Answer: $17,875
Step-by-step explanation:
take 27,500 and multiply it by 35% or .35
27500 x .35= 9625
take 9625 and subtract it from the initial value
27500 - 9625= 17875
Answer:
35 × $27500 = $9625
100 1
= $27500-$9625
=$17875
The sum of two numbers is 33.the larger number is 3 more than two times the smaller number.what are the numbers?
Answer: The numbers are 10 and 23
Step-by-step explanation:
Let the smaller number be x
And the larger number be y
Ist sentence;
1. The sum of two numbers is 33.
X + y= 33 .........eqn 1
2. second sentence
the larger number is 3 more than two times the smaller number.
Y = 3 +2x
Put y into eqn 1
X+ 3 +2x = 33
3x= 33- 3
3x= 30
X = 30/3
X= 10 and y= 3+ 2x
Y= 3+ 2(10)
Y = 3+ 20
Y= 23
Therefore the two numbers are 10 and 23
5( q + 27 ) - -30=95
STEPS:
First distribute the 5 through the parentheses to get 5q + 135. So the problem now reads 5q + 135 - (-30) = 95.
Now, minus a negative can be changed to plus a positive so - (-30) can be changed to +30 so our equation now reads 5q + 135 + 30 = 95.
Before adding or subtracting anything from both sides of the equation, make sure you simplify the left side as much as possible. Notice that we can add 135 and 30 to get 165 so the left side simplifies to 5q + 165 = 95.
Now we can simply subtract 165 from both sides of the equation to get 5q = -70.
Now simply divide both sides of the equation by 5 to get q = -14.
3y + 8 + (-7y) +9 expression in an equivalent. a) -10y +1 b) -4y + c) -9y d) 3y
Answer:
Step-by-step explanation:
3y + 8 +(-7y) + 9 =
3y + 8 - 7y + 9 =
-4y + 17
radio signals travel at a rate of 3 x 10^8 meters per second. how many seconds will it take for a radio signal to travel from a satellite to the surface of earth if the satellite is orbiting at a height of 3.6 x10^7 meters? Write the answer in scientific notation.
Answer:
[tex]time=1.2\times 10^{-1}\ second[/tex]
Step-by-step explanation:
Given:
The speed of the radio is [tex]3\times 10^{8}[/tex] meters per second.
The distance of the satellite from the earth is [tex]3.6\times 10^{7}[/tex] meter
The formula of the speed is
[tex]speed = \frac{distance}{time}[/tex]
For time the formula is.
[tex]time = \frac{distance}{speed}[/tex]
put distance and speed value in above equation.
[tex]time = \frac{3.6\times 10^{7}}{3\times 10^{8}}[/tex]
[tex]time = \frac{1.2 x 10^{7}}{10^{8}}[/tex]
[tex]time=1.2\times 10^{7}\times 10^{-8}[/tex]
[tex]time=1.2\times 10^{7-8}[/tex]
[tex]time=1.2\times 10^{-1}\ second[/tex]
Therefore, the radio will be take the time is [tex]1.2\times 10^{-1}\ second[/tex] or 0.12 seconds.
which if the following statements is true about the triangles below
Answer:
Step-by-step explanation:
ΔABC ≅ ΔABD by ASA
A card is drawn at random from a standard 52-card deck. What is the probability that it is an odd number (3,5,7,9) or a spade (or both)?
Answer:
The probability of selecting the given event = [tex]\frac{25}{52}[/tex]
Step-by-step explanation:
A card is drawn at random from a standard 52-card deck.
We have to find the probability of selecting an odd numbered card(3,5,7,9) or spade or both.For this we have to find the number of favourable cases.
Favorable cases = 13 (all the spades) + 12(4 odd numbered cards from each of the remaining 3 )
= 25
Final probability = [tex]\frac{number of favourable cases}{total number of cases}[/tex]
= [tex]\frac{25}{52}[/tex]
Hence the probability = [tex]\frac{25}{52}[/tex]
Which statement best describes the data in a scatter plot where the Y values are decreasing as the x-values are increasing
A. The data clock can be modeled by vertical line
B. The data tempest be modeled by a horizontal lThe data tempest be modeled by a horizontal line
C. The data can best be modeled by line with a positive slope
D. The data canvas be modeled by a line with a negative slope
Answer:
Option D is the right answer.Step-by-step explanation:
We need to find the option for which the value of the function will be increasing, with the increasing variable.
Vertical line means the value of the x is constant, for any y. Hence, it is not the answer.
