Given:AC is perpendicular to CB, angle DAB is congruent to Andre CAB.Prove triangle ABC is congruent to triangle ABD
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we have that
1) AC ⊥ CB and AD ⊥ DB -------> Given
2) Given
3) by definition of right angle
4) AB=AB ----------> by reflexive property
5) by complementary angles in a right triangle
6) by complementary angles in a right triangle
7) by substitution
8) ΔABC≅ ΔABD -------> by ASA congruence theoremRelated Questions
Which number would divide the numerator and the denominator of the firstfraction to yield the second fraction?
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Let the fraction to be divided be x.
[tex]\begin{gathered} \frac{10}{12}\div x=\frac{5}{6} \\ \text{Cross multiplying,} \\ x=\frac{5}{6}\times\frac{12}{10}=\frac{2}{2} \end{gathered}[/tex]Therefore, the fractional number which divide the first fraction is 2/2.
Which values of a, b, and c correctly represent the answer in simplest form? anipa 42 O a=3, b= 6, C = 10 0 0 a = 3,6= 3, C= 5 a= 5, b= 3, C= 3 O a= 10,b=6, C= 3
Answers
We can now compare the result of the left-hand side to that of the
right-hand side of the equation in the question
[tex]3\frac{3}{5}\text{ =a}\frac{b}{c}[/tex]It can be seen that a = 3
b= 3
c= 5
I need help with this bellwork
Answers
We have the point U(-5,-2)
Translated 2 units right means add 2 to the x coordinate
Translated 2 units up means add 2 to the y coordinate
The new point is U'
U'=(-5+2,-2+2)=(-3,0)
U'=(-3,0)
Can you help me or teach me how to do it?
Answers
We have an augmented matrix representing a system of equations.
As it has 4 columns and tow rows, we can see that the system has 3 variables (the last column is for the independent term) and 2 equations.
Then, it will have at least one degree of freedom: the value of all the variables will depend on the value of one of the variables.
We can translate the matrix to equations as:
[tex]\begin{gathered} \begin{cases}0x_1+1x_2-6x_3=4 \\ 1x_1-2x_2+10x_3={-2}\end{cases} \\ \\ \begin{cases}x_2-6x_3=4 \\ x_1-2x_2+10x_3={-2}\end{cases} \end{gathered}[/tex]NOTE: we can solve it using row operations but it is easier to understand in this in equation form rather than matrix form.
We can use the first equation to write x2 in function of x3:
[tex]\begin{gathered} x_2-6x_3=4 \\ x_2=6x_3+4 \end{gathered}[/tex]We can now replace x2 in the second equation and then write x1 in function of x3:
[tex]\begin{gathered} x_1-2x_2+10x_3=-2 \\ x_1-2(6x_3+4)+10x_3=-2 \\ x_1-12x_3-8+10x_3=-2 \\ x_1-2x_3=-2+8 \\ x_1-2x_3=6 \\ x_1=2x_3+6 \end{gathered}[/tex]We now see that we have two variables in function of the third one.
If we give x3 a value, then we can find the values of x1 and x2 that satisfy the equations for the value of x3 given.
Answer:
x1 = 2x3 + 6
x2 = 6x3 + 4
x3 is free
[Option A]
The cost of a pen is three times the cost of a pencil. The cost of 4 pencils and 3 pens is $9.75. What is the cost of a pencil?
Answers
ANSWER
[tex]\$0.75[/tex]EXPLANATION
Let the cost of the pen be x.
Let the cost of the pencil be y.
The pen costs 3 times as much as the pencil. This implies that:
[tex]x=3y[/tex]The cost of 4 pencils and 3 pens is $9.75. This implies that:
[tex]4y+3x=9.75[/tex]Substitute the first equation into the second equation:
[tex]4y+3(3y)=9.75[/tex]Simplify and solve for y:
[tex]\begin{gathered} 4y+9y=9.75 \\ 13y=9.75 \\ \Rightarrow y=\frac{9.75}{13} \\ y=\$0.75 \end{gathered}[/tex]That is the cost of a pencil.
