5 hours of math tutoring must be mixed with 5 hours of arts tutoring to make $45 per hour.
Mr. Robert charges $50 per hour for math tutoring and charges $40 per hour for language arts tutoring.
Let, he mixed x hours of math tutoring to 5 hours of arts tutoring.
Then, Income from x hours of math tutoring = $50x
Income from 5 hours of arts tutoring = 5×$40 = $200
Total mixed income in (x+5) hours = $(50x+200)
According to the question, in mixed process he make $45 per hour. So, for (x+5)hours he earns $(x+5)45
So, The equation becomes,
50x+200 = (x+5)45
⇒ 50x+200 = 45x+225
⇒ 50x-45x = 225-200
⇒ 5x = 25
⇒ x = 25/5
⇒ x = 5
So, 5 hours of math tutoring must be mixed.
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33. Three consecutive
integers exist such that five
times the first number is
equal to one more than twice
the sum of the second and
third numbers.
Which equation accurately
solves for the integers?
Let n represent the first
number.
The equation which accurately solves for the integers is; 5n = 2(2n +3) +1.
Which equation accurately solves for the integers?It follows from the task content that the first number is represented by n.
On this note, it follows that the second, and third numbers are; (n+1) and (n+2) respectively.
On this note, since five times the first number is equal to one more than twice the sum of the second and third numbers; we have;
5n = 2(n+1+n+2) +1
5n = 2(2n+3)+1.
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Question 1
At room temperature, one liter of water can dissolve over 300 grams of salt.
What is the solvent in this solution?
temperature
water
salt
grams
It's the water
The salt would be the solute that dissolves in the solvent.
Temp - is a factor
(affecting rate at which salt dissolves)
grams - unit of measure
Hope this helps!
Giving Brainliest to the first person who can accurately answer and explain these questions.
Answer:
It's A 48,736
Step-by-step explanation:
Answer:
48,856.11
Step-by-step explanation:
Compound interest is generally written as: [tex]A=P(1+\frac{r}{n})^{nt}[/tex] where P = principle amount, r = interest rate, n=compound periods, t = time. This is compounded continuously which can be defined as: [tex]A=Pe^{rt}[/tex]. If you're confused what e is, one of the definitions, is [tex]\lim_{x\to\infty}{(1+\frac{1}{x})^x[/tex]. This is essentially the very definition of continuous compound. It's when the amount of compounds (n in the equation) goes towards infinity. So using the previous defined equation simply plug the values into the equation.
[tex]A=(40000)e^{0.025*8}[/tex]
Multiply inside the exponent
[tex]A=(40000)*e^{0.2}[/tex]
raise e to the power of 0.2
[tex]A\approx40000*1.221[/tex]
Multiply
[tex]A=48,856.11[/tex]
Which choice represents the simplified exponential expression? (9^7)^4
Answer:
[tex]9^{28}[/tex]
Step-by-step explanation:
using the rule of exponents
[tex](a^{m}) ^{n}[/tex] = [tex]a^{mn}[/tex] , then
[tex](9^7)^{4}[/tex] = [tex]9^{7(4)}[/tex] = [tex]9^{28}[/tex]
The graph for the first equation of a ssystem is shown in orange the second equation is 3y+30= 6x
The solution to the system of equations is: (1, -8).
How to Find the Solution to a System of Equations?The solution is the coordinate of the point where both lines of the equations meet.
Second equation: 3y + 30 = 6x, rewrote in slope-intercept form:
3y = 6x - 30
y = 6x/3 - 30/3
y = 2x - 10 --> eqn. 1
Find the slope (m) and y-intercept (b) of the first graphed equation:
Slope (m) = change in y/change in x = rise/run = -4/2 = -2
The line intersects the y-axis at y = -6, so, the y-intercept, b = -6.
