1: -(5x + 7) + 1 = -5x -5
2: 4x - 7 + 2x = 2(3x - 3) - 1
3: -4x - 2 = -2(1 - 4x)
On a family trip, 100 miles were traveled at a rate of 60 miles per hour and another 30 miles at 40 miles per hour , what is the average speed for this trip
The average speed for the trip is calculated by using the formula of total distance divided by total time. For a total distance of 130 miles and total time of 2.42 hours, the average speed is approximately 53.72 mph.
Explanation:In order to find the average speed for the entire trip, we need to use the formula which is total distance travelled divided by the total time taken. The total distance travelled is 100 miles at 60mph plus 30 miles at 40mph, which results in 130 miles.
Now, to find the total time taken, we divide the distance travelled by the speed, which is 100 miles at 60mph results in 1.67 hours and 30 miles at 40mph results in 0.75 hours. Hence, the total time taken is the sum of these two times which is 2.42 hours.
Applying the formula for average speed, i.e., total distance divided by total time, we get 130 miles divided by 2.42 hours results in approximately 53.72 mph which is the average speed for the trip.
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At North parking garage it costs $5 to bring your car into the garage plus $2 for every hour the car is parked
The equation relating the total cost with the number of hours will be c = 2.25h + 5.
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have North parking garage where it costs $5 to bring your car into the garage plus $2.25 for every hour the car is parked.
Assume that [h] represents the number of hours the car was parked and [c] represents the total cost. Then, we can write the equation relating the total cost with the number of hours will be -
c = 2.25h + 5
Therefore, the equation relating the total cost with the number of hours will be c = 2.25h + 5.
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[The complete question is -
At the North parking garage it costs $5 to bring your car into the garage plus $2.25 for every hour the car is parked. If h, represents the number of hours the car was parked and c, represents the total cost, which equation would model this situation?]
find × in this proportion 16/X = x/4
x=
a. 64
b. 32
c. 16
d 8
Answer:
d
Step-by-step explanation:
The proportion given to us is
[tex]\frac{16}{x} =\frac{x}{4}[/tex]
Next we cross multiply to get
[tex]16*4=x*x[/tex]
[tex]64=x^2[/tex]
[tex]x^2=64[/tex]
Take the sqrt on both side to get x
so
[tex]\sqrt{x^2} = \sqrt{64}[/tex]
x=8
so the correct option is d .
A group of students is investigating whether copper is a better thermal conductor than steel. The students take a copper wire and a steel wire of the same length and diameter. They put equal lengths of wax on one end of each wire and dip the other end into a beaker of hot water. The length of wax left on the wires after 10 minutes is shown.
Experimental Observations
Copper Steel
Original length of wax: 3 cm 3 cm
Length of wax after 10 minutes: 0.7 cm 1.8 cm
What was the dependent variable in this experiment?
Type of wire used
Original length of wire
Original length of wax
Thermal conductivity of wire
The correct dependent variable in this experiment is the Length of wax after 10 minutes.
In the context of an experiment, the dependent variable is the variable that is being measured or tested in the experiment. It is the outcome that the experimenters are interested in observing to determine the effect of the independent variable.
In this case, the students are investigating the thermal conductivity of copper and steel wires by observing how much wax melts over a fixed period of time when the wires are heated. The independent variable is the type of wire used (copper or steel), as this is what the students are changing to see its effect on the dependent variable.
The dependent variable is the length of wax remaining after 10 minutes because this measurement is expected to change based on the thermal conductivity of the wire. The better the thermal conductor, the more heat will be transferred along the wire, and the more wax will melt. Since the students are measuring how much wax has melted (by subtracting the length of wax after 10 minutes from the original length), this is the dependent variable.
The original length of wire and the original length of wax are control variables; they are kept constant to ensure that any differences in the dependent variable are due to the independent variable (the type of wire) and not due to other factors. The thermal conductivity of the wire is a property being indirectly measured through the observation of the dependent variable. It is not directly measured and thus is not the dependent variable.
Which is the best approximation for the measure of angle XYZ?
A) 33.6°
B) 39.8°
C) 50.2°
D) 56.4°
Answer
39.8°
Explanation
To solve this we can use the trigonometric ratio tangent.
tan x = opposite / adjacent
= 10/12
= 0.8333...
x = tan⁻¹(0.8333..)
= 39.8°
The best approximation for the measure of angle XYZ in the given triangle is 39.8 degrees.
To solve this we can use the trigonometric ratio tangent.
