Answer:
y = 10x - 8
Step-by-step explanation:
The slope is "m", or how much the y-value changes on a line when the x-value changes by one.
The y-intercept is the y value of the line when it is intersecting the y-axis, or when the x-value is 0.
To find the slope, take 2 points from the graph and plug into the slope formula:
[tex]\frac{y_2-y_1}{x_2-x\\_1}[/tex]
I'll use (0, -8) and (1,2).
Plug into the formula.
[tex]\frac{2--8}{1-0}[/tex]
[tex]\frac{10}{1}[/tex]
10
Slope = 10
To find the y-intercept, look at the table. What is the y-value when the x-value is equal to 0?
-8
y-intercept: -8
Slope-Intercept form:
y = mx + b
m: slope
b: y-intercept
y, x: leave as variables
y = 10x - 8
Brian drove from Houston to New York, then to Chicago, then back to Houston. How far did he drive altogether?
Houston to NY= 1608
NY to Chicago=802
Chicago to Houston=1067
Write an equation in slope-intercept form that represents the data in the table.
The equation of the line that represents the data in the table is y = 30x + 30.
How to determine the equation of line from points?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept
From the data;
Point 1( 0,30 )
x₁ = 0y₁ = 30Point 2( 2,90 )
x₂ = 2y₂ = 90First, we determine the slope.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 90 - 30 )/( 2 - 0 )
Slope m = ( 60 )/( 2 )
Slope m = 30
Next, we determine the y-intercept b by substituting the given values into the equation of line formula.
y = mx + b
30 = (30)0 + b
30 = b
b = 30
Now, plug these values into y = mx + b to determine the equation of the line.
y = mx + b
y = 30x + 30
Therefore, y = 30x + 30 is the equation of the line.
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for part B how do I find the coordinate for A double prime after the rotation
When we rotate a figure 90° around a point, we need to check the difference in x and y coordinates between the point and the center of rotation.
Then these differences will swap among themselves.
The difference in x-coordinate between A and B is 1, so now this difference will be the difference in y-coordinate.
The difference in y-coordinate between A and B is 7, so now this difference will be the difference in y-coordinate.
So the coordinates of A'' will be:
[tex]B(-2,-1)\to A^{\doubleprime}(-2+1,-1+7)=A^{\doubleprime}(-1,6)[/tex]Also, the point will be in the third quadrant, so all coordinates are negative:
[tex]A^{\doubleprime}(-1,6)\to A^{\doubleprime}(-1,-6)[/tex]Therefore the answer is C.
(-5p+8)(-3p-5) pls help me solve this asappp
Step-by-step explanation:
(-5p + 8)(-3p - 5)
[tex]15p^2 +25p - 24p -40[/tex]
[tex]15p^2 +p -40[/tex]
Philip drove 66km from Liverpool to Sheffield at 80km/h.
How many minutes did this take him?
Answer:
49.5 minutes
Step-by-step explanation:
Amount of time that Philip took
= [tex]\frac{distance}{speed}[/tex]
= [tex]\frac{66km}{80km/h}[/tex]
= [tex]0.825h[/tex]
= [tex]49.5 min[/tex]
(2x+1)(x-2)(x+3)
please help
Answer: 2x^3 + 3x^2 - 11x - 6
Step-by-step explanation: simplified
Can someone explain how to answer this problem
Write an equation in point-slope form given the following: (1,2); m=7
thanks
Answer:
Step-by-step explanation:
Answer:
y-2 = 7(x-1)
Richard bought 3 slices of cheese pizza and 2 sodas for $8.75. Jordan bought 2 slices of cheese pizza and 4 sodas for $8.50. How much would an order of 1 slice of cheese pizza and 3 sodas cost?
An order of 1 slice of cheese pizza and 3 sodas cost will be $5.25.
Define simultaneous equation.Two or more algebraic equations that share variables, such as x and y, are said to be simultaneous equations. Since the equations are solved simultaneously, they are known as simultaneous equations.
