Rate = distance / time
Rate = 21 miles / 3 hours
Rate = 7 miles / hour
The answer is choice A. Hope this helps.
60 points! Please answer fast and show your work... Thank you!
You would like to purchase the car in 2 years. How much money will you need to invest at a 3.3% interest rate compounded annually in order to have $9500 in 2 years? Use the compound interest formula A = P (1 + i)n. (Round final answer to the nearest cent, but otherwise don’t round any intermediate values)
Answer:
$ 8902.72
Step-by-step explanation:
We would like to calculate the money which we need to invest at 3.3% rate compounded annually for two years . We know that ,
[tex]\longrightarrow \boldsymbol{ A = P \bigg(1+\dfrac{R}{100}\bigg)^n } [/tex]
where the symbols have their usual meaning . So here ,
Amount = $ 9500 time = 2 years Rate = 3.3% P = The money we need to invest (?)[tex]\longrightarrow \$ 9500 = P \bigg( 1+\dfrac{3.3}{100}\bigg)^2\\ [/tex]
Simplify RHS ,
[tex]\longrightarrow \$ 9500 = P \bigg(\dfrac{100+3.3}{100}\bigg)^2\\[/tex]
Simplify Nr . in RHS ,
[tex]\longrightarrow \$ 9500 =P\bigg(\dfrac{103.3}{100}\bigg)^2\\ [/tex]
Isolate P ,
[tex]\longrightarrow P = \dfrac{ \$9500\times 100\times 100}{103.3\times 103.3}\\[/tex]
Simplify ,
[tex]\longrightarrow \underline{\underline{\boldsymbol{ P = \$ 8902.72 }}}{} [/tex]
And we are done !
[tex]\bold{Formula: A = P(1 + \frac{r}{100})^{(n)}}[/tex]
Where
A = AmountP = PrincipalR = RateN = time compounded[tex] \bold{Solution : } \\ \\ \: \: \: \: \tt \: A = 9,500(1+\frac{3.3\%}{100})^{(2)} \\ \: \: \: \: \: \: \tt \: A = 9,500(1+ 0.033)^{(2)} \\ \tt \: A = 9,500(1.033)^{(2)} \: \: \\ \tt \: A = 10,137.34 \qquad \: \: \: [/tex]
therefore,I need $10,137.34 if would like to purchase the car.
2x+4/5-6=8
I need help ASAP
Answer:
x=33/5
Step-by-step explanation:
Let's solve your equation step-by-step.
2x+4/5 −6=8
Step 1: Simplify both sides of the equation.
2x+4/5−6=8
2x+4/5+−6=8
(2x)+(4/5+−6)=8(Combine Like Terms)
2x+−26/5=8
2x+−26/5=8
Step 2: Add 26/5 to both sides.
2x+−26/5+26/5=8+26/5
2x=66/5
Step 3: Divide both sides by 2.
2x/2=66/5/2
x=33/5
a. What is the slope.
b. What is the y-intercept.
c. Does the graph represent a proportional or non-proportional relationship? Explain and justify your reasoning.
Answer:
A: 2/3, B: 5, C: Yes because the slope is consistent.
Step-by-step explanation:
Helpppp hmmm guys sos plis stan nct help
Answer:
3
explanation:
[tex]\rightarrow \sf \sf \dfrac{36}{3a}[/tex]
[tex]\rightarrow \sf \sf \dfrac{36}{3(4)}[/tex]
[tex]\rightarrow \sf \sf \dfrac{36}{12}[/tex]
[tex]\rightarrow \sf \sf 3[/tex]
100 POINTS IF YOU CAN ANSWER THIS QUESTION WITH STEPS:
30% of the final exam
30% of 363/10(36)108/1010.870% of final exam:-
70% of 367/10(36)258/1025.8In the equation x square + 5x - 14 =0, the solutions are?
Answer:
-2,7
Step-by-step explanation:
[tex]\huge\bold\red{Answer:-}[/tex]
Step by step solution :
STEP 1 : Trying to factor by splitting the middle term
1.1 Factoring x2+5x-14
The first term is, x2 its coefficient is 1 .
