g(x) = x² + 2
h(x) = 3x - 2
Find g(a+3)
_____________________
Find
g(a+3)
g(x) = x² + 2
g(a+3) = (a+3)^2 +2
g(a+3) = (a+3)(a+3) +2
g(a+3) = a^2 +3a +3a+3*3 +2
g(a+3) = a^2 +6a +11
if each pair of flip flop coast c dollars which statment is true
The direct of arrow shows the direction less than 25
A) The speed limit downtown is 25 miles per hour
The statement is wrong beacuse the figure show the less than to 25 not equal to 25
B) The weight limit for the bridge is less than 25
The statement is correct
C) A child must be taller than 25inche
The statement is wrong beacuse the figure show the less than to 25 not greater than 25
D) A citizens must be 25 years old to run for congree
The statement is wrong because beacuse the figure show the less than to 25 not more than 25
Answer: B) The weight limit for the bridge is less than 25
Let event A = You make the first shot.Let event B = You make the second shot.What does P(BA) represent?A. The probability that you make the first shot, given that you makethe second shotB. The probability that you don't make the second shotC. The probability that you make either the first or the second shotD. The probability that you make the second shot, given that youmake the first shot
Given:
Event A = You make the first shot
Event B = You make the second shot
Let's determine what P(B|A) represents.
The probability that event B occurs given that event A has already occured is the conditional probability of event B.
This is represented by: P(B|A).
P(B|A) can be said to be the conditional probability that you make the second shot, given that you make the first shot.
Therefore, P(B|A) represents the probability that you make the second shot, diven that you make the first shot.
ANSWER:
D. The probability that you make the second shot, given that you make the first shot.
Find the area of the SIM circle round the to the nearest 10th used 3.144 pi do not include units with your answer 12 in
r = 12 units
[tex]\begin{gathered} \text{area}=\frac{1}{2}\times3.14\times12^2 \\ \text{area}=\frac{1}{2}\times3.14\times144 \\ \text{area}=\frac{452.16}{2}=226.08 \\ \text{area}=226.1 \end{gathered}[/tex]
A web music store offers two versions of apopular song. The size of the standardversion is 2.1 megabytes (MB). The size of thehigh quality version is 4.7 MB. Yesterday, thehigh quality version was downloaded twice asoften as the standard version. The total sizedownloaded for the two versions was 3335MB. How many downloads of the standardversion were there?Number of standard version downloads:?
Answer:
Number of standard version downloads: 290
Explanation:
• Let the number of downloads for the standard version(2.1MB) = s
Given that the high-quality version was downloaded twice as often as the standard version, then:
• The number of downloads for the high-quality version, (4.7MB) = 2s
The total size downloaded for the two versions was 3335MB.
[tex]\implies2.1s+2(4.7)s=3335[/tex]The equation above is then solved for s.
[tex]\begin{gathered} 2.1s+9.4s=3335 \\ 11.5s=3335 \\ s=\frac{3335}{11.5} \\ s=290 \end{gathered}[/tex]There were 290 downloads of the standard version.
I need help with this problem
Answer: x = 4
We are given two similar triangles
CB = XP
AB = RP
CB = 8
XP = 12
AB = 6
RP = 2x + 1
Using similarity triangle theorem
[tex]\begin{gathered} \frac{CB}{XP}\text{ = }\frac{AB}{RP} \\ \frac{8}{12}\text{ = }\frac{6}{2x\text{ + 1}} \\ \text{Collect the like terms} \\ 12\text{ x 6 = 8(2x + 1)} \\ \text{Open the parenthesis} \\ 72\text{ = 16x + 8} \\ 16x\text{ = 72 - 8} \\ 16x\text{ = 64} \\ \text{Divide both sides by 16} \\ \frac{16x}{16}\text{ = }\frac{64}{16} \\ x\text{ = 4} \end{gathered}[/tex]what is the value of r?
