The each base's length be 18 yards and 22 yards when a flower garden with a trapezoid shape is being planned by a landscaper.
Given that,
A flower garden with a trapezoid shape is being planned by a landscaper. She requests that the longer base be 7 yards longer than the height and that the shorter base be 3 yards longer. The flower garden is 150 square yards in size overall.
We have to find what will each base's length be.
We know that,
To be 3 yards longer than the height, the shorter base
b₁=h+3
To be 7 yards longer than the height, the longer base
b₂=h+7
Area of trapezoid=1/2(b₁+b₂)h
150=1/2(h+3+h+7)h
150=(2h+10)h/2
150=2h²+10h/2
150=2h²+5h
h²+5h-150=0
h²+15h-10h-150=0
h(h+15)-10(h+15)=0
(h-10)(h+15)=0
h=10 or h-15
h value should be positive.
So b₁=h+3=15+3=18
b₂=h+7=15+7=22
Therefore, The each base's length be 18 yards and 22 yards when a flower garden with a trapezoid shape is being planned by a landscaper.
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Is -5 2/3 the multiplicative inverse of 3/-17?
PLEASE HELP!!
Answer:
Yes
Step-by-step explanation:
Multiplicative Inverse of rational number:
When we multiply a rational number and its multiplicative inverse, we get 1
\(\sf -5 \dfrac{2}{3}=\dfrac{-17}{3}\)
Now,multiply this with (3/-17)
\(\sf \dfrac{-17}{3}*\dfrac{3}{-17} = 1\)
So, -5 2/3 is the multiplicatice inverse of 3/-17
find the missing angle measures.
Y = 63
Z = ?
X = ?
Can someone tell me the answer piz
Answer:
look at the photo I have sent
you wearing a mask right now???
can someone help me with this problem
Answer:
It should be 4 or (0,4)
Step-by-step explanation:
The y-intercept is just where one of the lines of the graph crosses the y-axis, which in the picture shows it crosses at (0,4)
Jennifer has already driven 160 miles on her trip to her grandparents' house. For every hour she travels, she drives an additional 55 miles. Which equation represents
the relationship between the total miles driven, y, and the number of hours, X.
Y=
Answer:
y=55x+160
Step-by-step explanation:
i might be wrong, but i think it would be y=55x+160
Answer:
y=55x+160
Step-by-step explanation:
she starts at 160 mi which is like your y-intercept so the "b" in y=mx+b. the slope or "m" would be 55 because thats how much she's travelling per 1 x or 1 hour
7
4
eaks
What is a solution to (x + 6)(x + 2) = 60?
O x = -6
x = -4
x = 4
x = 12
Answer:
x = 4
Step-by-step explanation:
(4+6)(4+2)
Add 4 and 6 to get 10.
10(4+2)
Add 4 and 2 to get 6.
10×6
Multiply 10 and 6 to get 60.
60
The power, P (watts) , of a car engine is proportional to the square of its speed, s ( m / s ) . When s = 30 , P = 1260 . Work out the power when the speed is 25 m / s
Answer:
875 Watts
Step-by-step explanation:
Given that :
P α s²
P = ks²
Where k is the proportionality constant
When ; p = 1260 ; s = 30
1260 = k * 30²
1260 = 900k
k = 1260 / 900
k = 1.4
Value of p ; when s = 25
P = 1.4 * s²
P = 1.4 * 25²
P = 1.4 * 625
P = 875 watt
Banners at the school’s store we’re on sale for $4 off the regular price. Mike brought 5 banners on sale and paid a total of $20. Write and solve an equation to find the regular price of one banner.
Answer:
$8Step-by-step explanation:
Let the regular price is x, then:
(x - 4)*5 = 20x - 4 = 20/5x - 4 = 4x = 4 + 4x = 8compare the 95% and 99% confidence intervals for the hours of sleep a student gets. in at least 2 sentences, explain the difference between these intervals and why this difference occurs.
Answer:
The 99% confidence interval will be wider than the 95% confidence interval because it encompasses a greater range of possible values, meaning that there is a lower chance of the true population parameter falling outside the interval. The 95% confidence interval means that if the study was repeated many times, 95% of the intervals constructed would contain the true population parameter, whereas the 99% confidence interval means that 99% of the intervals constructed would contain the true population parameter.
Step-by-step explanation:
Simplify m7m−4.
please please helpppp
Answer:
\(m^8-4\)
Step-by-step explanation:
\(Rule: a^b\cdot \:a^c=a^{b+c}\\=m^7m=m^{7+1}\\=m^{7+1}-4\\=m^8-4\)
A line of symmetry divides a figure into two equal halves in all aspects. State true or false.
The statement A line of symmetry divides a figure into two equal halves in all aspects is true.
