Answer:
2 and - [tex]\frac{1}{2}[/tex]
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 )
Given
3y = 6x + 9 ( divide all terms by 3 )
y = 2x + 3 ← in slope- intercept form
with slope m = 2
(i)
Parallel lines have equal slopes, thus
the slope of line t is 2
(ii)
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex], thus
the slope of line r is - [tex]\frac{1}{2}[/tex]
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
Megan is checking her tax bill for the last year. the tax rates were as follows: no tax on the £11000 of earning earnings in excess of £11000 and up to £43000 tasted at a rate of 20% earnings in excess of £43000 and up to 150000 taxed at a rate of 40% earnings over £150000 taxed at 45% last year meghan earned £158900 before tax how much tax did she pay in total?
Answer:
£53,205
Step-by-step explanation:
Megan paid ...
0 on the first £11,000
.20 of the next £43,000 -11,000 = £6400
.40 of the next £150,000 -43,000 = £42,800
.45 of the next £158,900 -150,000 = £4,005
So, her total tax bill is ...
£6,400 +42,800 +4,0005 = £53,205
Megan paid a total of £53,205 in tax.
Work out m and c for the line: y = 8 x
Answer:
m = 8 and c = 0
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 = 8x ← is in slope- intercept form, that is y = 8x + 0
with m = 8 and c = 0
find the area of the triangle that has a base of 5 inches in a height of 3 3/4 inches
Answer: 75/8= 9 3/8
Step-by-step explanation: Area = 1/2 X b X h
1/2 X 5 X 15/4 =
75/8=9 3/8
Which angles form a linear pair?
Answer:
b. is correct
PlZzzzz follow me guys...
help me lol abcdefghijklmnopqrstuvwxyz
Answer:
30 cans
Step-by-step explanation:
We can use ratios
15 cans x cans
---------------- = ------------------
7*2 people days 4*7 people days
Using cross products
15 * 28 = 14 * x
Divide by 14
15 * 28/14 = x
30 =x
Triangle ABE is similar to triangle ACD. AED and ABC are straight lines. EB and DC are parallel. AE = 5 cm, BC = 4.5 cm, BE = 4 cm, CD = 9 cm The area of quadrilateral BCDE is x cm2 The area of triangle ABE is y cm2 Find an expression for y in terms of x . Give your answer as simply as possible. (3 marks)
Answer:
y = 16x/65
Step-by-step explanation:
Given:
Triangle ABE is similar to triangle ACD. AED and ABC are straight lines
EB and DC are parallel
The area of quadrilateral BCDE = xcm²
The area of triangle ABE = ycm²
Find attached the diagram from the above information.
In similar triangles, the ratio of their corresponding angles are equal.
Also, the ratio of the area of the two triangles = square of ratio of the corresponding sides of the two triangles.
Area ∆ACD/area of ∆ABE = (DC/EB)²
Area ∆ACD/area of ∆ABE = [(area of quadrilateral BCDE +
area of ∆ABE)]/(area of ∆ABE)
(x+y)/y = (DC/EB)²
(x+y)/y = (9/4)²
x+y = (81/16)y
x = (81/16)y - y
x = (81y - 16y)/16
x = 65y/16
Making y subject of formula
16x = 65y
y = 16x/65
An expression for y in terms of x:
y = 16x/65
An expression for y in terms of x is :
y = 16x/65
Given:
Triangle ABE is similar to triangle ACD. AED and ABC are straight lines . EB and DC are parallel The area of quadrilateral BCDE = xcm² The area of triangle ABE = ycm²Consider, the image attached:
In similar triangles, the ratio of their corresponding angles are equal.
Also, the ratio of the area of the two triangles = square of ratio of the corresponding sides of the two triangles.
Thus,
Area ∆ACD/area of ∆ABE = (DC/EB)²
Area ∆ACD/area of ∆ABE =
[(area of quadrilateral BCDE + area of ∆ABE)]/(area of ∆ABE)
On substituting the given values:
(x+y)/y = (DC/EB)²
(x+y)/y = (9/4)²
x+y = (81/16)y
x = (81/16)y - y
x = (81y - 16y)/16
x = 65y/16
In terms of y:
16x = 65y
y = 16x/65
Therefore, an expression for y in terms of x: y = 16x/65
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Work out the area of a semicircle with radius 3 cm.
Give your answer in terms of t.