Answer:
168°
Step-by-step explanation:
The angels across from each other are vertical angles and vertical angles are congruent
r - 86 = 82 Add 86 to both sides
r = 168
find the distance between-8 1/3 and -5 1/2 write your answer as a fraction or mixed number
The given numbers are
[tex]-8\frac{1}{3},-5\frac{1}{2}[/tex]To find the distance between, we must subtract them. However, first, we need to transform each number into a normal fraction
[tex]-8\frac{1}{3}=\frac{8\cdot3+1}{3}=-\frac{24+1}{3}=-\frac{25}{3}[/tex]Using the same process, we have
[tex]-5\frac{1}{2}=-\frac{5\cdot2+1}{2}=-\frac{10+1}{2}=-\frac{11}{2}[/tex]Now, we subtract those fractions
[tex]-\frac{11}{2}-(-\frac{25}{3})=-\frac{11}{2}+\frac{25}{3}=\frac{-33+50}{6}=\frac{17}{6}[/tex]However, we need the result as a mixed number
[tex]\frac{17}{6}=2\frac{5}{6}[/tex]Therefore, the distance is 2 5/6.3. Write a quadratic equation such thatthe sum of its roots is -4 and theproduct of its roots is 24.
In a quadratic equation such as:
[tex]ax^2+bx+c=0[/tex]We can see that its roots are independent from the coefficient a, because:
[tex]\begin{gathered} ax^2+bx+c=0 \\ x^2+\frac{b}{a}x+\frac{c}{a}=0 \\ x^2+Bx+C=0 \end{gathered}[/tex]Another thing we know if that we can rewrite an quadratic equation using its roots by:
[tex]a(x-r_1)(x-r_2)[/tex]Which makes the linear coefficient B the same as the negative of the sum of the roots and the coefficien C the same as the product of the roots:
[tex]\begin{gathered} a(x-r_1)(x-r_2)=a(x^2-(r_1+r_2)x+r_1r_2)=a(x^2+Bx+C) \\ B=-(r_1+r_2) \\ C=r_1r_2 \end{gathered}[/tex]Thus, since we can choose the value of a, lets use a = 1 to make it simpler.
This makes:sum
[tex]\begin{gathered} B=-(r_1+r_2)=-(-4)=4 \\ C=r_1r_2=24 \end{gathered}[/tex]And the quadratic equations becomes:
[tex]x^2+4x+24=0[/tex]1. Each person in a large group of children with cell phones was asked, "How old were you when you first received acell phone?The responses are summarized in the table below.Age In YearsProbability0.030.0610111213141516170.110.230.230.1400110.080.01a.bMake a graph of the probability distributionThe bar centered at 12 in your graph represents the probability that a randomly selected person in this groupfirst received a cell phone at age 12. What is the area of the bar representing age 127 How does this compareto the probability corresponding to 12 in the table?What do you think the sum of the areas of all of the bars will be? Explain your reasoningWhat is the probability that a randomly selected person from this group first received a cell phone at age 12 or13?Is the probability that a randomly selected person from this group first received a cell phone at an age olderthan 15 greater than or less than the probability that a randomly selected person from this group first receiveda cell phone at an age younger than 12?d.e
Answers:
a. Graph
b. Area = 0.23
c. Sum = 1
d. P = 0.46
e. The probability that a person first received a cellphone at an age older than 15 is less than the probability that a person first received a cellphone at an age younger than 12.
Explanation:
a. To make the graph of a probability distribution, we will make a bar graph where the x-axis is the age and the y-axis is the probability. So, the graph is:
b. If each bar has a width of 1 unit and a height equal to the probability, the area of the bar centered at 12 will be equal to:
Area = Width x Height
Area = 1 x 0.23
Area = 0.23
So, the area of the bar is equal to the probability that a child first receives a cellphone at age 12.
