Answer:
a) Angle 1 = Value in degree = 95°
b)Angle 2 = Value in degree = 77°
c) Angle 3 = Value in degree = 85°
d) Angle 4 = Value in degree = 103°
Step-by-step explanation:
We use circle theorems to solve for this above question.
a) Angle 1 = Value in degree = 95°
Inscribed Angle is 1/2 of an Intercepted Arc
From the diagram, Angle 1 intersects at Arc B and Arc C
This means Angle 1 = (B + C)/ 2 =
Arc B = 100°
Arc C = 90°
Angle 1. = (100° + 90°)/ 2 = 190/ 2 = 95°
b)Angle 2 = Value in degree = 77°
From the diagram, Angle 2 intersects at Arc C and Arc D
Inscribed Angle is 1/2 of an Intercepted Arc
This means Angle 1 = (C+ D)/ 2
C = 90°
D = 64°
Angle 1. = (90° + 64°)/ 2 = 154/ 2 = 77°
c) Angle 3 = Value in degree = 85°
From the diagram, we can see that Angle 1 is opposite Angle 3, hence,
Opposite angles are supplementary which means their addition = 180°
Mathematically:.Angle 1 + Angle 3 = 180°
Angle 1 = 95°
95° + Angle 3 = 180°
Angle 3 = 180° - 95° = 85°
d) Angle 4 = Value in degree = 103°
From the diagram, we can see that Angle 2 is opposite Angle 4,
Hence,
Opposite angles are supplementary which means their addition = 180°
Mathematically:.Angle 2 + Angle 4 = 180°
Angle 2 = 77°
77° + Angle 3 = 180°
Angle 4 = 180° - 77° = 103°
Pls help ASAP! Given a polynomial f(x), if (x − 1) is a factor, what else must be true? f(0)= 1 f(1)=0 f(-1)=0 f(0)=-1
Answer:
f(1) = 0
Step-by-step explanation:
If you set x - 1 equal to 0 and solve, you get x = 1 when y is 0
Answer: x+1 plus the fator
Step-by-step explanation:
help i don't understand
Answer:
x = mn+y
Step-by-step explanation:
=> [tex]m = \frac{x-y}{n}[/tex]
Multiplying n to both sides
=> x-y = mn
Now, Adding y to both sides
=> x = mn+y
Answer:
x = m n + y
Step-by-step explanation:
Graph the inequality y > |x + 1| – 1. Which point is NOT part of the solution? (–1, 2) (1, −1) (–1, 0) (1, 3)
Answer:
(1,-1)
Step-by-step explanation:
If you try plugging in the numbers for x in the equation y > Ix + 1I - 1, you'll find the answer.
Bob goes shopping at his favorite store and finds a hat that is regularly priced at $40, but it is on sale for 20% off. The sales tax on the hat is 10% of the sale price. How much does Bob end up paying for the hat?
Answer:
$35.2
Step-by-step explanation:
Marked price of hat = $40
Sale discount = 20%
discount in $ = 20% of $40 = 20/100 * 40 = $8
Thus, sale price = marked price - sale discount = $40 - $8 = $32
Now it is given that there is sales tax of 10%
This sales tax will be applied on sale price
thus,
sales tax in dollars = 10% of sale price of hat = 10/100 * $32 = $3.2
Total price paid for hat = Sale price+ sales tax = $32 +$3.2 = $35.2
Thus, Bob ended up paying $35.2 for the hat.
Of the bundles delivered daily to the store, 1/3
consists of the morning edition of The Daily Sun.
Another 2 bundles are made up of the afternoon
edition of the same paper. Of the remaining
bundles, 1/2 is regional, one is a local
newspaper, and one is from another state. How
many bundles are delivered daily to the
bookstore?
