Let cheryl score "c", Adam score "a", Laura score "l" and Tom score "t", points.
Now, let's write equations for statements given.
Adam scores 8 more than Cheryl, so:
a = c + 8
or
c = a - 8
Laura scored twice as Adam, so:
l = 2a
Tom scores 10 less than Laura:
t = l - 10
or
t = 2a - 10
Altogether, they scored 66, so:
c + a + l + t = 66
Putting the 3 bold equations in the last one, we can solve for "a" first. Shown below:
[tex]\begin{gathered} c+a+l+t=66 \\ a-8+a+2a+2a-10=66 \\ 6a-18=66 \\ 6a=66+18 \\ 6a=84 \\ a=\frac{84}{6} \\ a=14 \end{gathered}[/tex]So,
c = a - 8
c = 14 - 8
c = 6
l = 2a
l = 2(14)
l = 28
t = 2a - 10
t = 2(14) - 10
t = 28 - 10
t = 18
So,
Adam = 14 points
Cheryl = 6 points
Laura = 28 points
Tom = 18 points
50 POINTS PLEASE SHOW WORK!!!! A radio telescope has a parabolic dish. Radio signals are collected at the focal point (focus) of the parabola. The distance from the vertex of the parabolic dish to the focus is 20 feet. The vertex of the dish is located at a point 30 feet above the ground and 80 feet to the east of a computer that reads and records data from the telescope. The diameter of the dish is 120 feet.
What is the depth of the parabolic dish?
In this exercise we have to use the knowledge of depth to be able to calculate the depth that is being seen by the telescope, in this way we can say that:
45 feet deep
First, knowing that the formula for the parabola is:
4py=x²
Now P is the distance from the vertex to the focus or to the directrix which is equal to 20, we can say that:
4(20)y=x²
80y=x²
Now we just should use individual knwon financial worth of X fashionable the maximum point of the dish, exist the measurement across object of the eating receptacle exist 120 extremities that is to say the maximum x, and we understand information that 120 extremities is heavy distance middle from two points the expansive -x and x, so those hopeful: -60 and 60.
80y=x²
80y=60²
80y=3600
y=45
Answer:
75ft
Step-by-step explanation:
We can let the parabola open upward......so we will have the form
4a ( y - k) = (x - h)^2
The distance from the vertex to the focus = 20 = a
We can let the vertex be ( 80, 30)
So we have the form
4(20) ( y- 30) = (x - 80)^2 simplify
80 ( y - 30) = ( x - 80)^2
Since the diameter is 120 ft...the radius is 60 ft.....so we can let one point on the parabola be ( 80 + 60 , a) =
(140 , a)......where a is the height of the dish....so we have that
80 ( a - 30) = (140 - 80)^2
80 ( a - 30) = (60)^2
80 ( a - 30) = 3600 divide both sides by 80
a - 30 = 45 add 30 to both sides
a = 75 ft = the height of the dish
Question 14 of 30The histogram below gives the distribution of test scores for a sample ofstudents in a school in Alaska. Which answer choice gives the number ofstudents that scored above 50.57
We need to find the number of students that scored above 50.57.
That number is given by the sum of all heights of the bars after 50.5:
Heights of the bars with scores above 50.5:
• bar labeled 1: ,100
• bar labeled 2: ,250
• bar labeled 3: ,200
• bar labeled 4: approximately ,190
• bar labeled 5: approximately ,60
Then, adding those values, we obtain:
[tex]100+250+200+190+60=800[/tex]Answer: D. 800
please help me please
There is no question, just some graphs, I can not explain if I don't know the question
ok
y = 2x
This is a positive line that increases from left to right, because the number 2 of the equation is positive.
So from the graphs that you send me, the right answer is the second one, it is an increasing line.
A graph increases from left to rigth if it goes up
A graph decreases from left to right if it goes down
Gavin and Jim win some money and share it in the ratio 1:3. Gavin gets £15. How much did Jim get?
