The length in feet of the pole is 13 ft.
What is Pythagoras theorem?The right-angled triangle's relationship between its three sides is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The square of a triangle's hypotenuse is equal to the sum of its other two sides' squares, according to the Pythagoras theorem. Let's learn more about the Pythagoras theorem, its proofs, and its equations before moving on to cases that have been solved using the triangle and square Pythagoras theorem. The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this.
Use the Pythagorean relationship:
c²= a² + b²
= 5² + 12²
= 25 + 144
= 169
c = 13
To know more about Pythagoras theorem ,visit:
brainly.com/question/343682
#SPJ13
6
Pens cost 20p each.
Rulers cost 60p each.
Saj buys some pens and some rulers.
He buys 8 rulers.
The total cost is £10
How many pens does he buy?
Answer:
26 pens
Step-by-step explanation:
Let P and R be the numbers of Pens and Rulers Saj purchases.
The cost of P Pens and R Rulers:
Pens = P(20p)
Rulers = R(60p)
P(20p) + R(60p) = £10
P(0.20) + R(0.60) = 10
R = 8
P(0.20) + (8)*(0.60) = 10
P(0.20) + 4.8= 10
P(0.20) = 5.2
P = (5.2/0.20)
P = 26 pens
CHECK:
8 Rulers = 8*(60p) = 480p
26 Pens = 26*(20p) = 520p
Total = £10
n is an integer. What are the possible values of n? A -2, -1, 0, 1, 2, 3, 4, 5, 6 B BUDE -2 < n ≤ 6 C -1, 1, 2, 3, 4, 5, 6 -2, -1, 0, 1, 2, 3, 4, 5 -2, -1, 0, 1, 2, 3, 4, 5, 6, 7 E -1, 0, 1, 2, 3, 4, 5, 6
Answer: Choice E
Explanation:
The given inequality means n is between -2 and 6. We exclude -2 itself, but include 6.
The set of integer values is -1, 0, 1, 2, ..., all the way up to 6.
What is DA equal to? Brainiest if correct and please show your answer.
Answer:
DA is equal to 25 or BAStep-by-step explanation:
ABC
ADC
Since we know that line CA is equal to line CA because of reflexive propertyAngle BAC and DAC are equal because of definition of an angle bisectorAngle ABC and ADC are equal because of definition of an angle bisectorThis will give us ASA, proving to us that all sides and angles are congruent (this was already given to us)So, if BA is 25, and we know that BA is congruent to DA, this tells us that DA is 25which pair of equations is a set of parallel lines ? a. y = x + 2 and y = 2 b. x = 2 and y = 4
Neither of the pairs of linear equations has the same slope in both lines, so we don't have parallel lines.
Which pair of equations is a set of parallel lines?A general linear equation is of the form:
y = m*x + b
Where m is the slope and b is the y-intercept.
Two linear equations are parallel only if both lines have the same slope and a different y-intercept.
In this case, the lines given are:
y = x + 2 and y = 2.
x = 2 and y = 4
Neither of these are particularly parallel lines (because in both pairs we have different slopes), so we conclude that there is no correct option.
Learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
y=3/5x+3 graph the line
We want to graph the line:
[tex]y=\frac{3}{5}x+3[/tex]For doing so, we will choose two different x-values, and we will find its correspondent y-values. This gives us two different points, and when we trace the line that passes through those points, we will have the line we wanted.
In this exercise, we will choose x=0, and x=5.
For x = 0
[tex]y=\frac{3}{5}(0)+3=0+3=3[/tex]This gives us the point (0,3).
For x = 5
[tex]y=\frac{3}{5}(5)+3=\frac{15}{5}+3=3+3=6[/tex]This gives us the second point: (5,6).
Now, graphing the points on a cartesian plane, and drawing the line between them, we obtain:
the length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of 8 cm/s. when the length is 7 cm and the width is 4 cm, how fast is the area of the rectangle increasing (in cm2/s)?
