Answer:
Minimum = (-3, -2)
Step-by-step explanation:
Standard form of a quadratic function:
[tex]f(x)=ax^2+bx+c[/tex]
If a > 0 the parabola opens upwards and the curve has a minimum point.
If a < 0 the parabola opens downwards and curve has a maximum point.
Given function:
[tex]f(x)=x^2+6x+7[/tex]
As a > 0, the parabola opens upwards and so the curve has a minimum point.
The minimum/maximum point of a quadratic function is its vertex.
Vertex form of a quadratic function:
[tex]f(x)=(x-h)^2+k[/tex]
Where (h, k) is the vertex.
To rewrite the given function in vertex form, complete the square.
Add and subtract the square of half the coefficient of the term in x:
[tex]\implies f(x)=x^2+6x+7 +\left(\dfrac{6}{2}\right)^2-\left(\dfrac{6}{2}\right)^2[/tex]
[tex]\implies f(x)=x^2+6x+7 +9-9[/tex]
[tex]\implies f(x)=x^2+6x+9+(7 -9)[/tex]
[tex]\implies f(x)=x^2+6x+9-2[/tex]
Factor the perfect square trinomial formed by x²+6x+9:
[tex]\implies f(x)=(x+3)^2-2[/tex]
Compare with the vertex form:
h = -3k = -2Therefore, the vertex is (-3, -2) and so the minimum value of the given function is (-3, -2).
Micaela and Elisa each Micaela and Elisa each improved their yards by planting rose bushes and geraniums they both bought their supplies from the same store. Micaela spent $122 on 14 rose bushes and. 8 geraniums Elisa spent $120 on 12 rose bushes and 12 geraniums. What is the cost of one geranium?
HELP ASAP
By solving a system of equations, we can see that each geranium costs 3 dollars.
What is the cost of one geranium?
First, let's define the two variables:
x = price of one rose bush.
y = price of one geranium
Now, with the information on the problem we can write two equations, thus, we will have a system of equations:
$122 = 14*x + 8*y
$120 = 12*x + 12*y
We want to solve that system, if we isolate x on the first equation we will get:
x = ($122 - 8y)/14
Now we can replace this on the other equation:
$120 = 12*($122 - 8y)/14 + 12*y
Now we can solve this for y.
14*$120 = 12*($122 - 8y) + 12*14*y
$1,680 = $1,464 + 72y
($1,680 - $1,464 )/72 = y = $3
Each geranium costs 3 dollars.
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1222445666161616145435463465364534534534
width= x length =2x+6. Two expressions to represent the perimeter
The two expressions to represent the perimeter of this rectangle include the following:
P = 2(2x + 6 + x).P = 2(3x + 6).What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
How to calculate the perimeter of a rectangle?Mathematically, the perimeter of a rectangle can be calculated by using this formula;
P = 2(L + W)
Where:
P represents the perimeter of a rectangle.L represents the length of a rectangle.W represents the width of a rectangle.Substituting the given variables into the given expression, we have;
P = 2(2x + 6 + x) ......expression 1.
For the second expression, we have:
P = 2(2x + 6 + x)
P = 2(3x + 6) ......expression 2.
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Complete Question:
The length of a rectangle is 2x+6 and the width is x. Write two expressions to represent the perimeter.
the ice rink sold 95 tickets for a total of 828.00. general admission tickets are $10.00 each and youth tickets are $8.00 each. how many of each did they sell
There were 61 youth tickets sold and 34 general admission tickets in linear equation .
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.GA= GENERAL ADMISSION =$10
Y= YOUTH =$8
GA+Y= 95
GA=95-Y
10GA+8Y=828
10(95-Y)+8Y=828
950-10Y+8Y=828
-2Y= 122 MULTIPLY BY (-1)
2Y= 122
Y= 61
GA= 34
There were 61 youth tickets sold and 34 general admission tickets.
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Please help! 10 points. If u don’t know don’t js answer for point I really need help. And please explain! Thank u!
Answer:
(b) √(4x+2)√(25x-4)
Step-by-step explanation:
Given two functions f(x) = √(4x+2) and g(x) = √(25x-4), you want the function fg.
SolutionThe product fg is a bit of shorthand notation:
[tex]fg = fg(x) = f(x)\cdot g(x)[/tex]
Substituting the given function definitions, we have ...
[tex]f(x)\cdot g(x) = \sqrt{4x+2}\cdot\sqrt{25x-4}[/tex]
The product of the radicals could be combined into one radical, but that has not been done in your answer choices. This means ...
