we have
f(x) = |x| – 4
Part b
f(4)
so
For x=4
substitute in the expression above
f(4) = |4| – 4
f(4)=4-4
f(4)=0
Part c
f(a+4)
so
For x=(a+4)
substitute
f(a+4) = |(a+4)| – 4
f(a+4)=a+4-4
f(a+4)=a
Use a calculator to help answer the question, Show that the point (6,1) is equidistant from points (9,0) and (3,0).The distance from (6,1) to (9,0) and the distance from (6,1) to (3,0) are both [ ] . Thus, (6,1) is equidistant from the two points.
First find the distance from (3,0) to (6,1)
We will use the distance formula
d = sqrt( (x2-x1)^2 + ( y2-y1)^2)
= sqrt( ( 6-3)^2 + ( 1-0)^2)
= sqrt( 3^2 + 1^2)
= sqrt( 9+1)
= sqrt(10)
Now we can find the distance between ( 6,1) and (9,0)
We will use the distance formula
d = sqrt( (x2-x1)^2 + ( y2-y1)^2)
= sqrt( ( 9-6)^2 + (0-1)^2)
= sqrt( 3^2+ (-1)^2)
= sqrt( 9+1)
= sqrt(10)
The distance is sqrt(10)
[tex]\sqrt[]{10}[/tex]In a raffle where 8000 tickets are sold for $2 each, one prize of $4200 will be awarded. What is the expected value of a single ticket in the raffle?
It is given that 8000 tickets are sold for $2 each, one prize of $4200 will be awarded.
The expected value is determined as
[tex]\frac{1}{8000\times4198}+\frac{7999}{8000\times-2}[/tex][tex]\frac{1}{8000\times4198}-\frac{7999}{8000\times2}=\frac{1}{8000}(\frac{2-33,579,802}{4198\times2})[/tex][tex]\frac{1}{8000}(\frac{-3183600}{796})=\frac{-3183600}{6368000}=-0.499[/tex]The expected value of a single ticket in the raffle is -0.499 dollar.
graph the line with the equation
we have the equation
y=-(1/2)x+7
Remember that
To graph a line we need al lest two points
so
Find the intercepts
step 1
Find the y-intercept (value of y when the value of x is zero)
For x=0
y=-(1/2)(0)+7
y=7
y-intercept is (0,7)
step 2
Find the x-intercept (value of x when the value of y is zero)
For y=0
o=-(1/2)x+7
(1/2)x=7
x=14
x-intercept is (14,0)
step 3
Plot the intercepts and join them to graph the line
using a graphing tool
see the attached figure
please wait a secon to draw the line
Given the function h described by h(x) = x + 2, find each of the following.h(0)=h(-7)=h( - 13)=h(10) =h(d + 4)=
Given the function h described by h(x) = x + 2, find each of the following:
h(0) = 0 + 2 = 2
h(-7) = -7 + 2 = -5
h( -13) = -13 + 2 = -11
h (10) = 10 + 2 = 12
h (d + 4) = d + 4 + 2 = d + 2 + 6
The cost of custom-made cookies at a bakery is shown on the graph below, where x represents the number of cookies and y represents the total cost.
The equation of a line is given by:
[tex]y=mx+b[/tex]where m is the slope and b is the y intercept. From the graph we notice that b=1. To find the slope we need to use the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Using the first two points on the graph (0,1) and (1,3) we have that the slope is:
[tex]m=\frac{3-1}{1-0}=\frac{2}{1}=2[/tex]Plugging the values in the first equation we have that the equationwe are looking for is:
[tex]y=2x+1[/tex]Where can I find L2 and L3 for a missing corresponding angles?
Answer:
Explanation:
Given:
<1=123.9°
<3=56.1°
Based on the given figure, the angles formed a straight line (Ex. <3 and <4). Angles on a straight line add up to 180°. So,
For <3 and <4:
We plug in what we know.
