To find the largest of two numbers when given their product and sum, we can use the quadratic formula. Let's denote the numbers as 'a' and 'b'. We know that 'a * b = 24' and 'a + b = 10'. We can rewrite the second equation as 'b = 10 - a' and substitute it into the first equation. Solving the quadratic equation, we find that the larger of the two numbers is 6.
Explanation:To find the largest of two numbers when given their product and sum, we can use the quadratic formula. Let's denote the numbers as 'a' and 'b'. We know that 'a * b = 24' and 'a + b = 10'. We can rewrite the second equation as 'b = 10 - a' and substitute it into the first equation.
Substituting 'b' into the equation 'a * b = 24', we get 'a * (10 - a) = 24'. Expanding and rearranging the equation, we have 'a^2 - 10a + 24 = 0'. Solving this quadratic equation, we find that the values of 'a' are 4 and 6. Therefore, the larger of the two numbers is 6.
531.75 is 75% of what amount
75% × X =531.75
X =531.75/75
X = 7.09
Answers
7.09
Check! Proof!
75% × 7.09
=531.75
Consider the expression below. Place the steps required to determine the sum of the two expressions in the correct order. 3x+6/x^2-x-6 + 2x/x^2+x-12
Answer:
Help with this please
Step-by-step explanation:
i have the attachment down there
Find the amount of the sales tax and the total cost. Round money answers to the nearest cent.
Cost of item: $560 tax rate: 8%
Sales tax=
Total cost=
Answer:
$604.80
Step-by-step explanation:
With 8% tax rate, multiply the cost of the item (560) by 8% (0.08)
560*.08 = 44.80 (sales tax)
Add the cost of item (560) and the sales tax (44.80)
560 + 44.80 = 604.80
in a probability experiment Eric flip a coin 36 times. The coin landed on head 24 times. What is the ratio of heads to tails in this experiment?
A.3/2
B.1/2
C.2/3
D.2/1
Answer:
2/3 is the correct answer so C. Hope this helps you. :)
Step-by-step explanation:
In this experiment, the ratio of heads to tails comes out to be 2/1.
Probability What is Probability?Probability is a way to gauge how likely something is to happen. Even while no event can be foreseen with absolute certainty, probability can be used to convey how likely it is that it will happen.
Formula of Probability:Probability is the ratio of the number of favourable outcomes to the total number of outcomes of an event.
The number of favourable outcomes for an experiment with 'x' and the total outcomes is represented by the symbol 's'. The following formula can be used to determine how likely an event is to occur.
Probability = Favourable Outcomes/Total Outcomes = x/s
Calculate the ratio:The total number of the outcomes are 36.
The total outcome for head is 24 times.
So, the total outcome for tail will be 36 - 24 = 12
The ratio of head to tail is = favourable outcome for heads/ favourable outcomes for tails.
Thus,
heads/ tails = 24/12
heads/tails = 2/1
Therefore, the ratio of heads to tails in the experiment is 2/1.
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Which could be the surface area of a cubic box that contains a baseball that has a diameter of 3 inches: 9 square inches, 18 square inches, 27 square inches, or 54 square inches?
Answer:
54 in²Step-by-step explanation:
Look at the picture.
The edge of the cube is equal to the diagonal of the sphere.
Therefore, the length of the cube's edge is 3 inches.
The formula of a surface area of a cube:
[tex]S.A.=6a^2[/tex]
Substitute a = 3 in:
[tex]S.A.=6(3^2)=6(9)=54\ in^2[/tex]
Plz help !! Need to graduate
Which graph represents the solution for the equation 4 3 x + 2 = 5x? A) A B) B C) C D) D
Answer:
A) A
Step-by-step explanation:
The equation of a line is given by
[tex]y=mx+q[/tex]
where
m is the slope of the curve
q is the y-intercept of the curve
The two lines given in the problem are:
[tex]y=\frac{4}{3}x+2[/tex] --> slope of 4/3 and y-intercept of +2
[tex]y=5x[/tex] --> slope of 5 and y-intercept of 0
By exclusion, we see that the correct answer is A. In fact:
- Option B is wrong, because one of the two lines has negative slope, while the two lines given in the problem have both positive slope
- Option C is wrong, because one of the two lines is flat (slope=0), while none of the two lines given in the problem has a slope of zero
- Option D is wrong, because again one of the two lines has negative slope
Option A is the correct one: in fact, we see that the black line has an y-intercept of +2 and a slope of 4/3, while the green line has a slope of 5 and an y-intercept of zero.
