Considering the volume of the given rectangular prism, the height is of 5.03 feet.
What is the volume of a rectangular prism?The volume of a rectangular prism of length l, width w and height h is given by:
V = lwh.
In this problem, we have that:
h = w - 1 -> w = h + 1.l = 2w = 2(h + 1) = 2h + 2.The volume is of 365 cubic feet, hence:
lwh = 365
(2h + 2)(h + 1)h = 365
(2h² + 4h + 2)h - 365 = 0
2h³ + 4h² + 2h - 365 = 0.
Using a cubic equation calculator, the height is of h = 5.03 feet.
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A student wants to sell 18 cookies for a fundraiser. She knows that she only has 3 days left to sell her cookies. Write an equation to find out how many cookies she must sell each day to reach her goal.
Answer:
6 cookies per day.
Step-by-step explanation:
if she is going to sell 18 cookies within 3 days, would divide that problem, (18 divided by 3) which will get you selling 6 cookies per day during that 3-day challenge.
5. A boy gets 29 marks out of 50 in his maths ex-
am. What percentage did he score?
Answer:
58%
Step-by-step explanation:
29 / 50 * 100% = 58 % ( rather pathetic score, huh?)
Answer:
58%
Step-by-step explanation:
the boy gets 29 marks out of 50
Then
He gets 29 × 2 marks out of 50 × 2
Then
He gets 58 marks out of 100
Therefore
He scored 58%
A 2-column table with 7 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries 15, 0, 3, 0, negative 3, 0, 15.
Predict which statements are true about the intervals of the continuous function. Check all that apply.
f(x) > 0 over the interval (−, 3).
f(x) ≤ 0 over the interval [0, 2].
f(x) < 0 over the interval (−1, 1).
f(x) > 0 over the interval (–2, 0).
f(x) ≥ 0 over the interval [2, ).
The statements that are true about the intervals of the continuous function are Options 2, 4 and 5
f(x) ≤ 0 over the interval [0, 2].f(x) > 0 over the interval (–2, 0).f(x) ≥ 0 over the interval [2, ).What is the statement about?Looking at the values given, the intervals which satisfies the condition are known to be:
f(x)<=0 over the interval [0,2]
f(x)>0 over the interval (-2,0)
f(x)>=0 over the interval [2,∞)
Because:
Since the table with x and f(x) values, we have to examine analyze the table and see the each option that is in line with f(x) or not .
Examine the values of x that is from -3 to 3, the f(x) values are both positive and negative . hence f(x)>0 is false over the interval (-∞,3)
Looking at the the interval from 0 to 2, the f(x) values are 0 and negative. Hence, f(x)<=0 over the interval [0,2]
When you look over the interval (-1,1), the f(x) values are said to be both positive and negative and as such, f(x)<0 is false over the interval (-1,1)
When you look at the interval (-2,0) , the f(x) is positive and as such, f(x)>0 over the interval (-2,0)
Looking at the interval [2,∞), f(x) is positive and as such, f(x)>=0 over the interval [2,∞)
Therefore, Option 2, 4 and 5 are correct.
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6. (04.05 MC)
Which Inequality matches the graph? (1 point)
-2x+3y>7
2x+3y <7
-3x+2y>7
3x-2y <7
3x - 2y < 7
=============================================================
Explanation:
The dashed boundary line goes through (1, -2) and (3, 1)
Find the slope of this line using the slope formula.
[tex](x_1,y_1) = (1,-2) \text{ and } (x_2,y_2) = (3,1)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{1 - (-2)}{3 - 1}\\\\m = \frac{1 + 2}{3 - 1}\\\\m = \frac{3}{2}\\\\[/tex]
The slope is 3/2 indicating we go up 3 and to the right 2.
--------------
Now use the point-slope template so we can determine the equation of the boundary line.
[tex]y - y_1 = m(x - x_1)\\\\y - (-2) = \frac{3}{2}(x - 1)\\\\y + 2 = \frac{3}{2}(x - 1)\\\\2(y+2) = 3(x-1) \ \ \text{ see note1 below}\\\\2y + 4 = 3x - 3\\\\2y - 3x = -3 - 4\\\\-3x+2y = -7\\\\3x-2y = 7 \ \ \text{ see note2 below}\\\\[/tex]
Note1: For this step, I multiplied both sides by 2 to clear out the fraction.
