Answer: The price increase = $2,860.
The price of the next model will be $57,860.
Step-by-step explanation:
Given: The next model sports car will cost 5.2% more than the current model.
Current model costs $55,000.
Price increase = 5.2% of (Cost of current model)
= (0.052) x ($55000)
= $ 2860
So, the price increase = $2860.
Price of the next model = Cost of current model + price increase
= $(55000+2860)
= $ 57,860
Hence, the price of the next model will be $57,860.
Find the slope of the line
Answer:
-1/4
Step-by-step explanation:
take two points (0, -2) & (-4, -1)
use the slope formula
(y₂ - y₁) / (x₂ - x₁)
(-1 + 2) / (-4 - 0) = 1/-4
y = -1/4x + b
slope is -1/4
Use cosine to find the missing value round to 2 decimal places #trigonometry
Answer:
1. 17.27 cm
2. 19.32 cm
3. 24.07°
4. 36.87°
Step-by-step explanation:
1. Determination of the value of x.
Angle θ = 46°
Adjacent = 12 cm
Hypothenus = x
Using cosine ratio, the value of x can be obtained as follow:
Cos θ = Adjacent /Hypothenus
Cos 46 = 12/x
Cross multiply
x × Cos 46 = 12
Divide both side by Cos 46
x = 12/Cos 46
x = 17.27 cm
2. Determination of the value of x.
Angle θ = 42°
Adjacent = x
Hypothenus = 26 cm
Using cosine ratio, the value of x can be obtained as follow:
Cos θ = Adjacent /Hypothenus
Cos 42 = x/26
Cross multiply
x = 26 × Cos 42
x = 19.32 cm
3. Determination of angle θ
Adjacent = 21 cm
Hypothenus = 23 cm
Angle θ =?
Using cosine ratio, the value of θ can be obtained as follow:
Cos θ = Adjacent /Hypothenus
Cos θ = 21/23
Take the inverse of Cos
θ = Cos¯¹(21/23)
θ = 24.07°
4. Determination of angle θ
Adjacent = 12 cm
Hypothenus = 15cm
Angle θ =?
Using cosine ratio, the value of θ can be obtained as follow:
Cos θ = Adjacent /Hypothenus
Cos θ = 12/15
Take the inverse of Cos
θ = Cos¯¹(12/15)
θ = 36.87°
Which graph shows all the values that satisfy 2/9x + 3 > 4 5/9 ?
Answer:
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In graphing inequalities, the first thing to do is graph the equation first irregardless of the inequality symbol. In the given problem, the equation to be graphed is f(x) = 2/9x + 3. Since it has a general form of y=mx + b, this is a linear function. Plot the graph by assigning arbitrary points of x, then you get the corresponding f(x) values. Graph the x values against the f(x) values. The blue line the attached picture will be formed.
Next, you solve the equation by finding x. Just don't mind the inequality symbol:
2/9 x + 3 > 4 5/9
2/9x > 4 5/9 - 3
2/9x > 14/9
x > 14/9 ÷ 2/9
x > 7
Hence, the value of x must be greater than 7. To show this in the graph, find the line where x=7. Create a partition using that line, then shade the rest of the portion where x is greater than 7 until infinity.
Hoped I helped
leave a like or rate please
Help on both questions please!! Ty
Find the measure of b.
0
3
27
Answer:
b= 126°
Step-by-step explanation:
OC= OB (radius of circle)
∠OCB= ∠OBC (base ∠s isos. △)
a= 27°
b= 180° -27° -27° (∠ sum of △OBC)
b= 126°
b= 2c (∠ at centre= 2 ∠ at circumference)
c= b/2 (divide by 2 on both sides)
c= 126° ÷2
c= 63°
2xsquered minus 8x minus 24
Answer:
x = 6 or x = -2
Step-by-step explanation:
Solve for x:
2 x^2 - 8 x - 24 = 0
The left hand side factors into a product with three terms:
2 (x - 6) (x + 2) = 0
Divide both sides by 2:
(x - 6) (x + 2) = 0
Split into two equations:
x - 6 = 0 or x + 2 = 0
Add 6 to both sides:
x = 6 or x + 2 = 0
Subtract 2 from both sides:
Answer: x = 6 or x = -2
Nine years ago, Tarah opened a savings account with her bank. She started with a balance of $359 and has not made any withdrawals or deposits since then. If her interest rate is 8% each year, how much interest has accrued using simple interest? Total Interest = $ What is Tarah's new total balance? New Balance Total = $
Answer:
Total- 617.48 Interest- 258.48
Step-by-step explanation:
First, we need to find out what 8% of 359 is.
