A.
[tex]6+\lbrack\frac{4}{9}+(-\frac{2}{9})\rbrack[/tex]Since both fractions have the same numerator, you can factorize 1/9 aout of the parentheses, because:
[tex]\begin{gathered} \frac{1}{9}\cdot4=\frac{4}{9} \\ \text{and} \\ \frac{1}{9}\cdot2=\frac{2}{9} \end{gathered}[/tex]Then you can simplify the expression as:
[tex]6+\frac{1}{9}\lbrack4+(-2)\rbrack=6+\frac{1}{9}\lbrack4-2\rbrack[/tex]Use f(x)=-x-8 and g(x) = x² + 8x − 15 to answer the following: a) f(1) + g(–3) b) g(−9) − f(–7)
ANSWER:
a) -37
b) 9
Given:
f(x)=-x-8 and g(x) = x² + 8x − 15
a) f(1) + g(–3)
f(1) = 1 - 8 = -7
g(-3) = -3² + 8(-3) - 15 = 9 - 24 - 15 = -30
f(1) + g(–3) = -7 + (-30)
= -7 - 30
-37
b) g(−9) − f(–7):
g(-9) = -9² + 8(-9) - 15 = 81 - 72 - 15 = -6
f(-7) = -7 - 8 = -15
Thus,
g(−9) − f(–7) = -6 - (-15)
= -6 + 15
= 9
Hello! I need some help with this homework question, please? I just need help with C or D Q2
C) Considering that f(x)=x² we can write the composite function f(f(x)) y plugging into the x-variable the function f(x) itself:
[tex]\begin{gathered} f(f(x)) \\ f\mleft(x\mright)=x^2 \\ f(f(x))=(x^2)^2 \\ f(f(x))=x^4 \end{gathered}[/tex]Now, let's find the Domain. Considering that this is a polynomial function that has no restraints nor discontinuity we can write out the following:
[tex]\begin{gathered} The\: domain\: of\: f\circ f\: is\: all\: Real\: numbers \\ D=\: \mleft(-\infty\: ,\: \infty\: \mright) \end{gathered}[/tex]How is the series 7 + 13 + 19+...+ 139 represented in summation notation?
Each term is 6 greater than the previous term.
First term is "7".
So,
a = 7
d = 6
Let's find the formula for the series,
[tex]\begin{gathered} a+(n-1)d \\ 7+(n-1)(6) \\ 7+6n-6 \\ 6n+1 \end{gathered}[/tex]We can immediately eliminate the firsst and third choice.
The variable is "t", so the general formula will be:
[tex]6t+1[/tex]How many terms are there?
The series starts from t = 1,
since 6(1) + 1 = 6 + 1 = 7
and 6(2) + 1 = 12 + 1 = 13
The terms match!
So, 2nd answer choice is correct!!
Answer[tex]\sum ^{23}_{t\mathop=1}(6t+1)[/tex]A shipment of computers arrived at. a warehouse.If each computers is valued at$995. What is the total value of the shipping?
Total number of computers = 20
Cost per a computer = $995
Total cost of 20 computers = 20 x $995
= $19,900
Find the value of x that will make A B5x + 20А.B3x + 60x = [?]
x = 20
Using the alternate exterior angles theorem, it was stated the exterior ang
2. The length of Sally's garden is 4 meters greater than 3 times the width. Theperimeter of her garden is 72 meters. Find the dimensions of Sally's garden.The garden has a width of 8 and a length of 28.
L = length
W = width
L = 4 + 3*W
The perimeter of a rectangle is the sum of its sides: 2L + 2W. Since it's 72, we have:
2L + 2W = 72
Now, to solve for L and W, the dimensions of the garden, we can use the first equation (L = 4 + 3*W) into the second one (2L + 2W = 72):
2L + 2W = 72
2 * (4 + 3*W) + 2W = 72
2 * 4 + 2 * 3W + 2W = 72
8 + 6W + 2W = 72
8W = 72 - 8
8W = 64
W = 64/8 = 8
Then we can use this result to find L:
L = 4 + 3W = 4 + 3 * 8 = 4 + 24 = 28
Therefore, the garden has a width of 8 and a length of 28.
