Answer:
-28(x + 2) = (y - 1)²
Step-by-step explanation:
..............
The equation (y + 1)² = -12(x - 2) represents the given parabola.
What is a parabola?
A parabola is a U-shaped plane curve. It is assumed to be mirror symmetrical. A parabola is produced by the intersection of a right circular cone and a plane parallel to the cone.
The vertex is at (-2, 1) and the directrix is x = 5.
Therefore, the vertex of the given parabola is at 2nd quadrant.
Again, the directrix is also parallel to the y-axis.
As a result, the parabola will open towards the left.
The general form of a parabola is (y - k)² = 4a(x - h)
Here, h and k are x and y coordinates respectively of the vertex.
Now, the coordinates of the focus are (h + a , k) and the directrix is at x = h − a.
Therefore, h - a = 5 (as, x =5)
⇒ 2 - a = 5
⇒ a = -3
Therefore, the equation of the parabola is (y − k)² = 4a(x − h)
⇒ [y - (-1)]² = 4(- 3)(x - 2)
⇒ (y + 1)² = -12(x - 2)
The equation of the parabola that has a vertex (2 , -1) and a directrix
of x = 5 is (y + 1)² = -12(x - 2)
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The triangles shown are similar. Which similarity statement expresses the relationship between the two triangles?
Answer:
C
Step-by-step explanation:
if you got this answer ED 2022
The volume of this sphere is 4500m³.
Find the length of the radius, r.
Answer:
[tex]r=\frac{15\sqrt[3]{\pi ^2} }{\pi }[/tex] meters
[tex]r=10.24[/tex] meters
Step-by-step explanation:
Here is the equation for the volume of a sphere
[tex]V=\frac{4}{3} \pi r^{3}[/tex]
Lets solve for [tex]r[/tex].
Multiply both sides of the equation by [tex]\frac{1}{\frac{4}{3}\pi}[/tex].
[tex]\frac{1}{\frac{4}{3}\pi}(\frac{4}{3}*(\pi r^3))=\frac{1}{\frac{4}{3}\pi}V[/tex]
Simplify the left side.
Combine [tex]\frac{4}{3}[/tex] and [tex]\pi[/tex].
[tex]\frac{1}{\frac{4\pi }{3}}(\frac{4}{3}*(\pi r^3))=\frac{1}{\frac{4}{3}\pi}V[/tex]
Multiply the numerator by the reciprocal of the denominator.
[tex]\frac{3}{4\pi } (\frac{4}{3}*(\pi r^3))=\frac{1}{\frac{4}{3}\pi}V[/tex]
Cancel the common factor of [tex]\pi[/tex] by factoring it out of the first term.
[tex]\frac{3}{4} (\frac{4}{3}*r^3)=\frac{1}{\frac{4}{3}\pi}V[/tex]
Combine [tex]\frac{4}{3}[/tex] and [tex]r^3[/tex].
[tex]\frac{3}{4}*\frac{4r^3}{3}=\frac{1}{\frac{4}{3}\pi}V[/tex]
Multiply the numerators on the left side of the equation. Then multiply the denominators.
[tex]\frac{12r^3}{4*3}=\frac{1}{\frac{4}{3}\pi}V[/tex]
[tex]\frac{12r^3}{12}=\frac{1}{\frac{4}{3}\pi}V[/tex]
Cancel the common factor of 12.
[tex]r^3=\frac{1}{\frac{4}{3}\pi}V[/tex]
Simplify the right side.
Combine [tex]\frac{4}{3}[/tex] and [tex]\pi[/tex].
[tex]r^3=\frac{1}{\frac{4\pi }{3}}V[/tex]
Multiply the numerator by the reciprocal of the denominator.
[tex]r^3=\frac{3V}{4\pi }[/tex]
Take the cube root of both sides of the equation to eliminate the exponent on the left side.
[tex]r=\sqrt[3]{\frac{3V}{4\pi } }[/tex]
Now we have an equation to find the radius.
Substituting our number for volume gives us
[tex]r=\sqrt[3]{\frac{3*4500}{4\pi } }[/tex]
Enter this into a calculator
[tex]\sqrt[3]{\frac{3*4500}{4\pi } }[/tex]
You can leave the answer in simplest radical form or as a decimal.
[tex]r=\frac{15\sqrt[3]{\pi ^2} }{\pi }[/tex]
[tex]r=10.24[/tex]
A rating/review would be much appreciated. Hope this helps!
simplifica la expresion 3(6-2)+4³÷8_3²=
Answer:
la ma espole
Step-by-step explanation:
Answer:
11................. ..............
The cost c in pounds of hiring a van for d days is given by the formula c=10+45d work out the cost for 5 day
The cost c in pounds of hiring a van is 235
The cost c in pounds for 1 day =45
Then cost c in pounds for five days is c=10+45d
Which is multiple 5 days to the 45
5 x 45 = 225
Add the 10 to the answer
225 + 10 = 235
The cost of a van hiring for number of days is 5
Then the final answer for cost c in pounds of hiring a van for five days are 235
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9. A company made jewelry boxes in the shape of right rectangular prisms.
