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We can relate an angle x to its opposite leg and its adjacent leg, by means of the trigonometric function tangent of x, like this:
[tex]\tan (x)=\frac{\text{opposite}}{\text{adjacent}}[/tex]Then we can find the value of the angle by applying the inverse function of tangent, like this:
[tex]x=\tan ^{-1}(\frac{opposite}{adjacent})[/tex]Let's replace the values from the figure into this equation to find x, like this:
[tex]\begin{gathered} x=\tan ^{-1}(\frac{25}{16}) \\ x\approx57.4 \end{gathered}[/tex]Then, x equals 57.4°
Related Questions
Given f(x) = 2x - 1 h(x) = x^2 + 1Find f[h(7)]
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Answer:
[tex]f\lbrack h(7)\rbrack\text{ = 99}[/tex]Explanation:
Given the functions:
[tex]\begin{gathered} f(x)=2x-1 \\ h(x)=x^2+1 \end{gathered}[/tex]We want to find:
[tex]f\lbrack h(7)\rbrack[/tex]First of all, we need to find:
[tex]f\lbrack h(x)\rbrack[/tex]This is done by inserting the value of h(x) into f(x)
So, we have:
[tex]\begin{gathered} f\lbrack h(x)\rbrack=2(x^2+1)-1 \\ =2x^2+2-1 \\ =2x^2+1 \end{gathered}[/tex]Substituting 7 for x in f[h(x)], we have f[h(7)]
[tex]\begin{gathered} f\lbrack h(7)\rbrack=2(7^2)+1 \\ =2(49)+1 \\ =98+1 \\ =99 \end{gathered}[/tex]Which is what we are looking for.
y = 2x divided by 6?
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Answer: I'm not sure if you're trying to find x or y, but y = x/3 and x = 3y
Step-by-step explanation:
Question 1 1. Which of the following is NOT a true statement? 1 point 21 22 23 24 25 26 27 28 O A. Angle 1 and Angle 5 are corresponding angles. w B. Angle 2 and Angle 7 are alternate interior angles. C. Angle 5 and Angle 8 are vertical angles. D. Angle 3 and Angle 7 are corresponding angles. O I e Type here to searchwhats the answer
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Note:
Corresponding agles are angles on corresponding (the same) side of the two lines intersected by the transversal
Alternate angles are angles on the opposite sides of the transversal
the vertex of the parabola below is at the point (3,2) and point (4,6) is on the parabola
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By using the vertex and the given point, we conclude that the quadratic equation is:
y = 4*(x - 3)^2 + 2
How to find the equation of the parabola?A quadratic equation with a vertex (h, k) and a leading coefficient A can be written as:
y = A*(x - h)^2 + k
In this case, we know that the vertex is (3, 2), replacing that in the general equation we get:
y = A*(x - 3)^2 + 2
We also know that the curve passes through (4, 6), so when x = 4, the value of y must be 6, replacing that in the quadratic equation we can find the value of A.
6 = A*(4 - 3)^2 + 2
6 = A*(1)^2 + 2
6 - 2 = A*1
4 = A
So we conclude that the quadratic equation is:
y = 4*(x - 3)^2 + 2
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I need help I already answered just to make sure
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The height of the tree is 13.82 m
Step - by - Step Explanation
What to find? Height of the tree.
Given:
• Angle of elevation = 62,°
,• Eye-level above the ground =160cm
,• Distance away from the tree = 6.5m
We need to first sketch the problem, to have a clearer picture of the question.
Change 160cm to meter
160 cm = 160/100 = 1.6 m
Height of the tree = 1.6 + x
We need to find the value of x.
From the sketch above;
Opposite =x
Adjacent =6.5
θ= 62°
Using the trigonometric ratio;
[tex]\tan \theta=\frac{opposite\text{ }}{\text{adjacent}}[/tex]Substitute the values.
