Answer:
a ≈ 117 cmStep-by-step explanation:
Using sine rule on triangle ABC as re - shown in the attachment below to get side AC first we have;
∠A = 34°, BC = 164cm, ∠B = 27°, AC = ?
AC/sin 27° = BC/sin 34°
AC/sin 27° = 164/sin 34°
AC = 164 * sin 27° / sin 34°
AC = 74.45/0.5592
AC = 133.14 cm
To get the side 'a', we will use the trig ratio SOH CAH TOA on the right angled ACD.
According to SOH,
sin 61° = a/AC
a = ACsin61°
a = 133.14 * sin 61°
a = 116.45
a ≈ 117 cm
The marked side is approximately 117 cm
please help! find the value of each shape
Answer:
see below
Step-by-step explanation:
red triangle= 36/2= 18
orange circle= 45- 18= 27
blue square= 53- 27= 26
Step-by-step explanation:
red= 18
yellow= 27
blue= 26
Cylinder a has a radius 2 cm and contains water to a height of 10cm cylinder b has a radius 5cm and is empty. Some of the water is poured from cylinder a to b the height is now the same
Answer:
h = 1.38 cm
Step-by-step explanation:
The question is at what value is the height of both cylinders the same:
The area of the circular base on each cylinder is:
[tex]Area=\pi r^2\\A=4\pi \ cm^2\\B=25\pi \ cm^2[/tex]
The initial volume in cylinder A is:
[tex]V=4\pi *10\\V=40\pi\ cm^3[/tex]
We have that Va + Vb = 40π. The height of water in each cylinder as a function of volume is:
[tex]h_A=\frac{V_a}{4\pi}\\h_B=\frac{V_b}{25\pi}[/tex]
If both heights are the same:
[tex]\frac{V_a}{4\pi}=\frac{V_b}{25\pi}\\V_b=\frac{25}{4}V_a \\V_a+V_b=40\pi\\V_a+\frac{25}{4}V_a=40\pi\\V_a=5.5172\pi\ cm^3[/tex]
The height 'h' is:
[tex]h=\frac{5.5172\pi}{4\pi}\\ h=1.38\ cm[/tex]
A preimage (2,-3) is translated to (3,2). What type of transformation has occured?
Answer:
Reflection.
Step-by-step explanation:
The reflection of the point (x,y) across the x-axis is the point (x,-y).
The reflection of the point (x,y) across the line y = x is the point (y, x).
Given the preimage (2,-3).
Step 1: Reflect (2,-3) accross the x-axis, to obtain: (2,3) Step 2: Reflect (2,3) accross the the line y = x to obtain: (3,2)Therefore, the type of transformation that has occured is Reflection.
Find The surface area of the pyramid
Answer:
85 ft^2
Step-by-step explanation:
Let us calculate the area of the triangles and the base.
For the triangles, we can use the area formula and get 5 • 3 which is 15. Since there are 4, we multiply it by 4 and get 60.
For the base, we have 5 • 5, which is 25. Adding it together, we get 85.
If you are stuck on how to find surface area, all you have to do is find the area of each side and add.
I hoped this helped!
Which graph represents a line with a slope of and a y-intercept equal to that of the line y = x – 2? A coordinate plane with a line starting at (negative 2, negative 4), passing through (0, negative 2) and (2, 1). A coordinate plane with a line passing through (negative 3, 0) and (0, 2). A coordinate plane with a line passing through (0, 2) and (2, negative 1). A coordinate plane with a line passing through (negative 3, 0) and (0, negative 2).
The slope of a line is the average rate of change of the line.
The graph that represents [tex]\mathbf{y = x - 2}[/tex] is graph (a)
The line equation is given as:
[tex]\mathbf{y = x - 2}[/tex]
To do this, we simply test the options until we get the correct graph
(a) Line that passes through (-2,-4) and (0,-2)
This means that:
[tex]\mathbf{(x_1,y_1) = (-2,-4)}[/tex]
[tex]\mathbf{(x_2,y_2) = (0,-2)}[/tex]
Substitute values for x1 and y1 in [tex]\mathbf{y = x - 2}[/tex]
[tex]\mathbf{-4 = -2 - 2}[/tex]
[tex]\mathbf{-4 = -4}[/tex]
This point is true for [tex]\mathbf{y = x - 2}[/tex]
Substitute values for x2 and y2 in [tex]\mathbf{y = x - 2}[/tex]
[tex]\mathbf{-2 = 0 - 2}[/tex]
[tex]\mathbf{-2 = - 2}[/tex]
This point is also true for [tex]\mathbf{y = x - 2}[/tex]
Hence, the graph that represents [tex]\mathbf{y = x - 2}[/tex] is graph (a)
See attachment for the graph of [tex]\mathbf{y = x - 2}[/tex]
Read more about linear functions at:
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Answer:
graph 4 i think
Step-by-step explanation:
11^-5 ÷ 11^-3 please help!!!!
