Answer:
[tex]\huge\boxed{\sf x\leq 2}[/tex]
Step-by-step explanation:
Given inequality:[tex]56-10x\geq 20+8x\\\\Subtract \ 20 \ from \ both \ sides\\\\56-20-10x\geq 8x\\\\36-10x\geq 8x\\\\Add \ 10x \ to \ both \ sides\\\\36\geq 8x+10x\\\\36\geq 18x\\\\Divide \ 18 \ to \ both \ sides\\\\2 \geq x\\\\OR\\\\x\leq 2\\\\\rule[225]{225}{2}[/tex]
[tex]\bf{56-10x\geq 20+8x }[/tex]
Subtract 8x on both sides.
[tex]\bf{56-10x-8x\geq 20 }[/tex]
Combine −10x and −8x to get −18x.
[tex]\bf{56-18x\geq 20 }[/tex]
Subtract 56 from both sides.
[tex]\bf{-18x\geq 20-56 }[/tex]
Subtract 56 from 20 to get −36.
[tex]\bf{-18x\geq -36 }[/tex]
Divide both sides by −18. Since −18 is <0, the inequality direction is changed.
[tex]\bf{x\leq \dfrac{-36}{-18} }[/tex]
Divide −36 by −18 to get 2.
[tex]\bf{x\leq 2 \ \ \to \ \ \ Answer}[/tex]
We conclude that the correct option is "C".
{ Pisces04 }simplify \sqrt{50} for maths please quick
Hello,
[tex] \sqrt{50} = \sqrt{2 \times 25} = \sqrt{2 \times 5 {}^{2} } = 5 \sqrt{2} [/tex]
Hey guys- need help in this one
Answer:
c
Step-by-step explanation:
[tex]x=5+i\sqrt{7} , y = 5-i\sqrt{7}\\ x^2-2xy+y^2=(x-y)^2\\ (x-y)^2=(2i\sqrt{7} )^2\\4.i^2.7\\-28[/tex]
Answer:
c
Step-by-step explanation:
given x = 5 + i[tex]\sqrt{7}[/tex] then y = 5 - i[tex]\sqrt{7}[/tex]
x² - 2xy + y² ← is a perfect square
= (x - y)² ← substitute values for x and y
= (5 + i[tex]\sqrt{7}[/tex] - (5 - i[tex]\sqrt{7}[/tex] )²
= (5 + i[tex]\sqrt{7}[/tex] - 5 + i[tex]\sqrt{7}[/tex] )²
= (2i[tex]\sqrt{7}[/tex] )²
= 2² × i² × ([tex]\sqrt{7}[/tex] )²
= 4 × - 1 × 7
= - 28
What term best describes 3x + 5?
Answer:
algebric expression
Answer:
Binomial
Step-by-step explanation:
Comment
Answer: Two terms make up the expression you are given (3x + 5) ).
When two terms are on either side of an isolated plus (or minus) sign, then the expression is called a Binomial.
a parabola passes through the points (2,8), (6,2), and (8,8). what is the x-coordinate of its vertex?
a) 4
b) 5
c) 7
d) cannot be determined
The x-value of the vertex of the given parabola is x = 5, so the correct option is b.
How to get the x-value of the vertex?
If we define the parabola by f(x), by looking at the table, we can read:
f(2) = 8f(6) = 2f(8) = 8So, notice that:
f(2) = f(8).
Then the x-coordinate of the vertex is the midpoint between 2 and 8.
x = (2 + 8)/2 = 5
The x-value of the vertex of the given parabola is x = 5, so the correct option is b.
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I need the answer please work out this tough question for me
Answer:
56
Step-by-step explanation:
Let N be the total number of spins.
Probability of A on Red and B on Red = 0.5 x 0 .6 = 0.3 (top branch of tree)
Therefore with N spins, the estimated number of times spinner A and spinner B land on red is 0.3N and we are given this as 84
So 0.3N = 84
N = 84/0/3 = 280
The probability of spinner A on blue and spinner B on blue is 0.5 x 0.4 = 0.2 (lowest branch of tree)
For 280 spins, the estimated number of times that both spinners land on blue is given by 0.2 x 280 = 56
Amy simplified this complex fraction problem.