3 cm
Answer:
Area = 4.5 π cm²
Step-by-step explanation:
Area of semicircle = [tex]\frac{\pi r^2}{2}[/tex]
Where r = 3cm
=> Area = [tex]\frac{\pi(3)^2 }{2}[/tex]
=> Area = [tex]\frac{9\pi }{2}[/tex]
=> Area = 4.5 π cm²
If f(x) = 2x, then f -1(x) =
0-2x
O 12x
OX-2
Answer:
What am I supposed to do
Step-by-step explanation:
When solving, you took the square root of both
sides of the equation. Consider this step when
completing the following statements.
The roots are imaginary because of the
1) negative radicand.
2) non perfect square radicand
3) need to identify + and - roots of the radicand
Answer:
Step-by-step explanation:
Negative Radicand
The roots of the equation are imaginary because of negative radicand.
What is an imaginary number?An imaginary number is a number that, when squared, has a negative result. Essentially, an imaginary number is the square root of a negative number and does not have a tangible value.
According to the given question.
We have to take square root both sides of the equation.
Then we get imaginary roots only when there is some negative number under the radical symbol. That is when the radicand is negative.
Hence, the roots of the equation are imaginary because of negative radicand.
Thus, option 1 is correct.
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I will give you brainliest!!! Solve the system of equations by graphing both equations with a pencil and paper y=x-3 y=-x+1
Answer:
A. (2,-1) i thought this is hard but its kind of easy actually
Step-by-step explanation:
so you just put the given options into the xs and ys.. so lets say we have (2,-1) 2=x -1=y
now put them into the equations.. y=x-3
-1=2-3( if this is true than this is the right answer)
y= -x +1
-1= -2 +1 (this is also correct)
which of the following statements must be true about this diagram check all that apply help asap
Answer:
i know that D is correct
How can this expression be written another way?
Apply the distributive property and the greatest common factor to write an equivalent expression
enter your answer by filling in the boxes
105+35m =
Answer:
35(3+1m)
Step-by-step explanation:
35(3+1m)
105+35m
Iff the hight of 1000 students are normally distributed with the mean of 68.5 inches and standard deviation of 2.7 inches how many of these students would you axpect to have hight? . Between 67.5 and 71.0 inches exclusive? . Greater then or equal to 74.0 inches?
Answer:
Step-by-step explanation:
Let x be the random variable representing the height of the students. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 68.5
σ = 2.7
the probability that a student's height is between 67.5 and 71.0 inches exclusive is expressed as
P(67.5 < x < 71.0)
For x > 67.5,
z = (67.5 - 68.5)/2.7 = - 0.37
Looking at the normal distribution table, the probability corresponding to the z score is 0.36
For x < 71.0
z = (71.0 - 68.5)/2.7 = 0.93
Looking at the normal distribution table, the probability corresponding to the z score is 0.82
Therefore,
P(67.5 < x < 71.0) = 0.82 - 0.36 = 0.46
The number of students whose height is between 67.5 and 71.0 inches is
0.46 × 1000 = 460 students
The probability that a student's height is greater than or equal to 74.0 inches is expressed as P(x ≥ 74)
P(x ≥ 74) = 1 - P(x < 74)
For x < 74,
z = (74 - 68.5)/2.7 = 2.04
Looking at the normal distribution table, the probability corresponding to the z score is 0.98
P(x ≥ 74) = 1 - 0.98 = 0.02
The number of students whose height are greater than or equal to 74.0 inches is
0.02 × 1000 = 20 students
Plz answer this question and I will mark you as brainliest
Answer: 3/8
Step-by-step explanation:
When you subtract fractions, you want them to have a common denominator.
[tex]\frac{36}{24}-\frac{27}{24} =\frac{9}{24}[/tex]
This answer is correct, but it is not in the simplest term. To get the simplest term, you want to divide the numerator and denominator by the same number.
[tex]\frac{9}{24} =\frac{3}{8}[/tex]
A cup of hot coffee will, over time, cool down to room temperature. The principle of physics governing the process is Newton's Law of Cooling. The temperature (in degrees Fahrenheit) of a cup of coffee can be modeled by the following equation: f(t)=80+120e^(-0.08t) Here the time t is measured in minutes after the coffee was poured into the cup. A. Explain, using the structure of the expression 80+120e^(-0.08t), why the coffee temperature decreases as time elapses (8 points). B. What is the temperature of the coffee at the beginning of the experiment (7 points)? C. Drinking coffee at 175 degrees can possibly burn your tongue. After waiting for 2 minutes, Leo became impatient and decided to drink the coffee. Will he be alright (7 points)? D. The ideal temperature to drink coffee is between 120 to 140 degrees, as many of the more subtle flavors of coffee are revealed. When is the best time for Leo to drink coffee (8 points)?
Answer:
A. Because the coefficient of time is negative .
The value of t decreases as time passes .
The temperature of the coffee decreases as time passes and the coffee will evemtually cool down to room temperature
B. At the beginning , t=0
Hence Temperature will be 80 + 120 = 200º
c. He wont be alright . High temperature , less time to cool down . So he wont be alright . Coffee might still be hot .
D. Assuming the temp is 130º
80 + 120ᵅ⁻⁰·⁰⁰⁸ˣ = 130
120ᵅ⁻⁰·⁰⁰⁸ˣ =130-80
120ᵅ⁻⁰·⁰⁰⁸ˣ =50
a-0.008x =(50/120)
0.008x = ln(0.416)
x = 10.962 =11mins
so he has to wait 11 mins to drink.
Step-by-step explanation:
f(t)=80+120e^(-0.08t)
-----------------------
A) Temperature decreases over time as the coefficient of time is negative (-0.08)B. t=0 ⇒ f(0)= 80 + 120*1 = 200 degC. t=2 ⇒ f(2)= 80+120*e^(-0.08*2) ≈ 182 degCoffee is still hot. He won't be alright. He needs to wait more
D. f(x)= 12080+120e^(-0.08x)= 120120e^(-0.08x)=40e^(-0.08x)=1/3-0.08x= ln(1/3)-0.08x= -1.0986x= -1.0986/-0.08x ≈ 14 minbest time is ≈ 14 min
write down the mathematical name of this shape
Answer:
parallelogram
Step-by-step explanation:
Its a parallelogram.
Answer
parallelogram
Step-by-step explanation:
This recipe makes 5 portions of fajitas. Carly has 700 g of chicken, 800 g of peppers, 200 g of onion, 50 g of spice mix and 16 tortillas. How much more of each ingredient will she need to make 15 portions by following this recipe?
Recipe:
Serves 5
400 g
chicken
600 g peppers
70 g onion
20 g spice mix
10 tortillas
?g chicken
? g peppers
? g onion
? g spice mix tortillas
Answer:
Chicken = 500 g
Peppers = 1 kg
Onions = 10 g
Spice mix = 10 g
Tortillas = 14
Step-by-step explanation:
5 × 3 = 15
What the recipe indicates she needs
400 × 3 = 1200
600 × 3 = 1800
70 × 3 = 210
20 × 3 = 60
10 × 3 = 30
Subtract what she needs from what she has
1200 - 700 = 500 g
1800 - 800 = 1000 g
210 - 200 = 10 g
60 - 50 = 10 g
30 - 16 = 14 tortillas
Answer:
qhdlqywylvly
Step-by-step explanation:hqiufqwbuif
MY LAST QUESTION WILL FOREVER BE GRATEFUL PLS HELP WILL GIVE BRANLIEST!! AT LEAST TAKE A LOOK!!!! PLS I AM BEGGING!!!
Given the diagram below, what statement can you NOT make?
A) m∠2 + m∠3 = 90
B) ∠5=∠3
C) ∠2=∠5
D) m∠4=90
Answer:
B
Step-by-step explanation:
∠ 2 + ∠ 3 = 90° ← True
∠ 5 = ∠ 3 ← False
∠ 2 = ∠ 5 ← True ( vertical angles )
∠ 4 = 90° ← True
Thus the statement that you cannot make is ∠ 5 = ∠ 3 → B
if i have 900 gallons of gas. how much tank does do we need to fill up 20?
Answer:
the answer is 18000
Step-by-step explanation:
900 gallons multiply 20
so our answer is =18000
Answer:
18000
Step-by-step explanation:
le
The graph shows two ratios from the table.
ty
9
Celery (x)
2
4
6
8
7
6
Carrots (y)
3
6
?
Carrots
5
4
3
Predict how many carrots you will need for the recipe if
you use 6 stalks of celery.
2
carrots
1
2 3
4 5 6 7 8 9 10
Celery
Answer:
9 carrots
Explanation:
There are different ways to solve these.
The first one is identify the pattern of the graph. You can see that the slope has 3 rises up and 2 runs to the right. So follow that point and you can see that the next coordinate is (6,9).
The second way is identify the pattern of the table. As you can see, the pattern goes like this: [tex]\frac{2}{3} ,\frac{4}{6} ,\frac{6}{y}[/tex]
2/3 = 2/3
4/6 = 2/3
6/y = 2/3
Solve the last one algebraically (cross-multiply first):
6/y = 2/3
2y = 18
y = 18 ÷ 2
y = 9
6/9 = 2/3 (correct)
Answer:
9 carrots
Step-by-step
HELP ME ASAP! PLS!!!!
Which triangle’s unknown side length measures StartRoot 53 EndRoot units?
(A)A right triangle with side length of 6 and hypotenuse of StartRoot 91 EndRoot.
(B)A right triangle with side length of StartRoot 47 EndRoot and hypotenuse of 10.
(C)A right triangle with side length of StartRoot 19 EndRoot and hypotenuse of StartRoot 34 EndRoot.
(D)A right triangle with side length StartRoot 73 EndRoot and hypotenuse 20.
Answer:
(B) A right triangle with side length of StartRoot 47 EndRoot and hypotenuse of 10
Step-by-step explanation:
I just took the quiz on edge
Answer:
B
Step-by-step explanation:
∆ABC is translated 6 units up and 3 units left to create ∆A'B'C'. If vertex A is at (-1, 2) and vertex B is at (1, 5), then vertex A' is at and vertex B' is at A.(5, 1) (-4, 8) B.(-2, 11) (-7, -1)
Answer:
(-4,8)
Step-by-step explanation:
(-1, 2) => (x, y)
is translated 6 units up => 2+6 = 8
3 units left => -1-3 = -4
the coordinates of A′ => (-4, 8)
would appreciate brainliest!
Need help with this didn’t understand it
Answer:
Ok, the solution to the first one. See below.
Step-by-step explanation:
[tex]1>3-d\\\\\mathrm{Add\:}d\mathrm{\:to\:both\:sides}\\\\1+d>3-d+d\\\\\mathrm{Simplify:}\\\\1+d>3\\\\\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\\\\1+d-1>3-1\\\\\mathrm{Simplify:}\\\\d>2[/tex]
See attachment below.
Best Regards!
12. Find the product: (88a + 80)(8a + 8) ( 1 ) 13. Find the product: (40y + zy)(4y + zy) ( 1 )
Answer:
(88a+80)(8a+8)
88a(8a+8)+80(8a+8)
704a²+704a+640a+640
704a²+1344a+640
(40y+zy)(4y+zy)
40y(4y+zy)+zy(4y+zy)
160y²+40zy²+4zy²+z²y²
160y²+44zy²+z²y²
Step-by-step explanation:
i hope this will help you
A flat surface that extends without end in all directions and is named by three points that are not on the same line is known as which geometric term? A. point B. ray C. line D. plane
Answer:
D...........................
The flat surface that extends without end in all directions and is named by three points that are not on the same line is known as D. Plane.
What is a plane?A flat form or a shape with two dimensions—length and width—is referred to as a two-dimensional shape. Shapes that are two-dimensional, or 2D, lack thickness.
We can represent all the two-dimensional figures in a plane some of them are, Triangles, Circles, Quadrilaterals, and Polygons.
A plane can also be represented as a surface, It can extend without end in all directions and is named after three points that are not on the same line.
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Alejandra has $600 in her checking account she wants to spend part of this money on a computer she wants to have at least 250 left in her checking account after buying the computer that in quantity shownCan be used to find t The amount of money in dollars the Alexandra can spend on her computer find the value of t
Answer:
350$
Step-by-step explanation:
600 = total in checking account.
250 = left in checking account after transaction.
600-250 = 350
meaning the most she can spend on a computer is 350$.
Answer:
t ≤ 350
Step-by-step explanation:
Which inequality represents all possible values of t ?
According to 3 sources I found online this should be correct! Let me know if anything else is needed asap!
What is the length of segment GH?
Answer:
4√5
Step-by-step explanation:
Distance formula: [tex]d = \sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]
Coordinates given:
H(8, 1)
G(0, -3)
d = [tex]\sqrt{(8-0)^2 + (1+3)^2}[/tex] = 4√5
Answer:
StartRoot 80 EndRoot
80 square root is the answer
Step-by-step explanation:
|GH|² = (8 - 0)² + (1 - (-3))²
|GH|² = 64 + 16
|GH|² = 80
GH = sqrt(80)
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Solve for the missing side of the triangle. 9.03 11.98 18.78 24.92
Answer:
11.98
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp/ hyp
sin 53 = x/15
15 sin 53 = x
11.97953265 = x
Read the following statement: x + 6 = 6 + x. This statement demonstrates:
Answer:
See below.
Step-by-step explanation:
This statement demonstrates the commutative property (of addition). This is because even though the order is switched, the result will remain unchanged and they are equal to each other.
Answer:
Commutative Property of addition
Step-by-step explanation:
This statement demonstrates the commutative property (of addition). means that no. After the order of your calculation, the end result will always be the same.
This is only applicable to addition and multiplication.
Hope this helps