.08 times 359 = 28.72. This is how much interest is gained in a year. Since she waited 9 years, we multiply 28.72 by 9 and get 258.48. This is the total interest.
Now we just add 258.48 and 359 to get 617.48.
Answer:
617.48
Step-by-step explanation:
SI = P x R x T / 100
SI = Simple Interest
P = Principal
R = Rate
T = Time
SI = 359 x 9 x 8 / 100
=> SI = 2872 x 9 /100
=> SI = 25848 /100
=> SI = 258.48
New Balance = Principal + Simple Interest
=> New Balance = 359 + 258.48
=> New Balance = 617.48
If the area of a circular pool is 300 square yards, what is its radius?
Answer:
radius = 9.77 yardsStep-by-step explanation:
Since the pool is circular
Area of a circle = πr²
where
r is the radius
From the question
Area = 300 square yards
To find the radius substitute the value of the area into the above formula and solve for the radius
That's
300 = πr²
Divide both sides by π
We have
[tex] {r}^{2} = \frac{300}{\pi} [/tex]
Find the square root of both sides
That's
[tex]r = \sqrt{ \frac{300}{\pi} } [/tex]
r = 9.7720502
We have the final answer as
radius = 9.77 yardsHope this helps you
5(x+1)=4x+21
solve please
Tyrone claims that the first step to simplfy this expression is to raise the numerator and denominator to the third power. Alisha claims that the first step to simplfy is to apply the qoutient of powers. Who is correct? Explain.
Answer:
Alisha's approach is simpler and less complicated
Step-by-step explanation:
Given:
(m^2*n^-3) / (m^6*n^-1)
Tyrone's approach.
(m^2*n^-3) / (m^6*n^-1)
(m^2*n^-3)^3 / (m^6*n^-1)^3
You can find the cube root of both the numerator and denominator in order to eliminate the third power
3√((m^2*n^-3)^3 / 3√(m^6*n^-1)^3
This will take us back to the original expression
(m^2*n^-3) / (m^6*n^-1)
= m^(2-6)*n^(-3+1)
= m^-4*n^-2
= 1/(m^4*n^2)
Alisha's approach.
(m^2*n^-3)/(m^6*n^-1)
= m^(2-6)*n^(-3+1)
= m^-4*n^-2
= 1/(m^4*n^2)
The approach of both of them are correct, however, Tyrone's approach will make the expression more complicated but they would still arrive at the same answer. 1/(m^4*n^2)
find square root of 2x2x3x3x4x4
square root = 24
Step-by-step explanation:
2x2x3x3x4x4 =576
Answer:
24
Step-by-step explanation:
2x2x3x3x4x4
= 2x3x4=24
amy bought a square table for her kitchen. The area of the table’s surface is 99ft². What is the best approximate length of one side of the table?
What value of a makes x/2 + 4= 8 true?
Answer:
x = 8
Step-by-step explanation:
x/2 + 4 = 8
x/2 = 8 - 4
x/2 = 4
x = 4*2
x = 8
Probe:
8/2 + 4 = 8
4 + 4 = 8
Answer:
x = 8
Step-by-step explanation:
Subtract 4 from each side to cancel out the positive 4. It should now look like this: x/2 = 4Multiply each side by 2. It should now look like this: x = 8Therefore, x equals 8.
