Answer:
The answer is (x + 5)(x - 5).
Step-by-step explanation:
Assuming that 25 is a perfect square so you can apply :
[tex](a + b)(a - b) = {a}^{2} - {b}^{2} [/tex]
Test :
[tex](x+5)(x-5) = {x}^{2} - 5x + 5x - 25 [/tex]
[tex](x+5)(x-5) = {x}^{2} - 25 [/tex]
Answer:
[tex]\boxed{(x-5)(x+5)}[/tex]
Step-by-step explanation:
x² - 25
Factor out square.
(x)² - (5)²
Apply difference of two squares formula.
a² - b² = (a-b)(a+b)
a = x
b = 5
x² - 25 = (x-5)(x+5)
In a group of 45 students, 5 study both Art and Biology. 8 study Biology but not Art. 9 study neither subject. Given that a randomly selected student studies Art, what is the probability the student studies Art and Biology?
Answer:
[tex]\frac{1}{9}[/tex]
Step-by-step explanation:
Data provided in the question
There is a total group of 45 students
Art + biology = 5
8 study biology but not Art
Neither subject studied = 9
Based on the above information, the probability of student that studies
art and biology is
Since there is a group of 45 students out of which 5 study both art and biology
So, the ratio is
4: 5
Now divide both sides by 5
So, now the ratio is
9:1
Therefore it means the probability is [tex]\frac{1}{9}[/tex]
I'll always give away 5 stars, thanks and Brainliest to the answer that's correct!
Naruto has a baseball card that is worth $45. The value of the card is increasing at the rate of 1.5% per year. How much will the card be worth in 15 years?
A: $366.17
B: $56.26
C: $89.21
D: $263.97
Answer:
a I believe sorry if I'm wrong
Answer:
I think its B: $56.26
PLEASE HELP ASAP THANKSSSS
Answer:
The correct answer is C
Step-by-step explanation:
As you can see Town A is on top of Town B this means that Town B has symetric points to town A. This also shows how Town A is Positively skewed.
Pleas answer in two minutes now
Answer:
I believe the answer is C.
The probability that my bus is late on any day is 0.2. The probability that it rains tomorrow is 0.4. If the weather and the bus are independent, what is the probability that it rains AND my bus is late?
Answer:
0.08
Step-by-step explanation:
The probability that the bus is late on any day is 0.2
The probability that it rains tomorrow is 0.4
The probability that it will rain tomorrow and the bus is late is the product of both individuals probabilities.
Therefore:
P(late & rains) = 0.2 * 0.4 = 0.08
Answer:
The probability that it rains and the bus is late is 1/7
Step-by-step explanation:
Practically, we can apply the Bayes’ theorem to solve this.
Mathematically, we use the Bayes’ problem as follows;
P( rain| late) = P(rain ^ late)/P(late) = P( late|rain) • P(rain)/[P(late|rain)P(rain) + P(not late|no rain)P(no rain)]
Where P(no rain) = 1-P(rain) = 1-0.4 = 0.6
P(on time) = 1-P(late) = 1-0.2 = 0.8
Kindly recall that P of raining = 0.4 and the probability that the bus is late is 0.2
Substituting these values into the Bayes’ equation above, we have;
P( rain| late) = (0.2)(0.4)/(0.2)(0.4) + (0.8)(0.6)
= 0.08/(0.08 + 0.48) = 0.08/0.56 = 1/7
Which equation represents a graph with a vertex at (-1,6)?
Answer:
B. [tex]y = 3x^2 -6x -3[/tex]
Step-by-step explanation:
Well, we can use the following formula to find the x coordianate of the vertex -b / 2a.
So let’s start with a)
-6 / 6
-1
A. is wrong because its vertex starts with -1.
b)
6 / 6
1
now that we have our x coordinate we can plug it into the equation to get our y.
3 - 6 - 3
So the y coordinate is -6.
Hence, the answer choice B. [tex]y = 3x^2 -6x -3[/tex]
look at the image below.
Work out angle x Triangles are not drawn to scale
Answer:
1) x = 71°, 2) x = 27°, 3) x= 32°
Step-by-step explanation:
1) Rectangle ABCD.
∠D = 90°
From ΔABE.
