The x-intercept and the y-intercept of the original equation of line 2x-5y=20 is (10,0) and (0,-4).
What is defined as the x and y intercepts?An intercept is a y-axis point by which the slope of a line passes. It is the y-coordinate of a point on the y-axis in which a straight line or a curve intersects. This is represented by the equation for a straight line, y = mx+c, where m is the slope as well as c is the y-intercept.The x-intercept occurs where y=0, and the y-intercept occurs where x=0.
2x-5y=20 is the original equation of the line.
1) Substitute 0 for y to obtain 2x - 5(0) = 20, that equals 2x = 20.
Now, find x by dividing all sides by 2, and x = 10, resulting in the x-intercept (10,0)
2) Substitute 0 for x to obtain 2(0) - 5y = 20, which equals -5y = 20.
Now, find y by dividing all sides by 5, and y = -4, implying that the y-intercept is (0,-4).
Thus, the x-intercept and the y-intercept of the original equation 2x-5y=20 is (10,0) and (0,-4).
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Graph they given functions FNG in the same rectangular coordinate system describe the graph of G is related to the graph of F
Functions given:
[tex]f(x)=4x[/tex][tex]g(x)=4x-4[/tex]Using a graphing calculator, we can find the graph of both functions:
The red line is representing f(x) graphically, while the blue line is representing g(x) graphically.
As they have the same slope, then f(x) is parallel to g(x).
Answer:
The functions are parallel.
factor each trinomial if the trinomial cannot be factored write prime. show ALL work1.) 2x^2+5x-122.) 6x^2-23x+7
1) the initial expression is:
[tex]2x^2+5x-12[/tex]To factor this expression we can use the cuadratic formula that is:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4(a)(c)}}{2(a)} \\ a=2 \\ b=5 \\ c=-12 \end{gathered}[/tex]so we replace the values and we get:
[tex]\begin{gathered} x=\frac{-5\pm\sqrt[]{5^2-4(2)(-12)}}{2\cdot2} \\ x=\frac{-5\pm\sqrt[]{121}}{4} \\ x=\frac{-5\pm11}{4} \end{gathered}[/tex]So now we have two solutions so:
[tex]\begin{gathered} x_1=\frac{-5+11}{4}=\frac{6}{4}=\frac{3}{2}=1.5 \\ x_2=\frac{-5-11}{4}=-\frac{16}{4}=-4 \end{gathered}[/tex]so the factor expression will be:
[tex](x-\frac{3}{2})(x+4)[/tex]2) the initial expression is:
[tex]6x^2-23x+7[/tex]so we repeat the same procedure so:
[tex]\begin{gathered} x=\frac{23\pm\sqrt[]{23^2-4(6)(7)}}{2(6)} \\ x=\frac{23\pm\sqrt[]{529-168}}{12} \\ x=\frac{23\pm\sqrt[]{361}}{12} \\ x=\frac{23\pm19}{12} \end{gathered}[/tex]So the two possible solutions are:
[tex]\begin{gathered} x_1=\frac{23+19}{12}=\frac{42}{12}=\frac{7}{2}=3.5 \\ x_2=\frac{23-19}{12}=\frac{4}{12}=\frac{2}{6}=\frac{1}{3}=0.33 \end{gathered}[/tex]so the factor form is:
[tex](x-\frac{7}{2})(x-\frac{1}{3})[/tex]Macy babysits the children in her neighborhood. For each family, she charges a flat fee plus a per hour charge as described by the data in the table.Which equation represents the total amount Macy charges for each family where x represents the number of hours she babysits? A. y = 4x + 71 B. y = 9x + 7 C. y = 4x + 36 D. y = 13x + 117
Answer:
B. y=9x+
Explanation:
To deermine tehe equation, pick two pairs of points from the table.
• The points are (8, 79) and (12, 115)
Substitute these points into the lope-ointercept form of the equation of a line.
[tex]y=mx+b[/tex]At (8,79): x=8 and y=79
[tex]79=8m+b[/tex]At (12, 115): x=12 and y=115
[tex]115=12m+b[/tex]Solve the two equations siultaneously fror m and b.
[tex]\begin{gathered} 79=8m+b \\ 115=12m+b \\ Subtract \\ -36=-4m \\ \implies m=\frac{-36}{-4}=9 \end{gathered}[/tex]Next, substitute m=9 into the first equation to solve for b:
[tex]\begin{gathered} 79=8m+b \\ 79=8(9)+b \\ b=79-72 \\ b=7 \end{gathered}[/tex]Substitute m=9 and b=7 into the slope-intercept form:
[tex]y=9x+7[/tex]The equation that represents the total amount Macy charges for each family where x represents the number of hours she babysits is:
[tex]y=9x+7[/tex]Option B is correct.
The function y=f(x)is graphed below. What is the average rate of change of the function f(x) on the interval−4≤x≤−1
STEP - BY - STEP EXPLANATION
What to find?
The average rate of change of the given function.
Given:
Step 1
State the average rate of change formula.
[tex]Average\text{ rate of change=}\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]Step 2
Determine the values of the function at the given interval.
Let x₁ = -4 and x₂ = -1
Locate f(x₁) and f(x₂) on the graph given.
f(x₁) = 4 and f(x₂)= -2
Step 3
Substitute the values into the formula and simplify.
[tex]Average\text{ rate of change=}\frac{-2-4}{-1+4}[/tex][tex]=\frac{-6}{3}[/tex][tex]=-2[/tex]ANSWER
Average rate of change = -2
Solve x for the following equation
2^-x =3 * 2^x
in words: 2 to the power of -x = 3 times 2 to the power of x
The solution of x for the exponential equation 2⁻ˣ =3 × 2ˣ would be x = - log 3 / log 2.
What are the properties of logarithms?There are four basic properties of logarithms:
logₐ(xy) = logₐx + logₐy.
logₐ(x/y) = logₐx - logₐy.
logₐ(xⁿ) = n logₐx.
logₐx = logₓa / logₓb.
The given exponential equation below is:
2⁻ˣ = 3 × 2ˣ
Take the logarithm on both sides of the equation,
log 2⁻ˣ = log 3 × 2ˣ
-x log 2 = log 3 + log 2ˣ
-x log 2 = log 3 + x log 2
x log 2 = - log 3
x = - log 3 / log 2
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Suppose a normal distribution has a mean of 18 abd a standard deviation of 4. A value of 24 is how many standard deviations away from the mean
Normal Distribution
The normal distribution can be described by two parameters: the mean and the standard deviation.
We are given the parameters of a normal distribution as follows:
Mean = 18
SD = 4
A value of 24 is 24 - 18 = 6 units away from the center of the distribution, or the mean value.
Calculating the ratio of 6 units by 4 units, we get 6 / 4 = 1.5
This means the given value is 1.5 standard deviations away from the mean
What line gets the proportionality between y and x of 4/3
3k-18 written as a product of 3
The answer is 6
If you divide 18 by 3 it's 6
Last semester, Jim earned an A in his 4-credit MATH 128 class, a B+ in his 3-credit ENG 152 class, a C- is his 2-credit COM 210 class, and a A- in his 5-credit HIST 151 class. What was his GPA for the semester? Be sure to use the following grade values in your calculation.
Jim's GPA for the last semester was 3.41.
What is the GPA?The Grade Point Average (GPA) is the summary of academic achievement in an academic period (semester).
GPA is computed as course unit value multiplied by grade points, divided by the sum of course units.
The Grade Point Average (GPA) may also be described as the cumulative GPA, that is, the sum of the grade points divided by the sum of the units.
Determining a student's GPA helps the school administrators to ascertain the student's academic progress, verifying areas for further improvement.
