The greatest common factor is 5 .
If you factor it out, the expression becomes 5 (4x + 7y) .
Answer: 55x^1 y^1
Step-by-step explanation:
Add 20+35= 55
x & y can't stand by it's self, so x^1 and y^1
So you take those answers and you got 55x^1 y^1
You must keep it in letters in alphabetic order or it's considered wrong.
Select which of these transformations is hardest for you to write using algebraic notation.
Then in the blank below offer your classmates some advice on how to write the transformation successfully.
The first transformation is the hardest to write using algebraic notation.
What is graph transformation?The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation.
Notice the first figure, the graph is translated 4 units to the left.
But, the second figure shows a vertical stretch of 2 times.
Let the function be y=f(x).
Then, the translation 4 units to the left using algebraic notation is written as:
y = f(x+4)
And, the vertical stretch of two times is:
y = 2f(x)
Clearly, the first transformation is the hardest to write using algebraic notation.
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Each serving ofsalad dressing uses 3 tablespoons of olive oil and 1 tablespoon of vinegar. A tablespoon of olive oil costs $0.13 and a tablespoon of vinegar costs $0.04. What is the cost of x servings of dressing in dollars?
The cost of x servings of dressing in dollars will be $0.43x.
According to the question,
We have the following information:
Each serving of salad dressing uses 3 tablespoons of olive oil and 1 tablespoon of vinegar.
Cost of 1 tablespoon of olive oil = $0.13
Cost of 1 tablespoon of vinegar = $0.04
So,
The cost of each serving of salad = Cost of 3 tablespoons of olive oil + cost of 1 tablespoon of vinegar
The cost of each serving of salad = 3*0.13 + 0.04
The cost of each serving of salad = $(0.39+0.04)
The cost of each serving of salad = $0.43
Now,
The cost of x servings of salad = $0.43x
(Note that if we have to find the cost of more than 1 product than the number has to be multiplied with the cost of one product.)
Hence, the cost of x servings of salad dressing is $0.43x.
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Which are the solutions of the equation x^4-5x^2-14=0? Use factoring to solve.
Answer:
x = ±√7 and x=±i√2
Step-by-step explanation:
x^4-5x^2-14=0
Factor
(x^2 - 7) ( x^2 +2) =0
Using the zero product property
x^2 -7 =0 x^2 + 2 =0
x^2 =7 x^2 = -2
Taking the square root of each side
(x^2)^1/2 =7^1/2 ( x^2)^1/2 = (-2)^1/2
x = ±√7 x=±i√2
Modeling with Mathematics:
A square-shaped parking lot with 100-foot sides is reduced by x feet on one side and extended by x feet on an adjacent side.
a) The area of the new parking lot is represpresented by (100+ x)(100 – x).
Find this product.
b) Does this area of the parking lot increase, decrease, or stay the same? Explain your thinking. (You can use example values for x to help explain.)
Answer:
a) Difference of squares:
[tex]10000 - {x}^{2} [/tex]
b) The area of the parking lot decreases because x^2 is subtracted from 10,000.
[tex]10000 - {1}^{2} = 10000 - 1 = 9999[/tex]
[tex]10000 - {2}^{2} = 10000 - 4 = 9996[/tex]
The following shape consists of a rectangle and a triangle. Determine its area.
Answer:
72 cm²
Step-by-step explanation:
You want the area of a shape consisting of a rectangle and a triangle. The rectangle is 7 cm long and 8 cm high. The triangle has a base of 8 cm and a height of 4 cm.
AreaThe area of the rectangle is ...
A = bh
A = (8 cm)(7 cm) = 56 cm²
The area of the triangle is ...
A = 1/2bh
A = 1/2(8 cm)(4 cm) = 16 cm²
Total areaThe total area is the sum of the areas of the parts:
total area = rectangle area + triangle area
= (56 cm²) +(16 cm²) = 72 cm²
The area of the shape is 72 cm².
