Answer:
Step-by-step explanation:
Hello,
[tex]2n^2+n-4=0\\\\\Delta=b^2-4ac=1^2-4*2*(-4)=1+32=33>0[/tex]
So there are 2 distinct real solutions.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
In the 2004 Olympic games Russia, China and the United States won a total of 96 gold medallions if the United States won 4 more medals than China and the medals achieved by the United States and Russia are twice those obtained by China determine the number of gold medals won by Russia
Answer:
28
Step-by-step explanation:
x = medals won by Russia
y = medals won by China
z = medals won by United States
Write a system of equations:
x + y + z = 96
z = y + 4
x + z = 2y
Substitute the second equation into the first and third:
x + y + y + 4 = 96
x + y + 4 = 2y
Simplify:
x + 2y = 92
x + 4 = y
Substitute for y:
x + 2(x + 4) = 92
x + 2x + 8 = 92
3x = 84
x = 28
Russia won 28 medals.
Which means China won 32 medals and the US won 36 medals.
¿Cuál es el área de un rectángulo, sabiendo que su perímetro mide 24 cm y que su base es el triple de su altura?
Answer:
El área del rectángulo es:
27 cm²
Step-by-step explanation:
Consideración:
La formula del perímetro de un rectángulo es:
p = 2(altura + base)
Planteamiento:
24 = 2(a+b)
b = 3a
a = longitud de la altura del rectángulo
b = longitud de la base del rectángulo
Desarrollo:
sustituyendo el valor de la segunda ecuación del planteamiento en la primer ecuación del planteamiento:
24 = 2(a + 3a)
24/2 = 4a
12 = 4a
a = 12/4
a = 3 cm
de la segunda ecuación del planteamiento:
b = 3a
b = 3*3
b = 9 cm
Comprobación:
de la primer ecuación del planteamiento:
24 = 2(3+9)
24 = 2*12
Respuesta:
la formula del área de un rectángulo es:
A = base * altura
A = 9cn * 3cm
A = 27cm²
The Area of rectangle is 27 unit².
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Perimeter = 24 cm
let the height of rectangle be x.
then the base= 3x
Now, Perimeter of rectangle= 2 ( l + w)
24 = 2( x+ 3x)
12 = 4x
x= 12/4
x= 3 units
So, length= 9 units and width= 3 units
Thus, Area of Rectangle= l x w
= 9 x 3
= 27 unit²
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The translated Question is:
What is the area of a rectangle, knowing that its perimeter measures 24 cm and that its base is three times its height?
Let f(x)=x2+10x+37 . What is the vertex form off(x)? What is the minimum value off(x)? Enter your answers in the boxes. Vertex form: f(x)= Minimum value of f(x):
Answer:
The vertex form is f(x) = (x + 5)² + 12
The minimum value of f(x) is point (-5, 12)
Step-by-step explanation:
1) The vertex form of a quadratic equation f(x) = x² + 10·x + 37, which is the form f(x) = a·(x - h)² + k is found as follows;
For the general form of the quadratic equation, f(x) = a·x² + b·x + c
h = -b/(2·a) and k = f(h)
Therefore, for f(x) = x² + 10·x + 37,
a = 1, b = 10
∴ h = -10/2 = -5
k = f(-5) = (-5)² + 10×(-5) + 37 = 12
The vertex form is f(x) = a·(x - h)² + k gives;
f(x) = 1·(x - (-5))² + 12 = (x + 5)² + 12
The vertex form is f(x) = (x + 5)² + 12
2) The minimum value of x is found when d(f(x))/dx = 0
d(f(x))/dx = d(x² + 10·x + 37)/dx = 2·x + 10
d(f(x))/dx = 0 = 2·x + 10
x = -10/2 = -5
We check that it is the minimum by f''(x) being positive;
f''(x) = d(2·x + 10)/dx = 2 which is positive and x = -5 is the x-coordinate of the minimum value of f(x)
The x-coordinate of the minimum value of f(x) minimum value is f(-5) = (-5)² + 10×(-5) + 37 = 12
Therefore, we have;
The minimum value of f(x) = (-5, 12)
Answer:
The vertex is (-5,f(-5)=12), The minimum value of f(x) is 12.
