[tex]2x^2 -5x-8 =0\\\\\implies x = \dfrac{ -(-5) \pm \sqrt{(-5)^2 - 4\cdot 2 \cdot (-8)}}{2 \cdot 2}\\\\\\\implies x = \dfrac{5 \pm \sqrt{89}}{4}\\\\\\\text{Hence}~ x = \dfrac{5 + \sqrt{89}}{4},~~ x = \dfrac{5 - \sqrt{89}}{4}[/tex]
Answer:
[tex]\sf \boxed{\sf x=\frac{5+\sqrt{89}}{4}}[/tex]
[tex]\sf \boxed{\sf x=\frac{5-\sqrt{89}}{4}}[/tex]
✰Step-by-step explanation✰ ⤵[tex]\sf 2x^2-5x-8=0[/tex]
☁ We'll solve this equation using The Quadratic Formula:
[tex]\boxed{\sf \cfrac{-b\pm \sqrt{b^2-4ac}}{2a}}[/tex]
A= 2, b= -5, c= -8
[tex]\sf x=\cfrac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\times \:2\left(-8\right)}}{2\times \:2}[/tex]
[tex]\mapsto \sf \sqrt{\left(-5\right)^2-4\times \:2\left(-8\right)}[/tex]
[tex]**\sf \left(-5\right)^2=5^2[/tex]
[tex]\mapsto \sf \sqrt{5^2+4\times \:2\times \:8}[/tex]
[tex]\mapsto \sf \sqrt{5^2+64}[/tex]
[tex]\mapsto \sf \sqrt{89}[/tex]
______________
[tex]\sf x=\cfrac{-\left(-5\right)\pm \sqrt{89}}{2\times \:2}[/tex]
☁ Now, we'll Separate solutions, first, we'll solve the equation when ± is plus:
[tex]\mapsto \sf \cfrac{-\left(-5\right)+\sqrt{89}}{2\times \:2}[/tex]
☁ Multiply 2*2 =4
[tex]\boxed{\sf \cfrac{5+\sqrt{89}}{4}}[/tex]
_________________
☁ Now solve the equation when ± is minus:
[tex]\mapsto \sf \cfrac{-\left(-5\right)-\sqrt{89}}{2\times \:2}[/tex]
☁ Multiply 2*2 =4
[tex]\boxed{\sf \cfrac{5-\sqrt{89}}{4}}[/tex]
[tex]\sf Solution \:1:\boxed{\sf x=\frac{5+\sqrt{89}}{4}}[/tex]
[tex]\sf Solution \:2:\boxed{\sf x=\frac{5-\sqrt{89}}{4}}[/tex]
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b. Symbols Write an expression for the number of feet in x inches.
Help!!
Answer:
x/12
Step-by-step explanation:
There are 12 inches in a foot.
feet in x inches = x/12
_____
With units, you have ...
(x in) × (1 ft)/(12 in) = x/12 ft
When the input of the function is -1, What is the output of the function?
Answer:
2
Step-by-step explanation:
The graph clearly shows that when x = -1, y = 2.
Thus, the output of this function is 2.
A restaurant offers a lunch special for $12 plus $3 tip for the server. Which expression represents the total cost for the special help mee now
Answer:
$15
Step-by-step explanation:
12+3+15
Answer:
Bill Amount: $12
Tip Percent: 25%
Divide By: 1
= $15
A survey 3,000 who bought a new car showed that 900 had problems. What is the relative frequency of the people that had problems. show steps for me
Answer:
30%
Step-by-step explanation:
Presuming that "survey 3,000" is the total and "900" is the factor who had problems then dividing the total amount by the amount of problems like equal the relative frequency of people that had problems
Math:
Amount of people you had problems / Amount of people who bought the new car.
900 / 3000 = 0.3
Now you need to multiply by 100% (because % in this case is a unit/measurement)
0.3 * 100% = 30%
There is a puddle 1.4 cm deep in your backyard. After one minute of rain, the puddle was 1.45 cm deep. The puddle was 1.5 cm deep after it rained for two minutes. If the pattern continues, how deep will the puddle be after it rains for 45 min?
Answer:
I know answer. give me money I will tell everything..
158) -.- A) P-3 in B) P-86 C) P-92 in D) P96 4
Answer:
P = 83 in
Step-by-step explanation:
For this one, all we need to do is substitute 7 for x and 4 for y:
3x + y = ?
3(7) + 4 =?
21 +4 = ?
21 + 4 = 25 in.
Now for the next one:
4y = ?
4(4) = ?
4(4) = 16
Now we solve the final side:
6x = ?
6(7) = ?
6(7) = 42
Now to find P, we must add them all together:
25 + 16 + 42 = 83
Therefore P = 83
Answer:
A) P = 83
Step-by-step explanation:
-=======================-
3x + y
3(7) + 4 =
21 + 4 =
25
-=======================-
6x
6(7)
42
-=======================-
4y
4(4)
16
-=======================-
25 + 16 + 42 = 83
Hope this helps.
Octavia is making cotton candy. She uses 17.5 cups of sugar to make 5 bags of cotton candy. At this rate, how many cups of sugar are used to make 1 bag of cotton candy?
Answer:
3.5 cups of sugar per bag.
Step-by-step explanation:
17.5/5
3.5 cups of sugar are used to make 1 bag of cotton candy
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
For 5 bags of candy = 17.5 cups of sugar needed
and, For 1 bags of candy
=17.5/ 5
=3.5 cups of sugar needed
hence, 3.5 cups of sugar are used to make 1 bag of cotton candy
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Can someone explain it step by step ?
Answer:
1. (x - 1) × (x + 3)
2. x = 3 and y = -2
Step-by-step explanation:
x² + 2x - 32x + 3y = 0; y = 3x - 11rewrite the equation:
y = 3x - 11; 2x + 3y = 0
solve y = 3x - 11 for the y:
y = 3x - 11
substitute 3x - 11 for y in 2x + 3y = 0;
2x + 3y = 0;
2x + 3y = 0
2x + 3 (3x - 11) = 0
11x - 33 = 0 (simplify both sides of the equation)
11x - 33 + 33 = 0 + 33 (add 33 to both sides)
11x = 33
11x/11 = 33/11 (divide both sides by 11)
x = 3
subtitute 3 for x in y = 3x - 11
y = 3x - 11
y = (3)×(3) - 11
y = -2
I showed one equation because the other is self explanatory, hope this helps.
9/10 - _ = 1/5 mathematics
Answer:
x=7/10
Step-by-step explanation:
1/5=2/10
9/10- =2/10
Substitute the blank with X
9/10- X =2/10
x=7/10
Answer:
7/10
Step-by-step explanation:
9/10 - _ = 1/5
Let's represent the unknown as x
Therefore,
9/10 - x = 1/5
9/10 - 1/5 = x
x = 9/10 - 1/5 = 7/10
Write the ratio as a fraction: 630kilometers in 5hours. Simplify your answer.
___ km/hour
Answer:
126/1=126
Step-by-step explanation:
630:5 as a fraction would be 630/5.
630/5 simplified would be 126/1.
Hope this helps :)
Answer:
630:5 would be 126:1
Step-by-step explanation:
To solve this we would divide 630 by five giving us 126, and divide 5 by 5 giving us one
Now we have 126:1, or 126 km/hour
A photo is 4 inches tall and 6 inches wide. To be proportional, how tall would the photo need to be if it were 10 inches wide?
Answer:
6[tex]\frac{2}{3}[/tex] inches tall
Step-by-step explanation:
4:6 = x:10
We can set it up like this:
[tex]\frac{4}{6}=\frac{x}{10}[/tex]
And then cross multiply & solve:
40 = 6x
6[tex]\frac{2}{3}[/tex] = x
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
divide £100 into 1:4
Answer: the answer is 25
Step-by-step explanation:
First do 100/1
Then do 1 x 100/1 x 4
so then divide 100 by 4 =
25/1 =
25
Brian has half of his investments in stock paying a 5% dividend and the other half in a stock paying 9% interest. If his total annual interest is $420, how much does he have invested?
The amount invested in each stock, the stock interest rate and the
duration of the investment, determines the interest.
Brian invested $3,000 in the stock that pays 5% dividend and $3,000 in the stock that pays 9% to make a total investment of $6,000.Reasons:
Let X represent the sum of the amount Brian invested, we have;
Amount invested in stock paying 5% dividend = [tex]\dfrac{X}{2}[/tex]
Amount invested in stock paying 9% dividend = [tex]\dfrac{X}{2}[/tex]
Total annual interest = $420
Required:
The amount invested in the stocks
Solution:
The amount invested is found as follows;
[tex]\dfrac{X}{2} \times 5\% + \dfrac{X}{2} \times 9\% = 420[/tex]
0.025·X + 0.045·X = 420
0.07·X = 420
[tex]\displaystyle \mathrm{The \ amount \ invested , \, X} = \frac{420}{0.07} = \mathbf{ 6,000}[/tex]
The amount he invested = $6,000 ($3,000 in each stock)
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Answer fast please!!!
The correct answer is C. 58
Hope this helps!
Step-by-step explanation:
the answer is 58 this is the result I hope I've helped
HELP THIS IS DUE TOMORROW!!!!,Use a balance scale to solve the
following equation for the value of b.
17 + b = 35
Answer:
Step-by-step explanation:
just do 35-17
Answer:
Step-by-step explanation:
first find b.
To find b, subtract 17 from 35.
35 - 17 = b
35 - 17 = 18
next, add 17 and 18 to see if it equals 35.
17 + 18 = 35
so, b = 18.
The profit at a chocolate shop can be represented using the function f(x)=3x−95, where x is the number of chocolate truffles sold each day. What is the slope and what does it represent?
Can someone explain how to do this.
Can somebody please help this is honestly due tomorrow
Answer:
I am almost completely sure its 4.
Step-by-step explanation:
I dont mind brainiests by the way
the capacity of a water tank is 1000 litres if 7/10 parts is emptied how many litres of water is left?
Answer:
700 liter
Step-by-step explanation:
because 1000 * 7/10 is 700
The graph of y = (x -k)? is shown below.
у
61
5
لما له
1
-3-2-1
1 2 3 4 5 6 7
X
1
-2
-3
What is the value of k?
Answer:
(7) 3 2 2x 23 xy y - 10 0 Solution The equation 2x2 23xyy2-100 has A2,B 23, and (1 13) as p3 (Example 2). 13: 271279. 2 m) long and 6 ft Step-by-step explanation:
The function f(t) = t2 + 4t - 14 represents a parabola.
Part A: Rewrite the function in vertex form by completing the square. Show your
work.
Part B: Determine the vertex and indicate whether it is a maximum or a minimum on
the graph. How do you know?
Part C: Determine the axis of symmetry for f(t).
Answer:
a: [tex]f(t)=(t+2)^2-18[/tex]
b: vertex: (-2, -18)
minimum
c: x = -2
Step-by-step explanation:
Completing the square is difficult to explain in words. but I'll try my best. Let me know if you need any more information.
Part A ===============
Start with the given function in this form:
[tex]f(x)=ax^2+bx+c\\t^2+4t-14[/tex]
We need an additional number, d, and we'll calculate it like this:
[tex]d=(\frac{b}{2a})^2 \\\\d=(\frac{4}{2(1)} )^2\\d=2^2\\d=4[/tex]
d needs to be added and subtracted at the same time. That way we do not change the value of the expression:
[tex]ax^2+bx+d-d+c\\\\t^2+4t+4-4-14[/tex]
And you can separate them like this to make it easier to read:
[tex](t^2+4t+4) + (-4-14)\\(t^2+4t+4)-18[/tex]
Finally, we need to factor the trinomial in the parenthesis. Because we've completed the square, it's now a perfect square trinomial. The factored form is just:
[tex](x+e)^2[/tex]
where e is half of b, or the square root of c. That looks like this in our case, and you can also expand it to make sure.
[tex](t+2)^2\\\\(t+2)(t+2)\\t^2+2t+2t+4\\t^2+4t+4[/tex]
Put that all together and you get the answer:
[tex]f(t)=(t+2)^2-18[/tex]
Part B ===============
Vertex form is this:
[tex]f(x)=a(x-h)^2+k[/tex]
where (h, k) is the vertex and a is the scale factor.
