How many solutions does 7(x - 2) + 5 = 3 (2x - 1) + 1 have?
Answer:
one, x = 7
Step-by-step explanation:
7(x - 2) + 5 = 3 (2x - 1) + 1
reduce:
7x - 14 + 5 = 6x - 3 + 1
x = 7
divide if possible
\( \frac{ - 14}{7} \)
A ∠A and ∠ B ∠B are supplementary angles. If m ∠ A = ( 8 x + 6 ) ∘ ∠A=(8x+6) ∘ and m ∠ B = ( 7 x + 24 ) ∘ ∠B=(7x+24) ∘ , then find the measure of ∠ B ∠B.
Answer:
< B = 94
Step-by-step explanation:
Remark
You should edit the question. The way you wrote it, , it looks like you have to square two binomials. That isn't the way it is given I don't think. You are told that A and B are supplementary. That means
A+B = 180
Equation
(8x + 6) + (7x + 24) = 180 Remove the brackets
Solution
8x + 6 + 7x + 24 = 180 Collect like terms
15x + 30 = 180 Subtract 30 from both sides
15x = 180 - 30
15x = 150 Divide by 15
x = 150 / 15
x = 10
Answer
What you need is <B
<B = 7x + 24
<B = 7*10 + 24
<B = 70 + 24
<B = 94
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Step-by-step explanation:
if the area of a box is 1 cm^2
then area of triangle is6 cm square
Decide if the following biconditional statement
is true or false;
A triangle is equilateral if and only if three sides
are congruent.
True
False
Answer:
True
Step-by-step explanation:
Pretty sure it's true.
At a basketball game, 3 out of every 10 people who enter the gym will be wearing hats. If 250 people attend the game, about how many of them will probably be wearing hats?
75 people
80 people
65 people
70 people
What is the volume and surface area of this cone?
Answer:
Volume = 261.8 cm³
Surface area = 254.2 cm²
Step-by-step explanation:
To calculate the volume of the cone, we have to use the following formula:
\(\boxed{V = \frac{1}{3} \pi r^2 h}\),
where:
V ⇒ volume
r ⇒ radius = 5 cm
h ⇒ height = 10 cm
Using the above formula and the provided measures, we get:
V = \(\frac{1}{3}\) × π × (5)² × 10
= \(\frac{1}{3}\) × π × 25 × 10
= 261.8 cm³
In order to calculate the surface area of the cone, we have to use the following formula:
\(\boxed{SA = \pi r^2 + \pi r l}\)
where:
SA ⇒ surface area
r ⇒ radius = 5 cm
l ⇒ slant length = \(\sqrt{r^2+h^2}\) = \(\sqrt{5^2+10^2}\) = 5√5 cm
Using the formula,
SA = π × (5)² + π × 5 × 5√5
= π × 25 + π × 25√5
= 254.2 cm²
what is 48 - 36 and then divided by 36
Answer
The result of 48 - 36 is 12. Then, if you divide 12 by 36, the result is 0.3333 or 1/3.
Step-by-step explanation:
sqrt( cos( x))* cos( 300* x)+ sqrt( abs( x)) - 9.3* (4- x^2) ^
The function g(x) does not pass through the origin
What are functions?Functions are ordered pairs, equations, tables, relations and graphs that relate the relationship between two or more quantities
The equation of the function is given as:
\(g(x) = \sqrt{\cos\left(x\right)}\cdot\cos\left(300x\right)+\sqrt{\left|x\right|}-0.3\left(4\ -x^2\ \right)^{0.001}\)
Next, we plot the graph of the function g(x)
See attachment for the graph of function g(x)
From the attached graph, we can see that function g(x) does not pass through the origin;
However, it covers the origin
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Provide an example and explain the steps to convert a fraction into a percent.
The most appropriate choice for percentage and fraction will be given by-
The process of conversion of fraction to percentage has been explained.
What is fraction and percentage?
Suppose there is a whole collection of objects and some parts of the objects are taken from the whole collection. Fraction represents those parts which are taken. In other words, part of a whole is called fraction. The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.
If a number is taken as fraction of 100 then the fraction is known as percentage.
To convert a fraction into percentage, we have to simply multiply the fraction with 100.
For example.
Suppose we have a fraction \(\frac{1}{4}\), we need to convert \(\frac{1}{4}\) to percentage.