__
Additional comment
You can see from the area formula that the area of a triangle is half the area of its enclosing rectangle. That is, the 4 cm high triangle on the right side of the figure effectively adds the area of a 2 cm wide rectangle with the same base.
The figure's area is equivalent to that of a rectangle 7+(4/2) = 9 cm wide and 8 cm high: (9 cm)(8 cm) = 72 cm², as above.
<95141404393>
what isss 1+2
please help im so confused
Answer:
3
Step-by-step explanation:
1 + 2 = 3
please mark this answer brainliest if it helped you in any way:)
Answer:
3
Step-by-step explanation:
1 + 2 = 3
Let break it down.
Lets say you have 1 apple
Your friend has 2 apples
All together you have 1 + 1 + 1 = 3 apples
what is the answer to (-6, 9), (7, -9)?
Answer:
100000000000000000000000000000
Step-by-step explanation:
what does x = to in the equation 4x +4<9x +8?
The given inequality is expressed as
[tex]4x\text{ + 4 }\leq\text{ 9x + 8}[/tex]The first step is to collect like terms. Thus, we have
[tex]\begin{gathered} 4x\text{ - 9x }\leq\text{ 8 - 4} \\ -\text{ 5x }\leq\text{ 4} \\ \end{gathered}[/tex]We would find x by dividing both sides of the inequality by - 5. Since - 5 is negative, the inequality symbol would be reversed. Thus, we have
[tex]\begin{gathered} \frac{-\text{ 5x}}{-\text{ 5}}\ge\frac{4}{-\text{ 5}} \\ x\text{ }\ge\text{ }\frac{-\text{ 4}}{5} \end{gathered}[/tex]To mail a letter to Vienna, Austria the post office charges a flat rate of $5.50 and an additional $0.25 for every ounce the letter weighs. The cost of mailing a letter is
determined by the equation y = 0.25x + 5.50, where y is the cost of the postage and x is the weight of the letter in ounces.
Step 1 of 2: Graph the equation by finding two points that satisfy the equation and plotting them on the graph. To plot a point, click on the appropriate position on
the graph. You may move a point by clicking and dragging.
Answer:
Step-by-step explanation:
See attached graph
Two pints selected are:
2 packages = $6
5 packages = $6.80
Two observers are standing on shore 20 mile apart at points A and B and measure the angle to a sailboat at a point C at the same time. one observer is 10 miles from the sailboat and the other observer is 25 miles from the sailboat. round to the nearest degree
Using the law of sines, supposing C = 30º, the angle of each observer with the sailboat is:
Observer A: 136º.Observer B: 14º.What is the law of sines?Suppose we have a triangle in which:
The length of the side opposite to angle A has length a.The length of the side opposite to angle B has length b.The length of the side opposite to angle C has length c.The lengths and the sine of the angles are related according to the following rule:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
The measure of angle B is found as follows:
sin(B)/10 = sin(C)/20
sin(B)/10 = 0.5/20 (sin(C) = 0.5)
sin(B) = 5/20
sin(B) = 0.25
B = arcsin(0.25)
B = 14º.
The measure of angle A is found as follows:
sin(A)/25 = sin(C)/20
sin(A)/25 = 0.5/20 (sin(C) = 0.5)
sin(A) = 12.5/20
sin(A) = 0.625
A = arcsin(0.625)
A = 136º.
Missing informationThe problem is incomplete, hence we suppose that the angle C is of 30º and problem asks for the angle measure of each angle.
(drawing is not to scale).
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Paul bought 1 7/8 m of fabric to make a shirt, while Rita bought 1 3/4 m to make her shirt. How much MORE fabric did Paula buy then Rita?
Fabric bought by Paul and Rita to make a shirt was 1 7/8 m and 1 3/4 m respectively , Paul bought 1/8 m more than Rita.
