Answer:
C) 3, 4, 5
Step-by-step explanation:
The rule for Pythagorean Triple is:
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
3, 4, 5 is one of the most commonly known triple and it proves the triple rule since
[tex] { 3}^{2} + {4}^{2} = {5}^{2} [/tex]
Find the kissing side round your answer to the nearest tenth
Answer:
x = 8.9
Explanation:
The sine ratio for 43 degrees gives
[tex]\sin 43^o=\text{opposite/hypotenuse}[/tex]Now, the side opposite to the 43 degree angle is x
find the domain of the graphed function. A) x ≥ - 4 B) - 4 ≤ x ≤ 4 C) x is all real numbers D) - 4 ≤ x ≤ 2
Given data:
The given graph.
The domain is the value of x, for the given function domain is,
[tex]-4\leq x\leq2[/tex]Thus, the domain is
the piecewise graph shows the price charged by a dog groomers based on a dog's weight what is the piecewise function that represents the graph?
Notice that the empty circle means that the point circled doesn't belong to the range of the function. Otherwise, the fulfilled circle means the point belongs to that range.
The first horizontal line represents the values of the function for x in the interval 0 < x ≤ 15 (notice the empty circle in point (0, 35) ).
Since this line is horizontal, it means that the function has the same value for all those x's:
f(x) = 35, for 0 < x ≤ 15
Now, let's look at the other horizontal line. It represents the values of the function for all x's in the interval 15 < x ≤ 40 (again, notice the empty circle in point (15, 40) ).
Again, since it's a horizontal line, the function has the same value for all those x's:
f(x) = 40, for 15 < x ≤ 40
Finally, the third line has a slope that we have to consider in order to find the form of the function for the last values of x.
We can find the slope in the following way:
1. first, we choose two points in this line whose coordinates are easy for us to identify. Let's take the points (40, 40) and (45, 50).
2. then, we calculate the difference between the y values of these two points:
y2 - y1 = 50 - 40 = 10
3. then, we calculate the difference between the x values of these two points (remember to take the second one minus the first one):
x2 - x1 = 45 - 40 = 5
4. now, we divide the y's differences by the x's differences (this will be the slope m):
m = (y2 - y1)/(x2 - x1) = 10/5 = 2
Now we know the slope m, we write the function of this line in the form:
f(x) - f(x0) = m * (x - x0)
f(x) - f(x0) = 2 * (x - x0)
Finally, to find the final form of this function, we choose any point in the line and use its x value replacing x0, and its y value replacing f(x0). Let's use the point (40, 40):
f(x) - f(x0) = 2 * (x - x0)
f(x) - 40 = 2 * (x - 40)
f(x) - 40 = 2x - 80
f(x) = 2x - 80 + 40
f(x) = 2x -40
Notice that this function for x = 40 has to assume the same value as the one we find for x = 40 using the function for the second horizontal line (f(x) = 40 ), because they both are defined for the same point:
f(x) = 2x -40
f(40) = 2*40 - 40 = 80 - 40 = 40
For this reason, as the second line already defines the function for x = 40, we can write the third part of the function only for values above x > 40.
Therefore, the function that represents the whole graph is:
f(x) = 35, for 0 < x ≤ 15
f(x) = 40, for 15 < x ≤ 40
f(x) = 2x -40, for x > 40
What can be concluded from the graph shown here?
The correct option regarding the skewness of the given distribution is:
The data is clumped to the right.
How to find the skewness of the distribution?To find the skewness of the distribution, we need to look at the mean and the median of the distribution.
The mean is the sum of all the observations in the distribution divided by the number of observations. The graph shows the number of times that each observation appears, hence the mean is found as follows:
Mean = (1 x 2 + 2 x 5 + 3 x 8 + 4 x 2 + 5 x 12 + 6 x 7 + 7 x 13 + 8 x 3 + 9 x 5 + 10 x 11)/(2 + 5 + 8 + 2 + 12 + 7 + 13 + 3 + 5 + 11) = 6.12.