Negative 2 and one-half divided by five-fourths = Negative five-halves divided by five-fourths = negative five-halves (five-fourths) = negative StartFraction 10 over 8 EndFraction. The quotient is negative five-fourths.
What errors did Amy make? Select all that apply.
Reciprocal the second fraction and perform multiplication instead addition.
What is fraction?
A number expressed as a quotient, in which a numerator is divided by a denominator.
Given:
Negative 2 and one-half divided by five-fourths = Negative five-halves divided by five-fourths = negative five-halves (five-fourths) = negative StartFraction 10 over 8 EndFraction.
As we see the calculations there is mistake which had amy made.
Amy should have reciprocal the second fraction before multiplication. As division is now allowed in fraction.
Also, She perform addition instead of multiplication.
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If sec x° = five thirds, what is the value of b? triangle lmn in which angle m measures 90 degrees, angle l measures x degrees, ln measures 20 units, and lm measures 3b units b = 4 b = 5 b = 6 b = 7
The correct answer is, b=4.
Given Information and To Find
It is given that in a right angled-triangle lmn,
∠m = 90°
∠l = x°
ln = 20 units
lm = 3b units
[tex]secx = \frac{5}{3}[/tex]
We have to find the value of b.
What is a right-angled triangle?
A right triangle is a triangle in which one of the angles is at a right angle or two of the sides are perpendicular, or more formally, an orthogonal triangle, formerly known as a right-angled triangle. Trigonometry's fundamental concept is the relationship between a right triangle's sides and other angles.
Applying Trigonometry
We know that in a right angled-triangle,
[tex]sec x=\frac{hypotenuse}{base}[/tex]
In this case, we have (refer to the diagram),
[tex]secx=\frac{ln}{lm}[/tex]
⇒ [tex]\frac{20}{3b} = \frac{5}{3}[/tex]
⇒ [tex]20(3) = 3b(5)[/tex]
⇒ [tex]15b = 60[/tex]
⇒ [tex]b=4[/tex]
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A model of a ship is built to scale of 1 cm:5 meters.The length of the model ship is 30 cm. What is the actual length of the ship?
Answer:
The actual length of the ship is 150 meters.
Step-by-step explanation:
The scale of the model is 1 cm:5 meters, which means that every 1 cm on the model represents 5 meters on the ship. Since the model ship is 30 cm long, that means it represents 150 meters on the real ship.
A certain test is designed to measure the satisfaction of an individual with his/her relationship. Suppose that the scores on this test are approximately normally distributed with a mean of 60 and a standard deviation of 8. An individual with a score of 50 or less is considered dissatisfied with his/her relationship. According to this criterion, what proportion of people in relationships are dissatisfied? Round your answer to at least four decimal places.
The probability that an individual will score of 50 or less is 0.06.
Given mean of 60 and standard deviation of 8.
We have to find the probability that individual will score 50or less.
Probability is the chance of happening an event among all the events possible. The probability lies between 0 and 1. The formula to calculate probability is as under:
Probability = number of items/total items.
We have to first find the z value from 50 to 60 which can be found as under:
z value=(50-60)/60
=-0.167
P value from 50 to 60 is 0.44
probability that the individual will score 50 or less is 0.5-0.44
=0.06
Hence the probability that the individual will score 50 or less is 0.06.
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Ms. johnson uses a statistics program to analyze all the data collected by her students during a lab experiment about acceleration due to gravity. the program reports =31.5 and . what is the variance of the data? round to the nearest tenth.
Since the variance is the square of the standard deviation, the variance here is 6.3.
A commonly used measure of dispersion is the standard deviation, which is simply the square root of the variance. Therefore, we just raise the standard deviation to the power of 2 to get the answer. We do as follows:
s = √v
(2.5)² = (√v)²
v = 6.25 = 6.3
So, Since the variance is the square of the standard deviation, the variance here is 6.3.
DISCLAIMER: The question was incomplete. Please find the full content below.
Question
Ms. Johnson uses a statistics program to analyze all the data collected by her students during a lab experiment about the acceleration due to gravity. The program reports a mean of 31.5 and a standard deviation of 2.5. What is the variance of the data?
