What is the solution to the following equation?
х+ (-21) = 8
О А. x= 27
B. х = 29
с. х = 13
D. х = 17
Answer:Option B
The solution to given equation is x = 29
Solution:Given that we have to find the solution of given equation
Given equation is x + (- 21 ) = 8
The value of the variable is found by adding, subtracting, multiplying or dividing both sides of the equation to simplify the equation and isolate the variable.
The goal is to have the variable on one side of the equation and numbers on the other.
From given equation,
x + ( -21) = 8
Let us first remove the brackets around -21
We know when we multiply a positive sign number with negative sign number, we get a negative sign number
x + 1( - 21 ) = 8
x - 21 = 8
Move -21 from L.H.S to R.H.S
x = 21 + 8
x = 29
Thus solution to given equation is x = 29 Thus Option B is correct
What Is the slope of y=3/4x-7
Answer:
[tex]m=\frac{3}{4}[/tex]
Step-by-step explanation:
This equation is in the form of y=mx+b
In this equation, m is the slope. m is the coefficient of x.
In the equation, [tex]y=\frac{3}{4} x-7[/tex]
[tex]m=\frac{3}{4}[/tex], which is the slope.
Answer:
m = 3/4
Step-by-step explanation:
This equation is in the form of y=mx+b
In this equation, m is the slope. m is the coefficient of x.
In the equation, y=\frac{3}{4} x-7
m=\frac{3}{4}, which is the slope.
PLEASE SOMEONE HELP ME ON THIS QUESTION!!!
Answer:
[tex]\frac{7}{3}[/tex]
Step-by-step explanation:
Im going to assume a faction greater than one means an improper fraction.
Converting [tex]2 \frac{2}{6}[/tex] gets [tex]\frac{14}{6}[/tex] which simplified is [tex]\frac{7}{3}[/tex]
at a clothing store, jackets are on sale for 30% off.sale tax is 5%.which expression will calculate the total cost of a jacket with an original price of x
The expression to calculate the total cost of a jacket with an original price of x is 0.7x + 5 % of 0.7x
Solution:
Given that at a clothing store, jackets are on sale for 30% off
Sales is 5 %
To find: Expression to calculate the total cost of jacket
Let "x" be the original price of Jacket
Price of jacket after offer = original price of Jacket - 30 % of original price
Price of jacket after offer = x - 30 % of x
Price of jacket after offer = [tex]x - \frac{30}{100}x = 0.7x[/tex]
The total cost of jacket is sum of price of jacket after offer and sales tax
total cost of jacket = price of jacket after offer + sales tax
total cost of jacket = 0.7x + 5 % of 0.7x
Thus the expression to calculate the total cost of a jacket with an original price of x is 0.7x + 5 % of 0.7x
Fifty students in the seventh grade are trying to raise at least $2000 for sports supplies. They already raised $750. How much should each student raise in order to meet the goal? Write your answer as an inequality.
Answer:
x ≥ 25
Step-by-step explanation:
In the seventh grade, fifty students are trying for sports supplies to raise at least $2000. They already have $750.
Let us assume that each student has to raise $x more to meet the goal.
Then, a total of 50 students will raise $50x more.
Therefore, the inequality to solve for x will be
750 + 50x ≥ 2000
⇒ 50x ≥ 1250
⇒ x ≥ 25 (Answer)
Final answer:
Each seventh grade student should raise at least $25 in order to collectively meet the goal of raising $2000 for their sports supplies after having already raised $750.
Explanation:
The goal amount for the seventh grade sports supplies fundraiser is $2000. They have already raised $750, leaving them with $1250 still needed to reach their goal. If there are 50 students working on the fundraiser, we can set up an inequality to determine how much money each student should raise minimally to meet the goal of $2000. Here's the inequality:
Let x be the amount each student needs to raise.
50x + $750 ≥ $2000
To solve for x, we subtract $750 from both sides of the inequality:
50x ≥ $2000 - $750
50x ≥ $1250
Now divide both sides by 50 to find the amount each student should raise:
x ≥ $1250 / 50
x ≥ $25
Therefore, each seventh grade student should raise at least $25 to meet the $2000 goal.
See if you're a genius by answering this question!
A 2-liter bottle of soda (67.6 ounces) costs $1.89. A case of twelve 12 ounce
cans of the same soda costs $2.99. Calculate the unit price (price/ounce) of each
item and determine which is the better bargain. Explain your answer.
