The equation which shows the volume of rectangular box is w² + 5w - 56 = 0.
What is defined as the rectangle?A rectangle is a two-dimensional (2D) shape with opposite sides that are parallel as well as equal to each other and four right angles.
The breadth (width) of a rectangle is the shorter side, and the length is the longer side.
The metal's length is 5 inches longer than its width. However, we fold up 1-inch flaps on every side, resulting in a 1-inch box height and an 2-inch decrease in length and width (1 inches on each side). Because the length and width both decrease in the same amount, the length remains 5 inches longer than that of the width.Then, the equations are as follows:
l = w + 5
The height of the box will be 1 inch which is cut and folded upward.
vol = l x w x h = 56 in³
Substitute the value of l in the equation.
56 = (w + 5)(w)(1)
56 = w² + 5w
w² + 5w - 56 = 0
Therefore, the equation which represent the volume of the rectangular box on 56 in.³ is w² + 5w - 56 = 0.
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Which answer choice is equal to -2x2 - 21x - 54?
Lucy’s chocolate bar is 46% cocoa. If the weight of the chocolate bar is 62 grams, how many grams of cocoa does it contain? Round your answer to the nearest tenth.
Answer: 28,5 grams of cocoa
Step-by-step explanation:
[tex]\frac{62*46}{100}[/tex]
About one eighth of the population is left-handed. In what size school would you expect to find about 50 left-handed students?
Answer:
400 students, 1/8 are left handed
Step-by-step explanation:
please help it's another urgent pt 2
Using the OR and AND operations, we have that:
a. The graph of the and operation is x > a, while the graph of the or operation is x > b.
b. The graph of the and operation is x > b, while the graph of the or operation is x > a.
c. The graphs of both operations are the same, given by x > a = x > b.
What is the result of the AND operation between two data-set?
The result of the AND operation between two data-set is the set that contains elements that belong to both sets.
What is the result of the OR operation between two data-set?
The result of the OR operation between two data-set is the set that contains elements that belong to at least one of the sets.
In item a, we have that a is to the right of b, hence:
b is plotted before a on the number line.The intersection is the values starting at a, as between b and a, there are x > b but not x > a, while for x > a, the values will belong to both sets.The or is the values starting at x > b, as they will already belong to one of the sets.Hence:
The graph of the and operation is x > a, while the graph of the or operation is x > b.
In item b, we have that a is to the left of b, hence:
a is plotted before b on the number line.The intersection is the values starting at b, as between a and b, there are x > a but not x > b, while for x > b, the values will belong to both sets.The or is the values starting at x > a, as they will already belong to one of the sets.Hence:
The graph of the and operation is x > b, while the graph of the or operation is x > a.
In item c, we have that a and b are the same point, hence, hence the graphs of both operations are the same, given by x > a = x > b.
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1. Which is the first step in solving
x 4 = 4
Subtract 4 from both sides.
Add 4 to both sides.
Add 4 to the left side.
Subtract 4 from the left side.
Answer:
I think to solve for X you have to place like terms on the other side like:
x4 = 4
x=4 - 4 (4 becomes negative)
x=0
help pleaseeeeeeeeeeeeeeeeeeee
6.2E15
Here ; E stands for "times 10 to the power of or simply it replaces 10^ "
An unknown distribution has a mean of 80 and a standard deviation of 12. A sample size of 95 is drawn randomly from the population.
Find the probability that the sum of the 95 values is less than 7,450. (Round your answer to 4 decimal places)
The probability that the sum of the 95 values is less than 7450 is 0.1002
Given Data :
An unknown distribution has a
Mean (μ) = 80
Standard Deviation (σ) = 12
Sample Size (n) = 95
is drawn from the population.
∑X ≈ N (95 * 80, [tex]\sqrt{95}[/tex] * 12)
= N (7600, 116.96)
The Probability that the sum of the 95 values is less than 7450 is given as follows :
P(∑x < 7450) = P [(∑x - μ) / s] < [(7450 - 7600) / 116.96
= P(Z < -1.282) = 0.1 (From Z table)
Hence, the probability that the sum of the 95 values is less than 7450 is 0.1002
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Write an equation in point-slope form if (-1, 2) is a point on the line and 1/4 is the slope.
The slope or gradient of a line is a number that describes both the direction and the steepness of line. The equation in point slope form if (-1,2) is a point on the line and 1/4 is the slope is y-2=[tex]\frac{1}{4}x+\frac{1}{4}[/tex].
What is a slope?A number that identifies the direction and steepness of a line is its slope or gradient. Letter m is frequently used to represent the slope.
