47 Dominic used the equation below to find d, the amount in dollars he would spend on gasolineto drive a distance of m miles.d =(3.5)Based on this equation, how much would Dominic spend on gasoline to drive a distance of180 miles?A $25.203.628B $21.00 - 2.94C $24.50 -343: 3.02D $28.00
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Answer
Explanation
The equation that
Related Questions
of what theorem is theorem 21 the converse?theorem21:if the opposite sides of a quadrilateral are equal then the figure is a parallelogram
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Theorem 1:
Opposite Sides Theorem Converse: If both pairs of opposite sides of a quadrilateral are congruent, then the figure is a parallelogram.
2. Write the equation of the graph below. y 57 4 3 2 1 -5 -4 -3,2 -1 0 1 2 .
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Cual es la coordenada-y del punto C ? What is the y-coordinate of pint C ?
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The y co-ordinate of the point C is 13.
Given, the points are :
A (2,4) = (x₁,y₁)
B (10,10) = (x₂,y₂)
Ratio of the length AC to CB is 3:1.
⇒ 3:1 = m:n
⇒ section formula C = (mx₂-nx₁/m-n) , my₂-ny₁/m-n)
substitute the values.
⇒ C = (3(10)-1(2)/3-1 , 3(10)-1(4)/3-1)
⇒ C = (30-2/2 , 30-4/2)
⇒ C = (28/2 , 26/2)
⇒ C = (14 , 13)
Hence the y coordinate of C is 13.
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Graph the inequality.3x+4y>4
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Given the inequality equation below:
[tex]3x+4y>4[/tex]Find the y-intercept
[tex]\begin{gathered} set\text{ x=0} \\ 3x+4y=4 \\ 3(0)+4y=4 \\ 4y=4 \\ y=\frac{4}{4}=1 \\ y-intercept\rightarrow(0,1) \end{gathered}[/tex]Find the x-intercept
[tex]\begin{gathered} set\text{ y=0} \\ 3x+4y=4 \\ 3x+4(0)=4 \\ 3x=4 \\ x=\frac{4}{3} \\ x-intercept\rightarrow(\frac{4}{3},0) \end{gathered}[/tex]Find the shaded area
[tex]\begin{gathered} set\text{ x=0, and y=0} \\ 3x+4y>4 \\ 3(0)+4(0)>4 \\ 0+0>4 \\ 0>4\rightarrow false \\ Shade\text{ the side of the line where \lparen0,0\rparen is not includedand use dot line} \end{gathered}[/tex]Hence, the graph is
Please please please help me
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The lines l, m, and n are parallel to each other and the value of x is 8.34.
What are parallel lines?Parallel lines are lines that are equidistant from each other and do not meet no matter how far they extend in either direction. Parallel lines form angles when crossed by a transversal and show some significant properties.
Angles that correspond are equal.Angles that are vertically opposite or vertically angled are equal.Interior angles that are opposite each other are equal.On the same side of the transversal, a pair of interior angles are supplementary.For the given question, we can see that lines l ║m ║n.
Therefore, (6x - 2)° = 52° [Vertically opposite angles are equal]
6x = 52 - 2
6x = 50
x = 50/6
x = 8.34
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4. Multiply the two polynomials using the destructive property.5. Are the two products the same when you multiply them horizontally?4. A)
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Given:
[tex](4x^2-4x)(x^2-4)[/tex]To multiply the two polynomials using the distributive property, we first follow the rule shown below:
For: (a+b)(c+d)=a(c+d)+b(c+d)=ac+ad+bc+bd
We let:
[tex]\begin{gathered} a=4x^2 \\ b=-4x \\ c=x^2 \\ d=-4 \end{gathered}[/tex]Now, we plug in what we know:
[tex]\begin{gathered} (4x^{2}-4x)(x^{2}-4) \\ =(4x^2)(x^2)+(4x^2)(-4)+(-4x)(x^2)+(-4x)(-4) \\ Simplify\text{ and rearrange} \\ =4x^4-16x^2-4x^3+16x \\ =4x^4-4x^3-16x^2+16x \end{gathered}[/tex]Therefore, the answer is:
[tex]=4x^4-4x^3-16x^2+16x[/tex]Jim invested $4,000 in a bond at a yearly rate of 4.5%. He earned $540 in interest. Howlong was the money invested? (just type the number don't write years)
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Answer:
3 years
Explanation:
The interest simple interest rate formula is
[tex]undefined[/tex]19. Which of the following regions represent the points in the solution of the inequality x ≤ 1? a. Left of the line x = 1 b. On and left of the line x = 1 c. On and right of the line x = 1 d. Right of the line x = 1
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ANSWER
b. On and left of the line x = 1.
EXPLANATION
The inequality is x less than or equal to 1. This means that the line x = 1 is included in the solution, which leaves us with options b or c.
To represent the values less than x = 1, we would take the values to the left of the line.
Hence, the region that represents the solutions of x ≤ 1 is on and left of line x = 1.
Determine The Domain for the relation below
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Answer:
The domain would be all real numbers.
Step-by-step explanation:
For Interval notation, it would be written as (-∝, ∝)
(I don't know what signs those are, but they are supposed to be infinity signs)
Domain is what x can or can't be. In the function that is in the image, the function is y=a constant. So, no matter what x is, y will always be the constant. So, x can be all real numbers.
Hope this helps!
The sum of three numbers is 106. The second number is 2 times the third. The first number is 6 more than the third. What are the numbers?First numberSecond number Third number
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Let's call the numbers a, b and c.
The first statement tells us that the sum of the three numbers is 106, so:
[tex]a+b+c=106.[/tex]The second statement tells us that the second number is two times the third so:
[tex]b=2c\text{.}[/tex]The final statement tells us that the first number is 6 more than the third, so:
[tex]a=c+6.[/tex]This gives us a system of three equations with three variables. Let's take the value of a given by the third equation, use it in the first one and isolate another variable:
[tex](c+6)+b+c=106,[/tex][tex]2c+b+6=106,[/tex][tex]2c+b=100,[/tex][tex]b=100-2c\text{.}[/tex]Let's take this value of b and use it in the second equation:
[tex]100-2c=2c,[/tex][tex]100=4c,[/tex][tex]c=25.[/tex]Now we know the exact value of c, so let's go back to the third equation:
[tex]a=25+6=31,[/tex]and now we also know the exact value of a, so let's go back to the second equation:
[tex]b=2(25)=50.[/tex]So, the first number (a) is 31, the second (b) is 50 and the third (c) is 25.
31+50+25=106.
A work shift for an employee at restaurant count of 8 hours what fraction of the employees work shift is represented by 2 hours
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Let:
T = Total number of hours = 8
n = Number of hours = 2
Therefore, the fraction is:
[tex]\frac{2}{8}=\frac{1}{4}[/tex]Answer:
[tex]\frac{1}{4}[/tex]What is the solution to the equation below? Round your answer to two decimal places.ln x = 0.2A.x = 1.58B.x = -0.70C.x = -1.61D.x = 1.22
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Given the equation:
[tex]\ln \left(x\right)=0.2[/tex]Apply the properties of logarithms:
[tex]e^{ln(x)}=e^{0.2}[/tex]Simplify:
[tex]x=e^{0.2}=1.22[/tex]Answer: D. x = 1.22
2 2 3 4 5 Enter an estimate. Round each mixed number to the nearest whole in your estimate. -38 4 9 Estimate: Find the difference and enter it in simplest form. 3 60
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To make the estimate of the substraction of the mixed numbers we use the fraction that is accompaning the whole number. If the number is less than 1/2 we say that the number is closer to the whole number before the fraction, if it is 1/2 or more then we add one to the whole number.
For the first number
[tex]5\frac{1}{4}\approx5[/tex]This is approximate to 5 because 1/4 is less than 1/2
For the second number
[tex]3\frac{8}{9}\approx4[/tex]This is approximate to 4 because 8/9 is greater than 1/2.
ESTIMATE
[tex]\begin{gathered} 5\frac{1}{4}-3\frac{8}{9}=\text{?} \\ 5-4\approx1 \end{gathered}[/tex]To pass a mixed number into a fraction we use the following procedure
[tex]a\frac{b}{c}=\frac{(a\cdot c)+b}{c}[/tex]Pass both mixed numbers
[tex]\begin{gathered} 5\frac{1}{4}=\frac{(5\cdot4)+1}{4}=\frac{20+1}{4}=\frac{21}{4} \\ 3\frac{8}{9}=\frac{(3\cdot9)+8}{9}=\frac{27+8}{9}=\frac{35}{9} \end{gathered}[/tex]To find the exact value
[tex]\frac{21}{4}-\frac{35}{9}=\frac{21\cdot9-35\cdot4}{9\cdot4}=\frac{49}{36}[/tex]answer
The exact value of the substraction is
[tex]\frac{21}{4}-\frac{35}{9}=\frac{49}{36}=1\frac{13}{36}[/tex]if the 4 in 47,502 was changed to a 7 how much would the value changed
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You have the following number given in the exercise:
[tex]47,502[/tex]According to the information given in the exercise, the digit 4 (located in the ten thousands place) was changed to a 7. Then now it is:
[tex]77,502[/tex]In order to find how much the value would change, you must find the difference (the difference, by definition, is the result of a subtraction).
