To create a consistent and independent system of equations with the solution (-1, -4), we generate two linear equations: 2x - 3y = 10 and 5x + 4y = -21, both of which are satisfied by the given solution.
Explanation:To construct an independent and consistent system of equations that has the solution (-1, -4), we can create two distinct linear equations where the point (-1, -4) satisfies both.
As an example, we choose two arbitrary linear equations, ensuring that they are not multiples of each other, and that they are satisfied by x = -1 and y = -4.
The general form of a linear equation is Ax + By = C.
For our first equation, we could have 2x - 3y = 2(-1) - 3(-4) = 10. To ensure the second equation is not a multiple of the first, we could choose 5x + 4y = 5(-1) + 4(-4) = -21.
The system of equations would then be:
2x - 3y = 105x + 4y = -21Evaluate the numerical expression. (2/5)^2 • 100 ÷ 2/3 + [2^4 ÷ (13 - 5)]
Answer:
14 /3- fraction
(Decimal: 4.666667)
Step-by-step explanation:
The value of the numerical expression is 26
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the expression be A = (2/5)^2 • 100 ÷ 2/3 + [2^4 ÷ (13 - 5)]
Now , on simplifying the equation , we get
A = ( 2/5 )² x 100 / ( 2/3 ) + [ 2⁴ / 8 ]
A = ( 4/25 ) x ( 100 x 3 ) / 2 + 2
So , the equation will be
A = 4/25 x ( 300/2 ) + 2
A = 4/25 x 150 + 2
A = 4 x 6 + 2
A = 24 + 2
A = 26
Therefore , the value of A is 26
Hence , The value of the numerical expression is 26
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Sarah lost her science book. Her school charges a lost book fee equal to 75% of the cost of the book. Sarah received a notice stating that she owed the school $60 for he lost book. How much did the school pay for the book.
Answer: the school paid $80 for the book.
Step-by-step explanation:
Let x represent the amount that the school paid for the book.
Her school charges a lost book fee equal to 75% of the cost of the book. It means that the amount that the school would charge on a book that cost $x is
75/100 × x = 0.75 × x = 0.75x
Sarah received a notice stating that she owed the school $60 for he lost book. It means that
0.75x = 60
x = 60/0.75
x = $80
Leah has a 22 ounce coffee. She drinks 7 ounces. Enter the percentage of ounces Leah has
left of her coffee. Round your answer to the nearest hundredth.
Answer:
The coffee Leah has left in percentage is 68.18%
Step-by-step explanation:
Given data
Total available coffee = 22 ounces
Amount She took out = 7 ounces
Let us carry out a simple subtraction arithmetic to find out the remainder
Hence remaining coffee = 22-7= 15
To expressing the remainder as a percentage we have
(15/22)*100=0.6818*100
= 68.1818%
To the nearest hundredths we have
= 68.18%
Answer: 68.18%
Step-by-step explanation:
Leah has a 22 ounce coffee and she drinks 7 ounces of the coffee. This means she will have:
22 - 7 = 15 ounces left.
The percentage of ounces of coffee Leah has left of her coffee will be the number of ounces left divided by the total number of ounces of coffee multiplied by 100. This will be:
= 15/22 × 100
= 0.6818 × 100
= 68.18%
The percentage of coffee Leah has left is 68.18%.
Kevin and Ethan are employees for a company. Ethan is making a salary of $34,200. Ethan is earning a salary that is 28% lower than the salary of Kevin. What salary is Kevin earning?
Answer:
$45,000
Step-by-step explanation:
Let Kevin's Salary=x
Ethan's Salary=$34,200.
Since Ethan is earning a salary that is 28% lower than the salary of Kevin.
Ethan is earning (100-24)%=76% of Kevin's Salary.
76% of Kevin's Salary=$34,200.
0.76x=34200
Divide both sides by 0.76
x=45000
Kevin's Salary is $45,000.
The sun casts a 70 foot shadow on a 30 foot tree. Find the angle of elevation to the nearest degree.