[tex]\tan 62=\frac{x}{6.5}[/tex]Cross-multiply.
x=6.5tan62°
x = 12.22 m
Height of the tree = 1.6 m + 12.22m
Height of the tree = 13.82 m
OR
Height of the tree = 1382 cm approximately.
the mean is 5.8the variance is 2.4We have to find the standard deviation and round it to one decimal place.
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To calculate the standard deviation given the variance, we just take the square root.
That because the variance is:
[tex]v=\sigma^2[/tex]And the standard deviation is:
[tex]\sigma[/tex]So, calculating the standard deviation:
[tex]\sigma=\sqrt[]{\sigma^2}=\sqrt[]{v}=\sqrt[]{2.4}=1.54919\ldots\approx1.5[/tex]Thus, the standard deviation is 1.5.
pls help no need for no need for long explanations just a summary
Answers
As shown in the figure:
There are two parallel lines of the triangle
Using the ratio and proportional to find the value of x
So,
[tex]\begin{gathered} \frac{x}{6}=\frac{9}{2} \\ \\ x=6\cdot\frac{9}{2}=\frac{54}{2} \\ \\ x=27 \end{gathered}[/tex]So, the answer is: x = 27
Which of the following pairs of numbers do not have a geometric mean of 12? A 11 and 13 B 20 and 7.2 C 3 and 48 D 5 and 28.8
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Answer
Option A contains two numbers that do not have a geometric mean of 12.
11 and 13 do not have a geometric mean of 12.
Explanation
The geometric mean of two numbers, a and b, is given as
Geometric mean = √(a × b)
So, we want to find which two numbers will have a geometric mean of 12
12 = √(a × b)
Taking the square of both sides, we see that
144 = (a × b)
So, whichever two numbers give a product of 144 is our answer.
Option A
11 × 13 = 143
Option B
20 × 7.2 = 144
Option C
3 × 48 = 144
Option D
5 × 28.8 = 144
Hope this Helps!!!
34 Sat purchased some art supplies and cord stock in order to make greeting cards. The graphbelow shows the relationship between the number of cards Sat makes and the total cost etthe materials used te make the cardsCost of Noking Greeting CardsTotal Cost(dollars)2 4 6 8 10Number of Cards MadeBased on the graph what will be the total cost of making 25 greeting cards?*2.50G$50.00N $52.50$15.00
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step 1
Find the slope
we have the points
(3,4) and (7,6)
m=(6-4)/(7-3)
m=2/4
m=$0.5 per card
the equation of the line in slope intercept form is equal to
y=mx+b
we have
m=0.50
b=?
point (3,4)
substitute
4=0.5(3)+b
b=4-1.50
b=2.50
y=0.50x+2.5
so
For x=25 cards
substitute
y=0.50(25)+2.50
y=15.00
answer is the option J4. A survey explored the relationship between gender and video game play. Which is not a reasonable interpretation of the data? Play Daily Do Not Play Daily Total Boys 45 5 50 Girls 12 38 50 Total 57 43 100 O A) More boys surveyed play video game daily than girls. TO B) Ignoring gender, a little more than half of the students surveyed play video games daily. Of the boys surveyed, 5% do not play video games daily. OD) Of the girls surveyed, exactly 24% play video games daily.
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Answer:
C.
Explanation:
Let's analyze each answer option:
Option A.
Taking into account the table, we can say that 45 boys play video games daily and 12 girls play video games daily, so more boys play video games daily than girls because 45 is greater than 12.
Option B.
In the same way, there is a total of 57 students that play video games daily and 43 that don't. Since 57 is a little higher than 50 (half of the 100 students surveyed), we can say that a little more than a half of the students surveyed play video games daily.
Option C.
There are 50 boys surveyed and from them 5 do not play video games daily, so the percentage of boys that don't play video games daily is:
[tex]\frac{5}{50}\times100=0.1\times100=10\text{ \%}[/tex]Option D.