The rate at which the area is increasing is 95cm/sec² .
Let us take the variable a to be the length of the rectangle and take the variable to b be the width of the rectangle.
We know that the area of the rectangle is given by A=a × b
Now differentiating with respect to t we get :
[tex]\frac{dA}{dt} = w\times\frac{da}{dt} +l\times\frac{db}{dt}[/tex]
Substituting the values we get that the rate of increase in the area is :
Rate of increase = (32 + 63) cm/sec² = 95 cm/sec²
A constant function is also regarded as linear in this sense because it is a polynomial of degree zero, or the zero polynomial.
A line segment represents the graph of a single variable.In this context, a function that is also a linearly map may be referred to as a homogeneous linear function or a linear form (the other meaning). In the context of linear algebra, the scalar-valued affine mappings are functions of degree 0 or 1.To learn more about area visit:
https://brainly.com/question/27683633
#SPJ4
Marques works in a department store selling clothing. He makes a guaranteed salary of $200 per week, but is paid a commision on top of his base salary equal to 10% of his total sales for the week. How much would Marques make in a week in which he made $750 in sales? How much would Marques make in a week if he made x dollars in sales?
The most appropriate choice for percentage will be given by -
Total salary of Marques in a week = $825
If Marques makes $x in sales, his total salary in a week = $([tex]750 + \frac{x}{10}[/tex])
What is Percentage?
Suppose there is a number and that number has to be expressed as a fraction of 100. The fraction is called percentage. For example 2% means [tex]\frac{2}{100}[/tex]
Here,
Guarantee salary of Marques = $200
Sales made by Marques in a week= $750
Percentage commission on total sales = 10 %
Commission received by Marques = [tex]\frac{10}{100} \times 750\\[/tex]
= $75
Total salary of Marques in a week = $(750 + 75)
= $825
If Marques makes $x in sales, his total salary in a week = $([tex]750 + \frac{10}{100}\times x[/tex])
= $([tex]750[/tex] + [tex]\frac{x}{10}[/tex])
To learn more about percentage, refer to the link -
https://brainly.com/question/24304697
#SPJ9
What is the answer to this ive been doing this all day and still cant figure it out
The proof explained below shows that the triangles are congruent by the AAS congruence theorem.
What is the AAS Congruence Theorem?The AAS congruence theorem states that two triangles can be proven to be congruent to each other if the two angles and a non-included side in one triangle is equal or congruent to two corresponding angles and a corresponding non-included sides in the other triangle.
This implies that, once the criteria needed prove that two triangles are congruent by the AAS congruence theorem are two pairs of congruent angles and a pair of non-included congruent sides.
Using the AAS congruence theorem, the two-column proof that shows each statement and the reason are explained below.
Statement Reason
1. CA bisects angle BAD 1. Given
angle B ≅ angle D
2. Angle CAB ≅ angle CAD 2. Congruent angles formed from bisection
3. Side AC ≅ side CA 3. Reflexive property
4. Triangle ABC ≅ triangle ADC 4. AAS congruence theorem
Thus, the above reasons and statements shows that the two triangles, triangle ABC and triangle ADC, are congruent by the AAS congruence theorem.
Learn more about AAS congruence theorem on:
https://brainly.com/question/3168048
#SPJ1
3. The diameter of a spherical balloon shrinks to one-half of its original size.How does this affect the volume?Hint: Test two scenarios and compare the volumes! Show your work!!A. The volume is cut in halfB. The volume doublesC. The volume is 1/8 the original volumeD. The volume is 1/4 the original volume
Answer:
C. The volume is 1/8 the original volume
Explanation:
Step 1. To find how the volume changes if the diameter is reduced to one-half of the original size, we will test two scenarios:
• In the first scenario, the diameter will be 2, and in the second scenario, the diameter will be one-half of 2 which is 1.
We will find the volume for these two cases and see how it changes.
Step 2. For a diameter of d=2.
