Answer:
1. a. b = - 8
b. x = 8
c. x = 11
d. x = 5
2. 12 soccer balls and 8 basketballs can be purchased.
Step by step explanation
a. [tex] - 14 + 6b + 7 - 2b = 1 + 5b[/tex]
Calculate the sum
[tex] - 7 + 6b - 2b = 1 + 5b[/tex]
Collect like terms
[tex] 7 + 4b = 1 + 5b[/tex]
Move variable to L.H.S and change it's sign
Similarly, Move constant to R.H.S and change its sign
[tex]4b - 5b = 1 + 7[/tex]
Collect like terms
[tex] - b = 8[/tex]
Change the signs on both sides of the equation
[tex]b = - 8[/tex]
-----------------------------------------------------------------
b. [tex] \frac{5x + 10}{ - 6} = - 5[/tex]
Apply cross product property
[tex]5x + 10 = - 5 \times ( - 6)[/tex]
Multiply the numbers
[tex]5x + 10 = 30[/tex]
Move constant to R.H.S and change its sign
[tex]5x = 30 - 10[/tex]
Calculate the difference
[tex]5x = 20[/tex]
Divide both sides of the equation by 5
[tex] \frac{5x}{5} = \frac{20}{5} [/tex]
Calculate
[tex]x = 4[/tex]
----------------------------------------------------------------
c. [tex] - 15 = \frac{ - 8x - 17}{7} [/tex]
Apply cross product property
[tex] - 15 \times 7 = - 8x - 17[/tex]
Multiply the numbers
[tex] - 105 = - 8x - 17[/tex]
Swap the sides of the equation
[tex] - 8x - 17 = - 105[/tex]
Move constant to R.H.S and change its sign
[tex] - 8x = - 105 + 17[/tex]
Calculate
[tex] - 8x = - 88[/tex]
Change the signs on both sides of the equation
[tex]8x = 88[/tex]
Divide both sides of the equation by 8
[tex] \frac{8x}{8} = \frac{88}{8} [/tex]
Calculate
[tex]x = 11[/tex]
------------------------------------------------------------------
D. [tex]5 = 6x + 5(x - 10)[/tex]
Distribute 5 through the parentheses
[tex]5 = 6x + 5x - 50[/tex]
Collect like terms
[tex]5 = 11x - 50[/tex]
Swap both sides of the equation
[tex]11x - 50 = 5[/tex]
Move constant to R.H.S and change its sign
[tex]11x = 5 + 50[/tex]
Calculate the sum
[tex]11x = 55[/tex]
Divide both sides of the equation by 11
[tex] \frac{11x}{11} = \frac{55}{11} [/tex]
Calculate
[tex]x = 5[/tex]
------------------------------------------------------------------
2.
Solution,
No.of students in soccer = x
No.of students in basketball = y
Total no.of students = 20
i.e x + y = 20 → equation ( i )
Cost of soccer ball = $ 7
Cost of basketball = $ 10
Total budget = $ 164
i.e 7x + 10 y = 165 → equation ( ii )
In equation ( i ),
x + y = 20
Move 'y' to R.H.S and change its sign
x = 20 - y
Put the value of x in equation ( i )
[tex]7(20 - y) + 10y = 164[/tex]
[tex]140 - 7y + 10y = 164[/tex]
[tex]3y = 164 - 140[/tex]
[tex]3y = 24[/tex]
[tex]y = \frac{24}{3} [/tex]
[tex]y = 8[/tex]
Now, put the value of y in equation ( i ) ,
x + y = 20
[tex]x + 8 = 20[/tex]
[tex]x = 20 - 8[/tex]
[tex]x = 12[/tex]
Hence, 12 soccer balls and 8 basketballs can be purchased.
Hope this helps...
Best regards!!
Answer:
1. b = -8
2. x = 8
3. x = 11
4. x = 5
hope that helpwd
Find the mean and standard deviation. Show all work. 1. X 0 1 2 3 4 P(x) .07 .38 .22 .13
Answer:
Mean = 2.14
Standard deviation = 2.40
Step-by-step explanation:
The calculation of mean and standard deviation is shown below:-
[tex]X = .07\times0 + 0.20\times 1 + 0.38\times 2 + 0.22\times 3 + 0.13\times 4\\\\ = 0 + 0.2 + 0.76 + 0.66 + 0.52[/tex]
= 2.14
So, the mean is 2.14
Now, For computing the standard deviation first we need to find out the variance which is shown below:-
Variance is
[tex]Var(X) = P(X^2) - [P(X)]^2\\\\ P(X^2) = .07\times (0^2) + .20\times (0^1) + .38\times (0^2) + .22\times (0^3) +0.13\times (0^4)[/tex]
After solving the above equation we will get
= 5.78
Now, the standard deviation is [tex]= \sqrt{Variance}[/tex]
[tex]= \sqrt{5.78}[/tex]
= 2.404163056
or
= 2.40
A+B=C? I don't get the formula...