In the same way, there are 50 girls surveyed, and 12 play video games daily, so the percentage of girls that play video games daily is:
[tex]\frac{12}{50}\times100=0.24\times100=24\text{ \%}[/tex]Therefore, the only option that is not a reasonable interpretation of the data is C. because the percentage of boys that don't play video games daily is 10% instead of 5%
Find the point slope Slope= 7Passing through (6,1)
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The point-slope form of a line always has the form:
[tex]y-y_0=m\cdot(x-x_0)[/tex]"m" represents the slope of the line; in our case, the statement of the problem says that
[tex]m=7[/tex]Besides, (x_0, y_0) is a point of the line. By the statement of the problem (again), we can choose:
[tex]x_0=6,y_0=1[/tex]Then, the point-slope form becomes:
[tex]y-1=7\cdot(x-6)[/tex]Dr. Hughes instructs her students to solve the equation, 2x - 5y = -20, for y. What is the correct first step?Add +5y to both sides of the equation.O Add -2x to both sides of the equation.Add +2x to both sides of the equation.Divide each term in the equation by -5.
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We have the following expression given:
2x -5y = -20
For this case the correct set in order to begin is add 5y in both sides
Add +5y to both sides of the equation.
Identify the type of polar graph for the equation: r = 2+2cos θ aLimacon with inner loop bCardioid cDimpled limacon dConvex limacon eRose Curve fCircle gLemniscate
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is choice a
iner loop Limacon
Identify the side lengths that form a right triangle.a. 12, 13, 16b. 15, 20, 21c. 9, 40, 42d. 10, 24, 26Identify the side lengths that form a right triangle.a. 3, 4, 8b. 30, 40, 45c. 5, 12, 13d. 6, 12, 133. do the side lengths of 8, 10, and 13 form a right triangle? 4. Determine if ▼ABC is a right triangle if AB=36, AC=48 and BC=60
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Answer:
d. 10, 24, 26
Explanation:
To identify the side lengths that form a right triangle, we check if it satisfies the Pythagorean theorem.
By the theorem:
[tex]\begin{gathered} a^2=b^2+c^2 \\ a\text{ is the hypotenuse, the longest side.} \end{gathered}[/tex]a. 12, 13, 16
[tex]\begin{gathered} 16^2=12^2+13^2 \\ 256=144+169 \\ 256\neq313 \end{gathered}[/tex]These side lengths do not form a right triangle.
b. 15, 20, 21
[tex]\begin{gathered} 21^2=15^2+20^2 \\ 441=225+400 \\ 441\neq625 \end{gathered}[/tex]These side lengths do not form a right triangle.
c. 9,40,42
[tex]\begin{gathered} 42^2=9^2+40^2 \\ 1764=81+1600 \\ 1764\neq1681 \end{gathered}[/tex]These side lengths do not form a right triangle.
d. 10, 24, 26
[tex]\begin{gathered} 26^2=10^2+24^2 \\ 676=100+576 \\ 676=676 \end{gathered}[/tex]These side lengths form a right triangle since both sides of the equation are the same.
Help - Classifying Quadrilaterals
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A square is all of these combined because each one could be a square, which means a square is each of these.
Answer:
A square is each of these because they may all be squares, hence a square is all of them.
Step-by-step explanation:
1 3/8 × 3 2/3=answer must be in simplest fraction form
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EXPLANATION
Given the fractions 1 3/8 and 3 2/3
First we need to turn both fractions into improper ones
[tex]1\frac{3}{8}=\frac{11}{8}[/tex][tex]3\frac{2}{3}=\frac{11}{3}[/tex]Now, multiplying both fractions:
[tex]\frac{11}{8}\cdot\frac{11}{3}=\frac{121}{24}[/tex]The answer is 121/24
Miguel has 225 base ball cards. He plans to keep 75 cards and give the rest to his friends.Can Miguel give an equal number of cards to 6 friends? Explain.
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We know what Miguel has 225 baseball cards, and he plans on keeping 75, while giving them the rest of them to his friends. We want to know if he can give an equal number to 6 of his friends.
