Given :
The foci of hyperbola are (8,0) and (-8,0) .
The difference of the focal radii = 6.
To Find :
The equation of the hyperbola.
Solution :
We know, distance between foci is given by :
2c = 8 - (-8)
c = 8
Also, difference between the foci or focal distance is given by :
2a = 6
a = 3
Now, we know for hyperbola :
[tex]b^2 +a^2 = c^2\\\\b^2={c^2-a^2}\\\\b^2 = 64-9\\\\b^2 = 55[/tex]
General equation of hyperbola is :
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\\\\\dfrac{x^2}{9}+ \dfrac{y^2}{55}=1[/tex]
Hence, this is the required solution.
factor completely 64^2 - 1
Answer:
4095
Step-by-step explanation:
find the slope
( 1,3) (4,9)
Answer:
2
Step-by-step explanation:
1. slope formula: [tex]\frac{y_{1}-y_{2} }{x_{1} -x_{2} }[/tex]
2. [tex]\frac{9-3}{4-1}[/tex]
3. [tex]\frac{6}{3}[/tex]
4. 2
Ty is placing CDs in boxes. There are a total of 7,200 CDs. Each box holds 90 CDs. How many boxes will Ty fill? A. 80 B. 70 C. 100 D. 90
Answer:
80 boxes.
Step-by-step explanation:
Total CDs available = 7200CDs
Amount of CD in each box = 90 CDs
To get the number of boxed Ty will fill, we will say;
90CDs = 1box
7200 CDs = x
Cross multiply
90 * x = 7200 * 1
90x = 7200
x = 7200/90
x = 80
Hence Ty will fill total of 80 boxes.
Answer:
80 CDS
Step-by-step explanation:
Total CDs available = 7200CDs
Amount of CD in each box = 90 CDs
To get the number of boxed Ty will fill, we will say;
90CDs = 1box
7200 CDs = x
Cross multiply
90 * x = 7200 * 1
90x = 7200
x = 7200/90
x = 80
Hence Ty will fill total of 80 boxes.
Someone please help on question 9
I will give you Brainliest
Answer:
(B). 38 cm³
Step-by-step explanation:
V = a² [tex]\frac{h}{3}[/tex]
a = 4.5 cm
h² = (6.1)² - ( [tex]\frac{4.5}{2}[/tex] )² = 32.1475
h = √32.1475 ≈ 5.67
V = (4.5)²( [tex]\frac{\sqrt{32.1475} }{3}[/tex] ) ≈ 38.27 ≈ 38 cm³
Answer:
[tex]38 cm^3[/tex]
Step-by-step explanation:
Given the slant height and a base side length of a right square pyramid, we can use these numbers to solve for the volume.
The formula for the volume of a square pyramid is generally known as:
[tex]V = 1/3 a^2h[/tex], where the variable 'a' represents the base side length and 'h' represents the height.
Since we are given the slant height, we can use Pythagorean's Theorem to calculate the height (non-slanted) when given a base side length by using the equation below:
[tex]a^2+b^2=c^2[/tex]
This is a special case because this is a right square pyramid, meaning we can use C squared and substitute that for the given slant height, 6.1 cm. The leg of the right triangle, which is [tex]\frac{s}{2}[/tex], takes place of 'b' which is 4.5. Now, given all of this, we can plug in our known values. Height is what we are solving.
[tex]h^2+\left(\frac{4.5}{2}\right)^2=6.1^2[/tex]
Now we will simplify and solve everything, and we get h; or the height, which equals 5.668977.
Now we can finally use the general formula to solve the volume of a square pyramid.
[tex]V = 1/3 a^2h[/tex]
Let's plug in everything now to find the volume — which we know that the height is approximately 5.66, and the base side length is 4.5.
[tex]V=\frac{1}{3}\left(4.5\right)^2\left(5.66\right)[/tex]
The volume from this formula equates to 38.205 cm³, or roughly 38 cm³, meaning the answer is B.
HELP!!!!! part A: Ms.Donaldson earns $18.80 per hour for the first 40 hours she works in a week. She earns 1 1/2 times that amount per hour for each out beyond 40 hours in a week. Last week Ms.Donaldson worked 45.5 hours. How much money did she earn? Part B: A health incurrence payment of 34.55 was deducted from Ms.Donaldson's earnings for the week. After the incurrence deduction, payroll taxes equal to 28% of the balance were deducted. What was the amount that Ms.Donaldson received afterwards?
