A restaurant added a new outdoor section that was 5ft wide 9ft long. What is the area of the new outdoor section?
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Given:
a.) A restaurant added a new outdoor section that was 5 ft wide 9 ft long.
Based on the given, Length and Width, presuming it's rectangular in shape, let's now determine the area:
[tex]\text{ Area = Length x Width}[/tex][tex]=\text{ 9 x 5}[/tex][tex]\text{Area = 45 ft}^2[/tex]Therefore, the area of the new outdoor section is 45 ft.²
Related Questions
Directions: Solve each equation. Check your solution(s) then indicate whether or not the solutions are extraneous.
Answers
we have
Part 3
[tex]3\mleft|x-2\mright|=18[/tex]step 1
Divide by 3 both sides
[tex]|x-2|=6[/tex]Solve the first case (positive)
[tex]\begin{gathered} +(x-2)=6 \\ x=6+2 \\ x=8 \end{gathered}[/tex]Solve the second case (negative)
[tex]\begin{gathered} -(x-2)=6 \\ x-2=-6 \\ x=-6+2 \\ x=-4 \end{gathered}[/tex]What is the common difference between successive terms in the sequence?2,8, 14, 20, 26
Answers
ANSWER
The common difference is 6
EXPLANATION
The common difference is the difference between each pair of consecutive element of the series:
[tex]\begin{gathered} 8-2=6 \\ 14-8=6 \\ 20-14=6 \\ 26-20=6 \end{gathered}[/tex]Each element is 6 integers apart from the previous one, The common difference is 6.
You can pick any question to solve. I really need help though...
If you solve all of it, I'll give you 115 points.
Answers
The simplification of the number 3⁷.3⁸/3¹⁹ is found as 1/3⁴.
What is meant by the term indices/ index?An index can be assigned to a number or a variable. A variable's index (or constant) is a value raised to a power of a variable. Indexes are also referred to as powers as well as exponents. It indicates how many times a provided number must be multiplied. The index specifies that a specific number (or base) be multiplied on its own an amount equal to a index raised to it.The given expression in the question is-
= 3⁷.3⁸/3¹⁹
By the power rule of the indices.
With the same base, the power of the number get added with sign.
= 3¹⁵/3¹⁹
Now, taking reciprocal.
= 3¹⁵.3⁻¹⁹
Subtract the powers.
= 3⁻⁴
Again take the reciprocal
= 1/3⁴
Thus, the simplification of the number is found as 1/3⁴.
To know more about the indices/ index, here
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The correct question is-
Simplify the given expression;
3⁷.3⁸/3¹⁹
Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (-1,6) and parallel to x + 3y = 7.a) The equation of the line in slope-intercept form is.(Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)
Answers
Answer:
[tex]y=\frac{1}{3}x+\frac{19}{3}[/tex]Step-by-step explanation:
Linear equations are represented in slope-intercept form by the following equation:
[tex]\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{slope} \\ b=\text{ y-intercept} \end{gathered}[/tex]If the line is parallel to x+3y=7, it means they have the same slope. Then, the slope would be;
[tex]\begin{gathered} x+3y=7 \\ y=\frac{x}{3}-\frac{7}{3} \\ \text{ Slope is the coefficient that goes with the ''x''} \\ \text{Slope}=\text{ }\frac{1}{3} \end{gathered}[/tex]Then, to find the y-intercept of the equation, substitute the slope and the given point, solve for b:
[tex]\begin{gathered} 6=\frac{1}{3}(-1)+b \\ b=6+\frac{1}{3} \\ b=\frac{19}{3} \end{gathered}[/tex]Hence, the equation would be:
[tex]y=\frac{1}{3}x+\frac{19}{3}[/tex]5-Which soda is the better deal? Coca-Cola $1.29 for 1.25 L O Pepsi $2.49 for 2 L 5b-What is the Unit Price for the better deal? Round to the nearest hundredth) Put your answer in the form 0.00 or .00, so if answer is 43 cents, its 0.43 or.43, if there is a dollar amount like 1.50, do not add zeros in front).
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We need to find the cost per liter for Coca and Pepsi and compare both solutions in order to answer the question.
In the first case (coca case), we have
[tex]\begin{gathered} 1.29\text{ dollars ----- 1.25 liters} \\ x\text{ ----------- 1 liter} \end{gathered}[/tex]then, we have
[tex]\begin{gathered} x=\frac{(1.29)(1)}{1.25} \\ x=\frac{1.29}{1.25} \\ x=1.032 \end{gathered}[/tex]By rounding down, 1 liter of coca cost $1.03.
