Answer:
x = -3
Step-by-step explanation:
The line y = 3 is a horizontal line. So a perpendicular line is a vertical line. The form of the equation for a vertical line is
"x = anumber"
The information we have to work with is the point (-3, 10) A point is in the form (x,y). So we know that x is -3 and y is 10.
We need the x.
x = -3
This is the equation of the vertical line through (-3,10). It is perpendicular to the horizontal line
y = 3.
Answer:
x = -3
Mia is decorating a ballroom ceiling with garland. If the rectangular ceiling is 63 feet by 60 feet, how much garland will Mia need to reach from one corner of the ceiling to the opposite corner?
Given the dimensions of the rectangular ceiling below
[tex]\begin{gathered} \text{length}=63\text{feet} \\ \text{width}=60\text{feet} \end{gathered}[/tex]Let us sketch out the image of the rectangle ceiling.
We are to solve for x, which represents the cost of garland Mia will need to reach from one corner of the ceiling to the opposite corner.
Let us now sketch out the triangular shape from the rectangle.
Using Pythagoras theorem to solve for x,
Therefore,
[tex]\begin{gathered} x^2=60^2+63^2 \\ x^2=3600+3969 \\ x^2=7569 \\ x=\sqrt[]{7569} \\ x=87\text{feet} \\ \therefore x=87feet \end{gathered}[/tex]Hence, the cost of garland Mia will need to reach from one corner of the ceiling to the opposite corner is 87feet.
Solve {3x+2y=15x−3y=8 by elimination. Express your answer as an ordered pair.
As given by the question
There are given that the system of equation:
[tex]\begin{gathered} 3x+2y=1\ldots(1) \\ 5x-3y=8\ldots(2) \end{gathered}[/tex]Now,
Multiply by 5 with the equation (1) and multiply by 3 with the equation (2)
Then,
[tex]\begin{gathered} (3x+2y=1)\times5=15x+10y=5\ldots(3) \\ (5x-3y=8)\times3=15x-9y=24\ldots(4) \end{gathered}[/tex]Now,
Subtract equation (4) from equation (3)
So,
[tex]\begin{gathered} 10y-(-9y)=5-24 \\ 10y+9y=5-24 \\ 19y=-19 \\ y=-1 \end{gathered}[/tex]Then,
Put the value of y into the equation (1)
So,
[tex]\begin{gathered} 3x+2y=1 \\ 3x+2(-1)=1 \\ 3x-2=1 \\ 3x=1+2 \\ 3x=3 \\ x=1 \end{gathered}[/tex]Hence, the answer as an ordered pair is (1, -1).
The pentagons ABCDE and PQRST are similar. Find the length x of RS.
Given:
Two pentagons are similar.
[tex]\begin{gathered} CD=6 \\ CB=2 \\ BA=3 \\ RQ=1.6 \\ QP=2.4 \\ RS=x \end{gathered}[/tex]Required:
To find the value of x.
Explanation:
Write proposition,
[tex]\frac{CD}{x}=\frac{CB}{RQ}[/tex]Substitute the given values, we get
[tex]\begin{gathered} \frac{6}{x}=\frac{2}{1.6} \\ 2x=6\times1.6 \\ 2x=9.6 \\ x=4.8 \end{gathered}[/tex]Final Answer:
The value of x is,
[tex]x=4.8[/tex]3. Ifx = 8, how much more wallpaper will you need for the living room than for the family room?(2 points each)a) What is the area of the living room when x = 8?Note: You will need tosubtract the area of theliving room from thefamily room.b) What is the area of the family room when x = 8?1c) Subtract the two areas to find how much more square feet the living room will require.
Question 4.
From the answers in part 1 and part 2, we have:
• Equation for the wallpaper of family room:
[tex]y=21x^2-21[/tex]• Equation for the wallpaper of the living room:
[tex]y=16x^2[/tex]Let's solve for the following:
• (a) Area of the living room when x = 8
Substitute 8 for x in the second equation which represents the area of the living room and evaluate:
[tex]\begin{gathered} y=16x^2 \\ \\ y=16(8)^2 \\ \\ y=16(64) \\ \\ y=1024ft^2^{} \end{gathered}[/tex]When x = 8, the area of the living room is 1024 square feet.
• (b). Area of the family room when x = 8.
Substitute 8 for x in the first equation which represents area of the familiy room and evaluate
[tex]\begin{gathered} y=21x^2-21 \\ \\ y=21(8)^2-21 \\ \\ y=21(64)-21 \\ \\ y=1344-21 \\ \\ y=1323ft^2 \end{gathered}[/tex]When x = 8, the area of the family room is 1323 square feet.
