Answer:
[tex]x=4,\:x=-\frac{3}{2}[/tex]
Step-by-step explanation:
[tex]x\left(2x-5\right)[/tex]
Apply the distributive law.
[tex]=x\cdot \:2x-x\cdot \:5[/tex]
[tex]=2x^2-5x[/tex]
[tex]2x^2-5x=12[/tex]
Subtract 12 from both sides.
[tex]2x^2-5x-12=12-12[/tex]
[tex]2x^2-5x-12=0[/tex]
Now, apply the quadratic formula.
[tex]x_{1,\:2}=\frac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\cdot \:2\left(-12\right)}}{2\cdot \:2}[/tex]
[tex]x_{1,\:2}=\frac{-\left(-5\right)\pm \:11}{2\cdot \:2}[/tex]
Separate the solutions.
[tex]x_1=\frac{-\left(-5\right)+11}{2\cdot \:2},\:x_2=\frac{-\left(-5\right)-11}{2\cdot \:2}[/tex]
Simplify.
[tex]x=4,\:x=-\frac{3}{2}[/tex]
Make a Prediction Predict the sum of -2 + 2. Explain
your prediction and check it using the number line.
Answer:
My prediction of the sum is 0.
Hope this helps :)
Step-by-step explanation:
It is 0 because if you owe 2 dollars and you pay it back with 2 dollars then you have 0 dollars owed.
--------------------> 2nd: 2 (positive two - move right)
<-------------------- 1st: - 2 (negative two - move left)
<----------l----------l-----------l----------l----------l--------->
-2 -1 0 1 2
George wants 42 liters of a mixture of water and 15% lemon juice. he has a mixture of 5% lemon juice and a mixture of 20% lemon juice. how many liters of the 5% and 20% mixtures should he mix to get what he wants? (round you answer to the nearest tenth if necessary.)
The amount of 5% lemon juice mixture and 20% lemon juice mixture that needed to be mixed is 14 liters and 28 liters, respectively.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Let the amount of 5% lemon juice mixture that is needed to be mixed be represented by x, then the amount of 20% lemon juice mixture will be represented by (42-x), because the total mixture is needed to be 42 liters.
Now, given that George wants 42 liters of a mixture of water and 15% lemon juice with a mixture of 5% lemon juice, and a mixture of 20% lemon juice. Therefore, we can write,
5% of x + 20% of (42-x) = 15% of 42 liters
0.05x + 0.2(42 - x) = (0.15×42)
0.05x + 8.4 - 0.2x = 6.3
0.05x - 0.2x = 6.3 - 8.4
-0.15x = -2.1
x = -2.1 / -0.15
x = 14
Further, the amount of mixture of lemon juice that is needed to be mixed can be written as,
5% lemon juice mixture, x = 14 liters20% lemon juice mixture, (42 - x) = 28 litersHence, the amount of 5% lemon juice mixture and 20% lemon juice mixture that needed to be mixed is 14 liters and 28 liters, respectively.
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a rectangele has and area of 48 in every dimension
A rectangular field is 35 m longer than it is wide. The length of the fence around
the perimeter of the field is 290 m.
a. 1+35= w
b.
1=w+35
21+2w=290
21+2w=290
C.
1=w+35
1+w=290
d. 1=w+35
Iw=290
Answer:
length = 90
width = 55
Step-by-step explanation:
Let W = width.
Let L = length.
L = W + 35
P = 2(W + L)
290 = 2(W + W + 35)
4W + 70 = 290
4W = 220
W = 55
L = W + 35 = 55 + 35 = 90
From midnight to 7:00 am, the temperature rose 1.1 C each hour. If the temperature at 7:00 am was -0.3 C, what was the temperature at midnight?
The temperature at midnight is -8°C.
How to calculate the temperature?Let the initial temperature be x.
It should be noted that there are 7 hours between midnight and 7am.
Therefore, the equation will be:
x + (1.1 × 7) = -0.3
x + 7.7 = - 0.3
x = -0.3 - 7.7
x = -8
The temperature at midnight is -8°C.
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need help with #3, and #4 please
The equation of the line from the given points marked on the graph is:
3. 3x+y+5=0
4. 3x+y+3=0
Given,
3.The points are:
(-1,-2) and (1,-8)
let the points be :
(-1,-2) = (x₁,y₁)
and (1,-8) = (x₂,y₂)
The equation of the line passing through the points (-1,-2) and (1,-8)
x - x₁/x₂-x₁ = y - y₁/y₂-y₁
For the given points, the equation is:
x-(-1)/1-(-1) = y-(-2)/-8-(-2)
x+1/2 = y+2/-6
-6(x+1) = 2(y+2)
-6x-6=2y+4
-6x-2y-6-4=0
-6x-2y-10=0
-2(3x+y+5)=0
3x+y+5=0 is the equation of the line.
