has a square garden with an area of 97 square feet feet. what is the length of each side of the garden
The length of one side of Colin's square garden, which has an area of 97 square feet, is approximately 9.85 feet.
Explanation:Colin has a square garden with an area of 97 square feet. The area of a square is calculated by squaring the length of one side (Side length * Side length = Area). Therefore, to find the length of one side of the square when you know the area, you would take the square root of the area.
In Colin's case, the area of the garden is 97 square feet, so the length of one side would be the square root of 97, which is approximately 9.85 feet.
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