The two variables are x and y as savings and cost, respectively. The inequality that represents the given sentence is x ≥ 14000 + y.
To represent an unknown number, letters and symbols are used which is known as variables.
The amount of savings and the costs are the unknowns, hence, we can assign a variable to each to represent them.
Let x = savings and y = cost.
Inequality demonstrates the relationship between quantities that are different from each other. The expressions in comparison can be separated by the symbol <, >, ≤, or ≥.
Let x = savings and y = cost.
The given sentence can be expressed as
x ≥ 14000 + y
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4. When triangle ABC is reflected across line AB, the
image is triangle ABD. Why are segment AD and
segment AC congruent?
D
A. Congruent parts of congruent figures are corresponding.
B. Corresponding parts of congruent figures are congruent.
C. An isosceles triangle has a pair of congruent sides.
D. Segment AB is a perpendicular bisector of segment DC.
(From Unit 2, Lesson 1.)
B
C
Corresponding parts of congruent triangles are congruent.
What do you mean by congruency?
In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. Formally speaking, two sets of points are said to be congruent if—and only if—they can be changed into one another by an isometry, which is a combination of rigid movements like translation, rotation, and reflection. This indicates that one item may be exactly aligned with the other object by moving and reflecting it, but not by resizing it. So if we can cut out and then perfectly match up two separate plane figures on a sheet of paper, they are congruent. The paper may be turned over.
Corresponding parts of congruent triangles are congruent.
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NEED HELP!
You are completing a math assessment. The number of questions you complete and the time it takes you to complete them have a proportional relationship, as shown in the table.
Number of Questions 2 5
Time (in minutes) 9 ?
How much time does it take to complete 5 questions?
11 minutes, 30 seconds
22 minutes, 30 seconds
3 minutes
12 minutes
The time taken to complete 5 questions is (option b) 22 minutes, 30 seconds
Given,
The number of questions = 2
Time taken to complete 2 questions = 9 minutes
Now,
The number of questions = 5
We have to find the time taken to complete 5 questions:
We can consider ratio here:
That is,
Number of questions : Time taken to complete
So,
2 : 9 and 5 : x
Lets equate:
2 : 9 = 5 : x
That is,
2x = 5 × 9
Now, divide 2 on both sides:
2x/2 = (5 × 9) / 2
Here,
x = 45/2
Then,
x = 22.5
Converting this into minutes, we get 22 minutes, 30 seconds.
That is,
The time taken to complete 5 questions is (option b) 22 minutes, 30 seconds
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REALLY EASY, WONT TAKE LONG + WILL GIVE BRAINLIEST AND A THANKS !
The order of the scale from smallest to the largest is:
The smallest = 1 inch to 3 yards
The middle : 1 inch to 1.1 yards
The largest : 1 inch to 1 yard
What is the order of the scale?A scale drawing is either a larger or smaller version of a diagram. A scale factor provides information on the unit of conversion between the original image and the scale drawing. A scale factor is the ratio of the length of the scale drawing to the length of the actual drawing.
The first step is to convert the given scale factors to the same units of measurement.
All of the measurements would be converted to yards
1 feet = 3 yards
1 inch to 3 yards
1.1 yards = 1 meter
1 inch to 1.1 yards
1 inch to 1 yard
The smallest = 1 inch to 3 yards
The next : 1 inch to 1.1 yards
The largest : 1 inch to 1 yard
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In a certain state's lottery, 22 balls numbered 1 through 22 are placed in a machine and 5 of them are drawn at random. If the 5 numbers drawn match the numbers that a player had chosen, the player wins $30,000. In this lottery, THE ORDER THE NUMBERS ARE DRAWN DOES MATTER. Compute the probability that you win the prize if you purchase a single lottery ticket.
The probability that you win a prize is 0.00003797372
How to determine the probability that you win a prize?From the question, we have the following parameters:
Sample Space = 1 to 22
This means that
Sample size, n = 22 i.e. the count of numbers from 1 to 22
The count of numbers to be drawn is 5
So, the individual probabilities are
P(1) = 5/22
P(2) = 4/21
P(3) = 3/20
P(4) = 2/19
P(5) = 1/18
The probability of winning is the product of the above
So, we have
p = 5/22 * 4/21 * 3/20 * 2/19 * 1/18
Evaluate
p = 0.00003797372
Hence, the probability is 0.00003797372
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Jennifer went to the mall and spent $120 on new clothes for her job. She bought 3 shirts that each cost the same amount and a pair of pants that cost $59. solve with just the equation
From the equation 3x + 59 = 120, the unit cost of the shirts is $20.33.
What is an equation?An equation is a mathematical statement used to equate two mathematical expressions.
To demonstrate equality, equations use the equation symbol (=).
The total amount spent on new clothes = $120
The number of shirts bought = 3
The cost of the pair of pants bought = $59
Equation of the situation is 3x + 59 = 120,where x = the unit cost of the shirts.
3x + 59 = 120
Subtract 59 from both sides:
= 3x + 59 - 59 = 120 - 59
Simplify both equations:
3x = 61
Divide both sides by 3:
3x/3 = 61/3
x = 20.33
Thus, we can conclude that the equation for the new clothes Jennifer bought at the mall shows that each shirt costs $20.33.
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15 - 700 < 1000?????
The given inequality is true as the value on the right side of the inequality is less than the value on the left side.
What is an equality?
Inequality is a relation which makes a comparison which is non-equal between two numbers or other mathematical .
We are given an inequality 15-700<1000
The left hand side of the inequality on solving becomes,
15-700= -685
Hence the inequality becomes -685<1000
as a negative value is always less than that of a positive values
Hence 15-700<1000
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im stuck pls pls help
Answer:
1) 5x-8
2) 2x(4x+3)
Step-by-step explanation:
Find the slope of the line that passes through the following points:
(1, -3)
(4, 0)
Work Shown:
[tex](x_1,y_1) = (1,-3) \text{ and } (x_2,y_2) = (4,0)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{0 - (-3)}{4 - 1}\\\\m = \frac{0 + 3}{4 - 1}\\\\m = \frac{3}{3}\\\\m = 1\\\\[/tex]
help please i don’t understand
Answer:
The correct option is B.
Find the measure of x.
65°
18
x = [?]
Round to the nearest hundredth.
Enter
Answer: 585
Step-by-step explanation: You can multiply both numbers and divide by 2 to get the answer
Decrease £16870 by 3%
Give your answer rounded to 2 DP.
We have that the Decrease of £16870 by 3% is mathematically given as
P=168193.9=>168193.90 2dp
Arithmetic
Question Parameters:
Decrease £16870 by 3% Give your answer rounded to 2 DP.
Generally the equation for the 3% of 16870 is mathematically given as
X=0.03*16870
X=506.1
Therefore Decrease £16870 by 3% we have
16870 - 506.1
P=168193.9
Answer:
= £16363.9
Step-by-step explanation:
- Decrease is a reduction and can be done only by subtraction in two ways;
Decreasing the percentage first;[tex] = (100 - 3)\% \\ = 97\%[/tex]
- Then multiply the result to the value being decreased;
[tex] = \frac{97}{100} \times 16870 \\ \\ = 16363.9 \: \: euros[/tex]
Decreasing from first principle;[tex] = \frac{3}{100} \times 16870 \\ \\ = 506.1 [/tex]
- Then reduce the original by the result:
[tex] = 16870 - 506.1 \\ = 16363.9 \: euros[/tex]
n(x)=-1-x+4 when x=-2, 0, 5
The value of the function n(x) = -1 -x + 4 when x = -2,0, and 5 are respectively.
Function:
A function is defined as a relationship between a set of inputs having one output each.
It can be represented as f(x).
Given,
Here we have the function
n(x) = -1 -x + 4
And we need to find the value of the function when x takes the values -2, 0 and 5.
To solve this one, then we have to put the value of x on the function and then we have to simplify it in order to get the value of the function.
For that first we have to put the value of x = -2, then we get,
n(-2) = -1 - (-2) + 4
n(-2) = -1 + 2 + 4
n(-2) = -1 +6
n(-2) = 5
Now we have to apply the value of x as 0, then we get the value of function as,
n(0) = -1 - 0 + 4
n(0) = -1 + 4
n(0) = 3
Finally we gave to apply the value of x as 5, then we get the value of n(5) as,
n(5) = -1 - 5 + 4
n(5) = -6 + 4
n(5) = -2
Therefore, the resulting values are 5, 3 and -2.
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The expression 15w+65 factored using the GCF is
THE GCF IN THE EXPRESSION IS 5 MEANING WE ARE GOING TO DIVIDE EACH AND EVERY TERM BY 5 .
[tex] = 5(3w + 13)[/tex]
ATTACHED IS THE SOLUTION
2. Khalid invests $6750 at 8.5% per annum. How much interest
has he earned and what is the total amount in his account after 4 years?
Directions: Simplify the following expressions. Refer to the rules for signed numbers in solving these problems.
Example: - 4 + 5 = +1 (the signs are different, take the difference (subtract) and place the sign of the larger number)
1. + 2 - (+3) =
2. + 11 + (-10) =
3. 3 + (-5 ) =
4. + 22 - 21 =
5. - 8 - (-44) =
6. -12 - (-6 ) + 3 =
7. + 16 -(-12) =
8. - 36 - (-36) =
9. -4 * 10 =
10. -1 * -1 =
11. + 7 * - 7 =
12. -4 / 4 =
13. -7 * -5 =
14. -10 * + 8 =
15. -2 * - 7 =
Step-by-step explanation:
remember, when 2 signs collide (like a mathematical operation and the sign of an operand of that operation), the following is always true (for additions/subtractions and multiplications/divisions) :
+ + = +
+ - = -
- + = -
- - = +
and don't forget : when a number or term is positive, we usually don't write the sign. only the mathematical operation.
1. 2 - 3 = -1
2. 11 - 10 = 1
3. 3 - 5 = -2
4. 22 - 21 = 1
5. -8 + 44 = 36
6. -12 + 6 + 3 = -3
7. 16 + 12 = 28
8. -36 + 36 = 0
9. -4 × 10 = -40
10. -1 × -1 = 1
11. 7 × -7 = -49
12. -4 / 4 = -1
13. -7 × -5 = 35
14. -10 × 8 = -80
15. -2 × -7 = 14
What is What is m∠DHG?
Answer: 72 degrees
Step-by-step explanation: We know that angle DHG and angle EHF are congruent due to the vertical angles theorem. Since these two angle measures are congruent, this also means that the expression 6(x-2) is congruent to 3x+30. To find the angle measure of DHG, we need to find x. We can set these two expressions equal to each other and solve for x.
6(x-2) = 3x+30
6x-12 = 3x + 30
-3x -3x
3x-12=30
+12 +12
3x=42
~divide by 3 on both sides~
x = 14
Now that we know our x variable, we can substitute 14 into the expression for angle DHG.
6(14-2)
6(12)
72.
Answer:
∠DHG = 72°
Step-by-step explanation:
As ∠DHG and ∠EHF are vertical angles, they are congruent.
What are vertical angles?
Vertical angles are formed when two lines intersect, creating opposite angles. Those opposites are congruent (equal).
Equation:
∠DHG = ∠EHF
[6(x - 2)] = (3x + 30)
Step 1: Distribute 6 through the parentheses.
[tex]\implies 6(x) + 6(-2) = 3x + 30[/tex]
[tex]\implies 6x - 12 = 3x + 30[/tex]
Step 2: Subtract 3x from both sides.
[tex]\implies 6x - 3x - 12 = 30[/tex]
[tex]\implies 3x - 12 = 30[/tex]
Step 3: Add 12 to both sides.
[tex]\implies 3x - 12 + 12 = 30 + 12[/tex]
[tex]\implies 3x = 42[/tex]
Step 4: Divide both sides by 3.
[tex]\implies \dfrac{3x}{3} = \dfrac{42}{3}[/tex]
[tex]\implies \boxed{x = 14}[/tex]
Step 5: Substitute the value of x into ∠DHG to find its measure.
[tex]\implies \angle DHG = 6(14 - 2)[/tex]
[tex]\implies \angle DHG = 6(12)[/tex]
[tex]\implies \angle DHG = \boxed{72^\circ}[/tex]
Therefore, the measure of ∠DHG is 72°.
PLEASE HELP PLEASEEE
Answer:
70
Step-by-step explanation:
[tex]56(5/4)=70[/tex]
Part Two:
For any long-distance call T-Mobile charges a base rate of $15 per month plus $0.05 a minute
that you are on the phone, while Verizon charges a base rate of only $10 per month, but charges
$0.10 per minute for long distance calls. Write the equation that represents the total cost for one month of long distance calls for each company, where y is total cost and x is the amount of minutes used:
T-Mobile:
Verizon:
Using an algebraic method, determine how many minutes the two plans will cost the same.
T-Mobile charges a base fee of $15 per month plus $0.05 for each minute. 300 minutes long would you need to call for them to charge the same amount.
Given that,
T-Mobile charges a base fee of $15 per month plus $0.05 for each minute you are on the phone for any long-distance call, while Verizon has a basic rate of only $10 per month but charges $0.10 for long-distance calls.
We have to find how long would you need to call for them to charge the same amount.
We can write the equation as
15+0.05x=0.10x
0.05x-0.10x=-15
-0.05x=-15
0.05x=15
x=15/0.05
x=300 minutes
Therefore, 300 minutes long would you need to call for them to charge the same amount.
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please help me 15 points for helping
a. The rate of change in length of baby grace is 0.75.
b. The linear equation for Baby Grace growth rate in point slope form is y - 20 = 0.75(x - 4)
a. The slope of the line for baby Claire growth is 0.8.
b. Baby girl Claire growth rate is faster than baby girl Grace growth rate.
How to form linear equation and find slope?Let's solve for the growth chart of baby grace.
Therefore,
a.
The rate of change in length of baby Grace can be found as follows:
rate of change = y₂ - y₁ / x₂ - x₁
Hence, using (4, 20)(6, 21.5)
rate of change = 21.5 - 20 / 6 - 4
rate of change = 1.5 / 2
rate of change = 0.75
b . The linear equation in point slope form can be found as follows;
y - y₁ = m (x - x₁)
where
m = slopeTherefore,
y - 20 = 0.75(x - 4)
Let's tackle the growth chart for baby Claire,
a.
slope of the line = y₂ - y₁ / x₂ - x₁
Using (4, 22)(14, 30)
slope of the line = 30 - 22 / 14 - 4
slope of the line = 8 / 10
slope of the line = 4 / 5 = 0.8
b.
Therefore, Baby Claire growth rate is faster than baby Grace.
This is because bay Claire growth rate is 0.8 and baby Grace is 0.75.
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What principal will bring Birr 637 interest at a rate of 7% in 2 years?
The principal with the given simple interest, rate of interest and time period is $4550.
Given that, interest = $637, rate of interest = 7% and time period = 2 years.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
We know that, simple interest = (P×R×T)/100
Put simple interest = $637, R=7% and T=2 years, we get
637 = (P × 7 × 2)/100
⇒ 14P=63700
⇒ P=63700/14
⇒ P= $4550
Therefore, the principal with the given simple interest, rate of interest and time period is $4550.
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Jan is twice as old as Jake. The sum of their ages is 5 times Jake's age decreased by 48.
How old are Jan and Jake?
Answer:
Jake = 24
Jan = 48
Step-by-step explanation:
J = Jan
X = Jake
2x + x = 5x - 48
2x = 4x - 48
-2x = -48
x = 24
Jake = 24
Jan = 48
$8.50 for 1 hrs how much will be for 6 hrs
Answer: 51
Step-by-step explanation:
8.50 x 6 = 51
Answer:
$51
Step-by-step explanation:
Since it's $8.50 per hour. Their asking you how many per 6 hours.
You multiply 8.50 x 6.
8.50 x 6= 51.
Find an equation of the line through the given pair of points.
(-7,-1) and (-2,-8)
Equation of the line through the given pair of points.(-7,-1) and (-2,-8) is
5y ++7x = -54
What is equation of line ?A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system. The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line. Any line's equation can be used to determine whether a given point is on the line or not. A linear equation with a degree of one is the equation for a line.
general equation of line is
[tex](y_{} -y_{1})=\frac{y_{2} -y_{1}}{x_{2} -x_{1}} (x_{} -x_{1})[/tex]
here [tex]x_{1} is -7 \\ y_{1} is -1[/tex]
y +1= [tex]\frac{y_{2} -y_{1} }{x_{2}- x_{1} }[/tex](x+7)
y +1= [tex]\frac{-7 }{5 }[/tex](x+7)
5y +5 = -7x -49
5y ++7x = -54
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Find the value of x and y. Show all of your work or explain how you get your answer.
Answer:
here,
2x=76 (because of adjacent angle)
76/2=x
x=38
again,
x+y=180(because of straight angle)
y=180-38
y=142
What is the slope of line a?
-4
-1/4
4
1/4
The slope of the given line a is found as 4.
What is described as the slope?A line's slope is the ratio of how much y increases even though x increases by some amount. The slope of a line indicates how steep it is, or how far y increases because x increases. The slope is stable (the same) throughout the line.If y is the vertical path on a graph and x is the horizontal direction, therefore this formula is: Slope = (Change in y)/(Change in x)For the given question;
The graph of the given line a is given.
Select any two points from the graph lying on the line.
(x, y) = (1, 1)
(x, y) = (2,5)
Thus, the slope will be;
Slope = m = (y - y)/(x - x)
m = (5 - 1)/(2 - 1)
m = 4/1
m = 4
Thus, the slope of the given line a is found as 4.
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2+22+222+2222+22222?
The answer for 2+22+222+2222+22222 is 24690
Answer:
22222222222
Step-by-step explanation:
222+22+2222+22²22
Please help fast ::: will mark as brainlist for answer
Answer:I think you should multiply by who many
Step-by-step explanation:
so 2.19x and 2.99x
Which plan to prove ∆ABD ≅ ∆CBD CANNOT be used based on the information in the diagram?
A. SSS
b. ASA
c. SAS
D. All of these plans are correct
The plan that cannot be used to prove that the two triangles are congruent based in the given information is: b. ASA.
How to Prove Two Triangles are Congruent?The following theorems can be used to prove that two triangles are congruent to each other:
SSS: This theorem proves that two triangles are congruent when there's enough information showing that they have three pairs of sides that are congruent to each other.ASA: This theorem shows that of two corresponding angles of two triangles and a pair of included congruent sides are congruent to each other.SAS: This theorem shows that if two triangles have two pairs of sides and a pair of included angle that are congruent, then both triangles are congruent to each other.The two triangles only have a pair of corresponding congruent angles, while all three corresponding sides are shown to be congruent to each other.
This means that ASA which requires two pairs of congruent angles, cannot be used to prove that both triangles are congruent.
The answer is: b. ASA.
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What is the equation of this line?
a. y=2/3x
b. y=−3/2x
c. y=−2/3x
d. y=3/2x
Solve for y.
y/4= 5.12
Help me please and ty <3
Answer: y = 20.48
Step-by-step explanation:
To get rid of the denominator under the y you must multiply the entire equation by 4.
y = 20.48
That's all :)
Answer:
20.48 :)
Step-by-step explanation:
To find y you need to do 5.12 multiplies by 4 which is 20.48. Hope this helps <3
