Answer:
I believe the terms would be 31, 35, 39.
Step-by-step explanation:
We know this because 43-27 is 16. since there are 3 terms missing, we divide the answer by 4, and you get 4. The number you get there is how many you add to each term to get the missing ones. For example, 27+4=31. The pattern is adding 4 to each term. Hope I helped!
Find the simplified product. b-5/2b X b^2+3b/b-5
The simplified product of [tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5}[/tex] is [tex]\frac{(b+3)}{2}[/tex]
How to simplify a product?The products can be simplified as follows;
Multiplying fraction,
[tex]\frac{x}{y} . \frac{a}{b} = \frac{xa}{yb}[/tex]
Therefore,
[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)}[/tex]
Hence,
Let's reduce the fraction by dividing
[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)} = \frac{(b^{2}+3b )}{(2b)}[/tex]
Therefore,
[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)} = \frac{(b^{2}+3b )}{(2b)} = \frac{(b(b+3))}{2b}[/tex]
Hence,
[tex]\frac{b- 5}{2b} X \frac{b^{2} + 3b }{b - 5} = \frac{(b-5)(b^{2} + 3b )}{(2b)(b-5)} = \frac{(b^{2}+3b )}{(2b)} = \frac{(b(b+3))}{2b} = \frac{b+3}{2}[/tex]
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Answer:
A, b+3/2
Step-by-step explanation:
1. y = 5 x Reflected across the x-axis 2. y = 5 –x+ 5 Reflected across the y-axis 3. y = 5 –x + 5 Translated down by 5 units 4. y = 5 –x – 5 Translated up by 5 units 5. y = –5 –x Translated left 5 units 6. y = 5 –x – 5 Translated right by 5 units
The matchup are:
1. Translated left 5 units - y = 5⁻ ˣ ⁻ ⁵ 2. Translated right by 5 units - y= 5⁻ ˣ ⁺ ⁵3. Translated up by 5 units - y = 5⁻ˣ + 54. Translated down by 5 units - y = 5⁻ ˣ -5 5. Reflected across the x-axis - y= - 5 ⁻ ˣ6. Reflected across the y-axis -y = 5ˣWhat is Translation and reflection?Reflection is known to be the turning over an object across a line and it is one where we do not need to change its size or shape.
While Translation is said to be sliding a figure into another direction and it is one where we do not need to change its size, shape or make.
The Translation and reflection matchup are given:
1. Translated left 5 units - y = 5⁻ ˣ ⁻ ⁵ 2. Translated right by 5 units - y= 5⁻ ˣ ⁺ ⁵3. Translated up by 5 units - y = 5⁻ˣ + 54. Translated down by 5 units - y = 5⁻ ˣ -5 5. Reflected across the x-axis - y= - 5 ⁻ ˣ6. Reflected across the y-axis -y = 5ˣSee full question below
Match each function formula with the corresponding transformation of the parent function y = 5-^x Please help ASAP!!
1. y = 5x
Translated left 5 units
2. y = 5–x + 5
Translated right by 5 units
3. y = 5–x – 5
Translated up by 5 units
4. y = 5–x+ 5
Translated down by 5 units
5. y = –5–x
Reflected across the x-axis
6. y = 5–x – 5
Reflected across the y-axis
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Which of the following is equivalent to
(16 3/2)^1/2 ?
O 6
O 8
O 12
O 64
Step-by-step explanation:
[tex] = { ({16}^{ \frac{3}{2} } )}^{ \frac{1}{2} } [/tex]
[tex] = { ({( {2}^{4}) }^{ \frac{3}{2} } )}^{ \frac{1}{2} } [/tex]
[tex] = {2}^{4 \times \frac{3}{2} \times \frac{1}{2} } [/tex]
[tex] = {2}^{ \frac{12}{4} } [/tex]
[tex] = {2}^{3} [/tex]
[tex] = 2 \times 2 \times 2[/tex]
[tex] = 8[/tex]
The answer is B.
5(b)
Joe has a bucket containing 1370cm³ of water measured to the nearest 10 cm³.
