The equations are e = 18+12t and a = 45+9t
Adrian will be father along in the book after 4 days. She will be 15 pages ahead of Ethan
Ethan's page number at the beginning of the month = 18
Adrian's page number at the beginning of the month = 45
Pages read by Ethan each day = 12 pages
Pages read by Adrian each day = 9 pages
Let e represent the page of the book that Ethan is on at the end of t days into the month. Let a represent the page of the book that Adrian is on at the end of t days into the month.
Formulating the equation we get the following:
e = 18 + 12t
a = 45 + 9t
Finding the page number of both Ethan and Adrian after 4 days by substituting the values in the equations we get:
e = 18+12(4)
e = 66
a = 45 + 9(4)
a = 81
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can you help me solve part A and B ASAP! THANKYOU
The shape comprises a semicircle, rectangle, and a trapezoid
A) The shape below will illustrate how the side length of the rectangle will be calculated
Part I is the semicircle of diameter
[tex]\begin{gathered} d=8\operatorname{cm} \\ r=\frac{d}{2} \\ r=\frac{8}{2}=4\operatorname{cm} \end{gathered}[/tex]From the diagram above
[tex]AB=r=4\operatorname{cm}[/tex]To find the missing side length of the rectangle , we will use the relation below
[tex]AB+BC+CD=12\operatorname{cm}[/tex]Where.
[tex]\begin{gathered} AB=4\operatorname{cm} \\ CD=3.5\operatorname{cm} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} AB+BC+CD=12\operatorname{cm} \\ 4+BC+3.5=12\operatorname{cm} \\ 7.5+BC=12\operatorname{cm} \\ BC=12-7.5 \\ BC=4.5cm \end{gathered}[/tex]The missing side length of the rectangle is = 4.5 cm
Hence,
The rectangle can be represented below as
The formula for the area of the rectangle is
[tex]\begin{gathered} A_{\text{rectangle}}=\text{length}\times breadth \\ \text{where,} \\ \text{length}=8\operatorname{cm} \\ \text{breadth}=4.5\operatorname{cm} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} A_{\text{rectangle}}=\text{length}\times breadth \\ A_{\text{rectangle}}=8\operatorname{cm}\times4.5\operatorname{cm} \\ A_{\text{rectangle}}=36\operatorname{cm}^2 \end{gathered}[/tex]Hence,
The Area of the rectangle = 36cm²
B) To calculate the area of the semicircle, we will use the formula below
[tex]\begin{gathered} A_{\text{semicircle}}=\frac{\pi\times r^2}{2} \\ \text{where,} \\ r=4\operatorname{cm} \end{gathered}[/tex]By substituting the values , we will have
[tex]\begin{gathered} A_{\text{semicircle}}=\frac{\pi\times r^2}{2} \\ A_{\text{semicircle}}=\frac{\pi\times4^2}{2}=\frac{16\pi}{2}=8\pi \\ A_{\text{semicircle}}=25.13\operatorname{cm}^2 \end{gathered}[/tex]Hence,
The area of the semicircle = 25.13 cm²
To calculate the area of the trapezoid, we will use the formula below
[tex]\begin{gathered} A_{\text{trapezoid}}=\frac{1}{2}(a+b)\times h \\ \text{where,} \\ a=8\operatorname{cm} \\ b=15\operatorname{cm} \\ h=3.5\operatorname{cm} \end{gathered}[/tex]The diagram below represents the trapezoid
By substituting the values, we will have
[tex]\begin{gathered} A_{\text{trapezoid}}=\frac{1}{2}(a+b)\times h \\ A_{\text{trapezoid}}=\frac{1}{2}(8\operatorname{cm}+15\operatorname{cm})\times3.5\operatorname{cm} \\ A_{\text{trapezoid}}=\frac{1}{2}(23\operatorname{cm})\times3.5\operatorname{cm} \\ A_{\text{trapezoid}}=\frac{80.5\operatorname{cm}}{2} \\ A_{\text{trapezoid}}=40.25\operatorname{cm}^2 \end{gathered}[/tex]Hence,
The area of the trapezoid is = 40.25cm²
To calculate the total area of the shape, we will use the formula below
[tex]\begin{gathered} \text{Total area=} \\ =A_{\text{SEMICIRCLE}}+A_{\text{RECTANGLE}}+A_{\text{TRAPEZOID}} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \text{Total area=}A_{\text{SEMICIRCLE}}+A_{\text{RECTANGLE}}+A_{\text{TRAPEZOID}} \\ \text{Total area}=25.13\operatorname{cm}+36\operatorname{cm}+40.25\operatorname{cm}^2 \\ \text{Total area}=101.38\operatorname{cm}^2 \end{gathered}[/tex]Hence,
The Total Area of the composite shape = 101.38cm²
Select all input values for which f(x) =3.
