[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{4}{5}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{5}{4}}\qquad \stackrel{negative~reciprocal}{+\cfrac{5}{4}\implies \cfrac{5}{4}}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{5}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-0}{2-(-2)}\implies \cfrac{5}{2+2}\implies \cfrac{5}{4} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{9}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{9-(-1)}{10-2}\implies \cfrac{9+1}{8}\implies \cfrac{10}{8}\implies \cfrac{5}{4}[/tex]
Answer: Im pretty sure it answer options 1 and 5
Step-by-step explanation: 1) (-2,0) and (2,5) 5) (2,-1) and (10,9)
its on edg.
29. A circle has a diameter of 16 inches.
What is the circumference of the
circle rounded to the nearest
hundredth? Use 3.14 for pi
A 50.24 inches
B 100.48 inches
C 200.96 inches
D 803.84 inches
Answer:
answer is A
Step-by-step explanation:
The formula for circumference of a circle using diameter is pi times "d". "d" means diameter. 3.14 x 16= 50.24
C = pi•d
C = 3.14(16)
C = 50.24 inches
Use the converse of the side-splitter theorem to determine
if TU || Rs. Which statement is true?
Answer:
Line segment TU is parallel to line segment RS because 32/36 = 40/45.
Step-by-step explanation:
The line segment TU is parallel to the line segment RS because 32 / 36 is equal to 40 / 45.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The converse theorem states that if TU || RS, then the ratio of the corresponding sides will be constant.
32 / 36 = 40 / 45 = 8 / 9 = constant
The line segment TU is parallel to the line segment RS because 32 / 36 is equal to 40 / 45.
Then the correct option is A.
The graph is given below.
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How do you calculate a weighted grade into a percentage?
For example, 64.97/ 75
Answer:
86%
Step-by-step explanation:
64.97/ 75 = 0.8662...
0.8662 x 100 = 86%
but it weighted so:
0.8662 x actual weighted % = % got out of weighted %
example:
Test is Weighted 25% out of 100%
0.8662 x 25% = 21 %
this case you got 21% out of 25% for the test
which congruency theorem can be used to prove that triangle abd is congruent to triangle dca
Answer:
SAS
Step-by-step explanation:
we know that
Triangles are congruent by SAS, if any pair of corresponding sides and their included angles are equal in both triangles
so
In this problem
we have that
the pair of corresponding sides AB with DC and AD with DA and their included angles ∠ BAD with ∠CDA are equal
therefore
Triangle ABD is congruent with triangle DCA by SAS congruency theorem
Answer:
sas
Step-by-step explanation:
i just did the assignment. please mark me brainliest!!!!!
Suppose the first equation in a system of two linear equations is 12x + 7y = 25. The second equation being which of these will cause the system to have no solution?
A.
12x + 7y = 20
B.
12x + 7y = 25
C.
12x + 9y = 20
D.
12x + 9y = 25
Answer:
A. 12x + 7y = 20
Step-by-step explanation:
Obviously, 12x + 7y cannot both be equivalent to unique [different] quantities.
Option A (12x + 7y = 20) would make the system of linear equations with 12x + 7y = 25 have no solution because the lines would be parallel and never intersect.
Second equation would make a system of linear equations with 12x + 7y = 25 have no solution. A system of linear equations will have no solution if the two lines represented by the equations are parallel, which means they have the same slope but different y-intercepts. Since the first equation is 12x + 7y = 25, we need a second equation with the same coefficients for x and y but a different constant term in order to represent parallel lines.
Option A (12x + 7y = 20) meets the criteria for causing the system to have no solution because it has the same coefficients for x and y as the first equation but a different constant term. This indicates that the lines are parallel and will never intersect, hence no solution exists for this pair of equations.
What is the greatest common factor of 8m, 36m3, and 12
ANSWER
GCF=4
EXPLANATION
The given monomials are:
[tex]8m = {2}^{3} m[/tex]
[tex]36 {m}^{3} = {2}^{2} \times {3}^{2} {m}^{3} [/tex]
[tex]12 = {2}^{2} \times 3[/tex]
The greatest common factor is the product of all the least powers of the common factors.
We can see that:
[tex] {2}^{2} [/tex]
is the common to all the factors.
Therefore the greatest common factor is
[tex] {2}^{2} = 4[/tex]
Answer: [tex]GCF=4[/tex]
Step-by-step explanation:
To find the Greatest Common Factor (GCF) of 8m, 36m³, and 12, you need to descompose them into their prime factors. Then:
[tex]8m=2*2*2*m=2^3*m\\\\36m^3=2*2*3*3*m^3=2^2*3^2*m^3\\\\12=2*2*3=2^2*3[/tex]
You can observe that the common factor with the lowest exponent is the following:
[tex]2^2[/tex]
Therefore, the Greatest Common Factor (GCF) of 8m, 36m³, and 12 is:
[tex]GCF=2^2\\GCF=4[/tex]
Simplify the expression (x^1/6)3
Answer:x^1/2
Step-by-step explanation:
x^1/6*3=
x^3/6=
x^1/2
Write an expression for the missing value in
the table.
Tom’s Age Kim’s Age
10 13
11 14
12 15
a ?
A a + 1 C a + 3
B a + 15 D a + 10
Answer:
C) a+3
Step-by-step explanation:
We are given the following data:
Tom's Age: 10 11 12 a
Kim's Age: 13 14 15
We have to evaluate Kim's age when Tom's age is a.
We have to build a relationship between Tim's age and Kim's age. If we look at their ages carefully we can see a pattern and their relation can be described as:
[tex]\text{Kim's age = Tim's age + 3}[/tex]
Thus, when Tim's age is a, we can compute Kim's age as:
[tex]\text{Kim's age = a + 3}[/tex]
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Answer:
iii) P=65h
iv) P=70h
Step-by-step explanation:
Payment of First day = $300
Number of hours = 5
Payment per hour = $60
Payment of First day = $240
Number of hours = 4
Payment per hour = $60
Payment of First day = $360
Number of hours = 6
Payment per hour = $60
Hence the rate of Payment for an hour is $60
Hence the rates
P=65h
and
P=70h
are more than the rate of payment made to labor.
Could you guys help me answer these two questions
Answer:
1. C. Jana
2. I. Matthew and Jake
Find the LCM of each pair of numbers 6 and 10
Answer:
LCM = 30
Step-by-step explanation:
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Which calculator correctly shows the quotient of
6.47 x 10-15
3.36 * 10-29
Answer:
the second one
Step-by-step explanation:
Answer:
the second one
Step-by-step explanation:
the one that says +14
If $190 is invested at an interest rate of 11% per year and is compounded continuously, how much will the investment be worth in 4 years? Use the continuous compound interest formula: A = Pert.
Answer:
295.01
Step-by-step explanation:
Use A = Pe^(rt)
$294.88 is the worth of the investment after 4 years.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that $190 is invested at an interest rate of 11% per year and compounded continuously.
We need to find the worth of the investment after 4 years.
[tex]A=Pe^{rt}[/tex]
A is the final amount
p is the principal amount
r is the rate of interest
t is the time.
[tex]A=190e^{0.11(4)}[/tex]
[tex]A=190e^{0.44}[/tex]
A=190×1.552
A=294.88
Hence, $294.88 is the worth of the investment after 4 years.
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What is an equation bof the line that is perpendicular to y-4=2(x-6);and passes through the point (-3,-5)
Answer:
y+5=-1/2(x+3)
Step-by-step explanation:
as perpendicular,
compare that given eqn with y-y1=m(x-x1),
m1=2
then,
perpendicular case,
m1×m2=-1
m2=-1/2
now,
as the eqn passes through point (-3,-5),
we know,
y-y1=m(x-x1)
then putting value,
y+5=-1/2(x+3)
Answer:
y + 5 = - [tex]\frac{1}{2}[/tex](x + 3)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line.
y - 4 = 2(x - 6) is in this form with slope m = 2
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex]
Hence the equation passing through (- 3, - 5) is
y - (- 5) = - [tex]\frac{1}2}[/tex] (x - (- 3)), that is
y + 5 = - [tex]\frac{1}{2}[/tex](x + 3) ← equation of perpendicular line
After you rewrite subtraction as addition of the
additive inverse, how can the like terms be
grouped?
[3a2 + (-3a2)] + (-5ab + 8ab) + [b2 + (-2b2)]
[3a2 + (-3a2)] + (-5ab + 8ab) + (b2 + 262)
© (3a2 + 3a2) + (-5ab + (-8ab)] + [b2 + (-262)]
(3a2 + 3a2) + (-5ab + (-262)] + [b2 + (-8ab)]
Answer:
(3a2 + 3a2) + [–5ab + (–8ab)] + [b2 + (–2b2)]
Step-by-step explanation:
Answer: c. (3a^2+3a^2)+[-5ab+(-8ab)]+[b^2+(-2b^2)]
for the second part: =a. 6a^2-13ab-b^2
Step-by-step explanation:
i did it
What is the y-intercept of a line that has a slope of –3 and passes through point (–5, 4)?
–17
–11
7
19
The y-intercept of a line that has a slope of –3 and passes through point (–5, 4) is -11.
What is the slope-intercept form of a line?The slope-intercept of a line is
[tex](y-y_{1})=m(x-x_{1})[/tex]
Here, [tex](x_{1},y_{1})[/tex] is the point through which the line passes and 'm' is the slope of the line.
Given, the line has a slope of –3 and passes through point (–5, 4).
Therefore, [tex](y-4)=-3[x-(-5)][/tex]
⇒ [tex](y-4)= -3(x+5)[/tex]
⇒ [tex](y-4)= -3x-15[/tex]
⇒ [tex]3x+y = -11[/tex]
⇒ [tex]y = -3x-11[/tex]
Comparing it with the standard form of equation, we get:
the y-intercept of the required line is -11.
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For f(x)=x-14 and g(x)=x^2+14 find (fog)(x). A. x^2+x B. x^2-28x+210 C. x^2 D. x^3-14x^2+14x
Answer:
C
Step-by-step explanation:
To evaluate (f ￮ g)(x)
Substitute x = g(x) into f(x)
f(x² + 14) = x² + 14 - 14 = x² → C
The value of (fog)(x) = x^2. So, option C is correct.
How to solve a composite function?The functions f(x) and g(x) are composite functions then,
(fog)(x) = f(g(x)).
Substitute g(x) in place of x in the function f(x).Simplify the equation.Calculation:Given that,
f(x) = x - 14
g(x) = [tex]x^2+14[/tex]
Then,
(fog)(x) = f(g(x))
= ([tex]x^2+14[/tex]) - 14
= x² + 14 - 14
= x²
Therefore, the value of (fog)(x) = x².
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Y=8x+40 substitute 3 for x
Answer:
[tex]\displaystyle 64 = y[/tex]
Step-by-step explanation:
[tex]\displaystyle y = 8[3] + 40; y = 24 + 40; 64 = 24 + 40[/tex]
I am joyous to assist you anytime.
Maggie needs to spend at least six hours each week practicing the piano. She has already practiced 3
hours this week. She wants to split the remaining
practice time evenly between the last two days of the week. Write an inequality to determine the minimum number of hours she needs to practice on each of
the two days
Final answer:
Maggie needs to practice at least 1.5 hours on each of the two remaining days.
Explanation:
To determine the minimum number of hours Maggie needs to practice on each of the two remaining days, we can set up an inequality based on the given information. Maggie needs to spend at least six hours each week practicing the piano, and she has already practiced three hours. Let's let x represent the number of hours she needs to practice on each of the remaining two days. The inequality can be written as:
3 + 2x ≥ 6
Solving for x, we subtract 3 from both sides of the inequality:
2x ≥ 3
Then, we divide both sides by 2 to solve for x:
x ≥ 1.5
Therefore, Maggie needs to practice at least 1.5 hours on each of the two remaining days.
Maggie must practice for at least [tex]$\dfrac{3}{2}$[/tex] hours each of the last two days.
Let x equal the number of hours Maggie practices each of the last two days. Since she Needs to practice at least 6 hours per week, and she already practiced 3 hours this week, she must practice for at least 6 - 3 = 3 more hours.
Splitting this time evenly between the two days means she practices x hours each day.
This can be expressed in the following inequality: [tex]$x + x \geq 3$[/tex] which combines the information about the minimum number of hours needed and the fact that she splits the remaining time evenly.
Simplifying the left side of the inequality gives [tex]$2x \geq 3$[/tex]. Dividing both sides by 2 gives [tex]$x \geq \dfrac{3}{2}$[/tex].
Thus, Maggie must practice for at least [tex]$\dfrac{3}{2}$[/tex] hours each of the last two days.
