Answer:
a = - [tex]\frac{9}{2}[/tex] , b = - [tex]\frac{25}{4}[/tex]
Step-by-step explanation:
To obtain the required form use the method of completing the square
add/ subtract ( half the coefficient of the x- term)² to x² - 9x
y = x² + 2(- [tex]\frac{9}{2}[/tex] )x + [tex]\frac{81}{4}[/tex] - [tex]\frac{81}{4}[/tex] + 14
= (x - [tex]\frac{9}{2}[/tex] )² - [tex]\frac{81}{4}[/tex] + [tex]\frac{56}{4}[/tex]
= (x - [tex]\frac{9}{2}[/tex] )²- [tex]\frac{25}{4}[/tex] ← in the form (x + a)² + b
with a = - [tex]\frac{9}{2}[/tex] and b = - [tex]\frac{25}{4}[/tex]
Answer:
a = 4.5
b = -6.25
Step-by-step explanation:
The given equation to us is ,
[tex]\implies y = x {}^{2} - 9x + 14[/tex]
And its given that it can we written in the form of ,
[tex]\implies (x + a) {}^{2} + b[/tex]
Where ,
a and b are constants .Therefore ,
[tex]\implies y = x^2 -9x + 14 [/tex]
Multiplying 9x by 2/2 ,we have ,
[tex]\implies y = x^2 -\dfrac{2}{2}\times 9 x + 14 [/tex]
Adding and subtracting (9/2)² ,
[tex]\implies y = \bigg\{ x^2 -\dfrac{2}{2}\times 9 x + \bigg(\dfrac{9}{2}\bigg)^2 \bigg\} +14 -\bigg(\dfrac{9}{2}\bigg)^2[/tex]
Therefore , we can write it as ,
[tex]\implies y = \bigg( x + \dfrac{9}{2}\bigg)^2 + 14 - 20.25 \\\\\implies \underline{\underline{ y = \bigg( x + \dfrac{9}{2}\bigg)^2 - 6.25 }}[/tex]
Hence the value of a is 9/2 and b is -6.25 .
Find the product.
(-2 x2 ) 3 ·3 x
Answer: -24x^7
Step-by-step explanation:
pemdas so you do parentheses first therefore getting (2x^2)^3x3x
remove the parentheses
do -8x^6x3x
after that you end up with -24x^7
Simplify (-2x^2) ^3 by raising each term by 3:
-2^3x^6
Now you have
-2^3 x^6 times 3x
-2^3 = -8
x^6 tomes x = x ^7
-8 x 3 = -24
Answer is -24x^7
Find the values of x and y. Round your answers to the nearest tenth if necessary,
Answer:
[tex]x=12,\\y=12\sqrt{3}[/tex]
Step-by-step explanation:
In any 30-60-90 triangle, the side lengths are in the ratio [tex]x:x\sqrt{3}:2x[/tex], where [tex]2x[/tex] is the hypotenuse, or longest side, of the triangle and [tex]x[/tex] is the side opposite to the 30 degree angle.
In the given 30-60-90 triangle, the longest side (hypotenuse) is marked as 24. Since [tex]x[/tex] is opposite to the 30 degree angle,
Therefore, we have:
[tex]x=\frac{24}{2},\\x=\boxed{12}[/tex]
Based on our side length ratio [tex]x:x\sqrt{3}:2x[/tex], [tex]y[/tex] is then:
[tex]y=x\sqrt{3}\text{ for}\implies x=12,\\y=\boxed{12\sqrt{3}}[/tex]
Answer:
[tex]\huge\boxed{x=12;\ y=12\sqrt3\approx20.8}[/tex]
Step-by-step explanation:
Look at the picture.
We have:
[tex]2a=24\\a=x\\a\sqrt3=y[/tex]
Therefore:
[tex]x=24:2=12\\\\y=12\sqrt3\approx12\cdot1.73=20.76\approx20.8[/tex]
What is the hardest math problem ever?
Step-by-step explanation:
this is the hardest I think
Someone please help me
[tex]( {9x}^{2} - 4)( {9x}^{2} + 4) \\ (3x - 2)(3x + 2)( {9x}^{2} + 4)[/tex]
What is the value of x |-16|
What is the solution for this inequality? -10x ≤ 40 A. x ≤ -4 B. x ≤ 4 C. x ≥ -4 D. x ≥ 4
Answer:
C. x ≥ -4
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
-10x ≤ 40
Step 2: Solve for x
[Division Property of Equality] Divide -10 on both sides: x ≥ -4Answer:
C. x ≥ -4
Step-by-step explanation:
To solve this inequality isolate the variable. Do this by using the properties of equality, specifically the division property. So, divide both sides by -10. This equals, x ≤ -4. However, whenever an inequality is divided or multiplied by a negative number the sign must be flipped. Therefore, the final answer is x ≥ -4.
it takes 5 girls to use 8 days to clean up a room. find the number of days that will be used by. 15 girls. 10 girls. 20 girls
HURRY I NEED HELP. ASAP.
