We have the following:
\(\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ a=5 \\ b=0 \\ c=-80 \end{gathered}\)replacing:
\(\begin{gathered} x=\frac{-0\pm\sqrt[]{0^2-4\cdot5\cdot-80}}{2\cdot5}=\frac{\pm\sqrt[]{1600}}{10}=\frac{\pm40}{10}=\pm4 \\ x_1=4 \\ x_2=-4 \end{gathered}\)Please look at the photo. Thank you!
The zeros with each multiplicity are given as follows:
Multiplicity one: x = 6.Multiplicity two: x = 11.Multiplicity three: x = -6 and x = -5.How to obtain the multiplicities?The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.
Considering the linear factors of the function in this problem, the zeros are given as follows:
(x + 6)³ -> zero at x = -6 with multiplicity of 3.(x - 11)² -> zero at x = 11 with multiplicity of 2.x - 6 -> zero at x = 6 with multiplicity of 1.(x + 5)³ -> zero at x = -5 with multiplicity of 3.More can be learned about the Factor Theorem at brainly.com/question/24729294
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which of these is an disadvantage of CT scan te
Answer:
It cannot be used to assess individual renal function or degree of obstruction. Sulfadiazine stones are also difficult to visualize on CT because of relatively low attenuation. It is relatively expensive.
Find the interest.
. 750$, 6.5%, 2years
Answer:
simple interest=$97.50.
compound interest= $100.668
Step-by-step explanation:
Given:
Principal (P) = $750
Rate (R) = 6.5% (in decimal form, 0.065)
Time (T) = 2 years
Simple Interest = Principal*Rate*Time
Using the formula, the simple interest is calculated as follows:
Simple Interest = $750*0.065*2 = $97.50
Therefore, the simple interest for $750 with a 6.5% interest rate over 2 years is $97.50.
Again:
Compound Interest = Principal*(1 + Rate)^(Time)-Principal
Using the same values as above, the compound interest can be calculated as follows:
Compound Interest = $750*(1+0.065)^(2)-$750
= $750*1.065^2 -$750
= $750 × 1.134225 - $750
= $850.66875-$750
= $100.668
Therefore, the compound interest for $750 with a 6.5% interest rate over 2 years is $100.668
Solve the system of equations.
2x-6y=8
x-3y=9
Plz help I’m superrr confused
Answer:
There is no solution to this system of equations. The lines do not intersect.
Step-by-step explanation:
Step 1 : See if either x or y can be eliminated.
2x-6y=8
2(x-3y=9)
2x - 6y = 8
2x - 6y = 18
There is no solution to this system of equations as they don't intersect. Notice how we can't cancel out the x or y without canceling the other unknown variable?
Proof : Rearranging the equations above into y = mx + b form, we get
Equation 1 : y = 1/3x - 4/3
Equation 2 : y = 1/3x - 3
A system of equations has no solution when the slopes are the same and both equations have different y intercepts.
Question 8(Multiple Choice Worth 2 points)
(Writing Two-Step Equations MC)
A new gaming chair costs $455.95. You have already saved $155.95 and earn $37.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
37.5 + 155.95w = 455.95; w = 8
37.5w + 155.95 = 455.95; w = 8
37.5w − 155.95 = 455.95; w = 16
37.5w − 455.95 = 155.95; w = 16
37.5w + 155.95 = 455.95; where w = 8; signifies the number of weeks required to babysit the business in order to purchase the gaming chair.
How do equations work?A mathematical formula that connects two expressions with the equals sign (=) expresses the equality of the two expressions. For instance, in English, an equation is any properly stated formula that consists of two expressions linked by the equals sign, whereas in French, an equation is described as containing one or more variables. To solve a variable equation, identify the values of the variables that cause the equality to hold true. The answer is known as the values of the variables that must satisfy the equality.
Equations can be categorized as identities or conditional equations.
w = (455.95-155.95)/(37.50)
=300/37.50
=8
So, number of weeks = 8
As a result, w = 8 and 37.5w + 155.95 = 455.95 is the solution.
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I need help on this problem please?
Answer:
yes ur friend is correct
Step-by-step explanation:
because the value of x .
The diagram only shows that angles M and B are supplementary ( add up to 180 degrees) and that angel 4x is adjacent to angel M.However, there is no information about the measure of angle B or angel M, so we cannot determine the value of x
Delivery of 5 large boxes, 3 small boxes; total weight 135 kilograms. And 7 large boxes, 9 smaller boxes total weight,279 kilograms. How much does each box weigh?
The weight of each of the boxes are:
Large box = 15.75 kg
Small box = 18.75 kg
How to solve simultaneous Equations?Let the weight of each large box be x
Let the weight of each small box be y.
Thus, if 5 large boxes and 3 small boxes have a total weight of 135 kilograms, then we have the equation:
5x + 3y = 135 -------(1)
Thus, if 7 large boxes and 9 small boxes have a total weight of 279 kilograms, then we have the equation:
7x + 9y = 279 ------(2)
Multiply eq 1 by 3 and eq 2 by 1 to get:
15x + 9y = 405 -----(3)
Subtract eq 2 from eq 3 to get:
8x = 126
x = 126/8
x = 15.75 kg
Thus:
5(15.75) + 3y = 135
3y = 135 - 78.75
3y = 56.25
y = 18.75 kg
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Calculate 50% of 7.9 giving your answer to one decimal place?
Answer:
4.0
Step-by-step explanation:
50% means half.
Divide by 2.
7.9 ÷ 2 = 3.95.
Round to the tenths place.
4.0
I hope this helps!
pls ❤ and mark brainliest pls!
Find the length of the diagonal of a rectangle. Round your answer to nearest tenth.
Answer:
19.2m
Step-by-step explanation:
"Slice" the rectangle into two right triangles (slice along the diagonal). Now you can use the Pythagorean theorem to calculate the length of the diagonal:
\(a^{2} +b^{2} =c^{2} \\12^{2}+15^{2} =c^{2} \\144+225=c^{2} \\\sqrt{369} =\sqrt{c^{2} }\\19.2m =c\)
If the random variable x is normally distributed with a mean equal to .45 and a standard deviation equal to .40, then P(x ≥ .75) is:
If the random variable x is normally distributed with a mean equal to 0.45 and a standard deviation equal to 0.40, then P(x ≥ .75) is 0.9227.
What is a Z-score?A z-score describes the position of a raw score in terms of its distance from the mean when measured in standard deviation units. The z-score is positive if the value lies above the mean and negative if it lies below the mean.
Given the problem above, we need to find what the z-score is when P(x ≥ .75).
The formula for calculating a z-score is given by:
\(Z=\dfrac{\text{x}-\mu}{\sigma}\)
Where:
x is the value of 0.75\(\mu\) is the mean of 0.45And \(\sigma\) is the standard deviation of 0.40Now,
\(Z=\dfrac{\text{x}-\mu}{\sigma}\)
\(Z=P(\text{x} \geq 0.75) = \huge \text(\dfrac{P(Z \geq (0.75 - 0.45)}{0.40}\huge \text)\)
\(Z= P\huge \text (\dfrac{Z \geq0.30}{0.40}\huge \text)\)
\(Z=P(Z \geq 0.75) = 1 - P(Z < 0.75)\)
\(Z=1 - 0.077337\)
\(Z\thickapprox 0.9227\)
Therefore, the z-score of P(x ≥ .75) is 0.9227.
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Which expression can be used to find the number of liters in 15 quarts?
The expression that can be used to find the number of liters in 15 quarts is 15 quarts/1 * 0.95 liters/1 quart
How to determine the expression?The volume is given as:
Volume = 15 quarts
In standard unit of conversion, we have:
1 quart = 0.95 liters
So, the equation becomes
Volume = 15 quarts/1 * 0.95 liters/1 quart
Hence, the expression that can be used to find the number of liters in 15 quarts is 15 quarts/1 * 0.95 liters/1 quart
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Last year it rained 23% of the days in a small town.
A) 23/100 B)1/23 C) 23/1000
D) 23/30
Answer: It would be A since percentage is out of 100
Can you please help me out with a question
Length = 7.679 units
Explanations:The length of an arc is given by the formula:
\(\text{Length = }\frac{\theta}{360}\times\text{ 2}\pi r\)\(\begin{gathered} \text{The radius, r = 4} \\ \theta=110^0 \\ \pi=\text{ 3.14159} \end{gathered}\)Substitute θ = 110, and r = 4 into the given formula:
\(\begin{gathered} \text{Length = }\frac{110}{360}\times2\times3.14159\times4 \\ \text{Length = }7.679 \end{gathered}\)Length = 7.679 units
Which best describes the relationship between the lines with equations 2x – 9y = 1 and x + 8y = 6?
A. perpendicular
B. neither perpendicular nor parallel
C. parallel
D. same line
9514 1404 393
Answer:
B. neither perpendicular nor parallel
Step-by-step explanation:
If the lines were perpendicular, the coefficients would be swapped and one negated. (You would have 8x -y = c, or 9x +2y = c in the system.)
If the lines were parallel, the coefficients in the two equations would only differ by a common factor. (Both equations would reduce to 2x -9y = c, or x +8y = c.)
The lines are not the same line (coefficients are different).
So, the only reasonable description is ...
neither perpendicular nor parallel
f(x)=x^2. What is g(x)?
Answer:
D, g(x) = 1/4 x^2
Step-by-step explanation:
You can try plugging in the x and y values into each equation. The answer to this would be D, where if you plug in 2 as the x value, you get 1/4 * 4 which equals 1. This also makes sense because 2x would have a narrower curve while 1/2x would have a wider curve.
=?
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21090 (x -1 ) + 109.07 = 1
)
The value of "x" which will satisfy the equation [{21090(x -1 ) + 109.07 } = 1] is 1.01.
As per the question statement, we are provided with an equation \([{21090(x -1 ) + 109.07 } = 1]\).
We are required to solve the above mentioned equation for "x", such that the value of x when substituted in the equation, satisfies the same.
To solve this question, we will simply use the methods of rearranging and opening up of brackets, as shown below.
\([{21090(x -1 ) + 109.07 } = 1] \\or, 21090x - 21090+109.07=1\\or, 21090x - (21090-109.07)=1\\or, 21090x - 20980.93=1\\or, 21090x=(1+20980.93)\\or, 21090x=20981.93\\or,x=\frac{21090}{20981.93}\\or,x=1.00515\\or,x=1.01\)
Therefore, the value of "x" which will satisfy the equation
[{21090(x -1 ) + 109.07 } = 1] is 1.01.
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Find the length of each side of the triangle. Check that the perimeter is equal to 20 inches.
Answer:
there is no picture
Step-by-step explanation:
Answer:
it depends on what triangle it is. if it an equilateral then the answer is 6.7 (20 divided by 3)
Step-by-step explanation:
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what is AE
AB=10
AE=2a + 10
ED=x + 3
CD=4
Enter you answer In the box
The given values into the equation AE = 2a + 10. Therefore, The value of AE is 3 - x.
To find the value of AE, we can substitute the given values into the equation AE = 2a + 10.
Given:
AB = 10
AE = 2a + 10
ED = x + 3
CD = 4
Since AB is a segment on the line, it can be divided into AE and ED. Therefore, AB = AE + ED.
We know that AB = 10 and CD = 4. So, if we subtract CD from AB, we get AE + ED = 10 - 4.
AE + ED = 6.
Now, we can substitute the value of ED, which is x + 3, into the equation: AE + x + 3 = 6.
To find the value of AE, we need to isolate it on one side of the equation. Let's subtract x and 3 from both sides:
AE = 6 - x - 3.
Simplifying further, we get;
AE = 3 - x.
Therefore, the value of AE is 3 - x.
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3. What is the length of AB?
pls help, dont put link pls
Please look at the graphs in the photo. Thank you!
(a). The graph of y = -f(x) is shown in the image below.
(b). The graph of y = g(-x) is shown in the image below.
How to draw the graph of the transformed functions?By reflecting the parent absolute value function g(x) = |x + 2| - 4 over the x-axis, the transformed absolute value function can be written as follows;
y = -f(x)
y = -|x + 2| - 4
Part b.
In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = rise/run
Slope (m) = -2/4
Slope (m) = -1/2
At data point (0, 5) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 5 = -1/2(x - 0)
g(x) = -x/2 + 5, -4 ≤ x ≤ 4.
y = g(-x)
y = x/2 + 5, -4 ≤ x ≤ 4.