So on multiplying \(\frac{1}{4}\) by 100, we obtain = \(\frac{1}{4} \times 100\) = 25%
So, \(\frac{1}{4}\) is equivalent to 25%
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3. John makes $7.25 per hour at work. If he works 17 hours a week, how much will he earn?
Answer:
He will earn $123.25
Step-by-step explanation:
You multiply $7.26 by 17.
Use the Law of Sines to solve the triangle. Round your answers to two decimal places. A = 100°, a = 122, c = 10 C= O B= O b =
The values of the triangle are approximately: B ≈ 75.33°, C ≈ 4.67°, and b ≈ 9.91.
To solve the triangle using the Law of Sines, we can use the formula:
a/sin(A) = c/sin(C)
Given that A = 100°, a = 122, and c = 10, we can substitute these values into the equation:
122/sin(100°) = 10/sin(C)
To find sin(C), we rearrange the equation:
sin(C) = (10 * sin(100°)) / 122
Using a calculator, we can evaluate sin(100°) ≈ 0.9848:
sin(C) = (10 * 0.9848) / 122
sin(C) ≈ 0.0813
To find the value of angle C, we take the inverse sine (sin⁻¹) of 0.0813:
C ≈ sin⁻¹(0.0813)
C ≈ 4.67°
Now, to find angle B, we can use the fact that the sum of the angles in a triangle is 180°:
B = 180° - A - C
B = 180° - 100° - 4.67°
B ≈ 75.33°
Finally, to find side b, we can use the Law of Sines again:
b/sin(B) = c/sin(C)
b/sin(75.33°) = 10/sin(4.67°)
Solving for b:
b = (10 * sin(75.33°)) / sin(4.67°)
b ≈ 9.91
Therefore, the values of the triangle are approximately: B ≈ 75.33°, C ≈ 4.67°, and b ≈ 9.91.
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People who have a positive attitude tend to be happier than those who have a negative or pessimistic attitude. A psychologist conducts an experiment to explore this relationship. He randomly selects 50 participants. He randomly divides those participants into two groups of 25. In one group, the participants are instructed to write down three positive statements each day. The members of the other group just go through their days as normal. After 3 weeks, the treatment group's happiness increased from an initial average of 7 to an average of 9 on a scale of 1 to 10. The control group's happiness average decreased from 7 to 5 on the same scale. (a) What is the independent variable in this study? writing positive statements or not O happiness the 50 participants O the 25 participants (b) What is the dependent variable in this study? O writing positive statements or not O happiness O the 50 participants the 25 participants (c) Suppose the parameter we wish to estimate is the mean increase (or decrease) in happiness (after the study minus before the study). For the treatment group, identify the point estimate. For the treatment group, calculate the margin of error of the point estimate. Assume that s = 1.2 and use a confidence level of 90%. (Use a table or technology. Round your answer to three decimal places.
(a) The independent variable in this study is writing positive statements may not. (b) The dependent variable in this study is happiness.
(c) the point estimate for the mean increase in happiness for the treatment group is 2 with a margin of error of 0.395.
(a) The independent variable in this study is writing positive statements or not, as this is the variable being manipulated to see its effect on the participants' happiness.
(b) The dependent variable in this study is the participants' happiness, as it is being measured to see if it is affected by the manipulation of the independent variable.
(c) Since the point estimate for the mean increase in happiness for the treatment group is:
9 - 7 = 2
The margin of error of the point estimate can be found;
Margin of error = z*(s√(n))
Where z is the z-score for the 90% confidence level, s is the standard deviation, and n is the sample size.
From the z-table, the z-score for the 90% confidence level will be 1.645.
Substituting the values;
Margin of error = 1.645*(1.2√(25))
Margin of error = 0.395
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Slope from two points
What is the slope for a line that passes through (10, 17) and (7, 8)?
Your answer
Answer:
slope is 3
Step-by-step explanation:
10,17
7,8
8-17=-9
7-10=-3
-9/-3=3
Given f(x) = 6(1 − x), what is the value of f(−7)?