Answer:
x=9
Step-by-step explanation:
Let total bundle=x
Morning edition of the daily sun=1/3x
=x/3
Afternoon edition of the daily sun=2
That leaves 2x/3 - 2, of which
x/3 - 1 are regional
1 is local
1 from another state
Sum everything
x = x/3 + 2 + x/3 - 1 + 1 + 1
x=2x/3 +3
x-2x/3=3
3x-2x/3=3
x/3=3
Cross product
x=3×3
x = 9
HELP ME PLEASEEEEEEEE
X Y
-2 11
-1 7
0 3
1 -1
2 -5
-2 = 16 times minus 2 plus 4y equals to 12
-1 = 16 times minus 1 plus 4y equals to12
0 = 16 times 0 plus 4y equals to 12
1 = 16 times 1 plus 4y equals to 12
2 = 16 times 2 plus 4y equals to 12
Therefore,
-2 = 16 * -2 + 4y = 12
-32 + 4y = 12
4y = 12 + 32
4y = 44
y = 44/4
y = 11
-1 = 16 * -1 + 4y = 12
-16 + 4y = 12
4y = 12 + 16
4y = 28
y = 28/4
y = 7
0 = 16 * 0 + 4y = 12
0 + 4y = 12
4y = 12 + 0
4y = 12
y = 12/4
y = 3
1 = 16 * 1 + 4y = 12
16 + 4y = 12
4y = 12 - 16
4y = -4
y = -4/4
y = -1
2 = 16 * 2 + 4y = 12
32 + 4y = 12
4y = 12 - 32
4y = -20
y = -20/4
y = -5
help please!!!! ty :)
Answer:
I think the answer should be 112
I'm guessing the supports in the water are equally distanced. Therefore, I'd divide 168 by four to get a singular distance between two supports. I got 42 yards.
Sean los ángulos a y B, donde la suma de la mitad de a mas la tercera parte de B es igual a 15. calcula el doble del cociente del seno de 3a y el coseno de 2B. Urgente pls a es alpha y B es beta por si acaso
Answer:
Supongo que tenemos dos ángulos A y B
"la mitad de A mas la tercera parte de B es igual a 15°" (también supongo que son grados)
A/2 + B/3 = 15°
A/2 = 15° - (B/3)
A = 30° - 2*(B/3)
Ahora queremos calcular:
2*sin(3*A)/cos(2*B)
pero podemos reemplazar A por lo que tenemos arriba:
2*sin(3*(30° - 2*(B/3)))/cos(2*B)
2*sin(90° - 2*B)/cos(2*B)
y como sabemos,
Sin( 90° - x) = Sin(90°)*cos(-x) + cos(90°)*sin(-x) = cos(-x) = cos(x)
entonces:
2*sin(90° - 2*B)/cos(2*B) = 2*cos(2*B)/cos(2*B) = 2*1 = 2.
(show all your working out)
Madeeha’s father won £149
He shared the money between his three children in the ratio 6:3:1
Madeeha was given the biggest share.
a) Work out how much money Madeeha was given.
b) She saved of her share.
How much did she save?
Answer:
She received £89.4
and she saved £67.05
Step-by-step explanation:
The complete question is as follows;
Madeeha’s father won £149.
He shared the £149 between his three children in the ratio 6:3:1. Madeeha was given the biggest share.
(a) Work out how much money Madeeha received.
(b) Madeeha saved 3/4 of her share.
Work out how much Madeeha saved.
Answer;
The total ratio is 6 + 3 + 1 = 10
Since madeeha was given the biggest share, that means she is given 6 out of 10 portions
So the amount she was given would be ;
6/10 * 149 = £89.4
Now we were told she saved 3/4
Amount saved would be 3/4 * 89.4 = £67.05
I Need the answer ASAP PLEASE HELPPPP What is 7/ 16 · 1 /2 ? A) 7/ 8 B) 7/ 32 C) 14/ 32 D) 7 /64
Answer:
B
Step-by-step explanation:
7/16 times 1/2 would be 7/32 because when you multiply fractions you multiply the top and the bottom like this
7 x 1
and 16 x 2
using this logic you can multiply both fractions to make
7/32
Answer:B) 7/ 32
alll you gotta do is multiply across and its already simplified
Which function is represented by this graph?
Answer:
Option B.
Step-by-step explanation:
From the given graph it is clear that it is a V-shaped graph. It means, it is the graph of absolute function.
The vertex form of an absolute function is
[tex]y=a|x-h|+k[/tex]
where, a is a constant and (h,k) is the vertex.