Answer:
B. x = -3
Step-by-step explanation:
f(x) = y
or however the vertical axis is called.
that is just something you always have to consider.
so, for what value of x does the functional curve ever reach the result (y) value of 3 ?
imagine a horizontal line you put through y = 3.
at what points is the functional graph touching or intersecting this line ?
at exactly 1 point. and that is at x = -3.
expressions for 50-42+10
Answer: look it up on calculator
Step-by-step explanation:
What is the complete factorization of 6x2 + 9x - 6?
A. 3(2x - 1)(x + 2)
B. (3x + 2)(2x - 3)
C. 3(x-2)(2x + 1)
D. 3(x-2)(2x - 1)
Answer: A. 3(2x−1)(x+2)
2.) The amount of sleep that elementary school children get per night follows a Normal distribution with a
mean of 9.5 hours and a standard deviation of 0.55 hours.
a.) Find the proportion of elementary school children who get between 9 and 10 hours of sleep per
night. Sketch the Normal curve and shade the area under the curve that is the answer to the
question.
The proportion of elementary school children who get between 9 and 10 hours of sleep per night is 0.6367 or 63.67%.
The amount of sleep that elementary school children get per night be denoted by X, X follows a Normal distribution with a mean of 9.5 hours and a standard deviation of 0.55 hours.
the proportion of elementary school children who get between 9 and 10 hours of sleep per night is equal to
P(9≤ X ≤ 10) = P((9 - 9.50)/0.55 ≤ Z ≤ (10 - 9.50)/0.55)
P(9≤ X ≤ 10) = P(-0.9091 ≤ Z ≤ 0.9091)
P(9≤ X ≤ 10) = 0.6367
P(X > 12) = P(Z>(12 - 9.50)/0.55)
P(X > 12) = P(Z>4.5455
P(X> 12) = 0.000
THere is zero possibility of student to get more than 12 houtrs of sleep
The proportion of elementary school children who get between 9 and 10 hours of sleep per night is 0.6367 or 63.67%.
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how can i find the angle of elevation of the sun to nearest degree?
SOLUTION
From the diagram at the right of the question, a right-angle has been formed already. So we will use SOHCAHTOA to find angle A. Looking at angle A, the opposite side is 140 ft and the adjacent side is 173 ft.
Using TOA, we have
[tex]\begin{gathered} TOA,tanA=\frac{opposite}{adjacent} \\ tanA=\frac{140}{173} \\ tanA=0.80924855 \\ A=tan^{-1}0.80924855 \\ A=38.98146539 \end{gathered}[/tex]Hence the answer is 39 degrees
What is the value of X in the equation 1/5x - 2/3y = 30, when y = 15?
Answer:
x = 200
Step-by-step explanation:
a) Simplify both sides of the equation.
1/5x - 2/3(15) = 30
1/5x + -10 = 30
1/5x - 10 = 30
b) Add 10 to both sides.
1/5x - 10 + 10 = 30 + 10
1/5x = 40
c) Multiply both sides by 5.
