Using basic mathematical operations such as addition and subtraction, they purchase 2054 more books for Oak Hill than Elm Street and Woodland combined.
Elm Street = 4,432 books
Oak Hill = 12,398 books
Woodland = 5,912 books
Using addition, we can determine how many books are purchased for Elm Street and Woodland combined by adding their values.
Elm Street + Woodland
4,432 + 5,912 = 10,344
Using subtraction, determine how many more books did they purchase for Oak Hill than Elm Street and Woodland combined.
Oak Hill - (Elm Street + Woodland)
12,398 - 10,344 = 2054 books
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Which is the equation of a line perpendicular to line AB?
Answer:
Step-by-step explanation:
y = -3x + 7
since the slope of the line AB = (4 - 2) /( 3 - (-3)) = 1/3
slope of line perpendicular to AB will be -3
Greg bought a blanket for $36.62, a flag for $11.25, and a glove for $17.75. He paid $60 and the rest he borrowed from his friend. If Greg got $4.38 in change from the cashier, how much did he borrow from his friend to pay for all the items?
Answer:
$10
Step-by-step explanation:
Let's begin with adding all of the items Greg bought.
36.62 + 11.25 + 17.75 = 65.62
Let the money paid to the cashier be x.
Now, it's stated he paid 60 dollars to the cashier and that he also got $4.38 back from the cashier.
Then, it must be that x=65.62+4.38
x=70
The money he borrowed from friend = 70-60=10
Therefore, the money Greg borrowed from his friend to pay for all the items is $10.
Greg borrowed $1.24 from his friend.
What is Unitary Method?A single unit's value may be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. We typically utilise this technique for math computations.
This approach allows us to calculate both the value of many units from the value of one unit and the value of many units from the value of one unit.
Given:
Greg bought a blanket for $36.62,
a flag for $11.25,
and a glove for $17.75.
Total expense of the objects he brought
= 36.62+ 11.25 + 17.75
= $65.62
He paid $60 then
=65.62 - 60 = $5.62 remaining
Also, he got $4.38 in change from the cashier
= 5.62 - 4.38
= $1.24.
Hence, Greg borrowed $1.24 from his friend.
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Write an equivalent expression by distributing the "-−" sign outside the parentheses: -(-8.2w+10) −(−8.2w+10)
The equivalent expression by distributing the sign outside the parentheses: -(-8.2w+10) −(−8.2w+10) will be 16.4w - 20.
How to calculate the value?It should be noted that bwsed on the information given, the expression is illustrated as:
-(-8.2w+10) −(−8.2w+10)
The signs should be taken into consideration. This will be:
-(-8.2w+10) −(−8.2w+10)
= 8.2w - 10 + 8.2w - 10
= 16.4w - 20
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Ava's sister is 9 years less than twice Ava's age b
Answer:
2b + 9
Hope this helps :)
Step-by-step explanation:
This equation shows the statement, "Ava's sister is 9 years less than twice Ava's age b."
i need help fast pleeeeas hurry
3 3/8 - 2 1/4 ÷ 1 1/2 - in the simplest form of a fraction
Answer:
1 7/8
Step-by-step explanation:
First convert mixed fraction to improper fraction. Then do division using KCF method. Then do subtraction.KCF method.
Keep the first fractionChange division to multiplicationFlip the second fraction[tex]\sf 3 \dfrac{3}{8}-2\dfrac{1}{4} \div 1\dfrac{1}{2}= \dfrac{27}{8}-\dfrac{9}{4}\div\dfrac{3}{2} \\\\[/tex]
[tex]\sf = \dfrac{27}{8}-\dfrac{9}{4}*\dfrac{2}{3}\\\\=\dfrac{27}{8}-\dfrac{3}{2}\\\\=\dfrac{27}{8}-\dfrac{3*4}{2*4} \ [\text{LCM of 2 and 8 is 8}]\\\\=\dfrac{27}{8}-\dfrac{12}{8}\\\\=\dfrac{27-12}{8}\\\\=\dfrac{15}{8}\\\\=1\dfrac{7}{8}[/tex]
a. Use your calculator to generate an arithmetic sequence with a common difference of -7 . How could you use a calculator to find the 6th term? The 8th term? The 20th term?
The 20th term of the arithmetic sequence is 122.
