Answer:
Step-by-step explanation:
identitiy property
Natasha and her two dogs were walking on a perfectly straight road when her two dogs ran away from her in opposite directions. Her beagle is now \dfrac{25}{4} 4 25 start fraction, 25, divided by, 4, end fraction meters directly to her right, and her labrador is \dfrac{51}{20} 20 51 start fraction, 51, divided by, 20, end fraction meters directly to her left. Which of the following expressions represents how far apart the two dogs are?
Answer:
[tex]\dfrac{74}{20}=3.7 meters[/tex]
Step-by-step explanation:
Hello!
1) Since no other data has been given. Suppose Natasha is in the center and the beagle is to the right.
[tex]\dfrac{25}{4} \:meters[/tex]
2) The labrador is [tex]\dfrac{51}{20}\: to\: the\: left.[/tex]
[tex]\dfrac{25}{4} -\dfrac{51}{20} =\dfrac{(5*25)-51}{20} \\\dfrac{(125-51}{20} =\dfrac{74}{20}[/tex]
Answer:
The answer is B :D hope this helps
Step-by-step explanation:
A circle with center A and radius three inches is tangent at C to a circle with center B, as shown. If point B is on the small circle, what is the area of the shaded region? Express your answer in terms of \pi.
Answer:
27π Sq in.
Step-by-step explanation:
Circle A is equal to 9π sq inches. (Radius squared times Pi), Segment BC is a radii of Circle B and the diameter of Circle A. Meaning Circle B's radius is 6 inches. The area of circle B would be 36π sq inches. Now we subtract Circle A's area from Circle B's area(36π sq in. - 9π sq in.), the area of the shaded region is 27π sq in.
Find the center and radius of x^2 – 18x + y^2 -10y = -6. part two write x2 – 18x + y2 -10y = -6 in standard form
Answer:
see explanation
Step-by-step explanation:
I will begin with part two, first.
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius.
Given
x² - 18x + y² - 10y = - 6
Using the method of completing the square
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(- 9)x + 81 + y² + 2(- 5)y + 25 = - 6 + 81 + 25, that is
(x - 9)² + (y - 5)² = 100 ← in standard form
with centre = (9, 5 ) and r = [tex]\sqrt{100}[/tex] = 10
from the figure below identify a)Obtuse vertically opposite angles b) A pair of adjacent complementary angles c) a pair of equal supplementary angles d) a pair of unequal supplementary angles e) a pair of adjacent angles that don’t form a linear pair
Answer:
a) BOC and AOD
b) BOA and AOE
c) BOE and EOD
d) BOA and AOD
e) AOE and EOD
Step-by-step explanation:
An obtuse angle is an angle that has more than 90° and vertically opposite angles are angle formed by two lines crossed. So, Obtuse vertically opposite angles are BOC and AOD
Adjacent angles are angles in which one angle is beside the other and complementary angles are angles whose sum is equal to 90°, so, a pair of adjacent complementary angles are BOA and AOE.
Supplementary angles are angles whose sum is equal to 180°, so BOE and EOD are equal suplementary angles and BOA and AOD are unequal supplementary angles
Finally, AOE and EOD are adjacent angles that don’t form a linear pair.
S and T are two-digit positive integers that have the same digits but in reverse order. If the positive difference between S and T is less than 40, what is the greatest possible value of S minus T
Answer :Answer: Did you get helped on this one?
Step-by-step explanation: okay yup yup have a good day OKAY
Step-by-step explanation: HAVE A GOOD ONE OKAY
If a watch store paid $125 per watch for a shipment of watches, and sold all but 15 watches from the shipment for $150 per watch, then, in terms of the number of watches in the shipment, y, what function describes the watch store’s profit, P, from the sales?
