ANSWER
A. y = 7383.3x
B. y = 17646.7x
C. Lesser altitude; 1257 feet
EXPLANATION
A. We want to write a proportional relationship between the time it took him to ascend and the total height he reached:
y = kx
where x = time taken
y = distance (height reached)
k = constant of proportionality
We have to find k for the relationship.
So, we have that:
[tex]\begin{gathered} 51683\text{ = k }\cdot\text{ }7 \\ \Rightarrow\text{ k = }\frac{51683}{7} \\ k\text{ = }7383.3\text{ ft/hr} \end{gathered}[/tex]This constant of proportionality (between distance and time) is called speed.
Therefore, the relationship for his ascent is:
y = 7383.3x
B. For his descent, we also have to find k in:
y = kx
We have that:
[tex]\begin{gathered} 52940\text{ = k }\cdot\text{ 3} \\ k\text{ = }\frac{52940}{3} \\ k=\text{ }17646.7\text{ ft/hr} \end{gathered}[/tex]Therefore, the relationship for his descent is:
y = 17646.7x
C. To find out if he reached a greater or lesser altitude than his starting point, we have to subtract his altitude during ascent from his altitude during descent.
If the value is positive then he ended up at a lesser altitude but if it is negative, he ended up on a greater altitude.
That is:
52940 - 51683
= 1257 feet
Since it is positive, that means that he descended more feet than he ascended and so, he ended up at a lesser altitude than his starting point, 1257 higher.
factorize the following if possible 5z^2+35z-90
Answer:
5z² + 35z - 90 = 0
5(z² + 7z - 18) = 0
z² + 7z - 18 = 0
(z - 2)(z + 9) = 0
r=−9, s=2
STEPS USING THE DIRECT FACTORING METHOD
5z²+35z−90
This quadratic equation can be resolved using a revolutionary direct factoring technique that does not rely on guesswork. The equation must have the form x2+Bx+C=0 to be solved using the direct factoring approach. To do this, multiply both sides of the equation by 5.
x²+7x−18=0
Let r and s be the factors for the quadratic equation such that x²+Bx+C=(x−r)(x−s) where the sum of factors (r+s)=−B and the product of factors rs=C
r+s=−7
rs=−18
When the average of the two integers is 1/2*-7=-7 /2, the sum of the two numbers r and s are exactly 7. You can also observe that the parabola symbolized by the quadratic equation y=x2+Bx+C has its axis of symmetry in the middle of r and s. An unknown quantity u separates the values of r and s from the center at an equal distance. Describe r and s about the variable u.
r=−7/2−u
s=−7/2+u
Put these in the product equation rs=-18 to solve for the unknown quantity u.
(−27−u)(−27+u)=−18
Simplify by expanding (a−b)(a+b)=a2–b2
49/4−u²=−18
Simplify the expression by subtracting 49/4 on both sides
−u2=−18−49/4=−121/4
To find the value of the unknowable variable u, simplify the expression by multiplying by 1 on both sides and taking the square root.
u2=121/4
u=±√121/4=±11/2
The factors r and s are the solutions to the quadratic equation. Substitute the value of u to compute the r and s.
r=−7/2−11/2=−9
s=−7/2+11/2=2
Therefore, r=−9, s=2
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2. (04.01) Which point could be removed in order to make the relation a function? (4 points) {(-9, -8), (-8, 4), (0, -2), (4,8), (0, 8), (1, 2)} (4,8) (0,8) (-9, -8) (1, 2)
Answer:
(0,8)
Step-by-step explanation:
What is needed in order to be a function?
A value of x cannot have more than one value of y. In this question, we have that for x = 0, there are 2 values of y: -2 and 8. So one of those can be removed.