Answer:
Do you know the answer
Step-by-step explanation:
Answer:
Step-by-step explanation:
67.6 oz cost $ 1.89
unit rate is : 1.89 / 67.6 = 0.027....rounds to 3 cents per oz
12 twelve oz cans.....thats (12 * 12) = 144 oz....for 2.99
2.99 / 144 = 0.0207....rounds to 2 cents per oz
the better bargain would be the 12 twelve oz cans because u save one penny more per oz then when ur buying the 2 liter bottle
plz help super fast 4 mins
Answer:
A. 10%
Step-by-step explanation:
Let events A nad B be:
A = an employee is a female
B = an employee is under the age of 30.
Use formula
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
There are 200 employees, 150 of them are female, then
[tex]P(A)=\dfrac{150}{200}=\dfrac{3}{4}=0.75[/tex]
There are 200 employees, 40 of them are under the age of 30, then
[tex]P(B)=\dfrac{40}{200}=\dfrac{1}{5}=0.2[/tex]
The probability of randomly selecting an employee who is a female or under the age of 30 is 85%, then
[tex]P(A\cup B)=0.85[/tex]
Thus,
[tex]0.85=0.75+0.2-P(A\cap B)\\ \\0.85=0.95-P(A\cap B)\\ \\P(A\cap B)=0.95-0.85=0.1[/tex]
Therefore, the probability of randomly selecting an employee who is a female and under the age of 30 is 0.1 or 10%.
What is the square root of the day of the month that Christmas falls on?
Answer:
5
Step-by-step explanation:
The day of the month Christmas falls on is 25th because Christmas falls on 25th December. The square root of 25 is 5 because 5 squared is 25
In the half-life function Q(t)=28550⋅((34)h)(th) Q ( t ) = 28550 ⋅ ( ( 3 4 ) h ) ( t h ) , what is the half-life, h h , if (34)h=12 ( 3 4 ) h = 1 2 ?
The half-life h is calculated to be approximately 2.41.
To determine the half-life h from the given half-life function:
[tex]\[ Q(t) = 28550 \cdot \left( \frac{3}{4} \right)^{\frac{t}{h}} \][/tex]
we need to solve for h in the equation:
[tex]\[ \left( \frac{3}{4} \right)^h = \frac{1}{2} \][/tex]
To solve for h , we take the natural logarithm (ln) of both sides of the equation:
[tex]\[ \ln \left( \left( \frac{3}{4} \right)^h \right) = \ln \left( \frac{1}{2} \right) \][/tex]
Using the logarithmic property [tex]\(\ln(a^b) = b \ln(a)\)[/tex], we get:
[tex]\[ h \ln \left( \frac{3}{4} \right) = \ln \left( \frac{1}{2} \right) \][/tex]
Now, solve for h :
[tex]\[ h = \frac{\ln \left( \frac{1}{2} \right)}{\ln \left( \frac{3}{4} \right)} \][/tex]
Calculate the natural logarithms:
[tex]\[ \ln \left( \frac{1}{2} \right) = \ln(0.5) \approx -0.6931 \\\[ \ln \left( \frac{3}{4} \right) = \ln(0.75) \approx -0.2877 \][/tex]
Now, divide these values to find h :
[tex]\[ h = \frac{-0.6931}{-0.2877} \approx 2.41 \][/tex]
So, the half-life h is approximately:
[tex]\[ h \approx 2.41 \][/tex]
Therefore, the half-life h rounded to the nearest hundredth is:
h = 2.41
plz help in the attachment below
Answer:
M(t) = 741·(1/2)^(t/5730)
Step-by-step explanation:
One way to write an exponential function is this:
value at time t = (initial value) · (multiplier over period)^(t/period)
Here, the initial value is given as 741 grams, and the time period is 5730 years. The multiplier over that period is 1/2, since half of the quantity remains after that time. The problem statement tells us that "value at time t" is M(t), so we have ...
M(t) = 741·(1/2)^(t/5730) . . . . . t in years; M(t) in grams
If (10,3) and (6,31) are two
anchor points on a trend line,
then find the equation of the
line.
Answer:
y = - 7x + 73
Step-by-step explanation:
y = mx + b m: slope b: y intercept
m = (y-y') / (x-x') = (31-3) / (6-10) = 28 / - 4 = -7
b = y - mx = 3 - (-7) x 10 = 73
equation: y = -7x + 73
check: 31 = -7 x 6 +73 = -42 + 73 = 31 (6,31)
A sequence is defined by the recursive formula f(n+1)=f(n)-2. If f(1)=18, what is f(5)?
