We need to find the value for x using the inverse operation:
Then:
[tex]\begin{gathered} 7-x=84 \\ \end{gathered}[/tex]Let us solve for x:
The x is subtracting, so it will add up to the other side:
[tex]7=84+x[/tex]Now, the 84 is positive, so it will be negative on the other side:
[tex]\begin{gathered} 7-84=x \\ x=-77 \end{gathered}[/tex]Hence, the solution for x is -77.
Find the four terms of the arithmetic sequence given the 13th term (a_{13}=-60) and the thirty third term (a_{33}=-160).Given terms: a_{13}=-60 and a_{33}= -160Find these terms:a_{14}= Answera_{15}= Answera_{16}= Answera_{17}= Answer
Given:
13th term = -60
33rd term = -160
Find:
14th, 15th, 16th, and 17th term
Solution:
For us to determine the 14 - 17th term, we need to identify the common difference in this arithmetic sequence. The formula is:
[tex]\frac{a_{33}-a_{13}}{33-13}[/tex]Let's plug in the values of a₃₃ and a₁₃ in the formula above.
[tex]\frac{-160-(-60)}{33-13}[/tex]Then, solve.
[tex]\frac{-100}{20}=-5[/tex]Hence, the common difference between the terms is -5.
So, the next 4 terms after a₁₃ are shown below:
[tex]\begin{gathered} a_{14}=-65 \\ a_{15}=-70 \\ a_{16}=-75 \\ a_{17}=-80 \end{gathered}[/tex]
help me with geometry proof, pls I did really bad on this homework and I need help, This is what I hard:State. Just.segment AB ll DC; Given
Answer:
Triangle ABC is congruent to DCE by SAS Theorem.
Step-by-step explanation:
Since AB is parallel to DC, we can say that BC is congruent to CE and AC is congruent to DE, then:
If two sides in one triangle are congruent to two sides of a second triangle, and also if the included angles are congruent, then the triangle is congruent.
Triangle ABC is congruent to DCE by SAS Theorem.
counselor at a summer camp are assigned beds to the campers Jackson is assign a bed and then Eva is assigned one are these two events dependent or independent
Solution;
The events are independent
Lily is making kool-aid. She uses 1/4 cup of sugar for every 2/3 cups of kool-aid. how 4many cups of sugar does she need to make 4 cups of kool aid. HELP PLS
Lily needs 3/2 cup of sugar to make 4 cups of kool-aid.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
Lily is making kool-aid. She uses 1/4 cup of sugar for every 2/3 cup of kool-aid which is given in the question.
We have to determine the number of cups of sugar she needs to make 4 cups of kool-aid.
Let the number of cups of sugar would be x she needs to make 4 cups of kool-aid.
As per the given information, we can write the ratio as:
1/4 cup of sugar : 2/3 cup of kool-aid = x cup of sugar : 4 cup of kool-aid
⇒ 1/4 ÷ 2/3 = x ÷ 4
⇒ (1/4) / (2/3) = x / 4
⇒ (1/4) × (3/2) = x / 4
⇒ 3/8= x / 4
⇒ x = (3 × 4)/8
⇒ x = 12/8
⇒ x = 3/2
Therefore, she needs 3/2 cups of sugar to make 4 cups of kool-aid.
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S
SOLUTION
Mr. McClary writes the equation 3(3x - 10) = 5(x + 10). The equation shows
the relationship between the perimeter of an equilateral triangle and the
perimeter of a regular pentagon. What is the perimeter of the pentagon?
A 20
B 50
C 100
D 150
Nikia chose A as the correct answer. How might she have gotten that answer?
The perimeter of pentagon is 150 so option D is correct.
Given:
Mr. McClary writes the equation 3(3x - 10) = 5(x + 10). The equation shows the relationship between the perimeter of an equilateral triangle and the perimeter of a regular pentagon.
3(3x-10) = 5(x+10)
9x - 30 = 5x + 50
9x - 5x = 30 + 50
4x = 80
divide by 4 on both sides
4x/4 = 80/4
x = 80/4
x = 20.
perimeter of pentagon = 5(x+10)
= 5(20+10)
= 5*30
= 150.
Therefore the perimeter of pentagon is 150 so option D is correct.
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A triangle is placed in a semicircle with a radius of , as shown below. Find the area of the shaded region.Use the value for , and do not round your answer. Be sure to include the correct unit in your answer.
Solution:
Given the figure below:
The area of the shaded region is expressed as
[tex]area\text{ of shaded region = area of semicircle - area of triangle}[/tex]step 1: Evaluate the area of the semicircle.
