Answer:
3
Step-by-step explanation:
:3
how can you find the slope of a line and use it to
solve problems?
Answer:
Step-by-step explanation:
1) Mark two points on the line in the graph.
2) Determine the rise and run. Rise ---> difference in y-coordinates. (y2-y1)
Run -----> difference in x-coordinates (x2 - x1)
3) Plugin the values in the below mentioned formula.
[tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
1.If slope = 0, then the line is parallel to x-axis.
2. If slope is undefined, then the line is parallel to y-axis.
3. If slope is +ve, then the line slant upwards and if slope = -ve, then the line slant downwards.
The ratio of the measures of the sides of a triangle is 3:4:5. Its perimeter is 48 inches. Find the scale factor as a decimal, and the measure of each side of the triangle.
Given:
The ratio of the measures of the sides of a triangle is 3:4:5.
Its perimeter is 48 inches.
To find:
The scale factor as a decimal, and the measure of each side of the triangle.
Solution:
Let x be the scale factor. Then the measures of sides of the triangle are 3x, 4x and 5x.
The perimeter of the triangle is 48 inches. It means the sum of all sides of the triangle is 48 inches.
[tex]3x+4x+5x=48[/tex]
[tex]12x=48[/tex]
Divide both sides by 12.
[tex]x=\dfrac{48}{12}[/tex]
[tex]x=4[/tex]
Now, the measures of sides are:
[tex]3x=3(4)[/tex]
[tex]3x=12[/tex]
Similarly,
[tex]4x=4(4)[/tex]
[tex]4x=16[/tex]
And,
[tex]5x=5(4)[/tex]
[tex]5x=20[/tex]
Therefore, the scale factor is 4 and the measures of sides are 12, 16 and 20.
Answer:
The scale factor is 4.
Sides are 12 inches, 16 inches, 20 inches.
Step-by-step explanation:
The ratio is 3 : 4 : 5 and the perimeter is 48 inches.
Let the scale is p.
The length of sides is 3 p , 4 p and 5 p.
So, the perimeter is
3 p + 4 p + 5 p = 48
12 p = 48
p = 4
So, the scale factor is 4.
Sides are 12 inches, 16 inches, 20 inches.
The 555 points plotted below are on the graph of y=\log_b{x}y=log
b
xy, equals, log, start base, b, end base, x.
Based only on these 555 points, plot the 555 corresponding points that must be on the graph of y=b^{x}y=b
x
y, equals, b, start superscript, x, end superscript by clicking on the graph.
Answer:
See attachment for graph
Step-by-step explanation:
See comment for correct question
Given
[tex]y = \log_bx[/tex]
Required
The corresponding points on [tex]y =b^x[/tex]
On the graph, we have:
[tex](x_1,y_1) \to (1,0)[/tex]
[tex](x_2,y_2) \to (2,1)[/tex]
[tex](x_3,y_3) \to (4,2)[/tex]
[tex](x_4,y_4) \to (8,3)[/tex]
[tex](x_5,y_5) \to (16,4)[/tex]
First, we solve for b in [tex]y = \log_bx[/tex]
Using laws of logarithm, the equivalent of the above is:
[tex]x = b^y[/tex]
[tex](x_2,y_2) \to (2,1)[/tex] implies that:
[tex]2 = b^1[/tex]
[tex]2 = b[/tex]
Rewrite as:
[tex]b =2[/tex]
So, the equation [tex]y =b^x[/tex] becomes:
[tex]y = 2^x[/tex]
Using the same values of x, we have:
[tex](x_1,y_1) = (1,2)[/tex]
[tex](x_2,y_2) = (2,4)[/tex]
[tex](x_3,y_3) = (4,16)[/tex]
[tex](x_4,y_4) = (8,256)[/tex]
[tex](x_5,y_5) = (16,65536)[/tex]
See attachment for graph
The points (1,2), (2,4), and (4,16) are plotted on the graph attached below and this can be determined by using the given data.
