Answer:
Step-by-step explanation:
The maximum possible distance between two posts for the fence will be given by HCF ( highest common factor ) of 24 and 64
24 = 8 x 3
64 = 8 x 8
highest common factor is 8 .
So distance between two poles ( maximum separation ) will be 8 m .
Ans : 8 m .
What is the slope of the line that passes through the points (-10, 8) and
(-15, – 7)? Write your answer in simplest form.
Answer:
[tex]slope=3[/tex]
Step-by-step explanation:
Use the following equation the find the slope:
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{rise}{run}[/tex]
Rise over run is the change in the y-axis over the change in the x-axis from one point to the other. This is also known as the "slope". Insert the known values:
[tex](-10_{x1},8_{y1})\\\\(-15_{x2},-7_{y2})\\\\\\\frac{-7-8}{-15-(-10)}\\\\\frac{-7-8}{-15+10}[/tex]
Solve:
[tex]\frac{-7-8}{-15+10}=\frac{-15}{-5}[/tex]
Simplify. Two negatives make a positive:
[tex]\frac{-15}{-5}=\frac{15}{5}[/tex]
Simplify fraction by dividing top and bottom by 5:
[tex]\frac{15}{5}=\frac{3}{1} =3[/tex]
The slope is 3.
:Done
The slope of the line that passes through the points (-10, 8) and (-15, -7) is 3 and thsi can be determined by using the point-slope formula.
Given :
The line that passes through the points (-10, 8) and (-15, -7).
The following steps can be used in order to determine the slope of the line that passes through the points (-10, 8) and (-15, -7):
Step 1 - The slope formula when two points are given is:
[tex]\rm m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]
where m is the slope and [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the points on the line.
Step 2 - Substitute the known terms in the above formula.
[tex]\rm m = \dfrac{-7-8}{-15+10}[/tex]
Step 3 - Simplify the above expression.
[tex]\rm m = \dfrac{15}{5}[/tex]
m = 3
For more information, refer to the link given below:
https://brainly.com/question/2514839
3) Find f(3) for the function below.
f(x) = 2x² – 3x
Answer:
9
Step-by-step explanation:
f(x) = 2x² – 3x
Let x=3
f(3) = 2 * 3^2 - 3*3
= 2 *9 - 9
= 18-9
= 9
Answer:
f(3) = 9Step-by-step explanation:
[tex]f(x) = 2x^2 -3x\\ f(3) = ?\\\\ f(3) = 2(3)^2 -3(3)\\ f(3) = 2(9) - 9\\ f(3) = 18- 9\\ f(3) = 9[/tex]
What is the perimeter of the figure shown?
Answer:
[tex]\boxed{16 units}[/tex]
Step-by-step explanation:
Hey there!
Well since all the sides are congruent and there are 8 sides we can make the following expression,
P = 2*8
P = 16
Hope this helps :)
Answer:
16
Step-by-step explanation:
The sides of this figure are equal to each other .
the permiter is the sum of the sides
The figure has 8 sides.
● P = 8 × 2
● P = 16
Drag a vertex of the triangle to change its shape.
Double-click or double-tap a vertex or side to prevent it from
changing.
Problem: Construct a triangle with interior angle
measures of 60° and 75°.
What is the measure of the third angle?
O 30°
2C = 41°
O 45°
48°
9.2
10
50°
ZA = 49°
6.0 ZB = 90°
Answer:
The correct option is;
45°
Step-by-step explanation:
By angle sum theorem, we have that the sum of angles in a triangle = 180°
Therefore, we have;
When the interior angles of the triangle are constructed to be 60° and 75°, we have by the angle sum theorem;
The third angle + 60° + 75° = 180°
Which gives;
The third angle = 180°- 60° - 75° = 180°- 135° = 45°
The measurement of the third angle by the angle sum theorem will be 45°
The correct option is ∠third angle = 45°.
the fastest land dwelling creature is the cheetah. fact or
opinion
Answer:
True.
Step-by-step explanation:
Cheetahs can reach speeds of 109.4–120.7 km/h (68.0–75.0 mph), and some have been recorded at over 80mph. The cheetah can accelerate from 0 to 96.6 km/h (60.0 mph) in under three seconds, though endurance is limited.
