Answer:
This looks a lot harder than it is, because with some clever observations we can quickly eliminate most solutions.
The first thing that springs to mind is a,b,c cannot all be odd, because then the LHS is even and the RHS is odd. Thus at least one of them must be even and therefore equal to 2. So let’s break this into two cases:
Case 1: c=2.
Hence we get
a(a+b)=122=2×61
Now a must be a positive prime factor of this number, and a+b is clearly more than a, so the only solution in this case is (a,b,c)=(2,59,2). Note here that we must check 59 is prime; fortunately it is.
Case 2: c≠2.
Now the RHS is odd, so a certainly can’t be even. But then b must be even, so b=2. Then we have
a(a+2)=120+c
Adding one to each side and factorising shows
(a+1)2=121+c
from which
c=(a+12)(a−10)
(if you are confused about this step think about difference of two squares factorisations).
But we know c is a prime number, so it can’t have any non-trivial factors. Thus one of the brackets must be 1, so a=11, which yields the solution (a,b,c)=(11,2,23). Once more we must check this solution is valid — again, it is, since 11 and 23 are prime. And those are the only two solutions since our cases cover every possibility.
Step-by-step explanation:
Answer:
1978
Step-by-step explanation:
This looks a lot harder than it is, because with some clever observations we can quickly eliminate most solutions.
The first thing that springs to mind is a,b,c cannot all be odd, because then the LHS is even and the RHS is odd. Thus at least one of them must be even and therefore equal to 2. So let’s break this into two cases:
Case 1: c=2.
Hence we get
a(a+b)=122=2×61
Now a must be a positive prime factor of this number, and a+b is clearly more than a, so the only solution in this case is (a,b,c)=(2,59,2). Note here that we must check 59 is prime; fortunately it is.
Case 2: c≠2.
Now the RHS is odd, so a certainly can’t be even. But then b must be even, so b=2. Then we have
a(a+2)=120+c
Adding one to each side and factorising shows
(a+1)2=121+c
from which
c=(a+12)(a−10)
(if you are confused about this step think about difference of two squares factorisations).
But we know c is a prime number, so it can’t have any non-trivial factors. Thus one of the brackets must be 1, so a=11, which yields the solution (a,b,c)=(11,2,23). Once more we must check this solution is valid — again, it is, since 11 and 23 are prime. And those are the only two solutions since our cases cover every possibility.
Which of the following is the coefficient in the algebraic expression 22y + z ?!
Answer:
22
Step-by-step explanation:
Answer:
22 is the coefficient.
Step-by-step explanation:
Because the coefficient is always beside the variable
For Ex: 10x
where x is your variable and 10 is your coefficient.
Hope my answer has helped you!
Which is the graph of g(x) = ⌈x + 3⌉? Image for option 1 Image for option 2 Image for option 3 Image for option 4
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]g(x)=\left|x+3\right|[/tex]
we know that
The graph is V-shaped
The vertex of the function is the point (-3,0)
The y-intercept is the point (0,3)
The graph in the attached figure
(20 Points)
Perform the indicated operations.
Answer:
5x-8/12y
Step-by-step explanation:
x+1
3y
+
x−2
4y
−(
x+3 /6y
=
30xy2−48y2
72y3
=
30x−48/72y
=
5x−8 /12y
13.5 is 15% of what number?
Answer:
90
Step-by-step explanation:
13.5/.15
To solve this you must use a proportion like so...
[tex]\frac{part}{whole} = \frac{part}{whole}[/tex]
15 is a percent and percent's are always taken out of the 100. This means that one proportion will have 15 as the part and 100 as the whole
We want to know out of what number is 13.5 15% of. This means 13.5 is the part and the unknown (let's make this x) is the whole.
[tex]\frac{13.5}{x} =\frac{15}{100}[/tex]
Now you must cross multiply
13.5*100 = 15*x
1350 = 15x
To isolate x divide 15 to both sides
1350/15 = 15x/15
90 = x
This means that 15% of 90 is 13.5
Hope this helped!
~Just a girl in love with Shawn Mendes
If x=-3 is the only x-intercept of the graph of a quadratic equation, which statement best discribes the discriminant of the equation?
Answer:
b² - 4ac = 0
Step-by-step explanation:
The nature of the roots of a quadratic equation are determined by the discriminant, that is
• If b² - 4ac > 0 then roots are real and distinct
• If b² - 4ac = 0 then roots are real and equal
• If b² - 4ac < 0 then roots are not real
x = - 3 indicates an equal root, hence b² - 4ac = 0
4(10x+2)-40x
Each step of the equation
Answer:
8
Step-by-step explanation:
We cannot solve this, since this is an expression, not an equation.
Lets simplify the expression
4(10x+2)-40x
Distribute the 4
40x +8 - 40x
8
Answer:
[tex]\displaystyle =8[/tex]
Step-by-step explanation:
Distributive property:
↓
A(B+C)=AB+AC
A=4, B=10x, and C=2
[tex]4*10x+4*2[/tex]
Simplify.
[tex]40x+4*2[/tex]
[tex]4*2=8[/tex]
[tex]40x+8[/tex]
[tex]40x+8-40x[/tex]
Group like terms
[tex]40x-40x+8[/tex]
Add numbers from left to right.
[tex]40x-40x=0[/tex]
[tex]\displaystyle 8[/tex], is the correct answer.
Hope this helps!
A regular convex polygon has eight sides. What is the measure of an exterior angle?
Answer:
The measure of one exterior angle is 45 degrees.
Step-by-step explanation:
The formula to find exterior angle of and shape is 360 degrees divided by n (number of sides the shape has). 360 divided by 8 = 45 degrees.
Answer:
Exterior angle = 45°
Step-by-step explanation:
We know that the sum of exterior angles of a polygon is 360 degrees.
Since here we a regular polygon with eight sides (which makes it an octagon) so this means that the interior angles each would be equal to:
[tex]\frac{(n - 2) \times 180}{n} \\ \frac{(8 - 2) \times 180}{8}\\ \frac{6 \times 180}{8} \\ \frac{1080}{8} [/tex] = 135 degrees
We know that each interior angle is supplementary to the exterior angle at the vertex.
So each exterior angle = [tex]180-135[/tex] = 45 degrees
enter the missing numbers in the boxes to complete the table of equivalent ratios
Time(min)
?
6
?
15
Distance(km)
6
18
24
?
Answer:
The ratio between 12 and 8 is 1.5, so you need to divide every other number by 1.5.
2/1.5=1.3
9/1.5=6
18/1.5=12
Hope this helps!
Step-by-step explanation:
The measure of angle A is 15 degrees and the length of side BC is 8. What are the lengths of the other two sides, rounded to the nearest tenth?
Answer:
AB=30.9 AC=29.9
Step-by-step explanation:
Rest of the answer is in the picture.
Answer:
AC= 29.9
AB= 30.9
What is the slope of the graph? Leave your answer as a reduced fraction.
Slope =
Identify the y-intercept. Write as a coordinate.
y-intercept =
Write an equation in slope-intercept form for the graph above.
y=
Answer:
-¼ = Slope
[0, 2] = y-intercept
y = -¼x + 2
Step-by-step explanation:
Your y-intercept is [0, 2] and your x-intercept is [8, 0] (not all the time your x-intercepts will be endpoints)]. Simply do rise\run until you hit another endpoint, starting from your y-intercept. As you can see, you go two blocks south, then eight blocks over east, since in this case, you are moving by increments of 2. If you were to recreate this graph in increments of 1, you would see that the simplification of -2\8, is -¼. That is why the rate of change is -¼. Do you understand?
the population of a city has increased by 15% since it was last measured. If the current population is 59.800, what was the previous population?
Answer:
about 50 000 i think sorry if this didnt hep
Step-by-step explanation:
To calculate the previous population before a 15% increase that resulted in a current population of 59,800, we use the formula: Previous Population = Current Population / (1 + Percentage Increase), which yields a previous population of approximately 52,000.
Explanation:The question pertains to determining what the previous population of a city was before it experienced an increase of 15%. Given that the current population is 59,800, we can calculate the previous population using the formula:
Current Population = Previous Population * (1 + Percentage Increase)
To find the Previous Population, we rearrange this formula:
Previous Population = Current Population / (1 + Percentage Increase)
By substituting in the given values:
Previous Population = 59,800 / (1 + 0.15)
Previous Population = 59,800 / 1.15
Previous Population = 52,000 (approximately)
Therefore, the previous population of the city was around 52,000 inhabitants before the 15% increase.
What is the slope and the y-intercept of the line on the graph below?
The slope is the amount of change in the value of y for every one unit increase in the value of x. Thus, what we are looking for is, if the value of x increases by 1, by how much will the value of y increase (or effectively decrease, if this value is negative)?
From the graph, we can see that as x increases, y decreases, therefor we know that this will be a negative number. Furthermore, if we look at the points (0, 1) and (4, 0), we can see that there has been a decrease of 1 unit (or an increase of -1 units) in the y-value for an increase of 4 units in the x-value. Thus, if we wanted to find how much the y-value increases for a one unit increase in the x-value we would have -1/4.
This also reflects the formula for the gradient being rise/run - there has been a 'rise' of -1 (negative since it has fallen rather than risen) and a 'run' of 4 (this refers to the amount of units in the x-direction).
Now we can see that either C or D is the answer.
To find the y-intercept, we simply look at what the y-value is when x = 0; looking at the graph, we can see that y = 1 when x = 0, thus the y-intercept is 1.
Given that the gradient is -1/4 and the y-intercept is 1, we can see that the answer is C.
Answer: OPTION C
(c) slope = Negative one-fourth, y-intercept = 1
slope = -1/4, y -intercept =1
Step-by-step explanation:
Explain how to convert a fraction to a percent.
Answer:
Convert the fraction to a decimal number. The fraction bar between the top number (numerator) and the bottom number (denominator) means "divided by." ...
Multiply by 100 to convert decimal number to percent. 0.25 × 100 = 25%
Step-by-step explanation:
Answer:
Divide the numerator by the denominator to get a decimal. Then move the decimal 2 places to the right and add the percent sign.
simplify ... 4xsquared x 4xsquared
Answer:
4X4=16
16X16=256
Step-by-step explanation:
Hi there! My name is Zalgo and I am here to provide you with your answer for today! So, 4x^2*4x^2 (4xSquared multiplied by 4xSquared) is quite simply. When you square a number, you are multiplying that number by itself (so, 4 times 4 equals 16). Once you have done that, you are left with 16 times 16. 16 multiplied by 16 is 256!
I hope that this answer helps! :D
"Stay Brainly and stay proud!" - Zalgo
(By the way, can you mark me as Brainliest? I'd greatly appreciate it! Thank you! :3)
How many solutions does the following equation have?
-6(x + 7) = -4.x - 2
Answer:
x=-20
Step-by-step explanation:
Given
-6(x+7)= -4x - 2
First of all, we have to solve brackets
So,
-6x-42=-4x-2
To find the solution of this equation, we have to isolate x on one side of the equation.
Adding 4x on both sides
-6x-42+4x = -2-4x+4x
-2x-42 = -2
Adding 42 on both sides
-2x-42+42 = -2+42
-2x=40
Dividing both sides by -2
-2x/2 = 40/-2
x = -20
The equation has only one solution which is x=-20 ..
simplify the polynomial by combining like terms
[tex]11x {}^{2} + 11x {}^{2} [/tex]
A.
[tex] - 12x {}^{2} [/tex]
B.
[tex]12x {}^{2} [/tex]
C.
[tex] - 24x {}^{2} [/tex]
D.
[tex]24x {}^{2} [/tex]
Answer:
22 x^2
Step-by-step explanation:
Simplify the following:
11 x^2 + 11 x^2
Hint: | Add like terms in 11 x^2 + 11 x^2.
11 x^2 + 11 x^2 = 22 x^2:
Answer: 22 x^2
none of your answers are correct.
find the total area for the regular pyramid
(please follow the answer set up in the picture)
Answer:
T.A. = 144 + 36√3
Step-by-step explanation:
The pyramid has a regular triangle for a base. The other three faces are isosceles triangles.
The height of base can be found by dividing it into two right triangles. We can either use properties of a 30-60-90 triangle, or use Pythagorean theorem.
h = 6√3
So the area of the base is:
A = 1/2 bh
A = 1/2 (12)(6√3)
A = 36√3
Similarly, the height of the three isosceles triangles can be found by dividing them into two right triangles and using Pythagorean theorem.
h = √(10² - 6²)
h = 8
So the area of the isosceles triangles is:
A = 1/2 bh
A = 1/2 (12)(8)
A = 48
So the total surface area of the pyramid is:
T.A. = 3(48) + 36√3
T.A. = 144 + 36√3
What is the product of -2x^3 + x - 5 and x^3 - 3x - 4 ? Show your work.
Is the product of x^3 - 3x - 4 and -2x^3 + x - 5 equal to the product of and ? Explain your answer.
For this case we must find the product of the following expressions:
[tex](-2x ^ 3 + x-5) (x ^ 3-3x-4)[/tex]
We apply distributive property, that is, we multiply term by term, taking into account that:
[tex]- * - = +\\- * + = -[/tex]
[tex]-2x ^ {3 + 3} + 6x^{3 + 1} + 8x ^ 3 + x ^ {1 + 3} -3x1 + 1 -4x-5x ^ 3 + 15x + 20 =\\-2x ^ 6 + 6x ^ 4 + 8x ^ 3 + x ^ 4-3x ^ 2-4x-5x ^ 3 + 15x + 20[/tex]
If we multiply:
[tex](x ^ 3-3x-4) (- 2x ^ 3 + x-5)[/tex]
We will obtain the same result because we would be applying the commutative property of multiplication.
ANswer:
[tex]-2x ^ 6 + 6x ^ 4 + 8x ^ 3 + x ^ 4-3x ^ 2-4x-5x ^ 3 + 15x + 20[/tex]
Answer:
2x^6+7x^4+3x^3-3x^2+11x+20
Step-by-step explanation:
.................. yw!! for nyone still wondering
Can someone give me the answer because I’m clueless
Answer:
D
Step-by-step explanation:
In year 0, we have 6.
In year 1, we have 6(4)
In year 2, we have 6(4)(4) or 6(4)^2
The 4 is the repeated factored
The answer is D
Please help I’m desperate for the answer
The domain is the input value of an equation/ graph, which is the X value.
The X value on a graph is the horizontal axis across the bottom.
The X-axis for this is the months, so the answer is The domain represents a 11-month period of flower production.
let h(x) = 2x + 5 and g(x) =8 - 3x. what is the value of h(g(1.5))?
Answer:
12
Step-by-step explanation:
g(1.5) is 8 - 3(1.5), or 8 - 4.5, or 3.5.
Then substitiute 3.5 for x in h(x) = 2x + 5: h(g(1.5)) = h(3.5) = 7 + 5 = 12
Your question asks what the value of h(g(1.5)) is.
Answer: 12To find the answer to your question, we're going to need to solve g(x) first, then plug in the answer from g(x) to h(x).
Lets solve:
We're going to plug in 1.5 to our "x" variables in the g(x) equation.
Your equation should look like this:
[tex]g(x)=8-3(1.5)[/tex]
Now, you solve:
[tex]g(x)=8-3(1.5)\\\\g(x)=8-4.5\\\\g(x)=3.5[/tex]
You should get 3.5
Once you're done solving g(x), we would plug in the answer we got from the G(x) equation into our h(x) equation.
Your equation should look like this:
[tex]h(x)=2(3.5) + 5[/tex]
Then, you solve:
[tex]h(x)=2(3.5) + 5\\\\h(x)=7+5\\\\h(x)=12[/tex]
Once you're done solving, you should get 12
This means that the value of h(g(1.5)) is 12.
12 should be your FINAL answer.
I hope this helps!Best regards, MasterInvestorWhich system below has no solution?
y = 4x and y = 2x - 3
y = -4x and y = 2x - 3
y = -4x and y = 2x + 3
y = -4-x and y = 2x - 3
it is multiple choice
The system of equations with y = -4x and y = 2x + 3 has no solution.
Explanation:The system of equations with y = -4x and y = 2x + 3 has no solution. To determine this, we can set the two equations equal to each other and solve for x:
-4x = 2x + 3
Adding 4x to both sides, we get:
0 = 6x + 3
Subtracting 3 from both sides, we get:
-3 = 6x
Dividing both sides by 6, we get:
-1/2 = x
Substituting x = -1/2 back into either equation will result in a false statement, indicating that the system has no solution.
Learn more about No solution to a system of equations here:https://brainly.com/question/30127282
#SPJ12
NEED HELP ASAP!
What is the value of x?
x =
The Intersecting Secant Theorem says
EC × ED = EB × EA
(x+4)(x+4+1) = (x+1)(x+1+11)
(x+4)(x+5)=(x+1)(x+12)
x^2 + 9x + 20 = x^2 + 13 x + 12
8 = 4x
x = 2
Check:
6(7)=42
3(14)=42, good
Answer: 2
Which is f(5) for the function –2x2 + 2x - 3?
Answer:
f(x)=-13
Step-by-step explanation:
-2x2+2x-3
-2(5)*2+2(5)-3
-10*2+10-3
-20+7=-13
I hope this helps!
Answer:
The value of f(5) is -43
Step-by-step explanation:
[tex]f(x)=-2x^2 + 2x - 3[/tex]
To find f(5) we plug in 5 for x in the given equation f(x)
Replace all x by 5
[tex]f(x)=-2x^2 + 2x - 3[/tex]
[tex]f(5)=-2(5)^2 + 2(5) - 3[/tex]
[tex]f(5)=-2(25) + 10 - 3[/tex]
[tex]f(5)=-50+ 10- 3=-43[/tex]
The value of f(5) is -43
what is the similarity ratio for two circles with areas 2pi m^2 and 200pi m^2
Answer:
The scale factor is equal to 10
Step-by-step explanation:
we know that
If two figures are similar. then the ratio of its areas is equal to the scale factor squared
Let
z ----> the scale factor
x ----> the area of the larger circle
y ---> the area of the smaller circle
so
[tex]z^{2}=\frac{x}{y}[/tex]
we ahve
[tex]x=200\pi \ m^{2}[/tex]
[tex]y=2\pi \ m^{2}[/tex]
substitute
[tex]z^{2}=\frac{200\pi}{2\pi}[/tex]
[tex]z^{2}=100[/tex]
[tex]z=10[/tex]
therefore
The scale factor is equal to 10
The radius of the larger circle is 10 times greater than the ratio of the smaller circle
Which best explains why this triangle is or is not a right triangle?
Answer:
D
Step-by-step explanation:
Using the converse of Pythagoras
If the square of the longest side equals the sum of the squares on the other 2 sides then the triangle is right.
longest side = 39
39² = 1521
36² + 15² = 1296 + 225 = 1521
The triangle is right since 36² + 15² = 39²
Answer:
This triangle is a right triangle:36² + 15² = 39².Step-by-step explanation:
If a ≤ b <c is the length of the sides of a right triangle, then:
[tex]a^2+b^2=c^2[/tex]
We have
[tex]a=15\ in,\ b=36\ in,\ c=39\ in[/tex]
Check the equality:
[tex]L_s=15^2+36^2=225+1296=1521[/tex]
[tex]R_s=39^2=1521[/tex]
[tex]L_s=R_s[/tex]
It's a right triangle.
PLEASE HELP LOL!!!!!!
first off, we know the angles at vertices C and F are right-angles, meaning both triangles are right-triangles.
we also know that sides AC = DF and BC = EF.
now, for right-triangles, if the two shorter legs are congruent in both triangles, the triangles are congruent by the Leg Leg theorem, namely LL.
Drag the tiles to the correct boxes to complete the pairs.
Using the properties of integer exponents, match each expression with the correct equivalent expression.
Answer:
1. [tex](-2^2)^{-6}[/tex] ÷ [tex](2^{-5})^{-4} \implies 2^{-32}[/tex]
2. [tex]2^4 . (2^2)^{-2} \implies 1[/tex]
3. [tex](-2^{-4}).(2^2)^0 \implies -2^8[/tex]
4. [tex](2^2).(2^3)^{-3} \implies 2^{-5}[/tex]
Step-by-step explanation:
1. [tex](-2^2)^{-6}[/tex] ÷ [tex](2^{-5})^{-4}[/tex] :
[tex] = \frac{ ( - 2 ^ 2 ) ^ { - 6 } } { ( 2 ^ { - 5 } ) ^ { - 4 } } = \frac{2^{-12}}{2^{20}} = 2^{-12-20}=2^{-32}[/tex]
2. [tex] 2 ^ 4 . ( 2 ^ 2 ) ^ { - 2 } [/tex] :
[tex]= 2^4 \times \frac{1}{2^4} = 1[/tex]
3. [tex](-2^{-4}).(2^2)^0[/tex] :
[tex]= (-2^4)^2 \times 1 = -2^8[/tex]
4. [tex](2^2).(2^3)^{-3}[/tex] :
[tex]= 2^4 \times \frac{1}{2^9} =\frac{1}{2^5} =2^{-5}[/tex]
Answer:
The answer is 1-2 2-4 3-4 and 4-3
Step-by-step explanation:
If Alessandra had 392,396 school books, what is the square root of half of her school books?
Answer:
Step-by-step explanation:
She likely has more books than the Library of Congress.
First of all you have to take 1/2 the number
(1/2) 392,396 = 196198
sqrt(196198) = 443 rounded to the nearest whole number.
evaluate f(x)=-x^-4 for x=3
The answer would be -0.012345679.
The first thing you would do is substitute 3 in for x, seeing that you've told us x = 3. After you've substituted x, the equation would look something like:
f(3) = -3^-4. From here, all you have to do is solve! -3 to the power of -4 equals -0.012345679. Therefor, f(3) = -3^-4 equals -0.012345679
Answer:
- [tex]\frac{1}{81}[/tex]
Step-by-step explanation:
Using the rule of exponents
• [tex]a^{-n}[/tex] ⇔ [tex]\frac{1}{a^{n} }[/tex]
Hence
f(3) =- [tex]3^{-4}[/tex] = - [tex]\frac{1}{3^{4} }[/tex] = - [tex]\frac{1}{81}[/tex]