The amounts are given as follows, using proportions:
i) Amount spent on entertainment: $240.
c) Monthly salary: $840.
What is a proportion?A proportion is a fraction of an amount, and this fraction is combined with the unit rates in the context of a problem along with basic arithmetic operations such as multiplication or division to find the desired amounts.
The ratio of food : travelling : entertainment = 4 : 2 : 3 means that:
4/9 of the investment was in food.2/9 of the investment was in travelling.3/9 of the investment was in entertainment.The amount spent on food $160 more than travelling, the total amount is obtained as follows:
(4/9 - 2/9)x = 160
2/9x = 160
2x = 160 x 9
x = 80 x 9
x = 720.
Then the amount invested in entertainment was of:
3/9 x 720 = 1/3 x 720 = $240.
He invests 6/7 of his monthly salary, as 1/7 is deposited, hence:
6x/7 = 720
6x = 720 x 7
x = 120 x 7 (simplifying both sides of the equality by 6)
x = $840.
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The table of ordered pairs (x, y) gives an exponential function.
Write an equation for the function.
X
-1
0
1
2
y
1
3
2
12
72
The equation for the function of the ordered pair is y =10x+2.
What is equation for the function?
An equation that has one solution for y for each value of x is referred to be a function. For each input of a particular type, a function assigns precisely one output. The names f(x) or g(x) are frequently used in place of y when naming functions. If our function's value is f(2), then we should calculate its value when x=2. Each functional equation contains some information about a function or several functions. An illustration of a functional equation is f (x) f (y) = x y, f(x) f(y) = x y.
Here in given order pair , let us take any two points,
[tex](x_1,y_1)=(0,2)\\(x_2,y_2)=(1,12)[/tex]
Now using slope formula,
=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> slope m =10/1 = 10
Now using equation formula,
=> [tex]y-y_1=m(x-x_1)[/tex]
=> y-2 =10(x-0)
=> y-2 = 10x
=> y=10x+2.
Therefore equation of the following order pair is y = 10x+2.
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Write equivalent fractions for 2/3 and 8/11 using the least common denominator.
Type the fractions, using a slash ( / ) to separate the numerator and denominator.
2/3 =
8/11 =
please give me the RIGHT answer immediately for the fractions using the least common denominator
The equivalent fraction for 2/3 and 8/11 is 22/33 and 24/33.
What is least common denominator?
The least common denominator (LCD) is the smallest number that can be a common denominator for a set of fractions. Also known as the lowest common denominator, it is the lowest number you can use in the denominator to create a set of equivalent fractions that all have the same denominator.
Given fractions are
2/3 and 8/11
L.C.M of 3 and 11 is 33.
We get,
2/3 ×11/11 = 22/33
and
8/11×3/3 = 24/33
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A wheel has a radius of 45 millimeters. Below is the table from the previous screen. About how many rotations does the wheel make when it travels 100,000 millimeters?
The number of revolutions taken by a wheel will be 353.68 millimeters.
What is the Circumference of a circle?The Circumference of a circle is defined as the product of the diameter of the circle and pi.
C = πd
where 'd' is the diameter of the circle
Given data as:
The radius of the wheel r = 45 millimeters
Circumference of wheel = Circumference of a circle
Circumference of wheel = 2πr =2π(45) = 282.74 millimeters
The distance traveled by wheel = 100,000 millimeters
Now, the number of revolutions taken by a wheel will be
⇒ distance traveled by wheel / Circumference of wheel
⇒ 100,000 / 282.74
⇒ 353.68
Thus, the number of revolutions taken by a wheel will be 353.68 millimeters.
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You spent less than $75. They purchased three pitchers of soda for $12.99 and pizzas for $6 each. How
many pizzas could the group purchase?
Answer:
6 pizzas
Step-by-step explanation:
12.99 times 3 which is the 3 pitchers of soda is 38.97
38.97 subtracted from 75 which is our total amount is 36.03
36.03 which is what we have left divided by 6 since each pizza is 6$ is 6.
What is the equation of the line containing the points (5, 2), (10, 4), and (15, 6)?
A. y = 2/5x
B. y = x - 3
C. y = 1/5x + 1
Answer: A
Step-by-step explanation:
The proof below may or may not be correct. If the proof is incorrect, determine the
first step number that is not justified and the reason it is not justified.