For this objective, we know what he will have to give to his friends an amount of:
[tex]undefined[/tex]Acetaminophen and liver damage. It is believed that large doses of acetaminophen
(the active ingredient in over the counter pain relievers like Tylenol) may cause damage to the
liver. A researcher wants to conduct a study to estimate the proportion of acetaminophen users
who have liver damage. For participating in this study, he will pay each subject $20 and provide
a free medical consultation if the patient has liver damage.
(a) If he wants to limit the margin of error of his 98% confidence interval to 2%, what is the
minimum amount of money he needs to set aside to pay his subjects?
(b) The amount you calculated in part (a) is substantially over his budget so he decides to use
fewer subjects. How will this affect the width of his confidence interval?
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Using proportions we can conclude that the researcher should recruit a minimum of 1509 subjects.
What is proportion?A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls).So, a study is being planned to determine the percentage of acetaminophen users who suffer liver injury.
With,
Level of confidence: 98%E=0.03 is the error margin.Then,
The z-value for 98% confidence is known Zₙ = 2.33.Calculation of the sample size: n = p(1 - p)(Zₙ/E)²In order to obtain the most cautious estimate, we should pick p = 0.5 because the researcher has no preconceived notions about what the sample proportion should be:
n = 0.5(1-0.5)(2.33/0.03)²1508.0277778 = 1509Therefore, using proportions we can conclude that the researcher should recruit a minimum of 1509 subjects.
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The correct question is given below:
It is believed that large doses of acetaminophen (the active ingredient in over the counter pain relievers like Tylenol) may cause damage to the liver. A researcher wants to conduct a study to estimate the proportion of acetaminophen users who have liver damage. If she wants to limit the margin of error of her 98% confidence interval to be no more than 3%, what is the minimum number of subjects that she needs to recruit? [Note: The researcher has no expectations about what the sample proportion should be ahead of time, so she – and you – should use p = 0.5 to get the most conservative estimate.]
When interest rates are low, some automobile dealers offer loans at 0% APR, as indicated in a 2016 advertisement by a prominent car dealership, offering zero percent financing or cash back deals on some models.Zero percent financing means the obvious thing—that no interest is being charged on the loan. So if we borrow $1,200 at 0% interest and pay it off over 12 months, our monthly payment will be $1,200/12 = $100.Suppose you are buying a new truck at a price of $26,000. You plan to finance your purchase with a loan you will repay over two years. The dealer offers two options: either dealer financing with 0% interest, or a $2,600 rebate on the purchase price. If you take the rebate, you will have to go to the local bank for a loan (of $23,400) at an APR of 6.5%.What would your monthly payment be if you took the rebate? (Round your answer to the nearest cent.)
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True or False? The end behaviors of each end of any quadratic function are always inthe same direction.
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In general, given a quadratic function,
[tex]\begin{gathered} f(x)=ax^2+bx+c \\ a,b,c\rightarrow\text{ constants} \end{gathered}[/tex]The end behaviors of each end of the function are given by the limits of f(x) when x approaches +/-infinite.
Therefore,
[tex]\lim_{x\to\infty}f(x)=\lim_{x\to\infty}ax^2=a\lim_{x\to\infty}x^2=a*\infty[/tex]and
[tex]\lim_{x\to-\infty}f(x)=\lim_{x\to-\infty}ax^2=a\lim_{x\to-\infty}x^2=a*\infty[/tex]Thus, the two limits are the same and depend on the sign of a.
Hence, the answer is True, the statement is True.The next model of a sports car will cost 3.4% more than the current model. The current model costs $36,000. How much will the price increase in dollars? What will be the price of the next model?
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ANSWER
[tex]\begin{gathered} 1224 \\ 37224 \end{gathered}[/tex]EXPLANATION
Given;
Current model costs $36000
$36000 is 100% of current price.