Answer:
Read this for more help!
Step-by-step explanation:
That is okay if you do not understand the formula. We all have troubles with math in one spot or in another. With the a²+b²=c², we would have to go really slowly. Just for you!
Let´s do an example. Say we have a triangle, and for this we need to know our square roots! Say we have this triangle, and it has both a 3 and a 4 on its sides. Now a triangle had 3 sides. 2 sides are smaller, and then it would have a larger side, which is called the hypotenuse! That is the side we would need to figure out, because the hypotenuse is the largest side of the triangle, and we only have the smaller sides(3 and 4).
So we need to work with the formula.
So let us plug the example into the formula.
There is no specific order to how we would be putting the sides in. 3 could be b or it could be a. Same goes for the 4. It really does not matter because you would be getting the same answer no matter what.
a²+b²=c²
3²+4²=c²
3²=9
4²=16
We need to add the two of those numbers, both 9 and 16 and we get 25. That is c². But we need c, because the hypotenuse is only c. So we need to take the square root of 25. And we get 5!
I will show you the equation again with 3 and 4 reversed.
4²+3²=c²
4²=16
3²=9
Like what we did above, we would get 25. And then take the square root! Same answer, so it really doesn't matter!
If you still do not understand this topic, you can always ask someone else who does, or go on khan academy, or search for more topics like this on BRAINLY! I hope this helped!
WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the normal distribution. The mean of the distribution is 15.0 minutes and the standard deviation is 3.5 minutes. What is the probability that a particular listener will tune in:
Complete question :
WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the normal distribution. The mean of the distribution is 15.0 minutes and the standard deviation is 3.5 minutes. What is the probability that a particular listener will tune in:
a. More than 20 minutes? b. For 20 minutes or less
Answer: 0.0764 ; 0.9236
Step-by-step explanation:
Mean (m) = 15 minutes
Standard deviation (sd) = 3.5
Z - score :
Z = (x - m) / sd
A) more than 20 minutes
P(X > 20) ; x = 20
Z > (20 - 15) / 3.5 = 5/3.5 = 1.429
P(z > 1.429) = 0.5 - P(0<z<1.43)
Using the z-table: 1.43 = 0.4236
0.5 - 0.4236 = 0.0764
2) 20 minutes or less :
P(X <= 20) ; x = 20
Z < (20 - 15) / 3.5 = 5/3.5 = 1.429
P(z < 1.429) = 0.5 + P(0<z<1.43)
Using the z-table: 1.43 = 0.4236
0.5 + 0.4236 = 0.9236
I am really confused... Please help me solve this question!
I hope this helps you
Helppppp pleaseeeeee
Answer:
(2, 2), (5, 3), (9, 4), and (13, 5).
Step-by-step explanation:
The inverse of a function makes it so that the x-values become y-values, and y-values become x-values.
The current coordinates are (2, 2), (3, 5), (4, 9), and (5, 13).
If the function were inversed, the coordinates would be (2, 2), (5, 3), (9, 4), and (13, 5).
Hope this helps!
For a class, Mrs. Hawk brought
in 7 different packages of
colored pens. The teacher
randomly selects 2 packages.
How many different
combinations are there?
Answer:
14
Step-by-step explanation:
7x2=14
which of the following shows 210 angles in standard position
The 210 angles in the standard position are shown in figure (A) option (A) is correct.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called an "Angle."
It is given that:
The measure of the angle:
= 210 degrees
The reference angle can be defined as the angle formed between the terminal side and the x-axis, known as the reference angle.
The angle between the x-axis and the y-axis is 90 degrees.
The angle between the y-axis and the negative x-axis is 90 degrees.
The angle between the negative x-axis and the arrow shown in the coordinate plane is 30 degrees.
Thus, the 210 angles in the standard position shown in figure (A) option (A) is correct.
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write down as decimal.
Answer:
iii) 5.7
iv) 27.85
vii) 0.609
viii) 40.0709
Step-by-step explanation:
hope this helps
Simplify
Pls help......
