Work out the equation of the line which has a gradient of 3 and passes through the point (-1,3)

Answers

Answer 1

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1\\ &&(~ -1 &,& 3~) \end{array} \\\\\\ % slope = m slope = m\implies 3 \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-3=3[x-(-1)] \\\\\\ y-3=3(x+1)\implies y-3=3x+3\implies y=3x+6[/tex]

Answer 2

Answer: y=3x+6

Step-by-step explanation: use y=mx+c

Related Questions

which of these equations represents functions? check all that apply

Answers

Answer:
Option B. y=7x^4 and Option D. y=2x+1

These funcionts pass the test of the verical line (it cuts the graph in only one point). Please, see the attached file.

Thanks

Jackie has a drawer with 20 buttons, each of different color. How many different ways can she choose three buttons for her bookbag?

Answers

To find all the different possible combinations, you multiply all the possibilities for each position.

1st - she as 20 different possible buttons
2nd - she would have 19 possible buttons
3rd-she would have 18 possible buttons

20 x 19 x 18=6840 possible ways to choose these buttons.

Using an algebraic rule, describe a translation 2 units to the left.

Answers

Answer:
point (x,y) translated 2 units to the left will give the point (x-2,y)
(x,y) = (x-2,y)

Explanation:
We will apply the translation on a given point.
Suppose that we have a point with coordinates (x,y).
We want to translate this point 2 units to the left. This means that we will move this point 2 units to the left.
Doing this, we will find that:
the x-value of the coordinate is decreased by 2
the y-value of the coordinate did not change as no translation occurred in the vertical axis.

Therefore:
a point (x,y) can be translated two units to the left to be (x-2 , y)

Hope this helps :)

For a point in the x-y plane,
(x,y)->(x-2, y)

For a function f(x), f(x)->f(x-h) where h is displacement to the right.
=>
f(x)->f(x+2)

the width of a rectangle is X and the length is twice he width. if the area of the rectangle is 162, what is X?

Answers

Final answer:

To find the value of X in a rectangle with width X and length 2X, we can use the area formula. By solving the equation, we find X = 9, making the width of the rectangle 9 units.

Explanation:

To find the value of X, we need to use the given information about the length and width of the rectangle. Let's assume the width of the rectangle is X. Since the length is double the width, it is 2X. The area of the rectangle is given as 162, so we can set up the equation:

Width × Length = Area

X × 2X = 162

Simplifying the equation, we get:

2X^2 = 162

Dividing both sides by 2, we have:

X^2 = 81

Taking the square root of both sides, we find:

X = ±9

Since the width cannot be negative, the value of X is 9. Therefore, the width of the rectangle is 9 units.

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Final answer:

The width of the rectangle is 9 units.

Explanation:

To find the width of the rectangle, we can set up the equation for the area. The width of the rectangle is X, and the length is twice the width, meaning the length is 2X. The formula for the area is length times width, so we have X * 2X = 162. Simplifying this equation gives us 2X^2 = 162. Dividing both sides by 2 gives us X^2 = 81. Taking the square root of both sides gives us X = 9. Therefore, the width of the rectangle is 9 units.

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here goes another question lol oops

Answers

Student 1 and 3.
[tex] - (5r - 3s + 1) = - 5r + 3s - 1[/tex]
Move the negative into the brackets,
positive becomes negative while two negatives make a positive.

1. -(5r - 3s + 1)
simplify....
-5r + 3s - 1

2. -5r + 3s + 1

3. -5r + 3s - 1

student 1 and student 3 have the equivalent equations.
Your answer is A. Student 1 and Student 3.

Write an equation that represents the data in the table x 5,10,15,20 y 17,22,27,32

Answers

they go up by 12
17-5=12
22-10=12
27-15=12
32-20=12

Which of the following is parallel to the line =6x + 1

Answers

Try this option:
common equation for line is y=kx+b, where k=tgα, b-number.
Rule: if y||y₁, then k=k₁.
It means that according to given conditions y₁=k₁x+b₁ ⇒ y₁=6x+b₁.

answer: y₁=6x+b₁

Lurinda ordered some boxes of greeting cards online. The cost of the cards is $6.50 + $3 where n is the number of boxes ordered and $3 is the shipping and handling charge. How much will Lurnda pay if she orders 8 boxes of cards

Answers

Answer:

$55

Step-by-step explanation:

Put 8 where n is in the equation and do the arithmetic.

cost = $6.50·n + 3

= $6.50·8 + 3 = $52 + 3

cost = $55

given abcd ac = 22 and ae= 2x-5 find the value of x

Answers

the complete question in the attached figure

we know that
if AC=22
then AE=AC/2----------> 22/2----------> AE=11
so
2x-5=11----------> 2x=16---------> x=16/2--------> x=8

the answer is x=8

The answer to this question is x=8... APEX

You are due a $750 paycheck at the end of the week (Friday), but want to get your hands on the cash on Monday. A payday lender offers to make this deal with you for a fee of 2% of the paycheck. What is the rate you are paying for this service? Assume a 365-day year.

Answers

Let R = rate, B = base and P = percentage

Use R = P/B

R = 0.02/750

Can you finish?

Assuming this is a simple discount note with a face value of $750, the interest that will be deducted is 2%*$750 = $15. Then the proceeds are $750 -15 = $735, and the effective annual rate is
.. 15/(735*(4/365)) ≈ 186.2%

If the area of a triangle is 5 5/6 feet and the base is 5 feet. What is the height?

Answers

[tex]\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh\quad \begin{cases} b=base\\ h=height\\ -----\\ A=5\frac{5}{6}\\ b=5 \end{cases}\implies 5\frac{5}{6}=\cfrac{1}{2}(5)h\implies \cfrac{5\cdot 6+5}{6}=\cfrac{5h}{2} \\\\\\ \cfrac{35}{6}=\cfrac{5h}{2}\implies 70=30h\implies \cfrac{70}{30}=h\implies \cfrac{7}{3}=h\implies 2\frac{1}{3}=h[/tex]

how can you use place -value blocks and a hundred chart to show the number that is ten more than 43? what is the number

Answers

The number that is ten more than 43 is 53

Represent the number with x.

A number x that is 10 more than 43 is then calculated using the following equation

x - 43 = 10

Add 43 to both sides of the equation

x - 43 + 43 = 10 + 43

Evaluate the sums

x = 53

Hence, the number that is ten more than 43 is 53

See attachment for the place value blocks

Answers

the area of a triangle = 1/2 base * height (basically half of a rectangle)

so 1/2 * 18 * 15.25 = 9*15.25 = 137.25

don't forget units so the answer is 137.25 inches squared

The area of the triangle is half the product of its base and height. The area of the triangle is 137.25 in².

What is the area of the triangle?

The area of the triangle is half the product of its base and height. It is given by the formula,

[tex]\rm \text{Area of triangle} = \dfrac{1}{2} \times base \times height[/tex]

As it is given that the base of the triangle is 15¹/₄ inches, while the height of the triangle is 18 inches. Therefore, the area of the triangle is,

[tex]\rm \text{Area of triangle} = \dfrac{1}{2} \times base \times height[/tex]

[tex]= \dfrac{1}{2} \times 15(1/4)\times 18\\\\\\ = \dfrac{1}{2} \times \dfrac{(15\times 4)+1}{4} \times 18\\\\\\= \dfrac{1}{2} \times \dfrac{61}{4} \times 18\\\\\\=137.25\rm\ in^2[/tex]

Hence, the area of the triangle is 137.25 in².

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a golf pro shop sells two types of shirts, the first for 100$ each and the other for 60$ each. last month the shop sold 50 of these shirts for a total of 4600$ how many 100$ shirts did they sell?

