It will take 6 years for the trees to be same height.
Step-by-step explanation:
Given,
Initial height of Type A = 7 feet = 7*12 = 84 inches
Growth rate = 2 inches per year
Let,
x be the number of years
Total height = T
T = 2x+84 Eqn 1
Initial height of Type B = 5 feet = 5*12 = 60 inches
Growth rate = 6 inches per year
T = 6x+60 Eqn 2
For same height;
Eqn 1 = Eqn 2
[tex]2x+84=6x+60\\84-60=6x-2x\\24=4x\\4x=24[/tex]
Dividing both sides by 4
[tex]\frac{4x}{4}=\frac{24}{4}\\x=6[/tex]
It will take 6 years for the trees to be same height.
Keywords: linear equation, division
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in the equation 6x^2+7x-49 how does 7x become -14x and 21x?
Answer:
See the explanation.
Step-by-step explanation:
Given function is [tex]6x^2+7x-49[/tex]
We will find its root by factoring.
In any quadratic function of the form [tex]ax^2+bx+c[/tex]
We will two numbers that when multiplied gives [tex]ac[/tex]. And when that two numbers are added it turns to [tex]b[/tex].
So, in [tex]6x^2+7x-49[/tex].
[tex]a=6,\ b=7.\ c=-49[/tex]
And [tex]ac=-294[/tex]
So, we need to find two numbers that when multiplied give [tex]-294[/tex],and when added give [tex]7[/tex].
Now, we can see
[tex]-14\times21=-294\\And\ -14+21=7[/tex]
In this manner, we can rewrite [tex]7x[/tex] as [tex]-14x+21x[/tex].
what are these answers
Answer:
.
Step-by-step explanation:
Will mark brainliest and 10 points
Answer:
Function 1 has a negative y-intercept, and Function 2 has a positive y-intercept.
Step-by-step explanation:
As shown by the graph, Function 1 has a negative y-intercept.
Function 2 y-intercept:
y = mx + b
y = -0.5x + b
1 = -0.5(2) + b
1 = -1 + b
b = 2
Function 2 has a positve y-intercept.
GUYS PLEASE HELP I WILL GIVE BRAINLEIST PLEASE GUY NEED THIS THANK YOU
enter the missing numbers in the boxes to complete the table of equivalent ratios.
length width
? 5
4 ?
6 ?
8 20
PLEASE HELP I NEED IT
Answer:
The pairs are [tex](2,5)[/tex], [tex](4,10)[/tex] and [tex](6,15)[/tex]
Step-by-step explanation:
We can see the given pairs have the same ratio.
Let us find the ratio of pair [tex](8,20)[/tex]
So, the common ratio is [tex]\frac{8}{20}=\frac{2}{5}[/tex]
Now, we will check each pair, Let the missing number be [tex]x[/tex]
Case-I
[tex](x,5)\\\frac{x}{5}=\frac{2}{5}\\ x=2[/tex] So,the pair is [tex](2,5)[/tex]
Case-II
[tex](4,x)[/tex]
[tex]\frac{4}{x}=\frac{2}{5}\\\\\frac{4}{x}=\frac{2\times 2}{5\times 2}=\frac{4}{10}\\ x=10[/tex]So, the pair is [tex](4,10)[/tex]
Case-III
[tex](6,x)[/tex]
[tex]\frac{6}{x}=\frac{2}{5}\\\\\frac{6}{x}=\frac{2\times 3}{5\times 3}=\frac{6}{15}\\x=15[/tex]So, the pair is [tex](6,15)[/tex]
Now, the required pairs are [tex](2,5)[/tex], [tex](4,10)[/tex] and [tex](6,15)[/tex]
Four more than seven times a number is the same as twenty less than three times the number. Find the number
Answer:
-6
Step-by-step explanation:
7x +4=3x-20
4x=-24
x= -6
The given problem can be translated into the equation 7x + 4 = 3x - 20. By solving this equation, we find out that the number x is -6.
Explanation:In this mathematical problem, we can define the number we are looking for as x. Based on the problem, we have the equation 7x + 4 = 3x - 20. This equation comes from the problem statement that 'four more than seven times a number is the same as twenty less than three times the number'.
Next, we can solve for x by subtracting 3x from both sides to get 4x + 4 = -20. Then, to isolate x, we subtract 4 from both sides to get 4x = -24. Finally, we divide by 4 on both sides and find that x = -6, which is the solution.
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Fiona cut fabric circles for an art project. She recorded the diameters of the circles in the table.
