Hey there! :)
Equation 1) -2x + y = 14
Equation 2) 4x - 6y = 4
Add 2x to both sides of equation 1 so that we can get the value of y.
y = 2x + 14
Now, plug the value of y into our second equation.
4x - 6(2x + 14) = 4
Simplify.
4x - 12x - 84 = 4
Add 84 to both sides.
4x - 12x = 4 + 84
Simplify.
-8x = 88
Divide both sides by -8.
x = -11
Now, plug our value of x into our first equation in order to find y.
-2x + y = 14
-2(-11) + y = 14
22 + y = 14
y = -8
Therefore, the systems of equation variables are : (-11, -8)
~Hope this helped! :)
⠀⠀⠀⠀
Value of x = - 11 Value of y = - 8⠀⠀⠀⠀
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➤ How to solve ?⠀⠀⠀⠀
For solving such questions we need to know the linear inequations .
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Liner inequations can be solved with many methods . But here as mentioned we have to solve with substitution method .
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Substitution method is the method of finding the value of one variable from equation 1 and then substituting the value in the equation 2 .
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Solution :⠀⠀⠀⠀
⠀⠀
-2x + y = 14 --- ( i )
⠀⠀⠀⠀
4x - 6y = 4
2 ( 2x - 3y ) = 4
2x - 3y = 4 / 2
2x - 3y = 2 --- ( ii )
As given , -2x + y = 14
➠ y = 14 + 2x
Now, we will substitute the value of y in eq ( ii )
⠀⠀⠀⠀
➠ 2x - 3y = 2
➠ 2x - 3 ( 14 + 2x ) = 2
➠ 2x - 42 - 6x = 2
➠ 2x - 6x = 2 + 42
➠ -4x = 44
➠ x = 44 / - 4
⠀⠀⠀⠀
➠ x = -11
⠀⠀⠀⠀
[tex]\sf{\underline{\boxed{\huge{\blue{\mathbb{x = - 11 }}}}}}[/tex]
substituting the value of x in equation ( i )⠀⠀⠀⠀
➠ -2x + y = 14
⠀⠀⠀⠀
➠ - 2 × - 11 + y = 14
⠀⠀⠀⠀
➠ 22 + y = 14
⠀⠀⠀⠀
➠ y = 14 - 22
⠀⠀⠀⠀
➠ y = - 8
⠀⠀⠀⠀
[tex]\sf{\underline{\boxed{\huge{\blue{\mathbb{y = -8}}}}}}[/tex]
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Rewrite a. an = 19 - 7(n-1)
Solution for an=19-7(n-1) equation:
Simplifying
an = 19 + -7(n + -1)
Reorder the terms:
an = 19 + -7(-1 + n)
an = 19 + (-1 * -7 + n * -7)
an = 19 + (7 + -7n)
Combine like terms: 19 + 7 = 26
an = 26 + -7n
Solving
an = 26 + -7n
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Divide each side by 'n'.
a = 26n-1 + -7
Simplifying
a = 26n-1 + -7
Reorder the terms:
a = -7 + 26n-1
7) Four workers are hired to harvest potatoes
from a field. Each is given a plot which is
5*8 feet in size. What is the total area of
the field?
Total area of the field is 160 ft^2
Step-by-step explanation:
Given
Total workers = 4
Each worker's share of area = 5*8 feet
We will find the area for each worker and then multiply the area with four to find the whole area of field as it was evenly distributed to workers
so,
[tex]Area\ given\ to\ one\ worker = 5*8\\= 40\ ft^2[/tex]
[tex]Total\ area = 40*4 = 160\ ft^2[/tex]
Total area of the field is 160 ft^2
Keywords: Area, Measurement
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Final answer:
The total area of the field being harvested by four workers, each with a plot of 5 by 8 feet, is 160 square feet.
Explanation:
The subject of this question is Mathematics, specifically, it involves calculating the total area of land worked by four workers. Each worker is given a plot that is 5 feet by 8 feet. To find the total area of the field that the four workers are harvesting, you multiply the area of one plot by the number of workers.
To calculate the area of one plot: Area = length * width = 5 feet * 8 feet = 40 square feet.