If the diameter is 2, the radius is:
[tex]\begin{gathered} r=d/2 \\ r=2/2 \\ r=1 \end{gathered}[/tex]Using the volume formula for a sphere:
[tex]V=\frac{4\pi}{3}r^3[/tex]In this case:
[tex]V=\frac{4\pi}{3}(1)^3[/tex]We will call this volume, V1:
[tex]V_1=\frac{4\pi}{3}[/tex]Step 3. Now we will find the volume for the second case in which the diameter is d=1.
The radius is:
[tex]\begin{gathered} r=d/2 \\ r=1/2 \\ \end{gathered}[/tex]Using the same formula for the volume:
[tex]V=\frac{4\pi}{3}(\frac{1}{2})^3[/tex]Solving the operations:
[tex]V=\frac{4\pi}{3}(\frac{1}{8})^[/tex]We will call this V2:
[tex]V_2=\frac{4\pi}{3}(\frac{1}{8})^[/tex]Step 4. As you can see, the first part of the previous expression is V1:
[tex]\begin{gathered} V_{1}=\frac{4\pi}{3} \\ V_2=\frac{4\pi}{3}(\frac{1}{8}) \end{gathered}[/tex]Therefore:
[tex]V_2=V_1(\frac{1}{8})[/tex]The second volume is the first volume multiplyed by 1/8 ⇒ it is 1/8 of the original volume.
Answer:
C. The volume is 1/8 the original volume
Type the number of the spelling rule that applies to the word.
noisy
Answer:
Step-by-step explanation:
if a word ends in a consonant plus "y" , we change "y" to "i" and add "es" to form the plural; "er" for comparative and "est" for superlative
noisiest and noisier
Answer:
Step-by-step explanation:
5
10 miles per hour equal feet per second
Let's recalll that:
• 1 mile per hour = 1.46667 feet per second
Therefore:
• 10 miles per hour = 1.46667 * 10 feet per second
,• 10 miles per hour = 14.6667 feet per second, Khalil!
-3/2 = -2/3w - 4/5 solve for w and simplify your answer as much as possible
Hello!
Here are all three solutions to the given equation.
Exact Form:
[tex]w=\frac{21}{20}[/tex]
Decimal Form:
[tex]w=1.05[/tex]
Mixed Number Form:
[tex]w=1\frac{1}{20}[/tex]
Hope this helps!
Question 10 of 183Consider the line y = -x +6.(a) Find the equation of the line that is parallel to this line and passes through the point (2, 6).(b) Find the equation of the line that is perpendicular to this line and passes through the point (2, 6).Note that a graphing calculator may be helpful in checking your answer.
Answer:
Part A:
[tex]y=-x+8[/tex]Part B:
[tex]y=x+4[/tex]Step-by-step explanation:
Part A:
Remember that two parallel lines have the same slope. This way, we can conclude that the slope of this particular line is:
[tex]m_a=-1[/tex]Since we already know that this line passes through point (2,6), we can use this point, the slope we've found and the slope-point form to get an equation for the line:
[tex]\begin{gathered} y-6=-1(x-2) \\ \rightarrow y-6=-x+2 \\ \\ \Rightarrow y=-x+8 \end{gathered}[/tex]Therefore, we can conclude that the equation of this line is:
[tex]y=-x+8[/tex]Part B:
Remember that the product between the slopes of two perpendicular lines is -1. This way, we'll have that:
[tex]\begin{gathered} -1\times m_2=-1 \\ \\ \Rightarrow m_2=1 \end{gathered}[/tex]Since we already know that this line passes through point (2,6), we can use this point, the slope we've found and the slope-point form to get an equation for the line:
[tex]\begin{gathered} y-6=(x-2) \\ \rightarrow y=x+4 \end{gathered}[/tex]Therefore, we can conclude that the equation of this line is:
[tex]y=x+4[/tex]a report on high school graduation stated that 85 percent of high school students graduate. suppose 3 high school students are randomly selected from different schools. what is the probability that none will graduate?
