Answers
Answer:
CF = 8.5
Step-by-step explanation:
Given 2 intersecting chords, then
The product of the parts of one chord is equal to the product of the parts of the other chord, that is
CF × DF = BF × EF , substitute values
CF × 14 = 7 × 17
14CF = 119 ( divide both sides by 14 )
CF = 8.5
Related Questions
I have this math problem I can't solve.
"Evelyn and Meredith decided to kayak 1 mile up and then back in the Humboldt channel.
The rate of the water flowing in the channel was 2 miles per hour. The total time it took them to kayak up and back was 3 hours and 40 minutes. Assuming they were padding their double kayak at a fairly consistent rate, find the rate Evelyn and Meredith were paddling.
Step 2 - Draw a picture to model the problem.
Step 3 - Label variables and create a table.
Step 4 - Write an equation to model the problem.
Step 5 - Solve the equation. Provide supporting work and detail.
Step 6 - Explain the results."
If you can help please do.
Answers
Evelyn and Meredith were paddling at a rate of [tex]\frac{3+\sqrt{493}}{11}mph[/tex] which is equivalent to 2.29mph approximately.
Step 2: See attached picture
Step 3: In this case we only have different variables, there is the rate at which Evelyn and Meredith were paddling, the rate at which they moved when rowing upstream, the rate at which they moved when rowing downstream, the time it took them to paddle upstream and the time it took them to paddle downstream.
v = rate at which Evelyn and Meredith were paddling.
[tex]v_{up}[/tex]= velocity at which they were moving when paddling upstream.
[tex]v_{down}[/tex]= velocity at which they were moving when paddling downstreamstream.
[tex]t_{up}[/tex]= time it took them paddling upstream.
[tex]t_{down}[/tex]= time it took them paddling downstream
Se attached picture for the table.
Step 4: Building this equation will require us to combine different equations into a single one. Let's start with the equation for the final rate at which they paddled when rowing upstream.
[tex]v-2=v_{up}[/tex]
When rowing upstream, the current will drag the kayak, so we subtract it from the rate at which they were rowing.
Let's find the final rat at which they moved when rowing downstream.
[tex]v+2=v{down}[/tex]
next, the problem tells us it took them 3 hours and 40 minutes to row up and down the channel so we can convert it into just hours like this:
[tex]40min*\frac{1hr}{60min}=\frac{2}{3}hr[/tex]
[tex]3hr+\frac{2}{3}hr=\frac{11}{3}hr[/tex]
so now we can build our equation for time.
[tex]t_{up}+t_{down}=\frac{11}{3}[/tex]
We also know that the rate is built by dividing the distance over the time it took them to travel the distance, so:
[tex]v_{up}=\frac{1}{t_{up}}[/tex]
[tex]v_{down}=\frac{1}{t_{down}}[/tex]
If we solved each of those equations for their respective times, we would end up with the following:
[tex]t_{up}=\frac{1}{v_{up}}[/tex]
[tex]t_{down}=\frac{1}{v_{down}}[/tex]
so we can now combine all the equations together so we get:
[tex]t_{up}+t_{down}=\frac{11}{3}[/tex]
[tex]\frac{1}{v_{up}}+\frac{1}{v_{down}}=\frac{11}{3}[/tex]
[tex]\frac{1}{v-2}+\frac{1}{v+2}=\frac{11}{3}[/tex]
So this equation models the problem.
