Answer:
Relationship: [tex]y =2.92x+4.23[/tex]
They are not proportional
The value is $33.43
Step-by-step explanation:
Given:
[tex]x = years[/tex]
[tex]y = amount[/tex]
When he retired, the expression is:
[tex](x_1,y_1) = (0,4.23)[/tex]
and the rate (m) is:
[tex]m = 2.92[/tex]
Solving (a): The relationship between y and x
This can be solved using the following point-slope formula:
[tex]y - y_1=m(x-x_1)[/tex]
Substitute values for x1, y1 and m
[tex]y - 4.23=2.92(x-0)[/tex]
[tex]y - 4.23=2.92(x)[/tex]
Make y the subject
[tex]y =2.92(x)+4.23[/tex]
[tex]y =2.92x+4.23[/tex]
Solving (b): Are they proportional?
No, they are not
A proportional relationship is expressed as:
[tex]y = mx[/tex]
By comparing this to [tex]y =2.92x+4.23[/tex]; they have different format
Solving (c): Value in 2010?
First, we determine the value of x in 2010
2000; x = 0
2001; x = 1
---
--
-
2010; x = 10
Substitute 10 for x in [tex]y =2.92x+4.23[/tex]
[tex]y = 2.92*10+4.23[/tex]
[tex]y = 29.2+4.23[/tex]
[tex]y = 33.43[/tex]
−11=r+4+4r Plz provide step by step
Answer:
R=-3
Step-by-step explanation:
-11=r+4+4r
-11=5r+4
-4 both sides
-15=5r
Divide 5 both sides
r=-3
Answer:
r=-3
Step-by-step explanation:
solve 15x + 60 < 240
Answer:
15x+60<240 is x<12
Step-by-step explanation:
Let's solve your inequality step-by-step.
15x+60<240
Step 1: Subtract 60 from both sides.
15x+60−60<240−60
15x<180
Step 2: Divide both sides by 15.
15x
15
<
180
15
x<12
Answer:
x<12
Step-by-step explanation:
The diagram shows 3 identical circles inside a rectangle.
Each circle touches the other two circles and the sides of a rectangle,
as shown in the diagram.
The radius of each circle is 28 mm.
Work out the area of the rectangle.
Give your answer correct to 3 significant figures.
Answer:
11700 mm²
Step-by-step explanation:
A rectangle is a quadrilateral with two equal, opposite and parallel sides. Each of the angles in a rectangle is 90°.
The horizontal distance of the rectangle = r + r + r + r = 4r
The vertical distance = r + h + r = 2r + h
Where h is the distance between the midpoint of the 2 up circles and the midpoint of the down circle.
Using Pythagoras:
(2r)² = h² + r²
h² + r² = 4r²
h² = 3r²
h = √3r²
h = r√3
Vertical distance = 2r + h = 2r + r√3
Area of rectangle = vertical distance * horizontal distance
Area = 4r * (2r + r√3) = 8r² + 4r²√3 = 4r²(2 + √3)
Substituting:
Area = 4r²(2 + √3) = 4(28²)(2 + √3) = 11703.711 mm²
Area = 11700 mm² to 3 s.f
HELP DUE IN 30 MIN
x =
Answer:
x=4
Step-by-step explanation:
21x+6=90(alternate angles)
21x=90-6
x=94/21
Therefore, x=4
Answer:
x=4
Step-by-step explanation:
21x+6=90
-6. -6
21x=84
/21. /21
x=4
Please help me with this question
9514 1404 393
Answer:
x = 7 1/3
Step-by-step explanation:
The smaller triangle is 6/9 = 2/3 the size of the larger triangle, so the left side is ...
(x -2) = (2/3)(8)
3(x -2) = 16 . . . . . multiply by 3 to clear fractions
3x -6 = 16 . . . . . . eliminate parentheses
3x = 22 . . . . . . . . add 6; next divide by 3*
x = 22/3 = 7 1/3 . . . . . feet
_____
* Note that we multiplied by 3, then divided by 3. If you're comfortable working with fractions and/or mixed numbers, these steps are unnecessary. The answer is simply x = 2 + 16/3 = 22/3.
