HELP PLEASE!
In this figure shown, EF is the mid segment of trapezoid ABCD. Find EF.
Answers
Answer:
x = 2
Step-by-step explanation:
EF = ½(BC + AD) => Trapezoid Midsegment theorem
Substitute
5x + 4 = ½((4x + 1) + (7x + 5))
5x + 4 = ½(4x + 1 + 7x + 5)
Multiply both side by 2
2(5x + 4) = 4x + 1 + 7x + 5
10x + 8 = 4x + 1 + 7x + 5
10x + 8 = 11x + 6
Collect like terms
10x - 11x = -8 + 6
-x = -2
Divide both sides by -1
x = 2
Related Questions
Evaluate 1/3m-1-1/2n when m=21 and n=12
Answers
Answer:
12
Step-by-step explanation:
Find the value of y. 108 degrees 40 degrees. x, y, z, w
Answers
Answer:
[tex] \frac{108}{2 } = 54[/tex]
The value of y for the given circle will be 54°.
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
The diameter is the longest line that can be drawn inside a circle.
In our daily life, we always see circle objects for example our bike wheel.
Area of circle = πr² and the perimeter of circle = 2πr where r is the radius of the circle.
In the given question by the circle theorem that if a curve makes a 2x angle then the extreme point will make the angle on circle as x.
So angle y = half of angle 108°
∠Y = 108°/2 = 54°
Angle w will also same as 54° because it also satisfies the theorem of the circle.
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Given two points P(sinθ+2, tanθ-2) and Q(4sin²θ+4sinθcosθ+2acosθ, 3sinθ-2cosθ+a). Find constant "a" and the corresponding value of θ when these two points coincide. (0 ≤ θ < 2π)
Show your work, thanks!
Answers
Answer:
[tex] \rm\displaystyle \displaystyle \displaystyle θ= {60}^{ \circ} , {300}^{ \circ} [/tex]
[tex] \rm \displaystyle a = - \frac{ \sqrt{3} }{2} - 1, \frac{\sqrt{3}}{2} - 1[/tex]
Step-by-step explanation:
we are given two coincident points
[tex] \displaystyle P( \sin(θ)+2, \tan(θ)-2) \: \text{and } \\ \displaystyle Q(4 \sin ^{2} (θ)+4 \sin(θ) \cos(θ)+2a \cos(θ), 3 \sin(θ)-2 \cos(θ)+a)[/tex]
since they are coincident points
[tex] \rm \displaystyle P( \sin(θ)+2, \tan(θ)-2) = \displaystyle Q(4 \sin ^{2} (θ)+4 \sin(θ )\cos(θ)+2a \cos(θ), 3 \sin(θ)-2 \cos(θ)+a)[/tex]
By order pair we obtain:
[tex] \begin{cases} \rm\displaystyle \displaystyle 4 \sin ^{2} (θ)+4 \sin(θ) \cos(θ)+2a \cos(θ) = \sin( \theta) + 2 \\ \\ \displaystyle 3 \sin( \theta) - 2 \cos( \theta) + a = \tan( \theta) - 2\end{cases}[/tex]
now we end up with a simultaneous equation as we have two variables
to figure out the simultaneous equation we can consider using substitution method
to do so, make a the subject of the equation.therefore from the second equation we acquire:
[tex] \begin{cases} \rm\displaystyle \displaystyle 4 \sin ^{2} (θ)+4 \sinθ \cos(θ)+2a \cos(θ )= \sin( \theta) + 2 \\ \\ \boxed{\displaystyle a = \tan( \theta) - 2 - 3 \sin( \theta) + 2 \cos( \theta) } \end{cases}[/tex]
now substitute:
[tex] \rm\displaystyle \displaystyle 4 \sin ^{2} (θ)+4 \sin(θ) \cos(θ)+2 \cos(θ) \{\tan( \theta) - 2 - 3 \sin( \theta) + 2 \cos( \theta) \}= \sin( \theta) + 2 [/tex]
distribute:
[tex]\rm\displaystyle \displaystyle 4 \sin ^{2}( θ)+4 \sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) - 6 \sin( \theta) \cos( \theta) + 4 \cos ^{2} ( \theta) = \sin( \theta) + 2 [/tex]