The area of the semicircle is expressed as
[tex]\begin{gathered} area\text{ of semicircle=}\frac{1}{2}\times\pi r^2 \\ where\text{ r is the radius of the circle} \end{gathered}[/tex]Thus, we have
[tex]\begin{gathered} area\text{ of semicircle = }\frac{1}{2}\times3.14\times4cm\times4cm \\ \Rightarrow area\text{ of semicircle =25.12 cm}^2 \end{gathered}[/tex]step 2: Evaluate the area of the triangle.
The area of the triangle is expressed as
[tex]\begin{gathered} area\text{ of triangle =}\frac{1}{2}\times base\times height \\ thus,\text{ we have} \\ area\text{ of triangle =}\frac{1}{2}\times8cm\times4cm \\ =16\text{ cm}^2 \end{gathered}[/tex]step 3: Evaluate the area of the shaded region.
Recall that
[tex]\begin{gathered} area\text{ of shaded reg}\imaginaryI\text{on = area of sem}\imaginaryI\text{c}\imaginaryI\text{rcle- area of tr}\imaginaryI\text{angle} \\ \end{gathered}[/tex]Thus, we have
[tex]\begin{gathered} area\text{ of shaded region = \lparen25.12 -16\rparen cm}^2 \\ =9.12\text{ cm}^2 \end{gathered}[/tex]Hence, the area of the shaded region is
[tex]9.12\text{ cm}^2[/tex]parallel linessolve for x
We have two parralel lines with angles 32x + 4 and 34x - 2
From the figure, the angles are corresponding angles
Corresponding angles are equal
That is,
34x - 2 = 32x + 4
Collect the like terms
34x - 32x = 4 + 2
2x = 6
Divide both sides by 2
2x / 2 = 6 / 2
x = 3
The answer is 3
What is the congruence correspondence, if any, that
will prove the given triangles congruent?
A) ASA
B)SAS
C) SSS
D) none
Answer:
A) ASA
Step-by-step explanation:
You want to know the relevant congruence postulate given the markings of angles and sides shown in the diagram.
MarkingsThe arc and hash marks show on the angles mean the angles with matching markings are congruent. Two angles are shown as congruent to their corresponding angles in the other triangle.
The hash mark on the sides mean the sides with matching markings are congruent. One side between the marked angles is shown as congruent to the corresponding side in the other triangle.
The letters A and S in the congruence postulate designations refer to corresponding Angles and Sides, respectively. So, two angles with a side between them would be identified as ASA.
The ASA congruence postulate applies.
Option A) ASA is the correct answer for the given triangle in the question. ASA is the congruence correspondence.
What is congruence correspondence?
Each triangle's vertices must match one another exactly. This expression signifies that each triangle's side and angle measurements match up with a side or angle of the other triangle. To have a one-to-one correspondence, triangles don't necessarily have to be congruent, but when they are, knowing the correspondence of the triangles is important to determine precisely which sides and which angles are congruent.
According to congruence postulate,
Angles with matching markings are congruent if an arc or hash mark appears on them. The relationship between two angles and the corresponding angles in the other triangle is demonstrated.
The hash marks on the sides indicate that the markings on the sides that match are consistent. The opposite triangle's equivalent side is shown to be congruent to the side between the highlighted angles.
The congruence postulate designations begin with the letters A and S, which stand for matching Angles and Sides, respectively. Therefore, ASA would be used to describe two angles with a side in between them.
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please answer this using the foil method[tex] {9x}^{2} + 60x + 100[/tex]
Answer
Given expression
[tex]9x^2+60x+100[/tex]By factorization, we have
[tex]\begin{gathered} 9x^2+30x+30x+100 \\ 3x(3x+10)+10(3x+10) \\ (3x+10)(3x+10) \end{gathered}[/tex]Now to check, using FOIL method, we have
F = First, i.e 3x(3x) = 9x²
O = Outer = 3x(+10) = +30x
I = Inner = +10(3x) = +30x
L = Last = +10(+10) = +100
Solve for n in the proportion 7/3 = n/21.
pls help. this is so confusing on how to find the p=S(t)=r+i part of the word problem.
Using a linear function, it is found that:
a) Sales are increasing at a constant rate of 30 purchases/month.
b) The linear function is: p = S(t) = 30t + 3990.
c) The total purchases will be of 5130 in June 2010.
d) The sales will be of 5400 in March of 2011.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For this problem, we have that:
The reference month is of April 2007, hence the intercept is of b = 3990.In 16 months, from April of 2007 to August of 2008, sales increased to 4470, hence the slope is given by: m = (4470 - 3990)/16 = 30.The slope of 30 is the constant rate of purchases per month, and the linear function is given by:
p = S(t) = 30t + 3990.