Answer:
Step-by-step explanation: step 5
they have not proved the ASA postulate i.e. they the are missing a step to proove angle BEF = angle CED (Verticle angles)
so, correct answer is step number 5 and reason 'missing prior step'
(x³-15)+(x-1) Divide using synthetic division
The quotient is x²+x+1 - 14/(x-1) after divide x³-15 by x-1.
What is synthetic division?
In algebra, synthetic division is a technique for manually dividing polynomials according to Euclid, requiring less writing and calculation than long division. Although the approach can be applied to division by any polynomial, it is often taught for division by linear monic polynomials.
The divisor is x - 1.The dividend is (x³-15).
Step 1:Take the constant term of the divisor with the opposite sign and write it to the left.
Write the coefficients of the dividend to the right (missed terms are written with zero coefficients).
Step 2:Write down the first coefficient without changes:
Step 3:Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
Step 4:Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).Add the obtained result to the next coefficient of the dividend, and write down the sum
Step 5:Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).Add the obtained result to the next coefficient of the dividend, and write down the sum.
We have completed the table and have obtained the following resulting coefficients: 1,1,1,−14.
All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.
The quotient is x²+x+1 and the remainder is -14.Therefore (x³-15)÷(x-1) = x²+x+1 - 14/(x-1)
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what is the factored form 8g^2+6g-9
Answer:
A.
Step-by-step explanation:
Why is every rhombus a parallelogram but not every parallelogram is a rhombus? Why is every square a rectangle but not every rectangle is a square? Why is every square a rhombus but not every rhombus
square?
A rhombus is a parallelogram because the opposite sides are parallel but every parallelogram is not a rhombus because all sides may not be equal. Every square is a rectangle because opposite sides are equal but not every rectangle is a square because all sides might not be equal. Every square is rhombus because all sides are equal but not every rhombus is a square because the angles might not be right angles.
We need to identify the properties of the given figure in order to answer why one figure can not be the other one:
A rhombus has all sides equal as well as parallel but all angles might not be right angles.
A square has all four sides equal and has 4 right angles.
A rectangle has equal opposite sides and 4 right angles.
A parallelogram has opposite parallel sides.
Hence, a rhombus can be a parallelogram because the opposite sides are parallel but every parallelogram can not be a rhombus because all sides may not be equal. Every square is a rectangle because opposite sides are equal but not every rectangle is a square because all sides might not be equal. Every square is rhombus because all sides are equal but not every rhombus is a square because the angles might not be right angles.
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The sum of two consecutive integers is less than -9. What is the smallest value that will make this true? Write and solve an inequality. Show your work using 3 or 4 steps.Use s as your variable. Round your initial answer to the nearest hundredth.
The value of the inequality when the sum of two consecutive integers is less than -9 is x < - 5.
How to calculate the value?It is vital to note that an inequality simply shows that the expressions aren't equal.
In this case, the sum of two consecutive integers is less than -9.
Let the integers be x and x + 1.
Therefore, x + x + 1 < -9
2x + 1 < -9
Collect like terms
2x < -9 - 1
2x < -10
Divide
x < - 10 / 2
x < - 5
The value is x < - 5.
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Can someone answer this?
The values indicated trigonometric functions are cot(β) = 0.14, cos(β) = 0.14, tan(90-β) = 0.14 and csc(β) = 1.01
How to find the trigonometric functions?Trigonometric functions are the periodic functions that denote the relationship between angle and sides of a right-angled triangle e.g sine, cosine, tangent, etc.
Given: tan(β) = 7
Thus, β = arc tan 7 = 81.87
(a) cot(β) = 1/tan(β) = 1/7 = 0.14
(b) cos(β) = cos 81.87 = 0.14
(c) tan(90-β) = tan(90-81.87) = tan 8.13 = 0.14
(d) csc(β) = 1/sinβ = 1/sin(81.87) = 1.01
Therefore, the value of the trigonometric functions are cot(β) = 0.14, cos(β) = 0.14, tan(90-β) = 0.14 and csc(β) = 1.01
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The sum of the angle measures of any triangle is 180°. Find the angle measures of a triangle if the second angle measures 7° less than twice the first, and the third angle measures 19° more than the second.