Now, since there are four workers each with a plot of this size, you multiply the area of one plot by the number of plots/workers:
Total area = 40 square feet/plot imes 4 plots = 160 square feet.
Therefore, the total area of the field being harvested by the four workers is 160 square feet.
Your friend was trying to complete this problem: There is a sale at the store and you have $50 to spend. Jeans cost $12 and shirts cost $8 If you buy 2 pairs of jeans and 3 shirts, will they have any money left over? if so how much? Their answer: No they will not have any money left because 2 pairs of jeans would cost $26 and 3 shirts would cost $24 and 26+24=50 so they would spend exactly the right amount. EXPLAIN their mistake! What did they do wrong? What should their answer have been?
Answer:
$48
Step-by-step explanation:
A pair of jeans= $12
Two pair of jeans= $12*2= $24
A shirt= $8
3 shirts= $8*3= $24
So it would be $24+$24= $48.
They made their mistake when calculating the cost of the jeans by getting $26 instead of $24.
solve for x
x- 2x (12 - 1/2) =2 (4-2x) +20
A.-14/9
B.-9/14
C.14/9
D.9/14
Answer:
A
Step-by-step explanation:
-22x=-4x+28
-18x=28
x=-28/18=-14/9
Micah deposits C dollars in a bank. The deposited amount earns an annual interest rate of r% and becomes D dollars in t years according to the formula Which formulas could be used to calculate t given C,D, and r
Answer:
[tex]t = \frac{100}{r} [\frac{D}{C} - 1][/tex]
Step-by-step explanation:
Assume that the deposited amount C dollars earn r% simple interest annually.
If after t years the deposited amount C dollars grows to D dollars, then we are asked to write a relation using the given terms to calculate t.
Now, using the formula of simple interest we can write
[tex]D = C(1 + \frac{t\times r}{100})[/tex]
⇒ [tex]1 + \frac{t \times r}{100} = \frac{D}{C}[/tex]
⇒ [tex]\frac{t \times r}{100} = \frac{D}{C} - 1[/tex]
⇒ [tex]t = \frac{100}{r} [\frac{D}{C} - 1][/tex]
So, this is the expression for t. (Answer)
Answer:
t= 100/r [d/c-1]
what is the slope of (-5,3 and (7,9) in fraction form?
Answer:
1/2
Step-by-step explanation:
you put it in slope form which is y1-y2/x1-x2 to get 9-3/7+5 which simplifies to 1/2
Given that point S is equidistant from the sides of triangle WXY, find the following measures.
SU - 5, 12, 13, or 18
M
m
Answer:
Step-by-step explanation:
5, 39, 24 just finished it
Answer:
[tex]SU=5\\\angle WXY = 24\°\\\angle SYW = 39 \°[/tex]
Step-by-step explanation:
According to the graph,
[tex]\angle WXT \cong \angle YXT[/tex]
So, [tex]m\angle YXT =12 \°[/tex]
By sum of angles we have
[tex]\angle WXY = \angle WXT + \angle YXT\\\angle WXY = 12 \° + 12\° = 24 \°\\\therefore \angle WXY 24\°[/tex]
By given, we know that
[tex]\angle UYS \cong \angle SYW\\\therefore \angle SYW = 39 \°[/tex]
By given, we know that side SU is a leg of the right triangle SUX, where the hypotenuse is 13 units, and the opposite angle is 12°. However, if you look closer, you would find that side ST is 5 units, and by GIven we know that ST = SU.
Therefore, SU = 5.
A company is selecting students for interviews at the career fair. The number of students selected from university A is given by Rx) = 4x + 5,
where x represents the number of days of the fair. The number of students selected from university B is given by g(x) = 2x + 8.
Which function best describes the total number of students selected at the career fair?
A
B.
C.
D.
h(x) = 6x + 13
h(x) = -2x + 3
h(x) = 2x - 3
f(x) = (4x + 5)(2x + 8)
Answer:
D) .h(x)= 6x+ 13
Step-by-step explanation:
We are given that,
Function representing number of students from A,
Function representing number of students from B,
It is required to find the total number of students in the fair.