What is arithmetic sequence?nth term = a1 + d(n - 1) so here:
20th term = -30 + 8(20 - 1)
- 30 + 152
[tex]a_{20}[/tex] = 122.
An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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Need da answer pls and thank u point will be 100
The lessons from Clare B. Dunkie's The Hollow Kingdom, and the quote it matches are:
"If you love her enough to give up your world for her, don't you think she would want to do the same for you?" - People are willing to make sacrifices for the people they care about.She looked around at the stars, the moon, the trees. These were things she could count on. - Nature can be a source of courage and comfort.What are some lessons from Clare B. Dunkie's The Hollow Kingdom?One lesson that we see is that people who care about someone, are able to make sacrifices to ensure the wellbeing of that person. We see it with the narrator saying that the person loved another so much that they sacrificed their world for that person.
Another less is that nature can often help us gain the courage we need to do something. This is shown with the subject looking to the moon and stars to back her up.
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Write the equation of each line in slope-intercept form. y/9 + x/3 = 2
The Slope-intercept form of the given equation is y = -3x + 18 .
An equation in Slope-intercept form is of the form
[tex]y = mx + b[/tex]
where m is the slope and b is the y intercept.
Now, the given equation is (y/9) + (x/3) = 2
Taking LCM on the left hand side of the equation, we get
⇒ [tex](3y+9x)/(2y) = 2[/tex]
⇒ 3y + 9x = 54
⇒ 3y = 54 - 9x
Dividing both side of the equation by 3, we get
⇒ y = [tex](54 - 9x)/3[/tex]
⇒ y = 18 - 3x
⇒ y = -3x + 18
∴ The equation y = -3x + 18 is in Slope-intercept form.
In the equation the slope is -3 and the y-intercept is 18.
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Consider the functions f(x)=4^x and g(x)=x-2. The function y is defined as y=f(g(x)) state the equation for y.
the equation for y will be y = 4ˣ / 16 when the function y is defined as y = f ( g ( x ) ).
We are given the functions:
f ( x ) = 4ˣ
g ( x ) = x - 2
Now, we have a function y defined as:
y = f ( g ( x ) )
Now, we need to find the equation for y.
We know that:
f ( g ( x ) ) = 4⁽ ˣ⁻ ² ⁾
f ( g ( x ) ) = 4ˣ / 4²
f ( g ( x ) ) = 4ˣ / 16
Therefore, we get that, the equation for y will be y = 4ˣ / 16 when the function y is defined as y = f ( g ( x ) ).
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Mt.Whitney is the highest peak in California at 14,949 feet. The city of El Centro, also in California, is 39 feet below sea level. What is the difference in elevation between in Mt. Whitney’s peak and city of El Centro?
Answer:
if the peak level is 14949 above sea level , so the difference in elevation is 14949 + 39 =14988 feet
#1: Jane has 6 feet of ribbon. If one
meter is about 3 feet, how many
meters of ribbon does Jane have?
O 12
02
O
O 1
Answer: jane has 1.5 meters of ribbon
Step-by-step explanation:
x2+6x−16 vertex form
Answer:
Hello,
Step-by-step explanation:
[tex]x^2+6x-16\\\\=x^2+2*3x+3^2-9-16\\\\=(x+3)^2-25\\[/tex]
Under her cell phone plan, Caroline pays a flat cost of $54.50 per month and $5 per gigabyte. She wants to keep her bill at $74 per month. Write and solve an equation which can be used to determine gg, the number of gigabytes of data Caroline can use while staying within her budget.
Answer:
5 gg
Step-by-step explanation:
Let us treat the number of gigabytes of data she can use (at max) per month as x.
We can say that [tex]54.5 + 5x = 74[/tex] will always be deducted from her and $5x per month for the extra data she uses.
[tex]54.5 + 5x = 74[/tex]
⇒ [tex]5x = 74 - 54.5[/tex]
⇒ [tex]5x = 25.5[/tex]
⇒ [tex]x = 25.5 / 5[/tex]
⇒ [tex]x = 5.1[/tex]
As she can only buy a fixed number of data, which cannot be a decimal, let us take the number directly below 5.1 - which is 5 - as the answer.