The first equation would be: y = -2x - 6 ---> eqn. 2
Subtract eqn. 2 from eqn. 1 to eliminate x
y = 2x - 10 --> eqn. 1
y = -2x - 6 ---> eqn. 2
2y = 0 - 16
2y = -16
y = -16/2
y = -8
Substitute y = -8 into eqn. 1 to find x:
-8 = 2x - 10
-8 + 10 = 2x
2 = 2x
2/2 = x
1 = x
x = 1
The solution is therefore: (1, -8).
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What number am I? If you divide me by 8, the quotient is 3.
Answer:
24
Step-by-step explanation:
[tex]8 * \frac{x}{8}=3 * 8[/tex]
x = 24
Answer:
24
Step-by-step explanation:
Let the number we are looking for = [tex]x[/tex].
∴ According to the question:
[tex]x[/tex] ÷ 8 = 3
• Multiply both sides by 8:
[tex]x[/tex] = 8 x 3
[tex]x[/tex] = 24
Question 4 of 5
Select the correct answer.
On a number line, point A is at -3.4 and point C is at 0.6. Point C divides AB in a ratio such that AC to CB is 4:7. What is the length of
AB?
O
AB = 4.2 units
AB = 11 units
AB= 2.8 units
AB= 7.6 units
Answer:
AB = 11 units
Step-by-step explanation:
a given ratio also tells us how many equally sized units there are in the whole (in this case the line).
the ratio 4:7 tells us therefore, that from the whole line 7 ratii units (of 7+4 = 11 ratio units) are on the side of CB.
4 ratio units (of the 11 ratio units) are on the side of AC.
AC is the distance between A and C.
that is
0.6 - -3.4 = 0.6 + 3.4 = 4 line units
aha ! the distance is 4 units on the number line, and the ratio tells us that AC is 4 ratio units.
so, line unit and ratio units are 1:1 the same.
that means that CB with 7 ratio units is then also 7 line units long.
so, the whole line AB is then 4 + 7 = 11 line units long.
Answer:
11 units
Step-by-step explanation:
correct on plato
For the given functions f and g find f•g and state it’s domain
f(x) = 3x - 6; g(x) = 8x +4
f.g and its domain is 24x²-36x-24; all real numbers.
Given, f(x) = 3x - 6; g(x) = 8x +4.
We need to find the value of f.g
What is a domain?The domain of a function; In mathematics, the domain of a function is the set of inputs accepted by the function.
Now, (f.g)(x)=(3x-6)(8x+4)
=24x²-48x+12x-24
=24x²-36x-24
Therefore, f.g and its domain is 24x²-36x-24; all real numbers.
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HELP
17x - 32y + 2.78y - 11,345x + 1/5x
Answer:
i think this is the answers
Step-by-step explanation:
-13.78xy
what is the perimeter of a rectangle with the of 10cm and width 20cm
Let sets A and B be defined as follows.
A= {c,d,e,f}
B is the set of odd numbers greater than 5 and less than 23 (a) Find the cardinalities of A and B. n(A) = n(B)=
There are 4 elements in the set A and 8 elements in set B that is n(A) = 4 and n(B) = 8
Cardinality of a setThis is the total number of elements in a set. Given the following sets;
A = {c, d, e, f}
B = {odd numbers greater than 5 and less than 23}
B = {7,9,11,13, 15, 17, 19, 21}
Since there are 4 elements in the set A and 8 elements in set B hence n(A) = 4 and n(B) = 8
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A principal of $5500 is invested in an account paying an annual rate of 7%. Find the amount in the account after 4 years if the account is compounded semiannually, quarterly, and monthly.
Answer:
Formulae is Future value, see in picture I've done example 1 for u.
► Math and Gymnastics
In a gymnastics competition, gymnasts compete
in events such as the balance beam, parallel bars,
vault, and floor exercise,
Leigh earned the following scores from the judges
for her balance beam routine.
9.30 9.20
Follow these steps to find Leigh's final score.
1. Order the scores from least to greatest.
9.20
9.30
9.20
9.00
Answer:
9.00,9.20,9.30
Step-by-step explanation:
how to convert each rate to a unit rate
Answer:
If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.
Step-by-step explanation:
Find an equation of each line given one point and the slope : (4, 8); slope 8
Step-by-step explanation:
in such a case the easiest approach might be using the point-slope form of a line equation :
y - y1 = m(x - x1)
with m being the slope, and (x1, y1) being a point on the line.
so, in our case that would be
y - 8 = 8(x - 4)
simplified this would be
y - 8 = 8x - 32
y = 8x - 24
FYI - this would be then the slope-intercept form (-24 would be the intercept point on the y-axis).
A formula for the normal systolic blood pressure for a man age A , measured in mmHg, is given as P=0.006A2−0.02A+120 . Find the age of a man whose normal blood pressure measures 128 mmHg.
The age of the man whose normal pressure measures 128 mmHg is approximately 38 years.
How do we determine the age of the man using a quadratic equation?The quadratic formula can be used to determine the age of a man whose normal blood pressure measures 128 mmHg. This can be expressed mathematically as:
[tex]\mathbf{ \dfrac{-b \pm\sqrt{b^2 - 4ac}}{2a}}[/tex]
From the given equation:
P = 0.006A² - 0.02A + 120
where;
P = 128128 = 0.006A² - 0.02A + 120
= 0.006A² - 0.02A + 120 - 128
= 0.006A² - 0.02A - 8
where:
a = 0.006 , b = - 0.02, and c = -8[tex]\mathbf{ \dfrac{-(-0.02) \pm\sqrt{(-0.02)^2 - 4(0.006)(-8)}}{2(0.006)}}[/tex]
[tex]\mathbf{ = \dfrac{(0.02) \pm 0.43863}{0.012}}[/tex]
= 38.2195 or -34.8862
Taking the positive integer value, the age of the man whose normal pressure measures 128 mmHg is approximately 38 years.
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Given the function r(x)=x−4x 9, find the values of x that make the function less than or equal to zero. write the solution in interval notation.
Inequalities help us to compare two unequal expressions. The solution that will make the value of the function r(x) less than equal to 0 is [3,∞).
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
To find the value of x that will make the function r(x)=x-4x+9 less than or equal to 0 solve the inequality,
x - 4x + 9 ≤ 0
x - 4x ≤ -9
-3x ≤ -9
x ≥ (-9)(-3)
x ≥ 3
Hence, the solution that will make the value of the function r(x) less than equal to 0 is [3,∞).
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Suppose that F(x) = x² and G(x) = 2/5 x². Which statement best compares the
graph of G(x) with the graph of F(x)?
A. The graph of G(x) is the graph of F(x) stretched vertically and
flipped over the x-axis.
B. The graph of G(x) is the graph of F(x) stretched vertically.
C. The graph of G(x) is the graph of F(x) compressed vertically and
flipped over the x-axis.
OD. The graph of G(x) is the graph of F(x) compressed vertically.
Answer: The graph of G(x) is the graph of F(x) compressed vertically.
Step-by-step explanation:
See attached image.
Each side of a hexagon is 10 inches longer than the previous side. What is the length
of the shortest side of this hexagon if its perimeter is 401 inches?
Answer:
The length of the shortest side of the pentagon would be:
40.2
Question 12 of 21
What is the domain of the exponential function shown below?
f(x) = 5.3x
Answer: All real numbers
Step-by-step explanation:
I assume you meant [tex]y=5.3^x[/tex].
In this case, the domain is the set of real numbers, as is with most standard exponential functions.
Can someone please assist me with this problem
The category in the pie chart that was chosen by 1/8 of those that were surveyed is documentary.
How to illustrate the pie chart?From the pie chart, it can be seen that comedy and drama have the highest fraction as they have 1/4 each.
Therefore, the percentage of those who choose comedy or drama will be:
= (1/4 + 1/4) × 100
= 2/4 × 100
= 50%
Lastly, if 24% chose news, the others that choose others will be:
= 1/3 × 24
= 8%
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Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x.
The given graph is a function.
The correct option is (B).
What is vertical line test?The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.
As we draw the vertical line then for one input x there is one output.