[tex]\boxed{fg=(\sqrt{4x+2})(\sqrt{25x-4})}[/tex]
A rectangular box is 17 cm wide and 26 cm high. If the
surface area of the box is 4238 square centimeters,
find the length of the box.
Answer:
3796 length of the box
Step-by-step explanation:4,238-26×17=3,796
Please help me 40 points and brainliest (show your work)
The actual width of Tyrone's patio using the scale drawing is 16 feet's
How to find the actual width of Tyrone's patio using scale drawing?The scale from the backyard to the drawing is 2 ft to 1 inches.
The width of the patio on the drawing is 8 inches.
Therefore, the width of the Tyrone's actual patio is as follows;
Hence,
1 inches = 2 feet's
8 inches = ?
cross multiply
actual length of Tyrone's patio = 8 × 2
actual length of Tyrone's patio = 16 feet's
Therefore, using the scale drawing, the actual length of Tyrone's patio is 16 feet's.
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712 can be divisble by both 2 and 3?
Answer:
no
Step-by-step explanation:
it is divisble by 1, 2, 4, 8, 89, 178, 356, 712
I only need the answer for Part 1, thank you.
a The absolute value of ax will be considered while for the second the absolute value of ax + b will be considered.
b The absolute value of ax will be considered while for the second the absolute value of ax + b will be considered.
Given data
a, b, c, and x be real numbers.
How to show the difference in solving |ax| + b = c and |ax + b| = c|ax| + b = c
The equation here contains the modulus sign only for ax hence only the absolute value of ax is considered.
|ax + b| = c
Here the modulus sign covers both ax and b hence the absolute values of ax + b is considered.
How to show the difference in solving |ax| + b ≤ c and |ax + b| ≥ c|ax| + b ≤ c
The equation here contains the modulus sign only for ax hence only the absolute value of ax is considered.
|ax + b| ≥ c
Here the modulus sign covers both ax and b hence the absolute values of ax + b is considered.
Note that absolute values do not consider the signs
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Find the slope between points (1,-1) and (2,-2)
Answer:
The slope should be -1.
----------------------------------
Hope this helps!
Have a great day and God bless! :)
================================================
Work Shown:
[tex](x_1,y_1) = (1,-1) \text{ and } (x_2,y_2) = (2,-2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-2 - (-1)}{2 - 1}\\\\m = \frac{-2 + 1}{2 - 1}\\\\m = \frac{-1}{1}\\\\\boldsymbol{m = -1}\\\\[/tex]
--------------------
Side notes:
Slope = rise/run
rise = change in y value = [tex]y_{2} - y_{1}[/tex]
run = change in x value = [tex]x_{2} - x_{1}[/tex]
Make sure you subtract in the same order each time.
The figure below shows points PQRS on a circle centre O. QP is produced to X Angle XPS = 77 and angle PSO = 68⁰. R Find the size of angle PQO. 0 68% 770 S X
Answer:
Step-by-step explanation:
Question Multiply. (−5 5/8)⋅(−2 1/3) What is the product? Enter your answer as a simplified mixed number in the box.
Answer:
[tex]13\frac{1}{8}[/tex]
Step-by-step explanation:
Given expression:
[tex]\left(-5 \frac{5}{8}\right) \cdot \left(-2 \frac{1}{3} \right)[/tex]
Convert the mixed numbers into improper fractions by multiplying the whole number by the denominator, adding it to the numerator of the fraction, and placing this as the numerator:
[tex]\implies -\dfrac{5 \cdot 8+5}{8} \cdot -\dfrac{2 \cdot 3+1}{3}[/tex]
[tex]\implies -\dfrac{40+5}{8} \cdot -\dfrac{6+1}{3}[/tex]
[tex]\implies -\dfrac{45}{8} \cdot -\dfrac{7}{3}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{b} \cdot \dfrac{c}{d}=\dfrac{a \cdot c}{b \cdot d}:[/tex]
[tex]\implies \dfrac{-45 \cdot -7}{8 \cdot 3}[/tex]
[tex]\implies \dfrac{315}{24}[/tex]
Convert the improper fraction into a mixed number:
[tex]\implies 315 \div 24 = 13\: \text{r}\:3[/tex]
[tex]\implies 13\frac{3}{24}[/tex]
[tex]\implies 13\frac{1}{8}[/tex]
Answer:
Product = 13 1/8
Step-by-step explanation:
The equation is,
→ (-5 5/8) × (-2 1/3)
Now the product of equation will be,
→ (-5 5/8) × (-2 1/3)
→ (-45/8) × (-7/3)
→ (-15 × -7)/8
→ 105/8
→ 13 1/8 {mixed fraction}
Therefore, the product is 13 1/8.