8 and 9 question, what is the volume of the gift box ?
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Given:
Find-:
The surface area of the box
Explanation-:
The surface area of the box is:
[tex]=ABCD+EFGH+EDCH+ABGF+ADEF+BCGH[/tex]So,
[tex]\begin{gathered} ABCD=EFGH \\ \\ EDCH=ABGF \\ \\ ADEF=BCGH \end{gathered}[/tex]So, surface area becomes:
[tex]=2(ABCD+EDCH+ADEF)[/tex]The formula of area is:
[tex]\text{ Area }=\text{ Length }\times\text{ Width}[/tex][tex]\begin{gathered} =2((15\times10)+(10\times2)+(15\times2)) \\ \\ =2(150+20+30) \\ \\ =2(200) \\ \\ =400\text{ in}^2 \end{gathered}[/tex]The wrapping paper area is 400in²
help please! American Fitness charges $50 per month of membership at its gym plus a one-time registration fee of $200. X Means what?Y Means what? Rule:
Answers
Explanation
Step 1
Let
x represents the number of months
y representes the total paid
Charges:
charges $50 per month =50x
one-time fee=200
total=200+5x
[tex]y=5x+200[/tex]I hope this helps you
Please assist me in finding the surface of this problem.
Answers
Given:
[tex]\begin{gathered} Base\text{ \lparen a\rparen = 2 cm} \\ Height\text{ \lparen h\rparen = 6 cm} \end{gathered}[/tex]Required:
The surface area of a hexagonal pyramid.
Explanation:
The surface area of the hexagonal pyramid with base a and a height h is given as,
[tex]\begin{gathered} Area\text{ = }\frac{3\sqrt{3}}{2}a^2\text{ + 3a }\sqrt{h^2}\text{ + }\frac{3a^2}{4} \\ \end{gathered}[/tex]Substituting the given value in the formula,
[tex]\begin{gathered} Area\text{ = }\frac{3\sqrt{3}}{2}\times\text{ \lparen2\rparen}^2\text{ + 3}\times2\times\sqrt{6^2\text{ + }\frac{3\times2^2}{4}} \\ Area\text{ = 47.86229} \\ Area\text{ }\approx\text{ 47.86 cm}^2 \end{gathered}[/tex]Answer:
Thus the surface area of the given hexagonal pyramid is 47.86 sq.cm.
A floor plan of Eva's new house has a scale of 1 in:12 feet. On the floor plan, Eva's bedroom is 3/4 in. by 7/8in.What is the actual area of Eva's bedroom?
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I need how finding the value of X for these boxs?
Answers
STEP - BY - STEP EXPLANATION
What to find?
The value of x.
Given:
Step 1
Recall the exterior angle theorem.
The exterior angle is equal to the sum of the two opposite interior angle.
Step 2
Use the theorem above to solve for the value of x.
That is;
[tex]\begin{gathered} x=47+39 \\ \\ x=86^\degree \end{gathered}[/tex]ANSWER
86 degree
Stan and Francine want to make soup. In order to get the right balance of ingredients for their tastes then bought 5 pounds of potatoes at $3.93 per pound, 4 pounds of cod for $2.37, and 4 pounds of fish broth for $2.34 per pound. Determine the cost per pound of the soup.
Answers
Answer:
[tex]\text{ \$2.96}[/tex]Explanation:
Here, we want to get the cost per pound of the soup
What we have to do here is, to sum up the costs and divide by the total pounds of ingredients
To get the cost of each ingredient, we have to multiply the number in pounds by each cost per pound
Mathematically, we have the cost per pound as follows:
[tex]\frac{5(3.93)\text{ + 4\lparen2.37\rparen + 4\lparen2.34\rparen}}{5+4_+4}\text{ = }\frac{38.49}{13}\text{ = \$2.96}[/tex]The sum of a number and three is five. Find the number.The number is ?
Answers
Given the description "The sum of a number and three is five", you need to remember the following:
- A Sum is the result of an Addition.
-The verb "is" indicates that it is an equation and, therefore, you must use this sign:
[tex]=[/tex]Let be "x" the unknown number.
