Answer:
Step-by-step explanation:
Parabola's equation is
y
=
1
16
(
x
−
7
)
2
+
1
and vertex is
(
7
,
1
)
.
Explanation:
Parabola is locus of a point which moves so that its distance from a given point calld focus and a given line ccalled directrix is always constant.
Let the point be
(
x
,
y
)
. Here focus is
(
7
,
5
)
and distance from focus is
√
(
x
−
7
)
2
+
(
y
−
5
)
2
. Its distance from directrix
y
=
−
3
i.e.
y
+
3
=
0
is
|
y
+
3
|
.
Hence equaion of parabola is
(
x
−
7
)
2
+
(
y
−
5
)
2
)
=
|
y
+
3
|
2
or
x
2
−
14
x
+
49
+
y
2
−
10
y
+
25
=
y
2
+
6
y
+
9
or
x
2
−
14
x
+
65
=
16
y
i.e.
y
=
1
16
(
x
2
−
14
x
+
49
−
49
)
+
65
16
or
y
=
1
16
(
x
−
7
)
2
+
65
−
49
16
or
y
=
1
16
(
x
−
7
)
2
+
1
Hence parabola's equation is
y
=
1
16
(
x
−
7
)
2
+
1
and vertex is
(
7
,
1
)
.
graph{(1/16(x-7)^2+1-y)((x-7)^2+(y-1)^2-0.15)((x-7)^2+(y-5)^2-0.15)(y+3)=0 [-12.08, 27.92, -7.36, 12.64]}
Until the scale was changed in 1995, SAT scores were based on a scale set many years ago. For Math scores, the mean under the old scale in the 1990s was 470 and the standard deviation was 110. In 2013 the mean was 515 and the standard deviation was 116. Gina took the SAT in 1994 and scored 500 on the Math test. Her cousin Colleen took the SAT in 2013 and scored 530 on the Math test. Who did better relative to their peers, and how can you tell? Group of answer choices Colleen—she scored 30 points higher than Gina. Gina—the standard deviation was bigger in 2013. Gina—her standardized score is higher than Colleen’s. Colleen—her standardized score is higher than Gina’s.
Answer:
Gina—her standardized score is higher than Colleen’s.
Step-by-step explanation:
Until the scale was changed in 1995, SAT scores were based on a scale set many years ago.
We solve this question using z score formula also know as standardized score formula which is given as:
z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.
For Gina
Gina took the SAT in 1994 and scored 500 on the Math test.
For Math scores, the mean under the old scale in the 1990s was 470 and the standard deviation was 110.
x = 500
μ = 470
σ = 110
Hence, the z score is given as:
z = 500 - 470/110
z = 0.27273
Gina's z or standardized score is 0.27273
For Colleen
Her cousin Colleen took the SAT in 2013 and scored 530 on the Math test.
In 2013 the mean was 515 and the standard deviation was 116.
x = 530
μ = 515
σ = 116
Hence, the z score is given as:
z = 530 - 515/116
z = 0.12931
Colleen's z or standardized score is 0.12931
The person who did better relative to their peers is Gina and this is because her standardized score is higher than Colleen’s.
What is the x-intercept of the line described by the equation? 14x - 8y = 56
Answer:
The x intercept is (4,0) and the y intercept is (0,-7)
Step-by-step explanation:
Answer:
Step-by-step explanation:
The x-intercept of a line is when the y-coordinate is 0. To find that point on this line, we first want to rearrange the equation into the form
[tex]y = mx + b[/tex]
we are given
[tex]14x - 8y = 56\\so, \\14x - 56 = 8y\\\frac{14x}{8} - \frac{56}{8} = \frac{8y}{8} \\y = \frac{7}{4}(x) - 7[/tex]
now, we can set y to 0 and solve
[tex]\frac{7}{4}(x) = 7\\7x = 28\\x = 4[/tex]
The x-intercept is (4, 0)
Help plz mportant!!! Choose the point-slope form of the equation below that represents the line that passes through the point (-1.6) and has a slope of -3.
а. y - 6 = -3x - 3
b. y - 6 = -3(x + 1)
c. y=-3x + 3
d. 3x+y=3
Answer:
B
Step-by-step explanation:
point slope uses the form y - y1 = m(x - x1)
m stand for slope. in this case it is -3
x1 is -1 and y1 is 6
when you plug it in, you get
y - 6 = -3(x - [-1])
which simplifies to your final answer: y - 6 = -3(x + 1)
x^2 − 15 = 1 please help
Answer:
x^2-15=1
x^2=16
4 x 4 = 16
THerefore...
x=4
Depending on how many choices there are -4 is also correct.