PLEASE HELP ME !!!?!????
what is the value of x?
please help!!
Answer: 20
Step-by-step explanation:
2001
(is A force of 200 is exerted on an area of 50meters square
Calculate the pressure exerted by the force.
Given : Force applied is given as : 200 N
Area : 50m²
We know that the pressure is the force applied perpendicular to the surface of an object per unit area. or
Pressure = Force/Area=> P = 200N / 50m²
=> P = 40Nm² or 40 pascal!!!!!!!Question 3 pls help!!!
Ln(x)=y (log(x)) what is y?
Answer:
Step-by-step explanation:
ln(xy²/z)
Jerry surveyed adult males to study the relationship between their High and the length of their Footwear both are measured in centimeters. he found the equation y equals 75 + 3.4 x in which tax is the foot length and why is the height to be a good fit for his data. Based on this equation what would be the expected foot length of an adult male who is 1.8 m tall round your answer to the nearest tenth
The expected foot length of an adult male who is 1.8 m tall is 30.8 cm.
How to illustrate the information?Based on the information given, Jerry surveyed adult males to study the relationship between their high and the length of their footwear both are measured in centimeters and he found the equation y equals 75 + 3.4 x.
This will be illustrated as:
y = 75 + 3.4x..
y = 1.8m = 180
Therefore, y = 75 + 3.4x.
180= 75 + 3.4x
180 = 75 + 3.4x
Collect like terms
3.4x = 180 - 75
3.4x = 105.
Divide
x = 105 / 3.4
x = 30.8 cm
Therefore, the expected foot length of an adult male who is 1.8 m tall is 30.8 cm.
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For each of the following polynomials given a power function that best represents the end behavior of the polynomial. Draw the arrows.
Answer:
the answer is the 3rd to the 4th power and
The end behavior of the polynomial y=-4x+8x-21'+3 is y = -4x^3.
What is degree of a polynomial?Degree of a polynomial is the highest power that its terms pertain (for multi-variables, the power of term is addition of power of variables in that term).
Thus, in the degree of the polynomial is 3 as the highest power in its terms is 3.
(power and exponent are same thing)
We are given that;
The functions (a) 1=3x-2x+12
(b) 1-10-8.x2
(c) y=6r-4r+x-120
(d) y=-3x+2x-4x+7
(e) y=5x+2x2
(f) y=-4x+8x-21'+3
Now,
To find the power function that best represents the end behavior of a polynomial, we need to look at the leading term (the term with the highest degree) of the polynomial.
(a) The leading term of this polynomial is 3x. So the power function that best represents its end behavior is y = 3x.
(b) The leading term of this polynomial is -8x^2. So the power function that best represents its end behavior is y = -8x^2.
(c) The leading term of this polynomial is 6r. So the power function that best represents its end behavior is y = 6r.
(d) The leading term of this polynomial is -3x^3. So the power function that best represents its end behavior is y = -3x^3.
(e) The leading term of this polynomial is 2x^2. So the power function that best represents its end behavior is y = 2x^2.
(f) The leading term of this polynomial is -4x^3. So the power function that best represents its end behavior is y = -4x^3.
Therefore, by polynomials the answer will be y = -4x^3.
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What are the domain and range of the function f(x) = x^2 + 5x + 4/ x+4
This is just a linear equation, then the domain is the set of all real numbers and the range is the set of all real numbers.
How to find the domain and range of the given function?Here we have the function:
f(x) = (x^2 + 5x + 4)/(x + 4)
The numerator can be rewritten if we find the zeros:
x = (-5 ± √( 5^2 - 4*1*4))/(2*1)
x = (-5 ± 3)/2
Then the zeros are:
x = (-5 - 3)/2 = - 4
x = (-5 + 3)/2 = -1
So the numerator can be rewritten to (x + 4)*(x + 1)
And the function is rewritten to:
f(x) = (x^2 + 5x + 4)/(x + 4) = (x + 4)*(x + 1)/(x + 4) = (x + 1)
This is just a linear equation, then the domain is the set of all real numbers and the range is the set of all real numbers.