The ratio of "vertical change" to "horizontal change" between (any) two unique points on a line is used to compute slope. Occasionally, the ratio is written as a quotient (also known as a "rise over run"), which produces the same number for every two unique points on the same line. A declining line has a negative "rise." The line might be useful, as determined by a road surveyor, or it might appear in a diagram that represents a road or a roof as a description or a design.
Given,
x1= -1
y1= 2
slope= 1/4
Substituting the values in the equation,
y-y1= m(x-x1)
y-2= [tex]\frac{1}{4}[/tex](x+1)
y-2= [tex]\frac{1}{4}x+\frac{1}{4}[/tex]
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(3, 4, 5, ...} is finite or infinite
The given set is (3, 4, 5, ...} is infinite set.
A set with an infinite number of elements is one that cannot be numbered. A set that has no last element is said to be endless. A set that can be put into a one-to-one correspondence with a suitable subset of itself is said to be infinite. No issue with the in-class assignment.
The stars in the clear night sky, water droplets, and the billions of cells in the human body are just a few examples of endless sets of objects that surround us. A set of natural numbers, however, serves as the best illustration of an infinite set in mathematics. There is no limit to the amount of natural numbers.
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The length of a rectangular garden is 5 m greater than the width. The area of the garden is 66 m² Find the dimensions of the garden.
L = 10 and w= 5 are the dimensions of the rectangular garden.
What is a rectangle, exactly?
The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.Let the width of the garden be a
Length of the garden = a + 5
Area = l * w
66 = ( a+ 5 ) * a
66 = a² + 5a
a² + 5a -66 = 0
a² + 11a - 5a - 66 = 0
a( a + 11 ) -5 ( a + 11) = 0
( a + 11 ) ( a - 5) = 0
so a + 11 = 0 ⇒ a = -11
a - 5 = 0 ⇒ a = 5
Width cannot be negative.
l = a + 5 = 10
w = 5
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HELP ASAP PLEASE!! FIND THE DOMAIN AND RANGE OF THJS GRAPH
The range is all the y-value or outputs of a function. In the case of a horizontal line, this is only one value.
The range is the y-intercept, -5.
The domain is all x-values or inputs of a function. For this graph, it is all real numbers (as you said).
The domain is all real numbers.
Can someone help me with this
Answer:
[tex]\sqrt{40}[/tex] would the answer to number 1.
(-1, 2) would be the answer to number 2.
the area of a sector is 5.024cm2 and the angle is 36°. what's the radius
Answer:
mark me brainlest
Step-by-step explanation:
The area of sector is = pi* r^2*β\360 …. . . .(1
Where
Pi=3.14
r = radius
β= angle=36
So. Put value in equation 1
5.024=3.14 * r^2*36/360
5.024*360/(3.14*36)= r^2
16=r^2
r=4
Howard's pawn shop bought an antique clock at the wholesale price of $725. Howard marked up the price of the clock 30%. What was the list price of the clock?
The list price of the clock is $375.50.
How to calculate the costFrom the information, Howard's pawn shop bought an antique clock at the wholesale price of $725. Howard marked up the price of the clock 30%.
The new price will be:
= $725 + (30% × $725)
= $275 + $82.5
= $357.5
Therefore, the list price of the clock is $375.50.
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if a number is divided by an d minused from an another number
This process required 3 to be subtracted 5 consecutive times, so again we see that 15 ÷ 3 = 5. The number that is being divided (in this case, 15) is called the dividend, and the number that it is being divided by (in this case, 3) is called the divisor. The result of the division is the quotient.
Division is a simple operation in which a number is divided. It's easiest to think of it as a number of objects being divided among a certain number of people.
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
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.............................
[tex]\frac{ {9}^{x + 1} - {3}^{2x} }{4 \times {3}^{2x - 1} } \\ [/tex]
ans : 6
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{9 {}^{(x + 1)} - 3 {}^{2x} }{4 \times 3 {}^{(2x - 1)} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{3{}^{2(x + 1)} - 3 {}^{2x} }{4 \times 3 {}^{(2x - 1)} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{3{}^{(2x + 2)} - 3 {}^{2x} }{4 \times 3 {}^{(2x - 1)} } [/tex]
here :
[tex]{ \sf {3}^{(2x+2)}=({3}^{2x - 1})\sdot (3³)} [/tex][tex]{ \sf {3}^{(2x)}=({3}^{(2x - 1)})\sdot (3¹)} [/tex][tex]\qquad \sf \dashrightarrow \: \cfrac{3{}^{(2x - 1)}(3 {}^{3} - 3 {}^{1}) }{4 \times 3 {}^{(2x - 1)} } [/tex]
[ taking [tex]{ \sf {3}^{(2x - 1)} } [/tex]common here ]
[tex]\qquad \sf \dashrightarrow \: \cfrac{27 {}^{} - 3 {}^{}}{4 } [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{24{}^{} {}^{}}{4 } [/tex]
[tex]\qquad \sf \dashrightarrow \: 6[/tex]
Need help with this was will off 30 points
The solution of the simultaneous equations is given by: x=0.60 and
y = 0.80 .
