The algebraic expression that represents the given sentence is:
8 (x + 5).
What are algebraic expressions?The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. The values a expressed in an unknown number using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression.
What is product of two numbers?In mathematics, a number that is obtained by multiplying two or more distinct variables together is referred to as the product.
Let us suppose the "a number", as x.
The sum of a number and 5 is represented as follows:
(x + 5)
The product of 8 and sum of a number and 5 is represented as follows:
8 (x + 5)
Hence, the algebraic expression that represents the given sentence is:
8 (x + 5)
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A y=x
The graph shown above is the graph of which parent function after a vertical shift up 1 unit?
y=x²
y=x³
Dy=x²
B
1
C
X
The equation for the graph after the shift would be y = x + 1. The answer is y = x + 1.
What happens when a function is shifted vertically?
Because this transformation involves adding a positive or negative constant to the function, a vertical shift, which moves the graph up or down, is the simplest shift. In other words, regardless of the input, the output result of the function receives the same constant.
The y-value adjusts when a function shifts vertically. While the y-value modifies the shift's magnitude, the x-value remains constant.
We add the value to the y-term if it changes upward. We shall deduct that amount from the y-term if it shifts downward.
The simplest transformation is a vertical shift, which entails moving the graph up or down. This is because this transformation only requires changing the function's sign from positive to negative.
The only variable that alters in vertical shifts of the fundamental linear equation y = mx + b is the b value, or the y-intercept.
The graph shown above is the graph of the parent function y=x after a vertical shift up 1 unit.
Hence, The equation for the graph after the shift would be y = x + 1. The answer is y = x + 1.
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3 (2 x - 7) = 3
How many solutions does this equation have?
Answer:
It has one solution, x = 4
Step-by-step explanation:
[tex]3(2x-7) = 3\\2x-7 = \frac{3}{3} \\2x-7 = 1\\2x = 8\\x = 4[/tex]
No other answer would work
An object is dropped from 28 feet below the tip of the pinnacle atop a 928-ft tall building. The height h the object after t seconds is given by the equation h=-16t^(2)+900. Find how many seconds pass before the object reaches the ground.
Answer: it takes 7.5 seconds for the object to reach the ground.
Step-by-step explanation:
The equation for the height of the object is h=-16t^2+900. To find the time when the object reaches the ground, we need to find the value of t when h=0.
Therefore, we can set h=-16t^2+900 = 0 and solve for t:
-16t^2+900 = 0
-16t^2 = -900
t^2 = 56.25
t = sqrt(56.25)
t = 7.5
So, it takes 7.5 seconds for the object to reach the ground.
La base de un cuadrado sin marco mide el doble de su altura si el marco tiene 2 pulgadas de ancho y su área es de 208 pulgada cuadradas encuentre las dimensiones del cuadrado sin marco
If the frame has 2 inches of width and its area is 208 inches of square. The dimensions of square without frame is 6.75 and 13.50.
Let the width of rectangle without frame is b.
Let the height of rectangle without frame is h.
Since the base of a square without frame is the double of its height. So
b = 2h...............(1)
The frame has 2 inches of width, so;
The width of rectangle with frame = b + 4
The height of rectangle with frame = h + 4
The area of the rectangle with frame = 208 inches of square
The formula of area of rectangle
A = Height × Width
(h + 4) × (b + 4) = 208
Putting the value of b from the equation 1
(h + 4) × (2h + 4) = 208
Simplify
h(2h + 4) + 4(2h + 4) = 208
2h^2 + 4h + 8h + 16 = 208
2h^2 + 12h + 16 = 208
Subtract 208 on both side, we get
2h^2 + 12h - 192 = 0
Taking common 2 from the equation, we get
h^2 + 6h - 86 = 0
After factoring the equation we get
h = (−3+√95, −3−√95)
h = 6.75, -12.75
The height can't be negative so we use the positive value of h.
Now putting the value of h in the equation 1.
b = 2×6.75
b = 13.50
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The complete question is:
The base of a square without frame is the double of its height, if the frame has 2 inches of width and its area is 208 inches of square. Find the dimensions of the square without frame.
