Answer:
(f-g)(5) = 14
Explanation:
Given the functions;
f(x) = 2x+7
g(x) = 3
f(x) - g(x) = 2x+7 -3
f(x)-g(x) = 2x+4
Substitute x = 5 int the result
(f-g)(x) = 2x +4
(f-g)(5) = 2(5) + 4
(f-g)(5) = 10+4
(f-g)(5) = 14
write the rule for the translation shown below using mapping notation
From blue to red:
Take any point.
C
We can see that point C moves 5 units to the right and 1 unit up
x+5, y+1
Mapping notation:
T:(x,y) ⇒ (x+5,y+1)
FIND THE MIDPOINT M OF THE LINE SEGMENT JOINING P= (-7,2) AND Q=(5,-6)
we need to know
(-7,2)= (x1,y1)
(5,-6)=(x2,y2)
the midpoint formula is
[tex]x_m=\frac{x_1+x_2}{2}=\frac{-7+5}{2}=\frac{-2}{2}_{}=1[/tex][tex]y_m=\frac{y_1+y_2}{2}=\frac{2-6}{2}=\frac{-4}{2}_{}=2[/tex]M=(1,-2)
is d=65t proportional or non proportional?
A proportional relationship can be said to be a relationship between two variables with equivalent ratios. Here the two variables vary directly with each other.
Thus, using the equation:
y = kx
where k is the constant
Here, we have:
d = 65t
where 65 is the constant of proportionality
We can say d varies directly as t
Therefore d = 65t is proportional.
ANSWER:
Proportional
6 The image at the right is a scale drawing of aparking lot. The length of each square on thegrid represents 0.5 cm. The actual parking lothas a perimeter of 84 m. Draw another scaledrawing of the parking lot using a scale from theparking lot to the drawing of 2 m to 1 cm. Justifywhy your drawing is accurate.
Answer:
Explanation:
We are told that on the grid
1 unit = 0.5 cm
and that actually, the perimeter of the parking lot is 84 cm.
Now on the drawing, the perimeter of the parking lot is
14 lines x 0.5 cm = 7 cm
This tells us that on the grid
7 cm = 84 m
which tells us that on the grid 1 cm is
1 cm = 84 m / 7 cm = 12 m
Therefore, the actual measurements of our parking lots are given by the following sketch.
Using the diagram below, classify the angle pairs as corresponding. alternate interior, alternate exterior, consecutive interior, consecutive exterior, or none.1-) what classification corresponds to angle 6 and 7 angle.
Because of the position of the angles, they are alternate exterior
Find the equation for the line that passes through the point (2-2), and that is perpendicular to the line with the equation - x + y = -3.
We are asked to find the equation of a line that is perpendicular to the line -x + y = -3 and passes through the point (2, -2)
Re-writing the given equation in slope-intercept form
[tex]y=x-3[/tex]Recall that the equation of a line in slope-intercept form is given by
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
Comparing the given equation with the above standard form we see that,
[tex]slope=m=1[/tex]Since we are given that the lines are perpendicular so the slope of the other line must be negative reciprocal of the given line.
[tex]m_2=-\frac{1}{m_1}=-\frac{1}{1}=-1[/tex]So the slope of the required equation is -1
Since we are also given that the line passes through the point (2, -2)
The point-slope form of the equation of a line is given by
[tex]y-y_1=m\mleft(x-x_1\mright)[/tex]Let us substitute the value of slope and the given point into the above equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-2)_{}=-1(x-2_{}) \\ y+2_{}=-1(x-2_{}) \end{gathered}[/tex]Solving the equation for y.
[tex]\begin{gathered} y+2_{}=-1(x-2_{}) \\ y+2_{}=-x+2_{} \\ y=-x+2-2 \\ y=-x \end{gathered}[/tex]Therefore, the required equation of the line is
[tex]y=-x[/tex]F(x)= cubed root of x-2 +3A. What is the domain of this function? Explain your answerB. What is the range
Given data:
[tex]F(x)=\sqrt[3]{x-2}+3[/tex]A. The domain of cube root function is all the real numbers because it is possible for three negatives to equal a negative. But this cannot apply for square functions.
