To get to his parent's house, Isaiah would have to drive due north 9 kilometers. To get to his grandparents' house, he would have to drive due east 12 kilometers. The straight-line distance between the parents' and grandparents' houses is __ kilometers.
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let us represent the question with a diagram for better understanding.
Using Pythagoras theorem
[tex]\begin{gathered} c^2=12^2+9^2 \\ c^2=144+81 \\ c=\sqrt[\square]{225} \\ c=15\text{ km} \end{gathered}[/tex]The distance between the parents and grandparent house = 15 km
Related Questions
9) Higher Order Thinking Make a conjecture about what happenswhen expressions are subtracted in the opposite order. What happenswhen the results are added? Support your conjecture with anexample in which several of the signs are negative.
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Let the two expressions are 6a + 12b - 15c and -2a + 2b + 8c. First, subtract the second expression from the first:
[tex]\begin{gathered} =6a+12b-15c-(-2a+2b+8c) \\ =6a+12b-15c+2a-2b-8c \\ =8a+10b-23c \end{gathered}[/tex]Now, subtract them in the reverse order, subtract the first from the second:
[tex]\begin{gathered} =-2a+2b+8c-(6a+12b-15c) \\ =-2a+2b+8c-6a-12b+15c \\ =-8a-10b+23c \end{gathered}[/tex]The second result is the negative of the first result.
Now, if the results are added then we get the answer zero.
[tex]\begin{gathered} =8a+10b-23c+(-8a-10b+23c) \\ =8a+10b-23c-8a-10b+23c \\ =0 \end{gathered}[/tex]Thus, we can say that when the expressions are subtracted in the opposite order, the results are negative of each other and when the results are added, we get zero as the answer.
Fitness The gym charges $180 for a yearly membership. There are currently1000 members. For every $5 increase in price, the gym will lose 10 members.How much should the gym charge to maximize its revenue?
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Solution:
Let the number of $5 increases be m. We get the following two equations:
new charge = 180 + 5n
membership = 1000 - 10n
thus, the revenue would be:
revenue = (180 + 5n)( 1000 - 10n)
Applying the distributive property, this is equivalent to:
[tex]180000+3200-50n^2[/tex]If we factor this equation, we obtain:
[tex]-50\mleft(n^2-64n-3600\mright)[/tex]notice that this is a parabola and the vertex will yield our answer. The n of the vertex is:
[tex]\frac{64}{2}=32[/tex]Applying this data into the first two equations, we get:
new charge = 180 + 5n = 180 + 5(32)= 340
membership = 1000 - 10n = 1000 - 10(32) = 680
So that, we can conclude that the correct answer is:
The new fee is $340.
Solve for h.
-3/4 - h + 1/3h - 2 = -4/3h -3
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Answer:
h = -3/8
Step-by-step explanation:
-3/4 - h + 1/3h - 2 = -4/3h -3
combine like terms
-2 = -8/4
-3 = -12/4
-2/3h - 11/4 = -4/3h -12/4
2/3h - 11/4 = -12/4
2/3h = -1/4
8/12h = -3/12
8h = -3
h = -3/8
it’s hard to see but y axis is height in feet and x axis is time in seconds anyways I need help with #21
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Q.21:
We are asked what f(3) = 32 means?
In Q.20, we are given the following function
[tex]f(x)=-2x^2+50[/tex]Where f(x) is the height (in feet) of the apple and x is the time in seconds.
If we substittute x = 3 seconds into the function, we get the corresponding height of the apple.
[tex]\begin{gathered} f(3)=-2(3)^2+50 \\ f(3)=-2(9)+50 \\ f(3)=-18+50 \\ f(3)=32 \end{gathered}[/tex]As you can see, the height of the apple is 32 feet at 3 seconds.
Therefore, the correct answer is the option (B)
The height of the apple at 3 seconds is 32 feet.
Identify the domain and range of the relation. Use a mapping diagram to determine whether the relation is a function.
{(-1, 5). (3, 4), (2, 5), (-1, -3)
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Answer:
domain: {-1, 2, 3}range: {-3, 4, 5}mapping diagram is attachedNOT a functionStep-by-step explanation:
You want to know the domain and range of the relation {(-1, 5). (3, 4), (2, 5), (-1, -3)}, and whether it is a function.
DomainThe domain is the list of x-values in the (x, y) pairs. We conventionally eliminate duplicates and put them in order.
{ -1, 2, 3} . . . . domain
RangeThe range is the list of y-values in the (x, y) pairs. Again, duplicates are eliminated, and they are put in order.