c. Since the area of each bar is equal to the respective probability, we get that the sum of the area of all bars should be equal to 1. In fact:
0.03 + 0.05 + 0.11 + 0.23 + 0.23 + 0.14 + 0.11 + 0.08 + 0.01 = 1
d. To know this probability, we need to add the probability that a person first received a cellphone at age 12 and the probability that a person first received a cellphone at age 13. So, the answer for this part will be:
P = P( Age 12) + P(Age 13)
P = 0.23 + 0.23
P = 0.46
e. The probability that a person first received a cellphone at an age older than 15 is equal to:
P(older than 15) = P(Age 16) + P(Age 17)
P(older than 15) = 0.08 + 0.01
P(older than 15) = 0.09
In the same way, the probability that a person first received a cellphone at an age younger than 12 is:
P(younger than 12) = P(Age 9) + P(Age 10) + P(Age 11)
P(younger than 12) = 0.03 + 0.06 + 0.11
P(younger than 12) = 0.2
Since 0.09 is lower than 0.2, we get that the probability that a person first received a cellphone at an age older than 15 is less than the probability that a person first received a cellphone at an age younger than 12.
Therefore, the answers are:
a. Graph
b. Area = 0.23
c. Sum = 1
d. P = 0.46
e. The probability that a person first received a cellphone at an age older than 15 is less than the probability that a person first received a cellphone at an age younger than 12.
An aquarium can be modeled as a right rectangular prism and it can hold 882 cubicinches of water when it is full. Its width is 7 in and height is 7 in. Find the length ofthe aquarium in inches. Round your answer to the nearest tenth if necessary.
Given: The dimension of an acquuarium modelled as a right rectangular prism as below
[tex]\begin{gathered} Volume=882in^3 \\ width(w)=7in \\ height(h)=7in \end{gathered}[/tex]To Determine: The length of the acquarium
Solution
The volume of a rectangular prism can be calculated using the formula below
[tex]Volume(rectangular-prism)=length\times width\times height[/tex]Let us substitute the given dimension into the formula above to calculate the length
[tex]\begin{gathered} 882in^3=l\times7in\times7in \\ 882in^3=l\times49in^2 \\ l=\frac{882in^3}{49in^2} \\ l=18in \end{gathered}[/tex]Hence, the length of the 18 inches
2. Cathy baked some cookies. She used 2 cups of chocolate chips, 1 cup of peanut butter chips, and 1 cup of butterscotch chips. How many cups of chips did she use in all?
She use 2 cups of chocolate, 1 cup pf penuts, 1 cup of butter chips and 1 cup of butterscotch, so she made in total:
[tex]2+1+1+1=5[/tex]She made 5 cups
Q3. Find the height of the top of the tower (labelled x) given the following scenario:I’m confused on how I should do it
The Solution:
Given the diagram below:
Considering right-angled triangle ABC,
we can apply the Trigonometrical Ratio as below:
[tex]\begin{gathered} \tan 25^o=\frac{y}{87} \\ \text{Cross multiplying, we get} \\ y=87\tan 25^o\ldots eqn(1) \end{gathered}[/tex]Similarly, considering right-angled triangle ABD,
we can apply the Trigonometrical Ratio as below:
[tex]\begin{gathered} \tan 40^o=\frac{x+y}{87} \\ \text{Cross multiplying, we get} \\ x+y=87\tan 40^o\ldots eqn(2) \end{gathered}[/tex]Now, putting eqn(1) into eqn(2), we get
[tex]x+87\tan 25^o=87\tan 40^o[/tex]Solving for x, we have
[tex]\begin{gathered} x=87\tan 40^o-87\tan 25^o \\ x=87(\tan 40^o-\tan 25^o) \end{gathered}[/tex][tex]x=87(0.8390996-0.4663077)=87\times0.37279=32.4329\approx32.43\text{ feet}[/tex]Therefore, the correct answer is 32.43 feet.