Given :
Logarithmic Function -- [tex]\rm y = log_b(x)[/tex] --- (1)
The following steps can be used in order to determine the corresponding points that must be on the graph [tex]\rm x = b^y[/tex]:
Step 1 - Now, substitute the value of x and y that is (2,1) in the expression [tex]\rm x = b^y[/tex].
[tex]\rm 2 = b^1[/tex]
b = 2
Step 2 - Now, substitute the value of b in the equation [tex]\rm y=b^x[/tex].
[tex]\rm y = 2^x[/tex] --- (2)
Step 3 - At (x = 1) the above expression becomes:
y = 2
Step 4 - At (x = 2) the expression (2) becomes:
y = 4
Step 5 - At (x = 4) the expression (2) becomes:
y = 16
The graph of [tex]\rm y = 2^x[/tex] is attached below.
For more information, refer to the link given below:
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Given quadrilateral ABCD, where the diagonals AC and BD intersect at point E. AE⎯⎯⎯⎯⎯⎯⎯≅EC⎯⎯⎯⎯⎯⎯⎯⎯AE¯≅EC¯ and BE⎯⎯⎯⎯⎯⎯⎯≅DE⎯⎯⎯⎯⎯⎯⎯⎯BE¯≅DE¯. Can you prove can you prove that the figure is a parallelogram? Explain.
Given:
In a quadrilateral ABCD, diagonals AC and BD intersect at point E.
[tex]AE\cong EC[/tex]
[tex]BE\cong DE[/tex]
To prove:
The figure is a parallelogram.
Solution:
We know that if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
In a quadrilateral ABCD, diagonals AC and BD intersect at point E.
[tex]AE\cong EC[/tex]
[tex]BE\cong DE[/tex]
Since the diagonals AC and BD of a quadrilateral ABCD bisect each other, therefore the quadrilateral ABCD is a parallelogram.
Hence proved.
What is a counterexample to this claim? Dividing a number by 2 always results in a smaller number.
Given:
Dividing a number by 2 always results in a smaller number.
To find:
The counterexample to the given claim.
Solution:
If 0 is divided by is divided by any non-zero real number [tex]a[/tex], then
[tex]\dfrac{0}{a}=0[/tex]
Let us consider the unknown number be 0. Then dividing a number by 2, we get
[tex]\dfrac{0}{2}=0[/tex]
Here, the result is not a smaller number because [tex]0=0[/tex].
Therefore, the counterexample to the given claim is "Dividing 0 by 2".
Answer:
-1
Step-by-step explanation:
A vertical light pole on a hillside casts a
shadow of 55 m long down the hill. If the
angle of elevation of the sun is 48.3° and the
angle of inclination of the hill is 21.4. Find
the height of the pole.
Answer: [tex]37.4\ m[/tex]
Step-by-step explanation:
Given length of shadow [tex]l=55\ m[/tex]
Hill inclination [tex]21.4^{\circ}[/tex]
Angle of elevation for sun [tex]48.3^{\circ}[/tex]
Suppose the length of the pole is [tex]h[/tex]
from the figure, and using sine rule. It can written
[tex]\Rightarrow \dfrac{55}{\sin 41.7^{\circ}}=\dfrac{h}{\sin 26.9^{\circ}}\\\\\Rightarrow h=55\cdot\dfrac{\sin 26.9^{\circ}}{\sin 41.7^{\circ}}\\\\\Rightarrow h=55\cdot 0.68011\\\Rightarrow h=37.40\ m[/tex]
Enter an equation in point-slope form for the line.
Slope is 4 and (-2,-1) is on the line.
The equation of the line in point slope form is:
Answer:
[tex]y+1=4(x+2)[/tex]
Step-by-step explanation:
Hi there!
Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where m is the slope and (x₁,y₁) is the given point
[tex]y-y_1=m(x-x_1)[/tex]
Plug in the slope and the point
[tex]y-(-1)=4(x-(-2))\\y+1=4(x+2)[/tex]
I hope this helps!