Answer:
\({:}\longrightarrow\tt f (x)=6 (1-x)\)
\({:}\longrightarrow\tt f (-7)=6 (1-(-7))\)
\({:}\longrightarrow\tt f (-7)=6 (1+7)\)
\({:}\longrightarrow\tt f (-7)=6(8)\)
\({:}\longrightarrow\tt f (-7)=48 \)
\(\therefore\sf f (-7)=48 \)
Answer:
:⟶f(x)=6(1−x)
{:}\longrightarrow\tt f (-7)=6 (1-(-7)):⟶f(−7)=6(1−(−7))
{:}\longrightarrow\tt f (-7)=6 (1+7):⟶f(−7)=6(1+7)
{:}\longrightarrow\tt f (-7)=6(8):⟶f(−7)=6(8)
{:}\longrightarrow\tt f (-7)=48:⟶f(−7)=48
\therefore\sf f (-7)=48∴f(−7)=48
ASAP SOMENW HELP ME PLS
Answer:
4.2
Step-by-step explanation:
Ok the points are (-1, 2) and (1, -2)
Put it in the formula
d = \(\sqrt{(1 - -1)^2 + (-2 - 2)^2} \\\sqrt{(2)^2 + (-4)^2} \\\sqrt{2 + 16} \\\sqrt{18} \\\)
√18 = 4.2426 ≈ 4.2
Hope this helps ya!!
An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.P(High- quality oil) = 0.3P(medium - quality oil)=0.4P (no oil)= 0.3What is the probability of finding oil (to 1 decimal)?
The probability of finding oil (to 1 decimal) is 0.7.
How are probabilities defined?Probability is a statistic that is used to show the possibility or chance that a certain event will occur. Probabilities can be expressed as fractions from 0 to 1, in contrast to percentages from 0% to 100%. The four main types of probability that mathematicians study are axiomatic, classic, empirical, and subjective. Given that the terms potential and probability are interchangeable, you could define probability as the probability that a particular event will take place.
To determine probability the Preliminary geologic , we obtain,
P(oil)=0.3+0.4
P(oil)=0.7.
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For what values of x will the result of 5x be greater than 25?
Answer:
x > 5
Explanation:
We are to determine the values of x that satisfies the condition:
\(5x>25\)To determine the values of x, we divide both sides of the inequality by 5.
\(\begin{gathered} \frac{5x}{5}>\frac{25}{5} \\ x>5 \end{gathered}\)Therefore, for any value of x greater than 5, the result of 5x will be greater than 25.
How to graph inequalities
Answer:
1) Rearrange the equation so "y" is on the left and everything else on the right.
2) Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)
3) Shade above the line for a "greater than" (y> or y≥) or below the line for a "less than" (y< or y≤).
Step-by-step explanation:
6. If T.> (MBC)= ADEF then how many units will the figure move up or down?
A. 6
B.O
C. 7
D. 10
Answer:
jhj
Step-by-step explanation:
On Tuesday, the Beef Market sold 400 pounds of prime rib steak at $9.98 per pound and 120 pounds of rib-eye steak at $6.49 per pound. What was the average cost in dollars per pound of the steaks sold on Tuesday
The average cost in dollars per pound of the steaks sold on Tuesday is 9.17 per pound.
Average cost:First step is to calculate the total cost for steaks
Total cost=400×$9.98 + 120×$6.49
Total cost=$4770.8
Second step is to calculate the total pound
Total pound=400 + 120
Total pound= 520
Third step is to calculate the average cost in dollars
Average cost=$4770.8 / 520
Average cost= 9.174615385
Average cost=9.17 per pound (Approximately)
Inconclusion the average cost in dollars per pound of the steaks sold on Tuesday is 9.17 per pound.
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You are choosing between two different cell phone plans. Plan 1, charges a rate of 20 cents per minute. Plan 2 charges a monthly fee of $49.95 plus 9 cents per minute. If x = the number of minutes used and y = total cost in Dollars!!!!!! A) Write system of equations to represent the total cost (in dollars) of each plan.Plan 1: Plan 2: B) What is the minimum number of minutes you would have to use in a month in order for the second plan to be preferable? minutes
We have two different plans
x is the number of minutes
y= total cost in dollars
Part A)
Plan 1
y=0.20x
Plan 2
y=0.09x+49.95
Part B
In order that the second plan will be preferable, is when the plan 2 is cheaper so we will have the next inequality
\(0.20x>0.09x+49.95\)Then we need to solve the inequality
\(0.20x-0.09x>49.95\)\(0.11x>49.95\)\(x>\frac{49.95}{0.11}\)\(x>454.09\)The nearest greater inter is 455
Therefore the minimum number of minutes you would have to use in a month in order for the second plan to be preferable is 455 minutes
Which statement best describes the table?
thankss :)
What’s 2 ways 3 people can share a 5 segment chewy fruit worm.?