Answer:
[tex]f(5)=10[/tex]
Step-by-step explanation:
A sequence is defined by the recursive formula [tex]f(n+1)=f(n)-2[/tex]
If [tex]f(1)=18,[/tex] then
for [tex]n=1: f(2)=f(1+1)=f(1)-2=18-2=16[/tex]
for [tex]n=2: f(3)=f(2+1)=f(2)-2=16-2=14[/tex]
for [tex]n=3: f(4)=f(3+1)=f(3)-2=14-2=12[/tex]
for [tex]n=4: f(5)=f(4+1)=f(4)-2=12-2=10[/tex]
Answer:
10!
Step-by-step explanation:
What is the equation of a line that is parallel to y=5/6x-10 and passes through (12,8)?
Answer:
y-8=5/6(x-12)
Step-by-step explanation:
y-y1=m(x-x1)
y-8=5/6(x-12)
The required equation of the line is [tex]\rm y = \dfrac{5}{6}x-2[/tex].
Given that,
The equation of the line is,
[tex]\rm y = \dfrac{5}{6}(x-10)[/tex]
It passes through the point (12, 8).
We have to determine
The equation of the line is parallel to the given line.
According to the question,
The equation of the line is,
[tex]\rm y = \dfrac{5}{6}(x-10)[/tex]
The slope of the line [tex]\rm m_1[/tex] is 5/6.
If the two lines are parallel to each other then the slope of these lines is the same.
[tex]\rm m_1 = m_2\\\\\dfrac{5}{6} = \dfrac{5}{6}[/tex]
Therefore,
The equation of line passes through the point (12, 8) is,
[tex]\rm( y -y_1) = m (x-x_1)\\\\(y-8) = \dfrac{5}{6} (x-12)\\\\6 (y-8) = 5(x-12)\\\\6y-48=5x-60\\\\6y = 5x-60+48\\\\6y = 5x-12\\\\y = \dfrac{5}{6}x- \dfrac{12}{6}\\\\y = \dfrac{5}{6}x-2[/tex]
Hence, The required equation of the line is [tex]\rm y = \dfrac{5}{6}x-2[/tex].
For more details refer to the link given below.
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The domain of f(x) is the set of all real values except 7, and the domain of g(x) is the set of all real values except –3. Which of the following describes the domain of (g o f) (x)?
all real values except x not-equals negative 3 and the x for which f (x) not-equals 7
all real values except x not-equals negative 3 and the x for which f (x) not-equals negative 3
all real values except x not-equals 7 and the x for which f (x) not-equals 7
all real values except x not-equals 7 and the x for which f (x) not-equals negative 3
Answer:
The last is the correct option
"all real values except x not-equals 7 and the x for which f (x) not-equals negative 3"
Step-by-step explanation:
Domain and Range of Functions
Given the function f(x), the domain of f is the set of all the values that x can take such f(x) exists. The range of f is the set of all the values that f takes.
We have a problem where we have to find the domain of a composite function. Let's recall that being f and g real functions, then
[tex]g\circ f=g(f(x))[/tex]
is the composite function of f and g.
We know the domain of f is the set of all real values except 7, and the domain of g is the set of all real values except –3.
Since f is the innermost function, the domain of the composite function is directly restricted by the domain of f. So, x cannot be 7.
Now, g takes f as its independent variable, and we know the domain of g excludes -3. It can be found that f(x) cannot be -3 because it will cause g not to exist.
Thus, the domain of [tex]g\circ f[/tex] is
All real numbers except x=7 and those where f(x)=-3
The last is the correct option
Jade uses 8 cups of flour to make 24 muffins at that rate how much flour will it take to make 30 muffins
Answer:
10 cups
Step-by-step explanation:
First, we need to find the unit rate. 24/8 equals to 3. 3 is the amount of flour per cupcake. 24 + 3= 27 + 3= 30. You added twice to get to 30. 8+2=10
What is the value of x in the equation 5x 3-4x2
Answer:
x^2(5x-4)
Step-by-step explanation:
5x^3-4x^2=x^2(5x-4)
5x+3+2y+x in expression
Answer:
6x+2y+3
Step-by-step explanation:
5x+3+2y+x
6x+2y+3
I need help am confused
Answer:
125, 119, 113, 107, 101
Step-by-step explanation:
All you have to do is keep subtracting 6 from the numbers.
125 - 6 = 119
119 - 6 = 113
113 - 6 = 107
107 - 6 = 101
Answer:
119,210,337,506,723
Step-by-step explanation:
x³-6 where x=5,6,7,8,9
5³-6=15-6=119
6³-6= 216-6=210
7³-6=343-6= 337
8³-6=512-6=506
9³-6= 729-6=723
In a school election, Juan received 4 times as many votes as Wayne, Neal recurved twenty less votes than Juan, and Kerry got half as many votes as Neal. The total votes cast in the election was 1,202. How many votes did Wayne receive?
Votes received by Wayne is 112
Solution:
To find: votes received by Wayne
Let the vote received by Wayne be "x"
Juan received 4 times as many votes as Wayne
Therefore,
Juan votes = 4 times as many votes as Wayne
Juan votes = 4x ---- eqn 1
Neal received twenty less votes than Juan
Neal votes = twenty less votes than Juan
Neal votes = Juan votes - 20
Neal votes = 4x - 20 ---- eqn 2
Kerry got half as many votes as Neal
Kerry votes = half of neal votes
Kerry votes = [tex]\frac{4x - 20}{2}[/tex] ---- eqn 3
The total votes cast in the election was 1,202
Wayne votes + Juan votes + Neal votes + Kerry votes = 1202
Plug in eqn 1 , eqn 2, eqn 3
[tex]x + 4x + 4x - 20 + \frac{(4x - 20)}{2} = 1202\\\\2x + 8x + 8x - 40 + 4x - 20 = 1202 \times 2\\\\22x - 60 = 2404\\\\22x = 2404 + 60\\\\22x = 2464\\\\x = 112[/tex]
Therefore votes received by Wayne is 112
Please can any one please help me with both of these
Answer:
Question 3: [tex]4x^3+x^2-12x-3[/tex]
Question 4: [tex]\frac{1}{2x}, x\neq 0[/tex]
Step-by-step explanation:
Question 3
g(x) * h(x) means to multiply both the functions given.
Also note the distributive property:
[tex](a+b)(n+p)=an+ap+bn+bp[/tex]
Now, lets multiply:
[tex]g(x)*h(x)=(4x+1)(x^2-3)\\=(4x)(x^2)-3(4x)+1(x^2)-1(3)\\=4x^3-12x+x^2-3\\=4x^3+x^2-12x-3[/tex]
The 2nd answer choice is right
Question 4
[tex](\frac{f}{g})(x)[/tex] means to divide both the functions and simplify, if possible. Lets do this:
[tex](\frac{f}{g})(x)=\frac{6x-3}{12x^2-6x}=\frac{3(2x-1)}{6x(2x-1)}=\frac{3}{6x}=\frac{1}{2x}[/tex]
This is the correct answer.
The restriction on the domain is any x value that we CANNOT PUT IN THE FUNCTION.
We know we cannot divide by 0, so what makes this fraction division by 0??
If we put x = 0, the function is undefined. So x CANNOT be 0.
Third answer choice is right.
During a basketball practice, Mai attempted 49 free throws and was on 25% of them. How many successful free throws did she make?
Mai made 12 successful free throws.
Step-by-step explanation:
Given,
Free throws made by Mai = 49 free throw
Successful throws = 25%
Number of successful throws = 25% of free throws
Number of successful throws = [tex]\frac{25}{100}*49[/tex]
Number of successful throws = [tex]\frac{1225}{100} = 12.25[/tex]
Rounding off to nearest whole number;
Number of successful throws = 12
Mai made 12 successful free throws.
Keywords: percentage, division
Learn more about division at:
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8 15 27 blank 20 find the blank number
the value of blank is 23.
Given series is,
8,15,27,_,20
We have to find the blank number.
Let the no. be x.
Since on observing the above series we find that the ratio of 15 to 8 is equal to the ratio of 27 to 15.
Hence, [tex]\frac{15}{8} =\frac{27}{15}=1.8[/tex]
This follows for the remaining terms also,
So, [tex]\frac{x}{27} =\frac{20}{x}[/tex]
[tex]x^{2} =20\times27\\x=\sqrt{540} \\x=23.23[/tex]
since, 23.23 is not a whole number so we take here 23.