The circumference of a circle is 11 pi ft. find its diameter, in feet
Answer:
11 feet
Step-by-step explanation:
Use the circumference formula, C = [tex]\pi[/tex]d
Plug in 11[tex]\pi[/tex] as C, and solve for d:
C = [tex]\pi[/tex]d
11[tex]\pi[/tex] = [tex]\pi[/tex]d
11 = d
So, the diameter is 11 feet
What is the value of y? 72
Answer:
D. 54
Step-by-step explanation:
54 + 54 = 108, and 72 + 180 equals 180 degrees.
This is due to the fact all angles in a triangle add up to 180 degrees.
can yaweeeeeeeee hlp
Answer:
( 25 x 100 )
option 1 is the answer
Step-by-step explanation:
Remaining options are not correct since they don't have 100 as a factor.
Volume of this hemisphere give answer to one decimal place
Answer:
[tex] \implies \rm Volume_{(Hemisphere)} = \dfrac{2}{3}\pi {r}^{3} \\ [/tex]
[tex]\implies \rm Volume_{(Hemisphere)} = \dfrac{2}{3} \times \dfrac{22}{7} \times 8 \times 8 \times 8 \\ [/tex]
[tex]\implies \rm Volume_{(Hemisphere)} = \dfrac{2}{3} \times \dfrac{22}{7} \times 512 \\ [/tex]
[tex]\implies \rm Volume_{(Hemisphere)} = \dfrac{22528}{21} \\ [/tex]
[tex]\implies \rm Volume_{(Hemisphere)} = 1072.8\: {cm}^{3} \\ [/tex]
hey are In 1990 oranges cost $0.56 per pound. In 2003 they cost $0.86 per pound. How 0 35. much did the oranges appreciate (percent of increase)?
SHOW YOUR WORK.
Answer:
Solution given:
in 1990
cost of orange[C.P]=$0.56
in 2003
cost of orange[S.P]=$0.86
now
increased price[profit]=S.P-C.P=$0.86-$0.56=$0.3
Now
increased percent [profit%]=?
we have
profit%=profit/c.p*100%
=0.3/0.56*100=53.57℅
Therefore
the oranges appreciated by 53.57%
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
Given:-are In 1990 oranges cost $0.56 per pound. In 2003 they cost $0.86 per poundFind:-percentage of increasing Solution:-we have, 1990 oranges cost $0.56 per pound. In 2003 they cost $0.86 per pound.
so,
C.P of 1990=0.56$c.p of 2003=0.86$[tex]\sf{increase_{(profit)}=0.86-0.56=0.3 }[/tex]
we know that,
[tex]\bold{ profit\%=\dfrac{profit}{C.P}×100 }[/tex]
According to the question,
[tex]\sf{percentage_{(profit)}=\dfrac{0.3}{0.56}×100 }[/tex] [tex]\sf{percentage_{(profit)}=\dfrac{5357}{100} }[/tex] [tex]\sf{percentage_{(profit)}=53.57\% }[/tex]What are the x-intercepts of the parabola?
A: (4.5, 0) and (5, 0)
B: (0, 4.5) and (0, 5)
C: (0, 5) and (0, 4)
D: (5, 0) and (4, 0)
Answer:
D: (5, 0) and (4, 0)
Step-by-step explanation:
The x-intercepts of a parabola are the points where the parabola intersect the x-axis (horizontal axis). Therefore, the y-value of the x-intercepts are always 0. Since coordinates are written (x, y), we can immediately eliminate answers B and C.
Next, we look at the x-coordinates of where the parabola intersects the x-axis. We can see clearly that the parabola crosses the x-axis at [tex]x=4[/tex] and [tex]x=5[/tex]. Therefore, the x-intercepts of the given parabola are (4, 0) and (5, 0).
Which of the following is perpendicular to 4x - 3y = 8?
Select one:
a. -8x + 12y = 7
b. 6x + 8y = 9
c. -4x - 3y = 8
d. -8x + 6y = 5
Answer:
a.-8x-12y
Step-by-step explanation:
i hope it will help u
The equation of line -4x - 3y = 8 is perpendicular to the given line of the equation which is the correct answer would be option (C).
