Solution:
The number of food items is given by the following expression:
4 cereal boxes + 6 cans+ t pieces of fruit+ 2 bags of rice
that is, she organizes
4+6+t+2 meals
this is equivalent to
(4+6+2)+t
this is equivalent to say
12 + t meals.
So that the correct answer is:
12 + t
given g(x)= -12f(x+1)+7 and f(-4)=2 fill in the blanks round answers to 2 decimal points as needed g( )=
We know the value of f(-4), which is 2
Let's think about a value of x in which we can calculate the value of f(x+1) using the given information (it means x+1 has to be equal to -4)
x+1=-4
x=-4-1
x=-5
Now use this value to calculate g(x)
[tex]\begin{gathered} g(-5)=-12\cdot f(-5+1)+7 \\ g(-5)=-12\cdot f(-4)+7 \end{gathered}[/tex]As we said, we already know the value of f(-4), use it to calculate g(-5)
[tex]\begin{gathered} g(-5)=-12\cdot2+7 \\ g(-5)=-24+7 \\ g(-5)=17 \end{gathered}[/tex]Find the coordinates of each point under the given rotation about the origin (-5, 8); 180
As given by the question
There are given that the point, (-5, 8).
Now,
The given coordinate of point (-5, 8) which is lies on the second quadrant.
Then,
According to the question,
Rotate it through 180 degree about the origin
Then,
The given coordinate move from 2nd quadrant to 4th, where the value of x is positive and y is negative
Then,
The new coordinat will be, (5, -8).
Hence, the coordinate is (5, -8).
Figure R = figure R". Describe a sequence of three transformations you canperform on figure R to show this. Show your work.
1) Rotate the figure 90º clockwise.
To rotate a figure 90º clockwise you have to perform the following transformation:
(x,y)→(y,-x)
So for each point of the figure you have to swich places between x and y.
And you have to multiply the x coordinate by -1.
R has 6 points:
(-4,-5)
(-7,-5)
(-7,-4)
(-5,-4)
(-6,-3)
(-2,-2)
First step: swich places between the coordinates of each point:
(x,y) → (y,x)
(-4,-5)→(-5,-4)
(-7,-5)→(-5,-7)
(-7,-4)→(-4,-7)
(-5,-4)→(-4,-5)
(-6,-3)→(-3,-6)
(-2,-2)→(-2,-2)
Second step, multiply the y-coordinate of the new set by -1
(y,x)→ (y,-x)
(-5,-4)→ (-5,4)
(-5,-7)→ (-5,7)
(-4,-7)→ (-4,7)
(-4,-5)→ (-4,5)
(-3,-6)→ (-3,6)
(-2,-2)→ (-2,2)
After the rotation, the figure moved from the 3rth quadrant to the 2nd quadrant.
composition of functions, interval notation
Given the functions:
[tex]\begin{gathered} g(x)=\frac{1}{\sqrt[]{x}} \\ m(x)=x^2-4 \end{gathered}[/tex]I would like to find their domain as well and then complete the answers:
[tex]\begin{gathered} D_g=(0,\infty) \\ D_m=(-\infty,\infty) \end{gathered}[/tex]For the first question: g(x) / m(x)
[tex]\begin{gathered} \frac{g(x)}{m(x)}=\frac{\frac{1}{\sqrt[]{x}}}{x^2-4}=\frac{1}{\sqrt[]{x}\cdot(x^2-4)}=\frac{1}{x-4\sqrt[]{x}} \\ x-4\sqrt[]{x}\ne0 \\ x\ne4\sqrt[]{x} \\ x^2\ne4x \\ x\ne4 \end{gathered}[/tex]As we can see, the domain of this function cannot take negative values nor 4, 0. So, its domain is
[tex]D_{\frac{g}{m}}=(0,4)\cup(4,\infty)[/tex]For the second domain g(m(x)), let's find out what is the function:
[tex]\begin{gathered} g(m(x))=\frac{1}{\sqrt[]{x^2-4}} \\ \sqrt[]{x^2-4}>0 \\ x^2>4 \\ x>2 \\ x<-2 \end{gathered}[/tex]This means that x cannot be among the interval -2,2:
[tex]D_{g(m)}=(-\infty,-2)\cup(2,\infty)[/tex]For the last domain m(g(x)) we perfome the same procedure:
[tex]m(g(x))=(\frac{1}{\sqrt[]{x}})^2-4=\frac{1}{x}-4[/tex]For this domain it is obvious that x cannot take the zero value but anyone else.
