The limit of the given expression lim x → 0 [4eˣ/2 − 4 − 2x − 12x² + x³] is determined as -2.
Limit of the function
The limit of the given expression is calculated as follows;
lim x → 0 [4eˣ/2 − 4 − 2x − 12x² + x³]
= (4e⁰)/2 - 4 - 2(0) - 12(0) + (0)
= (4)/2 - 4
= 2 - 4
= - 2
Thus, the limit of the given expression lim x → 0 [4eˣ/2 − 4 − 2x − 12x² + x³] is determined as -2.
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which inequality is represented by the graph
Answer:
This is your teacher if you do this again, I will contact your parents and you will get in big trouble.
Step-by-step explanation:
how do i solve log base 5 (x+9)=log base 5 (x+5)+1 solve for x and check both solutions to see if they are true or false
Step-by-step explanation:
[tex] log_{5}(x + 9) = log_{5}(x + 5) + 1[/tex]
[tex] \frac{ log(x + 9) }{ log(5) } = \frac{ log(x + 5) }{ log(5) } + 1[/tex]
[tex] log(x + 9) = log(x + 5) + log(5) [/tex]
[tex] log(x + 9) = log(5x + 25) [/tex]
[tex]x + 9 = 5x + 25[/tex]
[tex]x = - 4[/tex]
If we plug it in, it is true
A teacher randomly selects one student from a group of students. Fourteen students are wearing a black shirt, six students are wearing a red shirt, and nine students are wearing a blue shirt. What is the probability that the selected student is wearing a black shirt?
Answer:
14/29
Step-by-step explanation:
14/29 is the answer
What is the value of x?
to
x = [? ]°
Answer: 30
Step-by-step explanation:
(Assuming the line is a tangent)
A total of 10,800 pharmacy technicians were hired last year in particular country. This is 3% of all pharmacy technicians employed in the country. How many pharmacy technicians are employed in the country?
well, the total amount of technicians employed is 100% and that is "x" amount, now, we also know that 3% of of that is 10800, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 10800& 3 \end{array} \implies \cfrac{x}{10800}~~=~~\cfrac{100}{3} \\\\\\ 3x=1080000\implies x=\cfrac{1080000}{3}\implies x=360000[/tex]
i need help with this question
9 less than the sum of x and y
If we need to turn this into a mathematical expression:
Answer: (x + y) - 9
Step-by-step explanation:
9 less than the sum of x and y
(the sum of x and y) - 9
(x + y) - 9
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A hiking trail is shown as 14cm on a map the scale is 1:150000 how far in km is it in real life.
the scale says that each unit (cm/km/in/...) on the map is 150,000 times that unit so:
14cm on the map
= 150,000×14cm
= 2,100,000 cm
= 2100 km
(= 2.1 Mm)
6. If b>6, then 3b + 3 could be
A. 18
B. 19
C. 20
D. 21
E. 22
Answer:
E. 22
Step-by-step explanation:
Hello!
We know that b>6, and we are asked to find the possible values for 3b + 3.
Let's directly substitute 6 for b:
3(6) + 318 = 321Now, because b is greater than 6, and not equal to 6, any value greater than 21 will work.
The correct option is E. 22.
Find dy/dx of y = sin inverse ( x - 1 ).
[tex] \frac{1}{ \sqrt{1 - {(x - 1)}^{2} } } [/tex]
HELP ASAP!!!!! The graph compares temperatures and numbers of cyclists. The equation of the trend line for the scatterplot is y = 4x + 10. Predict the number of cyclists when the temperature is 12°C.
So
Put x ax 12°CHence
y=4(12)+10y=48+10y=58Option A
Answer:
Option A
Step-by-step explanation:
y=4x+10
So
Put x ax 12°C
Hence
y=4(12)+10
y=48+10
y=58
How many right angles are formed by perpendicular lines in spherical geometry?
A.
8
B.
6
C.
2
D.
3
Answer:
8
Step-by-step explanation:
I am good at math
What is the area of triangle ABC?
A(2,1) B(4,7) C(6,3)
Answer: 10
Step-by-step explanation:
It appears that [tex]\overline{AC} \perp \overline{BC}[/tex], so to check if this is the case, we can use the slope formula.
[tex]m_{\overline{AC}}=\frac{3-1}{6-2}=\frac{1}{2}\\m_{\overline{BC}}=\frac{3-7}{6-4}=-2[/tex]
Since these slopes are negative reciprocals, we can see that this is the case. So, we can take [tex]\overline{AC}[/tex] as the base of the triangle and [tex]\overline{BC}[/tex] as the height of the triangle, and then use the formula [tex]A=\frac{1}{2}bh[/tex].