∠EAB +∠ABE + ∠BEA = 180°
45 + 90 +∠BEA = 180
∠BEA = 45
∠BEA + ∠AED +∠DEC = 180 °, because ∠BEC is a straight angle
45 + x + 64 = 180
x = 71°
2) Δ XYZ is equilateral, all angles = 60°.
∠YZX = 60°.
∠YZW = 180°, because it is a straight angle.
∠YZX + ∠XZW= 180
60 + ∠XZW= 180
∠XZW = 120.
From ΔXZW
∠ZXW + ∠XWZ + WZX = 180
x + 33 + 120 = 180
x = 27°
3) In ΔPQR,
PQ = PR, so ∠PQR = ∠PRQ = 69°
∠PRQ + ∠PRS = 180, because ∠QRS = 180° as straight angle.
∠PRQ + ∠PRS = 180
69 + ∠PRS = 180
∠PRS = 111°.
From ΔPRS
∠PRS + ∠RSP + ∠SPR = 180
111 + 37 + ∠SPR = 180
111 + 37 + x= 180
x = 32
Which of the following investments could be represented by the function A = 250(1 + 0.08/12)12 × 4?
hello,
the first term is 250 so this is the initial invested amount
[tex](1+\dfrac{0.08}{12})^{12}=(1+\dfrac{8\%}{12})^{12}[/tex]
is to compute 8% annual interest compounded monthly (there are 12 months in a year)
and then multiply by 4 means that it is computed for 4 years so
finally the answer is
$250 is invested at 8% annual interest compounded monthly for 4 years
hope this helps
y=(x+9)÷(x-3)
Find the value of y when x=5
solution,
X=5
[tex]y = \frac{x + 9}{x - 3} \\ = \frac{5 + 9}{5 - 3} \\ = \frac{14}{2} \\ = 7[/tex]
hope this helps...
Good luck on your assignment..
Answer:
When x=5
Y=(5+9)÷(5-3)
= 14 ÷2
= 7
The admission fee at an amusement park is $20 for children and $35 for adults. On a certain day, 390 people entered the park, and the admission fees collected totaled $10650. How many children and how many adults were admitted? NUMBER OF CHILDREN= ? NUMBER OF ADULTS= ?
Answer:
Children = 200
Adults = 190
Step-by-step explanation:
Children = x
Adults = y
x + y = 390
x = 390 - y..............(1)
20x + 35y = 10650
Substituting
20(390-y) + 35y = 10650
y = 190
x = 390 - 190 = 200
Answer:
Step-by-step explanation:
Number of children = c
Number of adults = a
Total people = 390
a + c = 390 ------------------ (I)
Admission fee for 'c' children = 20 * c = 20c
Admission fee for 'a' adult = 35 * a = 35a
Total amount = $ 10650
35a + 20c = 10650 -------------(II)
Multiply equation (I) by (-20)
(I)*(-20) -20a - 20c = - 7800
(II) 35a + 20c = 10650 { Now add and so 'c' will be eliminated}
15a = 2850
a = 2850/15
a = 190
Plug in a = 190 in equation (I)
190 + c = 390
c = 390 - 190
c = 200
Number of children = 200
Number of adults = 190
An x-method chart shows the product a c at the top of x and b at the bottom of x. Below the chart is the expression a x squared + b x + c Consider the trinomial x2 + 10x + 16. Which pair of numbers has a product of ac and a sum of b? What is the factored form of the trinomial?
Answer:
The pair of numbers that has a product of ac and a sum of b = (+2, +8)
The factored form of the trinomial = (x+2) (x+8)
Step-by-step explanation:
ax² + bx + c = 0
This is in the form of a trinomial algebraic expression
Given trinomial: = ax² + 10x + 16
Where a = 1, b= 10, c= 16
To find the pair of numbers that has a product of ac and a sum of b, we would solve the equation.
Using factorisation method:
ac = a×c = 1×16 = 16
Let's find the factors of 16 whose sum gives +10 and product gives +16
Factors of 16 = 1, 2, 8, 16
+2 + +8 = +10
+2 × +8 = +16
The factors are +2 and +8
The pair of numbers that has a product of ac and a sum of b = (+2, +8)
x² + 10x + 16 = x + 2x + 8x + 16
x² + 10x + 16 = x(x+2) + 8(x+2)
= (x+2) (x+8)
The factored form of the trinomial = (x+2) (x+8)
Answer:
(x+2) (x+8)
Step-by-step explanation:
A man has a 10m X 10m square garden. In the center is a 2m X 2m square patch which he cannot use. He divides his usable space into four congruent rectangular patches, each of which measures
Answer:
4m X 6m
Step-by-step explanation:
This is because if there is a 2m square in the middle, there is 8 m of usable space left along both sides of the garden.