[tex]\begin{gathered} \angle3+\angle4=180 \\ 56.1+\angle4=180_{} \\ \text{Simplify and rearrange} \\ \angle4=180-56.1 \\ \angle4=123.9 \end{gathered}[/tex]For <2 and <1:
We plug in what we know.
[tex]\begin{gathered} \angle2+\angle1=180 \\ \angle2+123.9=180 \\ \angle2=180-123.9 \\ \angle2=56.1 \end{gathered}[/tex]Therefore, <2 = 56.1° while <4= 123.9°.
What is the factored form of this expression?x^3 + 27(32 – 3) (3 + 35 + 9)(1 + 3) (12 - 35 + 9)(2 + 3) (1 - 3.5 + 9)(t – 3)(x2 + 3r + 9
We have the following:
[tex]\begin{gathered} x^3+27 \\ x^3+3^3 \end{gathered}[/tex]now,
[tex]x^3+y^3=\mleft(x+y\mright)\mleft(x^2-xy+y^2\mright)[/tex]replacing:
[tex]x^3+3^3=\mleft(x+3\mright)\mleft(x^2-3x+9\mright)[/tex]The answer is the secondo option
members of the starting basketball team weigh 235,210,215,264,and 200 pounds. what is the average weight of starting team.
Consider that the average of any discrete data is defined as,
[tex]\text{Average}=\frac{\text{ Sum of Observations}}{\text{ Number of Observations}}[/tex]Here the data is the weight (in pounds) of the starting basketball team members,
[tex]235,210,215,264,200[/tex]So the corresponding mean wieght of a team member is calculated as,
[tex]\begin{gathered} \text{Average}=\frac{235+210+215+264+200}{5} \\ \text{Average}=\frac{1124}{5} \\ \text{Average}=224.8 \end{gathered}[/tex]Thus, the average weight of starting team member is 224.8 pounds.
Mama Gianaras pizza comes in two sizes, medium and large. The radius of a medium pizza is 8'' and the large is a 10''. what is the ratio of the circumferences? state answer as a fraction.
Explanation
[tex]\begin{gathered} C_m=2\pi *8 \\ C_l=2\pi *10 \end{gathered}[/tex][tex]\frac{C_m}{C_l}=\frac{2\pi *8}{2\pi *10}=\frac{8}{10}=\frac{4}{5}[/tex]Answer
4/5
On a hot day, Gabrielle poured 1/8 of a bucket of water into a plastic wading pool. A few minutes later she added another 1/2 of a bucket. How much water did Gabrielle pour into the pool?
5/8 of a bucket of water
Explanation:Initial amount poured = 1/8 bucket of water
An addition of 1/2 bucket into the the pool
Total amount of water in the pool = 1/8 bucket of water + 1/2 bucket of water
[tex]\begin{gathered} \frac{1}{8}+\frac{1}{2},\text{ }LCM\text{ = 8} \\ \frac{1(1)\text{ +4(1)}}{8} \end{gathered}[/tex][tex]=\frac{1+4}{8}=\text{ 5/8}[/tex]Total water in the pool is 5/8 of a bucket of water
As smart phones have grown in popularity, regular cell phones have fallen out of favor. As a result, one electronics retailer estimates that 17% fewer regular cell phones will be sold every year. If the retailer sells 162,147 regular cell phones this year, how many will be sold 10 years from now?If necessary, round your answer to the nearest whole number.
Initially, the retailer sells 162,147 regular cell phones
The retailer stimates, that every year sales will fall a 17%
meaning that after one year, sales will be:
162,147 * (1-0.17) = 134582.01
then, after 2 years, sales will be:
134582.01 * (1-0.17) = 111703.0683
which is the same as
[tex]162147\mleft(1-0.17\mright)^2=111703.0683[/tex]in that way, we can create the following formula:
[tex]162147\cdot(1-0.17)^y[/tex]where y is time in years,
now, if we replace y = 10 we can obtain the solution we are looking for
[tex]162147\cdot(1-0.17)^{10}=25158.795[/tex]rounding to the nearest whole number: 25,159
Angles X and Y are supplementary. Angle X measures 121.75° and angle Y measures (m − 9)°. Find m∠Y. 125.5° 58.25° 116.5° 67.25°
By the concept of supplementary angles the value of y = 58.25°. That is option C.