Diameter (cm) Frequency
2 3
2.25 3
2.5 4
2.75 4
3 2
3.5 2
Create a dot plot for the data in the table. Hover over each number on the number line. Then click and drag up to create the dots.
Answer:
2 : 3 dots up
2.25 : 3 dots up
2.5 : 4 dots up
2.75 : 4 dots up
3 : 2 dots up
3.25: 0 dots up
3.5 : 2 dots up
The dot plot for the considered data is plotted based on how many times each observation occured (given by frequencies), as plotted in the image attached.
How does dot plot works?Suppose we're measuring something whose values are numeric. For each value of that thing we observe, we plot a dot above that value in number line. Thus, the total number of dots in the dot plot tells us the total number of observations of the values of that thing we did.
Thus, suppose if we observed the value 'x', then we will make a dot above 'x'. If there is already a dot over 'x', then we will make a new dot over that dot.
If instead of only observations, the table of unique observation and frequency is given, then we plot dots that many times as the count written in the frequency table.
Thus, if its written that the value 2 has 3 has its frequency, then we plot 3 dots one over the other above the value 2 in the horizontal axis.
For this case, we're given the unique observation to frequency table as:
Diameter (cm) Frequency
2 3
2.25 3
2.5 4
2.75 4
3 2
3.5 2
That means, over the value 2, plot 3 dots (as diameter 2 occured 3 times), and so on, over the value 3.5, plot 2 dots.
The dot plot of the considered data is attached below.
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block 7 math test question 2
Answer:
The increasing quickly part is B.
The decreasing quickly part is D
The decreasing slowly part is A.
The constant part is C.
And the increasing slowly part is E.
Step-by-step explanation:
See the attached graph.
Here, the graph represents the viewing trend of a reality show. We have to match each phrase to the section of the graph it describes.
Now, the increasing quickly part is B.
The decreasing quickly part is D
The decreasing slowly part is A.
The constant part is C.
And the increasing slowly part is E. ( Answer )
A rectangle has a width of 8 and a perimeter of 40 what is the length of the rectangle?
Robert is purchasing some packs of chicken from the supermarket. The first pack weights 45 ounces . The second pack weights 3 pounds . Witch pack weights more
Answer:
3 pounds duh
Step-by-step explanation:
Answer: 3 pounds
Step-by-step explanation: 16 oz are in 1 pound and 1 pound times 3 = 3 pounds and 16 times 3 equals 48 and the pack weighs 45 oz therefore 3 pounds is heavier by 3 oz
In the figure, angle D measures 31⁰ and angle A measures 27⁰
1.The measurement of angle B is
A.59⁰
B.63⁰
C.90⁰
2. The measurement of angle F is
A.59⁰
B.63⁰
C.90⁰
Answer:
1)B:63°
2)A:59°
Step-by-step explanation:
1.ABC is a right triangle at C then angle ACB=90°(right angle)
Angle CAB=27°(see the given)
measure of the angles in any triangle is 180°
then angle CBA=
measure of all the angles - (measure ACB+measure CAB)
=180°-(90°+27°)
=63°
2. Same explanation of angle B:
in the right triangle DEF: angle DEF=90°
angle D=31°(given)
Then measure of angle A=180°-(angle E + angle D)
=180-(90+31)=59°
If f(x)=2x+5x and g(x)=3x-5,find (f+g)(x)
The answer is [tex](f+g)(x)=10x-5[/tex]
Step-by-step explanation:
Given that [tex]f(x)=2x+5x[/tex] and [tex]g(x)=3x-5[/tex]
To find : [tex](f+g)(x)[/tex]
Now, assign the value [tex]g(x)=3x-5[/tex] in [tex](f+g)(x)[/tex]
[tex](f+g)(x)=(f+3x-5)[/tex]
Also, assign the value [tex]f(x)=2x+5x[/tex] in [tex](f+g)(x)[/tex]
[tex](f+g)(x)=(2x+5x+3x-5)[/tex]
Now, adding the like terms , we get,
[tex](f+g)(x)=10x-5[/tex]
Thus, the value of [tex](f+g)(x)[/tex] is [tex](f+g)(x)=10x-5[/tex]
Answer:
[tex]10x-5[/tex]
Step-by-step explanation:
[tex]f(x)=2x+5x[/tex]
[tex]g(x)=3x-5[/tex]
[tex](f+g)(x)[/tex]
[tex]f(x)+g(x)[/tex]
[tex]2x+5x+3x-5[/tex]
[tex]10x-5[/tex]
Write an equation in slope-intercept form for the line perpendicular to y=−4x+1 that passes through the point (−7,1)
Answer:
all work is shown and pictured
Final answer:
To find the equation of a line perpendicular to y = -4x + 1 that passes through the point (-7, 1), determine the slope, use the point-slope form, and convert it to slope-intercept form.