Step 5: We can solve this equation by multiplying everything by the LCD
In this case the LCD is:
3(v-2)(v+2)
so, when doing the respective multiplications we end up with:
[tex]\frac{3(v-2)(v+2)}{v-2}+\frac{3(v-2)(v+2)}{v+2}=\frac{11(3)(v-2)(v+2)}{3}[/tex]
We can now simplify to get:
3(v+2)+3(v-2)=11(v+2)(v-2)
We can now do the respective multiplications to get:
[tex]3v+6+3v-6=11(v^{2}-4)[/tex]
and we can further simplify:
[tex]6v=11v^{2}-44[/tex]
Step 5: So we can now solve it by using the quadratic formula, first, we need to rewrite the equation in standard form:
[tex]11v^{2}-6v-44=0[/tex]
So we can now use the quadratic formula:
[tex]v=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}[/tex]
we substitute:
[tex]v=\frac{-(-6) \pm \sqrt{(-6)^{2}-4(11)(-44)}}{2(11)}[/tex]
and simplify:
[tex]v=\frac{6 \pm \sqrt{36+1936}}{22}[/tex]
[tex]v=\frac{6 \pm \sqrt{1972}}{22}[/tex]
[tex]v=\frac{6 \pm \sqrt{4(493)}}{22}[/tex]
[tex]v=\frac{6 \pm 2\sqrt{493}}{22}[/tex]
[tex]v=\frac{3 \pm \sqrt{493}}{11}[/tex]
this gives us two possible results:
[tex]v=\frac{3 + \sqrt{493}}{11}[/tex] and [tex]v=\frac{3 - \sqrt{493}}{11}[/tex]
Step 6: We only pick the first result since it's the positive result. We don't take the second one because a negative result represents the kayak moving in the opposite direction which is not how the situation was modeled.
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GIVE AN EXPLANATION PLEASE! 20 POINTS!! AND A BRAINLEEST IF TWO OR MORE PEOPLE HAVE ANSWERED IT. (FIRST COME FORST SERVE BASES + ANSWER HAS TO BE CORRECT)
Lily bought a pair of gloves and a shirt.
The gloves cost £4
She sold the gloves and the shirt for a total of £48
She made 100% profit on the cost of the gloves.
20% profit on the total cost.
Work out her percentage profit on the cost of the skirt.
Answer 1 decimal place.
Answers
witw6oweo6ssitsi5sutaurzhfztzjxisi5
y4+5y2+9 factorise please help me
Answers
[tex]\displaystyle\ y^4 +5y^2+9=(y^2+3)^2-y^2=(y^2-y+3)(y^2+y+3)[/tex]
Answer:
Solution given;
[tex] y^{4}+5y²+9[/tex]
keeping [tex]y^{4} and 9 together [/tex]
[tex]y^{4}+9+5y²[/tex]
[tex](y²)²+3²+5y²[/tex].....[I]
we have
a²+b²=(a+b)²-2ab
or
a²+b²=(a-b)²+2ab
same like that
[tex](y²)²+3²=(y²+3)²-6y² or (y²-3)²+6y²[/tex]
remember that while adding or subtracting the left term 5y² either adding 6y²or subtracting 6y²
should make the term perfect square
while subtracting it makes perfect square
so
we take
(y²)²+3²=(y²+3)²-6y²
again
substituting value of
(y²)²+3² in equation 1 and it becomes
(y²+3)²-6y²+5y²
solve like terms
(y²+3)²-y²
again
we have
a²-b²=(a+b)(a-b)
by using this.
(y²+3+y)(y²+3-y)
rearrange it
(y²+y+3)(y²-y+3) is a required factorisation form.
Choices:
One-sixth cups
Five-sixths cups
1 and two-thirds cups
1 and 5 / 6 cups
Answers
Answer:
Patel will require more orange juice = [tex]\frac{371}{660}[/tex] cups
Step-by-step explanation:
Patel needs the orange juice for his family = 3 cups
He needs more orange juice = 3 cups - Sum of juice squeezed from different oranges
[tex]=3-(\frac{13}{15}+\frac{1}{5}+\frac{9}{20}+\frac{5}{11}+\frac{7}{15})[/tex]
L.C.M. of the denominators = 660
[tex]=3-\frac{572+132+297+300+308}{660}[/tex]
[tex]=3-\frac{1609}{660}[/tex]
= [tex]\frac{1980-1609}{660}[/tex]
= [tex]\frac{371}{660}[/tex]
Therefore, amount of orange juice required more = [tex]\frac{371}{660}[/tex] cups
a set has 62 proper subsets how many elements has it for?
Answers
Answer:
6
Step-by-step explanation:
Total number of subsets is given as
[tex] {2}^{n} [/tex]
But the subset of a set consists of the proper subsets, an empty set and the set itself.