Class Course Grade Credit Hours Grade Value Total Grade
MATH 128 A 4 4.0 16 (4 x 4)
ENG 152 B+ 3 3.3 9.9 (3 x 3.3)
COM 210 C- 2 1.7 3.4 (2 x 1.7)
HIST 151 A- 5 3.7 18.5 (5 x 3.7)
Total 14 47.8
GPA = 3.41 (47.8/14)
Thus, for last semester, Jim's GPA was 3.41.
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4)PQRS is a rectangle. The length of the diagonal PR is 10cm. If PQ = 8cm, find the perimeter of the
rectangle.
The perimeter of the rectangle PQRS would be 28 cm which is the addition of all lengths of sides.
The given rectangle PQRS that has a length of the diagonal PR is 10 cm and PQ = 8 cm
What is the perimeter of the rectangle?The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.
To determine the perimeter of the rectangle.
Since opposite sides of the rectangle and diagonal are equal.
⇒ PQ = SR = 8 cm
⇒ PR = QS = 10 cm
⇒ PS = QR = x cm (suppose)
In the rectangle, all the angles are right angles
Now in △QRS,
Using Pythagoras' theorem, we have
QS² = QR² + SR²
10² = x² + 8²
x² = 100 - 64
x =√36
x = 6 cm
So length of PS = QR = 6 cm
The perimeter of the rectangle = PQ + SR + PS + QR
The perimeter of the rectangle = 8 + 8 + 6 + 6 = 28 cm
Therefore, the perimeter of the rectangle PQRS would be 28 cm.
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A mint milk shake contains 1.25 fluid ounces of milk for every 4 ounces of ice cream. A strawberry milk shake contains 1.75 fluid ounces of milk for every 5 ounces of ice cream. Which milk shake is thicker? Explain.?
Both milkshakes have the same thickness.
How to find the thickness of milk?
Given,
A mint milkshake contains 1.25 fluid ounces of milk for every 4 ounces of ice cream.A strawberry milkshake contains 1.75 fluid ounces of milk for every 5 ounces of ice cream.Solution:
Since the mint milkshake contains 1.25 fluid ounces of milk for every 4 ounces of ice cream,One ounce ice equal = 1.25 / 4 = 0.35 ounce of milk.Since the strawberry milkshake contains 1.75 fluid ounces of milk for every 5 ounces of ice cream,One ounce of ice equal = 1.75 / 5 = 0.35ounce of milk.Since both have an equal milk-ice ratio, both milkshakes have the same thickness.To learn more about ratios, refer
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What property of real numbers does each statement demonstrate? a + (-a) = 0 A Additive Inverse B Commutative Property of Addison c Associative Property of Addron o Distributive Property
solution
For this case the best way to solve this problem
a +(-a)=0
Is using the :
A. Additive inverse property
My family has 12 member coming for Christmas dinner. Each person eats an average of 4 lbs of food. How much food should I prepare?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Family
12 members
4 lb food per person
total food = ?
Step 02:
total food
[tex]\begin{gathered} \text{total food = 12 people}\cdot\frac{4lb}{\text{person}} \\ \end{gathered}[/tex]total food = 48 lb
The answer is:
You should prepare 48 lb of food
At an after-season sale on winter clothes, I found a bunch of really cute hats and scarves. I decided to buy two hats and two scarves for myself to have for next year. I spent $72. When I told my friends about the sale, they asked me to go back and get something for them. I ended up spending $46 on one hat and two scarves. What was the price of a single hat and a single scarf?Write two integers separated by comma, no spaces, no dollar sign
ANSWER
One hat costs $26 and one scarf costs $10
EXPLANATION
Let the price of one hat be h.
Let the price of one scarf be s.
Two hats and two scarves cost $72. This implies that:
[tex]2h+2s=72[/tex]One hat and two scarves cost $46. This implies that:
[tex]h+2s=46[/tex]From the second equation, make h the subject of the formula:
[tex]h=46-2s[/tex]Substitute that into the first equation and solve for s:
[tex]\begin{gathered} 2(46-2s)+2s=72 \\ 92-4s+2s=72 \\ \Rightarrow92-72=4s-2s \\ 2s=20 \\ \Rightarrow s=\frac{20}{2} \\ s=\$10 \end{gathered}[/tex]Substitute the value of s into the equation for h and solve for h:
[tex]\begin{gathered} h=46-2(10) \\ h=46-20 \\ h=\$26 \end{gathered}[/tex]Hence, one hat costs $26 and one scarf costs $10.
If you own a larger lawn, you must use more water to hydrate it.
Identify the independent variable.
Answer:
the independent variable is the lawn size
Step-by-step explanation:
Answer: The lawn size
Step-by-step explanation: The independent variable is the input which causes the output to change.
Need to know if I’m doing this right and understanding it
Solution
Intercepts : (0 , ) and (160, 0 )
Symmetry: x = 60
positive: (0 , 120)
negaive: (--∝ , 0) U (120 , +∝)
Increasing: (-∝ , 60)
Decreasng ; (60 , +∝)
Relatve extrema: (150
Is 2x-y=44x-2y=6 A Consistent and dependent?
Solution
We are given the two equations
[tex]\begin{gathered} 2x-y=4\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(1) \\ 4x-2y=6\ldots\ldots\ldots.\ldots\ldots\text{.}(2) \end{gathered}[/tex]Now, equation (1) x 2
[tex]\begin{gathered} 4x-2y=8\ldots\ldots.\ldots\ldots\ldots\ldots\ldots(1) \\ 4x-2y=6\ldots\ldots\ldots\ldots\ldots\ldots.\ldots(2) \end{gathered}[/tex]Equation (1) - equation (2)
[tex]\begin{gathered} (4x-4x)+(-2y-(-2y))=8-6 \\ 0+0=2 \\ 0=2 \end{gathered}[/tex]Which is never possible!
Therefore, the system of equation is NOT consistent.
Note:
Let us also draw the graph of the eqautionm given
Therefore, the system of equation is Inconsistent and Independent
Which decimal equivalent is NOT correct for the given set of numbers
EXPLANATION
Since the value 7/10 is equivalent to 0.7, not to 0.07, the last equivalence is NOT correct.
help me please
thank you
Part (a)
[tex]P(0)=0.7166(0)^2+6.267(0)+1.344 \approx 1.3[/tex]
Part (b)
[tex]P(5)=0.7166(5)^2+6.267(5)+1.344 \approx 50.6[/tex]
Part (c)
[tex]P(10)=0.7166(10)^2+6.267(10)+1.344 \approx 135.7[/tex]
Complete the remaining steps of the proof:given: -angle QSR is congruent to angle TRS-side PR is congruent to side PSProve:triangle QSR is congruent to triangle TRS. StatementsReasons1. Given1. PR = PSZQSR *ZTRS2. ZTSR * ZQRS 2.I3. SR RS3.4. AQSR SATRS4.Corresponding parts of congruent triangles arecongruent:: Base angles of an isosceles triangle are congruentReflexive property:: Side-Angle-Side (SAS) postulateAngle-Side-Angle (ASA) postulate
Write out the given parameter for the proofing
Given:
[tex]\begin{gathered} \Delta QSR\cong\Delta TRS \\ \vec{}PR\cong\vec{}PS \end{gathered}[/tex]From the given parameters, it can be seen that triangle PSR is an isosceles triangle because two sides (line PR and line PS) are equal
An isosceles triangle has two equal base angles.
[tex]\angle TSR\cong\angle\text{QRS(base angles of isosceles triangle are equal)}[/tex]Triangle QSR and triangle TRS has a common side which is line SR and line RS. This property is reffered to as reflective property
[tex]\vec{}SR\cong\vec{}RS(reflective\text{ property)}[/tex]From the above proofs, it can be seen the triangle QSR and triangle TRS have a same side and same angles
Therefore,
[tex]\Delta QSR\cong\Delta TRS(angle-side-angle(ASA)postulate)[/tex]Nothing
7x+19 (less than or equal too) 12
Answer:
x [tex]\leq[/tex] 17/7
Step-by-step explanation:
7x + 19 [tex]\leq[/tex] 12
Is the inequality you are trying to solve.
When solving an inequality, we solve it like a regular equation and do inverse operations by looking at the number and doing the opposite of whatever its operation is. Whatever happens on one side happens to the other. So you would first subtract 19 on both sides.
1. 7x + 19 [tex]\leq[/tex] 12
-19 -19
7x [tex]\leq[/tex] -17
the reason we subtracted was because the opposite operation to addition is subtraction as the number 19 had had a plus sign behind it
--
We would now divide as the operation opposite to multiplication is division and 7x is 7 times x
2. 7x [tex]\leq[/tex] -17
÷7 ÷7
x [tex]\leq[/tex] [tex]\frac{17}{7}[/tex] OR 2 [tex]\frac{3}{7}[/tex]
--
The answer is:
x [tex]\leq[/tex] 17/7
Hope this helped!
Geometry Angle of Depression and Angle of Elevation. 2. - 3.
2) We can draw this situation as:
We can now find the angle x.
We can use trigonometric ratios as:
[tex]\begin{gathered} \tan(x)=\frac{Opposite}{Adjacent}=\frac{23}{34} \\ x=\arctan(\frac{23}{34}) \\ x\approx34.08\degree \end{gathered}[/tex]3) We can draw this situation as:
We can find x as:
[tex]\begin{gathered} \tan(x)=\frac{Opposite}{Adjacent}=\frac{12}{17} \\ x=\arctan(12/17) \\ x\approx35.22\degree \end{gathered}[/tex]Answer:
2) 34.08°
3) 35.22°
For installation with a 300-kVA, 3-phase transformer, a 480-volt primary, and a 240-volt secondary. Calculate the maximum overcurrent protection value (not the fuse or circuit breaker rating) using the protection method for primary-only protection. (Round the FINAL answer to two decimal places.)
By using the protection method for primary-only protection, the maximum overcurrent protection (MOCP) is equal to 451.59 Amperes.
What is MOCP?In Electrical engineering, MOCP is an abbreviation for maximum overcurrent protection and it can be defined as the maximum allowable current rating that is required for any circuit breaker or fuse, in order to properly protect an electrical equipment, especially under uncertain or anticipated fault conditions.
Mathematically, the amount of current flowing through the primary winding of a three-phase transformer can be calculated by using this mathematical expression:
Current, I = 3-phase KVA/(1.73 × Voltage)
Substituting the given parameters into the formula, we have;
Current, I = 300,000/(1.73 × 480)
Current, I = 300,000/830.4
Current, I = 361.27 Amperes.
By using the protection method for primary-only protection, the maximum overcurrent with 25% above the current is given by:
Maximum overcurrent = 125% × Current
Maximum overcurrent = 125/100 × 361.27
Maximum overcurrent = 45,158.75/100
Maximum overcurrent = 451.5875 ≈ 451.59 Amperes.
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he Hamiltons are paving their driveway. They are paving a rectangular area and an area in the shape of a parallelogram to make it easier to turn around and pull out of the driveway. A sketch of the plan for their driveway uses a scale of 1 in. for every 3 ft. What is the actual area of the entire driveway they want to pave?
If they are paving a rectangular area and an area in the shape of a parallelogram to make it easier to turn around and pull out of the driveway. A sketch of the plan for their driveway uses a scale of 1 in. for every 3 ft. The actual area of the entire driveway they want to pave Is 1350 feet²
Actual areaFirst step is to find the length of both side
Actual length on side
Length = ( 5 + 4) × 3
Length = 9 × 3
Length = 27 feet
Actual length of the other side
Length = 16 2/3 × 3
Length = 16 ×3 +2/3 ×3
Length = 16×3+2
Length = 48 +2
Length = 50 feet
Now let determine the actual area of the whole driveway they want t0 pace
Actual area = 50 feet × 27 feet
Actual area = 1350 feet²
Therefore we can conclude that the actual area is 1350 feet².
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Joe has 3/4 cup of paint in a container. He uses 1/3 cup on a project and then adds another 1/2 cup. How much paint does he have now?
Answer:
Step-by-step explanation:
The cup of paint he has now is 11/12.
What is the amount of paint he has now?We are basically going to add or subtract the quantity of cup added or used respectively.
Initially, he has 3/4 cup of paint.
He uses 1/3 cup out of the 3/4 cup of paint, so we subtract 1/3 from 3/4:
= 3/4 - 1/3 = 5/12
He adds another 1/2 cup, so we add 1/2 to what we have left previously (5/12):
= 5/12 + 1/2 = 11/12
Therefore, the amount of paint he has now is 11/12 cup
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The ratio of boys to girls in Ms. Cunningham’s class is 2 to 3. There are 18 girls in the class. What is the TOTAL number of students in Ms. Cunningham’s class?
Responses
The total number of students(boys and girls) in Ms. Cunningham’s class are 30.
Number of girls in the class =18
The ratio of boys to girls in Ms. Cunningham’s class is 2 to 3
i.e. Ratio of boys and girls =2:3
Boys : Girls = 2 : 3
B/G = 2/3 -------1.
B/18 = 2/3
B = (18 x 2)/3
Boys = 12
Number of boys in the class = 12
Boy = 2x
12 = 2x
x = 12/2 = 6
number of girls in the class is 3x
3 x 6 = 18
Therefore, total number of students =12+18=30
The total number of students(boys and girls) in Ms. Cunningham’s class are 30.
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Evaluate the expression y=-4y^2 + 6y+9by th way that's y to the power of 2
we have the following:
[tex]y^2+6y+9[/tex]replacing, y = -4
[tex]\begin{gathered} (-4)^2+6\cdot(-4)+9 \\ 16-24+9=25-24=1 \end{gathered}[/tex]therefore, the answer is 1
19. Put these numbers in order from least to greatest: V36, V27, V16, V10, V8, V64(2 pts.)-2520 adenotto
EXPLANATION
Putting the numbers from least to greast give us:
8, 10, 16, 27, 36, 63
Santa owed $91 on a bill. By mistake Santa sent a check for $120. What is the balance on Santa's account?
ANSWER
[tex]\$29[/tex]EXPLANATION
To find the balance on Santa's account, we have to subtract the amount he owed from the amount on the check he sent.
Therefore, the balance on Santa's account is:
[tex]\begin{gathered} 120-91 \\ \Rightarrow\$29 \end{gathered}[/tex]That is the answer.
a ____ polynomial is a polynomial with a degree of 3
Let's understand some definitions first:
Polynomial - an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s). (oxford languages)
When we have 1 term, we call it a monomial.
When we have 2 terms, we call it a binomial.
When we have 3 terms, we call it a trinomial.
Now,
• When the power of a variable is 1, we call it a line:
[tex]\begin{gathered} x \\ 2x \\ \text{etc.} \end{gathered}[/tex]• When the highest power is 2, we call it a quadratic polynomial:
[tex]\begin{gathered} x^2 \\ 3x^2 \end{gathered}[/tex]• When the highest power is 3, we call it a cubic polynomial:
[tex]\begin{gathered} x^3 \\ -2x^3 \end{gathered}[/tex]Question
A ____ polynomial is a polynomial with a degree of 3
Answer
A cubic polynomial is a polynomial with a degree of 3