Explanation:
To find the equation of a line perpendicular to y = -4x + 1 that passes through the point (-7, 1), we first determine the slope of the perpendicular line. The slope of a line perpendicular to a line with slope m is the negative reciprocal of m. So, the slope is 1/4. Next, we use the point-slope form of a line y - y₁ = m(x - x₁) and plug in the point to find the equation in slope-intercept form, y = mx + b.
Plugging in (-7, 1) and slope 1/4 into the point-slope form, we get y - 1 = (1/4)(x + 7). Simplifying gives us y = (1/4)x + 2. Hence, the equation of the line perpendicular to y = -4x + 1 that passes through the point (-7, 1) is y = (1/4)x + 2.
A big cruise ship dropped anchor off the Caribbean island of Barbuda. The heavy anchor was released from a height of
54
5454 meters above the water's surface, and it fell at a constant rate. After
35
3535 seconds, the anchor was
9
99 meters below the water's surface.
How fast did the anchor drop?
meters per second
How long did it take the anchor to reach the water's surface?
seconds
54+9= 63 m = distance and time=35 sec hence, speed= 63/35=9/5=1.8 m/s
time taken to reach water surface= distance/speed=54/1.8=30 sec
solve the following formula c=1/2f(q+b) for q
Answer:q= (2C - fb)/f
Step-by-step explanation:
multiplying both sides by 2 we have,
2C = fb + fq,
subtract both sides by fb
fq = 2C - fb,
dividing both sides by f
q= (2C - fb)/f
Ms. Plumlee is making brownies. Ms. Sed is making brownies as well. Ms. Plumlee makes 12 brownies per hour. Ms. Sed makes 10 brownies per hour. After 24 hours, how many brownies does Ms. Plumlee and Ms. Sed make each?
Answer:
48
Step-by-step explanation:
After 24 hours, Ms. Plumlee makes 288 brownies and Ms. Sed makes 240 brownies.
Explanation:The mathematics problem involves calculating the total number of brownies made by Ms. Plumlee and Ms. Sed. Ms. Plumlee makes 12 brownies per hour, and Ms. Sed makes 10 brownies per hour. We need to find out the number of brownies each of them makes after 24 hours.
For Ms. Plumlee: 12 brownies per hour x 24 hours = 288 brownies.
For Ms. Sed: 10 brownies per hour x 24 hours = 240 brownies.
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Solve for x your answer must be simplified.
−7x>10
[tex]x< \frac{-10}{7}[/tex]
Solution:
Given inequality is –7x > 10.
To reduce this inequality to solve for x.
⇒ –7x > 10
Multiply by –1 on both sides of the inequality to reverse the expression.
⇒ –7x × (–1) < 10 × (–1)
⇒ 7x < –10
To simplify the expression, divide by 7 on both sides of the expression.
⇒ [tex]\frac{7}{7}x< \frac{-10}{7}[/tex]
⇒[tex]x< \frac{-10}{7}[/tex]
Hence [tex]x< \frac{-10}{7}[/tex].
- Rewrite - 7x +9y = 18 in slope-intercept form. Identify the slope and y-intercept
of the line.
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange - 7x + 9y = 18 into this form
Add 7x to both sides
9y = 7x + 18 ( divide all terms by 9 )
y = [tex]\frac{7}{9}[/tex] x + 2 ← in slope- intercept form
with slope m = [tex]\frac{7}{9}[/tex] and y- intercept c = 2
You plant 20 marigold seeds and 12 of them grow into flowers that bloom. If you plant 10 more marigolds, predict how many would bloom?
Answer:
I would predict that 6 marigolds would bloom
Marcus loves baseball and wants to create a home plate for his house. Marcus needs to calculate the area of the home plate at the ball field so he can reconstruct it when he gets home. Calculate the area of the polygon. (5 points)
Pentagon with square measuring 7 inches by 4 inches and two triangles with heights of 6 inches and 5 inches.