Horizontal line represents constant functions. Hence option B can not be the answer.
The data having a positive slope represents a increasing function with the increasing variable. Vice-versa for the data having a negative slope.
That is why option D will be the answer.
The correct option is d, which is the data canvas be modeled by a line with a negative slope.
Scatter plotA scatter plot is also known as a scatter chart, a scatter graph that uses dots to represent values for two different numeric variables. Each dot on the graph represents a particular on both the axis.
Given to usthe Y values are decreasing as the x-values are increasing
As we can see in the graph below with the decreasing value of y and increasing value of x, therefore, it will be a negative slope.
Hence, the correct option is d, which is the data canvas be modeled by a line with a negative slope.
Learn more about Scatter plots:
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What is 18,157 rounded to the nearest thousand
Answer:
18,000
Step-by-step explanation:
because its closer to 18,000 then 19,000.
Bobby’s football team received four five-yard penalties in the first quarter, which meant his team lost yardage in their progress toward the goal line. What was the change in their progression down the field as a result of these penalties?
Answer: they lost 20 yards.
Step-by-step explanation
Answer:
A -20
Step-by-step explanation:
Hans is at the observatory of the Empire State Building in New York City. The observatory is on the 86th floor of the building. Hans will take the elevator down from the 86th floor to the first floor, a distance of 320 meters. If the ride takes 50 seconds to descend, what is the rate of descent in meters per second?
Answer:
6.4 meters per second
Step-by-step explanation:
Rate of Change
If two variables x and t are to be related as the rate x changes when t changes, it can be expressed as:
[tex]\displaystyle v=\frac{x}{t}[/tex]
Hans takes a ride in the elevator down from the 86th floor to the first floor, a distance of x=320 meters in t=50 seconds. The rate of descent is
[tex]\displaystyle v=\frac{320}{50}[/tex]
[tex]v=6.4\ m/s[/tex]
I NEED HELP ASAP
Grandma bakes the world's best and favorite cookies. Grandma's cookies have a half-life of 2 hours. One day, Grandma baked a lot of cookies. If 2 days and 6 hours later, 2 cookies still remain, how many cookies did Grandma make?
A) 3.6 × 10^16
B) 4 dozen cookies
C) 268,435,456 cookies
D) 153 cookies
Answer:
C
Step-by-step explanation:
Write the function f(x)6x^2+7x+2 in vertex form, and identify its vertex
Answer:
Step-by-step explanation:
Complete the square to do this. This one is a bit of a pain because of the 7 as our linear term, but a little hard work never killed anyone!
The rules for completing the square are very strict and cannot be strayed from. The first rule is that the leading coefficient HAS to be a positive 1; ours is a positive 6 so we have to factor it out. Let's do that first then we can get to rule number 2.
Set the quadratic equal to 0, then move the constant over to the other side. This is not a rule, per se, but I teach it this way to avoid unnecessary confusion in an already confusing process.
[tex]6x^2+7x=-2[/tex] and to factor out the 6:
[tex]6(x^2+\frac{7}{6}x)=-2[/tex]
Now for rule #2: take half the linear term, square it, and add it to both sides. Our linear term is 7/6. Half of that is 7/12, and 7/12 squared is 49/144. BUT we cannot forget about that 6 hanging around out front, refusing to be ignored. It is a multiplier, so when we add 49/144 inside the parenthesis on the left, we have to add 6(49/144) to the right, giving us:
[tex]6(x^2+\frac{7}{6}x+\frac{49}{144})=-2+\frac{294}{144}[/tex]
We will rewrite now by simplifying. The left side can be written into a perfect square binomial (which is why we did this in the first place) and the right side can be added. The left side becomes
[tex]6(x+\frac{7}{12})^2[/tex]
The 7/12 comes from the square root of 49/144, and the x comes from the square root of x-squared. The right side requires a common denominator:
[tex]-2+\frac{294}{144}=-\frac{288}{144}+\frac{294}{144}=\frac{6}{144}=\frac{1}{24}[/tex]
So now we have
[tex]6(x+\frac{7}{12})^2=\frac{1}{24}[/tex]
Put evertyhing back onto the left side and set it back to equal y and you're done!
[tex]y=6(x+\frac{7}{12})^2-\frac{1}{24}[/tex]
Because the vertex form of a quadratic does not allow us to stray from the format "x -", we have to interpret our h coordinate as "x - (-7/12))" which is movement to the left. This gives us a vertex of
[tex](-\frac{7}{12},-\frac{1}{24})[/tex]
The solution to -2 x - 6 y equals 0
Answer:
x=-3y
Step-by-step explanation:
-2x-6y=0
x+3y=0
x=-3y
A baker is making an oversized sheet cake for a school dance. The recipe calls for 2 cups of sugar for every 3 cups of flour. How many cups of flour are needed, if she is using18 cups of sugar.
Answer:
2 cups of sugar
Step-by-step explanation:
Determine whether each mapping represents a function. Explain your reasoning.
Answer:
The first picture is a function and the second picture is not.
Step-by-step explanation:
Reason - In the first picture, there is no repeating value of x. In other words, every x value has a y value. However, in the second picture, the x value, 2 goes to 2 and -3.
115 On a coordinate plane, draw triangle ABC with vertices
A(-1, -1), B(3, -1), and C(-1, 2). Find the area of the triangle
in square units.
Final answer:
The area of triangle ABC with vertices A(-1, -1), B(3, -1), and C(-1, 2) is calculated using the determinant method and results in 6 square units.
Explanation:
To find the area of a triangle with vertices on a coordinate plane, you can use the formula that requires knowing the coordinates of all three vertices.
For triangle ABC with vertices A(-1, -1), B(3, -1), and C(-1, 2), we can use the determinant method:
The area of triangle ABC is ½ |x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)|. Substituting our given coordinates into this formula, we get:
Area = ½ |(-1)(-1 - 2) + 3(2 - (-1)) + (-1)((-1) - (-1))|
Area = ½ |(-1)(-3) + 3(3) + (-1)(0)|
Area = ½ |3 + 9 + 0|
Area = ½ × 12
Area = 6 square units
The area of triangle ABC is therefore 6 square units.
How is the factoring method GROUPING different from the factoring method GCF?
Answer:
Step-by-step explanation:
The basic concept for both is the same, except with grouping you have more than 3 terms and after factoring out what is common in each group, you are left with identical terms in a set of parenthesis that can then also be factored out. For example, this would be factoring by grouping (then I will show you a factoring by GCF to better illustrate the idea):
If our polynomial is
[tex]x^3-x^2+3x-3=0[/tex]
we could group those terms into groups of 2 (without changing their order at all) to get:
[tex](x^3-x^2)+(3x-3)=0[/tex]
and we factor out what's common in each group to get:
[tex]x^2(x-1)+3(x-1)=0[/tex]
You can see that the (x - 1) is common now and can be factored out, leaving us with
[tex](x-1)(x^2+3)[/tex] (the secod term now can be factored if you need the complete linear factorization, but it will lead to imaginary numbers).
An example of factoring out the GCF is to factor out what's common in all the terms. It HAS TO BE COMMON IN ALL THE TERMS to do it this way. For example, in the polynomial
[tex]6x^3-4x^2+2x-8=0[/tex] the GCF for all the terms is a 2, so that's all we can factor out. It has to factor out of every term every time, no exceptions:
[tex]2(3x^3-2x^2+x-4)=0[/tex]
The method of GCF factoring often just serves to simplify the polynomial down a bit, but sometimes will still require factoring.
Final answer:
Factoring by grouping is used for polynomials with four or more terms, arranging them into groups with common factors, while factoring by GCF involves finding the largest common factor for all terms in an expression.
Explanation:
Factoring by grouping and factoring by the Greatest Common Factor (GCF) are two methods used in algebra to simplify expressions or solve equations.
Factoring by GCF involves finding the largest factor that is common to all terms in an expression.
For example, in the expression 4x + 8, the GCF is 4, so we can factor it as 4(x + 2).
Factoring by grouping, on the other hand, is used when an expression has four or more terms.
The method involves grouping terms so that each group has a common factor that can be factored out.
For instance, with the polynomial x^3 + 3x^2 + 4x + 12, we group the terms into (x^3 + 3x^2) + (4x + 12).
We then factor out the GCF from each group, yielding x^2(x + 3) + 4(x + 3).
Recognizing that (x + 3) is common between the groups, we can then factor further to get (x^2 + 4)(x + 3).
what is the solution to 3x+5+4x=5x+27
｡☆✼★ ━━━━━━━━━━━━━━ ☾
3x + 5 + 4x = 5x + 27
7x + 5 = 5x + 27
- 5
7x = 5x + 22
- 5x
2x = 22
/2
x = 11
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Answer:
Step-by-step explanation:
3x + 5 + 4x = 5x + 27
collect like terms
7x - 5x = 27 -5
2x = 22
divide both side by 2
x = 11
slope of line (-3,-2) , (5,-2)
Answer:
0
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-2-(-2))/(5-(-3))
m=(-2+2)/(5+3)
m=0/8
m=0
Rewrite the equation 2x + 3y = 6 in slope-intercept form. y = -2 x + 6 y = - x + 2 y = 2 x + 6 3 y = -2 x + 6
Answer:
y=-2/3x+2
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Complete the inequality statement.
14 ft ____ 4 1/2 yd.
<
>
='
PLEASE ANSWER CORRECTLY
DO NOY ANSWER INCORRECTLY JUST FOT POINTS TY
Answer: 14ft > 41/2
Step-by-step explanation:
Your answer is:
14ft > 41/2yd
I hope this helped! If so, please mark brainliest!
Leah is masking a picture frame. The perimeter of her picture is 24 inches and the area is35 square inches. What are the lengths of the picture sides?
The sides are 7 inches and 5 inches. To get the perimeter, it's 7 +7 +5 + 5, which equals 24, and then 7 x 5 = 35 for the area.
wiple Choice which equation describes the relationship
20. Multiple
the table?
0 0 1 2 3 4 5 6
16 10 20 30 40 50 60 70
A. C= 10n
B. C= 10 +n
C. C= 10
D. C= 10 + 10n
answer:C=10+10n
proof: 10+10 (1)=20
10+10 (.6)=16
10+10 (-.4)=6
3. Matt bought 12 packages of hot dogs and hamburgers for a barbecue. Let x represent the number of packages of hot dogs, which cost $2.75 each. Let y represent the number of packages of hamburgers, which cost $3.20 each. Matt spent a total of $35.25. Write and solve a system of equations that can be used to represent the amount of hot dogs and hamburger packages Matt bought. Are there any constraints on your variables? Is the solution viable or non-viable?
Answer:
Matt bought 7 packages of hot dogs and 5 packages of hamburger.
Step-by-step explanation:
We are given the following in the question
Let x represent the number of packages of hot dogs.
Cost of one packet of hot dog = $2.75
Let y represent the number of packages of hamburgers
Cost of one packet of hamburgers = $3.20
Then, we can write the following equations:
[tex]x + y = 12\\2.75x + 3.2y = 35.25[/tex]
Solving the two equations,
[tex]2.75x + 2.75y = 33\\2.75x + 3.2y = 35.25\\\Rightarrow 0.45y = 2.25\\y = 5\\x = 7[/tex]
Thus, Matt bought 7 packages of hot dogs and 5 packages of hamburger.
The solution is viable.
Constraints to the system of equation:
[tex]x,y \geq 0 \\x + y = 12\\2.75x + 3.2y = 35.25[/tex]
two lines have the given equations. Use the LINEAR COMBINATION METHOD to solve.
2x-y=1
3x-y=-6
Using linear combination method, the solution to given system of equations are (-7, -15)
Solution:Linear combination is the process of adding two algebraic equations so that one of the variables is eliminated
Addition is used when the two equations have terms that are exact opposites, and subtraction is used when the two equations have terms that are the same.
Given system of equations are:
2x - y = 1 ---- eqn 1
3x - y = -6 ------ eqn 2
Subtract eqn 2 from eqn 1
2x - y = 1
3x - y = -6
(-) -------------
-x = 7
x = -7Substitute x = -7 in eqn 1
2(-7) - y = 1
-14 - y = 1
y = -14 - 1 = -15
y = -15Thus the solution to given system of equations are (-7, -15)
The triangle will be rotated 180° clockwise around the point (3, 4) to create A A'B'C.Which
characteristics of AA'B'C' will be the same for the corresponding characteristics of AABC? Select ALL that
apply.
The question is incomplete. Here is the complete question:
The triangle will be rotated 180° clockwise around the point (3, 4) to create A A'B'C.Which
characteristics of AA'B'C' will be the same for the corresponding characteristics of AABC? Select ALL that apply.
(A) The coordinates of A'.
(B) The coordinates of B'.
(C) The perimeter of Δ A'B'C'.
(D) The area of Δ A'B'C'.
(E) The measure of ∠B'.
(F) The length of segment A'B'.
Answer:
(C) The perimeter of Δ A'B'C'.
(D) The area of Δ A'B'C'.
(E) The measure of ∠B'.
(F) The length of segment A'B'.
Step-by-step explanation:
Given:
A triangle ABC rotated by 180° clockwise around the vertex C(3,4) to create Δ A'B'C.