• (c). Let's determine how much more square feet the living room will require.
Area of family room - area of living room = 1323 square feet - 1024 square feet = 299 square feet.
Therefore, you will need 299 more square feet of wallpaper for the living room than the family room
If a company has a dividend yield of 2.5%, a share price of $18 per share, how much will I receive in dividends if I own 10,000 shares? Do not include commas or the dollar sign in your answer.
In order to determine how much you will reiceive in dividens, you first calculate the price of your shares, which are 10,000 shares.
18(10,000) = 180,000
The cont of your shares are $180,000.
Next, you calculate the 2.5% of the previous cost, just as follow:
(2.5/100)(180000) = 4500
Hence, you will receive 4500 dollars due to the dividens of the price of your shares.
find p where f(x) = 2x ^ 3 + 5x ^ 2 + px + 8 where f(- 2) = 10
Explanation
Given the function
[tex]f\mleft(x\mright)=2x^3+5x^2+px+8[/tex]We can find the value of p when f(-2 )=10 below;
Therefore, we will have;
[tex]\begin{gathered} f(-2)=2(-2)^3+5(-2)^2+(-2)p+8=10 \\ -16+20-2p+8=10 \\ -4-2p+8=10 \\ -2p+4=10 \\ -2p=10-4 \\ -2p=6 \\ p=\frac{6}{-2} \\ p=-3 \end{gathered}[/tex]Answer: p = -3
There are 3 parts to this answer. A) list all rational zeros that are possible according to the rational zero theorem
we have the function
f(x)=x^3-3x^2-4x+12
p=12 ----> constant term
q=1 ---> leading coefficient
so
p/q=(+-1,+-2,+-3,+-4,+-6,+-12)/(+-1)
All possible rational zeros, according to the Rational Zero Theorem, are
-1,-2,-3,-4,-6,-12,1,2,3,4,6,12
Plans toPlans tovote "yes"vote "no"Totalon issue Qon issue QPlans tovote "yes"81220on issue P.Plans tovote "no" on141630issue PTotal222850The table shows a survey of 50 registered votersin a city. Each voter was asked whether theyplanned to vote “yes” or “no” on two differentissues. If a voter who plans to vote “yes” on issuePis randomly selected, what is the probability thatvoter also plans to vote "no" on issue Q?
Consider that the probability of an event is given by,
[tex]\text{Probability of an event}=\frac{\text{ No. of events favorable to the event}}{\text{ Total possible no. of outcomes}}[/tex]Consider the following events,
A = event that a voter plans to vote 'yes' on issue P
B = event that a voter plans to vote 'no' on issue Q
Then, given that event A has already occurred, the probability of occurrence of B, is given by,
[tex]P(\frac{B}{A})=\frac{P(A\cap B)}{P(A)}[/tex]Area = 496 in.? 25 in. X X 37 in.
EXPLANATION
Given the Trapezoid, we know that the Area is given by the following equation:
[tex]\text{Area}=\frac{(a+b)}{2}\cdot h[/tex]Where a=37in, b=25in
Replacing terms:
[tex]496=\frac{(37+25)}{2}\cdot x[/tex]Multiplying both sides by 2:
[tex]2\cdot496=(37+25)x[/tex]Adding terms and removing the parentheses:
[tex]2\cdot496=62x[/tex]Multiplying terms:
992=62x
Dividing both sides by 62:
[tex]\frac{992}{62}=x[/tex]Switching sides:
[tex]x=\frac{992}{62}[/tex]Simplifying the fractions:
[tex]x=16[/tex]Answer: x is equal to 16 inches.
The following quadrilateral is a trapezoid what is the length of the base of Wye V?
By the Trapezoid Midsegment Theorem, the midsegment of a trapezoid is parallel to each base and its measure is one half the sum of the lengths of the bases.