The probability that exactly none will graduate is [tex]0.003375[/tex].
What is probability?
Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes.
Step-by-step explanation:
Let [tex]X[/tex] be the random variable for the number of students who graduate.
Binomial distribution theorem tells that, [tex]P(X=x)=C(n , x)p^xq^{n-x}[/tex].
Here [tex]p=[/tex]probability of success on a single trial, [tex]q=[/tex]probability of failure on a single trial, [tex]n=[/tex] number of trials.
Given that [tex]p=0.85, q=1-p=1-0.85=0.15[/tex] and [tex]n=3.[/tex]
[tex]P(X=x)=C(3 , x)0.85^x0.15^{3-x}[/tex]
When [tex]3[/tex] students are randomly selected the probability that exactly none will graduate is given by,
[tex]P(X=0)=C(3 , 0)0.85^00.15^{3-0}[/tex]
[tex]P(X=0)=\frac{3!}{0!(3-0)!} 0.15^{3}[/tex]
[tex]P(X=0)=0.15^{3}[/tex]
[tex]P(X=0)=0.003375[/tex]
Hence the probability that exactly none will graduate is [tex]0.003375[/tex].
To learn more about probability from the given link
https://brainly.com/question/25870256
#SPJ4
Please help me, it is sooooo important
Answer:
1: figures a and b
2: figures a and b
3: figure a
Step-by-step explanation:
2 & 3:
all squares are rectangles, but not all rectangles are squares
Hope this helps!
suppose 52% of the students in a university are baseball players. if a sample of 436 students is selected, what is the probability that the sample proportion of baseball players will be greater than 45%? round your answer to four decimal places.
Probability of proportion will be greater than 3.18
What is meant by Probability of Proportion?Probability of Proportion: Probability represents the chances of some event happening. It is theoretical. Proportion summarizes how frequently some event actually happened
Population Proportion, p=0.52
sample proportion p'=0.45
sample size be n =436
probability of proportion will be greater than 52%
[tex]p(p' > 0.45)=p(p'-p\sqrt{p(1-p)/n} )[/tex]
[tex]=-p(z > (0.45-0.52)/\sqrt{0.52((1-0.52)/436}[/tex]
=P(z>-3.18)
probability of proportion will be greater than 3.18
To learn more about Probability of Proportions visit:
brainly.com/question/19261247
#SPJ4
A class measured the radius r, circumference C, and area A of various circular objects. The results are recorded in thistable. b. Does the equation A=1/2*r* C describe the relationships in the table? Explain your reasoning.YesNor (cm) C (cm) A (cm)42550
Equation:
A =1/2 * r * C
Replace with the values from the table and check the equation:
First row:
50 = 1/2*4*25
50= 50 TRUE
Second row:
78.5= 1/2*5*31.5
78.5= 78.75 FALSE
Since one equality is false, the equation Doesn't describe the relationship-
Answer : NO
Solve for X round to nearest tenth
Answer:
the answer for this question is 35.0
[tex]x^{2} + 2x _5=0[/tex]
Step-by-step explanation:
Substitute the values
a
=
1
,
b
=
−
2
, and
c
=
−
5
into the quadratic formula and solve for
x
.
2
±
√
(
−
2
)
2
−
4
⋅
(
1
⋅
−
5
)
2
⋅
1
Simplify.
x
=
1
±
√
6
Simplify the expression to solve for the
+
portion of the
±
.
x
=
1
+
√
6
Simplify the expression to solve for the
−
portion of the
±
.
What's a corner of a square? Two lines where they meet
Answer: A square is a shape with four equal-length sides and four corners that are all right angles.
Miguel is going to see a movie and is taking his 5 kids. Each movie
ticket costs $12 and there are an assortment of snacks available to
purchase for $5 each. How much total money would Miguel have to
pay for his family if he were to buy 5 snacks for everybody to share?