Jaycee Alvarez deposits $425 in a savings account at City Bank. The account pays an annual interest rate of 5.5 percent. She makes no other deposits or withdrawals. After three months the interest is calculated. How much simple interest does her money earn?
Answer:
$70.125
Step-by-step explanation:
First multiply $425*5.5/100*3 and you get:
$70.125
Find the length of the missing side of the right triangle below.
Answer:
your answer is a = + √105 .
If f(a) = 2a², find f(3)
Answer:
f(3) = 18
Step-by-step explanation:
f(a) = 2a²,
Let a = 3
f(3)= 2 * 3^2
= 2 * 9
= 18
Binomial (x – 6) and trinomial (–2x2 + x + 9) are the factors of which of the following polynomials?
Answer:
The polynomial is -2x³ + 13x² + 3x - 54.
Step-by-step explanation:
The binomial expression is: (x - 6)
The trinomial expression is: (-2x² + x + 9)
Multiply the two expressions to determine the resulting polynomial as follows:
[tex](x-6)(-2x^{2}+x+9)=x(-2x^{2}+x+9)-6(-2x^{2}+x+9)[/tex]
[tex]=-2x^{3}+x^{2}+9x+12x^{2}-6x-54\\=-2x^{3}+13x^{2}+3x-54[/tex]
Thus, the polynomial is -2x³ + 13x² + 3x - 54.
I need help with rational and irrational numbers here is the question.
Select all true statements about the square root of 2.
-It is a real number.
-It is an irrational number.
-It is a rational number.
-It is an integer.
-It is not a real number.
Answer:
The correct answer choices are:
1) It is a real number
2) It is an irrational number
Step-by-step explanation:
So we have the number:
[tex]\sqrt2[/tex]
First, let's define each of the terms:
Real numbers are all of the irrational and rational numbers. If a number is irrational or rational, then they are a real number. Any number that does not include the imaginary number i is real (you'll learn this eventually. It's actually really interesting!).
Irrational numbers are the numbers that do not terminate nor repeat. Examples include π or √3. Note that numbers like 1/3 which is .3333 is not irrational because they are repeating. π, on the other hand, does not repeat and never ends.
Rational numbers are the numbers that terminate or repeat. They also include the integers, whole numbers, and natural numbers.
So, the √2. First, it's real because it doesn't deal with imaginaries.
Next, use a calculator and calculate √2. We can see that it is about 1.41423562... This number does not repeat. And it does not terminate (end). In other words, √2 is a irrational numbers.
Since it is irrational, it cannot be rational. Since it's not rational, it cannot be an integer, whole number, or a natural number.
Therefore, the correct answer choices are:
1) It is a real number
2) It is an irrational number
Answer:
[tex]\Large \boxed{\mathrm{It \ is \ a \ real \ number.}} \\ \\ \Large \boxed{\mathrm{It \ is \ an \ irrational \ number.}}[/tex]
Step-by-step explanation:
[tex]\sqrt{2}[/tex]
Real numbers includes all the rational and irrational numbers.
Not real numbers include all the imaginary numbers.
Integers includes all whole numbers that are negative, positive, or zero.
Rational numbers can be expressed as the quotient of two integers.
Irrational numbers cannot be expressed as the quotient of two integers.
[tex]\sqrt{2}= 1.41421356237......[/tex]
The result of square root of 2 keeps going on.
It cannot be expressed as the quotient of two integers.
Therefore, the square root of 2 is an irrational number.
It is a real number since it is an irrational number.
1. Mateo is going to solve the equation below.
Which of the following represents the equation
after combining the like terms?