In the secon case (pepesi case), we have
[tex]\begin{gathered} 2.49\text{ dollars ------ 2 liters} \\ x\text{ ------------- 1liter} \end{gathered}[/tex]hence, x is equal to
[tex]\begin{gathered} x=\frac{(2.49)(1)}{2} \\ x=\frac{2.49}{2} \\ x=1.245 \end{gathered}[/tex]By rounding down, 1 liter of pepsi cost $1.25.
By comparing both solutions, we can see that Coca has a better price because $1.03 is less than $1.25.
An integer is 3 more than 4 times another. If the product of the two integers is 45, then findthe integers
Answers
Define the equations that describe the situation
[tex]\begin{gathered} x=4y+3 \\ x\cdot y=45 \end{gathered}[/tex]Clear x from the second equation
[tex]x=\frac{45}{y}[/tex]Make both equations equal
[tex]\begin{gathered} 4y+3=\frac{45}{y} \\ y(4y+3)=45 \\ 4y^2+3y=45 \\ 4y^2+3y-45=0 \end{gathered}[/tex]Solve the cuadratic equation
[tex]\begin{gathered} y=\frac{-3\pm\sqrt[]{3^2-4\cdot4\cdot(-45)}}{2\cdot4} \\ y=\frac{-3\pm\sqrt[]{9+720}}{8} \\ y=\frac{-3\pm27}{8} \\ y1=-\frac{30}{8}=-\frac{15}{4} \\ y2=\frac{24}{8}=3 \end{gathered}[/tex]As we are dealing with integers, the value of y is 3, now use one of the first equations to find x
[tex]\begin{gathered} x=\frac{45}{y} \\ x=\frac{45}{3} \\ x=15 \end{gathered}[/tex]The integers are 3 and 15
Create a multi-step equation(that requires at least 3 steps to solve). For the equation you create, include thefollowing things in your initial response:• The equation clearly written out• The mathematical work needed to solve the equation (be sure to show allsteps)• The solution to the equationFor each step in the solution process, write a brief sentence or two that explainsthe step. For example, you might write something like "I divided both sides of theequation by 2 to cancel out the multiplication by 2..."
Answers
SOLUTION
[tex]Given\text{ the question on the question tab;}[/tex]To create a multi-step equation
(that requires at least 3 steps to solve).
[tex]\begin{gathered} Writing\text{ out the equation;} \\ 9x-6=5x+18 \end{gathered}[/tex][tex]\begin{gathered} Solving\text{ the equation and giving brief sentence to explain the steps;} \\ 9x-6=5x+18 \\ Subtract\text{ 5x from both sides;} \\ 9x-5x-6=5x-5x+18 \\ 4x-6=18 \end{gathered}[/tex][tex]\begin{gathered} Add\text{ 6 to both sides} \\ 4x-6+6=18+6 \\ 4x=24 \\ Divide\text{ both sides by 4;} \\ \frac{4x}{4}=\frac{24}{4} \\ x=6 \end{gathered}[/tex]There is a population of 9,000 bacteria in a colony. If the number of bacteria doubles every 245 hours, what will the population be 980 hours from now?
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There is a population of 9,000 bacteria in a colony.
If the number of bacteria doubles every 245 hours, what will the population be 980 hours from now?
Recall that the exponential growth formula is given by
[tex]y=a\cdot b^x[/tex]Where a is the initial population, b is the rate of growth, and x is the time.
For the given case, we have
a = 9,000
b = 2 (doubles)
x = 980/245 = 4
Let us substitute these values into the above formula
[tex]\begin{gathered} y=a\cdot b^x \\ y=9,000\cdot2^4 \\ y=9,000\cdot16 \\ y=144,000 \end{gathered}[/tex]Therefore, the population of the bacteria will be 144,000 after 980 hours from now.