From the given graph it is clear that the vertex is at (7,-3). It means h=7 and k=-3.
[tex]y=a|x-(7)|+(-3)[/tex]
[tex]y=a|x-7|-3[/tex] ...(1)
It passes through (4,0).
[tex]0=a|4-7|-3[/tex]
[tex]3=3a[/tex]
[tex]1=a[/tex]
Put this in (1).
[tex]y=1|x-7|-3[/tex]
[tex]y=|x-7|-3[/tex]
Therefore, the correct option is B.
Trig work i don’t understand. pls help
Answer: A
Step-by-step explanation:
So we know that to find the area of a triangle you have to multiply the base times the height and divide it by two or multiply it by 1/2.Looking the information given it say that theta is equal to 26 degrees and the length of a or the hypotenuse is 25 and b which in this case is the base is 32. So the information gives us the base but now we need to find the height.
To find H we need to apply trigonometry solve for h the height.
As we could see theta which is 26 degrees is opposite the height and we know the hypotenuse length. So using soh cah toh we have to know that the length of h is going to be using the sin formula opposite over hypotenuse.
[tex]sin(26)=\frac{h}{25}[/tex] solve for h by multiplying both sides by 25.
h= 25 sin(26)
h= 10.96 is being rounded to the nearest hundredth because that is essential
Now we know H is equal to 10.96 which is the Height so now we have all the information we need the height and the base.
Multiply 10.96 by 32 and divide it by 2.
10.96 * 32 = 350.72
350.72 /2 = 176.36
The best answer is A because that is the only best approximation to 175.35.
The cross sectional area of a square shaped tunnel is 25m², the volume of the tunnel is 575m³. How long is the tunnel?
Answer:
23 mSolution,
Let the length of tunnel be 'l'
Area=25 m^2
Volume of tunnel= cross sectional area* length
[tex] or \: 575 = 25 \times l \\ or \: l = \frac{575}{25} \\ l = 23 \: m[/tex]
Hope this helps..
Good luck on your assignment..
What is the answer of .7 of which is 3.43
Answer:
4.9
Step-by-step explanation:
3.43/0.7
34.3/7=49
3.43/0.7=4.9
The value of x is approximately 4.9 when 0.7 (70%) of x is equal to 3.43.
We are given that 0.7 (which is the same as 70%) of a certain value (x) is equal to 3.43.
We represent "0.7 of x" as 0.7x.
So, the equation becomes:
0.7x = 3.43
To find the value of x, we need to isolate it on one side of the equation. To do this, we can divide both sides of the equation by 0.7:
(0.7x) / 0.7 = 3.43 / 0.7
The 0.7 on the numerator and denominator cancel out, leaving us with just x:
x = 3.43 / 0.7
Now, we perform the division:
x = 4.9
The value of x is approximately 4.9.
Hence, when 0.7 (70%) of 4.9 is calculated, it will be approximately equal to 3.43.
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Solve: -4 < -2x < 10
Explanation:
The expression -2x means -2 times x. To undo this, we divide all parts of the inequality by -2. Dividing by a negative number will flip the inequality sign. We go from "less than" to "greater than"
-4 < -2x < 10
-4/(-2) > x > 10/(-2) .... inequality signs flip
2 > x > -5
-5 < x < 2
This unknown number x is between -5 and 2. It cannot equal -5. It cannot equal 2.
7. In 2015 a club has 250 members who each
pay
$95 annual subscription.
In 2016 the membership increases by 4% and the annual subscription is
increased by 6%. What is the total income from subscriptions in 2016?
2015:
250 members
$95 annual subscription
2016
250 members + 4%
$95 annual subscription + 6%
Work:
250 x 1.04 = 260
95 x 1.06 = 100.7
260 x 100.7 = 26,182
Thus, the club makes $26,182 from 260 members who pay a subscription of $100.7
Work out the sum of the interior angles of any quadrilateral.
Answer:
The sum of the interior angles is 360 degrees.
Step-by-step explanation:
Simon has 160160160 meters of fencing to build a rectangular garden. The garden's area (in square meters) as a function of the garden's width xxx (in meters) is modeled by A(x)=-x(x-80)A(x)=−x(x−80)A, left parenthesis, x, right parenthesis, equals, minus, x, left parenthesis, x, minus, 80, right parenthesis What width will produce the maximum garden area?
