the prime numbers smaller than 50 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.
let's find the sums that give us 50:
3+47=50
7+43=50
13+37=50
19+31=50
so the answer is four different ways.
Find the equation of the line in slope intercept form that passes through the point with the given slope. Simplify your answer.
Point (0, 8); Slope = 8
Hello! Can you help with part A & B? Thank you!
we have the functions
[tex]\begin{gathered} g(x)=-2x^2+13x+7 \\ h(x)=-x^2+4x+21 \end{gathered}[/tex]Part A
Equate both equations
[tex]-2x^2+13x+7=-x^2+4x+21[/tex]Solve for x
[tex]\begin{gathered} -2x^2+13x+7+x^2-4x-21=0 \\ -x^2+9x-14=0 \end{gathered}[/tex]Solve the quadratic equation
using the formula
a=-1
b=9
c=-14
substitute
[tex]x=\frac{-9\pm\sqrt{9^2-4(-1)(-14)}}{2(-1)}[/tex][tex]x=\frac{-9\pm5}{-2}[/tex]The values of are
x=2 and x=7
The answer Part A
The distances are x=2 units and x=7 units
Part B
f(x)=g(x)/h(x)
so
[tex]f(x)=\frac{-2x^2+13x+7}{-x^2+4x+21}[/tex]Rewrite in factored form
[tex]\begin{gathered} f(x)=\frac{-2(x+\frac{1}{2})(x-7)}{-(x+3)(x-7)} \\ \\ f(x)=\frac{(2x+1)}{(x+3)} \end{gathered}[/tex]The given function has a discontinuity at x=7 (hole), a vertical asymptote at x=-3
and horizontal asymptote at y=2
find the value of given
The value of (p² + 1/p²) and (p + 1/p)²is 18 and 20 respectively.
The above question is from algebra section and is from the topic surds and indices.
One of the standard formula is
(a - b)² = a² - 2ab +b²
(i) Here the expression is
p - 1/p = 4 and we need to find the value of p² + 1/p²
(p - 1/p)² = p² + 1/p² -2p(1/p)
4² = p² + 1/p² - 2
16 + 2 = p² + 1/p²
p² + 1/p² = 18
(ii) we need to find the value of (p + 1/p)²
(a + b)² - (a - b)² = 4ab
(p + 1/p)² - (p - 1/p)² = 4p(1/p)
(p + 1/p)² - 4² = 4
(p + 1/p)² = 4 + 16
(p + 1/p)² = 20
Therefore, the value of (p² + 1/p²) and (p + 1/p)² is 18 and 20 respectively.
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Solve: 4,557 ÷ 22 A 27332 B 222073 C 207422 D 207322
plssss i really need a answer fast!!
C or D pretty sure it's d
PLEASE HELP ME!!!
How would I find the perimeter of this shape?
Explain your process and all steps
required.
Answer:
6x+8
Step-by-step explanation:
2 x 2x+3 = 4x+6
2 x x+1 = 2x+2
4x+6 + 2x+2 = 6x+8
Cathan and Jakove went out to eat, and the bill for their food was $24.50. If theyleft their server a 20% tip, what was the total cost of their dining experience? *
And the cost is $29,40
use the product to sum formula to help me solve this problem in trig
Explanation
The product-to-sum formula can be seen below.