Using ratios we can conclude that Jim will get £45.
What are ratios?In mathematics, a ratio shows how frequently one number appears in another. For instance, the ratio of oranges to lemons in a fruit plate would be eight to six if there were eight oranges and six lemons. Oranges make up 8:14 of the total fruit, whereas lemons make up 6:8 of the total fruit.So, the money Jim gets will be:
The ratio, that they got money in is 1:3.
Gavin:JIM = 1:3Gavin gets £15.Then Jim will bet:
£15 × 3£45Therefore, using ratios we can conclude that Jim will get £45.
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a circular field has area 14400 square feet what is the radius? a 12ft b 120ft c 720ft d 7200ft
The radius of the circular field with area 14400 square feet is 67.7ft
What is a circle?A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.
The radius of a circular field with an area of 14400 square feet can be calculated by the formula:
Area of a circle(A) = [tex]\pi r^{2}[/tex]
where A = 14400[tex]ft^{2}[/tex]
[tex]\pi[/tex] = constant which is 3.142
A = [tex]\pi[/tex][tex]r^{2}[/tex], where A = area of circle , r = radius
divide both sides by c
A/[tex]\pi[/tex] = [tex]r^{2}[/tex]
[tex]r^{2}[/tex] = A/[tex]\pi[/tex]
r = [tex]\sqrt{\frac{A}{\pi } }[/tex]
Substitute the values of A and [tex]\pi[/tex]
r = [tex]\sqrt{\frac{14400}{3.142} }[/tex]
r = 67.7ft
In conclusion the radius of the field is 67.7ft
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Interior and exterior angles
The measures of the interior and exterior angles ∠1, ∠2, ∠3, ∠4, ∠5, ∠7, ∠8, and ∠9 are 90°, 90°, 90°, 122°, 58°, 58°, 148°, 32°, and 148°, respectively.
We are given a triangle. One of the angles is 122 degrees, as shown in the diagram. We need to find all the interior and exterior angles. The vertically opposite angles are equal. The angle ∠4 is vertically opposite to the given angle. So, ∠4 = 122°. The angle ∠5 and the given angle form a linear pair. So, the angle ∠5 = 180° - 122° = 58°. The angle ∠6 is vertically opposite to the angle ∠5. So, the angle ∠6 = 58°. The angles ∠1, ∠2, and ∠3 are angles made by coordinate axes that are perpendicular to each other. So, the angles ∠1 = ∠2 = ∠3 = 90°. Now we use the angle sum property of a triangle. The sum of all the interior angles of a triangle is 180°. So, we can write the equation : ∠6 + ∠1 + ∠8 = 180°. So, ∠8 = 180° - (∠6 + ∠1) = 180° - (58° + 90°) = 180° - 148° = 32°. The angles ∠8 and ∠9 form a linear pair. So, ∠9 = 180 - 32° = 148°. The angle ∠7 is vertically opposite to the angle ∠9. So, the angle ∠7 = 148°.
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Use long division or a calculator to write 1/6 as a decimal. Then tell whether the decimal is terminating or repeating
It can be seen that it is a repeating decimal because the division is continuous
help meeeeeeeeeeeeeeeeeeee pleaseee rnnnn rn!!!!
Other than the unit of measurement i am genuinely confused by this because (as far as I know) there is no possible way of figuring this out. The unit is obviously meters but I have no idea what the answer is. You should ask your teacher to explain it to you because it's confusing.
3. Solve the expression when a= 0.25 and b = -1
36a + 42b - 18a + 6
Answer:
-31.5
Step-by-step explanation:
36(0.25)+ 42(-1)-18(0.25)+6
9-42-4.5+6
=-31.5
Urgent need of help!
The measure of the angle ∠ABD is calculated as 138° from the given data and figure.
What is triangle's angle sum property?The total of a triangle's three internal angles is 180 degrees, according to the angle sum property. When the values of the other two angles are known, the angle sum property is utilized to compute the measure of an unknown interior angle.
