Solve the quadratic equation
X^2+3x-70=0
Answers
Answer:
X can either be 7, or -10. You can prove this by plugging in the numbers yourself :)
Step-by-step explanation:
Please mark as brainliest
Related Questions
Graph two lines whose solution is (1, 4) .
Answers
The lines y = x + 3 and y = 2 · x + 2 pass through point (1, 4) on Cartesian plane.
How to graph two lines that pass through a given point on Cartesian plane
In this problem we must graph two lines that pass through point (x, y) = (1, 4). Lines can be represented by equations of following form:
y = m · x + b
Where:
x - Independent variable.y - Dependent variable.m - Slopeb - InterceptWe must choose two slope-intercept combinations to generate two different lines: (x, y) = (1, 4)
Line 1
4 = m · 1 + b
4 = m + b
m = 1
4 = 1 + b
b = 3
y = x + 3
Line 2
4 = m · 1 + b
4 = m + b
m = 2
4 = 2 + b
b = 2
y = 2 · x + 2
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When full, a car's petrol tank holds k litres. After using 15 litres, the remaining petrol is enough for the car to travel 344 km. if a car travels 8km litre find the value of k
Answers
Answer:
k = 58
Step-by-step explanation:
k = 15 litres + remaining petrol
Remaining petrol:
The car travels 8 km/litre.
344 km / (8 km/litre) = 43 litre
The car uses 43 litres to travel 344 km.
k = 15 + 43
k = 58
Write an equation of the line that passes through (2, −4) and (0, −4).
Answers
Answer: x⁰⁄₂ + 0 = y or x⁰⁄₂ = y
Step-by-step explanation:
Equation of a line is mx+b=y
m=slope
The slope is ʸ⁄ₓ or in this case ⁰⁄₂
b=where the line cross the y-axis which is 0, when it is 0 there is no use in write +0 after the equation, as there is no difference, but it is your choice
Write a sine function that has an amplitude of 2, a midline of 4 and a period of 2/3
Answers
A sine function that has an amplitude of 2, a midline of 4 and a period of 2/3 is write as:
y = 2 sin 3πx + 4How to write the sine functionThe sine function is written considering the general formula in the form
sine function, y = A sin wx + b
where
A = amplitude
w = 2π / period
b = midline
In the problem the values available are
A = 2
b = 4
period = 2/3
substituting the known values
sine function, y = A sin wx + b
sine function, y = 2 sin (2π / 2/3) x + 4
sine function, y = 2 sin (3π) x + 4
sine function, y = 2 sin 3πx + 4
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Which graph represents the solution set for the system x + y ≥ 5 and - 3x + 2y ≤-2.
Answers
Therefore , the solution of the given problem of inequality comes out to be graph 2 shows the solution for this system.
What does inequality really mean?
In mathematics, an inequality is a linear connection or a collection of numbers even when there is no equal sign. Equity always comes after equilibrium. When two numbers are not equal, inequality exists. Between equality and inequality, there exist differences. The most common symbol was chosen because when parameters aren't the same or comparable (). Values can be compared using a variety of disparities, no matter how few or numerous they are.
Here,
Given :
=> x + y ≥ 5
and
=> - 3x + 2y ≤-2
So,
=> x ≥ 5- y
=> - 3(5- y) + 2y ≤-2
=> -15 + 3y + 2y ≤-2
=> 5y ≤ 13
=> y ≤ 13/5
and
=> x ≥ 5- 13/5
=> x ≥ 12/5
Therefore , the solution of the given problem of inequality comes out to be graph 2 shows the solution for this system.
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reflect triangle a in the x axis to give triangle b. then, rotate your triangle b 90° around the origin to give triangle c.
i have drawn the triangles but i don't know what the single transformation would be.
Answers
Triangle a is a shape that is formed by connecting three points.