Answer:
Step-by-step explanation:
[tex]a^{-m}=\frac{1}{a^{m}}\\\\Therefore, \frac{1}{a^{-m}}=a^{m}[/tex]
[tex]11^{-5}[/tex] ÷ [tex]11^{-3} = 11^{-5} * 11^{3}\\\\[/tex] {[tex]a^{m}*a^{n} = a^{m+n}[/tex] }
[tex]11^{-5+3} \\\\= 11^{-2}[/tex]
Answer:
11^ -2 = 1 / 11^2 = 1/121
Step-by-step explanation:
11^-5 ÷ 11^-3
When the bases are the same, we subtract the exponents when dividing
11 ^ ( -5 - -3)
11 ^ ( -5+3)
11 ^ -2
We know that a^ -b = 1/a^b
1/ 11^2
1/121
triangle ABC has vertices A(5, 12) B(13, 13) and C (11,5). show that the triangle ABC is. scalene triangle
Answer:
AB =√( (13 - 5)² + (13-12)²) = √(8² + 1²) = √65
BC = √( (13 - 11)² + (13-5)²) = √(2² + 8²) = √68
AC =√( (11 - 5)² + (5-12)²) = √(6² + 7²) = √85
AB ≠ BC ≠ AC ∴ ABC is Scalene
Step-by-step explanation:
A scalene triangle is a triangle in which all the sides are different lengths.
In order to prove that ABC is scalene, we need to calculate the sidelengths and show them to be different.
The line between points A(x₁, y₁) and B(x₂, y₂) can be denoted AB.
the difference in x-coordinate is x₂ - x₁, and the difference in y-coordinates is y₂ - y₁.
this forms a triangle of length x₂ - x₁ and height y₂ - y₁ and the hypotenuse AB can be calculated using pythagoras' theorem:
AB = √((x₂ - x₁)² +(y₂ - y₁)²)
The triangle ABC with vertices A(5, 12) B(13, 13) and C (11,5) is a scalene triangle.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
The given three vertices of triangle ABC are A(5, 12) B(13, 13) and C (11,5).
We know that in a scalene triangle all the three sides lengths are different.
Let us find distance of AB,BC, CA
Distance=√(x₂-x₁)²+(y₂-y₁)²
A(5,12), B(13, 13)
AB=√(13-5)²+(13-12)²
=√8²+1²=√64+1=√65
B(13, 13) C (11,5).
BC=√(11-13)²+(5-13)²
=√4+64=√68
C (11,5).A(5,12),
CA=√(5-11)²+(12-5)²
=√(-6)²+(7)²
=√36+49=√85
The lengths of triangle ABC are different so the triangle is Scalene.
Hence the triangle ABC with vertices A(5, 12) B(13, 13) and C (11,5) is a scalene triangle.
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Please help me I’m desperate
Answer:
The firstStep-by-step explanation:
[tex]\frac29x+3>4\frac59\\{}\quad-3\quad-3\\\\\frac29x\ >\ 1\frac59\\\div\frac29\quad \, \div\frac29\\\\x>1\frac59\div\frac29\\\\x>\frac{14}9\times\frac92\\\\x>\frac{7}1\times\frac11\\\\x>7[/tex]
That means every x wich is greater than 7
For one month Siera calculated her home town’s average high temperature in degrees Fahrenheit. She wants to convert that temperature from degrees Fahrenheit to degrees Celsius using the function C of F = five-ninths (F minus 32) . What does C(F) represent?
Answer:
The answer is below
Step-by-step explanation:
A function shows relationship between variables usually between inputs (an independent variable) and outputs (a dependent variable).