Because the 2m square was in the middle, there is 8/2 = 4m along each width of the 4 small rectangles.
Becuase 4m is the width, there is 10 - 4 = 6m along each rectangle's length.
The 4m is the width, there is 10 - 4 = 6m along each rectangle's length. the area he will use is 4m x 6m.
What is reflexive property of congruence?The reflexive property of congruence says that the considered geometric quantity, whether it be angle, line segment, or shape etc, is congruent to itself.
Given information; A man has a 10m X 10m square garden. In the center is a 2m X 2m square patch we need to find which he cannot use.
He divides his usable space into four congruent rectangular patches.
If there is a 2m square in the middle, there is 8 m of usable space left along both sides of the garden.
The 2m square was in the middle, there is 8/2 = 4m along each width of the 4 small rectangles.
The 4m is the width, there is 10 - 4 = 6m along each rectangle's length.
Learn more about congruent triangles here:
https://brainly.com/question/16921692
#SPJ2
Find the difference.
(3x4 - 5x2 - 4)-( 2x3 x2 + 1)
w
3x4 - 2x3 - 4x2-5
a
Answer:
(3x4 - 5x2 - 4)-( 2x3 x2 + 1) is equals to -15
3x4 - 2x3 - 4x2-5 is equals to -7
Step-by-step explanation:
1.) (3x4 - 5x2 - 4)-( 2x3 x2 + 1)
3 x 4 = 12 5 x 2 = 10 12 - 10 = 2 2 - 4 = -2
2 x 3 = 6 6 x 2 = 12 12 + 1 = 13
-2 - 13 = -15
2.)3x4 - 2x3 - 4x2-5 is eaquals to -7
3 x 4 = 12 2 x 3 = 6 12 - 6 = 6 4 x 2 = 8
6 - 8 = -2 -2 - -5 = -7
Those were my answers
A 7-column table with 2 rows. Column 1 is labeled Sample with entries catfish, all fish. Column 2 is labeled 1 with entries 3, 20. Column 3 is labeled 2 with entries 5, 20. Column 4 is labeled 3 with entries 7, 20. Column 5 is labeled 4 with entries 5, 20. Column 6 is labeled 5 with entries 6, 20. Column 7 is labeled 6 with entries 8, 20. The mean number of catfish in all 6 samples is approximately 5.7. If 200 fish are in the pond, which proportion can be used to predict the number of catfish in the population? StartFraction 5.7 over 20 EndFraction = StartFraction x over 200 EndFraction StartFraction 5.7 over 20 EndFraction = StartFraction 200 over x EndFraction StartFraction 34 over 20 EndFraction = StartFraction x over 200 EndFraction StartFraction 8 over 20 EndFraction = StartFraction 20 over x EndFraction
Answer: The correct option is 5.7/20 = x/200
Step-by-step explanation: Please refer to the diagram attached for more details.
From the 7-column by 2-row table drawn, you can determine that the mean number of catfish as given in the question is derived as follows;
Mean = Summation of observed data / Number of observations
Mean = (3 + 5 + 7 + 5 + 6 + 8)/6
Mean = 34/6
Mean = 5.6667
Mean ≈ 5.7
Also the mean number of all fish is derived as follows;
Mean = Summation of observed data / Number of observations
Mean = (20 + 20 + 20 + 20 + 20 + 20)/6
Mean = 120/6
Mean = 20
Using relative frequency, we can confidently predict the number of catfish population in the pond. This simply means, if the mean number of catfish is 5.7 and the mean number of all fish is 20, then the relative frequency would be 5.7 over 20 of the total fish population.
Hence, if there is a total of 200 fish in the pond then to predict the proportion which would be catfish can be expressed as follows;
StartFraction 5.7 over 20 EndFraction = StartFraction x over 200 EndFraction.
OR better expressed as;
5.7/20 = x/200
Answer:
5.7/20 = x/200
Step-by-step explanation:
The points (0, –1) and (4, 5) lie on the straight line L.