YV and XW are the bases and GF is the midsegment. So:
[tex]\begin{gathered} GF=\frac{YV+XW}{2} \\ \text{this is } \\ 26=\frac{YV+24}{2} \end{gathered}[/tex]And solve for YV:
[tex]\begin{gathered} 2\cdot26=2\cdot\frac{YV+24}{2}_{} \\ 52=YV+24 \\ 52-24=YV+24-24 \\ YV=28 \end{gathered}[/tex]Answer: b. 28
Complete the square for the following equations:
1)6x^2+3x+9
2)x^2+5x+26
3)-x^2+6x+9
The complete square of the given numbers are-
Part a: 6(x + 1/4)^2 + 69/8
Part b: (x + 5/2)^2 + 27/2
Part c: -(x + 3)^2 + 18
What is meant by completing the square?A quadratic equation is represented as a mixture of quadrilaterals was using to form a square by the method of completing the square.The idea behind this method is to find a special value that, when added both to sides of a quadratic, produces a perfect square trinomial.For the given question
Part a: 6x^2+3x+9
Tale 6 commom;
6(x^2 + x/2 + 3/2)
Add and subtract 1/16 to the equation;
6(x^2 + x/2 + 1/16 - 1/16 + 3/2)
6((x^2 + x/2 + 1/16) - 1/16 + 3/2)
6((x + 1/4)^2 + 23/16)
6(x + 1/4)^2 + 69/8
Part b: x^2+5x+26
Add and subtract 25/4 to the equation;
x^2 + 5x + 25/4 - 25/4 + 26
(x^2 + 5x + 25/4) - 25/4 + 26
(x + 5/2)^2 + 27/2
Part c: -x^2+6x+9
Taking - 1 common.
-(x^2 - 6x - 9)
Add and subtract 9 in the equation;
-(x^2 - 6x + 9 ) - 9 - 9)
-((x^2 - 6x + 9 ) - 9 - 9)
-((x + 3)^2 -18)
-(x + 3)^2 + 18
Thus, the complete square of the umber are found.
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Answer: 123
Step-by-step explanation:
what you mean bae
what is the solution to the equation 2×+4=24
x = 10 is the solution to the equation
Here, we want to find the value of x.
To find the value of x, we need to bring like terms together.
[tex]\begin{gathered} 2x\text{ + 4 = 24} \\ \\ 2x\text{ = 24-4} \\ \\ 2x\text{ = 20} \\ \\ x\text{ = }\frac{20}{2} \\ \\ x\text{ = 10} \end{gathered}[/tex]Answer:
x=10
Step-by-step explanation:
24-4=20 divided by 2 is 10
3+4|3x+7> or = -89
Solve the inequality and graph, if possible
For the given inequality 3 + (4/3)x + 7 ≥ -89 the value of x ≥ (-297 / 4).
Graph of the given inequality is attached.
As given in the question,
For the given inequality we have:
3 + (4/3)x + 7 ≥ -89
Simplify the given inequality by taking all like terms together we have,
(4/3)x + 10 ≥ -89
Subtract 10 from both the side we get,
(4/3)x + 10 -10 ≥ -89 -10
⇒ (4/3)x ≥ -99
Multiply both the side by (3/4) we get,
x ≥ -99 × (3/4)
⇒ x ≥ (-297 /4)
Graph of the given 3 + (4/3)x + 7 ≥ -89 is attached .
Therefore, for the given inequality 3 + (4/3)x + 7 ≥ -89 the value of
x ≥ (-297 / 4).
Graph of the given inequality is attached.
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Please help me on my question It’s all one question
It is given that:
[tex]f(x)=\frac{2}{x};g(x)=3x+12[/tex]1) f(g(x)) will be:
[tex]f(g(x))=\frac{2}{g(x)}=\frac{2}{3x+12}[/tex]2)The domain will be all real numbers except x=-4.
