Answer:
D: 54 Divided by 6
Step-by-step explanation:
To find out how many 6 pound bags of food we can give away, we take the total amount of food and divide by 6
54/6
Logarithms- How to answer these questions?
Answer:
2. m = b³ (= 216)
3. logp(x) = -4
Step-by-step explanation:
2. The given equation can be written using the change of base formula as ...
... log(m)/log(b) + 9·log(b)/log(m) = 6
If we define x = log(m)/log(b), then this becomes ...
... x + 9/x = 6
Subtracting 6 and multiplying by x gives ...
... x² -6x +9 = 0
... (x -3)² = 0 . . . . . factored
... x = 3 . . . . . . . . . value of x that makes it true
Remembering that x = log(m)/log(b), this means
... 3 = log(m)/log(b)
... 3·log(b) = log(m) . . . . . multiply by the denominator; next, take the antilog
... m = b³ . . . . . . the expression you're looking for
___
3. Substituting the given expression for y, the equation becomes ...
... logp(x^2·(p^5)^3) = 7
... logp(x^2) + logp(p^15) = 7 . . . . . use the rule for log of a product
... 2logp(x) + 15 = 7 . . . . . . . . . . . . . use the definition of a logarithm
... 2logp(x) = -8 . . . . . . . . . . . . . . . . subtract 15
... logp(x) = -4 . . . . . . divide by 2
Answer:
For #3: [tex]\log_px=-4[/tex]
Step-by-step explanation:
I'm a little rusty on my logarithm rules for #2, but here's an explanation of #3.
Logarithms: the Inverse of ExponentsIn a sense, we can think of operations like subtraction and division as different ways of representing addition and multiplication. For instance, the same relationship described by the equation 2 + 3 = 5 is captured in the equation 5 - 3 = 2, and 5 × 2 = 10 can be restated as 10 ÷ 2 = 5 without any loss of meaning.
Logarithms do the same thing for exponents: the expression [tex]2^3=8[/tex] can be expressed in logarithms as [tex]\log_28=3[/tex]. Put another way, logarithms are a sort of way of pulling an exponent out onto its own side of the equals sign.
The ProblemOur problem gives us two facts to start: that [tex]log_p(x^2y^3)=7[/tex] and [tex]p^5=y[/tex]. With that, we're expected to find the value of [tex]\log_px[/tex]. [tex]p^5=y[/tex] stands out as the odd-equation-out here; it's the only one not in terms of logarithms. We can fix that by rewriting it as the equivalent statement [tex]log_py=5[/tex]. Now, let's unpack that first logarithm.
Justifying Some Logarithm RulesFor a refresher, let's talk about some of the rules logarithms follow and why they follow them:
Product Rule: [tex]\log_b(MN)=\log_bM+\log_bN[/tex]
The product rule turns multiplication in the argument (parentheses) of a logarithm into addition. For a proof of this, consider two numbers [tex]M=b^x[/tex] and [tex]N=b^y[/tex]. We could rewrite these two equations with logarithms as [tex]\log_bM=x[/tex] and [tex]\log_bN=y[/tex]. With those in mind, we could say the following:
[tex]\log_b(MN)=\log_b(b^xb^y)[/tex] (Substitution)[tex]\log_b(b^xb^y)=log_b(b^{x+y})[/tex] (Laws of exponents)[tex]\log_b(b^{x+y})=x+y[/tex] ([tex]\log_b(b^n)=n[/tex])[tex]x+y=\log_bM+\log_bN[/tex] (Substitution)And we have our proof.
Exponent Rule: [tex]\log_b(M^n)=n\log_bM[/tex]
Since exponents can be thought of as abbreviations for repeated multiplication, we can rewrite [tex]\log_b(M^n)[/tex] as [tex]\log_b(M\times M\cdots \times M)[/tex], where M is being multiplied by itself n times. From there, we can use the product rule to rewrite our logarithm as the sum [tex]\log_bM+\log_bM+\cdots+\log_bM[/tex], and since we have the term [tex]\log_bM[/tex] added n times, we can rewrite is as [tex]n\log_bM[/tex], proving the rule.
