The variables that
x + y = 2100
5 x + 7 y = 11700
Let x = total dollar amount of sales of phone;
y = total dollar amount of sales of computer
for total sales of phones anna earns 5% commission
So anna 's commission = 5% of x
= 0.05x
for total sales of computer anna earns 7% commission
So anna 's commission = 7% of y
= 0.07y
Given the total sales; x + y = 2100
And commission; 0.05x + 0.07y = 117; or 5x + 7y = 11700
Therefore the system of equations are
x + y = 2100 …….equation (1)
5 x + 7 y = 11700 ……equation (2)
In mathematics, a variable is a symbol and placeholder for any mathematical object. In particular, a variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set.
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GEOMETRY HONORS
Answer Options:
Valid: Law of Syllogism
Valid: Law of Detachment
No Valid Conclusion
please answer asap, thank you all so much
Answer:
17. Invalid
Step-by-step explanation:
It is invalid because not only the angles matter but also the measurement of the sides, if one side is bigger than the other, it cannot be a square.
5/9 (d - 12) = 10 A linear equation is shown above. Which of the following values of d is a solution to the equation?
For the given equation, the value of d = 30
How to solve an equation?To solve linear equations, utilize the steps that are provided below. Remove parenthesis from either side of the equation and combine similar phrases to make it simpler. To separate the variable term on one side of the equation, use addition or subtraction. To find the variable, use division or multiplication.
Divide both sides of the equation by the coefficient of variable: d-12 = 10÷ 5/9
Divide a fraction by multiplying its reciprocal: d 9 -12=10 x 9/5
Write as a single fraction: d-12 = (10 x 9) / 5
Calculate the product or quotient: d-12= 90 / 5
Reduce fraction to the lowest term by canceling the greatest common factor: d-12 = 18
Rearrange unknown terms to the left side of the equation: d=18+12
Calculate the sum or difference: d=30
Answer: d=30
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What is the image of the point (3,4)(3,4) after a rotation of 90^{\circ}90 ∘ counterclockwise about the origin?
The image of the point (3,4)(3,4) after a rotation of 90^{\circ}90 ∘ counterclockwise about the origin is (-3,4).
What is meant by the image of the points?A point's reflection
The mirror's "reflection" of the specified point P causes it to appear at an equal distance away on the other side of the line. To view this, move the point P. According to tradition, the "image" of point P is the reflection of point P across the line, which is designated by the term P' (pronounced "P prime").
As the rotation is counterclockwise around the origin,
the coordinates of the image will be - (-3,4)
The graph is attached at the end of the solution.
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Answer:
-4, 3
Step-by-step explanation:
(-8) x (-2/3) =
hellpp !
Answer:
(- 8) × (- 2/3) = 16/3 = 5 1/3
Hope this helps :)
Translate each sentence into an equation.
1. The sum of three times a and four is the same as five times a.
2. One fourth of m minus six is equal to two times the sum of m and 9.
3. The product of five and w is the same as w to the third power.
Translate each sentence into an equation. which are as follows the value of a is 2, the value of m is 13.71 and the value of w is the root of 5.
1. The sum of three times a and four is the same as five times a.
3a+4 = 5a
3a = 5a -4
4 = 5a-3a
4= 2a
2 =a
2. One-fourth of m minus six is equal to two times the sum of m and 9.
1/4m - 6 = 2 (m+9)
1/4m = 2m +18+6
1/4m = 2m + 24
2m -1/4 m = -24
7/4 m = -24
m = -24*4/7 = 13.71
The value of m is 13.71
3. The product of five and w is the same as w to the third power.
5*w = w.w.w
5 = w.w.w/w
5 = w.w
root of 5 = w
The value of w is the root of 5
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Given two terms of each arithmetic sequence, find a₁ and d . a₁₀ = 17 and a₁₄=34
The two terms of each arithmetic sequence [tex]a_{10}[/tex] = 17 ,[tex]a_{14}[/tex] =34 are d = 17/4 and a = -21.25.