collect like terms:
[tex]\rm\displaystyle \displaystyle 4 \sin ^{2}( θ) - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) + 4 \cos ^{2} ( \theta) = \sin( \theta) + 2 [/tex]
rearrange:
[tex]\rm\displaystyle \displaystyle 4 \sin ^{2}( θ) + 4 \cos ^{2} ( \theta) - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) + = \sin( \theta) + 2 [/tex]
by Pythagorean theorem we obtain:
[tex]\rm\displaystyle \displaystyle 4 - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) = \sin( \theta) + 2 [/tex]
cancel 4 from both sides:
[tex]\rm\displaystyle \displaystyle - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) = \sin( \theta) - 2[/tex]
move right hand side expression to left hand side and change its sign:
[tex]\rm\displaystyle \displaystyle - 2\sin(θ) \cos(θ)+\sin(θ ) - 4\cos( \theta) + 2 = 0[/tex]
factor out sin:
[tex]\rm\displaystyle \displaystyle \sin (θ) (- 2 \cos(θ)+1) - 4\cos( \theta) + 2 = 0[/tex]
factor out 2:
[tex]\rm\displaystyle \displaystyle \sin (θ) (- 2 \cos(θ)+1) + 2(- 2\cos( \theta) + 1 ) = 0[/tex]
group:
[tex]\rm\displaystyle \displaystyle ( \sin (θ) + 2)(- 2 \cos(θ)+1) = 0[/tex]
factor out -1:
[tex]\rm\displaystyle \displaystyle - ( \sin (θ) + 2)(2 \cos(θ) - 1) = 0[/tex]
divide both sides by -1:
[tex]\rm\displaystyle \displaystyle ( \sin (θ) + 2)(2 \cos(θ) - 1) = 0[/tex]
by Zero product property we acquire:
[tex] \begin{cases}\rm\displaystyle \displaystyle \sin (θ) + 2 = 0 \\ \displaystyle2 \cos(θ) - 1= 0 \end{cases}[/tex]
cancel 2 from the first equation and add 1 to the second equation since -1≤sinθ≤1 the first equation is false for any value of theta
[tex] \begin{cases}\rm\displaystyle \displaystyle \sin (θ) \neq - 2 \\ \displaystyle2 \cos(θ) = 1\end{cases}[/tex]
divide both sides by 2:
[tex] \rm\displaystyle \displaystyle \displaystyle \cos(θ) = \frac{1}{2}[/tex]
by unit circle we get:
[tex] \rm\displaystyle \displaystyle \displaystyle θ= {60}^{ \circ} , {300}^{ \circ} [/tex]
so when θ is 60° a is:
[tex] \rm \displaystyle a = \tan( {60}^{ \circ} ) - 2 - 3 \sin( {60}^{ \circ} ) + 2 \cos( {60}^{ \circ} ) [/tex]
recall unit circle:
[tex] \rm \displaystyle a = \sqrt{3} - 2 - \frac{ 3\sqrt{3} }{2} + 2 \cdot \frac{1}{2} [/tex]
simplify which yields:
[tex] \rm \displaystyle a = - \frac{ \sqrt{3} }{2} - 1[/tex]
when θ is 300°
[tex] \rm \displaystyle a = \tan( {300}^{ \circ} ) - 2 - 3 \sin( {300}^{ \circ} ) + 2 \cos( {300}^{ \circ} ) [/tex]
remember unit circle:
[tex] \rm \displaystyle a = - \sqrt{3} - 2 + \frac{3\sqrt{ 3} }{2} + 2 \cdot \frac{1}{2} [/tex]
simplify which yields:
[tex] \rm \displaystyle a = \frac{ \sqrt{3} }{2} - 1[/tex]
and we are done!
disclaimer: also refer the attachment I did it first before answering the question
A store manager claims that 60% of shoppers who enter her store make a purchase. To investigate this claim, she selects a random sample of 40 customers and finds that 40% of them make a purchase. She wants to know if the data provide convincing evidence that the true proportion of all customers who enter her store that will make a purchase differs from 60%. The P-value of this test is 0.0098. Interpret the P-value.
