The foci of the hyperbola is (0,3) and (0,-3).
Step-by-step explanation:
Given,
The equation of the hyperbola: [tex]\frac{(x-6)^{2} }{16} -\frac{(y+7)^{2} }{9} =1[/tex]
To find the foci of the given parabola
Formula
If the equation of the hyperbola: [tex]\frac{(x-h)^{2} }{a^{2} } -\frac{(y-k)^{2} }{b^{2} } =1[/tex]
The focus will be (0,±c) where c² = a²+b²
Now,
Here, a=3 and b=4
c² = 3²+4² = 25
or, c = ±5
Hence,
The foci of the hyperbola is (0,3) and (0,-3)
Answer:
(1, -7) and (11, -7)
or A on edge
Step-by-step explanation:
took the quiz
Is this correct?
Need help!!!!!
plz
Answer:
150
Step-by-step explanation:
the bases are 60 and the sides are 90
What’s the area and the perimeter
Area formula: a = l * w
a = 8 * 4.5
a = 36
Perimeter formula: p = 2l * 2w
p = 2(8) + 2(4.5)
p = 16 + 9
p = 25
Best of Luck!
Pat's average weekly income from her part time job was 15% more in September than it was in July. her average weekly income in July was 10% less than it was in August. if her average weekly income in September was $207, what was her average weekly income in August?
Her average weekly income in August was $200.
Step-by-step explanation:
To find the income in july :
Given that,
Her average weekly income in September was $207.Her part time job was 15% more in September than it was in July.Let,
'x' be the 100% of income she got in July.
Therefore, the income $207 in September is 115% of x.
⇒ 115% of x = 207
⇒ 1.15 × x = 207
⇒ x = 207 / 1.15
⇒ x = 180
∴ Her average weekly income in July was $180.
To find the income in August :
Given that,
Her average weekly income in July was 10% less than it was in August.We found that, $180 is the average weekly income in July which is 10% less than August.Let,
'y' be the 100% of income she got in August.
Therefore, the income $180 in July is 90% of y.
⇒ 90% of y = 180
⇒ 0.9 × y = 180
⇒ y = 180/0.9
⇒ y = 200
∴ Her average weekly income in August was $200.
her average weekly income in August was $200 .
Step-by-step explanation:
Let in July income was x , So in September :
⇒ [tex]x+\frac{15x}{100}[/tex]
According to question , her average weekly income in September was $207 i.e.
⇒ [tex]x+\frac{15x}{100}=207[/tex]
⇒ [tex]\frac{115x}{100}=207[/tex]
⇒ [tex]x=207(\frac{100}{115})[/tex]
⇒ [tex]x=180[/tex]
Now , average weekly income in July was 10% less than it was in August , let income of august = y, i.e.
Income in august = [tex]180+\frac{August(10)}{100}[/tex]
⇒ [tex]y=180 + \frac{y(10)}{100}[/tex]
⇒ [tex]\frac{9}{10}y=180[/tex]
⇒ [tex]y=\$200[/tex]
Therefore , her average weekly income in August was $200 .
What happens to the value of f(x) = log4x as x approaches 0 from the right?
Answer:f(x) approaches negative infinity
Step-by-step explanation:
N/A
Answer:
the 1st one is a (f(x) approaches negative infinity)
the 2nd one is c (f(x) approaches infinity)
Step-by-step explanation:
Let ABCD be a convex quadrilateral. Let P and Q be points on side AB such that AP = PQ = QB. Similarly, BR = RS = SC, CT = TU = UD, and DV = VW = WA.
The area of quadrilateral ABCD is 180. Find the area of hexagon AWTCSP.
Answer:
Isn't this an AoPS Problem?
Step-by-step explanation:
Match its group with its percentage or mean using the table below.