Joe Says
"If I tip my bucket of water in the cuboid container, it will never overflow"
Is Joe correct?
You must explain your answer
If the side length is greater than 11.11 cm then it will not overflow.
Otherwise, it will overflow.
If Joe tips the bucket of water in a cuboid container and the water is not overflowing then the cuboid container must be of volume greater than 1370 cm³.
We find the cube root of 1370 cm³.
[tex]\sqrt[3]{1370} \approx11.11[/tex]
Then the cuboid container should have a side of length greater than 11.11 cm.
Here the statement "If I tip my bucket of water in the cuboid container, it will never overflow" is correct or wrong based on the information that the container has a side length lesser or greater than 11.11 cm.
If the side length is greater than 11.11 cm then it will not overflow.
Otherwise, it will overflow.
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BC and DE are tangents to this circle. Work out the size of angle 0. Give reasons for your answer. A 52° B O D 27° E 0 C Not drawn accurately BC and DE are tangents to this circle . Work out the size of angle 0 . Give reasons for your answer . A 52 ° B O D 27 ° E 0 C Not drawn accurately
Answer:
Θ = 39°
Step-by-step explanation:
OA = OB ( radii of the circle ) , then
Δ AOB is isosceles with base angles congruent , that is
∠ ABO = ∠ BAO = 52°
the exterior angle of a triangle is equal to the 2 opposite interior angles.
∠ DOB is an exterior angle of the triangle , so
∠ DOB = ∠ ABO + ∠ BAO = 52° + 52° = 114°
the angle between a tangent and the radius at the point of contact is 90°, then
∠ OBC = ∠ ODE = 90°
the sum of the 4 interior angles of quadrilateral OBCD = 360°
∠ OBC + ∠ DOB + ∠ ODC + ∠ BCD = 360°
90° + 114° + (90 + 27)° + Θ = 360°
90° + 114° + 117° + Θ = 360°
321° + Θ = 360° ( subtract 321° from both sides )
Θ = 39°
can someone help me?
Answer:
think of each T in the original equation as an empty box, like this:
P( ) = 2( )² + ( ) - 7
when it says p(some number), it means replace all Ts in the equation with that number.
P( 0 ) = 2( 0 )² + ( 0 ) - 7 = 0 + 0 - 7 = -7
do the same for the rest <:)
for the second part, it's the same concept: every T is replaced with what's inside the parentheses.
so P( -t ) = 2( -t )² + ( -t ) - 7 = 2t² - t - 7
and so on and so forth.
Use 8a+16c.
What is the value of the expression when a = –5 and c = –1? Enter your answer in the box.
+
Carla babysits and tutors to make extra money. She babysits for $5 an hour and tutors for $10 an hour.
She can only work at most 15 hours a week. She wants to go on a trip with her friend and needs to
make $95 dollars this week to cover the cost of the trip. Write a system of inequalities to represent this
situation.
The system of inequalities to represent this situation will be x + y ≤ 15 and 5x + 10y ≤ 95.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Carla babysits and tutors to make extra money.
She babysits for $5 an hour and tutors for $10 an hour.
She can only work at most 15 hours a week.
Likewise, she wants to go on a trip with her friend and needs to make 95 dollars this week to cover the cost of the trip.
Then the system of inequalities to represent this situation will be
Let x be the number of babysits hours and y be the number of tutor's hours.
x + y ≤ 15
5x + 10y ≤ 95
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There are x boys in a class. If the
number of girls are 3x + 1, how many
boys and girls are in the class
altogether.
Answer:
4x+1
Step-by-step explanation:
3x+x+1=4x+1
Matt is trying to measure the height of a tree using
trigonometry. He is having trouble because of the
terrain around the tree. The horizontal distance
from the tree to Matt's eyes is 120 feet. The angle
of depression from the horizontal is 30°. Matt's
angle of sight to the top of the tree is 23°. What is
the height of the tree? (Round to the nearest foot.)