The nth term of a quadratic sequence is an² + bn where a and b are integers. The second term of the sequence is 8, and the fifth term is 65. What is the value of the tenth term in the sequence?
Step-by-step explanation:
When n = 2,
(2)²a + (2)b = 8.
=> 4a + 2b = 8.
When n = 5,
(5)²a + (5)b = 65.
=> 25a + 5b = 65.
4a + 2b = 8. => 10a + 5b = 20
25a + 5b = 65
- (10a + 5b = 20)
=> 15a = 45, a = 3.
Therefore 4(3) + 2b = 8, 2b = -4, b = -2.
We have a = 3 and b = -2.
Hence when n = 10,
an² + bn
= (10)²(3) + (10)(-2)
= 300 - 20
= 280.
The 10th term of the sequence is 280.
Answer:
The 10th term of the sequence is 280
Step-by-step explanation:
When n = 2,
(2)²a + (2)b = 8.
=> 4a + 2b = 8.
When n = 5,
(5)²a + (5)b = 65.
=> 25a + 5b = 65.
4a + 2b = 8. => 10a + 5b = 20
25a + 5b = 65
- (10a + 5b = 20)
=> 15a = 45, a = 3.
Therefore 4(3) + 2b = 8, 2b = -4, b = -2.
We have a = 3 and b = -2.
Hence when n = 10,
an² + bn
= (10)²(3) + (10)(-2)
= 300 - 20
= 280.
What is the area of the triangle?
24
10
26
units2
Can some one help me
Answer:
hey long time no see!
help help help ! (ITS DUE)
Answer:
y÷8
Step-by-step explanation:
The quotient is the result of division between two numbers.
SOOO its y÷8 because a quotient is a division problem and y and 8 are the variables in the equation!
2. Explain, in words, how you would solve this problem. Hint: you should get 1 point
a whole number answer.
9 – 24 = 4(3)
Your answer
Answer:
9-24=4(3)
-15=4×3
-15=12
Answer:
9-24= 4(3)
Multiply first
9-24=12
Then subtract the other digits in the side
-15=12
Step-by-step explanation:
Follow the PEMDAS rule which it to do which ever one of these first before furthering the math.
(Parentheses, exponents, multiply, division, addition and subtraction)
BUT hopefully there wasn’t a missing letter variable in the equation so you could get a single answer
[tex]\frac{a-3b}{a+2b} = \frac{4}{3}[/tex]
what is the value of a:b??
Answer:
[tex]a:b = -17:1[/tex]
Step-by-step explanation:
Given
[tex]\frac{a-3b}{a+2b} = \frac{4}{3}[/tex]
Required
Find a:b
[tex]\frac{a-3b}{a+2b} = \frac{4}{3}[/tex]
Cross Multiply
[tex]3(a-3b) = 4(a+2b)[/tex]
Open brackets
[tex]3a - 9b = 4a + 8b[/tex]
Collect Like Terms
[tex]3a - 4a = 8b+9b[/tex]
[tex]-a = 17b[/tex]
Divide through by -b
[tex]\frac{-a}{-b} = \frac{17b}{-b}[/tex]
[tex]\frac{a}{b} = \frac{17}{-1}[/tex]
[tex]\frac{a}{b} = \frac{-17}{1}[/tex]
Represent as a ratio
[tex]a:b = -17:1[/tex]
Picture is attached to it please help I need it
Answer:
x = 80, y = 100
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
Here n = 7 , then
sum = 180° × 5 = 900°
Sum the interior angles and equate to 900
y + 135 + 140 + 150 + 120 + 135 + 120 = 900, that is
y + 800 = 900 ( subtract 800 from both sides )
y = 100
x and y are adjacent angles and are supplementary, that is sum to 180°
x + y = 180
x + 100 = 180 ( subtract 100 from both sides )
x = 80
Thus x = 80 and y = 100
NEED HELP ASAP!!! please help me
please hurry! it's 4 a quiz
Answer:
AD∥BC,BD is the transversal line
⟹∠ADB=∠DBC (∵alternate angles)
⟹z=30
Step-by-step explanation:
Find the unknown side length. Simplify radical answers.
