Answer:
x = -1 ± √6
Step-by-step explanation:
[tex]x^{2} +2x - 5 = 0[/tex]
Lets use the quadratic formula → [tex]x = \frac{-b + \sqrt{b^{2} - 4ac} }{2a} \:or \frac{-b - \sqrt{b^{2}- 4ac } }{2a}[/tex]
So ,
[tex]x = \frac{(-2) + \sqrt{(2)^{2} - (4\times1\times-5) } }{2\times1} \:or \frac{(-2) - \sqrt{(2)^{2} - (4\times1\times-5) }}{2\times1}[/tex]
[tex]=> x = \frac{-2 + \sqrt{24} }{2} \:or \frac{-2-\sqrt{24} }{2}[/tex]
[tex]=> x = \frac{-2 + 2\sqrt{6} }{2} \:or \frac{-2 - 2\sqrt{6} }{2}[/tex]
Lets take 2 common from numerator.
[tex]=> x = \frac{2(-1 + \sqrt{6}) }{2} \:or \frac{2(-1-\sqrt{6}) }{2}[/tex]
Cancelling 2 from numerator & denominator gives
[tex]x = (-1+\sqrt{6} ) \: or (-1 - \sqrt{6} )[/tex]
Alyssa sold half of her comic books and then bought 8 more. She now has
12. How many did she begin with ?
Answer:
8 Books
Step-by-step explanation:
First find how many she had before buying 8 more-
12 - 8 = 4
Then multiply that by 2
4 x 2 = 8
The had 8 books to begin with
PLEASE PLEASE HELP ME I WILL MARK BRAINLIEST
Answer:
x = -25i
x = 25i
Tim and Ollie share some money in the ratio 2:5
Tim gets £80
Work out how much Ollie gets.
Answer:
£200
Step-by-step explanation:
The ratio is 2:5
we then have
80:x
Because one side of the ratio was multiplied by 40 we have to do the same to the other
20*5=200
therefore our new ratio is
80:200
Ollie gets £200
Which of the following is not a function?
Question 2 options:
{(1,2)(0,9)(3,4)(5,6)}
{(1,2)(3,4)(5,6)(7,8)}
{(1,5)(2,5)(3,5)(4,5)}
{(7,1)(2,4)(7,5)(8,3)}
Answer:D
Step-by-step explanation:
D, the X values repeat for 7.
Find f(-2), if f(x)=-3x^2-5x+11
Answer:
f(-2) = 9
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
f(x) = -3x² - 5x + 11
f(-2) is x = -2
Step 2: Evaluate
Substitute in x: f(-2) = -3(-2)² - 5(-2) + 11Exponents: f(-2) = -3(4) - 5(-2) + 11Multiply: f(-2) = -12 + 10 + 11Add: f(-2) = -2 + 11Add: f(-2) = 9The volume of a rectangular prism is 7/x-3/5x. If it has a width of 2/x and a height of 4/x, find the length of the prism?
a. 4/5
b. 32x²/40x
c. 4
d. 4x/5
The length of the rectangular prism is L = 4x/5
What is the volume of a prism?A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.
The volume of a prism is the product of its base area and height
Volume of Prism = B x h
where B = base area of prism
h = height of prism
Given data ,
The formula for the volume of a rectangular prism is V = lwh, where l, w, and h are the length, width, and height of the prism, respectively.
In this problem, we are given that the volume of the prism is 7/(x - 3/5x) and the width and height are 2/x and 4/x, respectively.
So we can substitute these values into the formula for the volume and solve for the length:
V = lwh
7/(x - 3/5x) = l * (2/x) * (4/x)
Multiplying both sides by (x - 3/5x), we get:
7 = l * 8/(5x² - 3x)
Simplifying, we get:
l = 56x²/(5x² - 3x)
Now we need to check if this solution satisfies the condition that the width is 2/x and the height is 4/x:
w = 2/x, h = 4/x
V = lwh = (56x²/(5x² - 3x)) * (2/x) * (4/x) = 7/(x - 3/5x)
So the solution is correct.
Hence , the length of the prism is 56x²/(5x² - 3x), which can be simplified to 32x²/40x or 4x/5
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Which of the following theorems cannot be used to prove two lines are
parallel?
Answer:
Option H
Step-by-step explanation:
Option F
If two lines are cut by a transversal so that a pair of corresponding angles are congruent, then the lines are parallel.
True.
Option G
If two lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the lines are parallel.
True
Option H
If two line are cut by a transversal so that a pair of vertical angles are congruent, then the lines are parallel.
Since, vertical angles don't prove the lines cut by a transversal are parallel.
So the statement is False.
Option J
If two lines are are cut by a transversal so that a pair of same side interior angles are supplementary, then the lines are parallel.
True.
What is the slope of the line
Write a system of linear inequalities represented by the graph.
Inequality 1:
Inequality 2:
Answer:
Inequality (1) → y > 2x
inequality (2) → x ≥ -2
Step-by-step explanation:
If the inequality (1) is a dotted line passing through origin.
