The temperature at the beginning of the week was = 65
and, the temperature now = 18.2
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
After one week, the temperature decreased by 46.8° with a
percent change of 72%.
let,
the temperature at the beginning of the week = x
so, we get,
x= 46.8/72*100
=65
i.e. the temperature at the beginning of the week was = 65
and, the temperature now = 18.2
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solve the quadratic equation numberically (using tables or x- and y- values ). (x+2)(x+3)=12 a.x=-1 or x=3 b. x=2 or x=-3 c. x=-6 or x=1 d. x=1 or x=-1
Answer:
c.
Step-by-step explanation:
[tex](x + 2)(x + 3) = 12 \\ {x}^{2} + 5x + 6 = 12 \\ {x}^{2} + 5x - 6 = 0 \\ (x + 6)(x - 1) = 0 \\ x = - 6 \: or \: x = 1[/tex]
PLEASE PLEASE PLEASE HELP ME IM BEgging YOUUU
Answer:
Step-by-step explanation:
answer is D my friend.
Consider the graph of the function f(x) = 2^x
Y-intercept of g(x) at (0,2) therefore correct option is D
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable is called a function.
Given is a function f(x) = 2ˣ
g(x) = 2f(x) = 2(2ˣ)
The y-intercept of g(x) = 2f(x),
Substitute in 0 for x and solve for y
y=2(2⁰)
Anything raised to 0 is 1.
y=2
Y-intercept in point form.
Hence, y-intercept of g(x) : (0,2)
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A pyramid is composed of six isosceles triangles and a hexagonal base. Each isosceles triangle has a height of 8 inches and a base of 6 inches. The area of the hexagonal base is 93.5 square inches.
What is the surface area of the pyramid?
Enter your answer in the box.
in²
The total surface area of the hexagonal pyramid is 237.5 in²
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.
The surface area of a solid figure is gotten by adding all the individual surfaces area.
Given the hexagonal pyramid with base of 6 inches and the each isosceles triangle has a height of 8 inches. Hence:
Area of pyramid base = 93.5 in²
The lateral face have 6 triangles faces, hence:
Area of each lateral face = 1/2 * base * height = 0.5 * 8 * 6 = 24 in²
Total area of lateral face = 6 * 24 in² = 144 in²
Total surface area = 144 in² + 93.5 in² = 237.5 in²
The surface area is 237.5 in²
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HELP???? PLEASE !
:(
Answer:
use the calculator
Step-by-step explanation:
that is for they event the calculator
Find the perimeter of the figure to the nearest hundredth.
The perimeter of the shape is 26.85 inches
What is perimeter ?A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference.
The shape consist of a rectangle joined with a semi circle.
Therefore the perimeter of the shape is calculated as:
7+7+ 5+ πd/2
where πd/2 is the circumference of the semi circle
= 7+7+5+(3.14× 5/2)
= 7+7+5+7.89
= 26.85 inches
therefore the perimeter of the shape is 26.85 inches
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b. Stockholders' equity as of December 31, 2003, assuming that assets decreased by $95,000 and liabilities decreased by $29,000 during 2003.
When assets declined by $95,000 and liabilities decreased by $29,000 from December 31, 2003 to December 31, 2004, there was a decrease of $124,000.
what is unitary method ?The device process is a method for addressing issues that entails first figuring out the price of a single unit, then multiplied a certain value to figure out the features offered. Simply put, the unit method is employed to obtain a single unit variable from a multitude that is passed. For example, 40 markers would cost 400 lakhs, which is equal to the cost than one pen. This procedure could follow a regular procedure. a single nation. anything has a distinct identity. Its adjoint and opposite are similar in terms of maths, algebra, mathematical physics, applied mathematics, or math of matrices or operators.
given
assets fell $95,000 in value.
liability reduction of $29,000
= $124000 lessening ($95,00 + $29,000)
When assets declined by $95,000 and liabilities decreased by $29,000 from December 31, 2003 to December 31, 2004, there was a decrease of $124,000.
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Translate and solve: Twelve more than p equals 6.
Answer:-6
Step-by-step explanation:
The solution to the equation "Twelve more than p equals 6" is p = -6.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The given equation is:
12 + p = 6
To solve for p, we need to isolate p on one side of the equation.