Answer:
The answer
D) D
Step-by-step explanation:
I knew this because one, i just did the test and two the previous answer that was given was incorrect
The cost of renting a private room at a restaurant is $400. There is also a charge of $25 for each person who attends. The total cost for Christian’s party at the restaurant was $775. Write an algebraic equation to represent the situation, than solve how many people people attended Christian’s party.
room=400
Ppl=25p
Total cost=775
775=25p+400 ⟨—— equation
775-400=25p
375/25=p
15=p
15 people attended his party
You and three friends are comparing the amount of money you have in your bank accounts. You have a balance of -$50, and your friends have balances of $20,
-$10, and $5. Which balance is the least?
Answer:
The least balance is your own because -50$ is the farthest from 0 on the number line
Step-by-step explanation:
which is the graph of y= ^3 sqrt x+1 -2
ANSWER
See graph in attachment.
EXPLANATION
The given function is
[tex]y = \sqrt[3]{x + 1} - 2[/tex]
The parent function is
[tex]y = \sqrt[3]{x} [/tex]
The transformation applied to this parent function is
[tex]f(x+1)-2[/tex]
That, is a shift to the left by 1 unit, and a downward shift by 2 units.
See attachment for correct choice.
Solve 5x 2 - 7x + 2 = 0 by completing the square. What are the solutions?
Answer:
[tex]x=\frac{2}{5}[/tex] or [tex]x=1[/tex]
Step-by-step explanation:
The given quadratic equation is
[tex]5x^2-7x+2=0[/tex]
Group the constant terms on the right hand side.
[tex]5x^2-7x=0-2[/tex]
[tex]5x^2-7x=-2[/tex]
Divide through by 5.
[tex]x^2-\frac{7}{5}x=-\frac{2}{5}[/tex]
Add the square of half the coefficient of x., which is [tex](\frac{1}{2}\times- \frac{7}{5})^2=\frac{49}{100}[/tex] to both sides of the equation.
[tex]x^2-\frac{7}{5}x+\frac{49}{100}=-\frac{2}{5}+\frac{49}{100}[/tex]
The left hand side is now a perfect square.
[tex](x-\frac{7}{10})^2=\frac{9}{100}[/tex]
Take the square root of both sides;
[tex](x-\frac{7}{10})=\pm \sqrt{\frac{9}{100}}[/tex]
[tex]x-\frac{7}{10}=\pm \frac{3}{10}[/tex]
[tex]x=\frac{7}{10}\pm \frac{3}{10}[/tex]
[tex]x=\frac{7-3}{10}[/tex] or [tex]x=\frac{7+3}{10}[/tex]
[tex]x=\frac{4}{10}[/tex] or [tex]x=\frac{10}{10}[/tex]
[tex]x=1[/tex] or [tex]x=\frac{2}{5}[/tex]
Answer:
[tex]x_1=1\\\\x_2=\frac{2}{5}[/tex]
Step-by-step explanation:
- You must divide the equation by 5:
[tex]x^{2}-\frac{7}{5}x+\frac{2}{5}=0[/tex]
- Add and subtract [tex](\frac{\frac{7}{5}}{2})^2[/tex]:
[tex]x^{2}-\frac{7}{5}x+(\frac{7}{10})^2+\frac{2}{5}-(\frac{7}{10})^2=0[/tex]
Therefore, you obtain:
[tex](x-\frac{7}{10})^2-0.09=0[/tex]
-add 0.09} to both sides:
[tex](x-\frac{7}{10})^2=0.09[/tex]
- Apply square root to both sides and solve for x:
[tex]\sqrt{(x-\frac{7}{10})^2}=\sqrt{\0.09}\\x-\frac{7}{10}=\sqrt{0.09}\\\\x_1=\frac{7}{10}+\sqrt{0.09}=1\\\\x_2=-\frac{7}{10}-\sqrt{0.09}=\frac{2}{5}[/tex]
What is ⅖x=4
And how do you solve it
Answer:x=10
Step-by-step explanation:
5/2 × 2/5 = 4/1 × 5/2
Multiply and simplify and x=10
The solution to the equation 2/5x = 4 is x = 10. You can find the solution by multiplying both sides of the equation by 5/2, which cancelled out the 2/5 on the left side, and then performing the operation on the right side.
