Help ASAP
The diagram shows a trapezium ABCD and a square PQRS.
AD=8cm
DC=3AB
The perimeter of the square is 24cm
The area of the square is half the area of the trapezium work out the length of AB
Answers
Answer:
AB = 2.25
Step-by-step explanation:
Perimeter of square = 4L
24 = 4L
L = 24/4
L = 6cm
Hence the side length of square is 6cm
Area of square = L^2
Area of square = 6^2
Area of square = 36 sq. cm
Area of square = 1/2 * Area of the trapezium
36 = 1/2 * (AB+3AB)*8
72 = (AB+3AB)*8
72 = 4AB * 8
72 = 32AB
AB = 72/32
AB = 2.25
Related Questions
What’s is the median number of guest at these parties
Answers
Answer:
21
Step-by-step explanation:
21 and 27
You are only given an option of 21, so take it.
Answer:
its 21
Step-by-step explanation:
Find the missing angle
Answers
90 minus 63 equals 37
Answer:
27 degrees
Step-by-step explanation:
x together with 63deg form a right angle (90deg)
x + 63 = 90
x = 90 - 63
x = 27
The product of 8 and the sum of a number and 12 is 240
Answers
Answer:
18
Step-by-step explanation:
Let the number be 'x'
Sum of 'x' and 12 = x +12
The product of 8 and the sum of a number and 12 = 8* (x +12)
= 8*x + 8*12
= 8x + 96
8x + 96 = 240
Subtract 96 from both sides
8x + 9 6 - 96 = 240 - 96
8x = 144
Divide both sides by 8
x = 144/8
x = 18
A fast food restaurant executive wishes to know how many fast food meals teenagers eat each week. They want to construct a 80% confidence interval with an error of no more than 0.07. A consultant has informed them that a previous study found the mean to be 5.8 fast food meals per week and found the standard deviation to be 1.3. What is the minimum sample size required to create the specified confidence interval
Answers
Answer:
The minimum sample size required to create the specified confidence interval is of 565.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.8}{2} = 0.1[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.1 = 0.9[/tex], so Z = 1.28.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Found the standard deviation to be 1.3.
This means that [tex]\sigma = 1.3[/tex]
Error of no more than 0.07. What is the minimum sample size required to create the specified confidence interval?
This is n for which M = 0.07. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.07 = 1.28\frac{1.3}{\sqrt{n}}[/tex]
[tex]0.07\sqrt{n} = 1.28*1.3[/tex]
[tex]\sqrt{n} = \frac{1.28*1.3}{0.07}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.28*1.3}{0.07})^2[/tex]
[tex]n = 565.1[/tex]
Rounding up:
The minimum sample size required to create the specified confidence interval is of 565.
How many degrees are in one external angle of a regular 12-gon?
Answers
9.A standard IQ test produces normally distributed results with a mean of 100 and a standard deviation of 15. A class of high school science students is grouped homogeneously by excluding students with IQ scores in either the top 15% or the bottom 15%. Find the lowest and highest possible IQ scores of students remaining in the class.(7)
Answers
Answer:
The lowest possible IQ scores of students remaining in the class is 84.46.
The highest possible IQ scores of students remaining in the class is 115.54.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 100 and a standard deviation of 15.
This means that [tex]\mu = 100, \sigma = 15[/tex]
Find the lowest and highest possible IQ scores of students remaining in the class.
Lowest:
The 15th percentile, which is X when Z has a pvalue of 0.15, so X when Z = -1.036.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.036 = \frac{X - 100}{15}[/tex]
[tex]X - 100 = -1.036*15[/tex]
[tex]X = 84.46[/tex]
Highest:
The 100 - 15 = 85th percentile, which is X when Z has a pvalue of 0.85, so X when Z = 1.036.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.036 = \frac{X - 100}{15}[/tex]
[tex]X - 100 = 1.036*15[/tex]
[tex]X = 115.54[/tex]
The lowest possible IQ scores of students remaining in the class is 84.46.
The highest possible IQ scores of students remaining in the class is 115.54.
Francis went to the sporting goods store and spent $75.15 on 6 items.
Five of those items were pairs of socks and each cost the same amount.
The 6th item was a soccer ball which cost $45. How much did each pair of
socks cost?
Answers
Answer:
$6.03
Step-by-step explanation:
The question is asking us how much each pair of socks cost. With the information we are given, we know that there are 5 pairs and that they all cost the same amount. If the total were just the 5 socks, we could easily divide the total by 5 to get the price of each pair but that's not the case. The soccer ball is included in the final cost. To overcome this, we just have to subtract the soccer ball's cost ($45) from the total.
