Answer:
The equation of line g is y = x/3 + 5
Step-by-step explanation:
Given that the line d passes through the points (-3, 1) and (9, 5) we have the equation of line d in slope and intercept form., y = m·x + c found as follows;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Where;
(x₁, y₁) = (-3, 1)
(x₂, y₂) = (9, 5)
[tex]Slope, \, m =\dfrac{5-1}{9-(-3)} = \dfrac{4}{12} = \dfrac{1}{3}[/tex]
The line, d, in point-slope form is y - 1 = 1/3(x - (-3))
Which gives;
y - 1 = 1/3·x + 3/3
y = 1/3·x + 1 + 1 = 1/3·x + 2
Given that line g is parallel to line d, we have;
Slope of line g = slope of line d = 1/3
Therefore, the equation of line g passing through point ^6, 7) in point-slope form is y - 7 = 1/3(x - 6) which gives;
y = x/3 - 2 + 7 = x/3 + 5
The equation of line g is y = x/3 + 5
The line f passing through point (-3, -3) is perpendicular to ling g, therefore, the slope = -1/m = -1(1/3) = -3
The point-slope form of the equation is y -(-3) = -3(x - (-3)) which gives;
y + 3 = -3·x - 9
Therefore, the equation of line f is y = -3·x - 9 - 3 = -3·x - 12
The equation of line f is y = -3·x - 12.
What are the zeros of the function y = 2x2 + 5x+2 ?
pls helppp!
Answer:
answer is a
Step-by-step explanation:
zeros are x intercepts
Answer:
A
Step-by-step explanation:
(2x+1)(x+2)
so
2x=-1
x=-1/2
x=-2
A
What is the solution to this system of linear equations? 3x – 2y = 14 5x + y = 32 (3, 5) (6, 2) (8, –1) (14, –18)
Answer:
work is shown and pictured
The solution to the system of linear equation is (x, y) = (6, 2)
3x - 2y = 14 (1)
3x - 2y = 14 (1)5x + y = 32 (2)
From (2)
y = 32 - 5x
Substitute y = 32 - 5x into (1)
3x - 2y = 14 (1)
3x - 2(32 - 5x) = 14
3x - 64 + 10x = 14
13x = 14 + 64
13x = 78
x = 78/13
x = 6
Substitute x = 6 into (2)
5x + y = 32 (2)
5(6) + y = 32
30 + y = 32
y = 32 - 30
y = 2
(x, y) = (6, 2)
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Using leaner combination method what is the solution to the system of linear equations 7x-2y=-20 and 9x+4y=-6
Answer:
x = -2 and y = 3
Step-by-step explanation:
In linear combination method we try one of the variables from bopth of equations by
first making the variable equal in vlaue
then either subtracting or adding the two equation as required to eliminate the variable.
_____________________________________________
7x-2y=-20 equation 1
and 9x+4y=-6 equation 2
we see that y has
has value -2 and +4
4 = 2*2
thus, if we multiply equation1 with 2 we will give value for variable y as 4y and hence y can be eliminated easily.
7x-2y=-20
multiplying the LHS and RHS with 2
2(7x-2y)=-20 *2
=> 14x - 4y = -40 eqaution 3
now that we have got 4y
lets add equation 2 and equation 3
9x +4y= -6
+14x - 4y = -40
________________________________
=> 23x + 0 = -46
x = -46/23 = -2
Thus, x = -2
substituitinng x = -2 in 7x-2y=-20
7*-2 -2y=-20
=> -14 -2y = -20
=> -2y = -20+14 = -6
=> y = -6/-2 = 3
Thus, y = 3
solution is x = -2 and y = 3
Find the domain of each function: g(x)= 1/x−9
Answer:
x ∈ R, x ≠ 9
Step-by-step explanation:
Given
f(x) = [tex]\frac{1}{x-9}[/tex]
The denominator of f(x) cannot be zero as this would make f(x) undefined.
To find the value that x cannot be, equate the denominator to zero and solve for x
x - 9 = 0 ⇒ x = 9 ← excluded value
Thus the domain is x ∈ R, x ≠ 9
NEED HELP NOWWW Which of the following is a monomial?
O A. 9/x
O B. 20x - 14
O C. 11 x^2
D. 20^9 - 7x
Answer: C
Step-by-step explanation:
A monomial is a expression where in it is x to the power of something, and x cannot be a denominator
PQRS is a parallelogram. Find the values of a and b. Solve for the value of c if c = a + b.
A. 5
B. 14
C. 0
D. 7
Answer:
a = 7
b = 7
c = 14 [Correct option is B. 14]
Step-by-step explanation:
Since the shape is a parallelogram, to solve this problem, use some of the properties of a parallelogram:
(i) Opposite sides are parallel and congruent. Being congruent means the sides are identical. In other words, they have the same length.
From the diagram, this means that sides PQ and SR are identical. i.e
=> PQ = SR
=> 6a + 10 = 8a - 4 [collect like terms and solve]
=> 14 = 2a
=> a = 7
(ii) Opposite angles are congruent. Angles PQR and PSR are identical. i.e
<PQR = <PSR = (9b + 2)°
Also,
<SPQ = <SRQ = (18b - 11)°
(iii) Consecutive angles are supplementary. The sum of any two angles that are not opposite to each other is 180°. i.e.
<SPQ + <PQR = 180°
<PQR + <QRS = 180°
<QRS + <RSP = 180°
.
.
.
Also,
<PSR + <SPQ = 180°
(9b + 2)° + (18b - 11)° = 180° [expand bracket and solve for b]
9b + 2 + 18b - 11 = 180
27b - 9 = 180
27b = 189
b = 7
Now, since a = 7 and b = 7;
c = a + b = 7 + 7 = 14
Therefore;
a = 7
b = 7
c = 14
5/16 = 15/18 is proportion
Answer:
False
Step-by-step explanation:
In a proportion, the two fractions are equal. Here the denominators are different for the same numerator, so the fractions are not equal. The given expression is not a proportion.
Find the product.
7xy(3x2y3)
PLEASES HELP!!! ASAP!!!
Answer:
21x³y^4
Step-by-step explanation:
7xy(3x^2y^3)=
21x³y^4
Answer:
21x^3y^4
Step-by-step explanation:
Multiply each term:
21x^3y^4
Plz mark me brainliest!!
Simplify (8j3 − 10j2 − 7) − (6j3 − 10j2 − j + 12).
Answer:
Step-by-step explanation:
8j^3-10j^2-7-6j^3+10j^2+j-12
2j^3+j-12
HELP JOHN CHEN I need help
Logan Chivery owns her own car. Her june monthly interest was $300. The rate is 8 1/2 percent. Logans principal balance at the beginning of June is $42,335.14.
Logan Chivery owns her own car. Her June monthly interest was $300. The rate is 8.5 percent. Logan's principal balance at the beginning of June is: (Use 360 days-do not round the denominator.)
A. $42,353.14
B. $42,335.14
C. $2,335.14
Answer: A. $42,353.14
Step-by-step explanation:
When taking a loan, we have to pay interest. The Simple Interest Formula is:
Simple Interest (I) = Principal (P) × Interest Rate (r)
Principal (P) is the borrowed amount.
Interest Rate (r) is the percent of the principal to be paid.
Time (t) is the length of time that money is borrowed.
If Logan Chivery has the monthly interest of $300 at a rate of 8.5% per year, first, we have to convert the year rate to the month of June rate.
30 days = 8.5÷360÷30 = 0.7083333333 interest rate
Then, find the Principal by using the formula
Simple Interest (I) = Principal (P) × Interest Rate (r)
4,2352.94×0.7083333333÷100=299.99
In the picture down below
Answer:
b
Step-by-step explanation:
The answer is b because we are looking for opposites
The opposite of +x is -x
While the opposite of -3 is +3
with this, we can switch them around.
this gives us the inverse of 3-x
One number is 5 times another. If their
difference is 96, find the numbers.
Answer:24
Step-by-step explanation:
24*5=120.
So the difference between 120-24=96.
The required number, one number is 5 times another and their difference is 96 is 24 and 120.
One number is 5 times another. If their difference is 96, To find the numbers.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements.
Let the number be x and y
According to the first condition,
One number is 5 times another.So,
y = 5x
Following the second condition,
their difference is 96. So,
y - x = 96 - - - - - (1)
Now put y = 5x in the above equation
5x - x = 96
4x = 96
x = 96/4
x = 24
Now put x = 24 in y = 5x
y = 5*24
y = 120
Thus the required number, one number is 5 times another and their difference is 96 is 24 and 120.
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For the inequality y+4x≤x2+2, where is the graph shaded and is the curve solid or dotted?
Answer:
The graph shaded outside the parabola and the curve is solid.
Step-by-step explanation:
The given inequality is
[tex]y+4x\leq x^2+2[/tex]
It can be rewritten as
[tex]y\leq x^2-4x+2[/tex]
The sign of inequality is [tex]\leq[/tex], so the curve is a solid line.
The related equation of line is
[tex]y=x^2-4x+2[/tex]
Table of values is
x 0 2 4
y 2 -2 2
Plot these points and draw a U-shaped curve.
Check the equality for (0,0).
[tex]0\leq (0)^2-4(0)+2[/tex]
[tex]0\leq 2[/tex]
This statement is true. So, (0,0) lies in the shaded portion.
So, shade the graph outside the parabola.
Someone help quick!!!
The diagram shows several points and lines. Which statements are true based on the diagram? Select two options.
A. Points K, M, and N are collinear
B. Points J, K, and Q are collinear
C. Points are is the intersection of the line KN and the line MQ
D. Find JQ, KM, and MQ all
intersect at point K
E. There is only one line that can be drawn through points L and P
Answer:
B, E
Step-by-step explanation:
J, K, Q are all on the same line: collinear
You can draw only one line through L and P
Answer:
b,e
Step-by-step explanation:
e2020
Fredo has a coupon for $1.00 off the price of a loaf of bread at the grocery store.After he arrived at the store,he found out the bread had already been marked down $2.00.what is the total discount on the price of the bread.
Answer:
$3 discount
Step-by-step explanation:
If Fredo originally had the markdown as $0 (meaning no change), then he arrived at the store, seeing the markdown was $2, the current markdown is $2.
Now that he has an extra $1 off, he gets 2+1 = $3 off the bread.
Hope this helped!
plz help me 3y+x=7
4x-2y=0
Answer:
x = 1
y = 2
Step-by-step explanation:
3y + x = 7 first equation
-2y + 4x = 0 second equation
multiplying by -4 the first equatión
-4(3y + x = 7)
-4*3y -4*x = -4*7
-12y -4x = - 28
and sum the second equation:
-12y - 4x = -28
- 2y - 4x = 0
-14y - 0 = -28
-14y = -28
y = -28/-14
y = 2
from the first equation:
3y + x = 7
3*2 + x = 7
6 + x = 7
x = 7 - 6
x = 1
Check:
from the second equation:
4x - 2y = 0
4*1 - 2*2 = 0
4 - 4 = 0
Choose the best estimate for the division problem below
6.7 /0.6
A. 16
B. 15
C. 11
Answer:
11
Step-by-step explanation:
6.7 / .6
Multiply top and bottom by 10
67/6
66/6 = 11 so this is close to 11
A 5-column table has 4 rows. The first column has entries A, B, C, Total. The second column is labeled X with entries 15, 5, 30, 50. The third column is labeled Y with entries 5, 8, 15, 28. The fourth column is labeled Z with entries 10, 7, 5, 22. The fifth column is labeled Total with entries 30, 20, 50, 100. Which two events are independent?
Answer:
hey! it's A and X on edge :)
Please answer this in two minutes
Answer:
[tex] x = 6.6 [/tex]
Step-by-step explanation:
Given ∆WXY,
<X = 15°
<Y = 23°
y = 10
x = ?
To find side x, use the Law of sines as shown below:
[tex] \frac{x}{sin X} = \frac{y}{sin Y} [/tex]
Plug in the values of y, Y, and X
[tex] \frac{x}{sin 15} = \frac{10}{sin 23} [/tex]
[tex] \frac{x}{0.2588} = \frac{10}{0.3907} [/tex]
Cross multiply
[tex] x*0.3907 = 10*0.2588 [/tex]
Divide both sides by 0.3907 to solve for x
[tex] \frac{x*0.3907}{0.3907} = \frac{10*0.2588}{0.3907} [/tex]
[tex] x = \frac{2.588}{0.3907} [/tex]
[tex] x = 6.624 [/tex]
[tex] x = 6.6 [/tex] (to nearest tenth)
7th grade-Post-test Summer Sc...
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Which of the following pairs are like terms? Select all that apply.
11a and 13a power of 2
18k and 18b
7x and 16x
17yz and 12y
9pq and 8qp
Answer:
9pq, 8qp, and 7x, 16y
Step-by-step explanation:
these pairs have the same variable and exponent. To be a like term, you have to have same variables and same exponents, so therefore 11a and 13a^2 can't be like terms.
Coffee is sold in two different sized canisters. The smaller canister has a diameter of 9 cm and a height of 12 cm. The larger canister is double the size of the small canister (i.e., the diameter and height are doubled). Calculate the volume and surface area of each canister and compare the results of doubling the dimensions.
Answer:
Below
Step-by-step explanation:
The canister has a cylindric form
The volume of a cylinder is given by the following formula :
V= r^2 * Pi *h
H is the heigth and r os the radius(half of the diameter)
Let Pi = 3.14
●●●●●●●●●●●●●●●●●●●●●●●●
V= 3.14*4.5^2 * 12
V= 763.02
V = 763 cm^3(after rounding to the nearest unit)
●●●●●●●●●●●●●●●●●●●●●●●●
The surface area of a cylinder is given by the followong formula:
Sa = 3.14*r^2*2 + Pi*d*h
r is the radius, d the diameter and h the heigth
Let Pi= 3.14
Sa= 3.14*4.5^2*2 + 3.14*9*12
Sa= 466.29 cm^2
Sa= 466 cm^2 ( after rounding to the nearest unit
●●●●●●●●●●●●●●●●●●●●●●●●
The dimensions of the second canister are the double of the first one
V= r^2*Pi*h
V= 9^2 *3.14*24
V= 6104.16 cm^3
V= 6104 cm^3 (after rounding to the neatest unit)
Sa= 2*3.14*r^2+ 3.14*d*h
Sa= 2*3.14*9^2 + 3.14*24*18
Sa= 1865.16 cm^2
Sa= 1865 cm^2 (after roundong to the nearest unit)
●●●●●●●●●●●●●●●●●●●●●●●●
The volume and the surface area of the second canister are bigger than the first one
Divide the second volume by the first one :
V2/V1= 6104/763 = 8
We deduce that the voulme of the second canister is greater 8 times than the first one
Do the same for the surface area
Sa2/Sa1 = 1865/466 = 4.002 = 4 (after rounding to the nearest unit)
The second surface area is greater 4 times than the first one
Answer:
Yeah, what they said above.
Step-by-step explanation:
Let $f(x)=x+5$ and let $g(x)=x^2+1$. Let $p(x)=g(x)+f(x)$ and let $q(x)=g(x)-f(x)$. Find $p(x)\cdot q(x)$.
Answer:
The data that we have is:
f(x) = x + 5
g(x) = x^2 + 1
p(x) = g(x) + f(x) = (x^2 + 1) + (x + 5) = x^2 + x + 6.
q(x) = g(x) - f(x) = (x^2 + 1) - (x + 5) = x^2 - x - 4
We want to find p(x)*q(x)
well, we can replace:
p(x)*g(x) = (g(x) + f(x))*(g(x) - f(x))
Now, you can recall the relationship:
a^2 - b^2 = (a + b)*(a - b)
then we have that:
(g(x) + f(x))*(g(x) - f(x)) = g(x)^2 - f(x)^2
now we can replace g(x) and f(x) by the expressions that we know:
g(x)^2 - f(x)^2 = (x^2 + 1)^2 - (x + 5)^2
now we can simplify this:
(x^2 + 1)^2 - (x + 5)^2 = (x^4 + 2*1*x + 1^2) - (x^2 + 2*5*x +5^2)
= x^4 + 2*x + 1 - x^2 - 10x - 25
= x^4 - x^2 - 8*x - 24
p(x)*q(x) = x^4 - x^2 - 8*x - 24
Answer:
x^4+x^2-10x-24
Step-by-step explanation:
WILL GIVE BRAINLEIST!!!!!
Find the surface area of the right triangular prism shown below.
Answer:
144 units²
Step-by-step explanation:
Surface area of a traingular prism is given as:
Area = 2(B.A) + P*L
Where,
B.A = base area of the triangular prism = ½*b*h
b = base of the triangular base = 4 units
h = height of the triangular base = 3 units
Base Area (B.A) = ½*4*3 = 2*3 = 6 units²
P = Perimeter of triangular face = sum of all sides the triangle = 3 + 4 + 5 = 12 units
L = length or height of prism = 11 units
Plug in all values into the formula for surface area of triangular prism = 2(B.A) + P*L
[tex] Area = 2(6) + 12*11 [/tex]
[tex] = 12 + 132 [/tex]
[tex] Surface Area = 144 [/tex]
Surface area of the triangular prism = 144 units²
Please help mee What is the smallest positive integer whose proper divisors add up to more than the integer itself?
Answer:
12
Step-by-step explanation:
The proper divisors of 12 are
1 2 3 4 6
Add those together you get 16
What does x equal in the equation 4x + (−3) = 5x + 3?
Answer:
x = -6
Step-by-step explanation:
First write the equation.
4x + -3 = 5x + 3
The isolate x in the equation. Add -4x to both sides.
4x + -3 + -4x = 5x + 3 + -4x
-3 = x + 3
Then add -3 to both sides.
-3 + -3 = x + 3 + -3
-6 = x
Now you have the value of x = -6.
Cheers.
Answer:
x = -6Step-by-step explanation:
4x + (−3) = 5x + 3+3 +3
4x = 5x + 6-5x -5x
-x = 6÷(-1) ÷(-1)
x = - 6Solve the system algebraically. 2x+ y - 10 = 0 x - y - 4 = 0 What is the value of y? 1/3 2/3 14/3
Answer:y = 2/3
Step-by-step explanation:
2x + y = 10
x - y = 4
-----------------add
3x = 14
x = 14/3
x - y = 4
14/3 - y = 4
-y = 4 - 14/3
-y = 12/3 - 14/3
-y = -2/3
y = 2/3 <==
Answer:
2x + y = 10
x - y = 4
-----------------add
3x = 14
x = 14/3
x - y = 4
14/3 - y = 4
-y = 4 - 14/3
-y = 12/3 - 14/3
-y = -2/3
y = 2/3 <==
Step-by-step explanation:
Jason is playing a trivia game with his friends. At the end of each round, his score updates to the square of 1 less than the previous round’s score. If he has 8 points in the first round, which of the following recursive formulas can be used to determine his score at the end of future rounds? Assume that the number of rounds is unlimited, and n is the number of rounds.
Answer:
8+n^2
Step-by-step explanation:
Answer:
f(n+1)=(f[n]-1)^2, where f(1)=8
Step-by-step explanation:
"it appears your explanation includes a link" so you don't get an explanation
please hellppp please someone help me fast
Tins of milk each of volume 77cm^3 and weight 170g
were packed into an empty carton of volume 1540cm^3
and weight 5ooo g.
How many tins of milk can be packed to fill the carton ?
What is the weight of the carton when packed with the tins of milk?
Answer:
1. 20 tins of milk
2. Weight of the Carton = 8,4kg ot 8400g
Step-by-step explanation:
Given
Volume of a Tin = 77cm³
Weight of a tin = 5000g
Volume of Empty Carton = 1540cm³
Weight of Empty Carton = 5000g
Calculating the number of tins of milk
To do this, we have to make use of the given volumes;
And this is done as follows;
[tex]Number = \frac{Volume\ of\ Empty\ Carton}{Volume\ of\ a\ Tin}[/tex]
Substitute 77cm³ for Volume of a Tin and 1540cm³ for Volume of an Empty Carton
[tex]Number = \frac{1540cm^3}{77cm^3}[/tex]
[tex]Number = 20[/tex]
Hence, 20 tins of milk will filled the empty carton
Calculating the weight of the Carton after filled with tins of milk
This is calculated as thus;
Total Weight = Weight of Empty Carton + Weight of Tins of Milk
Substitute 5000g for Weight of Empty Carton
Total Weight = 5000g + Weight of Tins of Milk
_________________________________________
Calculating Weight of Tins of Milk
Since 20 tins of milk will fill the empty carton, the
Weight of Tins of Milk = 20 * Weight of 1 Tin of Milk
Weight of Tins of Milk = 20 * 170g
Weight of Tins of Milk = 3400g
_________________________________________
Substitute 3400g for Weight of Tins of Milk
[tex]Total\ Weight = 5000g + 3400g[/tex]
[tex]Total\ Weight = 8400g[/tex]
In Kilograms:
[tex]Total\ Weight = 8.4kg[/tex]