Suppose you had d dollars in your bank account. You spent $22 but have at least $28 left. How much money did you have initially? Write and solve an inequality that
represents this situation.
a.) d-22 28; d 50
b.) d - 22 > 28; d > 50
c.) d + 22 s 28; d s 72
d.) d + 22 28; d 272
Hi there!
»»————- ★ ————-««
I believe your answer is:
d – 22 ≥ 28
d ≥ 50
»»————- ★ ————-««
Here’s why:
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[tex]\boxed{\text{Information Given:}}\\\\d - \text{Initial amount of money}\\\\\text{22 dollars was spent, and there are 'at least' 28 dollars left.}[/tex]
⸻⸻⸻⸻[tex]\boxed{\text{Setting up an inequality:}}\\\\\text{22 dollars was spent from the initial amount, 'd'.}\\\\d - 22\\\\\text{There are \textbf{at least} 28 dollars left. "At least" indicates a \underline{greater than or equal to} sign.}\\\\\rightarrow \boxed{d-22\geq 28}[/tex]
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[tex]\boxed{\text{Solving the inequality:}}\\\\d - 22\geq 28\\-------------\\\rightarrow d - 22 + 22 \geq 28 + 22\\\\\rightarrow \boxed{d \geq 50}[/tex]
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[tex]\text{Your answer should be: }\boxed{d-22\geq 28; \text{ }d \geq 50}[/tex]
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»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
An acute angle of a right triangle measures 30°, and the length of the triangle's hypotenuse is 10 ft. Find the missing angle measure and side lengths.
Answer:
missing angle <60 and side lengths 5, 5[tex]\sqrt{3}[/tex]
Step-by-step explanation:
we understand from the given information that the triangle in question is a special right triangle
and since this is a special triangle the side lengths follows :
the side length that sees <90 is represented by 2x
the side length that sees <60 is represented by x[tex]\sqrt{3}[/tex]
and the side length that sees <30 is represented by x
2x = 10 so x = 5 and x[tex]\sqrt{3}[/tex] = 5[tex]\sqrt{3}[/tex]
Which expression is equivalent to ((2x²) (3x) (4x)??
A.24x7
B.48x?
C.9677
D.576x12
Answer:
24x^4
Step-by-step explanation:
((2x²) (3x) (4x)
Add the exponents when multiplying
2*3*4 x^(2+1+1)
24x^4
help!! need to find the area
Answer:
10*5 +2(2*2)
50+8
58
Step-by-step explanation:
Answer:
58 units
Step-by-step explanation:
What’s the rate of change in this question y=0.860x+3.302
Answer:
The equation is in a linear form, which means its in y=mx + b
M is the slope.
Slope is a fancy word for rate of change.
Therefore, the slope/rate of change is...
.860
Evaluate:
18 (5n - 4) = [?]
Answer:
90n-72=0
Step-by-step explanation:
18×5n-18×4=0
Find sin 0
A. 16/20
B. 12/16
C. 12/20
D. 16/12
Answer:
16/20
Step-by-step explanation:
Since this is a right triangle
sin theta = opp side / hypotenuse
sin theta = 16/20
Answer:
A.
[tex]{ \tt{ \sin( \theta) = \frac{opposite}{hypotenuse} }} \\ \\ { \tt{ \sin( \theta) = \frac{16}{20} }}[/tex]
Identify the equation of the circle that has its center at (9, 12) and passes through the origin.
Answer:
(x-9)^2 +(y-12)^2 = 225
Step-by-step explanation:
First find the length of the radius
If is the distance from the center to the point
d = sqrt( (x2-x1)^2 + (y2-y1)^2 )
= sqrt( (0-9)^2 + (0-12)^2)
= sqrt ( 81+144)
= sqrt(225)
= 15
The equation for a circle is
( x-h) ^2+ (y-k)^2 = r^2
(x-9)^2 +(y-12)^2 = 15^2
(x-9)^2 +(y-12)^2 = 225
if a(b+c)=d and a, b, c and d are all integer, then which of the following must be true?
A. ab+c=d
B. ab+ac=d
C. a(b+c)>10
D. ab
Answer:
B. ab+ac=d
Step-by-step explanation:
Answer:
ab + ac = d
Step-by-step explanation:
a(b+c)=d
Distribute the a
ab + ac = d
need help with this!!
Answer:
{ 1,3,4,6,7}
Step-by-step explanation:
Do B∩C first
This is B intersect C which means what they have in common
B∩C = {3,6,7}
Then A∪(B∩C)
A union {3,6,7} which means join together ( combine with no duplicates) the two sets
{ 1,3,4,6,7}
Answer two questions about Equations A and B:
A. 3(x+2) = 18
B.
r + 2 = 6
1) How can we get Equation B from Equation A?