Answer:
5
Step-by-step explanation:
(0.000064)^5/6 divided by (0.00032)^6/5
(0.00032)^6/5=(0.000064)
and
(0.000064)^6/5=(0.00032)
so now we have (0.00032) divided by (0.000064)
which is 5!
hope this helps!
Answer: yes
Step-by-step explanation: no
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
the numbers of cars pf various colors in a parking lot
Answer: The speed of a car as it changes during a time.
B is the best example of continuous data.
Step-by-step explanation: The contrast between the definitions of continuous data vs. discreet data is that discrete data is counted, continuous data is measured.
A speedometer measures speed continuously, time is measured continuously.
Time can, however, be reported as discreet measurements in situations where that kind of data is needed. (not in this question)
A Number of cars is discreet.
Data from different workers or different days is not continuous.
ABC is a triangle in which DE ∥BC. Find ∠A
Answer:
∠A = 35°
Step-by-step explanation:
From the question above,
Sum of Angles on a straight line = 180°
180° = ∠BDE + ∠ADE
∠BDE = 105°
∠ADE = 180° - 105°
∠ADE = 75°
To find Angle ∠EBC and ∠DEB are alternate angles, this means that they are equal to each other
Hence, ∠EBC = ∠DEB
30° = 30°
Sum of Angles on a straight line = 180°
180° = ∠DEB + ∠BEC + ∠DEA
180° = 30° + 80° + ∠DEA
∠DEA = 180° -(30+ 80)°
∠DEA = 180° - 110°
∠DEA = 70°
It is important to note that the sum of Angles in a triangle = 180°
180° = ∠ADE + ∠DEA + ∠A
∠ADE = 75°
∠DEA = 70°
180° = 75° + 70° + ∠A
∠A = 180° - (75° + 70°)
∠A = 180° - 145°
∠A = 35°
The product of two numbers is 32. The first number, x, is one-half of the second number, y. Which system of equations can be used to find the two numbers? A system of equations. x y equals 32. x equals StartFraction one-half EndFraction y. A system of equations. x y equals 32. x equals y minus StartFraction one-half EndFraction. A system of equations. x plus y equals 32. x equals y minus StartFraction one-half EndFraction. A system of equations. x plus y equals 32. x equals StartFraction one-half EndFraction y.
Answer:
xy = 32
x = 1/2y.
Step-by-step explanation:
Let's say the two numbers are x and y.
The product of them is 32, so x times y is 32.
xy = 32.
x is 1/2 of y. So...
x = 1/2y
Your two systems are xy = 32 and x = 1/2y.
Hope this helps!
Answer:
The answer is A on edg 2021
A fruit bowl contains apples and bananas in the ratio 4 : 5. Two apples are removed changing the ratio to 2 : 3. Work out the total number of fruit that remain in the bowl.
Answer:
25
Step-by-step explanation:
Given that the ratio is 4 : 5 = 4x : 5x ( x is a multiplier ), then
4x - 2 : 5x = 2 : 3
Expressing the ratio in fractional form
[tex]\frac{4x-2}{5x}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )
3(4x - 2) = 10x , distribute left side
12x - 6 = 10x ( subtract 10x from both sides )
2x - 6 = 0 ( add 6 to both sides )
2x = 6 ( divide both sides by 2 )
x = 3
Thus initially there were
4x + 5x = 9x = 9(3) = 27 pieces of fruit
2 apples were removed, leaving 25
Answer:
25
Step-by-step explanation:
4 : 5. is ratio before two apples were removed.
2 : 3. is ratio after two apples were removed.
combing the two statements will give you the following mathematical statement:
4x-2:5x=2:3 solve for x
3(4x-2)=5x*2
12x - 6=
2x=6
x=3
then 4x + 5x = total ñô fruit
4(3) + 5(3) = total ñô fruit
27= total ñô fruit
remaining fruit=total ñô fruit - 2
remaining fruit=27-2
remaining fruit=25
a parabola had a vertex of (-5,0) and passes through the point (-3,1)
Answer:
Step-by-step explanation:
let the parabola be y=a(x+5)²+0
or y=a(x+5)²
∵ it passes through (-3,1)
1=a(-3+5)²
4a=1
a=1/4
so parabola is y=1/4(x+5)²
The mean annual tuition and fees for a sample of 11 private colleges was $26,500 with a standard deviation of $6,000. A dotplot shows that it is reasonable to assume that the population is approximately normal. You wish to test whether the mean tuition and fees for private colleges is different from $31,000.
i). State the null and alternate hypotheses.
ii). Compute the value of the test statistic and state the number of degrees of freedom.
iii). State a conclusion regarding H. Use the a = 0.05 level of significance.