A) P(y) = 125(y – 15) – 150y
B) P(y) = 15(125 – y) – 150y
C) P(y) = 150(y – 15) – 125y
D) P(y) = 15(150 – y) – 125y
Answer: C) P(y) = 150(y – 15) – 125y
Step-by-step explanation:
Hi, to answer this question we have to write an equation:
Profit = revenue - cost
Cost: a watch store paid $125 per watch for a shipment of watches
Cost = 125 y
Where y is the number of watches in the shipment
Revenue: sold all but 15 watches from the shipment for $150 per watch
Revenue = 150(y-15)
Profit(y) = 150(y – 15) – 125y
So, the correct option is:
C) P(y) = 150(y – 15) – 125y
Feel free to ask for more if needed or if you did not understand something.
Find the volume in cubic meters, of the 3-Dimensional composite
figure.
8m
5m
Answer:
890 m^3 to the nearest whole number.
Step-by-step explanation:
Volume = volume of the cylinder + volume of the hemisphere:
= π r^2 h + 1/2 * 4/3 π r^3
= π*5^2 * 8 + 1/2 * 4/3 π 5^3
= 890.12
Instructions: Find FS if BS=16.
Answer:
48
Step-by-step explanation:
FB:BS=2:1
[tex]\frac{FB}{BS} =\frac{2}{1} \\add~1~to~both~sides\\\frac{FB}{BS} +1=\frac{2}{1} +1=3\\\frac{FB+BS}{BS} =3\\\frac{FS}{BS} =3\\FS=3 \times~BS\\FS=3 \times~16=48[/tex]
Answer:
48
Step-by-step explanation:
Look at picture to see question
Suppose you are interested in testing wheter the mean earning of men in the general social survey is representative of the earning of the entire U.S. Male population. If there are 372 men in the general social survey sample and approximately 128 million men in the population, calculate the degrees of freedom for this single-sample t test.
Answer:
371
Step-by-step explanation:
According to the given situation the calculation of degrees of freedom for this single-sample t test is shown below:-
Degrees of freedom is N - 1
Where N represents the number of Men
Now we will put the values into the above formula.
= 372 - 1
= 371
Therefore for calculating the degree of freedom we simply applied the above formula.
La trayectoria de cierto satelitese ajusta ala grafica de la funcionf(x) igual6x al cuadradomenos 12donde x representael tiempo en días y f(x9 el recorrido en kilometroscuantos kilómetros habrá recorridoel sateliteal cabo de diez días desde su lanzamiento
Answer:
588 kilómetros
Step-by-step explanation:
La función con la que estamos trabajando según la pregunta es;
F (x) = 6x ^ 2 -12
Ahora, la pregunta que simplemente nos hace es encontrar el valor de F (x) dado que x = 10
Entonces, lo simple que hacemos aquí es hacer una sustitución de x = 10 Eso sería;
F (10) = 6 (10) ^ 2 - 12 = 600-12 = 588
Drag a statement or reason to each box to complete this proof.
If -5(x + 8) = -25, then x =
-3
What is the value of discontinuity of x^2+8x+4/x^2-x-6? Choices:
Answer:
-2
Step-by-step explanation:
Hello,
First of all, let's check the denominator.
[tex]x^2-x-6 \ \ \text{ *** How to factorise it ...? ***}\\\\\text{*** The product of the roots is -6=-2*3 and their sum is 1 ***}\\\\x^2-x-6=x^2-3x+2x-6=x(x-3)+2(x-3)=(x+2)(x-3)[/tex]
Now, let's see the numerator.
[tex]x^2+8x+4 \ \text{ *** -2 is not a zero as ***}\\\\(-2)^2+8*(-2)+4=4-16+8=-4\\\\\text{*** 3 is not a zero as ***}\\\\3^2+8*3+4=9+24+4=37\\[/tex]
So we cannot factorise the numerator with (x+2) or (x-3)
Then, -2 and 3 are the the discontinuities of the expression.