5 * (1/5x) = (5) * (40)
x = 200
Evaluate express your answer in exact simplest form9P4=
The formula for Permutation is,
[tex]^nP_r=\frac{n!}{\left(n-r\right)!}[/tex]The expression given is,
[tex]^9P_4[/tex]Given:
[tex]n=9,r=4[/tex]Plug in n = 9, r = 4
[tex]\frac{9!}{\left(9-4\right)!}[/tex]Simplify
[tex]\frac{9!}{5!}=\frac{9\times8\times7\times6\times5!}{5!}=9\times8\times7\times6=3024[/tex]Hence, the answer is 3,024.
What are the solutions to the inequality (x-3)(x=5)greater than or equal to 0
The solution of the inequality (x-3)(x-5) ≥ 0 is union of two intervals
(-∞,3] or [5,∞) that is x ≥5 or x≤3
What is an inequality and how to solve it?An inequality is a statement that compares two expressions using ≤, ≥, <, > .
We can solve an inequality by adding same number to both sides or by subtracting same number from both side. While adding or subtracting the sign of the inequality will not change.
Given inequality (x-3)(x-5) ≥ 0
It generates two cases either case1 is true or case 2.
Case1. (x-3)(x-5) ≥ 0 when (x-3) ≥0 and (x-5)≥0
⇒(x-3) ≥0 and (x-5)≥0
⇒ x ≥ 3 and x ≥ 5
⇒ x ∈ [3,∞) and x∈ [5,∞)
⇒ x ∈ [3,∞) ∩[5,∞)
⇒ x ∈ [5,∞)
∴ x is greater than or equal to 5
Case 2: (x-3)(x-5) ≥ 0 when (x-3) ≤0 and (x-5)≤0
⇒(x-3) ≤0 and (x-5)≤0
⇒ x ≤3 and x ≤ 5
⇒ x ∈ (-∞,3] and x∈ (-∞,5]
⇒ x ∈ (-∞,3] ∩ (-∞,5]
⇒ x ∈ (-∞,3]
∴ x is less than or equal to 3
Solution of the given inequality is case 1 or case 2
⇒ x ∈ [5,∞) or x ∈ (-∞,3]
⇒ x x ∈ (-∞,3] ∪ [5,∞)
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To solve the inequality StartFraction m over negative 7 EndFraction less-than-or-equal-to 14, what should be done to both sides? I NEED TO GET THIS DONE NOW HELP IM SO CONFUSED
To solve the inequality given by -n/7 ≤ 14 , -7 should be multiplied to both sides of the inequality .
Any monotonically rising function can, by definition, be applied to both sides of an inequality without changing their connection to one another (provided that both expressions are in the domain of that function).
If a monotonically falling function were applied to both sides of an inequality, the inequality relation would be reversed.The rules for the additive inverse and the multiplicative inverse for positive numbers serve as illustrations of the use of a monotonically declining function.If the function is strictly monotonic and the inequality is strict (a b, a > b), the inequality remains strict.If only one of these conditions is fulfilled, the resulting inequality is not strict. The conditions for both additive and multiplicative inverses really serve as a demonstration that a strictly monotonically dropping function is being applied.The inequality is -n/7 = 14
or, -n ≤ 14 × 7
or, -n ≤ 98
or, n ≥ -98
Therefore the first step is solve the inequality is to multiply both sides by 7.
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find the dimensions of the page that will require the minimum amount of paper
Let's use the variable x to represent the length of the paper and y to represent the width of the paper.
If there are margins of 1 inch along the sides and 3 inches along the top and bottom, and the area with printer matter is 27 in², we can write the equation:
[tex](x-2)\cdot(y-6)=27[/tex]Solving for x, we have:
[tex]\begin{gathered} x-2=\frac{27}{y-6} \\ x=\frac{27}{y-6}+2 \end{gathered}[/tex]Then, the equation that we want to minimize is the area equation, so:
[tex]\begin{gathered} A=x\cdot y \\ A=(\frac{27}{y-6}+2)\cdot y \\ A=(\frac{27+2(y-6)_{}}{y-6})y_{} \\ A=(\frac{27+2y-12}{y-6})y \\ A=(\frac{2y+15}{y-6})y \\ A=\frac{2y^2+15y}{y-6} \end{gathered}[/tex]The critical points of this function are:
y = 0 (one of the roots)
y = -15/2 (one of the roots)
y = 6 (function is not defined)
How much would a 5% tip be on a bill that cost $75.00?