Assuming the true population proportion of shoppers who will make a purchase is 0.60, the probability of obtaining a sample statistic of 0.40 in a random sample of 40 customers is 0.0098.
Assuming the true population proportion of shoppers who will make a purchase differs from 0.60, the probability of obtaining a sample statistic of 0.40 in a random sample of 40 customers is 0.0098.
Assuming the true population proportion of shoppers who will make a purchase is 0.60, the probability of obtaining a sample statistic as extreme as or more extreme than 0.40 in a random sample of 40 customers is 0.0098.
Assuming the true population proportion of shoppers who will make a purchase is different from 0.60, the probability of obtaining a sample statistic as extreme as or more extreme than 0.40 in a random sample of 40 customers is 0.0098.
Answers
Answer:
I do believe that it is Option B
(Assuming the true population proportion of shoppers who will make a purchase differs from 0.60, the probability of obtaining a sample statistic of 0.40 in a random sample of 40 customers is 0.0098.)
Step-by-step explanation:
This sample provide evidence that the grocery store manager overstated the true proportion P-value = 0.0333.
What is p-value?In null-hypothesis significance testing, the p-value is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct.
here, we have,
Given data in the question:
To test whether population proportion p is overstated;
Null hypothesis H₀ : p = (75%) = 0.75
Alternative hypothesis H₁ : = < (75%) < 0.75
Now, sample proportion p" = 64 / 100 = 0.64
From the dot plot below,
we will determine the p-value for test { P(p" < 0.64)}
The number of times p"<0.64 in 150 simulations is 5
Therefore:
P(p" < 0.64 ) = 5 / 150 = 0.0333
P-value = 0.0333
At 5% level of significance;
0.0333 < 0.05
Therefore, we reject null hypothesis H₀ at 5% level of significance,
We conclude that proportion of shoppers who bought bananas at least once in the past month is overstated.
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complete question:
A grocery store manager claims that 75% of shoppers purchase bananas as least once a month. Technology was used to simulate choosing 150 SRSs of size n = 100 from a population of shoppers where 75% buy bananas. The dotplot shows pˆ = the sample proportion of shoppers who bought bananas in the past month. A random sample of 100 shoppers from the store were selected and 64 bought bananas in the past month. Does this sample provide evidence that the grocery store manager overstated the true proportion? Justify your answer.
Question 4
1 pts
3. Aracelli has a class of kindergardeners. Each student gets a six oz cup of milk at
snack time. How many gallons of milk will she need to buy for a class of 23 students?
O 1.08 gallons
1.1 gallons
O 2 gallons
1 gallon
1 pts
Question 5
Answers
Answer:
There is a little over 1 gallon
Step-by-step explanation:
Can someone please help me
With Geometry
Answers
Answer:
4.2
Step-by-step explanation:
By intersecting chords theorem:
[tex]x \times 10 = 6 \times 7 \\ \\ 10x = 42 \\ \\ x = \frac{42}{10} \\ \\ x = 4.2[/tex]
2. Which equation describes a line that has
a slope of and a y-intercept of ?
A) 5y + 4x = 2
C) Sy - 4x = 2
B) 4x5y = 2
D) -5y - 4x = 2
Answers
Answer:
What?
Step-by-step explanation:
G8ve me more info and Ill answer again
A farmer A farmer sells 9.3 kilograms of pears and apples at the farmer's market.
4
5
of this weight is pears, and the rest is apples. How many kilograms of apples did she sell at the farmer's market?
Answers
Answer:
1.86
Step-by-step explanation:
Since decimals are the same as fractions, we can convert 4/5 to .80. And since "of" means multiply, we can convert .80 of 9.3 to:
.8 x 9.3 = 7.44
This is the amount of pears, so we subtract:
9.3 - 7.44 = 1.86
The weight of the apples is 1.86.
Renting video games from Store S costs $2.50 per game plus a monthly fee of $5.00. Renting video games from Store T costs $5.00 per game with no monthly fee. The monthly cost to rent video games depends on the number of video games, v, rented. ?