Answer:
give everyone one, then split the last two into thirds.
thats all i can think of so sorry :(
Step-by-step explanation:
Find the exact value of cosine (startfraction 5 pi over 6 endfraction) cosine (startfraction pi over 12 endfraction) sine (startfraction 5 pi over 6 endfraction) sine (startfraction pi over 12 endfraction)
The corrected exact values are cosine (5π/6) = -1/2, cosine (π/12) cannot be simplified further, sine (5π/6) = 1/2, sine (π/12) cannot be simplified further.
Let's correct the calculation of the exact values of the given trigonometric expressions:
1. Cosine (5π/6):
The angle 5π/6 is in the second quadrant. The reference angle for 5π/6 is π/6. Since the cosine function is negative in the second quadrant, the exact value is -cos(π/6) = -1/2.
2. Cosine (π/12):
The angle π/12 is not a special angle, so we cannot simplify it further using known exact values.
3. Sine (5π/6):
The angle 5π/6 is in the second quadrant. The reference angle for 5π/6 is π/6. The sine function is positive in the second quadrant, so the exact value is sin(π/6) = 1/2.
4. Sine (π/12):
The angle π/12 is not a special angle, so we cannot simplify it further using known exact values.
Therefore, the corrected exact values are:
cosine (5π/6) = -1/2,
cosine (π/12) cannot be simplified further,
sine (5π/6) = 1/2,
sine (π/12) cannot be simplified further.
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Please help i am super confused on what to do :)
Please explain how you got your answer too
Dont write something dum because i will report it i just need help on this question
Answer:
About 9.1 yards tall.
Step-by-step explanation:
So, we can draw the right triangle shown below:
We want to find h.
Since we know the angle and the side adjacent to the angle and we wan to find the opposite side, we will use the tangent ratio:
\(\displaystyle \tan(x^\circ)=\frac{\text{Opposite}}{\text{Adjacent}}\)
So:
\(\displaystyle \tan(20)=\frac{h}{25}\)
Therefore:
\(\displaystyle h=25\tan(20)\)
Use a calculator. Ensure your calculator is in the correct mode (degrees mode):
\(h\approx 9.1\text{ yards}\)
The goal post is around 9.1 yards tall.
Answer as soon as you see this. I need lots of help
Answer:
GFD = 132.7
Step-by-step explanation:
JIF and GFD are same side interior angles and when the lines are parallel, same side interior angles are equal
JIF = 132.7 so GFD = 132.7
In the diagram shown, we are given that JIF and GFD are parallel lines. However, these lines are also same side interior angles. This means that they will be equal to each other since they are parallel lines. Remember, parallel lines are coplanar lines that do not intersect.
So if JIF = 132.7°, then GFD also measures 132.7°.
Solving Logarithmic Equations
Answer:
optio 1
Step-by-step explanation:
i am copadent about that
Garden A has area 25 square meters. Garden B has area 58.7 square meters. The area of garden B is what percent of the area of garden A? First round the area of garden B to the nearest 10 square meters estamate the answer
Answer: The area of garden B is 234.8% of the area of garden A.
Step-by-step explanation:
Given: Garden A has area 25 square meters. Garden B has area 58.7 square meters.
The percent of the area of garden A is the area of garden B =
\(\dfrac{\text{area of garden B}}{\text{area of garden A}}\times100\)
\(=\dfrac{58.7}{25}\times100\%\\\\= 58.7\times4\%\\\\= 234.8\%\)
Hence, the area of garden B is 234.8% of the area of garden A.
What’s the area of a circle if the diameter is 25cm?
Answer:
≈ 490.87 cm²
Step-by-step explanation:
The area (A) of a circle is calculated as
A = πr² ( r is the radius )
Here diameter = 25, then r = 25 ÷ 2 = 12.5
A = π × 12.5² = 156.25π ≈ 490.87 cm² ( to 2 dec. places )
Answer: 490.87
Step-by-step explanation:
the radius is half of the diameter so radius = 12.5
do the following equation to find the area or a circle: A=πr2
plus in your numbers: A= π·12.52 and solve:
π·12.52≈490.87385