So, we have,
Total number of students =
i.e. Total number of students =
i.e. Total number of students =
i.e. Total number of students =
Hence, the function representing the total number of students in the fair is .
Thus, option D is correct.
Answer:
6x + 13.
Step-by-step explanation:
That is the sum of R(x) and g(x)
= 4x + 5 + 2x + 8
= 6x + 13.
Help!!! I don’t get this
i think u gotta multiply
Answer:
Use an app that can scan problems to solve
Step-by-step explanation:
12k + 5k − 11m + 13m
To simplify the expression 12k + 5k - 11m + 13m, we can combine like terms by adding the coefficients of the like terms. The simplified expression is 17k + 2m.
Explanation:The expression 12k + 5k - 11m + 13m can be simplified by combining like terms. Like terms have the same variables raised to the same powers. In this expression, the terms 12k and 5k are like terms because they both have the variable k. Similarly, the terms -11m and 13m are like terms because they both have the variable m.
To simplify, we can add the coefficients of the like terms:
12k + 5k - 11m + 13m = (12 + 5)k + (-11 + 13)m
Therefore, the simplified expression is 17k + 2m.
Identify the equivalent expression for
Square root of x +3
Answer:
sqrt(x+3)
Step-by-step explanation:
Solve the problem.
If $13,000 is borrowed at 5.8% simple interest for 10 years, how much interest will be paid for the loan?
Answer:
Interest =$7540
Step-by-step explanation:
p=$13000
r=5.8%
t=10yrs
i=p*r*t/100
=13000*5.8*10/1000
=130*58
= $7540
Need help answering this question tysm! (Picture attached)
Answer:
1 and 2 answers are correct
Step-by-step explanation:
2x-y= -8
x-y = -4
ADD BOTH (y is cancelled)
3x= -12
x= -4
-8+y=-8
y=0
-4-y = -4
Multiply all by -1
4+y=4
y=0
What is the domain and range of the following graph?
The parabola represents a firework’s arc. Teacher made a comment that neither time (x) nor height (y) can be negative. Don’t know if that has any effect on it.
Answer:
Domain f(x)={y:6≥y≤0}
Range of f(x)={x:x≤69}
Cross-check the location of point on your graph this is roughly estimation
The area of a rectangle is 27ft squared, and the length of the rectangle is 3ft less than twice the width. Find the dimensions of the rectangle.
Answer:
width =4.5ft
length=6ft
Step-by-step explanation:
w = x
L = 2x-3
area = L*w
27 = x(2x-3)
[tex]27=2x^{2} -3x[/tex]
[tex]2x^{2} -3x-27=0[/tex]
[tex]2x^{2} +6x-9x-27=0[/tex]
2x(x+3)-9(x+3)=0
(2x-9)(x+3)=0
2x-9=0
2x=9
x=9/2
x=4.5
L=2x-3=2*4.5-3 =9-3=6
The dimensions of the rectangle are; width = 4.5ft and length = 6ft.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
The length of the rectangle is 3ft less than twice the width.
Let width = x
Length = 2x - 3
The area of the rectangle = length × Width
27 = x(2x-3)
2x² - 3x = 27
2x² - 3x - 27 = 0
2x(x + 3) - 9(x + 3) = 0
(2x-9)(x+3)=0
The solutions are;
2x-9=0
2x=9
x=9/2
x = 4.5
(x+3) = 0
x = -3
The width cannot be negative.
So,
Length = 2x-3 = 2*4.5-3 = 9 - 3
Length = 6
Hence, The dimensions of the rectangle are; width = 4.5ft and length = 6ft.
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A hole the size of a photograph is cut from a red piece of paper to use in a picture frame.
On a coordinate plane, 2 squares are shown. The photograph has points (negative 3, negative 2), (negative 2, 2), (2, 1), and (1, negative 3). The red paper has points (negative 4, 4), (4, 4), (4, negative 4), and (negative 4, negative 4).
What is the area of the piece of red paper after the hole for the photograph has been cut?
17 square units
25 square units
39 square units
D47 square unitsthis is the ansswer
Answer:
D. 47 square units
Step-by-step explanation:
The area of the piece of red paper after the hole for the photograph has been cut is the difference between the area of large square and are of small square.