Explanation:To solve the equation 2/5x = 4, you'll first want to isolate the variable 'x' on one side of the equation. You can do this by dividing both sides of the equation by the coefficient of 'x', which is 2/5. However, instead of dividing by a fraction, it's easier to multiply by the reciprocal of the fraction.
So, we multiply both sides of the equation by 5/2. The 5/2 multiplied by 2/5 on the left side of the equation equals 1, leaving us with just 'x' on the left side of the equation.
So, you would have x = 4 * 5/2.
Now, we just perform the operation on the right side to find the value of 'x', and we get x = 20/2 = 10.
So, the solution to the equation 2/5x = 4 is x = 10.
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HELP ASAP! GIVING BRAINLIEST!!
∆ABC has A(-3, 6), B(2, 1), and C(9, 5) as its vertices. The length of side AB is
A) (50)^1/2
B) (65)^1/2
C) (105)^1/2
D) (145)^1/2
units. The length of side BC is
A) (50)^1/2
B) (65)^1/2
C) (105)^1/2
D) (145)^1/2
units. The length of side AC is
A) (50)^1/2
B) (65)^1/2
C) (105)^1/2
D) (145)^1/2
units.
∠ABC ≈ °
A) 55.21
B) 85.16
C) 105.26
D) 114.11
Answer:
1. Option A
2. Option B
3. Option D
4. Option C
Step-by-step explanation:
The given vertices of triangle ABC are A(-3, 6), B(2,1), C(9, 5).
We have to fine the distance AB, BC and AC.
To calculate the distance between two vertices we will use the formula
[tex]d=\sqrt{(x-x')^{2}+(y-y')^{2}}[/tex]
For the length of side AB
AB=[tex]\sqrt{(2+3)^{2}+(1-6)^{2}}=\sqrt{5^{2}+5^{2}}=\sqrt{50}[/tex]
Option A. is the correct option
For the length of side BC
[tex]BC=\sqrt{(9-2)^{2}+(5-1)^{2}}=\sqrt{7^{2}+4^{2}}=\sqrt{65}[/tex]
Option B is the answer.
For the length of side AC
[tex]AC=\sqrt{(9+3)^{2}+(5-6)^{2}}=\sqrt{12^{2}+(-1)^{2}}=\sqrt{145}[/tex]
Option D is the answer.
For ∠ABC we will use the formula [tex]tan\theta =\frac{m_{1}-m_{2}}{1+m_{1}m_{2}}[/tex]
Since angle ABC is formed by two sides AB and BC
So we will find the slopes of these two lines and find the angle
Now slope of AB, [tex]m_{1}=\frac{y-y'}{x-x'}=\frac{1-6}{2+3}=\frac{-5}{5}=-1[/tex]
Slope of BC, [tex]m_{2}=\frac{5-1}{9-2}=\frac{4}{7}[/tex]
[tex]tan\theta =\frac{m_{1}-m_{2}}{1+m_{1}m_{2}}[/tex]
[tex]tan\theta =\frac{(-1)-(\frac{4}{7})}{1+(-1)(\frac{4}{7})}=\frac{\frac{-11}{7}}{1-\frac{4}{7}}=\frac{\frac{-11}{7}}{\frac{3}{7}}=\frac{-11}{7}\times \frac{7}{3}=-\frac{11}{3}=-3.67[/tex]
[tex]\theta =tan^{-1}(-3.67)=74.75[/tex]
Since angle between them [tex]tan\theta[/tex] is negative that means angle theta will be obtuse angle.
