Answer:
x - 1
Step-by-step explanation:
(f + g)(x)=f(x) + g(x)
(f + g)(x)=(3x - 7) + (-2x - 6)
(f + g)(x)= 3x - 7 - 2x + 6
(f + g)(x)= 3x - 2x - 7 + 6
(f + g)(x)= x -1
Which answer is the explicit rule for the sequence 11,8.5,6,3.5,1
Answer: 3.5−2.5n
Explanation:
To find the common difference take the end term and subtract the first term:
8.5 -11 = -2.5
Take the third term and subtract the 3rd term to verify:
6-8.5 = -2.5 check
The formula for an arithmetic sequence is:
an = a1+d(n-1)
an = 11 -2.5(n-1)
Distribute:
an = 11 -2.5n+2.5
Combine terms:
answer = 13.5 - 2.5n
Explanation: Tread more on Brainly.com - https://brainly.com/question/13244259#read more find the common difference take the end term and subtract the first term:8.5 -11 = -2.5Take the third term and subtract the 3rd term to verify:6-8.5 = -2.5 check The formula for an arithmetic sequence is: an = a1+d(n-1)an = 11 -2.5(n-1)Distribute: an = 11 -2.5n+2.5Combine terms: answer = 13.5 - 2.5nAnswer:
Answer: 3.5−2.5n
remove all perfect squares from inside the square root
[tex] \sqrt{45} [/tex]
Answer:
3√5 or ≈6.7082
Step-by-step explanation:
1) √45
2) Factor out the perfect square: √3²×5
3) The root of a product is equal to the product of the roots of each factor: √3²√5
4) Reduce the index of the radical and exponent with 2: 3√5
5) Solution: 3√5 or ≈ 6.7082
after removing the perfect square factor from inside the square root of 45, we are left with 3√5.
To remove all perfect squares from inside the square root of √45, we need to factorize 45 and separate the perfect square factors.
The prime factorization of 45 is 3 × 3 × 5. Since 3 is repeated twice, it represents a perfect square factor.
We can rewrite the square root of 45 as the square root of (3 × 3 × 5). Using the property of square roots (√ab = √a × √b), we can simplify it as √(3 × 3) × √5.
The square root of 3 × 3 equals 3, so the expression simplifies to 3√5.
Therefore, after removing the perfect square factor from inside the square root of 45, we are left with 3√5.
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8. In order to qualify for the year-end tennis tournament,
Sam must win at least 60 percent of his matches this
year. To date, Sam has won 14 of his 18 matches. Of
Sam's 13 matches remaining in the year, what is the
least number that he must win in order to qualify for
the year-end tournament?
H 4
B. 5
C. 6
D. 7
E. 8
Answer:
(14 + x)/31 ≥ .6
14 + x ≥ 18.6
x ≥ 5
The correct answer is B.
Sam needs to win at least 5 more of his 13 remaining matches in order to achieve at least a 60% win rate and qualify for the year-end tournament.
Explanation:The question: how many of Sam's 13 remaining matches must he win to qualify for the year-end tournament by winning at least 60% of his matches this year, is a mathematics question related to percentage and probability. To solve it, you need to figure out the total number of matches Sam will play in the year and calculate what number constitutes 60% of that total. Sam is set to play a total of 31 matches (18 + 13). Sixty percent of 31 is 18.6, we will round this up to 19 as you cannot win portion of a match. Given that Sam has already won 14 matches, he needs to win at least 5 more of his 13 remaining matches (19-14 = 5) in order to win at least 60 percent of his matches for the year. So, the correct answer is 5.
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Help math question theres a graph
dang this is hard for me, let me think
Which point is an x-intercept of the quadratic function f(x) = (x – 4)(x + 2)?
