the general form of the line is
[tex]y=mx+b[/tex]where m is the slope of the line and b the y-intercept
we get the slope from the statement m=-6
[tex]y=-6x+b[/tex]now to find the value of b we replace the point (-2,4) and solve for b
[tex]\begin{gathered} (4)=-6(-2)+b \\ 4=12+b \\ b=4-12 \\ b=-8 \end{gathered}[/tex]now replace the value of b
[tex]y=-6x-8[/tex]and transform to the standard form placing the unknows on the same side
[tex]y+6x=-8[/tex]we can reorganize
[tex]6x+y=-8[/tex]then right option is Third option
A truck enters a highway driving 60mph. A car enters the highway at the same place 10 minutes later and drives 69mph in the same direction. From the time the car enters the highway, how long will it take for the car to pass the truck?The car will pass the truck in [___] minutes.
A truck enters a highway driving 60mph. A car enters the highway at the same place 10 minutes later and drives 69mph in the same direction. From the time the car enters the highway, how long will it take for the car to pass the truck?
The car will pass the truck in [___] minutes.
Remember that
the speed is equal to divide the distance by the time
s=d/t
d=s*t
when the car enter the highway--------> 10 min
so
distance of the truck is
60*(10/60)=10 miles
the equation of the distance at this moment is
y=60x+10
the equation of the distance of the car is
y=69x
equate both equations
69x=60x+10
69x-60x=10
9x=10
x=10/9 hours
convert to minutes
(10/9)*60=66.67 minutes
answer is
66.67 minutes
there are 100 cards in a hat numbered 1 to 100 the game is to draw one card out of the hat if the number you draw is odd you win $19.if the number you draw is even you win nothing. if you play the game what is the expected payoff
Answer:
Explanation:
There are 100 cards numbered 1 to 100.
• The number of even cards, E = 50
,• The number of odd cards, O = 50
The various probabilities are calculated below:
[tex]\begin{gathered} P(E)=\frac{50}{100}=\frac{1}{2} \\ P(O)=\frac{50}{100}=\frac{1}{2} \end{gathered}[/tex]Divide. Write your answer in the simplest form.6/5 divided by 7/6 ?????
SOLUTION
We want to solve 6/5 divided by 7/6, we have
[tex]\frac{6}{5}\div\frac{7}{6}[/tex]We change the division sign to multiplication and the second fraction reverses, we have
[tex]\begin{gathered} \frac{6}{5}\times\frac{6}{7} \\ =\frac{36}{35} \\ =1\frac{1}{35} \end{gathered}[/tex]Hence the answer is
[tex]1\frac{1}{35}[/tex]the cost to produce 7,500 widgets. cost of material= 3,500cost of labour=700what is the average cost of produce a single widget?
The material cost is 3,500 and the labour cost is 700 in producing 7,500 widgets.
The average cost to produce is the sum of the cost divided by the number of widgets.
This will be :
[tex]\frac{3500+700}{7500}=\frac{4200}{7500}=0.56[/tex]The answer is 0.56 per widget
what must be added to 40 to make 10²
Answer:
Step-by-step explanation:
Since 10^2= 100, you just have to subtract 40 from that:
100-40= 60 as answer
Grade 12 vectors 6.2 Q3 Let →v=⟨−1,5⟩.Sketch −2→v and 1/5→v
For this problem, we are given a vector and we need to sketch two variations of it.
The vector is:
[tex]v=<-1,5>[/tex]We need to sketch -2v and 1/5 v.
The coordinates for -2v are <2, -10> and for 1/5 v they are <-1/5,1>
Two similar pyramids have slant heights of 4 and 6.1) Find the scale factor.2) If the volume of the smaller pyramid is 48 meters cubed, what is the volume of the larger pyramid?
ANSWER
[tex]\begin{gathered} 1)\frac{3}{2}\text{ or 1.5} \\ 2)162m^3 \end{gathered}[/tex]EXPLANATION
1) The slant heights of the pyramids are 4 and 6.
The scale factor is the ratio of the corresponding sides of two figures, hence, the scale factor of the two pyramids is:
[tex]\begin{gathered} \frac{6}{4} \\ \Rightarrow\frac{3}{2}\text{ or 1.5} \end{gathered}[/tex]2) The ratio of the volumes of two similar figures is equal to the cube of their scale factor.
Let the volume of the bigger pyramid be p.
