Answer:
f(x) = (x+5)^2 +12
The minimum value is 12
Step-by-step explanation:
f(x)=x^2+10x+37
The vertex will be the minimum value since this is an upwards opening parabola
Completing the square by taking the coefficient of x and squaring it adding it and subtracting it
f(x) = x^2+10x + (10/2) ^2 - (10/2) ^2+37
f(x) = ( x^2 +10x +25) -25+37
= ( x+5) ^2+12
Th is in vertex form y = ( x-h)^2 +k where (h,k) is the vertex
The vertex is (-5,12)
The minimum is the y value or 12
Solve the homogeneous linear system corresponding to the given coefficient matrix.
[1 0 0 1]
[0 0 1 0]
[0 0 0 0]
(x1, x2, x3, x4) =________
This question is incomplete, the complete question is;
Solve the homogeneous linear system corresponding to the given coefficient matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set x4 = t and x2 = s and solve for x1 and x3 in terms of t and s.)
[1 0 0 1]
[0 0 1 0]
[0 0 0 0]
(x1, x2, x3, x4) =________
Answer:
the solution for the given system is; ( x₁, x₂, x₃, x₄ ) = ( -t, s, 0, t )
Step-by-step explanation:
Given the data in the question;
coefficient matrix
[tex]\left[\begin{array}{cccc} 1&0&0&1 \\ 0&0&1&0 \\ 0&0&0&0 \end{array}\right][/tex]
Now, from linear system;
[tex]\left[\begin{array}{cccc} 1&0&0&1 \\ 0&0&1&0 \\ 0&0&0&0 \end{array}\right] \left[\begin{array}{ccc}x_1\\x_2\\x_3\\x_4\end{array}\right] = \left[\begin{array}{ccc}0\\0\\0\\0\end{array}\right][/tex]
So, with the matrix, the associated equation is;
x₁ + x₄ = 0, x₃ = 0
Number of variables is 4 and ranked of the matrix is 2,
Hence, there are infinite solutions,
There are also two free variables;
from the question,
Let x₄ = t and x₂ = s be the free variables
so
x₁ + x₄ = 0
x₁ + t = 0
x₁ = -t
Therefore, the solution for the given system is;
( x₁, x₂, x₃, x₄ ) = ( -t, s, 0, t )
The probalityof raining today is 30% what is the probality tha it will nat rain?
you spend $40 on a meal for you and your friends. Sandwiches cost $5 and beverages cost $2 each. Write and equation in standard form where x is the number of sandwiches purchased and y is the number of beverages posted.
Will mark brainlest
find the domain and range of following
Answer:
Result:
{0, 3/7}
Decimal approximation:
{0, 0.428571}
Step-by-step explanation:
Find the norm...
and you know I wanna speedrun
help me plz plz!! It's due tomorrow will Mark u as BRAINLIEST
Answer: Mean(Mia)=34.33 Mean(Sophia)=35.667
Sophia's phone calls on average, are longer in length than Mia's phone calls.
Step-by-step explanation:
what is
3⋅f(−4)−3⋅g(−2)=
Answer:
[tex]3 * f(-8) - 3 * g(-2) = 6[/tex]
Step-by-step explanation:
Given
This question has a missing graph (See online)
Required
[tex]3 * f(-8) - 3 * g(-2)[/tex]
From the graph:
[tex]f(-8) = -2[/tex]
and
[tex]g(-2) = -4[/tex]
So, we have:
[tex]3 * f(-8) - 3 * g(-2) = 3 * -2 -3 * -4[/tex]
[tex]3 * f(-8) - 3 * g(-2) = 6[/tex]
A video game that usually costs $30.65 is marked down 60%. Kelvin determined that the new price of the game would be $18.39. Look at Kelvin's work and find his error. ($30.65)(0.60) = $18.39
*Please give an explanation longer than 1 sentence :,)
Answer:
Kelvin’s error is that when he got the final result, that was the amount that was marked down. He still needed to find the price after the original price was marked down by that number wich in this case is $18.39. So using one of his steps, 30.65(0.6)=18.39. We can subtract 30.65 (original price) and 18.39 (mark down price). You’d get 11.26 dollars as the final price.
can someone answer this i’ll give u a cookie PLEASE I NEED IT NOW
Answer:
its c
Step-by-step explanation:
please help! (listing BRAINLIST and giving points) :)
Answer:
sin∅ = 12/13
Step-by-step explanation:
use pythagorean theorem to find the missing side
a² + 5² = 13²
a² = 13² - 5²
a² = 169 - 25
a² = 144
a = 12
-----------------------------
Sin∅ = opp/hyp
sin∅ = 12/13
Can y’all help me on question 13?!
