The money spent by Mr. Dunston is $ 35.
Given that:-
Money spent by Mr. Dunston and Mr. Dolland = $ 45
Money spent by Mr. Dunston and Ms. Campbell = $ 65
Ms. Campbell spent 3 times as much as Mr. Dolland.
We have to find the money spent by Mr. Dunston.
Let the money spent by Mr. Dunston be $ x,
Let the money spent by Mr. Dolland be $ y and,
Let the money spent by Ms. Campbell be $ 3y
Hence, from the data given in the question, we can write,
x + y = 45 ...(1)
x + 3y = 65 ... (2)
By elimination method, we can write,
(2) - (1)
2y = 20
y = 10
x + 10 = 45
x = 45 - 10 = 35
x = 35
Hence, the money spent by Mr. Dunston is $ 35.
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I don't understand how to do this, pls help :(
Answer: A
Step-by-step explanation:
MODELING REAL LIFE The diagram shows the prices of two
types of ground-cover plants. A gardener can afford to buy 125
vinca plants and 60 phlox plants.
$1.20/plant Vinca $2.50/plant Phlox
a. Write an equation in standard form that models the possible
combinations of x vinca plants and y phlox plants the gardener
can afford to buy.
An equation that models the possible combinations is:
___ = 300.
Please help!
a.
A gardener can afford to buy 125 vinca plants and 60 phlox plants. $1.20/plant Vinca $2.50/plant Phlox.
The equation in standard form that models the possible combinations of x vinca plants and y phlox plants the gardener can afford to buy is
⇒ $1.20*x + $2.50*y
b.
An equation that models the possible combinations is
⇒ $1.20*125 + $2.50*60 = 300
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dont know how to do this either if u could feel free to help me
The graph that beast describes the slope of -2/3 passing through points (-1, 0) is in option c
How to determine the graph that matches the slope and the pointsInformation given in the question include
a linear function graph
The data is plotted as a linear function
What is linear function ?A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
The slope is represented as m, The slope by definition is the ratio change of the output values to the input values
the slope, m = -2/3
negative slopes slants from top left to bottom right as in a and c
from the graph, option c has points (-1, 0) and (0, -2/3)
m = (-2/3 - 0) / (0 - -1)
m = (-2/3) / (0 + 1)
m = -2/3
This matches with option C
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a) Find the circumference of a circle whose radius is 4 inches. Round to the nearest tenth.
b) Find the length of if mACB = 60º and the radius of the circle is 4 inches. Round to the nearest tenth.
Complete your work in the space provided.
The circumference of the circle is 25.1 inches.
The length of the arc ACB is 4.2 inches.
How to find circumference of a circle?The circumference of a circle is the perimeter of the circle.
Therefore,
circumference of a circle = 2πr
where
r = radiusHence,
circumference of a circle = 2 × 3.14 × 4
circumference of a circle = 8 × 3.14
circumference of a circle = 25.1 inches
The length of the arc ACB can be found as follows:
length of arc = ∅/ 360 × 2πr
length of the arc = 60 / 360 × 2 × 3.14 × 4
length of the arc = 60 / 360 × 25.12
length of the arc = 1507.2 / 360
length of the arc = 4.18666666667
length of the arc = 4.2 inches
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A company's policy is to spend no more than $350,000 a year for salaries. The president's salary is $110,000. The salaries of the eight other employees are equal. How much can be spent on each salary?
In tic-tac-toe, a 3 by 3 grid is filled with X's and O's. How many ways is there to fill the grid so that there is at least 4 of each symbol in the grid?
The number of ways to fill the tic-tac-toe grid, with at least 4 of each symbol in the grid, using the arrangements formula, is of:
252.
What is the arrangements formula?The number of possible arrangements that can be chosen from a set of n elements is given by the factorial of n, as follows:
[tex]A_n = n![/tex]
When the elements arranged can be repeated, the number of arrangements is presented as follows:
[tex]A_{n}^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1! \times n_2! \cdots n_3!}[/tex]
In which [tex]n_1, n_2, \cdots, n_n[/tex] represent the number of repetitions of each element.
For the tic-tac-toe grid, we have that the possible ways to organize the nine positions with at least four instances of each symbol is given as follows:
5 X's and 4 O's.4 X's and 5 O's.Hence the number of ways to fill up the grid is given as follows:
[tex]\frac{9!}{5!4!} + \frac{9!}{4!5!} = 2 \times 156 = 252[/tex]
Thus 252 ways to fill up the grid.
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Find the distance between the points (8,–2) and (8,7)
Answer:
9 units
Step-by-step explanation:
We see that on the x-axis, everything is equal.