Given the system of equations: 8x + 14y = 4 and -6x - 7y = - 10, what would youmultiply the bottom equation by to eliminate y when adding the two equationstogether?
We need to multiply the second equation by 2 to eliminate y when adding the two equations
i need help doing number 34 and 35 if you can please :(
The tangent of an angle, we will follow the steps below
Step 1: Write out the trigonometric ratio to obtain the tangent of an angle
[tex]\tan \emptyset=\frac{opposite}{adjacent}[/tex]From question 35
Step 2: Apply the tangent ratio
[tex]\begin{gathered} \tan A=\frac{\text{opposite}}{\text{adjacent}}=\frac{60}{100}=\frac{6}{10}=\frac{3}{5} \\ \tan A=\frac{3}{5}=0.6000 \end{gathered}[/tex]For tan B
[tex]\begin{gathered} \tan B=\frac{\text{opposite}}{\text{adjacent}}=\frac{100}{60}=\frac{5}{3} \\ \tan B=\frac{5}{3}=1.6667 \end{gathered}[/tex]the vertex of this parabola Is at parabola is at (2,-4)
Answer:
[tex]A=3[/tex]
Explanation: We are given two points, P1 is vertex and P2 is another point on the parabola:
[tex]\begin{gathered} P_1(2,-4) \\ P_2(3,-1) \end{gathered}[/tex]The general form of the equation of a parabola is:
[tex]y(x)=A(x\pm B)^2+C[/tex]Where A is the Coefficient of the parabola function which is responsible for compression and stretch, likewise B is responsible for the translation along the x-axis and C is responsible for translation along the y-axis.
We know that our function is translated 2 units towards the right and 4 units downwards:
Therefore:
[tex]\begin{gathered} B=-2 \\ C=-4 \end{gathered}[/tex]And this turns the parabola equation into:
[tex]y(x)=A(x-2)^2-4[/tex]Using P2 we can find the constant-coefficient as:
[tex]\begin{gathered} y(x)=A(x-2)^2-4_{} \\ P_2(3,-1) \\ \\ \\ \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} y(3)=A(3-2)^2-4=-1\rightarrow A-4=-1 \\ \because\rightarrow \\ A=3 \end{gathered}[/tex]Suppose that the local sales tax rate is 4% and you purchase a car for $18,000. How much tax is paid? What is the cars total cost?
Solution
Step 1:
Cost = $18000
Tax = 4% of $18000
Step 2
[tex]\begin{gathered} Tax\text{ = 4\% of \$18000} \\ \\ Tax\text{ = }\frac{4}{100}\text{ }\times\text{ \$18000} \\ \\ Tax\text{ paid = \$720} \end{gathered}[/tex]Step 3
[tex][/tex]101987006HR5SrOL4.3ON21.1 2 345 6 78 9 10Which of these statements are true for the scatter plot? Select all that apply.The scatter plot shows a negative association.The scatter plot shows a linear association.The scatter plot shows a positive association.The scatter plot shows no association.
The scatter plot shows a linear association.
The scatter plot shows a positive association.
Find the equation of the line. Write the equation of the line in standard form Vertical line through (-1,-1)
Solution
We have the following point given (-1, -1)
The equation of a line is given by:
y= mx+b
For this case since we have a vertical line the equation would be:
x= -1
Complete the function table for the given domain, and plot the points on the graph. (t) = -12 + 2.1 + 5 -1 0 1 2 3 Drawing tools Click on a tool to begin draving. EK Select f(x) Point Click on the Graph to place a Point HHHH 6 2 2 10 0
f(x) = -x^2 + 2x + 5
x -1 0 1 2 3
f(x) 2 5 6 5 2
The order in which you perform operations matters in a numerical expression. O A. True B. False
Answer:
A. True
Explanation:
Consider the numerical expression below:
[tex]9+2\times3[/tex]If we solve from the left to the right, we have:
[tex]9+2\times3=11\times3=33\text{ (Wrong Solution)}[/tex]This result is incorrect.