= GEOMETRY Area of a triangle Find the area of the triangle below. Be sure to include the correct unit in your answer. Explanation Check 7 cm 24 cm 25 cm 0 cm X cm² cm³ Ś ? ©2022 McGraw HilLLLS Oll Rights Rogon
We can use the base and the height of the right triangle as the two sides, to get the following area:
[tex]A=\frac{7*24}{2}=84[/tex]therefore, the area of the triangle is 84cm²
mario sketched a drawing of a dirt bike track he wants his dad to build. the brown area represents the track. Find the area of the track. round to the nearest tenth
brown area is the shaded area?
step 1
Find the area of the interior circle
[tex]A=\pi\cdot r^2[/tex]we have
r=20 ft
substitute
[tex]\begin{gathered} A=\pi\cdot20^2 \\ A=400\pi\text{ ft2} \end{gathered}[/tex]step 2
Find the area of the complete circle
r=35 ft
[tex]\begin{gathered} A=\pi\cdot35^2 \\ A=1,225\pi\text{ ft2} \end{gathered}[/tex]step 3
the shaded area is equal to the difference
[tex]\begin{gathered} A=1,225\pi-400\pi \\ A=825\pi\text{ ft2} \end{gathered}[/tex]assume pi=3.14
A=3.14*825=2,590.5 ft2
area is 2,590.5 square foot
C= 5\9 (F-32), determined C when F =77.
The formula for converting Celsius to Fahrenheit is expressed as
C = 5\9 (F-32)
If F = 77, it means that
C = 5/9(77 - 32)
C = 5/9 * 45
C = 5 * 5
C = 25
i need help with number 10. I have questions about the extreme and end behavior and symmetry
Answers:
Symmetry: about the origin
Extrema: No
End behavior: as x --> ∞, f(x) --> ∞ and as x --> -∞, f(x) --> -∞
Explanation:
The graph for f(x) = x³ is
Then, we can see that the graph is symmetric over the origin becuase
f(-x) = -f(x)
(-x)³ = -(x³)
-x³ = -x³
On the other hand, it doesn't have an extreme value, there are no maximum or minimum points in a given interval.
Finally, we can see that when x increases, f(x) increases, and when x decreases f(x) decreases. So, the end behavior is
as x --> ∞, f(x) --> ∞
as x --> -∞, f(x) --> -∞
The answers in blank boxes are either 1. The x intercept 2.The P intercept 3. The X coordinate of the the vertex4. The P coordinate of the vertex
Answer:
a) The startup cost of the company is the value of P when x equals zero.
Which is the P intercept on the graph.
[tex]\text{The P intercept}[/tex]b) The number of items they have to sell to break even is the value of x when the profit P equals zero.
This is the x-intercept on the graph.
[tex]\text{The x intercept}[/tex]c) The number of products they need to sell to maximize profit is the value of x at the maximum point on the graph.
This is the x coordinate of the vertex
[tex]\text{ The x coordinate of the vertex}[/tex]Explanation:
Given the revenue equation of the product;
[tex]P(x)=-2x^2+950x-14000[/tex]Graphing the equation.
a) The startup cost of the company is the value of P when x equals zero.
Which is the P intercept on the graph.
[tex]\text{The P intercept}[/tex]b) The number of items they have to sell to break even is the value of x when the profit P equals zero.
This is the x-intercept on the graph.
[tex]\text{The x intercept}[/tex]c) The number of products they need to sell to maximize profit is the value of x at the maximum point on the graph.
This is the x coordinate of the vertex
[tex]\text{ The x coordinate of the vertex}[/tex]May you please and give me the answer, im been stuck on it for 1 1/2 hours
Lets draw a picture of the problem:
The magnitude of the sum will the the magnitude of the red vector. Since we have a right triangle, we can apply Pytagorean theorem, that is,
[tex]\begin{gathered} c^2=2^2+4^2 \\ c^2=4+16 \\ c^2=20 \end{gathered}[/tex]Then, by applying square root to both sides, we have
[tex]\begin{gathered} c=\sqrt[]{20} \\ c=\sqrt[]{4\times5} \\ c=\sqrt[]{4}\times\sqrt[]{5} \end{gathered}[/tex]Therefore, the answer is
[tex]c=2\sqrt[]{5}[/tex]which correspondst to option 3 from left to right.