Converting 5/9 to whole number
The answer to your question is 0.55555555555
Solution: You simply divide 5 by 9 to get your whole number. In other words, 5/9 =0.55555555555
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The fraction 5/9 cannot be converted into a whole number because it results in a decimal number (approximately 0.55) upon division.
Explanation:In Mathematics, we have different types of numbers - whole numbers, fractions, decimals, etc. Here, you are asked to convert a fraction 5/9 into a whole number. However, it's essential to understand, that 5/9 cannot be converted into a whole number because it is less than 1.
For general understanding, a whole number can only be a non-negative number without any fractional or decimal parts, such as 0, 1, 2, 3, 4, and so forth. A fraction like 5/9 implies division, and when you divide 5 by 9, you get a decimal number (approximately 0.55), which is not a whole number.
Thus, the fraction 5/9 cannot be precisely converted into a whole number without rounding it off.
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what is the slope of the line that passing through point (2,3) and (-2,5)?
Answer:
[tex]\displaystyle \boxed{-\frac{1}{2}}[/tex]
Step-by-step explanation:
Slope formula:
↓
[tex]\displaystyle \frac{Y_2-Y_1}{X_2-X_1}[/tex]
[tex]\displaystyle Y_2=5\\\displaystyle Y_1=3\\\displaystyle X_2=(-2)\\\displaystyle X_1=2\\[/tex]
[tex]\displaystyle \frac{5-3}{(-2)-2}=\frac{2}{-4}=\frac{2\div2}{-4\div2}=\frac{1}{-2}=-\frac{1}{2}[/tex]
Therefore the slope is -1/2.
-1/2 is the correct answer.
Hope this helps!
What is the slope of a line is parallel to y = (1/2)x+ 3?
Answer here
Answer:1/2
Step-by-step explanation:
the slope of a line in an equation comes before x
since we know parallel lines have the same slope it is 1/2
At the end of the year, a library reported 32 books lost or stolen and 24 books were sent out for repair. If the library originally had 1,219 books, how many were left on the shelves or in circulation?
A. 1,219
B. 1,187
C. 1,163
D. 1,275
there were D. 1163 books left on the shelves or in circulation.
///////////////////////////////////////////////////////////////////////////
let us count the number of books that are NOT on the shelves now.
1st step: 32 + 24 = 56
2nd step: the total number of books minus the amount of books that are damaged or out: 1,219 - 56 = 1163
Answer:
C. 1,163
Step-by-step explanation:
Total books = books on shelves + books lost + books out for repair
What do we know
1219 = books on shelves + 32 + 24
1219 = books on selves + 56
Subtract 56 from each side
1219-56 = books on shelves - 56
1163 = books on shelves
An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown.
Which best describes the range of possible values for the third side of the triangle?
x < 12.5, x > 18.9
12.5 < x < 18.9
x < 6, x > 26
6 < x < 26
Answer:
Option D is correct.
Step-by-step explanation:
The length of 2 sides of triangle are given i.e 10 cm and 16 cm.
We need to find the range of the values of length of the third side.
Sum of 2 sides of triangle is greater than the 3rd side
so, 10+16 = 26
So, the length of third side should be less than 26
and we know that the length of third side should be greater than the absolute difference of other two sides
16-10 = 6
So, the length of third side should be greater than 6
Combining both we get 6<x<26
Hence Option D is correct.
The range of possible values for the third side of the triangle is 6 < x < 26
How to find third side of the triangleSide 1 = 10 cmSide 2 = 16 cmSide 3 = x cmSum of two sides is greater than third side10 + 16 = 26 cm
Length of third side is greater than difference between the two sidesDifference = 16 cm - 10cm
= 6 cm
Therefore, the range of value of the third side is x is greater than 6cm less than 26cm
6 < x < 26
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What is the largest fraction in each group?
5/6 29/36
Answer:
5/6 is larger
Step-by-step explanation:
5/6 * (6/6) = 30/36
30/36 > 29/36
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a triangle has two sides of lenghts 7 and 12 what value could the length of the third side be check all that apply
Answer:
Third length =
12-7 = 5
12+7 = 19
Third length can be only in this range
5Means the third length must be greater than 5 and less than 19.
Step-by-step explanation:
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Answer:
d
Step-by-step explanation:
Match the vocabulary word with the correct definition.
1. trapezoid
A trapezoid with legs of the same length.
2. bases of a trapezoid
A quadrilateral with at least one pair of parallel sides.
3. legs of a trapezoid
The parallel sides.
4. median of a trapezoid
The segment connecting the midpoints of the legs.
5. isosceles trapezoid
The nonparallel sides
Answer:
1. trapezoid
A quadrilateral with at least one pair of parallel sides.
2. bases of a trapezoid
The parallel sides
3. legs of a trapezoid
The nonparallel sides.
4. median of a trapezoid
The segment connecting the midpoints of the legs.
5. isosceles trapezoid
A trapezoid with legs of the same length.
Answer:
Trapezoid:A trapezoid is defined as a quadrilateral with at least one pair of parallel sides, when the trapezoid as equal legs, it's called an isosceles trapezoid.
Bases of a trapezoid:The bases of a trapezoid are the pair of parallel sides, both of them are called base, the longer one is the major base, and the shorter one is the minor base.
Legs of a trapezoid:The legs of a trapezoid are the nonparallel sides, because if they were parallel, that wouldn't be a trapezoid, it would be another quadrilateral.
Median of a trapezoid:The median of a trapezoid is a segment that connects the midpoints of the legs. Remember that medians are always line that intercept midpoints.
Isosceles trapezoid:As we said before, an isosceles trapezoid are those which have legs with equal legs. The name isosceles refers to equality.
Therefore, the right matches are
1. Trapezoid: A quadrilateral with at least one pair of parallel sides.
2. Bases of a trapezoid: The parallel sides.
3. Legs of a trapezoid: The nonparallel sides.
4. Median of a trapezoid: The segment connecting the midpoints of the legs.
5. Isosceles trapezoid: A trapezoid with legs of the same length.
Find The area of the trapezoid
Please help with questions 25-26
Answer:
Part 1) [tex]A=96\ cm^{2}[/tex]
part 2) [tex]A=40.8\ ft^{2}[/tex]
Step-by-step explanation:
Part 1)
we know that
The area of a trapezoid is equal to
[tex]A=(1/2)[b1+b2]h[/tex]
In this problem we have
[tex]b1=12\ cm[/tex]
[tex]b2=6+12+2=20\ cm[/tex]
[tex]h=6\ cm[/tex] ----> perpendicular distance between the two bases
substitute
[tex]A=(1/2)[12+20](6)[/tex]
[tex]A=96\ cm^{2}[/tex]
Part 2)
we know that
The area of a kite is equal to
[tex]A=(1/2)[D1*D2][/tex]
we have
[tex]D1=10.2\ ft[/tex]
[tex]D2=8\ ft[/tex]
substitute
[tex]A=(1/2)[10.2*8][/tex]
[tex]A=40.8\ ft^{2}[/tex]
Answer:
25) 96 cm²
26) 40.8 ft ²
Step-by-step explanation:
25) To find the area of trapezoid
Area of trapezoid = h(a + b)/2
Here a = 6 + 12 + 2 = 20 cm
b = 12 cm and h = 6
Area = h(a + b)/2
= 6(20 + 12)/2
= 96 cm²
26) To find the area of kite
Area of kite = pq/2
Where p and q are the two diagonals
Here p = 10.2 ft and q = 8 ft
Area = pq/2
= (10.2 * 8)/2 = 40.8 ft²
Find the midpoint of the line segment whose endpoints are (-2, 5) and (4, -9).Find the midpoint of the line segment whose endpoints are (-2, 5) and (4, -9).
The midpoint of the line segment with endpoints (-2, 5) and (4, -9) is found using the midpoint formula and is (1, -2).
Explanation:To find the midpoint of the line segment whose endpoints are (-2, 5) and (4, -9), you use the midpoint formula, which is derived from finding the average of the x-coordinates and the y-coordinates of the endpoints respectively.
The midpoint formula is:
( (x1 + x2) / 2, (y1 + y2) / 2 )
Plugging in our given endpoints (-2, 5) and (4, -9) into the formula, it becomes:
( (-2 + 4) / 2, (5 + (-9)) / 2 )
This simplifies to:
( 2 / 2, -4 / 2 )
And finally:
( 1, -2 )
Therefore, the midpoint of the line segment is at coordinates (1, -2).