B. For range put F(x) = y
[tex]\begin{gathered} y=\sqrt[3]{x-2}+3 \\ y-3=\sqrt[3]{x-2} \end{gathered}[/tex]Now, taking cube both sides we get
[tex](y-3)^3=x-2[/tex][tex]x=2+(y-3^{})^3[/tex]Thus, the range for the function is also all real numbers because value of x will be defined for every value of y.
Point P (2,1) is reflected across the y-axis. What is the coordinate of the reflected point, P'? A). (2,-1)B). (-2,1)C). (-1,2)D). (-1,-2)
Solution
For this case we have the following point:
P(2,1)
And we want to find the reflection across the y-axis so we can use the following formula:
(x,y) >>> (-x ,y)
Replacing we got:
B) (-2,1)
Please help. This is extra reference work. I don't know how to do it.
since by definition a parallelogram has two sets of opposite sides that are parallel and equal with each other, we can say that due to alternate angles, when we divide the parallelogram by its diagonal a pair of congruent angles appear like this
and due to alternate angles, we can also say that the corresponding angles will also be the same as this
Now since the diagonal is the same side for both triangles we can confirm that by the ASA theorem the two triangles are congruent.
[tex]\begin{gathered} \text{statement 1:} \\ AD\parallel BC \\ \text{reason 1:} \\ \text{Definition of parallelogram} \\ \text{statement 2:} \\ DC\parallel BA \\ \text{reason 2:} \\ \text{Definition of parallelogram} \\ \text{statement 3:} \\ \measuredangle DAC=\measuredangle ACB \\ \text{reason 3:} \\ \text{alternate angles } \\ \text{statement 4:} \\ \measuredangle DCA=\measuredangle BAC \\ \text{reason 4:} \\ \text{alternate angles } \\ \text{statement 5:} \\ AC=AC \\ \text{reason 5: } \\ \text{common side} \end{gathered}[/tex]Then due to 3,4 and 5 triangles, ADC and ABC are congruent by ASA theorem.
how to draw -360 degrees on a graph
Draw a graph of 360 degrees and move in a counterclockwise direction
Explanation:180 degrees is pi in radians.
Let -360 degrees be x radians, then
[tex]\begin{gathered} 180x=-360\pi \\ x=-\frac{360\pi}{180}=-2\pi \end{gathered}[/tex]We have -360 degrees when we move in a counterclockwise direction.
Check off all of the equations that would give no solutions
Answer:
5x + 10 = 5x - 15
6x - 8 = 2(3x - 3)
Explanation:
The equations that give no solutions are the equations that are equivalent to a false equality.
So, to find the answer, we need to solve each option:
5x + 10 = 5x - 15
5x + 10 - 5x = 4x - 15 - 5x
10 = -15 (False)
3x + 12 = 4x - 21
3x + 12 - 12 = 4x - 21 - 12
3x = 4x - 33
3x - 4x = 4x - 33 - 4x
-x = -33
x = 33
3(x + 4) = 3x + 12
3(x) + 3(4) = 3x + 12
3x + 12 = 3x + 12
5x + 10 = 6x - 8
5x + 10 - 10 = 6x - 8 - 10
5x = 6x - 18
5x - 6x = 6x - 18 - 6x
-x = -18
x = 18
2(3x - 4) = 6x - 8
2(3x) - 2(4) = 6x - 8
6x - 8 = 6x - 8
6x - 8 = 2(3x - 3)
6x - 8 = 2(3x) - 2(3)
6x - 8 = 6x - 6
6x - 8 - 6x = 6x - 6 - 6x
- 8 = - 6 (False)
Therefore, the answers are
5x + 10 = 5x - 15
6x - 8 = 2(3x - 3)
$34.31 divided by 12 gallons
step 1
Find out the unit rates
we have
34.31/12=$2.86 per gal
and
$2.90 per gallon
so
the better deal is the first option because is less
therefore
the answer is option ASolve Steps 1 through 3 2. Graph this function for 0 ≤ t ≤ 100. Choose the graph.
To find the remaining amount in grams of the radioactive isotope after 25 years, let us replace the "t" in the function with 25.
[tex]A(25)=300e^{-0.02813(25)}[/tex]Then, solve.
a. Multiply the exponents of the natural number e. The equation will become:
[tex]A(25)=300e^{-0.70325}[/tex]b. Apply the exponent on the natural number e. The equation will become:
[tex]A(25)=300(0.494974)[/tex]c. Multiply the two numbers 300 and 0.494974. The result is:
[tex]A(25)=148.4922\approx148.49g[/tex]Therefore, the amount of radioactive isotope remaining after 25 years is approximately 148.49 grams.
