Answer: B: 11 and 12
Step-by-step explanation:
- An integer is simply a whole number
- So consecutive integers are simply whole numbers that follow each other (ex: 1, 2, 3)
- The square root of 125 (in decimals) is 11.1803398875, meaning it is higher than 11 but less than 12
- So 11.1803398875 falls between 11 and 12, making the answer B
hope this helps :)
Solve each triangle – find any missing side and angle measures. Round answers to the nearest tenth.
Answer:
A = 55 degrees
B = 35 degrees
C = 90 degrees
side BA = 4.8 units
side AC = 2.7 units
side BC = 3.9 units
Step-by-step explanation:
Hello!
The things we know:
A = 55 degrees
C = 90 degrees
side BA = 4.8 units
AC = adjacent side
BC = opposite side
AB = hypothenuse
B = 180 - 55 - 90 degrees
B = 35 degrees
Let's find side AC
we can use the cos of theta.
cos(55) = AC/4.8
multiply 4.8 on both sides.
4.8cos(55) = AC
AC = 2.7 units
And now we just have to find BC
to calculate BC we can either use tangent or sin.
I will just use sin
sin(55) = BC/4.8
multiply 4.8 on both sides.
4.8sin(55) = BC
BC = 3.9
And now we know everything about the triangle
Hope I Helped!
Suppose A and B are 2x2 matrices and that AB = BA =
which of the following statements is correct?
The correct statement about the matrix is B. B^-1.
How to illustrate the matrix?From the information, it can be seen that the matrix is 2 by 2. Based on the information about the matrix, 1/3AB = 1/3BA.
From this, it can be depicted that the inverse of B illustrates that:
A(1/3B) = (1/3B)
This illustrates that the correct is B.
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Maria bought a stock for x dollars, and she sold it at a profit of 20 %. Write a
mathematical expression for the selling price.
Answer: 1.2x
Step-by-step explanation:
Profit = Selling price - Cost
She bought the stock at a cost of x dollars
Her profit was 20% of that, which is 0.2x dollars
Selling price = Profit + Cost = x + 0.2x = 1.2x
three pieces of piping are needed on construction site. The second piece needs to be 2m longer than the first, and the third piece needs to be 7m longer than the first, the combined length of the piping is 72m. Determine the lengths of the three pieces of pipe
Step-by-step explanation:
x + 2x + 7x
72 = 9x
72 - 9 = x
63 = x
63 ÷ 3 = 21
piece 1 = 21
piece 2 =21+2 = 23
piece 3 =21+7 = 28
21+23+28 = 72 This proves the above is correct.
Tim Hortons is hiring and offers $200 every week plus $5 per hour. McDonalds offers $300 every week plus $2 per hour. State the conditions under which Tim Hortons is the better employer.
Answer: After working for 33 [tex]\frac{1}{3}[/tex] hours a week
Step-by-step explanation:
Let us write equations to represent these two places. Let x be hours worked and y be money earned.
Tim Hortons:
$200 + $5x = y
McDonalds:
$300 + $2x = y
Now, to find the conditions of which Tim Hortons is the better employer (on the basis of money earned) we must find the interval that Tim Hortons pays more. This can be found by setting up another equation, or by graphing. I have shown both. See attached for the graph.
$200 + $5x > $300 + $2x
$5x > $100 + $2x
$3x > $100
x > [tex]\frac{100}{3}[/tex]
x > 33.3334
Tim Hortons is the better employer after an employee has worked for 33 [tex]\frac{1}{3}[/tex] hours a week.
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please help meeee ………..
Answer:
x = 5
Step-by-step explanation:
The equality of bases property says powers of the same base will be equal if and only if the powers are equal. This property is used to solve exponential equations.
Application[tex]\dfrac{(2)^x}{2}=16\qquad\text{copy of the original equation}\\\\2\times\dfrac{(2)^x}{2}=2\times16\qquad\text{multiply by 2 to isolate the base}\\\\2^x=32\qquad\text{simplify}\\\\2^x=2^5\qquad\text{rewrite the constant as a power of 2}\\\\\boxed{x=5}\qquad\text{use the Equality of Bases Property}[/tex]
__
Additional comment
Equating the exponents is fully equivalent to taking the logarithm of both sides of the equation, to that base.
[tex]\log_2(2^x)=\log_2(2^5)\ \Longrightarrow\ x=5[/tex]
You withdraw $140 from your savings account. then you withdraw $49 more. using an integer, which number represents your balance?
The integer represent the balance in your account is Z = + Y. The representation of integer is positive because withdrawal is always less then or equal to the amount present in the bank account.