Answer:
23°
Step-by-step explanation:
We apply Pythagorean theorem to determine the missing length, Hypotenuse:
[tex]h^2+b^2=H^2\\\\70^2+30^2=H^2\\\\H=\sqrt{5800}\\\\=76.15773\ ft[/tex]
This hypotenuse corresponds to the right triangle and the tree's height, corresponds to the angle of elevation:
-We apply the law of Sines;
[tex]\frac{a}{Sin \ A}=\frac{b}{Sin\ B}\\\\\\\frac{76.15773}{Sin \ 90}=\frac{30}{Sin\ h}\\\\h=Sin^{-1}\frac{30}{76.15773}\\\\=23.19859\approx 23\textdegree[/tex]
Hence, the angle of elevation is 23°
What are two numbers that equal to 28 in multiplication
Answer:
7*4
14*2
Step-by-step explanation:
Answer:
Answers will vary
Step-by-step explanation:
There are many possibilities, especially if you're going beyond whole numbers, meaning decimals work as well
Whole numbers
1 and 28
2 and 14
4 and 7
Decimals
3 and 9.33 or 9 1/3
5 and 5.6
6 and 4.67 or 4 2/3
8 and 3.5
9 and 3.11
10 and 2.8
These are just a few simple ones, it gets even more complicated if you have two numbers both with decimals
What is measure of angle P? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth. ° P Q R is a right triangle. Q is a right angle. P Q is equal to eight centimeters, Q R is equal to fifteen centimeters and P R is equal to seventeen centimeters.
Given:
In ΔPQR, ∠Q = 90°
PQ = 8 cm
QR = 15 cm and
PR = 17 cm
To find the value of ∠P.
Formula
By Trigonometric ratio we get,
[tex]tan \theta=\frac{opp}{adj}[/tex]
Now let us take ∠P = θ
With respect to θ, QR be the opposite side and PQ be the adjacent side.
So,
tan θ = [tex]\frac{QR}{PQ}[/tex]
tan θ = [tex]\frac{15}{8}[/tex]
θ = [tex]tan^{-1} (\frac{15}{8} )[/tex]
θ = 61.93° (approx)
Hence, the value of ∠P is 61.93° (approx).
Answer:
61.93°
Step-by-step explanation:
Using cosine law:
15² = 8² + 17² - 2(8)(17)cosP
225 = 353 - 272cosP
cosP = 8/17
P = 61.92751306
Jared worked 10 hrs in one week and earned $87.50 how many dollars per hour did he earn
Answer:
8.75 per hour
you would put the overall money earned and divide it by how many hours he worked
example:
87.50 ÷ 10 = 8.75
Leah and her children went into a bakery and will buy cupcakes and brownies. Each cupcake costs $4.75 and each brownie costs $3. Leah has a total of $65 to spend on cupcakes and brownies. Write an inequality that would represent the possible values for the number of cupcakes purchased, cc, and the number of brownies purchased, b.B.
Answer:
Step-by-step explanation:
C=Cupcakes
B=Brownies
$4.75 per cupcake...(4.75c)
$3.00 per brownies..(3b)
Leah has $65 only. ([tex]\leq[/tex] 65)
4.75c + 3b[tex]\leq[/tex] 65
how to find the area of a complex shape
Answer:
B. 114 cm²
Step-by-step explanation:
You want to know the area of a complex shape consisting of a triangle and a semicircle.
Areas of PartsThe shape can be divided at the dotted line into two shapes whose areas you have formulas for:
semicircle of radius 5 cmtriangle with base 15 cm and height 10 cmUsing the formulas for their areas, we find the area of each shape to be ...
A = (1/2)πr² . . . . . . area of semicircle with radius r
A = (1/2)π(5 cm)² = 25/2π cm² ≈ 39 cm²
A = (1/2)bh . . . . . . area of triangle with base b and height h
A = (1/2)(15 cm)(10 cm) = 75 cm²
Total areaThe sum of the areas of the parts is ...
total area = semicircle area + triangle area
total area = 39 cm² +75 cm²
total area = 114 cm²
The area of the complex shape is about 114 cm².
Can anyone help me out with this?
Can someone please help me?
its for geometry and i dont know it pls help
Hello.
The angle shown for 1 (and 3) is ∠40.
A straight line is shown, which is 180°. So the measure of ∠4 is 140°
The triangle shown is rotated about line m. A triangle with side lengths of 6 centimeters, 8 centimeters, and 10 centimeters is shown. The triangle is rotated about line m at the side with length 8 centimeters. What is the approximate base area of the resulting three-dimensional figure? Area of a circle: A = πr2
From the information given, the area of the circle is: "113 sq. cm".
What is the formula for the area of a circle?The formula to find the area of a circle is πr².
Using the side as the radius of the circle, we can calculate the area of the base area.
Note;
r = 6
Thus,
A = π * 6²
A = (22/7) * 36
A = 3.14285714286 * 36
Hence, The area of the circle A = 113.142857143 or 113 sq. cm.
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Diana has a 32 ounce bag of mixed nuts: 1/2 of the mix is peanuts, 1/9 of the mix is Brazil nuts, and 1/12 of the mix is cashews. How many of the bag are cashews
Answer:
2.67 ounce of cashews are in the mix.
Step-by-step explanation:
Since we are dealing with a 32 ounce bag of mixed nuts and 1/12 of this bag is cashews (1/12 of the mix),
Then:
1/12 × 32 ounce = The actual quantity of cashew nuts in the mix.