Among the options, we have: (0,8), which is the correct answer
Koharu pie dough recipe uses 6 oz of flour, 4 oz of butter, and 2 oz of water. Complete the sentences to describe the ratios in her recipe. The ratio of ____ to ____ is 3:2
Answer:
The ratio of flour to butter is 3:2
Step-by-step explanation:
:]
Put the correct number in each box 1/7 = 4/? = ?/56
Answer: 1/7 = 4/28 = 8/56
Step-by-step explanation: 7 timestables
Answer:
1/7=4/28=8/56
Step-by-step explanation:
From the pattern of the question we can see that the numerator of the second fraction is 4 and the previous fraction's numerator is 1 that means the fraction has been multiplied by 4. Therefore multiplying the numerator and denominator results in the answer 4/28. For the last fraction we can see that the denominator is 56 and is the double of 28 therefore doubling the whole second fraction we get our answer as 8/56. Overall equating all the three fractions we get the same answer 1/7 after minimizing the fraction.
Username: TNakashrai
What is the range shown in the graph below ?
Take into account that the range are all availables values of the function, that is, available values of the y coordinate in the graph.
As you can notice, such values are in the following interval:
range: (-∞,8]
Evaluate the polynomial function for the given values of the variable
ANSWERS
• P(2) = 11
,• P(-1) = 14
,• P(0) = 7
EXPLANATION
Every time we have to evaluate a function, what we have to do is replace the variable with the value and solve the operations.
Let's solve P(2),
[tex]P(2)=3(2)^2-4(2)+7[/tex]Solve the powers first,
[tex]P(2)=3\cdot4-4\cdot2+7[/tex]Then the products,
[tex]P(2)=12-8+7[/tex]And then the additions/subtractions,
[tex]P(2)=11[/tex]The process is the same for the other two values,
[tex]P(-1)=3(-1)^2-4(-1)+7=3\cdot1-4(-1)+7=3+4+7=14[/tex]And,
[tex]P(0)=3(0)^2-4(0)+7=3\cdot0-4\cdot0+7=0+0+7=7[/tex]Hence, P(2) = 11, P(-1) = 14 and P(0) = 7.
Box A weighs 212.04 kilograms. Box B weighs 212 1/4 kilograms Which statement is true?A) the box weigh the same amountB) Box B weighs 0.10 of a kilogram more than Box AC) Box A weighs 0.15 of a kilogram more than box BD) Vox b weighs 0.21 of a kilogram more than Box A
To be able to compare the weight of the boxes, we need to have their weight in decimal form:
Box A --> 212.04 kilograms
Box B --> 212 1/4 kilograms
Convert 212 1/4 to decimal:
[tex]\begin{gathered} \text{SINCE }\frac{1}{4}=0.25 \\ 212\frac{1}{4}=212.25 \end{gathered}[/tex]Box B --> 212.25
We can see that the weight of box B is more than the weight of box A, so we discard options A and C.
To find how much more is the weight of box B, we subtract the quantities:
[tex]212.25-212.04=0.21[/tex]Answer: Box B weighs 0.21 of a kilogram more than box A
2 The model shown below is a composite of tworectangular prisms.What is the volume of the model in cubic units?F 640 H 960G 512 J 1,280
Answer
Volume of the prism = 960 cubic units
Explanaion:
Step 1: Divide the two prism
Volume of a rectangular prism is
l x w x h
Where l = length, w= width, and h = height
The volume = full prism - cut prism
Full prism = 16 * 10 * 8
Full prism = 1280 cubic units
Cut prism = 8 * 10 * 4
Cut prism = 320 cubic units
Volume = 1280 - 320
Volume = 960 cubic units
Use the diagram to answer the question. 15 ft 120 ft2 10 ft A rectangular yard contains a 120-square-foot garden. If seeds are scattered uniformly over the yard, what is the probability that a seed lands in the garden?
area of the rectangle
[tex]\begin{gathered} \text{area}=\text{length}\times width \\ \text{area}=15\times10=150 \end{gathered}[/tex]area of rectangle is 150 sq ft, therefore the probability that a seed lands in the garden is
[tex]\frac{area\text{ garden}}{area\text{ rectangle}}=\frac{120}{150}=\frac{4}{5}[/tex]answer: 4/5
Ellie wants to save her weekly allowance to go to Disneyland, In 3
weeks she has $40. In 7 weeks, she has $60. Let x represent the
number of weeks and let y represent the total amount saved. Write
an equation in slope intercept form that represents this situation
The equation in slope-intercept form that represents the situation is y = 5x + 25.
In 3 weeks Ellie she saved $40 and $60 in 7 weeks.
