Step 1: Represent a with an unknown
Let a number be x
Step 2: Represent the given information with an equation
From the first statement, the sum of a number and seven is tripled can be represented with the equation below:
[tex](x+7)\times3[/tex]The second statement reflects that the result of the first statement is eight times a number. Eight times a number is
[tex]8\times x=8x[/tex]The result of the first statement and the second statement is
[tex](x+7)\times3=8x[/tex][tex]3x+21=8x[/tex]Step 3: Solve for the unknown
The solution of the unknown is as shown below:
[tex]\begin{gathered} 3x+21=8x \\ \text{collect like-terms} \\ 21=8x-3x \\ 21=5x \\ \text{divide through by 5} \\ \frac{21}{5}=\frac{5x}{5} \\ \frac{21}{5}=x \end{gathered}[/tex][tex]\begin{gathered} \frac{21}{5}=x \\ x=\frac{21}{5} \\ \operatorname{Re}-\text{write as a mixed fraction} \\ x=4\frac{1}{5} \end{gathered}[/tex]Hence, the number is 4 1/5
I need your help please
In order to calculate the price for each brand, calculate the quotient in between the price for n forks over the number of forks, just as follow:
Brand A:
3.89/72 = 0.05
Brand B:
6.62/96 = 0.07
Hence:
Unit price for brand A:
$0.05
Unit price for brand B:
$0.07
PLEASE ANSWER ALL THE QUESTIONS FOR 50 POINTS!!!!!
Answer:
a. 4.2 - 2.8 = 1.4
b. 72.1 - 45.6 = 26.5
c. 82.2 - 41.3 - 29.2 = 11.7
d. 17.1 - 11.7 - 0.8 = 4.6
e. 29.2 - 12.5 - 0.9 = 15.8
f. 21 - 14 = 7
g. 71 - 37 - 18 = 16
h. 50 - 19 - 8 = 23
i. 92 - 57 - 16 = 19
j. 44 - 18 - 9 = 17
HELP ASAP, IM DUE IN 4 HOURS
Rotate DEF 90° clockwise around the origin. Then translate D'E'F' to the right 5units and down 2 units. What are the coordinates of D''E''F''? Show and explain how you arrived at your answer.
Answer below and in attached graph Step by stepShow and explain:1) The rule for a rotation by 90° around the origin is (x,y)→(−y,x) so I moved the y to x and changed the sign, I moved x to y position. 2) to translate 5 units right and 2 units down, you add (+5, -2) to your current coordinates of D’ E’ and F’ giving D’’ E’’ F’’. Pre Image ➡️ D’ E’ F’ ➡️. D’’ E’’ F’’ (+5, -2)D (-5, -2) ➡️ (2, -5) ➡️ (7, -7)E (0, -2) ➡️ (2, 0). ➡️ (7, -2)F (-4, -6) ➡️ ( 6, -4). ➡️ (11, -6)Attached graph of pre image and transformations
Hi may you please help me
The value of x is 85° when a pair of parallel lines intersects another pair of parallel lines.
According to the question,
We have the following information:
A pair of parallel lines intersects another pair of parallel lines.
We have a figure where an angle is given as 85°.
Now, the following theorems would be helpful in finding the value of x:
When a pair of parallel lines is intersected by another line then the sum of two consecutive interior angles is 180°. (1)
When a pair of parallel lines is intersected by another line then the alternate interior angles are equal. (2)
Vertically opposite angles are equal. (3)
(Now, we will refer to these theorems by the number given in the brackets.)
Now, by theorem 3, we have vertically opposite angle as 85°.
Now, its alternate interior angle will also be 85°.
Now, 85° and x° are vertically opposite angles.
So, by theorem 3, we have the value of x as 85°.
Hence, the value of x is 85°.
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In the diagram below line FG is // to line HI, and line segments BC and AD intersect at E.
The measure of angle GBE = 3x+20, and the measure angle ECD = x.
The values of the angle x in the line segments is 40 degrees.
How to find the measure of angle?When parallel lines are are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.
Therefore, the line FG is parallel to line HI. The line segment BC and AD are the transversal lines that cut across the parallel lines FG and HI.