{-3, 4, 5} . . . . range
Mapping diagramThe mapping diagram is a visual aid that has domain values on the left, range values on the right, and arrows showing how the domain values map to the range values. Such a diagram is attached.
FunctionIf there are multiple arrow tails extending from any given domain value, the relation is not a function. This relation maps -1 to multiple values, so it is not a function.
Do you know anything about functions
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1)
Take into account that the equation of a line can be written as follow:
y = mx + b
where m is the slope and b the y-intercept.
the slope can be calculated as follow:
m=(y2 -y1)/(x2 - x1)
where (x1,y1) and (x2,y2)
For the given graph, consider the points (0,3) and (4,4)
Quadrilateral PFGH was created by dilating quadrilateral MBGK the length of MB = 4.2 and the
scale factor is 3, what is the length of the corresponding side, PF?
Thank youuu!!
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The corresponding length of the side PF will be 4.2.
What is scale factor? How it is used in Dilating coordinates?Scale factor is used to compare 2 quantities, indicating by how much one quantity is greater than the other. It is denoted by K. Mathematically-
K = a/b.
If a coordinate point (x, y) is dilated by a scale factor of [k], then the coordinate point after dilation will be - (kx, ky).
Given is Quadrilateral PFGH that was created by dilating quadrilateral MBGK such that the length of MB = 4.2 and the scale factor is 3.
When a length MB is dilated by a scale factor of 3, then the new length PF will be equal to -
PF = 3 x 4.2
PF = 12.6
The corresponding length of the side PF will be 4.2.
Therefore, the corresponding length of the side PF will be 4.2.
To solve more questions on dilation, visit the link below-
brainly.com/question/13439872
#SPJ1
Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $15 and same-day tickets cost $20. For one performance,there were 45 tickets sold in all, and the total amount paid for them was $825. How many tickets of each type were sold?Number of advance tickets sold: Number of same-day tickets sold:
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Let,
Number of Advance Tickets = a
Number of Same-Day tickets = s
Given,
Total 45 tickets sold
We can write
[tex]a+s=45[/tex]Also, each advance ticket cost $15 and same day tickets cost $20 for a total of $825. Thus, we can write:
[tex]15a+20s=825[/tex]We will multiply the first equation by - 15 and then add both equations. Then, solve for "s". The steps are shown below:
[tex]\begin{gathered} -15\times\lbrack a+s=45\rbrack \\ -15a-15s=-675 \\ ------------- \\ -15a-15s=-675 \\ 15a+20s=825 \\ ------------- \\ 5s=150 \\ s=\frac{150}{5} \\ s=30 \end{gathered}[/tex]Now, we can use this value of "s" and put it into Equation 1 and find the value of "a". Shown below:
[tex]\begin{gathered} a+s=45 \\ a+30=45 \\ a=45-30 \\ a=15 \end{gathered}[/tex]AnswerNumber of advance tickets sold: 15Number of same-day tickets sold: 30Alex is solving this system of equations: 5x + 4y = 1 4x + 2y = 8 He starts by rearranging the second equation to isolate the y variable: y = 4 - 2x. He then substitutes the expression 4 - 2.c for y in the first equation, as shown: Step 1: 5x +4(4-22) 1 Step2: 50 + 16 - 8x = 1 -32 = -15 Step 3: Step 4: I= -5 Step 5: y=4 - 2x Step 6: y=4-2(-5) Step 7: y= 14 Where did Alex make a mistake? Step 6
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Answer:
Step 4
Explanation:
The initial system of equation is:
5x + 4y = 1
4x + 2y = 8
So, if we take the second equation and isolate y, we get:
y = 4 - 2x
Then, replacing it on the first one, we get:
5x + 4(4 - 2x) = 1
Solving for x, we get:
5x + 4*4 - 4*2x = 1
5x + 16 - 8x = 1
-3x +16 = 1
-3x + 16 - 16 = 1 - 16
-3x = -15
Finally, dividing by -3, we get:
[tex]\begin{gathered} \frac{-3x}{-3}=\frac{-15}{-3} \\ x=5 \end{gathered}[/tex]Therefore, the mistake was made in step 4, because he didn't take into account the negative sign. So, the correct answer is x = 5 instead of x = - 5
Referring to the fig. Write the equation in standard form of the vertical line through the point (-1,0)
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Recall that the standard form of the equation of a vertical line is:
[tex]x+0y=C,[/tex]where C is a constant equal to the x-entry of all the points on the line.