C(F) = 5/9(F - 32) shows the relationship between C and F. C(F) is the temperature in degree Celsius for any temperature in Fahrenheit. This means that the function C(F) represents the conversion of temperature from Fahrenheit to degree Celsius.
Find the surface area of the prism.
Answer:
a). B = 24 yd²
b). h = 8 yd
c). S.A. = 240 yd²
Step-by-step explanation:
Area of the triangular base B = [tex]\frac{1}{2}(\text{Base of the right triangle})(\text{height of the base triangle})[/tex]
= [tex]\frac{1}{2}(8)(6)[/tex]
= 24 yd²
Height of the prism 'h' = distance between the triangular bases
= 8 yd
Perimeter of the triangular base = leg 1 + leg 2 + hypotenuse
= 8 + 6 + 10 = 24 yd
Surface area = 2B + Ph
= (2×24) + (24×8)
= 48 + 192
= 240 square yds
If a ∥ b and _____, then a ∥ c.
Answer:
b || c
Step-by-step explanation:
a can only be parallel to c is if c is parallel to either a or b as both a and b are parallel to each other. By the way || means that they are parallel lines.
Please help me in this question.Please!!!!
Answer:
[-3, -3]
Step-by-step explanation:
Simply divide the matrices together and you should find your solution.
are the two triangles similar? how do you know
Answer:
yes; by AA~
Step-by-step explanation:
The triangles are similar because vertical angles are congruent and alternate interior angles are both 39 degrees.
What percentage of students under age 15 travel to school by car? Round to the nearest whole percent. 11% 18% 41% 80%
Answer:
11%
Step-by-step explanation:
We need to fill the missing cells of the table first and are interested in first row for under age 15
1. 152- 65= 87 for the top left cell
2. 165- (87+60)= 18 for car column on same row
now we have number 18 and the total of the first row is 165:
18/165*100%= 10.9%So the first choice- 11% is the answer
Answer:
11% is the pecentage of students under the age of 15 that travel by car to school.
What is the scale factor ??
Answer:
3.5
Step-by-step explanation:
63 divided by 18 is 3.5
35 divided by 10 is 3.5
preform the operation and show work
Answer:
1 / (x² + 6x + 8)
Step-by-step explanation:
(x + 4) / (x² + 5x + 6) * (x + 3) / (x² - 16)
= (x + 4) / (x + 2)(x + 3) * (x + 3) / (x + 4)(x - 4)
↑ factor x² + 5x + 6 ↑ factor x² - 16 using difference of squares
= 1 / (x + 2) * 1 / (x - 4) ← x + 4 and x + 3 cancel
= 1 / (x + 2) * (x + 4) ← multiply
= 1 / (x² + 6x + 8) ← expand
please help ! Find all the missing angel measures in angel 1,4,7,10,13 the picture is attached above please help !! It’s for geometry (:
Answer: ∠1 = 52°, ∠4 = 40°, ∠7 = 100°, ∠10 = 49°, ∠13 = 65°
Step-by-step explanation:
There are three formulas you need to find the angles. Each formula is based on where the vertex lies.
On the circle: Measure of the angle = (1/2) the arc (Images 1-3)
∠4 = (1/2)°80 ∠10 = (1/2)(18° + 80°) ∠13 = (1/2)130°
= 40° = (1/2)98° = 65°
= 49°
Inside the circle: (1/2) Sum of the Big arc and Little Arc (Image 4)
∠7 = (1/2) (130° + 70°)
= (1/2)200°
= 100°
Outside the circle: (1/2) Difference of Big arc and Little Arc (Image 5)
∠1 = (1/2)[(62° + 130°) - (70° + 18°)]
= (1/2) (192° - 88°)
= (1/2)104°
= 52°
I can only add 5 attachments. If you want to see image 6 (which contains the measures for all of the angles), you will need to ask the question again. Sorry!