[tex]cosAsinB=\frac{1}{2}(sin(A+B)-sin(A-B))[/tex]Therefore, we can insert the values of the angles into the formula
[tex]\begin{gathered} Cos37.5sin7.5=\frac{1}{2}(sin(37.5+7.5)-sin(37.5-7.5)) \\ =\frac{1}{2}(sin45-sin30) \\ =\frac{1}{2}(\frac{\sqrt{2}}{2}-\frac{1}{2}) \\ =(\frac{\sqrt{2}}{4}-\frac{1}{4}) \\ =\frac{\sqrt{2}-1}{4} \end{gathered}[/tex]Answer:
[tex]\begin{gathered} A=2 \\ B=1 \end{gathered}[/tex]what’s the correct answer answer asap for brainlist
Answer:
A. 12
Step-by-step explanation:
Let p(x)=3x – 2 and q(x) = 2x + 5. Finda. p(x) – Q(x) =b. p(x) + q(x) =c. p(x)q(x) =
We are given the following functions;
[tex]\begin{gathered} p(x)=3x-2 \\ q(x)=2x+5 \end{gathered}[/tex]We shall find the values of the following;
[tex]p(x)-q(x)[/tex]We substitute for the values of each function and we'll have;
[tex]\begin{gathered} p(x)-q(x)=(3x-2)-(2x+5) \\ p(x)-q(x)=3x-2-2x-5_{} \end{gathered}[/tex]Take note that the negative sign in front of the parenthesis affects both values. Hence negative +5 becomes -5. We now have;
[tex]\begin{gathered} p(x)-q(x)=3x-2-2x-5 \\ p(x)-q(x)=3x-2x-5-2 \\ p(x)-q(x)=x-7 \end{gathered}[/tex](B):
[tex]p(x)+q(x)[/tex]Just like in part (a), we shall substitute for the value of each of the functions, as follows;
[tex]\begin{gathered} p(x)+q(x)=(3x-2)+(2x+5) \\ p(x)+q(x)=3x-2+2x+5 \\ p(x)+q(x)=3x+2x+5-2 \\ p(x)+q(x)=5x+3 \end{gathered}[/tex](C):
[tex]p(x)q(x)[/tex]In this case, we calculate the product of both functions, and we start by substituting for the value of each;
[tex]\begin{gathered} p(x)q(x)=(3x-2)(2x+5) \\ p(x)q(x)=3x\cdot2x+3x\cdot5-2\cdot(+2x)-2\cdot(+5) \end{gathered}[/tex]We can now simplify the above and we'll have;
[tex]\begin{gathered} p(x)q(x)=6x^2+15x-4x-10 \\ p(x)q(x)=6x^2+11x-10 \end{gathered}[/tex]ANSWER:
[tex]\begin{gathered} (a)=x-7 \\ (b)=5x+3 \\ (c)=6x^2+11x-10 \end{gathered}[/tex]please help me solve this please and thank you m8
We will hve the following:
[tex](5x+8)(x^3-x-4)=(5x^4-5x^2-20x)+(8x^3-8x-32)[/tex][tex]=5x^4+8x^3-5x^2-28x-32[/tex]compare the y-intercepts and the rates of change of the following items. y = -5x + 5 and a line which passes through the points (5, 0) and (-5, 5)
y-intercepts of line y = -5x + 5 is greater then a line which passes through the points (5, 0) and (-5, 5)
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
Here the points are (5, 0) and (-5, 5) and it is to find the equation of line passing through these points :
Now using slope formula to find the slope of line m :
m = (y₂-y₁)/ (x₂-x₁)
m = (5-0)/(-5-5)
m = 5/-10
m = -1/2
Let us first find the equation of the line using point-slope equation of line :
(y-y₁) = m(x-x₁)
Substituting all the values in above equation to get the equation of line :
(y-0) = -1/2(x-5)
2y = -x+5
2y = -x + 5
2y = -x +5
y = -x/2 + 5/2
Therefore, the equation of line passing through the points (5, 0) and (-5, 5) is y = -x/2 + 5/2 and its y-intercepts is 5/2
Now, the y-intercepts of line y = -5x + 5 is 5
That is, y-intercepts of line y = -5x + 5 is greater then a line which passes through the points (5, 0) and (-5, 5)
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The next model of a sports car will cost 3.1% less than the current model. The current model cost $54,000. How much will the price decrease in dollars? What will be the price of the next model?
Answer:
The price decrease will be $1,674
The price of the next model will be $52,326
Explanation:
Given the cost of the current model as $54,000.
We're told that the next model of the car will cost 3.1% less than the current model, let's go ahead determine the price decrease as seen below;
[tex]54000\times\frac{3.1}{100}=54000\times0.031=\text{ \$1,674}[/tex]We can see from the above that the price decrease is $1,674.
Let's go ahead and determine the price of the next model as seen below;
[tex]54000-1674=\text{ \$52,326}[/tex]Therefore, the price of the next model will be $52,326
5.(A.3A) The table represents some points on the graphof a linear function. What is the slope of thisfunction?х у-6-70-106-1312-16
The slope of a linear function can be obtained as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x1,y1) and (x2,y2) are points of the line.
