If v=-1, x=-2
and y= 3, find the value of:
3v + 2x
Answer:
-7
Step-by-step explanation:
3 v + 2 x
Where, v = -1 and x = -23 ( - 1) + 2 ( -2)
-3 - 4
-7
What value can you add in the blank in the expression x^2 + 6x + 7 +__ to complete the
square?
Answer:
2
Proof:
x^2 + 6x + 7 + 2 = x^2 + 6x + 9 = x^2 + 6x + 3^2 = (x + 3)^2
The value can you add in the blank in the expression [tex]x^2 + 6x + 7 +\textunderscore\textunderscore[/tex] to complete the square is 2
What is trinomial?"It is a polynomial which consists of three terms."
What is square trinomial?"A trinomial with degree 2"The general form of square trinomial is [tex]ax^{2} +bx+c[/tex] where a ≠ 0What is perfect square trinomial?"A square trinomial is a perfect square, if and only if it satisfies the condition b² = 4ac"
For given question,
We have been given a square trinomial.
[tex]x^2 + 6x + 7 +\textunderscore\textunderscore[/tex]
We need to find the number in the blank space, so that the given trinomial would be complete square.
Let 'm' be the required number.
So, the trinomial would be [tex]x^2 + 6x + (7 +m)[/tex]
Comparing above square trinomial with [tex]ax^{2} +bx+c[/tex],
we have a = 1, b = 6, c = 7 + m
We know, a square trinomial is a perfect square, if and only if it satisfies the condition b² = 4ac
⇒ b² = 4ac
⇒ 6² = 4 × 1 × (7 + m)
⇒ 36 = 4 × (7 + m)
⇒ 9 = 7 + m
⇒ m = 2
This means, we need to add 2 in the blank space.
So, the square trinomial would be,
[tex]x^2 + 6x + 7 + \underline {2}\\\\= x^2 + 6x + 9\\\\= (x + 3)^2[/tex]
Therefore, the value can you add in the blank in the expression [tex]x^2 + 6x + 7 +\textunderscore\textunderscore[/tex] to complete the square is 2
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A grapefruit is 8% heavier than an orange, and an apple is 10% lighter than the orange. By what percentage is the grapcfruit heavier than the apple?
Answer:
The grapefruit is 18% heavier than the apple.
Step-by-step explanation:
Orange defines the 100% in this situation.
We know that grapefruit is 8% heavier than an orange, so the weight of a grapefruit (in percentage) will be: 100% + 8% = 108%
And an apple is 10% lighter than the orange, then the weight (in percentage) of the apple will be: 100% - 10% = 90%
The difference between the two weights is then:
grapefruit - apple
108% - 90% = 18%
So the grapefruit is 18% heavier than the apple.
. What is the solution of the system of equations 3x + 2y = 4 and -2x + 2y = 24? *
Answer:
x= -4
y= -8
This will be the solution
What is the length of the base of a right triangle with an area of 15 square meters and a height of 3 meters? A. 5 m B. 10 m C. 30 m D. 45 m
Answer:
B.10
Step-by-step explanation:
15=1/2b(3)
30=3b
10= base
Find the Laplace Transform of the following function.
f(t) = 10 cos (12t+ 60°) u(t)
Answer:
L(f(t)) = [tex]\frac{5s - 60\sqrt{3} }{s^2 + 144}[/tex]
Step-by-step explanation:
f ( t ) = 10 cos ( 12t + 60°) u(t)
attached below is a detailed solution of the given problem
L(f(t)) = [tex]\frac{5s - 60\sqrt{3} }{s^2 + 144}[/tex]
If ∠1 = 3x, ∠2 = 5x + 18, and s ⊥ r, find m∠1.
I hope it will help you.
Answer:
x = 9
Step-by-step explanation:
angle <1 and angle <2 is complementary and their sum is 90 degrees
3x + 5x + 18 = 90 add like terms
8x + 18 = 90 subtract 18 from both sides
8x = 72 divide both sides by 8
x = 9 to find the measure of angle <1 replace x with the value we found
what is the equation of the line that has a gradient of 3 and passes through the point (-1,3)
Answer:
d
Step-by-step explanation:
You buy items costing $1900 and finance the cost with a fixed installment loan for 24 months at 8% simple interest per year.
1. What is the finance charge?
2. What is your monthly payment?
* Please explain how you got the answer*
9514 1404 393
Answer:
$304$91.83Step-by-step explanation:
1. The finance charge is found from the simple interest formula;
I = Prt
where P is the principal amount, r is the annual rate, and t is the number of years.
