Answer:
[tex]\large\boxed{(f+g)(x)=2x^2+\dfrac{3}{2}x-5}[/tex]
Step-by-step explanation:
[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=\dfrac{x}{2}-2=\dfrac{1}{2}x-2\\\\g(x)=2x^2+x-3\\\\(f+g)(x)=\left(\dfrac{1}{2}x-2\right)+(2x^2+x-3)\\\\=\dfrac{1}{2}x-2+2x^2+x-3\qquad\text{combine like terms}\\\\=2x^2+\left(\dfrac{1}{2}x+x\right)+(-2-3)\\\\=2x^2+1\dfrac{1}{2}x-5\\\\=2x^2+\dfrac{3}{2}x-5[/tex]
Help me out here please and thank u
Answer: C, -1.9
Step-by-step explanation:
Its obviously a negative, so it can't be D.
And it's a greater negative then A, so its not B.
And then A is just toooo far away.
So the answer is C
Hope this helps ;)
If f(x) = 2x2 +5/(x-2), complete the following statement:
f(3) = ______
Answer:
f(3) = 9
Step-by-step explanation:
when we have f(x) that means function of any number. when we have a number in that function we plug it in our equation for all X's. Therefore, when we have f(3) we plug it in to all X's which looks like this
[tex]f(3) = \frac{2 \times 2 + 5}{(3 - 2)} = 9[/tex]
notice how I multiplied at the top first. you also want to apply the rules of PEMDAS.
Hope this helps!
the sqaure of 9 less than a number is 3 less than the number
The student's mathematics problem requires solving a quadratic equation derived from the statement that the square of '9 less than a number' equals '3 less than the number'. By expanding, rearranging, and factoring the quadratic equation, we find that the number in question is 12.
Explanation:The student's question involves solving an algebraic equation to find an unknown number.
Let's denote the unknown number as x.
The problem states that the square of 9 less than the number is 3 less than the number itself.
This can be represented as the equation:
(x - 9)^2 = x - 3
To solve for x, we will follow these steps:
Expand the left side of the equation: x^2 - 18x + 81 = x - 3.Subtract x from both sides to set the equation to zero: x^2 - 19x + 84 = 0.Factor the quadratic equation: (x - 7)(x - 12) = 0.Find the values of x that make each factor equal to zero: x = 7 and x = 12.Therefore, the two possibilities for the unknown number are 7 and 12.
We must check which one satisfies the original equation, and we find that x = 12 is the correct solution.
=
2 1/3 divided by 3 equal what
Answer:
7/6 is the answer, or as a mixed fraction, 1 1/6
Step-by-step explanation:
Turn 2 1/3 into an improper fraction. This gives 7/3. Since dividing by 3 is the same as multiplying by 1/2, 7/3 * 1/2 multiply top and bottom with each other to get 7/6 as your answer.
Hope this helps!
Answer:
[tex]\frac{7}{9}[/tex]
Step-by-step explanation:
2[tex]\frac{1}{3}[/tex] ÷3
= [tex]\frac{7}{3}[/tex] ÷3
= [tex]\frac{7}{3}[/tex] x [tex]\frac{1}{3}[/tex]
= [tex]\frac{7}{9}[/tex]
3 digit largest number
Answer:
999 is the largest number that has 3 digits
Step-by-step explanation:
Amber is learning how to jump rope. She made 21 jumps the first day, 33
jumps the second day, and 45 jumps on the third day. If this pattern
continues, how many jumps will she be making on the eighteenth day?
OA) 225
OB) 209
OC) 69
OD) 57
Answer: 209 i think. hope it helped
Step-by-step explanation:
Answer:
225
Step-by-step explanation:
Each day she increased by 12 jumps. 12 x 17= 204 (you would multiply 12 by 17 instead of 18 since you wouldn't count the first day) 204+21=225
There are six __ triangles in a regular hexagon
A. Obtuse
B. Acute
C. Equilateral
D. Isosceles
Step-by-step explanation:
the correct answer is C equilateral hope this helps have a great day
There are six (C). Equilateral triangles in a regular hexagon
Equilateral triangles
An equilateral triangle exists in a triangle that has all its sides equal in length. Since the three sides are equal therefore the three angles, opposite to the equal sides, exist equal in measure.