Group of answer choices
50 in2
59 in2
85 in2
90 in2
Answer:
59 in2
Step-by-step explanation:
we know that
The area of the polygon is equal to the area of rectangle plus the area of two triangles
so
Find the area of rectangle
[tex]A_1=LW[/tex]
we have
[tex]L=7\ in\\W=4\ in[/tex]
substitute
[tex]A_1=(7)(4)=28\ in^2[/tex]
Find the area of triangle with height of 6 in
[tex]A=\frac{1}{2}bh[/tex]
we have
[tex]b=7\ in\\h=6\ in[/tex]
substitute
[tex]A_2=\frac{1}{2}(7)(6)=21\ in^2[/tex]
Find the area of triangle with height of 5 in
[tex]A=\frac{1}{2}bh[/tex]
we have
[tex]b=4\ in\\h=5\ in[/tex]
substitute
[tex]A_3=\frac{1}{2}(4)(5)=10\ in^2[/tex]
The total area is
[tex]A=A_1+A_2+A_3=28+21+10=59\ in^2[/tex]
Answer:
The answer is 59 in2
Step-by-step explanation:
A. Does the table represent a proportional relationship?
B. If the relationship is proportional, what is the constant of proportionality?
Total wight in pounds. 12 18 30 60
Number of books. 10 15 25 50
A. Yes the table represents a proportional relationship
B. The constant of proportionality is 1.2
Step-by-step explanation:
Two quantities are proportional if:
One of them is equal to the constant times the other oneIf x and y are proportion, then y = k x, where k is constant∵ Total wight in pounds ⇒ 12 , 18 , 30 , 60
∵ Number of books ⇒ 10 , 15 , 25 , 50
- Divide each two corresponding data to check if all they give
the same constant or not
∵ 12 ÷ 10 = 1.2
∵ 18 ÷ 15 = 1.2
∵ 30 ÷ 25 = 1.2
∵ 60 ÷ 50 = 1.2
- That means the total wight is equal to constant times the
number of books
∴ Total wight = 1.2 Number of books
∴ The total wight and the number of books are in a proportional
relationship
A. Yes the table represents a proportional relationship
∵ Total wight = 1.2 Number of books
∴ The constant of proportionality = 1.2
B. The constant of proportionality is 1.2
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witch of these is a correct expansion of (3x-1)(4x^2+5)
Answer:
12x^3 - 4x^2 + 15x -5
Mr Miller drove 568 miles last week. This week he drove 308 miles on Tuesday and 97 miles on Wednesday. What was the number of miles he drove in these two weeks?
The number of miles Mr Miller drive was 973 miles.
Step-by-step explanation:
Given,
Miles driven on first week = 568 miles
Miles driven on Tuesday this week = 308 miles
Miles driven on Wednesday this week = 97 miles
Total miles driven = Miles in first week + Miles on Tuesday + Miles on Wednesday
Total miles driven = 568 + 308 + 97 = 973 miles
The number of miles Mr Miller drive was 973 miles.
Keywords: addition
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HELP!! which is the measure of wx shown in the diagram below
Answer:
A. 25°
Step-by-step explanation:
We are given a circle and two intersecting lines of circle meets at s and form an angle 34° at S.
Also, we have W and X points on circle that form a minor arc and T and R makes a major arc of angle 93°.
In order to find the value of minor arc WX, we need to apply following formula:
Subtends angle on intersection of lines = [tex]\frac{Major Arc- Major Arc} {2}[/tex]
Plugging values in above formula, we get
34= [tex]\frac{93 - x }{2}[/tex]
On cross multiplication, we get
34 × 2 = 93-x
68 = 93 -x
x = 93-68
x= 25.
Therefore, measure of arc WX = 25°.Hope this helps and you understand !!!!!!
What is the slope OF THE GRAPH, not what is A slope, what is THE slope
Answer:
The slope is -3
Step-by-step explanation:
Hello!
Slope is measured by lattice points on the graph, and the formula is Rise/Run.
To calculate the slope of this graph, we must find two points that intersect coordinates. I will choose coordinates (0,2) and (1,-1).
Now to find the rise, we must find the difference in the y coordinates.
2 - (-1) 2 + 13To find the run, we must find the difference in the x coordinates.
0 - 1-1Now divide:
3/-1-3Linear relations are not functions when they appear graphically as:
horizontal lines
linear relations are always functions
vertical lines
Answer:
Vertical lines
Step-by-step explanation:
Linear relations are not functions when they appear graphically are vertical lines.
What is function?
" Function is defined as when the relation between variables are such that each input has one and only one output."
According to the question,
Linear relation are defined as y = ax + b
A. Horizontal lines is expressed by equation y = 0x + b
For each x = 0 , 1, 2, 3, .... value of y = b. For each input single output 'b' is defined.
Horizontal lines represent the function.
B. Linear relation represents straight line .
For example y = 2x +3
For each x we have single output y.