Hence the value of blank is 23.
For more details follow the link:
https://brainly.com/question/24873057
Ron and Hermione are lifting feathers into the air with magic. Hermione can lift a feather 3,525
centimeters (cm) into the air. That is 5 times as high as Ron can lift a feather.
How high can Ron lift a feather with his magic?
Answer:705 cm
Step-by-step explanation:
3525 divided by 5
=705
Ron’s feather flew 705 cm
Ron’s feather flew 705 cm with his magic.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Hermione can lift a feather 3,525 centimeters (cm) into the air. 5 times as high as Ron can lift a feather.
So
We have to 3525 divided by 5;
3525 / 5
=705
Hence, Ron’s feather flew 705 cm with his magic.
Learn more about the unitary method;
https://brainly.com/question/23423168
#SPJ2
Which television would cost you less money? A $429 television set with a 20% discount or a television set with no discount for $359?
Answer:
get the $429 with 20% off cuz its really only $343.2
Step-by-step explanation:
100%-20%=80%
80%=0.8
429x0.8=343.2
I need help trying to find out what is 73% of 83?
Answer:
60.59
Step-by-step explanation:
73%=0.73
0.73*83=60.59
60.59 is the number you're looking for.
Hope this helps, if not, comment below please!!!!
Please help! This is the third time I asked
Find k, the constant of proportionality, for the data in this table. Then write an equation for the relationship.
They equation needs to be in the form y=kx
K=
Equation:
Simply the expression 5a + 7 +3a -2
Answer:
8a+5
Step-by-step explanation:
Like terms and yea
Answer: 8a + 5
Step-by-step explanation:
Combining like terms makes you add 5a + 3a and +7 - 2
On a number line, what number is 2/3 of the way from 7 to 13?
Answer:
That would be about 11.667
The number that is 2/3 of the way from 7 to 13 on a number line is 11. This is found by calculating 2/3 of the distance between the two numbers and adding it to the starting number.
To find the number that is 2/3 of the way from 7 to 13 on a number line, you first calculate the distance between the two numbers, which is 13 - 7 = 6. Then you take 2/3 of that distance, which is 2/3 * 6 = 4. Lastly, you add this result to the starting number, in this case, 7, giving you 7 + 4 = 11. Therefore, the number that is 2/3 of the way from 7 to 13 is 11.
The graph of y= -4x + 7 is:
b and d can be eliminated because there are multiple solutions.
answer: A, because it shows all solutions to the equation
Answer: A line that shows the set of all solutions to the equation
Step-by-step explanation:
Given :
y = -4x + 7
The graph is a linear graph with negative slope.
the variable x could be any number , this means there could be as many solutions as possible.
this means that option B is out already.
Also , the equation is a graph and not a point , so option C and D are also out.
Option A will definitely fit in.
Write an linear equation that passes through (5,2) and (6,4)
Answer:
2x-y=8
Step-by-step explanation:
(6,4)-(5,2)=(1,2)
L: 2x-y=k
(5,2) -> L, k=8
2x-y=8
What are the exact solutions of x2 − x − 4 = 0, where x equals negative b plus or minus the square root of b squared minus 4 times a times c all over 2 times a?
A: x = the quantity of negative 1 plus or minus the square root of 15 all over 2
B: x = the quantity of 1 plus or minus the square root of 15 all over 2
C: x = the quantity of 1 plus or minus the square root of 17 all over 2
D: x = the quantity of negative 1 plus or minus the square root of 17 all over 2
Answer:C: x = the quantity of 1 plus or minus the square root of 17 all over 2
Step-by-step explanation:
Answer:
The answer is option C: x = the quantity of 1 plus or minus the square root of 17 all over 2
Step-by-step explanation:
The general form of the quadratic equation is ax² + bx + c = 0
The general solution of the quadratic equation is:
[tex]x=\frac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]
The given equation is x² − x − 4 = 0
So, a = 1 , b = -1 and b = -4
Substitute with a , b and c at the formula of the general solution.
The solution of the given equation = [tex]\frac{-(-1) \pm \sqrt{(-1)^2 - 4 * 1 * (-4)} }{2*1}= \frac{1\pm \sqrt{1 +16} }{2}=\frac{1\pm \sqrt{17} }{2}[/tex]
Comparing the solution with the given options
So, the answer is option C: x = the quantity of 1 plus or minus the square root of 17 all over 2