For the graph, since this is decaying, we know already that as the years go by, the amount of grams remaining decreases. Therefore, the graph should have a negative slope because we have an inverse relationship between time and the amount remaining.
Out of 4 graphs, Option B and Option D show this inverse relationship.
However, we know that the initial amount is 300 grams. This means at 0 years, the amount of the radioactive isotope should be 300 grams.
Between Options B and D, Option D shows the correct initial value which is 300 (3 dashes up). Hence, the graph of this function is best shown in Graph D.
To calculate the half-life, let's calculate first how many is half of the initial amount.
[tex]300\times\frac{1}{2}=150g[/tex]Half the initial amount is 150 grams. Let's take a look at the graph how many years will it take for the isotope to decay to 150 grams.
As we can see in the graph, in about 24.64 years, the radioactive isotope will be half of its initial amount. (Option C)
if a || b, m<2=63°, and m<9=105°, find the missing measure of m<14=?
Answer:
m∠14 = 138°
Step-by-step explanation:
∠2 = ∠5 = 63° (vertically opposite angles)
∠9 +∠8 = 180° (linear pair)
=> 105° + ∠8 = 180
=> ∠8 = 180° - 105° = 75°
∠5 + ∠8 + ∠11 = 180° (sum of angles in a triangle is 180)
=> 63° + 75° + ∠11 = 180°
=> 138° + ∠11 = 180°
=> ∠11 = 180° - 138° = 42°
∠11 + ∠14 = 180° (linear pair)
=> 42° + ∠14 = 180°
=> ∠14 = 180° - 42° = 138°
Hope you understood!!
write fraction or mixed number as a decimal 5 13/50
we have
5 13/50
write as decimal
so
step 1
Convert mixed number to an improper fraction
[tex]5\frac{13}{50}=5+\frac{13}{50}=\frac{250+13}{50}=\frac{263}{50}[/tex]step 2
Convert fraction into decimal number
so
[tex]\frac{263}{50}=5.26[/tex]therefore
the answer is
5.26Please guide me in the correct direction with attached pic. For p(x)=7+10x-12x^2-10x^3+2x^4+3x^5, evaluate the following;
Solution:
Given:
[tex]p(x)=7+10x-12x^2-10x^3+2x^4+3x^5[/tex]To find p(-3), substitute x = -3
[tex]\begin{gathered} p\left(x\right)=7+10x-12x^2-10x^3+2x^4+3x^5 \\ p(-3)=7+10\left(-3\right)-12\left(-3\right)^2-10\left(-3\right)^3+2\left(-3\right)^4+3\left(-3\right)^5 \\ p(-3)=-428 \end{gathered}[/tex]To find p(1), substitute x = 1
[tex]\begin{gathered} p\left(x\right)=7+10x-12x^2-10x^3+2x^4+3x^5 \\ p(1)=7+10\cdot\:1-12\cdot\:1^2-10\cdot\:1^3+2\cdot\:1^4+3\cdot\:1^5 \\ p(1)=0 \end{gathered}[/tex]To find p(5), substitute x = 5
[tex]\begin{gathered} p\left(x\right)=7+10x-12x^2-10x^3+2x^4+3x^5 \\ p(5)=7+10\cdot\:5-12\cdot\:5^2-10\cdot\:5^3+2\cdot\:5^4+3\cdot\:5^5 \\ p(5)=9132 \end{gathered}[/tex]Therefore, OPTION B is correct.
A pyramid has a base that is a right traingle with legs measuring 10 cm and 14 cm. The height of the pyramid is 9 cm.The volume of the pyramid is ___ cubic cm.
The volume formula is given by
V = 1/3 Bh where B is the area of the base and h is the height
The area of the base is the area of a triangle
B = 1/2 (10)*14 = 70 cm^2
V =1/3 (70cm^2) ( 9 cm)
C =210 cm^3
Rewrite (6x3 + 9x2 + 7)/(2x3 + 3x2) in the form q(x) + r(x)/b(x) where q(x) = quotient, r(x) = remainder, and b(x) = divisor.
