Final answer:
To find the value of x for the triangle to be isosceles, we set the lengths of any two sides equal to each other and solve for x. After testing different cases, we find that x equals 10 satisfies the condition for the triangle to be isosceles.
Explanation:
For a triangle to be isosceles, at least two sides must have equal length. We're given the side lengths as 3x, 5x - 12, and x + 20. We have two cases to consider to find the value of x for the triangle to be isosceles:
Case 1: 3x = 5x - 12
Case 2: 3x = x + 20 or 5x - 12 = x + 20
To solve for x in case 1, we equate the two expressions and solve as follows:
3x = 5x - 12
2x = 12
x = 6
However, if we substitute x = 6 into the third side (x + 20), we get a length of 26, which does not equal either of the first two sides. Therefore, x = 6 does not satisfy the condition for an isosceles triangle.
For case 2, we consider 3x = x + 20:
3x = x + 20
2x = 20
x = 10
By substituting x = 10 into 5x - 12, we get 50 - 12 = 38. We can see that two sides of the triangle are 30 and 30 (since 3x equals 3(10)), confirming that the triangle is isosceles with x equal to 10.
What is 0.666 in a fraction?
What is the simplified form of the following expression? (x10)(x2)
I'm pretty sure the answer would be x^12
URGENT MATH HELP!
Which shows the conversion of 0.21 millimeters to inches?
There is 0.03937 inch in 1 millimeter.
A.
0.21 mm × 0.03937 in./mm = 0.0083 inches
B.
0.21 mm + 0.03937 in./mm = 0.24937 inches
C.
0.21 mm ÷ 0.03937 in./mm = 5.34 inches
D.
0.21 mm × 0.03937 in./mm = 8.3 × 10^-2 inches
A trail mix has 4 cups of raisins, 3 cups of chocolate, 6 cups of peanuts, and 2 cups of cashews. Which ingredients are in the same ratio as cashews to raisins?
How many solutions x 2x 7 = 3x - 7?
Determine whether the dilation from A (blue figure) to B (green figure) is an enlargement or reduction, then find the scale factor of the dilation.
a. reduction; scale factor of 2/5
b. enlargement; scale factor of 5/2
c. reduction; scale factor of 2/3
d. enlargement; scale factor of 3/2
Answer:
Option B
Step-by-step explanation:
In the figure attached we have to find the scale factor of dilation of figure A to figure B.
Since figure A is smaller than figure B, it concludes figure A has been enlarged to form figure B.
Now we have to find the scale factor of enlargement.
Scale factor = [tex]\frac{\text{one side of the larger figure}}{\text{one side of the smaller figure}}[/tex]
= [tex]\frac{5}{2}[/tex]
Therefore option B is the correct answer.
A father and his daughter together weigh seven times the daughter's weight x. The father weighs 180 lbs. Which equation can be used to find the daughter's weight?
A. 180-7x = x
B. x -180 = 7x
C. 180 -x = 7x
D. 180 + x = 7x
...?
What is the lcm of 21, 84, 126?
The school’s guidance department compares the grade-point averages and standardized state test scores for 10 students in each grade. The table below shows the correlation coefficient for each data set.
Grade Level and Correlation Coefficient
9th grade 0.3
10th grade –0.1
11th grade 0.2
12th grade –0.8
For which data set(s) is a linear regression model reasonable?
~ 9th grade and 11th grade data sets
~ 10th grade data set
~ 10th grade and 12th grade data sets
~ 12th grade data set
Answer:
12th grade data set
Step-by-step explanation:
1)A discriminant of 0 indicates what type of roots?
A)Two Complex
B)One Rational Double
C)Two Rational
D)Two Irrational
2)The quadratic 2x2 + 6x + 3 has what type of roots?
A)Two Irrational
B)Two Complex
C)One Rational Double
D)Two Rational
3)The quadratic x2 + 20x + 100 has what type of roots?
Answer
A)Two Irrational
B)Two Rational
C)One Rational Double
D)Two Complex
4)What is the possible discriminant of the graph?(graph in the link)
A)0
B)–11
C)73
D)25
5)What is the possible discriminant of the graph?(Graph in the link)
A)0
B)17
C)25
D)–15
...?
For f(x) = 2x + 1 and g(x) = x2 – 7, find (f – g)(x).
