Answer:
x² + 10x + 25
explanation:
\(\hookrightarrow\) (5 + x)²
use the formula: (a+b)² = a² + 2ab + b²
\(\hookrightarrow\) x² + 2(5)(x) + (5)²
\(\hookrightarrow\) x² + 10x + 25
Solution:
\((5 + x)\² \\\\ \rightarrow (5 + x)(5 + x) \\\\ \rightarrow (5 \times 5) + (5 \times x) + (5 \times x) + (x \times x) \\\\ \rightarrow 25 + 5x + 5x + x^{2} \\\\ \rightarrow \bold{25 + 10x + x^{2} }\)
Determine whether each statement is always true, sometimes true, or
never true.
1. Every square is a rhombus.
2. Every rhombus is a parallelogram.
3. Every rectangle is a parallelogram.
4. The diagonals of a square are perpendicular.
5. If the diagonals of a quadrilateral bisect each other, then the
quadrilateral is a square.
6. If the diagonals of a quadrilateral are perpendicular, then the
quadrilateral is a rhombus.
7. The diagonals of a rectangle are congruent.
8. The diagonals of a rhombus bisect the vertex angles.
9. Some rectangles are rhombi.
10. Some rhombi are squares.
Here the statements 1, 2, 3, 4, 5, 7, 8, 10 are correct according to the rules of the shapes.
1: A rhombus is a quadrilateral with four equally sized sides. Each square is a rhombus since they all have four sides that are the same length. 2: Due to the parallel alignment of its opposing sides, every rhombus is a parallelogram. 3: It is true that all rectangles are parallelograms since they have two sets of parallel sides and two pairs of equal opposing sides. 4: The other is split into two equal halves by each bisector. 5: If a quadrilateral's diagonals are equal and bisect one another at right angles, it is a square. 7: Since the diagonals themselves are congruent, each bisected line segment is also congruent. 8: The diagonals split a rhombus's vertex angles into equal halves. The diagonals of a rhombus are at right angles to one another. 10: A square is a rhombus. Sometimes, this is accurate. When a rhombus has four right angles, it is true. So the statements 1,2,3,4,5,7,8,10 are correct.
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Calculate the surface area
To calculate the surface area of a rectangular prism, we need to find the area of each of its six faces and then add them up. In this case, the dimensions of the shape are:
Length = 8 cmWidth = 3 cmHeight = 6 cmRefer to the attachment below.
Three pairs of facesThere are three pairs of faces on a rectangular prism:
Two faces (top & bottom) with dimensions: Length × Width (8 cm × 3 cm).Two faces (front & back) with dimensions: Length × Height (8 cm × 6 cm).Two faces (left & right) with dimensions: Width × Height (3 cm × 6 cm).Finding the areaArea of Length × Width faces8 cm × 3 cm = 24 cm²
Since there are two of these faces, the total area is:
2 × 24 = 48 cm²
Area of Length × Height faces8 cm × 6 cm = 48 cm²
Since there are two of these faces, the total area is:
2 × 48 = 96 cm²
Area of Width × Height faces3 cm × 6 cm = 18 cm²
Since there are two of these faces, the total area is:
2 × 18 = 36 cm²
Adding the areas of the facesNow, add up the areas of all six faces:
Surface Area = 48 + 96 + 36 = 180 cm²
AnswerSo, the surface area of the rectangular prism is 180 cm².
________________________________________________________
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which table represents the expression 12 + x
Answer:
Table c represents the expression 12 + x
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Substitute each of the the values of x on column one into the expression on column two (12+1=13,12+2=14...........)
When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 3 kg, the acceleration of the object is 25 m/s^2. If the same force acts upon another object whose mass is 5 kg, what is this object's acceleration?
If the same force acts upon another object whose mass is 5 kg, the object's acceleration will be 1.667 m/s^2.
How can the acceleration be calculated?We were told that the constant force acts upon an object, and the acceleration of the object varies inversely with its mass, which can be interpreted as :
A = k/M
where M is the mass of the object.
A = acceleration
the k= proportionality constant
then we were told that mass is 3 kg, the acceleration of the object is 25 m/s^2
then substitute into the equation as:
25 =k*3
k= 25/3
then we were told that when mass is 5 kg, then acceleration will be ?
A= (25/3 )/5 = 1.667m/s^2.
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Jemma and Debra work as consults. They both get hired for jobs. Jemma charges a fee of $5 plus an additional $22 per hour. Debra charges $20 per hour. Write an expression that
Answer:
Jemma: 22x + 5
Debra: 20x
Step-by-step explanation:
what is 0.93333333333 as a fraction?