So we subtract $45 from $75.15, giving us $30.15, the total amount of all the socks. However we need to find out how much each pair costs and there are 5 of them, so we divide 30.15 by 5. This gives us the answer, $6.03.
Each pair of socks cost $6.03.
Simpler Explanation:
$75.15 - $45 = $30.15$30.15 / 5 = $6.03The answer is $6.03
Which graph represents a function
Answers
Find the value of x in the triangle shown below 8 2
Answers
Answer:
8.25
Step-by-step explanation:
(8x 8) + (2x2) = x ^2
64 + 4 = x2
x = √68
x = 8.25
Samantha, a business development representative at Apricot Inc., took her client out for a dinner that cost $180.75 before taxes. If she paid taxes of $18.08 on the meal, calculate the tax rate.
Answers
Answer:
10%
Step-by-step explanation:
Samantha is a business development representative
She took her client out for a dinner that costs $180.75 before taxes
She paid tax of $18.08 on the meal
The tax rate can be calculated as follows
= 18.08/180.75
= 0.1 ×100
= 10%
Hence the tax rate is 10%
please help me with this math assignment
Answers
Answer:
1)80%
2)210%
3)65%
4)105%
Answer:
80%
210%
65%
105%
Step-by-step explanation:
To solve for each of these equations, let's make them fractions first. The denominator will be 20 since that was the goal.
Elena did [tex]\frac{16}{20}[/tex] pushps.
Jada did [tex]\frac{42}{20\\}[/tex] pushups.
Lin did [tex]\frac{13}{20}[/tex] pushups.
Andre did [tex]\frac{21}{20}[/tex] pushups.
To convert this to percentages, let's multiply each by fraction by [tex]\frac{5}{5}[/tex]. This will give us a denominator of 100. The denominator will represent the percentage.
Elena did [tex]\frac{16}{20}[/tex] × [tex]\frac{5}{5}[/tex] = [tex]\frac{80}{100}[/tex] pushps. Elena did 80 percent of the pushups.
Jada did [tex]\frac{42}{20\\}[/tex] × [tex]\frac{5}{5}[/tex] = [tex]\frac{210}{100}[/tex] pushups. Jada did 210 percent of the pushups.
Lin did [tex]\frac{13}{20}[/tex] × [tex]\frac{5}{5}[/tex] = [tex]\frac{65}{100}[/tex] pushups. Lin did 65 percent of the pushups.
Andre did [tex]\frac{21}{20}[/tex] × [tex]\frac{5}{5}[/tex] = [tex]\frac{105}{100}[/tex] pushups. Andre did 105 percent of the pushups.
find the value of x. Pregunta matemática
Answers
Answer:
Ejercicios Resueltos
ANGULOS
1. Si el complemento de ángulo x es 2x, ¿Cuál es el valor de x en
grados?
Solución:
2x x 90 += °
3x 90
x 90 / 3
x 30
= °
= °
= °
2. Si el suplemento del ángulo x es 5x, ¿Cuál es el valor de x?
Solución:
5x+x=180
6x=180
x=180 /6
x=30
°
°
°
°
3- Determínese los dos ángulos x e y, cuya suma es 90 y cuya
diferencia es 10 .
°
°
Solución:
-Planteamos el sistema de ecuaciones:
x y 90
x y 10
+= °
−= °
-Resolvemos el sistema. Mediante el método de suma y resta
obtenemos:
2x 100
x 100 / 2
x 50
= °
= °
= °
-Hacemos la sustitución del valor encontrado de x en la primera
ecuación: 50 y 90
y 90 50
y 40
°+ = °
= °−
= °
°
∴La solución al problema es x 50 , y 40 =°= °
°
4. Hállense dos ángulos complementarios tales que su diferencia sea
30° .
Solución:
-Planteamos el sistema de ecuaciones:
x y 90
x y 30
+= °
−= °
-Resolvemos el sistema. Mediante el método de suma y resta
obtenemos:
2x 120
x 120 / 2
x 60
= °
= °
= °
-Hacemos la sustitución del valor encontrado de x en la primera
ecuación:
60 y 90
y 90 60
y 30
°+ = °
= °−
= °
∴La solución al problema es x 60 , y 30 = °= °
°
5. Hállense dos ángulos suplementarios tales que el uno sea 20 mayor
que el otro.