For this problem we just have to pick 2 points from the table (they don't have to be consecutive). I'll pick:
• x1 = 0
,• y1 = 4
,• x2 = 2
,• y2 = 14
And now we compute the slope:
[tex]m=\frac{14-4}{2-0}=\frac{10}{2}=5[/tex]The slope is 5 (third option)
1....
1) 3х = 27
2) 5х-2 = 25
3) (1/7)х = 49
4) 2х+8 = 1/32
5) 6х-4 = 36
6) 3х+2+3х = 90
2...
1) 2х = 32
2) 6х-3 = 36
3) (2/3)х = 1,5
4) 52х-1 = 0,2
5) 9х-1 = 81
6) 2х+1+2х = 96
Answer:
Step-by-step explanation:
3x=27
Find the radius of the given circle with the given central angle and arc length. Round your answer to the nearest tenth.
The arc length, when the central angle is measure in degrees, is given by:
[tex]s=2\pi r(\frac{\theta}{360})[/tex]In this case the arc length is 19.6 cm and the angle is 130°, plugging these values we have that:
[tex]\begin{gathered} 19.6=2\pi r(\frac{130}{360}) \\ r=(\frac{19.6}{2\pi})(\frac{360}{130}) \\ r=8.6 \end{gathered}[/tex]Therefore, the radius is 8.6 cm
Use the given information to find the unknown value:y varies inversely with a. When x = 4, then y= 4. Find y when I = 2.Iyy =help (numbers)
Inverse variation:
[tex]y=\frac{k}{x}[/tex]k is a constant
Use the given information (when x=4 y=4) to find the value of the constant:
[tex]\begin{gathered} 4=\frac{k}{4} \\ \\ \text{Multiply both sides of the equation by 4:} \\ 4\times4=4\times\frac{k}{4} \\ \\ 16=k \\ \\ \\ k=16 \end{gathered}[/tex]Then, the given relationship has the next equation:
[tex]y=\frac{16}{x}[/tex]Use the equation above to find y when x=2:
[tex]\begin{gathered} y=\frac{16}{2} \\ \\ y=8 \end{gathered}[/tex]Then, when x=2, y=8If the following function is continuous then what is the value of b?
For a function g(t) to be continuous at t = a:
1) The limit of g(t) must exist at t = a
2) g(a) must exist
3) The limit of g(t) at t = a must be equal to g(a)
[tex]undefined[/tex]How do I Simplify (6 — 4i) — (і +5)?
To simplify (6 - 4i) - (і +5), you have to apply associative property.
First step is to remove the parenthesis, then you have:
[tex]6\text{ - 4i - i + 5}[/tex]Now collect like terms:
[tex]\begin{gathered} 6\text{ + 5 - 4i - i} \\ =\text{ 11 - 5i} \end{gathered}[/tex]ANSWER:
[tex]11\text{ - 5i}[/tex]6pq³ x 2p⁹q²
solve this equation please and thanks
The resulting equation is 12[p^10][q^5].
The expression given to us is "6pq³ * 2(p^9)q²".The first term of the expression contains a constant that is 6.The first term of the expression contains a variable "p" raised to the power of 1.The first term of the expression contains a variable "q" raised to the power of 3.The second term of the expression contains a constant that is 2.The second term of the expression contains a variable "p" raised to the power of 9.The second term of the expression contains a variable "q" raised to the power of 2.We need to multiply the terms in the expression.In order to get the correct result, multiply the constants together and add the powers of the same variables.The final expression is "(6*2)[p^(1+9)][q^(3+2)]".The final expression is "12[p^10][q^5]".Hence, the resulting equation is 12[p^10][q^5].To learn more about equations, visit :
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To indirectly measure the distance across a lake, Jeremiah makes use of a couplelandmarks at points O and P. He measures NR, RP, and Q R as marked. Find thedistance across the lake (OP), rounding your answer to the nearest hundredth of ameter.