[tex]\text{Domain of f(g(x))=(-}\infty,-4)\cup(-4,\infty)[/tex]3)g(f(x)) will be:
[tex]\begin{gathered} g(f(x))=3f(x)+12 \\ =3(\frac{2}{x})+12 \\ =\frac{6+12x}{x} \end{gathered}[/tex]4) The domain of g(f(x)) is:
[tex](-\infty,0)\cup(0,\infty)[/tex]5) f(f(x)) is given by:
[tex]f(f(x))=\frac{2}{f(x)}=\frac{2}{\frac{2}{x}}=x[/tex]6)The domain of f(f(x)) is:
[tex](-\infty,\infty)[/tex]7) g(g(x)) is calculated as:
[tex]\begin{gathered} g(g(x))=3(g(x))+12=3(3x+12)+12 \\ =9x+36+12 \\ =9x+48 \end{gathered}[/tex]8)The domain of g(g(x)) is:
[tex](-\infty,\infty)[/tex]What is an equation of a parabola with the given vertex and focus? Vertex: (-2,5); focus: (-2,6)
ANSWER:
[tex]\left(x+2\right)^2=4\left(y-5\right)[/tex]STEP-BY-STEP EXPLANATION:
We can see that the vertex and the focus have the same coordinate in x, therefore, the equation of the parabola has the following form:
[tex]\left(x-h\right)^2=4p\left(y-k\right)[/tex]Where (h, k) is the vertex and p is the focal length, which we calculate as follows:
[tex]p=y_2-y_1=6-5=1[/tex]Now, we replace the vertex and the equation would finally be:
[tex]\begin{gathered} (x-(-2))^2=4\cdot1(y-5) \\ \\ \left(x+2\right)^2=4\left(y-5\right) \end{gathered}[/tex]I need help please quick it's for a project due tonight I need all the parts
From our answer, he raced 1 1/3 (4/3) hours at 90 mph and 2/3 hours at 60 mph
Here, we want to fill the table based on the information presented in the question
We proceed as follows;
We will fill the table, line by line
First line;
a) Rate mph is 90
b) Time at this rate is f hours
Second line;
a) Time is l hours
b) Distance is the product of the rate and 60 mph and the time l which is 60l
So let us set up the system of equations;
a)
[tex]f\text{ + l = 2}[/tex]b)
[tex]90\text{ F + 60 l = 160}[/tex]Now, we need to solve this system of equations simultaneously
We have this as;
[tex]\begin{gathered} f\text{ + l = 2} \\ 90f\text{ + 60l = 160} \\ \\ \text{From i;} \\ f\text{ = 2-l} \\ \\ 90\text{ (2-l) + 60l = 160} \\ 180-90l\text{ + 60l = 160} \\ 30l\text{ = 180-60} \\ 30l\text{ = 20} \\ l\text{ = }\frac{20}{30}\text{ = }\frac{2}{3} \\ \\ f\text{ = 2-}\frac{2}{3}\text{ = }\frac{4}{3} \end{gathered}[/tex]From our answer, he raced 1 1/3 (4/3) hours at 90 mph and 2/3 hours at 60 mph
How many solutions does the equation 6z + 1=2(3z -1) have?
Answer:
No solutions
Step-by-step explanation:
6z + 1 = 2(3z - 1)
6z + 1 = 6z - 2 (using pemdas you use the distributive property)
Next you want to combine like terms.
To get both z's on the same side you have to subtract it from one side. However, what you do to one side you must do to the other. Once you subtract 6z from both sides you are left with only numbers. Since you do not have a variable to solve for now this equation has no solutions.
Hope this helps!
The equation 6z + 1 = 2(3z - 1) has no solutions.
What is a solution?Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.
We have,
6z + 1 = 2(3z - 1)
Solve for z.
6z + 1 = 2 (3z - 1)
6z + 1 = 6z - 2
1 = -2
This means,
No solutions.
Thus,
There are no solutions.
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If you can buy one plantain for $0.49 then how many can you buy with $7.84
Let the unknown number of plantains be x.
It is given that one plantain costs $0.49. It is required to find the number of plantains that can be bought at $7.84.
Since one plantain can be bought for $0.49, it follows that x plantains will be bought for:
[tex]\$0.49\times x=\$0.49x[/tex]Equate this expression to the given price:
[tex]0.49x=7.84[/tex]Solve the equation for x:
[tex]\begin{gathered} 0.49x=7.84 \\ \text{Divide both sides by 0.49:} \\ \Rightarrow\frac{0.49x}{0.49}=\frac{7.84}{0.49} \\ \Rightarrow x=16 \end{gathered}[/tex]Hence, the required number of plantains that can be bought for $7.84 is 16.
The correct answer is 16 plantains.
Answer:
16
Step-by-step explanation:
1 plantain costs = $.49
how much can be bought from $7.84
7.84/.49 = 16 plantains
Select polynomial whose zeros and degree are given.Zeros: - 5(multiplicity of 3), 9(multiplicity of 2), - 2, 4Degree: 7
Given:
-5 (multiplicity of 3)
9 (multiplicity of 2)
-2 (multiplicity of 1)
4 (multiplicity of 1)
To make a polynomial with a given zeros and degrees, the first thing we need to do is to get the opposite values of the given zeros and add them to our variable x.
g (x) = 3x + 12 for x = 5
We will investigate how to evaluate a given function as per the indicated value of the independent variable.
A function is defined as a relationship between two variables ( x and y ). One of these variables mostly ( x ) is denoted as an independent quantity and ( y ) as the independent quantity.
A unique mathematical relationship is expressed between the two variables. Where, the independent variable ( x ) serves as an input to the function. The function is then evaluated on the basis of mathematical manipulation to give the output ( y ).