Answer:
1) [tex]\bar x = 6.2[/tex], 2) [tex]\bar x = 8.75[/tex], 3) [tex]\bar x = 4.5[/tex], 4) [tex]p = 40\,\%[/tex], 5) [tex]p = 60\,\%[/tex], 6) [tex]p = 10\,\%[/tex]
Step-by-step explanation:
1) Mean length of all fish in the sample:
[tex]\bar x = \frac{12+5+3+5+8+2+10+9+4+4}{10}[/tex]
[tex]\bar x = 6.2[/tex]
2) Mean length of adult fish in the sample:
[tex]\bar x = \frac{12+5+8+10}{4}[/tex]
[tex]\bar x = 8.75[/tex]
3) Mean length of juvenile fish in the sample:
[tex]\bar x = \frac{5+3+2+9+4+4}{6}[/tex]
[tex]\bar x = 4.5[/tex]
4) Percentage of sample that were adult fish:
[tex]p = \frac{4}{10}\times 100\,\%[/tex]
[tex]p = 40\,\%[/tex]
5) Percentage of sample that were juvenile fish:
[tex]p = 100\,\% - 40\,\%[/tex]
[tex]p = 60\,\%[/tex]
6) Percentage of sample that were juveniles over 8 inches long:
[tex]p = \frac{1}{10}\times 100\,\%[/tex]
[tex]p = 10\,\%[/tex]
The circumference of a circle is 48 pie units. What is the radius of the circle
Answer:
r = 24
Step-by-step explanation:
The formula for circumference is
C = 2*pi*r
48 pi = 2 * pi *r
Divide each side by 2pi
48 pi / 2pi = 2 * pi *r/ 2pi
24 = r
|3x−2|=19 please help quick thanks
Answer:
x=7,-17/3
Step-by-step explanation:
5x2 - 4x – 9 = 0
Master Product:
try
Answer:
Step-by-step explanation:
5×-9=-45
-9+5=-4
5x²-4x-9=0
5x²-9x+5x-9=0
x(5x-9)+1(5x-9)=0
(5x-9)(x+1)=0
x=-1,9/5
Question 1
4 pts
Which set of line segments could create a right triangle? (4 points)
O 15,30,35
O 15,36,39
O 15, 20, 29
O 5,15,30
Answer:
(B)15,36,39
Step-by-step explanation:
To determine which of the line segments could create a Right Triangle, we check if it satisfies the Pythagoras Theorem, taking the longest part to be the Hypotenuse in all cases.
By Pythagoras Theorem: [tex]Hypotenuse^2=Opposite^2+Adjacent^2[/tex]
In 15,30,35
[tex]35^2\neq 15^2+30^2\\1225\neq 1125[/tex]
In 15,36,39
[tex]39^2=36^2+15^2\\1521=1521[/tex]
In 15, 20, 29
[tex]29^2\neq 15^2+20^2\\841\neq 625[/tex]
In 5,15,30
[tex]30^2\neq 15^2+5^2\\900\neq 250[/tex]
We can see that only 15,36,39 satisfies the required condition and thus it could be used to create a right triangle.
What is the length of the hypotenuse of a right triangle with legs that are 7 and 8 inches long?
Answer:
square root of 113 or 10.63014581
Step-by-step explanation:
Answer:
[tex]\sqrt{113}[/tex]
Step-by-step explanation:
Using pythag theorem:
Length of the hypotenuse is [tex]\sqrt{7^{2}+8^2 }[/tex]
Thus [tex]\sqrt{113}[/tex]
Lyla made a scale drawing of a city park. She used the scale 1 millimeter = 1 meter. What is the scale factor of the drawing?
Answer:
1ml : 1m
Step-by-step explanation:
The scale factor of the drawing is the ratio of 1 milliliter and 1 meter; that is, 1ml : 1m.
You are a manager at a restaurant. The restaurant’s freezer needs to be kept at a temperature of −5°F. The last reading was −1°F.
How does the temperature need to change to reach the preferred reading?
It needs to decrease by 6°.
It needs to decrease by 5°.
It needs to decrease by 4°.
It needs to increase by 4°.
It needs to increase by 6°.
Answer:
It needs to decrease by 4°
Step-by-step explanation:
-1-4=-5
mark my brainliest? :)
Final answer:
The temperature needs to change by 4°F to reach the preferred reading at -5°F.