June 2010 is 3 x 12 + 2 = 38 months after April 2007, hence the purchases will be of:
S(38) = 30 x 38 + 3990 = 5130.
The sales will be of 5400 in t months after April 2007, for which:
S(t) = 5400
Hence:
30t + 3990 = 5400
t = (5400 - 3990)/30
t = 47 months.
One month shy of four year, hence in March of 2011.
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Summary
Give an example of a proportional relationship and write an equation that represents the relationship.
The proportional relationship is represented by the formula, y = kx, which demonstrates that y increases at the same rate as x does
Relationships between two variables that are proportional occur when their ratios are equal.
Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.The ratio of the constant values of two proportional quantities is known as the proportionality constant.When either the ratio or product of two changing values results in a constant, that pair of values is said to be in proportion.The Direct Variation and Inverse Variation types of proportions between the two provided values determine the value of the proportionality constant.The direct proportionality formula, y = kx, demonstrates that y increases at the same rate as x does. The cost per item (y), which is inversely proportional to the number of things purchased (x), is represented by the symbol y x.By using the indirect proportionality formula, y = k/x, it can be seen that when y rises, x falls, and vice versa.Therefore the proportional relationship is represented by the formula,
y = kx .
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Can anyone answer this
Answer:
add the number of sides then divide the number by the number of sides
Graph the line y= 3x - 5 using the slope and y-intercept.
Step-by-Step Solution
Step 1: Identify the slope and y-intercept of the line.
y = 3x-5
The slope is m = 1.
(Type an integer or a fraction.)
The required slope m is 3 and the y-intercept is - 5.
What is a y-intercept?On a graph, the y-intercept can be found by finding the value of y when x=0. This is the point at which the graph crosses through the y-axis.
· The y-coordinate of a point where a line, curve, or surface intersects the y-axis.
Given : The line y = 3x - 5
This is of the form y = mx + c which is the equation of the line.
On comparing these two equations
Thus the slope is 3 .
And y intercept is :
y = 3x - 5 and when x = 0
y =- 5.
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how much bags of fertilizer will brett need to cover the entire garden.
Area A = ?
Bag area covers = 54 ft2
Square Area S = 18ft X 18 ft
. = 324 ft2
Then now divide S/B
S/B = 324/54
. = 36/6
. = 6
Then answer is
Brett will need 6 bags of fertilizer
Larry and his brother wanted to put new carpet down in threerooms in his house. The three rooms measured 10' x 12, 13' x 15,and 12' x 12'. If the carpet Larry wants to use is $25.56 a sq. yd.and the roll of padding is $99 for a 30 sq.yd. roll, answer thefollowing questions. Remember that 1 square yard = 9 square feet.1. Total square footage to be covered with carpeting would besquare feet.2. How many square yards would that be?sq.yd.3. Based on the price of $25.56 a sq.yd., what would the total costbe for the carpeting? $4. To make sure Larry has enough padding, how many rolls wouldhe have to buy?What would that cost? $5. What would the total cost of the carpeting job be includingcarpet and padding? $
Find the area of each room and then add the three areas.
[tex]\begin{gathered} 10\times12=120 \\ 13\times15=195 \\ 12\times12=144 \\ \\ 120+195+144=459 \end{gathered}[/tex]The total square footage to be covered is 459.
Part 2)Since each square yard has 9 square feet, divide the square footage by 9 to find how many yards is that equal to:
[tex]\frac{459}{9}=51[/tex]Then, the area is equal to 51 square yards.
Part 3)The cost for each square yard is $25.56. Multiply that amount by 51 to find the total cost:
[tex]25.56\times51=1303.56[/tex]The total cost for the carpeting is $1303.56.
Part 4)Each roll of padding has 30 square yards. Since 51 yards must be covered, and two rolls would yield 60 square yards, then, the minimum amount of rolls needed is 2.
The cost for 2 rolls would be 2*$99 = $198.
Part 5)Add the cost of the two rolls of padding and the carpeting job to find the total cost:
[tex]\text{ \$}198+\text{ \$}1303.56=\text{ \$}1501.56[/tex]Then, the total cost of the carpeting job including the carpet and padding would be $1501.56.
Therefore, the answers are:
Part 1) 459 square feet.
Part 2) 51 square yards.
