Answer:
a) 5x and - 4x
Step-by-step explanation:
Explanation:-
Given equation is 4 x² + x -5
the factors of -20 = - 4 × 5
⇒ 4 x² + 5x - 4x -5
⇒ x ( 4 x +5) -1 ( 4x +5)
⇒ (x -1) (4 x +5)
Answer:
A :)
Step-by-step explanation:
If h(x) = 5 + x and k(x)=1/x
which expression is equivalent to (k•h)(x)?
Answer:
(k•h)(x) is 5/x + 1
Step-by-step explanation:
(k•h)(x) is the product of the functions h(x) = 5 + x and k(x) = 1/x.
This product (k•h)(x) is 5/x + 1
Answer:
1/(5+×)
Step-by-step explanation:
how do you round 8.97998
Answer:
to the nearest number that would be 9
Step-by-step explanation:
Answer:
To 1 d.p. = 9.0
Step-by-step explanation:
Because 9 is greater than 5 and is after the decimal point so you round up
The temperature in Ottawa starts at -4°C, rises 14°C, and then falls 8°C. What is the final temperature?
Answer:
2 degrees celsius
The final temperature in Ottawa is 2°C.
We have,
Given:
Initial temperature = -4°C
Temperature rise = 14°C
Temperature fall = -8°C
The formula to calculate the final temperature.
Final temperature = Initial temperature + Temperature rise + Temperature fall
Final temperature = -4°C + 14°C + (-8°C)
Simplify
Final temperature = -4°C + 14°C - 8°C
Final temperature = 2°C
Therefore,
The final temperature in Ottawa is 2°C.
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Circle P is shown. Line segment J K is a diameter, and line segment N O is a tangent that intersects the circle at point J. Point L is on the circle between points J and K. Point M is on the circle between points J and K. The measure of ∠KJN is 92°. What is the measure of Arc J M K? PLZZZ I need an explanation
Answer:
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the length of a rectangle is two feet greater then twice its width if the primeter is 25 find the width
Answer:
Step-by-step explanation:
Perimeter is simply length + width. They gave us that the length is 2 feet plus 2 times the width:
[tex]25=(2w+2)+W[/tex]
Subtract 2 from both sides to get 23 = 2w + w
Combine like terms to get 23 = 3w
Divide by 3 to get [tex]w=7 \frac{2}3}[/tex] feet
Find the least number which must be added to 6203 to obtain a perfect square.
Also, find the square root of the number so obtained.
Answer:
79
Step-by-step explanation:
78
---------
7 | 62 03
49
----------
148 | 13 03
11 84
-----------
19
-----------
78^2 = 6084.
We observe that 78^2 < 6203.
79^2 = 6241.
We observe that 79^2 > 6203.
Hence the number to be added to 6203 is 6241 - 6203 = 38.
6203 + 38 = 3241
= 79 * 79
= 79.
Therefore 38 should be added to 6203 to obtain a perfect square.
Add the polynomials: (-5 - 7x^2); (5 + 7x^3) *
0 - 14x15
O 10 + 14x^3
0 -7x^2 + 7x^3
OO
Answer:
[tex] - 7 {x}^{2} + 7 {x}^{3} [/tex]
Step-by-step explanation:
[tex]( - 5 - 7 {x}^{2} ) + (5 + 7 {x}^{3} ) \\ = - 5 - 7 {x}^{2} + 5 + 7 {x}^{3} \\ = - 7 {x}^{2} + 7 {x}^{3} [/tex]
Satnam is making a cake. he uses a batter made of 150g of dry ingredients.if the liquid has to be two sevenths of the total weight of the batter, how much liquid should he add? please help thank you
Answer:
Answer- 85.7 g
300:7= 42.85
42.85x2=85.7
Step-by-step explanation:
Answer:
42.85
Step-by-step explanation:
Since the liquid has to be 2/7 of the batter, and the batter is 150g, then that means we should multiply 2/7 by 150. This is thus 42.85
Please help! WILL mark as brainliest! I'm rly struggling
Answer:
Since we know the number 8 is in all 3 shapes we know D is 8. The clue after that tells us that C is brown. Since brown, purple, and orange are in the circle that means that D is either purple or orange but since the purple section has 5 and D is 8 we know that D is orange, B is purple, and B is 5. Since the blue section is only in the triangle, we know that F is blue. From the last clue we know that A is green. Since green and pink are in the rectangle only, G is pink. Using the third clue we know that E and F are 6 and 1 but we don't know which is which. Thankfully, since we know F is blue and the yellow section is 1, we can conclude that F is 6, E is yellow, and E is 1. We know that A and G are 3 and 4 but we don't know which is which, and we know C is 9. Since A's number is smaller than G's we know that A is 3 and G is 4.