What are supplementary angles?Angles that add up to 180 degrees are referred to as supplemental angles. For instance, angle 130° and angle 50° are supplementary angles since the sum of these two angles is 180°. Supplementary angles are two angles that add up to 18 0 180 circ 180. They frequently occur when they are on the same side of a straight line, for example. When two angles sum up to 180 degrees, they are complementary (a Straight Angle). They don't even have to be close to one another for the total to be 180 degrees. Examples: The additional angles of 40° and 140°. Supplementary angles are a pair of angles that always add up to 180 degrees. These two perspectives are referred to as complements of one another.
∠X + ∠Y = 180°
∠Y = 180° - 121.75°
∠Y = 58.25°
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Answer: the answer is B
Step-by-step explanation: i took the test and got it right
a. Determine whether the function relating the year to the number of viewers is linear or nonlinear for each show. b. Which show has more viewers in its sixth year? Show A or Show B?
Notice that:
1.- The number of viewers in millions of show A can be computed using the following expression
[tex]7(0.9)^t,[/tex]which is not a linear equation.
2.- The number of viewers of show B can be computed using the following expression:
[tex]5,000,000-(200,000t),[/tex]which is a linear expression.
Now, after 6 years, show A will have:
[tex]7(0.9)^6=3.72[/tex]millions of viewers and show B will have
[tex]5,000,000-200,000(6)=3,800,000[/tex]viewers.
Answer:
The function for Show A is nonlinear.
The function for Show B is linear.
Show B will have more viewers.
what is 4/6 divided by 3/12 the qotient is..........
Answer:
2 2/3
Explanation:
If 4/6 is divided by 3/12, we write the mathematical expression as:
[tex]\frac{4}{6}\div\frac{3}{12}[/tex]To obtain the quotient, we follow the steps below:
Step 1: Change the division sign to multiplication and take the inverse of the fraction after the division sign.
[tex]\frac{4}{6}\times\frac{12}{3}[/tex]Step 2: Reduce the terms where possible.
[tex]\begin{gathered} =\frac{4}{1}\times\frac{2}{3} \\ =\frac{8}{3} \\ =2\frac{2}{3} \end{gathered}[/tex]The quotient is 2 2/3.
the boiling point at atmospheric pressure of Ammonia is -28 1/10 °F and of propylene is -5÷ 9/10 °F. what is the difference In their boiling points?
The difference between the boiling points is the subtraction between them. The two boiling points are given in mixed fractions, to subtract them we need to subtract the integer part and the fractional part separately. With this in mind let's solve the problem:
[tex]\begin{gathered} -28\frac{1}{10}-(-53\frac{1}{10}) \\ -28\frac{9}{10}+53\frac{1}{10} \\ 25\frac{8}{10} \\ 25\frac{4}{5} \end{gathered}[/tex]The correct answer is the option "B".
On a map, the distance from Falls City, Texas to Pleasanton, Texas measure 2 centimeters. What is the actual distance if the scale on the map shows that 1 centimeter is equal to 30 kilometers?
1 cm --------------------- 30 km
2 cm -------------------- x
x = (2 x 30) / 1
x = 60 / 1
x = 60
Result: the distance between these cities is 60 km.
Given the graph of the function f(x), find x when f(x) =4
x = -1
Explanations:Note:
f(x) is the vertical axis of the graph
x is the horizontal axis of the graph
To get the value of x when f(x) = 4:
Locate the point on the graph that is on the "4" on the vertical axis and trace it downwards to get the value of x.
