Answer:
5m/s²
Step-by-step explanation:
Given :-
Initial Velocity = 40m/s Final velocity = 60 m/sTime = 4sTo Find :-
The acceleration .Solution :-
We know that the rate of change of velocity is called acceleration. Therefore ,
[tex]\sf\implies a = v - u / t \\ [/tex]
[tex]\sf\implies a = 60m/s - 40m/s/ 4 \\ [/tex]
[tex]\sf\implies a = 20m/s \div 4 \\[/tex]
[tex]\bf\implies a = 5m/s^2[/tex]
What is the measure of angle ABC?
Answer:
the answer is already in the question
D. 130°
D. 130
A parabola opens upward. The parabola goes through the point (3,-1),
and the vertex is at (2,-2).
Find the value of A for the parabola. Show your work. Use Part 1 and 2 to write the equation of the parabola.
Answer:
a=1
Step-by-step explanation:
Hopefully this helps :)
The equation of the parabola is: y = (x - 2)² - 2. Finding the value of A
The vertex of the parabola is at (2,-2). Since the parabola opens upward, the equation of the parabola will be of the form:
y = A(x - 2)² - 2
We can plug the point (3,-1) into this equation to find the value of A.
-1 = A(3 - 2)² - 2
Simplifying the right side of the equation, we get:
-1 = A - 2
Adding 2 to both sides of the equation, we get:
1 = A
Therefore, the value of A is 1.
Writing the equation of the parabola
The equation of the parabola is:
y = (x - 2)² - 2
To know more about parabola:
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helpppppppppppppppp//////////////////////////////////////////
Answer:
m(x)
Step-by-step explanation:
WILL GIVE BRAINLIEST AND 30 POINTS!
PLEASE SHOW WORK!
f(x)=x2+10 and g(x)=|x|
Find (f+g)(2).
Answer:
14
Step-by-step explanation:
[tex]f(x) = {x}^{2} + 10 \\ \therefore \: f(2) = {2}^{2} + 10 \\ \therefore \: f(2) = 4 + 10 \\ \therefore \: f(2) = 14 \\ \\ g(x) = |x| \\ \therefore \:g(2) = |2| \\ \therefore \:g(2) = 2 \\ \\ f(2) + g(2) = 14 + 2 \\ \red{ \bold{(f + g)(2) = 14}}[/tex]
Step by step Explanation:
[tex]f(x) = x2 + 10g(x) = 1[/tex]
[tex](f + g)(2).[/tex]
Step 1
The equation is in standard form.
[tex]xf = 10gx + x2[/tex]Step 2
Divide both sides by x.
[tex] \frac{xf}{x} = \frac{10gx + x2}{x} [/tex]Step 3
Dividing by x undoes the multiplication by x.
[tex]f = \frac{10gx + x2}{x} [/tex]Step 4
Divide x 2 + 10 g x by x.
[tex]f = 10g + \frac{x2}{x} [/tex]My Answer is.
[tex]\color{green}f \ = \frac{10g + \frac{x2}{x} }{f€g} x2 = {14}^{x} [/tex]Self Practice 5.3
1. Find the sum of the following arithmetic progression.
(a) -20, -15, -10, ..., 100
Answer:
5
Step-by-step explanation:
Have a phd in mathematics! Congrats on your first question!!!! Send me a brainlist :)
find the area of the trapezoid. helppppopop thank you
Answer:
[tex]\frac{4}{3}\:\mathrm{cm^2}[/tex]
Step-by-step explanation:
The area of a trapezoid can be found by multiplying the average of its bases and its height.
We're given:
One base of 4 cmOne base of 12 cmHeight of 1/6 cmTo find the average of a set of [tex]n[/tex] values, add all the values in the set and divide by [tex]n[/tex]. Therefore, to find the average of the two bases, we add 4 to 12 and divide by 2.
The average of the bases is therefore [tex]\frac{4+12}{2}=\frac{16}{2}=8[/tex]
Thus, the area of the trapezoid is [tex]8\cdot \frac{1}{6}=\frac{8}{6}=\boxed{\frac{4}{3}\:\mathrm{cm^2}}[/tex]
Does the data below describe a linear,
quadratic, or exponential function?
Answer:
Quadratic.
Step-by-step explanation:
Both linear and exponential equations are monotone increasing or monotone decreasing functions.
This means that, as the input increases, the output will only increase or only decrease, but never both.
