Answer: 14
Tap to view steps...
Step-by-step explanation:
Explain how you can use a table or graph to find the y-intercept.
The y-intercept is calculated using a table or a graph by substituting x = 0.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
The y-intercept value is calculated when the x-coordinate is zero.
Now,
Example:
(0, 3), (0. 5), (0, 7) are all y-intercepts of the graph.
Thus,
The y-intercept is calculated when x = 0.
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Draw 2 isosceles triangles ABC and DEF where AC=BC and DF=EF
The conclusions reached in steps 4 and 5 are invalid. This is a flawed argument for the existence of isosceles triangles.
An isosceles triangle contains what?An isosceles triangle has two equal sides and two equal angles as a result. The term comes from the Greek words iso (same) and skelos (leg). An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal.
Each step is valid, but the conclusion is not. At the end of step 4,
here are a series of isometric maps that lead A to D and C to F, as claimed..
After the final rotation in Step 5, the sequence of isometries takes B to E and C to F —but here’s the hitch—there is no reason why it should still take A to D, in fact it can’t take A to D unless the rotation angle is zero.
If the rotation angle in Step 5 is zero, then the isometries take [A,B,C] to [D,E,F] and the two triangles are indeed similar
But this requires the dilation in Step 2 to have made A′B′ congruent to DE , in other words, it requires assuming the triangles are similar before performing any of of the transformations.
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Question:
This is an invalid proof that all isosceles triangles are similar. Explain which step is invalid and why. 1. Draw 2 isosceles triangles ABC and DEF where AC = BC and DF = EF. 2. Dilate triangle ABC to a new triangle A'B'C' using center C and scale factor DF/AC so that A'C= BC - DF = EF. 3. Translate by directed line segment CF to take A'B'C' to a new triangle A" B" F. Since translation preserves distance, A"F = A'C=DF and B" F = BC = EF. 4. Since A"F=DF, we can rotate using center F to take A" to D. 5. Since B" F = EF, we can rotate using center F to take B" to E. 6. We have now established a sequence of dilations, translations, and rotations that takes A to D, B to E, and C to F, so the triangles are similar.
Trigonometric Identities (HELP)
Use the Reciprocal and Quotient Identities for 1&2
1: Find cscX if sinX= 2√5/5
2: Find cosA if tanA= √2/2 and sinA= -√3/3
Use the Pythagorean Theorem identities for 3&4
3: Find sinX if cotX= -√3/2 and cosX < 0
4: Find cotθ if cosθ= 1/7 and sinθ < 0
Use the cofunction and even-odd identities for 5&6
5: Find tan(-x) if cot(π/2 -x)= -1.84
6: Find cos(θ-π/2) if sinθ= -0.57
Simplify the Trigonometric expressions
7: secX ⋅ sin^2X + cosX
8:(sinθ + 1)(tanθ - secθ)
Prove the Trigonometric expression
1+sec^2X / 1+tan^2X= 1+cos^2X
1: cscX = 1/sinX = 5/2√5.
2: Using the reciprocal identity of tanA and sinA,
tanA/sinA = 1/cosA
√2/2 / -√3/3 = 1/cosA
-2√2/2√3 = 1/cosA
cosA = -2√3/2√2.
What are the responses to other questions?3: Using the Pythagorean theorem, sinX = √(1 - cos^2X)
√(1 - cos^2X) = √((1/cot^2X) - 1) = √((√3/2)^2 - 1) / (-√3/2)
sinX = √2/2.
4: Using the Pythagorean theorem,
cotθ = cosθ / sinθ = 1 / tanθ = 1 / (√(1 - cos^2θ) / cosθ) = cosθ / √(1 - cos^2θ) = 1 / (√(1 - (1/7)^2)) = √(48) / 7.
5: Using the cofunction identity, tan(-x) = -tan(x).
Using the identity that tan(π/2 -x) = cot(x),
-tan(x) = -1/cot(π/2 -x) = -1/(-1.84) = 1.84.