What are the coordinates of the quadrilateral STUV when reflected over the X-axis.
S(3,4), T(3,1), U(-2,1, V(-2,4)
Step-by-step explanation:
here is the answer friend
stackrel(harr)(AB) is perpendicular to 'stackrel(harr)(CD)'. How many
90° angles are formed by the intersection?
Answer:
4.
Step-by-step explanation:
A line AB is perpendicular to the line CD.
As shown in the diagram, there are four angles which measures 90°.
Identify the equivalent expressions of 4(2x + x – 3) – 3x + 3.
Answer:
9x - 9
Step-by-step explanation:
4(2x + x - 3) - 3x + 3
Simplify the expression, combine like terms in the parenthesis,
4(3x - 3) - 3x + 3
Distribute, multiply every term inside the parenthesis by the number outside of it;
(4)(3x) + (4)(-3) - 3x + 3
Simplify,
12x - 12 - 3x + 3
Combine like terms,
12x - 12 - 3x + 3
9x - 12 + 3
9x - 9
Which equation will solve the following word problem? Vanessa spent $87.00 on entertainment for the week. Her rent costs twelve dollars less than double that amount. How much does Vanessa spend on rent?
2 * $87 - $12 = R
2R = $87 + $12
2R - $12 = $87
2($87) - 2($12) = R
Answer:
2 * $87 - $12 = R
Step-by-step explanation:
Let R represent the cost of Vanessa's rent.
Vanessa spent $87.00 on entertainment for the week.
Her rent costs twelve dollars less than double that amount. Breaking it down, the expression "double that amount" is expressed as (2 × 87). Subtracting 12 from double that amount, the final expression would become
R = 2(87) - 12
R =
R = 174 - 12
The correct option is
2 * $87 - $12 = R
Compare the rates for different numbers of texts. If Roger's father wants to get a 600-text message plan, what is the difference in price for the Dial It Up and Ring Ring plans?
Answer:
[tex]\$6[/tex]
Step-by-step explanation:
Given
See comment for complete question
Required
The difference in the cost of 600 text messages plan
Representing the given data as; Cost to Number of text messages, we have:
[tex]Dial\ Up = \$5 : 100[/tex]
and
[tex]Ring\ Ring= \$8 : 200[/tex]
Multiply the dial-up by 6 to get the cost of 600
[tex]Dial\ Up = \$5 *6 : 100 * 6[/tex]
[tex]Dial\ Up = \$30 : 600[/tex]
So, the cost of 600 text messages is $30 --- for dial-up
Multiply the Ring Ring by 3 to get the cost of 600
[tex]Ring\ Ring= \$8 *3: 200*3[/tex]
[tex]Ring\ Ring= \$24: 600[/tex]
So, the cost of 600 text messages is $24 --- for Ring Ring
The difference (d) is:
[tex]d = \$30 - \$24[/tex]
[tex]d = \$6[/tex]
Which equation in slope-intercept form represents a line that passes through the point (5, -1) and is
parallel to the lin y = 2x - 7?
A) y=-11x-7
B) y= -1/2x-7
C) y= 2x-9
D) y= -9x-7
E) y= 2x-11
Answer:
E) y= 2x-11
Step-by-step explanation:
as we know the equation of line parallel to
y =2x-7 or, 2x-y-7=0 is 2x-y+k=0
as the line passes through the point (5,-1)
substituting the value of x and y in equation 2x-y+k=0
we get,
2×5-(-1)+k=0
or, 10+1+k=0
or, k=-11
hence putting the value of k in ep 2x-y+k=0
we get 2x-y-11=0
or, y=2x-11
Jacob went blueberry picking along a 3-mile walking path. He picked blueberries steadily along the walk. When he was finished, he had collected 50 ounces of blueberries.
How many ounces of blueberries did Jacob pick each mile?
Write your answer as a proper fraction or mixed number.
Answer:
16 2/3 ounces per mile
Step-by-step explanation:
50 ounces of blueberries/3 miles = 16.666 repeated
16.666 repeated = 16 2/3 ounces/mile
Find the surface area of the pyramid
I need help ASAP!
List the fractions and decimals in order least to greatest.
