Given:
The American marriage rate R, x years after 1960 is defined by the function
[tex]R(x)=-0.0065x^2 +0.23x + 8.47[/tex]
To find:
The year in which the marriage rate is the highest.
Solution:
We have,
[tex]R(x)=-0.0065x^2 +0.23x + 8.47[/tex]
It is a quadratic function with negative leading coefficient. So, it is a downward parabola and vertex of downward parabola is maximum.
If a quadratic function is [tex]f(x)=ax^2+bx+c[/tex], then
[tex]Vertex=\left(\dfrac{-b}{2a},f(\dfrac{-b}{2a})\right)[/tex]
In the given function,
[tex]a=-0.0065,b=0.23,c=8.47[/tex]
Now, x-coordinate of vertex is
[tex]-\dfrac{b}{2a}=-\dfrac{0.23}{2(-0.0065)}[/tex]
[tex]-\dfrac{b}{2a}=-\dfrac{0.23}{-0.013}[/tex]
[tex]-\dfrac{b}{2a}\approx 17.69[/tex]
It means the marriage rate is highest after 17 years of 1960.
[tex]1960+17=1977[/tex]
Therefore, the marriage rate is highest in year 1977.
please help me out....
What is the nature of the solution set to the following system of equations?
5x - y = 2
2x -0.5y = 3
O One solution at (-4,-4)
O Infinitely many solutions
O One solution at (-4,-22)
ONo solutions
Answer:
One solution at (-4, -22)
Step-by-step explanation:
5x - y = 2
y = 5x - 2 --(1)
2x - 0.5y = 3 --(2)
sub (1) into (2):
2x - 0.5(5x - 2) = 3
2x - 2.5x + 1 = 3
-0.5x = 2
x = -4
when x = -4, y = 5(-4) - 2 = -22
The nature of the solution set to the system of equations are,
⇒ One solution at (-4,-22).
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.
Given that;
The system of equations are,
5x - y = 2 .. (i)
2x - 0.5y = 3 .. (ii)
Now, We can simplify as;
From (i);
5x - y = 2
y = 5x - 2
Put above value in (ii);
2x - 0.5 (5x -2) = 3
2x - 2.5x + 1 = 3
- 0.5x = 2
x = - 4
From (i);
y = 5 × - 4 - 2
y = - 20 - 2
y = - 22
Thus, The nature of the solution set to the system of equations are,
⇒ One solution at (-4,-22).
Learn more about the mathematical expression visit:
brainly.com/question/1859113
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What is the product of a fraction multiplied by its multiplicative inverse? Justify your answer with an example
umm i dont get none of this to be honest
Use the diagram to find the measure of angle KHL.
Answer:
m∠KHL = 43°
Step-by-step explanation:
From the picture attached,
m∠KHL ≅ m∠GHL [Given in the picture]
Now substituting the values of the angles,
(3x + 1) = (5x - 27)
1 + 27 = 5x - 3x
28 = 2x
14 = x
m∠KHL = (3x + 1)° = (3 × 14) + 1
= 42 + 1
= 43°
Therefore, measure of ∠KHL = 43°
A car can travel 264 miles on 11 gallons of gasoline. How far can it travel on 2
gallons?
Answer:
The answer is 48 miles.
My Logic
If you divide 264 into 11, then you will get 24. 24 is the cars MPG. Then you can Multiply 24 by 2 and you get the answer. Hope this is helpful!
The high school band sells cured hams for a fundraiser. The first week of the
fundraiser, the club sells 8 cases of hams. Each case contains 10 hams. The goal is to
sell at least 20 cases. During the second week of the fundraiser, the club meets its
goal. Which graph of the inequality can be used to find the possible number of hams
sold the second week?