24 months is 2 years, so the interest charged is ...
I = $1900×0.08×2 = $304
The finance charge is $304.
__
2. The monthly payment will be the total amount due, divided by the number of months.
payment = ($1900 +304)/24 = $2204/24 ≈ $91.83
The monthly payment is $91.83.
The y value is two less than twice the x-value
Find the indicated Arc length in bold . Use 3.14 for pi!
The product of two consecutive negative integers is 600. What is the value of the lesser integer?
–60
–30
–25
–15
Answer:
-25
Step-by-step explanation:
-24×(-25)=600
Hope this helps! :)
Answer: It's -25
edg 2023
The set of lifespans of an appliance is normally distributed with a mean of 48 months and a standard deviation of eight months. What is the lifespan of an appliance that has a Z score of -3?
Answer:
24 months
Step-by-step explanation:
Given :
Mean = 48
Standard deviation = 8
Zscore = - 3
Using the relation :
Zscore = (x - mean) / standard deviation
Where, x = score
-3 = (x - 48) / 8
-3 * 8 = x - 48
-24 = x - 48
-24 + 48 = x
24 = x
Score = 24
Suppose you have a score that puts you 1.1 standard deviations below the mean. What is your percentile score?
Answer:
200000%
Step-by-step explanation:
.
How far does a train travel in 12 hours at 115 miles per hour?
1,509 mi
1,265 mi
1,380 mi
Answer:1380
Step-by-step explanation: 12x115
Answer:
1,380
Step-by-step explanation: 12 times 115 gives you the product of 1,380. :)
Hope this is helpful
can anybody help me? I'll give brainlest
9514 1404 393
Answer:
65°, 35°, 90°, 115°, 80°
Step-by-step explanation:
There are 9 of the longer tick marks in 90°, so each of them represents 10°. The shorter tick marks are halfway between, so are on multiples of 5°. This lets us make a list of the angle value associated with each of the letters.
A: 0 or 180
B: 65 or 115
C: 90
D: 145 or 35
E: 180 or 0
__
Using this list, we can find the measure of each angle by finding the positive difference of the corresponding angle values associated with each of its rays.
arc AOB = 65 -0 = 65°
arc DOE = 35 -0 = 35°
arc AOC = 90 -0 = 90°
arc EOB = 115 -0 = 115°
arc DOB = 145 -65 = 80°
Find the measure of the arc or angle indicated. Find QR Please help!!!
22. A trapezoid has an area of 24 square units. The height is 3 units and the length of one of the bases is 5 units. Find the length of the other base.
Answer:
Step-by-step explanation:
A trapezoid is a 4-sided figure with one pair of parallel sides. For example, in the diagram to the right, the bases are parallel. To find the area of a trapezoid, take the sum of its bases, multiply the sum by the height of the trapezoid, and then divide the result by 2, The formula looks like this:
area_trapezoid1.gif or area_trapezoid2.gif
Where b1.gif is base1.gif, b2.gif is base2.gif, h.gif is height and · means multiply.
Each base of a trapezoid must be perpendicular to the height. In the diagram above, both bases are sides of the trapezoid. However, since the lateral sides are not perpendicular to either of the bases, a dotted line is drawn to represent the height.
In Examples 1 and 3 below, the height is a side of the trapezoid since it is perpendicular to the base. In Example 2, the lateral sides are not perpendicular to the base, so a dotted line is drawn to represent the height.
20 points & Brainliest to the one who gets ALL of them correct! NEED HELP ASAP!!! Due today!!!
Verify these Identities & SHOW YOUR WORK:
1. cosx−cosxsin²x = cos³x
2. [tex]\frac{sinx}{1+cosx}[/tex] = [tex]\frac{1-cosx}{sinx}[/tex]
3. cos⁴b−sin⁴b = 1−2sin²b
4. [tex]\frac{siny+cosy}{siny}- \frac{cosy-siny}{cosy}[/tex] = [tex]\frac{secy}{cosy}[/tex]
5. (secx−tanx)² = [tex]\frac{1-sinx}{1+sinx}[/tex]
HELP!!!
Answer:
30
Step-by-step explanation:
Answer: go on mathaway!!!
Step-by-step explanation:
This dosent really help with ur question but mathaway is free and got me through math
Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.
