Answer:
2.52 m
Step-by-step explanation:
let the height be h m.
let the shorter ladder be x m away from the base of wall.
(x+1.96)²+h²=5.6²
x²+h²=4.2²
subtract
(x+1.96)²-x²=5.6²-4.2²
(x+1.96+x)(x+1.96-x)=31.36-17.64
(2x+1.96)(1.96)=13.72
2x+1.96=13.72/1.96=7
2x=7-1.96=5.04
x=5.04/2=2.52
One integer is 4 times another. If the product of the two integers is 144, then find the integers.
One possible set of answers is;
Another possible set of answers is:
Find the point at which the line with parametric equations x = 2 3t, y =-4t, z =5 t intersects the plane 4x 5y -2z=18
It looks like you have
[tex]\begin{cases}x=2+3t\\y=-4t\\z=5+t\end{cases}[/tex]
Substituting these in to the plane equation, we have
[tex]4x+5y-2z = 4(2+3t) + 5(-4t) - 2(5+t) = -2-10t = 18 \\\\ \implies-10t = 20 \implies t = -2[/tex]
When [tex]t=-2[/tex], we get the point
[tex]\begin{cases}x=2+3(-2)\\y=-4(-2)\\z=5+(-2)\end{cases} \implies (x,y,z) = \boxed{(-4,8,3)}[/tex]
Juan and Ari went to the farmers market to buy fruit. Juan’s bag of apples that he bought weighed StartFraction 31 over 7 EndFraction pounds. Ari’s bag of oranges that he bought weighed StartFraction 19 over 3 EndFraction pounds. Using compatible fractions, estimate how much heavier Ari’s bag is compared to Juan’s bag.
Answer:
approximately 2 lb
Step-by-step explanation:
Juan: 31/7
Ari: 19/3
Juan's fraction is close to 32/8 = 4
Ari's fraction is close to 18/3 = 6
6 - 4 = 2
Answer: approximately 2 lb
An envelope contains $1.20 in dimes and nickels. if the dimes were quarters and the nickels were dimes, there would be $1.35 more in the envelope. How many nickels are in the envelope?
The nickels in the envelope is $0. 12
How to determine the number
From the information given, we have that;
Dimes + nickels = $1. 20
1/4 dimes + dimes = $ 1. 35
Let dimes = d
Nickels = n
d + n = 1. 20 equation a
d/4 + d = 1. 35 equation b
Make 'd' subject from equation a
d = 1. 20 - n
Substitute into equation b
1. 20 - n/ 4 + 1. 20 - n = 1. 35
0. 3 - 0. 25n + 1. 20 - n = 1. 35
collect like terms
- 1. 25n = 1. 35 - 1. 5
- 1. 25 = - 0. 15
n = -0. 15/ -1. 25
n = 0. 12
Thus, the number of nickels in the envelope is $0. 12
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What is the divisor the dividend is 5/9
Answer
5/9 is the dividend
Step-by-step explanation:
Find the cube root of Z =1+i the power of 5
Answer:
Cube Root Calculator
Use this calculator to find the cube root of positive or negative numbers. Given a number x, the cube root of x is a number a such that a3 = x. If x positive a will be positive, if x is negative a will be negative. Cube roots is a specialized form of our common radicals calculator.
It will help you alot.
Step-by-step explanation:
Anu is a photographer and was recently hired to photograph a wedding in Hawaii. While there, Anu had some time to
explore the island and capture other beautiful pictures.
During the trip, Anu took a total of 1,200 photographs. Of these, 25% were wedding photos, 35% were pictures of Lanikai
Beach, and the rest of the pictures were taken at the Honolulu Zoo. How many of Anu's pictures were taken at the Honolulu
Zoo?
ANSWER: 480 out of 1200 were taken at the Honolulu Zoo.
7. stano. (2pt) Find the centers, foci, vertices and asymptotes of the hyperbola with equation given by: 16y²-x² - 6x - 32y = 57 And also sketch the hyperbola. (2pts)
The equation of parabola is a [tex]\frac{-(x+ 3)^{2}}{64} + \frac{ (y-1)^{2}}{4} = 1[/tex] and the coordinates of center is (0,0) And asymptote is become 16.