[tex]D_{m(g)}=(-\infty,0)\cup(0,\infty)_{}[/tex]please help me understand how to find the average rate of change of the function over the given interval and please show me work.
To answer this, you'll need to recall a formula for finding the rate of change of one variable with respect to another. Given f(x)=x^2 + x +1, the rate of change of the variable with respect to x is given by:
[tex]\begin{gathered} \frac{\differentialD yy}{\square}y}{dx}=n(ax^{n-1}),\text{ where n is the power of variable term, and a is the coefficient.}y}{\square}yy}{dx}=\text{nax}^{n-1} \\ So\text{ when f(x)=x\textasciicircum 2+x+1 is differentiated, we will arrive at } \\ \\ \frac{dy}{dx}=2x+1\text{ The average rate of change of the function within the range (-3,-2) means, we have to use x as -3 and also x as -2 into the derivative function } \\ x=-3 \\ \frac{\differentialD yy}{\square}y}{dx}=2(-3)+1=-6+1=-5y}{\square}y}{dx}=2(-3)+1=-6+1=-5 \\ \text{Also, } \\ x=-2 \\ \frac{\differentialD yy}{\square}y}{dx}=2x+1\text{ becomes}y}{\square}yy}{dx} \\ \\ \end{gathered}[/tex]How to find the (r) or difference in this scenario:
Aliens Away is a new video game where a player must eliminate a certain number of aliens on the screen by scaring them with an adorable house cat. When James plays the game, he eliminates 64 aliens in the first level and 216 aliens in the fourth level. If the number of aliens are destroyed in a geometric sequence from one level to the next, how many total aliens will James have wiped out by the end of the sixth level?
It is given that it is a geometric sequence, if I am not mistaken it is the explicit formula.
IF YOU COULD PLASE EXPLAIN:)
Total number of aliens James have wiped out by the end of the sixth level is 1330
The number of aliens eliminated in first level a = 64
The number of aliens eliminated in the fourth level = 216
The sequence is in geometric sequence
The nth term of the geometric sequence is
[tex]a_n=ar^{n-1}[/tex]
The fourth term is 216
216 = [tex]64r^3[/tex]
[tex]r^{3}[/tex] = 216/64
r = 3/2
Then we have to find the total alien James killed by the end of sixth level
Sum of n terms = [tex]\frac{a(r^n-1)}{r-1}[/tex]
Substitute the values in the equation
= [tex]\frac{64(1.5^6-1)}{1.5-1}[/tex]
= 665/0.5
= 1330
Hence, total number of aliens James have wiped out by the end of the sixth level is 1330
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I inserted a picture of the question, please give a VERY SHORT explanation
To multiply two polynomials we have to multiply each term in one polynomial by each term in the other polynomial, and then add the similar terms, as follows:
if two angles measure 90 and are complementary and congruent, the measure of each angle is
Leonardo, the answer is
45 degrees.
I need help figuring out how to find sides a and b using the law of sine
Given the triangle ABC below.
a is the side facing b is the side facing
c is the side facing
We ara interested in calculating the value of side a and b.
To do this, we need to apply the "sine rule"
Sine rule state that
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]Where
a is the side facing b is the side facing
c is the side facing
To calculate b,
B = 95 , b = ?
C = 48, c=100
[tex]\begin{gathered} \frac{b}{\sin B}=\frac{c}{\sin C} \\ \frac{b}{\sin 95}=\frac{100}{\sin \text{ 48}} \\ \\ b\text{ x sin48=100 x sin95} \\ b=\frac{100\text{ x sin95}}{\sin 48} \\ b=134.05 \end{gathered}[/tex]b = 134 ( to nearest whole number)
To calculate a:
A = 37, a = ?
C = 48, c=100
[tex]\begin{gathered} \frac{a}{\sin A}=\frac{c}{\sin C} \\ \frac{a}{\sin37}=\frac{100}{\sin 48} \\ a\text{ x sin48 = 100 x sin37} \\ a=\frac{100\text{ x sin37}}{\sin 48} \\ a=80.98 \\ \end{gathered}[/tex]a = 81 ( to the nearest whole number)
Question 3 (9 points)Find Pred then green)What is the probability that you select a red marble, then a green marbleP (red) -P (then Green) - (Total of marbles will be 1 less)P (red then green) = *Hint: Multiply
Solution
Step 1
Write out an expression for the probability
[tex]\text{The probaility of an event occurring= }\frac{\text{Number of required events}}{\text{Total number of events}}[/tex]Step 2
Define terms
Total number of events = 8 marbles
Number of required events = red then marble
Number of red = 2 marbles2
Number of green = 2 marbles
Note: The question is without replacement.