I need some help, having two units of ft and two angles is giving me some difficulty with knowing how to apply the trig identities
We will start from the top
We have a small right triangle with an angle of measure 30 degrees
and hypotenuse of length 30 feet
We will use the sine ratio to find its horizontal side which is a part of d
[tex]\sin (30)=\frac{d1}{30}[/tex]By using cross multiplication
[tex]\begin{gathered} d1=30\sin (30) \\ d1=15 \end{gathered}[/tex]Now we will work on the triangle which has an angle of measure 75 degrees
and the length of its hypotenuse is 200 feet
We will use the cosine ratio because d is adjacent to the angle of 75
[tex]\cos (75)=\frac{d-d1}{200}[/tex]By using cross multiplication
[tex]d-15=200\cos (75)[/tex]Add 15 to both sides to find d
[tex]\begin{gathered} d=15+200\cos (75) \\ d=66.76380902 \end{gathered}[/tex]The distance d = 66.76 feet
Graph the function given:A) g(x) = 2x -3
Given:
[tex]g(x)=2x-3[/tex]When x=-2
[tex]\begin{gathered} g(-2)=2(-2)-3 \\ g(-2)=-4-3 \\ g(-2)=-7 \end{gathered}[/tex]When x=0
[tex]\begin{gathered} g(0)=2(0)-3 \\ g(0)=-\text{3} \end{gathered}[/tex]When x=2,
[tex]\begin{gathered} g(2)=2(2)-3 \\ g(2)=1 \end{gathered}[/tex]Plot the points (-2,-7),(0,-3) and (2,1).
hey so if 1 is 1.50$ then how much is 2=?
If 1 is $1.50, then 2 = $3.00
Here, we have a relationship between the number and the currency value b
Thus;
if 1 is $1.50
then
2 is $x
To get x , we have;
1 * $x = 2 * $1.50
$x = $3.00
If the system has only one solution, then the system of equations are ____________
ANSWER:
2nd option: independent
STEP-BY-STEP EXPLANATION:
We have that systems of equations can be classified by the number of solutions.
If a system has at least one solution, it is said to be consistent, and if that consistent system has exactly one solution, it is said to be independent.
Therefore: If the system has only one solution, then the system of equations are independent.
The correct answer is the 2nd option: independent
write the slope intercept form of the equation (3,-4) and (-2,-4)
We know that a line is defined by two points. In this case, we need to find the line equation in the following form:
[tex]y=mx+b[/tex]We need to find the slope, m, and the y-intercept, b. To achieve this, we can use the two-point form of the line:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Now, we need to label those two points as follows:
• (3, -4) ---> x1 = 3, y1 = -4.
,• (-2, -4) ---> x2 = -2, y2 = -4.
And we can substitute those values into the two-point form of the line:
[tex]y-(-4)=\frac{-4-(-4)}{-2-3}(x-3)[/tex]Solving the given operations:
[tex]y+4=\frac{-4+4}{-5}(x-3)\Rightarrow y+4=\frac{0}{-5}(x-3)\Rightarrow y+4=0\cdot(x-3)[/tex]Then
[tex]y+4=0\Rightarrow y=-4[/tex]If we need to write the equation in the slope-intercept form, we have that m = 0, and b = -4, then, the equation will be:
[tex]y=0x+(-4)\Rightarrow y=0x-4[/tex]In summary, the slope-intercept form of the equation is equal to y = 0x - 4:
[tex]y=0x-4[/tex][We can notice that the line is parallel to the x-axis since the slope of the line is equal to 0, m = 0. The y-intercept (the point where the line passes through the y-axis) is equal to b = -4.]
A graph of the line is as follows:
Answer:
y = x + (-4)
Explanation:
slope intercept form=y=mx +b
slope of (3,-4) and (-2,-4) is 0
so the answer is y = x + (-4)
a rock is dropped in a vaccuum and has initial speed of 0 m/s. what is the rocks speed after 2 seconds?