Answer: A. $907.10
B. $628.236
Step-by-step explanation:
For the first 40 hours, Ms.Donaldson will earn: = 40 × $18.80 = $752.0
We are informed that Ms.Donaldson worked 45.5 hours, this means that she worked an extra 5.5 hours. The amount paid for the extra hour will be:
= 5.5 × 1.5 × 18.8
= $155.10
The amount she earned will be:
= $752.0 + $155.10
= $907.10
B. A health incurrence payment of $34.55 was deducted from Ms.Donaldson's earnings for the week. Therefore, the amount she will have after the deduction will be:
= $907.10 - $34.55
= $872.55
After the incurrence deduction, payroll taxes equal to 28% of the balance were deducted. What was the amount that Ms.Donaldson received afterwards?
This will be:
= $872.55 - (28% × $872.55)
= $872.55 - (0.28 × $872.55)
= $872.55 - $244.314
= $628.236
The United States government used to make coins of many different values
cont
3 cents
20 cents
$2
$5
For each coin, state its worth as a percentage of $1.
Type the answers in the boxes below.
1. cent
50
2. 3 cents
3
3. 20 cents
4. $2
Answer:
1. 50%
2. 3%
3. 20%
4. 200%
Step-by-step explanation:
Here, we want to find the worth of each coin as a percentage of $1
We simply divide the worth by $1 and multiply by 100%
$1 is same as 100 cents
Thus;
1. 50 cent
= 50/100 * 100% = 50%
2. 3 cents
= 3/100 * 100% = 3%
3. 20 cents
= 20/100 * 100% = 20%
4. $2
= 2/1 * 100% = 200%
help helppp help i need answerr thank Uuuuuuuuu
Answer:
see explanation
Step-by-step explanation:
(a)
The angles are vertical and congruent, that is
x - 10 = 125 ( add 10 to both sides )
x = 135
-------------------------------------------------
(b)
Supplementary angles sum to 180°
The angles are in the ratio 2 : 3 = 2x : 3x ( x is a multiplier ), then
2x + 3x = 180
5x = 180 ( divide both sides by 5 )
x = 36
thus
2x = 2 × 36 = 72
3x = 3 × 36 = 108
Then the 2 angles are 72° and 108°
Now you can mark them brainliest.
FIVE AND FOUR TENTHS AS A DECIMAL AND FRACTION
Answer:
Decimal: 5.4
Fraction: 27/5
A plumber charges his customers $25.70 per hour, h, plus a $54.50
service fee. On Tuesday, he earns $118.75 for fixing Mrs. Goodwill's
sink.
Mrs. Goodwill also hires an electrician to repair several damaged
outlets in her home. The electrician charges $35.22 for each individual
outlet repair, r, plus a $62 service fee.
If the electrician charges Mrs. Goodwill a total of $167.66, which
equation shows how to determine the number of individual outlet
repairs correctly?
A. 35.22-62r = 167.66
B. 35.22r -62 = 167.66
C. 35.22 +62r = 167.66
D. 35.22r + 62 = 167.66
Answer:
D
Step-by-step explanation:
multiplying 35.22 with r since this amount is charged for every repair and then adding 62 since that is the additional fee
Multiply
7z3 (2z2 – 4z).
A. 14z5 – 28z4
B. 9z5 – 11z4
C. 14z6 – 28z4
D. –14z
Answer:
solve it
Step-by-step explanation:
If the measurment of the angles of a triangle are 3b,2b,and 4b then what is the smallest angle
Given:
The measurement of the angles of a triangle are 3b,2b,and 4b.
To find:
The smallest angle.
Solution:
According to the angle sum property, the sum of all angles of a triangle is 180 degrees.
[tex]3b+2b+4b=180^{\circ}[/tex] [Angle sum property]
[tex]9b=180^{\circ}[/tex]
Divide both sides by 9.
[tex]b=20^{\circ}[/tex]
Now,
[tex]3b=3(20^{\circ})=60^{\circ}[/tex]
[tex]2b=2(20^{\circ})=40^{\circ}[/tex]
[tex]3b=4(20^{\circ})=80^{\circ}[/tex]
Therefore, the smallest angle is 40 degrees.
Michells aim to swim a total of 23 miles in 4 weeks. The table below shows the number of miles she swam in the first 3 weeks. How many more miles does Michelle have to swim in week 4 to reach her target?