A. –x2 + 2x – 6
B. 2x2 – 15
C. x2 – 2x – 8
D. –x2 + 2x + 8
HELP!! give me the correct answer
For the function, f(x) = 2x + 1 and g(x) = x² – 7, (f – g)(x) will be D. –x² + 2x + 8
How to calculate the functionTo find (f - g)(x), we need to subtract the function g(x) from the function f(x).
f(x) = 2x + 1
g(x) = x² - 7
(f - g)(x) = f(x) - g(x)
Substituting the given functions:
(f - g)(x) = (2x + 1) - (x² - 7)
Now let's simplify:
(f - g)(x) = 2x + 1 - x² + 7
Combining like terms, we have:
(f - g)(x) = -x² + 2x + 8
Therefore, the answer is D. -x² + 2x + 8.
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Tina has to pay 4 percent of the purchase price toward closing costs for her mortgage. If the purchase price is $275,000, what is the closing cost amount?
Answer:
Proportion states that two fractions or ratios are equal.
Let x be the closing cost amount.
As per the statement:
Tina has to pay 4 percent of the purchase price toward closing costs for her mortgage. If the purchase price is $275,000.
Purchased Price = $275,000
then, by definition of proportion :
[tex]\frac{4}{100}=\frac{x}{275000}[/tex]
By cross multiply we have;
1,100,000 = 100x
Divide both sides by 100 we have;
11,000 = x
or
x = $ 11,000
Therefore, the closing cost amount is, 11,000
Can someone smart help me here?
Solve the mathematical puzzle.
S is a three digit number.
Determine the digits of S from the clues.
All the digits are odd.
The last two digits add to make ten.
The first and last digits add to make eight.
The first two digits add to make twelve.
S is
What step in the construction of copying a line segment ensures that the new line segment has the same length as the original line segment?
To copy a line segment and ensure it has the same length as the original, use a compass to measure and create a duplicate line segment.
Explanation:To copy a line segment and ensure that the new line segment has the same length as the original, we can use a compass. Here are the steps:
Place the compass needle on one endpoint of the original line segment.Open the compass to the length of the original line segment.Without changing the compass width, place the compass needle on the other endpoint of the original line segment and draw an arc.Use the compass to measure the same length on the arc and draw a line segment connecting the two marks.By using this method, we can create a duplicate line segment with the same length as the original.
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Which of the following are quadratic functions?
Check all that apply.
a. y=2(x-3x^2+1)
b. y=5+2x
c. y=1/2x^2-13x+4
d. y= x/x-1 Which of the following are quadratic functions?
Check all that apply.
a. y=2(x-3x^2+1)
b. y=5+2x
c. y=1/2x^2-13x+4
d. y= x/x-1
Final answer:
The quadratic functions are: y = 2(x - 3x² + 1), y = 1/2x² - 13x + 4, and y = 1.
Explanation:
A quadratic function is a polynomial function of degree 2, which means its highest power of x is 2. The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.
Out of the given options, the quadratic functions are:
a. y = 2(x - 3x² + 1)
c. y = 1/2x² - 13x + 4
d. y = x/x - 1 (this can be simplified to y = 1)
The options b. (y = 5 + 2x) is not a quadratic function because it only has a linear term (power of x is 1).
Evaluate BC for A = 5, B = -4, and C = 2
What is the inverse of the function f(x) = 2x – 10? h(x) = 2x – 5 h(x) = 2x + 5 h(x) = x – 5 h(x) = x + 5
The inverse of a function is gotten by swapping the x and y coordinates.
The inverse of function f(x) is[tex]h(x) = \frac x2 + 5[/tex]
Given
[tex]f(x) = 2x - 10[/tex]
Rewrite as:
[tex]y = 2x - 10[/tex]
Swap x and y
[tex]x = 2y - 10[/tex]
Solve for y
[tex]2y = x + 10[/tex]
Divide by 2
[tex]y = \frac x2 + 5[/tex]
So, we have:
[tex]h(x) = \frac x2 + 5[/tex]
Hence, the inverse function is[tex]h(x) = \frac x2 + 5[/tex]
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What happened to the little boy who swallowed a silver dollar?