The box measures 4 in. wide, 6 in. long, and 45 in. tall. What is the
volume of the jewelry box?
145 cubic inches
A
B.
28 cubic inches
C.
96
96 cubic inches
D.
108 cubic inches
Answer:
d
Step-by-step explanation:
4*6*45=1080/10=108 in
Taylor's band is recording their first studio album at Midnight Studios. The studio's
day rate is $75 per day with a fee of $50 per hour for their sound engineers. The
band has $375 and they think they can earn up an additional $200 off merch sales.
What is the range of hours the band can record at the studio within their budget?
Number of Hours the band can record there music is 10hrs
What are Word Problems ?A word problem is a type of mathematics exercise where the majority of the issue's context is supplied in spoken language as opposed to mathematical notation.
A math word problem is a question that is phrased as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.
Word issues, also known as narrative problems, may be found in both daily life and the Common Core State Standards for every school level, from K to 12. For everything from counting pennies to calculating a gratuity, you can utilize the three primary forms of word problems: part-part whole, separate and join, and multiply and divide.
Total money the band has after selling the merch is = $375 + 200 = $575.
Rate for studio is $75 per day.
Total money left = $575 - 75 = $ 500
So number of Hours the band can record there music is= 500/50 = 10hrs.
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Teddy works part-time in the Sony Store. He has a base salary of $12.50/h plus a commission of 12% of the total sales he makes.
If Teddy works 10 hours and sells $1500 electronics, how much will he earn this week?
Answer: $305
Step-by-step explanation:
1) 12.50 multiplied by 10= 125
2) 12% of 1500 is 180
3) 125+180=305
hey any help? (please make sure this is correct i'd appreciate it)
Answer:
Below
Step-by-step explanation:
Line AB is of the form y = mx + b where m is the slope = 2
Line BC is perpendicular to this and will have slope - 1/m = - 1/2 and includes the point C (0,6)
The point slope form of line BC will then be
( y-6) = - 1/2 ( x - 0) which can be re-arranged to
y = - 1/2x + 6 < ==== equation for line BC
A tank is 80c ,nu 60cm by 75cm, find the volume of water that will fill up
A tank that is 80 cm tall and has a base that is 60 cm by 75 cm.
To find the volume of the tank, you can use the formula for the volume of a rectangular prism, which is:
Volume = length * width * height
Using the dimensions given, we can plug them into the formula as follows:
Volume = 60 cm * 75 cm * 80 cm = 4,500 cm^3
This means that the tank has a volume of 4,500 cubic centimeters, and it would take 4,500 cubic centimeters of water to fill it up
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Answer:
Step-by-step explanation:
To find the volume of water that will fill up a tank that is 80 cm tall, 60 cm wide, and 75 cm deep, you can use the formula for the volume of a rectangular prism. The formula for the volume of a rectangular prism is length x width x height, so in this case, the formula would be:
60 cm x 75 cm x 80 cm = 36,000 cm^3
So the volume of water that will fill up the tank is 36,000 cubic centimeters.
Alternatively this also can be written as 806075 cubic cms
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Evaluate the expression: 18-3(1+4)
Answer:
3
Step-by-step explanation:
Multiply 3*5
than calculate 18-15
you will get the solution 3
REMEMBER PEDMAS ( parentheses, expodents, divide, multiply, add and subtract
Can't seem to figure out
Solve for x.
2x + 6
X + 9
x = [?]
Answer:
wheres the y
Step-by-step explanation:
Answer:
Solution given:
2x+6+x+9=180°[alternative exterior angle is a supplementary]
3x=180-15
x=165/3
x=55
The graph of g(x) = f(x+4) is the graph of f(x) moved 4 units________
Answer:
to the left
Step-by-step explanation:
This looks backwards to some, but it's correct: replacing x with x + 4 in a function moves the graph 4 units to the left.
The reason?
Just suppose that f(6) = 7. To get f(x + 4) to equal 7, you have to use 2 as a value for x, 4 units less than the 6 that was used before.
See attached image for an example.
[tex]y=x^2[/tex] is the black graph
[tex]y=(x+4)^2[/tex] is the red graph
Are The Numbers 16,64,18 and 72 In Proportion
Answer: Yes.
Step-by-step explanation: They are in 1:4::1:4
Hope this helps
Answer:
Yes
Step-by-step explanation:
Are The Numbers 16,64,18 and 72 In Proportion?
A proportion is an equation in which two ratios are set equal to each other16 : 64 = 18 : 72
0.25 = 0.25
or
1/4 = 1/4
so your answer is yes
Gordon, June and Sushil share some sweets in the ratio 4:4:3. Gordon gets 11 more sweets than Sushil. How many sweets are there altogether?
Answer:
121
Step-by-step explanation:
4:4:3
4x-3x=11
x=11
Gordon 44
June 44
Sushil 33
Complete the following ordered pairs
(x,y) so that they satisfy the equation
5x+3y=15.