The second fastest land animal is the Pronghorn antelope at 98kph (60mph).
Answer:
It is a Fact because it can run 70mph or 112kph
30 points and brainliest for the right answer :) I would like to know how to do this, so an explanation would be nice :P Thanks for the help!
Answer:
Below
Step-by-step explanation:
● (a)
Let's determine the difference between the outputs of any two inputs that are one unit apart.
Let m be that difference.
2 and 3 are one unit apart since when you substract 2 from 3 you get 1.
● 3-2 = 1
Let's calculate m.
The output of 2 and 3 are respectively 45 and 53.
● m = 53 - 45
● m= 8
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's determine the difference between the outputs of any two inputs that are 2 units apart.
Let m' be that difference
3 and 1 are 2 units apart since when you substract 1 from 3 you get 2.
● 3-1 = 2
The outputs of 1 and 3 are respectively 37 and 53.
● m'= 53-37
● m' = 16
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's determine the difference between the outputs of two inputs that are 3 units apart.
Let m" be that difference
0 and 3 are 3 units apart since when you substract 0 from 3 you get 3.
● 3-0 = 3
Let's calculate m":
The outputs of 0 and 3 are respectively 29 and 53
● m" = 53-29
● m" = 24
■■■■■■■■■■■■■■■■■■■■■■■■■■
● m = 8
● m'= 16
● m" = 24
Notice that all these values are multiples of 8.
● 8 = 8×1
● 16 = 8×2
● 24 = 8×3
Notice that each time the difference m is multiplied by the units that are between the inputs.
This is explained by the fact that the function is a linear one.
When the input interval grows the difference between the outputs grows two.
Answer:
Step-by-step explanation:
find the equation of the linear function in the form of y=mx+b
m=y2-y1/x2-x1 =-3+11/-4+5=8
y=8x+29 ( when x=0, y=b=29)
out put : -3 and -11 -3-(-11)=8 which is 1 unit
out put : 21 and 5 21-5=16 which is 2 unit (2*8)
output :53 and 29 53-29=24 which is 3 units (3*8)
ratio of change = f(b)-(f(a)/b-a
at point -3 and -11 : f(-3)-f(-11)/-4+5=-3+11/1=8
at point 21 and 5 : 21-5/-1+3=16/2=8
the graph always increasing and always equal 8
Find the value of tetha in 2 cos 3 tetha = 1
Answer:
Step-by-step explanation: 2cos3 theta=1. Cos 3theta=1/2. Since cos 60°= 1/2. Therefore cos 3theta=cos 60°. Theta=20°.
can we chat girl in comment
How to do this question plz answer me step by step plzz plz
Answer:
£13496.80
Step-by-step explanation:
We can ignore the £ sign for now, that is just units.
If we decrease a number by 4.5%, we will have to find [tex]100-4.5=95.5[/tex]% of 14132.77.
We can easily do this by setting up a proportion.
[tex]\frac{x}{14132.77} = \frac{95.5}{100}[/tex]
Multiply 14132.77 by 95.5:
[tex]14132.77\cdot95.5=1349679.535[/tex]
Divide by 100:
[tex]1349679.535\div100=13496.79535[/tex]
Rounding this to two decimal places, it simplifies to 13496.80.
Hope this helped!
This rectangle has side lengths r and s.
For each expression, say whether it gives the perimeter of the rectangle, the area of the
rectangle, or neither.
1. rts
2. r.s
3. 2r + 2s
4.72 +82
Answer:
1.) Neither
2.) Area
3.) Perimeter
4.) Neither
Step-by-step explanation:
Given that the lengths of the rectangle are r and s
The perimeter of the rectangle will be:
Perimeter = 2r + 2s
Perimeter = 2(r+s)
While the area will be:
Area = r × s
Area = rs
For each expression, say whether it gives the perimeter of the rectangle, the area of the
rectangle, or neither.
1. rts = neither
2. r.s = Area of rectangle
3. 2r + 2s = Perimeter of rectangle
4.72 +82 = neither.
