b= 1.5
c= 5
To evaluate 2bc^2
we substitute b = 1.5 and c = 5 into the equation
[tex]\begin{gathered} 2bc^2 \\ \Rightarrow2x1.5x5^2 \\ \Rightarrow\text{ 2 x 1.5 x 25} \\ \Rightarrow75 \end{gathered}[/tex]The answer = 75
The first term of a geometric sequence is 6. The common ratio is 2. Find the7th term of the sequence using the explicit formula.
The geometric sequence is given by:
[tex]a_n=a\cdot r^{n-1}[/tex]where:
a = first term of the sequence
r = common ratio
so:
[tex]\begin{gathered} n=7 \\ a_7=6\cdot2^{7-1} \\ a_7=6\cdot2^6 \\ a_7=6\cdot64 \\ a_7=384 \end{gathered}[/tex]1) angle 1 and angle 2 are supplementary angles. If m 21 = (4x )° and m 22 = (8x), then find themeasures of these angles.
We know that
• Angle 1 and 2 are supplementary.
,• Angle 1 is equal to 4x, and angle 2 is equal to 8x.
Rember that supplementary angles are those which sum 180°,
[tex]m\angle1+m\angle2=180[/tex]Replacing all given expressions, we have
[tex]4x+8x=180[/tex]Now, we solve for x
[tex]\begin{gathered} 12x=180 \\ \frac{12x}{12}=\frac{180}{12} \\ x=15 \end{gathered}[/tex]With this value, we can find each angle.
[tex]\begin{gathered} m\angle1=4x=4\cdot15=60 \\ m\angle2=8x=8\cdot15=120 \end{gathered}[/tex]Therefore, the angles are 60° and 120°.A laptop has listed price of 629.95 before tax. If the sales tax rate is 6.5%, find the total cost of the laptop with sales tax included.
First, we find 6.5% of 629.95. Remember that 6.5% is equivalent to 0.065
[tex]0.065\cdot629.95=40.95[/tex]Then, we add the sales tax to the listed price
[tex]629.95+40.95=670.90[/tex]Hence, the total cost is $670.90.Write an explicit formula for an, then the nth term of the sequence 4, 12, 36, ....
The given sequence is 4, 12, 36
[tex]\begin{gathered} a(n)\text{ = a }\cdot r^{n\text{ - 1}} \\ \text{The common ratio of the sequence is 3} \\ \text{The first term = 4} \\ a(n)\text{ = 4 }\cdot3^{n\text{ - 1}} \end{gathered}[/tex]Which means "30 is the product of 6 and a number b"?A 30 = 6bB 30 x 6 = bC 30=b-6D 30 = 6 ÷b
SOLUTION:
Method:
30 is the product of 6 and a number b
'is' represents '='
'product' represent 'X'
Hence
30 is the product of 6 and a number b
30 = 6 X b
30 = 6b
Final answer: Option A
30 = 6b
3 plus (2 + 8) to the second power ÷4×(1/2) to the 4th power
We need to solve the expression above. To do that, the first step is to solve the operations inside the parenthesis:
[tex]3+10^2\colon4\cdot\frac{1}{2^4}[/tex]Then we need to calculate the powers.
[tex]3+100\colon4\cdot\frac{1}{16}[/tex]Now we need to calculate the division.
[tex]3+25\cdot\frac{1}{16}[/tex]We need to now perform the multiplications.
[tex]3+\frac{25}{16}[/tex]Finally we need to perform the sum.
[tex]\begin{gathered} \frac{16\cdot3+25}{16} \\ \frac{48+25}{16}=\frac{73}{16} \end{gathered}[/tex]The result of the expression is 73/16.
Given: f(x) = -x2 – 3x + 2 and g(x) = x2 + 4 10. Find -3f(x) 11. Find - g(x) - 5 12. Find (f + g)(x) 13. Find f(x) - g(x) 14. Find f (4x) 15. Find g(-x) - 5
Problem
Solution
10) -3 f(x)
[tex]-3(-x^2-3x+2)=3x^2+9x-6[/tex]11) -g(x)-5
[tex]-x^2-4-5=-x^2-9[/tex]12) (f+g)(x)
[tex]-x^2-3x+2+x^2+4=-3x+6[/tex]13) f(x) -g(x)
[tex]-x^2-3x+2-x^2-4=-2x^2-3x-2[/tex]14) f(4x)
[tex]f(4x)=-(4x)^2-3(4x)+2=-16x^2-12x+2[/tex]15) g(-x) -5
[tex](-x)^2+4-5=x^2+4-5=x^2-1[/tex]How is the graph of f(x)=x^2 translated to create the graph g(x)=(x-6)^2
Given data
The given function of the graph is
[tex]f(x)=x^2[/tex]The other given function of the graph is
[tex]g(x)=(x-6)^2=x^2+36-12x[/tex]The function of the graph is translated as
[tex]g(x)=f(x)+k_{}[/tex]Substitute the values in the above equation as
[tex]g(x)=x^2+k[/tex]all you need is in the photo please answer fast please DON'T DO STEP BY STEP PUT ONLY THE ANSWER Part b: what is the value of k? A) 1B) 2C)3
K = 2
From the graph, there is a vertical movement of 2 units
K = 2
Use the order of operations to simplify the given expression.(12÷3⋅3)^2
Problem Statement
The question gives us the following expression to simplify:
[tex](12\div3.3)^2[/tex]Solution
To solve this problem, we need to use PEDMAS.