In this case, knowing the value of the digits, you can set up the following subtraction:
[tex]70,000-40,0000[/tex]Solving the subtraction, you get the following difference:
[tex]=30,000[/tex]Therefore, the answer is:
[tex]30,000[/tex]Answer:30,000
(Please message me if I got this wrong)
Step-by-step explanation: Take 47,502 and turn it into 77,502. If you minus 47,502, you can see the difference/how much the value changed, which is 30,000
Simplify using the distributive property.8(y + 12)8 y + 9620 + y8 y + 1220 y
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Solution:
Concept:
The distributive property of multiplication states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then adding the two products together for the same result as multiplying the first number by the sum.
The expression is given below as
[tex]\begin{gathered} 8(y+12) \\ =8\times y+8\times12 \\ =8y+96 \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow8y+96[/tex]Is A= {9000, 5, 8, 119} a finite set?
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ANSWER
Yes, it is.
EXPLANATION
A finite set is a set that contains a finite number of elements. That is, the number of elements in a finite set are countable.
The set given is:
A = {9000, 5, 8, 119}
There are 4 elements in this set and hence, it is countable.
According to the definition of a finite set, this set is a finite set.
TRIGfind the following in triangle CAT.lineAT is 16.5angleT is 43degrees how do I solve?
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h= 22.6, CT =47º, CA=15.4
1) We're going to use trig ratios for that. So to find CT, the hypotenuse, and considering the angle 43º as our reference, we can write:
[tex]\begin{gathered} \cos (43)=\frac{adjacent}{\text{hypotenuse}} \\ \cos (43)\text{ =}\frac{16.5}{h} \\ \cos (43)h=16.5 \\ h=\frac{16.5}{\cos (43)} \\ h=22.5609\approx22.6 \end{gathered}[/tex]So the CT is equal approximately to 22.6.
2) Now let's find out the measure of angle C. The simplest way is to consider the fact that every triangle has the sum of its interior angles as 180º
90º +43º + C = 180º
133º + C = 180º
C =180º -133º
C = 47º
3) Let's focus on CA leg.
Concerning that, we can make use of another trig ratio. Since we know the measure of angle C
[tex]\begin{gathered} \tan (47)=\frac{opposite}{\text{adjacent}} \\ \tan (47)\text{ =}\frac{16.5}{CA} \\ CA=\frac{16.5}{\tan (47)} \\ CA\text{ =15.38649}\approx15.4 \end{gathered}[/tex]CA is approximately 15.4
8Σ-(-2): -1-i=1Evaluate each geometric series described. (Find the total sum)
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The given expression is
[tex]\sum ^8_{i\mathop=1}-(-2)^{i-1}[/tex]To solve this, we just have to replace each value of the sum in the expression, then we sum. Let's do it
[tex]\begin{gathered} -(-2)^{1-1}=-1 \\ -(-2)^{2-1}=-(-2)^1=2 \\ -(-2)^{3-1}=-(-2)^2=-4 \\ -(-2)^{4-1}=-(-2)^3=8 \\ -(-2)^{5-1}=-(-2)^4=-16 \\ -(-2)^{6-1}=-(-2)^5=-(-32)=32 \\ -(-2)^{7-1}=-(-2)^6=-64 \\ -(-2)^{8-1}=-(-2)^7=-(-128)=128 \end{gathered}[/tex]Now, we sum all these items
[tex]-1+2-4+8-16+32-64+128=85[/tex]Therefore, the total sum is 85.Find the derivative of the function y=(4x^ 3 -5x^ 2 )(3x^ 6 +2x^ 5 )10 two different ways. First, multiply the factors togethercollect like terms, then use the basic rules to find the derivative. Second, apply the Product Rule to the function as is currently written.