Answer:
Step-by-step explanation:
it would be a 20% tip
Answer:
3.75
Step-by-step explanation:
5% of 75 is 3.75
Round to nearest hundred thousand
449,387 rounds to _,and 350,030rounds to _.what is the estimate of 449,387+350,030
Answer:
800,000
Step-by-step explanation:
Rectangle A is 5 in by 7 in. If the scale factor is 4, what is the area of the new rectangle B? How does it compare with the first rectangle?
The area of rectangle B is 560 square inches.
What is the area of rectangle?Area of rectangle is the region occupied by a rectangle within its four sides or boundaries. The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle.
Given that,
Scale factor = 4
Rectangle A has
length = 5 inches
breadth = 7 inches
Area of a rectangle A = length×breadth
= 5×7
= 35 square inches
Scale factor is 4 so length and width of a new rectangle is
length = 5×4 = 20 inches
breadth = 7×4 = 28 inches
Area of a rectangle B = length×breadth
= 20×28
= 560 square inches
Hence, The area of rectangle B is 560 square inches.
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a bag contains 8 green marbles and 12 blue marbles. You draw a marble, return it to the bag and draw another. What is the possibility of drawing two green marbles
Answer:
2/5
Step-by-step explanation:
8+12=20
8/20 12/20
8 ÷ 4= 2
20÷4= 5
2/5
What’s 12:28 reduced
Answer: Reduce 12/28 to the lowest terms The simplest form of 12 28 is 3 7.
Step-by-step explanation: I hope this helps!
ANSWER QUICK I WILL GIVE BRAINLIEST!
the difference between a number and seven eighths exceeds negative two thirds f plus 7 over 8 is greater than 2 over 3 f minus 7 over 8 is less than or equal to negative 2 over 3 f minus 7 over 8 is greater than negative 2 over 3 f minus 7 over 8 is less than negative 2 over 3
The correct statement is f minus 7 over 8 is greater than negative 2 over 3. Option C
What are inequalities?Inequalities are defined as mathematical relation with an unequal comparison between two numbers, elements, quantities or mathematical expressions.
They are mostly used in the comparison of two numbers on the number line on the basis of their size of magnitude.
From the information given, we have that;
The difference between a number and seven eighthsIt also exceeds negative two thirdsLet the number be f
This is expressed as;
f - 7/8 > -2/3
This is written in word form as;
f minus 7 over 8 is greater than negative 2 over 3
Hence, the expression is f - 7/8 > -2/3
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Answer:
Step-by-step explanation:
c i have spoken
Solve one half equals one-fourth times the quantity y plus one-eighth end quantity for y.
y equals one half
y equals three fourths
y equals fifteen over eight
y equals three halves
Like can you do this quickly lol
The value of y in the equation 1/2 = 1/4y + 1/8y when solved is y = 4/3 .
A linear equation in one variable is defined as an equality between two expression either or both containing the variable .
A linear polynomial over a field, from which the coefficients are taken, can be reduced to a linear equation by equating it to zero.There is only one answer when there is only one variable. The term "linear equation" frequently alludes indirectly to this specific situation, in which the variable is appropriately referred to as the "unknown."When we say we've solved an equation, we mean we've found the value of the variable that, if we plugged it into the equation, would make it true or balanced.The given expression can be written a linear equation of the form :
1/2 = 1/4y + 1/8y
Simplifying the equation we get :
y = 4 / 3
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NEED HELP ASAP 9TH Grade
The equation that passes through the given points is the 3 option which is y = -3/2 x + 5
What are linear equation?A x + B y = C represents a two-variable linear equation in its standard form. As an illustration, the conventional form of the linear equation 2x + 3y = 5 It is rather simple to locate both intercepts when an equation is stated in this way (x and y). An algebraic equation with simply a constant and a first-order (linear) term, such as y = mx +b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Ax + b = 0, where a and b are two integers, and x is a variable, is an example of a linear equation with one variable. This equation has only one solution. 2x + 3 = 8, for instance.