A system of equations or simultaneous equations, usually referred to as an equation system, is a collection of finite equations for which common solutions are sought.
The elimination approach, which involves taking one of the unknowns out of each equation, is the most popular technique for solving simultaneous equations. The final step is to calculate the remaining unknown. If the coefficient of one of the letters is the same, regardless of sign, this is possible.The given pair of simultaneous equations are:
6 x + 8 y = 10
9 x + 6 y = 10.20
Now let us multiply the first equation by 6 and the second equation by 8 and subtract it from the first.
36 x + 48 y = 60
72 x + 48 y = 81.60
⇒ 36 x = 21.60
⇒ x = 21.60 ÷ 36
⇒ x = 0.60
Substituting the value in the first equation we get:
y= 0.80.
Hence the solution of the simultaneous equation is x=0.60 and
y = 0.80 .
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Every day, Angeni's cupcake store sells 5,000 cupcakes in chocolate and vanilla
flavors. If the chocolate flavor is 3 times as popular as the vanilla flavor, how many of
each cupcake does the store sell per day?
The number of vanilla and chocolate flavoured cupcakes sold every day is 1250 and 3750, respectively.
Let the number of vanilla-flavoured cupcakes be "x".The number of chocolate-flavoured cupcakes is 3*x.A ratio in mathematics describes how many times one number contains another. A number is an arithmetic value used to represent a quantity and to do computations. Numericals are written symbols that represent numbers, such as "3." A number system is a logical writing system for representing numbers with digits or symbols.The total number of cupcakes that are sold is 5,000.According to the question, x + 3x = 50004x = 5000x = 5000/4x = 1250The number of vanilla-flavoured cupcakes sold every day is 1250.The number of chocolate-flavoured cupcakes sold every day is 3750.To learn more about numbers, visit :
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Which statements accurately describe the function f(x) = 3(√18)x? Select three options.
The domain is all real numbers.
The range is y > 3.
The initial value is 3.
The initial value is 9.
The simplified base is 3√2.
Answer:
The domain is all real numbers.
The initial value is 3.
The simplified base is 3√2.
The statements accurately describe the function f(x) = 3(√18)x are:
The domain is all real numbers.
The initial value is 3.
The simplified base is 3√2.
What is Function?A function is an expression that illustrates the connection between two or more variables and numbers. A function defined by several subfunctions, each of which is applicable to a distinct interval in the domain, is said to be piecewise.
We have function,
f(x) = 3√18 x
now, simplifying the function we get
f(x) = 3 (3√2)x
f(x) = 9x√2
So, we can conclude that.
The domain is all real numbers.
The initial value is 3.
The simplified base is 3√2.
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I need help with this please and work out the problem
Answer:The answer is 425
Step-by-step explanation:
Which operations can be applied to a matrix in the process of Gaussian elimination?
a. replacing a row with the absolute values of that row
b. replacing a row with three times another row
c. replacing a row with twice that row
d. replacing a row with the sum of that row and another row.
e. swapping rows
(multiple answer are correct)
The following operations can be applied to a matrix during the Gauss Jordan elimination process:
(C) Replacing a row with twice the number of rows.(D) Substituting a row for the sum of that row and another row.(E) Row swapping.What is Gauss Jordan's elimination?Gaussian elimination, also known as row reduction in mathematics, is a method for solving systems of linear equations. It is made up of a series of operations performed on the corresponding coefficient matrix. This method can also be used to compute a matrix's rank, determinant of a square matrix, and inverse of an invertible matrix. The method is named after Carl Friedrich Gauss (1777-1855), though some special cases of the method were known to Chinese mathematicians as early as 179 AD, albeit without proof.During the Gauss Jordan elimination process, the following operations can be applied to a matrix:
Replacing a row with twice the number of rowsSubstituting a row for the sum of that row and another row.Row swappingTherefore, the following operations can be applied to a matrix during the Gauss Jordan elimination process:
(C) Replacing a row with twice the number of rows.(D) Substituting a row for the sum of that row and another row.(E) Row swapping.Know more about Gauss Jordan's elimination here:
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Which number has a 6 that is 1/10 the value of the 6 in 527.6?