What exactly is the SAS rule of similarity?SAS stands for Side-Angle-Side Similarity. If the proportion of the two sides of one triangle is the same as the proportion of the two sides of another triangle, and the angle inscribed by the two sides of both triangles is equal, two triangles are said to be similar.
Given: ΔACD and ΔBCD are isosceles.
AD ≅ AC
BD ≅ BC
∠BAC = 18°
∠BDC = 48°
We need to determine the measure of ∠ABD.
Since, AD ≅ AC
∠DAB = ∠BAC = 18°
Since, BD ≅ BC
∠BDC = ∠BCD = 48°
By triangle's angle sum property,
∠BDC + ∠BCD + ∠DBC = 180°
48° + 48° + ∠DBC = 180°
∠DBC = 84°
Also, ∠ABD = ∠ABC [By SAS rule of ΔABD + ΔABC]
From the figure we can see that,
∠DBC + ∠ABD + ∠ABC = 360°
84° + 2∠ABD = 360° [∵ ∠ABD = ∠ABC]
2∠ABD = 276
∠ABD = 138°
Therefore, the measure of the angle ∠ABD is calculated as 138° from the given data and figure.
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Pls do this for me asap
Answer:
The correct answer is B
Step-by-step explanation:
Two points determine a line. Find an equation of the line passing through the points.
(2,−7) and (5,−19)
An equation of the line is y=
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-19}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-19}-\stackrel{y1}{(-7)}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{2}}} \implies \cfrac{-19 +7}{3} \implies \cfrac{ -12 }{ 3 } \implies - 4[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{- 4}(x-\stackrel{x_1}{2}) \implies y +7 = - 4 ( x -2) \\\\\\ y+7=-4x+8\implies {\Large \begin{array}{llll} y=-4x+1 \end{array}}[/tex]
Solve the compound inequality.2x-5 33 and 3x-12-19Graph the solution on the number line:
Consider the system of inequalities,
[tex]\begin{gathered} 2x-5\leq3 \\ 3x-1\ge-19 \end{gathered}[/tex]Simplify the first inequality as follows,
[tex]\begin{gathered} 2x-5+5\leq3+5 \\ 2x\cdot\frac{1}{2}\leq8\cdot\frac{1}{2} \\ x\leq4 \end{gathered}[/tex]So, the solution to this inequality will be the set of points including and lying on the left of point 4 on the number line.
Simplify the second inequality as follows,
[tex]\begin{gathered} 3x-1+1\ge-19+1 \\ 3x\cdot\frac{1}{3}\ge-18\cdot\frac{1}{3} \\ x\ge-6 \end{gathered}[/tex]So, the solution to this inequality will be the set of points including and lying on the right of point -6 on the number line.
The solution to the compound inequality will be the common solution of both the inequalities, that is, the set of real numbers ranging from -6 to 4.
The solution can be seen on the number line as follows,
Carolina needs a total of $6.50 in quarters for a coin-operated car wash. He already has $1.50. Which equation can be used to find g, the
additional quarters Carolina needs in order to have enough money for the car wash?
Answer: 20 quarters
Step-by-step explanation:
As we look at this problem we can convert $6.50 dollars into 26 quarters. Us already knowing that Carolina has $1.50 (6 quarters) we can take the two numbers and minus both of them. 26 quarters ($6.50) - 6 quarters ($1.50) = 20 quarters($5.00)
Step-by-step explanation:
every $ is equivalent to 4 quarters.
every half-$ is equivalent to 2 quarters.
after all, 1 quarter = $0.25.
so, the equation is
4×1.5 + g = 4×6.5
or simplified
6 + g = 26
and from there we get then immediately that
g = 20
here is the 3rd one to do
For all three given expression; No, b is not equivalent to a and c.