In part A, we converted the given function into vertex form. Looking at that, you can see the vertex is at (-2, -18), and the scale factor is 1. When the scale factor is positive, the parabola faces upwards. When it's negative, the parabola faces downwards.
The scale factor is a positive 1 in this case, and if you picture that in your mind, the vertex is at the very lowest point, or the minimum, of the parabola.
Part C ==============
The axis of symmetry is always on the vertex, and that is because the vertex is the exact point where the parabola changes direction from positive to negative, or negative to positive.
The vertex of this parabola is (-2, -18), so the axis of symmetry is at x = -2.
Sorry if that got too long and hard to follow, I can clarify any part of it if needed.
Subtract and simplify. 12 3\8 − 9 1\8 =
Answer:
[tex]3\dfrac{1}{4} \ \ or \ \ 3,25[/tex]
Step-by-step explanation:
[tex]\displaystyle12 \frac{3}{8} -9\frac{1}{8} =12-9+\frac{3}{8} -\frac{1}{8} =3+\frac{2}{8} =3\frac{1}{4} \ \ or \ \ 3,25[/tex]
A store pays $306.56 for a refrigerator. The store marks up the price by 29%. What is the amount of the mark-up?
What is the quotient of 15a4b3/12a2b ? Assume that the denominator does not equal zero.
Answer:
[tex]\frac{5a^2b^2}{4}[/tex]
Step-by-step explanation:
Evaluate.
12⋅(1/4+1/3)power 2 +23 help ASAP
Answer:
325/12
Step-by-step explanation:
12(1/4 + 1/3)² + 23
12(7/12)² + 23
12(49/144) + 23
49/12 + 23
325/12 = 27 1/12 = 27.08333333
NEED HELP ASAP (ILL GIVE BRAINLIST)
Answer:
the answer is 33 9/11
Step-by-step explanation:
multiply the fractions
.
.
Answer:
33 9/11
Step-by-step explanation:
22 6/11 x 1 1/2
Convert into improper fractions.
248/11 x 3/2
Reduce the numbers with the greatest common factor 2.
124/11 x 3
Calculate
372/11
=33 9/11
Hope this helps :)
A loan is paid in 15 years with a total of $192.000. It had a 4% interest rate that compounded monthly. What was the principal?
Round your answer to the nearest dollar and do not include dollar sign
Select the geometric figure that correctly matches with the following formula:
A=[tex]\pi r^{2}[/tex]
Answer:
Circle
Step-by-step explanation:
The area of a circle is
[tex]\pi r^{2}[/tex]
A. circle
The area of a circle is 2[tex]\pi[/tex]r²
What is the formula for the circle?The Circle Formulas are expressed as,
the Diameter of a Circle. D = 2 × r. Circumference of a Circle. C = 2 × [tex]\pi[/tex] × r.Area of a Circle A = 2[tex]\pi[/tex]r²The collection of all points equidistant from a fixed point in a plane is called a circle.
the circle is a closed 2-dimensional figure in which the set of all the points in the plane is equidistant from a given point called the “center”. Every line that passes through the circle forms the line of reflection symmetry.
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write this fraction as a decimal use bar notation if neccesary
3 15/44
Answer:
3.34
Step-by-step explanation:
First step: 3x44=132, 132+15=147. Then use 147 as numerator and 44 as denominator.
Second step: Divide 147/44= 3.3409090909091, round and get 3.34.
Hope this helps.
Solve for b.
b+23=114
Enter your answer as a fraction in simplest form in the box.
b =
An equation is a collection of variables and constants. The value of b for the given equation b + 23 = 114 will be 91.
What is the equation?There are many different ways to define an equation.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
More than one variable may be present inside a linear equation.
As per the given equation,
b + 23 = 114
Add -23 both sides
b + 23 - 23 = 114 - 23
b + 0 = 91
b = 91
Hence "An equation is a collection of variables and constants. The value of b for the given equation b + 23 = 114 will be 91".
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"HKA
Erloka borrowed money from her brother to buy a new phone, and is paying off a fixed amount
each week
Answer:
$76
Step-by-step explanation: