Answer: 19 cm
Step-by-step explanation:
Substituting into the formula for the area of a trapezoid,
[tex]\frac{1}{2}(x-4)(x+4+x+9)=99\\\\\frac{1}{2}(x-4)(2x+13)=99\\\\(x-4)(2x+13)=198\\\\2x^2 +5x-250=0\\\\(2x+25)(x-10)=0\\\\x=-12.5, 10[/tex]
However, as x must be positive (since length must be positive), x=10. This means the length of the longer base is 19 cm.
An architect is designing a gazebo which base is a regular dodecagon. At what angle should he cut to frame the base?
Answer:
15
Explanation:
Note that a regular dodecagon is a 12 sided polygon with internal angles that are equal and sides of the same length.
So determine at what angle the architect should cut to frame the base, we have to divide 360 by 12 and divide the result by 2 as seen below;
[tex]\begin{gathered} \frac{360^{\circ}}{12}=30^{\circ}\text{ (degre}e\text{ per corner)} \\ \frac{30^{\circ}}{2}=15^{\circ\text{ }}(angle\text{ to be cut)} \end{gathered}[/tex]The angle that the architect should cut to frame the base is 15 degrees
Dm³ + n = rwhat does D equal?
Fill in the blank to make the two fractions equivalent. 4 = $ U A 30 ?
Given:
[tex]\frac{x}{30}=\frac{4}{5}[/tex]To find: The value of x (box)
Explanation:
Multiplying 30 on both sides. We get,
[tex]\frac{x}{30}\times30=\frac{4}{5}\times30[/tex]Solving we get,
[tex]\begin{gathered} x=4\times6 \\ x=24 \end{gathered}[/tex]Thus, the value of x is 24.
Final answer: The missing value is 24.
Which symbol correctly compares these fractions? -13\15 and -5\6 a: = b: > c:
Answer:
B
Step-by-step explanation:
None
is the reflection of a figure in the x axis equivalent to the rotation of that same figure 180° (clockwise) about the origin?
The reflection across x-axis has the following rule applied
[tex](x,y)\rightarrow(x,-y)[/tex]The rotation of 180° about the origin has the rule
[tex](x,y)\rightarrow(-x,-y)[/tex]In this case, the new image are not the same, that is to say
Therefore, they are not the same.
Sebastian bought cookies from his sister's scout troop. He bought 4 boxes of shortbread cookies and 3 boxes of peanut butter cookies. There are 20 shortbread cookies in each box but only 18 peanut butter cookies in each box. How many cookies did Sebastian buy in all?
Sebastian buy 134 cookies.
Given,
He bought 4 boxes of shortbread cookies
and, 3 boxes of peanut butter cookies.
There are 20 shortbread cookies in each box.
but only 18 peanut butter cookies in each box.
To find the how many cookies did Sebastian buy in all?
Now, According to the question:
Formulate the above conditions:
18 x 3 + 20 x 4
Calculate the product or quotient
54 + 20 x 4
54 + 80
= 134
Hence, Sebastian buy 134 cookies.
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The price of stock A at 9 am was $15.48 since then the price has been increasing at the rate of $0.11 each hour at noon the price of stock B was $16.23 it begins to decrease at the rate of $0.12 Each hour if the two rates continue in how many hours will the prices of two stocks be the same
How far will a train travel per hour if it travels 282 miles in 2 1/2 hour?
1) Gathering the data
282 miles
2 1/2 hour We can rewrite that as 2.5
2) Let's use a proportion, or rather a formula for that
282 miles ------- 2.5
x -------------------- 1
2.5x = 282
x=282 /2.5
x =112.8 miles per hour
In one 1 hour, this train is able to get 112.8 miles if this train maintains its velocity
An architect designs a house that is 10 m wide. The rafters holding up the roof are equal length and meet at an angle of 65°. The rafters extend 0.4 m beyond the supporting wall. How long are the rafters?
The length of the rafter when the architect design a house is 12.778m.
How to calculate the length?The information illustrates that the architect designs a house that is 10 m wide and that the rafters holding up the roof are equal length and meet at an angle of 65°.
The rafters extend 0.4 m beyond the supporting wall. Then, the length will be:
cos65° = BC / AC
cos 65° = (5 + 0.4)/x
cos 65° = 5.4/x
x = 5.4 / 0.4226
x = 12.778m
The length is 12.778m
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Can you please help me out with a question
Answer:
P = 80 units
Explanation:
Let's label some points in the triangle as:
Since the sides of the triangles are tangent to the circumference, we can write the following relationships:
XC = YC
AZ = AY
BX = ZB
So, the length of the missing side XC is equal to:
XC = YC = 14
On the other hand, the length of AB is the sum of the length of AZ and ZB, so we can calculate ZB as:
AB = AZ + ZB
26 = AY + ZB
26 = 18 + ZB
26 - 18 = ZB
8 = ZB
Because AZ and AY have the same length.
Finally, the measure of BX is equal to:
BX = ZB
BX = 8
Therefore, the perimeter of the triangle is:
Perimeter = AY + YC + AZ + ZB + BX + XC
Perimeter = 18 + 14 + 18 + 8 + 8 + 14
Perimeter = 80
So, the answer is 80 units.
Please help I am so bad at geometry
What is the value of x? O x = 21 O x = 28 x = 35 O x = 37
The value of the missing variable x is; x = 37
What is the value of the missing angle?Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line.
Now, from the given problem, we see that we have two parallel lines with a transversal crossing them Thus, we can say that the two given angles are corresponding angles and as such they are congruent. Thus;
3x + 4 = 115
3x = 115 - 4
3x = 111
x = 111/3
x = 37
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In a survey, 10 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $49 and standard deviation of $2. Find the margin of error at a 80% confidence level.
Give your answer to two decimal places
Given the data that we have here where the number of people in the survey is 10, s = 2 and mean = 49, the margin of error is given as 0.76
How to solve for the margin of errorThe margin of error can be used to provide the data that has to do with the amount of sampling error that would be in a given data statistic.
We would have to calculate the amount of error using the data that we have below.
We have the following values
number n = 10
mean u = 49
standard deviation sd = 2
The level of confidence c i = 80% = 0.80
we have to find the critical value
degree of freedom = 1 - 0.80
= 0.20
zα/2
= 0.20 / 2 = 0.10
= 1.383
The margin of error
= zα / 2 * s / √n
= 1.383 * 2/√10
= 1.383 x 2 / 3.623
= 1.383 x 0.552028
= 0.7634
The calculated margin of error is given as 0.7634
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The two triangles in the figure below are similar triangles. Solve for x.128846O 810O not enough information
Solution
step 1
Explain similarity
Both triangles are similar therefore the ratio of their corresponding sides must be equal.
Step2
State the corresponding sides
[tex]\frac{12}{x}=\frac{8}{4}[/tex]Step 3
Find x
[tex]\begin{gathered} 8x\text{ = 12}\times4 \\ x\text{ =}\frac{48}{8} \\ x=6 \end{gathered}[/tex]Hence option A
HELPDetermine the equation of the line shown in the graph:y = −1y = 0x = −1x = 0
in this problem we have a vertical line
The equation of a vertical line is equal to the x-coordinate of the point that passes through it
so
in this case
the equation of the line is
x=-1
y= 3x - 5 y= -6x + 4
The given system of equation:
y = 3x - 5 (1)
y = -6x + 4 (2)
We can solve the system of equation by using elimination method :
Elimination Method: In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.
Subtract the equation (1) & (2)
[tex]\begin{gathered} y-y=3x-5-(-6x+4) \\ 0=3x-5+6x-4 \\ 0=9x-9 \\ 9x=9 \\ x=\frac{9}{9} \\ x=1 \end{gathered}[/tex]So, we get x = 1
Substitute the value of x in the equation (1)
[tex]\begin{gathered} y=3x-5 \\ y=3(1)-5 \\ y=3-5 \\ y=(-2) \end{gathered}[/tex]y = (-2)
So, the solution of the system of equations are : (x,y) = (1,-2)
Answer: (x,y) = (1,-2)
The following two right triangles are similar.If side DE = 45, side HI = 36, and side DF = 30, what is the length of side HJ?A)21B)24C)20D)19
SOLUTION:
Step 1:
In this question, we are given the following:
The following two right triangles are similar.If side DE = 45, side HI = 36, and side DF = 30, what is the length of side HJ?
Step 2:
The details of the solution are as follows:
Since side DE = 45, side HI = 36, and side DF = 30.
Then, the length of side HJ =
[tex]\begin{gathered} Using\text{ Similar triangles, we have that:} \\ \frac{DF}{DE}=\frac{HJ}{HI} \\ Then,\text{ we have that:} \\ \frac{30}{45}=\frac{HJ}{36} \\ cross-multiply,\text{ we have that:} \\ 30\text{ x 36 = 45 x HJ} \\ Divide\text{ both sides by 45, we have that:} \end{gathered}[/tex][tex]HJ=\frac{30\text{ x 36}}{45}[/tex][tex]HJ\text{ = }\frac{1080}{45}[/tex][tex]HJ\text{ = 24 \lparen OPTION B \rparen}[/tex]the sequence has 100 term and the listing of number were as follow x, 7, 11, 15.......... 399 find the value of x
Answer:
x = 3
Step-by-step explanation:
Given the sequence x, 7, 11, 15, ... 399, where 399 is the 100th term, you want to know the first term, x.
Arithmetic sequenceThe differences of the first few terms are ...
11 -7 = 4
15 -11 = 4
This suggests an arithmetic sequence with a common difference of 4.
The first term, x, will be 4 less than the second term:
x +4 = 7
x = 7 -4 = 3
The value of x is 3.
__
Check
The n-th term of an arithmetic sequence with first term a1 = 3 and common difference d = 4 is ...
an = a1 +d(n -1)
an = 3 +4(n -1) = 4n -1
Then the 100th term is ...
a100 = 4(100) -1 = 399 . . . . consistent with the given information
The cafeteria prepares 80 meals a day for students if 3/8 of the meals are vegetarian, how many meals are are not vegetarian?
Meal prepared a day = 80 meals
Vegetarian meals will be
[tex]\text{vegetarian}=\frac{3}{8}\times80=\frac{240}{8}=30[/tex]Non vegetarian meals = 80 - 30 = 50 meals
Write and solve an equation. Do not forget to label your variable or your units
Mr. Thompson weighs 260 pounds and he loses 4 pounds each month.
The equation will be :
w = 260 - 4m
where w is the weight after m months
when w = 220 pounds, the number of months will be :
220 = 260 - 4m
4m = 260 - 220
4m = 40
m = 40/4
m = 10
The answer is 10 months
You earn $\$34.50$ selling items at a craft show. Newton earns $5$ times as much as you. Descartes earns $0.1$ times as much as Newton does. How much do the three of you earn in all?
All the three person earn $230.75 in all.
What is mean by Addition?
The process of combining two or more numbers is called the Addition.
Given that;
You earn in selling items = $35.50
Newton earn 5 times as much you.
Descartes earns 0.1 times as much as Newton does.
Now,
You earn in selling item = $35.50
Newton earn in selling = 5 x $35.50
= $177.5
Descartes earn in selling = 0.1 x $177.5
= $17.75
So, Total earn = $35.50 + $177.5 + $17.75
= $230.75
Therefore, All the three person earn $230.75 in all.
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Which steps should be used to graph the equation y-4 = 1/3 (x + 2)?
We have the following equation:
y - 4 = 1/3 (x + 2)
We clear y in order to be more unterstandable:
y - 4 = 1/3 (x + 2)
y = 1/3 (x + 2) + 4
y = 1/3 x + 2/3 + 4
y = 1/3 x + 2/3 + 12/3
y = 1/3 x + 14/3
Step 1In order to find the answer we are going to determine x value when y = 4:
y = 1/3 x + 14/3
4 = 1/3 x + 14/3
4 - 14/3 = 1/3 x
12 - 14 = x
-2 = x
Then, it passes through the point (-2 , 4), so we can discard options A and B (because it doesn't pass through (2, 4))
Step 2We know a linear equation is given by:
y = mx + b, where m and b are numbers: m is the slope of the line and b the y-intercept.
In this case y = 1/3 x + 14/3, the slope is 1/3. We know m is given by
m = Δy/Δx
Since in this case
m = 1/3 = Δy/Δx
Then
Δx = 3 and Δy = 1
That means that if it changes 3 units on the x-axis, then it changes 1 unit on the y-axis
. Suppose that in this process, 20% of the available raw sugar is changed to a refined sugar every 5 hrs. If a process begins with 1,000 pounds of raw sugar, write an exponential equation for the amount A of raw sugar (in pounds) t hrs after the process begins.
The exponential equation which represents the amount of raw sugar t hours after the process begins is; A = 1,000 (0.8)^(t/5).
Which equation represents the amount of raw sugar left t hours after the process begins?It follows from the task content that the amount of raw sugar left after the process begins is to be determined according to the information given.
Since, 20% of the available raw sugar is changed to a refined sugar every 5 hrs, it follows that only 80% of the raw sugar is left after each successive time interval period.
Hence, the exponential model of the situation is such that;
A = 1,000(0.8)^(t/5).
Where t = number of hours after the process begins.
Therefore, the required equation is; A = 1,000(0.8)^(t/5).
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624 students in a class took an algebra test.If 18 students passed the test, what percent passed?Answer:
The answer is 75%
What is the image point of (-6, -8) after the transformation R90° ory--r?
R90° transformation results in an image point that is (6, -8).
Describe Quadrant.The plane is divided into four infinite areas known as quadrants, each of which is bounded by two half-axes, using two-dimensional Cartesian axes.