Step 3
Get the required probabilities and the answer
[tex]\begin{gathered} Pr(\text{red marble) = }\frac{2}{8} \\ Pr(\text{green marble without replacement) =}\frac{2}{7} \end{gathered}[/tex]Hence the Pr(of red then green) is given as
[tex]\begin{gathered} =Pr(\text{red) }\times Pr(green\text{ without replacement)} \\ =\frac{2}{8}\times\frac{2}{7}=\frac{1}{14} \end{gathered}[/tex]Hence the probability of picking a red marble then a green marble = 1/14
In AOPQ, mZO = (6x – 14)°, mZP = (2x + 16)°, and mZQ = (2x + 8)°. Find mZQ.
Explanation
Step 1
the sum of the internal angles in a triangle equals 18o, so
[tex]\begin{gathered} (2x+16)+(6x-14)+(2x+8)=180 \\ 2x+16+6x-14+2x+8=180 \\ \text{add similar terms} \\ 10x+10=180 \\ \text{subtract 10 in both sides} \\ 10x+10-10=180-10 \\ 10x=170 \\ \text{divide both sides by 10} \\ \frac{10x}{10}=\frac{170}{10} \\ x=17 \end{gathered}[/tex]Step 2
now, replace the value of x in angle Q to find it
[tex]\begin{gathered} \measuredangle Q=(2x+8) \\ \measuredangle Q=(2\cdot17+8) \\ \measuredangle Q=(34+8) \\ \measuredangle Q=42 \end{gathered}[/tex]I hope this helps you
Ken wants to install a row of cerámic tiles on a wall that is 21 3/8 inches wide. Each tile is 4 1/2 inches wide. How many whole tiles does he need?
We have the following:
[tex]a\frac{b}{c}=\frac{a\cdot c+b}{c}[/tex]therefore:
[tex]\begin{gathered} 21\frac{3}{8}=\frac{21\cdot8+3}{8}=\frac{168+3}{8}=\frac{171}{8} \\ 4\frac{1}{2}=\frac{4\cdot2+1}{2}=\frac{8+1}{2}=\frac{9}{2} \end{gathered}[/tex]now, we divde to know the amount:
[tex]\frac{\frac{171}{8}}{\frac{9}{2}}=\frac{171\cdot2}{8\cdot9}=\frac{342}{72}=4.75\cong4[/tex]Therefore, the answer is 4 whole tiles
In the following expression, place a decimal point in the divisor and the dividend that is 4368÷6208 to create a new problem with the same answer as in question 11 that is 7 meters / 7
---------------------------------
436.8m -------------------> 62.08s
xm -------------------------->1s
Using cross multiplication:
[tex]\begin{gathered} \frac{436.8}{x}=\frac{62.08}{1} \\ \text{solve for x:} \\ x=\frac{436.8}{62.08} \\ x=7.036082474m \\ \end{gathered}[/tex]Solve the equation on the interval [0, 2\small \pi). Show all work. Do not use a calculator - use your unit circle!
SOLUTION
Write out the equation given
[tex]\cos ^2x+2\cos x-3=0[/tex]Let
[tex]\text{Cosx}=P[/tex]Then by substitution, we obtain the equation
[tex]p^2+2p-3=0[/tex]Solve the quadractic equation using factor method
[tex]\begin{gathered} p^2+3p-p-3=0 \\ p(p+3)-1(p+3)=0 \\ (p-1)(p+3)=0 \end{gathered}[/tex]Then we have
[tex]\begin{gathered} p-1=0,p+3=0 \\ \text{Then} \\ p=1,p=-3 \end{gathered}[/tex]Recall that
[tex]\cos x=p[/tex]Hence
[tex]\begin{gathered} \text{when p=1} \\ \cos x=1 \\ \text{Then } \\ x=\cos ^{-1}(1)=0 \\ \text{hence } \\ x=0 \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} \text{When p=-3} \\ \cos x=-3 \\ x=\cos ^{-1}(-3) \\ x=no\text{ solution} \end{gathered}[/tex]Therefore x=0 is the only valid solution on the given interval [0,2π).
Answer; x=0
why is height more specific measure than 'size'?
