Answer:
x = 3
Step-by-step explanation:
We are given the equation 4(x - 8) + 10 = -10 and are asked to find the solution, solution meaning to get x alone.
To do so, first distribute the 4 on the outside of the parenthesis to both values on the inside of the parenthesis :
4(x - 8)
(4 * x - 4 * 8)
4x - 32
4x - 32 + 10 = -10
Now combine like terms :
4x - 22 = -10
Now it's time to get x alone, first get rid of -22 by adding 22 to both sides :
4x = 12
Now get x alone by dividing both sides by 4 :
x = 3
The diameter of a $1 coin is 26.5 mm. Find the area of one side of the coin. Round to the nearest hundredth.
The area of one side of the coin is 41.605 mm².
Given that, the diameter of a $1 coin is 26.5 mm.
We need to find the area of one side of the coin.
What is the area of a circle formula?The area of a circle formula is A=πr².
Now, radius=26.5/2=13.25 mm.
Area of a coin=3.14×13.25=41.605 mm².
Therefore, the area of one side of the coin is 41.605 mm².
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find the common difference
9514 1404 393
Answer:
(a) 1/12
Step-by-step explanation:
The difference of adjacent terms is ...
1/4 -1/6 = 3/12 -2/12 = 1/12
7.
Which kind of function best models the data in the table? Graph the data and write an equation to model the data.
A. exponential; y = 3x – 1
B. linear; y = x – 1
C. quadratic; y = x2 – 1
D. linear; y = –x – 1
Answer:
D. linear; y = –x – 1
Step-by-step explanation:
Linear; y=-x - 1
The slope is negative since it’s decreasing. So it’s not the first equation. It’s not a quadratic equation because there is no forming U shape for this data. It’s not a exponential function because the slope is not 3 and a exponential function is in the form y=a(b)^x
...............................................................................................................................................
Answer:
The correct answer is D) linear; y = –x – 1
Step-by-step explanation:
To find this, use any values in the table and it will produce a true statement. This is how we check to see if a model is correct. See the two examples below for proof.
(4, 5)
y = -x - 1
-5 = -4 - 1
- 5 = -5 (TRUE)
(0, -1)
y = -x - 1
-1 = 0 - 1
-1 = -1 (TRUE)
a positive integer n is called special if n is divisible by 4, N+1 is divisible by 5 and n+2 is divisible by 6. how many special integers smaller than 1000 are there?
Answer:
17
Step-by-step explanation:
these positive integers are :
4, 64, 124, 184 ... , 964
964 = 4 + (n-1) (60)
964 = 4 + 60n -60
964 = 60n -56
60n = 1020
n = 1020/60
n = 17
so, the number of special integers smaller than 1000 are = 17
The digits n, n+1 and n+2 implies that the special numbers are consecutive i.e. they follow one another. The count of special numbers less than 1000 is 17.
Given that:
[tex]\{n,n+1,n+2\} = \{4,5,6\}[/tex]
[tex]Range = 1000[/tex]
First, calculate the LCM of 4, 5 and 6.
[tex]4 = 2 \times 2[/tex]
[tex]5 = 5[/tex]
[tex]6 = 2 \times 3[/tex]
So, the LCM is:
[tex]LCM = 2 \times 2 \times 5 \times 3[/tex]
[tex]LCM = 60[/tex]
This means that the special digit occurs after every other 60 digits (i.e. the difference between a special digit and another is 60)
To calculate the count of special digits, we make use of arithmetic progression formula
[tex]L = a + (n - 1) \times d[/tex]
Where
[tex]L = 1000[/tex] --- the last term
[tex]a = 4[/tex] --- the first special digit
[tex]d = 60[/tex] --- the common difference as explained above
So, we have:
[tex]L = a + (n - 1) \times d[/tex]
[tex]1000 = 4 + (n - 1) \times 60[/tex]
Collect like terms
[tex]1000 - 4 =(n - 1) \times 60[/tex]
[tex]996 =(n - 1) \times 60[/tex]
Divide both sides by 60
[tex]16.6 =n - 1[/tex]
Add 1 to both sides
[tex]1 + 16.6 =n[/tex]
[tex]17.6 =n[/tex]
Rewrite as:
[tex]n =17.6[/tex]
Remove the decimal part (do not approximate)
[tex]n =17[/tex]
Hence, the special numbers are 17 in total (that are less than 1000).
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Refer to picture
Need help on Q.8
Answer:
Rajan = 436.36 rupees and Kamal = 363.63 rupees
Step-by-step explanation:
Total ratio = 11/30
Amount to be shared = 800
Rajan = Individual ratio / Total ratio x the total amount to be shared
1/5 ÷11/30 × 800 = 436.36
Kamal = 1/6 ÷ 11/30 × 800 = 363.63
4) In the proof below, what is the missing reason?
