Which of the following equations could be used to solve the given equation?
9x + 26 + 7x - 17 = 2x + (-3x) + 5x
16x + 9 = 4x
16x + 11 = 4x
16x + 9 = 0
Answer:
16x + 9 = 4x
Step-by-step explanation:
9x+7x+26-17=2x-3x+5x
16x+9=4x
in the figure below, points d, e, and f are the midpoints of the sides of abc. suppose ac =72 df = 34 and ab =48. find the following lengths
Applying the triangle midsegment theorem, the following lengths are calculated as:
BC = 68
DE = 36
CE = 34
What is the Triangle Midsegment Theorem?According to the triangle midsegment theorem, the midsegment length is half the third side of a triangle.Triangles have three midsegments.Given:
AC = 72
DF = 34
AB = 48
Find BC:
BC = 2(DF)
SubstituteBC = 2(34)
BC = 68
Find DE:
DE = 1/2(AC)
DE = 1/2(72)
DE = 36
Find CE:
CE = 1/2(BC)
CE = 1/2(68)
CE = 34
Thus, applying the triangle midsegment theorem, the following lengths are calculated as:
BC = 68
DE = 36
CE = 34
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Is r = 6 a solution to the inequality below? 10 < r
Answer:
No
Step-by-step explanation:
10 is not less than 6, so 10 < r when r=6 is not true.
The water usage at a car wash is modeled by the equation W(x) = 5x3 + 9x2 − 14x + 9, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours. Write a function, C(x), to model the water used by the car wash on a shorter day. C(x) = 5x3 + 7x2 − 14x − 6 C(x) = 4x3 + 7x2 − 14x + 6 C(x) = 4x3 + 7x2 − 14x − 6 C(x) = 5x3 + 7x2 − 14x + 6
The committee spends $462 on costumes for 24 people. Each costume costs the same amount of money.
How much did each costume cost, in dollars?
Answer:
Step-by-step explanation: 462 Divided by 24 = 19.25$
Proof: 19.25 x 24 = 462
Answer: 19.25$
I need to find x and y
Using the same-side interior angles theorem,
\(8x+30+6x+24=180 \\ \\ 14x+54=180 \\ \\ 14x=126 \\ \\ \boxed{x=9}\)
Using vertical angles,
\(6(9)+24=10y+2 \\ \\ 78=10y+2 \\ \\ 10y=76 \\ \\ \boxed{y=7.6}\)
16-(-10) need help plz
Write an equation for the polynomial graphed below
The equation of the polynomial is P(x) = 1/27(x + 3)(x + 2)(x - 1)(x - 3)^2
How to determine the equation of the polynomialFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following readings:
A root of multiplicity 1 at x = -3 A root of multiplicity 1 at x = -2A root of multiplicity 1 at x = 1A root of multiplicity 2 at x = 3y-intercept = 2A polynomial is represented as
P(x) = a * (x - zero)^multiplicity
Using the above as a guide, we have the following:
P(x) = a * (x + 3)(x + 2)(x - 1)(x - 3)^2
The y-intercept is 2
So, we have
a * (0 + 3)(0 + 2)(0 - 1)(0 - 3)^2 = 2
This gives
a = -1/27
Hence, the expression is P(x) = 1/27(x + 3)(x + 2)(x - 1)(x - 3)^2
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What is 66 round to the nearest hundredth
Answer:
100
Step-by-step explanation:
66 is closer to 100 than to 0, therefore 66 rounds up to 100.
A sight-seeing tour bus can carry 68 people. If 330 people want to go sight-seeing on the bus, what is the minimum number of trips the bus will have to make to accommodate everyone?
The minimum number of trips the bus will have to make to accommodate everyone is 5.
To find the minimum number of trips the bus needs to make, we divide the total number of people by the capacity of the bus.
1. Divide the total number of people (330) by the capacity of the bus (68):
330 / 68 = 4.85 (rounded to the nearest whole number)
2. The result is approximately 4.85, which means that 4 trips will not be enough to accommodate everyone.
3. Since we can't have a fraction of a trip, we need to round up to the nearest whole number to ensure that everyone is accommodated.