a triangle has rotation symmetry that can take any of its verticles to any of its other vehicles. select all conclusions that we can reach from thisA. all sides of the triangle have the same lengthb. all angles of the triangle have the same measurec. a rotation of 60° will map the triangle to itselfd. a rotation of 120° will map the triangle to itself
Answers
In order for a triangle to be rotated in a symmetry that involves each rotation to matching vertices of the triangle, involves several of the options given in the list:
* All sides have the same length (we are dealing with an equilateral triangle)
* All angles ofthe triangle have the same measure (60 degrees each angle)
* A rotation of 60 degrees will map the traingle to itself (typical for a case of equilateral triangle)
* A rotation of 120 degrees will map the triangle with itself. (also in agreement with the answer immediately above, since 120 degree rotetion is the same as two consecutive 60 degree rotations)
Express cos -30 as a function of the reference angle.Question 13 options:-cos30cos210cos150cos30
Answers
The reference angle is the angle between the terminal side of the angle and the x axis. It is always positive
We know that cos ( -30) has a reference angle of 30 degrees
The cos is the x direction so cos (30) and cos (-30) will have the same value
cos (-30) = cos (30)
Answer: cos(30)
Susy has a square plot of grass in her backyard. Each side of the plot has a length of 14.5 feet. On one side, a semicircular fountain with a radius of 2.5 feet cuts into the plot of grass. She wants to put a brick border around the edge of the grass, so that it will also separate the grass from the fountain.What is the approximate length of the brick border?
Answers
Given:-
Susy has a square plot of grass in her backyard. Each side of the plot has a length of 14.5 feet. On one side, a semicircular fountain with a radius of 2.5 feet cuts into the plot of grass. She wants to put a brick border around the edge of the grass, so that it will also separate the grass from the fountain.
To find:-
What is the approximate length of the brick border?
The length of squares four sides is,
[tex]4\times14.5=58[/tex]All four sides of square are equall,
[tex]58-(2.5\times2)=53[/tex]Diameter of a circle is twice its radius,
[tex]\pi r=\pi2.5=7.85[/tex]Formula of circumference is,
[tex]2\pi r[/tex]So the length of brick is,
[tex]53+7.85=60.85[/tex]So the approximate length is 60.85ft.
You and three friends go to a baseball game. You each pay 2$ for a drink and x dollars for nachos. Use the distributive property to write and simplify an expression for the total the group pays.
Answers
You and three friends go to a baseball game.
So, there are a total of 4 persons.
You each pay $2 for a drink and x dollars for nachos.
Recall that the distributive property is given by
[tex]a\cdot(b+c)=a\cdot b+a\cdot c[/tex]For the given case, we have
a = 4
b = 2
c = x
Let us apply the distributive property to write and simplify an expression for the total the group pays.
[tex]\begin{gathered} 4\cdot(2+x)=4\cdot2+4\cdot x \\ 4\cdot(2+x)=8+4x \end{gathered}[/tex]Therefore, the simplified expression for the total amount that the group pays is
[tex]8+4x[/tex]Given: AB - DEDBEWhat additional information is needed to proveABEA - AEBDby Side-Angle-Side?O ZABE ~ ZDEBO ZBAE - ZEDBO AE - DBO ZACB - ZECB
Answers
We already know that BEA and EBD have a congruent side, we need to find another one and a corresponding congruent angle.
Notice that both triangles share the side BE. So, we already have two pairs of angles that are congruent.
To prove congruence of the triangles by SAS, we need that the angle formed by the two congruent sides is also congruent between the two, triangles, so
[tex]\angle BAE\cong\angle EDB[/tex]is the condition we are looking for
The correct answer is option B
Boyle's Law says that the volume of a gas varies inversely with the pressure. When the volume of a certain gas is 2 L, the pressure is 1165 kPa (kilopascals),What is the volume when the pressure is 466 kPa ?
Answers
SOLUTION
The volume of a gas varies inversely with the pressure
This is written as:
[tex]PV=k[/tex]Where k is a constant
When V=2L, P=1165kPa
Substitute these values into the above equation
[tex]1165\times2=k[/tex]It follows:
[tex]k=2330[/tex]Substituting the value of k into the equation gives
[tex]PV=2330[/tex]Find V when P=466kpa
Substitute P=466 into the equation PV=2330
[tex]466\times V=2330[/tex]Solve for V
[tex]\begin{gathered} V=\frac{2330}{466} \\ V=5 \end{gathered}[/tex]Therefore The required volume is 5L
Find the area of a triangle that has a base of 7 ft and a height of 6 ft
Answers
Area of a triangle = 1/2 * (Base *height )
Replacing your data
Area of the triangle = 1/2 * (7 *6 )
Area of the triangle = 21 ft^2
_______________
How many lines can be constructedperpendicular to AB that passthrough point D?.BсA. 0B. 1C. 2
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SOLUTION
To solve this question, we will try and visualize the image and see how many perpendicular lines can pass through point D to line AB.
Please note that perpendicular lines are lines that intersect at a right (90 degrees) angle.
From the above illustration, we see that it is one line (the yellow line) that is possible to be perpendicular from point D to line AB, any other line will not form at angle 90 to line AB.