Part 3) $1303.56
Part 4) 2 rolls for $198
Part 5) $1501.56
identify the set of numbers that best describes each situation explain your choice. 9. the amount of money in a bank account
The sets of the real numbers are
Whole numbers
Integers
Rational numbers
Irrational numbers
The whole numbers mean positive integers with zero
The integers mean positive , negative whole numbers, and zero
Rational numbers mean
Liam is setting up folding chairs for a meeting. If he arranges the chairs in 8 rows of the same length, he
has 3 chairs left over. If he arranges the chairs in 6 rows of that same length, he has 13 left over. How many
chairs does Liam have?
Liam has
chairs.
The most appropriate choice for linear equation will be given by-
Liam have 43 chairs
What is linear equation?
At first, we need to know the meaning of algebraic expressions.
Algebraic expressions consists of numbers and variables connected with addition,subtraction, multiplication and division sign.
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions with an equal to sign
A one degree equation is known as linear equation.
Let the number of chairs in one row be x
Number of chairs in 8 rows = 8x
3 chairs are left
Total number of chairs = 8x + 3
Number of chairs in 6 rows = 6x
13 chairs are left
Total number of chairs = 6x + 13
By the problem,
[tex]8x+3=6x+13\\8x-6x=13=3\\2x=10\\x=\frac{10}{2}\\x=5[/tex]
Number of chairs Liam has =
[tex]6\times 5 + 13\\30+13\\43[/tex]
Liam has 43 chairs
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Which graph correctly represents ? 1/5y - 1/2x > 2
A graph which represents the solution to this inequality is shown in the image attached below.
What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments (symbols):
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).Next, we would evaluate and simplify the given inequality in order to determine the graph which represent its solution as follows:
1/5y - 1/2x > 2
Subtracting 2 both sides, we have:
1/5y - 1/2x - 2 > 2 - 2
1/5y - 1/2x - 2 > 0
(2y - 5x - 20)/10 > 0
2y - 5x - 20 > 0
2y > 5x + 20
Dividing both sides by 2, we have:
y > 5x/2 + 10
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I will show you the pic
The general form of a linear equation is given by:
y = kx
where k is a constant.
From the given options you can notice that the only equation similar to the previous one is:
y = 1/6 x
Then, the previous equation is the linear equation.
Ron's Tea Shop has caffeinated tea and decaffeinated tea. During the lunchtime rush, the tea shop served 25 teas in all, 20% of which were caffeinated. How many caffeinated teas did the tea shop serve?
The number of caffeinated teas that the tea shop serve is 5.
How to calculate the percentage?Number of teas served = 25 teas.
Percentage that was caffeinated.= 20%
Therefore the number that was caffeinated will be the percentage multiplied by the number of teas. This will be:
= 20% × 25
= 0.2 × 25
= 5
Therefore, 5 are caffeinated
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Hello, I need some assistance with this homework question please for precalculusHW Q30
EXPLANATION
Since the degree is 6, the polynomial has 6 zeros:
Then, using the Complex Root Theorem, since the polynomial has 2 complex roots, thus the conjugate of 5 + i is 5 - i, and the conjugate of 7 - i is 7 + i:
In conclusion, the remaining zeros are: 5 - i, 7 + i
x f(x) −5 1 −4 0 −3 1 −2 2 −1 3 0 4 1 5 2 6 3 7 What are the vertex and range of the function?
The vertex is the turning point of a function while the range is the interval of the value of the function thus vertex of the given function is at (-4,0) while the range is [0,6].
What is the range and domain of a function?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.
The domain is for the independent variable while the range is for the dependent variable.
As per the given function,
x f(x) −5 1 −4 0 −3 1 −2 2 −1 3 0 4 1 5 2 6
The graph of this function has been plotted below,
The vertex is the point where the function is changing its sign of slope or turning point.
It is clear that at (-4,0) it is changing its slope of sign therefore (-4,0) will be the vertex.
The range is the interval where the function exists since the given function goes from y = 0 to y = 6 so [0,6] will be the range of the function.
Hence "The vertex is the turning point of a function while the range is the interval of the value of the function thus vertex of the given function is at (-4,0) while the range is [0,6]".
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Here is a vertical algorithm that we can use to find 60.19 – 47.52.Which place value column(s) will require regrouping?Please see image below.
Regrouping happens when we need to "borrow" value from the higher order digits to perform a subtraction properly. This happens on the tenths, because we need to subtract 5 from 1, which we can't do normally. So we need to regroup from the ones and tens, in order to solve the problem. The correct answer is B.
Find a point N on the segment with endpoints K(-2, -3) and L(4,3) that partitions thesegment, starting at point K, 1/3 of the way to point L.
