The equation ax = bx + 1 is the same as x = 1/(a - b) when solved for x. This means that x is equal to the reciprocal of the difference of a and b. This is the answer from the sample response.
Answer:
The equation ax = bx + 1 is the same as x = 1/(a - b) when solved for x. This means that x is equal to the reciprocal of the difference of a and b. This is the answer from the sample response.
Step-by-step explanation:
The end of a hose was resting on the ground, pointing up an angle. Sal measured the path of the water coming out of the hose and found that it could be modeled using the equation f(x) = –0.3x2 + 2x, where f(x) is the height of the path of the water above the ground, in feet, and x is the horizontal distance of the path of the water from the end of the hose, in feet.
When the water was 4 feet from the end of the hose, what was its height above the ground?
Answer:
3.2 feet
Step-by-step explanation:
The equation [tex]f(x)=-0.3x^{2}+2x[/tex] shows the height of water [[tex]f(x)[/tex]] and horizontal distance [[tex]x[/tex]].
Given the horizontal distance is 4 feet, they want to know the height.
Simply put 4 in [tex]x[/tex] of the equation and solve for [tex]f(x)[/tex]. So,
[tex]f(x)=-0.3(4)^{2}+2(4)\\f(x)=3.2[/tex]
So, the height of the water was 3.2 feet above the ground.
What unit of measurement would Guatemalans typically use to measure the weight of flour?
can someone explain how to find two positive numbers such that their product is 192 and the sum of the first plus three times the second is a minimum?
Which of the following represents this function written in standard form?
y=2(x+1)(x-6)
a. y=3x^2-10x-12
b.y=2x^2-10x+6
c. y=2x^2-5x-12
d. y=2x^2-14x+12
Which of the following represents this function written in standard form?
y=2(x+1)(x-6)
a. y=3x^2-10x-12
b.y=2x^2-10x+6
c. y=2x^2-5x-12
d. y=2x^2-14x+12
Answer:
[tex]y=2x^2-10x-12[/tex]
Step-by-step explanation:
[tex]y=2(x+1)(x-6)[/tex]
write the given function in standard form
Standard form is [tex]y=ax^2+bx+c[/tex]
[tex]y=2(x+1)(x-6)[/tex] multiply the parenthesis using FOIL method
[tex]y=2(x^2-6x+1x-6)[/tex]
multiply 2 inside the parenthesis
[tex]y=2(x^2-6x+1x-6)[/tex]
[tex]y=2x^2-12x+2x-12[/tex]
Combiene like terms
[tex]y=2x^2-10x-12[/tex]
in DEF DE=17 m angle =32 Find DF nearest tenth
Answer:
(A) 32.1
Step-by-step explanation:
It is given that in ΔDEF, DE=17 and m∠F=32, thus
Using the trigonometry, we have
[tex]sinx=\frac{Perpendicular}{Hypotenuse}=\frac{DE}{DF}[/tex]
⇒[tex]sin32^{\circ}=\frac{17}{DF}[/tex]
⇒[tex]DF=\frac{17}{sin32^{\circ}}[/tex]
⇒[tex]DF=\frac{17}{0.529}[/tex]
⇒[tex]DF=32.1[/tex]
Therefore, the value of DF is 32.1.
Hence option A is correct.
What does x equal
8=3+x/-6
My math homwork is asking me for the word form and the expanded form for 3.4 and 2.51,and i don't understand this. we just started it today and she my teacher gave us 3 pages of the math.
i need work shown write .569 as a percent
How do i write an akgebaric expression? Carrisa divided 40 grapes equally amoung f friends. How many grapes did each friend get?
How many friends?
40
____
X
40/ x
If i drove 34 times over a 7 mile bridge. how many miles in all did i drive?
2 1/7 into a improper fraction
How much of the circle is shaded? Write your answer as a fraction in simplest form?
Answer:
[tex]5/14[/tex]
Step-by-step explanation:
Let
x-----> the shaded area
we know that
[tex]x+\frac{1}{7}=\frac{1}{2}[/tex]
solve for x
Multiply by [tex]14[/tex] both sides
[tex]14x+2=7[/tex]
[tex]14x=7-2[/tex]
[tex]14x=5[/tex]
Divide by [tex]14[/tex] both sides
[tex]x=5/14[/tex] ----> fraction irreducible
Express x in terms of the other variables in the diagram below:
From the diagram below , x = t ( r - h ) / h
Further explanationFirstly , let us learn about trigonometry in mathematics.
Suppose the ΔABC is a right triangle and ∠A is 90°.
sin ∠A = opposite / hypotenusecos ∠A = adjacent / hypotenusetan ∠A = opposite / adjacentThere are several trigonometric identities that need to be recalled, i.e.
[tex]cosec ~ A = \frac{1}{sin ~ A}[/tex]
[tex]sec ~ A = \frac{1}{cos ~ A}[/tex]
[tex]cot ~ A = \frac{1}{tan ~ A}[/tex]
[tex]tan ~ A = \frac{sin ~ A}{cos ~ A}[/tex]
Let us now tackle the problem!