How much would Miguel have to pay if he bought a snacks for
everybody to share?
Total cost with 5 snacks:
Total cost with a snacks:
What is the value of x?
Answer:
5
Step-by-step explanation:
(10-x)+(12-x) HELPPPPPPPPPPPPPPPPPP
Answer:
x=-11
Step-by-step explanation:
Steps are in the attachment, but I couldn't include the last step.
The last step is to divide by -2 on both sides.
The final answer then will be x=-11
With the triangle below, find AB when CD is 15
Answer:
30 units
Step-by-step explanation:
point D is the midpoint of the bottom line, and we can infer 2 similar triangles from the markings on the triangle,
15 × 2 =ab
as CD is in the middle of the large triangle, the scale factor from the small triangle to the large triangle is 2.
Write an equation in slope-intercept form of the line that passes through the given points. PLEASE HELLLPPPPPPPPP.....
The equation of the table in slope intercept form is y = - 5 / 2x - 1
How to write equation in slope intercept form?Linear equation can be represented in various form, such as standard form, point slope form and slope intercept form.
But the equation of the table below will be represented in slope intercept form.
The equation in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, using (-4, 9)(-2, 4)
m = 4 - 9 / -2 + 4
m = - 5 / 2
Hence, let's find the y-intercept using (0, -1)
y = - 5 / 2x + b
-1 = - 5 / 2(0) + b
b = -1
Therefore, the equation is y = - 5 / 2x - 1
learn more on slope intercept form here:https://brainly.com/question/16772908
#SPJ1
If y= 4 1/4 when x= 3/4, find y when x= 4 1/2
when y = 17/4, x= 3/4
then assume y varies directly as x
then y =kx
k = y/x
k= 17/4× 4/3
k= 17/3
when x= 3/4, y = 27/34
What is variation?A variation is a relation between a set of values of one component and a set of values of other component.
Direct variation is a type of variation in which two variables go line in line with their values
y= kx where k is the proportionality constant
k = 17/3 when y = 17/4 and x= 3/4
using thesame value of k in the expression k=y/x
and x = 3/4, then
y= 27/34
learn more about direct variation from
https://brainly.com/question/25215474
# SPJ1
Which IRS form is provided at the end of the year by employers, so employees can use it to file taxes?
The IRS form is provided at the end of the year by employers, so employees can use it to file taxes is Form W-2.
What is Form W-2?Form W-2 can be described as the form that is been offered from the Internal Revenue Service which can be considered as the (IRS) tax form .
It should be noted that this form is been used in the United States so that the wages that is been paid to employees as well as their taxes can be reported. withheld from them
It should be noted that the form is been provided when the year is coming to an end by employers.
Read more about Form W-2 at:
https://brainly.com/question/25396013
#SPJ1
Given m ||n, find the value of x and y.
Answer: The correct answer is x=18 and y=59
Step-by-step explanation:
Opposite angles are congruent:
(6x+13) = (7x-5)
Solve for x:
6x+13−7x=7x−5−7x
−x+13−13=−5−13
−x=−18
x=18
Plug x value in for y:
Y=180-(7x-5)
Y=180-(126-5)
Y=180-121
Y=59
Given f(x)=x+2 and g(x)=4-x^2 find the following (g o f)(x)
Given functions are
[tex]\begin{gathered} f(x)=x+2 \\ g(x)=4-x^2 \end{gathered}[/tex]Then,
[tex]\begin{gathered} (g\circ f)(x)=g(f(x)) \\ =g(x+2) \\ =4-(x+2)^2 \\ =4-(x^2+4x+4) \\ =4-x^2-4x-4 \\ =-(x^2+4x) \end{gathered}[/tex]Thus,
[tex](g\circ f)(x)=-(x^2+4x)[/tex]1. What is the value of 18 + (-7) – (-5)
Answer:
16
Step-by-step explanation:
Two negatives make a positive:
18-7+5
Solve the problem left to right:
18-7=11
11+5=16