As given in the question,
Length of fabric bought by Paul to make his shirt = 1 7/8 m
Length of fabric bought by Rita to make his shirt = 1 3/4 m
Convert length of fabric into proper fraction
Paul fabric = 1 7/8 m
= 15 /8 m
Rita fabric = 1 3/4 m
= 7 /4 m
Length of Paul fabric more than Rita
Length of more fabric bought by Paul than Rita = (15 /8) - ( 7/4)
= (15/8) - (14/8)
= 1/8 m
Therefore, fabric bought by Paul and Rita to make a shirt was 1 7/8 m and 1 3/4 m respectively , Paul bought 1/8 m more than Rita.
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If a = -3x and b = -2i, then find the value of the ab² in fully simplified form.
The value of the expression ab² is 12x where a = -3x and b = -2i
How to evaluate the expression?From the question, the values of the variables are given as
a = -3x and b = -2i
The expression to calculate is then calculated as
ab²
Substitute the known values in the above equation
So, we have the following equation
ab² = (-3x) * (-2i)²
Evaluate the exponent
So, we have the following equation
ab² = (-3x) * -4
Evaluate the product
So, we have the following equation
ab² = 12x
Hence, the solution to the expression is 12x
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suppose the length of a rectangular room is (x + 4) meters and the width is (x - 4) meters, what expression that can be used to represent the area of the room?
Answer:
Step-by-step explanation:
area=l*w
(x+4)(x-4)
x^2-16 (use foiling)
There are 135 people in a sport centre.
73 people use the gym.
59 people use the swimming pool.
31 people use the track.
19 people use the gym and the pool.
9 people use the pool and the track.
16 people use the gym and the track.
4 people use all three facilities.
A person is selected at random.
What is the probability that this person uses at least 2 facilities?
4 + 12 + 5 + 15 = 36 persons utilize at least two facilities, with 4 of them using all three. Consequently, the likelihood that a randomly chosen individual who utilizes at least two facilities also uses all of them is
4/36=1/9
What is probability?
A probability is a numerical representation of the likelihood or chance that a specific event will take place.
If four people use all three facilities,
then 16 - 4 = 12 of them use the gym and the track but not the pool, and 9 - 4 = 5 of them use the pool and the track but not the gym.
The pool and gym are used by 19 - 4 = 15 individuals, however the track is not used.
4 + 12 + 5 + 15 = 36 persons utilize at least two facilities, with 4 of them using all three. Consequently, the likelihood that a randomly chosen individual who utilizes at least two facilities also uses all of them is
4/36=1/9
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In parallelogram ABCD, diagonals AC and BD intersect at point E, BE=x+21, and DE=4x.
What is BD?
Enter your answer in the box.
Answer:
BD = 56
Step-by-step explanation:
x + 21 = 4x
3x = 21
x = 7
x + 4x + 21
5x + 21
35 + 21
56
You are playing a game that uses two fair number cubes. If the total on the number cubes is either 6 or 10 onyour next turn, you win the game. What is the probability of winning on your next turn? Express your answer asa percent. If necessary, round your answer to the nearest tenth.O 1.2%O 13.9%O 77.8%O 22.2%
When rolling two dice the possible outcomes are:
Probability is calculated as follows:
[tex]\text{probability = }\frac{\text{ number of favorable outcomes}}{total\text{ number of outcomes}}[/tex]There is a total of 6x6 = 36 possible outcomes. From the table, we can see that 5 of them are a 6 and 3 of them are a 10. Then, the number of favorable outcomes is 5 + 3 = 8. Therefore, the probability of winning on your next turn is:
[tex]\begin{gathered} \text{probability = }\frac{8}{36} \\ \text{probability = }0.222 \\ \text{ Expressed as a percent, that is,} \\ \text{probability = }0.222\cdot100=22.2\text{ \%} \end{gathered}[/tex]2p+3/3=4p-7/2
what are all the steps to solve this problem?
it's 27/8 .........................