The width for maximum area will be 40 metres.
Given,Simon has 160 metres of fencing to build a rectangular garden.
The garden's area (in square meters) as a function of the garden's width x(in meters) is modeled by,
[tex]A(x)=-x(x-80)[/tex].
We know that perimeter of rectangle will be,
[tex]P=2(L+B)\\[/tex]
Here p is 160,
So,[tex]160=2(L+B)[/tex]
[tex]\L+B= 80[/tex]
Now we have the sum of length and width off the rectangular garden is 80.
Since,
[tex]A(x)=-x(x-80)\\[/tex]
So, [tex]A(x)=x(80-x)[/tex]
We know that the area of rectangle will be the product of length and , here in question width is [tex]x[/tex] so the length will be[tex](80-x)[/tex].
Now we have to calculate the width for which the area will be maximum.
The area will be maximum when the first derivative of area function will becomes zero.
So,
[tex]\frac{\mathrm{d} }{\mathrm{d} x} A(x)=\frac{\mathrm{d} }{\mathrm{d} x}(-x)(x-80)[/tex]
[tex]\frac{\mathrm{d} }{\mathrm{d} x}A(x)=\frac{\mathrm{d} }{\mathrm{d} x}(-x^{2} +80x)[/tex]
[tex]\frac{\mathrm{d} }{\mathrm{d} x}A(x)=-2x+80\\[/tex]
For maximum area ,
[tex]\frac{\mathrm{d} }{\mathrm{d} x}A(x)=0[/tex]
Hence,
[tex]-2x+80=0\\x=40[/tex]
Hence the width for maximum area will be 40 metres.
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The maximum area is 1600 sq meters.
Step-by-step explanation:The garden's area is modeled by a quadratic function, whose graph is a parabola.
The maximum area is reached at the vertex.
So in order to find the maximum area, we need to find the vertex's y-coordinate.
We will start by finding the vertex's x-coordinate, and then plug that into A(x).
The vertex's x-coordinate is the average of the two zeros, so let's find those first.
A(x)=0 -x(x-80)=0
↓ ↓
-x=0 or x-80=0
x=0 or x=80
Now let's take the zeros' average:
[tex]\frac{(0)+(80)}{2}=\frac{80}{2}=40[/tex]
The vertex's x-coordinate is 40. Now lets find A(40):
A(40)= -(40)(40-80)
= -(40)(-40)
= 1600
in conclusion, the maximum area is 1600 square meters.
If a sample of 234 customers were taken from a population of 3620 customers, could refer to the variance of how many of the customers' ages?
If a sample of 234 customers were taken from a population of 3620 customers, s^2 could refer to the variance of how many of the customers' ages?
A. 234
B. 3620
C. Both 234 and 3620
D. Neither 234 nor
3620
Answer: 234
Step-by-step explanation:
Sample distribution = 234 customers
Population distribution = 3620 customers
S^2 which in statistics refers to the same variance utilizes the sample data in estimating the variance value of a population.
The sample variance is given by:
s^2 = (x - mean) / n - 1
where ;
n = number of observation in sample
s^2 = sample variance
mean = statistical mean of sample data
n - 1, is used to account for the bias in our estimation or inference of a population statistics from sample data.
Which is the correct equation for calculating the kinetic energy of an object? K times E = m times g times h. K times E = one half m v squared. K times E = one half a t squared. K times E = one quarter g squared.
Answer:
KE = 1/2mv²
Step-by-step explanation:
The answer above is the formula for calculating kinetic energy. It is wise to remember it.
Answer:
Here is the answer np! :)
Step-by-step explanation:
The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 57 and a standard deviation of 7. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 50 and 57
Answer:
34%
Step-by-step explanation:
According to the empirical rule, 68% of all of the data in a normal distribution falls within one standard deviation of the mean.
Applying to this particular case, 68% of the requests fall within (50 - 7) and (50+ 7). The percentage of requests from 43 to 50 is equal to the percentage of requests from 50 to 57.