What is sequence?[tex]a_{10}[/tex] = 17
17 = a +9d.............1
[tex]a_{14}[/tex] =34
34 = a + 13d...........2
equating equation 1 and 2
17 = a +9d
34 = a + 13d
d = 17/4
d = 4.25 ..............3
from equation 3
a = -21.25
An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer.
16,18,26
Yes, the given set of numbers can be the measures of the sides of a triangle. The triangle is acute.
By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.
16 + 18 > 26
18 + 26 > 16
26 + 16 > 18
Hence, these set of numbers can be the measures of the sides of a triangle.
According to the Pythagorean Inequality Theorem, a triangle whose sides measure a, b, and c where c is the largest, the triangle can be characterized as:
acute if [tex]a^{2} + b^{2} < c^{2}[/tex]
obtuse if [tex]a^{2} + b^{2} > c^{2}[/tex]
right if [tex]a^{2} + b^{2} = c^{2}[/tex]
∴The longest side is 26.
Hence, a = 16, b = 18 and c = 26;
Consider [tex]a^{2} + b^{2[/tex] :
= [tex]16^{2} + 18^{2}[/tex]
= 580.
Now consider [tex]c^{2}[/tex] :
= [tex]26^{2}[/tex]
= 676.
Thus, [tex]a^{2} + b^{2} < c^{2}[/tex].
Hence, the triangle is acute.
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Find the sum.
2
3
+
1
5
Answer:
23+15 or 2/3+1/5
Step-by-step explanation:
23+15=48
2/3+1/5= 13/15
Add all numerators above the least common denominator then add the numbers
What is the conclusion of the given conditional
statement.
If it is a Thanksgiving, then we are not in
school.
Answer:
we are not in school
Step-by-step explanation:
Conditional: If it is a Thanksgiving, then we are not in school.
Hypothesis: If it is a Thanksgiving, then we are not in school.
Conclusion: If it is a Thanksgiving, then we are not in school.
Answer: we are not in school
The perimeter of a square is 4 times as
great as the length of any of its sides.
Determine if the perimeter of a square is proportional to its side length. Explain.
Answer:
Perimeter of a square is proportional to side length
Step-by-step explanation:
We have the relation p = 4a, p = perimeter, a = side length
This is the equation for a proportionate relationship of the form y = k.x where y ∝ x , y directly proportional to x => y varies as x varies and always by the same constant
k is known as constant of proportionality
Here k = 4
Let's say the side of square is 1. Then perimeter = 4
If side is increased to 2, then perimeter = 4 x 2 = 8
If side is increased to 3, then perimeter is 4 x 3 = 12
So perimeter increases by a factor of 4 for every unit increase in side length
Shaquana has a points card for a movie theater.
She receives 40 rewards points just for signing up.
• She earns 13.5 points for each visit to the movie theater.
• She needs 175 points for a free movie ticket.
How many visits must Shaquana make to earn a free movie ticket?
Which ordered pairs are solutions to the inequality y−3x<10?
(0,-4) , (0,-1) , (4,-1) are the ordered pairs are solutions to the inequality
y − 3x < 10 which is option (A) , (D) and (E) .
An inequality compares two values and indicates whether one is less than, greater than, or equal to another. a ≠ b indicates that a is not equal to b a < b indicates that a is less than b a > b indicates that a is greater than b (These two are known as strict inequalities) a ≤ b means that a is less than or equal to b a ≥ b means that a is greater than or equal to b.
We have to check whether the given options are the solutions to the inequality y− 3x < 10 . ...(1)
(A) If (0,-4) is the solution of given inequality y− 3x < 10 then it must satisfy the equation .
Putting x = 0 and y = -4 in equation (1) , we get
[tex]-4-3(0) < 10\\-4 < 10[/tex]
As the above condition is true so (0,-4) is the solution of given inequality
(B) If (-6,0) is the solution of given inequality y− 3x < 10 then it must satisfy the equation .