From the above explanation therefore, we can draw a conclusion that the correct answer is B.
Jordy bought 3 sets of 100 stamps, 2 sets of 20 stamps, 4 sets of 12 stamps, and 1 set of 10 stamps. How many stamps did Jordy buy?
Answers
Answer:
398 stamps
Explanation:
[tex]\begin{gathered} \text{3 sets of 100 stamps}=3\times100=300\text{ stamps} \\ \text{2 sets of 20 stamps}=2\times20=40\text{ stamps} \\ \text{4 sets of 12 stamps}=4\times12=48\text{ stamps} \\ \text{1 set of 10 stamps}=1\times10=10\text{ stamps} \end{gathered}[/tex]Therefore, the total number of stamps Jordy buys:
[tex]\begin{gathered} =300+40+48+10 \\ =398\text{ stamps} \end{gathered}[/tex]simplify the following expreission(2m^3 -5m+3m^2) + (4+5m^2-2m)
Answers
Answer:
[tex]2m^3+8m^2-7m+4[/tex]Explanation:
Given the expression:
[tex]\mleft(2m^3-5^{}m+3m^2\mright)+(4+5m^2-2m)[/tex]First, we open the brackets to get:
[tex]=2m^3-5^{}m+3m^2+4+5m^2-2m[/tex]Next, we collect like terms and simplify.
[tex]\begin{gathered} =2m^3+3m^2+5m^2-5m-2m+4 \\ =2m^3+8m^2-7m+4 \end{gathered}[/tex]Write all classifications that apply to the real number -5.O rational, integer, terminating decimalO rational, integer, whole number, natural number, terminating decimalO natural number, terminating decimal© rational, integer, natural number
Answers
Given the following question:
Classifications of -5
-5 isn't a whole number, since it's a negative
-5 is a integer
-5 is a rational number since it can be written as a fraction
-5 isn't a natural
-5 is a terminating decimal
Option A is your answer.
= √(x2 – x1)2 + (y2 – yı)2 when do i use this equation?
Answers
According to the given data we have the following expression:
√(x2 – x1)2 + (y2 – yı)2
The equation above is used to calculate the distance between the two points x1 y1 and x2 y2.
Distance is represented by letter D.
So the formula to calculate the distance would be:
d=√(x2 – x1)2 + (y2 – yı)2
The distance formula calculates the distance between two points in the coordinate plane. If (x1, y1) and (x2, y2) are the two points in question, the distance d between these two points is √((y2-y1)^2 + (x2-x1)^2
Solve for X 5 (3x + 1) = X -4 A. 9/14 B. 3/11 C. 1 D. 1/2
Answers
Solve for x:
[tex]5(3x+1)=x-4[/tex]To solve for x, we are going to use inverse operations to solve equatons.
Addition and subtraction are inverse operations, multiplication and division are inverse operations too.
Then,
[tex]\begin{gathered} As\text{ a first step, using distributive property:} \\ 15x+5=x-4 \\ 15x-x=-4-5 \\ 14x=-9 \\ x=-\frac{9}{14} \end{gathered}[/tex]Therefore, the correct answer would be A.
Sam takes 4 hours to peel 32 potatoes, while Josh takes 5 hours to peel 30 potatoes.How long is it going to take both Sam and Josh to peel 100 potatoes together
Answers
EXPLANATION
Given that it takes 4 hours to peel 32 potatoes, and 5 hours to peel potatoes to Josh, assuming that x represent the time, we can apply the following reasoning:
First, we need to compute the unit rate for Sam and Josh as follows:
[tex]\text{Sam rate=}\frac{32potatoes}{4\text{ hours}}=8\frac{potatoes}{\text{hour}}[/tex][tex]\text{Josh rate=}\frac{30\text{ potatoes}}{5\text{ hours}}=6\frac{potatoes}{\text{hour}}[/tex]Now, we can compute the time by multiplying each rate by the amount needed of time as shown as follows:
[tex]8x+6x=100[/tex]Adding like terms:
[tex]14x=100[/tex]Dividing both sides by 14:
[tex]x=\frac{100}{14}[/tex]Simplifying:
[tex]x=\frac{50}{7}=7.14\text{ hours}[/tex]It will take approximately 7 hours to peel 100 potatoes to Sam and Johh together.
ive got this due tomorrow and i literally CANNOT find the answer keys so imma need help in these three
Answers
13x=32+5x
First wee need to put all the terms on the same side of the equation remember if you change from one side to the other side of the equation the sign change
13x-5x=32
8x=32
we clear x
x=32/8
x=4
the solution is x=4
Solve a 2x + 6x z for X.