What is meant by the term equivalent expression?A string of numbers, factors, arithmetic calculations, and possibly exponents constitutes an algebraic expression.Equivalent expressions, as the name implies, are algebraic signifiers that, despite their appearance, turn out to be the same. And because they are the identical, they will produce the same results regardless of the numbers we replace for their variables.For the given question, the three expressions are-
a: 3(x - 1) + 4
Simplify the expression;
= 3x - 3 + 4
Add the constant
= 3x + 1 .....1
b: 3x - 1 ......2
c: 3(x - 2) + 7
Simplify the expression;
3x - 6 + 7
Add the constant
3x + 4 .....3
The result from eq 1, 2 and 3 are-
a = c ≠ b
Thus, No, expression b is not equivalent to a and c.
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can you help me with the fourth one marked as e
we have the equatiion
4x-5y=20
Convert to slope intercept form
y=mx+b
so
Isolate the variable y
step 1
subtract 4x both sides
4x-5y-4x=4x+20
simplify
-5y=-4x+20
step 2
Divide both sides by -5
so
-5y/-5=(-4x+20)/-5
simplify
y=(4/5)x-4what is the slope of a line perpendicular to the line whose equation is x+y=9
Answer:
perpendicular slope = 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
x + y = 9 ( subtract x from both sides )
y = - x + 9 ← in slope- intercept form
with slope m = - 1
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-1}[/tex] = 1
17.09+3.98 estimated
Answer:
21.07
Step-by-step explanation:
7. A line passes through (2, -1) and (8, 4). Writean equation for the line in point-slope form.Rewrite the equation in standard form using integers.y + 1 = %(x+ 2); -5x + 6y = -16•y-1=2(0x-2); -5x+ 6y= 16y-2=%0x+1);-5x+ 6y=17•y+1= %k-2);-5x+ 6y= -16
Recall that the equation of a line that passes through two points is given by the following formula:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1).[/tex]Notice that the above formula gives us the equation of the line in point-slope form. Substituting the given values in the above formula, we get:
[tex]y-(-1)=\frac{-1-4}{2-8}(x-2).[/tex]Simplifying the above result, we get:
[tex]y+1=\frac{5}{6}(x-2).[/tex]Now, taking the above equation to its standard form, we get:
[tex]\begin{gathered} 6y+6=5(x-2), \\ 6y+6=5x-10, \\ 6y-5x=-10-6, \\ -5x+6y=-16. \end{gathered}[/tex]Answer: [tex]y+1=\frac{5}{6}(x-2);-5x+6y=-16.[/tex]PLEASE SOMEONE HELP ASAP WILL GIVE ANYTHING
(Theoretical Probability MC)
Determine P(not yellow) if the spinner is spun once.
75%
37.5%
25%
12.5%
Answer:
Step-by-step explanation:
1. Percent means one out 100%
So:
100/8=12.5
2. Multiply by the number of spaces that are not yellow!
12.5*6=
75%
Answer: 75%
URGENT WILL GIVE BRAINLIEST! NEED THIS ANSWER ASAP + 100 PTS.
A neighborhood is trying to set up school carpools, but they need to determine the number of students who need to travel to the elementary school (ages 5-10), the middle school (ages 11-13), and the high school (ages 14-18). A histogram summarizes their findings: Which of the following data sets is represented in the histogram?