We can do this by subtracting 12 from both sides:
12 + p - 12 = 6 - 12
p = -6
Therefore,
The solution to the equation "Twelve more than p equals 6" is p = -6.
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Inga is solving 2x^2 + 12x -3=0. Which steps could she use to solve the quadratic equation? Select three options
To solve the quadratic equation 2x² + 12x - 3 = 0, the correct choices are option 1: 2(x² + 6x + 9) = 3 + 18 and option 3: 2(x² + 6x) = 3.
What is a quadratic equation?
Having the form ax² + bx + c = 0, quadratic equations are second-degree algebraic expressions. From the term "quad," which meaning square, comes the word "quadratic." A quadratic equation is a "equation of degree 2," to put it another way.
The given quadratic equation is 2x² + 12x - 3 = 0.
The first choice for solving the quadratic equation is -
2(x² + 6x + 9) = 3 + 18
Multiply 2 with every number of the other multiplier on the left side -
2·x² + 2·6x + 2·9 = 3 + 18
2x² + 12x + 18 = 3 + 18
Now, on simplifying it further -
2x² + 12x - 3 = 18 - 18
2x² + 12x - 3 = 0
The second choice for solving the quadratic equation is -
2(x² + 6x) = -3
Multiply 2 with every number of the other multiplier on the left side -
2·x² + 2·6x = -3
2x² + 12x = -3
2x² + 12x + 3 = 0
The third choice for solving the quadratic equation is -
2(x² + 6x) = 3
Multiply 2 with every number of the other multiplier on the left side -
2·x² + 2·6x = 3
2x² + 12x = 3
2x² + 12x - 3 = 0
The fourth choice for solving the quadratic equation is -
x + 3 = 21/2
Dividing 21 by 2 on right hand side -
x + 3 = 10.5
x + 3 - 10.5 = 0
x - 7.5 = 0
The fifth choice for solving the quadratic equation is -
2(x² + 6x + 9) = –3 + 9
Multiply 2 with every number of the other multiplier on the left side -
2·x² + 2·6x + 2·9 = -3 + 9
2x² + 12x + 18 = -3 + 9
Now, on simplifying it further -
2x² + 12x = -3 + 9 - 18
2x² + 12x = -12
2x² + 12x + 12 = 0
The sixth choice for solving the quadratic equation is -
(x + 3)² = 3/2
Apply the formula (a+b)² = a² + 2ab + b² on the left side and divide 3 by 2 on the right side -
x² + 6x + 9 = 1.5
x² + 6x + 9 - 1.5 = 0
x² + 6x + 7.5 = 0
Therefore, the correct choices are option 1 and option 3.
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Inga is solving 2x² + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Check all that apply.
2(x² + 6x + 9) = 3 + 18
2(x² + 6x) = –3
2(x² + =6x) = 3
x + 3 = 21/2
2(x² + 6x + 9) = –3 + 9
(x + 3)2 = 6/2
22. Volume of Water in a Reservoir.
A reservoir shaped like a
hemispherical bowl of radius 8 m is filled with water to a depth
of 4 m.
(a) Find an estimate S of the water's volume by approximating the
water with eight circumscribed solid cylinders.
(b) It can be shown that the water's volume is V = (320•pi)/3 m³.
Find the error |V-S| as a percentage of V to the nearest
percent.
On solving the provided question, we can say that Volume of cylinder, V = [tex]\pi r^2 X h[/tex] => V = 3.14 * 8*8*4 = 803.84 cubic m
what is cylinder?One of the most fundamental curved geometric forms is the cylinder, which is often a three-dimensional solid. It is referred to as a prism with a circle as its base in elementary geometry. Several contemporary fields of geometry and topology also define a cylinder as an indefinitely curved surface. A three-dimensional object known as a "cylinder" consists of curving surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure that has two bases that are both identical circles joined by a curving surface at the height of the cylinder, which is determined by the distance between the bases from the center. Examples of cylinders are cold beverage cans and toilet paper wicks.
here,
we have a cylinder
and,
radius, r = 8m
height, h = 4m
Volume, V = [tex]\pi r^2 X h[/tex]
V = 3.14 * 8*8*4 = 803.84 cubic m
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A certain type of lily plant is growing in a pond in such a way that the number of plants is growing
exponentially. The number of plants, N, in the pond at time t is modeled by the function N(t) = ab',
where a and b are constants and t is measured in months. The table shows two values of the function.
t
0
1
N(t)
150
450
Which equation can be used to find the number of plants in the pond at time t?