Caroline can use up to 5gg of data
Write a definite integral that represents the area of the region. (do not evaluate the integral.) y1 = x2 2x 3 y2 = 2x 12
The definite integral that represents the area of the region under the given curves is: [tex]\int\limits^3_{-3} {x^2-9} \, dx[/tex]
What is the area of the region under a curve?By performing a definite integral between the two locations, one can determine the area under a curve between two points. Integrate y = f(x) between the limits of a and b to determine the area under the curve y = f(x) between x = a & x = b. With the specified limits, integration can be used to calculate this area.Given:
[tex]y_1=x^2+2x+3[/tex][tex]y_2=2x+12[/tex]The points where the two intersect will be given by:
y₁ = y₂
=> x² + 2x + 3 = 2x + 12
=> x² + 3 = 12
=> x² = 9
=> x = ± 3
For x₁ = 3, y₁ = 2(3) + 12 = 18 => (x₁, y₁) = (3, 18)
For x₂ = -3, y₂ = 2(-3) + 12 = 6 => (x₂, y₂) = (-3, 6)
Now, for the area of the region under first curve [tex]y_1=x^2+2x+3[/tex]:
A₁ = [tex]\int\limits^3_{-3} {x^2+2x+12} \, dx[/tex]
For the area of the region under the second curve [tex]y_2=2x+12[/tex]:
A₂ = [tex]\int\limits^3_{-3} {2x+12} \, dx[/tex]
For the required area of the region bounded by the two curves will be given by:
A = A₂ - A₁ = [tex]\int\limits^3_{-3} {x^2+2x+3 - (2x +12)} \, dx[/tex]
A = [tex]\int\limits^3_{-3} {x^2-9} \, dx[/tex]
Refer to the image for the area so bounded by the curves.
Hence, The definite integral that represents the area of the region under the given curves is: [tex]\int\limits^3_{-3} {x^2-9} \, dx[/tex].
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Find the diameter and radius of a circle with the given circumference. Round to the nearest hundredth.
C = 124ft
A circle is a curve sketched out by a point moving in a plane. The radius and the diameter of the circle are 19.73 ft and 39.46 ft, respectively.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
Given that circumference of the circle as 124 ft. Therefore, the radius and the diameter of the circle can be written as,
Circumference of circle = 2 × π × (Radius of the circle)
124 ft = 2 × π × (Radius of the circle)
(Radius of the circle) = 124 ft/ (2 × π)
The radius of the circle = 19.73 ft
Diameter of circle = 2 × (Radius of the circle)
= 2 × 19.73 ft
= 39.46 ft
Hence, the radius and the diameter of the circle are 19.73 ft and 39.46 ft, respectively.
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I need help please I’m lost
Angle Pairs and their Relationships HW
4)
The measures of the angles m∠1 and m∠2 are: m∠1 = 109 and m∠2 = 71
What is Linear pair angles ?Linear pair angles are two angles which are adjacents and supplementary.
Given that: m∠2 and m∠1 form a linear pair
we know that the angles and are supplementary, which means that they add up to 180 degrees.
In order to solve for "x," we can write the following expression:
180 = (5x + 9) + (3x + 11)
8x = 180 - 20
x = [tex]\frac{160}{8}[/tex]
x = 20
Therefore, substituting, we get that the measures of the angles and are
m∠1 = 5(20) +9 = 109
m∠2 = 3(20) + 11 = 71
5)
the angle m∠2 = 86°
Given that m∠1 and m∠2 are vertical angles and m∠1 = (17x + 1) and m∠2 = (20x - 14)
Vertical angles are always congruent
m∠1 = 17x + 1
m∠2 = 20x - 14
Since ∠1 and ∠2 are vertical:
m∠1 = m∠2
17x + 1 = 20x - 14
Collect like terms
20x - 17x = 1 + 14
3x = 15
Divide both sides by 3
3x / 3 = 15/3
x = 5
m∠2 = 20x - 14
m∠2 = 20(5) - 14
m∠2 = 100 - 14
m∠2 = 86°
6)
The value of each angle that is p=119 and q=61
In light of this, the measure of an angle is P, which is three less than the measure of angle q.