-8x + 23 – 22x + 9 = 182
a. 14x + 32 = 182
b. -30x + 32 = 182
c. 14x + 14 = 182
d. -30x + 14 = 182
Answer: B
Step-by-step explanation: The answer would be B because both the 8x and 22x are both negative so once you add those two together you would get -30x so that cancels out A and C. SO now you move onto 23 and 9 well both of those are positive so you would add those together and get 32 so that cancels out D and only answer left is B
The equation that represents -8x + 23 – 22x + 9 = 182 after combining the like terms is b. -30x + 32 = 182 , where x = -5.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
The given equation is,
-8x + 23 – 22x + 9 = 182
Taking alike terms together we get,
-8x – 22x + 23 + 9 = 182
Solving we get,
– 30x + 32 = 182
Subtracting 32 both the side we get,
– 30x + 32 - 32 = 182 - 32
Solving we get,
– 30x = 150
⇒ x = -5
Thus, The equation that represents -8x + 23 – 22x + 9 = 182 after combining the like terms is b. -30x + 32 = 182 where, x = -5.
To learn more about equations:
https://brainly.com/question/12720088
#SPJ2
The Meyers, Kaplinsky, and Emdin family went to the county fair as a get-together. The Meyers family purchased 4 juice boxes and 2 BBQ sandwiches for $16. The Kaplinsky purchased 4 juice boxes and 3 BBQ sandwiches for $21. The Emdin family showed up late to the county fair and purchased 3 juice boxes and 3 BBQ sandwiches. How much money did the Emdin family spend on their meal?
Answer:
The Emdin family spent $19.5 on their meal
Step-by-step explanation:
Let
Juice boxes=x
BBQ sandwiches =y
The Meyers family purchased 4 juice boxes and 2 BBQ sandwiches for $16.
4x+2y=16
The Kaplinsky purchased 4 juice boxes and 3 BBQ sandwiches for $21.
4x+3y=21
4x+2y=16 (1)
4x+3y=21 (2)
Subtract (1) from 2
3y-2y=21-16
y=5
Substitute the value of y into (1)
4x+2y=16
4x+2(5)=16
4x+10=16
4x=16-10
4x=6
Divide both sides by 4
x=6/4
=1 2/4
=1 1/2
x=1.5
The Emdin family showed up late to the county fair and purchased 3 juice boxes and 3 BBQ sandwiches
3x+3y
Substitute the values of x and y
= 3(1.5)+3(5)
= 4.5 + 15
= $19.5
The Emdin family spent $19.5 on their meal
What is the equation of a line perpendicular to y = 2x - 6 that passes through (5, 4)
Answer: y=(-1/2)x-6.5
Step-by-step explanation:
y=2x-6
the perpendicular to this will have the opposite reciprocal slope.
The new equation will be
y=(-1/2)x-b
--------------------------
To find the y-intercept of the equation, we should substitute the point into the equation (5,4)
y=(-1/2)x-b
4=(-1/2)×5-b
4=-2.5-b
b=-6.5
------------------------------
so the equation will be y=(-1/2)x-6.5
Hi . Please show workings Solve for x in : 2(x+4)=50
Answer:
10.5
Step-by-step explanation:
[tex]2(x + 4) = 50 [/tex]
[tex]4x + 8 = 50 [/tex]
[tex]4x = 50 - 8[/tex]
[tex]4x = 42[/tex]
[tex]x = 42 \div 4[/tex]
[tex]x = 10.5[/tex]
Answer:
Simplifying
2(x + 4) = 50
Reorder the terms:
2(4 + x) = 50
(4 * 2 + x * 2) = 50
(8 + 2x) = 50
Solving
8 + 2x = 50
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-8' to each side of the equation.
8 + -8 + 2x = 50 + -8
Combine like terms: 8 + -8 = 0
0 + 2x = 50 + -8
2x = 50 + -8
Combine like terms: 50 + -8 = 42
2x = 42
Divide each side by '2'.
x = 21
Simplifying
x = 21
This took a long time to type and i think it is wrong but hope this helps. hint, hint.
What is the answer to -5+2/3 hurry please
Answer:
-4.33333333333
Step-by-step explanation:
Greetings from Brasil...