Let x and y represent the number of weeks and the total amount saved respectively.
The equation of a line in slope intercept form is given as:
y = mx + b where m is the slope and b is the y-intercept.
Now when x = 3, y = $40.
Therefore,
y = mx + b
40 = 3m + b --------------(1)
When x = 7, y = $60
y = mx + b
60 = 7m + b -------------(2)
Subtracting (1) from (2),
7m + b - 3m - b = 60 - 40
4m = 20
m = 5
So,
3m + b = 40
3(5) + b = 40
15 + b = 40
b = 25
Hence, the equation of the line in slope intercept form is y = 5x + 25.
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A right isosceles triangle has an area of 40.5 cm2. How tall is it?
Area = 40 cm^2
base = ?
height = x
Area = base * height / 2
bh = 2(40.5)
bh = 81 cm^2
81 3
27 3
9 3
3 3 height = 3 x3 x 3 base = 3
1
The height must be 27 cm and the base 3 cm.
a Is it possible to construct a triangle with lengths of 7, 54, and 45? EXPLAIN why or why not?
For a, b, and c to be the lengths of a triangle they must satisfy the following system of inequalities:
[tex]\begin{gathered} a+b>c, \\ a+c>b, \\ b+c>a\text{.} \end{gathered}[/tex]Now, notice that:
[tex]\begin{gathered} 7+54>45, \\ 45+54>7,\text{ } \\ 45+7=52<54. \end{gathered}[/tex]Since the given numbers do not satisfy the last inequality, then they cannot be the lengths of a triangle.
Answer: No it is not possible to construct a triangle with lengths 7, 54 and 45, because:
[tex]45+7<54.[/tex]Lewis uses cubes to represent each term of a pattern based on a recursive function. the recursive function defined is f(n+1)=f(n)+4, where n is an integer and n≥2. the number of cubes used in each of the first two figures is shown below. how many cubes does Lewis need in the third, fourth, and fifth figures of the pattern? fill in the blanks.figure 1: 9 cubesfigure 2: 13 cubesfigure 3: (blank)figure 4: (blank)figure 5: (blank)
Lewis uses cubes to represent each term of a pattern based on a recursive function. the recursive function defined is f(n+1)=f(n)+4, where n is an integer and n≥2. the number of cubes used in each of the first two figures is shown below. how many cubes does Lewis need in the third, fourth, and fifth figures of the pattern? fill in the blanks.
figure 1: 9 cubes
figure 2: 13 cubes
figure 3: (blank)
figure 4: (blank)
figure 5: (blank)
Let
f(0)=5
so
For n=0
f(1)=5+4=9
f(1)=9
For n=1
f(2)=9+4=13
f(2)=13
For n=2
f(3)=13+4=17
For n=3
f(4)=17+4=21
For n=4
f(5)=21+4=25
For n=5
f(6)=25+4=29
therefore
theanswer is
figure 3: 17figure 4: 21figure 5: 25please help me solve. I have 81 for blank 1 and 9 for blank 2. it is incorrect
We can further simplify
[tex]\sqrt[]{27}[/tex][tex]\begin{gathered} \sqrt[]{27}\text{ = }\sqrt[]{3\text{ x 9}} \\ \sqrt[]{27}\text{ = }\sqrt[]{3}\text{ x }\sqrt[]{9} \end{gathered}[/tex][tex]\begin{gathered} \sqrt[]{27}\text{ = }\sqrt[]{3}\text{ x 3 = 3 x }\sqrt[]{3} \\ \sqrt[]{27}\text{ = 3 }\sqrt[]{3} \end{gathered}[/tex][tex]\sqrt[]{3}\text{ x }\sqrt[]{27\text{ }}\text{ = }\sqrt[]{3}\text{ x 3}\sqrt[]{3}[/tex]The answers for the blank spaces are
[tex]\sqrt[]{3}\text{ and 3}\sqrt[]{3}[/tex]A grocery store sells a bag of 3 oranges for $2.16. What is the cost of oranges, in dollars per orange?