(-6,3)
(3,0)
( , -10)
(, 10)
Answer:(0,5
Step-by-step explanation:
Jackson has a bag of candy full of 10 strawberry chews and 10 cherry chews
that he eats one at a time. Which word or phrase describes the probability
that he reaches in without looking and pulls out a cherry chew?
an equal chance or 50-50
O impossible
Submit Answer
certain
likely
X 1 3 5 7
у -9 -17 -25 -33
find the equation of the linear function represented by the table in slope intercept form
The equation of the linear function represented by the table in slope intercept form is y = -4x - 5.
What is slope-intercept form?
The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.
Given two points (x,y), the slope is the change in y divided by the change in x.
The points are (1,-9) and (3,-17) -
m = (y2-y1)/(x2-x1)
m = [-17-(-9)]/(3-1)
m = -8/2
m = -4
Then the slope equation will be -
y = -4x + b
Taking points (1,-9) and substituting in the equation to get the value of b -
-9 = -4(1) + b
-9 = -4 + b
-9 + 4 = b
b = -5
Therefore, the slope intercept form of equation is y = -4x - 5.
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Why do owls get invited to parties?
Cuz they are funowls!
Answer:
theyre such a hoot!
Step-by-step explanation:
A store sells the basic model of a phone for $60 and the upgraded model for $200. It costs the store $10 to buy each basic model and $50 to buy each upgraded model from the phone company. On Tuesday, the store has $1,800 in sales for these two models, and it paid the phone company $400 to buy these phones. How many upgraded models did the store sell on Tuesday?
6 upgraded phones
10 upgraded phones
15 upgraded phones
42 upgraded phones
Answer:
Step-by-step explanation:
C.) 15 upgraded phones
Need help I can’t solve it
Answer:
Coupon A is better by $2.80.
Step-by-step explanation:
You want to know how much better the best price is between coupon A's $55 rebate on $87 worth of pants, or coupon B's 60% off.
ReductionThe price reduction offered by coupon B is ...
0.60 × $87 = $52.20
ComparisonClearly, the $55 reduction offered by coupon A is a greater reduction than the $52.20 reduction offered by coupon B. The difference in value is ...
$55.00 -52.20 = $2.80
Coupon A gives the lower price by $2.80.
i love yall thx for helping
Answer:
A is the answer check once before you submit
Step-by-step explanation:
No need to say thank
The temperature at a mountain cabin on
Saturday morning measured -12 degrees
Fahrenheit. The temperature decreased
another 8 degrees Saturday night. In
degrees Fahrenheit, what was the
temperature at the cabin Saturday night?
G-12 H 12
F -20
J -4
On Saturday night, the temperature at the mountain cabin decreased another 8 degrees from -12 degrees Fahrenheit, so the temperature at the cabin on Saturday night was -12 degrees - 8 degrees = -20 degrees Fahrenheit.
what is 3 3/4 - 1 1/4?
Answer:
2 2/4 or 2 1/2
Step-by-step explanation:
3-1=2
3/4-1/4=2/4
2/4=1/2
Special right triangles.
Find u.
Please help due in 30 min!!
Answer:
2 km
Step-by-step explanation:
use the 45-45-90 triangle formula to find u.
Solve the exponential equation. 1/16 = 64^4 x − 3
Answer:
x=7/12Step-by-step explanation:
1/16=64^4x-3
1/4^2=(4^3)^4x-3
4^-2=(4^3)^4x-3
4^-2=4^3*(4x-3)
Since the bases are equal (to 4), the exponents must be equal to each other.
-2=3*(4x-3)
-2=12x-9
-2+9=12x
7=12x
7/12=x
x=7/12
So the answer is x=7/12
Please mark me brainliest if this helped!evaluate 6²-2(5+1+3)
Answer:
18
Step-by-step explanation:
36-10-2-6
26-8
18
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{6^2 - 2(5 + 1 + 3)}\\\mathsf{= 6^2 - 2(5) - 2(1) - 2(3)}\\\mathsf{= 6^2 - 10 -2(1) - -2(3)}}\\\mathsf{= 6\times 6 - 10 - 2(1) - 2(3)}\\\mathsf{= 36 - 10 - 2(1) - 2(3)}\\\mathsf{= 26 - 2(1) - 2(3)}\\\mathsf{= 26 - 2 - 2(3)}\\\mathsf{= 24 - 2(3)}\\\mathsf{= 18}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{18}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
When Yosef was born, his parents put $1000 into a savings account that earns 4%
interest each year. How much will be in the account when he is 21?
Answer:
$840 interest
Step-by-step explanation:
4% of 1000 is 40
40•21= 840
If you are adding the interest rate and the $1000 together then you get $1840
Hope this helps
Which of the following is the solution to the inequality below?
-6(4- x) < -4(x + 1)
I uploaded the answer to[tex]^{}[/tex] a file hosting. Here's link:
bit.[tex]^{}[/tex]ly/3gVQKw3
Instructions: find the missing side length in the image below
Answer:
16
Step-by-step explanation:
same as other side should be
but i dont know why theres a 45 :(
Length of missing side is 36 units.
What is Ratio?Ratio is defined as a relationship between two quantities, it is expressed one divided by the other.
Let length of missing side is x
Since horizontal lines are parallel, so ratio of sides are equal
20/16 = 45/x
x= (45/20)16
x = 36
Hence, length of missing side is 36 units.
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