Answer:
[tex] \rm Numbers = 4 \ and \ -3.[/tex]
Step-by-step explanation:
Given :-
The sum of two numbers is 1 .
The product of the nos . is 12 .
And we need to find out the numbers. So let us take ,
First number be x
Second number be 1-x .
According to first condition :-
[tex]\rm\implies 1st \ number * 2nd \ number= -12\\\\\rm\implies x(1-x)=-12\\\\\rm\implies x - x^2=-12\\\\\rm\implies x^2-x-12=0\\\\\rm\implies x^2-4x+3x-12=0\\\\\rm\implies x(x-4)+3(x-4)=0\\\\\rm\implies (x-4)(x+3)=0\\\\\rm\implies\boxed{\red{\rm x = 4 , -3 }}[/tex]
Hence the numbers are 4 and -3
Step-by-step explanation:
[tex]numbers \: = x \: and \: y \\ x \times y = - 12......(1) \\ x + y = 1..... ..(2) \\y = 1 - x \\ put \: this \: in \: (1) \\ x(1 - x) = - 12 \\ x - {x}^{2} = - 12 \\ - x + {x}^{2} - 12 = 0 \\ factorise \\ {x}^{2} - 4x + 3x - 12 = 0 \\ x(x - 4) + 3(x - 4) = 0 \\ (x - 4)(x + 3) = 0 \\ x = + 4 \: or \: - 3 \\ thank \: you[/tex]
Two rectangles are similar. The first is 6 feet wide and 20 feet long. The second is 15 feet wide. What is the length of the second rectangle?
Answer:
50
Step-by-step explanation:
As they are similar, the ratio of the width should be equal to the ratio of length
6/15=20/x, x=50
If the graph of y=|x| is translated so that the point (1,1) is moved to (4,1) what is the equation of the new graph?
This question is solved using translation concepts, and doing this, it is found that the equation of the new graph is:
[tex]y = |x - 3|[/tex]
--------------------------
When a function f(x) is translated a units to the left, we get f(x - a).
--------------------------
In this question:
The original function is [tex]y = |x|[/tex]
Point (1,1) is moved to (4,1), that is, 3 is added to the x-coordinate, meaning that the function was shifted 3 units to the left.
Thus, the new equation is:
[tex]y = g(x) = f(x - 3) = |x - 3|[/tex]
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What is the circumference of the following circle?
ea
3 cm
a
t
D
cm
Show Calculator
your question is incomplete dear check it once
Identify the equation of the circle that has its center at (7, -24) and passes through the origin.
Answer:
[tex](x-7)^{2}[/tex] + [tex](y+24)^{2}[/tex] = [tex]625[/tex]Step-by-step explanation:
Verify that –(-x) is the same as x , for x = −4/5
Answer:
Step-by-step explanation:
-(--4,5)= -(4,5)= -4,5
What is the least common multiple of 4 and 12? O 4 O 12 O 24 o ) 48
Answer:
12
Step-by-step explanation:
Least common multiple means what is the smallest number that both numbers go into
List the prime factors
4= 2*2
12 = 2*2*3
The factors that are in needed to make both are 2 and 3
We need 2 of the 2's and 1 3
2*2*3 = 12
Answer:
12
Step-by-step explanation:
if tolu collects a loan of #250,000 from a bank at the rate of 11 whole number 1 over 2% interest how much will she pay as interest at the end of the year
Answer:
# 28750
Step-by-step explanation:
Intrest = P. A. * Intrest Rate * Time
Intrest = 250000 * 11.5/100 = 28750
Under his cell phone plan, Christopher pays a flat cost of $52 per month and $5 per
gigabyte. He wants to keep his bill at $75 per month. Which tape diagram could be
used to represent the context if x represents the number of gigabytes of data
Christopher can use while staying within his budget?
According to the given information, the tape diagram shown in option C is correct.
Use the concept of inequality defined as:
An inequality is a mathematical statement that uses the inequality symbol to indicate the relationship between two expressions. Both sides of an inequality sign have different expressions.
Given that,
The cost per month = $52
The cost per gigabyte = $5
He wants to keep his bill at $75 per month.
According to the given information the inequality expression be:
52 + 5x ≤ 75
Since now let x = 3
The LHS be:
52 + 15 = 67 < 75
Therefore,
The correct combination be:
52 + 5 + 5 + 5 < 75
Hence,
The tape diagram shown in option C is correct.
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Mike and Ken shared some stamps. \frac{1}{5} 5 1 of Ken's stamps were \frac{1}{3} 3 1 of Mike's stamps. If Mike gave Ken 24 stamps, Ken would have thrice as many stamps as Mike. Find the number of stamps each of them had in the beginning.
Answer:
Mike had 72 stamps
Ken had 120 stamps
Step-by-step explanation:
Given
[tex]M \to Mike[/tex]
[tex]K \to Ken[/tex]
[tex]\frac{1}{5} * K = \frac{1}{3} * M[/tex]
[tex]K + 24 = 3 * ( M - 24)[/tex]
Required
Find K and M
Make K the subject in: [tex]K + 24 = 3 * ( M - 24)[/tex]
[tex]K = 3 * ( M - 24) - 24[/tex]
Substitute [tex]K = 3 * ( M - 24) - 24[/tex] in [tex]\frac{1}{5} * K = \frac{1}{3} * M[/tex]
[tex]\frac{1}{5} * [3 * ( M - 24) - 24] = \frac{1}{3} * M[/tex]
Open brackets
[tex]\frac{1}{5} * [3M - 72 - 24] = \frac{1}{3} * M[/tex]
[tex]\frac{1}{5} * [3M -96] = \frac{1}{3} * M[/tex]
Multiply both sides by 15
[tex]3* [3M -96] = 5 * M[/tex]
[tex]9M -288 = 5M[/tex]
Collect like terms
[tex]9M -5M= 288[/tex]
[tex]4M= 288[/tex]
Divide both sides by 4
[tex]M= 72[/tex]
Substitute [tex]M= 72[/tex] in [tex]K = 3 * ( M - 24) - 24[/tex]
[tex]K = 3 * (72 - 24) - 24[/tex]
[tex]K = 3 * 48 - 24[/tex]
[tex]K = 120[/tex]
help me please
[tex] \frac{ \cos(80) }{ \sin(10) } + \frac{ \sin(20) }{ \cos(70) } = 2 \\ \\ \frac{ \cot(40) }{ \tan(50) } + \frac{ \cos(65) }{ \sin(115) } = 2[/tex]
Answer:
[tex] \frac{ \cos(80) }{ \sin(10) } + \frac{ \sin(20) }{ \cos(70) } = 2 \\ \frac{ \cos(90 - 10) }{ \sin(10) } + \frac{ \sin(20) }{ \cos(9 0 - 20) } = 2 \\ \frac{ \sin(10) }{ \sin(10) } + \frac{ \sin(20) }{ \sin(20) } = 2 \\ 1 + 1 = 2 \\ 2 = 2 \\ \\ \frac{ \cot(40) }{ \tan(50) } + \frac{ \cos(65) }{ \sin(115) } = 2 \\ \frac{ \cot(90 - 50) }{ \tan(50) } + \frac{ \cos(65) }{ \sin(90 + 65) } = 2 \\ \frac{ \tan(50) }{ \tan(50) } + \frac{ \cos(65) }{ \cos(65) } = 2 \\ 1 + 1 \\ = 2[/tex]
3025 to binary octal and base 5
Answer:
for binary 101111010001. for octal 5721. for base 5 - 44100
First get the gcf of 16x³ + 250 which is 2 then divide it which has the result of 8x³ + 125 then get the square root of 8x³ and 125
find the value of trigonometric ratio
Answer:
3/5
Step-by-step explanation:
Cos C = adjacent/hypotenuse
or, Cos C = 21/35 = 3/4
Answered by GAUTHMATH
I need help plss ( math ) SOMEONE ASAP
26a)729
b)2,457.6
c)3,500
d)8,100
e) 89,600
Step-by-step explanation:
just multiply first and divide with upper number to the lower
Please help me solve this last problem guys
Answer:
[tex]\frac{x+4}{4x-4}[/tex]
Step-by-step explanation:
Point slope formula.. help
========================================================
Explanation:
We'll need the slope first
m = slope
m = (y2-y1)/(x2-x1)
m = (0-(-4))/(-3-(-5))
m = (0+4)/(-3+5)
m = 4/2
m = 2
The slope is 2.
Next, pick either of the two given points to play the role of [tex](x_1,y_1)[/tex]
Let's say we picked on (-5,-4). The order doesn't matter so you could easily pick the other point as well.
We'll plug these items into the point slope equation below to solve for y.
[tex]y - y_1 = m(x - x_1)\\\\y - (-4) = 2(x - (-5))\\\\y + 4 = 2(x +5)\\\\y + 4 = 2x +10\\\\y = 2x +10-4\\\\y = 2x +6\\\\[/tex]
Or we could have picked on (-3,0). The m value stays the same (at m = 2)
[tex]y - y_1 = m(x - x_1)\\\\y - 0 = 2(x - (-3))\\\\y = 2(x +3)\\\\y = 2x+6\\\\[/tex]
This one takes a few less steps. Either way, we get to the same answer.
You only need to pick one of the points, but doing both of them helps show that the two points are on the same line. It helps confirm the answer.
-----------------------
Another way to check the answer is to plug the (x,y) coordinates into y = 2x+6 for each point.
So let's say we check (x,y) = (-5,-4)
y = 2x+6
-4 = 2(-5)+6 ... replace x with -5, replace y with -4
-4 = -10+6
-4 = -4
This confirms the first point. I'll let you check the second point.
Answer:
y = 2x+6
Step-by-step explanation:
Attached below is my graph
I graphed the two points, and formed a line
From the point (0,0), i counted the units till the first point the line touches on the y axis (6)
This is the y intercept
The slope-intercept form is written as y = mx+b
m = slope
b = y intercept
So so far we have y = mx + 6
The slope is the rise to the next point the line touches, over the run
You can see that as it rises 2, it runs 1
Rise / Run = 2/1 = 2
Slope = 2
Equation: y = 2x + 6
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
WILL MARK BRAINLIEST !!!
the polygons are similar. Find the scale factor of the smaller figure to the larger figure
Answer:
2:5
Step-by-step explanation:
10 boys cleared a piece of land for 21 days how many days will it take 7 boys to clear the same land if they work at the same rate
Answer:
it took 7 boys 21 days to clear a piece of land.
using Euclids division algorithm, find the largest number that divides 475 and 871 leaving 7 as the remainder in each case
Answer:36
Step-by-step explanation:
gcd(475-7,871-7)=gcd(468,864)=36
[tex]\begin{array}{c|c|c|c|c|c}&0&1&1&5&2\\468&864&468&396&72&\boxed{36}\\468&396&72&36&0\\\end{array}[/tex]
I need help to find y=
Answer:
I know but I will not tell you have to do by self
What is the distance between (-3, -4) and (2,2)
Answer:
I did for you but I don't know you will understand my HANDWRITING or not .
:(
can someone help me out with this 10 points and brainliest
Answer:
the first difference are all 20. (increases by 20 per week)
since the first differences of this relation are constant, it is a linear relation
Set up the ratio for cos(A)
Answer:
21/35
Step-by-step explanation:
Recall that Cos = Adjacent/Hypotenuse
We want to find Cos A
The adjacent of A is 21 and the hypotenuse is 35
So cos A would equal 21/35
Pls pls help me! What is it
Answer:
H
Step-by-step explanation:
Jackie
[tex] \sqrt{9} + \sqrt{25} = 3 + 5 = 8[/tex]
Jesse
[tex] \sqrt{9 + 25} = \sqrt{34} [/tex]
Taking the difference, we get the answer to be
[tex]8 - \sqrt{34} [/tex]
Q.5(b) The population {(P) in millions} of a country is estimated by the function, P=125e0.035t, t = time measured in years since 1990. (a) what is the population expected to equal in year 2000 (b) determine the expression for the instantaneous rate of change in the population (c) what is the instantaneous rate of change in the population expected to equal in year 2000.
Answer:
Hello,
Step-by-step explanation:
Q.5(b) The population {(P) in millions} of a country is estimated by the function, P=125e0.035t, t = time measured in years since 1990. (a) what is the population expected to equal in year 2000 (b) determine the expression for the instantaneous rate of change in the population (c) what is the instantaneous rate of change in the population expected to equal in year 2000.
[tex]P(t)=125*e^{0.035*t}\\a)\\P(2000)=125*e^{0.035*(2000-1990)}=177.38...\\\\b)\\P'(t)=125*0.035*e^{0.035*t}\\\\c)\\\\P'(2000)=125*0.035*e^{0.035*(2000-1990)}=6.2084...[/tex]
a number y cubed plus x squared decreased by 7
Step-by-step explanation:
It is read thus Y^3+X^2-7
The equation form from the given statement would be Y^3 + X^2 - 7.
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically.
For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4.
We have been given a statement as;
"A number y cubed plus x squared decreased by 7".
So, the equation form would be
Y^3 + X^2 - 7
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The complete question is
"A number y cubed plus x squared decreased by 7". write the expression.
Kathryn plants two different types of tomato plant. She records the number of tomatoes that she picks from each plant every day. Her records are shown below:
Plant A: 4, 6, 7, 3, 5, 2, 1, 3, 6, 5
Plant B: 5, 6, 7, 6, 8, 9, 6, 7, 7, 9
Which plant has the more consistent yield of tomatoes?
not enough information to tell
they produce about the same amount of plants
Plant A
Plant B
Answer:
Plant B
Step-by-step explanation:
When you compare the number of tomatoes she picks from plant B with plant A, you will notice that plant B has not produced less tomatoes than plant A in any day but it has either produced the same or more number of tomatoes.
Find the missing side
Answer:
[tex] \sqrt{(12) {}^{2} } + (7) {}^{2} \\ = 13.89[/tex]
Answer: x = 14
Step-by-step explanation:
[tex]h^2 = p^2 + b^2 \\x^2 = 12^2 + 7^2\\x^2 = 144+49\\x^2 = 193\\x = \sqrt{193} \\x = 13.89\\so, x = 13.9 \\so, x = 14[/tex]
4. If triangle ABC has the following measurements, find the measure of side c:
a = 5
B = 7
C = 42 degrees
9514 1404 393
Answer:
c ≈ 4.69
Step-by-step explanation:
The Law of Cosines is used for the purpose. It tells you ...
c² = a² +b² -2ab·cos(C)
c² = 5² +7² -2·5·7·cos(42°) ≈ 21.9799
c ≈ √21.9799 ≈ 4.688
The measure of side c is about 4.69 units.
Which statement best describes the function h(t) = 210 - 15t?
Oh is the function name; h(t) is the input, or independent variable; and t is the output, or dependent variable.
O h is the function name; t is the input, or independent variable; and h(t) is the output, or dependent variable.
O t is the function name; h(t) is the input, or independent variable; and h is the output, or dependent variable.
Ot is the function name; h is the input, or independent variable; and h(t) is the output, or dependent variable.
Answer:
h is the function name; t is the input, or independent variable; and h(t) is the output, or dependent variable.
Step-by-step explanation:
The explanation is in the answer.
h is the function name; h(t) is the input, or independent variable; and t is the output, or dependent variable is correct statement.
The given function is h(t) = 210 - 15t
The function is named h, and it takes an input value t (the independent variable) and produces an output value 15t (the dependent variable).
The function is often written as h(t) = 15t to make it clear that h is a function of t.
Hence, h is the function name; h(t) is the input, or independent variable; and t is the output, or dependent variable is correct statement.
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