°
Solución:
-Planteamos el sistema de ecuaciones:
x y 180
x y 20
+= °
=+ °
-Resolvemos el sistema:
(y 20 ) y 180
2y 180 20
2y 160
y 80
+ °+ =
= °− °
= °
= °
-Hacemos la sustitución del valor encontrado de y en la primera
ecuación: x 80 180
x 180 80
x 100
+ °=
= °−
= °
°
°
∴La solución al problema es:
x = °= ° 100 , y 180
TRIANGULOS
1.- ¿Cuánto miden cada uno de los ángulos interiores del siguiente
triángulo?
Solución:
Nota: La suma de los ángulos interiores de los triángulos es
180° .
((( A B C 180 ++= °
3x 5x 4x 180 ++ = °
12x 180 = °∴( ( (( A 22.5 , B 52.5 , C 30 , CBR 127.5 = ° = ° =° = °
x 15 = °
∴( ( A 45 , B 75 ,C 60 =° =°= °
°
°
°
°
°
°
2.- ¿Cuánto miden cada uno de los ángulos del siguiente triángulo?
Solución
a) Ángulo extendido
( ( B CBR 180 + = Esto debido a que son ángulos suplementarios
(B 15x 60 180 + − °=
(B 180 60 15x = °+ °−
(B 240 15x = °−
b) Suma de los ángulos interiores del triángulo
((( A B C 180 ++=
3x (240 15x) 4x 180 + °− + =
7x (240 15x) 180 + °− =
− + °= 8x 240 180− =− 8x 160°
x 7.5 =
∴( ( (( A 22.5 , B 52.5 , C 30 , CBR 127.5 = ° = ° =° = °
3.- Escribe la definición de bisectriz del triángulo.
Es la semirrecta que biseca el ángulo, es decir, divide el ángulo
en dos ángulos congruentes.
4.- ¿Qué es la mediatriz de un triángulo?
La mediatriz de un lado de un triángulo (y en general de un
segmento de recta), es la recta perpendicular a ese lado en su
punto medio.
5.- ¿Que es la mediana de un triángulo?
La mediana de un triángulo, es el segmento de la recta que une
un vértice con el punto medio del lado opuesto.
CUADRILATEROS
1.- ¿Qué cuadrilátero tiene las dos diagonales iguales y sus lados son
iguales dos a dos?
Rectángulo
2.- Si los ángulos de un cuadrilátero miden, respectivamente, 80º, 110º
y 70º, ¿Cuánto medirá el ángulo que falta?
100º
3.- ¿Cuál es el paralelogramo que tiene las diagonales perpendiculares?
Rombo
4.- ¿Cómo se llama el cuadrilátero que tiene dos lados paralelos?
Trapecio
5.- Encuentra el área del paralelogramo que tiene 5cm de base y 3 de
altura
A b*a
A 5*3
A 15
=
=
=
POLÍGONOS 1.- Cuatro ángulos interiores de un pentágono valen respectivamente
110°, 90°, 85° y 125°. ¿Cuánto vale el quinto ángulo?
Solución:
Si la suma de los ángulos interiores de un polígono es:
180°*(n-2)=180°*(5-2) = 540°, a lo que le se le resta los
valores de los ángulos que se dieron, consecuentemente, el
quinto ángulo vale 130°.
2.- ¿Cuántos lados tiene, en cada caso, el polígono cuyos ángulos
interiores suman respectivamente 1080°, 900°, 1260°?
Solución:
Despejando de la fórmula el valor de n, tenemos que:
. 2
180
suma angulos n = ° + , y esto aplicado a cada valor de la suma de los
ángulos internos, obtenemos que los valores de n son 8, 7 y 9
respectivamente.
3.- ¿Cuánto vale cada ángulo exterior de un octágono regular?
Solución:
Aplicando el teorema de que la suma de los ángulos exteriores
de un polígono es 360°, entonces cada ángulo exterior vale
360°/8 = 45°
4.- Calcular los ángulos exteriores de un triángulo rectángulo que tiene
un ángulo agudo doble del otro.
Solución:
Se tiene que la suma de los ángulos interiores es
180°*(n-2)= 180° y éste a su vez es igual a 90° + x + 2x,
despejando x de 3x = 90°, x= 30°, entonces los ángulos
interiores son 30°, 60° y 90°, teniendo como ángulos exteriores
150°, 120° y 90°.
Step-by-step explanation:
can someone help
me with this problem
Answers
Answer:
download QANDA thank youcos30= (root3)/2 cos45= (root2)/2 cos60= 1/2
so the correct answer is 30
Which expression is represented by the model?