Total number of subsets are 64
Therefore,
[tex] {2}^{n} = 64[/tex]
[tex] {2}^{n} = {2}^{6} [/tex]
Comparing both sides
[tex]n = 6[/tex]
SI SE EXTRAE UNA BOLITA DE UNA CAJA CERRADA CON UNA ABERTURA EN LA PARTE SUPERIOR DE LA MISMA.¿CUAL ES LA PROBABILIDAD DE EXTRAER UNA BOLITA DE COLOR SECUNDARIO? LA CAJA CONTIENE : TRES BOLAS DE COLOR PRIMARIO (1 BOLA ROJA,1 BOLA AMARILLA, 1 AZUL) DOS DE COLOR SECUNDARIO(1 NARANJA,1VERDE)
Answers
Answer:
La probabilidad es P = 0.4
Step-by-step explanation:
Sabemos que la caja tiene:
3 bolas de color primario (1 roja, 1 amarilla, 1 azul)
2 de color secundario (1 verde, 1 naranja)
Como la bola la sacaremos al azar, todas las bolas tienen exactamente la misma probabilidad de salir.
Queremos obtener la probabilidad de sacar una bolita de color secundario.
Esta probabilidad se calculará como el cociente entre el número de bolitas que cumplen este requisito (es decir, ser de color secundario, sabemos que hay dos de esas) y el número total de bolitas en la caja ( son 5)
La probabilidad es:
P = 2/5 = 0.4
Escribiendo esto en porcentaje (solo se lo multiplica por 100%) tenemos:
40%
Es decir, hay un 40% de posibilidades de sacar una bolita de un color secundario.
If an object looks the same
Answers
Answer:
I don't understand your question.............!
Step-by-step explanation:
Aubrey tiene un nuevo estuche de arte con forma de prisma rectangular. El estuche es de 12 cm por 20 cm por 5cm. Lo único dentro del estuche es un nuevo borrador rosa con las dimensiones que se muestran a continuación.
¿Cual es el volumen del estuche que no ocupa por el borrador?
Answers
Respuesta:
720 cm³
Explicación paso a paso:
El volumen de un prisma rectangular viene dado por:
V = largo * ancho * alto
Dimensión de la caja de arte = 12 por 20 por 5
Dimensión del borrador = largo * ancho * alto
Volumen del borrador = 2 por 4 por 0,5
Dimensión del estuche de arte que no contiene borrador:
(12 por 20 por 5) - (2 por 4 por 0,5)
(10 por 16 por 4,5)
Volumen de la caja que no contiene borrador:
10 * 16 * 4,5 = 720 cm³
Let ℤ be the set of all integers and let, (20) 0 = { ∈ ℤ| = 4, for some integer }, 1 = { ∈ ℤ| = 4 + 1, for some integer }, 2 = { ∈ ℤ| = 4 + 2, for some integer }, 3 = { ∈ ℤ| = 4 + 3, for some integer }. Is {0, 1, 2, 3 } a partition of ℤ? Explain your answer.
Answers
Answer:
[tex]\{0, 1, 2, 3\}[/tex] is a partition of Z
Step-by-step explanation:
Given
[tex]$$A _ { 0 } = \{n \in \mathbf { Z } | n = 4 k$$,[/tex] for some integer k[tex]\}[/tex]
[tex]$$A _ { 1 } = \{ n \in \mathbf { Z } | n = 4 k + 1$$,[/tex] for some integer k},
[tex]$$A _ { 2 } = { n \in \mathbf { Z } | n = 4 k + 2$$,[/tex] for some integer k},
and
[tex]$$A _ { 3 } = { n \in \mathbf { Z } | n = 4 k + 3$$,[/tex]for some integer k}.
