We are given domain of the function: 1 ≤ x ≤ 5.
Range: 0 ≤ f(x) ≤ 15.
Also included order pairs (1,4) and (5,15).
First order pair has domain 1, and second order pair has domain 5.
Both are included in domain of the given function.
Also, first order pair has range 4, and second order pair has range 15.
Both are included in range of the given function.
Option C. (3,8) has domain 3 and range 8 within the function.
But if we see option D. (5,10) also withing the function but we already given (5,15), that is range for domain 5 is 15.
So only C option is correct option.Answer:
D for plato users
Step-by-step explanation:
What is the justification for each step in the solution of the equation?
23x−13=2(x+2) Given
2x−1=6(x+2)
2x−1=6x+12 Distributive Property
2x=6x+13
−4x=13 Addition or Subtraction Property of Equality
x=−134
For this case we have the following equation:
[tex]\frac{2}{3}x-\frac{1}{3}= 2 (x + 2)\\[/tex]
If we multiply both sides of the equation by 3 we get:
[tex]2x-1 = 6 (x + 2)[/tex] ---> Multiplication Property of Equality
Applying the distributive property we have:
[tex]2x-1 = 6x + 12[/tex] ---> Distributive Property
Adding 1 on both sides of equality we have:
[tex]2x-1 + 1 = 6x + 12 + 1\\[/tex]
[tex]2x = 6x + 13[/tex] ---> Addition Property of Equality
Subtracting [tex]6x[/tex] on both sides we have:
[tex]-6x + 2x = 6x-6x + 13\\[/tex]
[tex]-4x = 13[/tex] ---> Subtraction Property of Equality
Finally, dividing by -4 on both sides we have:
[tex]\frac{-4x}{-4}= \frac{13}{-4}\\[/tex]
[tex]x = -\frac{13}{4}[/tex]---> Division Property of Equality
Using the formula r=d/t, where d is the didtance in miles, r is the rate, and t is the time in hours,at which rate must you travel to cover 185 miles in 2.5 hours
The rate of speed would be 74 mph
Explain why a vertical line is said to have undefined slope or no slope.
Five cats each ate 1/4 cup of cat food. How much food did the five cats eat?
Answer: Five cats ate 1 and a quarter of cat food.
Step-by-step explanation
Given:-
Cat food ate by one cat = 1/4 cup
Cat food ate by five cats =[tex]5\times \frac{1}{4} \text{ [Multiplying both sides with 5 ]}\\\\=\frac{5}{4}=\frac{4+1}{4}=\frac{4}{4}+\frac{1}{4}=1+\frac{1}{4}[/tex]=1 and 1/4 cup.
Therefore cat food ate by five cats = 1 and a quarter of cup.[ here a quarter =1/4]
A toy jeep is 12 1/2 inches long while an actual Jeep measures 18 3/4 ft long what is the value of the ratio length of a toy Jeep to the length of a actual Jeep
The length of toy jeep = [tex]12 \frac{1}{2}[/tex]
= [tex]\frac{25}{2}[/tex] inches
The length of actual Jeep = [tex]18 \frac{3}{4}[/tex] feet
We have to find the ratio length of a toy jeep to the length of actual jeep.
Firstly, we will make the dimensions of the both the given lengths same.
As 1 foot = 12 inches
[tex]18 \frac{3}{4}[/tex] feet = [tex]18 \frac{3}{4} \times 12[/tex] inches
=[tex]\frac{75 \times 12}{4}[/tex]
= 225 inches
So, the ratio length of toy jeep to actual jeep
= [tex]\frac{25}{2} \div 225[/tex]
= [tex]\frac{25}{2} \times \frac{1}{225}[/tex]
= [tex]\frac{1}{18}[/tex]
= 1:18
So, the ratio length of a toy Jeep to the length of a actual Jeep is 1:18.
Length of toy jeep = [tex]12\frac{1}{2}=\frac{25}{2}[/tex] inches
Length of actual jeep = [tex]18\frac{3}{4}=\frac{75}{4}[/tex] feet
Now to find the ratio between the two, we must convert both of them in same units. So, lets convert the actual jeep length in feet to inches.