In a regular hexagon, there are six equal sides and the number of triangles inscribed stands at six.Each side of the triangle constructed will be equal in measure. Thus, the triangle formed will be equilateral and every angle will measure. The solution will be, that there are six Equilateral triangles in a regular hexagon.Option(C). Equilateral exists the correct option.
To learn more about Equilateral triangles refer to:
https://brainly.com/question/16251591
#SPJ2
A. 127 cm^2
B. 144.5 cm^2
C. 172 cm^2
D. 50 cm^2
Answer:
144.5cm^2
Step-by-step explanation:
First find area of the rectangle
Area of a rectangle = L*B
= 9*13 = 117cm^2
Now find area of the triangle
Area of triangle. = 1/2 base * height
Height = 13 - 8 =5cm
Area of the triangle = 1/2 *11 *5 = 27.4
Now area of the who figure is area of rectangle + area of triangle
= 117 + 27.5
= 144.5cm^2
For this case we have that the area of the figure is given by the area of a rectangle plus the area of a triangle.
The area of a rectangle is given by:
[tex]A = a * b[/tex]
Where a and b are the sides of the rectangle.
According to the figure we have:
[tex]a = 13 \ cm\\b = 9 \ cm[/tex]
So, the area of the rectangle is:
[tex]A = 13 * 9\\A = 117 \ cm ^ 2[/tex]
On the other hand, the area of a triangle is given by:
[tex]A = \frac {1} {2} b * h[/tex]
Where b is the base of the triangle and h the height. According to the figure we have:
[tex]b = 13-8 = 5 \ cm\\h = 11 \ cm[/tex]
Substituting:
[tex]A = \frac {1} {2} 5 * 11\\A = 27.5 \ cm ^ 2[/tex]
Adding up we have the total area is:
[tex]A_ {t} = 117 \ cm ^ 2 + 27.5 \ cm ^ 2\\A_ {t} = 144.5 \ cm ^ 2[/tex]
Answer:
Option B
This the question complete the table below to show how to find the variance. After finding the variance, calculate the standard deviation
Answer:
Step-by-step explanation:ik
Final answer:
To find the variance, calculate the average of the squared differences between each data point and the mean. The standard deviation is found by taking the square root of the variance.
Explanation:
To calculate the variance, follow these steps:
Find the mean of the data set.
For each data point, subtract the mean and square the result.
Find the average of the squared differences.
To calculate the standard deviation, take the square root of the variance.
For example, if the data set is {2, 4, 6, 8, 10}, the mean is 6. The squared differences are {(2-6)^2, (4-6)^2, (6-6)^2, (8-6)^2, (10-6)^2}, which equals {16, 4, 0, 4, 16}. The average of the squared differences is (16+4+0+4+16)/5 = 40/5 = 8. Therefore the variance is 8. The standard deviation is the square root of the variance, so in this case, the standard deviation is √8 = 2.83.
factor and solve to find roots
x squared -x - 90 =0
[tex]x^2-x-90=0\\x^2+9x-10x-90=0\\x(x+9)-10(x+9)=0\\(x-10)(x+9)=0\\x=10 \vee x=-9[/tex]
4:x::5:15 SLOVE IT AND EXPLAIN
Answer:
x = 12
Step-by-step explanation:
Assuming you reqire the value of x that makes
4 : x equivalent to 5 : 15
Divide 5 by 4, that is 5 ÷ 4 = 1.25
Thus 1.25x = 15 ( divide both sides by 1.25 )
x = 12
Hence
4 : 12 = 5 : 15
Vertical? Obtuse? Straight? Or acute?
Answer:
d
Step-by-step explanation:
the angle is less than 90 degrees
Answer:
the correct choice is an acute angle have a great day
Step-by-step explanation:
Mr. Bryant is trying to figure out which class project to work on for community service. He surveyed the junior and senior students about their preferred project. The frequency table shows the responses of the students.
Juniors Seniors Total
Park Cleanup 30 26 56
Food Kitchen 50 34 84
Clothing Drive 10 50 60
Total 90 110 200
Determine the joint frequency of being a senior and wanting to have a park cleanup. Explain what this answer represents.