Putting x = -6 and y = 0 in equation (1) , we get
[tex]0-3(-6) < 10\\18 < 10[/tex]
As the above condition is not true so (-6,0) is not the solution of given inequality .
(C) If (-1,7) is the solution of given inequality y− 3x < 10 then it must satisfy the equation .
Putting x = -1 and y = 7 in equation (1) , we get
[tex]7-3(-1) < 10\\7+3 < 10\\10 < 10[/tex]
As the above condition is not true so (-1,7) is the not the solution of given inequality .
(D) If (0,-1) is the solution of given inequality y− 3x < 10 then it must satisfy the equation .
Putting x = 0 and y = -1 in equation (1) , we get
[tex]-1-3(0) < 10\\-1 < 10[/tex]
As the above condition is true so (0,-1) is the solution of given inequality.
(E) If (4,-1) is the solution of given inequality y− 3x < 10 then it must satisfy the equation .
Putting x = 4 and y = -1 in equation (1) , we get
[tex]-1-3(4) < 10\\-1-12 < 10\\-13 < 10[/tex]
As the above condition is true so (4,-1) is the solution of given inequality.
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(k^2-5k-2)(k^2+2) polynomial in standard form
Answer:
[tex]K^{4} -5k^{3} -10k-4[/tex]
Step-by-step explanation:
A not allowed
The students in a class were asked whether they preferred basketball,
netball or floorball. The ratio of students who preferred basketball to netball
to floorball was 10:9: 6. What percentage of students preferred netball?
Watch video
Answer>
Based on the given conditions, formulate: 9÷(6+10+9)
Calculate the sum or difference: 9/16+9
Calculate the sum or difference:9/25
Multiply a number to both the numerator and the denominator:9 x 4/25 x 4
Calculate the product or quotient: 36/100
Rewrite a fraction with denominator equals 100 to a percentage is 36%
therefore the percentage of the students preferred netball is 36%.
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100.One percent is one hundredth of a whole. It can therefore be written as both a decimal and a fraction. To write a percentage as a decimal, simply divide it by 100. For example, 50% becomes 0.5, 20% becomes 0.2, 1% becomes 0.01 and so on.Percentages are used widely and in many different areas. For example, discounts in shops, bank interest rates, rates of inflation and many statistics in the media are expressed as percentages. Percentages are important for understanding the financial aspects of everyday life.to know more about percentage ;
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Roxy and Randy are selling pancake breakfast plates to raise money for a class trip.
Roxy is selling plates for $5.00 and has already raised $175. Randy is selling plates for $3.50 and has already raised $250.
Which equation can be used to nd p, the number of plates that Roxy and Randy must sell so that the total amount raised is the same for both Roxy and Randy?
The total amount raised is the same for both Roxy and Randy if they sell 50 Plates.
Let the number of plate = 'p'
Roxy :
Selling price of plates = $5.00
Raised = $175
Total plates sold = 5.00p
Total amount raised = 5.00p + 175 ...eq.(1)
Randy :
Selling price of plates = $3.50
Raised = $250
Total plates sold = 3.50p
Total amount raised = 3.50p + 250 ...eq.(2)
Now we will equate the eq.(1) and eq.(2) to find the same amount raised by both Roxy and Randy ,
5.00p + 175 = 3.50p + 250
5.00p - 3.50p =250 - 175
1.5p = 75
p = 75/1.5
p = 50
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If DM = 26 and point G lies on the perpendicular bisector of DM¯¯¯¯¯¯¯, what is the value of r? Segment D M with point G between the endpoints. Segment D G has length R plus 3, and segment G M has length 4R minus 28. A. 10 B. 13 C. 30 D. 52
Applying the segment addition postulate, the value of r is determined as: A. 10.
What is the Perpendicular Bisector?A perpendicular bisector is a line segment which divides another line segment into two equal parts, that is, the segments formed have equal lengths.