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Given:
The given function is:
[tex]y=(4x^3-5x^2)(3x^6+2x^5)[/tex]First method: Multiplying factors and differentiating after arranging like terms together.
[tex]\begin{gathered} y=(4x^3-5x^2)(3x^6+2x^5) \\ =4x^3(3x^6+2x^5)-5x^2(3x^6+2x^5) \\ =12x^9+8x^8-15x^8-10x^7 \\ =12x^9-7x^{8^{}}-10x^7 \end{gathered}[/tex]Now we will differentiate y with respect to x by basic rules:
[tex]y^{\prime}=12(9)x^{9-1}-7(8)x^{8-1}-10(7)x^{7-1}[/tex]Solving further,
[tex]y^{\prime}=108x^8-56x^7-70x^6[/tex](b) Second method: Apply product rule to find the derivative:
Again,
[tex]y=(4x^3-5x^2)(3x^6+2x^5)[/tex]The product rule states:
[tex](uv)^{\prime}=u^{\prime}v+v^{\prime}u[/tex]Where u and v are the two factors multiplied.
So here we have:
[tex]\begin{gathered} u=4x^3-5x^2 \\ v=3x^6+2x^5 \end{gathered}[/tex]Finding the derivatives:
[tex]\begin{gathered} u^{\prime}=4(3)x^{3-1}-5(2)x^{2-1} \\ =12x^2-10x \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} v^{\prime}=3(6)x^{6-1}+2(5)x^{5-1} \\ =18x^5+10x^4 \end{gathered}[/tex]Now put the values in the product rule,
[tex]\begin{gathered} y^{\prime}=(uv)^{\prime} \\ =u^{\prime}v+v^{\prime}u \\ =(12x^2-10x)(3x^6+2x^5)+(18x^5+10x^4)(4x^3-5x^2) \end{gathered}[/tex]Simplifying further,
[tex]\begin{gathered} y^{\prime}=12x^2(3x^6+2x^5)-10x(3x^6+2x^5)+18x^5(4x^3-5x^2)+10x^4(4x^3-5x^2) \\ =36x^8+24x^7-30x^7-20x^6+72x^8-90x^7+40x^7-50x^6 \\ =108x^8-56x^7-70x^6 \end{gathered}[/tex]This is the derivative obtained.
From above two methods, we can see the derivative is same in both the cases.
Identify the parent function of f(x) = -×^2+2
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The given function is
[tex]f(x)=-x^2+2[/tex]The parent function refers to the simplest function possible.
Hence, the parent function is[tex]f(x)=x^2[/tex]16 ft.8 ftSurface Area =
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The point enter your response here is also on the graph of the equation.
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An equation that has a graph that is symmetric to the origin, has a reflection of each point through the origin, reflects across the x-axis and y-axis.
Therefore, if one point of the graph is (-4,1).
Reflected to both axis, we can find that another is is (-x,-y) = (-(-4), -1) = (4, -1)
So, the answer is the point (4, -1)
Solve for 2. Enter the solutions from least to greatest.x^2 - 3x - 40 = 0lesser x = [ ]greater x = [ ]
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
x^2 - 3x - 40 = 0
x1 = ?
x2 = ?
Step 02:
Quadratic equation:
roots:
x² - 3x - 40 = 0
(x - 8)(x + 5) = 0
x1 = 8
x2 = -5
The answer is:
lesser x = -5
greater x = 8
find the equivalent expression for x^1/2
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We want to find the equivalent expression for
[tex]x^{\frac{1}{2}}[/tex]Read as: x to the power of half
The equivalent expression for this is
[tex]\sqrt[]{x}[/tex][tex]x^{\frac{1}{2}}\text{ and }\sqrt[]{x}\text{ both have the same meaning}[/tex]ine temperaturtemperature at midnight?-53Allie scores 4 points in the first round of a card game. In the next round, she loses 6 points. Then she scores 4more points. How many points does Allie have after three rounds?on
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3
Allie scores 4 points in the first round of a card game. In the next round, she loses 6 points. Then she scores 4.
How many points does Allie have after three rounds?