You are on a treasure-diving ship that is hunting for gold and silver coins. You reel in a wire basket that contains gold and silver coins, among other things. The basket holds no more than 50 pounds of material. Each gold coin weighs about 0.5 ounce, and each silver coin weighs about 0.25 ounce. You want to know the different numbers of each type of coin that could be in the basket.
Answer:
Inequality equation:
0.03125x + 0.015625y ≤ 50 pounds
Step-by-step explanation:
We convert the ounces to pounds
1 ounce = 0.0625 pound
For the gold coin = 0.5 ounce
1 ounce = 0.0625 pounds
0.5 ounce = x
x = 0.5 × 0.00625 pounds
x = 0.03125 pounds
For the Silver coin = 0.25 ounce
1 ounce = 0.0625 pounds
0.25 ounce = x
x = 0.25 × 0.00625 pounds
x = 0.015625 pounds
The basket holds no more than 50 pounds of material.
Let the number of gold coins = x
The number of silver coins = y
Hence: our inequality equation:
0.03125x + 0.015625y ≤ 50 pounds
Mr. Park paid $85.00 for 4 shirts. Each shirt cost the same amount. What was the cost of each shirt in dollars and cents?
Answer:
I think you're supposed to do 85/4
Step-by-step explanation:
85 devided by 4
$21.25 for each shirt
hiii please help i’ll give brainliest if you give a correct answer ty!!
Given f(x) = 2x^2 – 9x + 2, g( x)= 1-6x, and
h(x) = x2 - 4, find (f o h) (2)
Answer:
The value of (f о h) (2) is 2
Step-by-step explanation:
Let us solve the question
In the composite function (f о h) (x) we substitute x in f(x) by h(x)
∵ f(x) = 2x² - 9x + 2
∵ h(x) = x² - 4
∵ We need to find (f о h) (2)
→ That means use x = 2
∴ x = 2
We will find at first h(2), then substitute x in f by the answer of h(2)
∵ x = 2
∵ h(2) = (2)² - 4
∴ h(2) = 4 - 4
∴ h(2) = 0
Now substitute x in f by 0
∵ x = 0
∵ f(0) = 2(0)² - 9(0) + 2
∴ f(0) = 0 - 0 + 2
∴ f(0) = 2
∴ (f о h) (2) = 2
On Friday, an art museum sold 720 adult tickets. The number of adult ticket sold was 9 times the number of children's ticket sold. On Saturday, the museum sold 6 times as many children's ticket as on Friday How many children ticket sold on saturday
Answer: 480 children's tickets
Step-by-step explanation:
On the Friday, 720 adult tickets were sold.
This number was 9 times the number of children's tickets sold. Number of adult tickets sold was therefore:
= 720/9
= 80 children's tickets.
On the Saturday, 6 times the above amount was sold:
= 6 * 80
= 480 children's tickets
What inverse trig function can be used to find the measure of angle A? (Will give Brainliest ❤️❤️)
9514 1404 393
Answer:
(b) sin⁻¹
Step-by-step explanation:
The relevant trig function relating angles to sides is ...
Sin = Opposite/Hypotenuse
Here, we have ...
sin(A) = 4/12 = 1/3
A = arcsin(1/30 = sin⁻¹(1/3)
The inverse sine function can be used to find the angle.
what is the slope of the line
Answer:
[tex]consider \: {1}^{st} and \: {3}^{rd} columns\\ slope = \frac{(96 - 32)}{(12 - 4)} \\ = \frac{64}{8} \\ slope = 8[/tex]
Read the caption thank you :)) if you know it let me know!
Answer:
∠ A = 50°
Step-by-step explanation:
In a parallelogram, consecutive angles are supplementary, sum to 180°
∠ A + 130° = 180° ( subtract 130° from both sides )
∠ A = 50°
Javier earned the following scores on his first five tests: 77, 89, 84, 80, and 85. What score did he earn on his last test to have a test mean of 84%?