Required
Is [tex]\{0, 1, 2, 3\}[/tex] a partition of Z
Let
[tex]k = 0[/tex]
So:
[tex]$$A _ { 0 } = 4 k[/tex]
[tex]$$A _ { 0 } = 4 k \to $$A _ { 0 } = 4 * 0 = 0[/tex]
[tex]$$A _ { 1 } = 4 k + 1$$,[/tex]
[tex]A _ { 1 } = 4 *0 + 1$$ \to A_1 = 1[/tex]
[tex]A _ { 2 } = 4 k + 2[/tex]
[tex]A _ { 2} = 4 *0 + 2$$ \to A_2 = 2[/tex]
[tex]A _ { 3 } = 4 k + 3[/tex]
[tex]A _ { 3 } = 4 *0 + 3$$ \to A_3 = 3[/tex]
So, we have:
[tex]\{A_0,A_1,A_2,A_3\} = \{0,1,2,3\}[/tex]
Hence:
[tex]\{0, 1, 2, 3\}[/tex] is a partition of Z
WILL GIVE BRAINLIEST
A graph has hours studied on the x-axis and test scores on the y-axis. Points are at (1, 3), (2, 6), (3, 5), (3, 8), (4, 5), (5, 8), (8, 9).
What statements describe this graph? Check all that apply.
The points are scattered.
The points are not connected.
The graph displays a discrete graph.
The graph displays the relationship of test scores to hours studied.
The graph represents the relationship between two sets of data.
Answers
Answer:
A,C,D.
Step-by-step explanation:
Answer:
Part A
Group A is a cluster of points with similar property or relationship.
Point B is an outlier. This is the point outside of the common relationship.
Part B
There is a negative tendency. As number of hours spent on computer games increase, the test scores decrease.
Step-by-step explanation:
so basically A, and B
Triangle D E F is reflected across D F to form triangle E G F. The lengths of sides E F and F G are congruent. To prove that ΔDEF ≅ ΔDGF by SAS, what additional information is needed? ∠DEF ≅ ∠ DGF ∠DFE ≅ ∠ DFG DE ≅ DG DG ≅ GF
Answers
Answer:
[tex]\angle DFE = \angle DFG[/tex]
Step-by-step explanation:
Given
See attachment for complete question
Required
What makes DEF and DGF congruent
We have:
[tex]EF = GF[/tex] --- this is indicated by the single line on both sides
Also:
[tex]DF = DF[/tex] --- both triangle share same side
For SAS to be true;
2 sides and 1 angle must be equal in either triangles
So far, we have:
[tex]EF = GF[/tex] ---- S
[tex]DF = DF[/tex] ---- S
The additional to complete the proof is:
[tex]\angle DFE = \angle DFG[/tex] ---- angle between the above sides
Reflection is a type of rigid transformation which requires the turning of an object, shape or figure about a reference point or line. Therefore, the needed additional information is ∠DFE ≅ ∠ DFG. Option B.
Reflection implies turning the given triangle DEF about its side DF, so as to produce an image with the same dimensions but different orientation.
The required proof by Side-Angle-Side (SAS) implies that the relations will be in respect of two of its sides and their included angle.
So that,
GF ≅ FE (given)
DF is the common side to triangles DEF and DFG.
DFG is the included side.
Thus;
∠DFE ≅ ∠ DFG (Side-Angle-Side postulate, SAS)
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Help please-- Given circle O below, if arc GH and arc HJ are congruent, what is the measure of chord line HJ?
Answers
Answer:
the answer is D
Step-by-step explanation:
Hope this helps :)
Given line segment AB with endpoints A(-1,7) and B(11, -1)
Find the length of AB.
Answers
Step-by-step explanation:
some to check if it correct
The length of the line segment AB is 8.48 unit.
What does length mean?The term used for identifying the size of an object or the distance from one point to another is known as length.
The length of the line segment having endpoints A (x1, y1) and B (x2, y2) can be determined using the formula,
[tex]AB=\sqrt{(x_{2} ^{2} -x_{1} ^{2} )+(y_{2} ^{2} - y_{1} ^{2} )}[/tex]
Given that x1 = -1, x2= 11, y1= 7, and y2= -1.
Substituting the given values in the above equation
[tex]AB=\sqrt{(11^{2}-(-1)^2 )+((-1)^2-7^2)}[/tex]
[tex]AB=\sqrt{72} = 8.48[/tex]
Hence, 8.48 unit is the length of line segment AB.