What is triangle?Triangle is a geometric figure with three sides and three angles. It is one of the basic shapes in geometry. Triangles are either right, acute, or obtuse, depending on the size of each angle. The sum of the angles in a triangle is 180 degrees. Triangles can be classified into equilateral, isosceles, and scalene triangles, depending on the length of the sides. All three types of triangles have various applications in mathematics, physics and engineering.
In order to reflect triangle a in the x axis, triangle b must be a mirror image of triangle a. To achieve this, each point in triangle a must be reflected across the x axis. This is done by multiplying the y coordinate of each point in triangle a by -1. As a result, triangle b will have the same three points as triangle a, except that the y coordinates of each point in triangle b will be the opposite of what they are in triangle a.
After reflecting triangle a in the x axis to form triangle b, the next step is to rotate triangle b around the origin 90°. This can be achieved by finding the coordinates of each point in triangle b, then rotating each point around the origin. To do this, the x coordinates of each point in triangle b remain the same, while the y coordinates are multiplied by -1. As a result, triangle c will be formed as a 90° rotation of triangle b around the origin.
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B) Find the 95% confidence interval for the mean Sales on days that have 12 employees working.
C) Find the 95% prediction interval for Sales on a day with 12 employees working.
Answers
To find the 95% confidence interval for the mean Sales on days that have 12 employees working, we would need to know the population standard deviation and the sample size. The formula for a 95% confidence interval for the mean is:
(sample mean) ± (critical value) x (standard deviation / sqrt(sample size))
Without the information about sample size, standard deviation and sample mean, it's not possible to find the exact 95% confidence interval for the mean Sales on days that have 12 employees working.
Similarly, to find the 95% prediction interval for Sales on a day with 12 employees working, we would need to know the population standard deviation, sample size, and the sample mean. The formula for a 95% prediction interval for a single observation is:
(sample mean) ± (critical value) x (standard deviation of the mean) x sqrt(1 + (1/sample size))
Again, without the information about sample size, standard deviation and sample mean, it's not possible to find the exact 95% prediction interval for Sales on a day with 12 employees working.
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Select the correct answer. What is the general form of the equation of a circle with its center at (-2, 1) and passing through (-4, 1)? A. x2 + y2 − 4x + 2y + 1 = 0 B. x2 + y2 + 4x − 2y + 1 = 0 C. x2 + y2 + 4x − 2y + 9 = 0 D. x2 − y2 + 2x + y + 1 = 0
Answers
Answer:
I think it's b. when you have a negative and a negative it becomes a positive
As the sample size gets larger; what happens to the size of the correlation that is needed for significance?
It gets smaller
It also gets larger
There no consistent relationship between sample size and the critical value for a significant correlation
It stays constant
Answers
The degree of correlation required for significance reduces as the sample size increases. As a result, the correlation size needed to determine significance will be smaller.
The size of our sample and the sample size has an impact on the significance of a sample link. For results to be relevant for high sample sizes, a minimal correlation is required. Fewer correlations and linkages are required for significance as the sample size increases.
Each sampling distribution's variability declines with the sample number and gradually moves toward leptokurtic behavior. The sample distribution's range is smaller than the range of the initial population.
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Which function is the inverse of f(x) = 2/3 x³ + 1?
Answers
The inverse of f(x) = 2/3 x³ + 1 is f^-1(x) = (3/2)(x-1)^(1/3).
Which function is the inverse of f(x) = 2/3 x³ + 1?The inverse of a function f(x) is a function that reverses the operation of the original function.The inverse of a function f(x) = 2/3 x³ + 1 can be found by switching the x and y values and then solving for x.In other words, we can set y equal to the original equation and solve for x.
Let y = 2/3 x³ + 1
We can then subtract 1 from both sides to get y – 1 = 2/3 x³
We can then divide both sides by 2/3 to get (y – 1) • (3/2) = x³
Finally, we can take the cube root of both sides to get the inverse function:
x = (y – 1)¹/₃ • (3/2)¹/₃
Therefore, the inverse of f(x) = 2/3 x³ + 1 is x = (y – 1)¹/₃ • (3/2)¹/₃.