Therefore linear relation represents function.
C. Vertical lines x = k , here for x=k there are many outputs y = 0,1, 2, 3....
Vertical line does not represent function.
Hence, linear relations are not functions when they appear graphically are vertical lines.
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5. An attacker swings a board with a mass of 2 kg toward a victim. The acceleration is 10 m/s2 when the board hits the victim. How much force did the board exert on the victim? Obj. 7.2
The force exerted on victim is 20 newton
Solution:
An attacker swings a board with a mass of 2 kg toward a victim
The acceleration is 10 [tex]m/s^2[/tex] when the board hits the victim
To find: Force exerted on victim
The force is given by formula:
[tex]F = mass \times acceleration[/tex]
From given,
[tex]mass = 2 \text{ kg }\\\\Acceleration = 10[/tex] [tex]m/s^2[/tex]
Substituting the values in formula,
[tex]Force = 2 \times 10 = 20[/tex]
Thus force exerted on victim is 20 newton
A mass of 2 kg and an acceleration of 10 m/s², the force is calculated to be 20 Newtons.
To determine the force exerted by the board on the victim, we can use Newton's second law of motion, which states:
⇒ Force (F) = Mass (m) x Acceleration (a)
Given that the mass of the board is 2 kg and the acceleration when it hits the victim is 10 m/s², we substitute these values into the equation:
⇒ F = 2 kg x 10 m/s²
⇒ F = 20 N
Thus, the board exerts a force of 20 Newtons on the victim.
Complete question:
An attacker swings a board with a mass of 2 kg toward a victim. The acceleration is 10 m/s² when the board hits the victim. How much force did the board exert on the victim?
What is the volume of a shipping cube with dimensions of 2 1/2 feet? 6 3/4 cubic feet 15 5/8 cubic feet 8 1/8 cubic feet
Answer:
The volume of shipping cube is [tex]15\frac{5}{8}\ cubic\ feet.[/tex]
Step-by-step explanation:
Given:
The dimensions of a shipping cube of 2 1/2 feet.
Now, to find the volume of shipping cube.
Side of cube = [tex]2\frac{1}{2}\ feet.[/tex]
Side = [tex]\frac{5}{2}\ feet[/tex]
So, to get the volume of cube we put formula:
[tex]Volume=(side)^3[/tex]
[tex]Volume=(\frac{5}{2})^3[/tex]
[tex]Volume=\frac{125}{8}[/tex]
[tex]Volume=15\frac{5}{8} \ cubic\ feet.[/tex]
Therefore, the volume of shipping cube is [tex]15\frac{5}{8}\ cubic\ feet.[/tex]
Answer:
b
Step-by-step explanation:
3 and19/12 simplified
Answer:
4 7/12
Step-by-step explanation:
3 19/12 = 3 + 19/12 = 3 + 12/12 + 7/12 = 3 + 1 + 7/12 = 4 7/12
While visiting Crimson Lake, Sally decided to go Kayaking. The rangers charge $8.50 per hour in addition to a $25.00 deposit to rent the kayak. If she rented the kayak from 11:30 a.m. to 2:30 p.m., write and solve a linear equation to find the total cost to rent the kayak.
The total cost to rent the Kayak will be $50.50
Step-by-step explanation:
Let h be the number of hours
Given
Charges per hour = $8.50
Renting Charges = $25.00
The renting charges are constant and will be used only once while the per hour charges will be calculated as number of hours change.
The function will be written as:
[tex]f(h) = 8.50h +25.00[/tex]
Here h is the number of hours.
From 11:30 AM to 02:30 PM makes three hours. So, to find the cost for 3 hours we have to put h = 3
[tex]f(h) = 8.5(3) + 25.00\\= 25.5+25.00\\= 50.5[/tex]
Hence,
The total cost to rent the Kayak will be $50.50
Keywords: Linear functions,, slope
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When Edna divides $35,286 by 7 using long division, is there is a remainder? If yes, what does the remainder mean?
Answer:
yes, the remainder is 6.
Step-by-step explanation:
the remainder is how many is left over if the divisor doesn't go perfectly into the dividend.
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The remainder of the division $35,286 by 7 using long division is 6.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example:
2 + 3x + 4y = 7 is an expression.
3x + 5 = 4 is an expression.
We have,
$35,286 ÷ 7
Now,
7) 35286 ( 540
-35
286
-280
6
7 x 5 = 35
7 x 40 = 280
We see that,
Using long division,
The remainder is 6.
Thus,
The remainder of the division $35,286 by 7 using long division is 6.
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