Answers

The answer would be 40. This can be found by using the formula "60s + 100t = 4,000" or replacing 40 into the formula above, which would mean there were 10 $60 shirts totaling $4,600 and 50 shirts.

Prepare 350g of a 2% lidocaine cream using a 1% lidocaine cream a 5% lidocaine cream

Answers

a) 1% lidocaine -x g, 0.01x pure lidocaine
5% lidocaine -y g, 0.05y pure lidocaine
(1)0.01x+0.05y=350*0.02
0.01x g we get from1% lidocoine and 0.05y g we get from 5% lidocoine

(2) x+y=350
x g is mass 1% lidocoine, we combine it with y g 5%,
so we get x+y, and we need 350g,
so x+y should be equal 350, x+y=350

we get system of 2 equations that we need to solve to find x and y

(1)0.01x+0.05y=350*0.02
(2) x+y=350

we can solve it by substitution, find x from (2) equation
x=350-y, substitute it into (1)
instead of x we put (350-y)
0.01(350-y)+0.05y=7
3.5-0.01y+0.05y=7
0.04y =3.5
y=87.5g 5% lidocaine

b)x=350-87.5=262.5 g 1% lidocaine
c) 350g =350000 mg

------------------------------------------------------------------
Define x and y:
------------------------------------------------------------------
Let x be the amount of 1% lidocaine needed.
Let y be the amount of 5% lidocaine needed.

------------------------------------------------------------------
Construct Equations:
------------------------------------------------------------------
x + y = 350

0.01x + 0.05y = 0.02 x 350
0.01x + 0.05y = 7

------------------------------------------------------------------
Solve x and y:
------------------------------------------------------------------
x + y = 350 ------------- (Equation 1)
0.01x + 0.05y = 7 ------------- (Equation 2)

------------------------------------------------------------------
From equation 1:
------------------------------------------------------------------
x + y = 350
x = 350 - y

------------------------------------------------------------------
Substitute x = 350 - y into equation 2:
------------------------------------------------------------------
0.01(350 - y) + 0.05y = 7
3.5 - 0.01y + 0.05y = 7
3.5 + 0.04y = 7
0.04y = 7 - 3.5
0.04y = 3.5
y = 87.5

------------------------------------------------------------------
Substitute y = 87.5 into equation 1:
------------------------------------------------------------------
x + y = 350
x + 87.5 = 350
x = 350 - 87.5
x = 262.5

------------------------------------------------------------------
Find x and y:
------------------------------------------------------------------
x = 262.6g (5% lidocaine cream)
y = 87.5g (1% lidocaine cream)

------------------------------------------------------------------
Convert 350g to milligram:
------------------------------------------------------------------
350g = 350 x 1000 mg
350g = 350 000mg

------------------------------------------------------------------
Answer:
(a) Amount of 5% lidocaine needed = 87.5g
(b) Amount of 1% lidocaine needed = 262.g
(c) 350g = 350 000mg
------------------------------------------------------------------

For her cell phone plan Heather pays $30 per month plus 0.05 protects she wants to keep her bill under $60 per month with any quality represents the number of texts T Heather can't spend each month while staying within her budget

Answers

Hi there!

Let the number of texts be represented by T.
The we get the following function of total cost:
Total cost = 30 + 0.05T.

Since Heather wants her bill to be under $60, the total cost must be smaller than 60. We get the following

30 + 0.05T < 60
Subtract 30 from both sides.

0.05T < 30
Divide by 0.05

T < 600. Therefore Heather can send a maximum of 600 texts (and then she pays a bill of $60)

In ∆ABC with m∠C = 90° the sides satisfy the ratio BC:AC:AB = 4:3:5. If the side with middle length is 12 cm, find: 1) The perimeter of ∆ABC; 2) The area of ∆ABC; 3) The height to the hypotenuse.

Answers

BC: 16
AC: 12
AB: 20

perimeter :
[tex]12 + 16 + 20 = 48[/tex]
area:
[tex](12 \times 16) \div 2 = 192 \div 2 = 96[/tex]
hope this helps

Jane goes to the fruit market every week. On Monday she buys 10 pears and 11 oranges for $10.05 By Friday she is out of fruit and goes back to the market to purchase 1 pear and one orange for $0.94 How much did Jane spend on 1 orange?

Answers

The answer may be 0.65, because 0.95(10)=9.40 and 10.05-9.40=0.65. I got the answer myself from yahoo

gloria went to the mall and spent 50 minutes shopping. then she. had lunch for 30 minutes. if gloria arrived at the mall at 11:00 a.m at what time did she finished lunch?

Answers

11:00am+50 minutes= 11:50
11:50am+ 30 minutes = 12:20

Gloria went to the mall and spent 50 minutes shopping. Then she had lunch for 30 minutes. If Gloria arrived at the mall at 11:00 A.M., at what time did she finish lunch?

Which polynomial represents the difference below? 7x8 + 8x6 - 2x + 9 - (4x8 + 3x7 + 3)

Answers

Use associativity and distributivity properties:
[tex]7x^8 + 8x^6 - 2x + 9 - (4x^8 + 3x^7 + 3)=(7-4)x^8-3x^7+8x^6-2x\\+(9-3)\\=3x^8-3x^7+8x^6-2x+6[/tex]
We are done.

Consider the difference of polynomials [tex](7x^8 + 8x^6 - 2x + 9) - (4x^8 + 3x^7 + 3).[/tex]

The first thing you have to do is take that "minus" sign through the parentheses containing the second polynomial (just change sign + to - and sign - to +):

[tex](7x^8 + 8x^6 - 2x + 9) - (4x^8 + 3x^7 + 3)=7x^8+8x^6-2x+9-4x^8-3x^7-3.[/tex]

Then combine terms with the same degree:

[tex]7x^8+8x^6-2x+9-4x^8-3x^7-3=(7x^8-4x^8)-3x^7+8x^6-2x+(9-3).[/tex]

Note that

[tex]7x^8-4x^8=(7-4)x^8=3x^8,\\ \\9-3=6.[/tex]

Thus,

[tex](7x^8 + 8x^6 - 2x + 9) - (4x^8 + 3x^7 + 3)=3x^8-3x^7+8x^6-2x+6.[/tex]

In the following function defined by an equation in the form y=ax^2+bx+c, identify the values of a, b, and c. y=-2x^2

a) A=-2, b=0, c=0
b) a=-2, b=-2, c=-2
c) a=0, b=-2, c=0
d) a=0,b=0, c=-2

Answers

[tex]\sf y=ax^2+bx+c[/tex]

[tex]\sf y=-2x^2[/tex]

'a' here is -2, 'b' is 0, and 'c' is also 0, anything multiplied by 0 is 0, adding 0 to anything keeps it the same. So the answer is A.

Final answer:

In the quadratic function y = -2x^2, the values of the coefficients a, b, and c are -2, 0, and 0, respectively.

Explanation:

In the quadratic equation y = ax^2 + bx + c, the coefficients a, b, and c represent specific values that dictate the curve's shape and position. Given the equation y = -2x^2, we can compare it to the standard form to determine its coefficients. It is evident that a is -2, b is 0 since there is no x-term, and c is also 0 because there is no constant term. Therefore, the correct answer is a=-2, b=0, c=0, which corresponds to option a.

find × if m<1=2×+10 and m<2=3×-6

Answers

∠1 = ∠2
2x +10 = 3x -6
16 = x . . . . . . . . . . . add 6-2x

Selection B is appropriate.

I need help!!! Pleasssse!!!!

The ratio of the length to the width to the height of a rectangular box of cereal is 6:2:7. The sum of the length and the width of the box is 24 centimeters. Find the surface area of the box of cereal

Answers

The sum of the length and width ratio units is 6+2 = 8. Since this stands for 24 cm, each ratio unit stands for 3 cm. The actual dimensions are
18 cm : 6 cm : 21 cm

The surface area (S) is given in terms of length (L), width (W), and height (H) by
S = 2(LW +H(L+W))
= 2((18 cm)*(6 cm) +(21 cm)*(18 cm +6 cm))
= 2(108 cm² +(21 cm)*(24 cm))
= 1224 cm²

The surface area of the box of cereal is 1224 cm².

Granny has some stickers.if she gives 6 stickers to each of her grandchildren,she will have 5 stickers left.if she gives 7 stickers to each of her grandchildren,she will need 2 more stickers.how many grandchildren does granny have?

Answers

sorry, but if you're in college, why do need to ask this question. this is like a 5th grade question.

Convert 15/9 to a decimal. A. 1.64 B. 1.67 C. 1.66 D, 1.69

Answers

15/9 = 1.6666... (where 6 repeats infinitely)

If we're rounding to 2 decimal places, 6 will round up to 7

Therefore, B. 1.67 is your answer

Which expression is equivalent to:

25a + 5b - 13

Answers

25a + 5b - 13

5(5a + b) - 13 is your answer

using the distributive property, we can distribute 5 to all terms within the parenthesis:

5(5a + b) - 13 = 25a + 5b - 13

5(5a) = 25a
5(b) = 5b

25a + 5b - 13 = 25a + 5b - 13 (True)

hope this helps

Answer:

The correct option is 4.

Step-by-step explanation:

The given expression is

[tex]25a+5b-13[/tex]

In option (1), the given expression is

[tex]20a+5a+b-13[/tex]

Combine like terms.

[tex]25a+b-13[/tex]

This expression is not equivalent to the given expression.

In option (2), the given expression is

[tex]20(5a+5b)-13[/tex]

Using distributive property.

[tex]100a+100b-13[/tex]

This expression is not equivalent to the given expression.

In option (3), the given expression is

[tex]30ab-13[/tex]

This expression is not equivalent to the given expression.

In option (4), the given expression is

[tex]5(5a+b)-13[/tex]

Using distributive property.

[tex]25a+5b-13[/tex]

This expression is equivalent to the given expression.

Therefore correct option is 4.

The ratio of french fries to packets of ketchup in Philip's bag is 8:1. What does this mean? A. There are 7 more french fries than packets of ketchup. B. For every 8 french fries, there is 1 packet of ketchup. C. For every 8 packets of ketchup, there is 1 french fry. D. There are 8 more french fries than packets of ketchup.

Answers

It's B. because the question says the ratio of fries to ketchup is 8 to 1 (for every 8 there is one)
In the question fries go firs and then ketchup, in tge rat 8 goes first and then 1

so if ratio of pens to book is 5 to one (5:1), than it means that for every 5 pens there is one book.

Brandon is twice as old as his brother Ryan. Ryan is one-eighth the age of their father. If their father is 52 years old, how old are Ryan and Brandon? (Please show work)

Ryan ________

Brandon ________

Answers

Ryan is 1/8 of 52 Ryan is 6.5 years old or
52 ÷ 8 = 6.5 6 years and 6 month old.

Brandon is 6.5 × 2
Brandon is 13 years old

Answer:

Brandon is 13 and Ryan is 6 and 1/2

Step-by-step explanation

Write the first four terms in the multiplication pattern given by the formula:

10 · 5n

Answers

we have that
an=10 * 5n---------------> an=50*n

then

for n=1
a1=50*1=50

for n=2
a2=50*2=100

for n=3
a3=50*3=150

for n=4
a4=50*4=200

the answer is
the first four terms are [50,100,150,200]

Can someone please help me? The measure of the reflex angle in rhombus ABCD is 260°. Find x. Thanks

Answers

Imagine that you kept drawing the circle around to include the entire angle. We know that the measure of that angle would be 360°, because there are 360° in a circle.

But instead, we stopped at 260°. We have x° left to get to 360°.

That's 360°-x°=260°.

x=100, so the answer is E

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