Answer:
x = - 2, x = 4
Step-by-step explanation:
Given
f(x) = (x - 4)(x + 2)
To find the x- intercepts let f(x) = 0, that is
(x - 4)(x + 2) = 0 ← in standard form
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4 → (4, 0 )
x + 2 = 0 ⇒ x = - 2 → (- 2, 0 )
Find the next three terms of each sequence 60,52,44
Answer:
36, 28, 20
Step-by-step explanation:
To find the three terms of each sequence, simply subtract 8 from each number. For an example, you can notice the pattern by subracting 52 from 60. The answer I recieved was 8. That shows that the pattern is to subtract 8 from the following number.
Hope this helped :)
Answer:68
Step-by-step explanation:each is by 8 so add 8 onto each number to find the total
Is -0.5 an integer? Explain.
Answer: the explanation is given below. The number is NOT an integer.
Step-by-step explanation: We are given to check whether the number -0.5 is an integer or not.
We know that
an integer is a number where the digits after the decimal are zero, or the denominator of its fractional form is 1.
The given number is
[tex]n=-0.5.[/tex]
Here, we can see that the digits after the decimal is 5, not zero. Also,
this number can be represented as a negative fraction with denominator not equal to 1 is as follows :
[tex]n=-\dfrac{5}{10}=-\dfrac{1}{2}.[/tex]
Therefore, this number is NOT an integer.
Use the quadratic formula to find both solutions to the quadratic equation
given below.
3x^2 - 7x - 1 = 0
which answers (in da pic)
HELP A BROTHA OUT!!!
The solutions to the quadratic equation 3x^2 - 7x - 1 = 0, using the quadratic formula, are x = [7 + sqrt(61)]/6 and x = [7 - sqrt(61)]/6.
Explanation:This question pertains to the solving of a quadratic equation using the quadratic formula. The quadratic formula is given by x = [-b ± sqrt(b^2 - 4ac)]/2a. In equation 3x^2 - 7x - 1 = 0, comparing it with the standard form of quadratic equation ax^2 + bx + c = 0, we can assign: a = 3, b = -7, and c = -1. Substituting these values into the formula, we get: x = [7 ± sqrt((-7)^2 - 4*3*(-1))]/2*3 = [7 ± sqrt(49 + 12)]/6 = [7 ± sqrt(61)]/6. So, the solutions to the equation are x = [7 + sqrt(61)]/6 and x = [7 - sqrt(61)]/6.
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find the equation of the circle: y-intercepts 4 and –8, contain (–12, –8)
[tex]\boxed{(x+6)^2+(y+2)^2=72}[/tex]
Step-by-step explanation:The center-radius form of the circle equation is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Here we know that the y-intercepts are:
[tex]y=4 \ and \ y=-8[/tex]
So:
[tex]\bullet \ If \ y=4, \ x=0 \\ \\ \\ (0-h)^2+(4-k)^2=r^2 \\ \\ \therefore \mathbf{(I)} \ h^2+16-8k+k^2=r^2 \\ \\ \\ \bullet \ If \ y=-8, \ x=0 \\ \\ \\ (0-h)^2+(-8-k)^2=r^2 \\ \\ \therefore \mathbf{(II)} \ h^2+64+16k+k^2=r^2 \\ \\ \\ \bullet \ If \ x=-12, \ y=-8 \\ \\ \\ (-12-h)^2+(-8-k)^2=r^2 \\ \\ \therefore 144+24h+h^2+64+16k+k^2=r^2 \\ \\ \therefore \mathbf{(III)} \ h^2+208+16k+24h+k^2=r^2[/tex]
So we have the following system of equations:
[tex]\left\{ \begin{array}{c}(I)\:h^{2}+16-8k+k^{2}=r^{2}\\(II)\:h^{2}+64+16k+k^{2}=r^{2}\\(III)\:h^{2}+208+16k+24h+k^{2}=r^{2}\end{array}\right.[/tex]