According to the given points
x = -1
So
y = (-3/2)(-1) + 5
y = 6.5
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the ratio of bots to girls in a school is nine : ten. what does this ratio mean. if there are 300 girls at the school, how many total students are at the school.
The number of the total students that are at the school is 570 if the ratio of boys to girls in a school is nine: ten and there are 300 girls at the school.
What is the ratio formula?The ratio formula is given as a:b = a/b for any two quantities, let's say a and b.
Given that a and b are separate amounts for two quantities, the combined total quantity is denoted as (a + b).
How are these ratio difficulties solved?Three steps are necessary to determine the ratio of three numbers:
Step 1: Add the ratio's numbers together to determine the total number of pieces.
Step 2: By dividing the given sum by the total number of parts, determine the value of each component in the ratio.
Step 3: Divide the original ratio by the sum of each component's values.
The ratio is given as 9:10 as boys to girls.
Number of girls = 300
Thus, girls will be 10x and boys will be 9x
then 10x = 300
⇒x = 30
Then we can calculate the number of boys as
9x = 9*30
=270
Thus, the total number of students in the school
= exact number of girls + exact number of boys
= 300 + 270
= 570
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Divide 2x2 7x â€"" 3 by 2x 5. which expression represents the quotient and remainder? x 1 x 1 â€"" x 1 x 1 â€""
The required solution of given polynomial equation is [tex]x+1-\frac{8}{2x+5}[/tex] .
Given polynomial equation is [tex]2x^{2}+7x-3[/tex] which is to be divided by [tex]2x+5[/tex]
In case of division of polynomials we Long division method to calculate final value of the given equation.
For solving given equation let us start from;
[tex]\frac{2x^{2} +7x-3}{2x+5}[/tex] = [tex]x+\frac{2x-3}{2x+5}[/tex]
[tex]x+\frac{2x-3}{2x+5}[/tex] = [tex]x+1 +\frac{-8}{2x+5}[/tex]
[tex]x+1-\frac{8}{2x+5}[/tex]
The final solution for given equation is [tex]x+1-\frac{8}{2x+5}[/tex]
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Here are Ryan's scores in nine French tests.
4
6
4
7
8
a
6
7
7
The mean of Ryan's nine scores is 6
Work out the value of a.
Answer:
a = 5
Step-by-step explanation:
the mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
= [tex]\frac{4+6+4+7+8+a+6+7+7}{9}[/tex] = 6 ( multiply both sides by 9 to clear fraction )
49 + a = 54 ( subtract 49 from both sides )
a = 5
problem 2 select all of the equations that represent a proportional relationship. (select all that apply.) the remaining length, , of a -inch rope after inches have been cut off: . the total cost, , after an sales tax is added to an item's price, : . the number of marbles each sister gets, , when marbles are shared equally among four sisters: . the volume, , of a rectangular prism whose height is cm and base is a square with side lengths cm: .
An equation represents proportional relationship when dividing the quantities of the equation results in a quotient that is always the same.
Equation: y = mx and m is a constant value, which means is the same.
A. Equation: 120 - x = L
Equation from alternative A is NOT proportional since the division of the quantities doesn't result in a constant.
B. Equation: 1.08p = t
Dividing total cost per item's price, will always give the sales tax, which is constant. So, this equation IS proportional.
t/p=1.08
C. Equation: x=m/4
This equation is proportional because dividing marbles per how much each sister gets, always gives the number of sisters:
m/x=4
D. Equation: V= 12s^2
This equation is NOT proportional because side length is squared, so it is not constant linearly.
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In the diagram AB = CD and CD = BC find BC
Answer:
BC = 10
Step-by-step explanation:
given CD ≅ BC , then
BC = CD , that is
3x + 1 = 13 - x ( add x to both sides )
4x + 1 = 13 ( subtract 1 from both sides )
4x = 12 ( divide both sides by 4 )
x = 3
Then
BC = 3x + 1 = 3(3) + 1 = 9 + 1 = 10
A triangle on a sphere could have ___ degrees.