Help I will make you a brainllest :)
Answer:
140
Step-by-step explanation:
Since m∠2 is 40°, then the m∠1 is also 40°. With that, ∠1 and ∠5 are supplementary, so we have 180 - 40 = 140°
Answer:
140
Step-by-step explanation:
done it before and had teacher show me answer sheet
I need help with this what is the answer
Answer:
5
Step-by-step explanation:
if u substitute the x's then u can see that it makes sense
ex. 5(1)+5 = 10 true
ex. 5(5)=5 = 30 true
hope this helps
You are given two offers for a monthly wage. Option A is to be paid one cent on the first day of the month, with your wages doubling each day (2 cents on day 2, 4 cents on day 3, 8 cents on day 4, etc.) for the rest of this 30 day month. Option B is to be paid $1 on the first day of the month, with your wages increasing $100 each day ($101 on day 2, $201 on day 3, $301 on day 4, etc.). Which option will give you more money by the end of the month? Make sure to support your answer.
Answer:
Option B.
Step-by-step explanation:
If you begin with one dollar a day there will get you more by the end of the month because on day 2 your on 201 already which is more than you get in that month with one cent.
The first option (A) will give you more money than option (B).
What are the geometrical progression series and arithmetic progression series?A geometric progression is a sequence in which any element after the first is obtained by multiplying the previous element by a constant which is called a common ratio denoted by r.
The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).
Given that
Case A). Doubling each day
1 + 2+ 4 + 8 + 16 .... it is form a GP series with common ratio (r) 4/2 = 2
Number of terms (n)
Sum = 30( [tex]2^{30}[/tex] - 1)/(2 - 1) = $2147483464.
Case B). Adding $100 each day
1 + (101 + 201 + 301 ....) it is form a ap series with common difference d = 201 - 101 = 100.
Number of terms = 29
Sum = 1 + 29/2 + [ 2 (101) + 28(100)] = $43530
Hence it is clear that case (A) will give you more money.
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Please answer it now in two minutes
Answer:
[tex]y=\frac{-5}{2}x+1.5[/tex]
Step-by-step explanation:
Well the equation we have [tex]y-4=\frac{-5}{2}(x-2)[/tex] is in slope-point form so we have to transfer it to slope intercept look at the first image below to see how I got [tex]y=\frac{-5}{2}x+9[/tex].
So we know that line T which is parallel to line S crosses through point (-1,4)
and we know that the slope stays the same and that its the y intercept has to change so the answer is [tex]y=\frac{-5}{2}x+1.5[/tex]. Look at the image second below.
this is the question click it
Answer:
C.
Step-by-step explanation:
5/8 = 20/32
20/32 ÷ 2 = 10/16
10/16 ÷ 2 = 5/8
Answer:
C
Step-by-step explanation:
You can see that both of the numbers are being multiplied by 4/4 which gives you a proportional relationship unlike the other answers there.
Every minute 2.5 gallons of water flows from the shower a family of four people showers for an average five minutes per person every morning how many gallons of water does a family use for showering every morning
Answer:
number of gallons of water the family will use every morning = 50 gallons
Step-by-step explanation:
Every minutes 2.5 gallons of water flows from the shower . The amount of water disperse by the shower for every 1 minutes is 2.5 gallons. The family using the shower are 4 in numbers . And each of them spend on average of 5 minutes showering .
Let us find how many gallons of water will flow for 5 minutes since family member spent an average of 5 minutes bathing every morning/. Therefore,
2.5 gallons = 1 minutes
? gallons = 5 minutes
cross multiply
number of gallons of water each family member uses every morning = 2.5 × 5 = 12.5 gallons
They are 4 family members in number since each person uses 12.5 gallons of water , 4 of them will use 4 × 12.5 = 50 gallons
Solve the equation by factoring:
x² – 5x = 14
a. x= -2 or 7
b. x= 2 and -7
C. X= -2 or -7
d. x = 2 or 7
Answer:
The two possible solutions are x = 7, or x = -2
which agree with answer a) in the list of options
Step-by-step explanation:
Start by moving all terms to one side of the equal sign, and then factoring out the constant term:
[tex]x^2-5x-14=0[/tex]
The constant term "-14" has ossible factors: (-1), (1) (-2), (2), (-7), (7), (-14), (14) and we look for a pair whose combining results in "-5" (the coefficient of the middle term. We find (-7) and (2) the appropriate factors, so we use then to split the middle term and then factor by grouping:
[tex]x^2-5x-14=0\\x^2-7\,x+2\,x-14=0\\x(x-7)+2(x-7)=0\\(x-7)\,(x+2) = 0[/tex]
Then if the product of these two binomial factors is zero, it means that the first binomial is zero, or the second one is zero. That is:
( x - 7 ) = 0 which means x = 7
or
( x + 2 ) = 0 which means x = -2
So the two possible solutions are x = 7, or x = -2
Answer:
a. -2 or 7Step-by-step explanation:
[tex]x^2-5x=14\\\\x^2-5x-14=0\\\\x^2+2x-7x-14=0\\\\x(x+2)-7(x+2)=0\\\\(x+2)(x-7)=0\\\\x+2=0\quad\vee\quad x-7=0\\\\x=-2\quad\vee\quad x=7[/tex]
Melanie began studying a sample of the chemical element einsteinium-253 which naturally loses its mass over time. The relationship between the elapsed time, t, in days, since Melanie started studying the sample, and the total mass remaining in the sample, M(t), in micrograms, is modeled by the following function: M(t)=169⋅(0.96)^t. How much percent does the chemical element lose weight by everyday?