What is the trigonometric ratio tangent?tan x = opposite side / adjacent side
We have given the,
Opposite side=10in
Adjacent side=12in
use this value in the gven formula
Therefore we get,
tanx = 10/12
tanx = 0.8333...
x = tan⁻¹(0.8333..)
x = 39.8°
Therefore, The best approximation for the measure of angle XYZ is 39.8 degrees.
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Your football team gained four yards on the first down into yards on the second down during its last possession which number is the additive inverse of yards gained
A-2
B -6
C 4
d 6
Answer:
B. -6
Step-by-step explanation:
There is a mistake in the question. It would have to say:
Your football team gained four yards on first down and two yards on second down during its last possession
So, your team gained 4 + 2 = 6 yards.
Calling x, the additive inverse of 6, the following equation must be satisfied:
6 + x = 0
x = 0 - 6
x = -6
Find the center and radius for the circle defined by the equation x^2 + y^2 + 5x -y + 2
Find the area in the right tail more extreme than z= 3.01 in a standard normal distribution
To find the area in the right tail more extreme than z= 3.01 in a standard normal distribution, we calculate the p-value as the probability of observing a value more extreme than the test statistic. In this case, the p-value is approximately 0.0103.
Explanation:The p-value, in statistics, measures the probability of obtaining results as extreme or more extreme than the observed data, assuming the null hypothesis is true. A smaller p-value suggests stronger evidence against the null hypothesis, typically indicating statistical significance and supporting the alternative hypothesis.
To find the area in the right tail more extreme than z = 3.01 in a standard normal distribution, we need to calculate the p-value.
The p-value is the probability of observing a value more extreme than the test statistic.
In this case, we use the formula P(Z > z) to find the area in the right tail. Using the information given, P(Z > 3.01) ≈ 0.0103.
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To find the area in the right tail more extreme than z= 3.01 in a standard normal distribution, we calculate the p-value as the probability of observing a value more extreme than the test statistic. In this case, the p-value is approximately 0.0103.
Explanation:The p-value, in statistics, measures the probability of obtaining results as extreme or more extreme than the observed data, assuming the null hypothesis is true. A smaller p-value suggests stronger evidence against the null hypothesis, typically indicating statistical significance and supporting the alternative hypothesis.
To find the area in the right tail more extreme than z = 3.01 in a standard normal distribution, we need to calculate the p-value.
The p-value is the probability of observing a value more extreme than the test statistic.
In this case, we use the formula P(Z > z) to find the area in the right tail. Using the information given, P(Z > 3.01) ≈ 0.0103.
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To find the area in the right tail more extreme than z= 3.01 in a standard normal distribution, we calculate the p-value as the probability of observing a value more extreme than the test statistic. In this case, the p-value is approximately 0.0103.
Explanation:The p-value, in statistics, measures the probability of obtaining results as extreme or more extreme than the observed data, assuming the null hypothesis is true. A smaller p-value suggests stronger evidence against the null hypothesis, typically indicating statistical significance and supporting the alternative hypothesis.
To find the area in the right tail more extreme than z = 3.01 in a standard normal distribution, we need to calculate the p-value.
The p-value is the probability of observing a value more extreme than the test statistic.
In this case, we use the formula P(Z > z) to find the area in the right tail. Using the information given, P(Z > 3.01) ≈ 0.0103.
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Sally is choosing what classes to take next year. She must take a math, a science, a fine arts, and a foreign language. If there are 4 math classes, 3 science classes, 5 fine arts classes, and 2 foreign languages classes to choose from, how many different schedules can she have?
the number of peaches, p, is three less then twice the number of grapes,g. which expression represents the number of peaches in terms of the number of grapes?
Veronica deposited $21 in a savings account that earns 2.4% simple interest. Which graph represents this scenario?
Answer:
The below graph represents this scenario.
Step-by-step explanation:
Given,
The deposited amount, P = $ 21,
Annual interest rate, r = 2.4 % = 0.024,
Thus, the simple interest after x years,
[tex]y=P\times r\times t[/tex]
[tex]=21(0.024)(x)[/tex]
[tex]=0.0504x[/tex]
If x-axis shows the number of years and y axis represents the simple interest after x years,
So, y = 0.0504x is a line passes through the origin which will show the given scenario,
( shown below )
Also, x ≥ 0 ( number of years can not be negative )
Jalen has a balance of $1870 on a credit card with an APR of 19.7%, compounded daily. About how much will he save in interest over the course of a year if he transfers his balance to a credit card with an APR of 16.5%, compounded monthly. (Assume that Jalen makes no payments or new purchases during the year, and ignore any possible late payment fees.)