There is only -2 in the list, this is the correct answer.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Nine-banded armadillos always give birth to quadruplets—four identical babies (called pups). Jenny’s armadillo has produced four female pups. Jenny realizes that each of those pups could eventually have four more armadillos.
a. How many armadillos would Jenny have if the four pups grew up to have four more pups each?
b. What if every generation of Jenny’s armadillos was female? How many armadillos would there be if you only count the ones in the 5th generation? Can you write a formula for the number of armadillos in any given generation? Please explain what each variable and each number in your formula means.
c. According to this formula the world should be overrun with armadillos after 20 to 25 generations. Why isn’t this true in real life?
Answer:
a. 16; b. aₙ = 4ⁿ⁻¹; c. predation and carrying capacity will limit the population
Step-by-step explanation:
a. The first female had 4 pups.
If each of them had 4 pups, there would be 4 × 4 = 4² = 16 pups.
b. 1st generation = 1 pup
2nd generation = 4 × 1 pup = 4 pups
3rd generation = 4 × 4 pups = 16 pups
4th generation = 4 × 16 pups = 64 pups
5th generation = 4 × 64 pups = 256 pups
The sequence is 1, 4, 16, 64, 256, …
We can also write it as 4⁰, 4¹, 4², 4³, 4⁴, …
Note that the exponent is one less than the number of the generation.
Thus, the general formula for the nth term, aₙ, is
aₙ = 4ⁿ⁻¹, where
n = the number of the generation
a = the number of pups in that generation.
c. a₂₅ = 4²⁵⁻¹ = 4²⁴ ≈ 281 000 000 000 000 or 281 trillion
The population would not reach that number because there would not be enough food for all those pups. Pups would die of starvation until their numbers equalled the carrying capacity of the ecosystem and would level off at that point.
There would also be increased predation by coyotes, bobcats, etc. This would also keep the population growth in check,
n the diagram below, points $A,$ $E,$ and $F$ lie on the same line. If $ABCDE$ is a regular pentagon, and $\angle EFD=90^\circ$, then how many degrees are in the measure of $\angle FDE$?
[asy]
size(5.5cm);
pair cis(real magni, real argu) { return (magni*cos(argu*pi/180),magni*sin(argu*pi/180)); }
pair a=cis(1,144); pair b=cis(1,72); pair c=cis(1,0); pair d=cis(1,288); pair e=cis(1,216);
pair f=e-(0,2*sin(pi/5)*sin(pi/10));
dot(a); dot(b); dot(c); dot(d); dot(e); dot(f);
label("$A$",a,WNW);
label("$B$",b,ENE);
label("$C$",c,E);
label("$D$",d,ESE);
label("$E$",e,W);
label("$F$",f,WSW);
draw(d--f--a--b--c--d--e);
draw(f+(0,0.1)--f+(0.1,0.1)--f+(0.1,0));
[/asy]
Answer:
18
Step-by-step explanation:
Each interior angle of a regular pentagon is 108 degrees. So Angle AED is 108 degrees. Since Angle AEF is a straight line (180 degrees), Angle FED is 72. This is because 180-108 = 72. Now, since a triangle has a total of 180 degrees, we add 72 and 90, because those are the 2 degrees we have calculated. This gives us a total of 162. Now, we subtract 162 from 180 to find out the degree of Angle FDE. This is 18. So our final answer is 18.
Sidenote: I hope this answer helps!
The properties of a pentagon and the given right triangle formed by
segments EF and FD give the measure of ∠FDE.
Response:
∠FDE = 18°Which properties of a pentagon can be used to find ∠FDE?The given parameters are;
A, E, F are points on the same line.