Answer:
14/15
Step-by-step explanation:
Answer:
I'm not very sure how I even got the answer, but the answer is 14/15
A rectangular garden measures 40m by 15m. A 1m flower bed is made round the two shorter sides and one
long side. A circular swimming pool of diameter 8m is constructed in the middle of the garden. Find
correct to the nearest square meter, the area remaining
Answer:
The area remaining, correct to the nearest square meter, is approximately 436 square meters.
Step-by-step explanation:
To find the area remaining, we need to subtract the area of the flower bed and the area of the pool from the total area of the garden.
The total area of the garden is:
40m x 15m = 600 square meters
The flower bed is 1m wide and runs along two shorter sides and one long side of the garden. So the area of the flower bed is:
(40m + 2 x 1m) x (15m + 2 x 1m) - 40m x 15m
= (42m x 17m) - (40m x 15m)
= 714 - 600
= 114 square meters
Now let's calculate the area of the pool. The diameter of the pool is 8m, so the radius is 4m. The area of the pool is:
π x (4m)^2
= 16π
≈ 50.27 square meters (rounded to two decimal places)
So the area remaining is:
600 square meters - 114 square meters - 50.27 square meters
≈ 435.73 square meters
Therefore, the area remaining, correct to the nearest square meter, is approximately 436 square meters.
I need to keep 20.0 mg of a drug in my system at a minimum and a Maximum of 140. mg. The half life of the drug that I put in my system is 16 hours. I have put 100.0 mg in my system by ingesting a pill. When is the earliest I should take the next 100.0 mg pill? When is the latest?
Answer:
Therefore, the earliest time to take the next pill is after 10.85 hours and the latest time is before 15.14 hours have passed.
Step-by-step explanation:
The concentration of the drug in your system after ingesting 100.0 mg can be calculated using the formula:
C = D / V
where C is the concentration, D is the dose, and V is the volume of distribution (assumed to be constant).
At the initial time, t = 0, the concentration is:
C(0) = 100.0 mg / V
After one half-life, t = 16 hours, the concentration is:
C(16) = C(0) / 2 = 50.0 mg / V
After two half-lives, t = 32 hours, the concentration is:
C(32) = C(16) / 2 = 25.0 mg / V
After three half-lives, t = 48 hours, the concentration is:
C(48) = C(32) / 2 = 12.5 mg / V
To find the earliest and latest times to take the next 100.0 mg pill, we need to calculate the concentration at those times and make sure it stays between 20.0 mg and 140.0 mg.
Let's first find the earliest time at which the concentration drops below 20.0 mg.
20.0 mg / V = C(16 + x) = 50.0 mg / V / (2^(x/16))
Solving for x:
2^(x/16) = 50.0 / 20.0 = 2.5
x/16 = log2(2.5)
x = 16*log2(2.5) = 16*0.678 = 10.85
So the earliest time to take the next pill is after 10.85 hours.
Now let's find the latest time at which the concentration goes above 140.0 mg.
140.0 mg / V = C(16 + x) = 50.0 mg / V / (2^(x/16))
Solving for x:
2^(x/16) = 50.0 / 140.0 = 0.3571
x/16 = log2(0.3571)
x = 16*log2(0.3571) = -15.14
So the latest time to take the next pill is before 15.14 hours have passed.
In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, what would the same 30 second commercial have cost during the first Super Bowl in 1967, when the CPI was 33.4? Round your answer to the nearest hundred dollars.
In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, when the CPI was 33.4 the estimated cost of a 30-second commercial during the first Super Bowl in 1967 would be approximately $68,900.
To calculate the cost of the 30-second commercial during the first Super Bowl in 1967, we can use the concept of inflation and the Consumer Price Index (CPI).
The CPI measures the average price change of a basket of goods and services over time. By comparing the CPI values of two different years, we can estimate the relative increase in prices due to inflation.
Given data:
Cost of a 30-second commercial in 2021 = $5.6 million
CPI in 2021 = 271.4
CPI in 1967 = 33.4
To calculate the cost in 1967, we need to adjust the 2021 cost for inflation using the CPI ratio:
Cost in 1967 = (Cost in 2021) * (CPI in 1967 / CPI in 2021)
Cost in 1967 = ($5.6 million) * (33.4 / 271.4)
Cost in 1967 ≈ $0.689 million
To round the cost to the nearest hundred dollars, we can multiply the cost by 100 and round it to the nearest whole number:
Cost in 1967 ≈ $68,900
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sequence three missing terms to comple 7444> →→19-
To complete the sequence "7444> →→19-", we need to find the missing terms that fit the pattern established by the given numbers. Let's analyze the sequence and identify any discernible pattern or rule.