Solving the ProblemWith those rules in hand, we're ready to solve the problem. Looking at the equation [tex]\log_p(x^2y^3)=7[/tex], we can use the product rule to split the logarithm into the sum [tex]\log_p(x^2)+\log_p(y^3)=7[/tex], and then use the product rule to turn the exponents in each logarithm's argument into coefficients, giving the equation [tex]2\log_px+3\log_py=7[/tex].
Remember how earlier we rewrote [tex]p^5=y[/tex] as [tex]log_py=5[/tex]? We can now use that fact to substitute 5 in for [tex]log_py[/tex], giving us
[tex]2\log_px+3(5)=7[/tex]
From here, we can simply solve the equation for [tex]\log_px[/tex]:
[tex]2\log_px+15=7\\2\log_px=-8\\\\\log_px=-4[/tex]
which expression is equivalent to 4 times the sum of 3 and x
Answer:
4(3+x)
Step-by-step explanation:
If any thing is in the brackets you need to do it first
so if you do 3 + x × 4 it will give yo 4x + 3 or 3 +4x
The given expression 4 (x + 3) is equivalent to the expression 4x + 12.
What is an equivalent function?The equivalent operations are those that have various forms but have the same outcome.
The expression is given below.
→ 4 (x + 3)
The expression can be written as
→ 4x + 12
The given expression 4 (x + 3) is equivalent to the expression 4x + 12.
More about the equivalent link is given below.
https://brainly.com/question/889935
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PLS HELP!!!!!! NOW PLS!!!!
Given that the points (-1, 5) and (2, 1) are vertices of a rectangle with sides parallel to the axes, how much longer is the length than the width?
A. 1 Unit
B. 2 Units
C. 3 Units
D. 4 Units
Answer:
The right answer is 1 unit or A
Step-by-step explanation:
what is 3/20 as a percentage
Answer:
15%
Step-by-step explanation:
Percent means out of 100. Lets get the denominator out of 100
3/20 * 5/5 = 15/100
This is 15%
Final answer:
To convert the fraction 3/20 to a percentage, first convert it to a decimal by dividing 3 by 20. Then, multiply the decimal by 100 to get the percentage.
Explanation:
To express 3/20 as a percentage, you can multiply the fraction by 100. The calculation is (3/20) * 100 = 15%. Therefore, 3/20 as a percentage is 15%. This means that 3 out of every 20 parts represent 15% of the whole. In percentage terms, it provides a convenient way to compare the fraction to 100, making it easier to understand its relative size or portion in relation to the total. In this case, 15% indicates the proportion of the whole that is represented by the fraction 3/20.
A regular dodecagon has 12 sides. What is the smallest angle of rotation about its center that carries a dodecagon onto itself?
Answer:
30°
Step-by-step explanation:
No. of sides in dodecagon = 12
No. of angles = 12
Since its regular, all sides and all angles are equal.
total rotational angle = 360°
since no. of angles = 12
and all angles are equal,
rotational angle at which, it will co - incide with itself = [tex]\frac{360}{12}[/tex]
= 30°
A regular dodecagon will be onto itself it is rotated about the central angle 30°.
Answer: 30°
Step-by-step explanation:
I is the origin and P is the (4,3). Rx and Ray are reflections around the x- and y- axes
(4,-8)
(-4,8)
(-4,-8)
Answer:
The correct option is 1. The image of (2,4) is (4,-8).
Step-by-step explanation:
The given rule is
[tex]R_x{\circ}D_{o,2}:(2,4)[/tex]
The transformations perform from right to left. [tex]D_{o,2}[/tex] means dilation with scale factor 2 and center of dilation is origin.
The given rule defines the dilation with scale factor 2 and center of dilation is origin followed by reflection across x-axis.