Explanation:
The current temperature of the restaurant's freezer is -1°F. To achieve the preferred temperature of -5°F, we need to calculate the difference between the two temperatures The temperature needs to change to reach the preferred reading is 5°. Thus,
Calculating the difference between the preferred temperature (-5°F) and the current reading (-1°F): -5 - (-1) = -5 + 1 = -4°F.Since temperatures are measured in terms of how much they deviate from zero, it needs to decrease, so the change will be positive: 4°F.Therefore, the temperature needs to decrease by 4°F to reach the preferred reading.
which of the following is equivalent to 3(2x-5)-4(x-3)=7
Answer:
A
Step-by-step explanation:
When we distribute, we get:
6x - 15 - 4x + 12 = 7
If we combine the like terms, we get:
2x - 3 = 7, which is A in your case. Hope this helps.
Corey drew a sketch of a paper hat
If a = 4 in and b = 3 in, what is the area of the sketch?
A.
84 in2
B.
60 in2
C.
40 in2
D.
21.5 in
Answer:
Not on there but it is 76in2
Step-by-step explanation:
Starting with the trapezoid. We know that a trapezoid can be split into 2 triangles and 1 rectangle. So the area of the trapezoid will be 4+32+4 which is 40 now that we know the trapezoid's area we can find the rectangle's area. The rectangle's area will be 12x3 which is 36. So, you would add both:40+36= 76in2.
(Angles) What is the measure of angle p, in degrees? *
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and we'll do it
Answer:
Third Answer or 62 degrees.
The measure of angle p can be found by subtracting the measures of angles q and r from 180 degrees.
Explanation:The measure of angle p can be determined by subtracting the measures of angles q and r from 180 degrees. Let's say angle q measures 50 degrees and angle r measures 70 degrees. By subtracting these values from 180, we can find that the measure of angle p is 60 degrees.
Learn more about Angle measurement here:https://brainly.com/question/33833061
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¿Cuál dígito debe ir en el recuadro para
que el siguiente número sea divisible
entre 2, 3 y 9? 8,? 48
Answer:
7
Step-by-step explanation:
English:
Which digit should go in the box to
make the next number divisible
between 2, 3 and 9? 8 ,? 48
Let x be the number, then the number will look like this:
8x48
This number is already divisible by 2, because it ends with an even number.
Now we need to check for divsibility by 3.
For this to be divisible by 3, the sum of the digit should be a multiple of 3.
[tex]8 + x + 4 + 8 = x +20[/tex]
We know if a number is divsible by 9, it is also divsible by 3.
So
[tex]x + 20=9,18,27,....[/tex]
The least positive solution is
[tex]x + 20 = 27[/tex]
[tex]x = 27 - 20[/tex]
[tex]x = 7[/tex]
Therefore 8748 is divsible by 2,3, and 9.
What is the area of the surface of a cookie was a diameter of 32 feet?
That would be [tex]\pi(32/2)^2\approx804.25\mathrm{ft^2}[/tex].
Hope this helps.
Sari had 3 times as much money as Raymond. If after she paid Raymond a certain number of dollars, she had $30 and Raymond had $42, which of these statements is correct?
A.
Sari originally had $18.
B.
Sari originally had $24.
C.
Sari paid Raymond $18
D.
Sari paid Raymond $24.
Answer:
D
Step-by-step explanation:
both A and B are false, because no value would allow Sari to pay Raymond and then still have 30 dollars so it has to be C or D
42 - 24 = 18 18 times 3 is 54, so this appears to work
30 + 24 = 54
42 - 18 = 24 24 times 3 is not 48, so C is incorrect
30 + 18 = 48
Which of the following is a dilation?
O (x, y)----(x, 3y)
O (x,y)--(3x, 3y)
O (x, y)--(x,y-3)
O (x, y)---(.5x, .4y)
O Both 2 & 4
What is the exact distance from (−4, −2) to (4, 6)? (4 points)
A 24
B88
C 100
D 128
I would say it’s B! I know it isn’t A because we can say no to A since it’s such a small number and (-4,-2) to (4,6) isn’t 24 nor bigger then 100 so the only possible answer is B
I hope this helps and makes sense!
If x = a sec and y = b tan then find b^2x x^2-a^2x y^2
How many solutions does this system have? 2x+8y=16,-3x+6y=30
Final answer:
To determine the number of solutions for the system of equations 2x+8y=16 and -3x+6y=30, the elimination method can be used. After multiplying and combining the equations, it is found that the system has a unique solution at (-4, 3). This means the two lines intersect at exactly one point.