"The sum of a number and three" can be represented with this expression:
[tex]x+3[/tex]Therefore, the equation is:
[tex]x+3=5[/tex]In order to find the value of "x", you need to apply the Subtraction Property of Equality by subtracting 3 from both sides of the equation:
[tex]\begin{gathered} x+3-(3)=5-(3) \\ x=2 \end{gathered}[/tex]Hence, the answer is: The number is 2.
At a historical landmark, candles are used to simulate an authentic atmosphere. A volunteer is currently putting new candles in the candle holders. On the east side, he replaced candles in 25 small candle holders and 16 large candle holders, using a total of 203 candles. On the west side, he replaced the candles in 3 small candle holders and 16 large candle holders, for a total of 137 candles. How many candles does each candle holder hold?
Answers
Let x be the number of candles in a small candle holder
Let y be the number of candles in a large candle holder
On the east side, he replaced candles in 25 small candle holders and 16 large candle holders, using a total of 203 candles:
[tex]25x+16y=203[/tex]On the west side, he replaced the candles in 3 small candle holders and 16 large candle holders, for a total of 137 candles:
[tex]3x+16y=137[/tex]System of equations:
[tex]\begin{gathered} 25x+16y=203 \\ 3x+16y=137 \end{gathered}[/tex]Elimination method:
1. Subtract equations:
2. Solve x:
[tex]\begin{gathered} 22x=66 \\ \frac{22}{22}x=\frac{66}{22} \\ \\ x=3 \end{gathered}[/tex]3. Use the value of x=3 to solve y:
[tex]\begin{gathered} 25x+16y=203 \\ 25(3)+16y=203 \\ 75+16y=203 \\ 75-75+16y=203-75 \\ 16y=128 \\ \frac{16}{16}y=\frac{128}{16} \\ \\ y=8 \end{gathered}[/tex]Then, each small candleholder holds 3 candles, and each large one holds 8 candlesWhich equation for the circle with center (4,8) and radius2?
Answers
ANSWER:
D. (x - 4)² + (y - 8)² = 4
STEP-BY-STEP EXPLANATION:
The equation of the circle has the following form:
[tex]\left(x−a\right)^2+\left(y−b\right)^2=r^2[/tex]Where (a,b) is the center and r is the radius, we substitute each value and obtain the correct equation:
[tex]\begin{gathered} \left(x-4\right)^2+\left(y-8\right)^2=2^2 \\ \\ \left(x-4\right)^2+\left(y-8\right)^2=4 \end{gathered}[/tex]So the correct answer is option D. (x - 4)² + (y - 8)² = 4
y=4x-7. find slope and Y- intercept
Answers
m = 4
y - intercept = -7
Explanation:y = 4x - 7
equation of line: y =mx + b
where m = slope
b = y-intercept
comparing both equations:
mx = 4x
m = 4
b = -7
y - intercept = -7
Lisa's Scrub-A-Dub Maid Service charges a initial fee of 20.00 plus 10.00 for every hour spent cleaning your home. Identify and state the starting charges and is this a growth or decay?
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Charges are= $20.00 + 10•N
Then answer is
Starting charges = $20
and
its a growth, because 10N is added
DAVIDPablo is studying the function f(x) shown in the graph. He claims that he can transform the function to include theordered pair (2, 2).86x)20-6-6Select the function that supports his claim.2US
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ANSWER
Function q(x) = f(x - 2) supports his claim
EXPLANATION
Function r(x) = f(x) - 2 would translate the graph 2 units down, so the vertex would be at (0,0)
Function s(x) = f(x) + 2 would translate the graph 2 units up, so the vertex would be at (0, 4) and the
Find the unknown number in the proportion 6/7 = x/95 Round your answer to the nearest hundredth.
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The given proportion is
[tex]\frac{6}{7}=\frac{x}{95}[/tex]To solve this proportion, we just have to multiply each side by 95.