The middle term is, +5x its coefficient is 5 .
The last term, "the constant", is -14
Step-1 : Multiply the coefficient of the first term by the constant 1 • -14 = -14
Step-2 : Find two factors of -14 whose sum equals the coefficient of the middle term, which is 5 .
-14 + 1 = -13
-7 + 2 = -5
-2 + 7 = 5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 7
x2 - 2x + 7x - 14
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-2)
Add up the last 2 terms, pulling out common factors :
7 • (x-2)
Step-5 : Add up the four terms of step 4 :
(x+7) • (x-2)
Which is the desired factorization.
Equation at the end of step 1 :
(x + 7) • (x - 2) = 0
STEP 2 : Theory - Roots of a product
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
2.2 Solve : x+7 = 0
Subtract 7 from both sides of the equation :
x = -7
Solving a Single Variable Equation:
2.3 Solve : x-2 = 0
Add 2 to both sides of the equation :
x = 2
Supplement : Solving Quadratic Equation Directly
Solving x2+5x-14 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Parabola, Finding the Vertex:
3.1 Find the Vertex of y = x2+5x-14
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is -2.5000
Plugging into the parabola formula -2.5000 for x we can calculate the y -coordinate :
y = 1.0 * -2.50 * -2.50 + 5.0 * -2.50 - 14.0
or y = -20.250
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = x2+5x-14
Axis of Symmetry (dashed) {x}={-2.50}
Vertex at {x,y} = {-2.50,-20.25}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-7.00, 0.00}
Root 2 at {x,y} = { 2.00, 0.00}
Solve Quadratic Equation by Completing The Square
3.2 Solving x2+5x-14 = 0 by Completing The Square .
Add 14 to both side of the equation :
x2+5x = 14
Now the clever bit: Take the coefficient of x , which is 5 , divide by two, giving 5/2 , and finally square it giving 25/4
Add 25/4 to both sides of the equation :
On the right hand side we have :
14 + 25/4 or, (14/1)+(25/4)
The common denominator of the two fractions is 4 Adding (56/4)+(25/4) gives 81/4
So adding to both sides we finally get :
x2+5x+(25/4) = 81/4
Adding 25/4 has completed the left hand side into a perfect square :
= x2+5x+(25/4)
= (x+(5/2)) • (x+(5/2))
= (x+(5/2))2
Things which are equal to the same thing are also equal to one another. Since
x2+5x+(25/4) = 81/4 and
x2+5x+(25/4) = (x+(5/2))2
then, according to the law of transitivity,
(x+(5/2))2 = 81/4
We'll refer to this Equation as Eq. #3.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
= (x+(5/2))2 is
= (x+(5/2))2/2
= (x+(5/2))1
=x+(5/2)
Now, applying the Square Root Principle to Eq. #3.2.1 we get:
x+(5/2) = √ 81/4
Subtract 5/2 from both sides to obtain:
x = -5/2 + √ 81/4
Since a square root has two values, one positive and the other negative
x2 + 5x - 14 = 0
has two solutions:
x = -5/2 + √ 81/4
or
x = -5/2 - √ 81/4
Note that √ 81/4 can be written as
√ 81 / √ 4 which is 9 / 2
Solve Quadratic Equation using the Quadratic Formula
3.3 Solving x2+5x-14 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 1
B = 5
C = -14
Accordingly, = B2 - 4AC
=25 - (-56)
= 81
Applying the quadratic formula :
-5 ± √ 81
x = —————
2
Can √ 81 be simplified ?
Yes! The prime factorization of 81 is
3•3•3•3
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 81 = √ 3•3•3•3 =3•3•√ 1
= ± 9 • √ 1
= ± 9
So now we are looking at:
x = ( -5 ± 9) / 2
Two real solutions:
x =(-5+√81)/2=(-5+9)/2= 2.000
or:
x =(-5-√81)/2=(-5-9)/2= -7.000
Two solutions were found :
x = 2 x = -7A helicopter was hovering over a shelter and was 800 ft above the ground. A medic was on the ground and was looking up at an angle of 65° to the helicopter. The medic’s eyes were 5.5 feet off the ground when looking at this angle of elevation. How far was the medic from the shelter?