Explanation:
The student is asking about the number of solutions for the system of equations 2x+8y=16 and -3x+6y=30. To find out how many solutions the system has, we can use either substitution, elimination, or graphing methods. Substitution involves solving one equation for one variable and then substituting that into the other equation. Elimination involves adding or subtracting equations to cancel out one of the variables, which can be followed by solving for the remaining variable. Graphing would involve plotting both equations and observing their intersection points.
For this specific problem:
Equation 1: 2x+8y=16
Equation 2: -3x+6y=30
If we try to use the elimination method, multiplying Equation 1 by 3 and Equation 2 by 2 would allow us to cancel out the x's:
Multiplying Equation 1 by 3: 6x+24y=48
Multiplying Equation 2 by 2: -6x+12y=60
Adding these equations together gives us:
36y=108, which simplifies to y=3. Substituting y=3 into Equation 1, we can solve for x:
2x+8(3)=16
2x+24=16
2x=-8
x=-4
Thus, the system has a unique solution (x, y)=(-4, 3), indicating that the two lines intersect at exactly one point.
What is the next term of the arithmetic sequence?
-6,-8, –10, –12, -14,
Answer:-16 Hope that helps
Step-by-step explanation:
What is the slope of the line that passes through the points (-8,-4) and (4, -4)?
Write your answer in simplest form.
Answer:
it is 0
Step-by-step explanation:
What’s the value of x in degrees
Answer:
92⁰
Step-by-step explanation:
a = 35⁰ ( vertically opposite )
b = 53⁰ (vertically opposite )
a + b + x = 180⁰ (Angle sum property of triangle)
35⁰ + 53⁰ + x = 180⁰
x = 180⁰ - 88⁰
x = 92⁰
Answer:
[tex]x = 97 \: \: degrees[/tex]
Step-by-step explanation:
[tex]a = 35 \\ b = 53 \\ (vertically \: \: opposite \: \: angles)[/tex]
[tex]35 + 53 + x = 180 \\ 86 + x = 180 \\ x = 180 - 83 \\ x =9 7 \: \: degrees[/tex]
sum of the angles in a triangle is 180 degrees.
hope this helps
brainliest appreciated
good luck! have a nice day!
Describe one method to calculating the area of the shaded region.
Answer:
Fine the area of the square, then the area of the circle. Subtract the area of the circle from the area of the square and you will get the remaining shaded area.
4) -8 – 3a = 46 whoever has best answer gets brainliest
Answer:
A= -18
Step-by-step explanation:
-8-3(-18)= 46= -18
Answer:
a=-18
Step-by-step explanation:
Let's break this down step by step.
-8-3a=46
Since 3a has a variable, a, we want to get it by itself. So the first step is to do the inverse operation and add 8 on both sides. That leaves this equation:
-3a=54
The 3a is -3a because of the subtraction sign in front. Now we divide on both sides because we want the variable, a, to be by itself. That leaves this simplified expression.
a=-18.
Now, let's work it out in context of the problem.
-8-3x-18=46
3x-18 is -54, and -8-(-54), it would become 46.
A wheelbarrow weighs 55 pounds. It can carry a load up to 1/2 ton. How many pounds does the wheelbarrow weigh when it is filled to capacity?
Answer:
1055 lbs.
Step-by-step explanation:
Since 1 ton is 2000 pounds, half a ton is 1000 pounds. The wheelbarrow weights 55 pounds in itself, so the total weight will be 1000 + 55 = 1055 lbs.
At a school picnic, students can choose their dessert. The desserts include 8 ice cream sandwiches, 9 chocolate frozen bananas, 12 ice cream cones, 11 frozen pops, 16 push-up sticks, and 14 shaved ice cones. If desserts are chosen at random, what is the probability that the first person in line will choose an ICE CREAM CONE? Please select one answer.
Answer:
[tex]\frac{12}{70}[/tex]
Step-by-step explanation:
Firstly add up the total number of Deserts.
8 + 9 + 12 + 11 + 16 + 14 = 70
There are a total of 12 ice cream cones
This can be represented as a fraction for your answer [tex]\frac{12}{70}[/tex]