The height of the tree will be 18.35 feet.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Matt is trying to measure the height of a tree using trigonometry.
He is having trouble because of the terrain around the tree.
The horizontal distance from the tree to Matt's eyes is 120 feet.
The angle of depression from the horizontal is 30°.
Matt's angle of sight to the top of the tree is 23°.
The diagram is given below.
Let x be the height of tree and AM be h.
The value of (h + x) will be
tan 30° = (x + h) / 120
x + h = 69.288
Then the value of h will be
tan 23° = h / 120
h = 50.94 feet
Then the height of the tree will be
⇒ h + x – h
⇒ 69.29 - 50.94.
⇒ 18.35 feet
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9. Solve for x: Please explain
Answer:
since the triangle has a line on 2 sides, it means that it is equal. Also, every triangle has 180 degrees so the missing degree is 70
Step-by-step explanation:
Figured it out
Answer:
x = 70°
Step-by-step explanation:
Since 2 sides are marked as congruent then the triangle is isosceles with 2 base angles being congruent , both 55°
the sum of the 3 angles in the triangle = 180° , so
x + 55° + 55° = 180°
x + 110° = 180° ( subtract 110° from both sides )
x = 70°
Find the length of the missing side. Leave your answer in simplest radical form.
Answer:
[tex]\sqrt{69}[/tex]
Step-by-step explanation:
from the pythagorean theorem:
[tex]a^2 + b^2 = c^2\\10^2 + b^2 = 13^2\\100 + b^2 = 169\\b^2 = 69\\b = \sqrt{69}[/tex]
what is 1,000,000,000 divided by -1,000
-1000000 that is the answer
hope this helps!
Last week, you went to the water park with friends on Monday, Wednesday, and Friday. If you stayed at the water park 3.5 hours each of those days, how many hours did you spend at the water park last week?
A. 15 hours
B. 9 hours
C. 5.5 hours
D. 10.5 hours
Answer: D. 10.5 hours
Step-by-step explanation:
3 days, 3.5 hours each
3.5 * 3 = 10.5 hours
Answer:
D. 10.5
Step-by-step explanation:
3.5 x 3 = 10.5
can someone please help me
Answer:
-6, 14, -26, 10x -4, -8x + -2x - 6
Step-by-step explanation:
So F(x) is setting that the values before the lines are equal to x and should be applied to the problem. Dont forget PEMDAS with these tho, they'll try to trick u like that.
So for the first one, f(0) you plug 0 where the x's are.
1.) 8(0)^2 +2(0) -6
0 + 0 - 6 = -6
2.) 8(2) +2(2) - 6
16+ 4-6= 20 - 6= 14
3.) 8(-2) + 2(-2) -6
-16 + -4 -6 = -26
On the ones where they leave the x there, you just have to leave the x. But don't forget distribution tho.
4.) 8(x+1) +2(x+1) -6
8x +8 + 2x + 2 -6
10x +10 -6 = 10x -4
5.) 8(-x) + 2(-x) -6
-8x + -2x -6
Step-by-step explanation:
the given function is f(x) = 8x² + 2x -6
f(0) = 8(0)² + 2(0) -6 = -6
f(2) = 8 (2)² + 2 (2) - 6 = 30
f(-2) = 8 (-2)² + 2 (-2) - 6 = 22
f (x+1) = 8(x+1)² + 2 (x+1) -6
= 8(x² +2x +1 ) + 2x -4
8x² + 16x +8 +2x -4 = 8x² + 18x + 4
f(-x) = 8(-x)² + 2 (-x) - 6
= 8x² -2x -6
An indoor running track is 200 meters in length. During a 3,000-meter race, runners must complete 15 laps of the track. An electronic timing device records the amount of time it takes each runner to complete a lap for every lap in the race. These are called lap times. The histograms below display the lap times for both Stefano and Alex, runners in the 3,000-meter race.