Answer:
0.72
Step-by-step explanation:
The answer is that because all you have to do is just 2.16 divided by 3. Equalling to 0.72. Now we just have to do 0.72 + 0.72 + 0.72 and that would equal $2.16.
plss mark me as a brainlist plss
What is the value of this expression: (−2)3 x 30 x (−4)−2
0
-3/2
-3/4
-1/2
3/2
3/4
1/2
The given expression (−2)3 x 30 x (−4)(−20) will have the value as -14400
In the above question, the following mathematical expression is given :
(−2)3 x 30 x (−4)(−20)
We need to find the value of the given expression by solving it using the BODMAS rule
According to the rule, first we'll solve the multiplication then subtraction
Therefore, we get
(−2)3 x 30 x (−4)(−20)
(-6) x 30 x (-)(-)80
We know, that (-) x (-) = +
and (-) x (+) = (-)
Therefore, we get
(-6) x 30 x (-)(-)80
(-6) x 30 x 80
-6 x 2400
- 14400
Hence, the given expression (−2)3 x 30 x (−4)(−20) will have the value as -14400
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The loudest sound measured one night during a hockey game was 112 dB. The loudest sound measured during a hockey game the next night was 118 dB. What fraction of sound intensity of the second game was the sound intensity of the first game?
Answer:
1/4
Step-by-step explanation:
I'm 95% sure that this is the answer. if im not correct, im sorry for wasting your time having to read all of this, and im sorry i couldnt help.
Aisha is trying to determine if △LMN and △PQR are similar, congruent, or neither using the information in the diagram.
Triangles L M N and P Q R are shown. The length of side L M is 11 and the length of P Q is 22. The length of M N is 7 and the length of Q R is 12. The length of N L is 6 and the length of R P is 12.
Which statement is true?
The statement that is true about the triangle is that D. The triangles are similar by the SSS similarity theorem.
How to illustrate the information?It should be noted that congruence simply refers to a scenario where there are the same triangles.
The SSS Similarity Theorem states that two triangles are similar if all three pairs of matching sides are proportionate.
Compare the shortest sides first, followed by the longest sides, when applying the SSS Similarity Theorem. Two triangles are similar if their corresponding side lengths are proportionate to one another.
Therefore, triangle LMN and PQR are the same.
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The triangles are not similar, but they are congruent.
The triangles are neither similar nor congruent.
The triangles are similar by the SAS similarity theorem.
The triangles are similar by the SSS similarity theorem.
Answer:
d) The triangles are similar by the SSS similarity theorem.
Solve the following system of equations using elimination. 2x + 5y = 12 -2x + 3y = 4
To solve a system of equation using elimination:
1. If it is necesary multyiply one of both equations for a number that makes each equation have an opposite term to the other equation.
In this case the equations already have opposite terms (2x and -2x)
2. Add equations:
3. Solve the variable in the result of substraction:
[tex]\begin{gathered} 8y=16 \\ y=\frac{16}{8} \\ \\ y=2 \end{gathered}[/tex]4. Use the value of the variable you get in the previus step to solve the other variable:
[tex]\begin{gathered} 2x+5y=12 \\ y=2 \\ \\ 2x+5(2)=12 \\ 2x+10=12 \\ 2x=12-10 \\ 2x=2 \\ x=\frac{2}{2} \\ \\ x=1 \end{gathered}[/tex]Then, the solution for the system of equations is x=1 and y=2simplify 3y-5y+10y-4y
To simplify 3y-5y+10y-4y, just add and subtract the coefficients of each term. That is, 3 - 5 + 10 - 4 = 4, which means that the final expression is 4y.
5/6x-2/3(x-2) + 1/2 please helppp
Answer:38
Step-by-step explanation:
Solve the equation _(4t+_) =6t+15
The given expression is : _( 4t + _ ) = 6t + 15
In the 6t + 15,
An automobile travels 415 miles on 16 2/3 gallons of gasoline.
a) How many miles per gallon does the car get on the trip? (Enter your answer as a simplified mixed number.)
b) How many gallons would be required for the car to travel 498 miles?
Choose the correct ordering of the numbers below from greatest to least.L. 779.56M. 29.7023N. 7.8695O. 0.8436P. 70.7540
When you order a number, you must check the number most in the left. The number L and the number M for example,
L. 779.56
M. 029.7023
In the hundreds place, L has a '7', and M has a '0', this means L is bigger than M.