ABCDE is a regular pentagon
∠EFD = 90°
Required:
The measure of ∠FDE
Solution:
The points A and E are adjacent points in the pentagon, ABCDE
Therefore;
line AEF is an extension of line side AE to F
Which gives;
∠DEF is an exterior angle of the regular pentagon = [tex]\frac{360 ^{\circ}}{5}[/tex] = 72°∠EFD = 90°, therefore, ΔEFD is a right triangle, from which we have;
The sum of the acute angles of a right triangle = 90°
Therefore;
∠DEF + ∠FDE = 90°
Which gives;
72° + ∠FDE = 90°
∠FDE = 90° - 72° = 18°
∠FDE = 18°
Learn more about the properties of a pentagon here:
https://brainly.com/question/15392368
26. A positive whole number is called stable if at least one of its digits has the same value
as its position in the number. For example, 78247 is stable because a
the 4th position. How many stable 3-digit numbers are there?
appears in
Answer:
OneStep-by-step explanation:
Given the value 78247 a s a stable number because at least one of its digits has the same value as its position in the number. The 4th number in the value is 4, this makes the number a stable number.
The following are the 3-digits stable numbers that appears in 78247
The first number is 824. This digits are stable numbers because 2 as a number is situated in the same place as the number (2nd position).
Hence, there are only 1 stable 3-digit numbers in the value 78247 since only a value exists as 2 in the value and there is no 1 and 3 in the value.
Solve the inequality 47.75 + x Less-than-or-equal-to 50 to determine how much more weight can be added to Li’s suitcase without going over the 50-pound limit. What is the solution set?
x Less-than-or-equal-to 2.25
x Less-than-or-equal-to 2.75
x Greater-than-or-equal-to 2.25
x Greater-than-or-equal-to 2.75
Answer: x Less-than-or-equal-to 2.25
Step-by-step explanation:
The given inequality: 47.75 + x Less-than-or-equal-to 50.
To determine: How much more weight can be added to Li’s suitcase without going over the 50-pound limit.
i.e. inequality for x.
[tex]47.75+x\leq50[/tex]
Subtract 47.75 from both the sides, we get
[tex]x\leq50-47.75\\\\\Rightarrow\ x\leq2.25[/tex]
So, the solution set is "x Less-than-or-equal-to 2.25"
Hence, the correct answer is "x Less-than-or-equal-to 2.25."
Answer
A x <_ 2.25
Step-by-step explanation:
How many real solutions In this problem
Answer:
D
Step-by-step explanation:
Given
y = x² + 1
y = x
Equating gives
x² + 1 = x ( subtract x from both sides )
x² - x + 1 = 0
Consider the discriminant Δ = b² - 4ac
with a = 1, b = - 1 and c = 1
b² - 4ac = (- 1)² - (4 × 1 × 1) = 1 - 4 = - 3
Since b² - 4ac < 0 then there are no real solutions
please help :) What is 96,989,200 written in scientific notation? A. 96.9892 × 10 to the 5 power B. 9.69892 × 10 to the 7 power C. 9.69892 × 10 to the 6 power D. 9.69892 × 10 to the 8 power
Answer: B. 9.69892 × 10^7
You'd have to move the imaginary decimal at the end of the number 96,989,200 seven times in order to get only one number that isn't zero before the decimal point.
What is the slope of the line shown below? (-2,3) (-4,-9)
Answer:
6Step-by-step explanation:
Let the points be A and B
A ( - 2 , 3 ) -------> ( x1 , x2 )
B ( -4 , -9 ) -------> ( x2 , y2 )
Now, finding the slope:
[tex]slope \: (m) = \frac{y2 - y1}{x2 - x1} [/tex]
Plug the values
[tex] = \frac{ - 9 - 3}{ - 4 - ( - 2)} [/tex]
Calculate
[tex] = \frac{ - 12}{ - 4 - ( - 2)} [/tex]
When there is a (-) in front of an expression in parentheses , change the sign of each term in expression
[tex] = \frac{ - 12}{ - 4 + 2} [/tex]
Calculate
[tex] = \frac{ - 12}{ - 2} [/tex]
Reduce the fraction with -2
[tex] = 6[/tex]
Hope this helps..
Best regards!!
2.) Evaluate 6a² if a = 4
Answer:
96
Step-by-step explanation:
We simply need to plug in a = 4 so 6a² = 6 * 4² = 6 * 16 = 96.
how to do this question plz
Answer:
48.