2 histograms. A histogram titled Alex apostrophe s 3,000 meter race lap times has lap times (seconds) on the x-axis, and frequency on the y-axis. 35 to 36, 1; 36 to 37, 5; 37 to 38, 4; 38 to 39, 4; 39 to 40, 1. A histogram titled Stefano apostrophe s 3,000 meter race lap times has lap times (seconds) on the x-axis, and frequency on the y-axis. 32 to 33, 1; 34 to 35, 1; 36 to 37, 1; 37 to 38, 4; 38 to 39, 5; 39 to 40, 1; 40 to 41, 2.
Using the histograms, which of the following is a correct comparison?
Neither runner had a lap time between 35 and 36 seconds.
Alex’s lap times show less variability than Stefano’s lap times.
The median lap time for both runners is in the 38–39 interval.
Both runners’ highest number of lap times in the 37–38 interval.
The true statement based on the histogram is
There were no lap times between 35 and 36 seconds.
The correct option is (A).
What is Histogram?A histogram is a graphical representation that organizes a group of data points into user-specified ranges.
Given:
indoor running track is 200 meters in length.
Also, a 3,000-meter race, runners must complete 15 laps of the track.
As, there no data for interval 35-36.
So, there were no lap times between 35 and 36 seconds.
Hence, The interval from 37 to 38 seconds saw the most lap times.
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Answer:
B. Alex's lap times show less variability than Stefano's lap times.
Step-by-step explanation:
A can't be right because Alex has a lap time between 35 and 36 seconds.
C can't be right because the median lap time for Alex isn't 38-39.
D can't be right because both runners have a higher frequency on lap times other than 37-38.
so it has to be B.
What is the nth term rule of the linear sequence below?
27, 25, 23, 21, 19, ...
Answer:
Step-by-step explanation:
Comment
This is an arithmetic series. It has the following givens.
a = 27 The first term
d = - 2 The difference between one term and the one behind it.
n = quite small
Tn = a + (n - 1)*d
tn = 27 - 2n + 2
tn = 29 - 2n
Write and solve a proportion to complete the statement. Round to the nearest hundreth if necessary.
1. 6km ≈ ?mi
2. 2.5 L≈ ?gal
3. 90lb ≈ ?kg
pls help
The conversion of the following units are done below.
6 km = 3.72 miles2.5 L = 0.65 gallons90 lb = 40.5 kgWhat is conversion?Conversion means to convert the same thing into different units.
We know the following unit's conversion.
1 km = 0.62 miles
6 km = 3.72 miles
1 L = 0.26 gallons
2.5 L = 0.65 gallons
1 lb = 0.45 kg
90 lb = 40.5 kg
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f(x)=x+2 g(x)=x-4
(f g)(x) =
O2x-2
O²-8
02-2x-8
Ọ x2+2x-8
Solve for (f g)(x)
Step-by-step explanation:
please mark me as brainlest
The new function (fog)x will be x - 2.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
To find (f g)(x), we need to evaluate f(g(x)).
First, we need to find g(x):
g(x) = x - 4
Next, we substitute g(x) into f(x):
f(g(x)) = f(x - 4)
Now we can simplify:
f(x - 4) = (x - 4) + 2
f(g(x)) = x - 2
Therefore, (f g)(x) = x - 2.
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Which of the following objects is considered to be one-dimensional because it ha length but no width or height?
A. Line segment
B. Point
C. Triangle
D.Cube
give me the answer
Given below is a magic square. Place the numbers
70 – 21 25 24 , ,, 95 –133 95 38
in the appropriate squares so that sum in each row, column and
diagonal is equal
The appropriate numbers to fill in the magic squares are;
Row 2, Column 2 = 21/133
Row 2, Column 3 = 24/38
Row 3, Column 2 = 70/95
Row 3, Column 3 = 25/95
How to use magic squares?
To solve this magic square, we will follow the procedures below;
Step 1; Convert all the numbers into lowest forms.Step 2; Find the sum of any column or row which is 34/19.Step 3; Put the numbers given in such positions that the sum of each row, column and diagonal is equal.Step 4; Write the numbers in their original form.When we follow those steps above, we will arrive at the following figures;
Row 2, Column 2 = 21/133
Row 2, Column 3 = 24/38
Row 3, Column 2 = 70/95
Row 3, Column 3 = 25/95
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What is the 25th term of this arithmetic sequence? 3,9,15,21,27
Answer:
75
Step-by-step explanation:
you need to divide numbers by 3
3×25=75
Answer:
147
Step-by-step explanation:
Arithmetic sequence:
a = first term = 3
d = common difference = second term - first term
= 9 - 3
d = 6
n = 25
[tex]\sf \boxed{\bf n^{th} \ term = a + (n-1) d}[/tex]
= 3 + (25 - 1)*6
= 3 + 24*6
= 3 + 144
= 147
80 pupils in a sports centre are surveyed. the pupils can only use the swimming pool and the gym. 32 pupils use the swimming pool. 43 pupils use the gym. 19 pupils use neither the swimming pool nor the gym. find the probability to select a pupil that uses the swimming pool but not the gym.
[tex]\frac{18}{80}[/tex] is the probability of pupil that uses the swimming pool but not the gym.
It is given that:
Total students are 80
32 pupils use the swimming pool
43 pupils use the gym
19 pupils use neither the swimming pool nor the gym
To know the pupils who use both add 32+43 = 75
75-61= 14 pupils use both
32-14 = 18 pupils use only the swimming pool
43-18= 29 pupils use only the gym
Hence, [tex]\frac{18}{80}[/tex] is the probability of pupil that uses the swimming pool but not the gym.
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Identify a pair of overlapping congruent triangles in the
diagram. Then use the given information to write a proof
to show that the triangles are congruent.
Proof
Given: AC = BC, LA = LB
Answer:
overlapping congruent triangles:
ΔACE ≅ ΔBCD
Proof:
given: AC ≅ BC, angle A ≅ angle B
angle ACB ≅ angle BCA by the reflexive property
ΔACE ≅ ΔBCD by the ASA triangle congruence property
(PLEASE HELP!) A rectangular photograph measures 24x19 cm. It is mounted on a card of size such that there is a 2 cm border all around. For the purposes of this question take the length of the photograph to be 24 cm.
If one of the borders must be 2 cm in width, determine the width of a possible length and width so that the inner and outer rectangles are similar.
Answer: The card is 28 cm by 23 cm
Check out the diagram below
Explanation:
I added 4 cm to each dimension of the "24 x 19". Why 4 instead of 2? Because we're effectively adding two copies of "2 cm" to each of the original length and width. Along the horizontal component, we have the left and right boundaries. Along the vertical component, we have the top and bottom boundaries. The diagram hopefully clears up any confusion you may have.
-40 represents the height of a subway 40 feet below ground level. 40 represents the height of a kite 40 feet above ground level what does the zero rpresent in this situation
Answer:
0 represents the ground level
A gas tank consists of a cylinder with a hemisphere on top. It is made of metal that is 1 cm
thick. It has an overall height of 90 cm and an external diameter of 20 cm. Calculate:
a the surface area of the tank
b the internal volume of the tank.
(Give answers correct to two significant figures)
The surface area of the cylinder is 5969.03 cm²
The internal volume is 23156.68 cm³
Given:
A gas tank consists of a cylinder with a hemisphere on top.
The thickness of the metal is 1 cm
The overall height is 90 cm
The external diameter is 20 cm
To Find
a) the surface area of the tank
We will add the area of the bottom circle of radius 10 cm (counting the 1 cm thickness in), the external surface area of cylinder of height (90 - 10) cm =80 cm and radius 10 cm, and the surface area of the hemisphere of radius 10 cm.