This means that:
[tex]\begin{gathered} \frac{p}{48}=(\frac{3}{2})^3 \\ \Rightarrow\frac{p}{48}=\frac{27}{8} \end{gathered}[/tex]Solve for p by cross-multiplying:
[tex]\begin{gathered} p=\frac{27\cdot48}{8} \\ p=162m^3 \end{gathered}[/tex]That is the volume of the larger pyramid.
Can you assist with #7 look ate the finished rest as a guide if necessary
We know that the segment DP is an angle bisector of angle BDC; this means that angle 1 has to be half angle BDC, that is:
[tex]m\angle1=\frac{1}{2}m\angle BDC[/tex]Plugging the expresions given for each angle we have:
[tex]\begin{gathered} 6x+6=\frac{1}{2}(15x) \\ 12x+12=15x \\ 15x-12x=12 \\ 3x=12 \\ x=\frac{12}{3} \\ x=4 \end{gathered}[/tex]Therefore, the value of x is 4
Jonathan goes out for dinner with his family. They want to give the waiter a 20% tip. Which expression represents the total cost of the bill, including tip, if the cost of the dinner is d dollars? *
Tip percentage = 20% = 20/100 = 0.2 (decimal form)
Cost of the dinner = d
The total cost of the bill:
Multiply the cost of the dinner by (1+0.20).
D (1+0.20)
d 1.20
1.2 d
Suppose 200 students were asked if they are right-handed or left-handed. The information is displayed in the following two-way table.Right-handedLeft-handedTotalMale681280Female10218120Total17030200Find P(male and left-handed). Enter your answer using two decimal places.
Step 1
From the given 2-way we are required to find the probability of getting a male and is left-handed,
Probability is written as;
[tex]Pr(event)=\frac{number\text{ of required events }}{Total\text{ number of events}}[/tex]Probability of male and left-handed is;
[tex]Pr(male\text{ and left handed})=\frac{12}{200}=0.12[/tex]Answer;
[tex]Pr(male\text{ and left-handed\rparen=0.12 to two decimal places}[/tex]Which of the following is the set C of the first 6 cube positive integers?
The set of numbers will be compound by the first 6 integers raised to 3. Find each of these values to know what is the correct answer.
[tex]\begin{gathered} 1^3=1\cdot1\cdot1=1 \\ 2^3=2\cdot2\cdot2=8 \\ 3^3=3\cdot3\cdot3=27 \\ 4^3=4\cdot4\cdot4=64 \\ 5^3=5\cdot5\cdot5=125 \\ 6^3=6\cdot6\cdot6=216 \end{gathered}[/tex]The set C of the first 6 cube positive integers is C={1, 8, 27, 64, 125, 216}. The correct answer is the third option.
Answer: Your answer is option 3. C={1, 8, 27, 64, 125, 216}
Step-by-step explanation:
Phyllis invested 54000 dollars, a portion earning a simple interest rate of 4% per year and the rest earning a rate of 7% per year. After one year the total interest earned on these investments was 3270 dollar. how much money did she invest at each rate
$54,000
a portion at simple interest 4%
another portion simple interest 7%
earned in one year $3,270
How much on each rate ?
Simple interest formula: P * r * t where P is the principal, r is the rate, and t is the time
Earnings at 4% = P1 * 0.04 * 1 = 0.04 P1
Earnings at 7% = P2 * 0.07 * 1 = 0.07 P2
Both add 3270, so we can write:
Equation 1: 0.04 P1 + 0.07 P2 = 3270
also both quantities invested add 54000, so we can write:
Equation 2: P1 + P2 = 54000
Solving Equation 2 for P1:
P1 = 54000 - P2
Using this value into equation 1:
0.04(54000 - P2) + 0.07 P2 = 3270
Solving for P2:
2160 - 0.04 P2 + 0.07 P2 = 3270
0.03 P2 = 3270 -2160 = 1110
P2 = 1110/0.03 = 37000
P2 = 37000
Using this value into the expression we found for P1:
P1 = 54000 - P2 = 54000 - 37000 = 17000
P1 = 17000
Answer:
She invested $17,000 at 4% and $37,000 at 7%
string Susan is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree. 44 90 feet 74 ft 87 ft 65 ft
In the picture we cna see a right triangle, so the height of the tree ould be estimate as:
[tex]\begin{gathered} \tan (44)=\frac{height}{90} \\ \text{height}=90\cdot\tan (44)\approx87ft \end{gathered}[/tex]The height of the tree is 87 ft
The maximum number of turning points or bumps of a nth degree polynomial is
A turning point is a point of the graph where the graph changes from increasing to decreasing or decreasing to increasing . A polynomial of degree n will have at most n−1 turning points
Answer:
[tex]n-1[/tex]Find the numerical value of the area under the normal curve given the following information:• to the right of z = 2.28
Getting the area under the normal distribution requires us to look into the z-table or z-distribution.
