[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})~\hspace{10em} slope = m\implies \cfrac{5}{6} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=\cfrac{5}{6}[x-(-3)]\implies y-4=\cfrac{5}{6}(x+3) \\\\\\ y-4=\cfrac{5}{6}x+\cfrac{5}{2}\implies y=\cfrac{5}{6}x+\cfrac{5}{2}+4\implies y=\cfrac{5}{6}x+\stackrel{\textit{LCD of 2}}{\cfrac{(1)5+(2)4}{2}}[/tex]
[tex]\bf y=\cfrac{5}{6}x+\cfrac{13}{2}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
an isosceles triangle has an angle that measures 140 degrees. which other angles could be in that isosceles triangle?
An Isosceles triangle means it has two sides that measures the same.
When we have two sides that measures the same also means that they have the same angles.
If one angel measures 140 that means that the other angles are 20 and 20
Because the angles of the triangle has to sum to 180
In an isosceles triangle, two angles are same and the sum of all angles is 180 degrees. If one angle is 140 degrees, the other two angles must sum to 40 degrees, and since they are equal, each would measure 20 degrees.
Explanation:In an isosceles triangle, two of the angles are equal, and the third angle, also known as the base angle, is different. The total sum of the angles in any triangle, including an isosceles triangle, is always 180 degrees. Thus, if one of the angles measures 140 degrees, the remaining two angles must sum up to 40 degrees. Since these two angles are equal (as it is an isosceles triangle), each of them would measure 20 degrees. Thus, in the given isosceles triangle, the other two angles would measure 20 degrees each.
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Find the value of x if m<4 = 2x + 20 and m<8 = 3x - 5. Use that info to calculate the exact measure of each angle.
Since m<4 and m<8 both add up to 180 degrees. Combine 2x + 20 and 3x - 5 and set it equal to 180. By subtracting 15 to the other side and dividing five to the other side you get x=33. Plug 33 back into the angle measurement separate equations to find degree angle measurement. Your welcome.
What is the median of
17,23,8,5,9,16,22,11,13,15,17,18
Answer:
15.5 or 15 1/2
arrange all numbers least to greatest and cross out each number until u get to the last two, once u get to the last two add them and divide them by two:
What is the prescribed dosage of a certain medicine for a 6-year-old child if the adult dosage of
the medicine is 180 milligrams?
What is C?
The formula below is used to calculate the correct dosage for a child:
C= a/(a+12) ∙ A
C = child’s dosage in milligrams
a = age of the child
A = adult dosage in milligrams
Show work
Answer:
The dose in milligrams of a 6-year-old child is 60.
Step-by-step explanation:
The formula is:
[tex]C = \frac{a}{(a+ 12)}A[/tex]
We know that
A= adult dosage in milligrams=180 milligrams
a = age of the child = 6 years-old
So the child’s dosage in milligrams is:
[tex]C = \frac{6}{(6+12)}*180[/tex]
[tex]C = \frac{1}{(3)}*180[/tex]
[tex]C = \frac{180}{(3)}[/tex]
[tex]C = 60\ milligrams[/tex]
Final answer:
To find the child's dosage of medicine, apply the formula C = a/(a+12) x A with a being the child's age and A the adult dosage. For a 6-year-old, the dosage is 60 milligrams.
Explanation:
To calculate the prescribed dosage of medicine for a 6-year-old child when the adult dosage is 180 milligrams, we use the formula C = a/(a+12) ⋅ A, where C is the child’s dosage in milligrams, a is the age of the child, and A is the adult dosage in milligrams.
Plugging the given values into the formula we get:
C = 6 / (6 + 12) ⋅ 180
C = 6 / 18 ⋅ 180
C = 1 / 3 ⋅ 180
C = 180 / 3
C = 60 milligrams
Therefore, the prescribed dosage for a 6-year-old child is 60 milligrams.
48j 5 k 2 ÷ (-3j 3 k)
where are the signs between the 5 and 48j, and k and 2? is at multiplication? cause you use parentheses only for that.
If it is multiplication... then 3j * 3k = 9jk
48j * 5 = 240j * k =240jk * 2 = 480jk / 9jk = 53.3333333333jk
What value of c makes the equation true? Assume x>0 and y>0 3√x^3/cy^4=x/4y(3√y) c = 12 c = 16 c = 81 c = 64
The value of c=12 will makes the equation true. for the given expression.
what is the value?Here in the question we have expression:
[tex]\dfrac{3\sqrt{x^3}}{cy^4}}=\dfrac{x}{4y^3\sqrt{y}}[/tex]
By solving the above equation we will get:
[tex]12\sqrt{x}=c\sqrt{y}[/tex]
So value of c=12 will makes the equation true. for the given expression.