Help please. Thank you
Answer:
D
Step-by-step explanation:
To figure out which ones is 15% of the number, we want to divide the number on the left of ratio, by the number on the right.
4/15=26%
5/33=15.15%
3/25=12%
1.5/10=15%
Answer:
[tex]\large \boxed{\mathrm{D. \ 1.5:10}}[/tex]
Step-by-step explanation:
4 is not 15% of 15.
15% × 15 = 2.25
5 is not 15% of 33.
15% × 33 = 4.95
3 is not 15% of 25
15% × 25 = 3.75
1.5 is 15% of 10.
15% × 10 = 1.5
Which equation can be used to solve the problem?
75 percent of what number is 150?
O
75 x 1
150 x 1
75
150
150 x 2 300
75x2 150
200x2 400
75 x2 150
75 x 2
100 x 2
150
200
Answer:
see below
Step-by-step explanation:
75% of what number is 150
75 150
----- = ---------
100 x
75*2 = 150
So multiply the left by 2/2
75*2 150
----- = ---------
100*2 x
150
------
200
Answer:
The last question
Step-by-step explanation:
I took the test
In how many ways can we put five identical fruits into three bowls? Note that the bowls may be empty.
So u have 5 fruits and 3 bowls
Divide 5 into 3 that would equal how many grams you would put in one bowl then measure that and then complete it by adding that amount into each bowl
Bethany sells roses and petunias. The expression 3r+2.5p3r+2.5p3, r, plus, 2, point, 5, p gives the cost (in dollars) of rrr roses and ppp petunias. What is the cost of 777 roses and 888 petunias? \$$dollar sign
Answer: The cost of 7 roses and 8 petunias is $41.
Step-by-step explanation:
Given, Bethany sells roses and petunias. The expression [tex]3r+2.5p[/tex], gives the cost (in dollars) of r roses and p petunias.
Now to find the cost of 7 roses and 8 petunias , put r= 7 and p= 8 in the above expression , we get
[tex]3(7)+2.5(8)=21+20\\\\=41[/tex]
Hence, the cost of 7 roses and 8 petunias is $41.
A geometric sequence has a common ratio of 22 and the 12th12th term is −12,288.−12,288.
What is the explicit rule that describes this sequence?
Answer:
Tₙ = -3(2)ⁿStep-by-step explanation:
The explicit rule for determining the nth term of a geometric sequence is expressed as Tₙ = arⁿ⁻¹ where;
a is the first term of the geometric sequence
r is the common ratio
n is the number of terms
If a geometric sequence has a common ratio of 2 and the 12th term is −12,288, then;
T₁₂ = ar¹²⁻¹
T₁₂ = ar¹¹
Given T₁₂ = -12,288 and r = 2, we can calculate the first term a
-12,288 = a2¹¹
a = -12,288/2¹¹
a = -12,288/2048
a = -6
Since the explicit rule for determining the nth term of a geometric sequence is expressed as Tₙ = arⁿ⁻¹, then for the sequence given, the explicit rule will be;
Tₙ = -6(2)ⁿ⁻¹
Tₙ = -6 * 2ⁿ * 2⁻¹
Tₙ = -6 * 2ⁿ * 1/2
Tₙ = -3(2)ⁿ
Hence the explicit rule that describes this sequence is Tₙ = -3(2)ⁿ
Find the measure of b.
Answer:
b = 80°
Step-by-step explanation:
The inscribed angle measuring 100°, is supplementary to the angle opposite it in the inscribed quadrilateral.
Thus, the angle is = 80°
Therefore, b + 80° = 180° (angle on a straight line = 180°).
Thus, b = 180° - 80° = 100°.
The measure of b is 80°.