So the angle between AB and BC = (180 - 74.75) = 105.26°
Therefore Option C. 105.26° is the answer.
If a + 1 = b, then b > a. true or false?
Answer:
TRUE, because you are adding a unit more to a, then by logic laws, the quantity grow.
Best regards
Answer:
b > a - True
Step-by-step explanation:
We are given the following expression and we are to determine whether [tex] b > a [/tex] is true or not:
[tex] a + 1 = b [/tex]
Considering the given equation, if we take both the variables on one side so we will get:
[tex] 1 = b - a [/tex]
Sign of the variable [tex]a[/tex] will change to negative while [tex]b[/tex] remains positive.
It means that [tex][/tex] is greater than [tex]a[/tex] (b > a) so it is true.
f(x)=3x + h f(h-1)=5
Answer: 4h - 3
Step-by-step explanation:
replace "x" with "h - 1" and simplify
f(x) = 3x + h
f(h - 1) = 3(h - 1) + h
= 3h - 3 + h
= 4h - 3
La Quintas population is about 954,000 and is decreasing at an annual rate of 0.1% Predict the population in 50 years
Answer:
907,450
Step-by-step explanation:
This is a problem of exponential decay. The population is decreasing at 0.1% per year.
The formula to figure this out is [tex]A=P(1+r)^t[/tex]
Where
A will be the future population (after 50 years)
P is the initial population (which is 954,000)
r is the rate of decrease (which is -0.1% or -0.001)
t is the time in years (which is 50)
Plugging these information into the formula and figuring out A will give us the answer. Shown below:
[tex]A=P(1+r)^t\\A=954,000(1-0.001)^{50}\\A=954,000(0.999)^{50}\\A=907,450.17[/tex]
Since fractional/decimal population is not feasible, we round it off.
The population in 50 years would be around 907,450
What is that answer to this question?
Answer:
c
Step-by-step explanation:
thats the answer
If 8x + 8y = 4 and 4x + 2y = 12, what is the value of x?
A) -5
B) -
11
2
C) 5
D)
11
2
the value of x = the answer is D 11/2
(I need help) - 2/3 divided by 4/6 = ?
If x = 14, which equation is true?
A 3(20- x) = 44
B 3(12-x) = 6
c 2(x - 3) = 22
D 2x-3 = 22
please I need help on this
Answer:
C
Step-by-step explanation:
Simply plug in x for all the questions to see if the x is the solution
A.) 3(20-14) = 44
3(16)=48
so A is incorrect
B.) 3(12-14) = 6
3(-2) = -6
so B is incorrect
C.) 2(14-3) =22
2(11) =22
C is correct
D.) 2(14)-3=22
28-3 = 25
so D is incorrect
Answer:
the answer would be 2(x - 3) = 22 (C)
Step-by-step explanation:
step 1:
2(x - 3) = 22
step 2: divide both sides by the equation 2
x - 3 = 11
step 3: move constant (3) to the right and change its sign
x = 11 + 3
step 4: add the numbers (11 and 3)
x = 14
brandon has 1 jill has 3 mark has 2 need Nicole has 4 and steve has 0 what is the mean
Answer: The mean is 2.
Step-by-step explanation:
The mean number is a group of numbers is the average. In this group, the numbers are 1, 3, 2, 4 and 0. The total of all of the numbers is 10. In order to calculate the average/mean you need to divide the total by the number of values, which is 10/5 = 2. The mean is 2.
Solve the inequality (n-7)>2n-3. Write the solution in set notation.
Answer:
- 4 > n and Notion form : [ -4 , -∞).
Step-by-step explanation:
Given : (n-7)>2n-3.
To find : Solve the inequality.
Solution : We have given
(n - 7) > 2 n - 3.