#7
DE is a midsegment of AABC. Find the value of x .
X =
B
A 6 E
D
X
C
Using the Midsegment Theorem, the value of x is: 6.
What is the Midsegment Theorem of a Triangle?The Midsegment Theorem states that in a triangle, the segment that connects the midpoints of two sides of the triangle is parallel to the third side and is half as long as the third side. In other words, the midsegment of a triangle is parallel to the third side and has half the length of the third side.
Therefore the ratio of DE to AB would be: 1/2
Ratio of EC to AC would be: x/(x + 6)
Thus:
x/(x + 6) = 1/2
Cross multiply
2x = x + 6
2x - x = 6
x = 6
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Write a quadratic given a vertex (11,2) and a point (9,3)
The equation of a quadratic equation with a vertex and a point is
y = 1/4 (x - 11)² + 2
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 6 is an equation.
We have,
Vertex = (11, 2)
Point = (9, 3)
The equation of a quadratic equation with a vertex and a point is
y = a (x - h)² + k
Where (h, k) is the vertex and (x, y) is the point.
Now,
(11, 2) = (h, k)
(9, 3) = (x, y)
Substitute.
y = a (x - h)² + k
3 = a (9 - 11)² + 2
3 = a x 4 + 2
3 = 4a + 2
3 - 2 = 4a
a = 1/4
Now,
The equation of a quadratic equation is y = 1/4 (x - 11)² + 2.
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What is the domain of the function
f(x) =
X+2
x≤-B
*>B
x2-6
Answer:
x ≥ -6
Step-by-step explanation:
Answer: x ≥-6
explanation: im pretty good at math
Find the percent of change when 51 is increased to 98. If necessary, round your answer to the nearest tenth.
a
48% decrease
b
48% increase
оооо
Ос
92. 296 decrease
Od
92. 29 increase
The percent of change when 51 is increased to 98, then there have increment of 92%. So the option d is correct.
The difference between a new and old amount, given as a percentage, is known as a percent change.
Calculating percent change involves determining the difference between the old and new quantities, dividing that difference by the old quantity, and multiplying that result by 100.
The number 51 is raised to 98; calculate the percentage change.
To start, subtract the new quantity from the previous one to determine the difference. 98 - 51 = 47, therefore the difference is 47.
The difference, 47, is then divided by the old amount, 51, yielding a result of 47/51=0.92.
Lastly, multiply the decimal by 100 × 0.92 to get the percentage change, which is increment of 92%.
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*PLEASE HELP SOON* Evaluate 5^x for each given value of x.
Each of the function should be evaluated as follows;
When x = 2, 5^x = 25.When x = 1, 5^1 = 5.When x = 0, 5^0 = 1.When x = -1, 5^-1 = 1/5.How to evaluate the function for each given value of x?In Mathematics, the valid and true solutions to any function are referred to as the domain (input value) and they can be determined by substituting the x-values contained in the table into the function.
When x = 2, the range (output value) for this function is given by:
Function, f(2) = 5^x = 5^2 = 25.
When x = 1, the range (output value) for this function is given by:
Function, f(1) = 5^x = 5^1 = 5.
When x = 0, the range (output value) for this function is given by:
Function, f(0) = 5^x = 5^0 = 1.
When x = -1, the range (output value) for this function is given by:
Function, f(x) = 5^x = 5^-1 = 1/5.
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Can’t figure this out need help
Answer: Hi! I believe your answer would be y = −5/7x − 5
Step-by-step explanation: I hope this helps!
Determine whether each pair of equations are equivalent. Explain your answer. 5x − 4 + 3x = 8 and 8x = 12
One afternoon Mr. And Mrs. Baxter and their 3 children were busy working outside in their garden. Mrs. Baxter was feeling hungry, so she went inside to the kitchen where there was a plate full of cookies. She ate 1/6 of the cookies and then went back to work. Mr. Baxter was feeling hungry, so he went inside and ate 1/5 of the remaining cookies and then went back to work. Next, Anna was feeling hungry, so she went inside and ate 1/4 of the cookies that were left on the plate and then went back to work. Then Tyler was feeling hungry, so he went inside, ate 1/3 of the cookies left on the plate and then went back to work. Finally, little Adam was feeling hungry, and he went inside and ate 1/2 of the remaining cookies, leaving 4 cookies on the plate. How many cookies were on the plate before anyone started feeling hungry?