4.The points are:
(-3,6) and (3,0)
let the points be :
(-3,6) = (x₁,y₁)
and (3,0) = (x₂,y₂)
The equation of the line passing through the points (-1,-2) and (1,-8)
x - x₁/x₂-x₁ = y - y₁/y₂-y₁
For the given points, the equation is:
x-(-3)/3-(-3) = y-6/0-6
x+3/6 = y-6/-6
-6(x+3) = 2(y-6)
-6x-18=2y-12
-6x-2y-18+12=0
-6x-2y-6=0
-2(3x+y+3)=0
3x+y+3=0 is the equation of the line
Hence we get the required equations of the line.
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HELP! (3x4)+ 52 MARKING BRAINLY!
Answer:
64
Step-by-step explanation:
[tex]3 \times 4\\= 12\\= 12 + 52\\= 64[/tex]
Answer:
64
Step-by-step explanation:
first 3 x 4 = 12
12+52=64
Converting units is always an exercise in linear relationships. how many inches is 2.50 m? (2.54 cm=1.0 inch)
There are 98.4252 inches in 2.50m.
Unit Conversion is defined as a process that involves multiplication and division by a numerical factor or a particular conversion factor.
For Example .Convert 2m into cm.
As we know that 1m=100cm
multiplying both sides by 2 we get
2m = 200 cm.
According to the question
It is given that 2.54 cm = 1 inch
[tex]1cm = \frac{1}{2.54} inch[/tex]
[tex]100cm=\frac{100}{254} inch[/tex]
[tex]1m = \frac{100}{2.54}[/tex] ( as 100cm = 1m)
we need 2.50 m So we multiply both sides by 2.50
[tex]2.50m=\frac{2.50*100}{2.54} \\\\ 2.50m=\frac{250}{2.54}[/tex]
[tex]2.50m=98.4252 inch[/tex]
Therefore , there are 98.4252 inches in 2.50m.
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what is 39/80 as a decimal
Answer:0.4875.
Step-by-step explanation:
Answer:
0.48750
explanation:
Solve for x in the given equation: 1/5 x = 2/5 What would be the inverse operation you would use to solve for x?
Translate each phrase into an algebraic expression: Jame has 20 more dollars than 3 times the amount Brittany has.
x = 20+ 3y
First order equations include linear equations. In the coordinate system, the linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). Multiple variables may be present in a linear equation. Linear equations in two variables, for example, are used when a linear equation contains two variables. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.
Jame = x
Brittany = y
x = 20+ 3y
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A fraction is equivalent to 2/3. The product of its numerator and denominator is 216. What is the fraction?
PLS ASAP AND TY IF U ANSWERED
Answer:
3.5 un
Step-by-step explanation:
to find the new length of the square using a scale factor of 1/7 you can just multiply 24.5 by 1/7
this is basically dividing 24.5 by 7
24.5 / 7 = 3.5
that is your answer
Find the derivative of the function using the definition of derivative. f(x) = kx d
Derivatives are essential for solving calculus and differential equation problems then the derivative of this function is [tex]$f^{\prime}(x)=k$[/tex]
What is meant by derivatives?The rate of change of a function with respect to a variable in Mathematics. Derivatives are essential for solving calculus and differential equation problems.
Given a traditional unbent position, f(x) = kx + d, where k is the pitch and (0, d) is the y-intercept.
a) Consider our position at two distinct points first:
f(x) = kx + d
f(x + h) = k(x + h) + d = kx + kh + d
Evaluate the derivative, then
[tex]$\lim h \rightarrow x \frac{f(x+h)-f(x)}{h}[/tex]
substitute the values in the above equation, we get
[tex]$&=\lim h \rightarrow x \frac{(k x+k h+d)-(k x+d)}{h} \\[/tex]
simplifying the above equation, we get
[tex]$&=\lim h \rightarrow x \frac{k h}{h} \\[/tex]
[tex]&=\lim h \rightarrow x k \\[/tex]
= k
Therefore, the derivative of this function is [tex]$f^{\prime}(x)=k$[/tex]
b. Since the actual function is linear, its part is all real numbers by definition.
c. Since the product is a constant function, its part is all real digits by meaning.
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the height of a frame is 2/3 times its width
The height of the frame is 1 m and the width is 1.5 meters.
The height and width are the two dimensions that are used to measure the perimeter of a rectangular frame.
The perimeter is defined as the sum of all sides of a polygon. For a rectangle it is equal to twice the sum of height and width.
Perimeter(p)=2×[height(h)+width(w)]
The given dimensions of the frame is that the height is [tex]\frac{2}{3}[/tex] the width.
Let us consider the width be x.
Hence height=[tex]\frac{2}{3} x[/tex]
Now perimeter =
[tex]2\times(x+\frac{2}{3}x) \\=\frac{10}{3} x[/tex]
But the given perimeter is 5 meter.