4. Therefore, the minimum number of trips the bus will have to make is 5, as it will require 5 full trips to transport all 330 people.
It's important to note that on the fifth trip, the bus will not be completely full, as only 10 people will be left to transport. However, this is the minimum number of trips needed to ensure that everyone can go sight-seeing on the bus.
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Solve by factoring:
x3+3x2+9x+27=0
Answer:
x = −3,3i, −3i
Step-by-step explanation:
PLSS HELP MEEE ITS MATH ND IDRK HOW TO ANSWER ITT
Answer: D is the answer. trust me.
Step-by-step explanation:
The problem that could be solved using the equation 10x+5=35 is option D: After a $5 discount, an order of 10 items cost $35. How much did each item cost?
To solve this problem, we can use the equation 10x + 5 = 35, where x represents the cost of each item. The $5 discount reduces the total cost of the 10 items by $5, so the total cost of the 10 items before the discount would be 10x. Therefore, we can set up the equation:
10x + 5 = 35
Subtracting 5 from both sides, we get:
10x = 30
Dividing both sides by 10, we get:
x = 3
So, each item cost $3 before the discount.
Answer:
A
Step-by-step explanation:
Evaluate the definite integral of sin^5(x)dx from 0 to pi/2.
Step-by-step explanation:
The definite integral of sin^5(x)dx from 0 to pi/2 can be evaluated using the method of substitution.
Let u = sin(x), then du = cos(x)dx
The integral becomes:
∫sin^5(x)dx = ∫u^5du from 0 to sin(π/2)
= (u^6)/6 evaluated at sin(π/2) and 0
= (sin^6(π/2))/6 - 0
= (1^6)/6
= 1/6
So, the definite integral of sin^5(x)dx from 0 to pi/2 is equal to 1/6.
How much would it cost to furnish a square room of 5m at N5.00 per square metre
(I need this answer before 6 march)
It would cost N125.00 to furnish a square room of 5m at N5.00 per square meter.
Describe the square meter.A square meter is a unit of measurement that denotes the surface area of a two-dimensional object or surface that is one metre long and one meter broad. It is frequently used to determine the dimensions of rooms, structures, and other areas as well as the surface area of land or other objects. The imperial method of measurement converts one square metre into 10.764 square feet. Science, engineering, and other fields frequently utilise the square metre, a core unit of the International System of Units (SI).
The area of the room is:
Area = 5m x 5m = 25 square meters
Then, we multiply the area by the cost per square meter:
Cost = 25 square meters x N5.00 per square meter = N125.00
Hence, it would cost N125.00 to furnish a square room of 5m at N5.00 per square meter.
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2
Let g(x) = x + 4x-7.
What is g(x) in graphing form?
(x + 2) - 7 = 4
O g(x) = (x + 2)²-7
Onone of the answer choices
x² + 4x-7=0
O g(x) = (x + 2)² - 11
The graphing form of the function g(x) is: C) none of the answer choices.
The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.
Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:
a = 1 (coefficient of x^2)
b = 4 (coefficient of x)
c = -7 (constant term)
Therefore, the graphing form of the function g(x) is:
C) none of the answer choices
None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.
In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.
The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C
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Based on a sample of 150 textbooks at the store, you find an average of 70.69 and a standard deviation of 29.6. The point estimate is: Incorrect (to 3 decimals) The 99 % confidence interval (use z*) is:______
Answer:
Step-by-step explanation:
Given that:
The sample size = 150
The sample mean = 70.69
The standard deviation = 29.60
The sample mean is equal to the point estimate of the population = 70.69
At 99% confidence interval level is:
∝ = 1 - 0.99
∝ = 0.01
The critical value:
\(Z_{\alpha/2} = Z_{0.01/2} \\ \\ Z_{0.005} = 2.58 \ using \ Z \ tables\)
The Margin of error = \(Z_{\alpha/2} \times \dfrac{\sigma}{\sqrt{n}}\)
\(= 2.58 \times \dfrac{29.6}{\sqrt{150}}\)
= 2.58 × 2.4168
≅ 6.235
At 99% confidence interval; the estimate of the population mean lies within the interval:
= \(\overline x - E < \mu \ < \overline x + E\)
= 70.69 - 6.235 < μ < 70.69 + 6.235
= 64.455 < μ < 76.925
= (64.455 , 76.925 )
Instructions
Is the point (21) a solution to the equations; y = -1/4x + 3/2 and y=-x+ 3? Show your work.