The inverse of f(x) = 2/3 x³ + 1 is denoted as f^-1(x). To find the inverse, we need to solve for x in terms of y, since the inverse of a function is a reflection of the function across the line y = x. To do this, we need to rearrange the equation, so that x is on the left side of the equation. We can start by subtracting 1 from both sides.This yields 2/3x³ = y - 1. We can then divide both sides by 2/3 to get x³ = (y - 1)/2/3. To solve for x, take the cube root of both sides. This yields x = cube root[(y - 1)/2/3]. Therefore, the inverse of f(x) = 2/3 x³ + 1 is f^-1(x) = cube root[(y - 1)/2/3].To learn more about the inverse of a function refer to:
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graph the line with slope 3 passing through the point (-4,-4)
Answers
The equation of the straight line passing through the point (-4, -4) with slope 3 can be written as y = 3x + 8.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is the line with slope 3 passing through the point (-4, -4)
The equation of the straight line passing through the point (-4, -4) with slope 3 can be written as follows. We can write -
y = 3x + c
For the point ( -4, -4), we can write -
- 4 = 3 x - 4 + c
c = - 4 + 12
c = 8
Therefore, the equation of the straight line passing through the point (-4, -4) with slope 3 can be written as y = 3x + 8.
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A hotel manager is adding a tile border around the rectangular pool. Let represent the width of the pool in feet. The length is
feet more than
times the width, as shown. Write two expressions that represent the perimeter of the pool.
LOADING... Click the icon for a diagram of the pool.
Question content area bottom
Part 1
Which expressions will give the perimeter of the pool? Select all that apply.
Answers
Substituting into the formula for the perimeter of a rectangle, the perimeter is [tex]2\left(n+3 \frac{1}{2} n +4 \frac{1}{2} \right)=2n+7n+9=\boxed{9n+9}=\boxed{9(n+1)}[/tex]
One cube has edge length 2 cm. A larger cube has edge length 5 cm. What is the ratio of the surface area of the smaller cube to the surface area of the larger cube in simplest form?
Answers
i think i onestly i think maybe 7 cm.
R varies directly with S and inversely with T. When s=5 and T=100, R=45. find the exact value of R when S= 13 and T=63
Answers
The value of R when S = 13 and T = 63 is 4361.5
What is Variation?A variation is a relation between a set of values of one variable and a set of values of other variables.
If R varies directly with S and inversely with T . This statement is represented in the form:
R = KS/T.
K is called proportionality constant
When R = 45 ,S = 13 and T = 100, then K=
K = RT/S
K = 45×100/5
K = 4500/5= 900
When S = 13and T = 63, then
R = KT/S
R = 900× 63/13
R= 56700/13
R = 4361.5
Therefore when S = 13 and T = 63, the value of R is 4361.5
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need someone to help do a flow proof
Answers
pls help I need to get a good grade
Answers
Answer:
3 1/2 cups of oats = 28 grams of fiber
Step-by-step explanation:
1 whole cup equals 8 grams (add halves for this)
8 x 3 = 24
24 + additional 4 from the remaining half makes 28 grams of fiber total.