The median is the middle term of the distribution. There are 68 terms in the distribution, hence the median is the observation in which the count reaches 34. Then:
Observation 1: Count 2.Observation 2: Count 2 + 5 = 7.Observation 3: Count 7 + 8 = 15.Observation 4: Count 15 + 2 = 17.Observation 5: Count 17 + 12 = 29.Observation 6: Count 29 + 7 = 36 > 34.Hence the median is of 6, which is less than the mean. Since the median is less than the mean, the data is right skewed, that is, clumped to the right.
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You want to build a deck in your back yard. The deck will be 14 feet long and 12 feet wide. If you will put railing along all four sides of the deck, how many feet of railing are needed?A) 26 feetB) 38 feetC) 52 feetD) 104 feet
C) 52 feet
Explanation:
Since the deck will be 14 feet by 12 feet and it has four sides, we can deduce that it's a rectangle.
Therefore all you need to do is sum up all the sides together
14 + 14 + 12 + 12 => 14 * 2 + 12 * 2 = 52 feet
An elevator ascends at a rate of 29.6 feet per second. If a building is 1,450 feet tall,
about how long would it take for the elevator to travel from the ground floor to the roof?
OA. 0.49 minute
O B. 0.82 minute
OC. 4.9 minutes
OD. 8.2 minutes
Elevator will take 0.82 minute for travel from the ground floor to the roof. (Option B is correct).
rate by an elevator ascends = 29.6 feet per second
height of the building = 1,450 feet
Time to travel from the ground floor to the roof is calculated as :
we use rate formula.
i.e
rate = distance/ time
time = distance/rate
time = 1450/ (29.6 feet/sec )
time = 1450/29.6
= 48.98sec
as we know
60 second = 1mint
1 second = 1/60 minutes
therefore,
time = (48.98 / 60) minutes
time = 0.8163
time = 0.812 minutes
Elevator will take 0.82 minute for travel from the ground floor to the roof. (Option B is correct).
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Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth. cos 12° = ____
Cos 12° expressed as an integer or as a decimal
[tex]\begin{gathered} \cos 12^0\text{ = 0.978} \\ \cos ^{}12^0\text{ = 0.99 (nearest hundredth)} \end{gathered}[/tex]Hence the value of cos 12° as a decimal to the nearest hundredth = 0.99
100 points asap
Tisha and her academic team are working to go to state finals. They must have a certain number of points, T, to advance. They have had three local matches, b, c and d, and will attend a district match. District match points count for four times the number of points than local matches do. Choose the equation that would help Tisha find how many points they need to earn in the district match, a, to advance.
a equals T over 4 minus b minus c minus d
a equals T minus b minus c minus d all over 4
a equals T plus b plus c plus d all over 4
a = 4(T − b − c − d)
The equation for Tisha and her team is a equals T plus b plus c plus d all over 4 or , a = (T-b-c-d)/4
An equation is created by joining two expressions with the equals sign ("=").
The expressions on each side of the equals sign are referred to as the equation's "left hand side" and "right hand side." In equations, the right side is commonly thought of as zero. This can be accomplished by subtracting the right hand from both sides, provided the generality is not compromised. An equation is comparable to a scale used to weigh stuff. The scale will balance and the weights will be regarded as being equal when the two pans are filled with the same volume of anything (such as grain).The points that are earned from the three local matches are b , c, and d.
points earned from the district game = 4a
The total points earned is T
Therefore forming the equation:
T = (4a + b + c + d )
Now we make a the subject of formula:
or , a = ( T - b - c - d) / 4
Therefore the required equation is a equals T plus b plus c plus d all over 4 .
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Answer:
a = (T-b-c-d)/4
Step-by-step explanation:
took test
i need help with this. please someone i’m begging lol
The inverse of the given equation is given by f⁻¹(x) = (x+8)²/49 - 8
What is an equation?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Equations are used to describe geometric shapes in Cartesian geometry. Since the investigated equations, such as implicit equations or parametric equations, have an unlimited number of solutions, the goal has changed. Now, one utilizes equations to analyze the attributes of figures rather than explicitly providing the solutions or counting them, which is impossible. The fundamental concept of algebraic geometry, a significant branch of mathematics, is presented here. Equations involving one or more functions and their derivatives are known as differential equations. By identifying a derivative-free formulation for the function, they may be resolved. Processes involving rates are modeled using differential equations.
given equation,
f(x) = 7√(x+8) - 8
y = 7√(x+8) - 8 (replace f(x) with y)
x = 7√(y+8) - 8 (interchange x and y)
y = (x+8)²/49 - 8 (solve for y)
f⁻¹(x) = (x+8)²/49 - 8 (replace y with f(x))
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at a local gym you can either pay $90 for money pass then pay for dollars each time you go to the gym or you can pay $13 each time you go with no monthly pass fee what is the cost where the two options are the same?