A. N(t) = 150(1)
B. N(t) = 450(1)
C. N(t) = 150(3)t
D. N(t) = 450(3)
We must identify the function N in order to determine the number of plants in the pond after time t. (t). N(t) = 150 + 450*t = 1,050 + 2,450*t = 3,750*t As a result, there are 3,750 plants in the pond at time t.
What is the equation that can be used to find the number of plants in the pond at time t?We must identify the function N in order to determine the number of plants in the pond after time t. (t).
Using the data in the table, solve this problem to determine the numerical values of a and b.
Write the equation N(t) for the case where t = 0:
N(0) = 150 = ab0
Anything multiplied by the zeroth power is equal to one. So:\s 150 = a.
Nice! Halfway there, I suppose.
Let's now write N(1) while keeping in mind that a = 150:
N(1) = 450 = 150b1
For b, use the formula 450/150 = b 3 = b.
Having established that a and b are equal, we can formulate the equation for N(t) as follows:
N(t) = 150 · 3t
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Carlos built a scale model of an airplane. The scale was 2:5. If the actual airplane was 100 feet long, how long was the model in inches?
Answer:
40 inches
Step-by-step explanation:
to find the actual model, you should apply the scale to the real length
2/5 * 100 = 200/5 = 40
What’s the sum of 6 and 7 and divide it by the sum of 10 and 3
Answer:
1
Step-by-step explanation:
(6+7)/(10+3)=1
so i get the first few parts but i don’t know how to answer the last part, could anyone help please?
i) Sketch, on a single diagram showing values of x from-180° to +180°, the graphs of
y = tan x and y = 4 cos x.
The equation : tan x = 4 cos x
has two roots in the interval -180° ≤x≤ 180°. These are denoted by a and ß, where a <ß.
ii) Show a and ß on your sketch, and express ß in terms of a
iii) Show that the equation tan x = 4 cos x may be written as 4 sin^2x+ sin x−4=0.
Hence find the value of ß-a, correct to the nearest degree.
i) The graph of y = tan x will be a periodic function with period of 180 degrees, with asymptotes at x = (n+1/2)π, where n is an integer. The graph of y = 4 cos x will be a cosine function with amplitude 4 and period 360 degrees.
ii) The roots of the equation tan x = 4 cos x, denoted by a and ß, can be found by solving the equation tan x = 4 cos x for x. The two solutions will be a and ß, where a <ß.
iii) The equation tan x = 4 cos x can be written as 4 sin^2x+ sin x−4=0 by using trigonometric identities. The value of ß-a can be found by using the quadratic formula on this equation. However, it's not possible to give you an exact value without the specific value of a.
(05.09 MC)
Quinn and Mila have to clean the house. It takes Quinn 8 hours to clean the house, while Mila can complete the task in 5 hours. Their mother says that it will take 6.5 hours to complete if they work together.
Part A: Write and solve an equation to determine how long it will take Quinn and Mila to complete the job together. You must show each step in solving to receive full credit.
Part B: Is their mother correct or incorrect? Use complete sentences and justify your answer.
(10 points)
The mother statement is incorrect because they both can finish the work in 3.07 hours.
And the equation is x(1/8 + 1/5) = 1.
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
Quinn and Mila have to clean the house.
Quinn cleans the house in 8 hours.
So, Quinn in 1 hour cleans: 1/8 part of the house.
Mila cleans the house in 5 hours.
Mila in 1 hour cleans: 1/5 part of the house
So, if they work together,
x(1/8 + 1/5) = 1
x = 40/13
x = 3.07 hours.
Their mother is incorrect.
Therefore, the equation is x(1/8 + 1/5) = 1.
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What are the range and domain of the function in the table below? x y -5 0 -3 2 -1 4 1 2 3 0 Domain: __________________________________ Range: __________________________________
Domain: 4 1 2 3 0
Range: -5 0 -3 2 -1
What is range & domain?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
here, we have,
given that,
x y
-5 0 -3 2 -1 4 1 2 3 0
let, y=f(x)
which is domain of x-range.
hence, Domain: 4 1 2 3 0
Range: -5 0 -3 2 -1
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Donna is a pacer in a marathon. She finishes 26.2 miles in 3 hours and 45 minutes while running a constant speed what is donnas speed in miles per hour to the nearest whole number
The donna's speed in miles per hour is seven miles per hour, rounded to the nearest whole number.
what is unitary method ?
