Answer:
a=25
b=40
Step-by-step explanation:
We can get two equations from these statements
1.a+b=65
2.a<b
therefore 2a=10+b
and 2a-10=b
substitute into original equation
a+(2a-10)=65
3a=75
a=25
b=65-25
=40
Assume our initial amount is $1000, the rate is 5% and it will only compound once per year. Our equation would look something like this:
The amount of money available after x number of years is given by y = 1000(1.05)ˣ
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the amount of money after x years. Assume our initial amount is $1000, the rate is 5% (0.05) and it will only compound once per year. The equation is given by:
y = 1000(1 + 0.05)ˣ
y = 1000(1.05)ˣ
The amount of money available after x number of years is given by y = 1000(1.05)ˣ
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if jimmy has 99 cups of cofe and drinks 50 how many does jimmy have
Answer:
jimmy
Step-by-step explanation:
Round the decimal to the nearest whole number, 14.2.
Answer:14.
Step-by-step explanation:
14.2 is closer to 14 than 15
Answer:
14
Step-by-step explanation:
The nearest whole number in 14.2 is 4.
Since 2 is less than 5, the 4 stays the same.
We get left with 14.
A cell phone tower covers a circular area with a radius of 15 miles.
(b) Will a person 11 miles west and 12 miles south of the tower have coverage? Explain.
A person 11 miles west and 12 miles south of the tower will not have coverage.
A circle is a closed curve that is drawn from a fixed point. This point is called the center. All points on the curve are equidistant from this center point.
The cell phone tower covers a circular area with radius 15 miles. This means that there will be coverage in all directions from center up to 15 miles.
The person is 11 miles west and 12 miles south of the tower.
Distance of person from center will be calculated using distance formula
[tex]d = \sqrt{(11^{2} + 12^{2} }[/tex]
∴ [tex]d = \sqrt{121 + 144}[/tex]
∴ [tex]d = 16.27[/tex] miles.
Since this distance is greater than the radius of circle (15 miles), the person will not have cell phone coverage.
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John walks away from his house down a straight street. The graph shows John's distance from his house over time. Describe his trip. Find John's speed on each section of the walk.
(lol please help, I don't know how to format this-)
Based on the graph (see attachment), John's speed on each section of the walk are as follows:
At the first interval, John's speed is equal to 4 km/h.At the second interval, John's speed is equal to 0 km/h.At the third interval, John's speed is equal to 1.5 km/h.What is speed?Speed can be defined as the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured as meter per seconds.
What is distance?Distance can be defined as the amount of ground covered (travelled) by a physical object over a specific period of time and speed, regardless of its direction, starting point or ending point.
How to calculate the speed?Mathematically, speed can be calculated by using this formula;
Speed = distance/time
Based on the graph (see attachment), John's speed on each section of the walk can be calculated as follows.
For the first interval, we have:
Speed = 6/1.5
Speed = 4 km/h.
For the first interval, we have:
Speed = 6/1.5
Speed = 4 km/h.
For the second interval, we have:
Speed = 6/0
Speed = 0 km/h.
For the third interval, we have:
Speed = 6/4
Speed = 1.5 km/h.
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Find the magnitude and direction of vector. →JK : J(-6,-4) and K(-10,-4)
The magnitude of vector →JK is 4
And the direction of vector →JK is given by an angle 360°
For given question,
Let J(-6, -4) = (x1, y1) and
K(-10,-4) = (x2, y2)
By distance formula, the magnitude of vector is,
[tex]|\vec{JK}|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\|\vec{JK}|=\sqrt{(-10+6)^2+(-4+4)^2}\\\\ |\vec{JK}|=\sqrt{(-4)^2}\\\\ |\vec{JK}|=4[/tex]
To find the direction of the vector JK:
[tex]tan\theta=\frac{y_2-y_1}{x_2-x_1} \\\\tan\theta=\frac{-4+4}{-10+6}\\\\ tan\theta=0\\\\\theta=0^{\circ}[/tex]
However, the angle is in the fourth quadrant, so we add 360° to obtain a positive angle.
Thus, 0° + 360° = 360°
Therefore, the magnitude of vector →JK is 4
And the direction of vector →JK is given by an angle 360°
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A group of friends wants to go to the amusement park. They have $89.50 to spend on parking and admission. Parking is $7.75, and tickets cost $27.25 per person, including tax. Write and solve an equation which can be used to determine pp, the number of people who can go to the amusement park.