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Answer: D). 6.3
Step-by-step explanation:
identify the domain of the function shown in the graph
0
x is all real numbers
Using it's concept, the domain of the square root function shown in the graph is:
[tex]x \geq 0[/tex]
What is the domain of a function?The domain of a function is the set that contains all possible input values for the function. In a graph, the domain is the set that contains the values of x.
Researching the problem on the internet, the graph is of the square root function, defined for [tex]x \geq 0[/tex], which is the domain of the function.
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What is the decimal expansion of the following fraction? 1/5
Answer:
0.2
Step-by-step explanation:
Answer:
0.2
Step-by-step explanation:
1 divided by 5 = 0.2
−6i⋅(6−2i)=minus, 6, i, dot, left parenthesis, 6, minus, 2, i, right parenthesis, equals Your answer should be a complex number in the form a+bia+bia, plus, b, i where aaa and bbb are real numbers.
The solution to the given product is:
-6i*(6 - 2i) = -12 - 36i
How to solve the given expression?
Here we want to solve:
-6i*(6 - 2i)
Here the thing that you need to remember is that i² = -1.
Expanding the product, we get:
-6i*(6 - 2i) = (-6i)*6 + (-6i)*(-2i)
= -36i + (6i)*(2i) = -36i + 12i² = -36i - 12
Then we conclude:
-6i*(6 - 2i) = -12 - 36i
That is the solution to the given expression.
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WILL GIVE BRAINLIEST IF YOU HELP MEE
Answer: A: Whole Number B:Integer and C: Rational are all correct.
For the question: In the figure, AB is divided into equal parts. The coordinates of point A are (2, 4), and the coordinates of point B are (10, 6). Match each pair of coordinates to the corresponding point on AB.
Answer:The coordinates of the point are (6 , 5).
For the question: Imani and Abedi drive to work. Imani drives 66 miles in 1.5 hours. Abedi drives 56 km in 1 hour 15 min. Work out the difference between their average speeds in km/h. 1 mile = 1.6 km
Answer:25.6 km/h
I couldn't help you on all of them, but I helped you on some. Hope this helps :D
Please help me with Algebra 2 questions (2).
#8: Simplify the expressions. Assume all variables are positive.
#11: Solve the equation.
8. The simplified form of the expression is [tex]- 5 x^{\frac{4}{5}}y^{3}[/tex]
11. The value of x is 4
Simplifying an expressionFrom the question, we are to simplify the give expression
The given expression is
[tex]y^{3}\sqrt[5]{32x^{4} } - 7\sqrt[5]{x^{4}y^{15} }[/tex]
[tex]y^{3} (32x^{4} )^{\frac{1}{5} } - 7(x^{4}y^{15} )^{\frac{1}{5}[/tex]
[tex]y^{3} \times 32^{\frac{1}{5} } x^{\frac{4}{5} } - 7 \times x^{\frac{4}{5}}y^{\frac{15}{5}}[/tex]
[tex]y^{3} \times 2^{5 \times} ^{\frac{1}{5} } \times x^{\frac{4}{5} } - 7 \times x^{\frac{4}{5}}y^{3}[/tex]
[tex]y^{3} \times 2 \times x^{\frac{4}{5} } - 7 \times x^{\frac{4}{5}}y^{3}[/tex]
[tex]2 x^{\frac{4}{5} } y^{3} - 7 x^{\frac{4}{5}}y^{3}[/tex]
[tex]= - 5 x^{\frac{4}{5}}y^{3}[/tex]
11. [tex]\frac{1}{2}(5x+7 )^{\frac{2}{3} } =\frac{9}{2}[/tex]
Multiply both sides by 2
[tex]2 \times \frac{1}{2}(5x+7 )^{\frac{2}{3} } =2 \times \frac{9}{2}[/tex]
[tex](5x+7 )^{\frac{2}{3} } =9[/tex]
Multiply both sides by a power of 3/2
[tex](5x+7 )^{\frac{2}{3} \times {\frac{3}{2} } } =9^{\frac{3}{2} }[/tex]
[tex](5x+7 )=3^{2 \times} ^{\frac{3}{2} }[/tex]
[tex]5x+7 =3^{3}[/tex]
[tex]5x+7 =27[/tex]
[tex]5x =27-7[/tex]
[tex]5x = 20[/tex]
[tex]x = \frac{20}{5}[/tex]
x = 4
Hence,
8. The simplified form of the expression is [tex]- 5 x^{\frac{4}{5}}y^{3}[/tex]
11. The value of x is 4
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2a. A quarterback throws a football from a position that is 10 yards from the goal line and 15 yards from the sideline. His receiver catches it at a position that is 50 yards from the same goal line and 5 yards from the same sideline. Find the distance of the throw.