Look at ΔADE in the attachment.
We will use the following formula to find relationship between variable t and h:
tan ∠A = opposite / adjacent
[tex]\tan \angle A = \frac{DE}{AD}[/tex]
[tex]\large {\boxed{ \tan \angle A = \frac{h}{t} } }[/tex] → Equation 1
Look at ΔABC in the attachment.
We will use the following formula to find relationship between variable r , t and x:
tan ∠A = opposite / adjacent
[tex]\tan \angle A = \frac{BC}{AB}[/tex]
[tex]\large {\boxed{ \tan \angle A = \frac{r}{x + t} } }[/tex] → Equation 2
Next we can substitute equation 1 to equation 2 :
[tex]\tan \angle A = \frac{r}{x+t}[/tex]
[tex]\frac{h}{t} = \frac{r}{x+t}[/tex]
[tex](x + t)h = r ~ t[/tex]
[tex](x + t) = \frac{(r ~ t)}{h}[/tex]
[tex]x = \frac{(r ~ t)}{h} - t[/tex]
[tex]x = \frac{(r ~ t)}{h} - \frac{(h ~ t)}{h}[/tex]
[tex]\large {\boxed {x = \frac{t(r - h)}{h}} }[/tex]
Learn moreCalculate Angle in Triangle : https://brainly.com/question/12438587Periodic Functions and Trigonometry : https://brainly.com/question/9718382Trigonometry Formula : https://brainly.com/question/12668178Answer detailsGrade: College
Subject: Mathematics
Chapter: Trigonometry
Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse , Triangle , Fraction , Lowest , Function , Angle
The following is a correspondence one is
A.{(a,1),(b,1),(c,1)}
B.{(1,a),(2,c),(3,d)
C.{(1,b),(2,c),(3,b)
D.{(a,b),(c,d),(b,d)
What is the length of segment LM?
Answer:
Step-by-step explanation:
From the given figure, we have
[tex]KN=NM[/tex]
⇒[tex]14x-3=25[/tex]
⇒[tex]14x=28[/tex]
⇒[tex]x=2[/tex]
Also, a is the angle bisector of ∠KNM and also it bisects the side KM such that KL=LM, thus
[tex]KL=LM[/tex]
Also, [tex]KL=9x+5[/tex]
Substituting the value of x in the above equation, we get
[tex]KL=9(2)+5[/tex]
[tex]KL=18+5[/tex]
[tex]KL=23[/tex]
Therefore, [tex]KL=LM[/tex]
[tex]LM=23[/tex]
Thus, the value of the segment LM is 23.
Which of the following expressions are equal to the one below?
(8+7) x 11
A. 8+ (7x11)
B. 11 x (8+7)
C. 8 x 11 - 7 x 11
D. 11 x 7 + 11 x 8
Tommy has a pet monkey. Every day, his monkey eats 4 apples in the morning. The monkey also eats two bananas for every banana that Tommy eats.
Write an equation to describe this situation where x is the number of bananas Tommy eats and y is the total number of pieces of fruit the monkey eats.
Answer:
The required equation is : [tex]2x+4[/tex]
Step-by-step explanation:
Tommy's monkey eats 4 apples in the morning. The monkey also eats two bananas for every banana that Tommy eats.
Let Tommy eats x bananas, then the monkey eats 2x bananas.
Then, the required equation will be :
[tex]2x+4[/tex]
For spring break this year your family decided to visit Michigan, but it snows the first weekend you are there. You decide to make a snowman. If the bottom ball is 3 feet across, the middle ball is 2 feet across, and the top is 1 foot across, how much snow is needed to build the whole snowman? Round your answer to the nearest cubic foot.
A)
19 cubic feet of snow
B)
31 cubic feet of snow
C)
511 cubic feet of snow
D)
1022 cubic feet of snow ...?
Answer:
A
Step-by-step explanation:
Final answer:
To find the amount of snow needed to build the snowman, we need to calculate the volume of each ball and then add them together. The total volume is 18.84 cubic feet, rounded to 19 cubic feet.So,Option A.19 cubic feet of snow is correct.
Explanation:
To find how much snow is needed to build the whole snowman, we need to calculate the volume of each ball and then add them together. The volume of a sphere can be found using the formula V = (4/3) * pi * r³, where r is the radius of the sphere.
The bottom ball has a diameter of 3 feet, so the radius is 3/2 = 1.5 feet. The volume of the bottom ball is (4/3) * 3.14 * (1.5³) = 14.13 cubic feet.
The middle ball has a diameter of 2 feet, so the radius is 2/2 = 1 foot. The volume of the middle ball is (4/3) * 3.14 * (1³) = 4.19 cubic feet.
The top ball has a diameter of 1 foot, so the radius is 1/2 = 0.5 feet. The volume of the top ball is (4/3) * 3.14 * (0.5³) = 0.52 cubic feet.
The total volume of the snowman is 14.13 + 4.19 + 0.52 = 18.84 cubic feet. Therefore, the answer is 19 cubic feet of snow.