Note2: Multiply both sides by -1 so that the x coefficient is positive
--------------
The key thing to pull away from the previous section is that the boundary line equation is 3x - 2y = 7
The question from here is: "What do we replace the equal sign with?"
We need to pick either < or > since we have a dashed boundary. We won't have an "or equal to" portion.
Let's assume the inequality sign is <
3x - 2y = 7 turns into 3x - 2y < 7
To see if this works, we'll plug in the origin (0,0) to get...
3x - 2y < 7
3(0) - 2(0) < 7
0 < 7
The last inequality above is true, so 3x - 2y < 7 is also true when x = 0 and y = 0. It tells us that the origin is in the shaded region. This matches with what the graph shows.
Therefore, we have confirmed that 3x - 2y < 7 is indeed the case.
You could pick other test points. However the origin is the easiest to work with in my opinion. If the boundary went through the origin, then you'd have to pick another point like (0,1).
If you want to use technology to verify the answer, then Desmos and GeoGebra are two good options to go for. See the screenshots below.
What are the coordinates of a point P(x, y)
reflected across the y-axis? Across the x-axis?
Use reflection notation to write your answer.
[tex]R_{x-axis}[/tex] means [tex]P(x,y) \longrightarrow P'(x,-y)[/tex].
[tex]R_{y-axis}[/tex] means [tex]P(x,y) \longrightarrow P'(x,-y)[/tex]
Match the systems of equations with their solution sets.
The Solution set 1 , 2 , 3, 4 matches with equations 4 , 1 , 2 , 3
What are System of Equations ?The system of equations are the set of equations that have common solution.
The set of equations given are
y+5 = x² - 3x
2x +y = 1
On subtracting equation 1 from 2
5 - 2x = x² -3x -1
x² -x -6 = 0
(x-3)(x +2) = 0
x = 3 , -2
At x = 3 , -2; y = -5 , 5
The set of equation are
y -17 = x²-9x
-x +y =1
-17 +x = x² -9x -1
x²-10x +16 = 0
x² - 8x -2x +16 = 0
(x -8) (x-2) = 0
at x = 2 ,8 ; y = 3 ,9
The set of equation is
y +12 = x²+x
x +y =3
12 - x = x²+x -3
x²+2x -15=0
x² +5x -3x -15 = 0
x(x+5) -3(x+5) = 0
(x-3)(x+5) = 0
x = 3 ,-5
At x = 3 , -5 , y = 0,8
The set of equation is
y-15 = -x² +4x
x +y = 1
-15 -x = -x²+4x -1
x²-5x -14 = 0
x² -7x +2x -14 = 0
x(x-7) +2(x-7) = 0
(x +2) (x-7) = 0
x = -2 , 7
at x = -2 , 7 ; y = 3 ,-6
Therefore the Solution set 1 , 2 , 3, 4 matches with equations 4 , 1 , 2 , 3
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Which equation accurately represents this statement? Select three options. Negative 3 less than 4.9 times a number, x, is the same as 12.8. Negative 3 minus 4.9 x = 12.8 4.9 x minus (negative 3) = 12.8 3 + 4.9 x = 12.8 (4.9 minus 3) x = 12.8 12.8 = 4.9 x + 3
Equations b,c, and e accurately represent this statement.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
The three equation accurately represents this statement is;
4.9 x-(-3) = 12.8
3+ 4.9 x = 12.8
12.8 = 4.9 x +3
Hence, equations b,c, and e accurately represent this statement.
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In Angle FGH, the measures of angles F, G, and
H, respectively, are in the ratio 4:4:10. Find
the measure of each angle.
Answer:
40 40 100°
Step-by-step explanation:
Is that TRIANGLE FGH?
the angles add to 180
180 / ( 4 + 4 + 10 ) = 10
then each angle is 4 x10 4 x 10 and 10 x10
a ramp is 17 feet long, rises 8 feet above, and a covers a horizontal distance of 15 feet as showed in the figure. the ratio of to is equal to tan B
Using relations in a right triangle, it is found that:
The ratio of 8 to 15 is equals to tan B.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.Researching the problem on the internet, we have that:
The side opposite to angle B has a length of 8 feet.The side adjacent to angle B has a length of 15 feet.Hence the tangent of B is:
tan(B) = 8/15.