6: Using the even-odd identity, cos(-θ) = cos(θ), and
sin(-θ) = -sin(θ),
cos(θ-π/2) = cosθcos(π/2) + sinθsin(π/2) = 0cos(π/2) + (-0.57)sin(π/2) = -0.57.
7: Using the identity sin^2X + cos^2X = 1,
secX ⋅ sin^2X + cosX = secX ⋅ (1 - cos^2X) + cosX = secX - secXcos^2X + cosX = secX + cosX.
8: Using the identity 1 + tan^2θ = sec^2θ,
(sinθ + 1)(tanθ - secθ) = (sinθ + 1)(tanθ - 1/cosθ) = (sinθ + 1)(tanθcosθ - 1) = (sinθ + 1)sinθ(tanθ/sinθ) - (sinθ + 1) = sinθ + sin^2θ - sinθ - 1 = sin^2θ - 1.
Proof:
Using the identity tan^2X = sin^2X / cos^2X,
1+sec^2X / 1+tan^2X = (1 + 1/cos^2X) / (1 + sin^2X / cos^2X) = cos^2X / (cos^2X + sin^2X) = cos^2X / (1) = 1 + cos^2X.
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If a figure is dilated by a factor of 3, the sides of the pre-image will be _ of the image's sides.
A. one-ninth the size
B. one-third the size
C. nine times the size
D. three times the size
Instructions Type an essay response to the following prompt. Completely explain all parts of your response and use the rubric to determine what you need to include in your essay. 1) In your own words, write a definition for sales tax. 2) If you buy a meal from a restaurant that costs $15.00, and the tax is 7%, how much do you pay in taxes? - Explain in detail, the steps you would take to solve this sales tax question.
1) The sales tax is an additional rate that is paid along with the cost of the meal.
2) The amount paid in taxes for a meal costing $15.00 and a rate of 7% is given as follows: $1.05.
How to obtain the sales tax?The sales tax is obtained applying the proportions in the context of this problem.
A proportion is applied as the sales tax is obtained with the multiplication of the cost of the meal by the decimal equivalent of the percentage of tax.
The decimal equivalent for a percentage of 7% is given as follows:
7/100 = 0.07.
Hence the amount of tax paid is given as follows:
0.07 x 15 = $1.05.
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ENRICHED: A random number generator is used to generate one integer between 70 and 200. Let J be the event of generating a multiple of 25, and let K be the event of generating a multiple of 70. What are the possible outcomes of each event?
J={ }
K= { }
J U K{ }
The possible outcomes for each event are given as follows:
J = {75, 100, 125, 150, 175, 200}.K = {70, 140}J U K = {70, 75, 100, 125, 140, 150, 175, 200}.How to obtain the possible outcomes for each event?
Event J is composed by the multiples of 25 that are between 70 and 200, hence we start at 75, as 25 x 3 = 75, and then keep adding 25 until we reach 200, as follows:
J = {75, 100, 125, 150, 175, 200}
Event K is composed by the multiples of 70 that are between 70 and 200, hence we start at 70, as 70 x 1 = 70, and then keep adding 70 until we reach 200, as follows:
K = {70, 140}.
The union set is composed by the elements that belong to at least one of these two sets, hence:
J U K = {70, 75, 100, 125, 140, 150, 175, 200}.
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Can someone please help?
Answer: The annual premium for a 27-year-old female purchasing a 20-Year Endowment insurance policy with a face value of $25,000 is $42.67.
Step-by-step explanation:
A medical study is conducted to determine which migraine treatment, A or B, provides faster relief. The study uses 10 volunteers who claim to suffer from migraines. Half of the volunteers are randomly assigned to use treatment A when they experience their first migraine. The other half are assigned to use treatment B. Then, after no treatment for one month, the treatments are reversed. The volunteers each record the amount of time it takes, in minutes, to experience relief from their migraine under each treatment. The data are displayed in the table. A 3-column table with 10 rows. Column 1 is labeled volunteer with entries 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Column 2 is labeled Treatment A with entries 10, 13, 13, 9, 13, 12, 14, 10, 8, 7. Column 3 is labeled Treatment B with entries 19, 18, 19, 15, 20, 16, 16, 16, 13, 17. What is the mean difference (A – B) and the standard deviation of the differences?