To learn more about length, use the link given below:
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Diego runs for 32 seconds at -8. meters per second .what is his finish point?
Answers
Answer:
The finishing point 4
Step-by-step explanation:
32/8=4
For how many integer values of M is M/30 strictly between 1/3 and 3/5?
Answers
Answer:
6 possible intergers brainliest me
Answer:
its 7
Step-by-step explanation:
Celsius to Fahrenheit
Answers
Step-by-step explanation:
149......hshdbhdhsbhsjsusvshhs
The given equation has been solved in the table. Step Statement 1 1 –7n + 11 = -10 2. -7n + 11 – 11 = -10 – 11 3 -7n = -21 4 = = =21 .In -7 -21 __7 5 n = 3 Use the table to complete each statement. In step 2, the In step 4, the property of equality was applied. property of equality was applied.
Answers
Answer:
In step 2, the subtraction property of equality was applied
In step 4, the division property of equality was applied
Step-by-step explanation:
Help me please!!! Thanks
Answers
Answer:
Cylinder H has the greater volume.
Step-by-step explanation:
Recall that the volume of a cylinder is given by:
[tex]\displaystyle V=\pi r^2h[/tex]
Where r is the radius and h is the height.
Cylinder H has a radius of 4.5 meters and a height of 3 meters. Thus, its volume is:
[tex]\displaystyle \begin{aligned} V&=\pi(4.5)^2(3)\\&=60.75\pi \\&\approx190.8518\text{ m}^3\end{aligned}[/tex]
Cylinder J has a diameter of 7 meters and a height of 4.5 meters. The radius is half the diameter, so Cylinder J's radius is 3.5 meters. Thus, its volume is:
[tex]\displaystyle \begin{aligned}V&=\pi(3.5)^2(4.5)\\&=55.125\pi \\&\approx 173.1803\text{ m}^3\end{aligned}[/tex]
Thus, Cylinder H has the greater volume.
What is the value of x to the nearest tenth?
A) 9.2
B) 7.2
C) 4.8
D) 12.0
Answers
Answer:
B. 7.2
Step-by-step explanation:
radius=24÷2= 12
other line =19.2÷2=9.6 because line from centre bisects chord and is perpendicular to it
Therefore: X²=√ 12²-9.6² ( theorem of Pythagoras)
X=7.2
Can someone help me with this math homework please!
Answers
Answer:
DOMAIN
input values belong to domainset of values for the independent variable is called the domainRANGE
output values belong to range set of values for the dependant variable is called the rangen a certain exam of grade ten, 75% students got high score in mathematics, 65%students got high score in English. If 6% of them did not get high score in both mathematics and English, then calculate: i. the percent of students who got high score in both the subjects. ii. the total number of students who got high score either in mathematics or in English if 300 students had attended the exam.
Answers
Answer:
thank you for the points
Step-by-step explanation:
Describe fully the graph which has equation x2 + y2 = 9
Answers
Answer:
The graph is a circle with a radius of 3 and a center of (0,0).
Step-by-step explanation:
Graph
The equation x² + y² = 9 represents a circle with center (0, 0) and radius = 3
What is equation?"It is a mathematical statement which consists of equal (=) symbol between two algebraic statements."
What is graph of a equation?"It is a set of points (x, y) which satisfy given equation."
For given question,
We have been given an equation x² + y² = 9
The graph of above equation as shown below.
We know, the equation of the circle with center (0, 0) and radius 'r' is, x² + y² = r²
We can write given equation as x² + y² = 3²
Comparing given equation with x² + y² = r² we have r = 3 units
The graph of above equation represents a circle with center (0, 0) and radius = 3
Therefore, the equation x² + y² = 9 represents a circle with center (0, 0) and radius = 3
Learn more graph of function here:
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The distance traveled (in meters) by an insect is modeled by the equation d=0.5t where d is the distance traveled in meters and t is the time in minutes. Find the distance traveled in 27.9 minutes.