Area of large square:
The length of the side of large square is
[tex]EF=|-4-4|=8\ units[/tex]
Area of large square [tex]=8^2=64\ un^2.[/tex]
Area of small square:
The length of the side of large square is
[tex]AB=\sqrt{(-3-(-2))^2+(-2-2)^2}=\sqrt{(-1)^2+(-4)^2}=\sqrt{1+16}=\sqrt{17}\ units[/tex]
Area of small square [tex]=\sqrt{17}^2=17\ un^2.[/tex]
Difference:
[tex]64 \ un^2-17\ un^2=47\ un^2[/tex]
A park designer wanted to place a fountain so that it was close to both the slide and the swings. Refer to the coordinate grid shown. Each unit on the grid represents 100 ft.
(A) find the distance from the slide to the foundation show your work.
(B) if each jump = 100ft, how far is it from the slide to the fountain?
Please show your work :)
Answer:
200 ft.
2 jumps
Step-by-step explanation:
The slide is placed at coordinates (-2,0) and the fountain is placed at coordinates (-2,-2).
(A) Therefore, using the distance between two known points formula, the distance from the slide to the fountain is given by
[tex]\sqrt{(-2 - ( -2))^{2} + (-2 - 0)^{2}} = \sqrt{(0 + 4)} = 2[/tex] units.
Now, given that each unit on the grid represents 100 ft.
So, the distance from slide to the fountain is (100 × 2) = 200 ft. (Answer)
(B) Now, if each jump = 100 ft, then the slide is 2 jumps apart from the fountain. (Answer)
We know the distance between two known points on the coordinate plane ([tex]x_{1},y_{1}[/tex]) and ([tex]x_{2},y_{2}[/tex]) is given by the following formula
Distance = [tex]\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2} )^{2}}[/tex]
The distance from the slide to the fountain is sqrt(29) units on the grid or 100*sqrt(29) feet. If each unit represents 100 ft, the distance is 100*sqrt(29) feet.
Explanation:To find the distance from the slide to the fountain, we need to determine the coordinates of both points on the grid. Let's assume the slide is located at point A (2,4) and the fountain is located at point B (7,6).
Using the distance formula, d = sqrt(([tex]x2 - x1)^2 + (y2 - y1)^2)[/tex], we can plug in the coordinates:
d = [tex]sqrt((7 - 2)^2 + (6 - 4)^2)[/tex] = sqrt(25 + 4) = sqrt(29).
So, the distance from the slide to the fountain is approximately sqrt(29) units on the grid or 100*sqrt(29) feet.
To determine the distance in feet if each unit on the grid represents 100 ft, we can simply multiply the distance by 100:
Distance = sqrt(29) * 100 = 100*sqrt(29) feet.
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Which number line shows the solution set to this inequality?
-2x +9< x-9
Answer:
B
Step-by-step explanation:
-2x + 9 < x - 9 simplifies to x < 6
Answer:
A is the answer
Step-by-step explanation:
Solve the equation and the answer would come out to be 6
open dot that goes to the right
Vince uses a coordinate plane to map an amusement park. The ordered pairs are locations of entrances to different rides at the park. He graphs and labels the ordered pairs. Then he connects the points to show the path around the park. What is the length of the path on the grid?
Please Help!