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if the m P=4x+1 and m Q=9x-3, find m Q
Answer:
4×9=36
1-3=-2
36÷2=18
Step-by-step explanation:
4×+1,9×-1.
4×9=36
1-3=-2
Identify which of the following numbers is an integer, rational and real number?
A.
−√5
B.
-1/2
C.
-50, 000, 000
D.
-1.5
From the given numbers :
Integers: -50,000,000
Rational numbers : -1/2 and -1.5
Real numbers : −√5 , -1/2, -50, 000, 000 , -1.5.
As given,
Given numbers:
A. −√5 :It is an irrational number.
Therefore belongs to real numbers.
B. -1/2 :In p/q form .
It is a rational and real number.
C. -50,000,000
It is a negative integer and real number.
D. -1.5 =-15 /10
=3/2
It is a rational and real number.
Therefore, from the given numbers :
Integers: -50,000,000
Rational numbers : -1/2 and -1.5
Real numbers : −√5 , -1/2, -50, 000, 000 , -1.5.
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what is the greatest possible error of 5.78 mi.?
Answer:
2.89
Step-by-step explanation:
GPE = U * 1/2
GPE = 5.78 * 1/2
GPE = 2.89
←
The surface area of a
three-dimensional figure is the sum of
the areas of all of its surfaces. Find the surface area of the
figure shown to the right.
The surface area of the figure is in².
4 in
4 in
10 in
Answer:
192 [in²]
Step-by-step explanation:
Area=(4*4)*2+(4*10)*4=192.
Suppose that the functions p and q are defined as follows.
p(x)=x² +6
q (x)=√x+9
Find the following.
(pg) (7) =
(9 °p) (7) = [
X
0/0
5
Answer:
Step-by-step explanation:
Here I need help with this question
C=5
Explain explain Explain
the length of a rectangle is 3 less than twice the width. The perimeter is 108 in. What is the length and width?
Answer:
19 in and 35 in
Step-by-step explanation:
Let the width be w and the length be 2w-3. Then,
[tex]2(w+2w-3)=108 \\ \\ 3w-3=54 \\ \\ 3w=57 \\ \\ w=19 \\ \\ \implies 2w-3=35[/tex]
Which of the following statements is true of the data displayed on this graph? 3 2 (2,5) (1,2) 2 77 (3,4) (3, 1) 3 (6,5) (5,3) 5 6 O The set of points on this graph is a relation and is a function. O The set of points on this graph is a relation but not a function O The set of points on this graph is a function but not a relation O The set of points on this graph is not a function and not a relation.
The set of points on this graph is a relation but not a function
We know that every function can be a relation but every relation cannot be a function.
A relation means the connection between the input and the output.
A function means that for every input there should only be one output.
Here, we have the data as:
(2,5), (1,2), (3,4), (3, 1), (6,5) and (5,3)
We can say that it is a relation as for every input, there is an output.
But, it is not a function.
This is because the input 3 has 2 outputs as 1 and 4 which is not possible in a function.
Therefore, the set of points on this graph is a relation but not a function.
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Sophie needed to get her computer fixed. She took it to the repair store. The
technician at the store worked on the computer for 4 hours and charged her $127 for
parts. The total was $227. Write and solve an equation which can be used to
determine x, the cost of the labor per hour.
Answer: 227=4x+127
x=$25
Step-by-step explanation:
227=4x+127 ==> equation
227-127=4x+127-127
4x=227-127
4x=100
4x/4=100/4
x=100/4
x=$25
x-y=-3
y-6=-1/4(x+12
Answer:
(0,3)
Step-by-step explanation:
x - y = -3
y = -1/4x + 3
x - (-1/4x + 3) = -3
x = 0
y = -1/4 x 0 + 3
y = 3
(0,3)
Answer: 24
Step-by-step explanation:
−3−6=−
4
1
(x+12)
Subtract 6 from −3 to get −9.
−9=−
4
1
(x+12)
Use the distributive property to multiply −
4
1
by x+12.
−9=−
4
1
x−
4
1
×12
Express −
4
1
×12 as a single fraction.
−9=−
4
1
x+
4
−12
Divide −12 by 4 to get −3.
−9=−
4
1
x−3
Swap sides so that all variable terms are on the left hand side.
−
4
1
x−3=−9
Add 3 to both sides.
−
4
1
x=−9+3
Add −9 and 3 to get −6.
−
4
1
x=−6
Multiply both sides by −4, the reciprocal of −
4
1
.
x=−6(−4)
Multiply −6 and −4 to get 24.
x=24