Based on the table, z = 2.28 is found encircled red on the table. Therefore, the area to the right of z = 2.28 is 0.98870.
Please not
translate the following expression into symbols: the whole numbers are a subset of the integers
Whole numbers: W
Integers: Z
the whole numbers are a subset of the integers:
To represent that an element is a subset of another elemet you use the symbol: ⊆
Then, you get the next:
[tex](W\subseteq Z)[/tex]Is the answer 0 or 17 ?!, how do i find n(a)
It is given that
[tex]n(B)=35,n(A\cap B)=17,\text{ n}(A\cup B)=52[/tex]To find the value of n(A) , use the formula
[tex]n(A\cup B)=n(A)+n(B)-n(A\cap B)[/tex]Substitute the values
[tex]52=n(A)+35-17[/tex][tex]n(A)=52-35+17=34[/tex]Hence the value of n(A) is 34.
whatvis the length of the hypotenuse3mm 4mm
Answer : x = 5
We are given two lengths of a right angle traingle
[tex]\begin{gathered} \text{Let the hypotenus be x} \\ \text{Opposite = 3mm} \\ \text{Adjacent = 4mm} \\ Apply\text{ pythagora's theorem} \\ \text{Hypotenus}^2=opposite^2+adjacent^2 \\ x^2=3^2+4^2 \\ x^2\text{ = 9 + 16} \\ x^2\text{ = 25} \\ \text{Take the squareroots of both sides} \\ x\text{ = }\sqrt[]{25} \\ x\text{ = 5} \end{gathered}[/tex]It doesn’t have a box on the picture for an answer because that thing has an error, but I still need help with finding the solutions.
Answer:
[tex]\log _a(\frac{\sqrt[]{3}}{10})=-0.0410[/tex]Step-by-step explanation:
Given the logarithms, find the following expressions:
[tex]\log _a(\frac{\sqrt[]{3}}{10})=\log _a\sqrt[]{3}-\log _a10[/tex]Using the rule for root logarithms:
[tex]\begin{gathered} \log _a\sqrt[p]{x}=\frac{\log _ax}{p} \\ \text{Solving the expression:} \\ \frac{\log_a3}{2}-(\log _a5\cdot\log _a2)=\frac{0.6131}{2}-(0.8982\cdot0.3869) \\ =-0.0410 \end{gathered}[/tex]Please write [tex]4 {x}^{2} + 9 {y}^{2} - 24x + 18y + 9 = 0[/tex]in standard form
I need help with this question to get the right answer
The blue region consists on the intersection of two regions. The region above the decreasing line, and the region below the increasing line. Those lines are
[tex]\begin{cases}y=x+8 \\ y=-\frac{1}{2}x\end{cases}[/tex]Those are the boundaries of those regions. Since both lines are dashed lines, the regions do not include those lines. The increasing line is the one with the positive slope
[tex]y=x+8[/tex]Since our region is below this line, the y values must be less than the values on this line, and the inequality that represents this region is
[tex]yThe decreasing line is the one with the negative slope[tex]y=-\frac{1}{2}x[/tex]Since our region is above this line, the y values must be greater than the values on this line, and the inequality that represents this region is
[tex]y>-\frac{1}{2}x[/tex]Combining those two regions, we have their intersection which is the desired blue region
[tex]y-\frac{1}{2}x[/tex]7x+9=-75 can someone please answer this I really need help
⇒I will use the additive inverse
[tex]7x+9-9=-75-9\\7x=-84\\\frac{7x}{7}=\frac{-84}{7} \\ x=-12[/tex]
For 5 cups of milk you need 4 cups of oatmeal, how many cups of oatmeal will be needed for 1 cup of milk?
The ratio milk-oatmeal has to stay the same; then, if x represents the cups of oatmeal we need for 1 cup of milk, we get:
[tex]\begin{gathered} \frac{5}{4}=\frac{1}{x} \\ \Rightarrow x=\frac{4\cdot1}{5}=\frac{4}{5}=0.8 \end{gathered}[/tex]The answer is 4/5 or 0.8 cups of oatmeal
Find the circumference of a circle with a diameter of meters. Use as an approximation for . Round your answer to the nearest whole meter. Enter only the number.