Answer:
first angle =35
second angle=63
third angle=82
What’s is 3/20as a decimal I need HELP!
how to find 3 to the power of x equals 2187?
i need a step by step detail on how to solve it.
Answer: [tex]x=7[/tex]
Step-by-step explanation:
[tex]3^x=2187\\\\x=\log_{3} (2187)\\\\x=7[/tex]
I need the abswer to 20005+56258
76263
Step-by-step explanation:
[tex] \: \: \: 20005[/tex]
[tex] + 56258[/tex]
___________
[tex] = 76263[/tex]
5(4 − 9 · 2) − 2( 3 · 2 + 4) + 7?
Answer: i think its -18
Step-by-step explanation:
5*(4-9*2)-2*(3*2+4)+7
= 5*(4-18)-2*(3*2+4)+7
= 5*(-14)-2*(3*2+4)+7
= 5*-14-2*(3*2+4)+7
= 5*-14-2*(6+4)+7
= 5*-14-2*(10)+7
= 5*-14-2*10+7
= -70-2*10+7
= -70-20+7
= -90+7
= -83
20 POINTS PLEASE HELP!!!
Solve the following system of equations. Show your work.
y=x−5
y=5x−17
Solution:
The solution to the system of equations y = x − 5 and y = 5x − 17 is x = 3 and y = -2
How to determine the solution to the system of equations?The system of equations is given as
y = x − 5
y = 5x − 17
Substitute y = x − 5 in the equation y = 5x − 17
So, we have
x - 5 = 5x − 17
Evaluate the like terms
4x = 12
Divide both sides by 4
x = 3
Substitute x = 3 in y = x − 5
y = 3 − 5
So, we have
y = -2
Hence, the solution is x = 3 and y = -2
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If a1=9 And an= 4an-1 then find the value of a5
If a₁ = 9 and aₙ = 4 + (aₙ - 1) in an arithmetic sequence, then the value of fifth term a₅ is equal to 25.
How to calculate an arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.From the information provided, we know that the common difference is equal to 4.
Substituting the given parameters into the formula, we have;
a₅ = 9 + (5 - 1)4
a₅ = 9 + 4(4)
a₅ = 9 + 16
a₅ = 25
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Complete Question:
If a₁ = 9 and aₙ = 4 + (aₙ - 1), then find the value of a₅.
Show me how to graph this by using key points step by step please and I will give you brainliest!
g(x)=log(6-3x)+1
Answer:
136-5x
Step-by-step explanation:
A dilation with scale factor 0.25 is performed on triangle 1 to produce triangle 2. Which statement MUST be true about the two triangles?
O Their corresponding sides have equal lengths, and their corresponding angles have equal measures.
• Their corresponding sides are parallel, and the angle measures of triangle 2 are 0.25 times the corresponding angle measures of triangle 1.
O Their corresponding sides are parallel, and their corresponding angles have equal measures.
O Their corresponding sides have equal lengths, and the angle measures of triangle 2 are 0.25 times the corresponding angle measures of triangle 1.
The correct statement is their corresponding sides have equal lengths, and the angle measures of triangle 2 are 0.25 times the corresponding angle measures of triangle 1.
What is property of similar triangle?
If the corresponding sides of two triangles have the same ratio and the corresponding angles are equal, then the triangles are similar.
They have parallel corresponding sides, and they have angles with the same measure.
hence, the correct statement is their corresponding sides have equal lengths, and the angle measures of triangle 2 are 0.25 times the corresponding angle measures of triangle 1.
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how could we determine the input value of t when W(t)=15 and the rule for function w is 2t+5
3. Consider the right triangle below in which a = 5 and b = 5.
A. Use the Pythagorean Theorem to solve for c.
Show your work!
B. What is the value of c rounded to the nearest hundredth?
C. What is the value of c in simplified radical form?
Answer:
Consider the right triangle below: State the Pythagorean Theorem as it relates to the above triangle. List the trig identities as they relate to the triangle above. Now suppose hypotenuse C represents a vector R, while sides B and A represent vector components Rx and Ry respectively. Redraw the triangle with the new labels below. Using Pythagorean Theorem, derive the equation for R.