The number of people who can go to the amusement park is 3 people
EquationTotal amount with the group of friends = $89.50Cost of parking = $7.75Cost of tickets per person =$27.25Number of people who can go to the amusement park = p89.50 = 7.75 + 27.25p
subtract 7.75 from both sides89.50 - 7.75 = 27.25p
81.75 = 27.25p
divide both sides by 27.25p = 81.75 / 27.25
p = 3
Therefore, the number of people who can go to the amusement park is 3 people.
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You can find the equation of a line through two points even if one point is not the y -intercept. Find the slope m of the line passing through the two points.Using either point, substitute for x, y , and m into y=m x+b . Solve for b and rewrite y=m x+b for the values of m and b . Write an equation in slope-intercept form for the line passing through each pair of points.
c. (-2,17) and (2,1)
1 = -4(2) + 9 is an equation in slope-intercept form for the line passing through points (-2,17) and (2,1)
What is a slope of line?A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.
The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.
Therefore,
m = y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.
Be aware that tan ∅ = y/x
We also refer to this tan as the line's slope
We have been asked to write an equation in slope-intercept form for the line passing through (-2,17) and (2,1)
First we will find the slope(m)
We know that slope = m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
For the pairs of points (-2,17) and (2,1)
⇒ m = [tex]\frac{1- 17}{2 - (-2)}[/tex]
⇒ m = [tex]\frac{-16}{4}[/tex]
⇒ m = -4
We know that the equation for slope(m) and y - intercept(b) of a line is given by :
y = mx + b
Here lets take equation 1 = -4(2) + b .Here x and y is substituted with the second two points.
⇒ 1 = -4(2) + b
⇒ 1 = -8 + b
⇒ b = 1 +8
⇒ b = 9
The equation in the slope intercept is as follows:-
1 = -4(2) + 9
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A year ago, a radio program was aired on r stations across the country. Today, the number of stations airing the radio program can be represented by the following expression: 0.82r Which set of statements is true?
A. The number of the stations airing the program increased by 18%. An equivalent expression that represents this situation is r+0.18r
B. The number of stations airing the program increased by 82%. An equivalent expression that represents this situation is r+0.82r
C. The number of stations airing the program decreased by 82%. An equivalent expression that represents this situation is r -0.82%
D. The number of stations airing the program decreased by 18%. An equivalent expression that represents this situation is r -0.18r.
The set of statements is true; B. The number of stations airing the program increased by 82%. the equivalent expression that represents this situation is r+0.82r.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
IT is given that year ago, a radio program was aired on r stations across the country.
Also Today, the number of stations airing the radio program can be represented by the following expression; 0.82r
Therefore, the equivalent expression that represents this situation is r+0.82r
Hence, The set of statements is true; B. The number of stations airing the program increased by 82%. the equivalent expression that represents this situation is r+0.82r.
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Find the coordinates of the centroid of the triangle with the given vertices. X(5,7), Y(9,-3), Z(13,2)
The coordinates of the centroid of the triangle with the given vertices X (5, 7), Y (9, -3), Z (13, 2) is (13 - 4,2) or (9, 2).
What is meant by the centroid of a triangle?The centroid is the object's center point. The centroid of a triangle is the point where the three medians of the triangle intersect. It is also defined as the point at which all three medians intersect. A median line connects the midpoint of a side and the opposite vertex of a triangle.
The midpoint D of XY is [tex]$\left(\frac{5+9}{2}, \frac{7-3}{2}\right)$[/tex] or (7, 2).
Note that DZ is a line that connects the vertex Z and D, the midpoint of XY. The distance from D(7, 2) to Z(13, 2) is 13 - 7 or 6 units.
If P is the centroid of the triangle XYZ, then [tex]$P Z=\frac{2}{3} D Z$[/tex].
So, the centroid is [tex]$\frac{2}{3}(6)$[/tex] or 4 units to the left of Z. The coordinates of the centroid (P) are (13 - 4, 2) or (9, 2).
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Consider the procedure used below to solve the given equation.
Given: 4(2x +5)-(3x-4)=15
Step 1: 8x+5-3x+4=24
Step 2: 5x + 9 = 24
Step 3: 5x = 24-9
Step 4: -5x = 15
Step 5:53= 15
Step 6: x=-3
Which statement about the solution of the given equation is true?