Next model will be 100% plus 3.4%;
[tex]\begin{gathered} 100+3.4=103.4 \\ =\frac{103.4}{100} \\ =1.034 \end{gathered}[/tex]t
[tex]\begin{gathered} 1.034\times36000 \\ =37224 \end{gathered}[/tex]Therefore, the increase in price;
[tex]\begin{gathered} 37224-36000 \\ =1224 \end{gathered}[/tex]Hence, the price increase in dollars is $1224 while the price of the next model is $37224
The round off errors when measuring the distance that a long jumper has jumped is uniformly distributed between 0 and 5.3 mm. Round values to 4 decimal places when possible.
The mean of this distribution is _____
The standard deviation is _____
The probability that the round off error for a jumper's distance is exactly 0.4 is P(x = 0.4) = ____-
The probability that the round off error for the distance that a long jumper has jumped is between 0 and 5.3 mm is P(1.2 < x < 3.4) = ____
The probability that the jump's round off error is greater than 4.16 is P(x > 4.16) = ____
P(x > 4.2 | x > 1.8) = ___
Find the 85th percentile____
Find the maximum for the lower quartile. ____
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Using the uniform distribution, it is found that:
The mean is of 2.65 mm.The standard deviation is of 1.53 mm.P(X = 0.4) = 0.P(1.2 < x < 3.4) = 0.4151 = 41.51%.P(X > 4.16) = 0.2121 = 21.51%.P(X > 4.2|x > 1.8) = 0.3257 = 32.57%.85th percentile: 4.505 mm.Lower quartile: 1.325 mm.Uniform probability distributionThe uniform distribution has two bounds, a and b, and all outcomes in the distribution are equally as likely.
In this problem, the bounds are as follows:
a = 0, b = 5.3.
Hence the mean is:
M = (a + b)/2 = (0 + 5.3)/2 = 2.65 mm.
The standard deviation is of:
[tex]S = \sqrt{\frac{(b - a)^2}{12}} = \sqrt{\frac{5.3^2}{12}} = 1.53[/tex]
The uniform distribution is continuous, hence the probability of an exact value is of 0.
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
Hence:
P(1.2 < x < 3.4) = (3.4 - 1.2)/(5.3 - 0) = 0.4151 = 41.51%.
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
Hence:
P(X > 4.16) = (5.3 - 4.16)/(5.3 - 0) = 0.2121 = 21.51%.
P(x > 4.2 | x > 1.8) makes the lower bound 1.8, hence:
P(X > 4.2|x > 1.8) = (5.3 - 4.16)/(5.3 - 1.8) = 0.3257 = 32.57%.
The 85th percentile is found as follows:
0.85 x (5.3 - 0) = 4.505 mm.
The lower quartile is the 25th percentile, hence:
0.25 x (5.3 - 0) = 1.325 mm.
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How to draw A Area Model For 29×56
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First, notice that:
[tex]29\text{ x }56=1624[/tex]now, we can write 29 as 20 + 9 and 56 as 50 + 6, so, we can draw the following rectangles:
Then, if we calculate the area of each of the rectangles, we get the following:
then, if we add all the areas together, we get:
[tex]1000+120+450+54=1120+504=1624[/tex]which is the same result as 29 x 56
solve for y please and thank uou
Answers
Similar triangles are triangles that maintain the same ratio even though they are of different scales. Their angles are however equal.