If that is done, we would observe that x = -1 when f(x) = 4
What is the range of the given function?{(-2, 0), (-4,-3), (2, -9), (0, 5), (-5, 7)}Ox|x=-5, -4, -2, 0, 2)O lyly = -9, -3, 0, 5, 7)Oxx-9, -5, -4, -3, -2, 0, 2, 5, 7)O lyly = -9, -5, -4, -3, -2, 0, 2, 5, 7)
The range of the function is the values of y-coordinates of the ordered pairs
Since the function is
[tex]\lbrace(-2,0),(-4,-3),(2,-9),(0,5),(-5,7)\rbrace[/tex]Then the values of y-coordinates are
[tex]\lbrace0,-3,-9,5,7\rbrace[/tex]Then the range should be
[tex]\lbrace y:y=-9,-3,0,5,7\rbrace[/tex]The 3rd choice
Draw the dilation of ABC using center P and a scale factor of 1/3. Draw the dilation of ABC using center A and a scale factor of 2. Explain how they are similar. 3
Both triangles are similar; while the first is a reduction, the second is an enlargement.
Let's begin by listing out the information given to us:
A(5,6), B(5,10), C(8,3)
A scale factor of 1 / 3 means the triangle will be smaller (reduction):
[tex]$$\begin{gathered}P=(2,3) \\A B=4 \Rightarrow A^{\prime} B^{\prime}=\frac{4}{3} \\B C=\sqrt{58} \Rightarrow B^{\prime} C^{\prime}=\frac{\sqrt{58}}{3} \\A C=\sqrt{18} \Rightarrow A^{\prime} C^{\prime}=\frac{\sqrt{18}}{3}=\sqrt{6}\end{gathered}$$[/tex]
A scale factor of 2 means the triangle will be bigger (enlargement):
[tex]$$\begin{gathered}A^{\prime \prime}=2 A=2(5,6)=(10,12) \\B^{\prime \prime}=2 B=2(5,10)=(10,20) \\C^{\prime \prime}=2 C=2(8,3)=(16,6)\end{gathered}$$[/tex]
Both triangles are similar; while the first is a reduction, the second is an enlargement
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hello I'm in the 7th grade and i need help with these word problems are you able to help and explain it to me so I can understand .. the title is called word Ratios
a) 12 goats ate 3 pizzas. To find goat per pizza, dividing the number of goats by the number of pizzas:
[tex]\frac{12\text{ goats}}{3\text{ pizzas}}=4\text{ }\frac{goat}{pizza}[/tex]b) 20 banks are robbed for a total of $50,000. To find the money per bank, divide the total money by the number of banks.
[tex]\frac{50,000}{20}=2500\text{ }\frac{\text{\$}}{bank}[/tex]c) In 86 years, 9 drops have formed. To find years per drop, divide the years by the number of drops.
[tex]\begin{gathered} \frac{86\text{ years}}{9\text{ drops}} \\ 9.6\text{ }\frac{years}{drop} \end{gathered}[/tex]d) 3 hippos eat 5 pumpkins
To find the number of pumpkins per hippo, divide 5 by 3.
[tex]\begin{gathered} \frac{5\text{ pumpkins}}{3\text{ hippos}}=1.7\text{ }\frac{pumpkins}{hippos} \\ \end{gathered}[/tex]how many square inches, 1 in. by 1 in., fit in an area if 1 square foot, 1 ft by 1 ft?
We have the following:
We must convert square feet to square inches
We have that 1 foot is equal to 12 inches
[tex]1ft^2\cdot\frac{(12in)^2}{(1ft)^2}=144in^2[/tex]Which means that one square foot equals 144 square inches.
Cost for assembling a smart phone is given in formula C(q) = 500 - 2q. Where C is cost, and q is cost for parts. If cost for parts equal $75, find total cost to assemble 1500 smart phones.
The total cost to assemble 1, 500 smart phones, given the cost formula, can be found to be $525,000
How to find the cost of the smart phones?The total cost of a smart phone is found by the formula, C(q) = 500 - 2q.