Find an equation of the line which is parallel to L and passes through the point (–2, 0).
Answer:
y = 3/2x + 3.
Step-by-step explanation:
With these two points, we can find the equation of line L.
y = mx + b
Slope: (5 --1) / (4 - 0) = 5 + 1 / 4 = 6 // 4 = 3/2
Intercept: [stated by the first pair of coordinates] (0, -1)
y = 3/2x - 1
Since the line is parallel to L, the slope is the same as line L.
y = 3/2x + b
The line passes through (-2, 0), so we can substitute the points into the equation and solve for b.
0 = 3/2 * -2 + b
b - 3 = 0
b = 3
So, the equation of the line which is parallel to L and passes through the point (-2, 0), is y = 3/2x + 3.
Hope this helps!
A grasshopper makes jumps that are either 17 or 19 cm in length, in either direction (forwards or backwards). Is it possible for the grasshopper to cover a distance of 101 cm in 100 jumps?
Answer: No. The grasshopper cannot cover exactly 101 cm in exactly 100 jumps.
Step-by-step explanation:
If the grasshopper makes 50 forward jumps of 19 cm and 50 backward jumps of 17 cm (in any order) the jumps total 950-850 for a net result of 100.
Changing to any other amount just gets farther away from the goal.
A system of equations yields no solution of integers.
x + y ==100
19x - 17y =101
You can try it, but the result has a decimal. This grasshopper cannot make partial jumps!
Five submarines sink on the same day, and all five go down at the same spot where a sixth had previously sunk. How might they all lie at rest so that each submarine touches the other five? To simplify, arrange six wooden matches so that each match touches every other match. No bending or breaking allowed.
Answer:
picture is attached
Step-by-step explanation:
there are many options but this is one
In an orchard the ratio of apple trees to pear trees is 2 : 5, and the ratio of pear trees to peach trees is 3 : 4. Work out the ratio of apple trees to pear trees to peach trees.
Answer:
5/8
Step-by-step explanation:
apple trees to pear trees=5/2 to peach trees=(5/2)/4=5/8
All of the following expressions simplify to 3, except _____.
-6 + 9
1 - (-2)
-9 ÷ (-3)
-5 - 2
Answer:
-5 - 2
Step-by-step explanation:
Solve each of the following
A is -6 + 9 which equals 3
B is 1 - (-2) which simplifies into 1 + 2 which equals 3
C is -9 / -3. the negatives cancel leaving 9/3 which is 3
D is -5 - 2 which simplifies into -5 + -2 which equals -7
If two lines meet at a right angle they are said to be _________ to each other.
Answer: perpendicular
Answer:
perpendicular
Step-by-step explanation:
If two lines meet at a right angle they are said to be perpendicular to each other.
Two lines are perpendicular when they intersect at a right angle.
I need help please help
Answer:
21u-16v+18w
Step-by-step explanation:
(7u-4v+4w) 14u-12v+14w
21u-16v+18w
Answer:
= 21u−16v+18w
Step-by-step explanation:
Let's simplify step-by-step.
7u−4v+4w−2(−7u+6v−7w)
Distribute:
=7u+−4v+4w+(−2)(−7u)+(−2)(6v)+(−2)(−7w)
=7u+−4v+4w+14u+−12v+14w
Combine Like Terms:
=7u+−4v+4w+14u+−12v+14w
=(7u+14u)+(−4v+−12v)+(4w+14w)
=21u+−16v+18w
Answer:
=21u−16v+18w
The police department uses a formula to determine the speed at which a car was going when the driver applied the breaks, by measuring the distance of the skid marks.The equation d=0.03r^2+r models the distance, d, in feet, r miles per hour (r is the speed of the car) Factor the equation. d=?
Answer:
0.03 feet
Step-by-step explanation:
d = 0.03r² + r
When d = 0: 0.03r² + r = 0
r(0.03r + 1) = 0
∴ r = 0
When r = 0: d = 0.03 feet
Complete the equation of the line through (-8,8)(−8,8)left parenthesis, minus, 8, comma, 8, right parenthesis and (1,-10)(1,−10)left parenthesis, 1, comma, minus, 10, right parenthesis.
Answer:
[tex]y = -2x - 8\\OR\\2x+y+8=0[/tex]
Step-by-step explanation:
Given that there are 2 points
[tex]A(-8,8)[/tex] and
[tex]B(1,-10)[/tex]
So, the coordinates are:
[tex]x_2 = 1\\x_1 = -8\\y_2 = -10\\y_1 = 8[/tex]
Equation of a line is given as:
[tex]y =mx+c[/tex]
where 'm' is the slope of the line, formula for 'm' is given as:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex](x,y)[/tex] are the points that satisfy the equation of the line.
[tex]c[/tex] is the [tex]y -[/tex] intercept.
Calculating the value of m using the given coordinates:
[tex]m=\dfrac{-10-8}{1-(-8)}\\\Rightarrow m=\dfrac{-18}{9} = -2[/tex]
So, the equation of line becomes:
[tex]y =-2x+c[/tex]
Now, putting the coordinates of point [tex]A(-8,8)[/tex]
[tex]8 =-2\times (-8)+c\\\Rightarrow 8 = 16+c\\\Rightarrow c = -8[/tex]
Please refer to the graph of given equation of line.
The equation of line is:
[tex]y =-2x+-8\\OR\\2x+y+8=0[/tex]
PLZ HELP!!!!WILL MARK BRAINLIEST AND 20 POINTS!!!
Answer: Find a common denominator on the right side of the equation
Step-by-step explanation:
You can see that they found the common denominator of 4 therefore that is the correct answer
find a18 of the arithmetic sequence 2, -5, -12, -19
Answer:
The 18th term of the sequence is -117.
Step-by-step explanation:
The given sequence is 2,-5,-12,-19
From this AP,
First term, a = 2
Common difference, d = -5-2 = -7
It is required to find the 18th term of the sequence. The nth term of an AP is given by :
[tex]a_n=a+(n-a)d\\\\a_{18}=a+17d\\\\a_{18}=2+17\times (-7)\\\\a_{18}=-117[/tex]
So, the 18th term of the sequence is -117.
Mrs. Brown has 11 more boys than girls in her class and has a total of 28 students. Which of the following systems of equations could be used to solve this problem?
Answer:
g=number of girls in the class b=number of boy in the class
g+b=28
g=11+b
Which of the following equations is graphed below?
Answer: 3rd answer choice
Step-by-step explanation:
Answer: 4th answer choice
Step-by-step explanation:
The play director spent 190190190190 hours preparing for a play. That time included attending 35353535 rehearsals that took varying amounts of time and spending 933493 \dfrac{3}{4}934393, start fraction, 3, divided by, 4, end fraction hours on other responsibilities related to the play. What question does the equation 35x+9334=19035x+93\dfrac{3}{4}=19035x+9343=19035, x, plus, 93, start fraction, 3, divided by, 4, end fraction, equals, 190 help answer?
Answer:
The equation above represents the total time the play director spent preparing for a play.
Step-by-step explanation:
The time spent by the play director for preparing for a play is, 190 hours.
Of these 190 hours, the director spent varying amounts of time attending 35 rehearsals for the play.
Let the varying amounts of time be denoted by, x.
The director also spent 3/4th of an hour, i.e. 45 minutes, on other responsibilities related to the play.
The equation provided is:
[tex]35x+\frac{3}{4}=190[/tex]
The equation above represents the total time the play director spent preparing for a play.
Which statement is true about the equations –3x + 4y = 12 and 1/4x-1/3y=1
Answer: No solution
Step-by-step explanation:
This system of equation has no solution because...
-3x+4y=12
1/4x-1/3y=1
[tex]-3x+4y-4y=12-4y[/tex]
[tex]-3x=12-4y[/tex]
[tex]\frac{-3x}{-3}=\frac{12}{-3}-\frac{4y}{-3}[/tex]
[tex]\frac{12}{-3}-\frac{4y}{-3}[/tex]
[tex]x=-\frac{12-4y}{3}[/tex]
substitute
[tex]\frac{1}{4}\left(-\frac{12-4y}{3}\right)-\frac{1}{3}y=1[/tex]
[tex]-1=1[/tex]
-1=1 is false so therefore this system has no solution
The graph of f(x) = 2x + 1 is shown below. Explain how to find the average rate of change between x = 2 and x = 5. (10 points) Graph of 2 to the power of x plus 1