In this case, y is the longest side in triangle 2 as 37.5 is the longest side in triangle 1
The ratio is thus:
[tex]\frac{y}{37.5}=\frac{16.5}{27.5}[/tex]Cross multiplying, we have:
[tex]\begin{gathered} 27.5y\text{ =37.5 x 16.5} \\ to\text{ get y, we divide both sides by 27.5} \\ \frac{27.5y}{27.5}\text{ = }\frac{\text{37.5 x 16.5}}{27.5} \end{gathered}[/tex]y = 22.5
Factor the Expression. If the expression cannot be factored, say so. 8.) x^2 - 4x - 12
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To factor an expression of the form:
[tex]x^2+bx+c[/tex]we find two numbers B and C that fulfills the following properties:
[tex]\begin{gathered} B+C=b \\ BC=c \end{gathered}[/tex]In this case we have b=-4 and c=-12. We can choose B=-6 and C=2. Then we write the expression as:
[tex]x^2-4x-12=x^2-6x+2x-12[/tex]and we factor the common factors in the first two and last terms:
[tex]\begin{gathered} x^2-4x-12=x^2-6x+2x-12 \\ =x(x-6)+2(x-6) \\ =(x+2)(x-6) \end{gathered}[/tex]Therefore:
[tex]x^2-4x-12=(x+2)(x-6)[/tex]A disk is in the form of square and measures 5.25inches on each side. Find the diagonal length of thedisk. I am taking geometry In the 8th grade and I am lost
Answers
Answer:
The diagonal length is 7.42 inches.
Explanation:
The disk with its diagonal is:
Then, we can look at the diagonal as the hypotenuse of a right triangle. Then, if we call D to the diagonal:
[tex]\begin{gathered} D^2=(5.25in)^2+(5.25)^2 \\ D=\sqrt{2(5.25in)^2}\approx7.42in \end{gathered}[/tex]Line segment AB is on square ABCD. Segment EF on equilateral triangle EFG is 12 units longer than AB. Square ABCD and triangle EFG have equal perimeters. What is the length of AB?
Answers
The length of segment AB when the line segment AB is on square ABCD is 36 units.
What is the length of segment AB?From the task content, the length of the line segment AB which is a side of the square ABCD is to be determined.
In this case, since the perimeters of triangle EFG and square ABCD are equal as given;
Let the length of segment AB = x.
Therefore, EF = x + 12.
Therefore, the perimeter of the equilateral triangle = 3(x +12).
While the perimeter of square ABCD is; 4x.
Therefore, since the perimeters are equal, we equate them and this will be:
3(x + 12) = 4x
3x + 36 = 4x
36 = x.
Therefore, the length is 36 units.
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Parallelogram ABCD was transformed to form parallelogram A'B'C'D'.У.101864D2-10-8-616 8 10a245-6881-101Which rule describes the transformation that was used to form parallelogram A'B'C'D'?O (x + 10, y + 3)0 (-x, y-3)O (x - 10.y-3)(x + 10. y-3)
Answers
Explanation
Step 1
to find the transformation, count the units moved in each axis
for x, (red line)
for y( green line)
[tex]\begin{gathered} \text{for x}\Rightarrow horizontal\Rightarrow from\text{ 2 to -8=-8-(2)=-}10 \\ \text{for y }\Rightarrow vertical\text{ }\Rightarrow\text{from 5 to 2, =2-5=-3} \\ so,\text{ the transformation is} \\ (x-10,y-3) \end{gathered}[/tex]Which answer choice below is a solution to this equation?7x + 5 – 2x = 2x – 7A. 2B. 0C. -4D. 8
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
[tex]7x\text{ + 5 - 2 x = 2 x- 7}[/tex]Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} 7\text{ x - 5 - 2 x = 2 x - 7} \\ 5x\text{ - 5 = 2x - 7} \\ collecting\text{ like terms, we have that:} \\ 5\text{ x - 2x = - 7 - 5} \\ 3\text{ x = - 12} \\ Divide\text{ both sides by 3, we have that:} \\ x\text{ =}\frac{-12}{3} \\ x\text{ = - 4 \lparen OPTION C \rparen} \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]x\text{ = - 4 \lparen OPTION C\rparen}[/tex]
-10 is no less than 2 times a number plus 14
Answers
Let the number be x.
Then according to the question,
[tex]\begin{gathered} -10\ge2x+14 \\ -10-14\ge2x \\ -24\ge2x \\ x\ge-12 \end{gathered}[/tex]Thus, the number should be greater than or equal to -12.