Answer:
c
Step-by-step explanation:
I said so and I did maths
What are the zeros? Please help
The total number of degrees in the center is 360°. If all five vertex angles meeting at the center are congruent, what is the measure of a base angle of one of the triangles?
Answer:
The measure of a base angle of one of the triangles is 54°
Step-by-step explanation:
In the isosceles triangle, the angle between the two equal sides called the vertex angle and the other two angles are equal and called base angles
∵ The total number of degrees in the center is 360°
∵ All five vertex angles meeting at the center are congruent
→ To find the measure of each vertex divide 360° by 5
∴ The measure of each vertex = 360° ÷ 5
∴ The measure of each vertex = 72°
∵ The base angles are equal in the isosceles triangle
∵ The sum of the measures of the angles of a triangle is 180°
→ Assume that the measure of each base angle is x
∴ x + x + 72° = 180°
∴ 2x + 72° = 180°
→ Subtract 72 from both sides
∵ 2x + 72 - 72 = 180 - 72
∴ 2x = 108
→ Divide both sides by 2 to find x
∴ x = 54
∴ The measure of each base angle = 54°
∴ The measure of a base angle of one of the triangles is 54°
Una caja contiene 3 bolas verdes, 5 bolas rojas y 2 bolas azules. Si se extraen al azar dos bolas sin reposición, ¿cuál es la probabilidad de que la primera sea azul y la segunda sea verde?
Responder:
1/15
Explicación paso a paso:
Dado que :
Número bolas verdes = 3
Número de bolas rojas = 5
Número de bolas azules = 2
Dibujo sin reemplazo; probabilidad de que el primero sea azul, el segundo sea verde
Probabilidad = resultado requerido / Total de resultados posibles
Resultados posibles totales = 3 + 5 + 2 = 10
P (1er azul) = número de azules / 10
P (1er azul) = 2/10 = 1/5
Sin reemplazo :
Total restante = 10 - 1 = 9
P (segundo verde) = número de verdes / 9 = 3/9
Probabilidad del primer azul y del segundo verde:
1/5 * 3/9 = 3/45 = 1/15
The probability that the first is blue and the second is green is 1/15
Probability is the likelihood or chance that an event will occur.
Probability = Expected outcome/Total outcomeIf a box contains 3 green balls, 5 red balls and 2 blue balls, the total number of balls is 10balls
Total outcome = 10 ballsIf blue is selected at first, the probability of selecting blue is 2/10 = 1/5If green is selected without replacement, the probability of selecting green will be 3/9Pr(selecting red and then green) = 1/5 * 1/3 = 1/15Learn more on probability here: https://brainly.com/question/24756209
3 years ago lower bought a new car for 21,700 when she traded the car into a dealer last week it was worth 13,020. Find the percent decrease in the car's value over the 3 year.
Answer:
1.67 percent
Step-by-step explanation:
Need help on this please and thank you
Step-by-step explanation:
a. 4/7t =56
4t= 392
t=98
b. 4=1/2 b -12
4+12=1/2 b
16=1/2 b
so, b =32
Jeyniel wrote the expression x^3/y^2. If x=4 and y=2; how much is the value of the expression? *
Answer:
The answer is 16
Step-by-step explanation:
X^3=64
Y^2=4
so 64 divided by 4 is 16
Answer:
16
Step-by-step explanation:
this might help you
Solve for g?
3=g/-4-5
its a 3g b but it's become to 4G ok and 4 -5 is -1 ok that's always question is
gary Sanchez struck out 112 times in 350 at bats. What PERCENTAGE of his at-bats were strike outs?
Answer:
it would be 32/100
Step-by-step explanation:
Answer:
32% of his bats were stuck out.
Step-by-step explanation:
A taxi company charges an initial fee of $1.95, plus $1.60 per mile driven. Shelly has $22.00 to spend on a taxi ride. Which inequality represents the number of miles, m, that Shelly can ride in a taxi
Answer:
Equation
1.95+1.6m ≤ 22
If solved
m ≤ 12.53
Step-by-step explanation:
SO we know the initial fee is 1.95
and for every mile driven, its $1.6
And we know that Shelly can spend less then or exactly the price of 22.
We know that m is miles driven
So we can make an equation
1.95+1.6m ≤ 22
1.95 can’t change since initial fee
1.6*m becuase its 1.6 for every mile driven and since “m” miles were driven, we multiply that by 1.6
Now it can’t go over 22 but it could be less than 22.