IT IS FOR NOW IM GIVING BRAINLIEST HRRY UP AND 10 POINTS Simplify the expression. What classification describes the resulting polynomial? (8x2 + 3x) − (12x2 − 1) A. linear binomial B. quadratic binomial C. quadratic trinomial D. linear monomial
Answer:
The equation would be a quadratic trinomial
Step-by-step explanation:
Step 1: Expand the equation to remove the brackets
0 = 8x² + 3x - 12x² + 1
Step 2: Collect like terms
0 = -4x² + 3x + 1
Step 3: Count number of terms
0 = -4x² + 3x + 1
1 2 3
Therefore there are 3 terms and this is a quadratic equation making the answer B, a quadratic trinomial
Solve D = ABC for C.
Answer:C=d/ab
Step-by-step explanation:
D=abc
D/ab=abc/ab (both side divided by ab)
Ab cancel by ab and c= d/ab remains
The solution of the given equation D = ABC for C will be D/(AB).
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
The equation must be constrained with some constraints.
As per the given equation,
D = ABC
The value of the above equation for C will be as,
D = (AB)C
C = D/(AB)
Hence "The solution of the given equation D = ABC for C will be D/(AB)".
For more about the equation,
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Suppose you roll a fair six-sided die 25 times. What is the probability that you roll 5 or more 6’s on that die?
A. 0.3883
B. 0.5937
C. 0.5
D. 0.4063
Answer:
D. P(5+ 6's) = 0.4063
Step-by-step explanation:
Binomial distribution.
For the distribution to be applicable, the experiment must
1. Have a know and constant number of trials
2. Probability of success of each trial remains constant (and known if available)
3. Each trial is a Bernoulli trial, i.e. with only two outcomes, success or failure.
4. Independence between trials.
Let
n = number of trials = 25
p = probability of success of each trial = 1 / 6
x = number of successes (0 ≤ x ≤ n) = 5
C(n,x) = number of combinations of picking x identical objects out of n
Applying binomial distribution
P(x,n) = probability of x successes in an experiment of n trials.
= C(n,x) * p^x * (1-p)^(n-x)
For n = 25 trials with probability of success (roll a 6) = 1/6
and x = 5,6,7,8,...25
It is easier to calculate the complement by
P(5+ 6's) = 1 - P(<5 6's)
= 1 - ( P(0,25) + P(1,25) + P(2,25) + P(3,25) + P(4,25) )
1- (
P(0,25) = C(25,0) * (1/6)^0 * (5/6)^25 = 0.0104825960103961
P(1,25) = C(25,1) * (1/6)^1 * (5/6)^24 = 0.05241298005198051
P(2,25) = C(25,2) * (1/6)^2 * (5/6)^23 = 0.1257911521247532
P(3,25) = C(25,3) * (1/6)^3 * (5/6)^22 = 0.1928797665912883
P(4,25) = C(25,4) * (1/6)^4 * (5/6)^21 = 0.2121677432504171
)
= 1 - 0.59373
= 0.40626
= 0.4063 (to 4th decimal place)
The number 16 has four fourth roots. In other words, there are four complex numbers that can be entered in the square in the equation below: __^4 = 16 Find them.
Answer:
Step-by-step explanation:
Hello, we know that the z complex solutions of
[tex]z^4=1[/tex]
are
1, i, -1, -i
so, the solutions of [tex]z^4=16=2^4[/tex] are
2, 2i, -2, -2i
Thank you
10 points please help
Answer:
[tex]\frac{14}{55}[/tex]
Step-by-step explanation:
note that
n! = n(n - 1)(n - 2) .... × 3 × 2 × 1
Given
[tex]\frac{8!9!}{5!12!}[/tex]
Cancel the terms from 8! ( 5 × 4 × 3 × 2 × 1 ) with the same terms from
5! ( 5 × 4 × 3 × 2 × 1 ) leaving
8 × 7 × 6 = 336 on the numerator
Similarly
Cancel the terms from 9! and 12!
leaving 12 × 11 × 10 = 1320 on the denominator, thus simplifies to
[tex]\frac{336}{1320}[/tex]
= [tex]\frac{14}{55}[/tex]
you have decided to hire a disc jockey for your party. the second dj you interviewed has 3 times as many songs as the first dj. the third dj had half as many songs as the second dj. write an expression to represent the number of songs the third has if the first dj had r songs. explain how you arrived at your answer
Answer:
The third DJ had (3r)/2 songs. Multiply r by 3 because the second DJ had 3 times as many as the first. Then divide that number by 2 because the third DJ has half as many.