[tex]\begin{gathered} \frac{x}{95}\cdot95=\frac{6}{7}\cdot95 \\ x=\frac{570}{7}\approx81.43 \end{gathered}[/tex]Therefore, the unknown number is 81.43, approximately.What is the domain and range of ƒ(x)=√7-x^2
Answers
SOLUTION
The function given is
[tex]f(x)=\sqrt{7-x^2}[/tex]The domain of a function is the set of input values (x-values) for which the function is defined or real.
To obtain the domain of the function above, we need to solve the expression in the square root.
[tex]\begin{gathered} 7-x^2\ge0 \\ \text{Then, subtract 7 from both sides} \\ 7-7-x^2\ge0-7 \\ -x^2\ge-7 \\ \text{Multiply both sides by -1} \\ x^2\le7 \end{gathered}[/tex]Take square root of both sides we have
[tex]\begin{gathered} \sqrt{x^2}\le\pm\sqrt[]{7} \\ \text{Then} \\ x^{}\le\pm\sqrt[]{7} \end{gathered}[/tex]Hence, the domain becomes
[tex]\begin{gathered} -\sqrt{7}\le\: x\le\sqrt{7} \\ or \\ \mleft[-\sqrt{7},\: \sqrt{7}\mright] \end{gathered}[/tex]Domain is [-√7,√7]
Similarly, for th range of f(x) we have
[tex]\begin{gathered} \mleft[0,\: \sqrt{7}\mright] \\ or \\ \: 0\le\: f\mleft(x\mright)\le\sqrt{7} \end{gathered}[/tex]Therefore
Range is [0,√7]
The area A, in square meters, of a rectangle with a perimeter of 80 meters is given by the equation A = 40w − w2, where w is the width of the rectangle in meters. What is the width of the rectangle if its area is 300 m2?
Answers
The equation for the area of the rectangle is given by:
A=40w - w²
But the value of the area A = 300
Substitute the value of A into the equation
300= 40w - w²
Rearrange the equation
w² - 40w + 300 = 0
The above is now a quadratic equation
To find the width, simply solve for w in the above quadratic equation.
Using the formula method to solve the above quadratic equation;
[tex]w=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]w² - 40w + 300 = 0
a=1 b=-40 and c=300
substitute the values into the formula and evaluate
[tex]w=\frac{-(-40)\pm\sqrt[]{(-40)^2-4(1)(300)}}{2(1)}[/tex][tex]=\frac{40\pm\sqrt[]{1600-1200}}{2}[/tex][tex]=\frac{40\pm\sqrt[]{400}}{2}[/tex][tex]=\frac{40\pm20}{2}[/tex][tex]=\frac{40}{2}\pm\frac{20}{2}[/tex][tex]=20\pm10[/tex]Either w = 20 + 10 or w= 20 - 10
w = 30 or w=10
This implies that there are two possible values for the width of the rectangle
Let's check our answer
p = 2l + 2w
80 = 2l + 2w
40 = l + w
If w = 30
l = 40 - 30 = 10
A = l x w = 10 x 30 = 300 m²
If w=10
l=40 - 10 = 30
A = l x w = 30 x 10 = 300 m²
Therefore, the width of the rectangle is either 30m or 10 m
Ms. Brooks put $1200 in a3retirement account that offers8% interest compounded annually.Ms. Brooks makes no additionaldeposits or withdrawals. How muchinterest will Ms. Brooks have earnedat the end of 2 years?
Answers
Solution
- We are required to find the compound interest on a $1200 invested in a retirement account if it is compounded annually at 8% interest for 2 years.
- In order to find the compounded interest, we use the formula:
[tex]\begin{gathered} A-P=I \\ \text{where,} \\ A=\text{ Amount compounded after n years} \\ P=\text{ Principal or Initial Amount} \\ I=\text{ Compounded interest} \end{gathered}[/tex]- But before we can use the above formula, we need to first calculate the Amount compounded. This can be gotten using the formula below:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \\ \text{where,} \\ n=\text{ The number of times the interest in compounded per year} \\ t=\text{ Number of years} \end{gathered}[/tex]- Thus, we can proceed to solve the question by first finding the Amount compounded over the 2 years and then going on to calculate the compound interest.