Hence, the given graph is function.
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Find the h.c.f of
[tex] {x}^{3} + {y}^{3} \: and \: \: {x}^{2} - xy + {y}^{2} [/tex]
The greatest common factor will be (x² – xy + y²).
Greatest common factorThis is a value or expression that can divide the given expressions without leaving a remainder.
Given the following expressions
x^3+^3 and x^2 - xy + y^2
Expand x^3+y^3
x^3+y^3 =(x + y)(x² – xy + y²).
Since (x² – xy + y²) is common to both expression, hence the greatest common factor will be (x² – xy + y²).
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The scale of a map says that 4 çm represents 5 km.
What distance on the map (in centimeters) represents an actual distance of 4
kilometers?
Answer:
3.2 km
Step-by-step explanation:
4cm÷5km=0.8 per cm to km
4km×0.8 km=3.2 km represents
Answer:
3.2 km
Step-by-step explanation:
[tex]\frac{4}{5} =\frac{x}{4}[/tex]
[tex]x=\frac{(4)(4)}{5} =\frac{16}{5} =3.2[/tex]
Hope this helps
The area of a rectangle is 119 square units. Find the length and width of the rectangular
Answer: 7 and 17
Step-by-step explanation:
Since the area of a rectangle is the product of the two sides, the product of these two numbers must be 119.
The factors pairs of 119 are 1 and 119, and 7 and 17.
x+7 and x-3 have a difference of 10. The difference of 7 and 17 is also 10. Hope this helped!
In the future, please take a less blurry photo because I had to guess the part where I think it said x-3.
Last week Sharon's mother order 60 roses for her shop this week she will order five times as many roses how many roses will she order write an expression and then find the solution
Answer:
60(5) = 300 :D
Step-by-step explanation:
First lets make the equation :)
Orders 60 roses
This week will order 5x as many as last week
60 x 5 OR 60(5)
60(5) = 300 :)
Have an amazing day!!
Please rate and mark brainliest!!
Use the demoivres theorem
The value of the given complex number is -1
De'moivres theorem
Given the polar form of a complex number expressed as:
[tex](cos\theta + isin\theta)^n\\[/tex]
This can also be expressed according to the de moivre's theorem as;
[tex]=(cos\theta + isin\theta)^n\\\\=(cosn\theta+isinn\theta)[/tex]
Given the expression below;
[tex](cos\frac{\pi}{6} + isin\frac{\pi}{6} )^{18}\\(cos18\cdot\frac{\pi}{6} + isin18\cdot\frac{\pi}{6} )\\(cos3\pi + isin3\pi)\\=-1[/tex]
Hence the value of the given complex number is -1
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g(x)= l2xl +2
find domain and range
The domain of the function g(x)=l2xl +2 is all real numbers and the range is from (0,∞).
Given g(x)= l2xl +2
First of all we know that modulas gives two values for x<0 and x>=0.
The function g(x) if opened gives two values.
for x>=0 g(x)=2x+2
for x<0 g(x)=-2x+2
because we have not told about the description about x so we can put any value in the function.
So the domain is all real numbers.
Now when we take g(x)=2x+2 for x>=0
putting x=0 we get 2 and rest are positive values so the value of g(x) keeps increasing as we increase the value of x. So here range is [2,∞).
Now take g(x)=-2x+2 for x<0
putting smallest number starting from zero but not 0 we will get a number near to 0 but not zero and because when a negative number multiplies with -2 it becomes positive and increase the value of g(x) so here the range becomes (0,∞).
When we talk about overall range it will be [2,∞) ∪(0,∞)
it will be (0,∞).
Hence the domain of the function g(x) is all real numbers and range is from 0 to infinity.
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Find the x-intercept of the graph of the linear equation y = −1
2
x + 3.
x-intercept
Answer:
Step-by-step explanation:
x intercept equals pi
Answer:
x intercept= 6
Step-by-step explanation:
Write the arithmetic series 3+9+15+21+27 using summation notation
Answer:
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