According to the statement
we have to find the centers, foci, vertices and asymptotes of the hyperbola from the given equations.
So, For this purpose,
Hyperbola is a a plane curve generated by a point so moving that the difference of the distances from two fixed points is a constant.
So, The given equation is:
16y²-x² - 6x - 32y = 57
So, rearrange it then
-x² - 6x - 32y + 16y² = 57
-(x² + 6x) + (16y² - 32y ) = 57
-(x² + 6x) + 16(y² - 2y ) = 57
-(x² + 6x + 9) + 16(y² - 2y +1 ) = 57 +1(16) + 9(-1)
-(x+ 3)² + 16 (y-1)² = 64
-(x+ 3)² + 16 (y-1)² = 64
divide whole equation by 64 then
[tex]\frac{-(x+ 3)^{2}}{64} + \frac{16 (y-1)^{2}}{64} =\frac{64}{64}[/tex]
then equation become
[tex]\frac{-(x+ 3)^{2}}{64} + \frac{ (y-1)^{2}}{4} = 1[/tex]
This become the equation of hyperbola.
So,
here coordinates of center is (0,0)
And asymptote is become 16.
So, The equation of parabola is a [tex]\frac{-(x+ 3)^{2}}{64} + \frac{ (y-1)^{2}}{4} = 1[/tex] and the coordinates of center is (0,0) And asymptote is become 16.
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In conducting a goodness-of-fit test, a requirement is that ________. Question content area bottom Part 1 A. the expected frequency must be at least five for each category B. the expected frequency must be at least ten for each category C. the observed frequency must be at least ten for each category D. the observed frequency must be at least five for each category
In conducting a goodness of fit test, a requirement is that the expected frequency must be at least ten for each category.
What is a goodness of fit test?In relation to the statistical model, the test tells how well it fits a set of observations.
The measures of the goodness of fit summarize the discrepancy between observed values and the values expected under the model in question.
Also, when conducting a goodness of fit test, a requirement is that the expected frequency must be at least ten for each category.
Therefore, the Option B is correct,
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Create a two-column proof: Given: EAB and DCB are two right triangles. The figure has BED≅ BDE. Point B is the midpoint of segment AC. Prove: EAB≅ DCB
The two-column proof that shows that ΔEAB ≅ ΔDCB by SAS congruence theorem is explained below.
What is the the SAS Congruence Theorem?The Side-angle-side congruence theorem (SAS) that states that two triangles that are have two pairs of corresponding congruent sides and a pair of included corresponding congruent angles are congruent to each other.
What is an Isosceles Triangle?Any triangle with two equal base angles is referred to as an isosceles triangle, The sides opposite these base angles are also congruent to each other.
Given the diagram below, the proof is expressed as follows:
Statement 1: ΔEAB and ΔDCB are two right triangles
Reason 1: Given
Statement 2: ∠EAB ≅ DCB
Reason 2: Right angles
Statement 3: ∠BED ≅ BDE
Reason 3: Given
Statement 4: ΔBED is an isosceles triangle
Reason 4: Definition of isosceles triangle
Statement 5: BE ≅ BD
Reason 5: Definition of isosceles triangle
Statement 6: ΔEAB ≅ ΔDCB
Reason 6: SAS
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If the volume of the cone is 180 in³, what is its surface area?
Answer:
Hi, to find the surface area of a cone is πrl
if your radius and length is given.
hope this helps (•‿•)
Apply the rule (-x, y - 2) to the following point, what is the result?