1. We have to solve the Parenthesis first.
2. After solving the Parenthesis, we can solve any other thing outside.
Implementation
1. Solving the Parenthesis:
We have a division and multiplication operation in the parenethesis. We must solve from left to right in this case since division and multiplication have the same priority.
Thus, we have:
[tex]\begin{gathered} 12\div3.3 \\ \text{Solving division first:} \\ 12\div3=4 \\ \\ \text{Solving multiplication next} \\ 4.3=12 \end{gathered}[/tex]2. Solving what is outside the parenthesis, we have:
[tex]undefined[/tex]Find the standard form of the equation of a circle Center (4,-2) and tangent to the line x=1
According to the given data we have the following:
circle Center (4,-2)
tangent to the line x=1
To finde the standard form of the equation we would have to make the following:
According to the data the center is (h,k)=(4,-2)
using the following formula we can find the equation:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Since the tangent line is x=1 and r=4-1=3
Therefore, the standard form of the equation of a circle
Center (4,-2) and tangent to the line x=1 would be the following:
[tex](x-4)^2+(y+2)^2=3^2[/tex]factor: 2x +28 .....
The equation given is,
[tex]2x+28.[/tex]The factor of the equation is obtained as,
[tex]2x+28=2(x+14)[/tex]In the equation given , two numbers 2 and 28.
We have to find the GCF which is greatest common factor of the two numbers,
[tex]2=2\times1[/tex][tex]28=7\times2\times2[/tex]The only number common from the two numbers factor are, 2.
And also when we open the bracket , we take 2 common for simplify the equation.
Therefore , the factor of the given equation is 2.
Hence verified from both sides.
An electrician charges a set fee for every house call and then charges an hourly ratedepending on how long the job takes. Let C represent the total cost of the visit whenthe electrician spends t hours at the house working. The table below has select valuesshowing the linear relationship between t and C. Determine the set fee for the housecall.t C2 2505 4306.5 520
Start by finding the slope, which will be the hourly rate the electrician charges using the formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]use points (2,250) and (5,430)
replace in the formula
[tex]\begin{gathered} m=\frac{430-250}{5-2} \\ m=\frac{180}{3} \\ m=60 \end{gathered}[/tex]now, use of the points to find the set fee using
[tex]\begin{gathered} C=mt+b \\ C=60t+b \end{gathered}[/tex]use point (6.5,520)
[tex]\begin{gathered} 520=60\cdot(6.5)+b \\ 520-390=b \\ 130=b \end{gathered}[/tex]The set fee is $130
Given the function g(x)=4x+3 and g-¹ (15)=k, find the value of k
We know that g(x) = 4x + 3, and that the value of the inverse function of g(x), g^-1(x) has a value of k when its argument is 15.
We can solve it by first calculating the inverse function.
We can start by writing:
[tex]\begin{gathered} g(x)=y\Rightarrow g^{-1}(y)=x \\ x=4y+3 \\ x-3=4y \\ \Rightarrow g^{-1}(x)=^{}y=\frac{x-3}{4} \end{gathered}[/tex]Now, when the argument is x = 15, we get:
[tex]\begin{gathered} g^{-1}(x)=\frac{x-3}{4} \\ g^{-1}(15)=\frac{15-3}{4}=\frac{12}{4}=3=k \\ \Rightarrow k=3 \end{gathered}[/tex]Answer: k = 3
1) Don works 18 hours a week. Which expression shows a good way to use rounding to estimate how many hours Don will work in 52 weeks? Name 5.1 B A 10 X 50 B 10 X 60 C 20 X 50 0 18 X 60
Since Don works 18 hours a week, we can round up to 20, and since we are estimating how many hours Don will work in 52 weeks, we can round down to 50, so we can estimate the total hours with the expression 20 x 50
How do I tell which of the following graphs I can expect the correlation coefficient to be closest to 1?Photo attached
Solution
If the correlation coefficient is close to 1, then the points is clustered around a line with positive slope
Correct option is A
(3,0) and(0,-7) Write an equation in standard form of the line that passes through the given points
Given the points ( 3 , 0 ) and ( 0 , -7)
The slope intercept form of the line y = mx + c
Where m is the slope and c is the y-intercept
The slope will be calculated as following:
[tex]m=\frac{0-(-7)}{3-0}=\frac{7}{3}[/tex]so, y = (7/3) x + c
C is the value of y when x = 0
So, using the point (0, -7)
when x = 0 , y = -7
so,
c = -7
so,
y = (7/3) x - 7
Multiplying all terms by 3
so,
3y = 7x - 21
so,
3y - 7x = -21
so, the standard form of the line :
3y - 7x = -21 or 7x - 3y = 21
For the following triangle, calculate the indicated trigonometric ratio of the given angle.
Explanation
the cosine of any angle is given by
[tex]\cos\theta=\frac{adjacent\text{ side}}{hypotenuse}[/tex]hence
Step 1
a) let
[tex]\begin{gathered} adjacent\text{ side=109} \\ hypotenuse=140 \\ angle\text{ = 39\degree} \end{gathered}[/tex]replace,
[tex]cos\text{ 39=}\frac{109}{140}[/tex]I hope this helps you
A diamond cutter has raw carats diamond that weighs 19.5 and from which two 5-carats diamonds will be cutHow much did the raw diamond weigh in milligramsHow much will each of two cut diamonds way in milligrams
Remember that
carats=ct
1 ct=200 mg
so
19.5 ct-----> convert to mg
19.5 ct=19.5*200=3,900 mg
5 ct -----> convert to mg
5 ct=5*200=1,000 mg
What is the probability that a patron had a sandwich but did not order soup
Solve for y16=5(y+6)-7ySimplify your answer as much as possible
Given the equation:
16 = 5(y + 6) - 7y
Let's solve the equation for y.
To solve for y, take the following steps:
• Step 1:
Apply distributive property
[tex]\begin{gathered} 16=5(y)+5(6)-7y \\ \\ 16=5y+30-7y \end{gathered}[/tex]• Step 2:
Combine like terms on the right side
[tex]\begin{gathered} 16=5y-7y+30 \\ \\ 16=-2y+30 \end{gathered}[/tex]• Step 3:
Subtract 30 from both sides:
[tex]\begin{gathered} 16-30=-2y+30-30 \\ \\ -14=-2y \end{gathered}[/tex]• Step 4:
Divide both sides by -2
[tex]\begin{gathered} \frac{-14}{-2}=\frac{-2y}{-2} \\ \\ 7=y \\ \\ y=7 \end{gathered}[/tex]Therefore, the value of y is 7.
ANSWER:
y = 7
What is the area of the trapezoid?3 in.15 in.14 in.5 in.9 in.square inches
Answer:
The area of the trapezoid is of 24 square inches.
Step-by-step explanation:
The trapezoid can be divided as:
A rectangle with base 3 inches and height 4 inches.
A right triangle with sides 3 inches and 4 inches.
The area of the trapezoid is the sum of the area of the rectangle with the area of the two right triangles.
Area of the rectangle:
The area of the rectangle with base b and height h is: A = b*h.
In this question, we have that b = 3, h = 4. So
A = b*h = 3*4 = 12
Area of the right triangle:
The area of a right triangle with sides a and b is: A = 0.5*a*b
In this question.
2 right triangles, each with a = 3, b = 4. So
A = 2*0.5*a*b = 3*4 = 12
Area of the trapezoid:
12 + 12 = 24
The area of the trapezoid is of 24 square inches.
Find the derivative :y = (x+3)/(2x+1)
given that
[tex]y=\frac{x+3}{2x+1}[/tex]Differentiating we get
[tex]\begin{gathered} \frac{dy}{dx}=\frac{(2x+1)-2(x+3)_{}}{(2x+1)^2} \\ =\frac{2x+1-2x-6}{(2x+1)^2} \\ =\frac{-5}{(2x+1)^2} \end{gathered}[/tex]Evaluate each expression below. Be sure to include IM notes (+/- and C/D) for each problem
a) -3 + (-1.5) = -3 - 1.5 = - (3 + 1.5) = -4.5
3
+
1.5
--------
4.5
b) -2 1/2 = -(2*2 + 1)/2 = -5/2
[tex]-\frac{5}{2}+\frac{2}{3}=\text{ }\frac{-5\cdot3\text{ + 2}\cdot2}{2\cdot3}=\frac{-15+4}{6}=\frac{-11}{6}[/tex]if DK equals a find K L M angle d l m equals 82 find M angle d k m m angle K a l equals 2x - 8 find X
1) Since DKLM is Rhombus then these are the valid properties:
• 4 congruent sides
2) If DK is 8 KL=?