24 cookies were on the plate before anyone started feeling hungry.
Let X be the number of cookies on the plate before anyone started feeling hungry.
After Mrs. Baxter ate 1/6 of the cookies, there were,
X - (X * 1/6) = 5/6X cookies left.
After Mr. Baxter ate 1/5 of the remaining cookies, there were,
5/6X - (5/6X * 1/5) = 5/6X- 1/6X = 4/6X cookies left.
After Anna ate 1/4 of the remaining cookies, there were,
4/6X - (4/6X * 1/4) = 4/6X- 1/6X = 3/6X cookies left.
After Tyler ate 1/3 of the remaining cookies, there were
3/6X - (3/6X * 1/3) = 3/6X- 1/6X = 2/6X cookies left.
After Adam ate 1/2 of the remaining cookies, there were,
2/6X - (2/6X * 1/2) = 2/6X- 1/6X = 1/6 cookies left.
We know, after Adam eats, 4 cookies are left, therefore,
1/6X = 4
So X = 4 *6 = 24
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The graph of y = In(x) was transformed by shifting 8 units left and 12 units up. Write an equation
The equation of the translated function for this problem is given as follows:
y = ln(x + 8) + 12.
What are the translation rules?The four translation rules are defined as follows:
Left a units: g(x) = f(x + a).Right a units: g(x) = f(x - a).Up a units: g(x) = f(x) + a.Down a units: g(x) = f(x) - a.The parent function in this problem is given as follows:
y = ln(x).
The translations in this problem, and their effects, are given as follows:
8 units left: x -> x + 8.12 units up: y -> y + 12.Hence the translated function is defined as follows:
y = ln(x + 8) + 12.
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Jamila ha p pencil. Haan ha 3 fewer pencil than Jamila. Naomi ha 4 time a many pencil a Haan. Write an expreion, in term of p, for the total number of pencil that the three children have. Write your expreion in it implet form.
The total number of pencils that the three children have is represented by the expression p + 3 + 4p. This expression can be simplified to p + 3 + 4p.
The total number of pencils that the three children have is represented by the expression p + 3 + 4p. This expression can be simplified to p + 3 + 4p.
Jamila has p pencils. Haan has 3 fewer pencils than Jamila, so Haan has (p - 3) pencils. Naomi has 4 times as many pencils as Haan, so Naomi has (4(p - 3)) pencils.
Therefore, the total number of pencils the three children have is p + (p - 3) + (4(p - 3)). This can be simplified to p + 3 + 4p.
The total number of pencils that the three children have is represented by the expression p + 3 + 4p. This expression can be simplified to p + 3 + 4p.
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Please help ASAP!!!!!!!!!
The correct linear model for the table is f(x) = 5x + 1.
What is the model for the table?We have to note that when we have a table of values, it is possible that we can be able to obtain the equation that can be able to model the function. We know that we can be able to write the line equation in the form y = mx + c
Where y = g(x) we can write the equation to obtain the slope of the line as;
m = y2 - y1/x2 - x1
Then we have;
1 - (-4)/0 - (-1)
5/1
m = 5
The correct equation of the line is therefore;
f(x) = 5x + 1
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I need help asap. I attached a imagine of the question.
Answer:
[tex]\boxed{n = - 5}[/tex]
Step-by-step explanation:
[tex]\textrm{We have the following equation:}\\\\\dfrac{n}{5}+\dfrac{\left(n-3\right)}{2}=n\\\\\textrm{ and we are asked to solve for n}[/tex]
Solution Steps
Multiply throughout by 10 which is the LCM of the denominators, 5 and 2
[tex]\dfrac{n}{5}\cdot \:10+\dfrac{n-3}{2}\cdot \:10=n\cdot \:10\\\\2n + 5(n-3) = 10n\\[/tex]
Expand the brackets: [tex]5(n-3) = 5n - 15\\\\[/tex]
The equation becomes:
2n + 5n - 15 = 10n
Add similar terms:
7n - 15 = 10n
Move 15 to the right side:
7n = 10n + 15
Move 10 to the left side
7n - 10n = 15
- 3n = 15
n = -15/3
[tex]\boxed{n = - 5}[/tex]
since 2005 the amount of money spent on restaurants in a certain country has increased at a rate of 4% each year in 2005 about 670 billion was spent on restaurants if the trend continues about how much money will be spent on restaurants in 2013 
Answer: Since 2005 the amount of money spent on restaurants in a certain country has increased at a rate of 4% each year. In 2005, about 670 billion was spent on restaurants.