Answers
Given data:
The given expression is a=2x+6xz.
the given expression can be written as,
a=2x(1+3z)
a/(1+3z)=2x
x=a/2(1+3z).
hus, the value of x is a/2(1+3z).
I need a tape diagram for the equation: 2 + 6x =32and another tape diagram for the equation: 7x + 1 = 15
Answers
Explanation:
2 + 6x =32
tape diagram:
Write an equation to describe the relationship shown in the graphrise/run = 80-____=___ ____-3 ____The equation of the line is y =____ x.
Answers
Answer
Rise/run = 20 miles/gallon
The equation of the line is y = 20x
Check Explanation for more.
Explanation
The rise-run is another name for the slope.
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For this question,
(x₁, y₁) and (x₂, y₂) are (3, 60) and (4, 80)
x₁ = 3
y₁ = 60
x₂ = 4
y₂ = 80
[tex]\text{Slope = }\frac{80-60}{4-3}=\frac{20}{1}=20[/tex]The equation of the line is y = 20x
Hope this Helps!!!
the figure to the right shows two parallel lines intersected by more than one transversal. let x = 34 degrees. find the measure of angles 1, 2 and 3.
Answers
Explanation
Step 1
as the horizontal lines are parallel, the angles (1) and x are congruents, so
[tex]\begin{gathered} m\measuredangle1=x \\ so,\text{replacing} \\ m\measuredangle1=34 \end{gathered}[/tex]Step 2
Now, we can see that angles (1) and (2) are complementary angesl (When two angles add to 90°)
so
[tex]\begin{gathered} m\measuredangle1+m\measuredangle2=90 \\ \text{replacing} \\ 34+m\measuredangle2=90 \\ \text{subtract 34 in boht sides} \\ -34+34+m\measuredangle2=90-34 \\ m\measuredangle2=56 \end{gathered}[/tex]Step 3
finally, angles (1) and angle (3) are supplementary angles (Two Angles are Supplementary when they add up to 180 degrees)
so
[tex]\begin{gathered} m\measuredangle1+m\measuredangle3=180 \\ \text{replace} \\ 34+m\measuredangle3=180 \\ to\text{ solve for x, subtract 34 in both sides} \\ -34+34+m\measuredangle3=180-34 \\ m\measuredangle3=146 \end{gathered}[/tex]i hope this helps you
A movie club surveyed 150 high school students. The students were asked how often they go to the movies and whether they prefer action movies or comedies.Thelr responses are summarized in the following table.Twice a month Three times a monthAction4527Comedy 6612or lessor more(a) What percentage of the students go to the movies three times a month or more?(b) What percentage of the students prefer action movies ?(a) 096Х5?(b) 1%Submit AContinue2021 McGraw Hill LLC. All Rights Reserved. Terms of Use Privacy Center
Answers
Answer:
(a) 26 %
(b) 48%
Explanation:
The total number of students is
[tex]45+27+66+12[/tex][tex]=150[/tex](a).
The total number of students that go to the movies three times or more is
[tex]27+12=39[/tex]Therefore, the percentage is
[tex]\frac{39}{150}\times100\%[/tex][tex]=26\%[/tex](b).
The total number of students that prefer action movies is
[tex]45+27=72[/tex]therefore, the percentage is
[tex]\frac{72}{150}\times100\%=48\%[/tex]Hence, to summerise:
(a) 26 %
(b) 48%
Which of the following are reasons used in proof that the angle bisector construction can be used to bisect any angle
Answers
In the construction we use the fact that all radius of a circle are congruent, so AB ≅ AC, as both segments are radius of the same circle.
In the same way, this let us write:
[tex]BD\cong CD[/tex]As, by reflexive property, we can write AD ≅ AD.
Then, we have triangles with 3 pairs of congruent sides, so they are congruent by the SSS postulate.
Then, because of CPCTC (corresponding parts of congruent triangles are congruent), the angle BAD is congruent to angle CAD, meaning that AD is a bisector of angle BAC.
Answer: Options A, C and D.
How many unit cubes fit in the figure below?7 units9 units5 units
Answers
step 1
Find the volume of the rectangular prism
V=L*W*H
substitute given values
V=5*9*7
V=315 unit3
therefore
the answer is 315 unit cubes option Abecause the volume of one unit cube is 1 unit3so315 unit cubes -----> volume is 315 unit3