Convert to slope-intercept from: y-3=6(x-5)
Answer:
y = 6x -27
Step-by-step explanation:
y-3=6(x-5)
Distribute
y-3 = 6x-30
Add 3 to each side
y-3+3 = 6x-30+3
y = 6x -27
This is in slope intercept form y=mx+b where m is the slope and b is the y intercept
Hey there! I'm happy to help!
Slope intercept form is y=mx+b. So, the first thing we want to do is isolate y on side of the equation.
y-3=6(x-5)
We use distributive property to undo parentheses.
y=3=6x-30
We add 3 to both sides.
y=6x-27
Now, this in slope intercept form.
Have a wonderful day! :D
what is the solution set
Answer:
b>11/13
Step-by-step explanation:
The way they use solution set is misleading
just think of it as "the answer"
8b-8>3-5b
13b>11
b>11/13
Answer:
Which properties of systems does a robot have? Which does it not have?
Step-by-step explanation:
The average life of individual is 70 years. With a standard deviation of 5.5 years. Assume that the lives of these individuals is normally distributed. a. Find the probability that a mean life of a random sample of 5 such turtles falls between 60 and 80 years. b. Find the mean data value that separates the top 10% from the rest of the means computed from a random sample of size 5.
Answer:
The answer is below
Step-by-step explanation:
Given that:
mean (μ) = 70 years, standard deviation (σ)= 5.5 years.
a) The z score measures how many standard deviation a raw score is above or below the mean. It is given as:
[tex]z=\frac{x-\mu}{\sigma}[/tex], for a sample size of n, the z score is: [tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]
Given a sample of 5 turtles, we have to calculate the z score for x = 60 and x = 80.
For x = 60:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{60-70}{5.5/\sqrt{5} } =-4.07[/tex]
For x = 80:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{80-70}{5.5/\sqrt{5} } =4.07[/tex]
The probability that a mean life of a random sample of 5 such turtles falls between 60 and 80 years = P(60 < x < 80) = P(-4.07 < z < 4.07) = P(z < 4.07) - P(z < -4.07) = 1 - 0 = 1 = 100%
b) The z score that corresponds to top 10% is -1.28.
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }\\\\-1.28=\frac{x-70}{5.5/\sqrt{5} }\\ x-70=-3\\x=70-3\\x=67\ years[/tex]
Identify the terms, like terms, coefficients and constants of the following expressions: a) 9 − z + 3 − 2z b) 7 − 5b + 1 terms: _____________ terms: ______________ like terms: ______ like terms: _______ coefficients: _____ coefficients: _____ constants: ______ constants: ______
Answer:
See below.
Step-by-step explanation:
a) 9 − z + 3 − 2z b) 7 − 5b + 1
terms: 9, -z, 3, -2z terms: 7, -5b, 1
like terms: 9 & 3; -z & -2z like terms: 7 & -1
coefficients: -1, -2 coefficients: -5
constants: 9, 3 constants: 7, 1
what is a coterminal angles
Answer: Coterminal Angles are angles who share the same initial side and terminal sides. Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians.
If f(x) = 3x^2 + 2 and g(x) = x^2- 9, find (f-g)(x).
O A. 4x2 - 7
O B. 2x2 +11
O c. 2x2 - 7
O D. 4x2 +11
Answer:
[tex] \boxed{\sf B. \ 2x^{2} + 11} [/tex]
Given:
f(x) = 3x² + 2
g(x) = x² - 9
To Find:
(f - g)(x)
Step-by-step explanation:
[tex]\sf (f -g)(x) = f(x) - g(x) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =(3x^{2} + 2) - (x^{2} - 9) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =3x^{2} + 2 - x^{2} + 9 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =3x^{2} - x^{2} + 2 + 9 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =(3x^{2} - x^{2}) + (2 + 9) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =2x^{2} + (2 + 9) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =2x^{2} + 11 [/tex]
You see Bonnie rock climbing El Capitan. On your telescope is a clinometer. The angle
of elevation is 20 degrees. You know you are standing 950 feet away from El Capitan.