Which means that:
The ratio of 8 to 15 is equals to tan B.
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Which is the slope-intercept equation of the line (-2,2) and (0,-4)?
Answer:
y=3x-4
Step-by-step explanation:
How many $4$-digit positive integers exist that satisfy the following conditions: (A) Each of the first two digits must be $1$, $4$, or $5$, and (B) the last two digits cannot be the same digit, and (C) each of the last two digits must be $5$, $7$, or $8$
Answer:
54 possibles
Step-by-step explanation:
Digit ONE 3 choices
Digit two 3 choices
digit three 3 choices
digit four 2 choices
3 x 3 x 3 x 2 = 54 choices meet all of the conditions
write an exponential function that includes the following given pair of points.
(-3,16) and (-2,8)
can anyone help me find its Area and perimeter? im so confused please also explain it!!
Topic= Measurement Area, volume & capacity
Answer:
See below
Step-by-step explanation:
Diameter of the semi circles = 15 - 3-3 = 9mm
radius = 4.5 mm
area of rectangle tha goes through the semicircles = 5 x 15 = 75 mm^2
area of two semicircles =
area of circle with radius 4.5 = pi r^2 = 63.62 mm^2
total area = 75 + 63.62 = `38.62 mm^2
Perimeter Two small side rectangles = 2 * (3+5+3) =26 mm
perimeter of cicle with diameter 9 = pi * d = 9pi = 28.27 mm
total perimeter = 54.27 mm
(check my math !)
Sulin has some $2 and $5 notes. The value of the notes add up to $58. There are 15 more $2 notes than $5 notes. How many $2 notes does Sulin have?
Answer:
t is number of 2 dollars
f is number of 5 dollars
2t+5f=58
f+15=t
2(f+15)+5f=58
simplify
2f+30+5f=58
simplify
7f+30=58
subtract
7f=28
f=4
substitute
4+15=t
4 five dollars
19 2 dollars
Hope This Helps!!!
A particular industrial product is shipped in lots of 20. Testing to determine whether an item is defective is costly, and hence the manufacturer samples his production rather than using a 100 percent inspection plan. A sampling plan constructed to minimize the number of defectives shipped to customers calls for sampling five items from each lot and rejecting the lot if more than one defective is observed. (If rejected, each item in the lot is tested.) If a lot contains four defectives, what is the probability that it will be rejected
The probability that the sample will be rejected if five items from 1 lot is selected is 26/15504.
Given Industrial product is product in lots of 20. If sample contains more than one defective then the lot will be rejected.
Probability is the chance of happening an event among all the events possible. The probability lies between 0 and 1. The formula of calculating probability is as under:
Probability= number of items/ total items.
Sample from 1 lot =5
Samples in 1 lot=20
Lot will be rejected when 1 sample, 2 sample , 3 sample, 4 sample or all the samples are defective.
Probability that the lot will be rejected=[tex](5C_{2} +5C_{3} +5C_{4} +5C_{5})/20C_{5}[/tex]
=(10+10+5+1)/15504
=26/15504
Hence the probability that lot will be rejected if the lot is rejected if more than one defective is observed is 26/15504.
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3x − 12y = −21,
−x + 4y = 7
find x and y intercept
A store carries chocolate, vanilla, peppermint, and lemon candies. One day, the store clerk notices that he has fifteen candies total. Furthermore, the number of peppermint and lemon candies together is twice the number of chocolate and vanilla candies together, and there are eight more peppermint candies than lemon candies. How many lemon candies are there
The total number of lemon candies is 1, solved using the linear equation in one variable 3l + 12 = 15, where l is the number of lemon candies.
We assume the number of chocolate candies to be c.
We assume the number of vanilla candies to be v.
We assume the number of peppermint candies to be p.
We assume the number of lemon candies to be l.
The total number of candies is given as 15.
This can be represented by the linear equation: c + v + p + l = 15 ... (i).
The number of peppermint candies and lemon candies together is given to be twice the number of chocolate and vanilla candies together.
This can be represented by the linear equation: p + l = 2(c + v) ... (ii).
There are eight more peppermint candies than lemon candies.
