The total amount will Perri need when she gets the keys for the house at closing is $41,860.
Estimation and Percentages
Perri is making a 7% down payment on the $364,000 purchase price of the condominium, so her down payment will be
0.07 x $364,000 = $25,480.
Perri estimates her closing costs to be 4.5% of the purchase price, which is 0.045 x $364,000 = $16,380.
Therefore, the total amount Perri will need when she gets the keys for the house at closing is the sum of the down payment and the closing costs, which is $25,480 + $16,380 = $41,860.
So the answer is (C) $41,860.
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Using long division to find each quotient.
(2x³ 3x² + 4x + 2) = (x + 2)
Answer:
Step-by-step explanation:
Here's the long division of (2x³ + 3x² + 4x + 2) ÷ (x + 2):
2x^2 - x + 6
x + 2 | 2x^3 + 3x^2 + 4x + 2
- (2x^3 + 4x^2)
--------------
- x^2 + 4x
- (- x^2 - 2x)
-------------
6x + 2
- (6x + 12)
--------
-10
Therefore, the quotient is 2x^2 - x + 6, and the remainder is -10.
The quotient represents the result of the division of the polynomial (2x³ + 3x² + 4x + 2) by the divisor (x + 2). In particular, the quotient 2x^2 - x + 6 represents the quadratic polynomial that, when multiplied by the divisor x + 2, gives the dividend 2x³ + 3x² + 4x + 2.
In other words, we have:
(2x³ + 3x² + 4x + 2) = (x + 2)(2x^2 - x + 6) - 10
The remainder -10 indicates that the division is not exact, and that there is a "leftover" term of -10 when we try to divide the polynomial (2x³ + 3x² + 4x + 2) by (x + 2).
Find the similarity ratio and the ratio of the perimeters of two regular octagons with areas of 48cm2 and 147cm2
The Simple ratio and the ratio of the perimeters of two regular octagons are approximately 1.472
The formula for the area of the regular polygon is:
Area = (2 + 2[tex]\sqrt{2}[/tex]) × [tex]s^{2}[/tex]
Where, s = length of the side of a polygon
consider two equations for the two octagons,
48 = (2 + 2[tex]\sqrt{2}[/tex]) × [tex](s1)^{2}[/tex]
147 = (2 + 2[tex]\sqrt{2}[/tex]) × [tex](s2)^{2}[/tex]
The length of each polygon is
s1 = [tex]\sqrt{\frac{48}{(2 + 2\sqrt{2} )} }[/tex] ≈ 3.079cm
s2 = [tex]\sqrt{\frac{147}{(2 + 2\sqrt{2} )} } }[/tex] ≈ 4.532cm
The similarity ratio is,
s2 ÷ s1 ≈ 1.472
The ratio of perimeters is,
8s2 ÷ 8s1 = s2 ÷ s1 ≈ 1.472
Therefore, the similarity ratio and the ratio of the perimeters are both approximately 1.472.
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1/2 + a = 1 3/4 = 7
1/2 + ? = 7
To solve the equation 1/2 + a = 1 3/4, we need to convert the mixed number 1 3/4 to an improper fraction:
1 3/4 = 4/4 + 3/4 = 7/4
Now we can rewrite the equation as:
1/2 + a = 7/4
To isolate the variable a, we need to subtract 1/2 from both sides:
a = 7/4 - 1/2
To add these two fractions, we need to find a common denominator, which is 4:
a = (7/4 - 2/4)
a = 5/4
Therefore, a = 5/4.
To solve the equation 1/2 + ? = 7, we can follow a similar approach. We need to isolate the variable on one side of the equation, so we need to subtract 1/2 from both sides:
? = 7 - 1/2
We need to find a common denominator to add these two fractions, which is 2:
? = (14/2 - 1/2)
? = 13/2
Therefore, the missing number is 13/2.
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Performance task prize patrol
A performance task is any educational activity or assessment that calls for students to perform in order to demonstrate their comprehension, competency, and knowledge.
How would you define activity?Mathematical activity includes the search for patterns as well as experimentation, description, fiddling, invention, picturing, conjecture, and guesswork.
A series of recurrent numbers, symbols, or shapes is referred to in mathematics as a pattern. Every kind of event or thing has a pattern that can be connected to it. A rule that distinguishes between items that are a part of a pattern and those that are not is known as a pattern.
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Complete question:
What is Performance task?
Problem 2
Let A= [ 9 2 -22]
[ 0 -2 0 ]
[ 1 0 -4 ]
a) find the characteristic polynomial of A
b) Find the two eigenvalues of A
(c) Find a basis for the eigenspace corresponding to the smallest eigenvalue. (d) Find a basis for the eigenspace corresponding to the largest eigenvalue.
{-2 2 22}
a) The characteristic polynomial of A is given by:
$$p_A(\lambda) = \lambda^3 - 5\lambda^2 + 18\lambda + 36$$
b) The two eigenvalues of A are:
$$\lambda_1=2, \lambda_2=-4, \lambda_3=9$$
c) A basis for the eigenspace corresponding to the smallest eigenvalue $\lambda_2=-4$ is given by the set of vectors:
$$\begin{bmatrix} 0\\1\\0 \end{bmatrix}, \begin{bmatrix} 2\\0\\1 \end{bmatrix}$$
d) A basis for the eigenspace corresponding to the largest eigenvalue $\lambda_3=9$ is given by the set of vectors:
$$\begin{bmatrix} 1\\0\\-4 \end{bmatrix}, \begin{bmatrix} -2\\2\\22 \end{bmatrix}$$
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On a bicycle, Carlota rides for 4 hours and is 26 miles from her house. After riding for 12 hours, she is 74 miles away. What is Carlota's rate?
Carlota's rate on a bicycle who is 74 miles away is approximately 6.1667 miles per hour.
Carlota's rate can be found by using the formula: rate = distance ÷ time. To find her rate for the first part of the trip, we can plug in the given values:
rate = 26 miles ÷ 4 hours rate = 6.5 miles per hour.To find her rate for the second part of the trip, we need to subtract the distance and time she had already traveled from the total distance and time:
74 miles - 26 miles = 48 miles12 hours - 4 hours = 8 hours.Then we can plug these values into the formula:
rate = 48 miles ÷ 8 hours rate = 6 miles per hour.Since Carlota's rate is the same for both parts of the trip, we can simply use the overall distance and time to find her rate:
rate = 74 miles ÷ 12 hoursrate = 6.1667 miles per hour.Therefore, Carlota's rate is approximately 6.1667 miles per hour.
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Use the remainder theorem to find the remainder when f(x) is divided by x-1. f(x). f(x)=2x^(3)+3x^(2)-12x+7
The remainder when f(x) is divided by x-1 is 0.
What is remainder theorem?Remainder Theorem states that given a polynomial function and a value for x, the remainder when the polynomial is divided by (x-a) is equal to the value of the polynomial when x=a. This theorem can be used to quickly and accurately find the remainder of a division problem, making it a very useful tool.
The remainder theorem states that if a polynomial f(x) is divided by x-a, then the remainder is f(a). In this case, we want to find the remainder when f(x) is divided by x-1. Therefore, we need to find f(1).
f(1) = 2(1)^(3) + 3(1)^(2) - 12(1) + 7
f(1) = 2 + 3 - 12 + 7
f(1) = 0
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Pls help me with this question! Thank you so much!
Answer:
420mm^3
Step-by-step explanation:
10mm×10.5mm=105mm
105mm×8mm=840mm^3
840mm^3÷2=420mm^3
The volume of this prism is calculated by this equation:
V = (area of a triangle)(height)
So plugging in the numbers it looks something like this
V = (10 x 10.5 x 1/2)(8)
V = (105 x 1/2)(8)
V = (52.5)(8)
V = 420 mm^3
In a video game each player earns 5 pts for reaching the next level and 15 pts for each coin collected. Make a table to show the relationship between the num of coins collected c and total pts p graph the ordered pairs and analyze the graph
Step-by-step explanation:
Refer to pic...........
Please helpppp I need this really really bad
The given exponential functions are classified as exponential growth or exponential decay above.
What is function?A function is a relation between a dependent and independent variable. We can write the examples of functions as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
Given is to check whether the given functions represent exponential growth or decay.
We can write the classified functions as -
{ 1 }. y = 500(0.30)ˣ exponential decay
{ 2 }. y = 500(1.70)ˣ exponential growth
{ 3 }. y = 0.3(500)ˣ exponential growth
{ 4 }. y = 500(0.30)ˣ - 6 exponential decay
{ 5 }. y = 0.3(1.7)ˣ - 2 exponential growth
{ 6 }. y = 500(0.30)ˣ ⁺ ⁸ exponential growth
{ 4 }. y = 500(0.30)ˣ ⁻ ⁶ exponential decay
Therefore, the given exponential functions are classified as exponential growth or exponential decay above.
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The equations y= -(x+7)(x+4) and y=-(x-(3) are equivalent. How can both x intercepts be determined if the equation y=-(x+7)(x+4) is given
Answer:
To find the x-intercepts of the equation y = -(x+7)(x+4), we need to set y = 0 and solve for x. So, we have:
0 = -(x+7)(x+4)
This equation will be true if either (x+7) = 0 or (x+4) = 0. Solving each of these equations, we get:
x+7 = 0 => x = -7
x+4 = 0 => x = -4
Therefore, the x-intercepts of the equation y = -(x+7)(x+4) are x = -7 and x = -4.
Now, we know that the equations y = -(x+7)(x+4) and y = -(x-3) are equivalent. This means that they have the same solutions, or the same x-intercepts. So, we can use the x-intercepts we found for the first equation to determine the x-intercepts of the second equation.
To find the x-intercepts of the equation y = -(x-3), we set y = 0 and solve for x:
0 = -(x-3)
This equation will be true if (x-3) = 0, which gives us:
x-3 = 0 => x = 3
Therefore, the x-intercept of the equation y = -(x-3) is x = 3, which is different from the x-intercepts of the equation y = -(x+7)(x+4). This means that the two equations are not equivalent.
Step-by-step explanation:
Answer:
x-intercepts can be found below
Step-by-step explanation:
The equation:
[tex]y=-(x+7)(x+4)[/tex]
Can also be written as:
[tex]y=-1(x+7)(x+4)[/tex]
In order to find the x-intercepts, we must set each of the factors equal to 0.
[tex]-1=0[/tex]
[tex]x+7=0, x=-7[/tex]
[tex]x+4=0, x=-4[/tex]
The x-intercepts are:
[tex](0,0)[/tex]
[tex](-7,0)[/tex]
[tex](-4,0)[/tex]
The equation:
[tex]y=-(x-3)[/tex]
Can also be written as:
[tex]y=-1(x-3)[/tex]
In order to find the x-intercepts, we must set each of the factors equal to 0.
[tex]-1=0[/tex]
[tex]x-3=0, x=3[/tex]
The x-intercepts are:
[tex](0,0)[/tex]
[tex](3,0)[/tex]
Question
Determine the value of x in the diagram.
The quadrilateral with the specified value for x has a 45° angle.
What is quadrilateral?A polygon with four sides, four angles, and four vertices is called a quadrilateral.
The Latin words quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral.
A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry.
The Latin words quadri, a variation of four, and latus, meaning "side," are the source of the name.
The exterior angles of the given quadrilateral are x°, 3x°, x°, and 3x°.
We are aware that a quadrilateral's total exterior angles are 360°.
Now, x°+3x°+x°+3x°=360°
8x°=360°
x°=45°
Therefore, the quadrilateral with the specified value for x has a 45° angle.
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DETAILS KAUFIALG 10 9.1.023. Specify the domain for the function. f(t)=(5)/(t^(2)+4) {t|t!=-4} {t|t>=0} {t|t!=4} {t|t!=-2 and t!=2} {all reals }
The correct domain for the function f(t)=(5)/(t^(2)+4) is {all reals}.
The domain of a function is the set of all possible inputs or values for the independent variable, t in this case. The function f(t)=(5)/(t^(2)+4) has a denominator of t^(2)+4. To find the domain, we need to determine the values of t that would make the denominator equal to zero, as those values would make the function undefined.
t^(2)+4=0
t^(2)=-4
t=±√(-4)
Since the square root of a negative number is not a real number, there are no real values of t that would make the denominator equal to zero. Therefore, the domain of the function is {all reals}.
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The dollar cost of producing x bagels is C(x) = 300 +0.25x - 0.4(x/1000)^3. Determine the cost of producing 2000 bagels. (Use decimal notation. Give your answer to one decimal place.)
C(2000) = $_______
The cost of producing 2000 bagels is $796.8.
To determine the cost of producing 2000 bagels, we need to plug in the value of x into the given equation and solve for C(x).
C(x) = 300 + 0.25x - 0.4(x/1000)^3
C(2000) = 300 + 0.25(2000) - 0.4(2000/1000)^3
C(2000) = 300 + 500 - 0.4(2)^3
C(2000) = 300 + 500 - 0.4(8)
C(2000) = 300 + 500 - 3.2
C(2000) = 796.8
Therefore, the cost of producing 2000 bagels is $796.8.
In general terms, profit is nothing more than revenues minus costs. This mathematically expressed is:
Profit = Revenues - Costs
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what is the answer to this?
HELP WORTH 10 POINTS
The picture shows the top view of a piece of glass.
A rectangular piece of glass is shown. The length is measured as 4 feet. The width is measured as 2 and one-half feet.
Which equations can be used to find the area, in square feet, of the piece of glass? Select all that apply.
A.
A
=
2
1
2
×
4
B.
A
=
5
2
+
4
C.
A
=
(
2
1
2
+
2
1
2
)
+
(
4
+
4
)
D.
A
=
5
2
×
4
E.
A
=
(
2
×
2
1
2
)
+
(
2
×
4
)
F.
A
=
2
1
2
+
4
The equation that can be used to determine the area of the glass is A = 2 1/2 x 4.
What is the equation that can be used to determine the area of the glass?A rectangle is a 2-dimensional quadrilateral with four right angles. A rectangle has two diagonals of equal length which bisect each other. The sum of interior angles is 360 degree and opposite sides are parallel
The area of the rectangle is the product of the length and the width.
Area of a rectangle = length x width
A = 4 x 2 1/2
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A restaurant is hosting a party for 901 guests. If each table can seat 6 guests, how many tables should the restaurant plan to use?
Answer:
151 tables
Step-by-step explanation:
If 1 table is used for 6 guests then for 901 guest we need to divide 901 by 6
901÷6= 150.15
Rounding of the answer 151 tables needed
Please solve it is due Thursday.
Answer:
A: x
Step-by-step explanation:
So with problems like this when it saids f(g(x) it wants you to plug those values in. In some cases you have a value where the x is but you don't so you can't solve g(x) so you move on to the next step. You plug in g(x)= x-1/2 everywhere there is a x in f(x). So our equation would be 2(x-1/2) + 1. Then you solve by canceling the 2 by dividing it out so we would have x-1 +1. Then you combine like terms which -1 +1 is 0 so our final answer would be x.
The Island of Paradis is divided into the following zones (Districts) which are given as follows Determine the total number of trips between the zones. Zone Production/Generation Attraction 1. Shinganshina 3643 3040 2. Utopia 3484 2524 3. Karanes 3156 2535 4. Trost 3204 4217 5. Krolva 2167 2122 6. Stohess 2542 1638 7. Ehrmich 2275 1245 8. Yarckel 2210 3714 9. Orvud 3597 4542 10. Mitras 3172 3754
Determine the total number of trips between the zone:
a. 1 and 6
b. 3 and 10
c. 5 and 10
d. 4 and 9
The total number of trips between the zone: a. 1 and 6 is 10863 trips. b. 3 and 10 is 12617 trips. c. 5 and 10 is 11215 trips. d. 4 and 9 is 15560 trips.