Here q is the cost of parts which is 75.
The assembly cost of a single phone is therefore:
= 500 - 2(75)
= 500 - 150
= $350
If there are 1, 500 smart phones, the total cost would be:
= 350 x 1, 500
= $525,000
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What congruence rule does the triangle follow? Please write the congruence statement triangle EFH is congruent to ________?
We can see here two triangles, and we can notice the following:
1. Since H is the midpoint of the segment EG, we can say that EH and HG are congruent segments.
2. Since these two triangles, namely, EFH and GFH share the same segment (HF), this side is also congruent to these two triangles.
3. Since EH is congruent to HG, and FH is congruent to itself, then EF is congruent to GF.
4. Angle E is congruent to angle G.
Therefore, we can say that:
Since we have that:
a. EF is congruent to GF
b. EH is congruent to GH
c. Angle E is congruent to angle G
We can conclude that the congruence rule, in this case, is SAS (Side-Angle-Side), because if two sides and the included angle are congruent to the corresponding parts of the other triangle, the triangles are congruent.
We also see that the three sides are congruent (and in this case, we can also conclude that the triangles are congruent by the rule SSS (side-side-side).
Likewise, we can also conclude that the triangle EFH is congruent to triangle GFH.
Which expression has a coefficient of 6? A. 2x + 6 B. 3x - 6 C. 2(x + 6) D. 6x + 3
A coefficient is a number that is multiplied by the variable.
From the given options, the variable is x, and the option that has the coefficient 6 is option D. 6x+3.
Since the number multiplied by the variable x is 6 in option D.
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph.
we have
f(x)=2x^4-4x^2
REmember that
The Leading Coefficient Test is the test which enables you to discover thebehavior of the graph in terms of rising and falling. This test utilizes the leading coefficientand whether the degree is odd or even to determine the behavior of the curves. The test goes as follows:
In this problem the leading coefficient is positive and even
sothe graph rises to the left and rises to the right.Hello, please I need urgent help with this math question
Given:
[tex]\sqrt[]{\frac{96}{8}}[/tex]Expand:
[tex]\sqrt[]{\frac{2^5\cdot3}{2^3}}[/tex]Simplify:
[tex]\sqrt[]{2^2\cdot3}[/tex][tex]=2\sqrt[]{3}[/tex]Therefore, the answer would be D. 2√3.
Mrs. Roberts bought 4 student movietickets and one adult ticket that cost $12.Write an expression to represent the totacost of the tickets. Let s represent eachstudent ticket
Total cost = 4s+12
student's ticket price = s
Number of students tickets= 4
Adult's tickets price = $12
Number of Adult's tickets = 1
Total cost = (number of students tickets x price of each student's ticket) + ( number of adult tickets x price of each adult ticket)
Total cost of the tickets (y)= 4s + 1(12)
y = 4s+12
in the following geometric sequence, find (i) the 7th term; (ii) the nth term:-1/3, 3/4, -9/8, .....
Given the geometric sequence:
[tex]-\frac{1}{2},\frac{3}{4},\frac{-9}{8},\ldots.[/tex]The common ratio will be:
[tex]r=\frac{3}{4}\div-\frac{1}{2}=\frac{3}{4}\cdot-2=-\frac{3}{2}[/tex]The general rule of the geometric sequence will be:
[tex]a_n=a_1\cdot r^{n-1}[/tex]so, a7 will be:
[tex]a_7=-\frac{1}{2}\cdot(-\frac{3}{2})^{7-1}=-\frac{1}{2}\cdot(-\frac{3}{2})^6=-\frac{729}{128}[/tex]And an will be:
[tex]a_n=(-\frac{1}{2})\cdot(-\frac{3}{2})^{n-1}_{}[/tex]what is the absolute value of -435 and 72
The absolute value of 72 is the distance between 72 and 0 on a number line.
There will be 72 point on the number line if we count. So,
Whats the correct answer answer asap
Answer:
the answer is c- best known mass