If a figure dilated by scale factor k and the center of dilation is origin, then
[tex](x,y)\rightarrow (kx,ky)[/tex]
The scale factor is 2,
[tex](x,y)\rightarrow (2x,2y)[/tex]
[tex](2,4)\rightarrow (4,8)[/tex]
If a figure reflected across x-axis, then x-coordinate remains the same but the sign of y-coordinate is changed.
[tex](x,y)\rightarrow (x,-y)[/tex]
[tex](4,8)\rightarrow (4,-8)[/tex]
Therefore image of (2,4) is (4,-8) and option 1 is correct.
can someone help me and explain how you did it?
Answer:
Step-by-step explanation: To find a y intercept you must find what y is when x is 0 so because it already tells you on the table the y intercept is 4. To find slope take 2 x intercepts and 2 y intercepts. For this well take the 0,4 and 5,1. The take the y from both pairs and minus them so it will look like 4 minus 1. Then draw a line under the equation under this line do the same thing but with the x's from both pairs so 0-5 then you will get as a result of both -3/5 as your slope.
Answer:
slope: -3/5
y-intercept: (0, 4)
slope-intercept form: y = -3/5x + 4
Step-by-step explanation:
Finding the slopeTo find the slope of this line, you would take two points from the table and substitute their coordinates into the slope formula.
Slope formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
I'm going to use the points (0, 4) and (5, 1). You can really use any point from the table. Substitute these points into the formula to find the slope.
(0, 4), (5, 1) → [tex]\frac{1-4}{5-0} \rightarrow \frac{-3}{5}[/tex]
This means the slope of the line is -3/5.
Finding the y-interceptThe y-intercept will always have the value of x be 0 (so the point is solely on the y-axis), so by looking at the table we can see that the y-intercept is at (0, 4).
Finding the slope-intercept formSince we have the slope and a point of the line, we must use point-slope form to find the equation of the line in slope-intercept form. Substitute in the point (0, 4) --you could use any point from the table-- and the slope -3/5 into the point-slope form equation.
point-slope form: y - y1 = m(x - x1) --you'll be substituting the point coordinates and slope into y1, x1, and m.
y - (4) = -3/5(x - (0))
Simplify.
y - 4 = -3/5x
Add 4 to both sides.
y = -3/5x + 4 is the equation of the line in slope-intercept form (you have both the slope and the y-intercept in this form).
the area of kens rectangular yard is 480 square feet. the yard is 24feet wide. in order to fence in the garden completely on all four sides,how many feet of fencing would ken need to buy.
Answer:
88 ft
Step-by-step explanation: Start with the formula for the area of a rectangle:
A = L*W, where L is the length and W is the width.
Here, the width is W = 24 ft, and the area i s 480 ft^2. Thus,
A = 480 ft^2 = L (24ft), which yields L = (480/24) ft = 20 ft.
The length of the fencing required is actually the perimeter of the yard, which is P = 2L + 2W.
Substituting 20 ft for L and 24 ft for W, we get:
P = perimeter of yard = amount of fending needed:
P = 2(20 ft) + 2(24 ft) = 88 ft
Ken would need 88 ft of fencing to enclose his entire yard.
Ken needs to buy 88 feet of fencing to enclose his rectangular yard, which has an area of 480 square feet and is 24 feet wide.
To find out how much fencing Ken would need to buy to enclose his rectangular yard, we first need to calculate the dimensions of the yard. We know the area of the yard is 480 square feet and the width is 24 feet.
To find the length, we use the following equation for the area of a rectangle (Area = length imes width):
480 square feet = length x 24 feet
By dividing both sides by 24 feet, we obtain:
length = 480 / 24
length = 20 feet
Now, to calculate the total amount of fencing needed, we add together the lengths of all four sides:
Total fencing = 2 imes (length + width)
Total fencing = 2 imes (20 feet + 24 feet)
Total fencing = 2 imes 44 feet
Total fencing = 88 feet
Therefore, Ken needs to buy 88 feet of fencing to enclose his yard completely on all four sides.