On adding both sides by 3
n - 7+ 3 > 2n .
n - 4 > 2n .
On subtracting b both sides by n
-4 > 2n -n.
- 4 > n.
So, we can say value of n is less than - 4 like -5,-6, -7 ........-∞
Notion form : [ -4 , -∞).
Therefore, - 4 > n and Notion form : [ -4 , -∞).
n = {n | n ∈ R, n < -4}
The given inequality is:
n - 7 > 2n - 3
Collect like terms
n - 2n > -3 + 7
-n > 4
Multiply both sides by -1 and change the sign to <
-1(-n) < -1(4)
n < -4
In set notation:
n = {n | n ∈ R, n < -4}
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Macy's is having a special on t-shirts. You can buy each at its regular price of $10.99, $11.90 and $10.08 or you can buy 3 t-shirts for $25. Julie bought one of each t-shirt at the sale price of $25. What percentage of the original total price did Julie save?
Answer:
24.2%
Step-by-step explanation:
The total regular price was:
$10.99 + $11.90 + $10.08 = $32.97
She paid:
$25
She saved: $32.97 - $25 = $7.97
Now we need to calculate what percent of $32.97 is $7.97.
To find what percent a number is of another number, divide the first number by the second number and multiply by 100.
percent saved = $7.97/$32.97 * 100 = 24.2%
Part (b)
Harry, Julie's best friend, also paid $25 for 3 t-shirts at a sale at another store. The sale price saved Harry 30% of the original price of the 3 t-shirts. What is the original price of Harry's 3 t-shirts? Who got the better deal?
Harry paid $25 and saved 30% over his original price. Let his original price be x. The original price was 100% of the original price since 100% means the whole amount. Since he saved 30%, that means he paid 70% of the original price.
70% of the original price = $25
70% of x = 25
70%x = 25
0.70x = 25
0.70x/0.70 = 25/0.70
x = 35.71
The t-shirts Harry bought had an original price of $35.71.
Harry got the better deal because he bought t-shirts with an original higher price for the same $25.
The ages of the guest on a museum tour are 32, 14, 18, 29, 65, 50, 48, 44, and 28. Find the five-number summary of the ages. Can you help cause there asking to show step by step
Answer:
1. Minimum Value = 14
2. First Quartile (Q₁) = 28
3. Median = 32
4. Third Quartile (Q₃) = 48
5. Maximum Value = 65
Step-by-step explanation:
The five-number summary includes five things that are:
1. Minimum Value
2. First Quartile (Q₁)
3. Median
4. Third Quartile (Q₃)
5. Maximum Value
So, Firstly arrange given data in ascending order:14, 18, 28, 29, 32, 44, 48, 50, 65
1. Minimum Value = 14
It can be found by arranging the data in ascending order, the first value we will get is the minimum value.
2. First Quartile is the middle value between Minimum value and Median of data after arranging data in ascending order.
First Quartile (Q₁) = 28
3. Median is the middle value of the data after arranging them in ascending order.
Median = 32
4. The third Quartile is the middle value between Median and Maximum Value of data after arranging data in ascending order.
Third Quartile (Q₃) = 48
5. Maximum Value is the largest value of the data or is the last value after arranging the data in ascending order.
Maximum Value = 65.
If f(x)= 2x + 5, which of these is the inverse of f(x)
Answer:
D. [tex]f^{-1}(x)=\frac{x-5}{2}[/tex]
Step-by-step explanation:
The given function is
[tex]f(x)=2x+5[/tex]
Let [tex]y=2x+5[/tex]
Interchange x and y.
[tex]x=2y+5[/tex]
Solve for y.