Given:
There is an expression given as below
[tex]\frac{6x^3+9x^2+7}{2x^3+3x^2}[/tex]Required:
We need to convert the given expression in form of q(x) + r(x)/b(x) where q(x) = quotient, r(x) = remainder, and b(x) = divisor.
Explanation:
Simplify the given equation
[tex]\frac{6x^3+9x^2+7}{2x^3+3x^2}=\frac{6x^3+9x^2}{2x^3+3x^2}+\frac{7}{2x^3+3x^2}[/tex]Simplify as
Final answer:
[tex]3+\frac{7}{2x^{3}+3x^{2}}[/tex]Find the nature of the roots of 2x2 - 3x - 12 = 0.Real and rationalReal and irrationalReal and equalComplex roots
Given:
[tex]2x^2-3x-12=0[/tex]Required:
To find the nature of the root.
Explanation:
Here
[tex]\begin{gathered} a=2 \\ b=-3 \\ c=-12 \end{gathered}[/tex]Now
[tex]\begin{gathered} b^2-4ac=(-3)^2-4(2)(-12) \\ =9-96 \\ =-87<0 \end{gathered}[/tex]The roots are complex.
Final Answer:
The roots are complex.
Find the percent increase. Round to the nearest percent. From 12 teachers to 48 teachers.
1) To find that out, we'll use proportions:
12 ---------------- 100%
48 --------------- x
Cross multiplying those ratios:
12x = 4800
x= 400
2) Now let's subtract from 100%
400% - 100% = 300
3) Then the increase was 300%
Juan earns $11.75 for each lawn he mows, and it takes him as of an hour to mow each lavvn. Which expression represents the number of hours it takes Juan to earn $141? o 141 – 11.75 x = 133 0 141 = x 11.75 = 2485 0 141 +11.75 = { = 228 o 141 = 11.75 x š = 8
E = 11.75t
t = number of hours or x
141 = 11.75x This is the answer
The first one is the answer
Nathaniel was completing the square in order to turn the general form of circle into standard form of a circle. His work is shown below. x2 + y2 + 6x – 10y - 2 = 0 x2 + y2 + 6x – 10y = 2 x² + 6x + + y2 – 10y +_ = 2 + + x2 + 6x + 9+ y2 – 10y + = 2 + 9 + Enter the numeric value that will be placed in both blanks to complete his step. I
Given the following expression
[tex]x^2+y^2\text{ + 6x - 10y - 2 = 0}[/tex]Firstly, we need to find the perfect square
[tex]\begin{gathered} \text{Collect the like terms} \\ x^2+6x+y^2\text{ - 10y = 2} \\ \text{ Find the p}\operatorname{erf}ect\text{ square} \\ x^2\text{ + (}\frac{6}{2}x)+y^2\text{ - (}\frac{10}{2}y)\text{ = 2} \\ x^2+3x+(3)^2+y^2-5y+(-5)^2\text{ = 2} \\ x^2+3x+9+y^2\text{ - 5y + 25 = 2} \\ \text{Add p}\operatorname{erf}ect\text{ square to both sides} \\ x^2+6x+y^2\text{ - 5y = 2 + 9 + 25} \end{gathered}[/tex]Select all the polygons that would be used in a net of the solid figure shown.
Three of the triangles are congruent and are isosceles triangles.
The third triangle has sides that are the bases of the congruent isosceles triangles.
Hence the third triangle is an equilateral triangle
So the correct options are:
isosceles triangle
and
equilateral triangle
Which ordered pair is a solution to the linear function y = 2x − 11?A) (1, -9)B) (0, -3)C) (1,5)D) (-2, 7)
To answer this question we have to verify if using the values of the ordered pair, the equation is true.
Try each option until you find one that meets this condition:
[tex]\begin{gathered} -9=2(1)-11 \\ -9=2-11 \\ -9=-9 \end{gathered}[/tex]In this case, the first option is the one that meets this condition.
It means that the correct answer is A. (1,-9).
3120 fans attended the final game of the season this was a 30% increase from the attendance at the first game of the season how many fans attended the first game of the season
let the number of attended the first game is x
30 % increment of x = 3120 ......( Given)
x + 30 % of x = 3120
[tex]\begin{gathered} x+x\times\frac{30}{100}=3120 \\ \frac{130x}{100}=3120 \end{gathered}[/tex][tex]\begin{gathered} x=\frac{31200}{13} \\ x=2400 \end{gathered}[/tex]thus, the answer is 2400 fans attended first game
Hello, I need some assistance with this homework question please for precalculusHW Q24
Given the graph
Explanation
Part A
The local minimum is s a point within an interval at which the function has a minimum value. This occurs at
Answer:
[tex]x=-2,6[/tex]Part B: The local minima are the y values of the above.
[tex]y=-4[/tex]George earns $50 every day plus a bonus of $5 per product he sells. His total daily earnings are at least $60. The situation can be modeled by this inequality: 50+59>(or more than) 60. Which number line represents the number of products George can sell in a day to satisfy the inequality?
We know that George earns $50 every day plus $5 per product.
If x is the number of products he sold, then his total daily earnings can be written as:
[tex]50+5x[/tex]We also know that this total daily earnings are at least $60, so we can combine with the previous expression and get:
[tex]50+5x\ge60[/tex]From this inequality, we can calculate the inequality for x:
[tex]\begin{gathered} 50+5x\ge60 \\ 5x\ge60-50 \\ 5x\ge10 \\ x\ge\frac{10}{5} \\ x\ge2 \end{gathered}[/tex]Answer: As the number of products (x) he sold are at least 2 (or "2 or more"), the right graph for the inequality is Option D.
Determine the correct answer about whether a Table of Values represents a Linear Function. Х 1 1 2 3 4 у 5 10 15 20 Table of Values represents a Constant Rate of Change x-values have a Constant Rate of Change y-values have a Constant Rate of Change Plot points on a Graph and see
Table of values represents a constant rate of change
Explanations:From the table:
The values of x are 1 , 2 , 3 , 4 , 5.
The corresponding values of y are 5, 10, 15, 20
For a linear function, there must be a constant rate of change:
That is, △y / △x should be constant
[tex]\begin{gathered} x_1=1,x_2=2,y_1=5,y_2=\text{ 10} \\ \frac{\triangle y}{\triangle x}=\text{ }\frac{y_2-y_1}{x_2-x_1} \\ \frac{\triangle y}{\triangle x}=\text{ }\frac{10-5}{2-1} \\ \frac{△y}{△x}=\text{ 5} \end{gathered}[/tex]Also considering:
[tex]\begin{gathered} x_3=3,x_4=4,y_3=15,y_4=20 \\ \frac{\triangle y}{\triangle x}=\text{ }\frac{y_4-y_3}{x_4-x_3} \\ \frac{\triangle y}{\triangle x}=\text{ }\frac{20-15}{4-3} \\ \frac{\triangle y}{\triangle x}=\frac{5}{1} \\ \frac{\triangle y}{\triangle x}=\text{ 5} \end{gathered}[/tex]In all the points considered, the rate of change is the same. This means that the table of values represent a constant rate of change, it therefore represents a linear function.
5. [-/1 Points]DETAILSCURRENMEDMATH11 2.9.012.MY NOTESASKYUse critical thinking to answer the following.You have given 5(5.5) tab with a strength of 1.25 mg per tablet. What total dosage (in milligrams) is this?mgeBook6. [-/1 Points]DETAILSCURRENMEDMATH11 2.9.013.MY NOTESASK YUse critical thinking to answer the following.The tablets your patient is to receive are labeled 0.1 mg, and you are to give6 (6.5) tab. What total dosage (in milligrams) is this?mgeBook0
Each tablet has a dosage of 1.25mg
You'll give the patient 5 and a half tablets, to calculate the total dosage of medicine you'll give the patient you can apply cross multiplication:
1tablet_____1.25mg drug
5.5tablets__xmg
[tex]x=\frac{5.5\cdot1.25}{1}=\frac{55}{8}=6.875[/tex]The total dosage is 6.875mg
Terrell buys 2 postcards during each day of vacation. After 9 days of vacation, how many total postcards will Terrell have bought?
Terrell went on a vacation and bought 2 postcards each day
This implies that he bought 2 postcards everday
He spent a total of 9 days
Total post card = No of days spent x number of postcards bought each day
Number of days = 9
Number of postcards =2
Total number of postcards = 9 x 2
Total number of postcards = 18
The answer is 18 postcards