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AB = 3(2x + 7), BC = 2x - 3, AC = 6x + 6
Answer:
^
Step-by-step explanation:
What's the most useless talent you have?
Knowing geometry is my useless talent
twisting my body 360 degrees
Need to solve for x
X+6=2x+5
Answer:
x=1
Step-by-step explanation:
x+6=2x+5
move the x to the right-hand side, and the 5 to the left-hand side (the sign will also change from a + to a -
6-5=2x-x
therefore, you will get:
x=1
Answer:
Step-by-step explanation:
x = 1
x + 6 = 2x + 5
6 - 5 = 2x - x
-1 = x
x = 1
--------------
check
1 + 6 = 2 × 1 + 5 (remember pemdas)
7 = 7
the answer is good
Find the missing coordinates such that the three vectors form an orthonormal basis for R3:
Coordinates is computed that:
a = 0
b = -0.8
c = 0
d = 0
e = 0
Calculating the missing coordinate in such a way that the three vectors for R3 are orthogonal:
\(\left[\begin{array}{ccc}0.6&a&b\\0.8&c&0.6\\1&-1&e\end{array}\right]\)
Any two vectors' dot product is zero and their norm is one on an orthogonal basis.
⇒ (-0.6, a, b) (0.8, b, c, -0.6)
⇒ -0.48 + ac - 0.6b = 0 → (1)
Similarly,
(0.8, c, -0.6) (d, -1, e)
⇒ 0.8d - c - 0.6c = 0 → (2)
Similarly,
(-0,6, a, b) (d, -1, e)
⇒ -0.6d - a + be = 0 → (3)
First Norm:
(0.6)² + a² + b² = 1
⇒ 0.36 + a² + b² = 1
⇒ a² + b² = 0.64 → (4)
Second Norm:
(0.8)² + c² + (-0.6)² = 1
⇒ 0.64 + c² + 0.36 = 1
⇒ c² + 1 = 1
⇒ c = 0
Now from equation (1), we can compute that:
(-0.48 + a) * (0 - 0.6b) = 0
⇒ -0.48 - 0.6b = 0
⇒ - (0.48 + 0.6b) = 0
⇒ 0.6b = -0.48
⇒ b = -0.48 / 0.6 = -0.8
∴ b = -0.8
From equation (4) we can compute that:
a² + b² = 0.64
⇒ a² + (-0.8)² = 0.64
⇒ a² = 0
∴ a = 0
Third Norm:
d² + 1 + e² = 1
d² + e² = 0 → (5)
From equation (3) we can infer that:
-0.6d - 0 + (-0.8e) = 0
⇒ -0.6d = 0.8e
⇒ d = -0.8e / 0.6
∴ e = -0.75d
Now we'll put this value in equation (5):
d² + (-0.75d)² = 0
⇒ d² + 0.5625d² = 0
⇒ d² (1 + 0.5625) = 0
⇒ d = 0
∴ e = 0
Therefore,
\(\left[\begin{array}{ccc}-0.6&0&-0.8\\0.8&0&-0.6\\0&-1&0\end{array}\right]\)
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Please explain how to do it too ill give brainliest
Answer:
x = 90
Step-by-step explanation:
The given diagram shows a circle with intersecting chords, KM and JL.
To find the value of x, we can use the Angles of Intersecting Chords Theorem.
According to the Angles of Intersecting Chords Theorem, if two chords intersect within a circle, the angle formed at the intersection point is equal to half the sum of the measures of the arcs intercepted by the angle and its corresponding vertical angle.
Let the point of intersection of chords KM and JL be point P.
As the chords are straight lines, angle x° forms a linear pair with angle JPM.
Note: We cannot use the Angles of Intersecting Chords Theorem to find the value of x directly, since we have not been given the measures of the arcs KJ and ML. Therefore, we need to use the theorem to find m∠JPM first.