Therefore:
[tex]\frac{10}{3} x=5\\or,x=5\times 3\div 10\\or,x=1.5[/tex]
Therefore the width is 1.5 meters.
Height=[tex]\frac{2}{3} \times 1.5\\[/tex]=1 meter.
So we can conclude that the width is 1.5 meters and the height is 1 meter.
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Problems.
87. the 4550 men in the arena comprised 85% of the people in
the arena. how many people were in the arena?
There are 5354 people were in the arena.
Percentage:
The term percentage is referred as a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.
The formula for calculating the percentage is,
Percentage = (Actual value/Total value) x 100
Given,
Here we have that, 4550 men in the arena comprised 85% of the people in the arena.
Now we need to find how many people were in the arena.
Let p be the number of people in Arena.
So, based on the percentage formula,
It can be written as,
=> 85% = (4550 / p) x 100
=> 85/100 = 4550 /p
=> 0.85 = 4550/p
=> 4550/0.85 = p
=> p = 5354
Therefore, there are 5354 people were in the arena.
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PLEASE HELP ME!
How do the graphs of y = f (x) + k, y = f(x – h), and y = -f(x) compare to the graph of the parent function f?
f(x) + k will shift the graph up k units.
For example, the notation f(x) + 5 will shift the curve up by 5
If k is negative, then the curve shifts down that amount
-------------------------
f(x-h) shifts the graph to the right h units
Example: f(x-2) shifts to the right 2 units
Another example: f(x+7) shifts left 7 units. In this case, h = -7
--------------------------
y = -f(x) is a reflection over the x axis
This is because we're multiplying each y coordinate by -1
A point like (1,2) reflects to (1,-2)
f (x) = 2x² - x - 12
Find f(8)
Will give brainliest and 5 star rating. Thank you. :)
Answer:
f(8) = 108
Step-by-step explanation:
Hello!
Substitute 8 for x in the equation.
Evaluatef(x) = 2x² - x - 12f(8) = 2(8)² - (8) - 12f(8) = 2(64) - 8 - 12f(8) = 128 - 8 - 12f(8) = 108f(8) is 108.
Find the measure of each marked angle. Assume the lines are parallel.
x+4=
9x-34=
The angles are 19; 101
What are parallel lines?Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect.
Given:
x+4, 9x-34
As, the lines are parallel
x+4 + 9x -34 = 180
10x + 30 = 180
10x = 150
x= 150/10
x=15
Hence, the angles are x+4 = 19; 9x-34 = 135 - 34 = 101
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Drama Teacher's Friend
Find the number that replaces each letter to complete the pattern in the
sequence. Use that number to replace the letter in the ordered pairs.
A =
1, 3, A, 7, 9, 11, B
3, C, 12, 24
2, 1, D, -1, -2, E, -4
F, 4, 9, 16, 25
7, 3,-1, G, -9
|||||||||||||||
E =
F =
G=
Answer:
hi 8jgvjig up uttgui86yghjEve and her mom are volunteering at an emergency relief center. To help prepare in case of a flood, they pack emergency kits with food and water. Eve puts 5 water bottles into each kit they pack. In all, she packs 125 water bottles.
Which equation can you use to find the number of emergency kits k Eve packs?
Answer:
Step-by-step explanation:
no. of emergency kits = x
bottles per kit = 5
total no. of bottles = 5x
which means,
5x = 125
125/5 = x
x = 25
Nilai dari sin 135, bantuin kakk pliss
Answer:
[tex] \frac{ \sqrt{2} }{2} \: or \: 0.7071[/tex]
Step-by-step explanation:
[tex] \sin(135) = \frac { \sqrt{2} }{2} \: or \: 0.7071 [/tex]
Elsa opens an account to save money for a family vacation. the account earns an annual interest rate of 4% 4 % . she earns $37 $ 37 in simple interest after 6 6 months.
Amount while opening account at rate of 4% for 6 months and earn simple interest $37 is $1850.
As given,
Simple interest amount earned by Elsa = $37
Annual interest rate R= 4%
Time T =6 months
Let P be the principal amount she put while opening account
Simple interest = (P × R × T) / 100
⇒37 ={P × 4 × (6/12)}/100
⇒P =(37 × 100) / 2
= $1850
Therefore, amount while opening account at rate of 4% for 6 months and earn simple interest $37 is $1850.
The complete question is:
Elsa opens an account to save money for a family vacation. The account earns an annual interest rate of 4%. She earns $37 in simple interest after 6 months. How much money did she put in the account when she opened it?
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5) One band rented a van to travel to Omaha. The band started out at 9:00AM, took a break at 9:32AM, and finally arrived in Omaha at 10:04AM. How many minutes did it take the band to reach Omaha?