4. FLOWERS Bethany placed a bouquet of roses in a vase full of water. Each day she recorded how much water had evaporated from the vase before refilling it. The results are shown in the table below. Over the course of five days how much water had evaporated? Use mental math to find your answer.
Answer:
A x 5
Step-by-step explanation:
Answer:
take all evaporation numbers and add them together to get the answer u r looking for
Step-by-step explanation:
A lot is in the shape of a trapezoid. The sum of the bases is 280 feet. If the area of the lot is 8,400 square feet, what is the distance across the lot, i.e., the altitude of the figure? The altitude of the trapezoid is feet.
Answer:
The altitude of the trapezoid is 60 feet.
Step-by-step explanation:
Trapezoid
Sum of the bases: B+b=280 feet
Area of the trapezoid: A=8,400 feet^2
Altitude of the trapezoid: h=?
The formula to calculate the area of a Trapezoid is:
A = (1/2) (B+b) h
Replacing the given values:
8,400 feet^2 = (1/2) (280 feet) h
(1/2) (280 feet) = (140 feet)
8,400 feet^2 = (140 feet) h
Solving for h: Dividing both sides of the equation by 140 feet:
8,400 feet^2 / (140 feet) = (140 feet) h / (140 feet)
60 feet = h
h = 60 feet
Answer: The altitude of the trapezoid is 60 feet.
Answer:
60
Step-by-step explanation:
In a geometric sequence {an}, if a1 = 4 and r = 0.2, the first 4 terms in the sequence are A) {4, .8, .16, .032,...}. Eliminate B) {4, 20, 100, 500,...}. C) {4, 4.2, 4.4, 4.6,...}. D) {4, 3.8, 3.6, 3.4,...}.
Hey man, your answer is (A) I took the test!!!
The first 4 terms in the sequence are :
A) { 4 , 0.8 , 0.16 , 0.032 , . . . }Further explanationFirstly , let us learn about types of sequence in mathematics.
Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.
[tex]\boxed{T_n = a + (n-1)d}[/tex]
[tex]\boxed{S_n = \frac{1}{2}n ( 2a + (n-1)d )}[/tex]
Tn = n-th term of the sequence
Sn = sum of the first n numbers of the sequence
a = the initial term of the sequence
d = common difference between adjacent numbers
Geometric Progression is a sequence of numbers in which each of adjacent numbers have a constant ration.
[tex]\boxed{T_n = a ~ r^{n-1}}[/tex]
[tex]\boxed{S_n = \frac{a( 1 - r^n ) }{1 - r}}[/tex]
Tn = n-th term of the sequence
Sn = sum of the first n numbers of the sequence
a = the initial term of the sequence
r = common ratio between adjacent numbers
Let us now tackle the problem!
Given:
a = 4
r = 0.2
Solution:
[tex]T_n = a ~ r^{n-1}[/tex]
[tex]T_1 = 4 \times 0.2^{1-1} = 4 \times 1 = 4[/tex]
[tex]T_2 = 4 \times 0.2^{2-1} = 4 \times 0.2 = 0.8[/tex]
[tex]T_3 = 4 \times 0.2^{3-1} = 4 \times 0.04 = 0.16[/tex]
[tex]T_4 = 4 \times 0.2^{4-1} = 4 \times 0.008 = 0.032[/tex]
Therefore , the first 4 terms in the sequence are :
A) { 4 , 0.8 , 0.16 , 0.032 , . . . }Learn moreGeometric Series : https://brainly.com/question/4520950Arithmetic Progression : https://brainly.com/question/2966265Geometric Sequence : https://brainly.com/question/2166405Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Arithmetic and Geometric Series
Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term
i’m in algebra 2 and it’s long division please help
[tex]\dfrac{5x^4+10x^3-7x+1}{x+2}=(5x^4+10x^3-7x+1):(x+2)[/tex]
[tex]_+\begin{matrix}(5x^4&+&10x^3&-&7x&+&1)&:&(x+2)&=5x^3-7\\-5x^4&-&10x^3\end{matrix}\\\overline{_+\begin{matrix}\ \ =&&&&=&\ \ \ -&7x&+&1\\&&&&&&7x&+&14\end{matrix}}\\\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\ 15}[/tex]
[tex]\dfrac{5x^4+10x^3-7x+1}{x+2}=(5x^4+10x^3-7x+1):(x+2)=5x^3-7+R(15)\\\\5x^4+10x^3-7x+1=(x+2)(5x^3-7)+15[/tex]
Final answer:
Long division is a method used to divide two polynomials in algebra. It involves arranging the dividend and divisor, determining the term of the quotient, subtracting and repeating until there are no more terms left to bring down.