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The correct value of [tex]\( c \)[/tex] that makes the equation true is [tex]\( c = 64 \)[/tex].
To find the value of [tex]\( c \)[/tex], we start by simplifying the given equation:
[tex]\[ 3\sqrt{\frac{x^3}{cy^4}} = \frac{x}{4y}(3\sqrt{y}) \][/tex]
First, we simplify the left side of the equation by applying the cube root to both the numerator and the denominator:
[tex]\[ \frac{3\sqrt{x^3}}{3\sqrt{cy^4}} = \frac{x}{4y}(3\sqrt{y}) \][/tex]
The cube root of [tex]\( x^3 \)[/tex] is [tex]\( x \)[/tex] , and the cube root of [tex]\( y^4 \)[/tex] is [tex]\( y \)[/tex] times the cube root of [tex]\( y \)[/tex], which is [tex]\( y \cdot y^{1/3} \)[/tex]. Simplifying further, we get:
[tex]\[ \frac{x}{3\sqrt{c} \cdot y} = \frac{x}{4y}(3\sqrt{y}) \][/tex]
Now, we simplify the right side of the equation:
[tex]\[ \frac{x}{3\sqrt{c} \cdot y} = \frac{x \cdot 3\sqrt{y}}{4y} \][/tex]
Since [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are positive, we can multiply both sides by [tex]\( 4y \)[/tex] to eliminate the denominators:
[tex]\[ \frac{4yx}{3\sqrt{c} \cdot y} = x \cdot 3\sqrt{y} \][/tex]
Simplifying, we get:
[tex]\[ \frac{4x}{3\sqrt{c}} = 3x\sqrt{y} \][/tex]
Now, we can divide both sides by [tex]\( x \)[/tex] since [tex]\( x > 0 \)[/tex]:
[tex]\[ \frac{4}{3\sqrt{c}} = 3\sqrt{y} \][/tex]
Next, we square both sides to eliminate the square root:
[tex]\[ \left(\frac{4}{3\sqrt{c}}\right)^2 = (3\sqrt{y})^2 \][/tex]
[tex]\[ \frac{16}{9c} = 9y \][/tex]
Since [tex]\( y > 0 \)[/tex], we can multiply both sides by [tex]\( 9c \)[/tex] to get rid of the denominator:
[tex]\[ 16 = 81cy \][/tex]
Now, we divide both sides by [tex]\( y \)[/tex]:
[tex]\[ \frac{16}{y} = 81c \][/tex]
Finally, we multiply both sides by [tex]\( y \)[/tex] to solve for [tex]\( c \)[/tex]:
[tex]\[ 16 = 81c \][/tex]
[tex]\[ c = \frac{16}{81} \][/tex]
[tex]\[ c = \left(\frac{2^4}{3^4}\right) \][/tex]
[tex]\[ c = \left(\frac{2}{3}\right)^4 \][/tex]
[tex]\[ c = \left(\frac{3}{2}\right)^{-4} \][/tex]
[tex]\[ c = 64 \][/tex]
Therefore, the value of [tex]\( c \)[/tex] that makes the equation true is [tex]\( c = 64 \)[/tex].
What are expressions equivalent to 12X+36Y?
To express 12X+36Y in different terms, we can use other variables or coefficients while maintaining the same relationship between X and Y. Two equivalent expressions are 4A+12B and 6C+18D.
To express the expression 12X+36Y in terms of equivalent mathematical expressions using different variables or coefficients, we can use any other variables or coefficients as long as they maintain the same relationship between X and Y. Here are two distinct expressions:
4A + 12B, where A is equivalent to X and B is equivalent to Y.6C + 18D, where C is equivalent to X/2 and D is equivalent to Y/2.For more such questions on equivalent expressions, click on:
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The probable question may be:
Express the expression 12X+36Y in terms of equivalent mathematical expressions using different variables or coefficients. Provide at least two distinct expressions that are equivalent to 12X+36Y.
150 is divisible by which of the following numbers:2,3,4,5,6,9 or 10
Answer: 150 is divisible by 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
I hope that this helps! :D
Answer:
2,3,5,6, and 10
Step-by-step explanation:
If you get a whole number when you divide by one of these numbers that means the number is divisible, if you get a fraction/decimal then it isn't divisible
which figure shows two congruent triangles
Hello there!