= 1/12 × 32
= 32/12
= 2.67 ounce of cashews are in the bag.
Answer:
2.666ounce is contained in the bag
Step-by-step explanation:
Given that 32 ounce of bag has mixed nuts of which 1/12 of this bag contain cashews.
(1/12 of the entire mix),
Hence,
1/12 × 32 ounce
= 1/12 × 32
= 32/12
= 2.666ounce of cashews are in the bag.
Your college fund has $65,000. It is currently in an account which pays 2.3% compounded monthly. How much money will you have in 15 years
Answer:
$91,749.04
Step-by-step explanation:
Lets use the compound interest formula provided to solve this:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
P = initial balance
r = interest rate (decimal)
n = number of times compounded annually
t = time
First, change 2.3% into a decimal:
2.3% -> [tex]\frac{2.3}{100}[/tex] -> 0.023
Since the interest is compounded monthly, we will use 12 for n. Lets plug in the values now:
[tex]A=65,000(1+\frac{0.023}{12})^{12(15)}[/tex]
[tex]A=91,749.04[/tex]
You will have $91,749.04 in 15 years.
The number part when a number and a variable are multiplied together in a term is called the _____.
Answer:
coefficient
Step by-step explanation:
If f(x) is discontinuous, determine the reason.[tex]f(x) = \left \{ {{x^2 + 4; x \leq 1} \atop {x+4; x \ \textgreater \ 1}} \right.[/tex]a. f(x) is continuous for all real numbersb. The limit as x approaches 1 does not exist c. f(1) does not equal the limit as x approaches 1 d. f(1) is not defined
Answer:
a. f(x) is continuous for all real numbers
Step-by-step explanation:
At x = 1
Piece 1:
f(x) = 1² + 4 = 5
Piece 2:
f(x) = 1 + 4 = 5
First piece ends at (1,5)
Second piece starts at (1,5)
So no discontinuity
Joe wants to rent an apartment with an initial monthly rent of $1,400. He has been told that the landlord raises the rent 1.25% each year. Using an exponential function ( or a method of your own) to model this situation, calculate the rent that Joe will have to pay for the 4th year of living in the apartment.
Answer: his pay for the 4th year is $1453.16
Step-by-step explanation:
The landlord raises the rent 1.25% each year. It means that the rent is increasing in geometric progression.
The formula for determining the nth term of a geometric progression is expressed as
Tn = ar^(n - 1)
Where
a represents the first term of the sequence.
r represents the common ratio.
n represents the number of terms.
From the information given,
a = $1,400
r = 1 + 1.25/100 = 1.0125
n = 4 years
The 4th term(year), T4 is
T4 = 1400 × 1.0125^(4 - 1)
T4 = 1400 × 1.0125^3
T4 = $1453.16
Using an exponential function, the rent Joe will have to pay for the fourth year, with a 1.25% annual increase, is approximately $1,453.38.
To calculate the rent Joe will have to pay for the fourth year of living in the apartment with an annual rent increase of 1.25%, we will use an exponential function. The general formula for compounded growth is given by:
Future Value = Present Value ×(1 + rate)number of periods
In Joe's case, the Present Value is the initial monthly rent of $1,400, the rate is 1.25% or 0.0125 when expressed as a decimal, and the number of periods is 3 years since we are calculating the rent at the start of the fourth year. Plugging these values into the formula:
Rent for the fourth year = $1,400 × (1 + 0.0125)3
Let's calculate that:
Rent for the fourth year = $1,400 × (1.0125)3
Rent for the fourth year approximately = $1,400 × 1.038128
$1,453.38
Hence, Joe will have to pay about $1,453.38 for the fourth year of rent.
Find the common ratio of the geometric sequence –1,-8, -64, ...
The common ratio of the geometric sequence –1,-8, -64, ... is 8. This is calculated by dividing a term in the sequence by its preceding term and is same across all consecutive terms.
Explanation:In a geometric sequence, the common ratio is found by dividing any term by its preceding term. Here, the sequence given is –1,-8, -64, ...
Let's calculate the ratio for this series: We divide the second term (-8) by the first term (-1), which is 8. Let's check it with the next terms, where we divide the third term (-64) by the second term (-8). We find the ratio to be 8 again.
Therefore, the common ratio of the given geometric sequence –1,-8, -64, ... is 8.
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The common ratio of the geometric sequence -1, -8, -64, ... is -8, which results from dividing any term of the sequence by its preceding term.
Geometric sequence: -1, -8, -64, ...
Common ratio:
To find the common ratio, we divide each term by its preceding term.