Answer:
ITS THE SECOND ONE
Step-by-step explanation:
the solution to -2x + 8 = -10
Answer:9
Step-by-step explanation:
-2x+8=-10
-2x=-18
X=9
Answer:
9
Step-by-step explanation:
Subtract
8
8
8
from both sides of the equation
−
2
+
8
=
−
1
0
-2x+8=-10
−2x+8=−10
−
2
+
8
−
8
=
−
1
0
−
8
-2x+8{\color{#c92786}{-8}}=-10{\color{#c92786}{-8}}
−2x+8−8=−10−8
2
Simplify
3
Divide both sides of the equation by the same term
4
Simplify
Solution
=
9Subtract
8
8
8
from both sides of the equation
−
2
+
8
=
−
1
0
-2x+8=-10
−2x+8=−10
−
2
+
8
−
8
=
−
1
0
−
8
-2x+8{\color{#c92786}{-8}}=-10{\color{#c92786}{-8}}
−2x+8−8=−10−8
2
Simplify
3
Divide both sides of the equation by the same term
4
Simplify
Solution
=
9
HELPPP
Solve for b 2 in A = h(b 1+b 2), if A = 16, h = 4, and b 1 = 3.
b 2 =
Answer:1
Step-by-step explanation: substitute all the corresponding terms so you get, 16=4(3+b2)
Then you multiply and get 16=12+4b2 then subtract 12 from both sides to get 4=4b2 and then divided both sides by 4 and you get 1=b2
Answer:1
Step-by-step explanation: A = h(b 1+b 2)
16=4(3+b2)
16/4=3+b2
4=3+b2
B2 =4-3=1
Elvira used 4 cups of grape juice, 1 1/2 cups of cranberry juice, and 1/2 cup of pineapple juice to make punch. One liter
is approximately equal to 4.23 cups.
Which measurement is closest to the number of liters of punch Elvira made?
Tobin is solving the equation 3 (x minus 1.25) = 11.25. His work is shown below.
3 (x minus 1.25) = 11.25. 3 x minus 3.75 = 11.25. 3 x minus 3.75 + 3.75 = 11.25 + 3.75. 3 x = 15. 3 x times 3 = 45 times 3. x = 135.
What mistake did Tobin make?
please need this asap!!
will give brainliest <3
Answer:
-0.02, -0.15, -0.2, -1.2
Step-by-step explanation:
The closer a negative number is to 0, the greater it is.
Answer:
-0.15,-0.02,-0.2,-1.2
I hope this helps
: What is the image after (3,7) is reflected over the x-axis?
Brainly
Got the question wrong cause the other answer here is the correct answer directly from Delta Math.
(-7, -3)
Enjoy and Happy Holidays!
can someone pls give me 2 mo brainlist
Answer:
i cant do dat because im broke sorry
Step-by-step explanation:
Evaluate:
7 - 3 + 10
Answer:
14
Step-by-step explanation:
7-3 = 4 4+10=14 therfore 14 would be the answer hope this helps
Can you solve?
|x+5|=12
What is the answer please
which pair of numbers shows an integer and its opposite?
1 point
A.7 , -7
B.7 , 1/7
C.-7 , 1/7
D.1/7 , 1/7
A jar can hold of a pound of flour. Austin empties of a pound of flour into the jar. What fraction of the jar is filled? Enter your answer in numerical form.
Answer:
2/3 of the jar was filled with flour
Step-by-step explanation:
The question is incomplete. Here is the complete question.
A jar can hold 3/4 of a pound of flour. Austin empties 1/2 of a pound of flour into the jar. What fraction of the jar is filled? Enter your answer in numerical form.
Given
Amount a jar can hold a = 3/4 of a pound of flour
If Austin empties 1/2 of a pound of flour into the jar, then the amount emptied into the jar b = 1/2 pounds
Fraction of jar filled will be expressed as b/a as shown;
b/a = (1/2)/(3/4)
b/a = 1/2 ÷ 3/4
b/a = 1/2 * 4/3
b/a = 4/6
Simplify to the lowest term
a/b = 2*2/2*3
a/b = 2/3
Hence 2/3 of the jar was filled with flour
It took everly 55 minutes to run a 10-kilometer race last weekend. If you know that 1 kilometer equals 0.621 mile, how many mintues did it take everly to run 1 mile during the race?
Answer:
8.9 minutes
Step-by-step explanation:
Converting Everly Kilometer race to miles
1 km = 0.621 miles
10 km =
10 × 0.621 miles
= 6.21 miles
Hence,
6.21 miles = 55 minutes
1 mile = x minutes
Cross Multiply
6.21 × x = 55 × 1
x = 55 minutes/6.21
x = 8.8566827697 minutes
Approximately = 8.9 minutes
I need help with another one! Thankyou guys this means alot to me
Answer:
9.5 = y
Step-by-step explanation:
You have to use the cosine function equation.
cos(38) = [tex]\frac{y}{12}[/tex]
Multiply 12 on both sides.