9514 1404 393
Answer:
(c) CPCTC
Step-by-step explanation:
Even if you don't know the meaning of CPCTC, you can eliminate the other choices because they refer to the whole triangle, not two corresponding angles.
Angles B and D are corresponding angles in the congruent triangles. The reason they are congruent is ...
Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
Gabriella has a smart phone data plan that costs $25 per month that includes 10 GB of data, but will charge an extra $15 per GB over the included amount. How much would Gabriella have to pay in a month where she used 5 GB over the limit? How much would Gabriella have to pay in a month where she used went over by x x GB?
find the next three sequence of 1,3, 9, 27,
Answer: 81, 243, 729
Step-by-step explanation:
STEP ONE: Find a pattern in the sequence
3 ÷ 1 = 3
9 ÷ 3 = 3
27 ÷ 9 = 3
As we can see from the given sequence, each number multiplies 3 to get the next term.
STEP TWO: Find the next three terms
27 × 3 = 81
81 × 3 = 243
243 × 3 = 729
Hope this helps!! :)
Please let me know if you have any questions
I need an explanation written out for (0.345)(2.1)
Thank you
Answer:
0.07245
Step-by-step explanation:
Just work out 345*21 and then divide by 10,000 because 0.345 is 3 digits from zero and 2.1 has 1 digit from zero, so total of 4 zeroes (10,000 since 10,000 has 4 zeroes).
16789047+65390-49532578=?
Answer:
-32678141
Step-by-step explanation:
Use a table of function values to approximate an x-value in which the exponential function exceeds the polynomial
function.
f(x) = 2^(5x-6)
h(x) = 3x^5 - 2x^3 - 4x + 7
x=4
x=7
x = 6
x=5
Answer: ¿Hablas español porque no entiendo esto? Si lo haces, ¿puedes decirme en español?
Step-by-step explanation:
Someone please explain this to me like you would a child
thank you
Answer:
12 degrees
Step-by-step explanation:
Answer:
15 degrees
Step-by-step explanation:
okay haha
so basically the cosine of an angle is the side adjacent to it, divided by the hypotenuse. the sine is the side opposite to that angle divided by the hypotenuse, and the tangent is the side opposite to that angle divided by the side adjacent to it.
in this case we are given the angle and the side opposite to it which is 10, and we are also given the hypotenuse of 39.
what trig function deals with opposite and hypotenuse?
the answer is sine
so we would find the sine of that angle which equals to opposite over hypotenuse:
sin(angle) = 10/39
but, they are asking for the inverse trig function. the inverse of sine is arcsin.
so :
arcsin(10/39) = angle
in a calculator, this would be equal to about 14.857 which is closest to 15.
Mr. Barry invested some money at 5% and amount half as great as 4%. His total annual income from both investments was $210. Find the amount invested at 4%
A) $1000
B) $1500
C) $2000
D) $2500
The amount invested at 4% is 1500.
How to estimate the amount invested at 4%?Let x be the amount invested at 4%.
2x be the amount invested at 5%.
0.04x + 0.05(2x) = 210
Multiply by 100 to eliminate decimals
4x + 5(2x) = 21000
Remove parentheses: (a) = a
[tex]4 x+5 \cdot 2 x=21000[/tex]
Multiply the numbers: [tex]$5 \cdot 2=10$[/tex]
4x+10x = 21000
Add similar elements:
4x+10x = 14x
14x=21000
Divide both sides by 14
[tex]$\frac{14 x}{14}=\frac{21000}{14}[/tex]
Simplifying the above equation, we get
x = 1500
The amount invested at 4% is 1500.
Therefore, the correct answer is option B) $1500.
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Can anyone help me with this?
I thing it lies on the negativity side of the number line between -2,24
what is the height of the water prism
Answer:
32 because I Don't know please vote my answer please
Answer:
12 (10) cm 937 637 = hafe 2929888389292822
factorize the expression:
mn² + mnp + 3mn + 3mp
Answer:
(mn+3m)(n+p)
Step-by-step explanation:
Answer:
(mn + 3m)(n + p)
Step-by-step explanation:
Factorize by grouping:
[tex]mn^2+mnp\\mn(n+p)\\\\3mn+3mp\\3m(n+p)\\\\(mn+3m)(n+p)[/tex]
please find the answer
there are options given below
plz give answer asap
Answer
33.3
Step-by-step explanation:
if u multiply the 2, and then find the ratio of them in comparison to the number under, you will find the rate decreases by 10 percent every time, the first situation it is 4/8 = 5/10, second situation is it 32/80= 4/10, and htis situation is most like 3/10, right ? so the answer would be 33.3 :)
write an equation of the function in the form y=a(b)^x -c that has a y intercept of -6, asymptote of y= -2 and goes through (2,-18)
Step-by-step explanation:
Asymptote: y = 2 y-intercept: (0,8)
Step-by-step explanation:
The given function is
f(x) = 6(0.5)^{x} + 2f(x)=6(0.5)
x
+2
This function is of the form:
f(x) = a {b}^{x} + cf(x)=ab
x
+c
where y=c is the horizontal asymptote.
By comparing , we have c=2 hence the horizontal asymptote is
y = 2y=2
To find the y-intercept, we put x=0 into the function to get:
f(0) = 6(0.5)^{0} + 2 = 6 + 2 = 8f(0)=6(0.5)
0
+2=6+2=8
Therefore the y-intercept is (0,8).
A parabola is graphed below.
What is the equation in vertex form of this parabola?
A
y=2(x−2)2−3
B
y=2(x+2)2−3
C
y=12(x−2)2−3
D
y=12(x+2)2−3
thank you so much! please hurry <3
Answer:
B
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here the vertex = (- 2, - 3 ) , then
y = a(x - (- 2))² - 3 , that is
y = a(x + 2)² - 3
To find a, substitute any point on the graph into the equation
Using the coordinates of the y- intercept (0, 5 )
5 = a(0 + 2)² - 3 ( add 3 to both sides )
8 = a(2)² = 4a ( divide both sides by 4 )
2 = a
y = 2(x + 2)² - 3 → B
8. Colleen times her morning commute such that there is an equal likelihood that she will arrive early or late to work on any given day. If she always arrives either early or late, what is the probability that Colleen will arrive late to work no more than twice during a five-day workweek
Solution :
Case I :
If Collen is late on [tex]0[/tex] out of [tex]5[/tex] days.
[tex]$= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} $[/tex]
[tex]$=\frac{1}{32}[/tex]
Case II :
When Collen is late on [tex]1[/tex] out of [tex]5[/tex] days.
[tex]$= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times ^5C_1$[/tex]
[tex]$=\frac{1}{32} \times 5$[/tex]
[tex]$=\frac{5}{32}[/tex]
Case III :
When Collen was late on [tex]2[/tex] out of [tex]5[/tex] days.
[tex]$= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times ^5C_2$[/tex]
[tex]$=\frac{1}{32} \times 10$[/tex]
[tex]$=\frac{5}{16}[/tex]
Therefore, the [tex]\text{probability}[/tex] that Collen will arrive late to work no more than [tex]\text{twice}[/tex] during a [tex]\text{five day workweek}[/tex] is :
[tex]$=\frac{1}{32} + \frac{5}{32} + \frac{5}{16} $[/tex]
[tex]$=\frac{1}{2}$[/tex]
Find the largest prime factor of 18! + 19! + 20!
Answer: Prime Factors for 18: 2, 3, and 3
Prime Factors for 19: 19
Prime Factors for 20: 2, 2, and 5
Can you mark brainlest
Step-by-step explanation:
Your classmate is unsure about how to use side lengths to determine the type of triangle. How would you explain this to your classmate?
Answer:
To determine the type of triangle using side lengths, you could use the converse of the Phythagorean theorem, acute triangle inequality theorem, and the obtuse inequality theorem. For example, if the square of the longest side of a triangle is greater than the sum of the squares of the other two sides, than its obtuse. And if the square of the longest side is less than the sum of the squares of the other two sides, then it would be acute. And if the square of the longest side is equal to the sum of the squares of the two other sides, then it would be a right triangle.
Step-by-step explanation:
it marks it correct on edge and it is not a sample answer.
have a jolly day!
When finding ordered pairs for a table of values for a function, the selection of x-coordinates can be
random
True
O False
Given positive integers x and y such that x doesn't equal y and $1/x+1/y=1/18$ what is the smallest possible value for x+y?