Assume that you take out a $2000 loan for 48 months at 3.5% APR. How much total interest will you have paid at the end of the 48 months? (Round your answer to the nearest cent.)
$
Step-by-step explanation:
Are you using a particular calculator for the class? For this class, is the payment expected to be compounded monthly?
There is a function in Microsoft Excel that will calculate the payment for you, but the answer is going to be slightly different for a business math class than a calculus-based statistics class.
The excel formula to calculate a payment is
=PMT(0.04/12,60,25000,0)
.04/12 is the interest APR on a monthly basis
60 is the number of months
25000 is the current amount owed
0 is the future balance after 60 payments
The answer from Excel is $460.41 -- ignore the negative sign for these purposes.
Multiply that number by the 60 months you pay and you get a total paid of $27,624.78
Remove the initial 25K and $2,624.78 is your interest amount.
By the way, I used the simplifying assumptions that the problem meant "interest rate" when it said "APR", and that the rate would compound monthly. In the actual loan industry, the interest rate is only part of the calculation for APR, a
146.08
Step-by-step explanation:
Let's start by figuring out the payment
effective rate: .035/12= .002916667
\begin{gathered}2000=x\frac{1-(1+.002916667)^{-48}}{.002916667}\\x=44.71\end{gathered}
2000=x
.002916667
1−(1+.002916667)
−48
x=44.71
then it's just
44.71*48-2000=146.08
Answer:
146.08
Step-by-step explanation:
Let's start by figuring out the payment
effective rate: .035/12= .002916667
[tex]2000=x\frac{1-(1+.002916667)^{-48}}{.002916667}\\x=44.71[/tex]
then it's just
44.71*48-2000=146.08
This is a rhombus. Solve for x, Then label each angle with its correct measures:
Answer:
Step-by-step explanation:
In the given rhombus, the value of x is 18.
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.
We know that;
Diagonal bisect the angles of a rhombus.
Hence, We can formulate;
⇒ (2x + 16)° = (3x - 2)°
Solve for x as;
⇒ 2x + 16 = 3x - 2
Subtract 2x both side,
⇒ 2x + 16 - 2x = 3x - 2 - 2x
⇒ 16 = x - 2
Add 2 both side,
⇒ 16 + 2 = x - 2 + 2
⇒ 18 = x
⇒ x = 18
Thus, The value of x in rhombus = 18
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For the sequence an = an-1 + an-2 and ai = 2, a2 = 3,
its first term is
its second term is
its third term is
its fourth term is
its fifth term is
Answer:
[tex]a_1 = 2[/tex]
[tex]a_2 = 3[/tex]
[tex]a_3 = 5[/tex]
[tex]a_4 = 8[/tex]
[tex]a_5 = 13[/tex]
Step-by-step explanation:
Given
[tex]a_n = a_{n-1} + a_{n-2}[/tex]
[tex]a_1 = 2[/tex]
[tex]a_2 = 3[/tex]
Solving (a): The first term
This has already been given as:
[tex]a_1 = 2[/tex]
Solving (b): The second term
This has already been given as:
[tex]a_2 = 3[/tex]
Solving (c): The third term
This is calculated as:
[tex]a_n = a_{n-1} + a_{n-2}[/tex]
[tex]a_3 = a_{3-1} +a_{3-2}[/tex]
[tex]a_3 = a_2 +a_1[/tex]
[tex]a_3 = 3 +2[/tex]
[tex]a_3 = 5[/tex]
Solving (d): The fourth term
This is calculated as:
[tex]a_n = a_{n-1} + a_{n-2}[/tex]
[tex]a_4 = a_{4-1} +a_{4-2}[/tex]
[tex]a_4 = a_3 +a_2[/tex]
[tex]a_4 = 5+3[/tex]
[tex]a_4 = 8[/tex]
Solving (e): The fifth term
This is calculated as:
[tex]a_n = a_{n-1} + a_{n-2}[/tex]
[tex]a_5 = a_{5-1} +a_{5-2}[/tex]
[tex]a_5 = a_4 +a_3[/tex]
[tex]a_5 = 8+5[/tex]
[tex]a_5 = 13[/tex]
Can y’all help me? Thanks :)
Answer:
Step-by-step explanation:
Soooo, by looking at the picture we can tell that it is a right trapezoid
The formula for the area is
(b1+b2)/2*h
(Base 1+ Base 2)/ 2 * height
Now we can plug in the numbers:
(5+15)/2*6
20/2*6
10*6
=60
1 gallon of paint per sq. foot
So Isha needs 60 gallons of paint
Ariana owns a food truck that sells tacos and burritos. She sells each taco for $4 and each burrito for $8.25. Ariana must sell at least $960 worth of tacos and burritos each day. Write an inequality that could represent the possible values for the number of tacos sold, tt, and the number of burritos sold, bb, that would satisfy the constraint.