Answer:
yes
Step-by-step explanation:
youre trying to find when -1/4x + 3/2 = -x+ 3
so if you set it up like that and then solve for x you get 2
then, you know that 2 is your x value so just plug in x into one of the equations to get the y value
(i used -x+3 bc its easier)
-2+3=y
y= 1
so your solution is (2,1)
also heres the graph
One shirt at H&M cost $7. what is the cost of 40 shirts
Answer:
$280
Step-by-step explanation:
7•40=$280
A system of equations is given.
Equation 1: 4x − 6y = 10
Equation 2: 9x + 2y = 7
Explain how to eliminate x in the system of equations.
Step-by-step explanation:
To eliminate x in the system of equations:
1. Multiply Equation 1 by 9 and multiply Equation 2 by -4, this gives:
Equation 1: 36x -54y = 90
Equation 2: -36x - 8y = -28
2. Add the two equations together to eliminate x:
(36x - 54y) + (-36x - 8y) = 90 - 28
Simplifying, we get:
-62y = 62
3. Solve for y:
y = -1
4. Substitute y = -1 into one of the original equations, say Equation 1:
4x - 6(-1) = 10
Simplifying, we get:
4x + 6 = 10
5. Solve for x:
4x = 4
x = 1
Therefore, the solution to the system of equations is x = 1 and y = -1. We can check that these values are correct by substituting them back into the original equations and verifying that they satisfy both equations.
Helpppppp meeee please and thank you
Find the area of the shaded region.
Please anyone help me!
Thank you
Answer:
7.26
Step-by-step explanation:
Here
Diameter=2m
Length =2.6m
Breadth=4m
Now
Area of circle=(22*2*2*4)/7
=22/7
=3.14m^2
again
Area of rectangle= lb
=2.6m*4m
=10.4m^2
So
Area of the shaded region is 10.4m^2-3.14m^2
=7.26m^2
The answer is 7.26 m².
To find the shaded area, subtract the area of the circle from the area of the rectangle.
(2.6 × 4) - (3.14 × 1²)10.4 - 3.147.26 m²What is 7/8 expressed as a percent? Enter your answer as a decimal.
Answer:
87.5% because calculator
Step-by-step explanation:
;)
Answer:
The Answer Is: D..! ) 0.875
Step-by-step explanation:
I Hope This Helped! Have a Great Day!
1. Given:pi x is prime.q: x is evenWhat is the truth value of p^ when x is replaced by 2?O png is falseOp^g is sometimes trueNot enough information is provided.O png is true
Okay, here we have this:
Considering the following table:
We know that P is true because 2 is prime, and we also know that Q is true because 2 is even, this mean that p^q is also true.
Finally we obtain that the correct answer is the last option.
true/false. when the population variance is not known (i.e., must be estimated from data), we use a z-statistic instead of a t-statistic for our hypothesis tests.
The given statement " when the population variance is not known (i.e., must be estimated from data), we use a z-statistic instead of a t-statistic for our hypothesis tests. " is false. Because in distribution of sample means, population variance is unknown.
When the population variance is not known and must be estimated from the data, we use a t-statistic instead of a z-statistic for our hypothesis tests.
This is because the distribution of the sample means follows a t-distribution when the population variance is unknown, whereas it follows a standard normal distribution (z-distribution) when the population variance is known.
The t-distribution has fatter tails than the z-distribution to account for the extra uncertainty introduced by estimating the population variance from the sample.
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show that the set of vectors in is orthogonal and (b)normalize the set to produce an orthonormal set.
An orthonormal set is a set of orthogonal unit vectors.
Normalization is the process of making unit vectors.