Answers
Answer:answer is 2.5v+5<5v A.k.a:A
Step-by-step explanation:
The lengths of three sides of a triangle are given. Classify each triangle as acute, right, or obtuse. 6,9,7
Answers
Right triangle : a^2+b^2=c^2
Acute triangle : a^2+b^2 > c^2
Obtuse triangle:a^2+b^2 < c^2
6^2+7^2 > 9^2
Square ABCD is translated 9 units to the right, followed by a translation 6 units down
Square ABCD is reflected across the y-axis, followed by a translation 6 units down
Square ABCD is translated 6 units down, followed by a translation 9 units to the right
Answers
Answer:
71
Step-by-step explanation:
ndndnrbrjen3n3nn3b2n2b2b
Find the area of a circle with a diameter of 31.
Answers
Answer:
hope this helps
Step-by-step explanation:
31 divided by 2 = 15.5 then do 15.5 x 15.5= 240.25 then you do 240.25 x 3.14 = 754.385
After solving the system of equations, what is the value of y?
6x+2y=-4
x-2y=4
Answers
Answer:
x=0, y=-2
Step-by-step explanation:
6x0=0
2(-2)=-4
so, -4=-4 so it is determined true
Then 0-2(-2), -2(-2)=4
subtract 0 from 4 which is 4
so, 4=4, so it is determined true
Solve -2 t + 5 ≥ -7.
please help im desperate
Answers
Answer:
The first ">" should be underlined in the equation.
..
The rules for solving inequalities are the same as those used for solving regular equations except for one important rule, that is, when you multiply both sides of an inequality by -1, the inequality sign reverses.
..
5-4x≥17
-4x≥12
-x≥3
Step-by-step explanation:
Answer:
-2t+5> -7-2t> -7-5t > -12/-2t> 6hope it helps.
stay safe healthy and happy.David wants to survey his friends about their favorite animal he distributes the following survey is this an appropriate survey for david to use
Answers
Answer:
Its A let me know if im wrong!
Answer:
Fourth option is most suitable here.
Please help me!! How do I do this?
Answers
Answer:
Taking 45 degree as reference angle
Then using sine rule
sin 45=
p/h
replacing the value of sin 45 degree by 1/root 2.so
1/root 2=9/c
doing cross multiplication
9*root 2=1*c
9 root 2 =c
therefore the value of c is 9 root 2
Step-by-step explanation:
what are the answers to problems 9 and 10 ?
Answers
Answer:
D. and F.
Step-by-step explanation:
Describe a congruence transformation that maps ABC to DEF
Answers
Answer:
A translation of 5 units to the right, followed by a reflection across the x axis.
1. Which equation describes a line with
y-intercept (0,5) that passes through the
point (2, 4)?
A) y = -2x + 6
C) y = 2x + 5
B) y = -x+5
D) y = x +5
Answers
please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answers
Answer:
∠ G ≈ 8.3°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan G = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{HI}{GI}[/tex] = [tex]\frac{1.1}{7.5}[/tex] , then
∠ G = [tex]tan^{-1}[/tex] ([tex]\frac{1.1}{7.5}[/tex] ) ≈ 8.3° ( to the nearest tenth )
19- What is the equation of the line that is perpendicular to the given line and has an x-intercept of 6? O y= 4 -10 86 8 10 x --**+ 8 O y=-3x+6 O y= 4X-8 O ya x-6 |(4,2) 5) 10.
Answers
Answer:
[tex]y=\frac{4}{3}x -8[/tex]
Step-by-step explanation:
So first find the slope of the given line
-2 - 4 = -6
4 + 4 = 8
-6 ÷ 8 = [tex]-\frac{3}{4}[/tex]
The slope of a line perpendicular to another line is the opposite reciprocal of the given slope.
The opposite reciprocal of [tex]-\frac{3}{4}[/tex] is [tex]\frac{4}{3}[/tex]
So now all we need to finish the slope intercept form y = mx + b is b, which is the y intercept.
[tex]y=\frac{4}{3}x+b[/tex]
Now that they give us the X intercept, you can plug in the values (6, 0).