In this case,
[tex]C=-1.[/tex]Therefore, the equation that represents the vertical line that passes through (-1,0) is
[tex]x+0y=-1.[/tex]
Answer:
[tex]x+0y=-1.[/tex]Can you help me find the roots of the quadratic equation by completing the square?
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Given
[tex]x^2-8x=9[/tex]Complete the square for x as shown below
[tex]\begin{gathered} x^2-8x+b=(x-a)^2 \\ \Rightarrow-8x=-2ax,b=a^2 \\ \Rightarrow a=4\Rightarrow b=16 \\ \Rightarrow x^2-8x+16=(x-4)^2 \end{gathered}[/tex]Thus,
[tex]\begin{gathered} \Rightarrow x^2-8x+16=9+16 \\ \Rightarrow(x-4)^2=25 \end{gathered}[/tex]After completing the square, the result is (x-4)^2=25Then, finding the roots of the quadratic equation,
[tex]\begin{gathered} (x-4)^2=25 \\ \Rightarrow(x-4)=\sqrt{25}=\pm5 \\ \Rightarrow x=4\pm5 \\ \Rightarrow x=-1,9 \end{gathered}[/tex]Hence, the roots are x=-1, and x=9Gavin looks at the second Model It and uses the variable h to write the expression8 + 3h. How many terms does the expression have? Which term is a product?Identify the variable and the coefficient and explain what each represents.
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the expression have 2 terms, 8 and 3h
The term that is a product is 3h
the variable is h and the coefficient is 3; that means the model height
and the product by 3 means that's the triple of h.
Answer:
Step-by-step explanation:
it is a linear expression with two terms.
term 3h is a product.
variable in the expression is represented by letter h
coefficient written along with a variable is 3
term 8 is a constant in the given linear expression
Given collinear points A B, and C such that point B is between A and C. Find the length of AB given that AB = 5x + 1, BC = 3x-4, and AC = x + 11
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Given collinear points A B, and C such that point B is between A and C.
Collinear points mean they all lie on the same plane.
AB = 5x + 1
BC = 3x-4
AC = x + 11
We are asked to find the length of AB.
To find the length of AB it is necessary to first find the value of x.
Let us draw this scenario to better understand the problem.
As you can see in the above figure, the sum of the length AB and BC must be equal to the length AC.
Mathematically,
[tex]AB+BC=AC[/tex]Let us substitute the given values
[tex](5x+1)+(3x-4)=x+11[/tex]Now let's solve the equation for x.
[tex]\begin{gathered} 5x+1+3x-4=x+11 \\ 5x+3x+1-4=x+11 \\ 8x-3=x+11 \\ 8x-x=11+3 \\ 7x=14 \\ x=\frac{14}{7} \\ x=2 \end{gathered}[/tex]Finally, the length of AB is
[tex]\begin{gathered} AB=5x+1 \\ AB=5\mleft(2\mright)+1 \\ AB=10+1 \\ AB=11 \end{gathered}[/tex]Therefore, the length of AB is 11.
What is the radius of a circle with a circumference of 48 inches? Give the exact value and the value rounded to the nearest tent.
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ANSWER
r = 24/π in ≈ 7.6 in
EXPLANATION
The circumference of a circle of radius r is,
[tex]C=2\pi r[/tex]So, if the circumference of this circle is 48 inches,
[tex]48in=2\pi r\Rightarrow r=\frac{48in}{2\pi}=\frac{24}{\pi}in\approx7.6in[/tex]Hence, the radius of this circle is 24/π inches, or 7.6 inches, rounded to the nearest tenth.
23. If the cube and rectangular box have the same volume, which equation can you use to find the height (h) of the box? (1) 63 = 6 x 12 xh (2) 62 = 6 x 12 xh (3) 63 = 6 + 12 + h (4) 6 = (6 x 12)h (5) h = 6 x 6 x 12
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We are given two figure, i) Cube, ii) rectangular box
The volume of any shape is calculated by multiplying height, width, length.
Volume = height x length x width
In the case of a cube, all the dimensions are the same. So volume would be = length x length x length
here, length = 6
So,
V(cube) = 6^3
For a rectangular box:
V(rect) = height x length x width
V(rect) = h x 12 x 6
As given, V(cube) = V(rect). Therefore,
6^3 = h x 12 x 6
Hence, the first option is correct.