From inspection of the given diagram:
\(m\overset\frown{JM}=30^{\circ}\)\(m\overset\frown{LK}=(2x - 30)^{\circ}\)Using the Angles of Intersecting Chords Theorem, we can calculate the measure of angle JPM (shown in orange on the attached diagram):
\(\begin{aligned}m \angle JPM &=\dfrac{1}{2}\left(m\overset\frown{JM}+m\overset\frown{LK}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+(2x-30)^{\circ}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+2x^{\circ}-30^{\circ}\right)\\\\&=\dfrac{1}{2}\left(2x^{\circ}\right)\\\\&=x^{\circ}\end{aligned}\)
As angle JPM forms a linear pair with angle x°, the sum of the two angles equals 180°:
\(\begin{aligned}m \angle JPM+x^{\circ}&=180^{\circ}\\\\x^{\circ}+x^{\circ}&=180^{\circ}\\\\2x^{\circ}&=180^{\circ}\\\\\dfrac{2x^{\circ}}{2}&=\dfrac{180^{\circ}}{2}\\\\x^{\circ}&=90^{\circ}\\\\x&=90\end{aligned}\)
Therefore, the value of x is 90, which means that the two chords intersect at right angles.
Consider the following equation.
x+2y=4
Step 2 of 2 : Determine the missing coordinate in the ordered pair (?,12) so that it will satisfy the given equation.
pleas
HELP IMMEDIATELY
Answer:
144ft^3
Step-by-step explanation:
To start, we have your formula: \(V=\frac{1}{2} (bh) (l)\)
b = base length of the triangle.
h = height of the triangle.
l = length of the prism
Fill in for each of those values:
\(V = \frac{1}{2} (6x6)(8)\)
\(V=\frac{1}{2} (36)(8)\)
\(V=(18)(8)\)
\(V=144\)
Your answer, because it is a 3D shape, should be cubed, so:
\(V=144ft^{3}\)
I need help!!!!!!!!!
Answer:
its b4 + 7b3 + 4b2 + b5 + 7b4+ 4b3= b5+8b4+11b3+4b2
Answer:
When multiplying, add the exponents, (example) remember if there is "7b" the exponent is one.
Multiply b^2 * b^3 = b^5 (add the exponent 2 + 3 = 5)
Multiply 7b * b^3 = 7b^4 (the exponent of 7b is one, add 1 + 3 for the exponent to become 4)
Multiply 4 * b^3 = 4b^3 (4 doesn't have a variable, the exponent will be 3)
b^2 * b*2 = b^4 (add exponents)
7b * b^2 = 7b^3 (add the exponents 1 + 2)
4 * b^2 = 4b^2
b^2 + 7b + 4
b^3 b^5 + 7b^4 + 4b^3
+
b^2 b^4 + 7b^3 + 4b^2
b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2
\(b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2\)
b^5 + 8b^4 + 11b^3 + 4b^2Help ASAP!!!!
Solve for X. Round to the nearest hundredth if necessary.
Answer:
11.47Step-by-step explanation:
Given : A right triangle
To do : Solve for x
Solution,
\(cos \: 55 = \frac{x}{20} \) ( by definition of cos function, adjacent / hypotenuse )
\(0.5736 = \frac{x}{20} \)
multiply both sides of the equation by 20
\((0.5736) \times 20 = x\)
Calculate the product
\(11.471 = x\)
Swipe both sides of the equation
\(x = 11.471\)
Round answer to nearest hundredth
\(x = 11.47\)
Hope this helps...
Best regards!!
Zoie is painting a picture that is 15 by 27 inches. She plans to frame it in a frame x inches wide.
1) Write a polynomial that will be the area of the framed picture.
2) What will be the area of the picture with the frame if x=3?
The polynomial area of the framed picture is (27 + 2x) * (15 + 2x) and the value is 693 square units
What are areas?The area of a shape is the amount of space on the shape
For most regular quadrilaterals, you multiply the side lengths to determine the area
How to determine the area of the framed picture?The given parameters are
Width = 15
Length = 27
Also, we have
Length of the frame = x
This means that the area of the framed picture is
Area = (Length + 2 * Length of the frame) * (Width + 2 * Length of the frame)
Substitute the known values in the above equation
Area = (27 + 2x) * (15 + 2x)
The value of the area when x = 3In (a), we have
Area = (27 + 2x) * (15 + 2x)
When x = 3, we have
Area = (27 + 2 x 3) * (15 + 2 x 3)
Evaluate
Area = 693
Hence, the area is 693 square units
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