A problem can be solved using the unitary method by first determining the value of a single unit, and then multiplying that value to determine the required value. Since it makes sense right away and can be performed mentally if the numbers add up, the unitary technique is frequently helpful for multiplying and dividing by fractions. This makes it a useful approach to explain or justify the often used written algorithms for fractions, particularly division by a fraction. Finding the value of a single unit, then multiplying it by the number of units to obtain the required value, is the unitary method's formula.
given
Donna runs marathons as a pacemaker. Her time to complete 26.2 miles is 3.75 hours.
In order to calculate her speed in miles per hour, we must divide the whole number of miles she ran by the total time it took her, which is,
= (26.2/3.75).
= 6.98 miles/hour.
The donna's speed in miles per hour is seven miles per hour, rounded to the nearest whole number.
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1:3 = 3:9 means and extremes?
Answer: they are equivalent ratios
Tell wether xy= 8 shows direct variation, inverse variation, or neither. Explain your reasoning
On solving the provided question, we can say that we have an equation, xy = 8 => x = 8/y; if x increases then y decreases, so it's a inverse variation
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
here,
we have an equation, xy = 8
x = 8/y
if x increases then y decreases, so it's a inverse variation
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Question 7
Jorge earned 91, 84, 87 on his first three out of four Algebra tests. He wants to get an
average of 90 in the class. What should he make on his last test to achieve this goal?
To earn an average score of 90, the score on the fourth test needs to be 98.
What is average?The core value of a set of data is expressed mathematically as the average of a list of data. It is defined mathematically as the ratio between the total number of units in the list and the sum of all the data. The term "mean" in statistics also refers to the average of a particular set of numerical data.
Given the score of the first three tests as:
91, 84, 87.
The average is given by the following formula:
Average = Sum of scores ÷ total number of tests
Let us suppose the score of fourth test as x.
Given that A = 90:
90 = (91 + 84 + 87 + x) ÷ 4
x = 98
Hence, the score on the fourth test must be equal to 98, to get an average score of 90.
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What is the domain of this function Y=sqrt(4-x)
Answer:(−∞,4],{x|x≤4}
Step-by-step explanation: Find the domain by finding where the equation is defined.
Detailed explanation and solution is available in the photo. I wish you success. If there is something you do not understand, please do not hesitate to ask :)
What is y = 4x^2 + 48x +135 in vertex form
Answer: search it up its a bit
Step-by-step explanation:
Anthony ordered two pizzas for a party. One was a small pepperoni pizza with a radius of 5 inches (5in.), and the other was a large cheese pizza with a 7in. radius. The circumference of the larger pizza is how much longer than the circumference of the smaller pizza?
The circumference of a circle is C=2πr.
Use π≈3.14 for the calculations.
Round your answer to the nearest hundredth.
The circumference of the larger pizza is 12.56 longer than the smaller pizza.
What is circumference?The length around the circle or the perimeter of the circle is called its circumference.
Given that, Anthony ordered two pizzas for a party. One was a small pepperoni pizza with a radius of 5 inches, and the other was a large cheese pizza with a 7 in. radius.
We need to find how much longer than the circumference of the smaller pizza,
We know that,
Circumference of a circle = 2πr.
Therefore,
Circumference of the larger pizza = 2 × 3.14 × 7 = 43.96 in
Circumference of the smaller pizza = 2 × 3.14 × 5 = 31.4 in
Therefore,
Subtracting the circumference of smaller pizza from larger pizza to get the difference = 43.96 - 31.4 = 12.56 in
Hence, the circumference of the larger pizza is 12.56 longer than the smaller pizza.
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A salesman sold 1500 worth of merchandise and received $75 in commssion for the sale. What percent of the sale was commision?
Answer:
5%
Step-by-step explanation:
1500 / 75 = 0.05 as a percentage its 5 %
Multiply the polynomials. 3x(x2 − 6x + 1)
The resulting polynomial is 3x³ - 18x² + 3x.
What is the polynomial?
A polynomial is defined as an expression that is composed of variables, constants, and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable).
3x(x² - 6x + 1) = 3x³ - 18x² + 3x.