Option A
$90 + $4 each time
Option B
$13 each time
Procedure
Equations
[tex]\begin{gathered} (1)\to C=90+4t \\ (2)\to C=13t_{} \\ \\ 90+4t=13t \\ 13t-4t=90 \\ 9t=90 \\ t=\frac{90}{9} \\ t=10 \end{gathered}[/tex]The cost would be
[tex]\begin{gathered} C=90+4\cdot10 \\ C=90+40 \\ C=130 \end{gathered}[/tex]The answer would be $130
A right triangle has vertices P(-2,5), Q(5,2) and R(8,9). Whatare the coordinates of the midpoint of the hypotenuse?
Answer:
D. (3, 7)
Explanation:
First, we need to draw the triangle to identify the hypotenuse, so using the points P(-2, 5), Q(5, 2), and R(8, 9), we get:
Therefore, the hypotenuse is side PR.
Then, the midpoint of a segment that goes from (x1, y1) to (x2, y2) is
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]So, replacing (x1, y1) = P(-2, 5) and (x2, y2) = R(8, 9), we get that the midpoint of the hypotenuse is
[tex](\frac{-2+8}{2},\frac{5+9}{2})=(\frac{6}{2},\frac{14}{2})=(3,7)[/tex]Therefore, the answer is D. (3, 7)
what number 14 is 70 percent of
Answer:
20
Step-by-step explanation:
70% of x = 14
0.7x = 14
x = 14/0.7
x = 20
For the attached blue bird, find the quadratic equation written in vertex form
The vertex form of a quadratic equation is expressed as
y = a(x - h)^2 + k
where
h and k are the x and y x and y coordinates of the vertex of the parabola.
a is the leading coefficent
From the information on the graph,
h = 13
k = 13
By substituting these values into the formula,
y = a(x - 13)^2 + 13
On the graph, when x = 26, y = 0
Substituting these values into the equation, we have
0 = a(26 - 13)^2 + 13
0 = a * 13^2 + 13
0 = 169a + 13
169a = - 13
a = - 13/169
a = - 1/13
By substituting a = - 1/13, h = 13 and k = 13 into the verte form equation, the quadratic equation written in vertex form is
y = - 1/13(x - 13)^2 + 13
Basil N. Thyme is putting in a triangular herb garden with sides of 2 yards, 3 yards and 4 yards. He needs to know the area of his garden so he would know how many herb plants to germinate in his greenhouse.. What is the area of his herb garden to the nearest square foot? (convert yards to feet.)
26.14 ft²
1) Considering that triangular herb:
2) Let's calculate the area of that triangle using the Heron formula so that we can not need to find the height:
2.1) Calculate the Perimeter:
2P = 2+3+4
2P = 9 yd
2 yards = 6 ft
3 yd = 9ft
4 yd = 12 ft
Converting into feet
9 yards = 27 feet
And the Semi perimeter (half the perimeter):
P = 9/2
27/2
Now we can plug that into Heron's Formula:
[tex]\begin{gathered} A=\sqrt[]{p(p-a)(p-b)(p-c)} \\ A=\sqrt[]{\frac{27}{2}(\frac{27}{2}-6))(\frac{27}{2}-9)(\frac{9}{2}-12)} \\ A=\frac{27\sqrt[]{15}}{4}\approx26.14 \end{gathered}[/tex]3)
So the area of that triangular garden is approximately 26.14 ft²
11.) A system of two linear equations can have no solution, onesolution, or infinitely many solutions. Draw graphs or write aparagraph explaining how a graph of the two equations wouldappear for each of these possibilities,Ihp
The solution of a system of two linear equations interprets the point of intersection of the two lines geometrically
When the two lines intersect each other at a point, then the system of two linear equations has a unique solution.