[tex]Subtract \ II \ from \ I \\ \\ \\\left\{ \begin{array}{c}h^{2}+16-8k+k^{2}=r^{2}\\-(h^{2}+64+16k+k^{2}=r^{2})\\---------------------\\h^{2}+16-8k+k^{2}-h^{2}-64-16k-k^{2}=r^{2}-r^{2}\end{array}\right.[/tex]
[tex]Simplifying: \\ \\ h^{2}+16-8k+k^{2}-h^{2}-64-16k-k^{2}=r^{2}-r^{2}\\ \\ 16-8k-64-16k=0 \\ \\ -24k-48=0 \\ \\ k=-\frac{48}{24} \\ \\ \therefore \boxed{k=-2}[/tex]
From (I):
[tex]h^2+16-8k+k^2=r^2 \\ \\ \\ For \ k=-2 \\ \\ h^2+16-8(-2)+(-2)^2=r^2 \\ \\ \therefore r^2=h^2+36 \\ \\ \\ Substituting \ k \ and \ r^2 \ into \ (III): \\ \\ h^{2}+208+16(-2)+24h+(-2)^{2}=h^2+36 \\ \\ Simplifying: \\ \\ 180+24h=36 \\ \\ 24h=36-180 \\ \\ 24h=-144 \\ \\ h=-\frac{144}{24} \\ \\ \therefore \boxed{h=-6}[/tex]
Finding the radius:
[tex]r^2=(-6)^2+36 \\ \\ r^2=36+36 \\ \\ r^2=72 \\ \\ \therefore \boxed{r=6\sqrt{2}}[/tex]
Finally, the equation of the circle is:
[tex](x-(-6))^2+(y-(-2))^2=72 \\ \\ \boxed{(x+6)^2+(y+2)^2=72}[/tex]
Answer:
[tex](x+6)^2 + (y+2)^2 = 72[/tex]
Step-by-step explanation:
We are given the following information in the question:
y intercept = 4, -8
The circle passes through the point (-12, -8)
Equation of circle:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
where r is the radius of circle, (h,k) is the center of circle.
The circle passes through the points (0,4), (0,-8_ and (-12,-8)
Putting these points in the equation of circle we get:
[tex]1) (0-h)^2 + (4-k)^2 = r^2\\h^2 + (4-k)^2 = r^2\\2) (0-h)^2 + (-8-k)^2 = r^2\\h^2 + (-8-k)^2 = r^2\\3) (-12-h)^2 + (-8-k)^2 = r^2\\[/tex]
Now, we have three equations in three variables.
Solving the three equations, we obtain:
h = -6, k = -2, r = [tex]6\sqrt2[/tex]
Putting these values in the equation of circle:
[tex](x-(-6))^2 + (y-(-2)) = (6\sqrt{2})^2\\(x+6)^2 + (y+2)^2 = 72[/tex]
The above equation is the required equation of circle.
Solve the inequality for v
56>8v
Answer: 2
Step-by-step explanation:
Answer:
7614
Step-by-step explanation:
c. What is the relationship between a + b and b + a?
d. What is the relationship between a - b and b - a?
Answer:
c. They are equal to each other.
d. They are the negative of each other.
Step-by-step explanation:
c. Adding c to d and d to c are the same and thus both expressions are equal. In addition, the numbers can be added in any order and will result in the same final answer. This is also known as commutative property.
d. a-b= -(b -a)
In this case, subtracting b from a is not equal to subtracting a from b. The order of terms in subtraction affects the final answer.
Find the x-intercept and the y-intercept of the graph of ax+by=c
Answer:
you need to show a picture of a graph for my answer to be acurate but I'll try.
Step-by-step explanation:
The x intercept is found by setting y = 0 in the above equation and solve for x. Hence, the x intercept is at (c/a , 0). The y intercept is found by setting x = 0 in the above equation and solve for x.
Noah is running a portion of a marathon at a constant speed of 6 mph. Complete the table to predict how long it would take him to run different distances at that speed and how far he would run in different time intervals.
Time in hours Miles traveled at 6mph
1.