Step-by-step explanation:
3x+6=18
3x=18-6
3x=12
x=4
What could be the coefficient of x once the variable term is isolated on one side of the equation? Check all that apply.
3x - 6(5x + 3) = 9x + 6
1. Distribute: 3x - 30x - 18 = 9x + 6
2. Combine like terms: -27x - 18 = 9x + 6
–36
–27
–24
24
27
36
Answer:
-36,36
Step-by-step explanation:
3x - 6(5x + 3) = 9x + 6
Distribute:
3x - 30x - 18 = 9x + 6
Combine like terms:
-27x - 18 = 9x + 6
There are two possible ways to isolate x
On the left
Subtract 9x from each side
-27x - 18 -9x = 9x-9x + 6
-36x -18 = 6
On the right
Add 27x from each side
-27x - 18 +27x = 9x+27x + 6
-18 =36x+ 6
what is the measure of m?
Answer:
[tex]n^{2} +18^{2} =x^{2}[/tex]
[tex]6^{2} +x^{2} =m^{2}[/tex]
[tex]6^{2} +18^{2} +n^{2} =m^{2}[/tex]
[tex]m^{2} =n^{2} +360[/tex]
[tex]n^{2} +36=m^{2}[/tex]
[tex]m=15[/tex]
OAmalOHopeO
“The length of a rectangle is two feet greater than twice its width. If the perimeter is 25 feet, find the width.” Which of the following translations is correct?
Answer:
b is the answer
Step-by-step explanation:
What action represents the "!" symbol on a TI 84 plus CE calculator for a Statistics problem??
Answer:
The "!" represents a factorial
Step-by-step explanation:
In math, a factorial when there is an ! followed by a number.
For example, 5! = 5 factorial.
To solve factorials, multiply every integer below the number before the factorial, including the number.
5! = 5 x 4 x 3 x 2 x 1 = 120.
Find P(blue and even).
A. 3/5
B. 1/10
c. 7/10
Answer: A. 3/5
Step-by-step explanation:
Assuming that they are colorful blocks,
There are in total 10 blocksThere are in total 2 blue blocksThere are in total 5 even blocksBlue blocks: 1, 2
Even blocks: 2, 4, 6, 8, 10
The net total of blue and even blocks:
2 + 5 = 7 blocksHowever, as we can see from above, the number [2] is repeated in both cases, thus we shall subtract one of them from the total number.
7 - 1 = 6 blocksWe analyzed at the beginning where there are 10 blocks in total. Then, utilizing the probability formula below:
6/10 = 3/5Hope this helps!! :)
Please let me know if you have any questions
Can someone help please and thank you
Answer:
b
Step-by-step explanation:
A researcher decides to find out whether giving students positive
reinforcement improves or impairs their grades. The researcher's sample
group consists of the following 8 students:
0 Jack
1 Tucker
2 Susie
3 Jill
4 Charianna
5 Trey
6 Ashton
7 Jordan
52197 66082 97867 49397 47924 78900 59414 64755 48733
Which of the following represents a 5-person group selected for the
treatment group using the first number in the line from a table of random
numbers above?
A. Charianna, Tucker, Jack, nobody, Ashton
B. Tucker, Susie, Trey, Ashton, Jordan
C. Trey, Susie, Tucker, Jordan, Ashton
D. Charianna, Tucker, Jack, Ashton, Trey
Answer: C. Trey, Susie, Tucker, Jordan, Ashton
========================================================
Explanation:
The random sub-sequence 52197 66082 helps directly determine who we pick.
The digit 5 is first of that sequence, so we pick Trey first (as he's the 5th student). Then we pick student #2 next, who is Susie.
Up next is student #1, and that would be Tucker
Up next is student #9, but the list only goes high as 7. So we skip over 9
Jordan is next up since 7 is the next digit
Finally, the last selection is Ashton because 6 follows after.
--------------
In other words, the sequence 52197 6 will lead to these selections in the order provided.
5 = Trey2 = Susie1 = Tucker9 = skip, since it's not on the list7 = Jordan6 = AshtonSide note: if we wanted a 6th student, then we'd have to skip over the next 6 since we cannot pick Ashton twice. The 6th selection would be Jack since he's student #0
Anybody knows the answers to the monomial functions ?
Step-by-step explanation:
A monomial function is an expression with only one term. ... For example, a polynomial function is the sum of many monomial functions; If there's only one term in a polynomial function, then it is a monomial function [2]. Monomial functions can take many forms: A monomial (a number by itself is a “monomial”).
This table shows the relationship of the total number of pieces of fruit to the number of bananas.
Why is StartFraction 6 Over 5 EndFraction not equivalent to Three-halves?
Given:
The table that shows the relationship of the total number of pieces of fruit to the number of bananas.
To find:
Why is [tex]\dfrac{6}{5}[/tex] not equivalent to [tex]\dfrac{3}{2}[/tex].
Solution:
If a, b, c are real numbers, then
[tex]\dfrac{a}{b}=\dfrac{a\times c}{b\times c}[/tex]
The given fraction is [tex]\dfrac{3}{2}[/tex]. It can be written as:
[tex]\dfrac{3\times 2}{2\times 2}=\dfrac{6}{4}[/tex]
The number 3 is multiplied by 2 to get 6. So, the 2 should also be multiplied by 2. The ratio should be [tex]\dfrac{6}{4}[/tex], not [tex]\dfrac{6}{5}[/tex].
Therefore, the correct option is A.
What value of x will make the equation true?
(Square Root of 5) (square root of 5)=x
Answer:
(2.236067978)(2.236067978)
=5 ans.
If this is incorrect forgive me
I hope this will help you
stay safe
Bob placed a 17- foot ramp against the side of a house so the ramp rested on a ledge that is 8 feet above the ground. How far was the base of the ramp from the house?
find the common difference in the linear sequence sequence 69,53,47,30
In order for the parallelogram to be a rhombus, x=? (7x+13)º
Answer:
x = 11
Step-by-step explanation:
The diagonals of a rhombus are perpendicular meaning that they create 90 degree angles
If they create 90 degree angles then 7x + 13 = 90
( Note that we've just created an equation that we can use to solve for x )
We now solve for x algebraically using the equation we created
7x + 13 = 90
Step 1 Subtract 13 from both sides
7x = 77
Divide both sides by 7
x = 11
Help Now Pleaseee!!!!
Find the volume of the sphere
Answer:
7235 using 3.14 for pi
7238 using the pi button
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
V = 4/3 pi (12)^3
V = 2304pi
Letting pi = 3.14
V = 7234.56 and rounding to a whole number
V = 7235
Using the pi button
V =7238.22947 and rounding to a whole number
V = 7238
Answer: 7238
Step-by-step explanation:
The formula used is 4/3πr³
Now let's substitute the radius: 12
4/3πr³
=4/3×π×12³
=4/3×π×1728
=7238.22947
but since we are rounding it to the nearest whole number the answer would be 7238
please explain this to me.
Answer:
Equation of line:- y=2x-7
slope(m)=2
slope of parallel line (m)=2
∴ Equation of parallel line:- y=2x+b
it passes through the point (-3,6)
6=2(-3)+b 6+6=b
b=12
∴ y=2x+12
OAmalOHopeO
convert into power notation -1/81
Answer:
-1/9^2 is the power notation for your questions
Step-by-step explanations
A running track has two semi-circular ends with radius 27m and two straights of length 90.6m as shown.
Calculate the total distance around the track rounded to 1 DP.
Answer:
350.85
Step-by-step explanation:
90.6*2 = 181.2
27*2 = 54 (diameter)
54*pi = 169.646003294
169.646003294 + 181.2 = 350.846003294
350.846003294 = 350.85
Find the equation of the line that passes through (1,6) and (3,10).
y=2x+4
y=-2x+4
y=-24-4
Oy-23-4
Answer:
m = (y2 - y1) / (x2 - x1) = (10 - 6) / (3 - 1) = 2 slope of line
y = m x + b standard form of straight line
y = 2 x + b where b is the intercept at x = 0
b = y - 2 x
b = 6 - 2 = 4 from our first equation
Also, b = 10 - 6 = 4 check from second equation
y = 2 x + 4 is our equation
Check if y = 6 and x = 1 then
y = 2 * 1 + 4 = 6 verifying the first point given
Instructions: Find the missing side lengths. Leave your answers as radicals in simplest
form.
Answer:
x = 40
y= 20
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 60 = 20 sqrt(3)/ x
x sin 60 = 20 sqrt(3)
x = 20 sqrt(3)/ sin 60
x = 20 sqrt(3)/ sqrt(3)/2
x = 20 *2
x = 40
tan theta = opp /adj
tan 60 = 20 sqrt(3)/y
y = 20 sqrt(3)/ tan 60
y = 20 sqrt(3) / sqrt(3)
y = 20