Given data -
Cost of 3 slices of cheese pizza and 2 sodas = $8.75
Cost of 2 slices of cheese pizza and 4 sodas = $8.50
Let x be the cost of 1 slice of cheese pizza
and y be the cost of 1 soda
According to the given data,
3x + 2y = $8.75 -------------equation 1
2x + 4y = $8.50 -------------equation 2
Equation 1 by equation 2 multiplied results in
6x + 4y = $17.5 ------------equation 3
By subtracting equation 2 from equation 3 to get the cost of 1 slice of cheese pizza, we will get
4x = $9
x = $2.25
By substituting the value of x in equation 2 so that we can get the cost of 1 soda, we will get
2*2.25 + 4y = $8.50
4.5 + 4y = $8.50
4y = $8.50 - 4.5
4y = $4
y = $1
To get the cost of 3 sodas, multiplying the value of y by 3
Therefore the cost of 3 sodas will be $1*3 = $3
The total cost of 1 slice of cheese pizza and 3 sodas cost = $2.25 + $3
= $5.25
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combine like terms algebra
Solve the equation 20 + 0.44x + 4 = 19 + 1.69x.
A. x = 4
B. x = 2.14
C. x = 5
D. x = 34.4
Answer: A
Step-by-step explanation: The starting equation is 24 + 0.44x = 19 + 1.69x,
First, combine the x's on the RHS, and the integers on the LHS.
1.69x - 0.44x = 1.25x
24 - 19 = 5
So the equation will be 1.25x = 5
Divide both sides by 1.25 to isolate the x.
x = 4
Select the step in the solution that shows the first error. Step 1: 5x – 3 = 2x + 6 Step 2: 3x – 3 = 2x + 6 Step 3: x – 3 = 6 Step 4: x = 3
The error is in step 2 that is 3x-3=2x+6 as in step 2 we shifted 2x to LHS side of calculation.
What is error?Error is the difference between a true value and an estimate, or approximate, representation of that value in applied mathematics. The difference between the mean of the entire population and the mean of a sample taken from that population is a frequent example in statistics. Three types of errors can occur when solving math problems: factual, procedural, and computational. Students can make a variety of math mistakes, and it's crucial to know how to avoid them and how to take lessons from them. An error is an inaccurate or incorrect action (from the Latin error, meaning "wandering"). An error is often used interchangeably with the word mistake. The term "error" in statistics describes the discrepancy between the computed value and the correct value.
Here,
5x-3=2x+6
3x-3=6
3x=9
x=3
The mistake is in step 2, which reads 3x-3=2x+6 because we shifted 2x to the LHS side of the calculation in step 1.
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a. Complete the area model and the
equation.
23 x 62 =
Answer:
Step-by-step explanation:
A parabola opening up or down has vertex 0, – 3 and passes through – 12,15. Write its equation in vertex form.
y = 0.125x² - 3 is equation of parabola in vertex form
The standard form of the parabola is [tex]y = ax^{2} + bx + c[/tex]
The vertex form of parabola is [tex]y = a(x-h)^{2} + k[/tex]
where h and k are vertex of parabola. The vertex formula is used to find vertex coordinate of parabola .
Vertex point of parabola are usually represented by (h, k).
Given that the vertex of parabola is 0, -3
(h, k) = (0, -3)
h = 0 and k = -3
substituting the values of h and k in vertex form of parabola,
[tex]y = a(x-0)^{2} -3\\y = ax^{2} - 3[/tex]
Parabola is also passing through (12,15) means it should satisfy vertex equation of parabola
[tex]15= a(-12)^{2} -3\\15+3 = 144a\\18 = 144a\\a = \frac{18}{144}\\\\a = 0.125[/tex]
Substituting value of a
Vertex form of parabola is [tex]y = 0.125x^{2} - 3[/tex]
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A 2 liter bottle filled is filled with water the water leaks 80 milliliters of water every 3 minutes will the bottle be empty in 1 hour why or why not?