Since, shaded area is above the dotted line,
Equation of the inequality will be in the form of y > mx +b
Here m = slope of the dotted line
b = y-intercept
Since, this line is passing through the origin,
Therefore, y-intercept = 0
Slope 'm' of the line = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{2}{1}[/tex]
m = 2
Inequality (1) → y > 2x
Second inequality is represented by the shaded area on the right side of the dark vertical line, x = -2,
Therefore, inequality 2 will be → x ≥ -2
Answer: x≽-2 and y>2x
24 birthdays in 100 days. What
percent of days are birthdays?
Answer:
24%
Step-by-step explanation:
24/100 =.24 which as a percent is 24%
Bentley spun a spinner with 4 equal sections labeled 1–4. The spinner landed on 1 three times, on 2 four times, on 3 six times, and on 4 three times. For which number is the experimental probability the same as its theoretical probability? Explain.
Answer:
2
Step-by-step explanation:
Experimental probability : (Number of times event occur / total number of trials)
Total Number of trials = (3 + 4 + 6 + 3) = 16
Experimental probability :
For 1: P(1) :
3/16
For 2 : P(2) :
4/16 = 1/4
For 3: P(3)
6 /16 = 3/8
For 4 : P(4)
3 / 16
Theoretical probability :
The Theoretical probability of 1, 2, 3 and 4 are the same ;
Theoretical probability =
(Required outcome / Total possible outcomes)
For each of 1 - 4
Theoretical probability = 1 /4
Experimental probability of P(2) = 1/ 4 and is Hence, the same as the Theoretical probability
Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions:
y > 3x + 10
y < -3/4x - 1
Part A: Describe the graph of the system, including shading and the type of lines graphed. Provide a description of the solution area.
Part B: Is the point (8, 10) included in the solution area for the system? Justify your answer mathematically.
Answer:
Part A:
I have attached the graph of this system of inequalities.
Part B:
Plug in (8,10) into both equations
10 > 3(8) + 10
10 > 24 + 10
10 > 34
This is false!
10 < (-3/4)(8) - 1
10 < (-3)(2) - 1
10 < -6 - 1
10 < -7
This is also false!
So, (8,10) is not included in the solution area for the system.
Step-by-step explanation:
Which is the midpoint of AB with A(-1, 5) and B(6, -3)?
Answer:
abcdef
Step-by-step explanation:
please answer for 20 points
Answer:
C
Step-by-step explanation:
whenever you see a (as in ax^2 + bx+c) as a number other than 1, you should see if you can factor that out
2(6x^2 -x -1)
= 2(3x+1) (2x-1)
Answer:
2\(3x+1)(2x-1\)
Step-by-step explanation:
1 point
3.) Jamal then says that there are other types of trends in the periodic
table and tells Nic about Atomic Radius. He looks at the same four elements
and points to the element with the largest atomic radius. Which should he
point to?
F
Ci
Br
I
Answer:
the largest one is f or francium.
I need help plz and thank u sm
Answer:
5x + 3
Step-by-step explanation:
Since we can see DC is the median of Triangle ABC
So it breaks the into two equal parts
Given
AD = 2x + 5
BD = 3x - 2
Now
AB = AB + BD
= 2x + 5 + 3x - 2
= 5x + 3
Hope it will help :)❤
brain list you
ω please
Answer:
C
Step-by-step explanation:
14. Higher Order Thinking: Lauren can drive her car 320 miles on 10 gallons of gasoline. Melissa can drive her car 280 miles on 8 gallons of gasoline. Who can drive farther on 40 gallons of gasoline? Complete the ratio tables to justify your solution.
Lauren can drive farther on 40 gallons of gasoline than Melissa because her car is more fuel efficient.
What is miles?
Miles are a unit of measurement used to measure distances, typically between two points. Miles are typically used to measure the length of a journey, such as how many miles it is from one city to another. Miles can also be used to measure the length of a route or the total distance that a person has traveled. In the United States, a mile is equal to 5,280 feet or 1.61 kilometers.
Lauren:
10 gallons : 320 miles
40 gallons : x miles
x = 1280 miles
Melissa:
8 gallons : 280 miles
40 gallons : y miles
y = 1120 miles
Since Lauren can drive 1280 miles on 40 gallons of gasoline, she can drive farther than Melissa, who can only drive 1120 miles on the same amount of gasoline. This is because Lauren’s car has higher fuel efficiency, meaning it uses less gasoline for the same distance.
In conclusion, Lauren can drive farther on 40 gallons of gasoline than Melissa because her car is more fuel efficient. This difference in fuel efficiency can be seen in the ratio tables, which show that Lauren can travel 160 miles farther than Melissa on the same amount of gasoline.
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RSTis graphed on a coordinate plane below. The triangle undergoes two
transformations and the new vertices are R"(4,2), S"(8,2), and T"(8,-6). Determine
the transformations and the order in which they were applied.
A. 90° counter-clockwise rotation, then reflected across the y-axis
B. Reflected across the y-axis, then a 90° counter-clockwise rotation
C. 90° counter-clockwise rotation, then reflected across the x-axis
D. Reflected across the y=x, then a 90° counter-clockwise rotation
Answer:C
Step-by-step explanation:
Transformation involves changing the position of a shape
The transformations and the order in which they were applied are:
A. 90° counter-clockwise rotation, then reflected across the y-axis
From the figure, the coordinate of RST is:
[tex]R= (2,4)[/tex]
[tex]S = (2,8)[/tex]
[tex]T =(-6,8)[/tex]
Using R to illustrate the transformation.