How is the theme of deception introduced twice in this scene?
Let x represent any year write an inequality in terms of x and 1822 that is true only for values of x that represent years before the year that Brazil started its war for independence and
What is the end behavior of f(x) = |3x - 2| + 4?
Answer:
It rises to the left and rises to the right.
Step-by-step explanation:
Evaluate the expression: |8|-|-2|
Thanks
A right triangle has side lengths AC = 7 inches, BC = 24 inches, and AB = 25 inches.
What are the measures of the angles in triangle ABC?
a) m∠A ≈ 46.2°, m∠B ≈ 43.8°, m∠C ≈ 90°
b) m∠A ≈ 73.0°, m∠B ≈ 17.0°, m∠C ≈ 90°
c) m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C ≈ 90°
d) m∠A ≈ 74.4°, m∠B ≈ 15.6°, m∠C ≈ 90°
Answer:
(C)
Step-by-step explanation:
It is given that a right triangle, ACB which is right angled at C has BC = 24 inches, and AB = 25 inches.
We know that m∠C=90°,
Using the trigonometry in ΔACB, we have
[tex]sinB=\frac{AC}{AB}[/tex]
Substituting the given values, we get
⇒[tex]sinB=\frac{24}{25}[/tex]
⇒[tex]B=sin^{-1}(0.96)[/tex]
⇒[tex]B=73.7^{\circ}[/tex]
Also, [tex]sinA=\frac{CB}{AB}[/tex]
Substituting the given values, we get
⇒[tex]sinA=\frac{7}{25}[/tex]
⇒[tex]A=sin^{-1}(0.28)[/tex]
⇒[tex]A=16.3^{\circ}[/tex]
Therefore, the measure of the angles in triangle ABC are m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C ≈ 90°.
Thus, option C is correct.
A jet ski company charges a flat fee of $24.00 plus $2.25 per hour to rent a jet ski. Another company charges a fee of $23.00 plus $2.50 per hour to rent the same jet ski.
Using a graphing calculator, find the number of hours for which the costs are the same. Round your answer to the nearest whole hour. (1 point)
A• 2
B• 8
C• 4
D•3
Let
x----------> charge per hour to rent a jet sky in dollars
y----------> the total cost to rent a jet sky in dollars
we know that
First Jet Sky Company
[tex]y=24.00+2.25x[/tex] ---------> equation [tex]1[/tex]
Second Jet Sky Company
[tex]y=23.00+2.50x[/tex] ---------> equation [tex]2[/tex]
we know that
To find the number of hours for which the costs are the same
equate equation [tex]1[/tex] and equation [tex]2[/tex]
The intersection both graphs is the solution of the problem
using a graph tool
see the attached figure
the intersection point is [tex](4,33)[/tex]
That means
For [tex]x=4\ hours[/tex]
the cost of the rent is [tex]y=\$33[/tex] in both companies
therefore
the answer is
[tex]4\ hours[/tex]
For 4 hours of booking, the charges paid to both the companies should be same. And the charge will be $ 30.
Let x be the number of hours of booking per jet ski.
First company charges $24.00 plus $2.25 per hour to rent a jet ski.
So, the total cost paid for x hours to the first company will be,
[tex]C_1=24+2.25x[/tex]
Second company charges a fee of $23.00 plus $2.50 per hour to rent the same jet ski.
So, the total cost paid for x hours to the second company will be,
[tex]C_2=23+2.5x[/tex]
Now, the charge paid to both the companies should be same. For this condition, the number of hours of booking per jet ski should be,
[tex]C_1=C_2\\24+2.25x=23+2.5x\\1=0.25x\\x=4[/tex]
Therefore, for 4 hours of booking, the charges paid to both the companies should be same. And the charge will be,
[tex]24+2.25\times4=\$33[/tex].
For visuals, refer the attached graph.
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Which of the following is a step in constructing a circle circumscribed about a triangle?
a. Use a compass to locate the intersection of the midpoint of each side.
b. Use the perpendicular bisectors to find the center of the circle.
c. Use a compass to locate the intersection of the altitude of each side.
d. Use the angle bisectors to find the center of the circle.
Answer:
Answer B is correct
One angle of an isosceles triangle measures 100°. which other angles could be in that isosceles triangle? choose all that apply. 20° 30° 50° 40° submit
Triangle is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
The other angles in the isosceles triangle are 40°.
Option D is the correct answer
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Isosceles triangle:
One angle = 100°
We know that,
In an isosceles triangle, there are two equal sides and two equal angles opposite to the equal sides.