1 feet = 12 inches.
So, [tex]\frac{75}{4}[/tex] feet = [tex]\frac{75}{4}\times12=225[/tex] inches
Ratio of length of toy jeep to actual jeep will be =
[tex]\frac{\frac{25}{2}}{225}[/tex]
[tex]\frac{25}{2\times225}[/tex]
[tex]\frac{25}{450}[/tex] = [tex]\frac{5}{90}[/tex]
ratio is : [tex]\frac{1}{18}[/tex] or 1:18
what the value of tge expression 30+(6÷3)+(3+4)
Remember to follow PEMDAS (Parenthesis, Exponents (and roots), Multiplication, Division, Addition, Subtraction)
First, solve the parenthesis
30 + (6/3) + (3 + 4)
30 + 2 + 7
Next, simplify. Combine like terms
30 + 2 + 7 = 39
39 is your answer
~Rise Above the Ordinary
Hello there!
Hint⇒⇒⇒⇒⇒⇒ You had to used PEMDAS.
P-Parenthesis
E-Exponents
M-Multiply
D-Divide
A-Add
S-Subtract
Explanation:
↓↓↓↓↓↓↓↓↓↓↓↓↓
[tex]30+(6/3)+(3+4)[/tex]
First you had to calculate with parenthesis first.
[tex](6/3)=2[/tex]
[tex]30+2+(3+4)[/tex]
Then you can calculate with parenthesis again.
[tex](3+4)=7[/tex]
[tex]30+2+7[/tex]
You had to add and subtract from left to right.
[tex]30+2+7=39[/tex]
[tex]=39[/tex]
Answer⇒⇒⇒⇒39
Hope this helps!
Thank you for posting your question at here on Brainly.
Have a great day!
-Charlie
Hayley begins solving this problem by combining like terms. 3x + 5x = 10 Which problem begins the same way? A) 5x = 20 Eliminate B) 2(x + 5) = 20 C) x 4 = 30 D) 4x ? 2x = 10
Answer:
In a linear equation of one variable there are two terms terms containing variable and constant.
Variable means term containing x,y,z which act as variables. and constant means any rational number . In higher classes you can include real number also.
The given equation is 3x + 5x = 10
So, the solution out of four options is A) 5x = 20.
Here variable is on one side of equation and constant on other side.
But Option (D) looks absolutely correct if we replace ? by either + sign or Negative (-) sign.
Answer:
D. [tex]4x-2x=10[/tex]
Step-by-step explanation:
We have been give an equation [tex]3x+5x=10[/tex]. The equation is solved by combining like terms. We are asked to choose the equation that an be solved by combining the like terms.
Let us check our given choices one by one.
A. [tex]5x=20[/tex]
We can see that equation A will be solved by dividing 20 by 5, therefore, option A is not correct choice.
B. [tex]2(x+5)=20[/tex]
We can see that equation B will be solved by dividing 20 by 5 and then subtracting 5, therefore, option B is not correct choice.
C. [tex]\frac{x}{4}=20[/tex]
We can see that equation C will be solved by multiplying 20 by 4, therefore, option C is not correct choice.
D. [tex]4x-2x=10[/tex]
We can see that equation D will be solved by combining like terms, therefore, option D is correct choice.
Sarah received a gift in a rectangular box with a volume of 240 in3. If the base of the box was 20 in2, how tall was the box? A) 2 inches B) 10 inches C) 12 inches D) 15 inches
Answer:
12 inches
Step-by-step explanation:
volume = length * width * height
volume = (length * width) * height
volume = (area of base) * height
height = volume/(area of base)
height = (240 in^3)/(20 in^2) = 12 in
Answer the box was 12 in bc 20x240divided by 4 =12
helpppppppp? please thank you
The x values are the same for both green dots, so you are looking at a simplified version of the distance formula.
d = sqrt( (x2 - x1)^2 + (y2 - y1)^2 )
Since x1 = x2 = 5, the first set of brackets = (5 - 5) = 0
d = sqrt( y2 - y1)^2 )
d = y2 - y1
y2 = 5
y1 = - 1
d = 5 - - 1
d = 6 Answer
What is the perimeter of the triangle shown on the coordinate plane, to the nearest tenth of a unit? A.24.8 units B.27.8 units C.28.5 units D.30.9 units
The answer is B I hope I helped
Answer:
the answer is B.28.7 hope i helped you learn something new
Step-by-step explanatio
Which of the following is equivalent to 17g – 2g?