As a rhombus, all of their sides are congruent. So KL = 8
The measure of the angle ∠DML = 82º then the measure of ∠DKM
The diagonals of the rhombus bisect the angle on the opposite side. So ∠DKM = 41º
The length of a rectangle is 3 times the width. The perimeter of the rectangle is 64meters. Find the length and the width of the rectangle.
Given
length = 3 x width
Perimeter = 64
Find
length and width of given rectangle
Explanation
Perimeter = 2(l + w)
64 = 2(3w+w)
64 = 2(4w)
64 = 8w
w = 8 m
Therefore, length = 3 x 8 = 24 m
Final Answer
length = 24m
Width = 8m
Mary made 1/4 of a batch of cookies in 1/10 of an hour. How many batchesof cookies can she make in one hour? What is the Unit rate?
Let's begin by listing out the information given to us:
1/4 batch of cookies = 1/10 hour
x batches of cookies = 1 hour
To solve for the number of batches of cookies in one 1 hour, we will use simple proportion
x * 1/10 = 1/4 * 1
4x = 10
x = 10/4 = 2.5
Hence, 2½ batches of cookies are done in 1 hour
2. What is the vertex of the function (x) = 1x – 34– 17 (A) (B) (C) (3,1) (39–1) (-3,-1) (-3,1)
if we have a function in the standard form as follows.
[tex]f(x)=|x\pm h|\pm k[/tex]Then the vertex is (h, k) or the point where the function changes the sign.
Therefore the vertex is (3, -1) or the option (B).
308 multiplied by p equals 209 .Find value of p.
The question can be written as;
308 * p= 209
To find the value of p divided both sides by 308
308p = 209
p= 209/ 308
p= 0.6786 ---------answer in 4 decimal places
Answer : p = 0.6786
D 45° y-- 35° 25° E F G 2x - 10° H
Given:
1) the angle FGD and angle DGE are supplementary angles.
[tex]\begin{gathered} \angle FGD+\angle DGE=180^{\circ} \\ y-35^{\circ}+25^{\circ}=180^{\circ} \\ y-10^{\circ}=180^{\circ} \\ y=190^{\circ} \end{gathered}[/tex]Also the line DE is parallel to GH and angle EDG and DGH formed supplementary angles.
[tex]\begin{gathered} \angle EDG+\angle DGE+\angle EGH=180^{\circ} \\ 45^{\circ}+25^{\circ}+2x-10^{\circ}=180^{\circ} \\ 60^{\circ}+2x=180^{\circ} \\ 2x=120^{\circ} \\ x=60^{\circ} \end{gathered}[/tex]Answer: x = 60 degree, y = 190 degree
2) the pair of angles of interior angles on the same sideof the transversal area supplementary.
[tex]\begin{gathered} 3x+x=180^{\circ} \\ 4x=180^{\circ} \\ x=45^{\circ} \end{gathered}[/tex]Answer: x = 45 degree.
3) The angle BEC and CEA are supplimetary angles.
[tex]\begin{gathered} \angle BEC+\angle DEC+\angle DEA=180^{\circ} \\ 90^{\circ}+\angle DEC+x=180^{\circ} \\ \angle DEC=90^{\circ}-x \end{gathered}[/tex]4) Angle GLK and angle EKL are supplementary,
[tex]\begin{gathered} \angle GLK+\angle EKL=180^{\circ} \\ \angle GLK+x=180^{\circ} \\ \angle GLK=180^{\circ}-x^{} \end{gathered}[/tex]5) B is parallel to D . and angle formed GFE and angle FED are supplementary,
[tex]\begin{gathered} \angle GFE+\angle FED=180^{\circ} \\ 40^{\circ}+5x+65^{\circ}=180^{\circ} \\ 5x=75^{\circ} \\ x=15^{\circ} \end{gathered}[/tex]Answer: x = 15 degree.
6) angle ABC and angle BCD are alternate angles and so they are equal.
[tex]\begin{gathered} \angle ABC=\angle BCD \\ x+15^{\circ}=45^{\circ} \\ x=45^{\circ}-15^{\circ} \\ x=30^{\circ} \end{gathered}[/tex]Answer: x = 30 degree.