However, by the order of operations, multiplication comes before addition, so we rightly have:
[tex]9+2\times3=9+6=15[/tex]We see that if we do not follow the order of operations, our results will not be accurate.
Therefore, the order in which you perform operations matters in a numerical expression.
The answer is True.
Instructions: Find the missing side. Round your answer to the nearest tenth. х 38° 30 X =
Let us call the third angle in the triangle y
y = 180 - 90-38 = 52 degrees ( sum of angles in a triangle is 180 degrees)
using trigonometric ratio
[tex]\sin \text{ 52=}\frac{\text{opposite}}{\text{hypothenuse}}[/tex]opposite = x
hypothenuse = 30
[tex]\begin{gathered} \sin 52\text{ =}\frac{x}{30} \\ x=\text{ 23.64032261} \end{gathered}[/tex]To the nearest tenth x = 23.6
Rewrite each of the following expressions so that they have no division
Using the law of indices,
[tex]\frac{1}{x^6}[/tex]will be
[tex]\frac{1}{x^6}=x^{-6}[/tex]Lin's mom bikes at a constant speed of 12 miles per hour. Lin walks at a constantspeed 1/3 of the speed her mom bikes. Sketch a graph of both of these relationships
ANSWER :
The graph is :
EXPLANATION :
From the problem we have the rates :
Lin's mom : 12 miles per hour
Lin : 1/3 of Lin's mom, that will be 12(1/3) = 4 miles per hour
Plot the points as (hour, miles).
(1, 12) and (1, 4)
Connect the points with the origin (0, 0)
That will be :
The black line represents Lin's mom and the orange line represents Lin.
The edge of a cube measures 11 m. Find the surface area.
In order to determine the surface area of the cube, use the following formula:
[tex]S=6a^2[/tex]where a is the length of the side of a cube a = 11 m.
Replace the value of a into the formula for S:
[tex]S=6(11m)^2=726m^2[/tex]Hence, the surface area of the given cube is 726m^2
Write your answer as a whole number and remainder. 38 : 5 = R
Answer
7 remainder 3
Explanation
38 : 5 can be written as 38/5
And we know that that will give
(38/5) = 7 remainder 3
Hope this Helps!!!
which statement best describes the changes to the graph when the coefficient of x^2 is multiplied by 1/2?A. the parabola will get narrower.B. the parabola will get wider.C. the parabola will shift to the right by 1/2 unit.D. the parabola will shift to the left by 1/2 unit.
B. The parabola will get wider
Explanatiion:The graph for the function x² is shown in the question
The graph x² is multiplied by 1/2. The new function becomes 1/2 x²
Let us plot the graph of 1/2 x² to compare with the graph of x² that has already been given
The graph of 1/2 x² is plotted above
As shown, it is obvious from the graphs of 1/2 x² and x² that the graph of 1/2 x² is wider than the graph of x²
Kristi Yang borrowed $12,000. The term of the loan was 150 days, and the annual simple interest rate was 6.5%. Find the simple interest due on the loan. (Round your answer to the nearest cent.)
For an initial ammount borrowed I, an term of the loan t, and an annual interest rate r, the simple interest S due on the loan is given by:
[tex]S=I\cdot r\cdot\frac{t}{365}[/tex]For I = $12000, r = 0.065 and t = 150 days, we have:
[tex]\begin{gathered} S=12000\cdot0.065\cdot\frac{150}{365} \\ S=12000\cdot0.065\cdot0.41096 \\ S=\text{ \$320.55} \end{gathered}[/tex]Find the value of c using the given chord and secant lengths in the diagram shown to right . c= (Round to the nearest tenth as needed .)