A.) (17 – 2) + g
B.) (17 – 2)g²
C.) (17 – 2) + g²
D.) (17 – 2)g
Hey there!!
Given equation :
17g - 2g
Let;s first look at something which is common in both the terms.
Yes, the alphabet which is common is the ' g '.
Now, let's apply distributive property.
... 17g - 2g
... g ( 17 - 2 )
Hence, the appropriate answer would be ' D '.
Hope my answer helps!
Joe rented a truck for ine day. There was a base fee of $15.99 and there was an additonal charge of 75 cents for each driven mile joe had to pay $183.24 when he returned the truck for how many miles did he drive the truck
PLZ help 20pts
Which graph represents the equation y=2/3x−2 ?
The slope-intercept form:
y = mx + b
m - slope
b - y-intercept
We have y = 2/3 x - 2
y-intercept = -2
Only the one graph has that y-intercept (look at the picture).
y = [tex]\frac{2}{3}x[/tex] - 2 means the line will intercept the y-axis at -2 and have a slope (rise over run) of 2 over 3.
Answer: C
The estimated insurance loss from a hurricane was $18.218.2 billion. This was $12.412.4 billion more than the loss from a tsunami three years later. What was the estimated insurance loss from the tsunami?
Answer:
If you are asking about the difference between the two, the difference is $5,805.80
Step-by-step explanation:
The question is in the attached. Thank yo
C Is your awnser! have a good day Pretty sure its C because theres only 1 line
a person who is entitled to social security benefits but is not receiving them would take his or her case to...
A: administrative court
B: Civil court
C: criminal on the state
D: It depends on the state
Answer:
A: administrative court.Step-by-step explanation:
An administrative court is specialize in administrative laws, its concern is mainly about public powers. Basically, the role of these type of courts is to ensure that officials are doing their job according to the law. Some of the issues that matters to an administrative courts are: taxation, dispensation of monetary benefits, environmental licenses, building inspection, child custody, immigration decisions, and more.
So, in this case we are talking about social security, someone is not receiving the benefits from it, so this means that a public institution is not working well, that's an administrative court jurisdiction, because it's in the public sector.
Find the system determinant of the given matrix. [2, 4] [3,-9]
[tex]\left[\begin{array}{ccc}2&4\\3&-9\end{array}\right]\\\\\det\left[\begin{array}{ccc}2&4\\3&-9\end{array}\right]=(2)(-9)-(4)(3)=-18-12=-30[/tex]
Answer:
-30 will be the determinant.
Step-by-step explanation:
We have to find the system determinant of the given matrix
[tex]\begin{bmatrix}2 & 4\\ 3 & -9\end{bmatrix}[/tex]
Determinant will be = 2(-9) - (4 × 3)
= -18 -12
= -30
Therefore, as per given options by you in the comments.
option A is the answer.
Which correctly describes the point of discontinuity of the function?
A real-valued univariate function f=f(x) has a jump discontinuity at a point [tex]x_0[/tex] in its domain provided that
[tex]\lim \limits_{x\to x_0^-}f(x)=A_1[/tex]
and
[tex]\lim \limits_{x\to x_0^+}f(x)=A_2[/tex]
both exist and that [tex]A_1\neq A_2.[/tex]
As you can see at x=-3,
[tex]\lim \limits_{x\to -3^-}f(x)=6,[/tex] [tex]\lim \limits_{x\to -3^+}f(x)=9[/tex] and [tex]6\neq 9.[/tex]
Therefore, there is a jump discontinuity at x=-3.
Answer: correct choice is A.
A cement bridge post is 24 inches square and 15 feet 9 inches in length. If the cement weighs 145 pounds per cubic foot, how much does one bridge post weigh? A. 9,280 pounds B. 9,222 pounds C. 9,135 pounds D. 8,700 pounds
Answer:
The answer is option (C), One cement bridge post weighs 9,135 pounds
Step-by-step explanation:
Step 1: Get the total volume of a cement bridge post
The cement bridge post is in the shape of a cuboid, therefor the volume of the cement bridge post can be expressed as;
Volume of cement bridge post=Base area×Length
where;
Base area=(24^2) inches square
1 foot=12 inches
Convert 24 inches to foot=24/12=2^2=4 feet²
Length=15 feet and 9 inches
1 foot=12 inches
Convert 9 inches to foot=9/12=0.75 feet
Total length=(15+0.75)=15.75 feet
replacing;
Volume of cement bridge post=(4×15.75)=63 cubic feet
Volume of cement bridge post=63 cubic feet
Step 2: Get the total weight of the cement bridge post
Total weight of the cement bridge post=Weight per cubic foot×total volume of the cement bridge post
where;
Weight per cubic foot=145 pounds per cubic foot
Total volume of the cement bridge post=63 cubic feet
replacing;
Total weight of the cement bridge post=(145×63)=9,135 pounds
One cement bridge post weighs 9,135 pounds
What steps would you take to construct an angle bisector? How many arcs would you make?
The steps are as follows:
1. Put the compass at one point on the vertex of the angle and draw an arc that intersects both sides of the angle.
2. Now, draw an arc from each of these points of intersection, in such a way that the arcs intersect in the interior of the angle. Keep the compass open in the same amount throughout this step.
3. Now, draw a ray/line from the vertex of the angle to the intersection point of the two arcs drawn during step 2.
How many arcs would you make? We will draw 3 arcs.
A bag of marbles contains 7 red, 5 blue, 4 red, and 2 yellow marbles. Jon selects a marble, replaces it, then selects another marble. What is the probability that Jon selects a red marble and then a yellow marble?
Question 2 options:
about 0.778 or 77.8%
0.5 or 50%
about 0.043 or 4.3%
0.25 or 25%
[tex]|\Omega|=18^2=324\\|A|=7\cdot2=14\\\\P(A)=\dfrac{14}{324}=\dfrac{7}{162}\approx0.043(=4.3\%)[/tex]
First, we find the total number of marbles.
We add up the red, blue, and yellow marbles:
The number of red marbles is 7 + 4 which equals to 11.
The number of blue marbles is 5.
The number of yellow marbles is 2.
To find the total number, we add these numbers together: 11 (red) + 5 (blue) + 2 (yellow) = 18. So, the total number of marbles is 18.
Second, we find the probability of each event - that is, picking a red marble and then a yellow marble.
Probability is the number of desired outcomes divided by the total number of possible outcomes.
The probability of picking a red marble, denoted as P(red) is the number of red marbles divided by the total number of marbles. So, P(red) = 11 / 18 which is about 0.611 or 61.1%.
The probability of picking a yellow marble, denoted as P(yellow) is the number of yellow marbles divided by the total number of marbles. So, P(yellow) = 2 / 18 which is about 0.111 or 11.1%.
Finally, we can find the answer to our question: What is the probability that Jon selects a red marble and then a yellow marble?
Because these are independent events (selecting a red marble does not affect the chance of selecting a yellow marble next), we can use the multiplication rule of probability to find the overall probability.
The multiplication rule states that the probability of two independent events both happening is the product of their individual probabilities. So the probability of picking a red marble and then a yellow marble, denoted as P(red and yellow), is P(red) * P(yellow).
P(red and yellow) = P(red) * P(yellow) = 0.611 * 0.111 which results in about 0.0679 or 6.8%.
So, the closest option is about 0.043 or 4.3% which seems to be incorrect as our calculated probability is different. There might be a mistake in the question or the provided options.
Graph x<2
please only answer if you know what your doing
This is the same concept as the previous question. The symbol (<) means it is a dashed line and shaded to the left.
Answer: B
if f(x)=2x and g(x)=1/x, what is the domain of (fg)(x)
Answer: all real #s except x=0
Step-by-step explanation:
Edge 2022
A party host is making identical party bags for guests using 44 bottles of bubbles, 89 stickers, and 55 pencils. What is the greatest number of identical party bags the host can make with the least amount of items leftover? Describe the contents of each bag.
Answer: 11 party bags with 1 sticker leftover
Each bag contains 4 bubbles, 8 stickers, and 5 pencils.
Step-by-step explanation:
Find the GCF of 44 (bubbles), 89 (stickers), and 55 (pencils)
44: 2 x 2 x 11
89: prime so choose 88 with 1 leftover
88: 2 x 2 x 2 x 11
55: 5 x 11
GCF = 11
Disregard the GCF to see how many of that item should go in each bag.
Bubbles: 2 x 2
Stickers: 2 x 2 x 2
Pencils: 5
△ABC is mapped to △A′B′C′ using the rule (x, y)→(−x, −y) followed by (x, y)→(x, −y) .
Which statement correctly describes the relationship between △ABC and △A′B′C′ ?
A. △ABC is congruent to △A′B′C′ because the rules represent a reflection followed by a rotation, which is a sequence of rigid motions.
B. △ABC is congruent to △A′B′C′ because the rules represent a rotation followed by a reflection, which is a sequence of rigid motions.
C. △ABC is not congruent to △A′B′C′ because the rules do not represent a sequence of rigid motions.
D. △ABC is congruent to △A′B′C′ because the rules represent a reflection followed by a reflection, which is a sequence of rigid motions.
Answer:
B. △ABC is congruent to △A′B′C′ because the rules represent a rotation followed by a reflection, which is a sequence of rigid motions.
Step-by-step explanation:
I just took the test, good luck! Have a wonderful day! :)
Transformation involves changing the position of a shape.
The correct statement is: (b) △ABC is congruent to △A′B′C′ because the rules represent a rotation followed by a reflection, which is a sequence of rigid motions.
The transformation rule is given as:
[tex]\mathbf{(x,y) \to (-x,-y)}[/tex], then:
[tex]\mathbf{(x,y) \to (x,-y)}[/tex]
The first transformation [tex]\mathbf{(x,y) \to (-x,-y)}[/tex] is 180 degrees rotation across the originThe second transformation [tex]\mathbf{(x,y) \to (x,-y)}[/tex] is a reflection across the x-axisRotation and reflection are both rigid transformation.
Hence, the correct option is (b):
Read more about rotation and reflection at:
https://brainly.com/question/15577335
Cristoble used synthetic division to divide the polynomial f(x) by x + 3, as shown on the table. What is the value of f(−3) ? −3 2 33 36 A synthetic division setup with respective columns containing the following numbers column 1 containing -3 as the divisor, column 2 containing 2, blank and 2, column 3 containing negative 5, negative 6, negative 11, and column 4 containing 3, 33, 36.There is a line above the numbers 2, negative 11 and 36.
Answer:
Remainder is 36.
Step-by-step explanation:
We are given that f(x) is divided by x+3 using synthetic division, and we are given with table attached in the image.
In synthetic division, first row represents the coefficients of dividend. From the given table, dividend is f(x)=[tex]2x^{2}-5x+3[/tex] and since f(x) is divided by x+3, divisor is -3.
First two numbers of last row represents coefficients of quotient and last most number of third row is remainder.
And we can write f(x) as (x+3)(2x-11)+36.
Hence remainder is 36 , when f(x) is divided by x+3.
Answer:
36
Step-by-step explanation:
this i believe is the settup u were describing
What is the value of x in the equation 3(2x + 4) = –6? (4 points)
–3
1
12
19
3.
The steps below show the incomplete solution to find the value of x for the equation
5x –2x –3 = –2 + 15:
Step 1: 5x –2x –3 = –2 + 15
Step 2: 5x –2x –3 = 13
Step 3: 3x –3 = 13
Which of these is most likely the next step? (4 points)
3x = 16
3x = 10
3x = 39
3x = 3
What are the values of m and n in the matrix addition below?
ANSWER
The correct answer is [tex]m=45,n=12[/tex].
EXPLANATION
We were given the matrix equation;
[tex]\left[\begin{array}{cc}n-1&6\\-19&m+3\end{array}\right] +\left[\begin{array}{cc}-1&0\\16&-8\end{array}\right] =\left[\begin{array}{cc}10&6\\-3&40\end{array}\right][/tex].
We must first simplify the Left Hand Side of the equation by adding corresponding entries.
[tex]\left[\begin{array}{cc}n-1+-1&6+0\\-19+16&m+3-8\end{array}\right]=\left[\begin{array}{cc}10&6\\-3&40\end{array}\right][/tex].
That is;
[tex]\left[\begin{array}{cc}n-2&6\\-3&m-5\end{array}\right]=\left[\begin{array}{cc}10&6\\-3&40\end{array}\right][/tex].
Since the two matrices are equal, their corresponding entries are also equal. we equate corresponding entries and solve for m and n.
This implies that;
[tex]n-2=10[/tex]
We got this equation from row one-column one entry of both matrices.
[tex]n=12[/tex]
Also, the row three-column three entries of both matrices will give us the equation;
[tex]m-5=40[/tex]
[tex]m=45[/tex]
Hence the correct answer is [tex]m=45,n=12[/tex].
The correct option is option 2
Sam initially invested $4,500 into a savings account that offers an interest rate of 3% each year. He wants to determine the number of years, t, for which the account will have less than or equal to $7,020.
Every year, Sam will have 103% of the amount from the previous year.
[tex]p\%=\dfrac{p}{100}\\\\103\%=\dfrac{103}{100}=1.03[/tex]
After the first year:
[tex]1.03\cdot\$4,500[/tex]
After the second year:
[tex]1.03\cdot1.03\cdot\$4,500=\$4,500(1.03)^2[/tex]
After the t-th year:
[tex]\$4,500(1.03)^t[/tex]
Therefore we have the inequality:
[tex]\$4,500(1.03)^t\leq\$7,020\ \ \ \ |\text{divide both sides by \$4,500}\\\\(1.03)^t\leq1.56\\\\(1.03)^{15}\approx15.56\\\\\text{therefore}\ t\leq15[/tex]
Answer: t ≤ 15.What is the equation of the following graph in vertex form?
Courtesy of Texas Instruments (2 points)
y = (x - 3)2 - 1
y = (x + 3)2 - 1
y = (x - 4)2 - 2
y = (x - 4)2 + 8
For this case we have:
The equation in vertex form of the parabola is given by:
[tex]y = a (x-h) ^ 2 + k\\[/tex]
The vertex is (h, k) and is given by the highest or lowest point of the parabola, in this case it is observed that it is [tex](h, k) = (- 3, -1)\\[/tex]
Thus, the equation is given by:
[tex]y = a (x - (- 3)) ^ 2 + (- 1)\\\\y = a (x + 3) ^ 2-1\\[/tex]
We look for the value of a, substituting a point of the parabola in the equation in the form of vertex, we will take the point [tex](x, y) = (0,8)\\[/tex]
Substituting we have:
[tex]8 = a (0 - (- 3)) ^ 2 + (- 1)\\\\8 = a (0 + 3) ^ 2-1\\\\8 = a (3) ^ 2-1\\[/tex]
[tex]8 = 9a-1\\\\8 + 1 = 9a\\\\9 = 9a\\[/tex]
[tex]a = \frac{9}{9}\\\\a = 1\\[/tex]
Thus, the equation of the parabola is given by:
[tex]y = (x + 3) ^ 2-1\\[/tex]
Answer:
[tex]y = (x + 3) ^ 2-1[/tex]
Answer:
y = (x + 3)2 - 1
Step-by-step explanation: