Answer:
EQUATION: 24 + 3X = 27. INEQUALITY: 2X - 6 < 18.
Step-by-step explanation:
For the equation:
"A number" means that we do not know what the number is yet. So it is a variable. I chose the variable, "X."
"The SUM of 24 AND" means we are adding 24 to something. So what we have so far is "24 + ..."
"3 times a number" means we are multiplying 3 by the unknown variable X. So 3X. What we have so far is "24 + 3X..."
"is 57" means that everything we've just stated equals 57.
Our entire equation is: 24 + 3x = 27.
For the inequality:
Inequalities mean that two expressions are NOT equal to each other.
"6 less than" means that we subtract 6. So we have,"6 - ..." so far.
"Double a number" means 2 times a number, which we are saying is X. So "2X."
" is less than 18" means that everything we just said is less than the value of 18.
So the whole inequality is: 2X - 6 < 18.
Evaluate f(3)
A. 18
B. 12
C. 4
D. 21
Answer:
the answer is c you will thank us later
a shop sells three types of boots (football, rugby and hiking) sales are usually in the ratio 6:2:3
last month 24 pairs of football boots were sold
how many boots altogether were sold last month
Answer:
44
Step-by-step explanation:
divide 24 by 6 then multiply it by all the number then add it all
please make me brainliest
A positive real number is 4 less than another. If the sum of the squares of the two numbers is 72, then find the numbers.
Answer:
Our two numbers are:
[tex]2+4\sqrt{2} \text{ and } 4\sqrt{2}-2[/tex]
Or, approximately 7.66 and 3.66.
Step-by-step explanation:
Let the two numbers be a and b.
One positive real number is four less than another. So, we can write that:
[tex]b=a-4[/tex]
The sum of the squares of the two numbers is 72. Therefore:
[tex]a^2+b^2=72[/tex]
Substitute:
[tex]a^2+(a-4)^2=72[/tex]
Solve for a. Expand:
[tex]a^2+(a^2-8a+16)=72[/tex]
Simplify:
[tex]2a^2-8a+16=72[/tex]
Divide both sides by two:
[tex]a^2-4a+8=36[/tex]
Subtract 36 from both sides:
[tex]a^2-4a-28=0[/tex]
The equation isn't factorable. So, we can use the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = 1, b = -4, and c = -28. Substitute:
[tex]\displaystyle x=\frac{-(-4)\pm\sqrt{(-4)^2-4(1)(-28)}}{2(1)}[/tex]
Evaluate:
[tex]\displaystyle x=\frac{4\pm\sqrt{128}}{2}=\frac{4\pm8\sqrt{2}}{2}=2\pm4\sqrt{2}[/tex]
So, our two solutions are:
[tex]\displaystyle x_1=2+4\sqrt{2}\approx 7.66\text{ or } x_2=2-4\sqrt{2}\approx-3.66[/tex]
Since the two numbers are positive, we can ignore the second solution.
So, our first number is:
[tex]a=2+4\sqrt{2}[/tex]
And since the second number is four less, our second number is:
[tex]b=(2+4\sqrt{2})-4=4\sqrt{2}-2\approx 3.66[/tex]
Answer:
[tex]2+4\sqrt{2}\text{ and }4\sqrt{2}-2[/tex]
Step-by-step explanation:
Let the large number be [tex]x[/tex]. We can represent the smaller number with [tex]x-4[/tex]. Since their squares add up to 72, we have the following equation:
[tex]x^2+(x-4)^2=72[/tex]
Expand [tex](x-4)^2[/tex] using the property [tex](a-b)^2=a^2-2ab+b^2[/tex]:
[tex]x^2+x^2-2(4)(x)+16=72[/tex]
Combine like terms:
[tex]2x^2-8x+16=72[/tex]
Subtract 72 from both sides:
[tex]2x^2-8x-56=0[/tex]
Use the quadratic formula to find solutions for [tex]x[/tex]:
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] for [tex]ax^2+bx+c[/tex]
In [tex]2x^2-8x-56[/tex], assign:
[tex]a\implies 2[/tex] [tex]b \implies -8[/tex] [tex]c\implies -56[/tex]Solving, we get:
[tex]x=\frac{-(-8)\pm \sqrt{(-8)^2-4(2)(-56)}}{2(2)},\\x=\frac{8\pm 16\sqrt{2}}{4},\\\begin{cases}x=\frac{8+16\sqrt{2}}{4}, x=\boxed{2+4\sqrt{2}} \\x=\frac{8-16\sqrt{2}}{4}, x=\boxed{2-4\sqrt{2}}\end{cases}[/tex]
Since the question stipulates that [tex]x[/tex] is positive, we have [tex]x=\boxed{2+4\sqrt{2}}[/tex]. Therefore, the two numbers are [tex]2+4\sqrt{2}[/tex] and [tex]4\sqrt{2}-2[/tex].
Verify:
[tex](2+4\sqrt{2})^2+(4\sqrt{2}-2)^2=72\:\checkmark[/tex]
Please halp due today its fill in the blanks dont do it randomly please
fill in the blanks with the words at the bottom
Which of the following graphs represent the dilation of
the given triangle XYZ with the center of dilation at the
origin with a scale factor 3?
Please I need it fast
Answer:
12y
Step-by-step explanation:
|x - 3|<5
Pls solve this you need to rewrite it without modulus sign and explain as well
Answer:
-2< x< 8
Step-by-step explanation:
|x-3|<5 <=> -5<x-3<5 <=> -2<x<8
..
Answer:
-2x<8
Step-by-step explanation:
|x-3|<5<=> -5<x-3<5 <=>-2<x<8
.....
The temperature rose by 15°C from morning till noon. If the temperature
was less than 50°C at noon, write and solve an inequality to show the
possible temperature in the morning (use t to represent the temperature
in the morning)
Please help meeee
Step-by-step explanation:
answer is in photo above
Convert 4years to months.
Answer:
56 months 12+12x2=56 hope this helps
Step-by-step explanation:
What is the decay factor in the exponential decay function y=a (1-r) t
Answer:
in this form, the "-r" would cause the result to decrease
I assume that the answer is "r"
if r = .1 (10 %) then 1-.1 = .9
if you have 100 items then y = 100(.9)^1 = 90
the total decreased by 10% ... y = 100(.9)^2 after 2 time periods
Step-by-step explanation:
Martin had 60kgs of sugar. He put the sugar weighing 3/4 kg. How many packets did he fill ??
Answer:
45kg
Step-by-step explanation:
60.3/4=45
Which of the following is the solution set for -3t + 11 > 20?
t < 3
t > 3
t < -3
t > -3
Answer:
t < -3
Step-by-step explanation:
-3t + 11 > 20
subtract 11 from both sides
-3t > 9
Divide both sides by -3
when multipying or dividing by a negative the inequality must be reversed
t < -3
A bicycle tire has a radius of 10 inches. To the nearest inch, how far does the tire travel when it makes 4 revolutions?
Answer: 251.2 inches.
Step-by-step explanation: You have to multiply 4*2*π*radius. So, simply multiply 4*2*3.14*10. It would come out as 251.2 inches.
(1.8 + 1.3) + 0.7 = 1.8 + (1.3 + 0.7) is an example of which property?
Answer:
Associative property
Step-by-step explanation:
The associative property is a math rule that says that the way in which factors are grouped in a multiplication problem does not change the product.
Hope this helps
Please help I really need ur help please
Answer:
y = 3x - 30
Step-by-step explanation:
First, put both equations into slope-intercept form.
x + 3y - 4 = 0
3y = -x + 4
y = (-1/3)x + (4/3)
2x + 5y - 20 = 0
5y = -2x + 20
y = (-2/5)x + 4
For a line to be perpendicular to y = (-1/3)x + (4/3), its slope should be the opposite and reciprocal of this line's slope.
The slope of y = (-1/3)x + (4/3) is (-1/3). The slope of a perpendicular line is 3.
To find the x-intercept of y = (-2/5)x + 4, plug in 0 for y and find x.
0 = (-2/5)x + 4
x = 10
The equation of the line right now is y = 3x + b
Plug in (10, 0) to find the y-intercept.
0 = 3(10) + b
b = -30
The equation of the line is y = 3x - 30
if shreeja wants to level her garden of length (2z+5) metre and breadth (2Z-3) metre, then the area of garden is ___________
Answer:
4z²+4z-15 Square Metre
Step-by-step explanation:
According To The Question,
Given, Shreeja wants to level her garden of length (2z+5) metre and breadth (2z-3) metre.Area Of Garden = Length × Breadth
Area Of Garden = (2z+5) × (2z-3)
Area Of Garden = 4z²-6z+10z-15
Area Of Garden=4z²+4z-15 Square Metre
pls help if I get this right you get brainlist if not you will get a 1 star
Answer:
(15+6)÷3
hope it helps!!
What is the solution to the system of equations?
Support your answer and justify your reasoning.
Answer in complete sentences.
Answer:
The solution to the system is (-2,6)
Step-by-step explanation:
I said the solution to the system is (-2,6) because that is where both lines cross, meaning that's the solution.
Hope this is hepful.
Is the following shape a rectangle? How do you know?
2 more than the sum of y and x as an algebraic expression
Answer:
(x+y)+2
hope this helps
1. Brad invested $2,300 in a corporate bond
that pays 14% interest compounded
continuously. How long will it take
Brad's investment to triple?
Given:
Principal value = $2300
Rate of interest = 14% compounded continuously.
To find:
The time taken by Brad's investment to triple.
Solution:
The formula for amount after the compound interest (Continuously) is:
[tex]A=Pe^{rt}[/tex]
Where, P is the principal, r is the rate of interest in decimal and t is the time period.
Triple of Brad's investment is
[tex]3\times \$ 2300=\$ 6900[/tex]
Substituting [tex]A=6900,P=2300\ r=0.14[/tex], we get
[tex]6900=2300e^{0.14t}[/tex]
[tex]\dfrac{6900}{2300}=e^{0.14t}[/tex]
[tex]3=e^{0.14t}[/tex]
Taking natural log on both sides, we get
[tex]\ln 3=\ln e^{0.14t}[/tex]
[tex]1.0986=0.14t[/tex] [tex][\because \ln e^x=x][/tex]
[tex]\dfrac{1.0986}{0.14}=t[/tex]
[tex]7.84714=t[/tex]
After approximating the value, we get
[tex]t\approx 7.85[/tex]
Therefore, Brad's investment will take 7.85 years to triple.
the answer to this question
Answer:
1 square unit
Step-by-step explanation:
Area of the shaded region
= Area of the triangle with base 3 units and height 1 unit - Area of triangle with base 1 unit and height 1 unit.
= 1/2 *3*1 - 1/2 *1*1
= 1.5 - 0.5
= 1 square unit
HELP PLEASE I WILL GIVE BRAINLY TO CORRECT ANSWER PLS.
2 The graphs of y = 3x + 7x – 4 and y + 2x = 10 intersect at the points A and B.
Find the coordinates of A and B.
You must show all your working and give your answers correct to two decimal places.
Answer:
Check the text of the exercise, there is something wrong
Step-by-step explanation:
y=10x-4
y=-2x+10
These are two stright lines, they meet in one point only, P(7/6, 23/3)
Need help -2<2×-3<1
Answer:
[tex]-2 < 2x - 3 < 1 \ = \ \frac{1}{2} < x < 2[/tex]
Step-by-step explanation:
[tex]-2 < 2x - 3 < 1\\\\-2 + 3 < 2x - 3 + 3 < 1 + 3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ adding \ by\ 3 \ ]\\\\1 < 2x + 0 < 4\\\\1 < 2x < 4\\\\\frac{1}{2} < \frac{2x}{2} < \frac{4}{2} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ divide \ by \ 2 \ ]\\\\\frac{1}{2} < x < 2[/tex]
Answer:
1/2 < x < 2
Step-by-step explanation:
-2<2x-3<1
Add 3 to all sides
-2+3<2x-3+3<1+3
1<2x<4
Divide all sides by 2
1/2 < 2x/2 <4/2
1/2 < x < 2
If x = 2.7, 5x = ____. (Input decimals only, such as 12.7.)
Answer:
5x=13.5
Step-by-step explanation:
Well, we know that 1x=2.7. So, if we want 5x we need to multiply 2.7*5 becuase 1x=2.7, so 5x=2.7*5.
Multiply. 2.7*5=13.5
So, 5x=13.5.
Hope this helps!
Answer:
13.5
Step-by-step explanation:
5x = ?
Replace 'x' with 2.7.
5(2.7) = ?
5(2.7) = 13.5
Hope this helps.
Please helpppp
Graph the system of inequalities {y>2x+1/ y>|x|. Which two quadrants does the solution lie in?
Answer:
Option (1)
Step-by-step explanation:
We have to graph the system of inequalities given.
y > 2x + 1 -----(1)
y > |x| --------(2)
For inequality (1),
Solution area will be the area above the dotted line y = 2x + 1
Similarly, solution area of the second inequality will be the area above the dotted lines of y = |x|
Solution area of the system of inequalities will be the common area of both the graphs of the given system.
That will lie in quadrants 1 and 2.
Option (1) will be the answer.
How would I do this?
Answer:
you can do it
Step-by-step explanation:
by using your brain
Mrs. Laser is building a new space for her chickens. She has 80 feet of fencing. What is the greatest fencing area she could create using fencing?
Answer:
400 ft^2
Step-by-step explanation:
It can be shown that a square area is the most efficient way in which to use fencing. If the area is not square, the area will inevitably be smaller.
Calculus is the tool most often used in higher math to solve optimization problems.
But the same goal can be achieved in this problem by working with constraints:
If x and y are the length and width respectively, then
2x + 2y = 80 ft, or x + y = 40, or x = 40 - y. This is one constraint.
The other constraint involves the area: A = x*y, or A = (40 - y)*y. To maximize this, we need to rewrite (40 - y)*y in standard form:
A = 40y - y^2, or, finally, A = -y^2 + 40 y. The coefficients of this quadratic are -1, 40 and 0; the axis of symmetry is thus
x = -b/ [2a], or, in this case, x = -40/[2*(-1)], or x = 20.
Thus, If x = 20, y = 20 also, proving that the shape of the enclosed yard is that of a square.
Then Mrs. L' 80 feet of fencing is sufficient to construct a 20 ft by 20 ft space, which comes out to a maximum area of 400 ft^2.
40 -
Instructions: Using the image, find the slope of the line. Reduce all fractions and enter using a forward slash (i.e.
"/"). If the slope is undefined, enter "undefined
Answer:
Δy = 5 Δx = 1
slope = [tex]\frac{5}{1}[/tex] = 5
Step-by-step explanation:
There are 30 students in Mr. Shawn’s class and 60% of the students are above 12 years old. How many students are above 12 years old?
Answer:
the answer is a 18 as 60 percent of 30 is 18
hope it helps
What is the value of x when h(x) = -3?
Answer and Step-by-step explanation:
The answer is -7 (A.)
This is determined by looking at the graph. If you to to the x-point of -3 units, you will see there is a point at a y-value of -7 (units down).
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