Step-by-step explanation:
Answer:
The third DJ had (3r)/2 songs. Multiply r by 3 because the second DJ had 3 times as many as the first. Then divide that number by 2 because the third DJ has half as many.
Step-by-step explanation:
just did
The sums of which two pairs from the table will give you the same result? For example, A + B = C + D.
Answer:
D + E = F + H
Step-by-step explanation:
We have to identify the two pairs from the give table which have the same result.
These pairs show the relation as A + B = C + D
We take a pair of expressions given in options (D) and (E)
By adding them,
D + E = (-4 + 9i) + (6 - 6i)
= 2 + 3i
Similarly we add the expressions given in options (F) and (H),
F + H = (-9 + 15i) + (11 - 12i)
= 2 + 3i
Therefore, D + E = F + H will be the answer.
If function g is defined by the equation y − 3x = -14, which equation represents the function in function notation?
Answer:
f(x) = 3x - 14
Step-by-step explanation:
note that y = f(x), thus rearrange the equation making y the subject.
Given
y - 3x = - 14 ( add 3x to both sides )
y = 3x - 14 , that is
f(x) = 3x - 14 ← in functional notation
A man lends 12,500 at 12% for the first
year, at 15% for the second year and at 18%
for the third year. If the rates of interest are
compounded yearly; find the difference
between the C.I. of the first year and the
compound interest for the third year.
Answer: $1398
Step-by-step explanation:
Given , Principal (P) = $12,500
Rate of interest for 1st year [tex](R_1)[/tex]= 12% =0.12
Rate of interest for 2nd year [tex](R_2)[/tex]= 15% =0.15
Rate of interest for 3rd year [tex](R_3)[/tex]= 18% =0.18
Interest for first year = [tex]I=P\times R_1\times T[/tex]
= [tex]12500\times 0.12\times 1[/tex]
= $1500
Now, For second year new principal [tex]P_2 = \$12,500+\$1,500 =\$14,000[/tex]
Interest for second year = [tex]I=P_2\times R_2\times T[/tex]
= [tex]14000\times 0.15\times 1[/tex]
= $2100
Now, For third year new principal [tex]P_3 = \$14000+\$2,100 =\$16,100[/tex]
Interest for third year = [tex]I=P_3\times R_3\times T[/tex]
= [tex]16100\times 0.18\times 1[/tex]
= $2898
Difference between the compound interest of the first year and the compound interest for the third year. = $2898 - $1500 = $1398
Hence, the difference between the compound interest of the first year and the compound interest for the third year is $1398 .
Two rectangles are similar. One has a length of 12 cm and a width of 9 cm, and
the other has a width of 8 cm. Find the length of the second rectangle. Round to
the nearest tenth if necessary.
A 12.3 cm
B 6 cm
C 10.7 cm
D 8 cm
Answer:
10.7
Step-by-step explanation:
Let x be the missing side.
The rectangles are similar. Wich means:
● 8/9 = x/12
Cross multiply
● 9x = 8×12
● 9x = 96
Divide both sides by 9
● 9x/9 = 96/9
● x = 10.666
Round it to the nearest unit
● x = 10.7
What is the quotient ? -4 /5 divide 2 A . - 1 3/5 B . -2 /5 c. 1/2 D . 1 3/ 5
Answer:
[tex] \boxed{ - \frac{2}{5} }[/tex]Option B is the correct option.