Answer:
90 cm²
Step-by-step explanation:
The shape can be divided in three rectangles.
Area = area of rectangle 1 + area of rectangle 2 + area of rectangle 3
✔️Area of rectangle 1 = L*W
L = 5 cm
W = 3 cm
Area = 5*3 = 15 cm²
✔️Area of rectangle 2 = L*W
L = 6 + 5 + 1 = 12 cm
W = 5 cm
Area = 12*5 = 60 cm²
✔️Area of rectangle 3 = L*W
L = 5 cm
W = 3 cm
Area = 5*3 = 15 cm²
✅Area of the shape = 15 + 60 + 15 = 90 cm²
A collection of 39 coins consists of dimes and nickels. The total value is $2.75. How many dimes and how many nickels are there?
Answer:
23 nickels and 16 dimes
Step-by-step explanation:
16 dimes = 1.60
23 nickels = 1.15
1.60 + 1.15 = 2.75
A skateboarding ramp is 13in. high and rises at an angle of 13°. How long is the base of the ramp? Round to the nearest inch.
===========================================================
Explanation:
The diagram is shown below. We know the vertical part of the triangle is 13 inches, which is the side opposite the reference angle 13 degrees. The adjacent side is unknown. We'll call it x. This is how long the base of the ramp is, which is the horizontal distance along the entire ramp. This distance is on the ground. The ramp itself is the hypotenuse but it seems like your teacher isn't wanting to know this value. So we'll ignore the hypotenuse.
We'll use the tangent rule to connect the opposite and adjacent sides.
tan(angle) = opposite/adjacent
tan(13) = 13/x
x*tan(13) = 13
x = 13/tan(13)
x = 56.309186365694
x = 56 inches is the approximate horizontal distance underneath the ramp
The base of the ramp is 57 inches long.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The tangent function relates the opposite side (height) and adjacent side (base) of a right triangle to the angle of elevation.
We know the opposite side is the height of the ramp, which is 13 inches, and the angle of elevation is 13 degrees.
Let the adjacent side (the base of the ramp) be "x".
The tangent of 13 degrees is equal to the opposite side divided by the adjacent side:
tan(13) = 13/x
To solve for x, we can multiply both sides by x:
x × tan(13) = 13
Then, we can divide both sides by tan(13):
x = 13 / tan(13)
x = 13 / 0.228
x= 56.99
Therefore, the base of the ramp is 57 inches long.
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HELPPPP I need help with this question!!!!
I think the 4th one but Im not too sure please forgive me if I'm wrong.
HELP ME PLEASEEEEEEEEEEEEEEEE
Answer:
[tex] \frac{2}{3} a - \frac{1}{6} = \frac{1}{3} \\ \frac{2}{3} a = \frac{1}{2} \\ 4a = 3 \\ a = \frac{3}{4} [/tex]
Suri and Carter want to start saving for the future. they each invest $4,000 into a certificate of deposit account. suri's investment earns 3% interest compounded annually. Carter's investment is 3% simple interest.
Two formulas:
Compound interest - A = P(1 + r/n)^nt
Simple interest = A = P(1 + rt)
A - final amount
P - initial principal balance
r - interest rate
n - number of times interest applied per time period
t - number of time periods elapsed
Suri --
A = 4,000(1+0.03/1)^5
A = $4,637.09
Carter --
A = 4,000(1+0.03*5)
A = $4,600
In 5 years, Suri makes $37.09 more than Carter
Four expressions are written in the table.
What value of n makes all of the expressions equivalent?
0
1
10
100
The following cylinder has a height of 7.2 in. and diameter of 6.8 in.
Cylinder with measures described in text.
What is the volume of the cylinder? Remember, the diameter of a circle is two times its radius.
Use 3.14 for π and round your answer to the nearest tenth.
Answer:
598.16
Step-by-step explanation:
Eh you should have the formula if not I can't really type it but ,trust, the answer is 598.16 in²
Answer:
261.3 in.
Step-by-step explanation:
HELP PLEASE!!!!
By which rule are these triangles congruent?
A) AAS
B) ASA
C) SAS
D) SSS
Answer:
ASA
Step-by-step explanation:
Both triangles contains two angles which indicate that it can only be the top 2 options.
Choose the solution set represented by the following graph.