Using the slope concept, it is found that the medic was 370.5 ft from the shelter.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
In this problem:
The vertical change is of 800 - 5.5 = 794.5 ft.The horizontal chnge is the distance d.The angle is of 65º.Hence:
[tex]\tan{65^\circ} = \frac{794.5]{d}[/tex]
[tex]d = \frac{794.5}{\tan{65^\circ}}[/tex]
[tex]d = 370.5[/tex]
The medic was 370.5 ft from the shelter.
More can be learned about the slope concept at https://brainly.com/question/18090623
Find the values of < and y.
(8x + 7)
5yº
(7y -- 34)
= (2x - 4)^
Answer:
x = 11
y = 17
Step-by-step explanation:
We know that opposite angles (or vertical angles) are equal.
So
8x + 7 = 9x - 4
Subtract 8x from both sides of the equation
8x - 8x + 7 = 9x - 8x - 4
7 = x - 4
Add 4 to both sides of the equation
7 + 4 = x - 4 + 4
11 = x
Looking at the other 2 angles,
5y = 7y - 34
Subtract 7 y from both sides of the equation
5y - 7y = 7y - 7y - 34
-2y = -34
Divide both sides by -2
-2y/-2 = -34/-2
y = 17
Answer:
Step-by-step explanation:
Vertically opposite angles are equal.
8x + 7 = 9x - 4 {Add 4 to both sides}
8x + 7 + 4 = 9x
8x + 11 = 9x {Subtract 8x from both sides}
11 = 9x - 8x
x = 11
7y - 34 = 5y {Add 34 to both sides}
7y = 5y + 34 {Subtract 5y form both sides}
7y - 5y = 34
2y = 34 {Divide both sides by 2
y = 34/2
y =17
2+4+2+ 6+4+5+4+6+3+2+2+1
Answer:
41
Step-by-step explanation:
2+4+2+ 6+4+5+4+6+3+2+2+1= 41
plz mark brainleist
[tex]\huge\boxed{41.}[/tex]
Given...
[tex]2+4+2+ 6+4+5+4+6+3+2+2+1=\boxed{?}[/tex]
Solution...[tex]\left[\begin{array}{ccc}2+4=6\\6+2=8\\8+6=14\\14+4=18\\18+5=23\\23+4=27\\27+6=33\\33+3=36\\36+2=38\\38+2=40\\40+1=40\end{array}\right][/tex]
Final answer...[tex]\huge\boxed{41.}[/tex]
[tex]\boxed{-----------------------------------}[/tex]
[tex]\boxed{Hope\;i\;helped!}\\\\\\\\\huge\boxed{Thanks,Plip.}[/tex]
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can i have some help
Answer:
£ 45.6
Step-by-step explanation:
Number of adults ⇒ 12
Number of children ⇒ 26
Total cost of tickets ⇒ £ 1804.80
Cost of an adult's ticket ⇒ £ 51.60
Cost of a ticket for child ⇒ ?
Let the cost of a ticket for child be x.
Therefore,
Total cost = cost of tickets for adults + cost of tickets for children
Total cost = (No. children × Cost of a ticket) + (No.adults × Cost of a ticket)
£ 1804.80 = 26x + 12 × £51.60
1804.80 = 26x + 619.2
1804.80 - 619.2 = 26x
1185.6 = 26x
Divide both sides by 26.
45.6 = x
So,
Cost of a ticket for child is £45.6
Step-by-step explanation:
12 x 51.60 you get the total cost for the adult tickets and all thats left is the total cost - adult ticket cost and then you get the child ticket wirth now all thats left is childs ticket cost % 26
julia’s dad bought a car for $15,000. the purchase price was seven-eighths of its retail price.
what is the decimal value of the discount given to julia’s father by the car dealership?