Explanation:
In algebra, long division is a method used to divide two polynomials. It is especially useful when the dividend (the polynomial being divided) has a higher degree than the divisor (the polynomial dividing the dividend).
Here's a step-by-step explanation:
Arrange the dividend and divisor in descending order.Determine the term of the quotient by dividing the leading terms of the dividend and divisor.Multiply the entire divisor by the term of the quotient and subtract it from the dividend.Repeat steps 2 and 3 until there are no more terms left to bring down.The result is the quotient and any leftover terms are the remainder.Let me know if you need further assistance or if there's anything else I can help you with!
Which of the function below is that inverse of f(x)=x^-25
Answer:
g⁻¹(x) = ±√(x + 25)
Step-by-step explanation:
g(x) = x² - 25 Rename g(x) as y
y = x² - 25
=====
Solve for x
y = x² - 25 Add 25 to each side
y + 25 = x² Take the square root of each side
x = ±√(y + 25) Switch x and y
y = ±√(x + 25) Rename y as g inverse
g⁻¹(x) = ±√(x + 25)
=====
See the graphs of g(x) and g⁻¹(x) below.
g(x) is the red line. g⁻¹(x) is the purple line.
Each graph reflects the other about the dashed line representing the function y = x.
Which number sentence is true
Answer:
B is the right one i bet u 100 point s
Answer:
B is the correct answer.
The brackets ║ represent absolute value. Absolute value is ALWAYS positive. I hope this helps you!
-Mikayla
Drag each tile to the correct box.
A scientist is studying the growth rates of three samples of bacteria in different conditions. The following three functions represent the number of bacteria in the three samples after x hours.
Order the samples by their average growth rate over the interval [1, 3], from least to greatest.
Answer: C < B < A
Step-by-step explanation:
First, let's evaluate the growth rate of A from [1, 3]
[tex]f(x) = 200\bigg(\dfrac{3}{2}\bigg)^1[/tex]
= 300
coordinate is (1, 300)
[tex]f(x) = 200\bigg(\dfrac{3}{2}\bigg)^3[/tex]
= 675
coordinate is (3, 675)
Average growth rate (AGR) is: [tex]\dfrac{675-300}{3-1} = \dfrac{375}{2} = 187.5[/tex]
AGR (A) = 187.5
*************************************************************************************
Next, let's evaluate the growth rate of B from [1, 3]
The coordinates are already provided as (1, 120) and (3, 480)
Average growth rate (AGR) is: [tex]\dfrac{480-120}{3-1} = \dfrac{360}{2} = 180[/tex]
AGR (B) = 180
*************************************************************************************
Lastly, let's evaluate the growth rate of C from [1, 3]
f(x) = 600(1.2)ˣ
f(x) = 600(1.2)¹
= 720
coordinate is (1, 720)
f(x) = 600(1.2)³
= 1036.8
coordinate is (3, 1036.8)
Average growth rate (AGR) is: [tex]\dfrac{1036.8-720}{3-1} = \dfrac{316.8}{2} = 158.4[/tex]
AGR (C) = 158.4
use the law of cosines to find each missing side
Answer:
29.03 units
Step-by-step explanation:
x^2 = 10^2 + 19^2 - 2*19*20 cos 122
= 100 + 361 - 720 * -0.52992
= 842.54
x = 29.03
What is the equation of the graph below?