Answer:
09
Step-by-step explanation:
A rectangular prism has a base area of 2 square feet and a height of 5 feet. What
is the volume of the prism in cubic feet?
10
15
12
11
Submit
This year, a small business had a total revenue of
$
62
,
100.
If this is
35
%
more than their total revenue from the previous year, what was the total revenue the previous year?
Answer:
21,735
Step-by-step explanation:
Which of the following correctly simplifies the expression 2 to the power of 3 multiplied by 3 to the power of 0 whole over 5, the whole squared.? (5 points)
2 to the power of 3 multiplied by 1 whole over 5, the whole squared. = 2 to the power of 6 multiplied by 1 squared over 5 squared. = 64 over 25.
2 to the power of 3 multiplied by 1 whole over 5, the whole squared. = 2 to the power of 5 multiplied by 1 squared over 5 cubed. = 32 over 125.
2 to the power of 3 multiplied by 0 whole over 5, the whole squared. = 2 to the power of 6 multiplied by 0 over 5 squared. = 0
2 to the power of 3 multiplied by 0 whole over 5, the whole squared. = 2 to the power of 5 multiplied by 0 over 5 cubed. = 0
9514 1404 393
Answer:
(a) 64/25
Step-by-step explanation:
The relevant properties of exponents are ...
a^0 = 1 . . . . a ≠ 0
(a^b)^c = a^(bc)
(ab)^c = (a^c)(b^c)
__
Your expression simplifies to ...
[tex]\left(\dfrac{2^3\cdot3^0}{5}\right)^2=\dfrac{2^{3\cdot2}\cdot1^2}{5^2}=\dfrac{2^6}{5^2}=\boxed{\dfrac{64}{25}}[/tex]
Please answer and explain.
Answer:
x = 13
Step-by-step explanation:
The sum of the exterior angles of a 4 sided polygon is 360
139+ 6x+9x+2x = 360
Combine like terms
139+17x=360
Subtract 139 from each side
17x = 360-139
17x = 221
Divide each side by 17
17x/17 = 221/17
x = 13
The following hypothetical data represent a sample of the annual numbers of home fires started by candles for the past several years.
5640, 5090, 6590, 6380, 7165, 8440, 9980
The population has a standard deviation equal to 1210. Assuming that the data is from a distribution that is approximately normal, construct a 90 % confidence interval for the mean number of home fires started by candles each year
Answer:
(6290.678 ; 7790.742)
Step-by-step explanation:
Given the data :
5640, 5090, 6590, 6380, 7165, 8440, 9980
The sample mean, xbar = Σx / n = 49285 / 7 = 7040.71
The 90% confidence interval :
Xbar ± Margin of error
Margin of Error = Zcritical * σ/√n
Since the σ is known, we use the z- distribution
Zcritical at 90% confidence = 1.64
Hence,
Margin of Error = 1.64 * 1210/√7
Margin of Error = 750.032
90% confidence interval is :
7040.71 ± 750.032
Lower boundary = 7040.71 - 750.032 = 6290.678
Upper boundary = 7040.71 + 750.032 = 7790.742
(6290.678 ; 7790.742)
Write the equation of the line that passes through the points
Y=2x+5
Answer:
Parallel means that the lines never intersect. If the equation of the new line is y=ax+b , then the system
y=ax+b
y=2x+5
needs to have no solutions. Subtracting the equations gives us
(a−2)x+(b−5)=0
In order for this to ever be 0 we need either a≠2 or b=5 , so to stop this from happening, we will require both a=2 and b≠5 .
Since our line now has the form y=2x+b , and (4,5) is on the line, then the equation
5=2⋅4+b
should be true. Since this implies that b=−3 , we have that the parallel line going through (4,5) has equation
y=2x−3
What is an equation of a line that goes through point (4,-5) and is parallel to y=2x+8?
Which line is parallel to the line y = 2x -4?
What is an equation for a line parallel to y = 5 x -5 and passing through the point (4,19)?
What is an equation for the line that is parallel to y= -4x