Therefore, the percentage of light bulb replacement requests numbering between 50 and 57 is 68/2 = 34%.
Which function represents g(x), a reflection of f(x) = Two-fifths (10)x across the x-axis? g(x) = Negative two-fifths(10)x g(x) = Negative two-fifths (one-tenth) Superscript x g(x) = Two-fifths (one-tenth) Superscript negative x g(x) = Two-fifths(10)-x
Answer:
The correct option is;
g(x) = Negative two-fifths(10)x
Step-by-step explanation:
The rule for the reflection across the x-axis is as follows;
Reflection about the x-axis
Pre-image point before reflection = (x, y)
Point of image after reflection = ((x, -y)
Therefore, the x coordinate remains the same while the y coordinate changes sign
For which given that f(x) = y = 2/5(10)x and g(x) = Reflection of f(x) across the x-axis, we have
Reflection about the x-axis
Pre-image point before reflection = (x, f(x))
Point of image after reflection = (x, g(x))
Hence g(x) = -f(x) = -2/5(10)x.
Answer:
A
Step-by-step explanation:
4.- En una pastelería han preparado 30 pasteles. Los van a colocar en bandejas de forma que en cada bandeja haya el mismo número de pasteles y no sobre ninguno. ¿De cuántas formas los puede colocar?
Answer:
7 formas
Step-by-step explanation:
En la pastelería, se han preparado 30 pasteles.
Cada bandeja contendrá la misma cantidad de pasteles.
Para encontrar de cuántas maneras puedes ponerlos, tenemos que encontrar los factores de 30. Ellos son:
1, 2, 3, 5, 6, 10, 15, 30
Esto significa que podemos tener:
30 bandejas que contienen 1 bandeja cada una
15 bandejas con 2 tortas cada una
10 bandejas con 3 tortas cada una
6 bandejas con 5 tortas cada una
5 pasteles que contienen 6 pasteles cada uno
3 bandejas con 10 pasteles cada una
2 bandejas con 15 tortas cada una
Esto significa que hay 7 formas de colocar los pasteles.
How many kilometers is it from the main gate to Manatee Springs? (Hint: To convert from
yards to kilometers, multiply by 0.0009144). Round answer to the nearest hundredth kilometer
Manatee Springs
Elephant
House
3,500 yds
- 200 yds
Tran Depot
2000
Bird Sanctuary
Main Gate
(SHOW WORK)
Answer:
6.04 km
Step-by-step explanation:
From the image attached, both triangles form are similar to each other because their corresponding angles are equal, therefore they are equiangular triangles. equiangular triangles have the same shape but different sizes and the ratio of their corresponding sides are equal.
Therefore since their corresponding sides are equal we can calculate the distance from the main gate to Manatee Springs. It is given by:
[tex]\frac{3500\ yards}{2000\ yards} = \frac{4200\ yards}{x}\\ x= \frac{4200\ yard*2000\ yards}{3500\ yards}=2400\ yards[/tex]
x = 2400 yards.
The distance from the main gate to Manatee Springs = x + 4200 yards = 2400 + 4200 = 6600 yards
The distance from the main gate to Manatee Springs = 6600 yards = (6600 * 0.0009144) km = 6.04 km
The distance from the main gate to Manatee Springs = 6.04 km
In 2004, the world's fastest knitter was able to knit 225 stitches in 3 min. How long would she take to knit a scarf that was 20 cm wide and 1.2 m long, if she used yarn that resulted in 1.6 stitches per centimetre?
It will take her 49.15 seconds to knit the scarf.
Since in 2004, the world's fastest knitter was able to knit 225 stitches in 3 min, to determine how long would she take to knit a scarf that was 20 cm wide and 1.2 m long, if she used yarn that resulted in 1.6 stitches per centimeter, the following calculation must be performed:
0.2 x 120 = Area 24 cm2 = Area 1.6 x 1.6 = 2.56 stitches per cm2 24 cm2 x 2.56 = 61.44 225/3 = 75 61.44 / 75 = 0.8192 1 = 60 0.8192 = X 0.8192 x 60 = X 49.15 = X
Therefore, it will take her 49.15 seconds to knit the scarf.
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which of the following sum in simplest form (radicals)
Answer:
9√2
Step-by-step explanation:
Easiest and fastest way is to plug it into a calc and calculate. If not, you will have to simplify the expressions to have a common root in order to add.
Answer:
9√2Option C is the correct option.
Solution,
[tex] \sqrt{8} + 3 \sqrt{2} + \sqrt{32} \\ = \sqrt{2 \times 2 \times 2} + 3 \sqrt{2} + \sqrt{2 \times 2 \times 2 \times 2 \times 2} \\ = 2 \sqrt{2} + 3 \sqrt{2} + 2 \times 2 \sqrt{2} \\ = 2 \sqrt{2} + 3 \sqrt{2} + 4 \sqrt{2} \\ =( 2 + 3 + 4 )\sqrt{2 } \\ = 9 \sqrt{2} [/tex]
Hope this helps...
Good luck on your assignment..
14.3p – 32.24 = 127.92 14.3p – 32.24 + 32.24 = 127.92 + 32.24 14.3p = 160.16 StartFraction 14.3 p Over 14.3 EndFraction equals StartFraction 160.16 Over 14.3 EndFraction.
Answer:
p = 11.2
Step-by-step explanation:
The computation is shown below:
Data provided in the question
2.6(5.5p – 12.4) = 127.92
Now
Distributive Propertyis
14.3p - 32.24 = 127.92
Addition Property is
14.3p = 127.92 + 32.24
Division Property is
14.3p ÷ 14.3 = 160.16 ÷ 14.3
p = 11.2
We simply find the value of p by applying the distributive property, addition property, and the division property and the same is to be considered
Answer:
The Answer is 11.2
Step-by-step explanation:
which one of the following is a type of face found on a platonic solid. A,regular hexagon, B. regular octagon, C.regular nonagon, D. regular pentagon
PLEASE NEED OF AN ANSWER
Answer:
B. regular octagon
I hope this will help you
What is the slope of the line through (-9, 6) and (-6, -9)? A/ ⅕ B/ 5 C/ -5 D/ -⅕
Answer:
-5
Step-by-step explanation:
We can find the slope between two points by using
m = (y2-y1)/(x2-x1)
= ( -9-6)/(-6 - -9)
=(-9-6)/( -6+9)
-15/3
-5
Answer:
C
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 9, 6) and (x₂, y₂ ) = (- 6, - 9)
m = [tex]\frac{-9-6}{-6+9}[/tex] = [tex]\frac{-15}{3}[/tex] = - 5 → C
Customers at your store select their groceries from shelves and then pay. Sales records and records of restocks for flaming roast coffee ( 1 lb size) are as follows: # of sales tues 5, we'd 8, thu 2, fri 19, sat 22, sun 15, mon 3, # of restock tue 6, wed 12, thurs 12, fri 18, sat 24, sun 0, mon0. What is the net change of how many bags are on the shelf, from the the beginning of tuesday to the end of monday?
Answer: - 2
Step-by-step explanation:
- - - - - - - - - - - T - - W - - TH - - F - - S - - S - - M
# of SALE - - - 5 - - 8 - - - 2 - - 19 - 22 - 15 - - 3
# of restock - 6 - - 12 - - 12 - - 18 - 24 - 0 - - 0
Calculating the change in shelf unit on a daily basis:
Change = difference in restock unit and the unit sold, that is, # RESTOCK - # SOLD
TUESDAY :
6 - 5 = 1
WEDNESDAY :
12 - 8 = 4
THURSDAY :
12 - 2 = 10
FRIDAY :
18 - 19 = - 1
SATURDAY :
24 - 22 = 2
SUNDAY :
0 - 15 = - 15
MONDAY :
0 - 3 = - 3
The net change equals the algebraic sum of all daily changes in shelf unit between Tuesday to Monday ;
[1 + 4 + 10 + (-1) + 2 + (-15) + (-3)]
[1 + 4 + 10 - 1 + 2 - 15 - 3]
[ 1 + 4 + 10 + 2 - 1 - 15 - 3]
= 17 - 19
= - 2
Number of bags decreased by 2