Final answer:
The joint frequency of being a senior and wanting to have a park cleanup is 26, which represents the number of seniors who preferred the project of park cleanup.
Explanation:
The joint frequency of being a senior and wanting to have a park cleanup can be determined by looking at the frequency table. According to the table, there are 26 seniors who want to have a park cleanup. Therefore, the joint frequency of being a senior and wanting to have a park cleanup is 26.
This answer represents the number of seniors who preferred the project of park cleanup. It shows the specific combination of being a senior (belonging to the senior students group) and wanting to have a park cleanup project.
Which expression is equivalent to
algebra II engenuity
Answer:
the correct answer is B
Answer:
second option
Step-by-step explanation:
Given expression is:
[tex]\sqrt[3]{64a^6b^7c^9}[/tex]
Converting the expression in the exponents of multiples of three
[tex]\sqrt[3]{4^3*a^6*b^6*b*c^9}[/tex]
Solving the radical
[tex]={4^{(3*\frac{1}{3})} *a^{(6*\frac{1}{3})}*b^{(6*\frac{1}{3})}*b^{(\frac{1}{3})}*c^{(9*\frac{1}{3})}}\\=4a^2b^2c^3\sqrt[3]{b}[/tex]
Hence,
2nd option is correct ..
20 points?please with explanation
WHAT IS 56+50×2= ???
Just follow PEMDAS
P=Parentheses
E=Exponents
M=Multiplication
D=Division
A=Addition
S=Subtraction
56+50*2
Do Multiplication first
56+50*2=56+100
56+100=156
Answer is 156
Answer:
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
56+50 × 2
Multiplication first then addition
50 × 2 = 100
56 + 100 = 156
What is the answer to this question
Answer:$0.46
Step-by-step explanation
there are 6 pens so divide 2.76 by 6
15/33=22/46
true or false?
Answer:
FALSE
Step-by-step explanation:
Let's use the denominator 33(46), or 1518.
Then 15/33 = 22/46 becomes:
690 726
--------- = ---------
1518 1518
Clearly, these two ratios are NOT equal, and so the statement is FALSE.
Answer:
false
Let's use the denominator 33(46), or 1518.
Then 15/33 = 22/46 becomes:
690 726
--------- = ---------
1518 1518
Clearly, these two ratios are not equal, and so the statement is false.
Find the exact value of sin15
The exact value of trigonometric function sin(15 degrees) is √6 - √2 divided by 4.
What is the exact value of sin15?To find the exact value of sin(15 degrees), we can use the sum-to-product trigonometric identity, which states that:
sin(A) + sin(B) = 2 × sin((A + B) / 2) × cos((A - B) / 2).
In this case, we can write sin(15) as sin(45 - 30) and use the identity.
First, we have sin(45 degrees) and sin(30 degrees), which are known values of √2/2 and 1/2, respectively. Plugging these values into the identity, we get sin(15) = 2 × sin(7.5) × cos(7.5).
Now, we can use the half-angle formulas for sine and cosine to simplify further. Sin(7.5 degrees) can be expressed as (√6 - √2) / 4, and cos(7.5 degrees) as (√6 + √2) / 4. So,
sin(15 degrees) = 2 × [(√6 - √2) / 4] × [(√6 + √2) / 4], which simplifies to (√6 - √2) / 4.
In conclusion, the exact value of sin(15 degrees) is (√6 - √2) / 4. This value can be derived using trigonometric identities and the half-angle formulas for sine and cosine.
Read more about trigonometric here:https://brainly.com/question/7331447
#SPJ1
The exact value of sin 15 is 0.2588.
Explanation:The exact value of sin 15 is 0.2588.
To find this value, we can use the fact that sin 30 = 0.5. Since 15 degrees is half of 30 degrees, we can use the half angle formula for sine to calculate sin 15.
Using the half angle formula, sin (15) = sqrt((1 - cos(30))/2) = sqrt((1 - sqrt(3)/2)/2) = 0.2588.
Learn more about Sine Function here:https://brainly.com/question/12015707
#SPJ1
Please help.. part a & b
Answer:
Part A
to the 10th power will be positive and to the 11th power is negative. When the exponent is even it will be positive. When it is odd it will be negative
Part B
The one with the negative enclosed will be positive. The second one, the exponent is only effecting the number and not the sign. The outcome will always be negative.