Answer:
the program I will get back to you on that date is approaching the
Step-by-step explanation:
the program I will get back to you on that date is approaching the
what is 1 1/2 divided by 1/6
Answer: 66/2 or in simplest form, 33/1
Step-by-step explanation:
11/2 divided by 1/6
*Keep the first fraction, flip the sign to multiplication, reciprocal or flip the fraction*
= 11/2 x 6/1
=66/2
=33/1
2. The Access to University course in the college has 252 full-time and 140 part-
time students enrolled this year. What fraction of students are studying part-
time?
Answer:
[tex]\frac{5}{14}[/tex]
Step-by-step explanation:
First, find the total number of students:
[tex]252+140=392[/tex]
Then, divide the number of students at hand by the total number:
[tex]\frac{140}{392}[/tex]
When possible, reduce the fraction to its simpliest form:
[tex]\frac{140}{392}\div\frac{28}{28}=\frac{5}{14}[/tex]
Priya practiced the violin for 152% as much time as Han practiced the piano hiw long did she practiced, if Han practiced for 74 minutes
To find the time that Priya spent practicing violin, calculate what is 152% of 74 minutes by multiplying 74 times 152/100:
[tex]\frac{152}{100}\times74=112.48[/tex]Therefore, Priya practiced for 112.48 minutes.
Math help please help
Answer:
2,6
Step-by-step explanation:
2km:0.2m .....................
Please help me! It is about proofs, SSS and SAS.
The two given triangles are congruent because of SAS.
What does congruency mean?In geometry, two figures or objects are congruent if their shapes and sizes match, or if one is the mirror image of the other. Both of the bread slices have the same shape and size when stacked on top of the other. Congruent refers to having the same precise size and shape. Having the same size and shape makes two shapes congruent. The mirror image of one shape is the same as the other if the two shapes are congruent.
The given triangles are RTP and STP
P is the midpoint of RS and TP is the altitude of triangle RTS.
In the triangles RTP and STP
TP = TP (common)
∠RPT = ∠ SPT (90°)
RP = SP (median divides the side equally)
So, both triangles are congruent using SAS property.
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Simplify each expression. Select the correct answer from the drop-down menu.
−6(3i)(−2i) =
2(3 − i)(−2 + 4i)
16+14i will the required simplified value as the expression is -6(3i)(-2i)=2(3-i)(4i-2) which is a complex number having imaginary and real part.
What is complex number?A complex number is one with the formula a + bi, where a and b are real numbers and I is an imaginary number. Complex numbers are those that are expressed as a+ib, where a,b are real numbers and I is an imaginary number known as "iota." (√-1) is the value of i. 2+3i is a complex number, for example, where 2 is a real number (Re) and 3i is an imaginary number (Im). A complex number is one that can be expressed as a + bi, where a and b are real numbers and I is an imaginary unit, and which solves the equation i² =-1. In this expression, a represents the complex's real part and b represents its imaginary part.
Here,
-6(3i)(-2i)=2(3-i)(4i-2)
-6(-6i²)
=36i²
=-36
2(3-i)(4i-2)
=2(12i-4i²-6+2i)
=2(14i+4-6)
2(14i-2)=-36
14i-2=-18
on simplifying,
16+14i will the required simplified value.
As the expression is -6(3i)(-2i)=2(3-i)(4i-2) which is a complex number with imaginary and real parts, the required simplified value is 16+14i.
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Answer:
−6(3i)(−2i) =
✔ –36
2(3 − i)(−2 + 4i) =
✔ –4 + 28i
Step-by-step explanation:
I need haled on this question so air was wondering what was the equation for r-c=p
The equation r-c= p represents the profit equation
What does the equation r-c = p stands for?Profit can be defined as the difference between revenue and cost i.e. revenue minus cost. The formula for profit can be written as:
p = r - c
where r is the revenue and c is the cost
Notice that the equation, r-c = p is the same as p = r-c when rearranged.
Therefore, the equation r-c=p stands for the profit equation
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Two friends drive off in different directions from the same place. One heads North at 30 miles per
hour, while the other heads East at 40 miles per hour.
Distance =
Complete an equation for the distance between the friends after t hours. Hint: Assume the starting
point is the origin.
An equation for the distance between the two friends after time (t) in hours is given by: c = 50t
Given,
Two friends drive off in different directions from the same place. One heads North at 30 miles per hour, while the other heads East at 40 miles per hour.
We have to find the equation for the distance between the friends after t hours.
Here,
The distance covered by each friend should be calculated as follows:
For the first friend heading North, we have;
Distance, a = speed × time
Distance, a = 30t
For the second friend heading East, we have:
Distance, b = speed × time
Distance, b = 40t
By applying Pythagorean theorem, the distance between these two friends after an amount of time (t) is given by:
Distance, c² = a² + b²
Distance, c² = (30t)² + (40t)²
Distance, c² = 900t² + 1600t²
Distance, c² = 2500t²
Distance, c = √(25 × 100t²)
Distance, c = √25t² × √100
Distance, c = 5t x 10
Distance, c = 50t
Therefore,
The equation for the distance between the friends after t hours is c = 50t
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A teacher buys packs of notebooks to give to their students. The tape diagram represents the ratio of brown notebooks to red notebooks. Brown notebooks Red notebooks Based on the ratio, if there are 24 red notebooks, what is the number of brown notebooks?
The number of brown notebooks is 40.
What is the ratio?
A ratio displays the multiplicity of two numbers. For example, if there are eight oranges and six lemons in a bowl of fruit, the orange-to-lemon ratio is eight to six. Similarly, the lemon-to-orange ratio is 6:8, and the orange-to-fruit ratio is 8:14.
We have,
24 red notebooks,
∴ 5/3 = x/24.
Cross-multiply, and we now have
120 = 3x.
Divide both sides by 3,
x = 120/3
x = 40
x = 40 brown notebooks.
Hence, the number of brown notebooks is 40.
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A number time 5 less that number has a product of -4. What are the two numbers?
Let the first number be x.
The second number is 5 times less than x => x - 5
Therefore, we can write the statement as
[tex]\begin{gathered} x\times(x-5)=-4 \\ x^2-5x=-4 \\ \therefore \\ x^2-5x+4=0 \end{gathered}[/tex]Solving the quadratic equation:
Let us replace -5x in the equation with -4x and -x to be able to factorize.
Hence,
[tex]\begin{gathered} x^2-4x-x+4=0 \\ x(x-4)-1(x-4)=0 \\ (x-4)(x-1)=0 \\ \text{Therefore} \\ x-4=0\text{ } \\ or \\ x-1=0 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} x=1 \\ or \\ x=4 \end{gathered}[/tex]Therefore, the number can be 1 or 4.
The second number can be
[tex]\begin{gathered} 1-5=-4 \\ or \\ 4-5=-1 \end{gathered}[/tex]Therefore, the pair of numbers can be
[tex](1,-4)\text{ or (4, -1)}[/tex]The area of this parallelogram is 49 square centimeters.y = ____ cm.
Answer:
7 cm
Explanation:
The area of a parallelogram:
[tex]A=\text{Base}\times Height[/tex]From the diagram:
• Base = y cm
,• Height = y cm
Thus:
[tex]\begin{gathered} y\times y=49 \\ y^2=49 \\ y=\sqrt{49} \\ y=7\operatorname{cm} \end{gathered}[/tex]The value of y is 7cm.
2 points
Question at position 5
Using the chart, which two students have the same unit rate? Explain how you know this.
Name Pages Read Number of Nights
Leah 45 3
Rose 48 4
Hannah 30 3
Philip 150 10
Leah and Philip have same unit rate.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The table is shown for the number of pages and number of nights.