{6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 2, 2}
{11, 11, 12, 5, 10, 7, 10, 8, 6, 11, 11, 12, 18, 14, 13}
{6, 5, 10, 12, 11, 7, 2, 14, 18}
{6, 14, 6, 8, 8, 19, 11, 12, 13, 10, 4}
Answer:
Step-by-step explanation:
The data set that is represented in the histogram is {5, 6, 5, 11, 12, 13, 12, 13, 14, 15, 11, 18, 17, 13} Definition of a histogram An histogram is a graph that organises numerical data. The histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval. the frequency is usually on the vertical axis while the class interval is usually on the horizontal axis.Explaining the graphLooking at the histogram,the age group of 5 - 10 have 3 children in the carpool. the age group of 11 - 13 have 7 children in the carpool. the age group of 14 - 18 have 4 children in the carpool. This means that there are 14 children in the carpool. The correct option should have 14 ages that range between 5 and 18. Here are the options of this question: A. {3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4} B. {5, 10, 4, 11, 12, 13, 12, 13, 12, 11, 14, 14, 19, 18} C. {5, 6, 5, 11, 12, 13, 12, 13, 14, 15, 11, 18, 17, 13} D. {3, 5, 10, 11, 13, 7, 18, 14, 4}To learn more about histograms, please check: brainly.com/question/13053780
Geometry!! Any help appreciated! Thank you
Answer:
this was in the other room and the
Step-by-step explanation:
times to go home and amen and keep me
Jack paid $46 for 4 pizzas. How much did he pay per pizza?
Answer:
$11.50
Step-by-step explanation:
46/4=11.5
In money have to make it the hundredths, so it's $11.50.
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Answer:
$11.50
Step-by-step explanation:
$46 ÷ 4 = 11.5
9 minus the quotient of 2 and x
Answer:
81x because 9x9=81x so 81x is your answer
what would the new points be after the transformation:
g(x)=f(-5x+10)
Answer:
There's nothing that can be done with the given information
Step-by-step explanation:
The volume of a cube is 2744m^3. What is the length of an edge of the cube?
Answer:14
Step-by-step explanation
The answer is PROBABLY a whole number.
(2) 10^3 = 1000; 20^3 = 8000. So the number is between 10 and 20; and closer to 10.
(3) Of the possible answers 11, 12, 13, and 14, only one of them has units digit 4 when raised to the 3rd power.
Answer:
L=14m
Step-by-step explanation:
volume of a cube =L×L×L
V=L³
2744=L³
L=³√2744
L=14m
The width of a rectangle measures (7r - 2s) centimeters, and its length measures
(r-5s) centimeters. Which expression represents the perimeter, in centimeters, of
the rectangle?
The perimeter of the given rectangle is 16r-14s centimeters.
Let width be represented by=w
Let length be represented by=l
Let perimeter be represented by=p
Then,
l=(r-5s)centimeters (Given in the question)
while w=(7r-2s)centimeters (Given in the question)
The formula for the perimeter of a rectangle= 2(l+b)
where l is the length while b is the breadth of the rectangle.
On putting values in the equation:
p=2(l+b)
p=2(l+w)
p=2[(7r-2s)+(r-5s)]
on opening the bracket 2 is multiplied by both terms.
p=2(7r-2s)+2(r-5s)
p=(2x7r-2x2s)+(2xr-2x5s)
p=(14r-4s)+(2r-10s)
p=14r-4s+2r-10s
p=14r+2r-4s-10s
p=14r+2r-(4s+10s)
p=14r+2r-(14s)
p=16r-(14s)
Thus,
p=16r-14s centimeters
The perimeter of the given rectangle is 16r-14s centimeters.
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Two planes at started to take off at the same time. Plane One took off from the tarmac going 375 mph at an angle of elevation of 40° and Plane Two took off from the tarmac going 400 mph at an angle of elevation of 35°. Which plane is rising faster? What would you change to make sure both planes rise at the same rate?
a. Since the vertical component of velocity v' = 241.05 mph > v" = 229.43 mph, the first plane is rising faster
b. I would change the angle of elevation of both planes
a. How to find which plane is rising faster?Two planes at started to take off at the same time. Plane One took off from the tarmac going 375 mph at an angle of elevation of 40° and Plane Two took off from the tarmac going 400 mph at an angle of elevation of 35°, to fidn which plane is rising faster, we compute their vertical component of velocity of the plane .