I think that it could be b but I'm not 100 percent sure
Kendall wants to use a credit card to purchase new furniture. His standard
APR is 22.65%, but his credit card is offering a promotional rate of 3% for six
months. The cost of the furniture, including sales tax, is $1,014. Assume that
Kendall has a previous unpaid balance, and his monthly payments apply to that
balance. How much will the promotional rate save Kendall in finance charges
during the six-month period?
Answer:
$199.98
Step-by-step explanation:
To calculate the amount that Kendall will save in finance charges during the six-month promotional rate period, we need to calculate the finance charges he would have incurred with his standard APR and then compare it to the finance charges he will incur with the promotional rate.
First, let's calculate the monthly finance charges with the standard APR. To do this, we need to know the average daily balance for each month. Assuming Kendall has a previous unpaid balance, let's say it is $500. And assuming he makes no other purchases, his average daily balance for each month would be:
$1,014 + $500 = $1,514The finance charges for each month with the standard APR would be:
$1,514 * (22.65/100) / 12 = $38.37
So, the total finance charges for the six-month promotional rate period with the standard APR would be:
$38.37 * 6 = $230.22
Next, let's calculate the finance charges with the promotional rate:
$1,514 * (3/100) / 12 = $5.04
So, the total finance charges for the six-month promotional rate period with the promotional rate would be:
$5.04 * 6 = $30.24
Finally, we can calculate the amount that Kendall will save in finance charges during the six-month promotional rate period:
$230.22 - $30.24 = $199.98
Therefore, Kendall will save $199.98 in finance charges during the six-month promotional rate period.
U= (1,2,3,4,5,6,7,8,9)
A=(1,2,5,6)
B=(2,3,4,6,7)
C=(5,6,7,8
Find (B’ n A) u c
Answer:
[tex](B'\cap A)\cup C=\{1,5,6,7,8\}[/tex]
Step-by-step explanation:
[tex]B'=\{1,5,8,9\}[/tex]
[tex](B'\cap A)=\{1,5\}[/tex]
[tex](B'\cap A)\cup C=\{1,5,6,7,8\}[/tex]
The complement of a set, notated with a prime symbol ('), are all other elements that are not in that set.
The intersection of two sets, notated by [tex]\cap[/tex], are just the elements that are contained in both sets.
The union of two sets, notated by [tex]\cup[/tex], are all the elements that are contained in both sets (any duplicates are not included).
(100 POINTS!) The measures of the exterior angles of an octagon are x°,2x°,3x°,4x°,5x°,6x°,7x°, and 8x°. Solve for X.
[tex]\textit{sum of all exterior angles in a polygon}\\\\ S=360^o \\\\[-0.35em] ~\dotfill\\\\ x+2x+3x+4x+5x+6x+7x+8x=360\implies 36x=360 \\\\\\ x=\cfrac{360}{36}\implies x=10[/tex]
Answer:
The exterior angles of an octagon add up to 360°. So, 8x° = 360°, and x = 45°.
On a math test there are multiple choice questions worth 4 points and open ended questions worth 6 points. Mr pills' first period class won a competition. and each student has 10 extra credit points added to their test score.
a. If Mai answered 13 mu tipple choice questions correctly and earned a total score of 92. how many open ended questions did she answer correctly?
b. If priya answered 4 open ended questions correctly and earned a total score of 94,how many multiple choice questions did she answer correctly?
c. Write an expression that will represent a students' score in first period who answers m multiple choice questions and e open ended correctly
A: Mai answered 5 open-ended questions correctly,
B: Priya answered 15 multiple-choice questions correctly,
C: expression for the condition is y = 10 + 4a + 6b.