When you talk about height, it is a more precise value that require a vertical distance from a referenced point. While 'size' is not specific whatsoever and it's more like a form of range.
what is 234,181 rounded to the nearest thousand
The figure 234,181 has the digit 4 in the thousands place.
Rounding to the nearest thouand would therefore be
234,000
This is because, the digit 1 that follows is not up to 5 and therefore is insignificant. So the digit 1 and the others after it are all rounded up to zeros.
8) What is the mass of the teddy bear if the toy car has a mass of 375 grams? 10 .S 0 4kg 3kg 1kg 2kg 000
The mass of the teddy is 1,225 grams
Here, we want to get the mass of the teddybear given the mass of the toy car
Since boith are on the scale, then it means they contribute to the mass on the scale
By reading the scale, we can see that the mass on the scale is 1.6 kg
As we know, 1000 g is 1 kg
It means 1.6 kg in g will be 1.6 * 1000 = 1,600 g
So, we can now subtract the mass of the toy car from this total to get the mass of the teddy
Mathematically, we have this as;
[tex]1600\text{ g - 375 g =1,225 g}[/tex]determine the area of the shaded regionA. 6 square unitsB. 19 square unitsC.20 square unitsD. 25 square units
area of the square:
[tex]\begin{gathered} a=l\times l \\ a=5\times5 \\ a=25 \end{gathered}[/tex]area of the rectangle
[tex]\begin{gathered} a=b\times h \\ a=3\times2 \\ a=6 \end{gathered}[/tex]area of the shaded region:
area of the square - area of the rectangle = area of the shaded region
[tex]25-6=19[/tex]answer: B 19 saquare units
Which points are separated by a distance of 4 units?A. (3,6) (3,9)B. (2,7) (2,3)C. (1,5) (1,3)D. (4,2) (4,7)
let us take the point (2,7) and (2,3) the distance between these two is
[tex]\begin{gathered} d=\sqrt[]{(2-2)^2+(7-3)^2} \\ d=\sqrt[]{4^2} \\ d=4\text{ unit} \end{gathered}[/tex]Hence these two points are separated by 4 units.
So option B is correct.
having trouble solving quadratic equations using factoring, examples are fine
Let's solve the quadratic equation using factorization:
x²-9x -22= 0
In order to solve using this method, we should beforehand factorize the polynomial:
The middle number is -9 and the last number is -22.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks? Let's think about two numbers that add up to -9 and multiply together to -22...
These numbers will be -11 and 2:
-11 +2= 9
-11*2= -22
So the factorization is:
(x+2)*(x-11) = 0
That means:
x + 2 =0
and
x - 11 = 0
Solving the equations:
x= -2
x= 11
S= {-2, 11}
What is the prime factorization of 84.(A)2 x 3 x 7(B)2^2 X 3 X 7(C)2 X 21
Answer:
84=2^2 x 3 x 7
Explanation:
A prime number is any number that has only two factors: 1 and itself.
To find the prime factorization of 84, we are required to express it as a product of its prime factors.
[tex]\begin{gathered} 84=2\times42 \\ 84=2\times2\times21 \\ 84=2\times2\times3\times7 \\ =2^2\times3\times7 \end{gathered}[/tex]
Therefore, the prime factorization of 84 is:
84=2^2 x 3 x 7
in the diagram segment AD and AB are tangent to circle C solve for x
A property ostates that if two lines that are tangent to the circle intersect in an external point, they are congruent, i.e. they have the same length.
[tex]\begin{gathered} AD=AB \\ x^2+2=11 \end{gathered}[/tex]From this expression we can determine the possible values of x. The first step is to equal the expression to zero
[tex]\begin{gathered} x^2+2-11=11-11 \\ x^2+2-11=0 \\ x^2-9 \end{gathered}[/tex]The expression obtained is a quadratic equation, using the queadratic formula we can determine the possible values of x:
[tex]\begin{gathered} f(x)=ax^2+bx+c \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]For our expression
[tex]x^2+0x+-9[/tex]The coefficients are
a=1
b=0
c=-9
Replace them in the formula
[tex]\begin{gathered} x=\frac{-0\pm\sqrt[]{0^2-4\cdot1\cdot(-9)}}{2\cdot1} \\ x=\frac{0\pm\sqrt[]{36}}{2} \\ x=\frac{0\pm6}{2} \end{gathered}[/tex]Now calculate both possible values:
Positive:
[tex]\begin{gathered} x=\frac{+6}{2} \\ x=3 \end{gathered}[/tex]Negative:
[tex]\begin{gathered} x=\frac{-6}{2} \\ x=-3 \end{gathered}[/tex]The possible values of x are 3 and -3
There were eight questions on Emily's math quiz, and she missed two questions.Which of the following diagrams represents the percentage of Emily's accuracy onthe quiz?A. 50%B. 75%C. 30%D. 10%
There are eight quartion in the quiz and two question missed. So Emily solved six question of the quiz.