This is a polynomial of degree 3. The coefficient of the x³ term is 3, the coefficient of the x² term is -18, and the coefficient of the x term is 3.
This is the product of two polynomials. The first one is 3x and the second one is (x² - 6x + 1).
When multiplying two polynomials, we distribute the coefficient of each term from the first polynomial to each term of the second polynomial and then add the results.
Hence, the resulting polynomial is 3x³ - 18x² + 3x.
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Hello I need help with my math please I need help with question to A and b thanks
Step-by-step explanation:
for what question ?
just in case, always remember Pythagoras
c² = a² + b²
with c being the Hypotenuse, a and b are the legs.
then there is the law of sine
a/sin(A) = b/sin(B) = c/sin(C)
a,b,c being the sides opposite of the A, B, C angles.
and as always : the sum of all angles in a triangle is always 180°.
1.
a)
angle A = 180 - 90 - 35 = 55°
a/sin(55) = 15/sin(90) = 15
a = 15×sin(55) = 12.28728066... m
b)
angle A = 180 - 90 - 25 = 65°
250/sin(65) = b/sin(90) = b = 275.8444797...
2.
a)
remember the trigonometric triangle with the up/down leg being sine (multiplied by the circle radius, which is the Hypotenuse of the triangle), and the left/ right leg being cosine (again multiplied by the Hypotenuse).
5 = 12×sin(x)
sin(x) = 5/12 = 0.416666666...
x = 24.62431835...°
b)
the same principle as for a), just now we need cosine.
12 = 15×cos(x)
cos(x) = 12/15 = 4/5 = 0.8
x = 36.86989765...°
3.
AB² = 125² + 65² = 15625 + 4225 = 19850
AB = sqrt(19850) = 140.890028... cm
angel C = 90°
125/sin(B) = 65/sin(A) = 140.890028.../sin(90)
sin(B) = 125/140.890028... = 0.887216801...
angle B = 62.52556837...°
angle A = 180 - 90 - 62.52556837... = 27.47443163...°
The total number of fence posts Edwin installs varies directly with the number of hours worked. He installs 40 fence posts in 8 hours.
Write a direct variation equation to represent this relationship.
Direct variation equation for the relationship is y = 4x
y is number of fence posts.
x is number of hours.
What is direct proportion?Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value.
Given,
Edwin installs 40 fence posts in 8 hours
Let the number of fence posts installed be y, x be the hours worked
x and y are in direct proportion,
then,
y/x = 40/5
y/x = 5
y = 5x
Hence, y = 5x is the direct variation equation of relationship.
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does the graph or equation represent a linear or nonlinear function? explain. y=1/3x-1
Answer: The graph of the equation y = 1/3x - 1 represents a nonlinear function. A nonlinear function is a function that is not a linear function, which means that the graph of the function is not a straight line. In this case, the equation y = 1/3x - 1 can be graphed and will not be a straight line, which means it is nonlinear. Additionally, the equation has an x in the denominator which is an indication that the function is nonlinear.
Step-by-step explanation:
Three times the sum of a number and 15 is at most 19
Let x be the number. Then, we have the inequality:
3(x + 15) ≤ 19
Expanding the left side:
3x + 45 ≤ 19
Subtracting 45 from both sides:
3x ≤ -26
Dividing both sides by 3:
x ≤ -8.67
So, the solution to the inequality is x ≤ -8.67, which means that the number x must be less than or equal to -8.67.
Find the value of the variables that make the matrix equation true.
{8 0 0} { 7x+3 0 0 }
{ 0 8 0} = { 0 9y-4 0 }
{ 0 0 8} { 0 0 5z-5}
The value of the variables that make the matrix equation true are x = 5/7, y = 4/9 and z = 13/5.
What is a matrix?A matrix is a rectangular array or table of numbers, symbols, or expressions that are organized in rows and columns to represent a mathematical object or an attribute of such an object in mathematics.
For instance, consider a matrix with two rows and three columns.
We are given the matrix as;
{8 0 0} = { 7x+3 0 0 }
{ 0 8 0} = { 0 9y-4 0 }
{ 0 0 8} = { 0 0 5z-5}
So, we have 7x + 3 = 8
7x = 5
x = 5/7
Also, 9y-4 = 8
9y = 4
y = 4/9
5z - 5 =8
z = 13/5
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