A. x - 3
B. x + 3
C. -x - 3
D. -x +3
Answers
Answer:
the correct answer is d. -x + 3
Answer:
The correct answer is d x - e
PLEASE HELPPP
what is the volume of this rectangular prism. ??
Brainlist + Five starts
Answers
Answer:
The answer is a
Step-by-step explanation:
it’s a because each dude is 1/2 and you add another one half that’s one and you keep on doing until the last one.
brainliest pls
I hope this helped and was right.
Step-by-step explanation:
Length: 6
width: 4
height:3
Formula :
Volume= l x w x h
6x4x3 =72
72 x 1/2= 36in3/A

HELP ASAP! I will mark Brainlist! Thanks (:
Answers
Answer:
Corresponding angles postulate
Answer:
definition of parrallel lines
Step-by-step explanation:
oh sorry. I understood it as parrallel
Nate Dogg's 4/5 of a mile in 1/6 hour. which fraction represents Nate speed in miles per hour.
Answers
Answer:
24/5
Step-by-step explanation:
(6) 4/5 ------------ per 1/6h (6)
24/5----------- per 1h
a cube has edge length 10 cm. starting at the vertices dots are placed along every edge at 1cm intervals. how many dots will there be in total once the pattern has been completed?
Answers
Answer:
120 dots
Step by step explanation:
In total there are 120 dots on the edges of a cube.
Given that, a cube has an edge length of 10 cm. Starting at the vertices dots are placed along every edge at 1 cm intervals.
We need to find how many dots will there be in total once the pattern has been completed.
How many edges are there in the cube?The number of edges in the cube is 12.
Now, the number of dots on an edge of 10 cm has 10 dots.
The total number of dots = Number of dots on an edge × Number of edges in a cube.
=10×12=120.
Therefore, in total there are 120 dots on the edges of a cube.
To learn more about the edges of the cube visit:
https://brainly.com/question/16256718.
#SPJ2
Find the missing angles
Answers
Answer:
See explanation:
Step-by-step explanation:
1: 180-50=130
3: vertical angles are the same, therefore 50
4: 180-50=130
5: angle 1 equals angle 5, therefore 130
6: 50
7: 50, angles 6 and 7 are vertical therefore equal
8: 180-50=130
I need to solve for x. The interior angles are 30 and 4x+2. The exterior angle is 8+6x.
Answers
Answer:
x + y + z = 180 (this is the first equation)
w + z = 180 (this is the second equation)
Now, rewrite the second equation as z = 180 - w and substitute that for z in the first equation:
x + y + (180 - w) = 180
x + y - w = 0
x + y = w
Step-by-step explanation:
Witch shows the expression ordered correctly from least value to greater value a b c or d
Answers
Determine whether the triangle is a right triangle 12, 10, 11...
Answers
Answer:
no it's not right angled
Step-by-step explanation:
thats because the left hand side is not equal to the right hand side
Answer:
You were on the right track: basically if a²+b²=c² is true , it's a right triangle...
a²+b²=c²
11²+10²=12²?
121+100=144?
221=144?
221≠144
Since they're not equal, the triangle isn't a right triangle.
Please solve these systems of equations by substitution.
1. x+y=7
x+2y=11
2. x+y=22
x+2y=48
3. x+y=45
x+2y=36
Answers
Step-by-step explanation:
x+ 2(7-x) = 11
x+14-2x = 11
-x = -3
x = 3
3+ y = 7
y = 4
x + 2(22-x) = 48
x + 44 -2x = 48
-x = 4
x = -4
-4 + y = 22
y = 26
y = 45-x
x + 2(45-x) = 36
x + 90 -2x = 36
-x = 54
x = -54
-54 + y = 45
y = 99
Answer:
1. x=3 and y=4
2. x=−4 and y=26
3. x=54 and y=−9
Step-by-step explanation:
1. x+y=7;x+2y=11
Step: Solvex+y=7for x:
x+y+−y=7+−y(Add -y to both sides)
x=−y+7
Step: Substitute −y+7 for x in x+2y=11:
x+2y=11
−y+7+2y=11
y+7=11(Simplify both sides of the equation)
y+7+−7=11+−7(Add -7 to both sides)
y=4
Step: Substitute 4 for y in x=−y+7:
x=−y+7
x=−4+7
x=3(Simplify both sides of the equation)
2. x+y=22;x+2y=48
Step: Solve x+y=22 for x:
x+y+−y=22+−y(Add -y to both sides)
x=−y+22
Step: Substitute−y+22 for x in x+2y=48:
x+2y=48
−y+22+2y=48
y+22=48(Simplify both sides of the equation)
y+22+−22=48+−22(Add -22 to both sides)
y=26
Step: Substitute26 for y in x=−y+22:
x=−y+22
x=−26+22
x=−4(Simplify both sides of the equation)
3. x+y=45;x+2y=36
Step: Solve x+y=45 for x:
x+y+−y=45+−y(Add -y to both sides)
x=−y+45
Step: Substitute−y+45 for x in x+2y=36:
x+2y=36
−y+45+2y=36
y+45=36(Simplify both sides of the equation)
y+45+−45=36+−45(Add -45 to both sides)
y=−9
Step: Substitute−9 for y in x=−y+45:
x=−y+45
x=−(−9)+45
x=54(Simplify both sides of the equation)
I hope this helped!