These are commonly numbered from 1 to 4, and are denoted by Roman numerals: the coordinates for I are I (+, +), II (-, +), III (-, -), and IV (+, -).
We are aware that there are four quadrants: I (x, y), II (-x, y), III (-x, -y), and IV (-x, -y) (x, -y)
We can infer that the points are in quadrant III from the supplied point, which is (-6, -8). (-x, -y).
Now, if we turn right 90 degrees and enter sector IV (x, -y), the supplied point will change to (6, -8)
hence, following the transformation of R90°, we have the image point is (6, -8).
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Emily and Andy each go to a hardware store to buy a wire. the table shows the relationship between the cost and the length of wire. Part A: Emily needs 24 ft of wire. how much will she spend on wire.Part B: Andy needs 13 yards of wire. how much will he spend on wire
Part A
If Emily needs 24 feet of wire, then she has to spend $14.4
Part B
If Andy needs 13 yards of wire, then he has to spend $23.4
From the given graph choose one option
The length of the wire = 120 inches
The cost of 120 inches of wire = $6
Cost of 1 inch of wire = 6/120
= $0.05
Part A
The length of the wire = 24 feet
Convert the feet to inches
24 feet = 288 inches
The cost of 288 inches of wire = 0.05×288
= $14.4
Part B
The length of the wire = 13 yards
Convert the yards to inches
13 yards = 468 inches
The cost of 468 inches of wire = 0.05×468
= $23.4
Hence,
Part A
If Emily needs 24 feet of wire, then she has to spend $14.4
Part B
If Andy needs 13 yards of wire, then he has to spend $23.4
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Complete the instructions to move from one point to another along the line
y = 2/3x + 1
___ ___ unit(s), then right 9 units.
Answer:
Step-by-step explanation:
the equation is written in slope intercept form
y= mx + b with m= slope and b= y-intercept
so in your equation
y=2/3x + 1,
the slope is 2/3 and the y-intercept is (0,1)
slope is also known as rise/run
so to move from one point to another, starting at (0,1) (since you know that point is on the line) you would move up 2 units and to the left 3 units.
hope this helped!
Given: I II m. Write a flowchart proof to show that ∠1 ≅ ∠3.
flowchart proof
1) Lines m and l are parallel ------> given
2) ∠1 ≅ ∠2 -----> by alternate interior angles
3) ∠3 ≅ ∠2 -----> by vertical angles
4) ∠1 ≅ ∠3 ----> by the transitive property
help me please......
There is the required value would be 6 in the box.
What is the Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
If you are in the partition XY in the ratio 3 to 4 from point X to point Y
To determine multiply the length of XY.
XY = 14 units then 3/7 of 14
= 3/7 × 14
Apply the multiplication operation,
= 42/7
Apply the division operation,
= 6
Hence, the required value would be 6 in the box.
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Lisa specializes in baking lemon cupcakes. She bakes 3 dozen cupcakes every hour. The cost (in dollars) of making n cupcakes is given by the function C(n) = 60 + 0.45n.
Consequently, it costs $62.70 to make cupcakes for two hours.
By making use of functions, We have: n(h) = 3h, The cost in terms of hours h is given by C(3h) = 60+1.35h, and Lisa's cost for making cupcakes for 2 hours is $62.70
According to the question, Lisa makes 3 dozen cupcakes an hour. To calculate how many she makes in h hours, we will apply the equality postulate as stated.
3 dozens = 1 hour
Hour = n(h)
Cross Multiplying,
n(h) × 1 = 3×h
n(h) = 3h
Therefore, n(h) = 3h is the function that predicts the number of cupcakes Lisa produces in h hours.
We shall locate the composite function C(n(h)) to obtain the cost function in hours.
C(n(h)) = C(3h) (3h)
If C(n) = 60 + 0.45n, then
By replacing n with 3h in the function as indicated, C(3h) is obtained;
C(3h) = 60+0.45(3h) (3h)
C(3h) = 60+1.35h
Thus, 60+1.35h is the cost function expressed in hours.
We will change h = 2 into the calculation C(h) = 60+1.35h to obtain the cost of baking cupcakes for 2 hours.
C(2) = 60+1.35(2) (2)
C(2) = 60+2.70
C(2) = 62.70
Consequently, it costs $62.70 to make cupcakes for two hours.
Complete Question:
Lisa specializes in baking lemon cupcakes. She bakes 3 dozen cupcakes every hour. The cost (in dollars) of making n cupcakes is given by the function C(n) = 60 + 0.45n. The function that models the number of cupcakes Lisa makes in h hours is n(h)=___. The cost in terms of hours h is given by ___. Lisa's cost for making cupcakes for 2 hours is___
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