To find the amount spent on restaurants in 2013, we can use the formula:
A = P(1 + r)^t
Where:
A = the final amount
P = the initial amount (670 billion)
r = the rate of increase (0.04 or 4%)
t = the number of years since the initial amount (8 years)
Plugging in the values, we get:
A = 670 billion (1 + 0.04)^8
A = 670 billion (1.04)^8
A = 670 billion * 1.4304
A = 951.8 billion
So, if the trend continues, about 951.8 billion will be spent on restaurants in 2013.
Step-by-step explanation:
Gary used to make bottles of glitter glue.
Bottles Glue Glitter
1 3.8 1.9
4
How much glue and glitter would he need to make 4 bottles?
Gary would need 15.2 oz glue and 3.8 oz of glitter to make 4 bottles.
Gary would need 6.8 oz glue and 4.9 oz of glitter to make 4 bottles.
Gary would need 7.8 oz glue and 5.9 oz of glitter to make 4 bottles.
Gary would need 15.2 oz glue and 7.6 oz of glitter to make 4 bottles.
Gary would need 15.2 oz glue and 7.6 oz of glitter to make 4 bottles.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
We have the information that,
Amount of glue needed for 1 bottle = 3.8 oz
Amount of glitter needed for 1 bottle = 1.9 oz
We have to find the amount of glue and glitter for 4 bottles.
Finding the product for 4 bottles.
Amount of glue needed for 4 bottles = 3.8 × 4 oz = 15.2 oz
Amount of glitter needed for 4 bottles = 1.9 × 4 oz = 7.6 oz
Hence Gary will need 15.2 oz glue and 7.6 oz of glitter to make 4 bottles.
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Consider the function f(x). Select all of the following that include a vertical stretch of f(x).
The vertical stretch of f(x) will be -2f(x), 5.5f(x) - 1, 7f(x)
As is well known, the vertical stretch of f(x) occurs when the value of the parameter is changed in the following general form:
When a constant c with a value larger than one is scaled across the board of a function, it results in a vertical stretch. It is written as the vertical stretch from the original function f(x) to the new, stretched function g(x)=cf(x) where c>1 g ( x ) = c f ( x ) where c > 1.
f(k(x-d)) = y = a+ c
when |a| exceeds 1 since The function is stretched vertically by a dilation factor of |a| when |a| > 1 (when a > 1).
Thus, we select F, D, and A.
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The full question:
Consider the function f(x). Select all of the following that includes a vertical stretch of f(x)
A. -2f(x)
B. 0.25f(x)
C. -f(x) + 6
D. 5.5f(x) - 1
E. f(x) + 9
F. 7f(x)
Use the long division method to find the result when 8x^{3}+6x^{2}+26x-128x
3
+6x
2
+26x−12 is divided by 4x-14x−1.
Answer:
4x^2-3x+1+18?=2x+3
Step-by-step explanation:
bnkjhhlhbghhbhbhlhby kjjn
The surface area of a cylinder is 24π m². The distance around the base of the cylinder is 3π meters and the diameter of a base of the cylinder is 4 meters. What is the height of the cylinder? Enter your answer, as a simplified fraction, in the box.
The height of the cylinder will be 6 meters.
What is a cylinder?One of the most fundamental curvilinear geometric shapes, a cylinder has traditionally been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In some modern branches of geometry, a cylinder may also be defined as an infinite curvilinear surface.
Given that the surface area of a cylinder is 24π m². The distance around the base of the cylinder is 3π meters and the diameter of the base of the cylinder is 4 meters.