{x | x R, x ≤ -2}
{x | x R, x > -2}
{x | x R, x < -2}
{x | x R, x ≥ -2}
Answer:
{x|x rx>-2}
Step-by-step explanation:
hope helpful answer
y = 3 sine (one-third x)
Answer:
B on edge
Step-by-step explanation:
A woman when working with her takes 2 hours to complete the housework, and takes 3 hours when working alone How long would it take the daughter to complete the housework if working alone?
The daughter will take 6 hours to complete the housework if working alone.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
A woman when working with her takes 2 hours to complete the housework and takes 3 hours when working alone.
Let's suppose y minutes taken by the daughter to complete the housework:
Rate for daughter = 1/x
1/3 + 1/x = 1/2
2x + 6 = 3x
x = 6 hours
Thus, the daughter will take 6 hours to complete the housework if working alone.
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What is the slope of the line represented by the equation y =4/5x-3?
A. -3
B. - 4/5
C. 4/5
D. 3
Answer:
4/5
Step-by-step explanation:
y =4/5x-3
The equation is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is 4/5
Answer:
4/5
Step-by-step explanation:
The slope will be in front of the x in slope intercept form.
What's the surface area of this figure? Pick one of the options.
If x=4 and y=5. The value of 3x-5y
Answer:
13, I believe :)
Step-by-step explanation:
3(4)-5(5)
multiply by the coefficient
=12-25
=-13
Find the final total value of a 5-year investment of $2600 at a simple annual rate of
3.53%
Answer:
A = $3,101.09
A = P + I where
P (principal) = $2,600.00
I (interest) = $501.09
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 3.53/100
r = 0.0353 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 2,600.00(1 + 0.0353/12)(12)(5)
A = 2,600.00(1 + 0.002941667)(60)
A = $3,101.09
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $2,600.00 at a rate of 3.53% per year compounded 12 times per year over 5 years is $3,101.09.
An auto repair shop charged a customer $496 to repair a car. The bill listed $96 for parts and the remainder for labor. If the cost of labor is $40 per hour, how many hours of labor did it take to repair the car?
The managers of a fast food chain want their products to be as similar as possible across locations. They suspect that the burgers at their Albuquerque branch have bigger parties than the burgers at the Santa Fe branch, so they take a sample of 7 patties from each restaurant and measure their weights in gransk
Albuquerque 11011 110 110 111 112 106
Santa Fe 107 111 110 108 109 110 109
The managers want to test if the parties in the Albuquerque branch have a higher average weight than the patties in the Santa Fe branch. Assume that all conditions for inference have been met
Which of these is the most appropriate test and alternative hypothesis?
a. Pairedt test with H>0 3
b. Pairedt test with H > 0
c. Pairedt test with Ht0
d. Two-sample t test with H. > 0
Answer:
H0 : μd = 0
H1 : μd > 0
Step-by-step explanation:
The scenario described above can be compared statistically using a paired test mean as the mean if the two groups are dependent, the two restaurants, Albuquerque and Santa Fe are both restaurant locations of a single restaurant company. Hence, to test the mean difference, we use the paired test statistic. Defined thus `
Null hypothesis ; H0 : μd = 0 and the Alternative hypothesis ; H1 : μd > 0
Answer:
Two Sample T test with Ha = Albernuque>Santa Fe
Step-by-step explanation:
Khan
What is the sum of the interior angle measures of a polygon that has 11 sides?
HINT: Sum= (n-2)180
Answer:
Step-by-step explanation:
no of sides (n)=11
sum=(n-2)180
=(11-2)180
=9*180
=1620
therefore sum of the interior angles of a polygon having 11 sides id 1620°.
Answer:
n= 1620
Step-by-step explanation:
I know the answer is correct I got the exact same question during the lessons.
Get brainly if right?
10 points!
Answer:
Tn = -13n +37
ordered list is 24, 11 , -2 , -15, -28 ,-41
ASAP:
Consider the word pROPOSITION. How many five letter words can be formed if two letters are alike and three letters are different? Consider the cases.
Answer:
The letters M, N, A , E appear twice and G, T appear once.
So, the first case was where all the letters were different, thus, the number of words formed were:
6C5 . 5!(further permutation) = 720
the second case was where there were two groups of two alike letters and one different letter. Thus, the number of words formed were:
2C1 . 4C2 . 3! = 72
the third case was where there were one group of two alike letters and three different letters.
Thus, the number of words formed were:
4C1 . 5C3 . 4!= 960
thus, the total number of words were:
720 + 72 + 960 = 1752
but this answer is wrong as the Real answer is 1824.
Step-by-step explanation: