Answer:
(3, 15) and (4, 12)
Step-by-step explanation:
x2 - 7x+12 = 0 factors to (x - 4)(x - 3) = 0, and so x: {3, 4}.
Since y= -3x + 24, y = 15 when x = 3 and y = 12 when x = 4. The solutions are thus (3, 15) and (4, 12). This is the third answer choice.
Answer:
see the explanation
Step-by-step explanation:
Y = –x2 + 4x + 12
y = –3x + 24
so
–x2 + 4x + 12 = –3x + 24
x^2 -7x + 12 = 0
(x - 4)(x - 3) = 0
x - 4 =0; x =4
x - 3 = 0; x= 3
y = –3x + 24 = -3(3) + 24 = -9+24 = 15 (when x = 3)
y = –3x + 24 = -3(4) + 24 = -12+24 = 12 (when x = 4)
answer
(3, 15) and (4, 12)
(give this a heart cause why not)
Find the number of digits in the square root of 61504.
Answer:
3
Explanation
There are 3 digits in the number 248 which is the square root of 61504.
√61504 = 248 --- 3 digits in 248
-13=-18+w/4 two step equation
Answer:
w = 20
Step-by-step explanation:
Add 18 on both sides:
[tex]\frac{w}{4} =5[/tex]
Multiply by 4 on both sides:
w = 20
Answer:
20
Step-by-step explanation:
Let's solve your equation step-by-step.
−13=−18+ w/ 4
Step 1: Simplify both sides of the equation.
−13=−18+ w/ 4
−13=−18+ 1/ 4 w
−13= 1/ 4 w−18
Step 2: Flip the equation.
1/ 4 w−18=−13
Step 3: Add 18 to both sides.
1/ 4 w−18+18=−13+18
1/ 4 w=5
Step 4: Multiply both sides by 4.
4*( 1/ 4 w)=(4)*(5)
w=20
A university's freshman class has 5000 students. 90% of those
students are majoring in Economics. How many students in the
freshman class are Economics majors?
Answer:
4,500
Step-by-step explanation:
To find the number of students majoring in economics, you must turn 90% into a decimal making it .9.
Then you multiply the decimal to how many students there are (5000x.9) and that gives you 4,500.
Which red triangle shows a 90° counterclockwise rotation of the blue triangle? Check all that apply. On a coordinate plane, a blue triangle has points (negative 1, 4), (negative 5, 4), (negative 1, 1). A red triangle has points (negative 4, negative 1), (negative 1, negative 1), (negative 4, negative 5). On a coordinate plane, a blue triangle has points (1, 1), (4, 5), (4, 1). A red triangle has points (negative 1, 1), (negative 1, 4), (negative 5, 4). On a coordinate plane, a blue triangle has points (0, 1), (4, 4), (4, 1). A red triangle has points (negative 4, 1), (negative 4, 4), (0, 1). On a coordinate plane, a blue triangle has points (negative 5, 4), (negative 1, 4), (negative 1), 1). A red triangle has points (1, 1), (4, 1), (4, 5). On a coordinate plane, a blue triangle has points (negative 2, 5), (4, 5), (4, 1). A red triangle has points (negative 1, 4), (negative 5, 4), (negative 5, negative 2).
Question:
1) Blue triangle points; (-1, 4), (-5, 4), and (-1, 1)
Red triangle points; (-4, -1), (-1, -1). and (-4, -5)
2) Blue triangle points (1, 1), (4, 5), (4, 1)
Red triangle points; (-1, 1), (-1, 4). and (-5, 4)
3) Blue triangle points (0, 1), (4, 4), (4, 1)
Red triangle points; (-4, 1), (-4, 4). and (0, 1)
4) Blue triangle points (-5, 4), (-1, 4), (-1, 1)
Red triangle points; (1, 1), (4, 1). and (4, 5)
5) Blue triangle points (-2, 5), (4, 5), (4, 1)
Red triangle points; (-1, 4), (-5, 4). and (-5, -2)
Answer:
The correctly rotated red triangles are those of (1), (2), and (5)
Step-by-step explanation:
In a 90° counterclockwise rotation, every x and y points of the original triangle are switched while the y is turned negative, as shown in the following equation;
(x, y) to (-y, x)
Therefore, the triangles that undergo a 90° counterclockwise rotation are as follows;
1) Blue triangle points; (-1, 4), (-5, 4), and (-1, 1)
Red triangle points; (-4, -1), (-1, -1). and (-4, -5)
(-1, 4) → (-4, -1)
(-5, 4) → (-4, -5)
(-1, 1) → (-1, -1)
Correctly rotated 90° counterclockwise
2) Blue triangle points (1, 1), (4, 5), (4, 1)
Red triangle points; (-1, 1), (-1, 4). and (-5, 4)
(1, 1) → (-1, 1)
(4, 5) → (-5, 4)
(4, 1) → (-1, 4)
Correctly rotated 90° counterclockwise
3) Blue triangle points (0, 1), (4, 4), (4, 1)
Red triangle points; (-4, 1), (-4, 4). and (0, 1)
(0, 1) → (0, 1) ≠ (-1, 0)
(4, 4) → (-4, 4)
(4, 1) → (-4, 1)
Not correctly rotated 90° counterclockwise
4) Blue triangle points (-5, 4), (-1, 4), (-1, 1)
Red triangle points; (1, 1), (4, 1). and (4, 5)
(-5, 4) → (4, 5) ≠ (-4, -5)
(-1, 4) → (4, 1)
(-1, 1) → (1, 1)
Not correctly rotated 90° counterclockwise
5) Blue triangle points (-2, 5), (4, 5), (4, 1)
Red triangle points; (-1, 4), (-5, 4). and (-5, -2)
(-2, 5) → (-5, -2)
(4, 5) → (-5, 4)
(4, 1) → (-1, 4)
Correctly rotated 90° counterclockwise.
Answer:
1,2,5
Step-by-step explanation:
100) 4030
What’s the greatest common factor
Answer: 10
Step-by-step explanation:
100/10=10
4030/10=403
For every pound a company spends on advertising, it spends £0.59 on its website. Express the
amount spent on advertising to its website as a ratio in its simplest form.
Answer:
100:59
Step-by-step explanation:
For every pound a company spends on advertising, it spends £0.59 on its website.
Amount Spent on Advertising = £1
Amount Spent on Website = £0.59
Therefore:
Amount Spent on Advertising : Amount Spent on Website
= 1 : 0.59
Multiply both sides by 100
= 100: 59
The ratio of the amount spent on advertising to its website as a ratio in its simplest form is 100:59 in its simplest form.
Answer:
£100 : £59
Step-by-step explanation:
The said company spends £0.59 on its website for every pound spent on advertisement. This implies that out of £1.00 spent on advertisement by the company, £0.59 is for website placements.
Thus, the rate of the amount spent on advertisement to amount spent on website is given as:
£1.00 : £0.59
To convert this to the nearest whole number, multiply through by 100, so that the ratio becomes;
£100.00 : £59.00
Therefore, the ratio expressed in its simplest form is £100 : £59
Rectangle A is a scale drawing of Rectangle B and has 25% of its area. If rectangle A has side lengths of 4 cm and 5 cm , what are the side lengths of rectangle B ?
Answer:
8 cm and 10 cm
Step-by-step explanation:
Hello, I can help you with this.
Step 1
According to the question there are two rectangles A and B,
Rectangle A is a scale drawing of Rectangle B and has 25% of its area
in other words
[tex]Area_{A}=0.25*Area_{B} (Equation\ 1)\\[/tex]
Step 2
Let
Rectangle A
length (1)= 4 cm
length (2)= 5 cm
[tex]Area_{A}=4\ cm * 5\ cm\\Area_{A}=20\ cm^{2}[/tex]
put this value into equation 1
[tex]Area_{A}=0.25*Area_{B} (Equation\ 1)\\\\20\ cm^{2} =0.25*Area_{B} \\divide\ each\ side\ by\ 0.25\\\frac{20\ cm^{2} }{0.25}=\frac{0.25}{0.25}*Area_{B}\\ Area_{B}=80\ cm^{2}[/tex]
Now, we know the area of rectangle B, to know its length we need to formule other equation
Step 3
[tex]Area_{B}=80\ cm^{2}\\length (1B)*length (2B)=80\ cm^{2} (equation\ 2)\\[/tex]
the ratio between the lengths must be constant, so the ratio of A must be equal to ratio in B, then
[tex]\frac{length(1A)}{length(2A)}=\frac{length(1B)}{length(2B)} \\\\\\frac{4}{5}= \frac{length(1B)}{length(2B)}\\0.8=\frac{length(1B)}{length(2B)}\\length(1B)=0.8*length(2B) (Equation 3)[/tex]
Step three
using Eq 1 and Eq 2 find the lengths
put the value of length(1B) into equation (2)
[tex]length (1B)*length (2B)=80\ cm^{2} (equation\ 2)\\\(0.8*length(2B)) (*length (2B)=80\ cm^{2} \\\\0.8*(length (2B))^{2} =80\ cm^{2}\\(length (2B))^{2} =\frac{80\ cm^{2}}{0.8} \\(length (2B))^{2}=100\\\sqrt{(length (2B))^{2}}=\sqrt{100\ cm^{2}} \\ length (2B)=10\ cm[/tex]
Now, put the value of length(2B) into equation 3 to know length (1B)
[tex]length(1B)=0.8*length(2B)\\length(1B)=0.8*10\ cm\\length(1B)=8 cm[/tex]
I really hope this helps you, have a great day.
Which is the correct first step in finding the area of the base of a cylinder with a volume of 140pi cubic meters and a height of 12 meters?
Answer:
CCCC
Step-by-step explanation:
Megan, Sally and Tom share £180 in the ratio 1:3:2 how much more does Sally recieve than Megan?
Answer: Sally recieves £60 more than Megan
Step-by-step explanation:
Add the ratio together 1+3+2=6
£180 divided by 6 = 30
Megan gets 30
Sally gets 30x3=90
Tom gets 30x2=60 30:90:69
a circle has a center located at 2 5 and passes through the point 10 3 answer
Determine the equation of the circle. Show how you arrived at your answer.
Write the equation of the tangent line to the circle at the point . Show how you determined your answer.
Answer:
[tex](x-2)^{2} +(y-5)^{2} =\sqrt{68}[/tex]
Step-by-step explanation:
Givens
The center of the circle is at (2,5).A point on the circumference is at (10,3).First, we need to find the radius, which is the distance between the given points.
[tex]d=\sqrt{(3-5)^{2} +(10-2)^{2} } =\sqrt{4+64}=\sqrt{68}[/tex]
Therefore, the radius of the circle is
[tex]r \approx 8.25[/tex]
The explicit form of the equation of the circle would be
[tex](x-2)^{2} +(y-5)^{2} =\sqrt{68}[/tex]
Help me with this!!! What is x
Answer:
58º
Step-by-step explanation:
Answer:
58 degrees
Step-by-step explanation:
x and 32 are complementary, which means they must add to 90 degrees.
x+32=90
Now, we have to solve for x. To do this, we need to get x by itself. 32 is being added on to x. To reverse this, subtract 32 from both sides, because subtraction is the opposite of division.
x+32-32=90-32
x=90-32
x=58
x is 58 degrees
The volume of a cylinder with base radius 3 cm and height 6 cm is
_______ π cubic centimeters.
Answer:
54 π cubic centimeters
Step-by-step explanation:
Formula for the volume of a cylinder: πr²h
π×3²×6=
9×6×π=
54π cm³
(3/5)/2=(1/4)/x solve for x
Answer:
[tex]x=\frac{6}{5}[/tex]
Step-by-step explanation:
[tex]\frac{3}{5} / 2=\frac{3}{10}[/tex]
[tex]\frac{3}{10} =\frac{1}{4} x[/tex]
[tex]x=\frac{6}{5}[/tex]
Answer:
x=
[tex] \frac{5}{6} [/tex]
Step-by-step explanation:
(3/5)/2=(1/4)x
3/10=1/4x
12x=10
x=10/12=5/6
Claire wants to find the mass of her suitcase. Which unit of measure would be best for her to use?
A. Tons
B. Liters
C. Meters
D. Kilograms
Answer: d
Step-by-step explanation:to s is to heavy and the others are for liquid and size
Answer:
D
Step-by-step explanation:
just makes the most sense
Use the unit circle to evaluate the six trigonometric functions of θ = -π.
Sin θ=
Cos θ=
Tan θ=
Csc θ=
Sec θ=
Cot θ=
Answer:
sin=0
cos=-1
tan=0
csc=undefined
sec=-1
cot=undefined
Step-by-step explanation:
On the unit circle, [tex]-\pi=\pi[/tex]. The sin of theta is therefore 0, the cosine is -1, and the tangent is 0/-1=0. Since the following functions are just the reciprocals of the previous ones, the cosecant is 1/0=undefined, the secant is 1/-1=-1, and the cotangent is 1/0= undefined. Hope this helps!
All six trigonometric ratios were calculated using a unit circle and comes out to be
[tex]sin(-\pi )= -sin\pi =0\\cos(-\pi )= cos\pi =-1\\tan(-\pi )= -tan\pi=0 \\cosec(-\pi )= -cosec\pi =infinity\\sec(\pi )= sec\pi =-1\\cot(-\pi )=-cot\pi=infinity[/tex]
I have attached a unit circle diagram.
What is a unit circle in trigonometry?In this unit circle corresponding values of sine and cosine have been written near the angle 'α' in form (cosα,sinα)
x-coordinate is cosα
y-coordinate is sinα
now,
one can find other trigonometric ratios
[tex]tan\alpha =\frac{sin\alpha }{cos\alpha } \\\\cot\alpha =\frac{1}{tan\alpha } \\\\cosec\alpha =\frac{1}{sin\alpha } \\\\sec\alpha =\frac{1}{cos} \\[/tex]
Hence, we can find the rest of the trigonometric ratios by using the coordinates (cosα,sinα) for a particular angle 'α'.
to get more about unit circle refer to the link,
https://brainly.com/question/16577559
A sector with a radius of 6 cm has a central angle measure of 4pi/9 in radians. What is the area of the sector?
Answer:
8πcm² = 8pi cm²
Step-by-step explanation:
The formula for area of a sector = ½r²θ
Where r = radius = 6cm
θ = central angle = 4pi/9 in radians = 4π/9
Area of the sector = 1/2 × 6² × 4π/9
Area of the sector = (144π/18)cm²
Area of the sector = 8πcm²
Therefore, Area of the sector =
8πcm² = 8pi cm²
Answer:
8πcm² = 8pi cm²
Step-by-step explanation:
trust
Note: The monthly loan payment was calculated at 119 payments of $330.38 plus a final payment of $329.73. Loan Balance: $25,000.00 Loan Interest Rate: 10.0% Monthly Loan Payment: $330.38 Number of Payments: 120 Cumulative Payments: $39,644.95 Total Interest Paid: $14,644.95 On average, what dollar amount of each monthly payment is interest? $ What percent of the total payments is total interest? %
Answer:
Average monthly interest = $ 122.04
% total interest =36.94 %
Step-by-step explanation:
There are 120 cumulative payments and the total interest paid was $ 14,644.95.
Hence, the average monthly interest is :
Average monthly interest = $ 14,644.95 / 120
Average monthly interest = $ 122.04
% total interest
= ($ 14,644.95) / $ 39,644.95 x 100
% total interest =36.94 %
A copy machine makes 32 copies per minute.how many copies does it make in 5 minutes and 15 seconds
Answer:
168
Step-by-step explanation:
You do 5 times 32 then divided 60 by 15 to figure out how much of 1 min is 15 sec its 1/4 so u do 1/4 of 32, 8 and add that to 5 times 32
A soccer player uses her head to hit a ball up in the air from a height of 1 meters with an initial vertical velocity of 5 meters per second. The height h in meters of the ball is given by h = −4.9t2 + 5t + 1, where t is the time elapsed in seconds. How long will it take the ball to hit the ground if no other players touch it? Enter the time to two decimal places.
Answer:
It will take 1.19 seconds for the ball to hit the ground if no other players touch it
Step-by-step explanation:
The height of the ball after t seconds is given by the following equation:
[tex]h(t) = -4.9t^{2} + 5t + 1[/tex]
How long will it take the ball to hit the ground if no other players touch it?
This is t when h(t) = 0. So
[tex]-4.9t^{2} + 5t + 1 = 0[/tex]
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
[tex]-4.9t^{2} + 5t + 1 = 0[/tex]
So [tex]a = -4.9, b = 5, c = 1[/tex]
So
[tex]\bigtriangleup = 5^{2} - 4*4.9*1 = 44.6[/tex]
[tex]t_{1} = \frac{-5 + \sqrt{44.6}}{2*(-4.9)} = -0.17[/tex]
[tex]t_{2} = \frac{-5 - \sqrt{44.6}{2*(-4.9)} = 1.19[/tex]
Since we want a time measure, the answer cannot be negative.
It will take 1.19 seconds for the ball to hit the ground if no other players touch it
What is the inverse function of f(x) equals X over X -2
Answer:
(2x)/(x-1)
x = y/(y-2)
(y-2)x = y
yx - 2x =y
yx-y = 2x
y(x-1) = 2x
y= 2x/(x-1)
use the rules of significant figures to simplify the following expression: 31.5 x 10.51
Answer:
31.5×10.51
315/10×1051/100
331065/1000
331.065
what should i get for my birthday ? answer quickly plz ( its on june 3rd ) ( i need help)
Answer:
thats so cool! Happy Birthday you should get some kind of dessert and pizza.
Step-by-step explanation:
Dessert: get some ice cream and something to go with it. TASTY
Pizza: pizza=happiness and happiness is what you should be on your bday!
In a certain town, the ratio of left-handed people to right-handed people 2:9 how many right-handed people would you expect to find in a group of 1320000 people?
Answer:
We are expected to find 1,080,000 right handed people in that group of people
Step-by-step explanation:
In this question, we are given the ratio of right handed to left handed people and we are asked to calculate the number of right handed people we can find in a given population.
First, we check the ratio given.
The ratio is said to be that of left handed individuals to right handed individuals and this sits at 2 to 9.
Thus out of 1,320,000 people , the number of right handed individuals will be ;
9/(2+9) * 1,320,000
9/11 * 1,320,000
= 1,080,000 people
Here is a probability scale:
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
There are 3 white counters and 2 black counters in a bag.
I take one of the counters at random.
Put a cross on the probability scale to show the probability
that I have chosen one of the white counters.
Answer:
see below
Step-by-step explanation:
You have 3 chances in 5 of drawing a white counter, so the probability is ...
3/5 = 0.6
Your mark will go at 0.6 on the probability scale.
All the ice cream sold has exactly one flavor and one treat. If a chocolate ice cream is picked at random, what is the probabilitly that it will have blue swirls
Answer:
Zero
Step-by-step explanation:
Since all the ice cream sold has exactly one flavor and one treat, a chocolate ice cream can't have a blue swirl. This means that the number of chocolate ice cream with blue swirl is zero. Therefor the probability is zero.
At an amusement park john wants to ride a rollercoaster that costs 19 tickets, a bumper car that costs 3 tickets, and a merry-go-round that costs 33 tickets. John had 31 tickets but lost 10 of them on a ride. How many more tickets does he need?
Answer:
John will need 34 more tickets to be able to go on all the rides he wants
Step-by-step explanation:
To solve this, we need to first of all know the total cost in terms of tickets of all the rides that john wants to have.
This will be
cost of roller coaster ride = 19 tickets
cost of bumper car ride = 3 tickets
cost of merry-go-round ride = 33 tickets
Total cost of rides = 19 + 3 + 33 =55 tickets
Next, we will need to find the number of tickets that John has left after losing 10 of them.
This will be 31 - 10 = 21 tickets left
To find the number of more tickets that John needs , we will subtract the number of tickets he has left from total ride ticket cost.
This will be 55-21 = 34 tickets.
Hence, John will need 34 more tickets to be able to go on all the rides he wants
Can someone help me please
Answer:
Step-by-step explanation:
I need help with question 9 please
Answer:
The population is everyone listed in the city phone directoy; the sample is the 75 people selected
Step-by-step explanation:
PLEASE HELP WILL MARK BRAINLIEST
Answer:
The original point is (5, -5). The new point would be (5, 3)
Step-by-step explanation:
-5+8= 3
Answer:
(5, -5)(5, 3)I hope I helped you! If my answer is correct, please mark me brainiest. Thanks!
What is the slope of the line perpendicular to the segment with endpoints (2,0) and (-6,3)?
A. 8/3
B. 3/4
C. -4/3
D. -3/8
Answer:
A line that passes (2, 0) and (-6, 3) has slope:
S1 = (-6 -2)/(3 - 0) = -4/3
Another line that is perpendicular with above line has slope:
S2 = -1/S1 = -1/(-4/3) = 3/4
=> Option B is correct
Hope this helps
:)
The segment with endpoints (2,0) and (-6,3) has a line perpendicular to it with a slope of 4/3.
What is the Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
From the general formula of the slope:
slope = (change in y) / (change in x)
The change in y is 3 - 0 = 3, and the change in x is -6 - 2 = -8. So the slope of the segment is:
slope = (3 - 0) / (-6 - 2) = -3/4
To find the slope of the line perpendicular to the segment, we know that it must have the opposite reciprocal slope. That is:
the slope of perpendicular line = -1 / slope of segment
slope of perpendicular line = -1 / (-3/4) = 4/3
Therefore, the slope of the line perpendicular to the segment with endpoints (2,0) and (-6,3) is 4/3.
Learn more about Linear equations here:
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