Step-by-step explanation:
[tex]\frac{24\sqrt{72} }{3\sqrt{2} }[/tex]
= (24 / 3) * [tex]\frac{\sqrt{72}} {\sqrt{2} }[/tex]
= 8 * [tex]\frac{\sqrt{72} * \sqrt{2}} {\sqrt{2} * \sqrt{2} }[/tex]
= 8 * [tex]\frac{\sqrt{144}} {2}[/tex]
= 8 * (12 / 2)
= 8 * 6
= 48.
Hope this helps!
In a survey men in a certain country (ages 20-29), the mean height was 62.8 inches with a standard deviation of 2.8 inches, what height represents the 99th percentile?
Answer:
the height that represents the 99th percentile is 69.324 inches
Step-by-step explanation:
Given that :
the mean height = 62.8 inches
standard deviation = 2.8 inches
For 99th percentile;
Let X be the random variable;
SO, P(Z≤ z) = 0.99
From the standard normal z tables
P(Z )= 2.33
The standard z score formula is :
[tex]z = \dfrac{X- \mu}{\sigma}[/tex]
[tex]2.33 = \dfrac{X- 62.8}{2.8}[/tex]
2.33 × 2.8 = X - 62.8
6.524 = X - 62.8
6.524 +62.8 = X
69.324 = X
X = 69.324
Therefore; the height that represents the 99th percentile is 69.324 inches
My state's lottery has 30 white balls numbered from 1 through 30 and 20 red balls numbered from 1 through 20. In each lottery drawing, 3 of the white balls and 2 of the red balls are drawn. To win, you must match all 3 white balls and both red balls, without regard to the order in which they were drawn. How many possible different combinations may be drawn?
Answer:
I dont give you the answer right away so you will read what i write and fully understand :D
Step-by-step explanation:
We are picking 3 balls from 30 balls, so its C(30,3) because the order of picking the balls doesnt matter. We also need to pick 2 balls from 20 balls, which is C(20,2). So the answer is C(30,3) * C(20,2).
Two choises! Pick the right one!
Answer:
The function has a maximum value of 3 that occurs at x = 1.
Step-by-step explanation:
First, note that the leading coefficient is negative. This means that the parabola will curve downwards. Because of this, the function has a maximum. The maximum value will simply be the vertex.
The formula for the x-coordinate of the vertex is -b/2a.
a=-3, b=6, c=0
Plug in the numbers:
x=-(6)/2(-3)
=-6/-6=1
Now, plug 1 back into the original function:
-3x^2+6x
-3(1)^2+6(1)
=-3(1)+6
=-3+6
=3
. What is the solution set for
|k - 6|+17 = 30
A. (-19, 7}
B. (-7, 19)
C. (-19, 19)
D. {-41, 19)
Answer:
Hope this is correct and helpful
HAVE A GOOD DAY!
Write 4x2 + 16x - 9 in vertex form. Write 5x2 - 10x + 4 in vertex form.
Hi king,
Write [tex]4x^{2} + 16x - 9[/tex] in vertex form:
f(x)=[tex]4x^{2} + 16x - 9[/tex]
f(x)=[tex]4(x+2)^{2} -25[/tex]
Write [tex]5x^{2} - 10x + 4[/tex] in vertex form:
g(x)=[tex]5x^{2} - 10x + 4[/tex]
g(x)=[tex]5(x-1)^{2} -1[/tex]
Have a great day.