Answer:
[tex]y=cos(x+\pi )[/tex]
Step-by-step explanation:
From the graph, we can see that y = -1 when x = 0.
So to check whether which of the given options is the equation of the given graph, we will set our calculator to the radian mode and then plug the value of x as 0.
1. y = cos(x + pi/2) = cos(0 + pi/2) = 0
2. y = cos(x+2pi) = cos(0+2pi) = 1
3. y = cos(x+pi/3) = cos(0+pi/3) = 1/2 = 0.5
4. y = cos(x+pi) = cos(0+pi) = -1
Therefore, the equation of this graph is y = cos(x+pi) = cos(0+pi) = -1.
7 1/3 ∙ x = 1.6 ÷ 6/11
x = __
Please Help!
Answer:
x= 0.4
Step-by-step explanation:
We need to solve and find the value of x
7 1/3x = 1.6 ÷ 6/11
Converting mixed fraction into improper fraction
22/3 x = 1.6 ÷ 6/11
Converting ÷ sign by X and reciprocating the term
22/3 x = 1.6 * 11/6
Now divide both sides by 3/22
x = 1.6 * 11/6 * 3/22
x = 1.6 * 1/2 * 1/2
x = 1.6/4
x = 0.4
S0, x= 0.4
what three things must a ordered pair have?
Answer: An x and y value, parenthesis around the values, and a comma in between them.
Examples of ordered pairs: (2, 5), (1872, 1683), (-3, 7), (7/8, -10/2)
The letters in the word Mississippi are put into a bag. What’s the probability of randomly selecting a vowel from the bag ?
- 3/11
- 2/11
- 1/11
- 4/11
Combine the like terms to create an equivalent expression. 3n+7−2
Answer:
3n+5
Step-by-step explanation:
What is the 41st term in sequence 8,10,12,14,.....?
Park Crest Middle School has a population of about 400 8th graders. Parkcrest is one of several middle schools in the state which has a total of 806, 240 8th graders. Use powers of 10 to estimate about how many times greater the States population of eighth-graders is compared to the number of 8th graders at Park Crest Middle School.
Answer:
[tex]8.05 * 10^{5}[/tex]
Step-by-step explanation:
Thinking process:
the population of Park Crest Middle School = 400 children
The population in the state = 806, 240 children
The difference:
[tex]806240 - 400\\= 805840[/tex]
Expressing the difference in standard form gives:
8.05 × 10⁵
You earn $8.60/hr. You work 32 hr/wk and your deductions are FICA (7.65%), federal tax withholding (10.6%), and state tax withholding (8.25%). How much do you have direct-deposited bi-weekly?
The amount that is direct-deposited bi-weekly is 404.30.
To calculate the bi-weekly direct deposit amount, we need to follow these steps:
1. Calculate the gross pay for a week:
Gross pay per week = Hourly wage * Hours worked per week
Gross pay per week = $8.60/hr * 32 hr/wk
Gross pay per week = $275.20
2. Calculate the total deductions per week:
Total deductions rate = FICA rate + federal tax rate + state tax rate
Total deductions rate = 7.65% + 10.6% + 8.25%
Total deductions rate = 26.5%
Total deductions per week = Gross pay per week * Total deductions rate
Total deductions per week = $275.20 * 26.5%
Total deductions per week = $73.049
3. Calculate the net pay for a week:
Net pay per week = Gross pay per week - Total deductions per week
Net pay per week = $275.20 - $73.049
Net pay per week = $202.151
4. Calculate the bi-weekly net pay:
Bi-weekly net pay = Net pay per week* 2
Bi-weekly net pay = $202.151 * 2
Bi-weekly net pay = $404.302
Since the net pay is calculated to the nearest cent, we can round the bi-weekly net pay to the nearest cent as well:
Bi-weekly net pay (rounded) = $404.30
Therefore, the amount that is direct-deposited bi-weekly is 404.30.