Answer: 0.125
Step-by-step explanation: Trust me
Snap ~ daddy_shadet
what is addition property of equality
Answer:
Additive property of equality states that if we add or subtract the same number to both sides of an equation, the sides remain equal.
4. An integer between -5 and -6
Answer:
The integers are the whole numbers, both positive and negative. The next integer after 5 is 6, so there is no integer between them. Since 5 and 6 are consecutive numbers, it is not possible to squeeze another integer between them. So, the answer is none.
Step-by-step explanation:
please mark me brainliest
Hey there!
-5 between (-6)
= -5 - (-6)
= -5 + 6
= 1
Therefore, your answer is: 1
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
I bought a sweater for 25% off and paid $30. What was the *original* price? Please explain.
well, the original price was "x", which oddly enough is the 100%, we also know that 25% off that is 30 bucks, so namely 100% - 25% = 75%, is 30 bucks, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 30&75 \end{array}\implies \cfrac{x}{30}=\cfrac{100}{75}\implies \cfrac{x}{30}=\cfrac{4}{3} \\\\\\ 3x=120\implies x=\cfrac{120}{3}\implies x=40[/tex]
Which inequality is shown on the number line below
Answer:
the first one
Step-by-step explanation:
tttt
Which inequality represents this sentence? Seven times four is greater than or equal to eight times three.
A. 7 • 4 ≥ 8 • 3
B. 7 • 4 ≤ 8 • 3
C. 7 • 4 < 8 • 3
D. 7 • 4 > 8 • 3
Step-by-step explanation:
Answer B
7 × 4=28
8×3=24
Thank me later
The height h (in feet) of an object dropped from a ledge after x seconds can be modeled by h(x)=−16x2+4. The object is dropped again from a different starting height so that it hits the ground 2 seconds later. Write a function g that models the path of the object the second time it is dropped.
Answer:
g(x) = - 16x² + 100
Step-by-step explanation:
Given the model:
First drop:
h(x) = - 16x² + 4
Second drop hits the ground 2 seconds later
Function g(x) to model the second drop:
-16t² + V0t + h0
h(x) = - 16x² + 4
0 = - 16x² + 4
16x² = 4
x² = 4/16
x² = 1/4
x = 1/2
2 seconds later :
X = 1/2 + 2
x = 2.5
0 = - 16(2.5)² + 0 + h0
0 = - 100 + h0
h0 = 100
Hence,
g(x) = - 16x² + 100
What is the percent of decrease from 84 to 21
Answer:
84 decreased to 21 is 25%
What is the value of x ?
5.5
9
11.5
13
Answer:
itz 5.5
Step-by-step explanation:
i just got it right
Write the point-slope form of the equation of the line that passes through the point (-1,5) and has a slope of -1. Include
your work in your final answer. Type your answer in the box provided to submit your solution.
Answer:
y= - x + 4
Step-by-step explanation:
The point-slope form of the equation of a line is:
y= m ( x - h )+ k
Where m is the slope and (h,k) is a point through which the line passes.
The slope of the line is m=-1 and it passes through (-1,5), thus the equation of the line is:
y=(-1) ( x - (-1) ) + 5
Operating:
y= - ( x + 1 ) + 5
y= - x - 1 + 5
Simplifying:
y= - x + 4
Can someone help with the last question I by accidentally pressed true tho
Answer:
The answer is True.
Step-by-step explanation:
-3x - 10 > -31
-3(5) - 10 > -31
-15 - 10 > -31
-25 > -31
True.
PLZZZZ HELP! write the equation in standard form y=3/4x - 4
Answer:
3x-4y = 16
Step-by-step explanation:
The sales tax in a major city is 6%. Find the total cost, including the tax charged on a purchase of 500$
Answer:
$530
Step-by-step explanation:
6% of 500 is 30. Add 500 and 30.
Please help, this is probably the last question I'll post for today!
Answer:
The answer is A.