Notice that triangles NPQ and NRQ are similar, then:
[tex]\frac{OP}{QR}=\frac{NP}{NR}.[/tex]Now, notice that:
[tex]PN=NR+RP.[/tex]Therefore:
[tex]\frac{OP}{QR}=\frac{NR+RP}{NR}.[/tex]Multiplying the above result by QR we get:
[tex]\begin{gathered} \frac{OP}{QR}\times QR=\frac{NR+RP}{NR}\times QR, \\ OP=\frac{NR+RP}{NR}\times QR. \end{gathered}[/tex]Substituting NR=125m, RP=65m, and QR=106.75m we get:
[tex]OP=\frac{125m+65m}{125m}\times106.75m.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} OP=\frac{190m}{125m}\times106.75m \\ =162.26m. \end{gathered}[/tex]Answer:
[tex]OP=162.26m.[/tex]
For y = 10*0.5^x , doesthis model exponential growth or decay? Explain how you know.
Answer:
Exponential decay
Explanation:
The exponential functions have the following form:
[tex]y=a\cdot b^x[/tex]If b is a number greater than 1, the equation models exponential growth, and if b is lower than 1, the equation models an exponential decay.
Since the equation is:
[tex]y=10\cdot0.5^x[/tex]We can say that the value of b is 0.5. 0.5 is lower than 1, so this equation models exponential decay.
DIRECTIONS: Use this information to answer Parts A and B.
Marisol deposits $5,000 in a savings account earning 5.75% simple interest per year.
Part A
How much interest will Marisol earn for a period of 5 years?
Part B
Marisol receives 8,450 when she close her savings account if she made no changes to the account, for how many years did Marisol keep the account open?
Answer: 287.&. Multiply 365 x 10 Great, you get 3650 . . . Multiply 287 by 3650 which then equals 1049375 . . . Wow! The interest will then be a total of 60929$ with the 8450 that she recieved that should equal 3 years total keeping it open . . .
Step-by-step explanation: Hope This Helps! Pls mark Branliest!
(Find the sum of the infinite geometric series 3 + 12 + 48 + 192 + ...
Given the Infinite Geometric Series:
[tex]3+12+48+192+...[/tex]You can find its sum by using this formula:
[tex]S=\frac{a_1}{1-r}[/tex]Where "r" is the common ratio and the first term is:
[tex]a_1[/tex]In this case, you can identify that each term is obtained by multiplying the previous term by 4. Therefore:
[tex]r=4[/tex]You can identify that:
[tex]a_1=3[/tex]Therefore, you can substitute values into the formula and evaluate:
[tex]S=\frac{3}{1-4}[/tex][tex]\begin{gathered} S=\frac{3}{-3} \\ \\ S=-1 \end{gathered}[/tex]Hence, the answer is: Option B.
Determine whether the value is from a discrete or continuous data set.Number of members present at a meeting is 6Is the value from A) discrete B) continuous
To answer this question we need to understand the difference between discrete and continous data:
• Discrete data can only take certain values along some interval.
,• Continuous data can take any value along some interval.
In this case we know that there will always be a integer number of people in the meeting, that is, we can only have certain values (we can't have 6.5 people in a meeting).
Therefore, this is a discrete data set.
Erin receives a 20% employee discount at the camera store where she works. She alsoreceives a $10 off the price on Wednesdays.a. Write a function e(p) that calculates Erin's new price after the employee discount(hint: what percent of the original price does she have to pay?)ep) =B. Write a function a(p) that calculates Erin's new price using her Wednesday discountonlya (p) =C. Write the function e(a(p))e a(p)) =D. What would Erin's final price be for a $400 camera she purchases on a Wednesday?
ANSWERS
A. e(p) = 0.8p
B. a(p) = p - 10
C. e(a(p)) = 0.8p - 8
D. $312
EXPLANATION
A. The employee discount is 20%. To the total price, which is 100%, we have to subtract the 20% to find the final price of the product. If the price is p, then the price after the employee discount would be,
[tex]e(p)=(1-0.2)p=0.8p[/tex]Hence, the function is e(p) = 0.8p
B. On Wednesdays, Erin gets a $10 discount on the price p of a product in the store, so if she buys on a Wednesday, she would pay a(p) = p - 10.
C. Now we have to find the function e(a(p)). This is a composition, where we have to replace p with a(p) in function e(p),
[tex]e(a(p))=0.8a(p)=0.8(p-10)=0.8p-0.8\cdot10=0.8p-8[/tex]Hence, the function is e(a(p)) = 0.8p - 8
D. If Erin buys a $400 camera on a Wednesday she will get both discounts: the employee discount and the Wednesdays discount. To find the final price for a selling price of p = 400, we have to use the function found in part C,
[tex]e(a(400))=0.8\cdot400-8=320-8=312[/tex]Hence, the final price for the $400 camera is $312, after both discounts.