What is a linear equation?Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
Both linear equations with one variable and those with two variables exist.
Given points on each multiple choice question = 4
points on each open-ended question = 6
extra credit for winners = 10 points
A. If Mai answered 13 multiple-choice questions correctly and earned a total score of 92,
the total score of multiple choice questions = 13*4
the total score of multiple choice questions = 52
score left = 92 - 52 - 10 (reducing 10 for extra points)
score left = 30
open-ended questions she answers correctly = 30/6
open-ended questions she answers correctly = 5
B: If Priya answered 4 open-ended questions correctly and earned a total score of 94,
the total score of open-ended questions = 4*6
the total score of open-ended questions = 24
the score left = 94 - 24 - 10 (reducing 10 for extra points)
score left = 60
multiple choice questions she answers correctly = 60/4
multiple choice questions she answers correctly = 15
C: an expression that will represent a student's score in first period,
let y be the total score,
a be the number of multiple choice questions answered,
the total score of multiple choice questions = 4a
and b be the number of open-ended questions answered,
the total score of open-ended questions = 6b
expression is,
y = 10 + 4a + 6b (adding 10 for extra points)
Hence Mai answered 5 open-ended questions correctly,
Priya answered 15 multiple-choice questions correctly,
and expression is y = 10 + 4a + 6b.
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Divide. (54t2−81t)÷(9t)
Answer:
The answer is 6t-9. This can be calculated by dividing the numerator (54t2−81t) by the denominator (9t). This gives 6t-9.
Step-by-step explanation:
Answer:
81t2+16
Step-by-step explanation:
(9t-4)(-9t-4) : Equation
Distribute parentheses using:(a + b)(c + d) = ac + ad + bc + bd.
Where : a=9t, b=-4, c=-9t, d=-4.
This leads to 9t(-9t) +9t (-4) -4- (9t) -4 (-4).
Now we have to Apply minus-plus rule.
Where: -(-a)=a.+(-a)=-a
-9t.9t - 9t.4 + 4.9t = 4.4
=81t2+16
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Eli's basketball team is having a Free-Throw Challenge in order to raise money for new uniforms. Eli's grandma pledges to give $10 as well as $2 for every free throw he makes. Which equation represents how much money (M) Eli's grandma will give depending on how many free throws (f)
Eli makes?
Answer:
M = 10 + 2f
Step-by-step explanation:
Please see the attachment for detail explanation
Find the perimeter of the figure.
Answer:
30
Step-by-step explanation:
Add all the sides and you get 30.
Hope this helps! Pls give brainliest!
Answer:
30
Step-by-step explanation:
6+9.5+6.5+4+4 = 30
Please solve for in this equation
Answer:
x = 4 rounded to the nearest whole number (actually 4.0801)
Step-by-step explanation:
The triangle formed by the sides of length 0.9x, 2.8x and 12 form a right triangle with the side of length 12 as they hypotenuse
By the Pythagorean theorem
c² = a² + b² where c = hypotenuse, a and b being the other two sides
Plugging in values we get
12² = (0.9x)² + (2.8x)²
144 = 0.81x² + 7.84x² = 8.65x²
Switching sides:
8.65x²= 144
x² = 144/8.65 = 16.6473
x = √16.6473= 4.0801
Rounded to the nearest integer, x = 4
The equation and the graph represent two functions. Use the equation y=4 and the graph to answer the questions.
When x is 4, is the output of the equation or graph greater?
What value for x produces the same output in both the graph and the equation?
When x is 4, the output of the equation is greater.
The value for x that produces the same output in both the graph and the equation is equal to 6.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).
Generally speaking, the graph of any proportional relationship such as the linear equation (y = 4) is characterized by a straight line that crosses the y-coordinate as shown in the image attached below.