What are the perpendicular lines?Perpendicular lines are two lines that cross one other and create a 90-degree angle.
The equation of the line below which is given in the question
4x - 3y = 8
We have to determine which is perpendicular to the given equation of the line
First, we need to find the slope of the given equation.
4x - 3y = 8
- 3y = - 4x + 8
Divided by -3 into both sides of the above equation,
y = (- 4/-3)x + 8/(-3)
y = (4/3)x - 8/3
Comparing the above equation with the standard form of line y = mx + b
Here m is the slope of the line, in this case, m = 4/3.
As per option (C),
- 3y = 8 + 4x
Divided by -3 into both sides of the above equation,
y = - 4/3x - 8/3
Here the slope of this line is - 4/3
Therefore, the equation of line -4x - 3y = 8 is perpendicular to the given line of the equation.
Hence, the correct answer would be option (C).
Learn about the perpendicular lines here :
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Steve's math homework took him 17 minutes. His science homework took him 22 minutes. How much time did it take Steve to finish his math and science homework?
Answer:
39 minutes for both
Step-by-step explanation:
22+17=39
Answer:
It took Steve 39 minutes to finish both his math and science.
Step-by-step explanation:
17+22=39
What is the area of this figure
Help please
Step-by-step explanation:
A you see here, we have 3 different shapes. a Triangle, a big and small rectangle. Lets start with the triangle.
between the 8 in's, theres a gap. 5+4=9,
9+8+8=25. we have the length of the triangle.
9*25 divided by 2= 112.5. thats are area of the triangle.
for the bigger rectangle, 20*9=180, the area of the rectangle, and the smaller rectangle at the bottom is 16.
Now we add:
112.5+180+16=308.5
hope this helps!
Which graph represents the function f(x) = √x+3 – 1?
Answer:
look at the png below
Step-by-step explanation:
Steve is traveling from Atlanta to Houston, a distance of 704 miles. If he divides the trip into two parts,
which the ratio of the parts is 2:5, how many miles does he drive in each section?
Answer:
201.14 , 502.85
Step-by-step explanation:
704/7 = 100.57
2*100.57 = 201.14
5*100.57 = 502.85
Determine wether the graph shows a positive correlation, negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in this situation.
Answer:
the answer is C.
Step-by-step explanation:
in this situation as time passes, the number of quarts picked decreases.
hope it helps!
Using the graph, determine the equation of the axis of symmetry.
Answer:
x = - 3
Step-by-step explanation:
The axis of symmetry passes through the vertex ( turning point ) of the graph and is a vertical line with equation
x = c ( c is the value of the x- coordinate of the vertex )
The vertex is (- 3, - 1 ) with x- coordinate - 3 , then
equation of axis of symmetry is x = - 3
What is the area of the label on a soup can that is 8 inches high and has a diameter of 4 inches? Round to the nearest hundredth. Assume the label wraps around the entire height of the can and does not overlap. SHOW WORK..
Answer:
Area of label = 100 inch² (Approx.)
Step-by-step explanation:
Given:
Height of label = 8 inches
Diameter of label = 4 inches
Find:
Area of label
Computation:
Design of label = Rectangle
So,
Width of label = 2πr
Width of label = 2(3.14)(4/2)
Width of label = 2(3.14)(2)
Width of label = 12.56 inches
Area of label = Height of label x Width of label
Area of label = 12.56 x 8
Area of label = 100.48
Area of label = 100 inch² (Approx.)