So this equation makes sense
If we solve it, it would be about m ≤ 12.53 miles
The table shows a relationship between the number of
tennis balls that fit into a given
number of cans.
Fill in the missing values to complete the table. Use
the spaces to the right to explain your values,
Answer:
What events or steps are described?
Do these things need to occur in a particular order?
Step-by-step explanation:
1. Donald usually runs the same distance daily for a total of 28 miles per week, training for a marathon. This week he was unable to run for 3 days How many miles was Donald able to run?
its urgent
12miles
Step-by-step explanation:
this is because 28 divide by 7 is 4 so 4 a day is 12 for 3 days
A city has 28 ambulances and 36 fire trucks . Find the ratio of the number of ambulances to the number of ambulances to number of fire trucks in simplest form
Answer:
28:35, which in fraction form is 28/35, but simplified is 4/5 or 4:5
Step-by-step explanation:
Bridget purchased 3 pairs of shoes online. The total bill of $126.81 included a $7.50 shipping charge and 6% tax on the total purchase. If the shoes that Bridget purchased were all priced the same, how much did each pair of shoes cost
Answer:
$37.
Step-by-step explanation:
Firstly, let's set the price of each pair of shoe to be x.
Since each pair of shoes costs the same, and there are three pairs, we can set the original price to be 3x.
Now, to apply the shipping charge, all we have to do is add 7.50 to 3x, getting 3x + 7.5.
Next, to apply a 6% tax, we can multiple the whole expression by (100% + 6%), getting (3x + 7.5) [tex]\cdot[/tex] 106%.
Since the whole bill foots to a total of $126.81, we can set the final equation to be:
[tex](3x + 7.5) \cdot 106\% = $126.81[/tex]
[tex](3x + 7.5) \cdot \frac{106}{100} = $126.81[/tex]
[tex]3x + 7.5 = $126.81 \cdot \frac {50}{53}[/tex]
[tex]3x = $119.6 - 7.5[/tex]
[tex]3x = 112.1[/tex]
[tex]x \approx \$37[/tex]
Hope this helped!
What is the solution to the equation x/3+x/6=7/2?
A. x=3/2
B. x= 7/3
C. x= 3
D. x= 7
Answer:
x=7
Step-by-step explanation:
A triangle ABC and its translated image XYZ are shown below.What relationship CANNOT be used to prove that triangle ABC is congruent to triangle XYZ?
Answer:
The answer is "Angle-Angle-Angle".
Step-by-step explanation:
Please find the image file in the attachment.
The angle of an image, composed of two rays at such a popular end-state, could be described. Angles with a tape measure are measured in degrees, When the three angles congruence between two triangles, that is NOT the congruence of a triangle. It seems to be the same (and similar form, yet we know nothing of their scale. We may call us comparable.
Elias has joined a game rental service. The membership has an initial fee of $35.00 and each game rental costs $5.00. This table shows the linear relationship between the total cost, y, and the number of games Elias rents, x. Fill in each box to correctly model the relationship between x and y.
Answer:
y=mx+b
y=35+5x
Step-by-step explanation:
A car is traveling at a rate of 32 miles per hour. At this rate, how many miles will the car will travel in 30 minutes?
Pls this will make my christmas
Answer:
32/2 is 16.
So.... 16 miles per 30 minutes
Step-by-step explanation:
Merry Christmas
Answer:
16 miles in a half hour
Step-by-step explanation:
divide the hour in half and then divide the 32 mph to get the 16 mph.
Exactly 512 tickets were sold for the talent show at Cypress Middle School. The number of student tickets sold was three times the number of adult tickets sold. How many adult and student tickets were sold?
Answer:
Number of adult tickets sold = 128
Number of student tickets sold = 384
Step-by-step explanation:
Given that:
There are two types of tickets:
1. Student tickets
2. Adult tickets
As per the question statement, number of student tickets sold were three times the adult tickets sold.
Let the number of adult tickets sold = [tex]x[/tex]
So, number of students tickets sold = [tex]3x[/tex]
Total number of tickets sold = Number of adult tickets sold + Number of student tickets sold = 512
[tex]\Rightarrow x+3x=512\\\Rightarrow 4x=512\\\Rightarrow x = 128[/tex]
Therefore, the answer is:
Number of adult tickets sold = 128
Number of student tickets sold = [tex]3\times 128[/tex] = 384