By critically observing the graphs of the equations, we can reasonably infer and logically deduce that they both would produce the same output (dependent value or y-value) at the ordered pair (4, 6).
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A rectangular prism has a volume of 120 in³. What is the height of the prism? What is the
surface area of the prism?
Show your work.
Given that the volume of the rectangular prism is 120 cubic inches, we can write the equation:
l * w * h = 120
where l, w, and h are the length, width, and height of the prism, respectively.
Since the length is 3 and the width is 10, we can plug in these values into the equation:
3 * 10 * h = 120
Solving for h, we get:
h = 120 / (3 * 10) = 120 / 30 = 4
So the height of the rectangular prism is 4 inches.
To find the surface area of the rectangular prism, we can add up the areas of all six faces:
2 * l * w + 2 * w * h + 2 * h * l
Plugging in the known dimensions, we get:
2 * 3 * 10 + 2 * 10 * 4 + 2 * 4 * 3 = 60 + 80 + 24 = 164 square inches
So the surface area of the rectangular prism is 164 square inches.
Answer: Hight 4 inch, surface area 164 square inch
Step-by-step explanation: multiply with l * w * h
* = x
Demarco and Tanya have received information about three separate mortgage offers. In two or three paragraphs, describe your recommendation for the best financial choice in their situation. Evaluate each of the three offers, compare and contrast their effectiveness, and explain the offer that works best. As you explain your answer, support it using reasons and evidence from the calculations you made based on the information provided in this guide for Analyzing Mortgage Options. pls try to be original
Best Mortgage Option 3 because this mortgage option offers a lower interest rate.
Why Option 3 was recommendedAfter reviewing all three mortgage options available to Demarco and Tanya, I would recommend that they choose option 3. This option offers a lower interest rate compared to the other two options and a longer loan term, which means that their monthly payments will be lower and more manageable for their budget. Additionally, option 3 offers a fixed interest rate, which provides them with more stability and predictability in their mortgage payments, as opposed to options 1 and 2 that offer adjustable interest rates.
Option 1 has the highest interest rate and the shortest loan term, making their monthly payments the highest of all three options. Option 2 offers a slightly lower interest rate, but it still higher compared to option 3, and has a shorter loan term compared to option 3, making their monthly payments still relatively high.
In conclusion, the best financial choice for Demarco and Tanya would be option 3. Its lower interest rate, longer loan term, and fixed interest rate make it the most affordable and stable option for them in the long run.
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The manager of a store that specializes in selling tea decides to experiment with a new blend. She will mix some Earl Grey tea that sells for $6 per pound with some Orange Pekoe tea that sells for $4 per pound to get 200 pounds of the new blend. The selling price of the new blend is to be $5.50 per pound, and there is to be no difference in revenue from selling the new blend versus selling the other types. How many pounds of the Earl Grey tea and Orange Pekoe tea are required?
The amount of Earl Grey tea to mix is 225 pounds.
The amount of Orange Pekoe tea to mix is 75 pounds.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let x be the amount of Earl Grey tea to mix.
So, the amount of Orange Pekoe tea to mix = 300-x
then, 6x+4 (300-x) = 5.5 x 300
6x+1200-4x=1650
2x=450
x=225
and, amount of Orange Pekoe tea to mix = 300-225=75
Thus, the amount of Earl Grey tea to mix = 225 pounds
and, the amount of Orange Pekoe tea to mix=75 pounds.
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Is j = 1 a solution to the inequality below? 4 > j
Answer:
yes
Step-by-step explanation:
4 > j ( substitute j = 1 )
4 > 1 ← is a true statement
so j = 1 is a solution to the inequality
Amy will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $40 and costs an additional $0.70 per mile driven. The second plan has no initial fee but costs $0.90 per mile driven.
For what amount of driving do the two plans cost the
same?
What is the cost when the two plans cost the same?
The two plans cost the same when the amount is $200.
What are equations?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
Let us suppose the miles driven = x.