On the y-axis, there are -2 and 7.
So we are finding the distance between -2 and 7
|-2|+|7|=9
So the distance between the points is 9 units.
Solve 7x+23x-5=6(5x+8). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA. x=
OB. The equation has infinitely many solutions.
OC. The equation has no solution.
Please helppppppppppp
Answer:
1
2
[
x
2
2
−
x
3
3
]
2
0
=
1
2
[
(
4
2
−
8
3
)
−
(
0
)
]
=
1
2
(
−
2
3
)
=
−
1
3
Step-by-step explanation:
When we add any two multiples of 5 and 10 we sometimes,always or never get a number ending in 2.
Sometimes
Never
Always
Answer:
Never
Because for example; 25(the multiple of 5) + 20(the multiple of 10) equals 45
Answer:
Step-by-step explanation:
never
Rapunzel's team participated in a total of 143 wrestling matches. Rapunzel participated in 67 percent of the wrestling matches. What fraction of the wrestling matches did Rapunzel participate in?
Using the percentage, Rapunzel participated in 9581/100 matches.
In the given question we have to find the fraction of the wrestling matches did Rapunzel participate in.
Rapunzel's team participated in a total of 143 wrestling matches.
Rapunzel participated in 67 percent of the wrestling matches.
Total matches = 143
Participated in = 67%
Total number of matches in which Rapunzel participated is
= 143*67%
= 143* 67/100
= 9581/100
Rapunzel participated in 9581/100 matches.
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In their October 2003 issue, Consumer Reports evaluated the price and performance of 23
models of cordless phones. Computer output gives these summaries for the prices:
a. Were any of the prices outliers? Explain how you made your decision.
b. One of the manufacturers advertises a cordless phone “economy-priced at only $31.95”.
Would you consider that to be a very low price? Explain.
Considering the five number summary of the data-set, we have that:
a. None of the prices were outliers, as all the prices are within 1.5 IQR of the quartiles.
b. That is not a very low price, as it is above the first quartile, while very low prices have to be 1.5 IQR below the first quartile.
How to identify outliers on the five number summary?The outliers, considering the five number summary of a data-set, are the values that are more than 1.5 Interquartile Ranges from the quartiles, that is, either:
1.5 IQR below the first quartile, which is a low outlier.1.5 IQR above the third quartile, which is a higher outlier.The interquartile range of a data-set is the difference between the third quartile and the first quartile, hence, for the given data-set:
IQR = Q3 - Q1 = 110 - 30 = 80.
Hence the bounds for outliers are given as follows:
Low outliers: 30 - 1.5 x 80 = -90. (there will be no low outliers).High outliers: 110 + 1.5 x 80 = 230.Since the maximum value of 200 is less than 230, there are no outliers in the data-set.
Missing InformationThe five number summary is given by the image at the end of the answer.
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Solve for x X/11=2
x=?
Answer:
x = 22
Step-by-step explanation:
Solve for x:
x/11 = 2
multiply both sides by 11:
11(x/11) = 11(2)
x = 22
Answer:
x = 22
Step-by-step explanation:
[tex] \sf \frac{x}{11} = 2[/tex]
Use cross multiplication.
[tex] \frac{x}{11} = \frac{2}{1} \\ \\ \sf x = 2 \times 11 \\ \\ \sf \: x = 22[/tex]
Find a number that is 6 times as large as 9 minus 3
The required number is 1 which represents "6 times as large as 9 minus 3".
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is reasoning.
We have to determine the number that is "6 times as large as 9 minus 3".
Let the required number would be x
Translate the phrase "6 times as large as 9 minus 3" into the algebraic form :
⇒ 6 × x = 9 - 3
⇒ 6x = 6
⇒ x = 6 / 6
⇒ x = 1
Thus, the required number is 1 which represents "6 times as large as 9 minus 3".
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Do you think the blue dot represents the y-intercept of this line? Why or why not?
Answer:
No, the point is on the x-axis, it is not a y-intercept.
1. Ryan says that if a number is divisible by both 2 and 5, then it is also divisible by 10. Do you agree
with Ryan? Explain.
Answer: Yes
Step-by-step explanation:,
The factors of 10 are 2 and 5 any number divisible by 10 will also be divisible by both 2 and 5.
Hope this helps! ^-^ Have a good day! :)
Answer:
Yes, Because factors of 10 are 1,2,5,10.
So all numbers divisible by 10 must be divisible by 2 and 5.
Step-by-step explanation:
Find all zeros of f(x) = x³ - 4x² - 5x + 14. Enter the zeros separated by commas. Enter exact values,
using radicals and/or fractions if necessary, not decimal approximations.
Question Help: Message instructor
Check Answer
Jump to Answer
Answer: x=-2, x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]
Step-by-step explanation:
f(x) = x³ - 4x² - 5x + 14
-2 | 1 -4 -5 14
-2 12 -14
1 -6 7 0
x³ - 4x² - 5x + 14 = (x+2)(x²-6x+7)
x²-6x+7=0
x²-6x+9-2=0
(x²-6x+9)-2=0
x²-6x+9=2
x²-3x-3x+9=2
x(x-3)-3(x-3)=2
(x-3)²=2
x-3=[tex]\sqrt{2}[/tex], -[tex]\sqrt{2}[/tex]
x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]
Hence, zeroes are x=-2, x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]
Step-by-step explanation:
our first "suspicion" for a factoring is an integer factor of the constant term : 14.
14 = 2 × 7 or -2 × -7
I started to try 2 or -2 and found that -2 is indeed a zero solution.
so, the first factors are
f(x) = (x + 2)(x² + ...)
let's divide (x³ - 4x² - 5x + 14) by (x + 2) to get the x² term.
x³ - 4x² - 5x + 14 ÷ x + 2 = x² - 6x + 7
- x³ + 2x²
--------------
0 -6x² - 5x
- -6x² - 12x
----------------
0 7x + 14
- 7x + 14
------------
0 0
f(x) = (x + 2)(x² - 6x + 7)
the zeros for x² - 6x + 7 we get from the general solution for a quadratic equation
ax² + bx + c = 0
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (6 ± sqrt((-6)² - 4×1×7))/(2×1) =
= (6 ± sqrt(36 - 28))/2 = (6 ± sqrt(8))/2 =
= 3 ± sqrt(8/4) = 3 ± sqrt(2)
x1 = 3 + sqrt(2)
x2 = 3 - sqrt(2)
so, the zeros are
-2, 3 - sqrt(2), 3 + sqrt(2)
K=2; f(x)=-x^3 -2x ^2+3 answer
The value of the function f(x) = [tex]x^3-2x^2+3[/tex] when x = 2 is f(2) = 3
The given function is
f(x) = [tex]x^3-2x^2+3[/tex]
The function is the mathematical statement which represents the relationship between one variable and another variable. If one variable is dependent variable the other variable will be independent variable.
The given function is
f(x) = [tex]x^3-2x^2+3[/tex]
The value of x = 2
Then substitute the value of x in the function
f(x) = [tex]x^3-2x^2+3[/tex]
f(2) = [tex]2^3-2(2)^2+3[/tex]
Solve the power of each terms
f(2) = 8 - 8 + 3
Do the arithmetic operations
f(2) = 3
Hence, the value of the function f(x) = [tex]x^3-2x^2+3[/tex] when x = 2 is f(2) = 3
The complete question is:
Find the value of f(x) = [tex]x^3-2x^2+3[/tex] , when x = 2
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PLEASE HELP DUE RIGHT NOW
WILL MARK BRAINLIEST IF YOU HELP
please actually help though dont just comment for points, or put links i will report you
Answer: : (4 – 5) – (13 – 18 + 2).
Step-by-step explanation:
hoped dat helped
its in the picture♡
Answer:A. (10 x 3) + 8
Answer:
A : ( 10 * 3 ) + 8
Hope this helps!
Step-by-step explanation:
10 friends, each donate 3 pieces of clothing, ( 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 ) or ( 10 * 3 ), plus the 8 pieces of clothing Emily is donating. ( 10 * 3 ) + 8.
4y=16x-4 in standard form?
The standard form of linear equation is 4x - y = 1.
What is the standard form of a linear equation?
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).
The slope intercepts form a linear equation is y = mx + c, where m is the slope and c is y-intercept of the line.
Given linear equation is:
4y=16x-4
Subtract 16x from both sides:
4y - 16x = -4
Divide both sides by -4
-y + 4x = 1
4x - y = 1
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To go to the theater you would pay $8.00 for each ticket you purchase. Which answer choice correctly represents the algebraic expression for the cost of t tickets?
A. 8t
B. 8 + t
C. 8 – t
D.
The algebraic expression that correctly represents the cost of t tickets is 8t , the correct option is (a) .
In the question ,
it is given that
the cost of 1 ticket for the theater is = $8.00
let the number of ticket be = t
so , the cost for t tickets = (cost of 1 ticket ) × ( number of tickets )
Substituting the values of number of tickets and cost of 1 ticket ,
we get ,
cost for t tickets = 8 × t
= 8t
Therefore , The algebraic expression that correctly represents the cost of t tickets is 8t .
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The equation m = 4b represents the time in minutes (m) it takes a chef to cook a certain number of bacon cheeseburgers (b).
Determine the constant of proportionality.
one fourth
1
4
8
For given equation, the constant of proportionality is 4
In this question, we have been given an equation m = 4b that represents the time in minutes (m) it takes a chef to cook a certain number of bacon cheeseburgers (b).
We need to determine the constant of proportionality.
We know that the the constant of proportionality is nothing but the ratio of two proportional values.
In this case the time a chef needs to cook depend on the number of bacon cheeseburgers (b).
So, m is directly proportional to the b
Therefore, the constant of proportionality is 4
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Answer:
The answer is 4
Step-by-step explanation:
I hope this helps!!
A town's population is 43,200. About 125 people move out of the town each month. Each month, 175 people on average move into town. A nearby town has a population of 45,900. It has no one moving in and an average of 175 people moving away every month. In about how many months will the populations of the towns be equal? Write an equation to model the situation. Then solve the equation and answer the question.
The equation to model the situation is given below. And the months will the populations of the towns be equal will be 12.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A town's populace is 43,200. Around 125 individuals move out of the town every month. Every month, 175 individuals on the normal move into town. A close by the town has a populace of 45,900. It has nobody moving in and a normal of 175 individuals moving away consistently.
Let y be the total population and x be the number of months. Then the equations are given as,
y = (175 - 125)x + 43200
y = 50x + 43200 ...1
y = -175x + 45900 ...2
From equations 1 and 2, then we have
50x + 43200 = - 175x + 45900
50x + 175x = 45900 - 43200
225x = 2700
x = 2700 / 225
x = 12
The months will the populations of the towns be equal will be 12.
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can someone help with this? there is also a part two. picture is provided :) (not pt 2)
Solution of the given equation x² -6x +10 =0 using quadratic formula or perfect square method is same in complex number and is equal to 3 + i or 3 - i.
As given in the question,
Given equation is:
x² -6x +10 = 0
Complex number i² = -1
Using perfect square method:
x² -6x + 9 +10 -9 =0
⇒x² -6x +9 =-1
⇒ (x - 3)² = (i)²
⇒x-3 = ± i
⇒ x= 3 ± i
Using quadratic formula,
x = [ -(-6) ±√ (-6)² -4(1)(10)] / 2(1)
=( 6 ± √-4)/ 2
= (6± √4i²) /2
= (6 ± 2i) / 2
= 3 ± i
Therefore, solution of the given equation x² -6x +10 =0 using quadratic formula or perfect square method is same in complex number and is equal to 3 + i or 3 - i.
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Select the correct answer.
Given: ZNMY
ZPOB
Prove: ZXMN ZAOP
kk
M
ZXMY and ZAOB are right angles because that information is given. This means that ZXMN is complementary to ZNMY and
ZAOP is complementary to ZPOB by the linear pair theorem. Since ZNMY ZPOB, by the congruent complements theorem.
ZXMN ZAOP.
Where is the error in the proof? Select all that apply.
O The given cannot be used to state that ZAOB is a right angle.
The linear pair theorem cannot be used to state ZXMN is complementary to ZNMY.
The linear pair theorem cannot be used to state ZAOP is complementary to ZPOB.
The congruent complements theorem cannot be used to state that ZXMN
ZAOP.
The given cannot be used to state that ZXMY is a right angle.
The linear pair theorem cannot be used to state ZAOP is complementary to ZPOB.
What is complementary angles?Complementary angles are two angles with a combined angle of 90 degrees, whereas supplementary angles have a combined angle of 180 degrees.
A good that adds value to another good or service is said to be complimentary. To put it another way, they are two items that the client uses in tandem with one another. For instance, cereal and milk or a DVD and a DVD player.
Because the three angles of a triangle sum up to 180° and the right angle has already taken up 90°, the two non-right angles in a right angled triangle are complimentary. We say two angles "Complement" one other when their sums equal 90 degrees. because a complete angle is what is considered to be the right angle.
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Pls help giving brainliest
Answer:5) gcf=6 lcm=42 | 6) gcf=2 lcm=270 | 7) gcf=2 lcm=224
Step-by-step explanation:
Solve for x.
5^x +25^x+125^x=-5
Answer:
No solutionStep-by-step explanation:
Given5ˣ + 25ˣ + 125ˣ = - 5Each exponent on the left side is a positive number and therefore their sum is positive too.
But we have a negative value on the right.
This is not possible, hence no solutions.
parallel lines, traversal, and algebra
need help!