If f is continuous everywhere, f'(3) = 0 and f" (3) = 4, then there must be a local minimum at z = 3.
Answer:
True
Step-by-step explanation:
f'(3) = 0 says the tangent line at x = 3 is horizontal.
f"(3) = 0 means the graph of f is concave up at x = 3.
Together, these tell you the graph has a local minimum at x = 3. The graph is U-shaped at the point where x = 3.
A line passes through the points (–5, –4) and (0, 4). What is its equation in slope-intercept form?
Considering the expression of a line, the equation of the line that passes through the pair of points (-5,-4) and (0,4) is y=8/5x + 4.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:
m= (y₂ - y₁)÷ (x₂ - x₁)
Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, the value of the ordinate to the origin b can be obtained.
Equation in slope-intercept form in this caseBeing (x₁, y₁)= (-5, -4) and (x₂, y₂)= (0,4), the slope m can be calculated as:
m= (4 - (-4))÷ (0 - (-5))
m= (4 + 4)÷ (0 +5)
m= 8÷ 5
m= 8/5
Considering point 2 and the slope m, you obtain:
4= 8/5×0 + b
4= 0 +b
4= b
Finally, the equation of the line is y=8/5x + 4.
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For which value of 0 is sin 0=-1?
y
sin 270° = sin 3π/2 = -1, the value of 0 is 270° or 3π/2.
Given,
sin 0 = -1
We have to find the value of 0.
Lets see the trigonometric table for sin.
sin 0 = sin 0 = 0sin 30°= sin π/6 = 1/2sin 45° = sin π/4 = 1/√2sin 60° = sin π/3 = √3/2sin 90° = sin π/2 = 1sin 180° = sin π = 0sin 270° = sin 3π/2 = -1sin 360° = sin 2π = 0From the above table we get the value of sin 0
The value -1 is for sin 270° which is equal to sin 3π/2
That is,
sin 270° = sin 3π/2 = -1, the value of 0 is 270° or 3π/2.
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help me pleaseeeeeeeeeeeeeeeeee !!!!!!!!!!!!!!!!!!!!!!
help me pleaseeeeeeeeeeeeeeeeee !!!!!!!!!!!!!!!!!!!!!!
Answer:
Vertex: (-2, 3) Axis of symmetry: x = -2 The parabola opens downward.
Step-by-step explanation:
Barney just bought stock in Purple Dinosaur Industries. He paid a total of $7,380. The price of the stock is $12 for one share. How many shares did he buy?
The number of shares he buy is $615.
Given that Barney just bought stock in Purple Dinosaur Industries and he paid a total of $7,380 and the price of the stock is $12 for one share.
We want to find the number of shares Barney buys.
The total amount barney should pay is $7380.
The price of the stock for one share is $12.
The total number of shares barney buy is 7380/12=615.
Hence, the number of shares barney should buy when he paid a total $7380 and the price of stock for one share is $12 is $615.
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I need examples of surds
Describe the characteristics of each set of numbers
that make up the set of integers.
Numerous other sorts of numbers exist, including natural, whole, rational, real, and integers. Positive and negative numbers, but not decimals or fractions, make up the category of integers.
Q What are integers in mathematics?
ANS An integer is a whole number without any fraction or decimal part.
The traits of each group of numbers are as follows:
Negative numbers are those that are less than zero.The set of integers includes zero.Numerical categories cross over one another.Integers must be written with an ellipsis ("") and inside a bracket ({}).Use a number line when adding or subtracting numbers.Please help geomatry 9th grade
The statements that are a result of corresponding parts of congruent triangles being congruent are:
EFGH has four congruent sidesDiagonal FH is perpendicular to side FEAngle FEH is congruent to angle FGHWhat is an isosceles triangle?An isosceles triangle is a type of triangle with two equal sides and angles. The other types of triangle includes;
Equilateral triangleRight angle triangleScalene triangleFrom the figure;
Sides EFGH are congruent, that is, equal
Since Sides EFGH are congruent, it can not be a rectangle, it is a square.
Triangle FGH and FEH are both isosceles triangle.
Diagonal FH bisects triangle FGH and FEH
So therefore, the isosceles triangle FGH and FEH are congruent and bisected by diagonal FH.
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