The height of the cylinder will be calculated as:-
Surface area = 2πrh
24π = 2πrh
r x h = 12
The diameter is 4 meters so the radius is 2 cm.
r x h =- 12
h = 12 / r
h = 12 / 2 = 6 meters
The height of the cylinder will be 6 meters.
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Determine if the conditions stated would result in a unique quadrilateral.
Select Yes or No for each statement.
Four sides and one angle, three sides and two included angles, or two neighboring sides and three angles, to construct a unique quadrilateral.
What is meant by unique quadrilateral?
If the two diagonals and three sides of a quadrilateral are known, it is possible to create it in a singular way. If the two neighboring sides and three angles of a quadrilateral are known, it can be built in an original fashion.
A polygon called a quadrilateral has four sides, four angles, and four vertices. If the size of a quadrilateral's sides and diagonal are known, it is possible to create it in a singular way.
They must have the same number of sides as angles because they are polygons and have four angles. Every quadrilateral has inner angles that sum to 360 degrees.
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What fraction in simplest form is 28 hours out of a week
A department store receives a shipment of
3 boxes of glass ornaments. There are
25 ornaments in each box. Lucas opens the
boxes and finds that 6 of the ornaments are
broken. Based on this shipment, what
prediction can Lucas make about the next
shipment of ornaments?
F A delivery of 4 boxes will contain 4 more
broken ornaments than a delivery of
3 boxes.
G A delivery of 5 boxes will contain 6 more
broken ornaments than a delivery of
3 boxes.
H A delivery of 6 boxes will contain 6 more
broken ornaments than a delivery of
3 boxes.
JA delivery of 7 boxes will contain 10 more
broken ornaments than a delivery of
3 boxes.
The prediction that Lucas can make about the next shipment of ornaments is that H. A delivery of 6 boxes will contain 6 more broken ornaments than a delivery of 3 boxes.
How to calculate the word problem?It should be noted that a word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
In this case, since the department store receives a shipment of 3 boxes of glass ornaments and there are 25 ornaments in each box.
Lucas then opens the boxes and finds that 6 of the ornaments are broken. This implies that there are 2 broken for each box.
In this case, a delivery of 6 boxes will contain 6 more broken ornaments than a delivery of 3 boxes.
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If $\angle A=20^\circ$ and $\angle AFG=\angle AGF,$ then how many degrees is $\angle B+\angle D?$
The angles b and d have 80° degrees.
Trigonometry is the branch of mathematics that studies and defines the relations between the side lengths and angles of a triangle.
One key fact to know in all trigonometry problems is that all angles within a normal triangle = 180 degrees.
By creating algebraic equations based on the information given in the question, we can find missing values using this key fact.
Given:
Angle a = 20 deg
Angle b = Angle d = x
x = ?
We know that since two angles are equal, it is an isosceles triangle.
Using algebra and the given information, we create an equation:
20+2x=180
2x=180-20
2x=160
x=80
Therefore, we know that angles b and d are 80° degrees.
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2x²+4x+5=ax²+(2b-6)x+c what does a,b,c represent
Answer: A=2 B=4 C=5
Step-by-step explanation:
I NEED HELP ON THIS ASAP!!!!
Answer:
see below
Step-by-step explanation:
v=πr² (h/3)
h=3v/πr²
original equation measures v using bottom circle area multiply the height.
the equation for the height reverses the multiplication using volume divided by the area, so the result is a linear measurement.
I need help with my math homework
Answer:
6 = D
7 = F
8 = A
9 = B
10 = C
Have a nice day ;)
what is (5x+6)-(2x+5).
a researcher reported that for 100 college students, the mean was 80 and the standard deviation was 12.6. how is the standard deviation best interpreted?
It can be interpreted as the average distance between each data point and the mean value of 80 for the 100 college students.
Standard deviation is a measure of the spread of values in a set of data, calculated as the square root of its variance. It indicates how much variation or dispersion there is from the mean of the set.
The standard deviation is a measure of the variability or dispersion of the data set around the mean. In this case, it can be interpreted as the average distance between each data point and the mean value of 80 for the 100 college students.
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