Solve: e^(2x+5) = 4
mc001-1 .j pg
mc001-2 .j pg
mc001-3 .j pg
The Answer Is C, x=((ln4)-5)/(2)
Answers
The value of the logarithm equation is given by x = [ ln ( 4 ) - 5 ] / 4
What is Logarithm?The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm
The properties of Logarithm are :
log A + log B = log AB
log A − log B = log A/B
log Aⁿ = n log A
Given data ,
Let the logarithm equation be represented as A
Now , the value of A is
e⁽ ²ˣ ⁺ ⁵ ⁾ = 4 be equation (1)
On simplifying the equation , we get
Taking logarithm on both sides of the equation , we get
2x + 5 = ln ( 4 )
On simplifying the equation , we get
ln ( 4 ) = 2x + 5
Subtracting 5 on both sides of the equation , we get
2x = ln ( 4 ) - 5
Divide by 2 on both sides of the equation , we get
x = [ ln ( 4 ) - 5 ] / 4
Hence , the equation is x = [ ln ( 4 ) - 5 ] / 4
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ou are tasked to perform a linear regression using the least-squares method on the following (x,v) data points: (6,7) (8,9) (13,17) From the list of answers, pick the point that will be part of the regression line Hint: Find the equation of the line (slope, intercept) as you did in the regression assignment: Then for a (X1, Y1) given below; replace the value of X in the equation with the value of X1, and find out if you get the value of Y1. If you do (meaning the equivalence is true), that point is part of the regression line: (0,01) (9.11) (6,7)
(8,9)
Answers
The point that will be part of the linear regression line is (6,7).
The least-squares method is used to perform a linear regression on the given data points (6,7), (8,9), and (13,17). This method finds the line of best fit through the set of data points by minimizing the sum of the squares of the differences between the observed values and the predicted values from the line. To check whether a point is part of the regression line or not, we can substitute the x value of the point into the equation of the line and see if it gives the corresponding y value.
In this case, point (6,7) is part of the regression line because it satisfies the equation of the line.
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Complete the following statements with the correct words Note: Correct spelling is important. func a. If s(t) is a distance (or height or position) function, then s'(t) would be a velocity b. If c(x) is a cost function, then c'(x) would be called the cost x c. If y(t) is a velocity function, then v'(t) would be a acceleration function
Answers
Velocity, marginal cost, and acceleration are derivatives of displacement, cost, and velocity functions.
The velocity of an object or particle describes how far it has moved or displaced over time. If the function s(t) determines the position of an object, then the velocity is its first derivative. And, this is written as s'(t). The initial blank is therefore filled with velocity.
The cost difference between producing one more product or serving one more customer is known as the marginal cost. As a result, it can be calculated by dividing the change in overall costs by the change in energy output. So, the cost function's derivative is the marginal cost. If the cost function is c(x), then its derivative c'(x) is the marginal cost. The second blank is filled with marginal cost.
Acceleration is the time-dependent derivative of velocity. If v(t) is the velocity, then the acceleration is v'(t). The third blank is filled with acceleration.
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Three specimens of Alloys A, B, C containing copper and zinc are melted together to create an ingot containing 20% copper and 40% zinc. What are the percentages X and Y of copper and zinc in the alloy A?
Answers
Answer:
X=10%
Y=30%
Step-by-step explanation:
The required percentages X and Y of copper and zinc in alloy A are given as 10% and 13.34%.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
Percentage of copper in A = 1/2 [percentage of copper in ingot]
= 1/2 × 20% = 10%
Percentage of zinc in A = 1/3 [percentage of zincin ingot]
= 1/3 × 40% = 13.34%
Thus, the required percentages X and Y of copper and zinc in alloy A are given as 10% and 13.34%.
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The question seems to be incomplete,
Complete question.
Three specimens of Alloys A, B, and C containing copper and zinc are melted together to create an ingot containing 20% copper and 40% zinc. What are the percentages X and Y of copper and zinc in alloy A when copper is half of the copper in the ingot and zinc is 1/3 of the zinc in the ingot?
Can somebody please tell me how do we solve this? Thank you.
Answers
A repair man charges an inspection fee plus $20 dollars per hour. A customer with a coupon for 40% off the inspection fee pays $110 for a 4-hour repair. How many hours are worked when a customer pays $90 without a coupon?