Six standard 6-sided dice are rolled, and the resulting numbers are multiplied together. What is the probability that the product is divisible by 125?
Answer:
1453/23328
Step-by-step explanation:
Since we are going to have at least three 5's to obtain a number divisible by 125, the number of ways we can combine exactly three 5's is ⁶C₃. The number of ways we can combine the remaining dice without containing a five is 5³, since there are 3 remaining dice. So, for exactly three 5's , we have ⁶C₃ × 5³. Similarly, for exactly four 5's, we have ⁶C₄ × 5² (5² since there are two dice left). Also, for exactly five 5's, we have ⁶C₅ × 5¹ (5¹ since there are one die left). Finally, for exactly six 5's, we have ⁶C₆ × 5⁰(5⁰ since there are no dice left without a five).
So, for at least three 5's, we have ⁶C₃ × 5³ + ⁶C₄ × 5² + ⁶C₅ × 5¹ + ⁶C₆ × 5⁰
= 20 × 125 + 15 × 25 + 6 × 5 + 1 × 1
= 2500 + 375 + 30 + 1
= 2906 ways
The total number of ways of combining the six dice is 6⁶
So, the probability of obtaining a product divisible by 6 is thus P = 2906/6⁶ = 2906/46656
= 1453/23328
Using the binomial distribution, it is found that there is a 0.0536 = 5.36% probability that the product is divisible by 125.
The product will be divisible by 125 in two outcomes:
3 of the dices result in 5, as [tex]5^3 = 125[/tex]6 of the dices result in 5, as [tex]5^6 = 5^3 \times 5^3[/tex]For each dice, there are only two possible outcomes, either the result is 5, or it is not. The results of the dices are independent, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
Six dices are rolled, hence [tex]n = 6[/tex].Each number is equally as likely, hence the probability of a 5 being rolled, that is, a success, is [tex]p = \frac{1}{6} = 0.1667[/tex].The probability that the product is divisible by 125 is:
[tex]p = P(X = 3) + P(X = 6)[/tex]
Hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{6,3}.(0.1667)^{3}.(0.8333)^{3} = 0.0536[/tex]
[tex]P(X = 6) = C_{6,6}.(0.1667)^{6}.(0.8333)^{0} \approx 0[/tex]
Then:
[tex]p = P(X = 3) + P(X = 6) = 0.0536 + 0 = 0.0536[/tex]
0.0536 = 5.36% probability that the product is divisible by 125.
A similar problem is given at https://brainly.com/question/24863377
On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below and to the right of the line is shaded. Which linear inequality is represented by the graph? y ≤ 2x + 4 y ≤ one-halfx + 3 y ≥ One-halfx + 3 y ≥ 2x + 3
Answer: [tex]y \leq \frac{1}{2} x+3[/tex]
Step-by-step explanation:
If a function has a positive slope, that means the y value is increasing with respect to x. As you go down the x-axis, the y value will continuously increase.
First you want to plot the two sets of coords that they gave you, or else you wont know what the line looks like. Or, you could visually do it in your head. We're going down -4 on the x-axis and down 1 on the y-axis. Then for our second coords, we are going to 0 on the x-axis, then up 3 on the y-axis.
You could plot this for yourself, but im going to do it in my head for simplicity. We also need to find the slope of this function in order for us to find the y-intercept. The slope is change in y divided by the change in x. Subtract the initial position from the final position.
3 - 1 = 2
0 - (-4) = 4
2/4 = 1/2
The new equation is:
[tex]y=\frac{1}{2} x+b\\plugin(0,3)\\3=\frac{1}{2} (0)+b\\b=3[/tex]
Everything is shaded below and to the right of the line. They said the line was solid, so that means less than or equal to, [tex]\leq[/tex]
Answer:
B
Step-by-step explanation:
if z (3,-1) is the midpoint of line segment of coordinate x (5,2) and y (a,b) then find the value of a and b. I need it fast if u tell fast I'll mark ur Brainliest. It's a deal
Answer:
the coordinates of y are (1,-4)
Step-by-step explanation:
by using midpoint formula
z(x,y)=([tex]\frac{x1+x2}{2}[/tex],[tex]\frac{y1+y2}{2}[/tex])
putting the values of coordinates
(3,-1)=[tex]\frac{5+a}{2}[/tex],[tex]\frac{2+b}{2}[/tex]
separating the coordinates
3=[tex]\frac{5+a}{2}[/tex] and -1=[tex]\frac{2+b}{2}[/tex]
3×2=5+a and -1×2=2+b
6=5+a and -2=2+b
6-5=a and -2-2=b
1=a and -4=b
so the actual coordinates of y are (1,-4)
i hope it will help you
What is the final amount if 1885 is increased by 5% followed by a further 18% increase?
Give your answer rounded to 2 DP.
Answer:
Answer = 2,335.52
Step-by-step explanation:
Given amount : 1,885
Finding 5% of 1,885 = 0.05 * 1,885
5% of 1885 = 94.25
Now 1885 increased by 5% = 1,885 + 94.25= 1,979.25
Finding further 18% of 1,979.25 = 0.18 * 1,979.25
18% of 1979.25 = 356.265
Final amount = 1,979.25 + 356.265
Final Amount = 2,335.515
Now Rounding off the answer to 2 decimal points we get:
Answer = 2,335.52
(As the third digit after decimal is 5 so previous will be added b 1)
An equilateral triangle has an apothem measuring 2.16 cm
and a perimeter of 22.45 cm.
What is the area of the equilateral triangle, rounded to the
nearest tenth?
2.7 cm
4.1 cm2
16.2 cm2
24.2 cm
2.16 cm
Answer:
d) 24.2 cm²
Area of equilateral triangle A = 24.22 cm²
Step-by-step explanation:
Step(i):-
Perimeter of equilateral triangle = 3 a
Given Perimeter of equilateral triangle = 22.45 cm
now 3 a = 22.45
Dividing '3' on both sides,we get
a = 7.48 cm
Step(ii):-
Area of equilateral triangle
[tex]A = \frac{\sqrt{3} a^{2} }{4}[/tex]
[tex]A = \frac{\sqrt{3} (7.48)^{2} }{4}[/tex]
A = 24.22 cm²
Conclusion:-
Area of equilateral triangle A = 24.22 cm²
Answer:
The answer is 24.2
Step-by-step explanation:
on edg. 2020
Evaluate the difference between 55.4 and 4.11.
Hey there!
The word "difference" means 'SUBTRACT' in mathematical terms. Now that we know the definition we could solve for this equation!
New equation: "55.4 - 4.11 = ?"
55.4 - 4.11 = 51.29
Thus, your answer is: 51.29
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
What is the range of the function?
The function f(x) = (x - 4)(x - 2) is shown.
10
O all real numbers less than or equal to 3
O all real numbers less than or equal to - 1
O all real numbers greater than or equal to 3
O all real numbers greater than or equal to - 1
Answer:
The range of the function is all real numbers greater than or equal to -1.
Step-by-step explanation:
Second order polynomials are continous and have an absolute maximum or minimum that restricts the set of the range associated with the function. A fair approach to estimate the range is rewritting the expression into parabola form, which is:
[tex]y - k = C \cdot (x-h)^{2}[/tex]
Where:
[tex]C[/tex] - Vertix parameter, dimensionless. If [tex]C > 0[/tex], then vertix is an absolute minimum, but if [tex]C < 0[/tex], vertix is an absolute maximum.
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
[tex]h[/tex] - Location of the vertix with respect to the independent variable, dimensionless.
[tex]k[/tex] - Location of the vertix with respect to the dependent variable, dimensionless. This value restrics the set corresponding to the range of the polynomic function.
First, we have to expand polynomial into its standard form:
[tex]y = (x-4)\cdot (x-2)[/tex]
[tex]y = x^{2}-6\cdot x +8[/tex]
Now, we are going to complete the square and factorize the resultant expression until parabola form is obtained:
[tex]y = x^{2}-6\cdot x + 9 -9 + 8[/tex]
[tex]y = (x-3)^{2} -1[/tex]
[tex]y + 1 = 1 \cdot (x-3)^{2}[/tex]
Since the vertix parameter is positive, then vertix is an absolute minimum. The location of the vertix with respect ot the depedent variable is [tex]k = -1[/tex]. Therefore, the range of the function is all real numbers greater than or equal to -1.
Type the expression that results from the following series of steps: Start with t, add 6, multiply by 2, then subtract 5.
Answer:
2(t+6)-5
Step-by-step explanation:
The unknown number is t
=> Adding 6 will make it t+6
=> Multiplying 2 will make it 2(t+6)
=> Subtracting 5 will make it 2(t+6)-5
When x^3 + 2x^2 - 7x + a is divided by (x-2) the remainder is 4. Find the value of a. Please help
Answer:
a = - 8
Step-by-step explanation:
A polynomial divided by factor (x - h) has a remainder given by f(h)
Here the divisor is (x - 2), thus f(2) gives the remainder, that is
2³ + 2(2)² - 7(2) + a = 4 ← 4 being the remainder
8 + 8 - 14 + a = 4, that is
12 + a = 4 ( subtract 12 from both sides )
a = - 8
You guys I don’t even know how to start this help please!!!
Use the right triangle below to solve.
Which trig function should be used to find side AB if you know the measure of angle A and side CB?
A sine
B cosine
C tangent
D none of these
option A
use sin because it's formula is opposite/hypotenuse
=BC/AB
HERE'S YOUR ANSWER GIRLFRIEND ♥️♥️
Don't forget to follow
You know the opposite side of the angle and want to find the hypotenuse
Sin(angle) = opposite/ hypotenuse
You would use the sine function
Find the area of the circle R=3ft
Answer:
28.27 ft²
Step-by-step explanation:
Area of the circle is equal to πr².
Where r is the radius.
π(3)²
9π = 28.274334
The area of the circle is 28.27 ft² approximately.
Answer:
see below
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
A = pi (3)^2
A = 9pi
Letting pi be approximated by 3.14
A = 9 * 3.14
A=28.26 ft^2
If we use the pi button
A = 28.27433388 ft^2
another screenshot one... sowwwwyyy im really having trouble lolz
Answer:
the one that is a continuous line and starts in the num 4 in the y
Step-by-step explanation:
Answer:
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Instructions: Find the equation of the line through point (−4,1) and parallel to y=−12x−2. Use a forward slash (i.e. "/") for fractions (e.g. 1/2 for 12). Y=
Answer:
y = - 12x - 47
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 12x - 2 ← is in slope- intercept form
with slope m = - 12
Parallel lines have equal slopes, thus
y = - 12x + c ← is the partial equation
To find c substitute (- 4, 1 ) into the partial equation
1 = 48 + c ⇒ c = 1 - 48 = - 47
y = - 12x - 47 ← equation of parallel line
The required equation of the line is y = -12x - 47
What is the slope-point form of equation of the line?"The equation of the line having slope m and passing through points (p, q) is (y - q) = m(x - p)"
What is the slope-intercept form of the line?"y = mx + c, where m is the slope and c is the Y-intercept of the line."
For given question,
We have been given a point (-4, 1)
The required line is parallel to the line y = -12x - 2
Comparing above equation with slop-intercept form of the line.
m = -12
Let m1 be the slope of the required line.
We know that the slope of parallel lines is equal.
⇒ m1 = m
⇒ m1 = -12
Now we find the equation of the required line by using slope-point form.
Let (p, q) = (-4, 1)
By using slope-point form,
⇒ (y - q) = m1(x - p)
⇒ (y - 1) = -12(x - (-4))
⇒ y - 1 = -12x - 48
⇒ y = -12x - 47
Therefore, the required equation of the line is y = -12x - 47
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Factorize x^3-10x^2-53x-42
Answer:
(x+1)(x-14)(x+3)
Step-by-step explanation:
The first step in factorising polynomials is to find the smallest factor first. The way to do this is with trial and error. Lets see if x+1 is a factor.
According to the factor theorem, (x-a) is a factor of P(x) if and only when P(a) = 0
In this case we will use f(x) = ((x)^3)-((10x)^2)-53x-42
f(-1) = 0
Therefore (x+1) is a factor of the polynomial.
Now we divide the polynomial with (x+1) via long division to get (x^2)-11x-42.
We now factorise (x^2)-11x-42 using whatever method you would like. I'm going to use the AC method, where we find a number that multiplies to AC and adds to B, In this case AC = -42, and B = -11.
Therefore (x^2)-11x-42 factosied is (x-14)(x+3)
Now merge (x+1) with (x-14)(x+3)
The final answer is (x+1)(x-14)(x+3)
If this has helped, please consider making this the Brainliest answer!
Answer:
(x+1)(x+3)(x-14)
Step-by-step explanation:
=> x³-10x²-53x-42
We'll break 10x² and -53x into parts
=> x³+x²-11x²-11x-42x-42
Taking common
=> x²(x+1)-11x(x+1)-42(x+1)
Taking x+1 as common will make it
=> (x+1)(x²-11x-42)
Using mid term break formula
=> (x+1)(x²-14x+3x-42)
=> (x+1)[x(x-14)+3(x-14)]
Taking (x-14) as common
=> (x+1)(x+3)(x-14)
This is the required factorized form.
Hope it helps :)
(I'LL MARK U BRAINLIEST BUT PLS HELP FIRST)
Care packages cost $6.25 each and certificates cost $4.50 each. Mr. Fernandes has a budget of $550 to purchase both care packages and certificates. If he purchases 45 certificates, what is the maximum number of care packages he can purchase?
A) State maximum number of care packages he can purchase
B)Explain how you got it
Answer:
55
Step-by-step explanation:
find how much it costs to buy 45 certificates, subtract that from the original budget then divide that by 6.25 and remove the decimals
Answer:
He can buy up to 55 care packages
Step-by-step explanation:
c = certificates
p = packages
6.25p + 4.50c ≤ 550
c = 45
6.25p + 4.50(45) ≤ 550
6.25p + 202.50 ≤ 550
Subtract 202.50 from each side
6.25p + 202.50 -202.50 ≤ 550-202.50
6.25p ≤ 347.50
Divide each side by 6.25
6.25p/6.25 ≤ 347.50/6.25
p ≤ 55.6
Since we cannot buy part of a care package
p ≤55
Gracie owns a deferred annuity. The contract is tied to a market index, which was at 1000 when Gracie purchased the product and reached 1250 five years later at the end of the contract's crediting term. The 25 percent index gain is the basis for the amount of interest credited to the contract. What kind of annuity does Gracie own?
Answer:
Point to point indexed annuity.
Step-by-step explanation:
An indexed annuity is linked to specific index performance. Point to point indexed annuity is the one which gives interest on the basis of index percentage change. The interest credit is calculated by taking the percentage change between the beginning and end points of the index.
Consider the function represented by the graph. On a coordinate plane, a straight line with a negative slope begins on the y-axis at (0, 9) and exits the plane at (8, 1). What is the domain of this function?
Answer:
The domain of y = f(x) is [0,8]
Step-by-step explanation:
Since the straight line with negative slope begins on the y-axis at (0. 9) and exits the plane at (8, 1), we get is domain from the minimum and maximum values of x for which the function is valid.
So, the minimum value of x at which the function is valid is x = 0 and the function is y = f(0) = 9.The maximum value of x at which the function is valid is x = 8 and the function is y = f(8) = 1.
So, the domain of the function y = f(x) is [0,8]
Answer:
y = f(x) is [0,8]
Step-by-step explanation:
Which polynomial represents the sum below?
Answer:
D
Step-by-step explanation:
Combine like terms
3x^2 + 5x^2=8x^2
12x+7x=19
=3
Rewrite the equation by completing the square.
x2 – 2x + 1 = 0
Answer:
Step-by-step explanation:
What is the y-intercept of f(x)=(3/5)^x?
Answer: y-intercept = 1
Step-by-step explanation:
Make x equal to 0 and youll get the y-intercept. If you take something to the power of 0, you will always get 1.
The mean length of 9 childrens' big finger is 8.5cm. The mean length of 7 adults' big finger is 16.4cm. What is the mean length (rounded to 2 DP) of these 16 people's big finger?
Step-by-step explanation:
(8.5 cm + 16.4 cm) ÷ 16
= 24.9cm ÷ 16
= 1.25
= 1.25 cm