The values of the variables, x and y in the angles formed by the parallel lines that have a common transversal are;
x = 4°, y = 10°
11. x = 9°, y = 12°
12. x = 14°, y = 5°
13. x = 8°, y = 11°
14. x = 16°, y = 23°
15. x = 9°, y = 13°
What are parallel lines?Parallel lines are lines that maintain the same distance from each other along their lengths.
From the figure, we get;
(29·x - 3) and (15·x + 7) are linear pair angles, therefore;
(29·x - 3) + (15·x + 7) = 180°
44·x + 4 = 180
x = (180 - 4)/44 = 4
x = 4°
(15·x + 7) and (13·y - 17) are same side exterior angles between parallel lines, therefore;
(15·x + 7) + (13·y - 17) = 180°
(15×4 + 7) + (13·y - 17) = 180°
67 + 13·y - 17 = 180°
50 + 13·y = 180
13·y = 180 - 50 = 130
y = 130 ÷ 13 = 10
y = 10°
11. (18·x - 44)° and (8·x - 10)° are same side exterior angles, therefore;
(18·x - 44)° + (8·x - 10)° = 180°
26·x - 54 = 180
x = (180 + 54)/26 = 9
x = 9°
(8·x - 10)° and (13·y - 38)° are linear pair angles, therefore;
(8·x - 10)° + (13·y - 38)° = 180°
(8 × 9 - 10)° + (13·y - 38)° = 180°
62 - 38 + 13·y = 180
13·y = 180 - (62 - 38) = 156
y = 156 ÷ 13 = 12
y = 12°
12. (9·x - 2)° and (5·x + 54)° are corresponding angles, therefore;
(9·x - 2)° = (5·x + 54)°
(9·x - 2)° = (5·x + 54)°
9·x - 5·x = 54 + 2 = 56°
4·x = 56°
x = 56° ÷ 4 = 14°
x = 14°
(9·x - 2)° and (10·y + 6)° are linear pair angles, therefore;
(9·x - 2)° + (10·y + 6)° = 180°
(9 × 14 - 2)° + (10·y + 6)° = 180°
124 + 6 + 10·y = 180
10·y = 180 - 130 = 50
y = 50 ÷ 10 = 5
y = 5°
13. The angle to which the angle (8·x - 1)° is an alternate interior angle is a corresponding angle to the angle (11·x - 25)°, therefore;
(8·x - 1)° is congruent to angle (11·x - 25)°
(8·x - 1)° = (11·x - 25)°
11·x - 8·x = 25 - 1 = 24
3·x = 24
x = 24 ÷ 4 = 8
x = 8°
Angles (15·y - 48)° and (8·x - 1)° are linear pair angles, therefore;
(15·y - 48)° + (8·x - 1)° = 180°
(15·y - 48)° + (8 × 8 - 1)° = 180°
(15·y - 48)° + 63° = 180°
15·y + 15° = 180°
15·y = 180° - 15° = 165°
y = 165° ÷ 15 = 11°
y = 11°
14· The angle (4·x + 4)° and (7·x - 44)° are alternate exterior angles, therefore;
(4·x + 4)° = (7·x - 44)°
7·x - 4·x = 44° + 4° = 48°
3·x = 48°
x = 48° ÷ 3 = 16°
x = 16°
The vertical angle to angle 39° is a linear pair angle to the angle (8·y - 43)°
Therefore;
39 + 8·y - 43 = 180°
8·y = 180 + 43 - 39 = 184
y = 184 ÷ 8 = 23
y = 23°
15. The diagram indicates that the angles (15·x - 26)° and (12·x + 1)° are congruent, therefore;
(15·x - 26) = (12·x + 1)
(15·x - 12·x) = (26 + 1)
3·x = 27
x = 27 ÷ 3 = 9
x = 9°
The vertical angle to (2·x + 1) is therefore;
12·x + 1 = 12 × 9 + 1 = 109
The angle sum property indicates that we have;
28° + 109° + (4·y - 9)° = 180°
(4·y - 9)° = 180° - (28° + 109°) = 43°
(4·y - 9)° = 43°
(4·y)° = 43° + 9° = 52°
y = 52°/4 = 13°
y = 13°
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(-42n+28p)(-1/4) simplify. Assume that no denominator equals zero
The value of (-42n+28p)(-1/4) is 249n/4
What are fractions?A fraction represents a part of a whole or, more generally, any number of equal parts. A fraction describes how many parts of a certain size there are, for example, one-half, three-fifths, three-quarters.
A fraction has a denominator and numerator. There are three types of fraction. Proper, improper and mixed fraction
Opening the parentheses of the equation
(-42n+ 28p)(-1/4).
= -42n× -1/4+ 28× -1/4
= (42n×-7)/4
= -294n/4
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