What is the product? enter your answer as a fraction, in simplified form, in the box. −1/4⋅(−6/11)?
yeah it would be 3/11 i just did the test
Harry’s team has won 13 less than 6 times as many games as it has lost. The team lost n games. What expression could you use to find the number of games the team has won?
In the week before and the week after a holiday there were 10,000 total deaths and 4968 of them occurred in the week before the holiday.
a) construct a 90% confidence interval estimate of the proportion of deaths in the week before the holiday to the total death in the week before and the week after the holiday
b) based on the result does there appear to be any indication that people can temporarily postpone their death to survive the holiday
The confidence interval is calculated based on the given values and can help determine if deaths are temporarily postponed during holidays.
Explanation:To construct a confidence interval estimate of the proportion of deaths in the week before the holiday to the total deaths in the week before and after the holiday, we can use the formula:
p ± z √(p(1- p/ n)
where p is the sample proportion, z is the z-score, and n is the sample size.
In this case, the sample proportion is p = 4968/10000 = 0.4968.
The z-score corresponding to a 90% confidence interval is approximately 1.645. The sample size is n = 10000.
Substituting these values into the formula, we get:
0.4968 ± 1.645 √((0.4968 * 0.5032) / 10000)
Calculating this expression gives us the confidence interval estimate.
Based on the result, we can assess whether there is an indication that people can temporarily postpone their death to survive the holiday. If the lower limit of the confidence interval is significantly lower than the proportion of deaths in the week after the holiday, it suggests that there is a decrease in deaths in the week before the holiday. However, if the lower limit is close to or higher than the proportion of deaths in the week after the holiday, it indicates that there is no evidence of a significant decrease in deaths before the holiday.
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if you drive your car constant speed of 45 miles per hour, how long will it take to travel 378 miles
(only subject im bad at) What is the Least Common Denominator (LCD) of 7/8 and 1/6 ?
alice leaves her house and walks to school she walks 45 meters south and 336 meters east. how far is Alice from her house?
Alice's distance from her home is 339 meters.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Alice leaves her house and walks to school she walks 45 meters south and 336 meters east.
We can write the Alice's distance from her home as -
{x} = √(45)² + (336)²
{x} = √(2025 + 112896)
{x} = 339 meters
Therefore, Alice's distance from her home is 339 meters.
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1000 millimeters equals what =
Find the equation of a circle in standard form where C(6, -2) and D(-4, 4) are endpoints of a diameter. ...?
A heart beats 8 times in 3 seconds.About how many times will a cats heart beat in 2 minutes
The measures of each exterior angle in a regular hexagon is (4x + 15)°. Find the value of x. Show equations and all work that leads to your answer.
...?
Solve the problem. Susan purchased some municipal bonds yielding 7% annually and some certificates of deposit yielding 9% annually. If Susan's investment amounts to $19,000 and the annual income is $1590, how much money is invested in bonds and how much is invested in certificates of deposit? a. $13,500 in bonds; $5500 in certificates of deposit b. $5500 in bonds; $13,500 in certificates of deposit c. $13,000 in bonds; $6000 in certificates of deposit d. $6000 in bonds; $13,000 in certificates of deposit
...?
Susan invested $6,000 in municipal bonds and $13,000 in certificates of deposit. For the bond investment scenario, given the increase in market interest rate to 9%, you would pay less than $10,000 for the bond. The calculation shows you would be willing to pay approximately $9,724.77.
Explanation:To solve Susan's investment problem, we can set up a system of equations using the information provided in the problem. Let x be the amount invested in municipal bonds and y be the amount invested in certificates of deposit (CDs). We can then set up the following equations:
x + y = $19,000 (Total investment amount)
0.07x + 0.09y = $1,590 (Total annual income from investments)
Now, we solve the system of equations. Multiplying the second equation by 100 to get rid of decimals:
7x + 9y = 159,000
Next, we can multiply the first equation by 7 to help us eliminate one variable:
7x + 7y = 133,000
Subtracting the modified first equation from the second equation:
9y - 7y = 159,000 - 133,000
2y = 26,000
y = $13,000
Using y = $13,000 in the first equation:
x + 13,000 = 19,000
x = $6,000
Therefore, Susan invested $6,000 in municipal bonds and $13,000 in certificates of deposit.
Regarding the bond investment scenario:
a. Since the market interest rate has risen to 9%, higher than the bond's 6% interest rate, you would expect to pay less than $10,000 for the bond.
b. To calculate the price you would be willing to pay, you need to find the present value of the expected payment from the bond one year from now:
The expected payment is $10,000 (the face value) plus $600 (the final interest payment), which totals $10,600.
Using the market interest rate of 9%, the present value (PV) formula is:
PV = Payment / (1 + market interest rate)
PV = $10,600 / (1 + 0.09)
PV = $10,600 / 1.09
PV ≈ $9,724.77
Therefore, you would be willing to pay approximately $9,724.77 for the bond.
Write the equation of a line in slope-intercept form from the graph below.
Write the equation of a line in slope-intercept form from the graph below.
Answer: Y=x or y=1x
Step-by-step explanation:
Slope of 1 y-intercept of (0,0)