Any number squared is a positive.
x=4, x=-4
Step-by-step explanation:
A triangular bike path is exactly 9 miles long. If each of the three connecting paths is a whole-number of miles long, which could be the lengths of the paths?
Answer:
2 miles, 3 miles, 4 miles
Step-by-step explanation:
could yu PLZZZZZZ mark brainliest
Answer:
2 miles, 3 miles, 4 miles
1 $40.00 shirt is on a 10% off sale rack, What is the final price of the shirt 8.25%
tax is applicable?
Answer:
$38.97
Step-by-step explanation:
100% - 10% = 90% = 0.9
$40 × 0.9 = $36
100% + 8.25% = 108.25% = 1.0825
$36 × 1.0825 = $38.97
a person who weighs 120 pounds on earth weighs 20 pounds on the moon. How much does a 93-Ib. person weigh in the moon
Answer:
15.5 pounds on the moon
Step-by-step explanation:
hope this helps
need brainlyest plz
THANKS!!
Answer:
15.5 lb
20 is a sixth of 120, and 15.5 is a sixth of 93
Question #1 Find the unit rate if the graph below
A
150
135
120
105
90
75
Toys
60
45
30
15
3 6 9 12 15 18 21 24 27 30
Cartons
Answer:
The unit rate is 5 toy per carton on the graph
The cost of Ken's car wash was $24.00. If he wants to give his detailer a 15% tip, about how much of a tip should he leave?
Which expression represents a quadratic expression in standard form? *
5x-4
-21-x^2
-15+2x-x^2
x^2-2x-63
A penguin walks 10 feet in 6 seconds. At this speed how far does the penguin walk in 45 seconds?
Find the y-intercept of a line that passes through the point (-5,-6) and has a slope of 2.
Answer:
The y intercept is 4
Step-by-step explanation:
Given:
-Given point: (-5,-6)
-Slope of 2
1) Put the equation into point-slope form y - y1 = m(x - x1)
With the given, we can plug it all in using this formula!
-y1 = -6
-x1 = -5
m = 2
(you would change these negative numbers into positives because the equation shows them being subtracted! remember that two negatives make one positive!)
y+6= 2(x+5)
2) Simplify
y+6= 2(x+5)
y+6=2x+10
y=2x+4
With y=2x+4, set x to 0 because the y intercept is where x is equal to 0 and you get 4!
what is the point do these equation intersect x+4y=15 and 4x+5y=16
4/5x - 1/10 = 3/10 what is the value of x
Answer:
x=1/2 or 0.5
Step-by-step explanation:
Hope this helps and have a great day :)Write in simplest form: what is 2^-3 in simplest form
Answer: 1/8
[tex]2^{-3}=\frac{1}{2^{3} }=\frac{1}{8}[/tex]
Step-by-step explanation:
Answer:
1/8
Step-by-step explanation:
Solve one third plus seven ninths equals
Answer:
1 1/9 0r 10/9
Step-by-step explanation:
the least common denominator or LCM of the two denominators:
LCM of 3 and 9 is 9
For the 1st fraction, since 3 × 3 = 9,
1
3
=
1 × 3=3
3 × 3=9
= 3/9
Likewise, for the 2nd fraction, since 9 × 1 = 9,
7
9
=
7 × 1=7
9 × 1=9
=7/9
Add the two fractions:
3
9
+
7
9
=
3/9+ 7/9=10/9
So, 1/3 + 7/9 = 10/9
In mixed form: 1 1/9
There are between 24 and 40 students in a class,
The ratio of boys to girls is 4:7
How many students are in the class?
Answer:answer is 387
Step-by-step explanation:ok got it
Answer:
There are 33 students in the class.
Step-by-step explanation:
geometry work help find the value of x
Answer:
110⁰!!
Step-by-step explanation:
so this is an isosceles triangle! the base angles are always equal to each other. since 35 is a vertical angle, the base angle vertical to that would be 35. and since base angles ALWAYS equal each other, they would both be 35.
35+35=70, 70 is the base angles added up
180-70=110
c=110
Researchers collected data on calories per serving for 77 brands of breakfast cereal. The histogram displays the data
30
25-
20
1
Frequency
15
What is the approximate center of this distribution?
The center of the distribution is between 120 and 130
calories.
The center of the distribution is between 90 and 100
calories.
The center of the distribution is between 110 and 120
calories.
The center of the distribution is between 80 and
90 calories.
The center of the distribution is between 130 and 140
calories.
10
-
50 60 70 80 90 100 110 120 130 140 150 160
Calories
Histogram attached
Answer and explanation:
To find the center of the distribution, we find the mean of the distribution.