O The first mistake was made in Step 1.
O The first mistake was made in Step 2.
O The first mistake was made in Step 3.
O The answer is correct. Can you please show me the work please?
Answer:
A. The first mistake was made is Step 1
Step-by-step explanation:
The first mistake was in Step 1. Take a look below to see how Step 1 should've been.
4(2x +5)-(3x-4)=15
Use distributive property.
4(2x +5)-(3x-4)=15
8x+20-3x+4=15
Hope this helps!
Please mark as brainliest if correct!
Have a great day! :)
Solve for x in the equation below.
Round your answer to the nearest hundredth.
Do not round any intermediate computations.
Answer:
Get natural log on both sides and subtract 8 to subject the unknown x.
Step-by-step explanation:
Since this seems to be a quiz-type question I cannot provide a direct answer.But I may help you to get it on your own with some effort from your side.You may follow these steps. I hope you have a calculator to simplify the terms.[tex]\begin{aligned}\\e^{x+8} &= 15\\\\ln(e^{x+8}) &=\small ln(15)\\\\(x+8) ln(e)&=\small ln(15)\\\\x+8&=\small ln(15) \cdots\cdots\cdots[ ln(e) = 1]\\\\x&=\small ln(15) -8\end{aligned}[/tex]
Let me know the answer.Answer:
x = -5.29
Step-by-step explanation:
e^(x+8) = 15
==> take log of both sides
log(e) * (x+8) = log(15)
==> divide both sides by log e (log(15)/log(e) = 2.70805)
x + 8 = 2.70805
==> subtract both sides by 8
x = -5.29 (rounded to the nearest tenth)
Peter and Patty are very competitive and they both are saving money in their piggy banks. Peter has $90 and
Patty has $120. Patty's mom gives her a bonus of 20% of what she already has and Patty adds it to her piggy
bank. Peter's dad tells him that he will give him a bonus so that Peter has the same total as Patty. What percent of
Peter's money must the bonus from his dad be?
Answer any of the following if you know one but not the other!!
1. If the terminal side of angle θ, in standard position, passes through the point (4, -7), what is the numerical value of sinθ?
2. Given tanθ = 3/2 and angle θ is in quadrant III, find the exact value of sinθ in simplest radical form using a rational denominator.
3. Why is it true that sin(θ) = cos (90 - θ) and cos(θ) = sin (90 - θ)?
Step-by-step explanation:
1.
the length of the terminal side from (0, 0) to (4, -7) is the radius of the circle, while
x = 4 = cos(theta)×radius
y = -7 = sin(theta)×radius
so,
sin(theta) = -7/radius
radius² = (4 - 0)² + (-7 - 0)² = 4² + 7² = 16 + 49 = 65
radius = sqrt(65)
sin(theta) = -7/ sqrt(65) = -0.868243142...
FYI
theta = -60.2551187...°
or 299.7448813...°
2.
tan(theta) = 3/2
so,
sin(theta)/cos(theta) = 3/2
2×sin(theta) = 3×cos(theta)
square both sides
4×sin²(theta) = 9×cos²(theta)
completing the square
4×sin²(theta) + 9×sin²(theta) = 9×cos²(theta) + 9×sin²(theta)
13×sin²(theta) = 9×(cos²(theta) + sin²(theta)) = 9
sin²(theta) = 9/13
sin(theta) = 3/sqrt(13)
to make it a rational denominator we multiply by
sqrt(13)/ sqrt(13)
and we get
sin(theta) = 3×sqrt(13)/13
3.
because the sum of all angles in a triangle is 180°.
one angle is theta.
then we have the 90° angle at the origin (or center of the circle).
and that leaves 180 - 90 - theta = 90 - theta for the third angle.
this triangle can be flipped with putting 90 - theta in place of theta.
the flipped triangle is equivalent to the original triangle (all angles and side lengths are identical between the 2 triangles).
the baseline (radius) is the same length in both triangles.
in that flipped triangle the side formerly sin(theta) is now cos(90-theta) and cos(theta) is now sin(90-theta).
Point B is the center of a circle, tangent to the y -axis, and the coordinates of Point B are (3,1) . What is the area of the circle?
A π units ² D 6 π units²
B 3 π units² E 9 π units²
C 4 π units ²
The area of the circle with center located at Point B (3, 1) and tangent to the y-axis is 9π units^2. The answer is E.
The area of a circle is the area enclosed by the circle. It is the product of the square of the radius and the constant π. The Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159.
Area of circle = πr^2
To know the radius of a circle given its center and tangent line to it, find the distance between the the center and the point of tangency. As the radius is the distance from the center of the circle to any point in the circumference of the circle
If the circle is tangent to y-axis, then the radius is the absolute value of the x-coordinate.
r = 3 units
Using the formula for the area of a circle:
Area of circle = πr^2
Area of circle = π(3 units)^2
Area of circle = 9π units^2
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8.1 + u/7 = -3.1
Please help, Thanks!!
Help please, I’m needing help with these questions
The equation of the line perpendicular to y = -²/₃x + 5 and passing through the point (6, -7) is; y = ³/₂x - 16
What is the equation of the line in slope intercept form?We want to find the equation of the line perpendicular to y = -²/₃x + 5 and passing through the point (6, -7).
Now, the slope that is perpendicular to that line is;
m = -1/(-²/₃) = 3/2
Thus;
Equation of the new line is;
y - (-7) = 3/2(x - 6)
y + 7 = 3x/2 - 9
y = ³/₂x - 16
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Felicia bought 4.5 bags of candy for her party baskets. Each bag has 146 pieces of candy. If she has 9 party baskets, how many pieces of candy will each party basket have?
Each party basket will have 73 pieces of candy
How to calculate the number of candies in each basket ?Felicia has 4.5 bags of candy for her party basket
Each bag has 146 pieces of candy
She has 9 party baskets, the number of candies in each party basket can be calculated by multiplying 4.5 by 146 and dividing the result by 9
4.5 × 146/9
= 657/9
= 73
Hence there are 73 pieces of candy in each basket
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Write 35 - 9 as the product of the GCF of 35 and 9 and another sum. Make sure you check your work.
Answer:
Step-by-step explanation:
Mark decided to make Christmas presents for his classmates. he bought 10lb of two types of candies: caramel candies for $2.80 per pound and chocolate candies for $3.50 a pound.
Write a function f(x) that presents the total cost of the candy, where x is the weight of the less expensive candy.
Answer:
10 times 3.50 + 10x= f(x)
Step-by-step explanation:
35+28
f(x)= 63
The function f(x) that presents the total cost of the candy will be f(x) = 35 - 0.70x.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
Mark decided to make Christmas presents for his classmates. he bought 10lb of two types of candies: caramel candies for $2.80 per pound and chocolate candies for $3.50 a pound.
Let x be the number of pounds of caramel candies and (10 - x) be the number of pounds of chocolate candies. Then the equation is given as,
f(x) = 2.80x + 3.50(10 - x)
f(x) = 2.80x + 35 - 3.50x
f(x) = 35 - 0.70x
The function f(x) that presents the total cost of the candy will be f(x) = 35 - 0.70x.
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Simplify 2¾+(3⅜-1½) please I need your help now, and I want you to explain it accordently ,am waiting
Answer:
1⁷/15
Step-by-step explanation:
2¾(3⅜-1½)
using the rule of BODMAS
change the fractions in the bracket into improper fraction
2¾(27/8-3/2)
find LCM of the fractions in the bracket
2¾(27-12)/8
2¾(15/8)
convert the other mixed fraction to an improper fraction
11/8(15/8)= 5.15625~ 5.2
Which answer shows how to correctly multiply 2×4×(−6)?
Answer:
-48
Step-by-step explanation:
2 x 4 = 8
8 x -6 = -48
Simplify each complex fraction.
1/1+ x / y
The simplification form of the given complex fraction [tex]\frac{1}{1+\frac{x}{y} }[/tex] is equal to
(y)/ (y +x).
As given in the question,
Given complex fraction is equal to [tex]\frac{1}{1+\frac{x}{y} }[/tex]
Simplify the given complex fraction by taking the least common multiple of the denominator,
[tex]\frac{1}{1+\frac{x}{y} }\\\\\\= \frac{1}{\frac{y+x}{y} } \\\\\\=\frac{ (1)(y)}{y+ x} \\\\= \frac{y}{y+x}[/tex]
Therefore, the simplification form of the given complex fraction [tex]\frac{1}{1+\frac{x}{y} }[/tex] is equal to (y)/ (y +x).