If two linear equations in the given system represent two lines parallel to each other, then the system becomes inconsistent and in that case, it has no solution.
If the system is dependent i.e. there is only one linear equation in two variables, then every point on the line is the solution of the equation.
So, in that case, it has infinitely many solutions.
Learning Log9-11-20Provide a complete written response to the prompts. You must include any graphs or sketchesthat apply1. Explain how the points of intersection of graphs of functions can be determined (orverified) using the multiple representations of a system of equations. Provide examples anda sketch.I
Previous concepts
We need to take in count that the intersection or the values of x that satisfy a system equations represent the solutions.
We have 3 possible cases when we have a system of equations:
1) One Solution
2) No solutions
3) Infinite solutions
Also we know that if we have one or more solutions then the system would be consistent otherwise would be inconsistent.
Solution
Let's analyze the situation with examples.
1) Case 1: One solution.
We have the following system of equations :
[tex]y=3x+2,y=-2x+1[/tex]We can graph both equations and we can see this:
And as we can see we have an intersection point (-0.2, 1.4) with just one solution for this case.
2) Case 2: No solutions
We have the following system of equations : y = 3x + 2, y = 3x + 1
4
A drilling crew dug to a height of -32²/12
feet during their first day of drilling. On
the second day, the crew dug down 192²/23
feet more than on the first day. Describe
the height of the bottom of the hole after
the second day.
The the height of the bottom of the hold after second day is 1517.45 feet.
What is height?
Height is a way to measure someone or something from base to top or head to toe
Day 1 height = -[tex]32^{2}/12[/tex] feet
Day 2 height = [tex]192^{2} /23[/tex] more than first day
=36864/23+(-1024/12)
=1602.78-85.33
=1517.45 feet
Therefore, the height of the bottom of the hole after the second day is 1517.45 feet.
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Which of the following best describes the climate and vegetation of the savanna?
What’s the correct answer answer asap for brainlist
Option (D) "Few trees, mostly grass, rich soil, cold winters, the average rainfall and good for agriculture" perfectly describes the climate and vegetation of Savana.
What is the climate & vegetation of Savana?The savanna also spelled savanna, is a type of vegetation that thrives in hot, seasonally dry climates and is distinguished by an open tree canopy (i.e., scattered trees) above a continuous understory of tall grass (the vegetation layer between the forest canopy and the ground). Scrub, grasses, and sporadic trees make up the savanna vegetation, which is found near water sources such as aquifers, seasonal rivers, and water holes. Additionally, it has few trees and is primarily grass, with rich soil, cold winters, average rainfall, and favorable agricultural conditions.Animals and plants must adjust to extended dry spells. Many plants, such as the acacia tree with its tiny, waxy leaves and thorns, are xerophytic.Therefore, option (D) "Few trees, mostly grass, rich soil, cold winters, the average rainfall and good for agriculture" perfectly describes the climate and vegetation of Savana.
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Answer:
C
Step-by-step explanation:
Its the Little Rain
Find the maximum and minimum values of the function for this region.
For a discontinuous function ,maximun value is found by replacing every region for the values x ,y
So then for x≤2. and y≤1 and f(x,y) = x +y
theres a maximum value but no minimum ( because is minus infinite). The maximum value for this area is
x+y = 2+1= 3
Now for area y ≥-2x -3
rearrange the equation as y+2x ≥ -3
is the equation of a plane , the plane or area that goes over the straight line y= -2x-3.
So now replace y = -2x-3 in the function f(x,y) = x+y
then f(x,y)= x -2x-3 = -x-3
Now the third region is y≥ 2x -3
this is the area over a line with slope positive equal to 2
now replacing again for this area we find
f(x,y) = x+y = 2x-3 +x = 3x -3
because x≤2. So then replace x by 2 in f(x,y) to find the maximum value
f(x,y) in 2nd region is f(x,y) = -x-3= -2-3= -5
f(x,y) in 3rd region is f(x,y) = 3x -3= 3•2 -3= 3
Finally in conclusion, the máximum value is 3 , the minimum value is -5
HELP PLEASEEEEEEEEEEE!! ILL MARK BRAINLIEST
The answer is follows,
[tex]-3^5[/tex] = -243
[tex](-3)^5[/tex] = -243
[tex]\left(-3^5\right)[/tex] = -243
[tex]-\left(-3\right)^5[/tex] = 243
An exponent is a number or letter written above and to the right of the base of a mathematical expression.