1/2
1 1/3
1 1/2
9
4 1/2
Answer:
[tex]\begin{array}{cc}\text{Time}&\text{Distance}\\ \\1&6\\ \\\dfrac{1}{2}&3\\ \\1\dfrac{1}{3}&8\\ \\1\dfrac{1}{2}&9\\ \\9&54\\ \\4\dfrac{1}{2}&27\end{array}[/tex]
Step-by-step explanation:
Noah's running speed = 6 mph.
Use formula [tex]D=v\cdot t,[/tex] where
D is the distance,
v is the speed,
t is the time.
If [tex]t=1[/tex] hour, then [tex]D=6\cdot 1=6[/tex] miles.
If [tex]t=\dfrac{1}{2}[/tex] hour, then [tex]D=6\cdot \dfrac{1}{2}=3[/tex] miles.
If [tex]t=1\dfrac{1}{3}[/tex] hours, then [tex]D=6\cdot 1\dfrac{1}{3}=6\cdot \dfrac{4}{3}=8[/tex] miles.
If [tex]t=1\dfrac{1}{2}[/tex] hours, then [tex]D=6\cdot 1\dfrac{1}{2}=6\cdot \dfrac{3}{2}=9[/tex] miles.
If [tex]t=9[/tex] hours, then [tex]D=6\cdot 9=54[/tex] miles.
If [tex]t=4\dfrac{1}{2}[/tex] hours, then [tex]D=6\cdot 4\dfrac{1}{2}=6\cdot \dfrac{9}{2}=27[/tex] miles.
So, the table is
[tex]\begin{array}{cc}\text{Time}&\text{Distance}\\ \\1&6\\ \\\dfrac{1}{2}&3\\ \\1\dfrac{1}{3}&8\\ \\1\dfrac{1}{2}&9\\ \\9&54\\ \\4\dfrac{1}{2}&27\end{array}[/tex]
Please find attached the answers in the attached diagram
Average speed is the total distance travelled per time.
Average speed = total distance / total time
Noah's average speed is 6mph
From the above formula, the formula to determine miles run is average speed x time
Total miles he ran in 1 hour = 6 x 1 = 6 miles
Total miles he ran in 1/2 hours = 6 x 1/2 = 3 miles
Total miles he ran in 1 1/3 hours = 6 x 4/3 = 8 miles
The formula to determine total time: total distance / average speed
Time it took Noah to run 1 1/2 miles = 3/2 ÷ 6 = 1/4 miles
Time it took Noah to run 9 miles = 9 ÷ 6 = 1 1/2 miles
Time it took Noah to run 4 1/2 miles = 9/2 ÷ 6 = 3/4 miles
Please find attached an image of the table used in answering this question
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What is the ratio of birds to eggs? Choose 1 answer: (Choice A) 3 :4, (Choice B) 4 :3 (Choice C) 3 :5 (Choice D) D 5 :3
Answer:
1 2/3 an egg to a bird
Step-by-step explanation:
because there are 5 eggs and divide 5 by 3 you get 1 2/3 and there are 3 birds so each gets 1 2/3rds an egg
Answer:
C) 3:5
Step-by-step explanation:
The question asks for the ratio of birds to eggs. It's asking how many birds there are in comparison to the number of eggs. The key to ratios is paying attention to which is listed first.
There are 3 birds, and 5 eggs, therefore the ratio is 3:5
79 plus what equals 90
Answer:
11
Step-by-step explanation:
90=79+x
-79-79
_________
11=x
In a sample of 94 widgets, 4 were defective. How many defective widgets would you expect in a sample of 282 widgets?
Answer:
12
Step-by-step explanation: 282 divided by 94 = 3
4x3=12
Answer:
12 defective widgets
Step-by-step explanation:
Here we calculate the "experimental probability:" 4 defective widgets out of 94 widgets comes out to a probability of being defective of 4/94, which of course could be reduced.