Tracy opened a savings account and deposited $600.00. The account earns 4% interest,compounded annually. If she wants to use the money to buy a new bicycle in 3 years, howmuch will she be able to spend on the bike?Round your answer to the nearest cent.
The compound interest formula is:
[tex]C(n)=P\lbrack(1+i)^n-1\rbrack[/tex]Where:
C(n) is the interest generated after n periods
P is the principal value, the values deposited initially.
i is the annual interest rate in percentage terms.
n is the number of compounding periods.
In this case:
P = $600.00
i = 0.04 (converted from percentage to decimal by dividing by 100
n = 3 years
Then:
[tex]C(3)=600.00\lbrack(1+0.04)^3-1\rbrack[/tex]Then solve:
[tex]C(3)=600\lbrack1.04^3-1\rbrack=600\lbrack1.124864-1\rbrack=600\cdot0.124864=74.9184[/tex]This is the amount of interest generated over 3 years. The total amount then will be the initial amount plus the interest generated:
[tex]600+74.9184=674.9184[/tex]Rounded up to the nearest cent, the amount she will be able to spend after 3 years is $674.91
x-y=3, 2x-y=5 what’s the solution
Answer:
x = 2, y = -1
Solve the following system:
{-y + x = 3 | (equation 1)
-y + 2 x = 5 | (equation 2)
Swap equation 1 with equation 2:
{2 x - y = 5 | (equation 1)
x - y = 3 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{2 x - y = 5 | (equation 1)
0 x - y/2 = 1/2 | (equation 2)
Multiply equation 2 by 2:
{2 x - y = 5 | (equation 1)
0 x - y = 1 | (equation 2)
Multiply equation 2 by -1:
{2 x - y = 5 | (equation 1)
0 x + y = -1 | (equation 2)
Add equation 2 to equation 1:
{2 x + 0 y = 4 | (equation 1)
0 x + y = -1 | (equation 2)
Divide equation 1 by 2:
{x + 0 y = 2 | (equation 1)
0 x + y = -1 | (equation 2)
Collect results:
Answer: |
| {x = 2
y = -1
I believe that this is truly the answer.
multiply the following decimals-0. 8 • (-0.3) • (-0.4) = -0. 096
Remember when we multiply negative numbers we need to be careful in the sign
[tex]-0.8\cdot-0.3\cdot-0.4=-0.096[/tex]Remember when we multiply decimals, first multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.
Let f be a differentiable function with f(2)=-3 and f'(2)=-4.
The value of differentiable function g(x)=x³ × f(x) if f(2)=-3 and f'(2)=-4 is -68.
If the derivative of a function exists at every point inside its domain, the function is said to be differentiable. In particular, f′(a) exists in the domain if a function f(x) is differentiable at x = a.
Given function
g(x)=x³ × f(x)
FInd out -
Value of g′(2) = ?
If f(2) = -3 and f'(2) = -4.
Let us apply the product rule of differentiation of a product of two functions. The product rule states that
d/dx (fg) = d/dx (f) × g + f × d/dx(g)
or
(fg)'(x) = f'(x) × g(x) + f(x) × g'(x).
Observe that if g(x) = x³ × f(x) then
g'(x) = 3x² × f(x) + x³ × f'(x).
Thus, g'(2) = 3 × 2² × f(2) + 2³ × f'(2)
Put the value of f(2) and f'(2)
= 3 × 4 × (-3) + 8 × (-4)
= -36 - 32
= - 68.
Therefore , If f(2)=-3 and f'(2)=-4, the value of the differentiable function g(x)=x³ × f(x) is -68.
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What is the estimated probability that at least two of the puppies will befemale?A. 6/10 = 60 %B. 5/10 = 50 % C. 7/10 = 70 % D. 4/10 = 40 %
Answer:
C. 7/10 = 70 %
Explanation:
We are asked to find the total number of outcomes that give us at least 2 female puppies.
Now outcomes 1,2,4,5,7,9, and 10, which are 7 outcomes in total, give us at least two female puppies. Therefore, we can say 7 out of 10 times we get at least 2 female supplies and hence the probability is
[tex]\frac{7}{10}=70\%[/tex]