First find the length of the segment KL
Apply the formula for distance between two points as;
d = √{y2-y1}^2 + {x2-x1}^2 where
y1= -3 , y2 = 3 , x1 = -2 and x2 = 4
d= √ {3--3}^2 + { 4--2}^2
d= √ 9^2 + 6^2
d= √ 81 + 12
d= √93 = 9.6
So the length of the segment is 9.6
From point K {-2, -3} , find 1/3 of the length to locate point L
This will be : 1/3 * 9.6 =3.2
This means point L is 3.2 units from point K, now apply the distance formula to find x and y coordinates for L, where K is {-2,-3} and L {x,y}
d = √{y2-y1}^2 + {x2-x1}^2
3.2 = √{y--3}^2 + {x--2}^2
3.2 =√ {y+3}^2 +{x+2}^2
3.2^2 = {y+3}^2 + {x+2}^2
10.3 = y^2 + 6y + 9 + x^2 +4x +4
10.3 = y^2 + 6y +x^2 +4x +9+4
10.3 = y^2 + 6y +x^2 +4x +13
0=y^2 +6y +x^2 +4x +13-10.3
0= y^2 +6y +x^2 +4x +2.7
y^2 + 6y +x^2 +4x +2.7 = 0
{-0.9,-0.5)
let k(x)=3h(x)+4x^4/g(x). given the following table of values, find k'(-1)
k(x)=3h(x)+4x^4/g(x). given the following table of values, k'(-1) will be 3.
What is differentiation?A function's sensitivity to change with respect to a change in its argument is measured by the derivative of a function of a real variable in mathematics. A crucial calculus technique is the derivative. the procedure for determining a function's derivative, or rate of change, in mathematics. Differentiation is the method used to calculate a function's derivative. The derivative is the rate at which two variables, x and y, change relative to one another.
Given Data
k(x) = -3h(x) + [tex]\frac{4x^{4} }{g(x)}[/tex]
k(x) = -3h'(x) + 4[tex]\frac{4x^{3} g(x)- x^{4}g'(x) }{gx^{2} }[/tex]
k'(-1) = -3h'(-1) + 4 [tex]\frac{4g(-1)-g(-1)}{g(-1)^{2} }[/tex]
k'(-1) = -3(-1) + 4(0)
k(-1) = 3 + 0
k'(-1) = 3
k(x)=3h(x)+4x^4/g(x). given the following table of values, k'(-1) will be 3.
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Solve the equation for all complex and real solutions. Use potential zeros and synthetic division[tex]5x^4+7x^3+119x^2+175x-150=0[/tex]
Answer: the complex solutions are:
Step-by-step explanation: x = 5i , -5i , 3/5 ,-2
If g(x)=5x, h(x)=√x, find the composition.
(g . h)(0)
( g . h ) ( 0 ) = _____
The value of the composition (g . h)(0) is 0
What is a function?A function can be defined as a mathematical law, expression of rule that explains the relationship between two variables in an equation.
These variables are;
The independent variableThe dependent variableThe functions are;
g(x) = 5xh(x) = √xThe composite function is gotten by substituting the value of x of the independent variable in the function.
The composite function (g . h)(0) is determined by substituting the value of x as h(x) in the function g(x), we get;
(g . h) = 5√x
Now, substitute the value of x as 0, we have;
(g . h)(0) = 5√0
Find the square root
(g . h)(0) = 5(0)
Find the product
(g . h)(0) = 0
Hence, the value is 0
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if you could give me the answer without explantion i would be happy to leave a good review
The coordinates of the fourth side are (6, -8)
Explanation:Let the coordinate of the fourth side be (x, y)
The diagonals of a parallelogram bisect eachother, so the midpoint of (-3, -2) and (x, y) is equal to the midpoint of (4, -4) and (-1, -6)
[tex]\begin{gathered} (\frac{x-3}{2},\frac{y-2}{2})=(\frac{4-1}{2},\frac{-6-4}{2}) \\ \\ (\frac{x-3}{2},\frac{y-2}{2})=(\frac{3}{2},-5) \\ \\ \frac{x-3}{2}=\frac{3}{2}\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(1) \\ \\ \frac{y-2}{2}=-5\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots.(2) \end{gathered}[/tex]Solving these equations:
x - 3 = 3
x = 3 + 3 = 6
and
y - 2 = -10
y = -10 + 2 = -8
The coordinates are (6, -8)
Round 0.4275 to the nearest thousand
we have
0.4275
if we round to the nearest thousand, we look at the third digit of our number
0.4275
do you know the answer now?
0.42 is not correct
and only 2 decimals will be rounded to the nearest hundreth
becuase we have a 5 after 7, the number will be rounded up
0.428
this is the answer
if we would have for example
0.3521
the rounded to the nearest thousand would be 0.352