But we can go ahead and calculate the expected number of defective widgets by mult. that 282 widgets by the probability 4/94:
282 4
------- * ------- = 12
1 94
In this sample of 282 widgets, we could expect that 12 will be defective.
solve the equation. 31-12n=211
Answer:
Step-by-step explanation:
31 - 12n = 21l Subtract 31 from both sides.
31-31-12n =211-31 Do the subtraction
-12n = 190 Divide by -12
-12n/-12 = 190/-12
n = -15.333333
Solve m² + 8m = -3 by completing the square.
(Use a comma to separate multiple values.)
What the answer for this?
Answer:
Step-by-step explanation:
m² + 8m = -3
(m² + 8m+16) -16 = -3
(m+4)² = 13.....continue
Given: 3x + 1 = -14; Prove: x = -5
Answer:
x = -5
Step-by-step explanation:
Solve for x:
3 x + 1 = -14
Subtract 1 from both sides:
3 x + (1 - 1) = -14 - 1
1 - 1 = 0:
3 x = -14 - 1
-14 - 1 = -15:
3 x = -15
Divide both sides of 3 x = -15 by 3:
(3 x)/3 = (-15)/3
3/3 = 1:
x = (-15)/3
The gcd of -15 and 3 is 3, so (-15)/3 = (3 (-5))/(3×1) = 3/3×-5 = -5:
Answer: x = -5
Answer:
Step-by-step explanation:
3x + 1 = -14;
substr 1 : 3x+1-1 = - 14 -1
3x = -15
divid by 3
x = -5
Julio wants to calculate 200,000 300,000. When he used
his calculator to multiply, it showed the result below:
6E-10
Write the number shown on the calculator display in
standard form
OA) 60,466,176
OB) 600,000,000
OC) 6,000,000,000
OD) 60,000,000,000
Answer:
D = 60,000,000,000
Step-by-step explanation:
When "E" appears on a calculator , it means exponential and it is used to denote numbers that are too big or small to appear on the calculator screen in their decimal form.
Therefore 6E-10 means 6 exponential 10 , mathematically written as 6^10
which is 60,000,000,000
An app developer projects that he will earn 230$ for every 100 apps downloaded .which of the following equation can be used to be represented the proportional relationship between the number of apps ,x,and the total earnings
V
The developer would earn $50.00 if 20 apps are downloaded. Similarly, they can calculate earnings for any other number of app downloads using this equation.
To represent the proportional relationship between the total earnings (y) and the number of apps downloaded (x), we can use the formula for direct variation, which is:
[tex]\[ y = kx \][/tex]
Where:
- [tex]\( y \)[/tex] represents the total earnings,
- [tex]\( x \)[/tex] represents the number of apps downloaded, and
- [tex]\( k \)[/tex] is the constant of proportionality.
In this scenario, the app developer earns $20.00 for every 8 apps downloaded. This means that for every 8 apps downloaded, the earnings increase by $20.00. So, the constant of proportionality [tex](\( k \))[/tex] is the rate at which earnings increase per app downloaded.
To find the value of [tex]\( k \)[/tex], we can divide the total earnings by the number of apps downloaded:
[tex]\[ k = \frac{y}{x} \][/tex]
Given that the developer earns $20.00 for every 8 apps downloaded, we can substitute these values into the equation:
[tex]\[ k = \frac{20}{8} \][/tex]
[tex]\[ k = 2.5 \][/tex]
Now that we have the value of [tex]\( k \)[/tex], we can rewrite the equation with this value:
[tex]\[ y = 2.5x \][/tex]
This equation represents the proportional relationship between the total earnings [tex](\( y \))[/tex] and the number of apps downloaded [tex](\( x \))[/tex]. It shows that for every additional app downloaded, the total earnings increase by $2.50, maintaining a consistent rate of increase.
This equation allows the app developer to predict their earnings based on the number of apps downloaded. For example, if 20 apps are downloaded, the total earnings can be calculated as:
[tex]\[ y = 2.5 \times 20 = 50 \][/tex]
So, the developer would earn $50.00 if 20 apps are downloaded. Similarly, they can calculate earnings for any other number of app downloads using this equation.