Answer:
Step-by-step explanation:
Given that:
Sample size n = 11
Sample Mean X = 26500
standard deviation = 6000
Population mean [tex]\mu[/tex] = 31000
the null and alternate hypotheses are being stated as follows:
[tex]H_o : \mu = 31000[/tex]
[tex]H_1 : \mu \neq 31000[/tex]
The value of the test statistic can be computed as:
[tex]Z = \dfrac{\bar x - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \dfrac{26500 - 31000}{\dfrac{6000}{\sqrt{11}}}[/tex]
[tex]Z = \dfrac{-4500}{\dfrac{6000}{3.3166}}[/tex]
Z = −2.4875
Z = −2.49
The degree of freedom df = n- 1
The degree of freedom df = 11 - 1
The degree of freedom df = 10
At the level of significance ∝ = 0.05
[tex]t_{\alpha/2}[/tex] = 0.025
From the t distribution table at [tex]t_{\alpha/2, 10}[/tex] and critical value = -2.49;
The p-value = 0.0320
Decision Rule: Reject null hypothesis if p -value is lesser than the level of significance
Conclusion:We reject the null hypothesis , therefore, we conclude that there is no sufficient information to that the mean tuition and fees for private colleges is different from $31,000
divide 0.377 ÷ 2.9 dosto please solve it
48 - 8x equivalent expression
Answer:
8(6-x)
Step-by-step explanation:
Both 48 and 8 can be divisible by 8.
48 ÷ 8 = 6
8 ÷ 8 = 1
Therefore you get the answer 8(6-x)
as the simplest form.
Hope this helps.
PLEASE help me solve this question! I really need to solve this question ASAP! No nonsense answers, and please attach the solution.
Answer:
{-0.5, 0.1}
Step-by-step explanation:
multiply the 8 on the left with x/x so you can write left hand as [tex]\frac{1-8x}{x}[/tex]cross multiply to get rid of the fractions: [tex]5x = (1-8x)(5x+2)[/tex]simplify into a regular quadratic equation: [tex]-20x^2 - 8x +1 =0[/tex]use the quadratic formula to get the answers:[tex]x = \frac{8 \pm \sqrt{(-8)^2 - 4 \cdot -20 \cdot 1}}{-40} = \frac{8 \pm 12}{-40}[/tex]
so x is 20/-40 = -0.5 or x = -4/-40 = 0.1
points Q and R are midpoints of the sides of triangle ABC. Triangle A B C is cut by line segment Q R. Point Q is the midpoint of side A B and point R is the midpoint of side A C. The lengths of A Q and Q B are 4 p, the length of Q R is 2 p + 3, and the length of C B is 6 p minus 4. The lengths of A R and R C are congruent. What is AQ? 10 units 14 units 20 units 32 units
Answer:
AQ = 20 units
Step-by-step explanation:
I tried figuring in the pic below..
Similar triangles are triangles whose corresponding measures are proportional. All of their corresponding angles are also congruent. There are theorems and postulates that prove triangle similarity. Usually they requrie at least three parts of each triangle. The symbol for similarity is ~.
We have two triangles in the figure. ΔAQR and ΔABC. We will prove first that they are similar.
Answer:
20
Step-by-step explanation:
RQ is 1/2 of CB, so 2(2p+3)=6p-4. This would make p=5. Then, 5*4=20.
(also it is right on edgenuity)
HELP ASAP MATH PLS!!!!!
Answer:
A
Step-by-step explanation:
We know that because the second plane flies 15 miles less, it has to be either A or B, because they have -15 at the end.
It cannot be B, because in B, the second plane has a -w in the equation. However, in the word problem, the second plane flies with the wind, not against it. Therefore, it must be A.
Can you help me plz
Answer:
[tex]\boxed{\sf y=6}[/tex]
Step-by-step explanation:
There are 5 identical squares.
The area of one square is [tex]\sf s^2[/tex].
[tex]\sf{y^2 } \times \sf{5}[/tex]
[tex]\sf 5y^2[/tex]
The area of the whole shape is 180 cm².
[tex]\sf 5y^2=180[/tex]
Solve for y.
Divide both sides by 5.
[tex]\sf y^2=36[/tex]
Take the square root on both sides.
[tex]\sf y=6[/tex]
Samuel is solving the equation 3 (x minus 1) + 4 = 2 minus (x + 3). Which equivalent equations might Samuel use? Check all that apply.