This can be represented by the linear equation: p = l + 8.
Substituting p = l + 8 in (ii), we get,
l + 8 + l = 2(c + v),
or, 2(l + 4) = 2(c + v),
or, c + v = l + 4.
Substituting c + v = l + 4, and p = l + 8, in (i), we get:
l + 4 + l + 8 + l = 15,
or, 3l + 12 = 15,
or, 3l = 15 - 12 = 3,
or, l = 3/3 = 1.
Therefore, the total number of lemon candies is 1, solved using the linear equation in one variable 3l + 12 = 15, where l is the number of lemon candies.
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3. Segment RU is an angle bisector. m/QRU = 70°.
What is mzQRS?
Q
70°
□A 70°
B 140°
C 35°
OD 20°
A
U
S
PLS HELP ME OUT
Answer:
b - 140
Step-by-step explanation:
an angle bisector divides an angle in half
so
half of the angle is 70
the other half is 70
so
70 + 70 = 140
b is your answer
Answer: B. 140°
Step-by-step explanation:
Hi!
An angle bisector just cuts the angle in half.
Therefore, if one half is 70°, the other half is also 70°!
To find the measure of the angle just add them!
70° + 70° = ?
= 140°
So, your answer is B. 140°
Hope this helps and have a great day!
triangle abc is equal to
triangle pqr, angle p=8X+4,
angle a=5x+16 , and angle
q=10x+2. find angle r
a. 36
b.not enough info
c. 42
d 102
Answer:
d. 102°
Step-by-step explanation:
We can use the relations ...
corresponding angles in congruent triangles are congruentthe sum of angles in a triangle is 180°to write equations that let us find x and all of the angles in ∆PQR.
Corresponding anglesThe congruence relation ∆ABC ≅ ∆PQR tells us that ∠P = ∠A. Using the given expressions for these angles, we have ...
∠P = ∠A
8x +4 = 5x +16
3x = 12 . . . . . . . . . subtract (5x+4)
x = 4 . . . . . . . . . divide by 3
Then the measure of angle P is ...
∠P = 8x +4 = 8(4) +4 = 36 . . . . . degrees
Other anglesAngle Q in ∆PQR is given as ...
∠Q = 10x +2 = 10(4) +2 = 42 . . . . . degrees
Then the measure of angle R needed to make the total of angles in ∆PQR be 180° is ...
∠R = 180° -36° -42° = 102°
Angle R is 102°.
__
In summary:
x = 4∠P = ∠A = 36°∠Q = ∠B = 42°∠R = ∠C = 102°If there are 36 eggs in 3 egg cartons, how many eggs are in 6 egg cartons? eggs
Step-by-step explanation:
36 eggs in 3 cartons.
now we double the cartons, so, we need to double the eggs too, because there is a direct relationship between cartons and the number of eggs.
so. in 2×3 cartons are then 2×36 = 72 eggs.
I have a bag with blue marbles and yellow marbles in it. At the moment, the ratio of blue marbles to yellow marbles is 8:5. If I remove 12 blue marbles and add 21 yellow marbles, the ratio will be 1:3. How many blue marbles were in the bag before I removed some
There were 15 blue marbles in the bag before removing some
Let B=blue marbles and Y= yellow marbles
The ratio of B to Y is
[tex]\frac{B}{Y} =\frac{8}{5}[/tex]
If we remove 12 blue marbles and add 12 yellow marbles,
the ratio will be
[tex]\frac{B-12}{Y+21} =\frac{1}{3}[/tex]
[tex]3(B-12)=1(Y+21)[/tex]
[tex]3B-36=Y+21\\[/tex]
[tex]3(\frac{8}{5}Y)-36=Y+21[/tex]
[tex]\frac{24}{5}Y-Y=21+36[/tex]
[tex]\frac{19}{5}Y=57[/tex]
[tex]Y=\frac{57*5}{19}\\[/tex]
[tex]Y=15[/tex]
[tex]B=\frac{8}{5} (15)\\B=24[/tex]
Hence, there were 15 blue marbles in the bag before removing some
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Write an equation of the perpendicular bisector of the segment with the endpoints (3,5) and (9,−1). HELP!!!!!