A line of symmetry does indeed divide a figure into two equal halves in all aspects. When a figure has a line of symmetry, it means that if you were to fold the figure along that line, both halves would match exactly. This implies that the two halves of the figure are mirror images of each other, and they are congruent in terms of shape, size, and all other aspects.
The concept of symmetry is widely used in various fields, including mathematics, art, and design. Figures that possess symmetry often have an aesthetically pleasing and harmonious appearance.
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Using the 100/50/20 Rule for daily fluid requirements (DFR). Calculate the following questions, do not round the patient's weight but round all final answers to a whole number. 1-10 kg = 100ml/kg/day 11-20 kg = 50ml/kg/day (+ 1000 mL/day for 1* 10kg) Over 20kg = 20mL/kg/day (1500 mL/day for 1s 20kg) 18. An infant weighs 11 pounds. What is the required amount of fluid per day in ml? I 19. A child weighs 31 lbs and 8 ozs. What is the required amount of fluid per day in ml? If no oral fluids are consumed, what is the hourly IV flow rate to maintain proper hydration?
18. An infant weighs 11 pounds which is equivalent to 4.98 kg. Using the 100/50/20 Rule, the required amount of fluid per day for an infant between 11-20 kg is 50 ml/kg/day. So, the required amount of fluid per day in ml is 4.98 kg x 50 ml/kg/day = 249 ml/day.
19. A child weighs 31lbs and 8 ozs which is equivalent to 14.21 kg. Using the 100/50/24 Rule, the required amount of fluid per day for a child over 20 kg is 20 ml/kg/day. So, the required amount of fluid per day in ml is 14.21 kg x 20 ml/kg/day = 284.2 ml/day.
If no oral fluids are consumed, the hourly IV flow rate to maintain proper hydration would be: 284.2 ml/day / 24 hours/day = 11.8 ml/hour.
Daily Fluid Requirements (DFR)The question is about fluid requirements for infants and children, and it is using the 100/50/20 Rule for Daily Fluid Requirements (DFR) to calculate the required amount of fluid per day for different weight ranges. The 100/50/20 Rule is a guideline used to determine the appropriate amount of fluid that infants and children should receive on a daily basis based on their weight. The rule states that for infants and children up to 10 kg, the recommended fluid intake is 100 ml/kg/day, for those between 11-20 kg it is 50 ml/kg/day, and for those over 20 kg it is 20 ml/kg/day.
The question also asking about the hourly IV flow rate to maintain proper hydration if no oral fluids are consumed.
This subject is part of pediatrics, more specifically in the field of fluid and electrolyte balance and management.
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Here's an equation I need to solve:
x/2 +3 = 10
The first step is to subtract 3 from both sides:
x/2 = 7
What step do you do next to solve for x?
divide by 2
subtract 7
multiply by 2
add 7
Answer:
you multiply both sides by 2.
Step-by-step explanation:
Im in advanced math and we have been doing this for a while.
Temperature
Use the example data set to accurately graph this data, interpret the graph, write the analysis, and write the conclusion. When writing your analysis and conclusion, be sure to answer the
Unfortunately, you have not provided the example data set that you would like to graph, analyze, and conclude. Therefore, I will provide general steps on how to accurately graph data, interpret the graph, analyze it, and conclude.
Graph the data set on the appropriate graph. For example, if you have time series data, plot it on a line graph. If you have categorical data, plot it on a bar graph. Ensure to use appropriate labeling for the x-axis and y-axis, including units.
Interpret the graph Analyze the graph by observing its key features such as the shape, trend, and distribution. For example, observe if there is a positive, negative, or no correlation. If there is a trend, is it linear or non-linear What is the range and variability of the data Write the analysis Write the analysis based on your observations State whether the hypothesis was supported or rejected and how the data set contributed to understanding the research question or the phenomenon being studied.
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3×=21, the value of ×is
✽ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ✽
➷ \(x + 3 = 21\)
➷ \(x = 21 - 3\)
➷ \(x = 18\)
✽
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ May ♡
Create proof for the following argument
~C
D ∨ (F ⊃ C)
C ∨ ~D /F ⊃ C
To create a proof for the given argument, we can use the method of deduction. F ⊃ C is true based on both methods of proof.