Using the distance formula,
[tex]AC=\sqrt{(6-2)^{2}+(3-1)^{2}}=\sqrt{16+4}=2\sqrt{5}\\BC=\sqrt{(4-6)^{2}+(7-3)^{2}}=\sqrt{4+16}=2\sqrt{5}[/tex]
So, the area is [tex]\frac{1}{2}(2\sqrt{5})(2\sqrt{5})=\boxed{10}[/tex]
Parallel lines q and q are cut by transversal r forming 4 angles at each intersection. At the intersection of lines r and q, clockwise from top left, the angles are: 1, 2, 4, 3. At the intersection of lines r and s, clockwise from top left, the angles are: 5, 6, 8, 7.
Use the diagram to complete the statements.
Angles 1 and 5 are
because they are
angles.
Angles 4 and 6 are
because they are
angles.
Using the vertically opposite angles theorem and corresponding angles theorem, we have proven that alternate exterior angles are congruent
Angle theoremsFrom the question, we are to prove that alternate exterior angles are congruent.
In the given diagram, examples of alternate exterior angles are
∠1 and ∠8
∠2 and ∠7
Now, we will prove that ∠1 = ∠8
In the diagram, we can observe that
∠1 = ∠4 (Vertically opposite angles theorem)
and
∠4 = ∠8 (Corresponding angles theorem)
Then,
By the substitution property of equality
∠1 = ∠8
Hence, alternate exterior angles are congruent
Here is the complete and correct question:
Consider parallel lines cut by a transversal. Parallel lines q and s are cut by transversal r. On line q where it intersects line r, 4 angles are created. Labeled clockwise, from uppercase left: angle 1, angle 2, angle 4, angle 3. On line s where it intersects line r, 4 angles are created. Labeled clockwise, from uppercase left: angle 5, angle 6, angle 8, angle 7.
Explain which theorems, definitions, or combinations of both can be used to prove that alternate exterior angles are congruent.
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Answer:
Step-by-step explanation:
Parallel lines q and q are cut by transversal r forming 4 angles at each intersection. At the intersection of lines r and q, clockwise from top left, the angles are: 1, 2, 4, 3. At the intersection of lines r and s, clockwise from top left, the angles are: 5, 6, 8, 7.
Use the diagram to complete the statements.
Angles 1 and 5 are
✔ congruent
because they are
✔ corresponding
angles.
Angles 4 and 6 are
✔ supplementary
because they are
✔ same-side interior
angles.
Tess has a garden that is 4 1/2 feet wide and 6 3/4 feet long. How many feet of fencing does she need to put around all sides of her garden?
Answer:
11.25
Step-by-step explanation:
6 3/4 + 4 1/2
For each of the descriptions below, create a system of linear inequalities (please help will mark brainliest for whoever answers correctly!)
Answer:
hope you can understand
value of the discriminant for the equation -3x=-x^2+2x
Using the GCF factor the given expression: 21xy + 14y
7(3xy + 2y)
7y(3x + 2)
3(7xy + 14y)
7xy(3 +2)
ASAP
Since 7y is common to both factors, therefore the GCF of the expression is 7y. The factored form will be 7y(3x + 2)
Greatest common factor of an expressionThe greatest common factor is the value that will divide an expression without leaving a remainder.
Given the expression 21xy + 14y
Find the factors
21xy = 7 * 3 * x * y
14y = 7 * 2* y
From the factors above, it is clear that 7 and y are the greatest common factors.
Since 7y is common to both factors, therefore the GCF of the expression is 7y. The factored form will be 7y(3x + 2)
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Factor out
21xy=3×7×y×x14y=2×7×ySo
7y is common hence 7y is GCFNow factor up
7y(3x+2)Option B
please help please help
Answer:
angleEAF=angleBAC (शिर्षभिमुख कोण भएर)
10x+90+5x=180 (सरल कोण भएर)
or, 15x+90=180
or, 15x=180-90
or, 15x=90
or, x=90÷15
or, x=4
Answer:
x=6
Step-by-step explanation:
90°+5x+10x=180°
90°+15x=180°
15x=180°-90°
15x=90°
x=90/15
=6
10×6=60
5×6=30
60°+30°=90°
90°+90°=180°
x=6 QED
Select the correct choice that completes the sentence below.
The expression
f(x+h)-f(x)
h
is called the
of f.
Answer:
difference quotient
Step-by-step explanation:
PLEASE HELP!!!!!!!!!! I'll NAME BRAINLIEST!!!!!!
Classify the expression by the number of terms.
5y^2-8+6y^4
Answer:
5x2-2x+1 The highest exponent is the 2 so this is a 2nd degree trinomial.
Step-by-step explanation: Also pls answer by question
What is the area of the hexagon below?
What is the surface area of this 3d character based off the illustration. Can you provide explanation. Thank you.
The surface area of this 3d character based off the illustration will be 289.
How to explain the surface area?It should be noted that the surface area simply means the amount of space that covers the outside of a shape.
Here the length of the shape is 17 and the width is also 17 as well. It should be noted that the width and length are determined by looking at the axis of the shapes drawn.
In this case, the area will be:
Length × Width
= 17 × 17
= 289
In conclusion, the surface area is 289.
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In a year, a hospital admitted 4500 patients. If of the patients had heart or lung diseases,
how many patients had heart or lung diseases?
Answer:
4500
Step-by-step explanation:
all of them were admitted.
Which property is demonstrated in the equation 2 + 5 + 7 = 2 + 7 + 5
15+ 2x = 5 + 3x
what's the answer
Answer:
x = 10
Step-by-step explanation:
rewrite this equation with x on the left and numbers on the right
2x - 3x = 5 - 15
-x = -10
x=10
give brainliest, please!
hope this helps :)
The value of x is x = 10
To solve a first degree equation, first: we add or subtract like terms. Finally, we split the terms of both equalities.
- In this equation, we're going to subtract the like terms -- and on the other side of the equation, we're going to also subtract the real terms.
Resolution15 + 2x = 5 + 3x
2x - 3x = 5 - 10
-1x = -10
x = 10
So, the correct value is x = 10
Helpppppp asap with this
Answer:
I have no clue, cant lie to you. God Bless you though.
Step-by-step explanation:
What is the solution to this system of equations? 2x+y-5z=4 x+3y+z=5 3x-y-4z=-11
For the given linear system equations, the value for the variables are: x=-2, y=4, and z=-5 - Option C.
System of Linear Equations
System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.
The question gives:
2x+y-5z=4 (1)
x+3y+z=5 (2)
3x-y-4z=-11 (3)
First, you should sum equations 1 and 2. The results will be:
3x+4y-4z=9 then you have a new equation (4).
3x-y-4z=-11 (3)
3x+4y-4z= 9(4)
Now, you should multiply equation (3) by -1, then you will have:
-3x+y+4z=+11 (3)
3x+4y-4z=9 (4)
After that, you should sum the previous equations: (3) and (4).
5y=20
y=4
For find z, you should multiply equation 2 by -2. After that, you should sum equations 1 and 2.
2x+y-5z=4 (1)
-2x-6y-2z=-10 (2)
Thus, you will have:
-5y-7z=-6, like y=4 you have
-5*4-7z=-6
-20-7z=-6
-7z=14
z=-2
If z=-2 and y=4 from equation 2, you can find x.
x+3y+z=5
x+3*4-2=5
x+12-2=5
x+10=5
x=5-10
x=-5
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Which conversion factor should be used to convert the 152.5 g to moles?
Answer:
Step-by-step explanation:
You will need to know the gram weight per mole from the periodic table for the element ( or the molecule of elements) in question.
First draw the line on the graph. Then reflect each vertex of quadrilateral across the line to produce quadrilateral .
A four quadrant graph with a line and a quadrilateral with vertex.
Vertex Preimage Coordinates Vertex Image Coordinates
A (-3,-2) A' (-2,-3)
B (-2,-1) B' (-1,-2)
C (-1,-2) C' (-2,-1)
D (-1,-4) D' (-4,-1)
The equation of the line about which the quadrilateral is reflected will be y = x.
What is a reflection of the point?It is the image of the point which is located in the opposite direction of a given point.
The rule of the refection is given will be
Firstly, the rule for reflecting a point about the line y = x is;
While reflecting on the line y = x, we get the reflected points by swapping the coordinates.
First, draw the line on the graph. Then reflect each vertex of quadrilateral across the line to produce quadrilateral.
Vertex Preimage Coordinates Vertex Image Coordinates
A (-3,-2) A' (-2,-3)
B (-2,-1) B' (-1,-2)
C (-1,-2) C' (-2,-1)
D (-1,-4) D' (-4,-1)
The diagram is given below.
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