Write two numbers that multiply to the value on and add to the value on bottom
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xy = 66
x + y = 17
x = 11
y = 6
11 times 6 = 66
11 plus 6 = 17
Answer is 11 and 6
There is a question that is what is this ordered pair a solution for the inequality. The equation is x+y< -4; (0, 0). If you could explain how to solve it and what the answer is that would be amazing. Thank you
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We have to replace x by the first value of the ordered pair in this case 0. And replace y by the second value of the ordered pair in this case is 0. So we get the following question.
[tex]is\text{ }0+0=0<-4\text{?}[/tex]as 0 is not less than -4 we get that (0,0) is not a solution of the inequality
Martin, a carpenter wants to make a spice rack for the kitchen. He cuts a 16.24 feet long plank into 5 pieces of equal length. What is the length of each piece of wood ? Round to the nearest hundredth. Solve using long division.
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Let's divide the 16.24 feet long plank by 5 to be able to determine the length of each piece of wood.
Using Long Division Method:
Therefore, the length of each piece when a 16.24 feet long plank is being cut into 5 pieces is 3.248 feet. Rounding off to the nearest hundredth, it will be 3.25 feet.
can you please solve thisOptions for the first box: 'AD' or 'DE'
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If AD/DB = AE/EC, we can state that the line segment DE is parallel to BC, since they link endpoints for AD and AE, and DB and EC, respectively
Please solve quicklyyyy and show all work. Note** a and b are not answer choices they are different steps and sections. PLEASE HELPPP MEE
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a)
x - intercepts: 2 and -1/2
Point = (3, -14)
quadratic formula:
y = a(x -2)(x + 1/2)
we need to solve for a.
-14 = a(3 - 2)(3 + 1/2)
-14 = a(7/2)
a = - 4
so:
y = -4(x -2)(x + 1/2)
y = -4x^2 + 6x + 4
b)
x - intercept = -2 = (-2, 0)
point: (-1, 4)
We can plug both points into two separated equations, as follows:
4 = a(-1)^2 + b(-1) + c (EQUATION 1.)
0 = a(-2)^2 + b(-2) + c (I'll multiply this equation by -1 in order to add the 2 equations together and get rid of c)
4 = a - b + c
0 = -4a + 2b - c
_____________
4 = -3a + b
a = 1/3b - 4/3**
Now we plug back in to the first equation to find c.
4 = 1/3b - 4/3 - b + c
c = 2/3b + 16/3 **
Now we plug one last time on the equation 1 with all b variables:
4 = 1/3b - 4/3 - b + 2/3b + 16/3
b =
evaluate the following leaving your answers in standard form (5 * 10 raise to power 6) x (1.2 * 10 raise to power 5)
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Answer:
(5*10^6)x(1.2*10^5)
(5*1,000,000)x(1.2x100,000)
5,000,000x120,000
600,000,000,000
(t + 7) = 16 what value for t makes this equation true
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answer: t = 9
For the following in functions of the quantity of t minutes
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Part A
Given
[tex]Q(t)=400(2)^{\frac{t}{4}}[/tex]Solution
We ask to double the time i.e
[tex]\begin{gathered} 800=400(2)^{\frac{t}{4}} \\ \text{Divide both sides by 400} \\ \frac{800}{400}=\frac{400}{400}(2)^{\frac{t}{4}} \\ \\ 2^1=(2)^{\frac{t}{4}} \\ \\ 1=\frac{t}{4} \\ \\ \text{cross multiply} \\ t=1\times4 \\ t=4 \end{gathered}[/tex]Part B
Given
[tex]y=10(\frac{1}{2})^{\frac{t}{12}}[/tex]Solution
The half-life would be 5
[tex]\begin{gathered} y=10(\frac{1}{2})^{\frac{t}{12}} \\ 5=10(\frac{1}{2})^{\frac{t}{12}} \\ \text{divide both sides by 10} \\ \\ \frac{5}{10}=\frac{10}{10}(\frac{1}{2})^{\frac{t}{12}} \\ \\ \frac{1}{2}=(\frac{1}{2})^{\frac{t}{12}} \\ \\ 1=\frac{T}{12} \\ \text{cross multiply} \\ T=1\times12 \\ T=12 \end{gathered}[/tex]A conical beaker has a base radius of 8 cm and a height of 15 cm. A conical tank full of acid is a similar shape to the beaker. The beaker can be filled with acid from the tank exactly 1728 times. Work out the base radius and height of the tank
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Step-by-step explanation:
V = pi×h/3 (R² + Rr + r²) where "V", "h", "R" and "r" are volume, height, larger "rim" radius, and smaller base radius of the conical cylinder (here beaker and tank).
since the beaker and the tank are similar, this means that there is one constant scaling factor for all the corresponding lines between the 2 shapes.
that means that
height of beaker × f = height of tank
has the same "f" as
base radius of beaker × f = base radius of tank.
the same for R ("rim" radius).
and so on.
that means that in the volume formula for the tank the factor "f" is brought in as f³ (product of "f" in "h" and of "f²" in every radius term of the summary terms in the brackets).
so,
Vtank = Vbeaker × f³
therefore,
1728 = f³
f = 12
and the base radius of the tank is
8 × 12 = 96 cm
the height of the tank is
15 × 12 = 180 cm
What is the best estimate for 56.23 - 45.9?A.9B.10C.11D.15
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Step 1:
Write the expression
56.23 - 45.9
Step 2:
To estimate, you will round each decimal number to the nearest whole number.
[tex]\begin{gathered} 56.13\text{ }\approx\text{ 56} \\ 45.9\text{ }\approx\text{ 46} \end{gathered}[/tex]Step 3:
Next, estimate
[tex]\begin{gathered} =\text{ 56 - 46} \\ =\text{ 10} \end{gathered}[/tex]Final answer
Option B
10
6) The storeroom of the apex company measures 28ft. By 25ft.& has a 12ft. High ceiling. How many cubic ft of storage space does the apex company have?
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In order to find the volume, we will use the next formula
[tex]V=l\times w\times h[/tex]where l is the length, w is the width and h is the height.
In our case
l=28 ft
w=25 ft
h=12 ft
we substitute the data
[tex]V=28\times25\times12=8400ft^3[/tex]The volume is 8400 cubic feet
PLEASE HELP I’M BAD WITH ANGLES AND I DESPERATELY NEED TO GET THESE QUESTIONS RIGHT.
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1. Consider that the sum of the angles is equal to 90°, then, you have:
30° + 44° + x = 90° simplify left side
74° + x = 90° subtract 74° both sides
x = 90° - 74°
x = 16°
2. As in the previous excersice:
x + 74° = 90°
x = 90 - 74°
x = 16°
3. The sum of the angles is equal to 180°.
134° + x = 180°
x = 180° - 134°
x = 46°
4. The given angles are congruent because they are vertical, then:
x = 59°
4(x - 3)= 16 - 3x Solve for X
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The given equation is expressed as
4(x - 3)= 16 - 3x
The first step is to expand the parentheses on the left by multiplying the terms inside the parentheses with the term outside. We have
4x - 12 = 16 - 3x
The nest step is to add 3x and 12 to both sides of the equation. We have
4x + 3x - 12 + 12 = 16 + 12 - 3x + 3x
7x = 28
Dividing both sides of the equation by 7, we have
7x/7 = 28/7
x = 4
Tara wants to prove that a second pair of corresponding angles from KJN and LJM are congruent. Determine a second pair of corresponding angles from KJN and LJM that are congruent. Then explain how you know that the two are congruent.
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For similar angles, the ratio of corresponding angles are equal
∠JKN and ∠LKM
Explanation:Triangle KJN is similar to triangle LJM.
For similar angles, the ratio of corresponding angles are equal.
From part A, we have been given a pair of corresponding angles:
∠KJN corresponds to ∠LJM
The angles are equal
∠K correponds to ∠L
∠JKN corresponds to ∠LKM
∠N corresponds to ∠M
∠JNK corresponds to ∠JML
A second pair of corresponding angles from triangle KJN and traingle LJM could be:
∠JKN and ∠LKM
OR
∠JNK and ∠JML
Any of the above pairs could be chosen
Find the volume of a right circular cone that has a height of 6ft and a base with a radius of 9.7ft. Round your answer to the nearest tenth of a cubic foot.
Answers
We can express the volume of a cone with the equation:
[tex]V=\frac{1}{3}A_bh=\frac{1}{3}\pi r^2h[/tex]where Ab is the area of the base, r is the radius of the base and h is the height of the cone.
Then, replacing with r=9.7 ft and h=6 ft, we get:
[tex]\begin{gathered} V=\frac{1}{3}\pi\cdot(9.7ft)^2\cdot(6ft) \\ V=\frac{1}{3}\pi\cdot94.09ft^2\cdot6ft \\ V\approx591.2ft^3 \end{gathered}[/tex]Answer: the volume is 591.2 cubic feet.