84%
88%
86%
89%
Answer:
88
Step-by-step explanation:
it meets the mean
Answer:
88%
Step-by-step explanation:
:)
Given: F(x) = x +3 ; G(x) = 2x^2 -4 Find (f*g)(x)
I seriously need help with this
Answer:
(f*g)(x) = (x +3)(2x² -4) =2(x+3)(x²-4) or = 2x³ + 6x² - 4x -12
Step-by-step explanation:
F(x) = x +3
G(x) = 2x^2 -4
(f*g)(x) = f(x) * g(x)
(f*g)(x) = (x +3)(2x² -4) =2(x+3)(x²-4) or = 2x³ + 6x² - 4x -12
The function (f x g)(x) is equal to 2x³ + 6x² - 4x -12.
What is a function?A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.
The function (f x g)(x) is calculated as,
F(x) = x +3
G(x) = 2x² -4
(f x g)(x) = f(x) x g(x)
(f x g)(x) = (x +3)(2x² -4) =2(x+3)(x²-4)
(f x g)(x) = 2x³ + 6x² - 4x -12
Therefore, the function (f x g)(x) is equal to 2x³ + 6x² - 4x -12.
To know more about function follow
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Megan is trying to break the school's long jump
record. To what level of accuracy and precision
should her jump be measured?
I need help!!
Which of the following expression is equal to y/x^2?
Sara sold 461 tickets for a school play. Student tickets cost $3 and adult tickets cost $4. Sara’s sales totaled $1624.How many adult tickets and how many student tickets did Sara sell?
Answer:
220 student and 241 adults
Step-by-step explanation:
x+y=461
3x+4y=1624
y=-x+461-----> 3x+4(-x+461)=1624
-x+1844=1624
+x -1624
x=220
3(220)+4y=1624
660+4y=1624
4y=964
y=241
There are 241 adult tickets and 220 student tickets did Sara sell.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Sara sold 461 tickets for a school play.
And, Student tickets cost $3 and adult tickets cost $4. Sara’s sales totaled $1624.
Let number of adult tickets = x
And, Number of student tickets = y
Hence, We get;
⇒ x + y = 461 .. (i)
And, 4x + 3y = 1624 .. (i)
Multiply by 3 in (i);
⇒ 3x + 3y = 1383 .. (iii)
Subtract form (ii);
⇒ x = 241
And, From (i);
⇒ x + y = 461
⇒ 241 + y = 461
⇒ y = 461 - 241
⇒ y = 220
Thus, There are 241 adult tickets and 220 student tickets did Sara sell.
Learn more about the mathematical expression visit:
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Point E on the diagonal of the rectangle ABCD, AE:EC=3:1, and AB:BC=5:4. Find the ratio of DE to BE
Answer:
3.88 : 3.25 ≈ 13 : 11
Step-by-step explanation:
I don't know what are you in, geometry or algebra? I'll post my way of solution. It may need some calculator calculation that I can't give detail of steps here. I just like to explore something, wish it help.
suppose D is the origin, DA = 4 and AB = 5
A (0,4) B(5,4) C(5,0) D(0,0)
AE/AC = 3/4 (i.e. AE/EC = 3/1)
parallel of EF with DC and EG with BC
CF/BC = CE/AC = 1/4
CF = BC x 1/4 = 4 x 1/4 = 1
DG/DC = AE/AC = 3/4
DG = DC x 1/4 = 5 x 3/4 = 15/4
coordinator of E (3.75 , 1)
length of DE = √3.75² + 1² = 3.88
length of BE = √1.25² + 3² = 3.25
DE : BE = 3.88 : 3.25 ≈ 13: 11 (3.88/13 ≈ 0.29, 3.25/11 ≈ 0.29)
Determine the input, output and function of the following question
K=3H-11
Answer:
do we need to explain in words or numbers
Step-by-step explanation: