The length of BD is 9 units when considering the idea of a line segment's midpoint.
What is midpoint of line segment ?A midpoint is a point that lies on a line connecting two other locations and is in the middle of the line. The midpoint is the point on the middle of the line that is equally distant from the two points if a line is drawn connecting the two points. The midpoint is the point B that lies halfway between any two points, let's say A and C. As a result, measuring the length of the line segment and dividing it by two will yield the midway.
According to the given information :
AE = 18, DE = 5
However, D is the middle of CE
CE = 2 × 5 = 10
The line CE will become 10
But AE is the total length of the line segment and it is equal to 18
AE = AC + CE
AC = AE - CE
AC = 8
If AC = 8 , BC = 1/2AC
BC = [tex]\frac{8}{2}[/tex]
BC = 4
The BD becomes BC + CD
BD = 9 units
The length of BD is 9 units when considering the idea of a line segment's midpoint.
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Paige deposited $1,277
in a savings account.
How much would she
have in the account
after 3 years at an
annual simple interest
rate of 4%?
Answer:
Below
Step-by-step explanation:
The original amount + interest
1277 + 1277 * .04 * 3 = 1430.24 dollars
Select the correct number from each drop-down menu to show the values of and y.
The angle x of the triangle is 68 degrees and the side y is 7.5 units.
How to find the angles of a triangle?The triangle ABC is a right angle triangle because it has one angle as 90 degrees. The sum of the angles in the triangle is 180 degrees.
The angle ECD is congruent to angle ACB(vertically opposite angles).
Therefore,
∠ECD ≅ ∠ACB
Hence,
x = 180 - 90 - 22
x = 68 degrees.
using trigonometric ratios, let's find y
cos 22 = adjacent / hypotenuse
sin 22 = 2y - 1 / 15
cross multiply
15 cos 22 = 2y - 1
2y - 1 = 13.9077578185
2y = 13.9077578185 + 1
2y = 14.9077578185
divide both sides by 2
y = 14.9077578185 / 2
y = 7.45387890925
Therefore,
y = 7.5 units
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Does (-4, -1) make the inequality 12x + 9y < 1 true?
yes
Submit
no
The answer for this equation is true.
Putting x=-4 and y=-1,
12(-4) + 9(-1) = -48-9= -57 which is smaller than 1.
What is an equation?
In mathematics, an equation is a formula that expresses equality by connecting two expressions with an equal sign. Equations and their cousins in other languages may have subtly different meanings. For example, in French an equation is defined as containing one or more variables, whereas in English any well-formed expression consisting of two expressions joined by an equal sign is an equation.
To solve an equation involving variables, it is necessary to determine which values of the variables make the equation true. The variables for which the equation must be solved are also called unknowns, and the values of the unknowns that satisfy the equation are called the solution of the equation. There are two types of equations: identities and constraints. The ID applies to all values of the variable. Constraint expressions apply only to specific values of variables.
Therefore, The answer for this equation is true.
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(1, 3) and (-3,-5)
Write a linear equation that passes through the given two points
Answer:
y = 2x + 1
1. Find the slope; (change in y values)/(change in x values)
Slope = (-5 - 3)/ (-3 - 1) = -8/-4 = 2
2. Find the y-intercept (b) using the slope intercept formula: y = mx + b
m = 2 and using point (1, 3) , solve for "b"
y = mx + b
3 = 2(1) + b
3 = 2 + b
1 = b
3. Write the linear equation: y = 2x + 1
Step-by-step explanation:
Write and solve an equation that represents the following math sentence.
Twenty-six equals the sum of 13.5 and the quotient of a number and 2.5.
26 equals 13.5 plus m over 2.5; m = 5
26 equals 13.5 plus m over 2.5; m = 31.25
26 = 13.5 + 2.5m; m = 5
26 = 13.5 + 2.5m; m = 31.25
The equation is 26 = 13.5 + 2.5 m, and the value of m is 5, so option C is correct.
What is equation?Equations are statements in mathematics containing the equals (=) sign flanked on either side by two algebraic expressions. The relationship between the expressions printed on the left and right sides is shown to be equal in this way.
Given:
Twenty-six equals the sum of [tex]13.5[/tex] And the quotient of a number and [tex]2.5.[/tex]
Write the equation in mathematical form,
26 = 13.5 + quotient × 2.5
Assume the quotient is m then,
26 = 13.5 + 2.5 m,
Solve the equation to get the value of m,
26 - 13.5 = 2.5 m,
m = 5
Therefore, the equation is 26 = 13.5 + 2.5 m, and the value of m is 5.
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what numbers when miltiplied equal -120, added/subtracted gives 7?
Numbers when multiplied equal -120, added/subtracted gives 7 .
What is quadratic formula?
The quadratic formula in elementary algebra is a formula that yields the answer to a quadratic problem. In addition to the quadratic formula, additional methods of solving quadratic equations include factoring, completing the square, graphing, and others.
Two equations
x y = 7
x + y = 7
solving for one variable
y = 7/x
applying the one variable
x + 7/x = 7
multiplying both sides by x
x^2 + 7 = 7x
rewriting to a quadratic equation
x^2 - 7x + 7 = 0
applying the quadratic formula
x = 1/2 (7 + square root 21) and y = 1/2 (7 - square root 21)
approximate answer
x ~ 5.79129 and y ~ 1.20871
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what is the answer to –87 × –9 =
help meeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeee!!!!!
Answer:
Step-by-step explanation:
a.) The population is years measured after 2000 so 2000 is 0. Any number to the 0 power is 1 so the population is 23.1 (million).
28.3 = [tex]23.1e^{0.0152t}[/tex]
1.22510823 ≈ [tex]e^{0.0152t}[/tex]
ln 1.22510823 ≈ 0.0152t
t≈13.4 million
This is geometry
Find the missing length indicated
Note: Not drawn to scale
Answer:
? = 9
Step-by-step explanation:
First, deduce the length top part of the left side.
8 - 6 = 2
So, we can now label that top part 2.
Finally, compare the ratios of the sides.
2 : 6 = 3 : ?
2 * (3/2) : 6 * (3/2) = 3 : ?
? = 6 * (3/2)
? = 9
Why do translations produce parallel lines?
Choose the correct answer below.
O A. Translations do not change the y-intercept of the line, so the
original line and the transformed line are always parallel.
OB. Translations do not change the slope of the line, so the
original line and the transformed line are always parallel.
OC. Translations change both the slope and the y-intercept of
the line an equivalent amount, so the original line and the
transformed line are always parallel.
O D. Translations do not change the slope or y-intercept of
the line, so the original line and the transformed line are
always parallel.
Answer:
OB
Step-by-step explanation:
The slopes are not changed.
See the picture of the 2 graphs. The slopes are the same,, but the y intercepts are different, so the lines are parallel.
A solid has volume 6 cubic units and surface area 22 square units. The solid is dilated, and the image has surface area 198 square units.
Answer:
162 units³
Step-by-step explanation:
Original solid:
V = 6 units³
SA = 22 units²
Dilated solid:
V = ?
SA = 198 units²
The ratio of the areas is 198/22 = 9
The ratio of the area is the square of the scale factor.
The scale factor is:
scale factor = √9 = 3
The ratio of the volumes is the cube of the scale factor.
ratio of volumes = 3³ = 27
The dilated volume is:
6 × 27 = 162 units³
Answer: 162 units³
Rectangle jklm is similar to rectangle wxyz . what is the scale factor of a dilation from jklm to wxyz ? enter your answer as a decimal in the box.
If the rectangle JKLM is similar to rectangle WXYZ , then the scale factor is 1.5 .
In the question ,
two rectangle figures are given ,
the rectangles JKLM and WXYZ are similar ,
So , to find the scale we consider the ratio of the sides of the rectangle .
the ratio of the sides is ⇒ ZW/JM = WX/JK
Substituting the values of ZW = 13.5 , JM = 9 , WX = 18 and JK = 12 ,
we get ,
13.5/9 = 18/12
⇒ 1.5 = 1.5
So , the rectangles are similar and the scale factor is = 1.5 .
Therefore , the scale factor is 1.5 .
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You have leased production space that is 275 ft x 200 ft. The property owner charges $5 per square foot to calculate the annual cost. How much is the annual cost?.
The annual cost is $275,000.
What is annual cost ?
Annual Costs refers to the sum of 1) Authorized Services for each Fiscal Year. 2) Administrative Costs; 3) any sums required to make up for actual or anticipated Special Tax Delinquencies for the current or preceding Fiscal Year.
The charge per square foot is $5.
The total square feet leased
=275ft x 200ft
=55,000 square ft.
The total cost of the annual rent is
=55,000 x $5
=$275,000
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√3x +2=3√2x-2
Solve for X
The value of x for the given expression is, x = 4 / (3√2 - √3).
What is solving an equation?
A General Rule for Equation Solving:
Simplify each side of the equation by removing parentheses and combining like terms.
To separate the variable term on one side of the equation, use addition or subtraction.
To find the variable, use division or multiplication.
Given;
√3x + 2 = 3√2x - 2
⇒
3√2x - √3x = 2 + 2
(3√2 - √3)x = 4
Divide both sides by 3√2 - √3
⇒ x = 4 / (3√2 - √3)
Hence, the value of x for the given expression is, x = 4 / (3√2 - √3).
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Let’s say that Charlotte wants to have money left over after buying the concert ticket. Complete the statement to write an inequality that represents Charlotte having money left over after buying the ticket.
The inequality that represents Charlotte having money left over after buying the ticket. is
8m + 20 < 68
What is inequality?Inequality is a means of representing the relationship existing between the left hand side and right hand side of equations, using other terms aside exactly using only "equal to"
Having left over means that the the cost of the ticket should be less than the amount Charlotte has
Therefore, 8m + 20 should be less than 68 and this represented by
8m + 20 < 68
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Use the model to answer the question.
Two 10 by 10 grids are connected, creating a rectangle with 20 columns. 1 columns are shaded. 4 rows are shaded. 8 squares are in the overlap.
Which is the missing factor that makes the equation true?
___ × 0.4 = .08
A. 0.02
B. 0.2
C. 2
D. 20
Answer:
D
Step-by-step explanation:
if u calculate 20×0.4 it will give you 8
the 0 before 8 is insignificant
Answer:
B. 0.2
Step-by-step explanation:
(?) x 0.4 = .08
Reverse math
.08 divided by 0.4
A bin at a department store contains blue and red blankets. The ratio of blue blankets to red blankets is 4 to 1. What percent of the blankets in the bin are blue?
The percentage of the blue blanket will be 25%.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that a bin at a department store contains blue and red blankets. The ratio of blue blankets to red blankets is 4 to 1.
The percentage of the blue blanket will be calculated as,
Percentage = 1 / 4
Percentage = 0.25
Percentage = 0.25 x 100 = 25%
Therefore, the percentage of the blue blanket will be 25%.
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Which of the following equations describes the graph shown below?
(1) y = log5 x
(3) y = log, x
(2) y = log₂ x
(4) y = log₁ x
The graph shown in the question is representing the equation y = log x, so option 3 is correct.
What is a graph?A collection of objects is arranged in a graph, where some object pairings are conceptually "linked." Each pair of connected vertices is referred to as an edge, and the objects are represented by mathematical abstractions known as vertices.
Given:
The graph is shown in the image,
Put the value of x and y from the graph to the equation as shown below,
x = 1, y = 0
Put in option 1,
y = log5 x
0 = log5
0 = 0.69
Again, put in option 2,
y = log x
0 = log1
0 = 0
Hence, it is the correct option.
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Sally is going to furniture shopping using her credit card. if her credit card has a limit of $2000 and she is currently holding a balance of $763 how much can she afford to spend on Furniture?
make an inequality.
She can spend a maximum of $2763.
How to calculate how much can she afford to spend on Furniture?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.
The credit card works as there can be a negative balance in the card. For example if Sally has a shortage of money and she is in need of some, she can take money from her credit card and then repay it later.
Sally already has $763 in her possession in this situation, and her credit card can only have a $2000 balance.
So Sally can spend $763 which she already has in her hand and then spend a maximum of $2000 using her credit card.
Given,
credit card limit = 2000
current balance = 763
2000+763=2763
So She can spend a maximum of $2763.
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6. Danielle wants to construct different triangles with angle measures of
90°, 45°, and 45°, but she was only able to draw the triangle shown
at the right.
What mistake might Danielle have made?
Danielle didn't change the length of triangle then he draw that infinite triangles with given measure.
What is right triangle?
A right triangle is a triangle with one angle at a right angle, meaning that two of its sides are perpendicular. It is also known as a right-angled triangle, an orthogonal triangle, or more commonly as a rectangled triangle. Trigonometry's foundation is the right triangle's relationship between its sides and other angles. it.
Given:
Danielle wants to construct different triangles with angle measures of
90°, 45°, and 45°. She was only able to draw the triangle shown at the right.
She did not consider that the triangle could be enlarged or reduced, while keeping the same angle measures, to make a different triangle.
Hence, Danielle didn't change the length of triangle then he draw that infinite triangles with given measure.
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can u tell me answer I can't cause my trial is over
Answer:
no your trail is not over
Which equation is written in slope-intercpet form and has a slope of -5 and a y intercept of 5?
The equation written in slope-intercept form withn a slope of -5 and a y-intercept of 5 is y = -5x + 5
What is an intercept?intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.
equation of straight line in slope intercept form is given as
y = mx + c
where m = slope and c = y-intercept
from the question, it means m = -5 and c = 5
substituting we have,
y = -5x + 5
In conclusion, the equation in slope-intercept form is y = -5x + 5
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please help:
find m<t explain your reasoning
The value of m∠T in the triangle is 65°
How to find m∠T in the triangle?
The congruence of any two figures is generally understood as two figures which can perfectly overlap each other. Congruent triangles are triangles that are perfect copies of one another.
Given: ΔABC and ΔRST
If the two triangles ABC and RST are arranged, two angles and a side of one are respectively equal to two angles and the corresponding side of the other (AAS). Thus, the triangles are congruent. This implies:
∠A = ∠R, ∠B = ∠S, |AB| = |RS| .Also, ∠C = ∠T, |AC| = |RT| and |BC| = |ST|
Thus, <R = 41°, ∠S = 74°,
<R + ∠S + ∠T = 180° (Sum of angle in a triangle)
41 + 74 + ∠T = 180
115 + ∠T = 180
∠T = 180 - 115
∠T = 65°
Therefore, m∠T = 65°
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Destiny buys a duffel bag priced at $38. Shipping and handling are an additional cost, of 10% of the price. How much shipping and handling will Destiny pay?
Answer: 41.8
Step-by-step explanation:
38 x 0.10 = 3.8
3.8 + 38 = 41.8
41.8
A scientist measures the distance in feet between animals and surface of a pond. positive number represents distance above the surface and negative numbers represent decent below the surface. A fish is located at -1/2 foot. a snail is located at the opposite of -1/2 foot what number is represents the location of the snail in feet
A number which represents the location of the snail in feet is 1/2 feet.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
Note: The opposite of a given number on a number line is the number on the other side of zero (0) and the same distance from zero (0).
Based on the information provided above, we can reasonably infer and logically deduce that the snail is located at the opposite of -1/2 foot on the number line. Therefore, the opposite of -1/2 foot would be 1/2 foot.
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A couch is on sale for $81.60, which is 24% off the original price
What’s the original price?
Answer: It should be $101.18
Step-by-step explanation:
You would basically subtract the 81.60 to the 24% making it 19.58. then from the 19.58 you add the 81.60 and there you go!
Rebekah manages a yoga studio that charges each customer a one-time initial fee of \$35$35dollar sign, 35 and an additional fee of \$12$12dollar sign, 12 per class taken. Rebekah's goal is for each customer to spend at least \$100$100dollar sign, 100 at the studio, and she wants to know the minimum number of classes a customer needs to take to meet that goal. Let ccc represent the number of classes a customer takes. 1) which inequality describes this scenario?.
The required inequality that represents the given situation is 35+12C≥100.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.
Both mathematical phrases, equations, and inequalities are created by connecting two expressions.
The equal sign (=) indicates that two expressions in an equation are believed to be equivalent.
The symbols >,<, ≥, ≤ or ≠ indicate that the two expressions in inequality are not always equal.
So, initial payment = $35
$12 in additional fees for each class
The minimum goal is $100.
There are C classes in total.
Minimum target: One-time starting charge + (Additional fee per class) x (Number of classes)
The scenario's inequality is as follows:
35 + 12C ≥ 100
Therefore, the required inequality that represents the given situation is 35+12C≥100.
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4x + y = -7 solve for y
Answer: -7
Step-by-step explanation:
First, simplify the equation and make y isolated.
4x + y = -7
y = -7 - 4x
Plug in 0 for x.
y = -7 - 4(0)
y = -7
A popular act commands $250,000 for a single appearance plus 20% of ticket sales and 10% of concession receipts. If ticket sales are $1,250,000 and concession receipts are $400,000, what will the act be paid for their performance?.
The required will the act be paid for their performance is $540,000.
Explain percentage.In mathematics, a percentage is a number or ratio that can be communicated as a negligible portion of 100. In the event that we need to compute percent of a number, partition the number by the entire and duplicate by 100. Consequently, the rate implies, a section for every hundred
How will the act be popular paid for their performance?The total amount that should be paid is the sum of the single appearance fee, the 20% of ticket sales and the 10% of concession receipts.
We have,
single appearance = $250,000
sales =$1,250,000
concession receipts = $400,000
Total amount = single appearance + (10% of sales) + (10% ofconcession receipts)
Then,
Total amount = $250,000 + (20% x 1,250,000) + (10% x $400,000) = $540,000
Thus, required total amount is $540,000.
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The quotient of a number, 2, and 21 is 42.
Which equation and value of & represent this relationship?
The equation will be written as (42/2) = 21.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the quotient of a number, 2, and 21 is 42. The equation of the quotient will be written as,
42 / 2 = 21
Here the value 42 when divided by 2 will give 21.
Therefore, the equation will be written as (42/2) = 21.
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