Step-by-step explanation:
[tex] \mathrm{ - \frac{4}{5} \div 2}[/tex]
[tex] \mathrm{dividing \: a \: negative \: and \: a \: positive \: equals \: a \: negative \:. \: ( - ) \div ( + ) = ( - )}[/tex]
[tex] \mathrm{ - \frac{4}{5} \div 2}[/tex]
[tex] \mathrm{dividing \: is \: equivalent \: to \: multiplying \: with \: the \: reciprocal}[/tex]
[tex] \mathrm{ - \frac{4}{5} \times \frac{1}{2} }[/tex]
[tex] \mathrm{reduce \: the \: numbers \: with \: G.C.F \: 2}[/tex]
[tex] \mathrm{ - \frac{2}{5} }[/tex]
Hope I helped!
Best regards!
The quotient of -4 /5 divide 2 would be equal to -2/5 in simplified form.
What are the Quotients?Quotients are the number that is obtained by dividing one number by another number. We can use the fact that division can be taken as multiplication but with the denominator's multiplicative inverse.
We have been given that -4 /5 divide 2
Thus, we have to divide the terms as;
-4 /5 ÷ 2
Therefore, -4 /5 x 1/ 2
-2/5
Hence, the quotient of -4 /5 divide 2 would be equal to -2/5 in simplified form.
Learn more about the quotient;
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On a cold February morning, the temperature of the radiator fluid in Stanley’s car is . When the engine is running, the temperature of the fluid goes up per minute. Approximately how long will it take before the radiator fluid temperature reaches ?
Answer:
18.18 min
Step-by-step explanation:
The complete question is
On a cold February morning, the radiator fluid in Stanley’s car is -18F. When the engine is running, the temperature goes up 5.4 F per minute. Approximately how long will it take before the radiator fluid temperature reaches 80 F?
The initial temperature of the engine [tex]T_{1}[/tex] = -18 F
rate of increase in temperature r = 5.4 F/min
Final temperature [tex]T_{2}[/tex] = 80 F
Difference in temperature ΔT = [tex]T_{1} -T_{2}[/tex] = 80 - (-18) = 98 F
time taken to reach this 80 F will be = ΔT/r
where ΔT is the difference in temperature
r is the rate of change of temperature
time taken = 98/5.4 = 18.18 min
The volume of a sphere whose diameter is 18 centimeters is
π cubic centimeters. If its diameter were reduced by half, its volume would be
of its original volume.
Answer:
volume before reducing is 8 times the volume after reducing
Step-by-step explanation:
volume before reducing=
V=4/3πr³=
V=4/3π(9)³=972π cm³
diameter reduced to half=18/2=9 cm
radius=d/2=9/2=4.5 cm
volume of sphere when diameter reduced by 1/2=
V=4/3πr³
v=4/3 (π)(4.5)³=121.5π
volume before reducing is 8 times the volume after reducing
Answer:
The volume of a sphere whose diameter is 18 centimeters is 972 π cubic centimeters. If its diameter were reduced by half, its volume would be 1/8 of its original volume.
Step-by-step explanation:
Correct for plato :)
explanation pls? step by step i get confused on these questions! thank you!
Answer:
5xyz
Step-by-step explanation:
10x^2 y^2z and 15xyz^2
Rewriting
2*5*x*x*y*y*z and 3*5 *x*y*z*z
What is common to both terms
5 x y z
The greatest common factor is 5xyz
Answer:
the GCF is 5(xyz)
Step-by-step explanation:
For the numbers, you want to find the largest number that both of the coefficients can be divided by. I'm not sure if your answer choices include variables, but if they do, its only xyz, nothing can be squared because both equations have different variables squared.
Please answer ASAP. The question is down below
Answer: A
Step-by-step explanation:
Notes: Dividing by a fraction means to multiply by its reciprocal.
The denominator cannot equal zero.