Answers
Without a coupon and paying $90 the customer was attended for 2 hours
How to find the number of hours the customer paid forWhen a customer with a coupon for 40% off the inspection fee pays $110 for a 4-hour repair the inspection fee is calculated
customer's pay = (inspection fee * 40% off the inspection fee) + charge per hour * number of hours
40% off means the customer paid 60% of the fees
let the inspection fee be x
110 = (x * 0.60) + 20 * 4
110 = 0.6x + 80
110 - 80 = 4x
0.6x = 30
x = 50
a customer without a coupon
let the number of hours be y
customer's pay = inspection fee + charge per hour * number of hours
90 = 50 + 20 * y
90 = 50 + 20y
20y = 90 - 50
20y = 40
y = 2
the customer spent 2 hours
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Solve for C. Explain your steps for brainliest
Answers
Answer:
[tex]\sf \frac{2A-hb}{h}=c[/tex]
Step-by-step explanation:
[tex]\sf A=\frac{1}{2}h(b+c)[/tex]
First, multiply both sides by 2.
[tex]\sf 2A=h(b+c)[/tex]
Solve the brackets.
[tex]\sf 2A=hb+hc[/tex]
Subtract h b from both sides.
[tex]\sf 2A-hb=hc[/tex]
Divide both sides by h.
[tex]\sf \frac{2A-hb}{h}=c[/tex]
What is the prime factorization of 24? 2 x 6 3 x 8 22 x 4 23 x 3
Answers
Its pair factors are (1, 24), (2, 12), (3, 8), and (4, 6). The prime factorization of 24 gives 2 x 2 x 2 x 3 = 23 x 3, where 2 and 3 are the prime factors of 24. The sum of factors of 24 is 60. The correct answer is 24 = 2³×3
More prime factorization of 24:So, the prime factorization of 24 are 2 × 2 × 2 × 3 or 23 × 3, where 2 and 3 are the prime numbers. Learn more about factors and prime factors here with us in BYJU’S and also download BYJU’S – The Learning App for a better experience. What are the factors of 24? Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.
There are many ways to factorization 24 but we have to pick one:
There is a picture of what the solution is to factorization of 24.
Therefore, the correct answer is 24 = 2³×3
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the straight line l has equation x-y =3
the curve c has equation 3x^2 -y^2+xy=9
l and c intersect at the points p and q
find the coordinates of the midpoint of pq
Answers
Answer: The Midpoint of P and Q are (-0.5, -3.5)
Step-by-step explanation: To find the coordinates of the intersection points of the line and the curve, we can substitute the equation of the line into the equation of the curve and solve for x and y.
From the equation of the line: x - y = 3, we can see that y = x - 3
Substituting this into the equation of the curve:
3x^2 - (x-3)^2 + x(x-3) = 9
Now we can simplify and group
3x^2 - x^2 + 6x - 9 + x^2 - 3x = 9
3x^2 + 3x - 9 = 9
3x^2 + 3x = 18
3x(x+1) = 18
x(x+1) = 6
We can see that x = 2 and x = -3 are the solutions.
Substituting the x value back into the original equation of the line to find the y coordinate:
x = 2 => y = 2 - 3 => y = -1
x = -3 => y = -3 - 3 => y = -6
So the intersection points are (2,-1) and (-3,-6)
To find the midpoint of these two points, we take the average of their x and y coordinates:
x = (2 + -3) / 2 = -0.5
y = (-1 + -6) / 2 = -3.5
so the midpoint of the two intersection points is (-0.5, -3.5)
Answer:
Point, [tex](p,q)[/tex], is [tex](\frac{-1}{2} ,\frac{-7}{2} )[/tex].
Step-by-step explanation:
Given the equations [tex]x-y=3[/tex] and [tex]3x^{2} -y^{2} +xy=9[/tex] . Find where they intersect and find the midpoint, [tex](p,q)[/tex], of the two intersection points. To find find points of intersection, you can either set up these equations as a system and solve algebraically or you can use a graphing calculator to graph the functions and see where they cross.
I will set up these equations as a system of equations,
[tex]\left \{ {{x-y=3} \atop {3x^{2} -y^{2} +xy=9}} \right.[/tex]
I will solve the top equation for [tex]x[/tex], and substitute it into the bottom.