The probability that the person is male or married is?
[tex]|\Omega|=257\\|A|=129+136-68=197\\\\P(A)=\dfrac{197}{257}\approx76.7\%[/tex]
Given the parent function f(x) = 2^x, which graph shows f(x)+1?
Step-by-step explanation:
f(x) + n - move the graph n units up
f(x) - n - move the graph n units down
f(x + n) - move the graph n units to the left
f(x - n) - move the graph n units to the right
====================================================
We have f(x) = 2ˣ.
g(x) = f(x) + 1 - move the graph of f(x) one unit up.
(look at the picture)
Leticia stretched for 8 minutes and then jogged around her block several
times. It takes her 6 minutes to run around the block once. She spent 38
minutes exercising. How many times did Leticia jog around the block?
Choose two answers: one for the equation that models this situation and one
for the correct answer.
A. Equation: 6 + 8x = 38
B. Answer: 5 times around the block
O
C. Equation: 8 + 6x = 38
D. Answer: 4 times around the block
Answer:
Step-by-step explanation:
c, b, because 6 multiplied by x will equal the amount of time she spent running around the block plus the 8 minutes stretching, if you solve for x the answer is also 5 times around the block
Subtracting the stretching time from the total exercise time gives the jogging time, which when divided by the time per lap, gives the total laps. Leticia jogged around the block 5 times.
The question asks how many times Leticia jogged around the block given that she stretched for 8 minutes and then jogged, with each lap taking 6 minutes to complete, and she spent a total of 38 minutes exercising.
To solve this problem, we need to first determine how much time she spent jogging after stretching. To do this, we subtract the time spent stretching from the total exercise time:
38 minutes total - 8 minutes stretching = 30 minutes jogging.
Next, we divide the jogging time by the time it takes to run around the block once: 30 minutes jogging / 6 minutes per lap = 5 laps. The correct equation that models this situation is C.
Equation: 8 + 6x = 38 and the correct number of times she jogged around the block is B. Answer: 5 times around the block.
will give brain less
Which of the following ordered pairs could be the y-intercept of a function? (1, 2) (-3, 2) (5, 0) (0, 0)
Answer:
(0, 0)
Step-by-step explanation:
The y-intercept refers to the point where the graph of a function intersects or crosses the y-axis. The value of x is usually zero at this particular point since the y-axis has the equation;
x = 0
From the alternatives given, the ordered pair (0, 0) could be the y-intercept of a function since x has a value of 0.
what is the distance between the points 4,10 and -3,-14 on the coordinate plane
Answer:
25
Step-by-step explanation:
Here we are supposed to find the distance between two coordinates ( 4,10) and (-3,-14).
Let us do this step by step with detailed explanation.
We will use distance formula in order to find the distance between them. The distance formula is given as
[tex]D=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} }[/tex]
Here we have
[tex]x_{2}=-3\\x_{1}=4\\y_{2}=-14\\y_{1}=10\\[/tex]
Replacing them in the formula we get
[tex]D=\sqrt{(-3-4)^{2} +(-14-10)^{2} }\\D=\sqrt{(-7)^{2} +(-24)^{2} }\\D=\sqrt{49+ 576 }\\D=\sqrt{625 }\\D=25\\[/tex]
Hence our distance is 25 units
Final answer:
The distance between the points (4,10) and (-3,-14) on the coordinate plane is 25 units, calculated using the distance formula.
Explanation:
The distance between the points (4,10) and (-3,-14) on the coordinate plane can be found using the distance formula, which is derived from the Pythagorean theorem. The distance formula is √((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are the coordinates of the two points.
To calculate the distance:
Substitute the coordinates into the formula: √((-3 - 4)² + (-14 - 10)²).Simplify the expressions inside the parentheses: √((-7)² + (-24)²).Square the numbers: √(49 + 576).Add the results: √625.Take the square root: √625 = 25.The distance between the points is 25 units.
the average of five number is 25.if four of the numbers are 30,29,25 and 20,the average of the three larger numbers are
Answer:
28
Step-by-step explanation:
There are five numbers so the average must be x/5.