7 3/8 + (-4 1/2) ÷ (-5 2/3) Please Explain
Answer:
7 3/8 + (-4 1/2) ÷ (-5 2/3) = 8 23/136
Step-by-step explanation:
1) First I turned all the mix numbers into improper fractions:
7 3/8 ----> ( 7(8)+3/8) = 59/8, 4 1/2 ----> (4(2)+1/2) = 9/2, 5 2/3 ----> (5(3)+2/3) = 17/3
So now it should look like this: 59/8 + (-9/2)÷(-17/3)
2) Now our goal is to divide both of the improper fractions (-9/2)÷(-17/3),
- We first apply our fraction rule: -a/-b = a/b (when we have two negatives they cancel out each other and make a positive)
Our Case, From this:-9/2 ÷ -17/3 = To This: 9/2 ÷ 17/3
3) Now we can divide the fractions using this rule: a/b ÷ c/d = a times d / b times
Our Case, From This: 9/2 ÷ 17/3 To This: 9(3)/2(17) Which Gives Us: 27/34
(9 x 3 = 27, 2 x 17= 34)
So now it looks like this: 59/8 +27/34
4) Our look goal is to have the same denominator (which is the bottom part of the fraction) which are 8 and 34
To find it we find the LCM or Least Common Multiple of 8 and 34
(The LCM of a, b is the smallest positive number that is divisible by both a and b) which in this case a and b are 8 and 34
LCM is 136
5) We adjust our two fractions based on the LCM,
(Multiply each numerator ( top part of the fraction) by the same amount of needed to multiply its corresponding denominator to turn it to the LCM 136.
From This: 59/8 and 27/34 To This: 1003/136 and 108/36 ( 59(17)/8 (17) = 1003/136, 27(4)/34(4) = 108/306
6) Finally we can add the numerator (1003 and 108) together: 1003+108= 1111 and now we are left with 1111/136
Then we turn our improper fraction back into a mix number: 1111/138= 8 23/136
Answer:
[tex]\frac{1111}{136} = 8 \frac{23}{136}[/tex]
Step-by-step explanation:
We want to simplify:
[tex]7 \frac{3}{8} + \frac{ -4 \frac{1}{2} }{ -5 \frac{2}{3} }[/tex]
First, convert all the fractions to improper fractions:
[tex]\frac{59}{8} + \frac{ - \frac{9}{2} }{ - \frac{17}{3} } \\\\= \frac{59}{8} + \frac{27}{34}[/tex]
Find the LCM of the denominators:
[tex]\frac{(17 * 59) + (4 * 27)}{136} \\\\ = \frac{1003 + 108}{136}\\ \\= \frac{1111}{136} \\\\= 8 \frac{23}{136}[/tex]
Select the correct answer.
Which of the following represents a function?
Answer:
D.
Step-by-step explanation:
A function is when each x-value has only 1 y-value.
A: When x = 5, there are two values for y.
B: When x = -3, there are two values for y.
C: When x = -4, there are two y-values.
D: Each x-value has exactly one y-value.
So, your answer should be D.
Hope this helps!
Option (D) is accurate since the fourth option's x value has exactly one y value.
D. {(₋7,9), (₋4,₋9), (5,15), (7,19)}
What are functions?
Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.
When we say that a variable quantity y is a function of a variable quantity x, we indicate that y depends on x and that x's value determines what y's value will be. This reliance can be expressed as follows: y = f (x)
Given,
In the first case, y has two different values of 13 and 17, which is not permitted in a function, with the same value of x = 5. The first case is not a function as a result.
For the same value of x = 3 in the second case, y has two different values of 1 and 1, which is not permitted in a function. The second example is therefore not a function.
In the third case, for the same value of x = ₋4, y has two different values of 52 and 16 which is not allowed in a function. Therefore, third case is not a function.
Here, in the fourth situation, no x value is identical and there is only one possible y value.
Hence we get the answer as {(₋7,9), (₋4,₋9), (5,15), (7,19)} which represents the function.
Learn more about "functions" here-
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In a local ice sculpture contest, one group sculpted a block into a rectangular based pyramid. The dimensions of the base were 3 m by 5 m, and the pyramid was 3.6 m high. Calculate the amount of ice needed for this sculpture.
Answer:
18m square
Step-by-step explanation:
Formula for rectangular- based pyramid is L x W x H divided by 3
= 3 x 5 x 3.6 divided by 3 = 18
So you would need 18 m square for the sculpture