Answer:
The length is 52 units
Step-by-step explanation:
we know that
The length of the path. is equal to the perimeter of polygon A.B.C.D.E.F
[tex]P=A.B+B.C+C.D+D.E+E.F+A.F[/tex]
The formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
step 1
Find the distance A.B
we have
[tex]A(-7,7),B(6,7)[/tex]
substitute in the formula
[tex]d=\sqrt{(7-7)^{2}+(6+7)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(13)^{2}}[/tex]
[tex]d_A_B=13\ units[/tex]
step 2
Find the distance B.C
we have
[tex]B(6,7),C(6,-2)[/tex]
substitute in the formula
[tex]d=\sqrt{(-2-7)^{2}+(6-6)^{2}}[/tex]
[tex]d=\sqrt{(-9)^{2}+(0)^{2}}[/tex]
[tex]d_B_C=9\ units[/tex]
step 3
Find the distance C.D
we have
[tex]C(6,-2),D(3,-2)[/tex]
substitute in the formula
[tex]d=\sqrt{(-2+2)^{2}+(3-6)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(-3)^{2}}[/tex]
[tex]d_C_D=3\ units[/tex]
step 4
Find the distance D.E
we have
[tex]D(3,-2),E(3,-6)[/tex]
substitute in the formula
[tex]d=\sqrt{(-6+2)^{2}+(3-3)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(0)^{2}}[/tex]
[tex]d_D_E=4\ units[/tex]
step 5
Find the distance E.F
we have
[tex]E(3,-6),F(-7,-6)[/tex]
substitute in the formula
[tex]d=\sqrt{(-6+6)^{2}+(-7-3)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(-10)^{2}}[/tex]
[tex]d_E_F=10\ units[/tex]
step 6
Find the distance A.F
we have
[tex]A(-7,7),F(-7,-6)[/tex]
substitute in the formula
[tex]d=\sqrt{(-6-7)^{2}+(-7+7)^{2}}[/tex]
[tex]d=\sqrt{(-13)^{2}+(0)^{2}}[/tex]
[tex]d_A_F=13\ units[/tex]
step 7
Find the perimeter
[tex]P=A.B+B.C+C.D+D.E+E.F+A.F[/tex]
substitute the values
[tex]P=13+9+3+4+10+13[/tex]
[tex]P=52\ units[/tex]
how to write three hundred fifty and ninety-four thousandths in standard form?
Answer:
It is 3.5 x 10^2 and 9.4x10^4
Step-by-step explanation:
350 = 3.5 x 10^2
which implies 3 - hundred
5 - tens
0 - units
94000 = 9.4x10^4
which implies 9 - ten thousand
4 - thousand
0 - hundred
0 - tens
0 - units
Answer:
Repost: 350.94
Step-by-step explanation:
three hundred: 3__
fifty: _5_
And: Is for the decimal point
Ninety (Thousandths): ___.9_
Four (Thousandths): ___._4
Now just put it all together and you get 350.94
Hopes this helps in the future ^_^
2. Compare CH3Cl and CCl4. Explain why one is polar and one is nonpolar. Be sure to use
the term symmetry in your explanation.
Answer:
Step-by-step explanation:
CH3Cl is polar while CCl4 is non polar.
When we consider whether something is polar or not we have to consider the following:
-Molecular symmetry
-Polar bonds (based on Electronegativity)
-Whether or not all the bonds are equal in magnitude
So for CCl4:
-All of the bonds are equal, in that all the electronegativity differences (delta EN) are the same.
-There are polar bonds as the delta EN between Cl (EN = 3.0) and C (EN=2.5) is 0.5 which means the bond is polar covalent
But when we look at the symmetry of the molecule (by drawing the lewis structure) there are no lone pairs, meaning that the molecule is symmetrical and therefore, it is non polar.
For CH3Cl:
-There are polar bonds here whether between C-H or C-Cl like above, both delta EN are greater than or equal to 0.5
-But, all of the bonds are not equal in strength. Cl (3.0) atoms have much higher electronegativity values than H (2.1) and there for they will "pull" the electrons closer and polarize the molecule. Therefore, the differences in bonds causes this molecule to be asymmetrical, and hence polar.
CH3Cl is polar due to an uneven electron distribution and net dipole moment, due to the different atoms attached. In contrast, CCl4 is nonpolar because it's symmetrical with the dipole moments cancelling out.
Explanation:The compounds CH3Cl and CCl4 vary in their polarities due to their molecular geometry, leading to different symmetries. CH3Cl has a tetrahedral shape but is polar because of the presence of the electronegative Chlorine atom and three Hydrogen atoms, creating an uneven distribution of electrons and thereby, a net dipole moment. On the other hand, CCl4 is also tetrahedral, but it's nonpolar due to its symmetry. As it has four Chlorine atoms evenly distributed around the Carbon atom, the dipole moments cancel out each other leading to no net dipole moment.