Determine the accuracy of Emily.
[tex]\frac{6}{8}\times100=75[/tex]So Emily's accuracy is 75% and option B is correct.
Which points are on the graph of y = cot x? (Select all that apply)A. (/3 , √3/2)B. (/2 , 0)C. (0 , )D. (/4 , 1)E. ( , 0)
Solution:
The graph function is given below as
[tex]y=cotx[/tex]The graph is given below as
Therefore,
The points on the graph are
[tex]\begin{gathered} \Rightarrow(\frac{\pi}{4},1) \\ \Rightarrow(\frac{\pi}{2},0) \end{gathered}[/tex]OPTION B AND option D are the right answers
Lee Ann is planning a bridal shower for her best friend. At the party, she wants to serve 3 beverages, five appetizers, and three desserts, but she doesn't not have time to cook. She can choose from 9 bottle drinks, 9 Frozen appetizers, and 12 prepared desserts at the supermarket. How many different ways can lie and pick up the food and drinks to serve at the bridal shower?
2328480 ways
ExplanationWe want to find out how many ways there are to select an item. The combination formula is a formula to find the number of ways of picking "r" items from a total of "n" items.
This number is given by:
[tex]undefined[/tex]The angle of elevation to the top of a Building in New York is found to be 7 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building.
_________ feet
The height of the building is 649.44 feet
Given,
The angle of elevation of the building from ground = 7°
The distance from base of the building to the angle = 1 mile
We have to find the height of the building:
As this information are noted, we will get a right angled triangle(image attached).
So, by trigonometry:
Tanθ = opposite side / adjacent side
here,
θ = 7 degree
opposite side = x
adjacent side = 1 mile
Then,
Tanθ = opposite side / adjacent side
tan(7°) = x / 1
x = tan(7°) × 1
x = 0.123 × 1
x = 0.123 miles
1 mile = 5280 feet
Then,
0.123 miles = 0.123 × 5280 = 649.44 feet
That is,
The height of the building is 649.44 feet.
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what does -1 3/4+4.7=
-1 3/4 + 4.7 = -1.75 + 4.7 = 2.95
3/4 = 0.75, so -1 3/4 is -1.75
-1.75 + 4.7 = 2.95
Answer: 2.95
Darell made a scale drawing of a shopping center. The parking lot is 4 centimeters wide in the drawing. The actual parking lot is 40 meters wide. What scale did Darell use?
Answer:
1 cm to 10 m
Step-by-step explanation:
4 cm to 40 m = 1 cm to 10 m
Fill in the table using this function rule.
Answer:
-8, 2, 12, 22
Step-by-step explanation:
[tex]y = 5x+2\\y = 5(-2)+2\\y=-10+2\\y=-8[/tex]
[tex]y = 5x+2\\y = 5(0)+2\\y=0+2\\y=2[/tex]
[tex]y = 5x+2\\y = 5(2)+2\\y=10+2\\y=12[/tex]
[tex]y = 5x+2\\y = 5(4)+2\\y=20+2\\y=22[/tex]
p and q are roots of the equation 5x^2 - 7x +1. find to value of p^2 x q +q^2 x p and (p/q)+(q/p)
1) Let's find the roots of the equation: 5x² -7x +1
5x² -7x +1
2) Calling x_1 =p and x_2= q
Plugging them into the (p/q)+(q/p) expression, dividing the fractions. And then rationalizing it we'll have finally:
[tex]\frac{\frac{7+\sqrt[]{29}}{10}}{\frac{7-\sqrt[]{29}}{10}}+\frac{\frac{7-\sqrt[]{29}}{10}}{\frac{7+\sqrt[]{29}}{10}}=\frac{7+\sqrt[]{29}}{10}\cdot\frac{10}{7-\sqrt[]{29}}\text{ +}\frac{7-\sqrt[]{29}}{10}\cdot\frac{10}{7+\sqrt[]{29}}\text{ =}\frac{39}{5}[/tex]