The speed depends on the acceleration, but the acceleration in this case is practically null and constant, therefore the speed will not present any change.
Which means that atfer 2 seconds, the speed did not undergo any change.
Mrs. Dinson has 9 pencils on her desk. She has 3 pencils in a box. To find the number of pencils she has altogether, Mrs. Dinson writes 9 +3 = 12. What other addition fact could Mrs. Dinson use?
The sum of two equal addends will always yield the same result.
1) Considering that Mrs. Dinson has 9 pencils on her desk and 3 in a box, we can use the following addition fact:
The sum of two equal addends will always yield the same result.
That's why 9 +3 will always yield 12 as well as 3 + 9 =12
What is the difference of the fractions? Use the number line to help find the answer.1/5 - 3/4-1 -18 -16 -1420200620 20 20 2016 1820 201 x1920112011201920
We are asked to find the following difference of fractions
[tex]\frac{1}{5}-\frac{3}{4}[/tex]Let us first find the difference
[tex]\frac{1}{5}-\frac{3}{4}=\frac{4\cdot1-5\cdot3_{}}{20}=\frac{4-15}{20}=-\frac{11}{20}[/tex]So, the difference of the fractions is -11/20
Now let us identify the difference by using the given number line
Classify the following quantities as either discrete or continuous.temperature:number of passengers on a bus:number of Cheetos in a bag
temperature Continuous
number of passengers Discrete
number of Cheetos on a bag Discrete
Volume of a swimming pool Continuous
How do I get the answer to this? -42——- =-3
We have to solve the expression -42/(-3).
We can start by cancelling the negative signs:
[tex]\frac{-42}{-3}=\frac{42}{3}[/tex]We also know that 3 is a factor of 42: we can see that 14 times 3 is equal to 42, so 42/3 = 14:
[tex]\frac{-42}{-3}=\frac{42}{3}=14[/tex]Answer: 14
hi! i need to create a two column proof for reaching the answer:) the answer is XY=327ft
Statement Reason
0. XA = 500 ft Given
,1. AC = 500 ft Given
,2. BC = 327 ft Given
[tex]4.\angle BAC\cong\angle XAY\text{ }\ldots\ldots\ldots\ldots\ldots\text{Vertical angles}[/tex]5. A is the midpoint of XC XA = AC
[tex]6.\angle BCA\cong\angle YXA\ldots\ldots\ldots\ldots\ldots\ldots\ldots.\ldots.\text{ Alternate interior angles}[/tex][tex]7.\Delta\text{BAC}\cong\Delta YAX\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots.\text{ ASA}[/tex][tex]8.XY\cong BC\ldots\ldots\ldots\ldots\ldots\ldots\ldots....\ldots\ldots\ldots\ldots\ldots\Delta\text{BAC}\cong\Delta YAX[/tex][tex]9.XY=BC\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots..\ldots\ldots\ldots.....\ldots\ldots XY\cong BC[/tex]10. XY = 327 ft XY = BC
What is an equation of the line that passes through the points (8,-4) and (6,-5)?Put your answer in fully reduced form.
The expression for the equation of the line with the given two coordinates
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Given pair of coordinates : (8,-4) & (6,-5)
Substitute the value and simplify
[tex]\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ \text{Substitute x}_1=8,x_2=6,y_1=(-4),y_2=(-5) \\ y-(-4)=\frac{-5-(-4)}{6-8}(x-8) \\ y+4=\frac{-5+4}{-2}(x-8) \\ y+4=\frac{1}{2}(x-8) \\ y=\frac{x}{2}-\frac{8}{2}-4 \\ y=\frac{x}{2}-4-4 \\ y=\frac{x}{2}-8 \\ 2y=x-16 \\ x-2y-16=0 \end{gathered}[/tex]Answer : Equation of line is : x-2y-16=0