We have
[tex]R= (2,4)[/tex]
First, R is rotated 90 degrees counterclockwise
The rule of this transformation is:
[tex](x,y) \to (-y,x)[/tex]
So, we have:
[tex](2,4) \to (-4,2)[/tex]
Next, the point is reflected across the y-axis.
The rule of this transformation is:
[tex](x,y) \to (-x,y)[/tex]
So, we have:
[tex](-4,2) \to (4,2)[/tex]
From the question, we have the coordinate of R" to be;
[tex]R: =(4,2)[/tex] --- same as the result of the above sequence
Hence, option (A) is correct
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Which set of ordered pairs does not represent a function? Delta math
Answer:
The first set of ordered pairs is a function, because no two ordered pairs have the same first coordinates with different second coordinates. The second example is not a function, because it contains the ordered pairs (1,2) and (1,5). These have the same first coordinate and different second coordinates
Select the correct shapes.
Select the shapes that are similar to shape A.
Answer: Its the pink one and the green one
hope that was helpful!
Step-by-step explanation:
Answer:
pink, dark blue, and red
Step-by-step explanation:
Evaluate y=5x+7, for x=3.
how do i solve 9/10 y = -36
Answer:
-40
Step-by-step explanation:
Multiply both sides by the reciprocal of 9/10 to get rid of the fraction
[tex]\frac{10}{9}[/tex]×[tex]\frac{9}{10}[/tex]×y=-36 ×[tex]\frac{10}{9}[/tex]
y=-36×[tex]\frac{10}{9}[/tex]
y=[tex]\frac{-360}{9}[/tex]
y=-40
someone help. Simplify: (1/a)^3
Answer:
1/a3 is the simplify expression for the equation
Una torta de queso para 4 personas presisa 300g de queso, 10ml de leche, 100g de azucar, 100g de mantequilla y 50g de harina, si queremos hacer una tarta para 6 personas, qué cantidad de ingredientes necesitaremos?
Answer:
Por tanto, la cantidad de ingredientes necesarios para 6 personas es:
450 g de queso, 15 ml de leche, 150 g de azúcar, 150 g de mantequilla y 75 g de harina.
Step-by-step explanation:
Por lo tanto:
Para queso
4 personas = 300g de queso
6 personas = x
Cruz multiplicar
4x = 6 × 300g
x = 6 × 300 g / 4
x = 450 g de queso
Por 10ml de leche
4 personas = 10 ml de leche
6 personas = x
Cruz multiplicar
4x = 6 × 10 ml
x = 6 × 10 ml / 4
x = 15 ml
Por 100 g de azúcar
4 personas = 100 g de azúcar
6 personas = x
4x = 6 × 100g
x = 6 × 100 g / 4
x = 150 g de azúcar.
Por 100 g de mantequilla
4 personas = 100 g de mantequilla
6 personas = x
4x = 6 × 100g
x = 6 × 100 g / 4
x = 150 g de mantequilla
Por 50 g de harina
4 personas = 50 g de queso
6 personas = x
4x = 6 × 50g
x = 6 × 50 g / 4
x = 75 g de queso.
Por tanto, la cantidad de ingredientes necesarios para 6 personas es:
450 g de queso, 15 ml de leche, 150 g de azúcar, 150 g de mantequilla y 75 g de harina.
6th grade math help me plz
hi
can you answer this and explain please
Answer:
B
Step-by-step explanation:
Inequalities of the type | x | ≤ a, have solution of the form
- a ≤ x ≤ a , so
| x | ≤ 4
- 4 ≤ x ≤ 4
The values of x are between - 4 and + 4, but can equal - 4 and 4 since the symbol is ' less than or equal to '
This is indicated on a number line by solid circles, where not equal to are denoted by open circles.
Thus the solution is Graph B
A group of students went on a field trip. There were 3 boys for every 4 girls inthe group. If there were 20 girls, how many students in all went on the field trip? 10 points
Answer:
15 boys
Step-by-step explanation:
start by dividing 20 by 4
you get 5
5 times 3 next
now you have 15
Answer:
25 girls and boys
Step-by-step explanation:
There are 3 boys for every 4 girls
To find the rate we must
Divide 20 by 4 then multiply that by 3
20 divided by 4 is 5
5 times 3 is 15
15 boys went on the field trip
20 girls went on the field trip
The total number of students is 25 girls and boys
what is 1/4 of 84 and hury please
Answer:
21
Step-by-step explanation:
A caterer prepares twice as many pizzas as she usually prepares for a large party. The caterer usually prepares 6 pizzas. The caterer also estimates that each party guest will eat
1
2
of a pizza.
Drag and drop each expression into the correct boxes to complete the explanation.
The expression that represents how many guests the pizzas can serve is .
How many party guests will the pizzas serve? Drag and drop the number of guests into the box.
The pizzas can serve guests.