Answer:
1 hour and 4 minutes
Step-by-step explanation:
A person's grade in school is generally identified by a number. give an example of a situation in which grade level is treated as categorical.
The grade level is treated as categorical when a principal wants to know the number of students from each grade will be participating in a performance.
Variables can be classified into quantitative and categorical. Quantitative variables are those which carry numerical values. Even though a person's grade in school is generally identified by a number, it is a categorical variable. Categorical variables classify data into different groups as the grade level. The grade level categorizes students into different grades and each grade level represents a particular grade only.
Any variable which is partly qualitative and represents groups of data are called categorical variables. Also grade level is ordinal. An example of a situation in which grade level is treated as categorical is when a principal wants to know how many students from each grade will be participating in a performance. Other examples of categorical variables are race, gender, age group, etc.
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solve the simultaneous equation
-4x+3y=1
6x-y=2
Answer:
x = 1/2, y = 1
Step-by-step explanation:
Let's change the equation,
→ 6x - y = 2
→ y = 6x - 2
Then the value of x will be,
→ -4x + 3y = 1
→ -4x + 3(6x - 2) = 1
→ -4x + 18x - 6 = 1
→ 14x = 1 + 6
→ x = 7/14
→ [ x = 1/2 ]
Hence, the value of x is 1/2 (or) 0.5.
Now the value of y will be,
→ y = 6x - 2
→ y = 6(1/2) - 2
→ y = 3 - 2
→ [ y = 1 ]
Hence, the value of y is 1.
Answer:
x = ¹/₂
y = 1
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}-4x+3y=1\\\:\:\:\:\:\:6x-y=2 \end{cases}[/tex]
Multiply the second equation by 3:
[tex]\implies 3 \cdot 6x-3 \cdot y = 3 \cdot 2[/tex]
[tex]\implies 18x-3y=6[/tex]
Add this to the first equation to eliminate the term in y:
[tex]\begin{array}{lrr}&-4x+3y & = 1\\+ & 18x-3y& = 6\\\cline{2-3} & 14x \phantom{-3x)} & = 7\end{array}[/tex]
Solve for x:
[tex]\begin{aligned}\implies 14x & = 7\\\\\dfrac{14x}{14} & = \dfrac{7}{14}\\\\\implies x & = \dfrac{1}{2}\end{aligned}[/tex]
Substitute the found value of x into the first equation and solve for y:
[tex]\begin{aligned}-4x+3y & =1\\x=\dfrac{1}{2}\implies -4\left(\dfrac{1}{2}\right)+3y & =1\\-\dfrac{4}{2}+3y & =1\\-2+3y & =1\\-2+3y+2 & =1+2\\ 3y & =3\\\dfrac{3y}{3} & =\dfrac{3}{3}\\\implies y & =1\end{aligned}[/tex]
Therefore, the solution to the given system of equations is:
x = ¹/₂ and y = 1
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(-13,2)(-17,9) find the slope of the line through each pair of points
Work Shown:
[tex](x_1,y_1) = (-13,2) \text{ and } (x_2,y_2) = (-17,9)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{9 - 2}{-17 - (-13)}\\\\m = \frac{9 - 2}{-17 + 13}\\\\m = \frac{7}{-4}\\\\m = -\frac{7}{4}\\\\[/tex]
A slope of -7/4 means that we move down 7 and to the right 4.
By paying $1500 cash and the balance is equal monthly payments, how many months would it take to pay for a car costing $12,495?
The monthly installments need to be paid is $10995.
To determine the number of months needed to pay off the remaining balance. We need to know the monthly installment.
What is installments?When you get an installment loan, you get the money you borrowed or the item you bought right away.
You pay it off in installments, which are regularly scheduled payments that may include interest. For a set number of months, or years, you generally owe the same amount on every installment. When the loan is fully repaid, the account is permanently closed.Now, as per the question;
Amount paid in cash = $1500
Remaining balance which is to be paid as monthly installments
= $12495 - $1500
=$12495 − $1500
=$10995
Thus, the monthly installments are $10995.
Now, to determine the number of months needed to pay off the remaining balance. The monthly installment is need to be known.
As a result, information on monthly installments is lacking.
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The complete question is-
What necessary piece of information is missing that prevents solving the problem? By paying $1500 cash and the balance in equal monthly payments, how many months would it take to pay for a car costing$12,495?
Please help loll and show your work if you can
First order equations include linear equations. In the coordinate system, the linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). Multiple variables may be present in a linear equation. Linear equations in two variables, for example, are used when a linear equation contains two variables. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.
10) -6(-5+r) = 102
30 -6r =102
-6r = 72
r = -12
11) -1 = x - 4 +4
x =-1
12) 0 = -6x -2x
-8x = 0
x= 0
13)5n+ 4n =9
n =1
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Options are PR = 18, 14, 9 and 11 please help me with which it is