We have a function g ( x ) defined as follows:
[tex]g\text{ ( x ) = 3x + 12}[/tex]We are to evaluate the above function for the indicated value of the input ( independent variable ) - x as follows:
[tex]x\text{ = 5}[/tex]The process of function evaluation always start with the substitution of the indicated value of independent variable ( x ) into the function relation as follows:
[tex]g\text{ ( 5 ) = 3}\cdot(5)\text{ + 12}[/tex]Then we go about applying the basic mathematical operation defined in the relationship expressed. Keeping in mind the order in which each mathematical operator is to be performed i.e PEMDAS rule!
We will go ahead and solve our parenthesis and evaluate the function g ( x ) at x = 5 as follows:
[tex]\begin{gathered} g\text{ ( 5 ) = 15 + 12} \\ g\text{ ( 5 ) = 27} \end{gathered}[/tex]For the indicated value of the independent variable ( x = 5 ) the function g ( x ) outputs the the value of:
[tex]27\ldots\text{ Answer}[/tex]
The area of a square rug is 64 square feet. What is the perimeter of the rug?
Given data
Area of a square = 64 square feet
To find the perimeter of a rectangle, you need the length of its sides.
You can find the length of a square from the area of the square given below.
[tex]\begin{gathered} \text{Area of a square = L}^2 \\ L\text{ = length of the side} \\ \text{Next, substitute the value of area to find the length.} \\ 64=L^2 \\ \text{Next, to find the length, find the square root of both sides.} \\ \sqrt[]{64\text{ }}\text{ = }\sqrt[]{L^2} \\ L\text{ = 8 ft} \end{gathered}[/tex]Use the formula below to find the perimeter.
The perimeter of a square = 4L
= 4 x 8
= 32 feet
A quadrilateral has vertices P(-2,3) Q(4,3) R(4,1) S(-2,1). Whats the most specific classification of this quadrilateral?
To find the classification of the quadrilateral with the given vertices you can ubicate in a plane the vertices (x,y):
The vertices form a rectanglefind the midpoint of the points (3,3) and (-2,-5)
⇒To find the midpoint use the formula:
⇒[tex]M(\frac{x_{1}+x_{2} }{2} ,\frac{y_{1} +y_{2} }{2})\\M(\frac{3+(-2)}{2} ,\frac{3+(-5)}{2} )\\\\M(\frac{3-2}{2},\frac{3-5}{2} )\\M(\frac{1}{2} ,\frac{-2}{2} )\\M(\frac{1}{2} ,-1)[/tex]
Your midpoint M is given above .
GOODLUCK!!!
Answer:
Midpoint formula : ([tex]\frac{x1 + x2}{2}[/tex] , [tex]\frac{y1 + y2}{2}[/tex])
the given points are (3,3) and (-2,-5).
(3 = x1, 3 = y1) and (-2 = x2, -5 = y2).
we place them in the formula.
([tex]\frac{3 + -2}{2}[/tex] , [tex]\frac{3 + -5}{2}[/tex])
(1/2 , -2/2)
(0.5, -1) is the midpoint.
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Determine which if any of the triangles are similar. If they are then give the scale Factor
EXPLANATION
The triangles that are similar are the first and the third one. {△ABC and △RST}
The scale factor can be obtained by dividind two corresponding sides, as for instance, the hypotenuses, 12/6= 2
The scale factor is 2
4. Johnny's Cab charges a fixed cost of $3.75 plus $1.25 per kilometer.a.Write an equation that relates the fare to the distance travelled.b.What is the total cost for a 21-km ride?
a.
- The independent value is $3.75.
- The dependent value is $1.25 because it depends on the kilometer ride.
- Let us set x for each kilometer.
- Let us set F for the toral fare
Then, we can write the next equation that relates the fare to the distance.
[tex]F=3.75+1.25x[/tex]b.
If we want to find the total cost for a 21-km ride. Then, we need to set x=21 on the equation.
Hence,
[tex]\begin{gathered} F=3.75+1.25(21) \\ F=30 \end{gathered}[/tex]Hence, a 21-km ride has a total cost of $30.