Total rupees withdraw from saving account is $149
Let total amount in account before withdrawing is X= $500
Amount left after withdraw the money is calculated by a
AMOUNT LEFT = TOTAL AMOUNT - WITHDRAW AMOUNT
So, put the values then
Y= X($500) - $149
Y= $500 - $149
Y= $351
If we represent the balance of saving account in the integer form then it become the Z = + Y. The representation of integer is positive because withdrawal is always less then or equal to the amount present in the bank account.
So, The integer represent the balance in your account is Z = + Y. The representation of integer is positive because withdrawal is always less then or equal to the amount present in the bank account.
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A tape diagram. 0 dollars is 0 percent. Question mark dollars is 23 percent. 52 dollars is 100 percent.
Jared has earned 23% of the $52 he needs to buy a new jacket. Find 23% of $52.
Answer:Jared has earned 23% of the $52 he needs to buy a new jacket. Find 23% of $52.Which expression can you use to find 23% of 52? ✔ 0.23 × 5223% of $52 is $✔ 11.96.An easy way to check your answer is to use the friendly ✔ 25%and divide 52 by ✔ 4to get ✔ 13
Step-by-step explanation:
The radius of a sphere is 3 inches. Which represents the volume of the sphere?
• 12t cubic inches
• 367 cubic inches
• 647T cubic inches
• 817 cubic inches
Answer:
Step-by-step explanation:
The formula for the volume of a sphere of radius r is V = (4/3)(pi)r^3.
Here, with r = 3 in, the volume is
V = (4/3)(3.14)(3 in)^2, or V = 36(pi)(27 in)^3 = 36pi in^3
x^2/0.35-x=1.3*10^-5
Solve for x
The solution to the value of x in the given equation is x = 0.00212658 or x = -0.00213958
Solving algebraic equations:The process of solving the unknown value of an algebraic equation involves equating the values of the unknown to the constant value.
Given that:
[tex]\mathbf{\dfrac{x^2}{0.35-x}= 1.3 \times 10^{-5} }[/tex]
[tex]\mathbf{x^2 = 1.3 \times 10^{-5} (0.35-x) }[/tex]
x² = 4.725 × 10⁻⁶ - 1.3 × 10⁻⁵x
= [tex]x^2 + 1.3\times10^{-5}x - 4.725 \times 10^{-6}[/tex]
= x²+0.000013x-0.000004725
Solving for (x) by using the quadratic equation:x = 0.00212658 OR x = -0.00213958
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Which graph represents the function f (x) = StartFraction 3 x minus 2 Over x minus 2 EndFraction?
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 0.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the left in quadrant 2, and the other curve opens down and to the left in quadrant 4. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 1.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the left in quadrant 2, and the other curve opens down and to the left in quadrant 4. A vertical asymptote is at x = negative 2, and the horizontal asymptote is at y = 4.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 3.
The graph which represents the rational function is; On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 3.
Which graph represents the rational function?It follows from the task content that the rational function given is; f(x) = 3x-2/x-2.
Hence, since the numerator and denominator polynomials are of the same order, it follows that the horizontal asymptote is the quotient; 3/1 = 3.
Additionally, the vertical asymptote of the function is the value of x which renders the denominator equal to 0 and consequently, the function undefined.
Hence, x -2 = 0 and x= 2.
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Answer: THE PERSON ABOVE IS CORRECT!!
The answer is D.) On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 3.
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Mason is a songwriter who collects royalties on his songs whenever they are played in
a commercial or a movie. Mason will earn $30 every time one of his songs is played in
a commercial and he will earn $80 every time one of his songs is played in a movie.
Mason earned a total of $470 in royalties on 9 commercials and movies. Write a
system of equations that could be used to determine the number of commercials and
the number of movies on which Mason's songs were played. Define the variables that
you use to write the system.
Answer:479
Step-by-step explanation:470+9=479
We can write the system of equation that determines the number of commercials and the number of movies on which Mason's songs were played as → 30x + 80y = 470 and x + y = 9. The variables used in the system of equations are -
x - Number of times his song played in a commercial
y - Number of times his song played in a movie.
What is equation modelling?
Equation modelling is a method of writing a mathematical relation from a mathematical statement for mathematical analyses of the problem given.
Given is Mason who collects royalties on his songs whenever they are played in commercials or movies.
Assume that his song played in 'x' commercials and 'y' movies.
Cost per song when played in commercial = $30
Then for 'x' commercials, total cost will be = $30x
Cost per song when played in movie = $80
Then for 'y' movies, total cost will be = $80y
Total money earned through both = $470
We can write the system of equation that determines the number of commercials and the number of movies on which Mason's songs were played as -
30x + 80y = 470
The total number of commercials and movies combined -
x + y = 9
The variables used in the system of equations are -
x - Number of times his song played in a commercial
y - Number of times his song played in a movie.
Therefore, We can write the system of equation that determines the number of commercials and the number of movies on which Mason's songs were played as → 30x + 80y = 470 and x + y = 9. The variables used in the system of equations are -
x - Number of times his song played in a commercial
y - Number of times his song played in a movie.
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Can someone help me?
Alex and Bobby are in the woods and are standing 240
yards apart.. Both boys spot a plane with angles of
elevation of 40 degrees and 45 degrees respectively. How
far from the plane is Bobby? Round to the nearest tenth of
a yard. Enter a number answer only.
The distance from Bobby to the plane is 154.7 yards.
How to find the distance of the plane to Bobby using angle of elevation?Sine law can be used to find the distance of the plane to Bobby.
Therefore,
x / sin 40 = 240 / sin 95
cross multiply
Hence,
x sin 95 = 240 sin 40
divide both sides by sin 95
x = 240 sin 40 / sin 95
x = 240 × 0.64278760968 / 0.99619469809
x = 154.08 / 0.9961
x = 154.683264732
x = 154.7 yards
Therefore, the distance from Bobby to the plane is 154.7 yards.
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help me please!!! 30 points
Answer:
17 square centimeters.
Step-by-step explanation:
Divide the rectangle into a 3x5 rectangle and a 2x1 rectangle.
(3x5)+(2x1)=17
17 square centimeters.
Fiona divided 3x2 5x-3 by 3x 2. the expression represents the remainder over the divisor. what is the value of a? -5 -1 1 5
The value of a is -5 if the provided polynomial is divided by (3x + 2) option first -5 is correct.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a polynomial:
3x² + 5x - 3
Which is divided by (3x + 2)
= (3x² + 5x - 3) ÷ (3x + 2)
[tex]\rm = \dfrac{\left(3x^2+5x-3\right)}{\left(3x+2\right)}[/tex]
[tex]\rm =x+\dfrac{3x-3}{3x+2}[/tex]
[tex]\rm =x+1+\dfrac{-5}{3x+2}[/tex]
[tex]\rm =x+1-\dfrac{5}{3x+2}[/tex]
By comparing with the given remainder.
a = -5
Thus, the value of a is -5 if the provided polynomial is divided by (3x + 2) option first -5 is correct.
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For what values of k will the function f(x) = 9x² + 4x + k have 1 real roots.
Hello,
Answer:
for k = 4/9
Step-by-step explanation:
a = 9 ; b = 4 ; c = k
we search Δ = 0 (because 1 real root)
Δ = b² - 4ac = 4² - 4 × 9 × k = 16 - 36k
Δ = 0 ⇔ 16 - 36k = 0 ⇔ 36k = 16 ⇔ k = 16/36 = (4 × 4)/(4 × 9) = 4/9
⇒ k = 4/9
Answer:
[tex]\{\frac{4}{9} \}[/tex]
Step-by-step explanation:
First off, we are given a parabola by definition:
[tex]f(x) = 9x^2 + 4x + k \\ a = 9, b = 4, c = k;[/tex]
Since [tex]a > 0[/tex], our parabola has an upward opening.
Should we think about it graphically, it will be no wonder that we should pay our attention to the points of the parabola intersecting the abscissa axis. In other words, we need our vertex to intersect the x axis only once per se.
The vertex:
[tex]V_{x} = \frac{-b}{2a} = \frac{-4}{2 * 9} = - \frac{2}{9} \\ V_{y} = 9V_{x}^2 + 4V_{x} + k = 9(- \frac{2}{9})^2 + 4(- \frac{2}{9}) + k = 9 * \frac{4}{9^2} - \frac{8}{9} + k = \frac{4}{9} - \frac{8}{9} + k = - \frac{4}{9} + k[/tex]
As a result, our [tex]V_{y}[/tex] is parametric. [tex]k = \frac{4}{9}[/tex] suits us because [tex]V_{y} = - \frac{4}{9} + \frac{4}{9} = 0[/tex]. If [tex]k > \frac{4}{9}[/tex], we do not have any roots at all. We have two roots if [tex]k < \frac{4}{9}[/tex].
the ratio equivalent to tan P and tan Q
Answer:
Tan p is 20/21
Tan q is 21/20
Step-by-step explanation:
Tan is short for tangeant.
tangeant means opposite/adjacent
the opposite of vertices p is 20.
the adjacent of vertices p is 21.