Solution:
The circumference of a circle is expressed as
[tex]\begin{gathered} circumference=\pi\times d \\ where\text{ d}\Rightarrow diameter\text{ of the circle} \end{gathered}[/tex]Given that the diameter of the circle is 13 meters, we have
[tex]d=13[/tex]By substitution, we have
[tex]\begin{gathered} circmference=\pi\times13 \\ where\text{ }\pi=3.14 \\ thus, \\ circumference=3.14\times13 \\ =40.82 \\ \therefore \\ circumference\approx41\text{ meters} \end{gathered}[/tex]Hence, the circumference of the circle, to the nearest meter, is
[tex]41[/tex]Joan's expenses for a month were: rent, $680; transportation,$265; food, $487; clothing, $95; utilities, $240; and otheritems, $55. What was the total for her expenses?
For finding out the total of Joan's expenses for a month, we need to add up all her expenses:
[tex]\text{Rent + Transportation + Food + Clothing + Utilities + Other items}[/tex]Now you can calculate the Joan's expenses, this way:
[tex]680+265+487+95+240+55\text{ }[/tex]eight times some number increased by 9 is -10
Let x represent some number.
The phrase "eight times some number" can be expressed as 8x. If that quantity is increased by 9, we can represent it as 8x+9. If that expression is equal to -10, then we can write down the equation 8x+9=-10.
Therefore, the phrase "eight times some number increased by 9 is -10" can be written using algebraic languaje as:
[tex]8x+9=-10[/tex]Randy spins the arrow on a spinner with 5 equal sections labeled A, B, C, D, and E. Then, he rolls a 6-sided number cube with sides numbered 1 through 6. What is the probability that the arrow will stop on the letter A and the number cube will show the number 4?
This is a probability question
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of required outcomes and the total number of outcomes.
Step 1:
Find the probability of selecting Letter A from the spinner
The number of total outcomes = 5
number of required outcome =1
[tex]Probability\text{ that the arrow spins on A=}\frac{1}{5}[/tex]Step 2: Find the probability that a number 4 is selected
The number of total outcomes = 6
number of required outcome =1
[tex]probability\text{ that a number 4 is selected=}\frac{1}{6}[/tex]Step 3: Find the probability that the arrow will stop on the letter A and the number cube will show the number 4
[tex]P=\frac{1}{5}\times\frac{1}{6}=\frac{1}{30}[/tex]The probability is 1/30
I need help knowing how the graph would look like with a polynomial with roots 4,-2 and 7 thanks!
Answer:
Explanation:
Here, we want to get the graph of the polynomial
To get that, we have the expression of the polynomial as follows:
[tex]\begin{gathered} if\text{ x = 4 , a linear factor is x-4} \\ x\text{ = -2, a linear factor is x+2} \\ x\text{ = 7 , a linear factor is x-7} \end{gathered}[/tex]Thus, we have the polynomial expression as follows:
[tex](x-4)(x+2)(x-7_)[/tex]Now, we can have the plot as shown below:
We have the y-intercept at y = 56
The price per pound of potatoesincreased by 5% this month compared to the price last month. If the price per pound of potatoes last month was d dollars, which one of the following expressions shows the price per pound of potatoes this month?A: d- 0.05dB: d+ 0.05C: 0.05dD: 1.05d
Answer:
D: 1.05d
Explanation:
The price per pound last month = d dollars
The price increased by 5% this month compared to the price last month.
Therefore, the price this month will be:
[tex]\begin{gathered} d+(5\%\text{ of }d)=d+0.05d \\ =(1+0.05)d \\ =1.05d \end{gathered}[/tex]The expression that shows the price per pound of potatoes this month is 1.05d.
The correct option is D.
Divide the polynomial by the monomial denominator by writing the fraction as the sum (or difference) of fractions. Simplify your answer, if possible.2x2 - 4x + 3-- 2x
Given the following question:
[tex]\frac{2x^2-4x+3}{-2x}[/tex][tex]\begin{gathered} \frac{2x^2-4x+3}{-2x} \\ 2x^2\div-2x=-x \\ -x+\frac{-4x+3}{-2x} \\ -4x\div-2x=2 \\ -x+2+\frac{3}{-2x} \\ -x+2-\frac{3}{2x} \end{gathered}[/tex]Your answer is "-x + 2 - 3 / 2x"