First round: 4 points (positive)
Second round = lose 6 points (negative)
Third round = scores 4 (positive )
Add and subtract all the points
4-6+4 = 2
Jeremiah can drink 64 fluid ounces of coffee in 4 days. How many Quarts of coffee can he drink in 1 hour.help explain please:)
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1 quart = 32 fluid ounces
Therefore, 64 fluid ounces = 2 quarts
Jeremiah can drink these 2 quarts in 4 days meaning he drinks
[tex]2\frac{\text{quarts}}{4\text{days }}=0.5\frac{\text{quarts}}{\text{days}}[/tex]Now, there are 24 hours in a day; therefore, the number of quarts Jeremiah drinks in 1 hour is
[tex]\frac{0.5\text{quarts}}{24\text{hours}}=\frac{1}{48}\frac{\text{quarts}}{\text{days}}[/tex]or in decimal form, this is 0.021 quarts in an hour.
Given a∥b , and c is not parallel to a or b, which statements must be true? Select each correct answer. m∠4=m∠8 the measure of angle 4 equals the measure of angle 8 m∠7=m∠10 the measure of angle 7 equals the measure of angle 10 m∠8=m∠9 the measure of angle 8 equals the measure of angle 9 m∠2=m∠7 the measure of angle 2 equals the measure of angle 7
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The true statements from the given options about the congruent angles are; m∠4 = m∠8 and m∠2 = m∠7
How to identify congruent angles?From the image, the figure consists of three horizontally oriented lines, with two of them parallel and having a common transversal.
Option A; m∠4 and m∠8 are corresponding angles formed between line a and line b.
Given the line a is parallel to line b, we have; m∠4 ≅ m∠8 by corresponding angles theorem
m∠4 = m∠8 is true by definition of congruency
Option B; m∠7 and m∠10 are alternate interior angles
Given the line c is not parallel to line b, we have; b ∦ c
Therefore; m∠7 ≠ m∠10 by the inverse of the alternate interior angles theorem
Thus; m∠7 = m∠10 is False
Option C; m∠8 and m∠9 are alternate interior angles formed between non parallel lines.
Thus; m∠8 ≠ m∠9
m∠8 = m∠9 is false
Option D; m∠2 and m∠7 are alternate exterior angles, Thus;
m∠2 ≅ m∠7 by alternate exterior angles theorem
m∠2 = m∠7 is true, by definition of congruency
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Write the equation, (2)x+(3)y=(24) in slope-intercept form
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the equation in slope- intercept form:
y = -2x/3 + 8
Explanation:
GIven: (2)x+(3)y=(24)
To write in slope intercept form, we apply the formula for a linear equation:
y = mx + c
where m = slope, c = intercept
2x + 3y = 24
Make y the subject of formula by taking x to the other side of the equation:
3y = -2x + 24
Divide through by 3:
[tex]\begin{gathered} \frac{3y}{3}=\frac{-2x}{3}+\frac{24}{3} \\ y\text{ = }\frac{-2x}{3}+8 \end{gathered}[/tex]when we compare the above equation with the equation of line, they are in alignment.
Hence, the equation in slope- intercept form:
y = -2x/3 + 8
Nina deposited $20.59 in her checking account. Later that week, she wrote a checkfor one-third the amount in the account, and then another check for $9.74. If shehad $108.60 left in her account, how much did she have to begin with.
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1) Reading carefully, we can do it step by step.
2) She had deposited $20.59 and wrote a check, since she wrote a check we can understand that as a debit so we can write out the following:
[tex]\begin{gathered} 20.59-\frac{20.59}{3}= \\ 20.59-6.86 \\ 13.7 \end{gathered}[/tex]Note that we rounded off to the nearest hundredth.
2.2) So now, she wrote another check, i.e. -$9.74
[tex]\begin{gathered} \$13.7-\$9.74 \\ \$4 \\ 108.60 \\ 108.60+\mleft(20.59-6.86-9.74\mright)=112.59 \end{gathered}[/tex]When 9 and 2/3 is written in simplest radical form, which value remains under the radical?36927
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Given
[tex]9^{\frac{2}{3}}[/tex]To write it in the simplest form and to find which value remains under the radical.
Explanation:
It is given that,
[tex]9^{\frac{2}{3}}[/tex]It is known that,
[tex]x^{\frac{m}{n}}=\sqrt[n]{x^m}[/tex]That implies,
[tex]\begin{gathered} 9^{\frac{2}{3}}=\sqrt[3]{9^2} \\ =\sqrt[3]{3\times3\times3\times3} \\ =3\sqrt[3]{3} \end{gathered}[/tex]Therefore, the simplest form of the expression is,
[tex]3\sqrt[3]{3}[/tex]and the value that remains under the radical is 3.