P + q = 180 ( By definition of supplementary)
p = 2q -3
Substitute the value
Then ,we get
2q - 3 + q =180
3q = 180 + 3
3q = 183
q= [tex]\frac{183}{3}[/tex]
= 61
then, if you substitute q's value, you get
p= 2(61) - 3 = 122 - 3 = 11.9
Hence, p= 119 and q= 61
7)
The value of x is 19°
Given that : ∠DBE =2x - 1
∠CBE =5x – 42 and BD is perpendicular to AC.
A right angle is formed when two lines are perpendicular.
∠DBE + ∠CBE = 90
90 = (2x - 1) + (5x - 42)
7x = 133
x = 19°
8)
The value of x and y are : x= 26° and y= 9°.
As a linear pair, (5x - 17)° + (3x - 11)° = 180°.
or, 8x - 28°= 180°
8x = 180° + 28°
Therefore, the value of x is 26°.
Now,
3x - 11°= 3×26°-11° = 67°
Again,
67°+90°+(2y+5)° = 180° { being linear pair}.
157°+2y+5° = 180°
or, 2y + 162° = 180°
or, 2y = 180° - 162°
y = [tex]\frac{18}{2}[/tex]
Therefore, the value of y is 9°.
The value of x is 26° and y is 9°.
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List the domain and range of each relation. (0,4)_,(4,0),(-3,-4),(-4,-3)
Range - { 4 , 0 , -4 , -3 } is the domain and range of each relation.
What does the math term domain mean?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.What is domain and range mathematics?
A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
Domain - { 0, 4 , -3 , -4 }
Range - { 4 , 0 , -4 , -3 }
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Do the equations ;x + 2 = 6
and ;(*+ 2) = 6 represent the same situation?
Explain.
The given equations have in one, (1/5) is the coefficient of x, in the second equation, (1/5) is the coefficient of (x + 2), while both equations equals 6. Therefore, the value of x is different in both equations which do not represent the same situation.
How the given equations be evaluated?The given equations are presented as follows;
[tex]\frac{1}{5} \cdot x + 2 = 6...(1)[/tex]
[tex] \frac{1}{5} \cdot (x + 2) = 6...(2)[/tex]
Solving each equation for x gives;
For equation (1), x = 5×(6 - 2) = 20
x = 20
For equation (2), we have;
x = 6 × 5 - 2 = 28
x = 28
Given that the value of x in the given equations are different, the situations are different.
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c. Find the 9 th term of the geometric sequence from part (b).
The 9th term of the geometric sequence can be determined by using the nth term of geometric sequence formula: an=arn-1
Geometric sequence is the series of number in which each term is determined by multiplying the common ratio with the preceding term.
In the formula, an=arn-1, a is the first term, n is the number of terms, and r is the common ratio.
The geometric sequence from the part b is 2,4,8,…
The first term a = 2
The common ratio r = 2
The number of term n = 9
Hence, to find the 9th term,
a9=2(2)9-1
a9=2(2)8
a9=512
The 9th term of the geometric sequence 2,4,8,… is 512
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What is the average rate of change, please simplify your answer (PICTURE BELOW)
Answer:
[tex]{ \tt{change = \frac{y_{b} - y _{a} }{x _{b} - x _{a} } }} \\ \\[/tex]
xb is 4; yb is 16 [from graph (4, 16)]xa is 1; ya is 2 [from graph (1, 2)][tex]{ \tt{ change = \frac{16 - 2}{4 - 1} }} \\ \\ = { \tt{ \frac{14}{3} }} \\ \\ = 4 \frac{2}{3} [/tex]
12x + 8x + 3 + x
Is it
3x+12
-9x+6 2/3
21x+3
24x
-15x+8.3
Answer:
see explanation
Step-by-step explanation:
a bit more info is needed so this may be wrong.
so first you add up the x values which is 12x+8x+x=21x
then you can see we have a problem, we dont know the x value so the answer would be 21x +3
but we can go a bit further to get an answer as 3(7x+1)
this is also known as factorisation.
so ans: 3(7x+1)
Jim thinks that the value of a baseball card can be modeled by a decay formula and that the value will decrease at a rate of 0.2% each year. The card was originally valued at $250 in 2007.
What would Jim expect the value of the card to be in 2018?
Answer: $244.55
A = $250 ; r=0.002 t= 11 [From 2007 to 2018 , t=2018-2007]
PLEASE I NEED HELP QUICK EASY POINTS
Answer: f(-1) = -12
Step-by-step explanation:
To solve, we will substitute t for -1 into the function.