Compounded Amount:
We can find the compounded amount as follows:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \\ A=1200(1+\frac{8}{100\times1})^{2\times1} \\ \\ A=1200(1+\frac{8}{100})^2 \\ \\ A=1399.68 \end{gathered}[/tex]-
Compounded interest
[tex]\begin{gathered} I=A-P \\ I=1399.68-1200 \\ \\ \therefore I=199.68 \end{gathered}[/tex]Final Answer
The interest is $199.68
This scale balanced with 18 on the left side and 9b onthe right side. Your teacher changed the scale, but didnot have time to restore the balance.Find the number to divide by on the left that makes thescale balance. Then complete the equation.
Answers
The initial balance was 18 and 9b, so we can write an equation and find the value of b:
[tex]\begin{gathered} 18=9b \\ b=\frac{18}{9} \\ b=2 \end{gathered}[/tex]So if the value of b is 2, let's calculate the missing value in order to rebalance the equation:
[tex]\begin{gathered} 18\colon x=3b \\ \frac{18}{x}=3\cdot2 \\ \frac{18}{x}=6 \\ 6x=18 \\ x=\frac{18}{6} \\ x=3 \end{gathered}[/tex]So the number to divide on the left is 3.
Write the fraction in lowest terms. Use the method of dividing by a common factor.35/45A) 7/9B) 5/9C) 7/5D) 35/45
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Answer: We have to write the fraction in the lowest terms, by dividing it by the common factor:
[tex]\frac{35}{45}[/tex]The common factor for both numerator and the denominator is 5, therefore, after dividing by it, the new fraction becomes:
[tex]\frac{35}{45}=\frac{\frac{35}{5}}{\frac{45}{5}}=\frac{7}{9}[/tex]The answer, therefore, is Option(A).
Use the graph to answer the question. find the asymptotes of the graph of the function select all the apply A. x=-2B. x=-1C. x=1 D. y=0
Answers
An asymptote is a line that a curve approaches, as it heads towards infinity.
For the given function: The curves of the function approach to the asymptote x= -2 (graph of the function never touches x= -2):
Asymptote: x= -2
amal went to PetSmart to get his hamster an exercise ball. There was a small ball with a 6 inch diameter and a 12 inch one. The volume of the large ball halfeight timesfour timestwice
Answers
The volume of the large ball is eight times the volume of the small ball
Explanation:Given:
the diameter of the smaller ball = 6 inch
The diameter of the larger ball = 12 inch
To find
The volume of the larger ball in relation to the smaller one
A ball is spherical, we will be using the volume of a sphere:
[tex]Volume\text{ of a sphere = }\frac{4}{3}\pi r^3[/tex]For the smaller ball:
[tex]\begin{gathered} diameter\text{ = 2\lparen radius\rparen} \\ radius\text{ = diameter/2 = 6/2 = 3 in} \\ \\ Volume\text{ of the smaller ball = }\frac{4}{3}\pi\times3^3 \end{gathered}[/tex]For the larger ball:
[tex]\begin{gathered} diameter\text{ = 12 in} \\ radius\text{ = 12/2 = 6} \\ \\ Volume\text{ of the larger = }\frac{4}{3}\pi\times6^3 \end{gathered}[/tex][tex]\begin{gathered} The\text{ ratio of larger ball to smaller ball = }\frac{\frac{4}{3}\pi\times6^3}{\frac{4}{3}\pi\times3^3}\text{ = 216/27} \\ \\ The\text{ ratio of larger ball to smaller ball = 8} \\ \\ \frac{volume\text{ of larger ball}}{volume\text{ of smaller ball}}=\text{ 8} \end{gathered}[/tex]The volume of the large ball is eight times the volume of the small ball
Which is a possible location for point C so thatARST is similar to ACAB?6T.4.B54NW1ONx-65 -4 -3 -2 -1 0 1 2 3 4 5 6- 4 3 4 G 9SR0 (-2, 1)(-2, 0)(3,0)(3, 1)