A. none of these
B. 13.95 meters
C. 55.8 meters
D. 1.395 meters
Answers
Answer:
B. 13.95 meters
Step-by-step explanation:
The question is just asking you to talk the amount of time taken, and divide it in half.
d= 0.5(27.9)
plz help ASAP with explanation
Answers
Answer:
The height of the tank in the picture is:
19.5 cmStep-by-step explanation:
First, to know the height of the tank, we're gonna change the unit of the volume given in liters to cm^3:
1 liter = 1000 cm^3So:
1.2 liters = 1200 cm^3Now, we must calculate the height of the tank that we don't know (the other part that isn't with water), to this, we can use the volume formula clearing the height:
Volume of a cube = long * wide * heightNow, we must clear the height because we know the volume (1200 cm^3):
Height = volume of a cube / (long * wide)
And we replace:
Height = 1200 cm^3 / (12 cm * 8 cm)Height = 1200 cm^3 / (96 cm^2)Height = 12.5 cmRemember this is the height of the empty zone, by this reason, to obtain the height of the whole tank, we must add the height of the zone with water (7 cm) that the exercise give us:
Heigth of the tank = Height empty zone + height zone with waterHeigth of the tank = 12.5 cm + 7 cmHeigth of the tank = 19.5 cmIn this form, we calculate the height of the tank in 19.5 cm.
(9-3)+18÷9
show your work
Answers
(9-3)+18÷9
= 6+18÷9
= 6+2
= 8
Answer:
8
Step-by-step explanation:
Well, we need to use order of operations. Since there are parenthesis, we solve what is inside that first. So, 9-3=6. We have solved one part of the equation. There are no exponents so division comes next. 18/9=2. Now we are left with 6+2. 6+2=8. Therefore, your final answer is 8.
It took Sarah 4 days to write a paper, she wrote 12 pages on day 1, 15 pages on day 2 and 9 pages on day 3. If she wrote 12 pages per day , how many pages did she write on the fourth day ?
Answers
Answer:
Option A
Step-by-step explanation:
Sarah took 4 days to write a paper.
She wrote 12 pages per day, so total number of pages she wrote in 4 days = 12 × 4
= 48 pages
On day 1, she wrote number of pages = 12
On day 2, she wrote number of pages = 15
On day 3, she wrote number of pages = 9
On day 4, she wrote number of pages = P
She wrote total number pages in 4 days = 12 + 15 + 9 + P
= 36 + P
Therefore, P + 36 = 48
P = 48 - 36
P = 12
She wrote 12 pages on day 4.
Option A is the answer.
[tex] \frac{x}{2} + \frac{6}{x } = 4[/tex]
using quadratic equation....help me if you can
Answers
find the size of each of the unknown angles.
plz solve this question fast as soon as possible with solution.
Answers
Answer:
Angle a = 80°, Angle b = 55°, Angle c = 45°, Angle d = 80°
Step-by-step explanation:
To find the measure of Angle a, we add 55 and 45, then subtract the sum from 180.
180 - 100 = 80
Angle a is 80°.
Then, we solve for Angle b. Line segment CD is congruent to Line AB, so Angle b is congruent to 55°.
After that, we find Angle c. Line segment AC is congruent to Line segment BD, so Angle c is congruent to 45°.
Lastly, we solve for Angle d using the same method we used for Angle b and Angle c. Angle d is congruent to Angle a, so it measures 80°.
So, Angle a = 80°, Angle b = 55°, Angle c = 45°, Angle d = 80°.
What is 1/4 in feet?
Answers
Answer:
0.25 feet
7.62 centimeters
3 inches
Step-by-step explanation:
Not really a clear question-
consider the two triangles shown below are the two triangles congruent
Answers
Answer: Yes
Step-by-step explanation: Let's first find the missing angle in the second triangle and to find this angle, remember that the sum of the measures of a triangle is 180 degrees so you should find that our missing angle is 67°.
Now, notice that we have two angles and the included side of one triangle
congruent to two angles and the included side of a second triangle.
Therefore, we can say the triangles are congruent by ASA.