Solve the following equation for bn + 3Gb = qb
To determine an equation and make b the subject:
[tex]n+3Gb=qb[/tex][tex]\begin{gathered} n+3Gb=qb \\ \text{make b the subject of the formula} \\ 3Gb-qb=-n \\ b(3G-q)=-n \\ \text{divide both side by 3G-q} \end{gathered}[/tex][tex]\begin{gathered} b(3G-q)=-n \\ \frac{b(3G-q)}{3G-q}=-\frac{n}{3G-q} \\ b=\frac{-n}{3G-q} \end{gathered}[/tex]Hence the value of b in the above expresion is
[tex]b=\frac{-n}{3G-q}[/tex]
A local theater sold 135 tickets to a matinee play with a total revenue of $2,367.00where they charged $25.00 for an adult ticket and $13.00 for a child's ticket. Usingthe variables a and c to represent the number of adult tickets sold and the number ofchildren's tickets sold respectively, determine a system of equations that describes thesituation.Enter the equations below separated by a comma.How many adult tickets were sold?How many children's tickets were sold?Pls see the picture
Given:
• Total number of tickets sold = 135
,• Total revenue = $2,367.00
,• Cost of each adult ticket = $25.00
• Cost of each child ticket = $13.00
Let's write a system of equations that describes this situation.
Let a represent number of adults tickets sold.
Let c represent number of children tickets sold.
We have the system of equations:
• a + c = 135
,• 25a + 13c = 2367
Let's solve the system using substitution method.
• Rewrite the first equation for a.
Subtract c from both sides:
a + c - c = 135 - c
a = 135 - c
• Substitute (135 - c) for a in equation 2:
25(135 - c) +13c = 2367
Apply distributive property:
25(135) + 25(-c) + 13c = 2367
3375 - 25c + 13c = 2367
3375 - 12c = 2367
• Subtract 375 from both sides:
3375 - 3375 - 12c = 2367 - 3375
-12c = -1008
Divide both sides by -12:
[tex]\begin{gathered} \frac{-12c}{-12}=\frac{-1008}{-12} \\ \\ c=84 \end{gathered}[/tex]Substitute 84 for c in any of the equations:
a = 135 - c
a = 135 - 84
a = 51
We have:
a = 51, c = 84
Therefore, 51 adult tickets and 84 children tickets were sold.
ANSWER:
• System of equations:
a + c = 135, 25a + 13c = 2367
• Number of adult tickets sold = 51
,• Number of children tickets sold = 84
Drag each example to the correct mathematical property listed.DRAG & DROP THE ANSWERAdditive IdentityAdditive Inversea.l=a12. = 1a + 0 = aa +(-a) = 0Multiplicative IdentityMultiplicative Inverse
Explanation:
[tex]\begin{gathered} a\text{ }\times\text{ }\frac{1}{a}\text{ }=\text{ 1} \\ \frac{1}{a\text{ }}is\text{ the invers of a} \\ This\text{ is }Multiplicative\text{ inverse} \end{gathered}[/tex][tex]\begin{gathered} a\text{ + (-a)} \\ -a\text{ is the inverse of a} \\ So\text{ this is additive inverse} \end{gathered}[/tex][tex]\begin{gathered} a\text{ + 0 = a} \\ \text{Adding zero to a number gives back same number} \\ \text{This is additive identity} \end{gathered}[/tex][tex]undefined[/tex]your cell phone bill is $24.99 per month plus $0.16 for each text you send or receive. you have at most $29 to spend on your cell phone bill. What is the maximum number of texts you can send or receive next month?
The maximum number of texts to send or received in next month will be
25.
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
Cell phone bill = $24.99 per month
Cost of each text to send or receive = $0.16
Now,
You have at most $29 to spend on your cell phone bill.
Let number of text to send or receive = x
So, We can formulate;
$24.99 + $0.16x < $29
Solve for x as;
$24.99 + $0.16x < $29
Subtract 24.99 we get;
$0.16x < $29 - $24.99
$0.16x < $4.01
Divide by 0.16 we get;
x < 25.06
After rounding we get;
x < 25
Thus, The maximum number of texts to send or received in next month will be 25.
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It takes 15 minutes to paint 1/15 of the fence. How long is it going to take her to paint the whole entire fence
For this problem, we were informed that 1/15 of the fence was painted in 15 minutes. We need to calculate the time it will take to paint the whole fence, assuming that the same speed is maintained.
In order to do that we need to assign a variable "t" to the time it will take to paint the fence, then we need to multiply the fraction 1/15 with this variable, and make it equal to 15 minutes, then we need to solve for "t". This is done below:
[tex]\begin{gathered} \frac{t}{15}=15 \\ t=225\text{ minutes} \end{gathered}[/tex]The process of painting the whole fence will take 225 minutes at that rate.