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2. Open Response The table shows the amount
spent on tomatoes at three different stands
at a farmer's market. Which stand sold their
tomatoes at the least expensive price per
pound, and what is that price? Round to the
nearest cent, if necessary. (Lesson 1)
Stand Weight (lb) Cost ($)
A
2.00
B
C
100
NATA/W
3.45
14.85
Stand C sold their tomatoes at the least expensive price per pound that price is 2.70 per pound.
The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
We have to determine the price of sold tomatoes at the least expensive price per pound.
The price of sold tomatoes at stand A:
⇒ 2/(3/4) = 2/0.75 = 2.67 per pound.
The price of sold tomatoes at stand B:
⇒ 3.45/(5/4) = 3.45/1.25 = 2.76 per pound.
The price of sold tomatoes at stand C:
⇒ 14.85/(11/2) = 14.85/5.5= 2.70 per pound.
Here is the least expensive price per pound at stand C.
Hence, the stand C sold their tomatoes at the least expensive price per pound that price is 2.70 per pound.
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I need help asap!!!!
the answer is negative 41
Simplify:
PLEASE HELP
(3^2 x 3^3) 5
a
3^10
b
3^30
c
3^25
d
9^10
Answer:
1215
Step-by-step explanation:
What is the equation of the slant asymptote of the rational function?
f(x)=10x3−15x2+x−15x2−2
Responses
y=x−3
y equals x minus 3
y=2x−115
y equals 2 x minus fraction 11 over 5
y=2x−3
y equals 2 x minus 3
y=x−115
The equation of the slant asymptote of the rational function is; y = 2x - 3
What is the equation of the slant asymptote of the rational function?We want to find the equation of the slant asymptote of the rational function given as;
f(x) = (10x³ - 15x² + x - 1)/(5x² - 2)
To solve this question, we will divide the numerator by the denominator. The result (not including the remainder) will be the equation of the slant asymptote.
We can tell the first term of the quotient will be 2x since 10x³/5x² = 2x. Thus, the answer from the given options will be either 2x − 3 or 2x − 11/5.
The easiest method to apply here is to simply multiply these options by the denominator to get;
(5x² − 2) (2x − 3) = 10x³ − 15x² − 4x + 6
(5x² − 2) (2x − 11/5) = 10x³ − 11x² − 4x + 22/5
So the answer must be 2x − 3
Thus, the equation of the slant asymptote of the rational function is; y = 2x - 3
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If x2-x-2 > 0, which of the following is the solution set for x?
Ox>-1
Ox>2
O -1 < x < 2
Ox< -1 or x> 2
O No solutions are possible.
Solving the quadratic inequality, the solution set for x is given as follows:
x < -1 or x > 2.
When a function is positive and when it is negative?A function is positive when it is above the x-axis.A function is negative when it is below the x-axis.For this problem, the inequality is given by:
x² - x - 2 > 0.
To graph a quadratic inequality, first we have to find the roots of the quadratic function, hence:
x² - x - 2 = 0
(x - 2)(x + 1) = 0.
Hence the roots are:
x - 2 = 0 -> x = 2.x + 1 = 0 -> x = -1.As the graph given at the end of the answer shows, any concave up quadratic function is positive to the left and to the right of the roots, hence the solution set for the inequality is:
x < -1 or x > 2.
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marking brainliest if a/2-3/2+22 what is A
The value of a cannot be determined because the expression is not an equation
How to determine the value of a?The expression is given as:
a/2 - 3/2 + 22
The above is an expression, and not an equation
For the value of the variable a to be solved, the expression must be an equation
Equations are mathematical expressions that are represented by the equal to or equality sign i.e =
Examples of equations are:
a + b = c
y = mx + c
Ax + By = C
y = ax^2 + bx + c
y = x
Hence, the value of a cannot be determined because the expression is not an equation
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Evaluate each finite series for the specified number of terms. 1+2+4+ . . . . ; n=5
Solving the question with the help of geometrical progression, we get that the value of this finite series is 31.
A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
As we know the formula for geometric progression is:
aₙ = a₁ r ⁿ⁻¹
Where , a₁ is the first term and r is the ratio , and n is the number of terms.
Here, the ratio is 4/2 = 2
Here, a₅ = 1 . 2⁵ ⁻ ¹ = 2⁴ = 16
a₄ = 1 . 2⁴ ⁻ ¹ = 2³ = 8
Now, We should calculate the value 1 + 2 + 4 + 8 + 16 = 31.
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