In this case, -8 ÷ (-1) = 8 and -64 ÷ (-8) = 8.
Therefore, the common ratio is 8.
0). Where is Point B on the number line?
Answer: point B should be the 2nd number on the number line.
Step-by-step explanation:
the answer is shove it up your whole
hAHA JK ITS B
6 x 1 x 5 x 1/10 as a decimal
Answer:
30.10
Step-by-step explanation:
The length of a rectangle is 8 inches longer than half of its width.The area of the rectangle is 18 square inches.How many inches wide is the rectangle
Answer:
The correct answer is 2 inches.
Step-by-step explanation:
Let l inches and w inches be the length and width of a rectangle respectively.
According to the given problem, l - 8 = [tex]\frac{w}{2}[/tex].
Area of the rectangle is given to be, according to the question, 18 square inches.
Thus l × w = 18
⇒ l × (2l - 16) = 18
⇒ 2 [tex]l^{2}[/tex] - 16l - 18 = 0
⇒ [tex]l^{2}[/tex] - 8l - 9 = 0
⇒ ( l - 9) ( l + 1) = 0
The possible values of l are 9 and -1. As the length cannot be equal to -1, thus the value of the length is 9 inches.
Width of the rectangle is 2 inches.
Vicente has a prism-like water tank whose base area is 1.2 square meters. He bought 6 goldfish at the store, and the store owner told him to make sure their density in the tank isn’t more than 4 fish per cubic meter. Vicente needs to figure out how high to fill the water in the tank. What is the lowest possible height so the fish aren’t too crowded?
Answer:
1.25 m.
Step-by-step explanation:
Given,
Area of base = 1.2 m²
Number of gold fish = 6
Density of the tank should be = 4 fish/m³
Height of the tank= ?
4 fish = 1 m³
6 fish = 1.5 m³
Volume required for 6 fish is 1.5 m³
V = area of base x height
1.5 = 1.2 x h
h = 1.25 m
Hence, height of the tank is equal to 1.25 m.
Answer:
1.25
Step-by-step explanation:
Hello Mr. White drove 15 miles in July. He drove 8 times as many miles in September as he did in July. He drove 3 times as many miles in August as he did in September. How many miles did Mr. White drive in August? And that is my question I don't get it
Answer:
360 miles
Step-by-step explanation:
15 times 8= 120 miles I. September
Times 3 in August=360 miles
What is the next term of the geometric sequence?
2,−10,50,...
Answer:
-250
Step-by-step explanation:
I don't know for sure but I hope it's correct.
Answer:
-250
Step-by-step explanation:
What kind of slope does the following line have?
+
Answer:
horizontal and vertical
Step-by-step explanation:
if its the plus?
Amelia is 3 years older than Caleb, and Caleb is 2 years more than half of Amelia's age. The system of equations represents this situation. A = 3 + C C = 2 + 0.5A How old is Amelia? How old is Caleb?
Step-by-step explanation:
Simple
If Amelia is 10 years old and so half of Amelia age = 5
Caleb is 2 years more so = 5 + 2 = 7
It means Caleb age = 7
And Amelia age = 10
The cylinder shown has a radius of 3 inches. The height is three times the radius. Find the volume of the cylinder. Round your solution to the nearest tenth
Answer:
254.5 Inches Cubed
Step-by-step explanation:
Formula for Finding the Volume of a Cylinder: [tex]V=\pi r^2h[/tex]
The radius is 3 inches.
[tex]r=3[/tex]
The height is three times the radius.
Multiply the radius by three to get the height.
[tex]h=3*3\\h=9[/tex]
The height is 9 inches.
Use the formula to find the volume.
[tex]\pi (3)^29= \pi (9)9=81\pi[/tex]
The exact volume is 81[tex]\pi[/tex] inches cubed.
[tex]81 * \pi[/tex] ≈ 254.47
254.47 ≈ 254.5
The volume of the cylinder should be about 254.5 inches cubed.
Bryant’s pool contains 13,000 gallons of water.
The maximum rate at which the city allows pools to be drained is 720 gallons per hour.
Write a function that represents the number of gallons of water left in Bryant’s pool t hours after he starts draining, if he drains the pool at the maximum rate.
Answer:
13000=t720
Step-by-step explanation:
720 x t = 13000
The function that represents the number of gallons of water left in Bryant’s pool t hours after he starts draining is 13,000 - 720t.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given Bryant’s pool contains 13,000 gallons of water. The maximum rate at which the city allows pools to be drained is 720 gallons per hour. Therefore, the equation can be written as,
Water left = 13,000 - 720t
Hence, the function that represents the number of gallons of water left in Bryant’s pool t hours after he starts draining is 13,000 - 720t.
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