Orthonormal VectorsA set of vectors in which each vector is orthogonal to every other vector in the set is called an orthogonal set of vectors.
Two vectors are orthogonal when their dot product equals zero.
An orthonormal set is one in which each vector has length 1 and is orthogonal.
The process of creating a vector of length 1 in the same direction of the original vector is called "normalization".
An orthonormal set of vectors that is a basis of a vector space is quite useful. We can use the Gram-Schmidt process to transform a basis of a vector space (which may not be orthogonal) into an orthonormal basis.
To normalize vectors to produce an orthonormal set of vectors, we calculate the length of the vector and divide the vector by its length, to obtain a unit vector.
Since the question asked about "how to normalize vectors to produce an orthonormal set" that implies that the vectors already form an orthogonal set.
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The given question is incomplete,
So , I take another question, The question is:
How to normalize vectors to produce an orthonormal set?
If x = 4 cm, what is the surface area of the geometric shape formed by this net?
A.
70 cm2
B.
30 cm2
C.
25 cm2
D.
96 cm2
a rectangle has a length of 22 feet less than 6 times its width. if the area is of the rectangle is 868 square feet,find the length of the rectangle
Answer:
Length=62 feet
Step-by-step explanation:
L x W =area area= 868 L=6W-22
868=W x (6W-22)
868=6W^2-22W
reorder equation
6W^2-22W-868=0
Factor
(3W-42)(2W+20.7)=0
3W=42
W=14, then L=6(14)-22=62
Check:
62x14=868
The length of the rectangle is 62 feet.
Given,
A rectangle has a length of 22 feet less than 6 times its width.
The area of the rectangle is 868 square feet.
We need to find the length of the rectangle.
What is the area of a rectangle?It is given by:
A = Length x width
What is middle-term factorization?We have,
ax² + bx + c
a x c = p x q
The sum of p and q must be equal to b.
Find the length of the rectangle.
L = 6W - 22 ______(1)
Find the width of the rectangle.
Width = W ______(2)
Find the area of the rectangle.
A = L x W
868 square feet = L x W
From (1) and (2)
868 = (6W -22) x W
868 = 6W² - 22W
6W² - 22W - 868 = 0
Solve for W.
6W² - 22W - 868 = 0
Using middle-term factorization.
2( 3W² - 11W - 434 ) = 0
3W² - 11W - 434 = 0
3W² - ( 42 - 31 )W - 434 = 0
3W² - 42W + 31W - 434 = 0
3W ( W - 14 ) + 31 ( W - 14 ) = 0
3W + 31 = 0
3W = - 31
W = - 31 / 3 ( Can not be a negative)
W - 14 = 0
W = 14
Putting W = 14 in (1)
L = 6W - 22
L = 6 x 14 - 22
L = 84 - 22
L = 62
Thus the length of the rectangle is 62 feet.
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For which real a is the following lim true?
Answer:
a=1
Step-by-step explanation:
Both for nominator and denominator, as the n goea to infinity only the gratest degree becomes meaningful. So that, 'a' must be equal to coefficient of n^4. So the answer is a=1.
A pack of gatorade states that 4 tablespoons of mixture should be added for every 7 cups of water. If the container holds 56 cups of water in it, how much should be added to the water?
What is the meaning of "the universal class V is a proper class"?
The statement "the universal class V is a proper class" means that class V, which represents the universal set that contains all sets, is not itself a set but rather a proper class.
We have,
In set theory, a proper class is a class that is not a set.
A class is a collection of objects, and a set is a class that can be a member of other classes.
On the other hand, a proper class cannot be a member of another class.
The statement "the universal class V is a proper class" means that class V, which represents the universal set that contains all sets, is not itself a set but rather a proper class.
This means that V cannot be an element of any other class or set within the context of the set theory being considered.
The concept of proper classes is used to prevent paradoxes and contradictions that can arise when unrestricted comprehension is allowed in set theory.
Thus,
The statement "the universal class V is a proper class" means that class V, which represents the universal set that contains all sets, is not itself a set but rather a proper class.
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