Now, a rotation is a rigid motion transformation. In rigid transformation, the size, length, angle measures, perimeter and area of the figure doesn't change and remains the same as the original figure.
Rotation only changes the position of the points on the figure.
Here, as the triangle ABC is rotated about vertex C, the position of vertex A and B will change. But, the angles made by each of the vertices will remain same. Also, the side lengths of the triangle will remain the same. So, the perimeter and area will also not change. As the point of rotation is point C, the vertex C' will be same as vertex C.
So, the correct options are (C), (D), (E), and (F).
Please help me with this I’m crying
Answer:
640 cm²
Step-by-step explanation:
The ratio between the area two similar polygon are the ratio between their sides squared.
Given side S₁ and side S₂, you can find the area of the second shape by multiplying the area of the first shape by a factor of (S₂/S₁)².
This might sound confusing if you're not used to hearing math terms so lets solve it in this problem.
The side of the first trapezoid is 5cm, so S₁ = 5
The side of the second trapezoid is 20cm so S₂ = 20.
The ratio between them is 20/5=4
To find the area of the second shape, we just have to multiply the area of the first one by the ratio², ie. (S₂/S₁)².
40(4)² = 40(16) = 640 cm²
Karina read a total of 20 2/4 pages in her science and social studies books combined she read 12 3/4 pages in her science book how many pages did she read in her social studies book
Answer:
8 1/4
Step-by-step explanation:
20 2/4
-
12 3/4
__________
8 1/4
7 1/4
You subtract 20 and 2/4 by 12 3/4 and you get 8 1/4
In ΔQRS, RS = 19, SQ = 20, and QR = 18. Which statement about the angles of ΔQRS must be true?
Triangle with sides RS=19, SQ = 20, AND QR = 18 must have unequal angles as triangles with unequal sides have unequal angles.
A triangle with unequal sides is known as the Scalene triangle. As mentioned in the question triangle QRS has unequal sides of length RS = 19, SQ = 20, and QR = 18.
Then we can say that triangle Δ QRS is a Scalene triangle.
A scalene triangle has unequal angles. It has no line of symmetry present in a scalene triangle.
In a scalene triangle, the angle opposite to the longest side is the greatest.
Hence, we can say that the angles of Δ QRS are unequal.
For more details about Triangles,
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The correct statement is that at least two angles of ΔQRS are equal, and one angle is different.
Here,
In a triangle, the sum of the measures of the three interior angles is always 180 degrees.
This is known as the triangle angle sum property.
Therefore, if we know the lengths of two sides of a triangle, you can determine the measure of the third angle using the Law of Cosines or the Law of Sines.
In the case of ΔQRS, we can use the Law of Cosines to find the measure of angle ∠Q:
Cos(∠Q) = (RS² + QR² - SQ²) / (2 * RS * QR)
Cos(∠Q) = (19² + 18² - 20²) / (2 * 19 * 18)
Cos(∠Q) = (361 + 324 - 400) / (2 * 19 * 18)
Cos(∠Q) = 285 / 684
Cos(∠Q) ≈ 0.416667
Now, to find the measure of ∠Q, we take the inverse cosine (arccos) of 0.416667:
∠Q ≈ arccos(0.416667) ≈ 65.392°
Now that we know the measure of ∠Q, we can find the measures of the other angles:
∠R = 180° - ∠Q - ∠S
∠R = 180° - 65.392° - ∠S
And
∠S = 180° - ∠Q - ∠R
∠S = 180° - 65.392° - (180° - 65.392° - ∠S)
∠S = 180° - 65.392° - 180° + 65.392° + ∠S
∠S = 2 * 65.392° - ∠S
2 * ∠S = 2 * 65.392°
∠S = 65.392°
So, the measures of the angles in ΔQRS are approximately:
∠Q ≈ 65.392°
∠R ≈ 49.608°
∠S ≈ 65.392°
As we can see, two of the angles (∠Q and ∠S) are equal, while the third angle (∠R) is different.
Therefore, the correct statement is that at least two angles of ΔQRS are equal, and one angle is different.
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I need help with Algebra 2a
Answer:
Step-by-step explanation:
Summation means that you are adding together all the numbers that result from putting in the numbers 5-11 for i:
(-7 - 6(5)) + (-7 - 6(6)) + (-7 - 6(7)) + ( -7 - 6(8)) + ( -7 - 6(9)) + ( -7 - 6(10)) + ( -7 - 6(11)) which gives you the numbers:
-37 + -43 + -49 + -55 + -61 + -67 + -73 = -385