To determine the total number of trips between the zones, we can simply do addition of the production/generation and attraction values for the two zones in question. Based on the values in the table:
a. For zones 1 and 6, the total number of trips would be 3643 + 3040 + 2542 + 1638 = 10863 trips.
b. For zones 3 and 10, the total number of trips would be 3156 + 2535 + 3172 + 3754 = 12617 trips.
c. For zones 5 and 10, the total number of trips would be 2167 + 2122 + 3172 + 3754 = 11215 trips.
d. For zones 4 and 9, the total number of trips would be 3204 + 4217 + 3597 + 4542 = 15560 trips.
Therefore, the total number of trips between the zones are: a. 10863 trips between zones 1 and 6 b. 12617 trips between zones 3 and 10 c. 11215 trips between zones 5 and 10 d. 15560 trips between zones 4 and 9.
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Assume that each package of a company contains 4 products and the number of defective products in one package has the following distribution: X 0 3 4 1 2 Р 0.02 0.14 0.34 0.36 0.14 1. Find the average and the standard deviation of the number of defective products in a package. Answer: E(X) 2.46 Answer: 0(X) = 0.9635 2. Suppose that the numbers of defective products are independent between packages . Find the probability that there are not greater than 859 defective products in 359 package. Answer: 0.0934
The probability that there are not greater than 859 defective products in 359 packages is 0.9999.
We are given that;
Distribution: X 0 3 4 1 2 Р 0.02 0.14 0.34 0.36 0.14 1
0(X) = 0.9635 2
Now,
We need to know the probability of success for each package, which is the probability of having a defective product. Assuming that each product has an equal chance of being defective, we can calculate this probability by dividing the number of defective products by the number of products in a package. In this case, we have:
[tex]p = \frac{0.02 + 0.14 + 0.34 + 0.36 + 0.14}{4} = 0.25[/tex]
This means that each product has a 25% chance of being defective, and each package has a binomial distribution with n=4 and p=0.25.
To find the average and the standard deviation of the number of defective products in a package, we can use these formulas³:
[tex]$$E(X) = np$$$$\sigma(X) = \sqrt{np(1-p)}$$[/tex]
Plugging in the values of $n$ and $p$, we get:
[tex]$$E(X) = 4 \times 0.25 = 1$$$$\sigma(X) = \sqrt{4 \times 0.25 \times (1-0.25)} = \sqrt{0.75} \approx 0.866$$[/tex]
Therefore, the average number of defective products in a package is 1, and the standard deviation is 0.866.
To find the probability that there are not greater than 859 defective products in 359 packages, we need to use the binomial distribution again, but with different values of n and p. In this case, we have:
[tex]$$n = 359 \times 4 = 1436$$$$p = 0.25$$[/tex]
We want to find the probability that [tex]$X \leq 859$[/tex], where [tex]$X$[/tex] is the number of defective products in 1436 trials. We can use this formula:
[tex]$$P(X \leq k) = \sum_{i=0}^{k} \binom{n}{i}p^i(1-p)^{n-i}$$Plugging in the values of $n$, $p$, and $k$, we get:$$P(X \leq 859) = \sum_{i=0}^{859} \binom{1436}{i}0.25^i(1-0.25)^{1436-i}$$[/tex]
Therefore, by probability the answer will be 0.9999.
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Kendra has $7. 35 in her purse. She needs at least $2. 87 more to buy a special bead. What is the total amount, x, she needs for the bead? Which inequalities can be used to represent the situation?
Kendra needs to have at least $7.35 in her purse and needs to accumulate at least $2.87 more to shop for the special bead.
To discover the total amount Kendra needs to shop for the special bead, we add the amount she already has in her purse to the amount she needs to shop for the bead:
x = $7.35 + $2.87
x = $10.22
Thus, Kendra needs a total of $10.22 to shop for the special bead.
To represent the scenario as inequalities, we can use the subsequent:
Let y be the amount Kendra wishes to buy the unique bead, then:
Kendra has at least $7.35: y + $7.35 ≥ y
Kendra needs at the least $2.87 more: y + $2.87 ≤ x
Combining these inequalities, we get:
y + $7.35 ≥ y
y + $2.87 ≤ x
Therefore, Kendra needs to have at least $7.35 in her purse and needs to accumulate at least $2.87 more to shop for the special bead.
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Please somebody help me it’s due today
The value of the segments DB = 23.32 in, RK = 18.22 in and YK = 6.83 in.
What is Pythagoras Theorem?The Pythagorean Theorem states that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the triangle's legs.
The connection between the four edges of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem.
For the given figure we see the right triangle DHB.
Here, DH = 20 in and HB = 12 in.
Using the Pythagoras theorem we have:
DB² = DH² + HB²
DB² = 20² + 12²
DB² = 400 + 144
DB = 23.32
For the right triangle RHK we have:
HR = 16 and HK = 8.72
Using the Pythagoras theorem:
RK² = 16² + 8.72²
RK= 18.22
Also, KY = YK = 6.83 in.
Hence, the value of the segments DB = 23.32 in, RK = 18.22 in and YK = 6.83 in.
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-9x^2(-3x^5 +5x -5) what is the anwser
Suzie's Desserts offers its customers 5 dessert options. The prices are: $5.00 $9.00 $9.00 $6.00 $6.00 $9.00 $9.00 What is the mean absolute deviation of the prices? If the answer is a decimal, round it to the nearest ten cents
We can write the mean absolute deviation as -
1.63.
What is absolute deviation?Absolute deviation or mean absolute deviation is the measure of how far a given data element is from a given mean value of the data.
Given is that Suzie's Desserts offers its customers 5 dessert options. The prices are: $5.00 $9.00 $9.00 $6.00 $6.00 $9.00 $9.00.
The formula for absolute deviation is -
[tex]$\frac {1}{n} \sum \limits_{i=1}^n |x_i-m(X)|[/tex]
We can calculate the mean as -
(5 + 9 + 9 + 6 + 6 + 9 + 9)/7 = 7.57
We can write the absolute deviation as -
Absolute deviation =
1/7(5 - 7.57 + 9 - 7.57 + 9 - 7.57 + 6 - 7.57 + 6 - 7.57 + 9 - 7.57 + 9 - 7.57) = 1.63
Therefore, we can write the mean absolute deviation as -
1.63.
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Please help me find the answer to this question
The measure of Angle D in a parallelogram is 88 degrees.
Explain about parallelogram ?
A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and parallel to each other. The opposite angles are also equal in measure.
Properties of a parallelogram:
Opposite sides are parallel.Opposite sides are equal in length.Opposite angles are equal in measure.Consecutive angles are supplementary, i.e. their sum is 180 degrees.Diagonals bisect each other.According to the question:
Since EFDM is a parallelogram, we know that opposite angles are equal. Therefore,
Angle E = Angle M
Angle D = Angle F
We're given:
Angle E = 16x + 12
Angle D = 18x - 2
So we have:
Angle M = 16x + 12
Angle F = 18x - 2
The sum of the angles in a parallelogram is 360 degrees. Therefore, we have:
Angle E + Angle F + Angle D + Angle M = 360
Substituting the given values, we get:
(16x + 12) + (18x - 2) + (16x + 12) + (18x - 2) = 360
72x + 20 = 360
72x = 340
x = 5
Now we can find the values of Angle E, Angle D, Angle F and Angle M:
Angle E = 16x + 12 = 16(5) + 12 = 92 degrees
Angle D = 18x - 2 = 18(5) - 2 = 88 degrees
Angle F = Angle D = 88 degrees
Angle M = Angle E = 92 degrees
Therefore, the measure of Angle D is 88 degrees.
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HELPPPP PLEASEEEEEE ASAP
Answer: I remember this question very well. I believe that the correct answer is 99.7%
68% of data falls between 15 and 25.
95% of data falls between 10 and 30.
99.7% of data falls between 5 and 35.
The length of interstate 90 from west coast to east coast is 153.5 miles more than 2 times the length of interstate 15 from southeast California to northern Montana. Let m be the length of interstate 15. Which expression can you use to represent the length of interstate 90
In response to the given query, the result we have is As a result, the expressions following statement may be used to explain how long Interstate 90 is: 2m + 153.5
what is expression ?Multiplying, dividing, adding, and subtracting are all mathematical operations. As an example, consider the following expression: Expression, mathematics, and a numeric value Numbers, parameters, and functions are the components of an expression in mathematics. Using opposing words and phrases is possible. An expression, sometimes referred to as an algebraic expression, is any mathematical statement that includes variables, numbers, and a mathematical action between them. For instance, the expression 4m + 5 is made up of the expressions 4m and 5, as well as the variable m from the previous equation, all of which are separated by the mathematical symbol +.
Let L represent the length of I-90. We are informed that
L = 2m + 153.5
where m is Interstate 15's length.
As a result, the following statement may be used to explain how long Interstate 90 is:
2m + 153.5
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Hi due today pls help! Ty!
red counter to blue
There are 15 blue counters in the bag.
What are ratios and proportions?
Two quantities are compared to form a ratio. An equality of two ratios is a proportion.
We know that the initial ratio of red counters to blue counters was 4:5. Therefore, we can write:
4x : 5x
We also know that 10 more red counters were added to the bag. Therefore, the new number of red counters in the bag is:
4x + 10
The ratio of red counters to blue counters then became 6:5. Therefore, we can write:
(4x + 10) : y = 6 : 5
We can simplify this equation by cross-multiplying:
5(4x + 10) = 6y
20x + 50 = 6y
Dividing both sides by 6, we get:
y = (20x + 50)/6
Simplifying, we get:
y = (10x + 25)/3
Since y has to be a whole number, 10x + 25 has to be divisible by 3. The only value of x that satisfies this condition is x = 2.
Therefore, the initial number of red counters was 4x = 8, and the initial number of blue counters was 5x = 10.
After adding 10 more red counters, the new number of red counters was 18, and the new ratio of red counters to blue counters was 6:5.
To find the new number of blue counters, we can use the equation we derived earlier:
y = (10x + 25)/3
Substituting x = 2, we get:
y = (10(2) + 25)/3 = 15
Therefore, there are 15 blue counters in the bag.
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Question 1 Solve the following inequality: 5(3y+1)<15 Answer in interval notation.
The solution to the inequality 5(3y+1)<15 in interval notation is (-∞, 2/3).
To solve the inequality 5(3y+1)<15, we need to isolate the variable y on one side of the inequality. Here are the steps to do so:
1. Start with the given inequality: 5(3y+1)<15
2. Distribute the 5 on the left side: 15y+5<15
3. Subtract 5 from both sides: 15y<10
4. Divide both sides by 15: y<10/15
5. Simplify the fraction: y<2/3
Now, we can write the solution in interval notation. Interval notation uses parentheses or brackets to indicate the range of values that satisfy the inequality. In this case, the solution is all values of y less than 2/3, so we use the notation (-∞, 2/3).
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The lenght of a rectangular floor is twice its breadth if the perimeter of the floor is 216 m find it length and breadth
As per the perimeter, the length of the rectangular floor is 72 meters, and the breadth is 36 meters.
Now we can use the formula for the perimeter of a rectangle to write an equation in terms of x and solve for x.
Perimeter of the rectangle = 2(length + breadth)
Given that the perimeter is 216 m, we can substitute the values of length and breadth in terms of x to get:
216 = 2(2x + x)
Simplifying this equation, we get:
216 = 2(3x)
Dividing both sides by 2, we get:
108 = 3x
Solving for x, we get:
x = 36
Now that we have the value of x, we can use it to find the length and breadth of the rectangular floor.
Length = 2x = 2(36) = 72 m
Breadth = x = 36 m
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