Since point G lies on the perpendicular bisector of segment DM, therefore:
DG = GM
Given the following:
DM = 25
GM = 4r - 28
DG = r + 3
Therefore:
DG + GM = DM [segment addition postulate]
Substitute
r + 3 + 4r - 28 = 25
Combine like terms
5r - 25 = 25
5r = 25 + 25
5r = 50
5r/5 = 50/5
r = 10
Thus, applying the segment addition postulate, the value of r is determined as: A. 10.
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Solve for y.
A. 12
B. 13.5
C. 9
D. 10.5
Answer: C
Step-by-step explanation:
180° = 96° + 8y + 12
180° = angles on a straight line
180 - 96 - 12 = 8y
8y = 180 - 96 - 12
8y = 72
y = 72 / 8
y = 9
How do I find angle x?
The value of x is 280
How to determine the angleFrom the information given, we have that;
Angle at the circumference = xAngle at the center = 140It is important to note that, the angle subtended by an arc at the center is twice the angle subtended at the circumference.
Example;
If AOB is the angle at the circumference and ACB is the angle at the center
Then, we have that;
Angle AOB = 2 × Angle ACB
2(140) = x
expand the bracket
x = 280
Thus, the value of x is 280
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What is the slope of the line passing through the points
(2,5) and (4, 1)?
Answer:
-2
Step-by-step explanation:
Slope = rise/run
[tex]\mathrm{Slope} = \frac{y_2-y_1}{x_2-x_1}\\m=\frac{1-5}{4-2}\\1 - 5 = -4\\4 - 2 = 2\\=\frac{-4}{2}\\ =-2[/tex]
In this problem, you will investigate the relationships among three points of concurrency in a triangle.
a. Draw an acute triangle and find the circumcenter, centroid, and orthocenter.
Construct an acute triangle and find the centroid (medians), circumcenter (perpendicular bisectors), and orthocenter (altitudes). Take note of how these three centers interact with one another from the figure.
What are acute triangles?
An acute angle triangle (also known as an acute-angled triangle) is a triangle with all of its interior angles being acute angles. Remember that an acute angle is one that is less than 90°.
A triangle with three acute angles is known as an acute triangle. An obtuse triangle has one obtuse angle and two acute angles. Because the angles of a triangle in Euclidean geometry must sum to 180°, no Euclidean triangle can have more than one obtuse angle.
Construct an acute triangle and find the centroid (medians), circumcenter (perpendicular bisectors), and orthocenter (altitudes). Take note of how these three centers interact with one another from the figure.
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If 3% of a number equals 2, find 9% of that number.
Answer:
6
Step-by-step explanation:
2/.03 = 66.66...7 times .09 = 6
The number is 66.67. And the 9% of the number 66.67 will be 6.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Let the number be 'x'. Then the equation is given as,
3% of x = 2
0.03 x = 2
x = 2 / 0.03
x = 66.67
Then the 9% of that number is calculated as,
⇒ 9% of 66.67
⇒ 0.09 x 66.67
⇒ 6
The number is 66.67. And the 9% of the number 66.67 will be 6.
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| Identify the prime statements in the below compound statement
9 is odd and 9 is divisible by 3
A composite number is one that is greater than one and contains more than 2 factors.
For example, the number four can always be factorized in a variety of ways. As a result, the factors of 4 have been 1, 2, and 4. It contains more than two elements. As a result, 4 is a composite number.For the given statement;
9 is divisible by 3 can be written as;
9/3 = 3 ; as 3 is the prime number, the statement is regarded as prime statement.
For, 9 is odd.
As, 9 is not a prime but a composite number, the statement is considered as the compound statement.
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State the property that justifies each statement.
If x=5 and b=5 , then x=b .
Each assertion is backed up by property. This same transitive property of equality supports this.
What exactly is the transitive property?If x, y, and z are really the three quantities, as well as x is connected with y by some rule, and y is connected to z by the same rule, we can say x is connected to z using the same rule.
According to the given data:x=5
b=5
x=b.
That transitive property that equality justifies this.
because :
Transitive Property of Equality show If a = b and b = c, then a = c.
so in the given statement the x=5 and b=5 so x=b.
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-1.4 + (-1.2) thanks
Answer:
-2.6
Step-by-step explanation:
−
7
4
p+(−
7
2
p)+
7
1
1
Answer: god please help the world
Step-by-step explanation: we are struggling
Answer: -6/7p+1/7
Step-by-step explanation: thank god I'm smart lol... I'm a big brain!!!
Refer to ®N . Identify each.
b. a diameter
The diameter is the length of the line passing through the center and touching two points on the circle's edge.
What is the diameter?In geometry, a circle's diameter is any straight line segment that passes through the center of the circle and has endpoints on the circle. It is also referred to as the circle's longest chord. Both definitions apply to a sphere's diameter.
The diameter is defined as the length of a line passing through the center and touching two points on the circle's rim.
A circle's diameter extends from one side to the other, with its midpoint in the center. Divide the radius of the circle by two to get the diameter.
A circle's diameter divides the shape in half. The radius of a circle is half the length of its diameter (or, conversely, the diameter of a circle is twice the length of its radius).
The complete question is:
Identify each
b. a diameter
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i’m doing my geometry homework with the equation 1/2h(b1+b2) but i can’t figure this one out. please help
Answer:
Step-by-step explanation:
to find the bottom base you add the two numbers that make it
5+18=23
now put everything in the formula
[tex]\frac{1}{2}*12(12+23)\\[/tex]
parathesis first
12+23=35
[tex]\frac{1}{2} *12*35[/tex]
multiply in order
6*35
210
Step-by-step explanation:
i’m doing my geometry homework with the equation 1/2h(b1+b2) but i can’t figure this one out. please help
1/2h (b1 + b2) is the formula for finding the area of the figure (trapezoid)
1/2 * 12 (18 + 5 + 12)=
6 * 35=
210 units²
i don’t know how to do this
1-8. For each equation below, find y if x = 2. y=7- |x| a. b. y=x²-1 C. y = √√x+14
The values of the function for x = 2.
for y = 7- |x| ; y = 5for y = x²-1 ; y = 3for y = √x+14; = 4What is defined as the linear equation in two variables?A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers as well as the coefficients of x and y, i.e. a and b, are not equal to zero. A solution this, is a specific point on the graph where when the x-coordinate is multiplied by a and the y-coordinate is multiplied by b, the sum of these two values equals c.Part a: y = 7- |x|
The modulus function returns the magnitude and absolute value of a number, regardless of whether it is positive or negative. The modulus function is represented by y = |x| or f(x) = |x|, where f: R ---> R and x ∈ R.
Put x = 2 in the function;
y = 7- |2|
y = 7 - 2
y = 5
Part b: y = x²-1
put x = 2
y = 2²-1
y = 3
Part c: y = √x+14
Put x = 2
y = √2+14
y = √16
Squaring both side;
y = 4
Thus, the values for the function are obtained.
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Which of the following situations could be represented by a graph with a y-intercept of -8?
A. Hal bought $8 worth of supplies, then sold x buttons for $3 each. His profit is y dollars.
B. Mr. May has 3 sticks left, and each student needs 8 sticks to make their craft project. There are x students, and they need y sticks in all.
C. Kim ran 3 laps clockwise and 8 laps counterclockwise, for a total of 5 miles of the track. The track is x miles long and she ran a total of y laps.
D. Jian bought 8 packs of paper and sold 3 origami swans. His current profit is -$5. A pack of paper costs x dollars and he sells the swans for y dollars.
The situation given that can be represented by a graph with a y-intercept of -8 is A. Hal bought $8 worth of supplies, then sold x buttons for $3 each. His profit is y dollars.
How to use the y-intercept?The y-intercept is a figure in the linear equation that shows the original number of units before the value of x either started to increase or to decrease and therefore cause a change in x.
The situation where Hal bought $8 worth of supplies would be represented by the y-intercept of -8 because the $8 that Hal bought represents his total profit before he sells anything. That total profit is -8 because Hal has spent -$8 but has not sold anything.
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