3 x minus 3 + 4 = 2 minus x minus 3
3 x minus 1 + 4 = 2 minus x + 3
3 x minus 3 + 4 = 2 minus x + 3
3 x + 1 = negative x minus 1
3 x + 3 = negative x + 5
3 x + 1 = negative x + 5
Answer: 3 x minus 3 + 4 = 2 minus x minus 3
3 x + 1 = negative x minus 1
Step-by-step explanation:
A and D. Edge 2020
The required equation that Samuel used is 3x -3 + 4 =2- x -3. option A is correct.
Samuel is solving the equation 3 (x minus 1) + 4 = 2 minus (x + 3). Which equivalent equations might Samuel use, is to be determined.
The equation is the relationship between variables and represented as[tex]y = ax +b[/tex] is an example of a polynomial equation.
Given equation is [tex]3(x-1) +4 =2 -(x+3)[/tex]
Simplification of the above equation,
opening the parenthesis on both sides
step 1⇒ 3x - 3 + 4 = 2 - x - 3
step 2⇒ 3x + 1 = -x - 1
Transposition of -x to the left side and +1 to the right side
step 4 ⇒ 3x +x = -1 -1
4x = -2
Transposition of 4 to the denominator of -2.
step 5⇒ x = -2/4
x = -1/2
Thus , Step 1 3x -3 + 4 =2- x -3 is the equivalent equation used by the samuel.
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PLEASE HELP THANK YOUUUU Your group has $120 available for the banquet. Any other costs must be covered from selling tickets for the event. You decided to take care of the major cost first–hall rental and caterer. Each caterer you approach is associated with a specific hall. Caterer One charges $45 per person. The cost of using the hall is inclusive. Caterer Two charges $250 for hall rental plus $28 per person. Cater Three charges $500 for hall rental plus $20 per person. 1. Write the equation to represent the cost of each caterer. Use C to represent cost and n to represent number of people. (3 marks)
Answer:
The cost C, of hosting the banquet with the services of Caterer One is;
C = $ 45·n
The cost C, of hosting the banquet with the services of Caterer Two is;
C = $250 + $ 28·n
The cost C, of hosting the banquet with the services of Caterer Three is;
C = $500 + $ 20·n
Step-by-step explanation:
The information includes;
The amount available to the group for the banquet = $120
The number of people attending the banquet = n
The cost incurred in hosting the banquet = C
The major costs in hosting the banquet are hall rental and caterer
The cost per caterer are as follows;
Caterer One
The cost per person including the hall = $45
Therefore, the cost incurred, C, in hosting the banquet using caterer one is equal;
C = n × $45 = $ 45·n
Caterer Two
The hall rental = $250
The cost per person = $28
Therefore, the cost incurred, C, in hosting the banquet using caterer two is equal;
C = $250 + n × $28 = $250 + $ 28·n
Caterer Three
The hall rental = $500
The cost per person = $20
Therefore, the cost incurred, C, in hosting the banquet using caterer three is equal;
C = $500 + n × $20 = $500 + $ 20·n.
Answer:
The cost C, of hosting the banquet with the services of Caterer One is;
C = $ 45·n
The cost C, of hosting the banquet with the services of Caterer Two is;
C = $250 + $ 28·n
The cost C, of hosting the banquet with the services of Caterer Three is;
C = $500 + $ 20·n
Step-by-step explanation:
The information includes;
The amount available to the group for the banquet = $120
The number of people attending the banquet = n
The cost incurred in hosting the banquet = C
The major costs in hosting the banquet are hall rental and caterer
The cost per caterer are as follows;
Caterer One
The cost per person including the hall = $45
Therefore, the cost incurred, C, in hosting the banquet using caterer one is equal;
C = n × $45 = $ 45·n
Caterer Two
The hall rental = $250
The cost per person = $28
Therefore, the cost incurred, C, in hosting the banquet using caterer two is equal;
C = $250 + n × $28 = $250 + $ 28·n
Caterer Three
The hall rental = $500
The cost per person = $20
Therefore, the cost incurred, C, in hosting the banquet using caterer three is equal;
C = $500 + n × $20 = $500 + $ 20·n.
The radius of a cylindrical water tank is 5.5 ft, and it’s height is 10 ft. What is the volume of the tank?
Answer:
950.33 ft³
Step-by-step explanation:
The volume of a cylinder is denoted by: V = πr²h, where r is the radius and h is the height.
Here, the radius is r = 5.5 ft and the height is h = 10 ft. Plug these into the formula:
V = πr²h
V = π * 5.5² * 10 ≈ 950.33 ft³
The answer is thus 950.33 ft³.