Answer:
Hello,
[tex]\boxed{Answer: 75}[/tex]
Step-by-step explanation:
x,y integers, x,y >0 ,x≠y
[tex]\dfrac{1}{x} +\dfrac{1}{y} =\dfrac{1}{18}\\\\\dfrac{x+y}{xy} =\dfrac{1}{18}\\\\x+y=\dfrac{xy}{18}\\\\x=\dfrac{18y}{y-18}\\x=\dfrac{18y-324 +324}{y-18}\\x=18+\dfrac{324}{y-18}\\[/tex]
[tex]\dfrac{1}{x} +\dfrac{1}{y} =\dfrac{1}{18}\\\\\dfrac{x+y}{xy} =\dfrac{1}{18}\\\\x+y=\dfrac{xy}{18}\\\\x=\dfrac{18y}{y-18}\\x=\dfrac{18y-324 +324}{y-18}\\x=18+\dfrac{324}{y-18}\\\begin{array}{|c|c|c|c|}y-18&y&x&x+y\\---&---&---&---\\1&19&18+324=342&362\\2&20&18+162=180&200\\3&21&126&147\\4&22&99&121\\6&24&108&132\\12&30&45&75\\18&36&36&72\\\end{array}\\\\\\\boxed{Answer: 75}\\\\[/tex]
please solve part c.d.e and f
SEE THE IMAGE FOR SOLUTION
HOPE IT HELPS
HAVE A GREAT DAY
[tex]\sqrt{x^{2} +4x+4[/tex] -3=0
Answer:
Given,
[tex] \sqrt{ {x}^{2} + 4x + 4} - 3 = 0 \\ = > \sqrt{ {x}^{2} + 4x + 4} = 3 \\ = > {( \sqrt{ {x}^{2} + 4x + 4} })^{2} = {3}^{2} \\ = > {x}^{2} + 4x + 4 = 9 \\ = > {x}^{2} + 4x + 4 - 9 = 0 \\ = > {x}^{2} + 4x - 5 = 0 \\ = > {x}^{2} + 5x - x - 5 = 0 \\ = > x(x + 5) - 1(x + 5) = 0 \\ = > (x - 1)(x + 5) = 0 \\ \\ \sf \: either \: x - 1 = 0 \: \: \: \: \\ = > x = 1 \: \: \\ \\ \sf \: or \\ x + 5 = 0 \\ = > x = - 5 \\ \\ \green{ \boxed{ \bf \: \: \: \: \: x = 1 \: \: or \: - 5}}[/tex]
But if we put the value of x = 5 then it doesn’t satisfy the equation.
So,
X = 1
Answer:
The answer is [tex]x=1[/tex].
Step-by-step explanation:
To solve this problem, start by factoring the equation using the perfect square trinomial rule, which is states that the middle term is the first term multiplied by the last term, and then multiplied by 2. The formula for the perfect square trinomial rule looks like [tex]a^2+2ab+b^2[/tex], where [tex]a=x[/tex] and [tex]b=2[/tex]. The equation will look like [tex]\sqrt{(x+2)^2}-3=0[/tex].
Next, pull out the terms from under the radical, assuming positive real numbers, which will look like [tex]x+2-3=0[/tex]. Then, simplify the equation by subtracting 3 from 2, which will look like [tex]x-1=0[/tex]. Finally, add 1 to both sides of the equation, and the answer will be [tex]x=1[/tex].
Question 12
What is the value of x in the following equation?
2/3x + 2 = 4
Sally and Mia run a furniture making company. They work together to build and paint custom dressers.
Sally charges a $100 flat fee for each dresser she builds, plus $420 for each hour she spends building.
Mia charges a $150 flat fee for each dresser she paints, plus $390 for each hour she spends painting.
a) Represent what Sally charges for one dresser as a polynomial. Remember to define any variables!
b) Represent what Mia charges for one dresser as a polynomial. Remember to define any variables!
c) Write a new SIMPLIFIED polynomial that represents their total charges, together, for one dresser.
Answer:
y = 250 + 810x
Step-by-step explanation:
Let
y = total charges
x = cost per hour
Sally: building
y = 100 + 420x
Mia: painting
y = 150 + 390x
Find their total charges of building and painting
Add the total charges of both of them
y = 100 + 420x + 150 + 390x
y = 250 + 810x
What is the length of the altitude of the equilateral triangle below?
A. /240
B. 144
C. 12
D. 4
E. 12/3
F. 4/3
Answer:
its C option which is 12
Answer:
A
Step-by-step explanation:
Using Pythagoras' identity in either of the 2 right triangles
a² = (4[tex]\sqrt{3}[/tex] )² + (8[tex]\sqrt{3}[/tex] )² = 48 + 192 = 240 ( take square root of both sides )
a = [tex]\sqrt{240}[/tex] → A
1. Ms. Rogers earns $___ each month. She pays 25% of her earnings, or $____ in federal taxes and 6% of her earnings, or $____ in state taxes. She pays ____ % of her earnings, or $____ for insurance. After these deductions, Ms. Rogers takes home $_____
131.76
8
175.68
549
2,196
1,339.56
Answer:
2,196; 549; 131.76; 8; 175.68; 1339.56
Step-by-step explanation:
2,196 is the biggest number, so use that as the first number.
.25x2196=549
.06x2196=131.76
.08x2196=175.68
2196-(549+131.76+175.68)=1339.56