Mean= sum of all values/number of values
To calculate the mean of the distribution using the histogram(attached) with given frequencies, we find the mid point of each class and multiply by its frequency to get the sum of the values(estimated) and then divide by the number of values(sum of the frequencies of the classes)
midpoint of 50-60=50+60/2=55
midpoint of 70-80=150/2= 75
midpoint of 80-90=170/2=85
midpoint of 90-100=190/2=95
midpoint of 100-110=210/2=105
Midpoint of 110-120=230/2=115
Midpoint of 120-130=250/2=125
Midpoint of 130-140=270/2=135
Midpoint of 140-150=290/2=145
Midpoint of 150-160=310/2=155
Sum of the values= 55*frequency= 55*3+75* 2+85*1+95*7+105*17+115*29+125*10+
135*2+145*3+155*3
Sum of all values =8605
Number of values= 3+2+1+7+17+29+10+2+3+3=77
Mean= 8605/77= 111.753
Therefore the center of the distribution is between 110 and 120 calories.
There are a total of 24 people at Camp Float-Away. If 4 of the people are counselors, what is the ratio of campers to counselors?
Answer:
5:1
Step-by-step explanation:
Since there are 4 counselors, the other 20 people are campers. You divide 20 by 4 (to determine how many campers equal 1 counselor) and you get 5. So 5:1
5x+4=2(x+2)
please help me i tried it and i got it wrong I got 2/5
Answer: x= 0
Step-by-step explanation:
5x + 4 = 2(x + 2) First distribute on the right side of the equation
5x + 4 = 2x + 4 Subtract 2x from both sides
-2x -2x
3x + 4 = 4 Subtract 4 from both sides
-4 -4
3x = 0 Divide both side by 3
x = 0
Find the unit rate. Round your answer to the nearest hundredth.
357 miles in 5 hours
miles per hour
Answer:
71.4 mph
Step-by-step explanation:
357/5
71.4
Answer:
71.40
Step-by-step explanation:
357/5= 71.4 or 71.40 to the nearest hundredth.
Can someone help me with the questions in the picture?
i need help with this
Answer:
1st - Yes ; 2nd - Yes ; 3rd - Yes ; 4th - No
Step-by-step explanation:
You buy 6 items for $25.60. About how much did you spend?
$125
$145
$75
$150
Answer: About $150.
Explanation: Each item cost $25.60, so I multiplied it into six, equalling about $150.
Find x and the lengths of sides JM, MN, and JN. Triangle JMN is an isosceles triangle with side JM ≅ side MN. JM = 2x - 5, MN = 3x -9, and JN = x - 2.
Answer:
x = 4
JM ≅ MN = 3
JN = 2
Step-by-step explanation:
In an isosceles triangle, two of the sides are equal. Given the lengths of sides of triangle JMN as JM, MN, and JN where JM ≅ MN
Given
JM = 2x - 5
MN = 3x -9, and
JN = x - 2.
Since JM≅ MN then;
2x - 5 = 3x-9
Collect like terms;
2x-3x = -9+5
-x = -4
multiply both sides ny -1;
-(-x) = -(-4)
x = 4
For side JM;
JM = 2x-5
JM = 2(4)-5
JM = 8-5
JM = 3
Since JM ≅ side MN, hence;
MN = 3
For side JN;
JN = x-2
JN = 4-2
JN = 2
Answer:
good job
Step-by-step explanation:
ACD is a triangle and B is a point on AC.
BC = 10cm
Angle ACD = 770 Angle BDC = 26°
Angle DAC = 40°
(a) Find the length of BD
(b) Find the size of angle ABD
(c) Find the length of AD
Answer:
< ABD
Step-by-step explanation:
<ACD=770<BDC=26<DAC=40 then. <ABD=770+26+40= 796+40= 836Stefanie swam four-fifths of a lap in the morning and seven-fifteenths of a lap in the evening. How much farther did Stefanie swim in the morning than in the evening?
A 3-gallon jug of orange juice costs $10.44. What is the cost of the orange juice per quart?
A.
$1.07
B.
$0.87
C.
$2.06
D.
$0.98
Answer:
B. $0.87
Step-by-step explanation:
Divide $10.44 by 12 (how many quarts are in 3 gallons) to get the answer.
Simplify the expression.
Can someone explain to me how to get the answer? Thanks!
Answer:
11x^2+2x+9
Step-by-step explanation:
2+(2+6)⋅x^2+2x+3x^2+7
2+(8)⋅x^2+2x+3x^2+7
2+8x^2+2x+3x^2+7
9+8x^2+2x+3x^2
9+8x^2+2x+3x^2
11x^2+2x+9