A. 1432.986
B. 982.46
C. 54.6
D. 36
The number that has a 6 that is 1/10 the value of the 6 in 527.6 is B. 982.46.
How to illustrate the information?It should be noted that we are to simply find the place value of the numbers.
In 527.6, the place value is 1/10.
On the other hand, in 982.46, the place value is 1/100.
Therefore, the number that has a 6 that is 1/10 the value of the 6 in 527.6 is 982.46.
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Corresponding angles examples
Answer:
The opening and shutting of a lunchbox, solving a Rubik's cube, and never-ending parallel railway tracks are a few everyday examples of corresponding angles.
HOPE IT'S HELPS YOUYou bought f pounds of fruit today. Today, you bought 3 times as many pounds of fruit as you bought yesterday. Which expression correctly shows how many pounds of fruit you bought yesterday? is it
f + 3
3f
3 ÷ f
f ÷ 3
or
none of the above
The answer would be 3f.
What is the perimeter of quadrilateral EFGH?
Answer:
54 units
Step-by-step explanation:
From G to H, use the Pythagorean Theorem:
[tex]3^2+4^2=\sqrt{25} =\fbox{5}[/tex]
From G to F, just count:
[tex]\fbox{11}[/tex]
From H to E, use the Pythagorean Theorem:
[tex]12^2+5^2=\sqrt{169}=\fbox{13}[/tex]
From F to E, use the Pythagorean Theorem:
[tex]15^2+20^2=\sqrt{625}=\fbox{25}[/tex]
Now, add up all the answers:
[tex]5+11+13+25=\fbox{54}[/tex]
y = ²√x - 3
X
-10
-4
-2
4
y
Answer:
di mo po alam yan
oh di po kayo makain tindi tagalog
It is so hot that Craig's cousins ask him to make creamy mango smoothies. First, Craig blends 5 cups of mango, 1 quart of yogurt, and 3 cups of crushed ice. Then, he divides the smoothie evenly among 6 large glasses. How many cups of smoothie does he put in each glass?
Answer:
2 Cups
Step-by-step explanation:
First of all you need to add all of the ingredients together, which would total 12 cups of smoothie. Also important to add is that 1 quart is 4 cups. Then you have 12/6 which equals 2!
The cups of smoothie in each glass is 2 cups.
How many cups of smoothie is in each glass?In order to determine the number of cups of smoothie that would be put in each glass, it should be ensured that the measures of the ingredients are in the same unit.
The first step is to determine the total cups of smoothie that Craig makes.
In order to determine the total cups, quart has to be converted to cups
1 quart = 4 cups
Total number of cups = 5 + 4 + 3 = 12 cups
The next step is to determine the cups in each glass.
Cup of smoothie in each glass = total number of cups of smoothie / total number of large cups
12 / 6 =2 cups.
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Q. You work for a food wholesaler that provides ingredients for restaurants and other food
producers. A large-scale bakery needs 72 pounds of raisins. The raisins come in 12-ounce
boxes. A total of 24 boxes will fit in a case. How many cases of raisins should you ship to
them?
The cases that would be shipped is 4.
How many cases would be shipped?The first step is to convert pounds to ounce
1 pound = 16 ounce
16 x 72 = 1152 ounces
The next step is to determine how many boxes would be needed.
Boxes needed = 1152 / 12 = 96 boxes
The third step is to determine the number of cases that would be shipped.
Cases that would be shipped = 96 /24 = 4
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What is 2/3 x 9 in fraction?
Answer: it would be 18/3 or
Step-by-step explanation:
2/3 x 9 = ?
1) You multiple both numerator and denominator: 2x9 / 3x1 = 18/3
2) Find the GCF ( greatest common factor) for both numbers. Which is
3) Then divide both the numerator and denominator by 3 to simplify to it's lowest term: 18÷3= 6 and 3÷3= 1 which gives a fraction of 6/1 or
What is the range of the function f(x) = x^2– 1 over the interval of -1 ≤ x < 3? Give your answer in interval notation.
Answer:
[0, 8)
Step-by-step explanation:
To find the range, compute the values of the function at the edges of the interval.
The interval edges are -1 and 3
f(x = -1) = (-1)² - 1 = 1 - 1 = 0.
f(x = 3) = 3² - 1 = 9 - 1 = 8 but does not include 3 so
so range of f(x) : 0 ≤ f(x) < 8
Note that we cannot have f(x) ≤ 8 only < 8 since the interval does not include x = 3
Range in interval notation is [0, 8)
The use of the square brackets on the left means the number is included in the interval; so 0 is included ( ≥ ).
The round brackets on the right mean that the number is not include (< 8 )