The answer is the first option.
Remember that congruent = same size and same shape, and this is the only option that has both of those things. In the second and forth options, the sizes are different making those options not correct. In the 3rd option, the shape is slightly different since one triangle is not as stretched out as the other.
I hope this was helpful and have a great day!
Since the two sides and one angle in figure 1 are the same as a result they are congruent.
What is the congruent triangle?Congruent triangles are those that are exactly the same size and shape. Congruent is represented by the symbol ≅ When the three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle, they are said to be congruent.
While the similarity law for triangles is defined as the law to prove that two triangles have the same shape, it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.
Thus, the two sides and one angle in figure 1 are the same as a result they are congruent.
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plz help to do it of math
A leap year consists of 366 days.
52 weeks + 2 days.
These 2 days can be: (mon,tue),(tue,wed),(wed,thu),(thu,fri),(fri,sat)(sat,sun)(sun,mon)
Thus, the total number of cases = 7.
The number of cases in which we get Friday = 2(Thu, Fri)(Fri, Sat).
Therefore the required probability = 2/7.
Sam solved the proportion
3 = 5, but she has some mistakes in her solution.
Read her steps carefully, and then answer the questions.
Step 1: (x + 5)1 = 4(x + 2)
Step 2: x + 5 = 4x + 8
Step 3: 5 = 3x + 8
Step 4:
3= 3x
Step 5: -1=1
Mill
Part A: In which step did Sam make her first mistake?
Part B: What is Sam's first mistake?
Select one answer for Part A, and select one answer for Part B.
Answer:
A. Step One
B. She multiplied straight across in the proportion instead of diagonally
Step-by-step explanation:
Answer:
A. Step One
B. She multiplied straight across in the proportion instead of diagonally
How can you justify that the diagonals of a rhombus bisect opposite interior angles?
Answer:
the opposite sides are of equal length; - the diagonals bisect each other; - the opposite angles are congruent; - the sum of any two consecutive angles is equal to 180 . Rhombis (plural of rhombus) have additional properties. Theorem 1. In a rhombus, the diagonals are the angle bisectors.
Step-by-step explanation:
The diagonals of a rhombus bisect opposite interior angles because they create congruent triangles that have equal corresponding angles.
Explanation:The question addresses a geometry concept about the properties of a rhombus. To justify that the diagonals of a rhombus bisect opposite interior angles, we can consider the definition of a rhombus as a special type of parallelogram where all four sides are of equal length. Additionally, we know that in a parallelogram, opposite sides are parallel. By drawing the diagonals of a rhombus, we create congruent triangles because of the properties of parallelograms and the fact that all sides of a rhombus are equal. Each diagonal will bisect the angle from which it is drawn because in these congruent triangles, the corresponding angles are equal. This means that the diagonals bisect each other and they bisect the opposite interior angles into equal parts.
The polynomial 24x3 − 54x2 + 44x − 99 is factored by grouping. 24x3 − 54x2 + 44x − 99 24x3 + 44x − 54x2 − 99 4x(____) − 9(____) What is the common factor that is missing from both sets of parentheses?
Answer: [tex]6x^2+11[/tex]
Step-by-step explanation:
Given the polynomial of degree 3:
[tex]24x^3 - 54x^2 + 44x -99[/tex]
You can observe make two groups or two terms each:
[tex](24x^3 + 44x) - (54x^2 + 99)[/tex]
The Greatest Common Factor (GCF), is the highest number that divides into two or more numbers without leaving remainder.
You can observe that the GCF of both set are factored out ([tex]4x[/tex] and [tex]9[/tex]), then, you can find the common factor that is missing from both sets of parentheses with this procedure:
[tex](\frac{24x^3}{4x}+\frac{44x}{4x})-(\frac{54x^2}{9}+\frac{99}{9})=(6x^2+11)-(6x^2+11)[/tex]
You can observe that the common factor that is missing from both sets of parentheses is:
[tex]6x^2+11[/tex]
115) Working alone, it takes Sebastian nine hours to
pick forty bushels of apples. Eduardo can pick
the same amount in 11 hours. How long
would it take them if they worked together?
It will take them 20 hours, since the question is asking how long it will take them when working together you add each of their hours together,9+11=20
Ummmmm don’t pay any attention to the writing there just so he problem for me please.I really need help
I dont know how to help you bud give me a geometry and I could maybe solve it lol
The measurement of 2 and justification
M<2=105. They must add up to 180.
The measure of an angle is 78° less than the measure of its complement. What is the measure of the angle?