To add or subtract fractions we can use the following expression:
A/B + C/D = A.D/BD + C.B/BD- 5 and - 5/1 is the same
- 5 + 2/3 = - 5/1 + 2/3
(-5.3)/(1.3) + (2.1)/(1.3)
(- 15 + 2)/3
- 13/3Simplify the radical. 4^√10 A)√20 B)4√10^5 C)2√5 D)2√10^5
Answer:
80.145817
Step-by-step explanation:
4√10 = 80.145817
Please help I don’t get
Answer:
Answer: 25
The problem is saying that f of x is equal to 13, which means you insert 13 for every x in the equation:
[tex]f(13) = 2(13) - 1[/tex]
Multiply 2 by 13 to get 26:
[tex]f(13) = 26 - 1[/tex]
Subtract 1 from 26 to get 25:
[tex]f(13) = 25[/tex]
I hope this helps. Let me know if you have any questions!
Ship A and Ship B are 120 km apart when they pick up a distress call from another boat. Ship B estimates that they are 70 km away from the distress call. They also notice that the angle between the line from ship B to ship A and the line from ship A to the distress call is 28°. What are the two possible distances, to the nearest TENTH of a km, from ship A to the boat?
Answer:
147.5 km and 64.4 km
Step-by-step explanation:
a=120 km
b=70 km
β=28 degrees ( ∘)
b^2=(a^2)+(c^2)−2ac*cosβ
70^2 =(120^2 )+(c^2)−2⋅ 120⋅ c⋅ cos(28∘ )
(c^2 ) −211.907c+9500=0
note p, q, and r are replacement variables in the Pythagorean theorem since a, b, and c are already in use
p=1;q=−211.907;r=9500
D=(q^2 ) −4pr=(211.907^2 )−4⋅1⋅9500=6904.75561996
D>0
[tex]c_{1,2}[/tex] = (−q± [tex]\sqrt{D}[/tex] )/2p=(211.91±[tex]\sqrt{6904.76}[/tex])/2
[tex]c_{1,2}[/tex] =105.95371114±41.5474295834
([tex]c_{1}[/tex]−147.501140726)([tex]c_{2}[/tex]−64.4062815596)=0
[tex]c_{1}[/tex]=147.501140726
[tex]c_{2}[/tex]=64.4062815596
Question 1
n+ 19 = 40
What does n equal?
Answer:
Hey there!
n+19=40
-19=-19
n=21
Let me know if this helps :)
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ n = 21}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{n + 19 = 40}[/tex]
Move 19 to right hand side and change it's sign
⇒[tex] \sf{n = 40 - 19}[/tex]
Subtract 19 from 40
⇒[tex] \sf{n = 21}[/tex]
Hope I helped!
Best regards!!
Heather cut away 6.22 meters of rope. Before that, she had 9 meters of rope. How much rope does Heather have left?
Answer:
2.78 meters
Step-by-step explanation:
Subtract 6.22 from 9
9 - 6.22
= 2.78
So, she had 2.78 meters of rope left
Answer:
[tex]\huge\boxed{\mathrm{2.78\ meters}}[/tex]
Step-by-step explanation:
Heather had = 9 meters
She cut away = 6.22 meters
Heater have left:
=> 9 - 6.22
=> 2.78 meters
If you are given the functions f(x) = 3x + 1... Can you find the input value if f(x) = 10
Answer:
Input value: 3
Step-by-step explanation:
If I'm understanding the question correctly it would look like this.
[tex]10 = 3x + 1[/tex]
Next: Subtract one
[tex]9 = 3x[/tex]
Divide by three to get x.
[tex]x = 3[/tex]
Step-by-step explanation:
[tex]\huge{\purple{\underline{\underline{\bf{\pink{Answer}}}}}}[/tex]
In this we have give the value of x = 10
[tex]f(x) = 3x + 1[/tex]
[tex]f(10) = 3(10) + 1[/tex]
[tex]f(10) = 30 + 1[/tex]
[tex]f(10) = 31[/tex]
so the value of x is 31
hope it helps
Find the circumference of a circle with a radius of 6 inches. Round your answer to the nearest hundredth
Answer: 37.70 inches
Step-by-step explanation:
Forumla for circumference: C = 2πr
C = 2π(6)
C = 12π
C= 37.6991118431
C = 37.70 (rounded)