Looking at the sequence, we can observe that each number is decreasing by a certain value. In this case, the first number is 7444, and the second number is 19, indicating a decrease of 7425. Now, we need to continue this pattern.
To find the third missing term, we subtract 7425 from 19, resulting in -7406. Therefore, the third missing term is -7406
To find the fourth missing term, we subtract 7425 from -7406, resulting in -14831. Therefore, the fourth missing term is -14831.
To find the fifth missing term, we subtract 7425 from -14831, resulting in -22256. Therefore, the fifth missing term is -22256.
Therefore, the completed sequence is:
7444> →→19- → -7406 → -14831 → -22256
Each term in the sequence is obtained by subtracting 7425 from the previous term.
It's important to note that this solution assumes a linear pattern in which the same subtraction value is applied to each term. However, without additional context or information about the sequence, there could be alternative patterns or interpretations.
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is 12 - x = -y a linear equation
Answer:
Yes
Explanation:
Given the equation
\(12-x=-y\)Multiply both sides of the equation by negative,
\(\begin{gathered} -(12-x)=-(-y) \\ y=x-12 \end{gathered}\)Therefore, the equation is a linear equation.
Initially 100 milligrams of a radioactive substance was present. After 5 hours the mass had decreased by 2%. If the rate of decay is proportional to the amount of the substance present at time t, determine the half-life of the radioactive substance
Answer:
The half-life of the radioactive substance is 135.9 hours.
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the perimeter of a semicircle protractor is 14.8cm,find it's radius
The radius of the semicircle protractor is approximately 4.693 cm.
Given,Perimeter of a semicircle protractor = 14.8 cm.
To find:The radius of a semicircle protractor.Solution:We know that the perimeter of a semicircle protractor is the sum of the straight edge of a protractor and half of the circumference of the circle whose radius is the radius of the protractor.
Circumference of a circle = 2πrWhere, r is the radius of the circle.If the radius of the semicircle protractor is r, then Perimeter of a semicircle protractor = r + πr [∵ half of the circumference of a circle =\((1/2) × 2πr = πr]14.8 = r + πr14.8 = r(1 + π) r = 14.8 / (1 + π)r ≈ 4.693\) cm.
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Solve for x. You must show all of your work to receive credit.
Answer:
x = 6
Step-by-step explanation:
If an item is marked 15% off to a sale price of $12.75 ,What is the price of the item before the discount
Answer:
$85
Step-by-step explanation:
Divide 15% by $12.75
Change 15% into a decimal by multiplying it by 100
$12.75/0.15= $85
The table displays the scores of students on a recent exam. Find the mean of the
scores to the nearest 10th.
From the Table display of scores and students on a recent exam, The mean of the scores to the nearest 10th is 83.7.
To find the mean of the scores, we need to calculate the sum of the products of each score and its corresponding number of students, and then divide it by the total number of students.
Here's the calculation:
(70 * 6) + (75 * 3) + (80 * 9) + (85 * 5) + (90 * 7) + (95 * 8) = 420 + 225 + 720 + 425 + 630 + 760 = 3180
Total number of students = 6 + 3 + 9 + 5 + 7 + 8 = 38
Mean = Sum of products / Total number of students = 3180 / 38 ≈ 83.7 (rounded to the nearest tenth)
Therefore, the mean of the scores is approximately 83.7.
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Which equation is equivalent to 2 Superscript 4 x Baseline = 8 Superscript x minus 3?
2 Superscript 4 x Baseline = 2 Superscript 2 x minus 3
2 Superscript 4 x Baseline = 2 Superscript 2 x minus 6
2 Superscript 4 x Baseline = 2 Superscript 3 x minus 3
The equivalent exponential equations are given as follows:
\(2^{4x} = 2^{3(x - 3)}\)
How to obtain the equivalent exponential expression?The exponential expression for this problem is defined as follows:
\(2^{4x} = 8^{x - 3}\)
The number eight is the third power of 3, that is:
8 = 2³.
The power of a power rule is used when a single base is elevated to multiple exponents.
Then the simplified expression is obtained keeping the base, while the exponents are multiplied.
Meaning that the equivalent expression on the right side of the equality in this problem is given as follows:
\(8^{x - 3} = (2^3)^{x - 3} = 2^{3(x - 3)}\)
Meaning that the correct option is given by the fourth option.
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a turtle swims 15 kilometers in 9 hours how long does it take the turtle to swim 18 kilometers?
Answer:
10.8 hours or 648 minutes
Step-by-step explanation:
1. Find a factor of 15 and 18 kilometers. A similar factor is 3.
2. Find how long it will take the turtle to swim 3 kilometers.
3. Divide 9 by 5 which is how long it takes to swim three hours. (Keep it in a fraction for now)
4.Multiply 9/5 by 6 to get 18 hours; which is 10.8 hours.
A sculpture is in the shape of a square pyramid. The sculpture has a height of 6 meters and a volume of 50 cubic meters. Find the side length of the square
base.
5 meters
2 meters
12 meters
10 meters
Answer : a link for your answer https://quizlet.com/140197143/surface-area-and-volume-surface-area-of-rectangular-pyramids-flash-cards/
Step-by-step explanation:
Answer:
5 meters
Step-by-step explanation:
Need help asap! Please help worth many points
Answer:
8x-4
Step-by-step explanation:
multiply 2x-1 * 4
What is the surface area?
5 yd
4 yd
5 yd
6 yd
6 yd
On Monday, a baker made cookies. He had enough cookies to completely fill 2
equal-sized trays. He sells the cookies for $3 each.
2 3 4 5
12
At the end of the day on Monday, the trays are pictured above. How much mone
did the baker earn selling cookies on Monday?
10
4 78910
12
Answer:
Step-by-step explanation:
it is my first time doing dis so it is 12.
A parent is buying two types of chocolate truffles for their family. The oldest child can eat twice as much as their younger siblings and prefers white chocolate (W), the younger three like dark chocolate (D) and the spouse likes white chocolate (W). Five white chocolate truffles (W) cost the same as three dark chocolate truffles (D). If the parent bought 6 white chocolate truffles(W) and 10 dark chocolate truffles (D), and spent $34.00, how much was each dark chocolate truffle
Answer:
Each chocolate truffle is $2.125
Step-by-step explanation:
Honestly, I'm not 100% sure if this is correct, and I am truly sorry if this is wrong, but its worth a try :)
Maria purchased a car for $8599. If the rate of depreciation is 2.5%, what will the value of the car be after four years? Round your answer to the nearest hundredth.
Answer:
$ 7770.81
Step-by-step explanation:
2.5 % each year means the car retains 97.5 % ( or .975 in decimal) of its value per year
8599 ( .975) ^4 = $ 7770.81
This exercise demonstrates a connection between the curl vector and rotations. Let B be a rigid body rotating about the z-axis. The rotation can be described by the vector w = ωk, where ω is the angular speed of B, that is, the tangential speed of any point P in B divided by the distance d from the axis of rotation. Let r = ⟨x, y, z⟩ be the position vector of P.(a) By considering the angle θ in the figure, show that the velocity field of B is given by v = w × r.(b) Show that v = −ω y i + ω x j.(c) Show that curl v = 2w.
The relation between curl vector and rotations is v = wdj
What is curl vector?A vector field is a vector field's curl. The tendency of particles at point P to spin about the axis that faces the direction of the curl at P is measured by the curl of a vector field at P. If and only if its curl is zero, a vector field with a simply linked domain is considered conservative.
Let v represent the particle's velocity as a vector.
vector v=ui+vj+wk
curl v =
curl v = \(\left[\begin{array}{ccc}i&j&k\\d/dx&d/dy&d/dz\\u&v&w\end{array}\right]\)
= (dw/dy - dv/dz )i - (dw/dx - du/dz)j + (dv/dx - du/dy )k
Now by comparing with rotational matrix ,
We know that w = rotational matrix
\(w_{x}\) = 1/2 (dw/dy - dv/dz )
\(w_{y}\) = 1/2 (dw/dx - du/dz)
\(w_{z}\) = 1/2 (dv/dx - du/dy )
w = \(w_{x} i +w_{y} j + w_{z} k\)
w = 1/2[ (dw/dy - dv/dz )i + (dw/dx - du/dz)j + (dv/dx - du/dy )k]
w = 1/2 curl v , rotation = 1/2 curl v
let B be a rigid rotating about z axis
w = w.k
tangential speed =wk *di
v = wdj
curl of v= \(\left[\begin{array}{ccc}i&j&k\\d/dx&d/dy&d/dz\\0&w_{x} &0\end{array}\right]\)
v = wdj ,
The relation between curl vector and rotations is v = wdj
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a car tire with radius 12 in. does 80 revolutions in a minute. how far does the car travel ?
Answer:
Travel distance in one minute is 6028.8 inches or 502.4 feet or 167.5 yards=======================
GivenTire has radius of 12 in;Tire does 80 revolutions per minute.To findTravel distance in one minuteSolutionUse circumference formula to find the tire circumference:
C = 2πrC = 2*3.14*12 = 75.36 inFind the distance by multiplying the number of revolutions by circumference:
d = 80*75.36 in = 6028.8 inConvert the inches to feet, or yards, considering 12 in = 1 foot and 3 feet = 1 yard:
6028.8/12 = 502.4 feet502.4 /3 = 167.5 yardsthe axis of symmetry for the graph of the function f(x)=1/4x2+bx+10 is x=6 what is the vale of 6?
Considering the vertex of the quadratic equation, it is found that the value of b is of b = 3.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
y = ax^2 + bx + c
The vertex is given by:
\((x_v, y_v)\)
In which:
\(x_v = -\frac{b}{2a}\)\(y_v = -\frac{b^2 - 4ac}{4a}\)The axis of symmetry is of \(x = x_v\). In this problem, we have that a = 0.25 and x_v = 6, hence:
b/2a = 6.
b/0.5 = 6
b = 6 x 0.5
b = 3.
The value of b is of b = 3.
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Using the Law of Sines to solve the triangle
How do I do it?
The values of ∠B, a and c in the triangle are 68°, 8.1 and 13
What is a triangle?triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.
If ABC is a triangle, then it is denoted as ∆ABC, where A, B and C are the vertices of the triangle. A triangle is a two-dimensional shape, in Euclidean geometry, which is seen as three non-collinear points in a unique plane.
The sum of he interior angles of the triangle is 180°
so that, ∠A + ∠B + ∠C =180
37 + ∠B + 75 = 180
∠B = 180 - 112
∠B = 68°
Using sine rule to find a and c
a/sinA = b/sinB = c/sinC
tto find a
a/SinA = b/sinB
substitute A, B and b o fin a
a/sin37 = 12/sin68
cross multiply
a sin68 = 12 sin 37
a sin68 = 12(0.6018)
a(0.9271) = 7.221
a = 7.221/0.9271
a = 8.4
to find c
b/sin B = c / sin C
12/sin68 = c/sin75
cross multiply we have
c sin 68 = 12sin(75)
c(0.9271) = 12(0.9659)
c = 12.5
In conclusion the values of A, a and c are 68°, 8.4 and C 12.5
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the accompanying data file contains 40 observations on the response variable y along with the predictor variables x and d. consider two linear regression models where model 1 uses the variables x and d and model 2 extends the model by including the interaction variable xd. use the holdout method to compare the predictability of the models using the first 30 observations for training and the remaining 10 observations for validation.
The holdout method is a common approach to assess the performance of a model on new, unseen data.
What is linear regression models?Linear regression is a statistical technique used to model the relationship between a dependent variable and one or more independent variables. In simple linear regression, the relationship is modeled using a straight line, while in multiple linear regression, the relationship is modeled using a hyperplane in higher dimensions. Linear regression models are widely used in various fields, including finance, economics, social sciences, and engineering, to analyze and predict the behavior of a dependent variable based on one or more independent variables. The basic idea behind linear regression is to find the best-fitting line or hyperplane that minimizes the sum of the squared differences between the predicted values and the actual values of the dependent variable. This best-fitting line or hyperplane is called the regression line or regression hyperplane.
Here,
The basic idea is to split the available data into two parts: a training set and a validation set. The training set is used to fit the model, while the validation set is used to evaluate its performance. The holdout method can help us estimate how well the model will generalize to new data.
To compare the predictability of two linear regression models using the holdout method, we would follow these steps:
Split the data into a training set and a validation set. In this case, we would use the first 30 observations for training and the remaining 10 observations for validation.
Fit the first linear regression model using the training data. This model uses the variables x and d as predictors.
Fit the second linear regression model using the training data. This model extends the first model by including the interaction variable xd as a predictor.
Predict the response variable y for each observation in the validation set using both models.
Compare the predicted values to the actual values of y in the validation set. We can use metrics such as mean squared error (MSE) or R-squared to assess the performance of each model.
Choose the model that performs better on the validation set. This model is expected to have better predictability on new, unseen data.
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Multiply.
(2x+6)²
NEED ANSWER ASAPP
Answer:
4x² + 24x + 36
Step-by-step explanation:
(2x + 6)² = (2x + 6)(2x + 6) = 4x² + 12x + 12x + 36 = 4x² + 24x + 36