[tex]\dfrac{5a^3bc}{8ab^3}\div\dfrac{-ab^2}{6a^5b}\cdot \dfrac{2a^2b^3}{3b}\qquad \rightarrow a\neq 0,b\neq 0\\\\\\=\dfrac{5a^3bc}{8ab^3}\cdot\dfrac{6a^5b}{-ab^2}\cdot \dfrac{2a^2b^3}{3b}\\\\\\=\dfrac{5\cdot 6\cdot 2\quad a^3\cdot a^5\cdot a^2\quad b\cdot b\cdot b^3\quad c}{8\cdot -1 \cdot 3\quad a\cdot a\qquad b^3\cdot b^2\cdot b \quad}\\\\\\=\dfrac{-60a^{10}b^5c}{-24a^2b^6}\\\\\\=\dfrac{-5a^8c}{2b}[/tex]
Allie, Ben, and Cliff plant ceilings in the neighborhood park. Ali plans 40% of the total number of ceiling, then place 45% of the total number of seed wings, and Cliff plans the rest of the siblings. If Cliff +84 siblings how many seedling do the three boys play together
Answer:
The number of seedlings the three boys planted together is 560 seedlings
Step-by-step explanation:
The possible information in the question are;
Percentage of the seedlings planted by Ali = 40%
Percentage of the seedling planted by Ben = 45%
The percentage of the seedling planted by Cliff = The rest of the seedling
The number of seedling planted by Cliff = 84 siblings
Therefore, the percentage of the seedling planted by Cliff = 100% - 45% - 40% = 15%
Given that Cliff planted 15% of the seedlings, we have;
15% of seedlings Cliff planted = 84
Let X = the total number of seedlings
15/100 × X = 0.15×X = 84
X = 84/0.15 = 560
The total number of seedlings = The number of seedlings the three boys planted together = 560 seedlings.
This table represents a quadratic function.
What is the value of “a” in the function’s equation?
A. -1/2
B. 1/2
C. 2
D. 1
Answer:
I think 1/2 is the ans
Step-by-step explanation:
quadratic function equation
would help
PLEASE HELP!!!
Which expression shows a way to find the area of the following rectangle?
Answer:
B
Step-by-step explanation:
This rectangle appears to have 7 boxes on the bottom, and 3 box for the side.
Since area is base×height
It would be 7×3
Find the total surface area.
Answer:
160cm²
Step-by-step explanation:
To find the surface area of this prism, you just need to add up the areas of each side. To simplify the calculations a bit, we can take multiples of the sides which are the same. For example, here we have two equal trapezoids on each end, so we can multiply the area by two when adding.
The work is in the attachment.
What is the slope of the line that cuts through the points (1, 2) and (5, 4)?
Answer:
[tex]slope=\frac{1}{2}[/tex]
Step-by-step explanation:
Use the following equation:
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{rise}{run}[/tex]
Rise over run is the change in the y-axis over the change of the x-axis, otherwise known as the slope.
Insert the values:
[tex](1_{x1},2_{y1})\\(5_{x2},4_{y2})[/tex]
[tex]\frac{4-2}{5-1}=\frac{2}{4} =\frac{1}{2}[/tex]
The slope is [tex]\frac{1}{2}[/tex].
:Done
Answer:
1/2
Step-by-step explanation:
The formula for slope is: y1-y2/x1-x2
The points given are: (x-coordinate, y-coordinate)
In the formula:
y1 is the y-coordinate of the first point
y2 is the y-coordinate of the second point
x1 is the x-coordinate of the first point
x2 is the x-coordinate of the second point
This said, we can plug our points in.
2-4/1-5
Subtract.
-2/-4
Simplify.
-1/-2
The negatives will cancel each other out.
1/2
The slope of the line that cuts through the points (1,2) and (5,4) is 1/2.
what is the value of 14 - a² given a = -3? A. 23 B. 11 C. 8 D. 5
Answer:
The answer is D. 5
Step-by-step explanation:
14-(-3)^2=
14-9=5
The value of f(a) = 14 - [tex]a^{2}[/tex] at x = -3 is 5.
We have the following function of [tex]a[/tex] -
f(a) = 14 - [tex]a^{2}[/tex]
We have to determine the value of this function at a = -3.
What is the value of f(x) = 2x - 3 at x = 3?\The value of f(x) = 2x - 3 at x = 3 can be calculated as follows -
f(3) = 2 x 3 - 3 = 6 - 3 = 3
According to the question -
f(a) = 14 - [tex]a^{2}[/tex]
Now, the value of the function f(a) can be calculated as follows -
f(- 3) = 14 - [tex](-3)^{2}[/tex]
f(- 3) = 14 - 9
f(- 3) = 5
Hence, the value of f(a) = 14 - [tex]a^{2}[/tex] at x = -3 is 5.
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