A large patio brick weighs 4 38 pounds. A small patio brick weighs 2 13 pounds.How much more does the large brick weighs
Answer:
2.25
Step-by-step explanation:
You have to subtract 2.13 from 4.38
Example: 4.38-2.13
The graph of an equation is shown below:
Based on the graph, which of the following represents a solution to the equation?
A) (−2,−3)
B) (3, 1)
C) (1, 3)
D) (3, 2)
A glazier is setting supports in parallel segments to prevent glass breakage during storms. What are the values of x and y? Justify your conclusions.
Answer:
m∠y=50°
m∠x=50°
Step-by-step explanation:
we know that
The angles in matching corners are called corresponding angles. When the two lines are parallel Corresponding Angles are equal
so
m∠y=50° -----> by corresponding angles
and
The angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles. When the lines are parallel, the alternate interior angles are equal.
so
m∠x=m∠y -----> by alternate interior angles
so
m∠x=50°
therefore
m∠y=50°
m∠x=50°
PLEASE HELP!!!
-x/4 - 2 = x + 1
Answer:
-x/4-3=x
Step-by-step explanation:
Answer:
-12/5
Step-by-step explanation:
-x/4-2=x+1
-x/4-x-2=1
-x/4-x=1+2
-x/4-x=3
-1/4x-4/4x=3
-5/4x=3
x=3/(-5/4)
x=(3/1)(-4/5)
x=-12/5
Mei and Anju are sitting next to each other on different horses on a carousel. Mei's horse is 3 meters from the center of the
carousel. Anju's horse is 2 meters from the center. After one rotation of the carousel, how many more meters has Mei
traveled than Anju?
Answer:
[tex]2\pi \approx 6.28\ meters[/tex]
Step-by-step explanation:
Mei's horse is 3 meters from the center of the carousel. After one rotation, Mei travelled
[tex]l_M=2\pi r=2\pi \cdot 3=6\pi\ meters[/tex]
Anju's horse is 2 meters from the center. After one rotation, Mei travelled
[tex]l_A=2\pi r=2\pi \cdot 2=4\pi\ meters[/tex]
The difference in their travelled distances is
[tex]l_M-l_A=6\pi -4\pi =2\pi \approx 6.28\ meters[/tex]
Mei travels 6.28 meters more than Anju in one rotation.
In one rotation, Mei's horse travels a distance of
2 * 3.14 * 3 = 18.84 meters.
In one rotation,
Anju's horse travels a distance of 2 * 3.14 * 2 = 12.56 meters.
Therefore, Mei travels 18.84 - 12.56 = 6.28 meters more than Anju in one rotation.
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Equivalent expression of 7 square root 5
Answer:19
Step-by-step explanation:
Subtract then add
Which of the following fractions is equivalent to 4/20
A. 3/15
B. 2/12
C. 1/10
D. 3/19
Please answer QUICKLY.
3/15 is equivalent to 4/20
A rectangle has an area of 90 square centimeters and a height of 12.5 centimeters. What is the length of the base?
Answer: l = 7.2
Step-by-step explanation:
90/12.5 = 7.2
7.2 * 12.5 = 90
Answer:
length of the rectangle is 7.2 centimeters.
Step-by-step explanation:
Area of the rectangle has been given as 90 square centimeters.
Height of the rectangle = 12.5 centimeters
Now we have to calculate the length of the rectangle.
Since, Area of the rectangle = Length × height
90 = 12.5 × length
Length = [tex]\frac{90}{12.5}[/tex]
= 7.2 centimeters
Therefore, length of the rectangle is 7.2 centimeters.
A dairy farmer ideally produces 800 gallons of milk per day. This total can fluctuate by as much as 40 gallons in either
direction. What is the maximum and minimum expected daily production?