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1: i am thinking of a number. When it is increased by 7, it equals 21. what is my number
N = 28
N = 14
N = 7
N = 147
2: i am thinking of a number. It is multiplied by 9. The product is 27. What is my number
N = 36
N = 18
N = 3
N = 4
3: Translate the following sentence into an equation. Then solve the equation
The difference of a number and 7 an 21
21 - 7 = n; n =14
n + 7 = 21 ; n=14
n + = 21 ; n = 28
21 - 7 = n; n =14
Answer:
N = 14
Step-by-step explanation:
Let the number be N. Then:
N + 7 = 21
Now solve this equation for N:
Subtract 7 from both sides. We get:
N = 14
Answer:
1. n = 14
2. n = 3
3. n - 7 = 21; n = 28
Mark is slicing a tomato for 4 members do his family. Each person will get 1/6 of the tomato. What fraction of the tomato will Mark slice. Use fraction strips as needed.
Answer:
4*1/6=2/3
Step-by-step explanation:
we have 4 of 1/6
so 1/6 +1/6 +1/6 +1/6=4*1/6=4/6=2/3
Renae likes to make pizza dough on the weekends. She has 8 1/3 cups of flour. She needs 5/6 of a cup for each pizza.How many pizzas can she make?
Answer:
She can make 10 pizzas.
Step-by-step explanation:
8 1/3=25/3
(25/3)/(5/6)=(25/3)(6/5)=150/15=10
The data below shows the age distribution of cases
of a certain disease reported during the year at a
hospital
34 17 25 37 19 19 27 19 44 24
24 22 32 12 13 16 18 14 12 16
14 17 10 16
20 15 15 10 10
14 17 20 18 19 13 13 B 18 30
24 34 44 31 43 40 28 31 18 22
15 31 18 27 35 35 20 32 38 32.
22
Organising the data into a frequency distribution
lor table, calculate the coefficient of Skewness
and kur tosis and interpret your results
Answer:
I would line up the numbers in order
The coefficient of skewness is 0.26, indicating slight positive skewness and the kurtosis is approximately -0.84, indicating a platykurtic distribution.
We have,
To calculate the coefficient of skewness and kurtosis, we first need to organize the data into a frequency distribution table.
Age | Frequency
10 | 3
12 | 2
13 | 4
14 | 5
15 | 5
16 | 5
17 | 4
18 | 6
19 | 4
20 | 3
22 | 4
24 | 4
25 | 1
27 | 3
28 | 1
30 | 2
31 | 4
32 | 3
34 | 3
35 | 3
37 | 1
38 | 1
40 | 1
43 | 1
44 | 2
To calculate the coefficient of skewness, we use the formula:
Coefficient of Skewness = (mean - mode) / standard deviation
Mean = (10 * 3 + 12 * 2 + 13 * 4 + ... + 44 * 2) / 100 ≈ 20.49
Mode = 18 (the most frequent value in the dataset)
Standard Deviation
= √[((10 - mean)² * 3 + (12 - mean)² * 2 + ... + (44 - mean)² * 2) / 100]
≈ 9.63
Coefficient of Skewness = (20.49 - 18) / 9.63 ≈ 0.26
To calculate the kurtosis, we use the formula:
Kurtosis = ∑[((x - mean) / standard deviation)⁴ * frequency] / (n * standard deviation⁴) - 3
Kurtosis = [((10 - mean) / standard deviation)⁴ * 3 + ((12 - mean) / standard deviation)⁴ * 2 + ... + ((44 - mean) / standard deviation)⁴ * 2] / (100 * standard deviation⁴) - 3 ≈ -0.84
Interpretation:
Coefficient of Skewness:
The coefficient of skewness is positive (0.26), indicating that the data is slightly skewed to the right (positively skewed). This means that there is a longer tail on the right side of the distribution.
Kurtosis:
The kurtosis value is approximately -0.84. Since it is less than 3, the distribution is considered platykurtic. This means that the distribution has lighter tails and is flatter compared to a normal distribution.
Thus,
The coefficient of skewness is 0.26, indicating slight positive skewness and the kurtosis is approximately -0.84, indicating a platykurtic distribution.