Step-by-step explanation:
3+6=9
-5-9=-14
-14/2
Hope this helps! :)
Answer:
Answer is A. -7
Step-by-step explanation:
-5-(3+6)/2. PEMDAS (Parenthesis)
-5-9/2 Add/Subtract & Slash and dash = -5 + -9 = -14
-14/7= -7/1 which is just -7
the image shows this famous mondrian painting. the rectangle in the top left is red, the one in the bottom left is blue and the one in the bottom right is yellow. the remaining ones are white. how many rectangles are the altogether in the painting?
The number of rectangles in the paintings shown is: 7 rectangles.
What is a Rectangle?A rectangle is a quadrilateral shape with four sides and four angles.
A rectangle has two opposite sides that are equal to each other and are parallel as well. Also, the interior angles formed by the sides are right angles.
Thus, from the paintings there are:
1 red rectangle4 white rectangles1 blue rectangle1 yellow rectangleTherefore, the number of rectangles in the paintings shown is: 7 rectangles.
Learn more about rectangles on:
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Mangojuicecosts$8.50perquartandbananajuicecosts$6.20perquart.Tyler wants to make a mixture of mange and banana juice that sells for $5.50 per quart. How many quarts "q" of mango juice should he mix with 4 quarts of banana juice to make mango-banana juice at that price? Which equation below represents the situation?
Answer:
There is no possible combination that will result in mango-banana juice that costs $5.50 per quart if its two ingredients cost $8.50 and $6.20 per quart.
Step-by-step explanation:
the equation you need to solve is:
let M = quantity of mango juice
$8.50M + (4 x $6.20) = (4 x $5.50) + $5.50M
$8.50M + $24.80 = $22 + $5.50M
$24.80 - $22 = $5.50M - $8.50M
$2.80 = -$3M
M = $2.80 / -$3 = -0.933 ⇒ the quantity of mango juice cannot be negative
how to complete the square of: 3x^2-6x-12=0
Answer:
exact form:
x=±√5+1
decimal form:
x = 3.23606797..., -1.23606797...
Step-by-step explanation:
Use the formula (b/2)^2 in order to create a new term. Solve for x by using this term to complete the square. ---- :))
Answer:
x = √5 + 1, x = -√5 + 1
Step-by-step explanation:
We want the coefficient of x^2 to be 1, so let's divide either side by 3;
3x^2 - 6x - 12 = 0 => Divide either side by 3
3x^2/3 - 6x/3 - 12/3 = 0/3 => Simplify
x^2 - 2x - 4 = 0
Let's try to form a perfect square;
(x^2 - 2x + ? ) - 4 = 0
|
1/2(- 2) = (- 1)^2 = 1
(x^2 - 2x + 1) + 4 - 1 = 0
(x - 1)^2 - 5 = 0
(x - 1)^2 = 5
For x - 1 = √5 : x = √5 + 1
For x - 1 = - √5 : x = -√5 + 1
There were approximately 3 x 10^5 firefighters in the United States in 2012. The average salary of a firefighter was $45,000. About how much did all firefighters in the United States earn from their salary altogether in 2012? Express your answer using scientific notation
Given the number of firefighters and the average salary, the total salary altogehter is about $1.35 x 10^10
What is scientific notation?Scientific notation is used simplify large numbers into smaller numbers. In order to transform a number into a scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.
3 x 10^5 x 4.5^4 = 13.5 x 10^9
= 1.35 x 10^10
To learn more about scientific notation, please check: brainly.com/question/25334755
What is y = x 2 + 10 x + 28 in vertex form?
Answer:
=12x+28
Step-by-step explanation:
The distance between San Antonio and Houston is 190 miles. Nicholas and Rose each drove
2
5
of the total distance. If Charlie drove the rest of the distance, how many miles did Charlie drive?
The distance droved by Charlie is about 38 miles
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
The distance between San Antonio and Houston is 190 miles. Nicholas and Rose each drove 2/5 of the total distance.
Distance droved by Nicholas = Distance droved by rose = (2/5) * 190 = 76 miles
Distance droved by Charlie = 190 - 76 - 76 = 38 miles
The distance droved by Charlie is about 38 miles
Find out more on equation at: https://brainly.com/question/2972832