The sum of the three angles in the isosceles triangle is 180.
We already have,
One angle = 100°
The other two should be equal.
The sum should give us 180°.
Now,
40 + 40 = 80
100 + 80 = 180°
Thus,
The other angles in the isosceles triangle are 40°.
Option D is the correct answer
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Find the equation of a line in standard form that passes through the point (0,3) and is parallel to y=8x-3
Michael rented a truck for one day. there was a base fee of $19.95 , and there was an additional charge of 96 cents for each mile driven. michael had to pay $147.63 when he returned the truck. for how many miles did he drive the truck?
Which equations have the same value of x as 2/3(6x+12)=-24? Check all that apply.1. 4x+8=24 2. 9x+18=-24 3. 4x+12=-24 4. 18x+36/2=-24 5. 4x=-36 6. 4x=-32 7. x=-9 8. x=-8
Final answer:
After solving the original equation 2/3(6x+12)=-24, we find x = -8. Comparing this solution with the provided equations, the ones that have the same value for x are 9x+18=-24, 18x+36/2=-24, and x=-8.
Explanation:
To find which equations have the same value for x as 2/3(6x+12)=-24, we must first solve the original equation to find the value of x it yields:
2/3(6x+12) = -24
Multiply both sides by 3/2 to eliminate the fraction:
6x + 12 = -24 * (3/2)
6x + 12 = -36
Subtract 12 from both sides:
6x = -48
Divide by 6:
x = -8
Now we will compare this solution with the other equations:
4x+8=24 -> Does not match.9x+18=-24 -> When solving for x, we get x=-8, which matches.4x+12=-24 -> Does not match.18x+36/2=-24 -> Simplify to get 9x+18=-24, x = -8, matches.4x=-36 -> Does not match.4x=-32 -> Does not match.x=-9 -> Does not match.x=-8 -> Directly given the solution, which matches.Therefore, the equations that have the same value of x as the original equation are 9x+18=-24, 18x+36/2=-24, and x=-8.
The following triangle CAT is transformed using a translation: Triangle CAT is shown. C is at 0, 0, A is at negative 2, 1, T is at negative 1, 4. Which could be coordinates of C'A'T' after the translation? (4 points) Select one: a. C=(0,0), A=(2,1), T=(1,4) b. C=(2,0), A=(0,1), T=(1,4) c. C=(0,0), A=(−1,−2), T=(−4,−1) d. C=(−2,0), A=(−1,0), T=(−4,1)
the answer would be b. C=(2,0), A=(0,1), T=(1,4)
all x's move 2 to the right and no change in y
Solution: If a shape is being translated neither it's shape nor size changes.When we translate a shape we just move a shape or geometrical figure by certain distance either horizontally or vertically or both horizontally and vertically.
Coordinates of Triangle CAT is →C(0,0), and A(-2,1), and T(-1,4).
In option (a) vertices C has not been translated , but A and T are translated.Which is Untrue because we have to move all the vertices by same value. But x and y can have different value.
In option (b) all the coordinates C,A,and T is being translated along→ x by 2 units , horizontally right, but not translated in vertical direction.
C(0,0)⇒C(0+2,0+0)→C(2,0)
A(-2,1)⇒C(-2+2,1+0)→C(0,1)
T(-1,4)⇒C(-1+2,4+0)→C(1,4)
In option C, Coordinates of A and B are changed but not of C, So in this case translation can't happen.
In option D , C is being translated 2 units horizontally left , but amount of translation in A and T are different.
So , Option (b) is true.
how do you solve the equations:
-(1+4m)-6m=-81
and
238=-5(6v-7)-7
Line l has a _____ slope.
positive
negative
undefined
0
Answer: positive
Step-by-step explanation:
The slope of a line is given by:-
[tex]m=\dfrac{\text{rise}}{\text{run}}[/tex]
From the given picture, it can be seen that the rise in the line l is positive since the change in the y coordinates increases as we from left to right.
Similarly we can see that the run in the line l is positive since the change in the x coordinates increases as we from left to right.
By using above formula, the slope of line m is positive.
Find the ratio a:b, if it is given that ... 2a-3b/5 = a+b/3
use the triangle to answer the question.
Which equation shows a correct relationship of trigonometric functions?
sin x/cos y=0
sin x/ cos x =0
sin x/ cos x =1
sin x/ cos y =1
Help please thanks!!!!!!!!!!!
Answer:
P represents the population in year 0
Step-by-step explanation: