Given:
The two end points of a line are (2,10) and (3,-5).
To find:
The equation of the line in the slope intercept form.
Solution:
The slope intercept form of a line is
[tex]y=mx+b[/tex]
Where, m is slope and b is the y-intercept.
The two end points of a line are (2,10) and (3,-5). So, the equation of the line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-10=\dfrac{-5-10}{3-2}(x-2)[/tex]
[tex]y-10=\dfrac{-15}{1}(x-2)[/tex]
[tex]y-10=-15(x-2)[/tex]
On further simplification, we get
[tex]y-10=-15x+30[/tex]
[tex]y=-15x+30+10[/tex]
[tex]y=-15x+40[/tex]
Therefore, the slope intercept form of the given line is [tex]y=-15x+40[/tex].
Jess has 60 ounces of an alloy that is 40% gold. How many ounces of pure gold must be added to this alloy to create a new alloy that is 75% gold?
Answer:
84 ounces of pure gold
Step-by-step explanation:
Jess has 60 ounces of an alloy that is 40% gold. How many ounces of pure gold must be added to this alloy to create a new alloy that is 75% gold?
Pure gold = 100% gold
Let the number of ounces of pure gold = x
Hence, we have the equation
40% × 60 ounces + 100%× x ounces = 75%(60 + x)ounces
= 0.4 × 60 + 1x = 0.75(60 + x)
= 24 + x = 45 + 0.75x
Collect like terms
x - 0.75x = 45 - 24
0.25x = 21
x = 21/0.25
x = 84 ounces
Therefore, we need 84 ounces of pure gold
84 ounces of pure gold must be added
The first is to write out the parameters
Jess has 60 ounces of alloy
40% of this alloy is pure gold
The number of ounces that should be added can be calculated as follows;
Let y represent the unknown
40/100(y)(60) + 100/100(y)= 75/100(60+y)
24 + y= 0.75(60+y)
25 + y= 45 + 0.75y
24 - 45= 0.75y -y
-21= -0.25y
y= 21/0.25
y= 84
Hence the number of ounces of pure gold required is 84 ounces
Please see the link below for more information
https://brainly.com/question/3922146?referrer=searchResults
Tell whether the lines through the given points are parallelperpendicular, or neither Line 1: (1, 0), (7, 4) Line 2: (7, 0) , (3, 6) The slope of line 1 is The slope of line 2 is
Answer:
The lines are perpendicularStep-by-step explanation:
We determine whether lines are parallel or perpendicular by getting their slopes
For line 1; (1, 0), (7, 4)
Slope m = 4-0/7-1
M1 = 4/6
M1 = 2/3
Hence the slope of M1 is 2/3
For Line 2; (7, 0) , (3, 6)
M2 = 6-0/3-7
M2 = 6/-4
M2 = -3/2
Take the product of the slopes
M1 * M2 = 2/3 * -3/2
M1M2 = -1
Since the product of their slope is -1, hence the lines are perpendicular
What is the area of the following trapezoid? 14 mm 10 mm 28 mm 210 mm 2 280 mm 2 O 420 mm 2 O 140 mm 2
Answer:
210 mm2
Step-by-step explanation:
you add both the bases and then height ;)
Square Areas
The dots on the grid are all one unit apart.
1. The square shown here can be described
as a 3/5 square. Find its area.
.
Show all your reasoning
Answer:
The area will be "34 unit²".
Step-by-step explanation:
The diagram is missing throughout the given question. Below is the figure attached.
According to the question,
The side of squares will be:
= [tex]\sqrt{(5)^2+(3)^2}[/tex]
= [tex]\sqrt{25+9}[/tex]
= [tex]\sqrt{34} \ units[/tex]
Hence,
The area of square will be:
= [tex](side)^2[/tex]
= [tex](\sqrt{34} )^2[/tex]
= [tex]34 \ unit^2[/tex]
What is the scale factor of the dilation from A to B?
Answer:
1
Step-by-step explanation:
The scale factor of the dilation from A to B is, 1.67
What is the scale factor ?Scale factor is a mathematical term, which we use to scale 2-dimensional and 3-dimensional shapes. Scale factor is a measure of similar figures. Those figures who look the same but are in different sizes.
For example, Two spheres look similar but could have different radii.
Given that,
Two parallelograms
A & B
First one has side length = 4.5 unit
Second one has side length = 7.5 unit
For calculating scale factor, we need to found ratio of two sides length
Scale factor = 7.5/4.5
= 1.66666
Hence, the scale factor is 1.67
To know more about Scale factor check:
https://brainly.com/question/26903822
#SPJ2
What is an
equation of the line that passes through the points (-4,-4) and (4, 6)?
Answer:
Step-by-step explanation:
1.) Find the slope
[tex]\frac{y_2-y_1}{x_2-x_1} = \frac{6-(-4)}{4-(-4)}= \frac{6+4}{4+4} = \frac{10}{8}=\frac{5}4}[/tex] = m2.) Use the slope-point form for a line
[tex]y-y_0=m(x-x_0)[/tex]
Pick any point (-4,-4) or (4,6) into [tex]y_0 and x_0\\[/tex]
but your equation is y= 5/4x+1
A coat is on sale for 30% off the original price of 120$.what is the amount of discount
Answer:
36
Step-by-step explanation:
You do 120 multiplied by .3 to get 36. This makes the discount amount is $36 which also means you only pay $84 for the coat.
4. Asia is designing a triangular-shaped window with a height of 15 inches and
an area of 135 square inches. What is the length of the base of the window?
Answer:
18in
Step-by-step explanation:
Given data
Height h= 15 in
Area= 135 in^2
The expression for the area is given as
Area= 1/2 Base * Height
substitute
135= 1/2* Base*15
135= 7.5 Base
Base= 135/7.5
Base= 18 in
Hence the base is 18in
Maggie has $16 to spend on lunch for the week. she has spent $4 so far. which inequality shows how much she can spend for the rest of the week?
The measure of one interior angle of a parallelogram is 5 times the measure
of another angle. What's the measurement of the larger interior angle?
Answer:
Step-by-step explanation:
The sum of these adjacent angles must sum to 180 degrees (also the sum of all angles must be 360)
a+5a=180
6a=180
a=30
The larger angle is 5a so the larger angle is
5(30)=150 degrees.
Select the correct answer from the drop-down menu. A line with a slope of -2 crosses the y-axis at (0, 3). The equation of the line is . A. -3x + y = 3, B. 3x + y = 2 C. 2x + y = 3 D. 2x + y = 2
(Someone help please)
Put these numbers in order, from least to greatest.
3.5
-1
4.8
-1.5
-0.5
-4.2
0.5
-2.1
-3.5
Answer:
-4.2,-3.5,-2.1,-1.5,-1,-0.5,0.5,3.5,4.8
Answer:
0.5, 3.5, 4.8, -0.5, -1, -1.5, -2.1, -3.5, -4.2
Step-by-step explanation:
hope this helps :)
Ken wants to buy two shirts. The original price of the first shirt is $34, and the original price of the second shirt is $28. Ken will use one of the two discount coupons shown to buy the shirts. Coupon 1 Coupon 2 Buy one shirt at the original price and receive half off the price of a second shirt of equal or lesser value. Take 20% off the original price of each shirt, Based on this information, which statement is true?
Write the equation of the line graphed below.
Answer:
x=1
Step-by-step explanation:
I WILL GIVE BRANLIEST HELP FAST DUE IN 10 MINS 56yx^3-32yx+16y
Answer:
8y(7x^3-4x+2)
Step-by-step explanation:
Group and factor out the greastest common factor then combine
Answer:
this is my alt here ya go champ
Step-by-step explanation:
PLEASE HELP DUE AT MIDNIGHT!
Answer:
D or A i think
Step-by-step explanation:
pls mark brainliest
Answer:
B. Angle 2 and Angle 7 are alternate interior angles.
Step-by-step explanation:
Angle 2 and Angle 7 are actually alternate exterior angles. They are on opposite sides of the transversal and so the "alternate" part is correct, however, alternate interior angles are ones on the inside of the transversal, like angles 4 and 5.
A rectangle has a perimeter of 18. The height of the rectangle is 4 cm. What is the area of the rectangle?
Answer:
20
Step-by-step explanation:
Perimeter of rectangle= 2l+2h so 2l+2(4)=18. SO 2l=10. l=5
Area=bh
(5)(4)=20cm
The temperature at 6 a.m. was -12°F. At 11 a.m. the temperature was 0°F. Which of the following shows the temperature change from 6 a.m. to 11 a.m.?
Answer:7 - 9 = -2
Step-by-step explanation:
Please Help!!!!!! You have twice as many nickels as pennies. you have $1.10. how many of each coin do you have? Solve each problem using a system of equations.
20 Observa el trapecio isosceles PQRS en el plano cartesiano.
0
1
2
3
4
5
6
7
8
9
10
A. ¿Cuántas unidades mide el lado QR?
B. ¿Cuál es la distancia entre los puntos PyR?
Recuerda contestar todas las partes de la pregunta en el espacio provisto.
Answer:
The answer is below
Step-by-step explanation:
La distancia entre dos puntos A(x₁, y₁) y B(x₂, y₂) en el plano cartesiano se da como:
[tex]AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
El paralelogramo que se muestra en el diagrama tiene vértices en P (3, 6), Q (7, 6), R (9, 2) y S (1, 2)
a) La distancia entre Q y R viene dada por:
[tex]QR=\sqrt{(9-7)^2+(2-6)^2} =\sqrt{20}=2\sqrt{5} \ units[/tex]
b) La distancia entre P y R viene dada por:
[tex]QR=\sqrt{(9-3)^2+(2-6)^2} =\sqrt{52}=2\sqrt{13} \ units[/tex]
Card
#3
Find the area of the shaded region
shape: triangle
2
6 cm
shapesquare
Area formula:
Note: Round to the Final Answer
nearest hundredth (include Units!)
Checked by Teacher
Answer:
19,27 cm^2
Step-by-step explanation:
area of triangle = (6 x 3)/ 2 = 9 cm^2
circle area : 3^2 x 3,14 = 28,27 cm^2
area of shaped region = 28,27 - 9 = 19,27 cm^2
An item is regularly priced at $80 Barbado add a discount of 25% off the regular price how much did Bob pay
Answer: $60
Step-by-step explanation:
Given
The price of an item is $80
The discount on it is 25%
Net payable price =Regular Price- discount
[tex]\Rightarrow \text{Net Payable Price(P)}=80-25\%\ \text{of}\ 80\\\Rightarrow P=80(1-0.25)=80\times 0.75\\\Rightarrow P=\$60[/tex]
Solve 3x - y = 3 and 2x - y = 2 by substitution method
Answer:
x = 1
y = 0
Step-by-step explanation:
3x - y = 3
2x - y = 2 , then y = 2x - 2
substitute for y:
3x - (2x - 2) = 3
combine like terms:
x + 2 = 3
subtract 2 from both sides of the equation:
x = 1
y = 2(1) - 2 = 0
Answer:
x=5, y=8
Step-by-step explanation:
let 3x-y=3 be [1]
and 2x-y = 2 be [2]
Change up [2] to:
2x=2+y
2x-2 = y and name this [3]
Sub [3] into [1]
3x-(2x-2)=3
3x-2x-2=3
x-2=3
x=5
Sub x=5 into [3]
2(5)-2=y
10-2=y
8=y
find l of the following cone
Answer:
[tex] l = \sqrt{261}\: in[/tex]
Step-by-step explanation:
Height of the cone h = 15 in
Radius of the cone r = 12/2 = 6 in
We need to find slant height (l) =?
[tex] \because l = \sqrt{ {r}^{2} + {h}^{2} } \\ \\ \therefore l = \sqrt{ {6}^{2} + {15}^{2} } \\ \\\therefore l = \sqrt{36 + 225} \\ \\\therefore l = \sqrt{261} \\ [/tex]
Answer:
l = √261 in
Step-by-step explanation:
Hope this helps
What is the decimal equivalent of
−
5
6
?
−
1.2
− 1.2
−
0.8
¯
3
− 0.8 3 ¯
0.8
¯¯¯3
0.8 3 ¯ 0.8\3
1.2
Answer:
kwkwkjwsjsjsssjsj
Step-by-step explanation:
ksksossoslsksmssmmssmsk
PLEASE HELP ASAP
An isosceles trapezoid has an area of 25 square units and a height of 5 units. Find the sum of the bases of the trapezoid.
Complete your work in the space provided.
Answer:
5 units because 5 times 5 is 25
How do you factor a quadratic equation completely?
Answer:
A Method For Simple Cases
Step 1: Find two numbers that multiply to give ac (in other words a times c), and add to give b.
Step 2: Rewrite the middle with those numbers:
Step 3: Factor the first two and last two terms separately:
Step-by-step explanation:
Venita is sewing new curtains. The table below shows the relationship between the number of stitches in a row and the length of the row.
Sewing
Number of stitches
Length (cm)
5
1
15
3
20
4
30
6
What is the relationship between the number of stitches and the length?
Answer:
The number of stitches is 5 times the length.
Step-by-step explanation: i took edge
PLEASE HELP! QUICK EASY POINTS!! LOOK AT THE IMAGE!
Answer:
0.2 and 11.8
Step-by-step explanation:
Find the slope of the line graphed
Answer:
I believe it is 2