2b. Explain how you created the two points in order to find the distance.
The calculated distance of this throw is given as 41.23 meters.
How to solve for the distance of the throw.
In order to solve for this, we have to make use of the formula for calculating distance.
This is given as:
[tex]\sqrt{(x^{2}-x^{1} ) } (y^{2} -y^{1} )[/tex]
This is substituted as
sqr(50-10)²+(5-15)²
= √40² +√ -10²
= √1700
= 41.23
b. The points were created to find the distance by making use of yards from the goals and the yards from the sidelines.
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□ 1. What is the prime factorization of 15x³y²?
Answer:
3*5*(x^3)*(y^2)
Step-by-step explanation:
Since we don't know what x and y are, we can leave them as they are. Now we just find the prime factorization of 15, which is 3*5.
Using the quadratic formula to solve 5x = 6x²-3, what are the values of x?
Answer:
[tex] \boxed{\sf{x = \frac{5 \pm \sqrt{97} }{12} }}[/tex]
Step-by-step explanation:
[tex]\sf{5x = 6 {x}^{2} - 3 }[/tex]
[tex]\sf{0 = 6 {x}^{2} - 3 - 5x }[/tex]
[tex]\sf{0 = 6 {x}^{2} - 5x - 3 }[/tex]
a = 6b = - 5c = - 3[tex] \sf{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} }[/tex]
[tex]\sf{x = \frac{ - ( - 5) \pm \sqrt{ { - 5}^{2} - 4(6)( - 3)} }{2(6)} }[/tex]
[tex]\sf{x = \frac{5 \pm \sqrt{ 25 + 72} }{12} }[/tex]
[tex]\sf{x = \frac{5 \pm \sqrt{97} }{12} }[/tex]
A bag contains 4 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, find the probability that a blue marble will be drawn. a. One-third c. StartFraction 1 Over 7 EndFraction b. StartFraction 1 Over 11 EndFraction d. StartFraction 3 Over 14 EndFraction Please select the best answer from the choices provided A B C D
The probability of selecting a blue marble is 3/14. Hence, option D is the right choice.
The probability of any event is the chance of the occurrence of that event. It is given as the ratio of the number of favorable outcomes to the event to the total number of outcomes possible in the experiment.
If we consider an event A, the number of favorable outcomes to event A be n, and the total number of outcomes be S, then the probability of event A is given as:
P(A) = n/S.
Let us take the event of selecting a blue marble from the experiment of selecting a marble randomly from the bag be A.
The number of outcomes favorable to event A (n) = 3 {3 blue marbles}.
The total number of outcomes (S) = 14 {Total number of marbles in the bag = 4 red + 3 blue + 7 green = 14 marbles}.
Therefore, the probability of selecting a blue marble is,
P(A) = n/S = 3/14.
Hence, option D is the right choice.
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Scores on a graduate school entrance exam follow a normal distribution with a mean of 560 and a standard deviation of 90. What is the probability that a randomly chosen test taker will score between 490 and 560
[tex]P(490 < X < 560)[/tex]= 0.3133
Given: μ = 560
σ = 90
To find: P (490 < X < 560)
Normal distributions are symmetric, unimodal, and asymptotic. A normal distribution is determined by two parameters the mean and the variance. A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution. It's always easy to solve questions in terms to standard normal
Hence, converting normal distribution to standard normal gives:
P(490 < X < 560) = [tex]P(\frac{560-560}{90}[/tex]≤ [tex]\frac{X-\mu}{\sigma} < \frac{640-560}{90})[/tex]
= P(0 ≤ Z < 0.888)
= P (z<0.89) - P(z ≤ 0)
Using standard normal table,
= 0.8133 - 0.5
P(490 < X < 560) = 0.3133
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HALP
x =x=x, equals
^\circ
∘
Answer:
90°+x = 180°(angles on a straight line)x=180°-90°x=90°THERE ARE A LOT OF WAYS TO WORK THE ANSWER OUT BUT THAT ONE IS SIMPLE AND EASY TO UNDERSTANDStep-by-step explanation:
HOPE THIS HELPS!!helllppppppppppp please
The equation of the line with a slope of -3 and passing through the point (3, 16) is y = -3x + 25
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The equation of a line is:
y = mx + b
Where m is the slope and b is the y intercept.