so tan p= 20/21
The opposite of vertices q is 21
the adjacent of vertices q is 20
so tan q is 21/20
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!! GEOMTREY
Answer:
[tex]m\angle{ABC}=144^{\circ}[/tex]
Step-by-step explanation:
By using Angle Addition Postulate, it holds:
[tex]m\angle{ABD}+m\angle{DBC}=m\angle{ABC}[/tex]
Substitute [tex]m\angle{ABD}=76^{\circ}[/tex] and [tex]m\angle{DBC}=68^{\circ}[/tex] into the equation:
[tex]76^{\circ}+68^{\circ}=m\angle{ABC}[/tex]
Add the measures:
[tex]m\angle{ABC}=144^{\circ}[/tex]
help meeeeeeeeeeeeeeeeee
Let x = number of hours washing cars
Let y = number of hours landscaping
System of equations:
[tex]10x+8y=84\\\\x=2y[/tex]
help asap grade 5 math help fast help quick !!!
Answer:
B and D
Step-by-step explanation:
A
[tex]\frac{5}{6}[/tex] × 13 = [tex]\frac{5(13)}{6}[/tex] = [tex]\frac{65}{6}[/tex] = 10 [tex]\frac{5}{6}[/tex] < 13
B
4 × 13 = 52 > 13
C
[tex]\frac{3}{4}[/tex] × 13 = [tex]\frac{3(13)}{4}[/tex] = [tex]\frac{39}{4}[/tex] = 4 [tex]\frac{3}{4}[/tex] < 13
D
[tex]\frac{10}{10}[/tex] × 13 = 1 × 13 = 13
Band D are equal to or greater than 13
Which graph shows the solution to y2-2x+10?
write each polynomial in standard form. Then give the leading coefficient. You may need to combine like terms before writing the polynomial in standard form.
18y^5-3y^8+10y
Answer: y(-3y^7+18y^4+10)
Step-by-step explanation:
help me out plsss I need to turn this in now
Answer:
Complementary angles are:
∠ORS and ∠SRQ
Supplementary angles are:
∠ORP and ∠PRQ
Which of the lines is the graph of x=1−y?
Answer:
y = -x + 1
(Image of what graph looks like is attached)
Step-by-step explanation:
x = 1 - y can be rewritten into y = mx + b format.
x = 1 - y (subtract 1 from both sides)
x - 1 = -y (multiply by -1 to both sides)
y = -x + 1
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20 POINTS
A circle has a diameter of 24cm. What is its circumference?
Use 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer
Answer:
c = 75.36 cm
Step-by-step explanation:
The equation of the circumference is:
[tex]c=\pi d[/tex] In which "d" represents the measurement of the diameter
in this case d= 24cm, π = 3.14
Calculate the circumference:
[tex]c=\pi d=(3.14)(24)=75.36cm[/tex]
Hope this helps
A circle has a diameter of 24cm. The circumference of the circle is c = 75.36 cm.
What is the circumference of the circle?The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.
The circumference of the circle = 2πr
Given information;
A circle has a diameter of 24cm.
"d" represents the measurement of the diameter, so
d= 24cm, π = 3.14
Radius = d/ 2 = 12
Calculate the circumference:
The circumference of the circle = 2πr
= 2 ( 3.14 ) ( 12)
= 75.36
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What is the difference of the rational expressions below?
4x 2x
9
9
O A.
6x
O B.
2x
O C.
O D. Ex
Answer:
B
Step-by-step explanation:
[tex]\frac{4x}{9}[/tex] - [tex]\frac{2x}{9}[/tex]
since the denominators are common , then subtract the numerators, leaving the common denominator.
= [tex]\frac{4x-2x}{9}[/tex]
= [tex]\frac{2x}{9}[/tex]
PLEASE HELP
This table contains an Arithmetic Sequence. Find the missing terms in the table.
if m²+1/m = 4, find m²+ 1/m²
A) The solution to m² + (1/m²) is gotten as; 14
B) The solution to m³ + ¹/₃ is gotten as; 52.312
How to simplify Algebra?We are given the algebraic equation;
(m² + 1)/m = 4
Multiply through by m to get;
m² + 1 = 4m
m² - 4m + 1 = 0
From online quadratic equation calculator, we have;
m = 3.732 or 0.268
A) Thus;
m² + (1/m²) = 3.732² + (1/3.732²)
⇒ 14
B) m³ + ¹/₃ gives;
3.732³ + (1/3) = 52.312
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Select the correct answer. What is one root of this equation? 2x^2-4x+9
Answer:
1±i sqrt(7/2)
Step-by-step explanation:
For this equation you would need to use quadratic formula: x=(-b+-square root b^2-4ac)/2a
Answer:the answer is option E (see pic)
Step-by-step explanation:
One root would be: x =(4-√88)/-4=1+1/2√ 22 = 1.345