Question1. 2.3 , 2 4/5 , 2.6
Question 2. 0.5 , 3/16 , 0.75 , 5/48
Who ever helped me thank you :D
Answer:
Q1: 2.3, 2.6, 2 4/5
Q2: 5/48, 3/16, 0.5, 0.75
Step-by-step explanation:
that should be correct sorry if im wrong
Answer: The answer is already completed
Step-by-step explanation:
what is the formula for finding the length of a line on the cartesian plane.
Answer:
Step-by-step explanation:
distance = square root [ [tex](x2-x1)^{2}[/tex] + [tex](y2-y1)^{2}[/tex] ]
where you have two points on the line
Point 1 = P1 = (x1,y1)
point 2 = P1 =(x2,y2)
a bag contains 3 white balls and 4 red balls. A.second bag contains 4 white balls and 3 red balls. If a bag is picked at random from each bag. Find the probability that both are white
Answer:
12/49 chance that they are both white
Step-by-step explanation:
We have 2 events going on:
The first bag that contains: 3 white, 4 red
The second bag that contains: 4 white, 3 red
First let's find the probability of picking a white ball from each individual bag (not combing the chances yet):
For the 1st bag, there are 3 white balls out of 7 balls (add 3 and 4).
That means there's a 3/7 chance you'll get a white ball from the 1st bag.
For the 2nd bag, there are 4 white balls out of 7 balls (add 4 and 3).
That means there's a 4/7 chance you'll get a white ball from the 2nd bag.
To find the probability of getting both white from both of the bags, multiply 3/7 & 4/7:
3/7 * 4/7 = 12/49
You can't simplify 12/49 further, so that's your answer!
Hope it helps (●'◡'●)
Answer:
2/6Step-by-step explanation:
_______________________________hope it helps________the answer is... 2/6
Type the correct answer in the box. Use numerals instead of words.
Consider this expression.
Hello!
|m² - 7| + n² =
= |-2² - 7| + 5² =
= |-4 - 7| + 5² =
= |-11| + 5² =
= 11 + 5² =
= 11 + 25 =
= 36
Good luck! :)
Answer:
28
Step-by-step explanation:
Use a calculator to find the cross products. Compare the cross products and determine if the ratios form a proportion. Write “Y” if the ratios do form a proportion, and write “N” if the ratios do not form a proportion.
1. 3/12 and 10/30
2. 7/16 and 42/66
3. 13/70 and 39/200
4. 16/34 and 80/170
5. 11/12 and 66/72
6. 14/17 and 112/134
7. 2/3 and 120/190
8. 23/99 and 115/495
The relationship between miles and kilometers is shown in the table below.
Miles
Kilometers
18.2
29.12
29.5
47.20
34.1
54.56
52.8
84.48
How many miles are in 19.08 kilometers?
11.925
17.48
20.68
30.528
Answer:
Step-by-step explanation ithink your are correct because that there 19.08+18.3=11.925
Answer:
11.925
Step-by-step explanation:
pLZ HELPPPPPPPPPPPPPPPPPPPPPPPPP.
Answer:
x^4+4x^3+6x^2+7x+2
Encontrar la magnitud de la velocidad angular de un disco de 0.75 rev/así como la magnitud de su desplazamiento angular Si su movimiento duró 180 segundos
Answer:
La magnitud de la velocidad angular es 0.026 rad/s y la magnitud del desplazamiento angular es 4.71 rad.
Step-by-step explanation:
Podemos encontrar la magnitud de la velocidad angular (ω) del disco con la siguiente ecuación:
[tex] \omega = \frac{\theta}{t} [/tex]
En donde:
θ: es el desplazamiento angular = 0.75 rev
t: es el tiempo = 180 s
Primero debemos cambiar las unidades del desplazamiento angular de revoluciones a radianes:
[tex] \theta = 0.75 rev*\frac{2\pi rad}{1 rev} = 4.71 rad [/tex]
Entonces, la velocidad angular es:
[tex] \omega = \frac{4.71 rad}{180 s} = 0.026 rad/s [/tex]
Por lo tanto, la magnitud de la velocidad angular es 0.026 rad/s y la magnitud del desplazamiento angular es 4.71 rad.
Espero que te sea de utilidad!
11. What is the value of y when 10y-5=20
Answer:
y = 2.5
Step-by-step explanation:
Given
10y - 5 = 20 ( add 5 to both sides )
10y = 25 ( divide both sides by 10 )
y = 2.5
Answer:
5/2
Step-by-step explanation:
The given equation to us is ,
[tex]\implies 10y -5 = 20 [/tex]
Add 5 both sides ,
[tex]\implies 10y -5 +5 = 20 +5 \\[/tex]
[tex]\implies 10y = 25[/tex]
Divide both sides by 10 ,
[tex]\implies 10y \div 10 = 25\div 10 \\[/tex]
[tex]\implies \boxed{ y = \dfrac{5}{2}}[/tex]
Write in the form a to the power of k, where a is a prime number and k is rational
[tex]\sqrt[4]{27}[/tex]
The answer is 3 to the 3/4 power.