Here for our data, we can see that first we have:
x = -8
y = 13
Then x increases to x = -6, and y decreases to y = 9
Then x increases to x = -4 and y increases to y = 13
Then this function is not monotone increasing nor monotone decreasing, so the data can not describe a linear nor an exponential function.
Then the correct option is quadratic.
The transformation from the function ƒ(x) = 3x to the function ƒ(x) = 3x + 4 indicates:
Answer:
Moving 4 to the right on the x axis
A bag contains 6 black tiles, 5 white tiles, and 4 blue tiles. Event A is defined as drawing a white tile from the bag on the first draw, and event B is defined as drawing a black tile on the second draw. If two tiles are drawn from the bag, one after the other without replacement, what is P(A and B) expressed in simplest form? A. 4/45 B. 1/7 C. 4/15 D. 5/14
Answer:
5/14
Step-by-step explanation:
There are 15 tiles in total
5 white| 6 black | 4 blue
event A results in the subject pulling a white tile and not replacing it
5-1= 4
so the first answer should be 4/15
event B results in the subject pulling another tile, a black one and not replacing it.
6-1= 5
given this answer, there is one less tile in the total, since we removed another tile.
So our answer would be-
5/14 or D
log_(5)(x-4)=1-log_(5)(x-8)
Answer:
x = 3, x = 9
Step-by-step explanation:
When solving this problem, keep the general format of a logarithm in mind:
[tex]b^x=y\\log_b(y)=x[/tex]
Where, (b) represents the base, (x) is the exponent, and (y) is the evalutaor. Please note that others might use slightly different terminotoly than what is used in this answer.
One is given the following expression, and is asked to solve for the parameter (x);
[tex]log_5(x-4)=1-log_5(x-8)[/tex]
First, manipulate the exquestion such that all of the logarithmic expressions are on one side. Use inverse operations to do this.
[tex](log_5(x-4))+(log_5(x-8))=1[/tex]
Now use the Logarithmic Base Change rule to simplify. The Logarithmic Base Change rule states the following;
[tex]log_b(x)=\frac{log(x)}{log(b)}[/tex]
Remember, if no base is indicated in a logarithm, then the logarithm's base is (10). Apply the Logarithmic Base Change rule to this problem;
[tex]\frac{log(x-4)}{log(5)}+\frac{log(x-8)}{log(5)}=1[/tex]
Now remove the denominator. Multiply all terms in the equation by the least common denominator; ([tex]log(5)[/tex]) to remove it from the denominator on the left side.
[tex](\frac{log(x-4)}{log(5)}+\frac{log(x-8)}{log(5)}=1)*(log(5))[/tex]
[tex]log(x-4)+log(x-8)=log(5)[/tex]
All logarithms have the same base, the left side of the equation has the addition of logarithms. This means that one can apply the Logarithm product rule. The logarithm product rules the following;
[tex]log_b(x*y)=(log_b(x))+(log_b(y))[/tex]
This rule can be applied in reverse to simplify the left side of the equation. Rather than rewriting the product of logarithms as two separate logarithms being added, one can rewrite it as one logarithm getting multiplied.
[tex]log(x-4)+log(x-8)=log(5)[/tex]
[tex]log((x-4)(x-8))=log(5)[/tex]
Now used inverse operations to bring all of the terms onto one side of the equation:
[tex]log((x-4)(x-8))=log(5)[/tex]
[tex]log((x-4)(x-8))-log(5)=0[/tex]
Similar to the Logarithm product rule, the Logarithm quotient rule states the following;
[tex]log_b(x/y)=(log_b(x))-(log_b(y))[/tex]
One can apply this rule in reverse here to simplify the logarithms on the left side:
[tex]log((x-4)(x-8))-log(5)=0[/tex]
[tex]log(\frac{(x-4)(x-8)}{5})=0[/tex]
The final step in solving this equation is to use the Logarithm of (1) property. This property states the following:
[tex]log_b(1)=0[/tex]
When applying this property here, one can conclude that the evaluator must be equal to (1), therefore, the following statements can be made.
[tex]log(\frac{(x-4)(x-8)}{5})=0[/tex]
[tex]\frac{(x-4)(x-8)}{5}=1[/tex]
Inverse operations,
[tex]\frac{(x-4)(x-8)}{5}=1[/tex]
[tex](x-4)(x-8)=5[/tex]
[tex](x-4)(x-8)-5=0[/tex]
Simplify,
[tex](x-4)(x-8)-5=0[/tex]
[tex]x^2-12x+32-5=0[/tex]
[tex]x^2-12x+27=0[/tex]
Factor, rewrite the quadratic expression as the product of two linear expressions, such that when the linear expressions are multiplied, the result is the quadratic expression:
[tex]x^2-12x+27=0[/tex]
[tex](x-3)(x-9)=0[/tex]
Now use the zero product property to solve. The zero product property states that any number times (0) equals (0).
[tex]x=3,x=9[/tex]
Hello,
I suppose the question is solve for x.
[tex]\displaystyle log_5\ (a)=\dfrac{ln (a)}{ln (5)} \\\\log_5(x-4)=1-log_5(x-8)\\\\\dfrac{ln(x-4)}{ln(5)} =1- \dfrac{ln(x-8)}{ln(5)}\\\\ln(x-4)=ln(5)-ln(x-8)\\\\ln(x-4)+ln(x+8)=ln(5)\\\\ln((x-4)*(x-8))=ln(5)\\\\(x-4)*(x-8)=5\\\\x^2-12x+27=0\\\\\Delta=12^2-4*27=36=6^2\\\\x=9\ or\ x=3\\\\Sol=\{3,9\}\\[/tex]
For Moderators,
this is a mathematical resolution without any bla-bla sentences that you will easily find. (I can not do it sorry)
Which equation is NOT true?
Answer:
[tex]{ \bf{15x + 30 = 180}}[/tex]
If two boxes of cereal and a jug of milk cost $8.50, and three boxes of cereal and two jugs of milk cost $14.00, how much does a box of cereal cost?
Answer:
$3
Step-by-step explanation:
Let c represent the cost of a box of cereal and let m represent the cost of a jug of milk.
Create a system of equations:
2c + m = 8.5
3c + 2m = 14
Solve by elimination by multiplying the top equation by -2:
-4c - 2m = -17
3c + 2m = 14
Add them together and solve for c:
-c = -3
c = 3
So, a box of cereal costs $3
A box of cereal cost $3 if two boxes and a jug of milk cost $8.50, and three boxes and two jugs of milk cost $14.00.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, two boxes of cereal and a jug of milk cost $8.50, and three boxes of cereal and two jugs of milk cost $14.00
Let c stand for the price of a box of cereal and m for the price of a milk jug.
The obtained system of equations is as follows,
2c + m = 8.5
3c + 2m = 14
Multiply the top equation by -2 to reach the solution by elimination:
-4c - 2m = -17
3c + 2m = 14
Put them all together to find c:
-c = -3
c = 3
Thus, a box of cereal cost $3 if two boxes and a jug of milk cost $8.50, and three boxes and two jugs of milk cost $14.00.
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Traveling from City 1 to City 2, a pilot planned a southeast course along the path labeled d. Instead, a storm forced the pilot to travel 32 miles south, then 24 miles east to reach City 2. How many extra miles was the pilot forced to fly?
A. 13 mi.
B. 14 mi.
C. 16 mi.
D. 17 mi.
Answer:
C. 16 mi.
Step-by-step explanation:
This situation forms a right triangle: the distances 32 miles south and 24 miles east are the legs, and the original southeast course is the hypotenuse.
Use the pythagorean theorem, a² + b² = c² to solve for c, the length of the southeast course.
a² + b² = c²
32² + 24² = c²
1600 = c²
40 = c
So, the southeast course is 40 miles long.
Find how many miles the pilot traveled on the alternate route:
32 + 24
= 56
Find the difference in extra miles:
56 - 40
= 16
So, the pilot was forced to fly 16 extra miles.
The correct answer is C. 16 mi.
Answer:
16
Step-by-step explanation:
On Edge 2022
What is -2y + -4y. Simplify the answer.
Step-by-step explanation:
Explanation is in the attachment
hope it is helpful to you
Answer:
[tex]-2y+\left(-4\right)y[/tex][tex]=-2y-4y[/tex][tex]=-6y[/tex][tex]-----------[/tex]
hope it helps...
have a great day!!
nth term of an AP is given by an expression 7n-2,find the common difference of this sequence if fisrt term of sequence is 1? a.2 b.-2 c-7 d7
Step-by-step explanation:
there is something wrong with what your write here as problem description.
either there is something missing in the main expression, or in the answer options.
given your nth-term expression 7n-2, none of the 4 answer options can fit.
so, I thought, maybe there was a typo.
the possible interpretations of the expression could be
7n - 2
7(n-2)
[tex] {7}^{n} - 2[/tex]
[tex] {7}^{n - 2} [/tex]
we know that
a1 = 1
a2 = either
a1 + 2 = 3
a1 - 2 = -1
a1 + 7 = 8
a1 - 7 = -6
so, we can eliminate both negative answer options, because they would cause only negative sequence elements, but the main expression (neither of the 4 possibilities) does not allow that.
but also none of the 4 possibilities of the expression delivers any of the 4 values for a2 as described above.
7×2 - 2 = 14 - 2 = 12
7(2-2) = 7×0 = 0
7² - 2 = 49 - 2 = 47
[tex] {7}^{2 - 2} = {7}^{0} = 1[/tex]
similar not for a3.
so, if I consider your answer options right, we have 4 possible arithmetic sequences:
1. 1, 3, 5, 7, 9, 11, 13, 15, ...
2. 1, -1, -3, -5, -7, -9, -11, -13, ...
3. 1, 8, 15, 22, 29, 36, 43, 50, ...
4. 1, -6, -13, -20, -27, -34, -41, ...
the nth term expression is for
a. an = 2n - 1
b. an = 2×(-n) + 3 = 2×(-n + 1) + 1
c. an = 7n - 6
d. an = 7×(-n) + 8 = 7×(-n + 1) + 1
so, please pick the right expression from this list, and then use the answer option with the same letter.
Jayce travels 30 miles per hour in her car. How many miles does she travel in 4 hours?
Answer:
Step-by-step explanation:
Answer:
hello there
here is your answer:
120 miles
Step-by-step explanation:
because every 30 mile jayce drives is by 1 hour.
jayce travels for 4 hours so that 120 miles
also because you can mutiply 30*4=120
hope this helps have a good day bye
plz tell the answers in the correct order
Answer:
a) 120°
Step-by-step explanation:
i think this is the right answer
express 26 divide 4 +root3 in form a +b root3 where a and b are integres
Answer:
8 - 4[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Given: [tex]\frac{26}{4 + \sqrt{3} }[/tex]
To express the given question in the form a + b[tex]\sqrt{3}[/tex], we first have to rationalize the denominator of the expression.
Rationalizing the denominator, we have;
[tex]\frac{26}{4 + \sqrt{3} }[/tex] * [tex]\frac{4 - \sqrt{3} }{4 - \sqrt{3} }[/tex] = [tex]\frac{104 -26\sqrt{3} }{16 -4\sqrt{3} + 4\sqrt{3}- 3 }[/tex]
= [tex]\frac{104 - 26\sqrt{3} }{16 - 3}[/tex]
= [tex]\frac{26(4 - \sqrt{3} }{13}[/tex]
= 2(4 - [tex]\sqrt{3}[/tex])
= 8 - 4[tex]\sqrt{3}[/tex]
The required form of the given question is therefore 8 - 4[tex]\sqrt{3}[/tex]
What is the other solution to the equation (Algebra ll) *URGENT*
Given:
The equation is:
[tex]3-2|0.5x+1.5|=2[/tex]
One solution of this equation is -2.
To find:
The another solution of the given equation.
Solution:
We have,
[tex]3-2|0.5x+1.5|=2[/tex]
It can be written as:
[tex]-2|0.5x+1.5|=2-3[/tex]
[tex]-2|0.5x+1.5|=-1[/tex]
Divide both sides by -2.
[tex]|0.5x+1.5|=0.5[/tex]
After removing the modulus, we get
[tex]0.5x+1.5=\pm 0.5[/tex]
Case I:
[tex]0.5x+1.5=0.5[/tex]
[tex]0.5x=0.5-1.5[/tex]
[tex]0.5x=-1[/tex]
Divide both sides by 0.5.
[tex]x=-2[/tex]
Case II:
[tex]0.5x+1.5=-0.5[/tex]
[tex]0.5x=-0.5-1.5[/tex]
[tex]0.5x=-2[/tex]
Divide both sides by 0.5.
[tex]x=-4[/tex]
One solution of the given equation is [tex]x=-2[/tex] and the another one is [tex]x=-4[/tex].
Therefore, the correct option is B.
A car is sold for $7560 at a loss of 10%. What is the original cost of the car?
Answer:
car(c.p)=$8400
Step-by-step explanation:
L%=(c.p-s.p)100%
c.p
10%=(c.p-7560)100%
c.p
10c.p=100c.p-756,000
(10-100)c.p= -756,000
-90c.p= -756,000
-90 -90
c.p=8400
solve the equatiuon =
Find the measure of the indicated angle
Answer:
yes
Step-by-step explanation:
The diagram shows a cylinder of diameter 6 cm and height 20 cm what is the volume in cm3
Answer:
565.2cm³
Step-by-step explanation:
the radius= 6/2= 3 cm
the height= 20cm
the volume= 3.14× 3²×20
= 3.14×180= 565.2 cm³
Check the picture below.
Someone please help me out
Answer:
[tex] {x}^{3} + 5 {x}^{2} - x - 5 \\ {x}^{2} (x + 5) - 1(x + 5) \\ (x + 5)( {x}^{2} - 1)[/tex]
Find the product
14/4 • 33/10 =
Answer:
Step-by-step explanation:
[tex]\frac{14}{4}*\frac{33}{10}=\frac{7}{2}*\frac{33}{10}\\\\ =\frac{7*33}{2*10}\\\\=\frac{231}{20}\\\\=11\frac{11}{20}[/tex]
One side of a rectangle is 2 yd longer than two times another side. The area of the rectangle is 84 yd2. Find the length of the shorter side.
Answer:
6 yds
Step-by-step explanation:
If we label the shorter side as x, the longer side can be represented as 2x + 2. Now, we can write an equation to model the situation. The area of a rectangle is the sides multiplied by each other:
84 = x(2x + 2)
84 = 2x^2 + 2x
Since all terms are divisible by two, we can divide both sides by it:
42 = x^2 + x
We can write the quadratic equation in standard form:
x^2 + x - 42 = 0
Now, we can factor. We are looking for numbers that multiply to -42 and add to 1. These numbers are 7 and -6. Factored the equation would be written as followed:
(x + 7)(x - 6) = 0
Using the zero-product property, we can obtain two equations and solve them:
x + 7 = 0
x = -7
x - 6 = 0
x = 6
Since the side of a rectangle can't be negative, the answer must be 6 yds.
Il y a 5ans Thomas avait 5 fois l'âge de benoit aujourd'hui Thomas a 3 fois l âge de Benoît quel est l'âge de benoit
Répondre:
Benoit a 10 ans
Explication étape par étape :
Laisser :
Âge de Thomas = x
Benoit age = y
il y a 5 ans :
x - 5 = 5 (y - 5)
x - 5 = 5y - 25 - - (1)
Aujourd'hui :
x = 3y - - (2)
Mettez x = 3y dans (1)
3 ans - 5 = 5 ans - 25
Recueillir des termes similaires
3 ans - 5 ans = - 25 + 5
-2a = - 20
Diviser les deux côtés par - 2
y = 10
Solve the following pair of linear equations using substitution method
[tex] x-3y = 13[/tex]
[tex]x+2y=8[/tex]
Answer:
(10, - 1 )
Step-by-step explanation:
Given the 2 equations
x - 3y = 13 → (1)
x + 2y = 8 → (2)
Rearrange (1) making x the subject by adding 3y to both sides
x = 3y + 13 → (3)
Substitute x = 3y + 13 into (2)
3y + 13 + 2y = 8
5y + 13 = 8 ( subtract 13 from both sides )
5y = - 5 ( divide both sides by 5 )
y = - 1
Substitute y = - 1 into (3) for corresponding value of x
x = 3(- 1) + 13 = - 3 + 13 = 10
solution is (10, - 1 )
Problem: Construct a triangle with interior angle measures of 60° and 60°. Let one of the side lengths be 10. What are the lengths of the other sides?
Answer:
Step-by-step explanation:
Given a triangle with angles 60° and 60°. Let the third angle be represented by x, so that;
x + 60° + 60° = [tex]180^{o}[/tex] (sum of angle in a triangle)
x + 120 = [tex]180^{o}[/tex]
x = [tex]180^{o}[/tex] - 120
x = 60°
Thus, since the third angle of the triangle is 60°, then the triangle is an equilateral triangle. For an equilateral triangle, all sides are equal and all its angles are equal. So that the other sides of the triangle is 10 each.
<ABC ≅ <BAC ≅ < ACB ≅ 60°
AB = BC = AC = 10 cm
The required construction for the question is attached to this answer for more clarifications.
Answer:
It's an obtuse angle
Step-by-step explanation:
Solve for x. Round to the nearest tenth, if necessary.
Answer:
X would be 63.9
Hope it helps
Step-by-step explanation:
The value of the variable 'x' using the cosine formula will be 63.9 units.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The value of 'x' is given by the cosine of the angle ∠QSR. And the cosine of an angle is the ratio of the base and hypotenuse of the right-angle triangle. Then we have
cos 35° = x / 78
x = 63.9
The value of the variable 'x' using the cosine formula will be 63.9 units.
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