[tex]x-5=2y[/tex]
Divide both sides by 2
[tex]\frac{x-5}{2} =y[/tex]
Hence [tex]f^{-1}(x)=\frac{x-5}{2}[/tex]
Answer: OPTION D
Step-by-step explanation:
To find the inverse of the function given in the problem, you must apply the proccedure shown below:
1- Rewrite the function:
[tex]y=2x+5[/tex]
2- You must solve for x from the functionn, as following:
Subtract 5 from both sides of the function.Divide both sides of the function by 2. Then:[tex]y-5=2x\\\\x=\frac{y-5}{2}[/tex]
Rewrite the function as following (Substitute [tex]x=f^{-1}(x)[/tex] and [tex]y=x[/tex]:[tex]f^{-1}(x)=\frac{x-5}{2}[/tex]
Write the expressions for when you translate the graph of y= x one unit up, one unit down, one unit to the left, one unit to the right
Answer:
Step-by-step explanation:
One unit up: y = x + 1
One unit down: y = x - 1
One unit to the left: y = x + 1
One unit to the right: y = x - 1
Final answer:
To translate the graph of y = x, add or subtract from either x or y in the equation; for example, translating one unit up is expressed as y = x + 1.
Explanation:
To translate the graph of the function y = x in various directions, we apply different transformations to the equation. For each translation, there's a specific algebraic manipulation:
One unit up: y = x + 1One unit down: y = x - 1One unit to the left: y = x + 1One unit to the right: y = x - 1Shifting a graph vertically involves adding or subtracting from the y-value, while shifting horizontally involves adding or subtracting from the x-value before it is plugged into the function.
Determine the Median of 40 49 62 56 68 39 50 61 54 44
The median is 52 you can put this in a stat line in a graphing calculatior
Given the even number of data set, the median which is the average of the middle two numbers in the arranged data set is 52.
What is Median?Median is simply the middle value in a set of variables arranged in a descending or ascending order.
Given the data set; 40 49 62 56 68 39 50 61 54 44.
First, we arrange is ascending order.
39 40 44 49 50 54 56 61 62 68
Since it is an even number set ( 10 )
We find the average of the middle two numbers
Median = ( 50 + 54 ) / 2
Median = 104 / 2
Median = 52
Therefore, the given the even number of data set, the median which is the average of the middle two numbers is 52.
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If 4 students share 30 ft.² wall equally how many square feet of the wall will be painted by each student
Answer:
7.5 ft²/student
Step-by-step explanation:
This is a "unit rate" problem.
30 ft²
------------------ = 7.5 ft²/student
4 students
Each student will paint 7.5 ft² of the wall.
Adrian has 5 times as many stickers as Derrick. If Adrian has 325 stickers, how many stickers does Derrick have?
Answer: 1625
Step-by-step explanation: If Adrian has 5 times as many times is a keyword to know its multiplication. 325x5=1625
Derrick has 65 stickers.
Explanation:To find out how many stickers Derrick has, we need to divide the number of stickers Adrian has by 5. Since Adrian has 325 stickers, we divide 325 by 5.
325 ÷ 5 = 65.
Therefore, Derrick has 65 stickers.
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A drawer is filled with 9 black shirts, 6 white shirts, and 5 gray shirts.
One shirt is chosen at random from the drawer. Find the probability that it is not a white shirt.
Write your answer as a fraction in simplest form.
Answer:
There is a 7/10 chance that it is not white
Step-by-step explanation:
To find this, start by finding the number of total shirts.
9 + 6 + 5 = 20
Now find the number that are not white.
9 + 5 = 14
Now divide the number of non-white by the number in total.
14/20
And simplify the fraction.
7/10
Final answer:
The probability of choosing a shirt that is not white from the drawer is 7/10, since there are 14 non-white shirts out of a total of 20 shirts.
Explanation:
The question asks to find the probability that a shirt chosen at random from a drawer is not white, given that there are 9 black shirts, 6 white shirts, and 5 gray shirts. To tackle this, we'll look at the total number of shirts and then subtract the number of white shirts from this total to find how many shirts are not white. The total number of shirts is 9 (black) + 6 (white) + 5 (gray) = 20 shirts. The number of shirts that are not white would be 20 (total) - 6 (white) = 14 shirts. Therefore, the probability of choosing a non-white shirt is 14 (non-white shirts) divided by 20 (total shirts), which simplifies to 7/10. This fraction is already in its simplest form.