Now,
The unit rate to read the number of pages for Leah;
⇒ 45 / 3 = 15
The unit rate to read the number of pages for Rose;
⇒ 48 / 4 = 12
The unit rate to read the number of pages for Hannah;
⇒ 30 / 3 = 10
The unit rate to read the number of pages for Philip;
⇒ 150 / 10 = 15
Thus, Leah and Philip have same unit rate.
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Transversal c intersects lines a and b. Prove that a // b in each case.
The required solutions are m∠1 + m∠7 = 143° + 37° = 180° and 'a' is parallel to 'b' due to the same-side exterior angle.
Transversal c intersects lines a and b which is given in the question.
As per the given figure,
m∠1 + m∠7 = 143 degrees + 37 degrees = 180 degrees
m∠1 = 143° and m∠7 = 37°.
First, we can write m∠1 + m∠7 and then substitute angles with their actual degree measure:
143° + 37° = 180 degrees
The first statement will be:
m∠1 + m∠7 = 143° + 37° = 180°
Exterior indicates that both angles are on the same side, or outside, of the parallel lines.
Angles a, b, c, and d in the figure are outside of the parallel lines.
We can then state;
a and b are parallel since they both agree with the same-side exterior theorem.
As a result, 'a' and 'b' are parallel because they both satisfy the same-side exterior theorem.
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i 45° 1030 909 600 9. Is the pentagon a regular pentagon?
internal angles of the polygon
angle a = 180 - 45 = 135°
angle b = 180 - 90 = 90°
angle c = 180 - 60 = 120°
angle d = 540 - 135 - 90 - 120 - 77 = 118°
angle e = 180 - 103 = 77 °
angle x = 180 - 118 = 62°
the polygon is not a regular polygon because the measure of its angles are different
Alizeh invests $9,000 in an actively managed mutual fund that has an annual expense ratio of 1.1%. The investment earns a 5% rate of return. How much does she pay in fees for her actively managed fund?
As per the given interest rates, she have to pay $103.95 in fees for her actively managed fund.
Interest:
Interest means the amount to be paid on the borrowed money or the amount received on the money lent.
Given,
Alizeh invests $9,000 in an actively managed mutual fund that has an annual expense ratio of 1.1%. The investment earns a 5% rate of return.
Here we need to find the fees for her actively managed fund.
First we have to change rate of return percent to decimal form,
That is,
5% = 0.05
Now, we have to multiply the amount and decimal to get Alizeh 's profit,
=> 9000 x 0.05
=> 450
Therefore, the fund's total after 1 year, including initial investment and profit is
=>9000 + 450
=> 9450.
Now, we have to change fee percent that is the expense ratio into decimal form,
=> 1.1% = 0.011
Therefore, the fees for her fund is,
=> 9450 x 0.011
=> 103.95
Therefore, she have to pay $103.95 for her managed fund.
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Which value of y makes this equation true?
Which value of y makes this equation true?
12y - 1/2 = 9y +8/5
A. 1/6
B. 1/2
C. 2
D. 6
On solving the given equation the value of y=7/10 so this value the given equation will be true as the definition of solution of equation says ,"A solution to an equation is a number that can be plugged in for the variable to make a true number statement. "
What is solution to equation?A number that can be entered for the variable to produce a true number statement is the solution to an equation. One-step equations can be solved in four different ways: by adding, subtracting, multiplying, and dividing. In an equation, both sides will remain equal if we add the same amount to each side. Systems of equations can be solved using one of three techniques: graphing, substitution, or elimination. Simply plot the given equations on a graph and locate the point(s) where they all intersect to solve a system by graphing. You can find the values of the variables you are solving for by finding the coordinate of this point.
Here,
12y - 1/2 = 9y +8/5
3y=8/5+1/2
3y=(16+5)/10
3y=21/10
y=7/10
According to the definition of an equation's solution, "A solution to an equation is a number that can be plugged in for the variable to make a true number statement," the value of y will be 7/10 when the given equation is solved.
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