84°
51°
6°
12°
The measure of the angle is 6°
A complementary angle consists of two angles who's sum is 90 degrees. Since there are two we know this for sure:
1st angle: x (unknown value)
2nd angle: x-78 (78 less then its complement)
total: 90
If we put the equation together we get: x+x-78= 90
x+x-78+78=90+78
2x=168
2x/2=168/2
x=84
Now we know that x = 84, know we gonna find the 2nd angle:
1st: x=84
2nd: 84-78 = 6
total: 84+6=90
39 POINTS!! ALGEBRA. PLEASE HELP, I AM FAILING AND THIS IS DUE IN AN HOUR.
Answer:
Question 10: [tex]f(x)=1/2x-1[/tex] Question 13: [tex]f(-2)=-1[/tex] Question 11: [tex]f(8)=60[/tex]
Step-by-step explanation:
For Question 10:
The functionis in the form of [tex]f(x)[/tex]. We know the slope is [tex]\frac{1}{2}[/tex] (rise 1 run 2)and the y intercept is -1 (where the line goes through the y axis). We can then put the function is slope intercept form ([tex]y=mx+b[/tex]) and we would have [tex]f(x)=1/2x-1[/tex].
For Question 13:
To evaluate the function[tex]f(x)=\frac{3}{2} x-4[/tex] for [tex]f(-2)[/tex] we need to plug -2 into the function as x. [tex]f(-2)=\frac{3}{-2} (-2)-4[/tex]. [tex]\frac{3}{-2}[/tex] times -2 would equal 3 because the negatives cancle out. 3-4 equals -1 so the solution is [tex]f(-2)=-1[/tex].
For question 11:
Same as question 13. plug 8 into x in [tex]f(x)=x^2-4[/tex]. This would be [tex]f(8)=(8)^2-4[/tex]. 8 squared is 64 and 64-4 is 60. Therefore [tex]f(8)=60[/tex].
Please help and show work
Answer:
Coordinates of A': will NOT be the same
Coordinates of C': will NOT be the same
Perimeter of ABC: will be the same
Area of A'B'C': will be the same
Measure of ∠B: will be the same
Slope of A'C': will be the same
Step-by-step explanation:
We have a triangle ABC that will be translated (moved) 2 units down, 3 units to the right.
Since the triangle is moved, then the coordinates of every summit (A, B and C) will be affected. So,
Coordinates of A': will NOT be the same
Coordinates of C': will NOT be the same
However, since the triangle is only moved, not transformed in any way, not scaled up/down for example the following will remain the same:
Perimeter of ABC: will be the same
Area of A'B'C': will be the same
Measure of ∠B: will be the same
Since the triangle is only translated, not rotated or reflected the following will remain the same:
Slope of A'C': will be the same
w+x=z make x the subject of the formula
Answer:
x = z - w
Step-by-step explanation:
Given
w + x = z ( isolate x by subtracting w from both sides )
x = z - w
Answer:
x = z - w
Step-by-step explanation:
Take w to the other side and subtract with z to make x the subject
Which of the following is a polynomial function in standard form with zeros at -8, -1, and 3?
Answer:
Option A is correct.
Step-by-step explanation:
Zeros at -8, -1 and 3 means these are the factors of the polynomial.
x=-8, x=-1 and x =3
It can be written as:
x+8=0, x+1=0 and x-3=0
Factors can be written as:
(x+8)(x+1)(x-3)=0
Multiplying the first two terms and then their product with third terms:
[tex](x(x+1) +8(x+1))(x-3) =0\\(x^2+x+8x+8)(x-3)=0\\Adding\,\, like\,\, terms\,\,:\,\,\\(x^2+9x+8)(x-3) =0\\x(x^2+9x+8) -3(x^2+9x+8)=0\\x^3+9x^2+8x-3x^2-27x-24=0\\Adding\,\, like\,\, terms\,\,:\,\,\\x^3+9x^2-3x^2+8x-27x-24=0\\x^3+6x^2-19x-24=0\\or\,\,f(x) = x^3+6x^2-19x-24[/tex]
So, Option A is correct.
solve the equation 6+1/5q=10
Answer:
q = 20
Step-by-step explanation:
1/5q = 4
q = 20
What are the solutions of the following system?
X+y = 25
| 2x+y= -5
(0,-5) and (-5,5)
(0,-5) and (5, -15)
(0, -5) and (-4, 3)
(0, -5) and (4, -13)
Final answer:
The solutions of the given system can be found by solving the equations simultaneously using the method of substitution. The solution is (x, y) = (-30, 55).