12cos(38) = y
Solve.
9.46 = y
Answer:
9.5
Step-by-step explanation:
y is the adjacent side of the given 38 degree angle. You are given the hypotenuse of right angle triangle. So the trig function that you need to use is the Cosine
Cos(38) = y / 12
multiply both sides by 12
12*cos(38) = 12*y/12
12*cos(38) = y
12*0.7880= y
y =9.456
Antonio, Lucas y Darío compraron un refresco de 5/2 (2litros y 1/2) que piensan repartir en partes iguales. a) ¿Qué fracción de litro le corresponde a cada uno? b) Una vez repartido el refresco llego Benjamín a quien van a convidarle. ¿Cuánto debe convidarle cada uno para que los cuatro tengan la misma cantidad de refresco?
Answer:
a) A Antonio, Lucas y Darío le corresponde cada uno [tex]\frac{5}{6}[/tex] litros.
b) Antonio, Lucas y Benjamín deben convidar cada uno [tex]\frac{5}{24}[/tex] litros.
Step-by-step explanation:
a) Antonio, Lucas y Darío compraron un refresco, el cual reparten en tres partes iguales. Por tanto, la fracción de litro para cada persona es la capacidad del refresco dividido por el número de personas. Es decir:
[tex]x = \frac{\frac{5}{2}\,L }{3}[/tex]
[tex]x = \frac{5}{6}\,L[/tex]
A Antonio, Lucas y Darío le corresponde cada uno [tex]\frac{5}{6}[/tex] litros.
b) En primer lugar calculamos la fracción correspondiente a cuatro personas:
[tex]x = \frac{\frac{5}{2}\,L }{4}[/tex]
[tex]x = \frac{5}{8}\,L[/tex]
Ahora, procedemos a calcular la diferencia entre el escenario calculado en a) y el resultado anterior:
[tex]\Delta x = \frac{5}{6}\,L-\frac{5}{8}\,L[/tex]
[tex]\Delta x = \frac{40-30}{48} \,L[/tex]
[tex]\Delta x = \frac{10}{48}\,L[/tex]
[tex]\Delta x = \frac{5}{24}\,L[/tex]
Este resultado corresponde a la fracción que Antonio, Lucas y Darío deben convidar cada uno a Benjamín. Entonces, Antonio, Lucas y Benjamín deben convidar cada uno [tex]\frac{5}{24}[/tex] litros.
What's 2(a-2)=3(a-5)
11kx+13kx= 6 for x
a: x=4/k
b:x=1/4k
c:x=4k
d:x=k/4
i have no clue smh
24kx = 6
kx = 6/24
kx = 1/4
x = 1/4/k
x = 1/4k
A) X = 1/4k or the first option.
There are 48 students in the dass. They arrange their desks in rows with 8 desks in each row.
How many rows are there?
Answer:
6 rows
Step-by-step explanation:
We know that 48 desks are split up into rows of 8
If we divide the 48 total desks by the 8 desks in each row... we find the number of rows.
48/8 = 6
Find the solutions to x2 = 20.
Answer:
X=+2^5 A
Step-by-step explanation:
whats the slope of this?
Answer: -3
Step-by-step explanation:
Chestnut is trying to break his school record for eating the most hot dogs in 10 minutes he needs to eat more than 72 hot dogs to break his record after 1 minute Joy has eaten 71 for the hot dogs lady represent the number of hotdogs Joy East per minute for the next 9 minutes
Find the slope of the line passing through the points (-9, 4) and (-9, -9)
Answer:
There is no slope, it is undefined and the line would continue to go up from the position x= -9
brainliest if correct please
If the difference when −15 is subtracted from a number is twice the difference when 24 is subtracted from the same number, what is the value of the number?
Answer:
The number is 39
Step-by-step explanation:
Let the unknown number be x:
[tex](x-(-15))=2(x-24)\\x+15=2x-24\\39=x\\\therefore x=39[/tex]
REALLY NEED HELP PLEASE!!
Step-by-step explanation:
sum of angles in triangle is 180
so 80 + 40 + angle 2 = 180 angle 2 = 60