(-3,5)
O (-5,-5)
O (3, 3)
O (-5,3)
O (-3,7)
Answer:
[tex] - 3 \times - 1 = 3 \\ \\ 5 - 2 = 3[/tex]
Step-by-step explanation:
3,3
Answer: Second Choice. (3, 3)
Step-by-step explanation:
Given point
(x, y) = (-3, 5)
Given the rule for application
(-x, y - 2)
Determine the new x-value
x = -3
-x = - (-3) = 3
Determine the new y-value
y = 5
y - 2 = (5) - 2 = 3
Therefore, the result is [tex]\Large\boxed{(3,~3)}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
In politics, marketing, etc. we often want to estimate a percentage or proportion p. One calculation in statistical polling is the margin of error - the largest (reasonble) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%). In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 32% with a margin of error of 2.5%. Describe the conclusion about p using an absolute value inequality. The answer field below uses the symbolic entry option in Mobius. That lets you type in a vertical bar | to represent absolute values. Also, when you type in < and then =, the symbolic entry option will automatically convert that to ≤ . In the same way, if you type in > and then =, the symbolic entry option will automatically convert that to ≥. Be sure to use decimal numbers in your answer (such as using 0.40 for 40%). __________
Answer:
yes yes yes yes yes Yes Yes you are cute
Five interlocked, colored rings make up the Olympic symbol. The rings are
blue, black, red, yellow, and green and represent Africa, the Americas, Asia,
Australia, and Europe. The symbol looks like this:
1. In how many ways could the five colors of the Olympic symbol have been
arranged among the rings?
Answer:
120
Step-by-step explanation:
5 rings 5 colors
for the first ring there are 5 colors to choose from
4 colors for the second
3 for the third
2 for the fourth
1 for the last one
so 5! = 120
on a unit circle, the terminal point of 0 is (1/2, square root 3/2). what is sin 0?
A. square root 3/2
B. 1/2
C. square root 3/3
D. square root 3
Answer: A
Step-by-step explanation:
[tex]\sin \theta[/tex] is equal to the y-coordinate.
Answer: square root 3/2
Step-by-step explanation:
If 2 angles have the same angle measure they are said to be what
2 angles that have the same angle measure are congruent.
Given that the two angles have the same angle measure.
Congruence is a term reserved for geometry. Two metrics are congruent when you can perfectly map to each other by mirroring, rotating, and translating without distortion.
We know that two shapes or objects are congruent if they have the same shape and the same size. For two angles to be congruent, they must coincide when they are overlapped. This is only possible if the two angles are equal.
Therefore, if two angles have the same measure, then they are said to be congruent.
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Sports clubs have increasingly been acknowledged as important settings for health promotion. The term sport club is synonymous with organized sport and both are considered to consist of environments that support the healthy behaviors of its athletic members. One of the member Sanjaya pays rupees 500 in advance on his account at a sports club ,each time he visits the club 10 rupees is deducted from his account. Q6. Which of the following equation represent the left balance of sanjaya’s y after visiting x number of days? * A) y=500+10x B) y=10+500x C) x=500-10y D) y=500-10x NO RESPONSE
The linear equation that represent the left balance of sanjaya’s y after visiting x number of days is:
y = 10x + 500.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.From the data given, we have that:
The y-intercept is of 500.The slope is of 10.Hence the balance is given as follows:
y = 10x + 500.
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Merina is scheduled to make two loan payments to Bradford in the amount of $1,000 each, two months and nine months from now. Merina doesn't think she can make those payments and offers Bradford an alternative plan where she will pay two equal amounts seven months from now followed by another equal payment seven months later. Bradford determines that 8.5% is a fair interest rate. Using the second unknown equal payment as your focal date, what are the equal payments?
well, we're assuming all along that Merina owes Bradford $2000, because in the 1st scenario, she was going to pay twice $1000.
on the 2nd scenario, she'll be paying the same $2000 but split 7 months from now and then 7 months later, same 2000 bucks, at which point Bradford applied 8.5% interest.
using those assumptions, since the wording is not quite clear, we can say that Merina is simply paying 2000 bucks plus the 8.5%
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8.5\% of 2000}}{\left( \cfrac{8.5}{100} \right)2000}\implies 170 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\stackrel{principal}{2000}~~ + ~~\stackrel{interest}{170}}{2}\implies \stackrel{\textit{two equal payments of}}{1085}[/tex]
What is the mean absolute deviation of this? 1 is 2 sundaes.
Using it's concept, the mean absolute deviation of the data-set is of 2 sundaes.
What is the mean absolute deviation of a data-set?The mean of a data-set is given by the sum of all observations divided by the number of observations.The mean absolute deviation of a data-set is the sum of the absolute value of the difference between each observation and the mean, divided by the number of observations.The mean absolute deviation represents the average by which the values differ from the mean.The mean for this problem is:
(4 + 6 + 2 + 4)/4 = 4
Hence the MAD is:
(|4-4| + |6-4| + |2-4| + |4-4|)/4 = 1
Since each unit represents 2 sundaes, the mean absolute deviation is of 2 sundaes.
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Question 8 of 10
Factor the polynomial: -5x³ - 10x² - 15x
OA. 5x(x²+2x-3)
OB. -5x(-x2 - 2x - 3)
C. -5x(x2 + 2x - 15)
OD. -5x(x2+2x+3)
Which of the following would be an acceptable first step in simplifying the expression
sinx/1- cosx?
A. sinx - sinx/1- cos x
B. 1/cscx - cosx
C. Cannot be simplified further
D. sin x(1+cosx)/(1-cosx)(1+cosx)
Answer: A
Step-by-step explanation: Because it can be simplified twice.
Show all work to write the expression in simplified rational exponent form:
[tex]\sqrt[4]{17x^{2}}[/tex]
(Fourth root of 17 x squared)
Answer:
[tex](17x)^{\frac{2}{4}}[/tex]
Step-by-step explanation:
There's not much work to show for this problem, but I'll explain it for you
Use the exponent rule for roots to combine the 4 and the 2 like a fraction
2 on the top and 4 on the bottom
[tex](17x)^{\frac{2}{4} }[/tex]
That's it! Pretty easy
Good Luck!
pls mark brainliest
QUESTION IS DOW BELOW 5 POINTS EACH PLEASE HELP PLEASE HELP PLEASE HELP
a. Central angle in the circle is: Angle BAC
b. A major arc is: Arc BEC
c. A minor arc is: Arc BC
d. measure of arc BEC is: 260°
e. m(BC) = 100°
What is a Central Angle?A central angle has two of its sides as radii of the circle, forming an angle at the center of the circle, where the vertex is at the center of the circle.
What is a Major Arc?A major arc has a measure that is greater than 180 degrees. That is, it is more than half a circle (semicircle). Thus, measure of major arc > 180 degrees.
What is a Minor Arc?A minor arc has a measure that is less than 180 degrees. That is, it is not more than half a circle (semicircle). Thus, measure of minor arc < 180 degrees.
a. Central angle in the circle is: Angle BAC
b. A major arc in circle A is: Arc BEC
c. A major arc in circle A is: Arc BC.
d. Measure of arc BEC = 360 - 100 [according to the central angle theorem]
Measure of arc BEC = 260°.
e. Measure of angle BAC = 100° [given]
Measure of arc BC = angle BAC [according to the central angle theorem]
Measure of arc BC = 100°
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Reagan has a part-time job walking dogs. She makes $12.20 per hour. If she earns $106.75 this week, how many hours does she work?
Answer:
8.75
Step-by-step explanation:
106.75 divided by 12.20= 8.75
Question is on the paper
Note: Spam/Irrelevant answers will be blocked and reported
The dimensions based on the area given are 15cm by 20cm.
How to calculate the sides?From the information given about the rectangle, the area is given as 300cm² and the margins are given as 1.5 and 2.
Therefore, the dimensions will be:
(1.5 × x) × (2 × x) = 300
1.5x × 2x = 300
3x² = 300
x² = 300/3
x² = 100
x = 10
Therefore the dimensions will be:
= 1.5x = 1.5 × 10 = 15
= 2x = 2 × 10 = 20
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We minimize the total area of the sheet
[tex]S = xy[/tex]
constrained by
[tex](x-4)(y-3) = 300[/tex]
Solve the constraint equation for [tex]y[/tex].