Given:
h(t) = (t + 7)(t - 1)
Substitute:
h(-1) = (-1 + 7)(-1 - 1)
Add and subtract:
h(-1) = (6)(-2)
Multiply:
f(-1) = -12
Bo the baker makes the best cookies! His recipe for triple-chip cookies uses 1/2 cups of chocolate chips, 3/4 cup of butterscotch chips, and 5/8 cup of peanut butter chips. Yum! How many cups of chips does Bo use to make one batch of triple-chip cookies?
Answer:
1/2 + 3/4 + 5/8
4/8 + 6/8 + 5/8 = 15/8 or 1 7/8 cups
Step-by-step explanation:
probably right dunno
This is one batch right? if so shud be right
For each function, determine whether y varies directly with x . If so, what is the constant of variation?
a. 5 x+3 y=0
-5/3 is the constant of variation where y varies directly with x.
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
A DIRECT VARIATION is a mathematical relationship between two variables that can be stated mathematically by an equation in which one variable equals a constant times the other. y = kx
⇒ 5 x+3 y=0
⇒ 3y= -5x
⇒ y = -5x/3
Thus, y = -5/3 × x, here k is constant = -5/3
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Name the geometric terms modeled by a wall and the floor. (Blank 1) Blank 1 options two lines intersecting in a point • two lines intersecting in a line • two planes intersecting in a line three planes intersecting in a point
Answer: Two planes intersecting in a line
Explanation:
The wall and floor are two different planes. They meet up to form a line which is the crease between them.
A plane is a flat surface without any bends or curves to it. In theoretical terms, planes go on forever in all directions. Realistically there are limits of course. The wall or floor cannot go on forever.
Another example of two planes would be found in a book. Each page is a plane. Two adjacent pages meet up to form a line (i.e. the spine of the book is a line).
Read the problem. Identify what you need to know. Then organize the data to solve the problem.
There are 10 sophomore, 8 junior, and 9 senior members in student council. Each member is assigned to help plan one school activity during the year. There are 4 sophomores working on the field day and 6 working on the pep rally. Of the juniors, 2 are working on the field day and 5 are working on the school dance. There are 2 seniors working on the pep rally. If each activity has a total of 9 students helping to plan it, what is the probability that a randomly selected student council member is a junior or is working on the field day?
F. 1/5
G. 4/18
H. 5/9
J. 2/3
Using the combination formula, the committee can be selected in 1,211,760 ways.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
Combination formula is the number of different combinations of x objects from a set of n elements.
In this problem:
There are 10 sophomore, 8 junior, and 9 senior members in student council.
They are independent, so we can just multiply them, thus;
T = 18!/ 2! 16! x 12!/ 2! 10! x 10!/ 3! 7!
T = 1,211,760
Hence, The committee can be selected in 1,211,760 ways.
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Silas pays 8% interest on his $22,000 college loan and 11% interest on his $10,000 car loan. What average interest rate does he pay on the total $32,000 he owes? Round your answer to the nearest tenth of a percent.
The average interest rate does he pay on the total $32,000 he owes is 9. 5%
How to determine the average
From the information given, we have that;
8% interest on his $22,00011% interest on his $10,000Given the total pay he owes as;
= $22, 000 +$ 10, 000
= $32, 000
The average interest rate is expressed as;
= sum of interest rate for college loan and car/ number of interest rate
Substitute the values
= 8 + 11/ 2
= 19/ 2
Find the quotient
= 9. 5%
Thus, the average interest rate does he pay on the total $32,000 he owes is 9. 5%
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Position and label the following triangle on the coordinate plane.
right ΔJ K L with legs JK and KL so that JK is a units long and leg KL is 4 b units long
The right angle triangle ΔJ K L with legs JK and KL has been plotted below where the third side will be √(16b² + a²).
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
Given the triangle ΔJ K L
Base = a and Perpendicular = 4b
By Pythagoras theorem,
Hyp² = Base² + Perp²
Hyp² = a² + (4b)²
LJ = √(16b² + a²).
Hence "The right angle triangle ΔJ K L with legs JK and KL has been plotted below where the third side will be √(16b² + a²)".
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