Answer:
The chemical element loses 4% of its weight everyday
Step-by-step explanation:
Here, we are interested in knowing the percentage weight loss of the chemical each day.
The key to answering this is looking at the expression inside the bracket.
We can express M(t) = 169•(0.96)^t as
M(t) = 169•(1-0.04)^t
So what this means is that we need to find the percentage value corresponding to 0.04 since it is a constant term here
Mathematically, 0.04 is same as 4/100, so we can clearly say that the constant percentage loss is 4%
Answer:
0.96
Step-by-step explanation:
The exponential function modeling the mass of the sample is of the form M(t)=A⋅Bt. Therefore, AAA determines the initial mass of the sample (when Clemence began studying it) and BBB determines the daily change in the mass of the sample.
The mass of the sample is multiplied by \it{0.96}0.960, point, 96 every day. Since 0.96<10.96<10, point, 96, is less than, 1, the mass of the sample shrinks by a factor of 0.960.960, point, 96 every day.
Every day, the mass of the sample shrinks by a factor of 0.960.960, point, 96.
Please help!!me don’t understand
Answer:
x=45
Step-by-step explanation:
the sum of straight angle=180
2x+45+x=180
3x=180-45
3x=135
x=135/3=45
Answer:
45 degree
Step-by-step explanation:
Since it is an straight line it means all of the added angles together equal 180
2x+45+x=180
3x+45=180
3x=135
x=135/3
x=45
9a
+ 6b
Help please
Answer:
3(3a+2b)
Step-by-step explanation:
9a+6b
3 times 3a=9a
3 times 2b=6b
Answer:
3(3a+2b)
Step-by-step explanation:
9a+6b
3²•a+(2.3)b
3(3²•a/3 +2•3b/3)
3(3²-¹ •a +2b)
3(3a+2b)
What is the volume of the cone with a diameter of 4ft and height 4ft round to the nearest cubic foot
Answer:
67
Step - Step - Explanation
What is 220% of 400? A. 88 B. 880 C. 8,800 D. 88,000
Answer:
The correct answer is B. 880
Step-by-step explanation:
220%=2.2
2.2(400)=880
Answer:
B. 880
Step-by-step explanation:
220% × 400
= 220/100 × 400
= 88000/100
= 880
a) (Triangle)ABC, given that AB = 16 cm, BC = 63 cm and
AC = 65 cm how do we find if it is a right angled
Answer:
Δ ABC is right angled
Step-by-step explanation:
If the triangle is right then the longest side squared will equal the sum of the squares on the other 2 sides.
longest side = 65, then
65² = 4225
16² + 63² = 256 + 3969 = 4225
Since 65² = 16² + 63² then Δ ABC is right
Answer:
We can know if it is a right angled triangle by using the Pythagoras theorem ( a²+b²=c²)
Step-by-step explanation:
To identify, we can take the largest length of the triangle as hypotanuse( that is, AC:65) And the rest as base and perpendicular ( 63 and 16 cm)
By applying Pythagoras theorem,
AB²+BC²= AC² ; (63)²+(16)²= (65)²
63² is 3969, 16² is 256… 65² is 4225.
Now, if 63²+16²:65²… then the triangle mentioned is a right angled triangle.
3969+256=4225
LHS = RHS, So, triangle ABC is a right angled triangle as it satisfies the condition of Pythagoras theorem.