[tex](x-4)(y-3) = 300 \implies y-3 = \dfrac{300}{x-4} \implies y = 3 + \dfrac{300}{x-4} = \dfrac{3x+288}{x-4}[/tex]
Substitute this into [tex]S[/tex] and find the critical points.
[tex]S = \dfrac{3x^2+288x}{x-4} = 3x + 300 + \dfrac{1200}{x-4}[/tex]
[tex]\dfrac{dS}{dx} = 3 - \dfrac{1200}{(x-4)^2} = 0[/tex]
[tex]\implies \dfrac{1200}{(x-4)^2} = 3[/tex]
[tex]\implies (x-4)^2 = 400[/tex]
[tex]\implies x-4 = \pm20[/tex]
[tex]\implies x=-16 \text{ or } x = 24[/tex]
Of course [tex]x[/tex] can't be negative, so the page dimensions that minimize [tex]S[/tex] are [tex]x=24[/tex] and [tex]y=18[/tex].
Divide
8x⁴-6x³+2÷2x²+3
WhenWhen we divide 8x⁴ - 6x³ + 2 by 2x² + 3 The result obtained is 4x² - 3x - 6 remainder 9x + 20
What is quotient?Quotient is the result obtained when division operation is carried out.
For example when 6 is divided by 2, the result obtained is 3. Thus, the quotient is 3
How to divide 8x⁴ - 6x³ + 2 by 2x² + 3To divide 8x⁴ - 6x³ + 2 by 2x² + 3, we shall apply the long division method. This is illustrated below:
4x² - 3x - 6
2x² + 3 | 8x⁴ - 6x³ + 2
-(8x⁴ + 12x²)
-6x³ - 12x² + 2
-(-6x³ - 9x)
-12x² + 9x + 2
-(-12x² - 18)
9x + 20
Thus, the result obtained when we divide 8x⁴ - 6x³ + 2 by 2x² + 3 is 4x² - 3x - 6 remainder 9x + 20
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Please I need the answer this is due in on monday!!
The number sets that each number belong too are given as follows:
1. Rational.
2. Irrational.
3. Rational.
4. Whole.
5. Whole.
6. Integer.
What is the classification of the number -4.2?It is a terminating decimal, hence it is a rational number.
What is the classification of the number 3 times square root of 5?The square root of 5 is not exact, hence it is a non-terminating decimal, meaning that is an irrational number.
What is the classification of the number 5/3?It is a fraction, hence it is a rational number.
What is the classification of the number 9?It is a positive non-decimal number, hence it is a whole number.
What is the classification of the square root of 16?The square root of 16 is of 4, which is a positive non-decimal number, hence it is a whole number.
What is the classification of the square root of -8/2?The result of the division is of -4, which is a negative non-decimal number, hence it is an integer number.
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In a flower garden of rose and sunflower, 40% of flowers are rose. if there are 120 sunflower in the garden, total of how many flowers are there in the garden?
Answer:
200
Step-by-step explanation:
If 40% are roses than 60% must be sunflowers (40% + 60% = 100%)
We are trying to find 60% of some number is 120.
Let n = the total number of flowers
.6n = 120 Divide both sides by .6
n = 200
100 000 , 10 000 , 1000 , 100 , A , B
The two missing numbers in the pattern are:
A=___?
B=___?
The two missing numbers in the pattern are 10 and 1
How to determine the missing numbers?The sequence is given as:
100 000 , 10 000 , 1000 , 100 , A , B
From the above sequence, the next term is the quotient of the current term and 10.
So, we have:
A = 100/10 = 10
B = A/10 = 10/10 = 1
Hence, the two missing numbers in the pattern are 10 and 1
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Sam drove from his house to college. When he stopped at college, he saw on the instrument panel of his car that he covered 26.5km. What is the displacement?
Answer:
instruments are very important to the direction of the personal information and concerns about the direction