what is the value of the expression below? (8^5/3)^1/5
Answer:
8^1/3
Step-by-step explanation:
(8^5/3)^1/5
8^5/3×1/5
8^5/15
8^1/3
Answer:
Step-by-step explanation:
Exponent Rule: [tex](a^{m})^{n}=a^{m*n}[/tex]
[tex](8^{\frac{5}{3}})^{\frac{1}{5}}= 8^{\frac{5}{3}}*{\frac{1}{5}}\\\\\\=8^{\frac{1}{3}}\\\\= \sqrt[3]{8} \\\\= \sqrt[3]{2*2*2}\\\\= 2[/tex]
Line ab and cd (if presented in the picture) are straight lines. Find x (the pictures are not scaled)
Answer:
[tex]x + 2x + 34 + 20 = 180 [/tex]
Answer:
x=42
Step-by-step explanation:
Statement Reason
1. m∠AOB = 180° — Def. of straight ∠
2. m∠AOE + m∠EOF + m∠FOB = m∠
AOB —- Parts − whole Postulate
3. x + 2x+34° + 20° = 180° —- Substitution
4. x = 42°. —- Algebra
This is statement and reason! (no problem rsm people)
1/2a=11
a=? P.S I am not in high school I am in 4TH GRADE!!!
Answer:
a: 1/22
Step-by-step explanation:
cross multiply 1/2a=11
which will give 22a=1
divide both sides by 22
to give a=1/22
Matt covers a distance of 300 miles in 10 hours. Given that he covers an equal distance every hour, find the distance covered by him in 4 hours.
Which expression is equivalent to 6(3n-4)?
1)9n-10
2)18n-24
3)18n-4
4) 3n-24
Answer:
[tex]18n - 24[/tex]
Step-by-step explanation:
[tex]6(3n - 4) = 18n - 24[/tex]
Answer:
18n-24
Step-by-step explanation:
6(3n-4)
Open the brackets .......
(6×3n)-(6×4)
=18n_24
Please help me with this question please and thank you ❤️
Answer:
x = -1
Step-by-step explanation:
3x - 1/9 (27) = 18
3x - 3
Divide both sides be 3
x = -1
Answer:
x = 7
Step-by-step explanation:
to solve this equation we are given the value of y which 27. just substitute 27 for y in the equation :
3x - 1/9(27) = 18
3x - 3 = 18
3x = 21
x= 7
What is the solution to the system of equations represented by these two lines?
Question 7 options:
(0, 4)
(2, 0)
(4, 2)
(2, 3)
The answer is: (2, 3) :)
What is the function rule for the line?
Answer:
y =2/3x -2
Step-by-step explanation:
The y intercept is -2
The slope is
m = (y2-y1)/ (x2-x1)
Using the points (0,-2) and (3,0)
m = ( 0 - -2)/(3 -0)
= (0+2)/(3-0)
= 2/3
The slope intercept form is
y = mx+b where m is the slope and b is the y intercept
y =2/3x -2
Consider the following 8 numbers, where one labelled
x
is unknown.
12, 46, 31,
x
, 49, 24, 41, 14
Given that the range of the numbers is 63,
work out 2 values of
x
.
Put the data set in order:
12, 14, 24, 31, 41, 46, 49
In order to find a value of x using the range, x has to be on either end of the data set. Meaning:
x, 12, 14, 24, 31, 41, 46, 49 or 12, 14, 24, 31, 41, 46, 49, x
Since the range is the highest value minus the lower value, you can set two equations for x:
x - 12 = 63
x = 75
49 - x = 63
x = -14
Thus, x = 75, -14
Two values of x are -14 & 75
What is range of numbers ?The difference between highest and lowest numbers of the set of numbers is called the range of numbers.
What are the values of x ?The given values are 12, 46, 31, 49, 24, 41, 14
Arranging all the values in ascending order we get,
12, 14, 24, 31, 41, 46, 49
If x will be included, then x is in the 1st position or in the last position.
Then the values are x, 12, 14, 24, 31, 41, 46, 49 or 12, 14, 24, 31, 41, 46, 49, x
The range of the number is 63
So, we get two equations from it.
1 ) 49-x = 63
2 ) x-12 = 63
Solving eq. (1) we get, x = 49-63 = -14
Solving eq. (2) we get, x = 63+12 = 75
So the values of x are -14 & 75
Learn more about range of number here :
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