What is the vertical component of velocity?The vertical component of velocity is v' = vsinФ where
v = speed and Ф = angle of elevationFor the first plane
v = 375 mph and Ф = 40°So, v' = vsinФ
= (375 mph)sin40°
= (375 mph) × 0.6428
= 241.05 mph
For the second plane
v = 400 mph and Ф = 35°So, v" = vsinФ
= (400 mph)sin35°
= (400 mph) × 0.5736
= 229.43 mph
Since v' = 241.05 mph > v" = 229.43 mph
So, the first plane is rising faster
b. What would you change to make sure both planes rise at the same rate?To make both planes rise at the same rate, I would change the angle of elevation of both planes
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in larg cities, people often take taxi to get from one place to another. what is the cost per mile of taxi ride how much is 47-mile taxi ride
People in large cities use taxis to get from one location to another; the cost is $25.20 every 36 miles, and a 47-mile taxi ride will cost $32.9.
What is the multiplication and division rule?Multiplication Rule If events A and B occur in the same sample space, the probability of both A and B occurring is equal to the probability that A occurs multiplied by the probability that B occurs, given that A has occurred.
Returning to the previous example, the first response is correct because it follows the BODMAS principles, which state that division can be done before multiplication and must be done before addition. Multiplication happens before addition.
Given,
Cost every 36 miles = 25.20
Cost of one mile = Cost for 36 miles / 36
Cost of one mile = 25.20/36
Cost of one mile = 0.7
Cost of 47 miles = Cost of one mile × 47
Cost of 47 miles = 0.7 × 47
Cost of 47 miles = 32.9
47 miles taxi ride will cost 32.9
The complete question is:
In large cities people out and take taxis to get from one place to another the cost is $25.20 every 36 miles how much is a 47 mile taxi ride
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Which of the following coordinate points have undergone an enlargement and reduction? Select all that apply.Group of answer choices(5, -1) --> (10, 2) --> (20, 4)(1, 1) --> (6, 6) --> (1, 1)(4, 9) --> (20, 34) --> (20/45, 1)(3, 0) --> (9, 0) --> (18, 0)(0, -5) --> (0, 5) --> (0, 30)
By definition, you know that dilations have a scale factor, this is labeled k. To dilate something in the coordinate plane, multiply each coordinate by the scale factor.
If there is a reduction, then 0 < k < 1.
If there is an enlargement, then k > 1.
[tex](x,y)\rightarrow(kx,ky)[/tex]So, you have
[tex]\begin{gathered} (5,-1)\rightarrow(5\cdot2,-1\cdot-2)=(10,2) \\ \text{ k is not the same for both coordinates of the point} \end{gathered}[/tex][tex]\begin{gathered} (1,1)\rightarrow(6\cdot1,6\cdot1)=(6,6) \\ \text{In this case, k = 6 and k > 1 then the coordinate points have an enlargement} \\ (6,6)\rightarrow(\frac{1}{6}\cdot6,\frac{1}{6}\cdot6)=(1,1) \\ \text{In this case, k = 1 and 0< k < 1 then the coordinate points have an reduction} \end{gathered}[/tex][tex]\begin{gathered} (4,9)\rightarrow(4\cdot5,9\cdot\frac{34}{9})=(20,34) \\ \text{ k is not the same for both coordinates of the point} \end{gathered}[/tex][tex]\begin{gathered} (3,0)\rightarrow(3\cdot3,3\cdot0)=(9,0) \\ \text{In this case, k = 3 and k > 1 then the coordinate points have an enlargement} \\ (9,0)\rightarrow(2\cdot9,2\cdot0)=(18,0) \\ \text{In this case, k = 2 and k > 1 then the coordinate points have an enlargement} \end{gathered}[/tex][tex]\begin{gathered} (0,-5)\rightarrow(-1\cdot0,-1\cdot-5)=(0,5) \\ \text{ In this case, k = -1, and by definition k > 0} \end{gathered}[/tex]Therefore, the correct answer is
[tex]B\text{.}(1,1)\rightarrow(6,6)\rightarrow(1,1)[/tex]