Given that the line has a slope of -3 and passes through (3, 16), hence:
y - 16 = -3(x - 3)
y = -3x + 25
The equation of the line with a slope of -3 and passing through the point (3, 16) is y = -3x + 25
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Need help not good at math what so ever.
A triangle is a plane figure which has three sides and angles. Thus the sum of internal angles of a triangle is [tex]180^{o}[/tex]. Thus the answers to the missing values are:
7. x = [tex]108^{o}[/tex]
8. x = [tex]133^{o}[/tex]
9. x = [tex]124^{o}[/tex]
10. x = [tex]62^{o}[/tex]
11. x = [tex]74^{o}[/tex]
12. x = [tex]77^{o}[/tex]
13. a = [tex]35^{o}[/tex]
14. b = [tex]74^{o}[/tex]
15. c = [tex]66^{o}[/tex]
The sum of the internal angles of a triangle is [tex]180^{o}[/tex]. Thus in a given question, the required value for each missing value is:
7. Let the unknown inter nal angle ne represented by r, so that;
70 + 38 + r = [tex]180^{o}[/tex]
r = [tex]180^{o}[/tex] - 108
r = 72
So that,
x + a = [tex]180^{o}[/tex] (sum of angles on a staight line)
72 + a = [tex]180^{o}[/tex]
a = [tex]180^{o}[/tex] - 72
= [tex]108^{o}[/tex]
a = [tex]108^{o}[/tex]
8. x = 39 + 94 (Sum of two opposite interior angles is equal to an exterior angle)
x = [tex]133^{o}[/tex]
9. x = 43 + 81 (Sum of two opposite interior angles is equal to an exterior angle)
x = [tex]124^{o}[/tex]
10. x + 19 = 81 (Sum of two opposite interior angles is equal to an exterior angle)
x = 81 - 19
x = [tex]62^{o}[/tex]
11. 41 + x = 115 (Sum of two opposite interior angles is equal to an exterior angle)
x = 115 - 41
x = [tex]74^{o}[/tex]
12. x = 41 + 36 (Sum of two opposite interior angles is equal to an exterior angle)
x = [tex]77^{o}[/tex]
13. 33 + 112 + a = [tex]180^{o}[/tex] (sum of angles on a staight line)
a = [tex]180^{o}[/tex] - 145
= [tex]35^{o}[/tex]
14. b + 71 + a = [tex]180^{o}[/tex] (sum of angles on a staight line)
b = [tex]180^{o}[/tex] - 106
b = [tex]74^{o}[/tex]
15. c + 71 + 43 = [tex]180^{o}[/tex] (sum of angles on a staight line)
c = [tex]180^{o}[/tex] - 114
c = [tex]66^{o}[/tex]
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I have $230 and I’m at a bookstore. I love books, so I want to buy as many as I can. The books I want to buy each cost $17. At most, how many books can I buy and still have at least $25 left for dinner?
Answer:
12 books
Step-by-step explanation:
Lets set aside $25 for dinner first.
Amount left = $230 - $25 = $205
Number of books able to buy = amount left ÷ cost per book
= $205 ÷ $17
= 12.058 books
Of course, you cant buy .058 books , that wont make sense, so you take the highest possible WHOLE number, which in this case, is 12 books.
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Answer:
-3
Step-by-step explanation:
Define two points on the line:
[tex]\textsf{let}\:(x_1,y_1)=(0,4)[/tex][tex]\textsf{let}\:(x_2,y_2)=(2,-2)[/tex]Substitute the defined points into the slope formula and solve for m:
[tex]\begin{aligned} \textsf{slope}\:(m) & = \dfrac{y_2-y_1}{x_2-x_1}\\\\ \implies m & =\dfrac{-2-4}{2-0}\\\\ & =\dfrac{-6}{2}\\\\ & =-3\end{aligned}[/tex]
Therefore the slope of the given line is -3.