Doing the same procedure with the other, we get the following order:
[tex]\begin{gathered} 779.56>70.7540>29.7023>7.8695>0.8436 \\ L>P>M>N>O \end{gathered}[/tex]The pentagons ABCDE and PQRST are similar.
Find the length x of TP.
Answer:x=3
Step-by-step explanation: if they are similar lets say for instance BD is congruent to QS.
so TP is congruent to AE and AE is three so TP has to be three.
hope this helps!
The result obtained from measuring length is called a/an __________ measurement and is stated in __________ units.
The result obtained from measuring length is called a linear measurement and is stated in linear units.
The linear measurement is the distance between the two objects or points. The linear measurement is a single dimension measurement
The unit of the measurement of the length is called linear units. In US system of measurements the linear units are feet, yard and inch etc..,In metric system the linear units are meter, centimeter, decimeter etc..
Therefore the result obtained from measuring length is called a linear measurement and is stated in linear units.
Hence, the result obtained from measuring length is called a linear measurement and is stated in linear units.
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What must x equal if a ∥ b? Explain.
The value of x should be equal to 23
Given
Angle at the top is 86
also equation 3x + 17
The lines are parallel
We know if a transverse line is drawn across two parallel lines then 3 types of angles would form namely Corresponding angle, alternate angle, Opposite angle.
From the geometry the angle 86 and the equations 3x + 17 are alternative angles.
Since alternative angles are equal 86 will be equal to 3x + 17
Now equating both
86 = 3x + 17
86 - 17 = 3x
69 = 3x
x = 23
Hence the value of x is equal to 23
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Answer: x=23
Step-by-step explanation:
Im not going to bore you with long algebra but basically 86-17=3x
69=3x inverse you get 23
what is 576.984 round in to the nearest tenths
Answer: 577
Step-by-step explanation:
Answer:
577.0
Rounded to the nearest 0.1 or
the Tenths Place.
Step-by-step explanation:
576.984
You rounded to the nearest tenths place. The 9 in the tenths place rounds up to 10 because the digit to the right in the hundredths place is 8.
Because the tenths place was rounded up from 9 to 10, the tenths place becomes 0 and the ones place is increased by 1. When a 9 is rounded up to 10, that place value becomes 0 and we add 1 to the previous place value.
577.0
When the digit to the right is 5 or greater we round away from 0.
576.984 was rounded up and away from zero to 577.0
Please help me with this question
Answer:
The cost of a card is 4 dollars
The cost of a baseball is 18 dollars
Step-by-step explanation:
13c + 9b = 214
3c + 8b = 156
(13c + 9b = 214) × -8
( 3c + 8b = 156) × 9
-104c - 72b = -1712
27c + 72b = 1404
-------------------------------
-77c = -308
÷-77 ÷-77
--------------------
c = 4
3c + 8b = 156
3(4) + 8b = 156
12 + 8b = 156
-12 -12
----------------------
8b = 144
÷8 ÷8
------------------
b = 18
I hope this helps!
Find the least common denominator of
8/x²+11x+28
and
-2/x^2+4x
The least common denominator of 8/( x²+11x+28 ) and -2/ (x^2+4x) is (x+4).
We have to find the least common denominator of 8/x²+11x+28 and -2/x^2+4x. We can solve this problem by following a few steps.
The denominator of both terms is, x²+11x+28 and x²+4x.
First of all, we have to find the factors of these two terms.
Let's find the factors of x²+11x+28.
x²+11x+28 = x²+11x+28
Or, x²+11x+28 = x²+ 4x+ 7x+ 28 [ we have to break the middle term in such a way as the product of consecutive terms must be 28 ]
Or, x²+11x+28 = x (x+4) +7 (x-4) [ we have to take ( x+ 4) as acommon ]
Or, x²+11x+28 = ( x+4 )( x+7 ).................(1)
Now find the factors of x²+4x.
x²+4x = x (x+4)..................(2) [ We have to take x as a common ]
Therefore, the common term between (1) and (2) is ( x+4 ). So, the least common denominator is ( x+4 ).
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