Explanation:
The solutions of the given system of equations can be found by solving it simultaneously. We have the following equations:
X+y = 25
| 2x+y= -5
To solve this system, we can use the method of substitution or elimination. Let's use the method of substitution:
From equation 1, we can express y in terms of x as: y = 25 - xSubstitute this value of y into equation 2: 2x + (25 - x) = -5Simplify the equation: x + 25 = -5Solve for x: x = -30Substitute this value of x back into equation 1 to find y: y = 25 - (-30) = 55Therefore, the solution to the system is (x, y) = (-30, 55).
Please help the year is almost over and I need help with this or I will fail and get held back and my sisters will tease me!!!! 20 points
Answer:
The total weight of the packages of fruit that weigh less than half a pound is, 7/8.
Step-by-step explanation:
This reason being is because 2 of the 1/8ths are under 1/2 of a pound, and the 1/4th and the 3/8 is all under 1/2 of a pound. You add the 2 1/8ths together and get 2/8 + the 3/8 = 5/8. Then you add the 5/8 together with the only 1/4th and you get 7/8, as your answer.
Hope this helps!! :)
Find the local and global extrema for the graph of ƒ(x) = x3 – 6x2.
Answer:
Global extrema: none. Local extrema: (0, 0) and (4, -32)
Step-by-step explanation:
ƒ(x) = x3 – 6x2 should be written as ƒ(x) = x^3 – 6x^2. Use " ^ " to denote exponentiation, please.
One way to answer this problem would be to make a careful graph of ƒ(x) = x^3 – 6x^2. Notice that this graph begins in Quadrant III and ends in Quadrant I; this is one outcome of its being an ODD function. The graph will increase, reach a peak (a local max), decrease, reach a valley (a local min) and then grow from then on.
Another way is to use calculus. You don't say what course you're in, so I can't be sure that calculus would make sense to you.
Find the first derivative of ƒ(x) = x^3 – 6x^2. It is f '(x) = 3x^2 - 12x. Set this derivative = to 0 and find the roots. Hint: find the roots of 3x^2(x - 4). They are x = 0 and x = 4. At x = , y = f(0) = 0. Thus, the local max is
(0, 0). At x = +4, y = f(4) = 64 - 6(16) = -32. Thus, the local min is at (4, -32 ).
This graph rises without bound as x goes to ∞, and decreases without bound as x goes to -∞. Thus, there is neither a global max nor a global min.
What should be done to x^2 + 15x in order to create a perfect square?
[tex]\bf \qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf x^2+15x+\boxed{?}^2\implies \stackrel{\textit{we know the middle term is}}{2\sqrt{x^2}\cdot \sqrt{\boxed{?}^2}\implies 2x\boxed{?}}\qquad then\qquad 2x\boxed{?}=15x \\\\\\ \boxed{?}=\cfrac{15x}{2x}\implies \boxed{?}=\cfrac{15}{2}\qquad \impliedby \textit{we should add that much \underline{squared}} \\\\[-0.35em] ~\dotfill\\\\ x^2+15x+\left( \cfrac{15}{2} \right)^2\implies \left(x+ \cfrac{15}{2} \right)^2[/tex]
Lorenzo is moving from New York to California. he will drive 2641 miles from his old Home to his new home. every hour he will drive 60 miles. about how many days will it take him to get to his new home if he drives for 8 hours a day?
Answer:
Every hour he drives 60 miles and if he drives 8 hours a day ( 8x60 ), that means that he drives 480 miles a day. Then you would do, 2641 / 480, to find the number of days it should take. The answer is around 5.5 days.
Given that p is an integer, q = -12 and the quotient of
p
q
is -3, find p.
A) -36
B) -4
C) 4
D) 36
Answer: D
Step-by-step explanation:
Find the total area of the solid figure
Answer:
126 ft²Step-by-step explanation:
We have
2 rectangles 3ft × 5ft
2 rectangles 5ft × 6ft
2 rectangles 3ft × 6ft
The formula of an area of a rectangle:
A = lw
l, w - dimensions of a rectangle
Calculate:
A₁ = (3)(5) = 15 ft²
A₂ = (5)(6) = 30 ft²
A₃ = (3)(6) = 18 ft²
The total area of the solid figure:
A = 2A₁ + 2A₂ + 2A₃ = 2(A₁ + A₂ + A₃)
Substitute:
A = 2(15 + 30 + 18) = 2(63) = 126 ft²
Σ20/n=1(3n+2) = what