OA. 160
OB. 200
OC. 180
OD. any number of
Answer:
the anwser is 180
Step-by-step explanation:
Ahmed recorded a temperature drop of 2 degree F and a second temperature drop of 3 degree F. What is the total change in temperature?
Answer:
a drop of 5 degree F, or -5 °F
Step-by-step explanation:
You want to know the total change in temperature after a drop of 2 degree F and a second temperature drop of 3 degree F.
ChangeThe total change will be the sum of changes.
We can figure the total drop in temperature as the sum of drops:
2 °F +3 °F = 5 °F . . . . the total drop in temperature
If we use negative values to represent temperature drops, then the total change can be written as ...
(-2 °F) +(-3 °F) = -5 °F . . . . . the total change in temperature
__
Additional comment
We often find it convenient to use negative numbers to represent decreases, drops, amounts below some reference level, and so on. Positive numbers can be used for the same purpose if we define the meaning of a positive number in the context.
Here, we can identify a temperature drop by saying it is a drop of 5 degrees, where a positive temperature drop means a change to a lower value. Or, we can say it is a change of -5 degrees, where a positive change is defined as a change to a higher value.
Defining the meaning of positive and negative numbers is especially important when an "improvement" is a reduction in some value (cost, for example). A positive improvement may mean a negative change, and vice versa.
HELP HELP HELP What is the x-intercept of the line with this equation −5x+15y=15 ?
<3
Answer: (-3, 0)
Step-by-step explanation: Isolate the y variable, so you get 15y = 15 + 5x, then divide by 15, y = 1 + 1/3x. To get the x intercept, the y has to be equal to 0, so we get 0 = 1 + 1/3x.
0 = 1+1/3x
-1 = 1/3x
-3 = x
Answer:
x = - 3
Step-by-step explanation:
To get the x intercept, y has to be equal to 0.
- 5·x + 15·y = 15
- 5·x + 15·0 = 15
- 5·x = 15
x = 15/(- 5)
x = - 3
when a plumber is called the cost of the service call is 65$ for them to show up at your house, plus an additional $30 per hour
PLEASE SOLVE ALL OF THEM I WILL GIVE U THE WORLD
Answer:
Step-by-step explanation:
y=30x+65
y=30(3)+65
y=90+65
y=155
5. What is the main doman and range of the roller coaster? (Hint: you should express these as a compound inequality or in interval notation
Answer:
If you’re in the mood for a scary movie, you may want to check out one of the five most popular horror movies of all time—I am Legend, Hannibal, The Ring, The Grudge, and The Conjuring. Figure 1 shows the amount, in dollars, each of those movies grossed when they were released as well as the ticket sales for horror movies in general by year. Notice that we can use the data to create a function of the amount each movie earned or the total ticket sales for all horror movies by year. In creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the domain and range. In this section we will investigate methods for determining the domain and range of functions such as these.
Step-by-step explanation:
Please help! Really struggling on this subject! ASAP
Given the function below, determine the following.
f(x)= 10x +8
Find f(5).
Find f(-7).
Find a if f(x) = 88.
Answer:
Solutions Below.
Step-by-step explanation:
These questions test on the concept of Functions Substitution.
Function SubstitutionFunction Substitution is about giving an input (domain) to a function to produce an output (range)
Example: f(x) = 9x , f(9) = 9(9) = 81
ApplicationWe are given the following function:
f(x) = 10x + 8, where we can express it as
y = 10x + 8
Now we can find the value of f(5) by substituting x = 5 into the function. (Meaning: Find the value of y when x = 5.)
f(5) = y = 10(5) + 8 = 50 + 8 = 58
Next, applying the same concept, we can find the value of f(-7) by substituting x = - 7 into the function. (Meaning: Find the value of y when x = -7.)
f(-7) = y = 10(-7) + 8 = -70 + 8 = - 62
This last question requires us to work in reverse, where we find the value of x when f(x) = y = 88.
f(x) = y = 10x + 8
10x + 8 = 88
10x = 88 - 8
10x = 80
x = 80 ÷ 10 = 8