[tex]x-y=3 = > x=3+y[/tex]
Now substitute [tex]x=3+y[/tex] for x into the bottom equation. Solve for y,
=> [tex]3x^{2} -y^{2} +xy=9[/tex]
=>[tex]3(3+y)^{2} -y^{2} +(3+y)y=9[/tex]
=> [tex]3(y^{2}+6y+9) -y^{2} +y^{2}+3y =9[/tex]
=>[tex]3y^{2}+18y+27 -y^{2} +y^{2}+3y =9[/tex]
=> [tex]3y^{2}+18y+27+3y =9[/tex]
=> [tex]3y^{2}+21y+27 =9[/tex]
=>[tex]\frac{3y^{2}+21y+27 =9}{3}[/tex]
=>[tex]y^{2}+7y+9 =3[/tex]
=>[tex]y^{2}+7y+6 =0[/tex]
=> [tex](y+1)(y+6)=0[/tex]
=>[tex]y=-1[/tex] or [tex]y=-6[/tex]
Now plug these values for [tex]y[/tex] into [tex]x=3+y[/tex].
When y=-1:
[tex]x=3+(-1)[/tex]
=> [tex]x=2[/tex]
When y=-6:
[tex]x=3+(-6)[/tex]
=> [tex]x=-3[/tex]
The solution to the system (points of intersection) is [tex](-3,-6)[/tex] and [tex](2,-1)[/tex]. I also attached a graph of the intersection points.
Now to find the midpoint of the two intersection points, [tex]midpoint=(\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} )[/tex]
[tex](x_{1},y_{1}) = > (-3,-6)[/tex]
[tex](x_{2},y_{2}) = > (2,-1)[/tex]
=>[tex]midpoint=(\frac{-3+2}{2} ,\frac{-6+(-1)}{2} )[/tex]
=>[tex](\frac{-1}{2} ,\frac{-7}{2} )[/tex]
Thus, the point, [tex](p,q)[/tex], is [tex](\frac{-1}{2} ,\frac{-7}{2} )[/tex].
Which of the following choices is equivalent to 2 - x > 5(x - 4)?
A. 2- x > 5x + 20
B. 2- x > 5x - 4
C. 2- x > 5x - 20
D. 2- x > x - 20
Answers
Answer:
Step-by-step explanation:43
Answer: C
Because 5(x - 4) is equal to 5 times x and 5 times -4, which is 5x - 20
Convert:
63 decimeters 58 millimeters
= millimeters
Please help I don’t understand this
Answers
Answer:
6358 mm
Step-by-step explanation: multiply the value of decimeters by 100,
we get 6300 mm and then we add the 58 mm in 6300 mm.
100 POINTS ANSWER RIGHT!11
Find the slope of the line.
Answers
Rollins read books create expression
Answers
When Rollins read books it is a expression in which the number of books he has completed is, N = P/( a × b )
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.
For example, 2x+3
In given problem,
we have to make relationship between number of books he has completed, how many pages he can read per minute and daily how many minutes he reads book.
suppose,
the number of books he has completed = N
pages he can read per minute = a
time spent on reading per day = b
Total page in a book = P
N = P/( a × b )
Hence, The expression is N = P/( a × b )
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when you combine all the baking soda recipes from the recipes that use exactly 1 1/4 teaspoons how much baking soda will you have in all
Answers
Answer:
When you combine all the baking soda recipes from the recipes that use exactly 1 1/4 teaspoons, you will have the same amount of baking soda that was used in all the recipes.
Step-by-step explanation:
In other words, if you have X number of recipes that each use 1 1/4 teaspoons of baking soda, you will have X*1.25 teaspoons of baking soda in total.
It is important to notice that the question is asking about the amount of baking soda used in those exact recipes that calls for 1 1/4 teaspoons and not about the total amount of baking soda you would end up with after making all the recipes. Therefore, the total amount of baking soda you would have after making all the recipes would depend on how much was used in each recipe and how many were made .