How high up is Bonnie?
Answer:
≈ 345.8 ft
Step-by-step explanation:
There is a right triangle formed by Bonnie's height (h) the ground and the angle of elevation.
Using the tangent ratio in the right triangle
tan20° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{h}{950}[/tex] ( multiply both sides by 950 )
950 × tan20° = h , thus
h ≈ 345.8 ft ( to 1 dec. place )
In a group of 25 people, only three languages are spoken – English, Spanish and German. If there is at least one person who speaks all the three languages, how many people can interact with each other in English and German? 4 people speak two languages but do not speak Spanish One fifth of the group speaks more than one language.
Answer:
x + a=5
Step-by-step explanation:
Let
number of people who speak only English = E
the number of people who speak only German = G
the number of people who speak only Spanish = S
the number of people who speak only English & German but not Spanish = x
the number of people who speak only English & Spanish but not German = y
the number of people who speak only German & Spanish but not English = z;
the number of people who speak only German & Spanish & English = a
Find the the value of (x + a).
Statement 1: 4 people speak two languages but do not speak Spanish.
x = 4.
x+a
Value for a is unknown.
(x + a). Insufficient.
Statement 3: One-fifth of the group speaks more than one language.
x + y + z + a
= 25/5
= 5
value of (x + a) unknown
Insufficient.
Putting (1) and (2) together
x + y + z + a = 5
x = 4 and a=1,
we have only one possible solution from
x + y + z + a = 5
x + a
= 4 + 1
= 5.
Sufficient.
blake bought two iced coffees at dutch bros. He originally had $13.50 and now has $9 Write and solve an equation to find out how much each iced coffee cost
if he had $13.50 and now he has $9 all you have to do is minus $13.50 by 9 like this 13.50-9=4.50 the ice coffee costs $4.50 simple.
If you still have a question and don't understand this please ask again thank you.
What are three collinear points on line l?
points A, B, and F
points A, F, and G
points B, C, and D
points B, F, and G
Answer:
Points A, F, and G are three collinear points on line l.
Step-by-step explanation:
Answer:
Points A, F and G
Step-by-step explanation:
what is meaning of rate?
Answer:
1.a measure, quantity, or frequency, typically one measured against another quantity or measure.
Step-by-step explanation:
2.a fixed price paid or charged for something.
Answer:
a measure, quantity, or frequency typically one measured against another quantity or measure.
Assign a standard or value to (something) according to a particular scale.Please Explain step-by-step
An algebra class contains 30 students. Forty
percent of the students in the class are girls. How
many boys are in the class?
Answer:
algebra es muy buena materia
Functions f(x) and g(x) are shown: f(x) = x2 g(x) = x2 − 8x + 16 In which direction and by how many units should f(x) be shifted to match g(x)? Left by 4 units Right by 4 units Left by 8 units Right by 8 units
Answer:
Shift right by 4
Step-by-step explanation:
Given f(x)=x^2
g(x)= x^2-8x+16
Using
Horizontal Shift theorem dealing with the question
If the graph were to be move to to the right, we must use of graph f (x-L)
Where L= 4 and
NOTE:
POSITIVE L MAKES GRAPH SHIFT RIGHT
2) NEGATIVE MAKES GRAPH SHIFT LEFT
g(x)= x^2-8x+16
If we factorize this we have
(x-4)(x-4)
Since the two terms are the same we have (x-4)^2
Then it can move by factor of 4 to the right since constant 4 can be substracted from the parents function
Answer:
Left by 4
Step-by-step explanation:
graph x^2 and x^2 − 8x + 16 on Desmos . com
you start at f(x) and end at g(x)
identify the terms of each expression 7 + 5 p + 4r + 6 s
LaShawn solved the equation below to the determine the solution.
3 x minus 8 = negative x + 4 (x minus 2)
Answer:
x = all real numbers.