Please help with this!!! 8 points!!!
Answer:
d
Step-by-step explanation:
4a=5b+5 2a=3b+2. solve using the method of elimination
please help !*
Answer:
a = 2.5, b = 1
Step-by-step explanation:
Given the 2 equations
4a = 5b + 5 → (1)
2a = 3b + 2 → (2)
Multiplying (2) by - 2 and adding the result to (1) will eliminate a
- 4a = - 6b - 4 → (3)
Add (1) and (3) term by term to eliminate a
0 = - b + 1 ( add b to both sides )
b = 1
Substitute b = 1 into either of the 2 equations and solve for a
Substituting into (2)
2a = 3(1) + 2 = 3 + 2 = 5 ( divide both sides by 2 )
a = 2.5
Answer:
a = 2.5
b = 1
Step-by-step explanation:
4a = 5b + 5 and 2a = 3b + 2
→ Multiply the second equation by 2
4a = 6b + 4
→ Subtract this new equation from the first one
0 = b - 1
→ Find b by adding 1 on both sides
b = 1
→ Substitute b into one of the equation
4a = ( 5 × 1 ) + 5
→ Simplify
4a = 10
→ Divide both sides by 4
a = 2.5
A man serves 6 customers in 30 minutes. How many customers can be served in 2 hours?
Answer:
24
Step-by-step explanation:
2 hours * 60 minutes/hour = 120 minutes
120 minutes / 30 minutes = 4
120 minutes is 4 times 30 minutes, so he can serve 4 times as many people.
4 * 6 customers = 24 customers
Answer: 24
A man serves 6 customers in 30 minutes. There are 24 customers who can be served in 2 hours.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
A man serves 6 customers in 30 minutes. we want to find how many customers can be served in 2 hours.
We know that
2 hours x 60 minutes/hour = 120 minutes
120 minutes / 30 minutes = 4
120 minutes is 4 times 30 minutes, so he can serve 4 times as many people.
= 4 x 6 customers
= 24 customers
Learn more about the unitary method;
https://brainly.com/question/23423168
#SPJ2
Find the measure of the missing angle using the exterior angle sum theorm.
Answer:
28°
Step-by-step explanation:
Theorem: the exterior angle of a triangle is equal tobthe sum of opposite interior angles of the triangle
therefore,
55 = unknown angle + 27
let the unknown angle be x
55 = x + 27
isolating x
x = 55 - 27
x = 28
thus, the missing angle is 28°
I WILL GIVE BRAINLIEST I NEED HELP NOW!!! I PROMISEThe table shows the relationship “Kevin read 35 pages per hour.”
Hours (h)
Pages (p)
1
35
2
70
3
105
4
140
5
175
Which statements are correct? Check all that apply.
The variable h is the independent variable.
The variable p is the independent variable.
The number of pages read increases as the amount of time decreases.
The number of hours spent reading causes a change in the number of pages read.
The variable p is the dependent variable.
The variable h is the dependent variable.
The more pages that are read, the less time it takes.
Answer:
The correct answers are:
The variable p is the independent variable.
The number of hours spent reading causes a change in the number of pages read.
The variable p is the dependent variable.
Step-by-step explanation: Hope this helps :)))
These two statements are correct and applicable
(1) The number of hours spent reading causes a change in the number of pages read.
(2) The variable p is the dependent variable.
What is a variable?"A Variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters x, y, and z are common generic symbols used for variables."
What is a dependent variable?"A dependent variable is the variable that changes as a result of the independent variable manipulation."
What is a linear graph?"A Line graph is a graphical display of information that changes continuously over time. A line graph may also be referred to as a line chart. Within a line graph, there are points connecting the data to show a continuous change. A Line graph has two axes(X- axis and Y-axis)"
We have,
Kelvin read 35 pages per hour
According to the question,
Number of hours increasing, number of pages also increasing
∵ The table data shows linear graph
We can clearly say that from a line graph definition,
These two are correct and applicable to Kelvin's situation
(1) The number of hours spent reading causes a change in the number of pages read.
(2) The variable p is the dependent variable.
Learn more about Line graph and variable here
https://brainly.com/question/20106471
https://brainly.com/question/20291071
#SPJ2