~ an aesthetics lover
In packing for a trip, Sarah puts three pairs of socks - one red, one blue, and one green - into one compartment of her suitcase. If she then pulls four individual socks out of the suitcase, simultaneously and at random, what is the probability that she pulls out exactly two matching pairs
Answer:
1/5 or 20%
Step-by-step explanation:
This problem can be easily solved by finding the probability of her picking one matching pair to leave in the suitcase (which results in pulling out exactly two matching pairs)
For the first sock, it does not matter what sock she picks.
For the second sock, there is only 1 out of the 5 socks left that would match the first one picked. Therefore, the probability that she pulls out exactly two matching pairs is 1/5 or 20%
a:b=7.2
How many times larger is a than b?
Does anyone understand this?
PLEASE HELP ASAP
Answer:
3.5 times as large
Step-by-step explanation:
The ratio can be written using a colon or a fraction bar. In the latter case, simplifying the fraction gives you your answer:
a : b = 7 : 2 = 7/2
'a' is 7/2 = 3.5 times as large as 'b'
Does this graph show a function? Explain how you know.
5
-5
-5
A. No; there are y-values that have more than one x-value.
B. No; the graph fails the vertical line test.
C. Yes; the graph passes the vertical line test.
D. Yes; there are no y-values that have more than one x-value.
Answer:
Option (C).
Step-by-step explanation:
To check a graph whether it's a function or not we use a vertical line test. In this test first we draw a vertical line on the given graph. If this line intersects the graph at more than one point, the graph is not a function.
In the given parabola, opening upwards passes the vertical line test.
Therefore, this graph shows a function.
Option (C) will be the answer.
Option (c) Yes; the graph passes the vertical line test. And
(d) Yes; there are no y-values that have more than one x-value are correct options. Hence, a given graph is a function.
This is a graph of [tex]y = x^2[/tex]
Which is a graph of parabola.
To determine the given graph is a function or not, we do a vertical line test.
The vertical line test says that if a vertical line intersects a graph more than once, then that graph is not a function. And in this case, y-values have more than one x-values.
Let’s draw a vertical line in the given graph (attached below)
We see that the vertical line touches the graph only at once. That’s why it is a function, and so there are no y-values that have more than one x-value.
Hence, the given graph is a function and option (3) and (4) are correct options.
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Help please!! Thank you
Answer:
25 ( A)
pls mark me as BRAINLIEST
stay at home stay safe
and keep rocking
Answer:
A
Step-by-step explanation:
The first ten primes are
2,3,5,7,11,13,17,19,23,27
so the number is
2*3*5*7*11*13*17*23*27
so
2*11 is 22, so 22 divides the number
2*3 is 6, so 6 divides the number
2 is there so 2 divides the number
So the only one is 25.
fins the zeroes of the quadratic equation : 4√ 5 x^ 2 - 24x - 9√ 5
10th grade Cbse chapter 2 : Polynomials
pls give the step by step explanation so that i can understand
Answer:
Step-by-step explanation:
Hello,
First of all, we know that the solution of the following equation
[tex]ax^2+bx+c=0[/tex]
are
[tex]\dfrac{-b\pm\sqrt{b^2-4ac}}{2a} \ \text{ when } \Delta=b^2-4ac \geq 0[/tex]
I would suggest that you try to apply this formula first and check the solution only after you try.
Let's apply it in this case, we have:
[tex]a=4\sqrt{5} \\ \\ b=-24 \\ \\ c= -9\sqrt{5}[/tex]
[tex]\Delta=b^2-4ac=24^2+4*9*5=1296 \\ \\ \sqrt{\Delta}=36 \ \text{ and the solutions are } \\ \\ \\ x_1=\dfrac{24-36}{8\sqrt{5}}=\dfrac{-12}{8\sqrt{5}}=\boxed{\dfrac{-3}{2\sqrt{5}}} \\ \\x_2=\dfrac{24+36}{8\sqrt{5}}=\dfrac{60}{8\sqrt{5}}=\boxed{\dfrac{15}{2\sqrt{5}}}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
If f(x) = -8x - 6 and g(x) = x+8 , what is (f • g) (- 7)
Answer:
hello:
Step-by-step explanation:
If f(x) = -8x - 6 and g(x) = x+8 , (f • g) (- 7)= f(g(-7))
but g(-7)=-7+8=1
(f • g) (- 7)= f(1) =-8(1)-6 =-14