25= x/5
x= 125
30+29+25+20 = 104
Therefore the final number of the five must be 125-104=21
The 3 largest are still 30,29,25.
So their average is (30+29+25)/3
= 28
The average of the three larger numbers is 28
Let y be the 5th number.
Next, we shall determine the value of y. This can be obtained as follow:
Data: 30, 29, 25, 20 and yAverage = 25y =?Average = Sum of data / number of data
25 = (30 + 29 + 25 + 20 + y) / 5
25 = (104 + y) /5
Cross multiply
25 × 5 = 104 + y
125 = 104 + y
Collect like terms
y = 125 – 104
y = 21
Thus, the correct data are: 30, 29, 25, 20, 21
Finally, we shall determine the average of the three larger numbers.
Data: 30, 29, 25, 20, 21Three large numbers: 30, 29, 25Average =?Average = Sum of data / number of data
Average = (30 + 29 + 25) / 3
Average = 84 / 3
Average = 28
Therefore, the average the three larger numbers is 28
Lean more about average (i.e mean): https://brainly.com/question/4256636
What is the area of the mombus shown below?
Answer:
A
Step-by-step explanation:
The area (A) of a rhombus is calculated as
A = half the product of the diagonals
here AC = 13 and BD = 15 ← diagonals, hence
A = 0.5 × 13 × 15 = 97.5 units² → A
Answer:
Its A. 97.5
Step-by-step explanation:
just took the test
Solve the exponential equation. (½)x = 32
Answer:
x = - 5
Step-by-step explanation:
Using the rule of exponents
• [tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]
Given
[tex](1/2)^{x}[/tex] = 32
[tex]\frac{1}{2^{x} }[/tex] = 32
[tex]2^{-x}[/tex] = [tex]2^{5}[/tex]
Since the bases are equal, both 5, equate the exponents
Hence x = - 5
an exercise class has two options a $25 pass for all sessions during the month or $3 per lesson write an equation to model the cost of going to the exercise class for a month using a pass and another equation for paying a fee for each lesson
Answer:
With pass cost = $25
Without pass cost = 3x number of days going the the class
Answer:
[tex]y =25[/tex] and [tex]y=3x[/tex]
Step-by-step explanation:
Given : An exercise class has two options a $25 pass for all sessions during the month or $3 per lesson
To Find: write an equation to model the cost of going to the exercise class for a month using a pass and another equation for paying a fee for each lesson.
Solution:
Let the total cost be y
Option 1) a $25 pass for all sessions during the month
So, equation for option 1 : [tex]y =25[/tex]
Option 2) $3 per lesson
Let x be the number of lessons
So, cost of x lessons = 3x
So, Total cost: [tex]y=3x[/tex]
So, equation for option 2 : [tex]y =3x[/tex]
Hence an equation to model the cost of going to the exercise class for a month using a pass and another equation for paying a fee for each lesson is [tex]y =25[/tex] and [tex]y=3x[/tex]
William deposited 375$ into a bank account earning 2.1% simple interest. what is his new account balance be in 12 years
[tex]\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$375\\ r=rate\to 2.1\%\to \frac{2.1}{100}\dotfill &0.021\\ t=years\dotfill &12 \end{cases} \\\\\\ A=375[1+(0.021)(12)]\implies A=375(1.252)\implies A=469.5[/tex]
The new account balance in 12 years can be calculated using the simple interest formula. William's new balance after 12 years will be $469.50, after earning a simple interest of $94.50 on his initial deposit of $375.
Explanation:William's new account balance in 12 years can be calculated using the simple interest formula, which is: Principal (P) x Rate (R) x Time (T).
We already know from the question that the principal (P) is $375, the rate (R) is 2.1% or 2.1/100 = 0.021, and the time (T) is 12 years.
Plugging these values into the formula, we get:
Simple Interest (SI) = PRT
= $375 * 0.021 * 12
= $94.50.
The new balance in the account would be the sum of the initial amount and the simple interest earned. Therefore, the new balance = $375 (Initial deposit) + $94.50 (Interest) = $469.50.
https://brainly.com/question/32543341
#SPJ11