Given that,
The first plan has an initial fee of $40 and costs an additional $0.70 per mile driven. This is represented as:
A = 40 + 0.70x
The second plan has no initial fee but costs $0.90 per mile driven.
B = 0.90x
The two plans cost the same when A = B:
40 + 0.70x = 0.90x
40 = 0.90x - 0.70x
40 = 0.20x
x = 200
The two plans cost the same when the amount is $200.
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3 over 5 meters =. centimeters
Answer:
60
Step-by-step explanation:
3/5 = 0.6 meters = 60 cm
A small fair charges different admission for adults and children; it charges $2.75 for adults, and $0.25 for children.
On a certain day, the total revenue is $6,962.50 and the fair admits 4900 people.
How many
adults and children were admitted?
Answer: Let's call the number of adults admitted "A" and the number of children admitted "C". We know that:
A + C = 4900 (total number of people admitted)
And the total revenue is:
2.75A + 0.25C = $6,962.50
We can use the first equation to solve for one of the variables in terms of the other:
C = 4900 - A
Substitute this expression for C into the second equation:
2.75A + 0.25(4900 - A) = $6,962.50
Expand and simplify the right side:
2.75A + 1225 - 0.25A = $6,962.50
2.5A = 5737.5
Solve for A:
A = 2298
So there were 2298 adults and 4900 - 2298 = 2602 children admitted.
Step-by-step explanation:
write the following expression in terms of logs of x, y and z: log x√√x/z
The equation in terms of log(x), log(y) and log(z) is,
log x + 1/4 log y -1/2 log z.
What is logarithmic expression?A logarithmic equation is one in which a variable-containing expression's logarithm is used as a solution. If you can write both sides of the equation as powers of the same number, that will help you answer exponential equations.
here, we have,
log x√√y/z = log(x√(√y)/z)
Consider, the given logarithmic expression,
we get,
By using the logarithmic rule: log(ab) = log(a) + log(b)
So, log(x√(√y)/z)
=logx + log(√(√y)/z)
=log x + 1/2 log (√y)/z
=logx + 1/2 log (√y) - 1/2 log z
= log x + 1/4 log y -1/2 log z
Hence, the expression in terms of x , y and z is, log x + 1/4 log y -1/2 log z.
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What is the range of the function shown on the graph above?
From the graph the range of the function is obtained as option 1: -5 ≤ y ≤ 8.
What is the range of data?
The range of data is defined as a measure of the difference between the maximum value of data and the minimum value of data.
From the graph, the following observations are made -
The endpoints of the graph have closed circles this means that, the endpoints are inclusive of the range.
For closed circles the inequality symbols used is (≤,≥).
The y-axis values suggests the range of the function.
The minimum y-axis value in the fourth quadrant is -5.
The maximum y-axis value in the first quadrant is 8.
The range of the function is [-5 , 8]
Therefore, the range is found to be -5 ≤ y ≤ 8.
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According to this diagram, what is sin 28°?
28°
OA. 17
15
OB.
B. 15
8
O C. 17
D. 15
OE
F.
8
15
8
17-
15
62°
90°
00
8
Answer:
sin 28 = 8 /17
Step-by-step explanation:
Since this is a right triangle, we can use trig functions.
sin theta = opp side / hypotenuse
sin 28 = 8 /17
Write an expression having only two terms that is
equivalent to 2x - 3. Explain how you wrote the
expression and how you can check that it iS equivalent.
Answer:
2X-3=0
2X=3
X=3/2
Step-by-step explanation:
Answer:
2x- 3 = 0
2x=3
x = 3/2
Step-by-step explanation: best of luck to you
Find the scale factor.
ABCD~EFGH
Answer:
0.67
Step-by-step explanation:
10/15＝0.666666......
＝0.67
Lexi MUST spend $100 and get 100 animals. $15 for 1 dog, $1 for 1 cat, and 25 cents for each mice.
thank you to whoever helps <33