(-3, -4) and (-5, y); m = -9/2
Answers
Answer:
the answer would be y= -40
Please help i am giving away brainliset
A machinist creates a spacer by drilling a 3 cm diameter hole through the middle of a cylinder that has a diameter of 5 cm and a height of 0.5 cm. What is the volume of the finished spacer to the nearest tenth cm3?
A. 1.6 cm^3
B. 6.3 cm^3
C. 12.6 cm^3
D. 19.7 cm^3
No dam links
Answers
Answer:
Step-by-step explanation:
Find the difference of the volume of outer cylinder and volume of inner cylinder.
Outer cylinder:
diameter = 5 cm
r = 5/2 = 2.5 cm
h = 0.5 cm
Volume = πr²h
= 3.14 * 2.5 *2.5 * 0.5
= 9.8125 cm³
Inner cylinder:
diameter = 3 cm
r = 3/2 = 1.5 cm
h = 0.5 cm
Volume = 3.14 * 1.5 *1.5 *0.5
= 3.5325 cm³
Volume of the finished space = 9.8125 - 3.5325
= 6.28
= 6.3 cm³
Answer:
6.3 cm³
Step-by-step explanation:
4 by 4 by 4: 64 cubes; you can cover the bottom with 4 by 4 5 16 cubes and you can fit 4 such layers. 2 by 16 by 2: 64 cubes; you can cover the bottom with 16 by 2 5 32 cubes and you can fit 2 such layers. 2 by 4 by 8: 64 cubes; you can cover the bottom with 2 by 4 5 8 cubes and you can fit 8 such layers.
HELP I CANT DO THIS-
Answers
2. F. 160
3. D. Triangular prism
4. H. 30 boxes
5. C. Equilateral Triangle
Please help me, and please do not make a download, because I cannot download anything on my computer. THank you!!!
Answers
Answer:
(A)48
(B)volume of one of the small cubes is 1/64cm^3
c)3/4x1x1=3/4cm^3
Step-by-step explanation:
What is the slope of a line parallel to the line with equation 5x + 3y = 7?
−7/3
−5/3
−3/5
5/3
Answers
Answer:
so first we have to make it to y- intercept form
5x + 3y = 7
3y = 7 -5x since we moved to the other side of the equal sign it turns negative
now divide both sides by 3 becuase y needs to have no number in front of it
3y divided by 3
7 divided by 3
-5 divided by 3
now its y = 7/3 - 5/3x
now we need to reorder the terms so its y = mx + b
y = -5/3x + 7/3 or 2.3
mx equals slope so -5/3 is the slope
Step-by-step explanation:
Answer:
−5/3
Step-by-step explanation:
Parallel lines have the same slope. So to find the parallel line you must first find the slope of the original line. Do this by putting the equation into slope-intercept form. Once the equation is in the slope-intercept form it is, [tex]y=-\frac{5}{3}x+\frac{7}{3}[/tex]. Therefore, the correct answer is −5/3.
- 5 (-2x+10) = 10
equation with parentheses
Answers
Answer: x=6
Step-by-step explanation:
−
5
(
−
2
+
1
0
)
=
1
0
−
5
(
−
2
x
+
10
)
=
10
−5(−2x+10)=10
Solve
1
Distribute
−
5
(
−
2
+
1
0
)
=
1
0
−
5
(
−
2
x
+
10
)
=
10
−5(−2x+10)=10
1
0
−
5
0
=
1
0
10
x
−
50
=
10
10x−50=10
2
Add
5
0
50
50
to both sides of the equation
3
Simplify
which expression is equivalent to the expression -3(4x - 2) - 2x?
A- -8x
B- -16x
C- -14x -2
D- -14x + 6
Answers
Answer:
D is the answer
Step-by-step explanation:
You just distribute the negative three and combine like terms