The answer is: $404.30.
A customers photo cell phone bill this month is $50 and 50 Cent the company charges a monthly fee of $18 +5 cents for each car used in to represent the number of calls
Morita works in a florist shop and makes flower arrangements. She outs 10 flowers in each case, and 2/10 of the flowers are daisies. If Morita makes 4 arrangements, how many daisies does she need. Show how you can check your answer. Last weekend, Morita used 10 daisies to make flower arrangements. How many flowers other than daisies did she use to make the arrangements? Explain your reasoning.
Answer:
8 daisies
Step-by-step explanation:
You have to multiply the amount of vases by daisies.
Answer:
Givens
Morita outs 10 flowers in each case.2/10 of the flowers are daisies.Morita makes 4 arrangements.We know that Morita arranges 4 cases, each of them has 10 flowers.
So, if there are 2/10 daisies per case, that means each can contains 2 daisies.
But, she did 4 arrangements. There are 2x4 = 8 daisies in total.
Now, last weekend, Morita used 10 daisies to make flower arrangements, and we know she tend to use 2/10 of the flowers as daisies, that means this fraction represents daisies,
[tex]\frac{2}{10}x=10\\ x=\frac{100}{2}\\ x=50[/tex]
Therefore, there are 50 flowers in total.
What is 2pi/ 5radians in degrees
Answer:
2/5 * pi radians = 72 degrees
Step-by-step explanation:
To convert radians to degrees, we multiply by 180/pi
2 * pi/5 * 180/pi =
The pi/pi cancels leaving
2/5 * 180
360/5
72
2/5 * pi radians = 72 degrees
Answer fast!!!!!!!!!!!
There are 90 students in Grade 5, and 10% of them were absent today.In Grade 6, 15% of the 80 students were absent today.What was the total number of students in the two grades who were present today?
Answer:
21 students
Step-by-step explanation:
90 x .10 = 9
80 x .15 = 12
9 + 12 = 21 students
in the figure above CD is the perpendicular bisector of AB. three students explained how they proved ADC is congruent to BDC
who's explanation is incorrect??
Answer:
All explanations are correct
Step-by-step explanation:
In triangle ABC, CD is the perpendicular bisector of AB, thus using ΔADC and ΔBDC,
AC=BC ( Since CD is perpendicular to AB, therefore C is equidistant from both A and B)
∠ADC=∠BDC=90°(CD perpendicular AB)
CD=CD( Reflexive property)
therefore, by SAS rule of congruency,
ΔADC≅ ΔBDC,
Also, In the same triangles, AC=BC ( Since CD is perpendicular to AB, therefore C is equidistant from both A and B)
CD=CD( Reflexive property)
AD=BD (D is the midpoint and divides AB into two equal halves)
Thus, by SSS rule of congruency,
ΔADC≅ ΔBDC,
Thus, all the three explanations are correct.
In the given case, we can conclude that All explanations are correct
In triangle ABC, let CD be the perpendicular bisector of AB. We can use the properties of triangles to demonstrate that ΔADC is congruent to ΔBDC.
AC=BC: This holds true because CD is perpendicular to AB, making point C equidistant from both A and B.
∠ADC=∠BDC=90°: Since CD is perpendicular to AB, both angles ADC and BDC are right angles.
CD=CD: This is a reflexive property, stating that any line segment is equal to itself.
By applying the SAS (Side-Angle-Side) rule of congruency using the above properties, we can conclude that ΔADC is congruent to ΔBDC.
Furthermore, we can establish that in these congruent triangles:
AC=BC (since C is equidistant from A and B due to CD being perpendicular to AB).
CD=CD (reflexive property).
AD=BD (as D is the midpoint of AB).
Hence, using the SSS (Side-Side-Side) rule of congruency, we can also conclude that ΔADC is congruent to ΔBDC.
Therefore, all three explanations correctly demonstrate the congruence of these triangles.
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