Some families spend their incomes according to budget plans. If a family used the plan
below as a basis, about how much would it spend for clothing?
Shelter.
Food
Clothing
Operation
Savings
Other Expenses.
$525
Monthly
Income
.26%
.28%
7%
. 10%
. 9%
20%
100%
O $35.75
O $36.75
O $53.20
$75.00
O none of these
Using proportions, it is found that the family would spend $36.75 on clothing.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The family has a budget of $525, and spends 7% of it in clothing, hence the amount is given by:
A = 0.07 x 525 = $36.75.
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Alice, Bob, and Carol were riding their bikes along the same path at different speeds. Alice's speed was twice Bob's speed, and Carols' speed was one-third that of Alice's speed. What was Carol's speed, in miles per hour, if Bob's speed was 9 miles per hour
Carol's speed is computed to be 6 miles/hour, solved using the equation (3x)/2 = 9.
We assume Carol's speed to be x miles/hours.
Carol's speed is given to be one-third of Alice's speed.
Then Alice's speed is three times Carol's speed, that is, Alice's speed = 3x miles/hour.
Alice's speed is given to be twice Bob's speed.
Then Bob's speed is half of Alice's speed, that is, Bob's speed = (3x)/2 miles/hour.
But, Bob's speed is given to be 9 miles per hour.
Therefore, we get the equation:
(3x)/2 = 9.
To find Carol's speed, we solve this equation as follows:
(3x)/2 = 9,
or, {(3x)/2}*2 = 9*2 {Multiplying both sides by 2},
or, 3x = 18 {Simplifying},
or, 3x/3 = 18/3 {Dividing both sides by 3},
or, x = 6 {Simplifying}.
Therefore, Carol's speed is computed to be 6 miles/hour, solved using the equation (3x)/2 = 9.
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(please answer quick, i'm timed!!)
What is the simplest form of StartRoot 1,764 EndRoot?
A] 21
B] 42
C] 3^2(7^2)
D]2^2(3^2)(7^2)
Squares are the results of multiplying a value by itself. The correct option is B.
What is square root?Squares are the results of multiplying a value by itself. Whereas the square root of a number is a value that when multiplied by itself yields the original value. As a result, both are vice versa approaches. For example, the square of 2 is 4 and the square root of 4 is 2.
The number 1764 in the form of prime factors can be written as,
1764 = 2×2×3×3×7×7×1
Therefore,
√1764 = 2×3×7 = 42
Hence, the correct option is B.
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Answer: d}2^2(3^2)(7^2)
Step-by-step explanation: I did the quiz
Solve the system, enter the smallest x coordinate first
The solutions to the system of equations are given as follows: (1, -3) and (-4,2).
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The equations are given as follows:
(x + 3)² + (y + 2)² = 17.x + y = -2.From the second equation:
y = -2 - x.
Replacing in the first:
(x + 3)² + (y + 2)² = 17.
(x + 3)² + (-2 - x + 2)² = 17
x² + 6x + 9 + x² = 17
2x² + 6x - 8 = 0
2(x² + 3x - 4) = 0
2(x + 4)(x - 1) = 0.
Then the solutions for x are:
x + 4 = 0 -> x = -4.x - 1 = 0 -> x = 1.The solutions for y are:
When x = 1, y = -2 - 1 = -3.When x = -4, y = -2 -(-4) = 2.Hence the solutions are:
(1, -3) and (-4,2).
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Can someone help me pls
Answer:
(d) x = (5±√53)/2
Step-by-step explanation:
The given quadratic equation is in standard form, so the coefficients are readily identified. The solution is given by the quadratic formula based on those coefficients.
Quadratic formulaThe solution to the quadratic equation ax² +bx +c = 0 is given by the formula ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
ApplicationThe given equation has coefficients a = 1, b = -5, c = -7, so the solutions given by the formula are ...
[tex]x=\dfrac{-(-5)\pm\sqrt{(-5)^2-4(1)(-7)}}{2(1)}=\dfrac{5\pm\sqrt{25+28}}{2}\\\\\boxed{x=\dfrac{5\pm\sqrt{53}}{2}}[/tex]