[tex]0=8+b[/tex]
b = -8
Rick bought a fan for his living room he was looking at it while he was installing it wondered to himself what the angle between each blade measured. The fan has 3 blades evenly spaced. What is the angle between each blade and what type of angle are they?
Answers
Answer:
The angle between the two blades is 120 degree.
Step-by-step explanation:
number of blades = 3
The blades are equally spaced.
The total angle around a circle is 360 degree.
So, the angle between the two blades is given by
[tex]\theta =\frac{360}{n}\\\theta =\frac{360}{3} = 120^{o}[/tex]
The table shows two options provided by a high-speed Internet provider.
Setup Fee ($) Cost per Month ($)
Option 1 80 30
Option 2 No setup fee $40
Part 1 out of 2
In how many months will the total cost of both options be the same? What will that cost be?
In months the total cost of both options will be the same. That cost will be $.
Answers
Answer:
8 months and $320
Step-by-step explanation:
To find when 30m + 80 = 40m, isolate m.
30m + 80 = 40m
Subtract 40m from both sides.
-10m + 80 = 0
Subtract 80 from both sides.
-10m = -80
Divide both sides by -10
m = 8
To find the cost, substitute 8 as m in one of the equations.
40(8) = 320
Work backward to solve.
What is the starting position (x, y)?
Answers
Tyler has a plant that is 24 inches tall. Fionas plant is 13 inches taller than Tyler's plant. How tall is fionas plant?
Answers
Answer:
37 inches
Step-by-step explanation:
to get 37 inches, you need to add 24 and 13. so 24+13 would equal 37.
A limousine costs $75000 new, but it depreciates at a rate of 12% per year. How many years would it take to be worth $45000? Round to the nearest year.
Answers
Number of years to make a worth of $45000 with Depreciation rate of 12% and Total worth $45000 is 4 years
Years= 4 year
What is Depreciation?The term depreciation refers to an accounting method used to allocate the cost of a tangible or physical asset over its useful life. Depreciation represents how much of an asset's value has been used. It allows companies to earn revenue from the assets they own by paying for them over a certain period of time.
Given that:
limousine costs $75000
Depreciation rate = 12% per year= 0.12
Total worth= $45000
By using the formula for year we have
total worth = cost of object [tex](1- Depreciation \;rate)^{year}[/tex]
45000= 75000x [tex](1-0.12)^{year}[/tex]
0.6= [tex](0.88)^{year}[/tex]
Now taking log on both side we have
log 0.6= year x log0.88
-0.2218 = year x -0.05551
year= 4.049
year≈ 4 year(rounding off nearest year)
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The average mass of a certain type of microorganism is 2.4x10^-6 grams. What is the approximate total mass, in grams, of 5x10^3 of these microorganisms?
a. 1.2X10^-4
b. 1.2X10^-3
c. 1.2X10^-2
d. 1.2X10^-1
Answers
The total mass of 5 x 10³ microorganisms is 1.2 x [tex]10^{-2}[/tex].
Option C is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Mass of an organism = 2.4 x [tex]10^{-6}[/tex] grams
The total mass of 5 x 10³ microorganism.
= 5 x 10³ x 2.4 x [tex]10^{-6}[/tex]
= 12.0 x [tex]10^{3 - 6}[/tex]
= 12 x [tex]10^{-3}[/tex]
= 1.2 x [tex]10^{-2}[/tex]
Thus,
The total mass is 1.2 x [tex]10^{-2}[/tex]
Learn more about expressions here:p
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Escribe en lenguaje simbólico las siguientes expresiones, teniendo en cuenta que llamamos x a la edad de María. La edad que tenía María hace 3 años. El doble de la edad que tendrá María dentro de 10 años. La tercera parte de la edad que tenía María hace 1 año.
Answers
Answer:
i don't know that language sorry
Step-by-step explanation:
Order the expressions by value from least to greatest.
|2-9| |4| |6+4| -|7|
Answers
Answer:
-|7|, |4|, |2-9|, |6+4|
Step-by-step explanation:
I think this is correct
Shane can run the length of a football field (100 yards) in 12 seconds what's shanes speed?
Answers
Answer:
8 1/3 or 8.33 yards per second
Step-by-step explanation:
100/12 = 8 1/3