Answers
the triangle RST, we can measure the sides, and we get:
if we want the triangle ABC to be similar, has to be a right angle so the value of X has to be -2 or 3. let's see the triangles we have on each option:
So, triangles A and C have the same proportions that triangle RST, (half of each side)
so the correct option is between these two, now if we rotate the triangle RST, we get a similar triangle that A. (rotate until the side SR is vertical)
so the answer is: (-2,1)
Find the x- and y-intercepts of the equation. h(x)=2x−9
Answers
y-intercept is
[tex]h(0)=-9[/tex]The point is (0,-9)
x-intercept is
[tex]h(x)=0\Rightarrow2x-9=0\Rightarrow x=\frac{9}{2}[/tex]x-intercept is
[tex](\frac{9}{2},0)[/tex]Acheetah ran 195 yards in 6 seconds. What was the cheetah's average speed in miles per hour? Express the answer rounded to the nearest mile per hour._ 195 yd ? mi 6 sec 1 hr The yard unit needs eliminated The second unit needs eliminated Conversion Factors: 1 mi = 1760 yd 1 min = 60 sec, 1 hr = 60 min 1mi 7 mi 195 yd 60 sec 60 sec 60 min 1 min 1 hr 6 sec 1760 yd 1 hr 195 x 60 x 60 ? mi 6x1760 1 hr
Answers
The cheetah covered a distance of 195 yards in 6 seconds . The cheetah average speed in miles per hour can be computed below
Let us convert to the units we want to represent our final answer
1760 yards = 1 miles
195 yards = ?
cross multiply
distance in miles = 195/1760 miles
lets us convert the time
1 minutes = 60 seconds
6 seconds = 6/60 = 1/10 minutes
60 minutes = 1 hour
1/10 minutes = ? hour
cross multiply
[tex]\frac{\frac{1}{10}}{60}=\frac{1}{600}\text{ hours}[/tex]Therefore, the average speed will be
[tex]\begin{gathered} \text{speed =}\frac{dis\tan ce}{\text{time}} \\ \text{speed}=\frac{\frac{195}{1760}}{\frac{1}{600}}=\frac{195}{1760}\times\frac{600}{1}=\frac{117000}{1760}=66.4772727273\approx66\text{ miles per hr} \end{gathered}[/tex]a scientist have two solutions which she has labeled solution a and solution B each contain salt she knows that solution a is 70% salt and solution B is 95% so she wants to obtain 160 oz of a mixture that is 75% so how many ounces of each solution should she use
Answers
Solution:
Let x = the number of ounces of Solution A
Let y = the number of ounces of Solution B
then we have the system of the equation:
x + y = 160 EQUATION 1
0.70 x + 0.95 y = 0.75(160) = 120 EQUATION 2
Solving for y in equation 1, we obtain:
y = 160-x EQUATION 3
replacing the above on equation 2, we get:
0.70 x + 0.95(160-x) = 120
this is equivalent to:
0.70 x + 152 - 0.95x = 120
this is equivalent to
152-120 = 0.95 x -0.70 x
this is equivalent to:
32 = 0.25 x
solving for x, we get:
[tex]x\text{ = }\frac{32}{0.25}\text{ = 128 }[/tex]now, replacing the above into the equation 3, we obtain:
y = 160-x = 160 - 128 = 32
then, we can conclude that the correct answer is:
x = the number of ounces of Solution A = 128 ounces
y = the number of ounces of Solution B = 32 ounces.
Marsha uses a coordinate plane to design a triangular flag у 8 E 7. 6 5 4 3 2 1 G 0 1 2 3 4 5 6 7 8 What are the coordinates for triangle EFG? A (0,1) B (1,1) C ( 37) D(5,6) E (6,5) F (7,3)
Answers
Given
To find the coordinates of the vertices E, F, G of the given triangle.
Now,
From the given figure, the coordinates of the points E, F, G are listed as,
[tex]\begin{gathered} E(x,y)=E(3,7) \\ F(x,y)=F(6,5) \\ G(x,y)=G(1,1) \end{gathered}[/tex]Hence, the coordinates are (1,1), (3,7), (6,5).