Below is the proof:
1. ~C
2. D ∨ (F ⊃ C)
3. C ∨ ~D / F ⊃ C
4. Assume F
5. C ∨ ~D 3,4 Disjunctive syllogism (DS)
6. C 5,1 Disjunctive syllogism (DS)
7. F ⊃ C 4-6 Conditional introduction (CI)
Alternatively, we can use the method of indirect proof. Below is the proof:
1. ~C
2. D ∨ (F ⊃ C)
3. C ∨ ~D / F ⊃ C
4. Assume ~ (F ⊃ C)
5. F 4, indirect proof (IP)
6. C ∨ ~D 3,5 Disjunctive syllogism (DS)
7. Assume C
8. C 7, direct proof (DP)
9. Assume ~C
10. ~D 6,9 Disjunctive syllogism (DS)
11. D ∨ (F ⊃ C) 2 Addition (ADD)
12. Assume D
13. F ⊃ C 12,11 Disjunctive syllogism (DS)
14. C 5,13 Modus ponens (MP)
15. ~D ⊃ C 10,14 Conditional introduction (CI)
16. ~D 6,8 Disjunctive syllogism (DS)
17. C 15,16 Modus ponens (MP)
18. C 7-8, 9-17 Proof by cases (PC)
Therefore, F ⊃ C is true based on both methods of proof.
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Consider the following function. g ( x ) = x 3 − 6 A) Find its average rate of change over the interval [ − 2 , 2 ] . B) Compare this rate with the instantaneous rates of change at the endpoints of the interval.
A- The average rate of change of g(x) over the interval [-2, 2] is 4, B- the instantaneous rates of change at the endpoints are different from the average rate of change over the interval.
A) To find the average rate of change of the function g(x) over the interval [-2, 2], we need to compute the difference quotient:
average rate of change = [g(2) - g(-2)] / [2 - (-2)]
First, we find the values of the function at the endpoints of the interval:
g(-2) = \(-2^{3}\) - 6 = -14
g(2) = \(2^{3}\) - 6 = 2
Substituting these values into the
average rate of change = (2 - (-14)) / (2 - (-2)) = 16 / 4 = 4
Therefore, the average rate of change of g(x) over the interval [-2, 2] is 4.
B) To compare this rate with the instantaneous rates of change at the endpoints of the interval, we need to find the derivatives of the function at x=-2 and x=2 using the power rule of differentiation:
g'(x) = 3\(x^{2}\)
g'(-2) = 3\(-2^{2}\) = 12
g'(2) = 12
The instantaneous rate of change at x=-2 is 12, and the instantaneous rate of change at x=2 is also 12. These values are equal to the average rate of change over the interval [-2, 2], which is 4.
This means that the function g(x) is not a linear function over the interval [-2, 2], and the instantaneous rates of change at the endpoints are different from the average rate of change over the interval.
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3. Which phrase best describes the function of the ATP molecule?
1. Carries energy
2. Destroy energy
3. absorbs energy
4. none of the above
Answer:
1.) Carries energy
Step-by-step explanation:
A good summary of an ATP molecule is a molecule that transfers energy between cells... meaning it carries energy from cell to cell. Furthermore, energy cannot be destroyed, and cannot be absorbed, only changed and transformed. This leaves us with two options, (1. Carries energy, and 4. None of the above). Since we already have a basic understanding of what an ATP molecule does, we can confidently determine that the correct answer is that an ATP molecule can best be described as carrying energy.
Multiply. Write your answer as a fraction in the simplest form 3 x 7/12
\(3\times \dfrac 7{12} = \dfrac{3 \times 7}{12}=\dfrac{3 \times 7}{3 \times 4} = \dfrac 74\)
Convert 0.0045 to a percent.
Select one:
0.045%
0.45%
4.5%
45%
Answer: 0.045%
Step-by-step explanation:
Brigid is picking strawberries at the Pick-Your-Own Farm. Her goal is to pick 5 bushels of strawberries. She has already picked 1
1
2
bushels, and she picks at a rate of
5
8
bushel per hour. The scenario is represented as
5
8
h + 1
1
2
= 5, where h is the number of hours she picks. How many more hours will it take Brigid to fill 5 bushels of strawberries?
2 and StartFraction 3 Over 16 EndFraction hours
2 and StartFraction 3 Over 16 EndFraction hours
5 and three-fifths hours
10 and two-fifths hours
Answer:
We can start by isolating the variable "h".
5 8 h + 1 1 2 = 5
Subtracting 11/2 from both sides:
5 8 h = 5 - 1 1 2
Simplifying:
5 8 h = 8 1 2
Dividing both sides by 5/8:
h = 8 1 2 ÷ 5 8
Converting the mixed number to an improper fraction:
h = (8 x 8 + 1) ÷ 5 8
h = 65/8
Now, we can convert this fraction to a mixed number:
h = 8 1/8
Brigid has already picked for 8 1/8 hours, so the amount of time needed to pick the remaining strawberries is:
5 - (1 1/2 + 5/8 x 8) = 5 - (3 5/8) = 1 3/8
Therefore, Brigid still needs to pick for 1 3/8 hours to fill 5 bushels of strawberries. The answer is 1 and 3/8 hours or 2 and 3/16 hours (if simplified).