What is meant by exponent?The number of times a number is multiplied by itself is referred to as its exponent. For instance, 2 to the third (written as 23) means: 2 x 2 x 2 = 8. An exponent is a number that is superscripted over another number. In other words, it denotes that the base has been raised to a certain level of power. Other names for the exponent include index and power. If m is a positive number and n is its exponent, the expression mn denotes that m has been multiplied by itself n times. Power is defined in mathematics as a base number raised to the exponent, where the base number is the factor multiplied by itself and the exponent is the number of times the same base number is multiplied.To learn more about exponent, refer to:
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10. Determine whether the question can be answered using permutations or combinations.Explain your choice then answer the question. (3 points each)a.On a sailboat there are 6 signal flags. The order the flags are strung on the mastdetermines the signal being sent. How many 3-flag signals can the captain send?b. You are taking an online geometry quiz in which 6 questions are randomly selected froma test bank of 50 questions. How many versions of the quiz are possible?
a.
The question can be answered using the permutations because the order of the flag strung on the mast determines the signal being sent.
Since there are 6 signal flags and the captain has to send a 3-signal flag. So, the number of signals that can be sent are:
[tex]\begin{gathered} _6P_3=\frac{6!}{\left(6-3\right)!} \\ =\frac{6\times5\times4\times3!{}}{3!} \\ =6\times5\times4 \\ =120 \end{gathered}[/tex]Thus, the answer is 120.
b.
The question can be answered using the combination because the questions are randomly selected.
Since the total number of questions is 50 and the number of questions that have to be selected is 50.
So, the number of versions of the quiz that are possible are:
[tex]\begin{gathered} _{50}C_6=\frac{50!}{\left(50-6\right)!6!} \\ =\frac{50\times49\times48\times47\times46\times45\times44!}{44!6!} \\ =\frac{50\times49\times48\times47\times46\times45}{6\times5\times4\times3\times2\times1} \\ =\frac{11441304000}{720} \\ =15890700 \end{gathered}[/tex]Thus, the answer is 15890700.
1/3 |2x+3|-1 is less than or equal to 8
Adding 1 to both sides gives
[tex]\frac{1}{3}|2x+3|\leq9[/tex]and then multiplying both sides by 3 gives
[tex]|2x+3|\leq27[/tex]At this point, this absolute value inequality can be decomposed into two separate inequalities
[tex]\begin{gathered} -(2x+3)<27 \\ (2x+3)<27 \end{gathered}[/tex]We first solve the first inequality.
Multiplying both sides by -1 reverses the sign of the inequality and gives
[tex]2x+3>-27[/tex]subtracting -3 from both sides we get
[tex]2x>-30[/tex]and finally dividing both sides by 2 gives
[tex]x>-15.[/tex]That is the first solution, the second solution is given by the second inequality 2x+ 3 <27.
Subtracting 3 from both sides and then dividing the equation by 2 gives
[tex]x<12[/tex]Hence, the solution to our inequality is
[tex]-15
Hi please help me thanks!
Answer:
Year Jessica Tom Who earns more?
1 $400 $400 They earn the same amount
2 $408 $400 Jessica earns more
3 $416 $400 Jessica earns more
Step-by-step explanation:
At simple interest, the amount of interest is the same each year
First year: Since compounding takes place only at the end of the year, both of them earn the same amount of interest
Interest earned = 20,000 x 0.02 = $400
Same for both boxes for first year
Both of their deposits will increase by $400 to $20,400
For second year
Jessica's interest is calculated on 20,400 = 20,400 x 0.02 = $408
Her deposit value at the end of year 2 = 20, 400 + 408 = $20,808
Tom's interest is calculated on the original deposit since it is simple interest. So in year 2, Tom still makes $400.
In year 2 Jessica earns more interest than Tom
Jessica: $408
Tom : $400
For third year, Jessica's interest is calculated on her deposit value of 20,800 = 20,800 x 0.02 = $416
Tom's interest for 3rd year is the same as for the previous years = $400
So in third year, Jessica earns more
solve2(5t-25)+5t<-80
You have the following inequality:
2(5t - 25) + 5t < -80
In order to solve the previous inequality, proceed as follow:
Expand the factor left side and simplify like term:
2(5t) - 2(25) + 5t < -80
10t - 50 + 5t < -80
15t < -80 + 50
15t < -30
Divide by 15 both sides and simplify:
t<-30/15
t<-2
Hence, the solution to the given inequality is t<-2
Brand A has a recognition value worth 43$ billion more than brand B. If the total value of these two brands is 107$ billion, find the value of each of the brands.
The value of Brand A is $75 billion and Brand B is $32 billion.
What is an expression?An expression is used to illustrate the relationship between the variables.
Let brand B value = x
Brand A has a recognition value worth 43$ billion more than brand B. This will be x + 45
The total value of these two brands is 107$ billion.
The expression to find the value is for each brand will be:
x + x + 43 = 107
2x + 43 = 107
Collect like terms
2x = 107 - 43
2x = 64
Divide
x = 64/2
x = 32
Brand B is $32 billion
Brand A = x + 43 = 32 + 43 = $75 billion.
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Turica has 4 different pen colors: Red, purple, blue, and green. She has 8 pens of each color. She selects a pen at random.What is the probability she will select a green pen?A: 1/2B: 1/3C: 1/4D: 1/32
If y varies directly as x, and y is 48 when x is 6, which expression can be used to find the value of y when x is 2?48O y - 3 (2)O y = 4g (2)(48)(B)O y--(48)(6)
The phrase y varies directly as x can be understood that y gets bigger when x gets bigger as well, this can be written as,
[tex]\frac{y_1}{x_1}=\frac{y_2}{x_2}[/tex]then, using the point (6,48) find the value when x is 2,
[tex]\frac{48}{6}=\frac{y_2}{2}[/tex]clear for y2,
[tex]y_2=\frac{48}{6}(2)[/tex]Answer:
[tex]y_=\frac{48}{6}(2)[/tex]Write the mixed number -5 4/9 as a decimal
Write the mixed number -5 4/9 as a decimal
we have the number
5 4/9
step 1
convert to an improper fraction
5 4/9=5+4/9=49/9
and
49/9=5.444444...
Part 2
we have the number
7/-35-------> is the same that -7/35
simplify
Divide by 7 the numerator and denominator
-1/5
Find out an equivalent fraction
Multiply by (3/3)
-3/15
therefore
we have
7/-35
-7/35
-1/5
-3/15
decimal number
-1/5=-0.20
Taylor's dad lifted 80°g of weight how much more did Taylor's dad left than Davin record your answering grams
The weight that Taylor's dad lifted higher will be 30g.
What is weight?It should be noted that weight simply means the mass that a body contains.
From the information, Taylor's dad lifted 80g of weight and Davin's dad lifted 50g of weight.
The weight that Taylor's dad lifted more than Davin's dad will be:
= Weight of Taylor's dad - Weight of Davin's dad
= 80 - 50
= 30g
The difference is 30g.
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Taylor's dad lifted 80g of weight and Davin's dad lifted 50g of weight. How much more did Taylor's dad lift than Davin?
Find each angle measure in the figure. (x + 30) and The angle measures are Use the equation to justify your answer. x + (x +30) + 2x =
Answer:
37.5, 75 and 67.5 degrees
Explanation:
The sum of angle in the given triangle is 180 degrees
Hence;
x + x + 30 + 2x = 180
4x + 30 = 180
4x = 180 - 30
4x = 150
x = 150/4
x = 37.5 degrees
Get angle 2x
2x = 2(37.5)
2x = 75 degrees
Get angle x + 30
x + 30 = 37.5 + 30
x = 30 = 67.5 degrees
Hence the angles of the triangle are 37.5, 75 and 67.5 degrees