ANSWER
c = 6.4
EXPLANATION
The intersecting chords theorem says that the product of one secant segment and its external segment is equal to the product of the other secant segment and its external segment.
One secant segment is (9+19) and its external segment is 9. The other is (13+c) and its external segment is 13:
[tex]9\cdot(9+19)=13\cdot(13+c)[/tex]Solving for c:
[tex]\begin{gathered} 9\cdot28=13^2+13c \\ 252=169+13c \\ 252-169=13c \\ 83=13c \\ c=\frac{83}{13} \\ c=6.3846\ldots \\ c\approx6.4 \end{gathered}[/tex]can you help with this one its has 11 part to it
Recall that the limit of a function exists if
[tex]\lim_{x\to n^+}f(x)=\lim_{x^\to n^-}f(x).[/tex]Now, from the graph, we get that:
[tex]\begin{gathered} \lim_{x\to0^-}f(x)=0, \\ \lim_{x\to0^+}f(x)=0, \end{gathered}[/tex]therefore:
[tex]\lim_{x\to0}f(x)=0.[/tex]Answer: [tex]True.[/tex]which square root is a whole number ?
Let's find the square root of all to find which is a whole number
√254 = 15.937
√255 =15.967
√256 =16
Hence √256 is a whole number
The correct option is C.
A patient that you are tending to cannot exceed 500 Cal per meal. You notice that on the label the meal has 21grams of fat, 68 grams of carbohydrates, and 40 grams of protein. On average fat has 9 Cal/g, carbohydrates have4 Cal/g, and protein has 4 Cal/g.a) How much energy would the patient consume if they would eat the whole meal?b) What is the unit symbol of the answer?c) Are they within the 500 Cal limit? Input Y for yes and N for no
To determine the total amount of calories consumed in that meal, we have to multiply the number of grams of each type of nutrient by the energy provided by each gram of that nutrient.
We are given that 1 gram of fat has 9 calories, therefore, 21 grams of fat have:
[tex]9\times21\text{ calories=189 calories}[/tex]1 gram of carbohydrates gives 4 calories of energy, therefore, 68 grams have
[tex]68\times4\text{ calories= }272\text{ calories.}[/tex]1 gram of protein has 4 calories, therefore, 40 grams of protein has:
[tex]40\times4\text{ calories=160 calories.}[/tex]The mean has a total of:
[tex](189+272+160)\text{ calories=621 calories.}[/tex]Answer:
A) 621 Cal.
B) Cal.
C) N.
Your mom paid $8 for 10 Granny Smithapples and bought some Golden Deliciousat 60 cents an apple. If her average cost is$0.66 per apple, how many GoldenDelicious apples did she buy?
First, let's calculate the price of each Granny Smith apples, by dividing the cost by the number of apples:
[tex]undefined[/tex]Determine the area of the figure: 1.5 cm 5 cm 5.5 cm Your answer
We can add the are of the 3 rectangle, so we get that the area is:
[tex]A=1.5\cdot5+1.5\cdot5+1.5\cdot0.5=15.75\operatorname{cm}[/tex]Gabriella is a 11 years younger than Mikal the sum of their ages is 51 what is mikhails age
Answer:
30
Step-by-step explanation:
11 plus 30 is 51 therefor your sum is 30
Create an expression that can be used to find the value of x
There are two possible expressions that can help to calculate "x"
First
[tex]\begin{gathered} \text{ cos 28 = }\frac{42}{x} \\ \text{ } \end{gathered}[/tex]Second
[tex]\text{ sec 28 = }\frac{x}{42}[/tex]Both are possible to find "x".
order the numbers from least to greatest -2 3/4 negative 1/3 0.2 negative two negative 1 and 1/2 -0.8
So the numbers we have are:
-2, 3/4, -1/3, 0.2, -1, 1/2 & -0.8
So the numbers from least to greatest go as follows:
-2, -1, -0.8, -1/3, 0.2, 1/2, 3/4