Therefore,
3x + 20 + x = 180 (Same interior angles)
Same interior angles are supplementary. That is the angles sum up to 180 degrees.
Therefore,
3x + 20 + x = 180
4x + 20 = 180
4x = 160
divide both sides by 4
x = 160 / 4
x = 40 degrees
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Find the error in the calculations below, if there is one:
Line (1): -5x/4-7/2<-3/8
Line (2): 10x + 28<-3
Line (3): 10x < - 31
Line (4): x < -31/10
Line (5):
The error occurs in the second line, the correct solution is x > -5/2.
What is inequality?The relation between two unequal expressions is defined as inequality.
Given inequality is -5x/4 - 7/2 < -3/8.
The solution of the inequality is:
-5x/4 - 7/2 < -3/8
10x + 28 > 3
10x > -25
x > -25/10
x > -5/2
Hence, the error occurs in the second line, the correct solution is x > -5/2.
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Two 50 foot tall radio towers are 3000 feet apart. Find the angle of depression from the top of one tower to the base of the other.
Answer:
Explanation:
The diagram representing the two towers is given below:
m=p*Vwe have
p=m/V
Solve for m
That means-----> isolate the variable m
Multiply both sides by V
p*V=(m/V)*V
Simplify
p*V=m
rewrite
m=p*V
Using the properties of equality, the value for m in the equation is: m = pV.
How to Apply the Properties of Equality to Solve for a Variable?For any given equation, to solve for a variable in the equation, we have to isolate the variable to one side of the equation in order to determine its value. To do this, several properties of equality need to be applied to isolate the variable to one side of the given equation.
Given the equation, p = m/V, we need to isolate the variable m to one side of the equation in order to solve for m.
p = m/V
Multiply both sides of the equation by V
p × V = m/V × V [multiplication property of equality]
Simplify the equation:
pV = m
m = pV
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Below is the change received by Julia after buying a magazine.She paid for the magazine using a £10 note. Work out the price of the magazine.
pls provide the picture below, because of that its an incomplete answer
3(x+3)= x +13 ansewr!
Answer: x=2
Step-by-step explanation:
1. Distribute
2. Subtract 9 from both sides
3. Simplify
4. Subtract x from both sides
5. Simplify
6. Divide both sides by the same factor
7. Simplify
Solve the system using linear combination.
41
(5x + 3y
3x - 6y = 9
=
We want to eliminate the variable y. What number should we multiply times the first
equation, so that when we add the two equations, we can eliminate the variable y?
The solution of system of equation is x = 2 and y = 7. We should multiply first equation with 2 so that when we add the two equations, we csystem of equation an eliminate the variable y.
What is system of equation?
Two or more equations that share variables are said to be .
For instance, consider two equations where x and y are shared:
x + y = 6
3x + y = 2
We might be able to solve equations that have the same number of variables. Where the lines intersect in this case is the answer (1,5)
Given system of equation:
5x + 3y = 41,
3x - 6y = 9
Lets multiply the first equation with 2, we get
10x + 6y = 82
Adding these equation with second given equation we get,
10x +6y +(3x - 6y) = 82 + 9
13x = 91
x = 91/13
x = 7
putting the value of x in any one equation
3(7) -6y = 9
y = 2
Therefore, the x and y in the given system of equation are 7 and 2 respectively.
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Jenny love to plant flowers.she has $30 to spend on flower plant flats .find the number of flats she can buy of the cost $4.98 each
Answer:
6
Step-by-step explanation:
We can round $4.98 up to $5.
Then do $30 / $5 = 6
Go back and check if 6 works:
$4.98 × 6 = $29.88 which is less than $30.
So the answer is 6
Select the correct answer from each drop-down menu. a cash card has a starting value of $25. if the card is not used within the first year of its purchase, the value on the card begins to decrease by $2.50 per month. the relationship between the number of months after the first year and the amount remaining on the card is . the independent variable is the . the dependent variable is the .
The equation that represent the relationship between the number of months and the amount remaining on the card is: y = 25 - (2.50x)
a) the independent variable is the: Number of month after the first year
b) the dependent variable is the: Amount remaining on the card
To solve this problem, we have to state the equation using the information of the problem.
Information about the problem:
Starting value= $25Decrease= $2.50 per monthWriting the equation according to the information gave, we have:
y = 25 - (2.50x)
Where:
Amount remaining on the card = yNumber of month after the first year = xThe relationship between the number of months after the first year and the amount remaining on the card is: linear and inverse because when the number of months after the first year increases (x), the amount remaining on the card (y) will decrease.
The "y" variable is the dependent variable, because it will change according to the number of months passed after the first year (x).
The "x" variable is the independent variable, because it doesn't depend on any other value, just the number of months passed after the first year.
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
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Determine the missing number in the equation.
The equation 4 times 7 equals 4 times 10 in parentheses minus 4 times blank
Answer:
The missing number is 3.
Step-by-step explanation:
1. For the sake of the equation, let's represent the missing number as y. Then write the equation: 4*7=(4*10)-4*y
2. Follow according to the order of operations, then you should get the result of 28=40-4y
3. Swap -4y and 28 in the equations: 4y=40-28 which goes to 4y=12.
4. Find y by dividing the rest of the equation by 4: y=3
Silvia has 20 tomato plants and 30 bean plants. She wants to put the plants in rows so that each row has the same number of tomato plants and the same number of bean plants. What is the greatest number of rows Silvia can plant?
The greatest number of rows Silvia can plant as per given number of plants and condition is equal to 10.
As given in the question,
Silvia is going to plant 20 tomato plants and 30 bean plants.
Total tomato plants = 20
Total bean plants = 30
If Silvia would like to plant, the plants in rows where each row has the same number of tomato plants and each row has the same number of bean plants.
Then, the greatest number of rows Silvia can plant is equal to greatest common factor of 20 and 30.
20 = 2×2×5
30 = 2×3×5
Greatest common factor of 20 and 30 = 2×5 = 10
Therefore, the greatest number of rows Silvia can plant as per given number of plants and condition is equal to 10.
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Use the table to answer the question. Number of cases ordered Number of rolls of paper towels 1 12 3 36 5 60 10 120 A restaurant is placing an order for paper towels. The data table shows the amount of paper towel rolls compared to the number of cases. At which ratio in the data table does the constant of proportionality appear? Write your answer as an ordered pair
Paper towels are being ordered by a restaurant. The data table compares the number of cases to the quantity of paper towel rolls. 1:12 ratio does the proportionality constant appear at in the data table.
Given that,
There is a table.
Paper towels are being ordered by a restaurant. The data table compares the number of cases to the quantity of paper towel rolls.
We have to find what ratio does the proportionality constant appear at in the data table.
The table is
Number of cases ordered | Number of rolls of paper towels
1 | 12
3 | 36
5 | 60
10 | 120
Therefore, 1:12 ratio does the proportionality constant appear at in the data table.
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Write an equation of the line through (-3,- 6) having slope17/16Give the answer in standard form.The equation of the line is
The equation of a line in Standard form is:
[tex]Ax+By=C[/tex]Where "A", "B" and "C" are Integers ("A" is positive).
The Slope-Intercept form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
In this case you know that:
[tex]m=\frac{17}{16}[/tex]And knowing that the line passes through the point
[tex]\mleft(-3,-6\mright)[/tex]You can substitute values and solve for "b":
[tex]\begin{gathered} y=mx+b \\ -6=(\frac{17}{16})(-3)+b \\ \\ \\ -6=-\frac{51}{16}+b \\ \\ -6=-\frac{51}{16}+b \\ \\ -6+\frac{51}{16}=b \\ \\ b=-\frac{45}{16} \end{gathered}[/tex]Then, the equation of this line in Slope-Intercept form is:
[tex]y=\frac{17}{16}x-\frac{45}{16}[/tex]Now that you have this equation, you can write it in Standard form as following:
[tex]\begin{gathered} y+\frac{45}{16}=\frac{17}{16}x \\ \\ \frac{45}{16}=\frac{17}{16}x-y \\ \\ \frac{17}{16}x-y=\frac{45}{16} \end{gathered}[/tex]The answer is:
[tex]\frac{17}{16}x-y=\frac{45}{16}[/tex]Find the slope of each line.
1)2x-5y=20
2) 2x-3y=-9
Answer:
1)2/5
2)2/3
Hope this helps!
Answer:
1. m=2/5
2. m-2/3
Step-by-step explanation:
given circle K with diameter IJ and radius KG. GH is tangent to K at G. If GH =6 and KH =8, solve dor KG. Round your answer to the nearest tenth if necessary. If the answer cannot be determined click cannot be determined.
EXPLANATION:
We are given a circle K with radius KG. Note here that line KJ and line KG are both radii of the circle given.
Also we know that a line tangent to a circle at the point of intersecting with the radius forms a 90-degree angle with the radius.
We can now extract the following triangle from the diagram provided;
We now have a right triangle which we shall solve by use of the Pythagorean theorem;
[tex]a^2+b^2=c^2[/tex]Where we have c as the longest side (hypotenuse) and then a and b are the two other sides. Substituting into the equation above now gives us;
[tex]\begin{gathered} a^2+b^2=c^2 \\ KG^2+6^2=8^2 \\ KG^2+36=64 \end{gathered}[/tex]Subtract 36 from both sides;
[tex]\begin{gathered} KG^2+36-36=64-36 \\ KG^2=28 \end{gathered}[/tex]Take the square root of both sides;
[tex]\begin{gathered} \sqrt[]{KG^2}=\sqrt[]{28} \\ KG=5.2915 \end{gathered}[/tex]Rounded to the nearest tenth, the answer is;
ANSWER:
[tex]KG=5.3[/tex]A graph of a linear function has a slope of -1/3 and contains the point (0, 2). Which of these represents the equation of this function?
slope intercept equation is represented below
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} 2=-\frac{1}{3}(0)+b \\ b=2 \\ y=-\frac{1}{3}x+2 \end{gathered}[/tex]Arthur sits in the park reading a newspaper, then starts walking home at a constant pace. He stops for bagels, then walks the rest of the way home. What does the X axis represent. What does the y-axis represent?
Based on the information provided about Arthur, we have the following:
The x-axis of the graph would represent the amount of time that Arthur spends on his way home.The y-axis of the graph would represent the distance covered by Arthur from a reference position (home).What is a graph?In Mathematics, a graph can be defined as a type of chart that is commonly used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis (x-coordinate) and y-axis (y-coordinate).
What is distance?Distance simply refers to the amount of ground that is covered or travelled by a physical object (body) over a particular period of time and speed, irrespective of the physical object's direction, starting point, or ending point.
In conclusion, the distance covered by a physical object (body) over a particular period of time can be plotted by using a position-time graph as shown in the image attached below.
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You have discovered another alien. Find the correct rescue path before answering this question.
When the spaceship starts from a point on the y axis, what is the y-intercept of the line of travel?
the x-coordinate of the spaceship
the y-coordinate of the spaceship
the y-coordinate of the alien
the distance from the spaceship to the alien
From the problem we can get that the y intercept of the line of travel is the y coordinate of the spaceship.
Given,
You have discovered another alien. Find the correct rescue path .
When the spaceship starts from a point on the y axis, we have to find the y intercept of the line of travel.
y-intercept;
A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis. This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.
Here,
From the problem we can get that the y intercept of the line of travel is the y coordinate of the spaceship.
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Use the conditional statement "If it is January, then there is snow." for questic
17. Identify the hypothesis:
18. Identify the conclusion:
Hypothesis: It is January and Conclusion: There is snow
What is hypothesis and conclusion?The initial clause, or "if," of a conditional statement is the hypothesis. The second, or "then," component of a conditional statement is the conclusion. The theory led to the conclusion.
An if-then statement, also known as a conditional statement, is a set of hypotheses followed by a conclusion. As indicated, this is pq. Read this: if p, then q. If the hypothesis is correct but the conclusion is untrue, a conditional statement is false.
Conditionals are in the form if P, then Q.
P is the hypothesis.
Q is the conclusion.
If It is January, then there is snow.
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How many solutions does this equation have?
-7k 2k= -9k
no solution
one solution
infinitely many solutions
Submit
Answer:
1 answer
Step-by-step explanation:
when the terms are collected
[tex]4k = 0[/tex]
[tex]k = 0[/tex]
Find the distance between C & D. C = (8, -3) and D = (-9, -6) CD= [?] Round to the nearest tenth. Hint: Use the distance formula.
The distance between C and D is 17.26 units
What is meant by distance?
Distance is a numerical or qualitative measurement of the distance between two objects or places. Distance can refer to a physical length or an estimate based on other factors in physics or common use (e.g. "two counties over"). Because spatial cognition is a rich source of conceptual metaphors in human thought, the term is frequently used metaphorically to mean a measurement of the amount of difference between two similar objects (such as statistical distance between probability distributions or edit distance between text strings) or a degree of separation (as exemplified by distance between people in a social network). The concept of a metric space is used in mathematics to formalize most such conceptions of measurement, both real and metaphorical.
Distance CD = √{(-9-8)² + (-6+3)²}
= √{(-17)² + (-3)²}
= √{289 + 9}
= √298
= 17.26 units
Hence, the distance between C and D is 17.26 units
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Answer: 17.3
Step-by-step explanation:
solving one step inequalities using addition subtraction multiplication and division
To begin with
we have the inequality
[tex]4>x-2[/tex]To solve
Step 1: we will collect like terms
[tex]4+2>x[/tex]simplify the inequality above
[tex]\begin{gathered} 6>x \\ \text{Re}-\text{arranging} \\ x<6 \end{gathered}[/tex]Hence, the answer is
[tex]x<6[/tex]To draw the shape
Part B is correct
A parabola can be drawn given a focus of (-5, -1) and a directrix of y=7. Write the equation of the parabola in any form.
A parabola with focus of (-5, -1) and a directrix of y=7 has the equation of the parabola as: (x + 5)² = 8 (y - 3)
How to write the equation of parabola with directrix of y = 7 and focus of (-5, -1)Quadratic equation = parabolic equation, when the directrix is at y direction is of the form:
(x - h)² = 4P (y - k)
OR
standard vertex form, y = a(x - h)² + k where a = 1/4p
The focus
F (h, k + p) = (-5,-1)
h = -5
k + p = -1
P in this problem, is the midpoint between the focus and the directrix
P = (-1 - 7) / 2 = -4
p = -4
the vertex
v(h, k)
h = -5
k + p = -1, k = 3
v(h, k) = v(-5, 3)
substitution of the values into the equation gives
(x - h)² = 4P (y - k)
(x - -5)² = 4 * 2 (y - 3)
(x + 5)² = 8 (y - 3)
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17. What are the roots of the equation s² - 7 = 74?
18. One of the roots of x² - 8x = 0 is 8. What is the other root?
paanswer po ngaun
w solution if meron po sana
Answer:
17. s = 9
18. x = 8x^(½)
Step-by-step explanation:
s² - 7 = 74?
s² = 74 + 7
s² = 81
√(s²) = √(81)
s = 9
x² - 8x = 0
x² = 0 + 8x
x² = 8x
√(x²) = √(8x)
x = 8x^(½)
OR by factoring
x²−8x=0
x(x−8)=0
x=0 or x−8=0
x=0 or x=8
Jayden multiples -4yx 1/5y and gets an answer of -4/5y. How can you tell without multiplying that his answer is incorrect
Multiplication is not possible with so similar variables in the denominator, in the given fractions and hence the answer is incorrect.
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions.So, -4y × 1/5y:
The answer to this multiplication is -4/5y.Which is a wrong answer.We can easily observe in the second term that the denominator is 5y and in the 1st term there is no denominator, so 1 will be represented as a denominator.And y will not be present.Hence, multiplication is not possible with so similar variables in the denominator, in the given situation.Theefore, multiplication is not possible with so similar variables in the denominator, in the given fractions and hence the answer is incorrect.
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Percy has $200 in a savings account that earns annually.
How much will he have in total in 1 year?