Step-by-step explanation:
If it’s the right answer I’ll give u brainliest
Answer:You are correct
Step-by-step explanation:
Here is a explanation so it can be clearer
Proportionality, In algebra, equality between two ratios. ... The term proportionality describes any relationship that is always in the same ratio. The number of apples in a crop, for example, is proportional to the number of trees in the orchard, the ratio of proportionality being the average number of apples per tree.
If you are reading this hope you have a wonderful day and may your dreams come true!Good luck!
Hope this helped!
Tell me if it’s wrong!
lfu29
In a right triangle, cosine a = 0.352 and sine a = 0.936. what is the approximate value of tangent a?
Answer:
Step-by-step explanation:
Divide
the cosine and the sine to get the tangent.
Answer:
2.65909090
Step-by-step explanation:
tangent of an angle can be defined in terms of the cosine and sine value of the angle such that: \(tan(\theta)=\frac{sin(\theta)}{cos(\theta)}\), this can be used to explain why tan(theta) is undefined at some angles, which is just when cos(theta) = 0.
Anyways, we can plug in the values of cosine and sine to get:
\(tan(a) = \frac{0.936}{0.352}\)
Divide:
\(tan(a) = 2.65\overline{90}\)
PLZZZZZZZZZZ HLPPPPPPPPP MEEEEEEEEEEEE
Answer:
2 roots.
Step-by-step explanation:
The roots are the same things as the x-intercepts. From -4 to 3, there are two times when the polynomial intersects the x-axis. So, there are 2 roots.
Hope this helps!
Please help this is really hard
Answer:
The new pic will be like this , i think .
Step-by-step explanation:
Good night ^*^
Choose the correct answer from the given four options:In an AP if a = –7.2, d = 3.6, an = 7.2, then n
2
4
3
5
Answer:
n=5
Step-by-step explanation:
by using
n=(an-a)/a+1
substituting values
n= 7.2-(-7.2)/3.6 +1
n=5
A woman bought some large frames for $19 each and some small frames for $9 each at a closeout sale. If she bought 27 frames for $343, find how many of each type she bought.
Let x be the number of large frames and y be the number of small frames that a woman bought from the closeout sale.Therefore, the two equations that we can use to solve the problem are:
x + y = 27 ...(1)and19x + 9y = 343 ...(2)Multiplying equation (1) by 9 and subtracting it from equation (2), we get:19x + 9y = 343 ...(2)- (9x + 9y = 243) ...(3)10x = 100x = 10Thus, the woman bought 10 large frames
.Substituting x = 10 in equation (1), we get:10 + y = 27y = 27 - 10y = 17Thus, the woman bought 17 small frames. Therefore, the woman bought 10 large frames and 17 small frames.
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help plz lol? 15 ponts :)
Answer:
The scale factor is 2.
Step-by-step explanation:
Divide 2 by 1 then you get 2. I got the 2 and the one from the shapes. So don’t get confused ;)
5. Use synthetic substitution evaluate (x^4 + 3x^2 -2) at f(-4)
The value of f(-4) when the function is x⁴+3x²-2 is 292.
Given that,
The function as x⁴+3x²-2.
We have to find the value of f(-4)
A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f from a set A (the function's domain) to a different set B (the function's co-domain) is referred to as a function.
Take the function
f(-4)=(-4)⁴+3(-4)²-2
f(-4)=256+3(16)-2
f(-4)=246+48-2
f(-4)=294-2
f(-4)=292
Therefore, the value of f(-4) when the function is x⁴+3x²-2 is 292.
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What kind of transformation converts the graph of f(x)=-x-1 into the graph of g(x)= -5x-5? vertical stretch horizontal stretch vertical shrink horizontal shrink
The transformation that converts the graph of f(x)=-x-1 into the graph of g(x)=-5x-5 is a horizontal stretch. A horizontal stretch is a transformation that expands the horizontal distance between two points, and it compresses the vertical distance between two points.
When two functions have the same form as f(x) and g(x), the first step is to determine the ratio of the coefficients of x. The ratio of the coefficients of x in g(x) to the coefficients of x in f(x) is -5/-1 = 5.
Because the ratio of the coefficients of x is 5, the graph of g(x) is a horizontal stretch of the graph of f(x) by a factor of 5. The transformation stretches the graph to the right because the value of x is multiplied by 5.
The transformation affects the horizontal axis rather than the vertical axis. A horizontal stretch happens when a function's domain is compressed by a factor of b to create a new function with a horizontal stretch factor of b.
Therefore, the transformation that converts the graph of f(x)=-x-1 into the graph of g(x)=-5x-5 is a horizontal stretch, which compresses the vertical distance between two points while expanding the horizontal distance between two points.
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Graph a system of equations with the solution (-4, 6). Be sure to record the equations represented on your graph