The equation of the perpendicular bisector of the segment with the endpoints (3,5) and (9,−1) is y = x + 8
Equation of a lineThe equation of a line in slope intercept form is expressed as;
y = mx + b
The equation of the perpendicular bisector will be given as y = -1/m x+ b
where
m is the slope
b is the y-intercept
Determine the slope
Slope = -1-5/9-3
Slope = -6/6
Slope = -1
For the y-intercept
-1 = -1(9) + b
-1 = -9 + b
b = 8
Determine the equation
y = -1/m x + b
y = -1/(-1) x + 8
y = x + 8
Hence the equation of the perpendicular bisector of the segment with the endpoints (3,5) and (9,−1) is y = x + 8
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Calculate the ninth term of the sequence:
3, 8, 13, 18, 23, 28, 33, 38, ...
Answer:
43
Step-by-step explanation:
sequence: +5
∴ninth term of sequence = 38+5
= 43
35.149 = 30+5+0.1+ ____ +0.009
how to find the missing sum
Answer:
0.04
Step-by-step explanation:
30+5+0.1+0.009 is 35.109
35.149 - 35.109= 0.04
35.149 = 30+5+0.1+ ____ +0.009
= 30 + 5 + 0.1 + x + 0.009
= 35.109 + x
x is the unknown value, so what number add to the 35.109 gives 35.149? That's what we're after.
35.149 = 35.109 + x
- 35.109 both side
0.04 = 0 + x
Thus, x = 0.04
(35.109 - 35.109 cancles each other & we get x on its own because 0.04 - 0 gives you 0.04)
Hope this helps!
for what values of b will f(x)=log b x be a decreasing function?
Answer:
Step-by-step explanation:
if another line is perpendicular to the line shown on the graph, what must be its slope
It's B
Slope is negative, the other must be positive due to m1 x m2 = - 1
m1 = -2/5
The diagram shows a gradient of -2/5. So, the
reciprocal of this valve to make - 1 is 5/2 (which is the - 2/5 flipped upside down, but positive)
-2/5 x 5/2 = - 10/10 (or - 1)
Thus, the perpendicular line to this has a gradient of 5/2.
Hope this helps!
Consider the line shown on the graph below. Enter the equation of the line in the form y = mx + b where m is the slope and b is the y-intercept. Enter the equation of the line in the form y=mx + b where m is the slope.
Hello!
We know the y-intercept (b) is 160. So let's find the slope!
Slope = rise / run
Slope = 120 - 160 / 1 - 0
Slope = -40/1 = -40
Forming the equation :
y = mx + b
y = -40x + 160
∴ The equation of the line in slope-intercept form is y = -40x + 160.
Find the value of x:
X
4
10
Applying the definition of similar triangles, the value of x is determined as: 12.5.
What are Similar Triangles?In a triangle like the one shown above, the line that intersects the two sides of the triangle divides the two sides of the triangle to form similar triangles. Thus, their corresponding sides are proportional to each other.
Therefore, we would have:
(x + 5) / 5 = (10 + 4) / 4
(x + 5) / 5 = 14/4
4(x + 5) = 5(14)
4x + 20 = 70
4x = 70 - 20
4x = 50
x = 50/4
x = 12.5
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Part B Which value is closest to the product 0.04 × 8.01?
A. 32
B. 3.2
C. 0.032
D. 0.32
Answer:
D
Step-by-step explanation:
this is because when multipled you get 0.3204 so u round and it becomes 0.320
Answer:
D
Step-by-step explanation:
0.04 x 8.01 = [tex]\dfrac{4}{100} . \dfrac{801}{100}[/tex]
[tex]=\dfrac{3204}{10000}\\\\\\0.3204[/tex]
PLEASE HELP I AM REALLY CONFUSED
Answer:
Step-by-step explanation:
y = 3 (x-1)(x+ 7 ) this graph will intercept the x axis when y = 0
0 = 3 ( x-1)(x+7) so you can see this = 0 when x =1 or when x = -7
these are the x-axis intercepts
the vertex will be right in the middle between the intercepts found above ....... at x = -3
plug this value in to find the y coordinate 3 ( -3-1)(-3+7) = -48
vertex is -3, -48
the axis of symmetry is the value of the x coordinate of the vertex
x = - 3
direction of opening will be upward.....
see attached graph