15. TRIANGLES Find the dimensions of a triangle if the base is 2/3 the measure of the height and the area is 12 square centimeters. (Lesson 4-3)
The dimensions of the triangle with a base that is 2/3 of its height and an area of 12 square centimeters are a base of 4 centimeters and the height of 6 centimeters.
Explanation:The question asks for the dimensions of a triangle. We are given that the base is 2/3 of the height and the area is 12 square centimeters. The formula for the area of a triangle is 1/2 * base * height. Since we know that the base is 2/3 of the height, we can denote the height as 'h' and the base as (2/3)h. From here, we can set up the equation 12 = 1/2 * (2/3)h * h, which simplifies to 12 = 1/3 * h². Solving for 'h', we find the height is √36 or 6 centimeters. Given the base is 2/3 of the height, the base, therefore, is 4 centimeters.
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Determine the x values that cause the function to be (a) Zero, (b) Positive and (c) Negative, then d) sketch a graph of the function.
Fill in the missing number to complete the factorization:
x 3 + x 2 - 21x - 45 = (x + 3)(x - 5)(x +
Missing number to complete the factorization is 3.
What is factorization?Factorization can be defined as the process of breaking down a number into smaller numbers which when multiplied together arrive at the original number. These numbers are broken down into factors or divisors.
Given expression
[tex]x^{3}+x^{2} -21x-45=(x+3) (x-5) (x+a)[/tex]
Let a be the missing number
(x + 3) (x - 5) (x + a)
= [tex](x^{2} -5x+3x-15)(x+a)[/tex]
= [tex](x^{2} -2x-15)(x+a)[/tex]
[tex]x^{3}+x^{2} -21x-45=x^{3} +x^{2} a-2x^{2} -2xa-15x-15a[/tex]
By comparing the expressions
-2xa - 15x = -21x
⇒ -2xa = -6x
⇒ a = 3
[tex]x^{2} (a-2) = 1x^{2}[/tex]
⇒ a - 2 = 1
⇒ a = 3
-15a = -45
⇒ a = 3
Hence, missing number to complete the factorization is 3.
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What is 0.021 in fraction form?
what is the answer to 8y - 1 = 31
Is 8.92 greater or less than 8.9
What is another name for 34/8 as a mixed number??
How do u simplify 2/5 x 6/7? and what the answer?
I really need help solving this whole problem.
Jimmy was 12 years old in 2014 and now in 2016 he is 15 how did he grow 3 years in 2 years?
A. HE WAS BORN ON MAY 1ST
B. HE WAS BORN ON DECEMBER 23RD
C. HE WAS BORN ON NOVEMBER 15TH
D. HE WAS BORN ON JANUARY 20TH
What is the greatest common factor of 34n and 8n^2?
The greatest common factor of 34n and 8n² is 2n, as both expressions share the variable n and the highest common numerical coefficient is 2.
The greatest common factor (GCF) of two algebraic expressions can be found by identifying the highest powers of common factors in the terms. For the expressions 34n and 8n², both terms have n as a common factor. Since we want the greatest common factor, we take the highest power of n that appears in both terms, which is n (not n² because n is the highest power in the least degree term, 34n). Next, we find the GCF of the numerical coefficients 34 and 8, which is 2. Therefore, the greatest common factor of 34n and 8n² is 2n.
Which statement is modeled by the expression?
150/k
The Henderson family drove 150 miles each day of their vacation. If their vacation lasted for k days, then 150/k is the total number of miles they traveled on their vacation.
The cafeteria has a capacity of 150 seats. If k is the number of people in the cafeteria at lunch time, then 150/k is number of seats that were not used at lunch time.
A librarian had 150 books to be placed on shelves with an equal number of books on each shelf. If k is the number of shelves to be used, then 150/k is the number of books on each shelf.
Cory had 150 dollars in his savings account. He withdrew k dollars to buy a catcher's mitt. He then had 150/k dollars left in his savings account.
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The answer would be A librarian had 150 books to be placed on shelves with an equal number of books on each shelf. If k is the number of shelves to be used, then 150/k is the number of books on each shelf.
Explanation: Lets see Option 1 is obviously out Option 2 does not make
sense When it comes to option 3 that makes the most sense Option 4 could be right but option 3 is the best and correct answer
So that's your answer
Hope This Helps :)
-Sprinkles