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Josef is on a planning committee for the eighth-grade party. The food, decoration, and entertainment costs a total of $350. The committee has $75 already. If the committee sells the tickets for $5 each, at least how many tickets must be sold to cover the remaining cost of the party?
Answer:
At least 55 tickets must be sold to cover the remaining cost of the party.
Step-by-step explanation:
Total money needed for the party = $350
The money already with the committee = $75
Now, the money yet to be collected = Total Party Budget - Money present
= $350 = $75 = $275
Now, the cost of 1 ticket = $5
Let us assume the number of tickets sold to cover the cost of party = m
⇒ The cost of m tickets = 5 m
The renaming cost = Total cost of m tickets
or, 5 m = $275
⇒ m = 275/5 = 55
or, m = 55
Hence, at least 55 tickets must be sold to cover the remaining cost of the
party by Josef.
- 5 = 1/(x + 12)
Solve the equation for y
Answer:
x=-61/5
Step-by-step explanation:
-5=1/(x+12)
x+12=-1/5
x=-1/5-12
x=-1/5-60/5
x=-61/5
Solve for x
X+(x+4)=28
Answer: x = 12
Step-by-step explanation:
First you must simplify:
x + (x + 4) = 28
Reorder the terms:
x + (4 + x) = 28
Remove parenthesis around (4 + x):
x + 4 + x = 28
Reorder the terms:
4 + x + x = 28
Combine like terms: x + x = 2x
4 + 2x = 28
Solving
4 + 2x = 28
Now we must solve for the variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + 2x = 28 + -4
Combine like terms: 4 + -4 = 0
0 + 2x = 28 + -4
2x = 28 + -4
Combine like terms: 28 + -4 = 24
2x = 24
Divide each side by '2'.
x = 12
Simplifying
x = 12
Hope this helps! :)
What is the measure of each interior angle of a regular hexagon?
Answer:
120°
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
A hexagon has 6 sides, thus
sum = 180° × 4 = 720°
To find the measure of each interior angle divide by 6, that is
interior angle = 720° ÷ 6 = 120°
Answer: 120°
Step-by-step explanation: Let's start by finding the sum of the measures of the interior angles. The sum of the measures of the interior angles of a polygon can be found using the formula 180 (n - 2) where n represents the number of sides in the polygon.
Since a regular hexagon has 6 sides, we can plug a 6 in for n in our formula and we have 180 (6 - 2) where 6 represents the number of sides. We can simplify this by subtracting 2 from 6 inside the parentheses to get 180 (4) which is 720.
So the sum of the measures of the interior angles of a regular hexagon is 720°.
However, we want to know the measure of each interior angle. Since the angles of a regular hexagon are all congruent, we simply divide the sum of the measures of the angles which is 720 by the number of angles or sides which is 6 to get 120.
So the measure of each interior angle of a regular hexagon is 120°.
So the formula for finding the measure of each interior angle of a regular polygon is simply the sum of the interior angles 180 (n - 2) divided by the number of sides which is n.
Image provided.
What is the value of the discriminant of the quadratic equation -2x =-8x+8, and what does its value mean about the number
of real number solutions the equation has?
Final answer:
The value of the discriminant is 36, which means that the quadratic equation -2x = -8x + 8 has two distinct real solutions.
Explanation:
The given equation -2x = -8x + 8 can be rearranged into a quadratic equation: -8x + 8 + 2x = 0. Combining like terms gives: -6x + 8 = 0. To find the discriminant of this quadratic equation, we look at the coefficient of x^2, which is 0. Since the discriminant D = b^2 - 4ac, where a = coefficient of x^2, b = coefficient of x, and c = constant term, in this case, a = 0, b = -6, and c = 8. Plugging these values into the formula, we have: D = (-6)^2 - 4(0)(8) = 36 - 0 = 36.
The value of the discriminant is 36. The discriminant tells us about the number of real number solutions the equation has. If the discriminant is positive (D > 0), then the equation has two distinct real solutions. If the discriminant is zero (D = 0), then the equation has one real solution. If the discriminant is negative (D < 0), then the equation has no real solutions.
In this case, since the discriminant is positive (D = 36), the quadratic equation has two distinct real solutions.