So, the surface area of the cylinder is
[tex]\pi\times(10)^2+2\times\pi\times 10\times 80+ 2\times \pi \times (10)^2[/tex]
= π×(100+1600+200)
= π×(1900)
= 5969.03 cm²
b) To find the internal volume of the tank we find the internal volume of the hemisphere with an internal radius (10-1)=9 cm,
the internal volume of the cylinder of radius 9 cm and height (80-1) cm
= [tex]\frac{4}{3}\times \pi \times 9^3[/tex]+[tex]\pi\times 9^2\times 79[/tex]
= 23156.68 cm³
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To eliminate the × terms and solve for y in the fewest steps by which constants should be equations be multiplied by before adding the equations together
To eliminate the y terms and solve for x in the fewest steps, you can multiply the equations by appropriate constants so that the coefficients of the y terms in Both equations have the same magnitude but opposing signs. So to eliminate the y terms and solve for x in the fewest steps, you should multiply the first equation by 2 and the second equation by 3x
In this instance, you can do the following steps:
Start with the original equations:
Equation 1: 2x + 3y = 8
Equation 2: 3x - 2y = 4
To eliminate the y terms, multiply Equation 1 by 2 and Equation 2 by 3:
Multiply Equation 1 by 2:
2(2x + 3y) = 2(8)
4x + 6y = 16
Multiply Equation 2 by 3:
3(3x - 2y) = 3(4)
9x - 6y = 12
Now, add the two modified equations together to eliminate the y terms:
(4x + 6y) + (9x - 6y) = 16 + 12
4x + 9x + 6y - 6y = 28
13x = 28
Finally, solve for x by dividing both sides of the equation by 13:
x = 28/13
Therefore, to eliminate the y terms and solve for x in the fewest steps, you should multiply the first equation by 2 and the second equation by 3x
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The probable question may be:
To eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before adding the equations together? The first equation should be multiplied by 2 and the second equation by 3. x.
can someone please help and explain its due in a littleee
[tex]f(x) = {x}^{2} - 3x + 2 [/tex]
••••••••••••••••••••••••••••••••••••••••put x = (-1)
[tex] f( - 1) = {( - 1)}^{2} - 3 \times ( - 1) + 2 \\ \\ 1 + 3 + 2 \\ \\ 6.[/tex]
••••••••••••••••••••••••••••••••••••••••put x = (z)
[tex] f(z) = {z}^{2} - 3 \times z + 2 \\ \\ {z}^{2} - 3z + 2 \\ \\ {z}^{2} - 2z - z + 2 \\ \\ z(z - 2) - 1(z - 2) \\ \\ (z - 1)( z -2 ) \\ \\ (z - 1) = 0 \: \: , \: \: (z - 2) = 0\\ \\ z = 1 \:, \: 2[/tex]
••••••••••••••••••••••••••••••••••••••••put x = (x+1)
[tex]f(x + 1) = {x}^{2} - 3x + 2 \\ \\ {(x + 1)}^{2} - 3 (x + 1) + 2 \\ \\ {x}^{2} + 1 + 2x - 3x - 3 + 2 \\ \\ {x}^{2} - x \\ \\ x(x - 1) \\ \\ x(x - 1) = 0 \\ \\ x - 1 = \frac{0}{x} \\ \\ x - 1 = 0 \\ \\ x = 1.[/tex]
•••••••••••••••••••••••••••••••••put x = (√2 + 1 )
[tex]f( \sqrt{2} + 1) = {x}^{2} - 3x + 2 \\ \\ {( \sqrt{2} + 1) }^{2} - 3( \sqrt{2} + 1) + 2 \\ \\ 2 + 1 + 2\sqrt{2} - 3 \sqrt{2} - 3 + 2 \\ \\ 3 - 1 \sqrt{2} - 1 \\ \\ 2 - \sqrt{2} \\ \\ 2 - 1.4 (optional \: \: \: steps)\\ \\ 0.6 \: \: [/tex]
Which transformation would be a horizontal reflection and a dilation of scale factor ½ of the L shape?
The transformation which would be a horizontal reflection and a dilation of scale factor ½ of the L shape is as in the attached image.
What is horizontal reflection and dilation?The term horizontal reflection with respect to transformation in mathematical context simple means that the shape is reflected over the vertical axis(y-axis as mirror). The dilation of a scale factor of ½ simply means that the shape reduces to half it's original size.
Hence, it follows that the attached image represents the transformation.
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