Step-by-step explanation:
3 x minus 8 = negative x + 4 (x minus 2)
3x - 8 = -x + 4(x - 2)
3x - 8 = -x + 4x - 8
3x - 8 = 3x - 8
3x - 3x = -8 + 8
0 = 0
Since the result is a true statement, but 0 = 0, x is equivalent to all real numbers.
Hope this helps!
Answer:
Step-by-step explanation:
I need help please so if you could help that would be nice. Also i will make brainliest
Chad and his family went to the beach. First, they swam in the ocean for 1 hour and 15 minutes. Then they built sand castles for 45 minutes and played volleyball for 1 hour and 30 minutes. When they finished playing volleyball, it was 3:30 P.M. What time did Chad's family get to the beach?
Answer:
12:00
Step-by-step explanation:
so if you add up all the time they were there like this 1 hour + 15 +45+1 hour +30 you will get 3 hours and 30 minutes so then you subtract the the time from the time like this 3:30 so they went at 12:00
A trader bought a bag for 125gh cedis. he later sold it at a profit of 30%. What is his selling price
Answer:
162.5 Cedis
Step-by-step explanation:
Cost Price= 125
Profit % = 30%
Selling price=?
Selling price= Cost price+ profit
Profit = ?
[tex]profit \% = \frac{profit}{cost \: price} \times 100[/tex]
[tex]30 \% = \frac{x}{125} \times 100[/tex]
[tex]30 \% = \frac{100x}{125} \\ 30 \times 125 = 100x[/tex]
[tex]3750 = 100x \\ \frac{3750}{100} = \frac{100x}{100} \\ x = 37.5[/tex]
Profit = 37.5 gh Cedis
Selling price= 125+37.5
Selling price= 162.5 gh Cedis
The selling price of a bag is 162.5Cedis.
It is required to find the selling price.
What is profit?The profit is defined as the amount gained by selling a product, and it should be more than the cost price of the product.
Given that :
Let the profit be x.
Cost Price= 125
Profit % = 30%
profit%=profit/cp*100
30=profit/125*100
3750=100x
x=37.5
profit=37.5
Selling price= Cost price+ profit
Selling price=125+37.5
Selling price=162.5ghcedis
So, the selling price of a bag is 162.5Cedis.
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This data set is ages at first job. 14, 14, 16, 16, 17, 17, 18, 20, 21, 23 Construct a boxplot. Make sure to include labels.
Answer:
Please find attached the required box and whiskers plot
Step-by-step explanation:
The numbers are given in arranged order as follows;
14, 14, 16, 16, 17, 17, 18, 20, 21, 23
The five number summary are;
The minimum value = 14
The maximum value = 23
The first quartile, Q₁, is the (n + 1)/4th term or the 2.75th term = 14 + 0.75×(16 - 14) = 15.5
The second quartile, Q₂, (the median) is the (n + 1)/2th term or the 5.5th term = 17
The third quartile, Q₃, is the 3(n + 1)/4th term or the 8.25th term = 20 + 0.25×(21 - 20) = 20.25.
HELP ASAP WILL MARK BRAINLIEST!!!!!! Use the number line below, where RS=9y+2, ST = 4y+9 and RT = 115. a. What is the value of y? b. Find RS and ST. a. What is the value of y?
Answer: y = 7
Step-by-step explanation:
Answer ASAP please, Will give brainliest.
Answer:
see below
Step-by-step explanation:
The measure of a minor arc is the same as the angle that forms it.
1. Since ∠GBJ = 90°, the answer is 90°.
2. ∠HBI = 180° - 151° = 29° so the answer is 29°.
3. ∠HBJ = 180° so the answer is 180°.
4. The reflex angle ∠GBI = 90 + 151 = 241° so the answer is 241°/
5. Since ∠GBJ = 90°, the reflex angle ∠GBJ = 360 - 90 = 270° so the answer is 270°.
6. ∠GBH = 180 - 90 = 90° so the reflex angle ∠GBH = 360 - 90 = 270° so the answer is 270°.