1.64285714286
Round up the number
Answer: 1.6 or 2
Step-by-step explanation:
If you are rounding it to the nearest tenths then the answer is 1.6 but if you are rounding to the nearest whole number then its 2.
Can someone please help me?
There is a profit made by the Mia in that particular month of the amount $350.
What is meant by the term revenue?The total amount of money produced by sale of products or services connected to the company's main operations is referred to as revenue.The total earnings as well as profit of a company is referred to as income or net income.Net revenue along with net income are both useful in determining a company's financial strength, although they are not exchangeable.For the given question,
The table is given for the revenue and expenses made by Mia.
The total revenue made by Mia in that particular month is $9,550.
The total fixed expenses are $9,000.
The variable expense is $200.
Thus, the difference in the expense is-
Difference = Revenue - fixed expense - variable expense
Difference = $9,550 - $9,000 - $200.
Difference = $350
As, the difference is positive there is profit made by Mia.
Thus, there is a profit made by the Mia in that particular month of the amount $350.
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a new over-the-counter medicine to treat a sore throat is to be tested for effectiveness. the makers of the medicine take two random samples of 25 individuals showing symptoms of a sore throat. group 1 receives the new medicine and group 2 receives a placebo. after a few days on the medicine, each group is interviewed and asked how they would rate their comfort level 1-10 (1 being the most uncomfortable and 10 being no discomfort at all). the results are below. find the 95% confidence interval in the difference of the mean comfort level. is there sufficient evidence to conclude that the new medicine is effective? assume the data is normally distributed with unequal variances. (round answers to 4 decimal places) make sure you put the 0 in front of the decimal. average group 1
A confidence interval exists "a range of values that's likely to contain a population value with a certain degree of confidence.
In case the 95 % confidence interval would be given by
[tex]$0.582 \leq \mu_1-\mu_2 \leq 3.178$[/tex]
What is meant by confidence interval?A confidence interval exists "a range of values that's likely to contain a population value with a certain degree of confidence. It exists often denoted a % whereby a population means lies between an upper and lower interval".
The margin of error exists the range of values below and above the sample statistic in a confidence interval.
Normal distribution, exists a "probability distribution that exist symmetric about the mean, showing that data near the mean exists more frequent in occurrence than data far from the mean".
[tex]$\bar{X}_1=5.84$[/tex] represent the sample mean 1
[tex]$\bar{X}_2=3.96$[/tex] represent the sample mean 2
n 1 = 25 represent the sample 1 size
n 2 = 25 represent the sample 2 size
[tex]$s_1=2.211334$[/tex] sample standard deviation for sample 1
[tex]$s_2=2.35372$[/tex] sample standard deviation for sample 2
[tex]$\mu_1-\mu_2$[/tex] parameter of interest.
The confidence interval for the difference of means exists given by the following formula:
[tex]$\left(\bar{X}_1-\bar{X}_2\right) \pm t_{\alpha / 2} \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}} \text \dots{ (1) }$$[/tex]
The point of estimate for [tex]$\mu_1-\mu_2$[/tex] exists just given by:
[tex]$\bar{X}_1-\bar{X}_2=5.84-3.96=1.88$$[/tex]
In order to estimate the critical value [tex]$t_{\alpha / 2}$[/tex] we require to estimate first the degrees of freedom, given by:
[tex]$d f=n_1+n_2-1=25+25-2=48$$[/tex]
Since the Confidence is 0.95 or 95 %, the value of [tex]$\alpha=0.05$[/tex]and α 2 = 0.025, and we can utilize excel, a calculator or a table to estimate the critical value. The excel command would be: " = -T.INV (0.025, 48) ". And we see that [tex]$t_{\alpha / 2}=2.01$[/tex]
In order to replace into formula (1), we get
[tex]$1.88-2.01 \sqrt{\frac{2.211334^2}{25}+\frac{2.35372^2}{25}}=0.582$[/tex]
[tex]$1.88+2.01 \sqrt{\frac{2.211334^2}{25}+\frac{2.35372^2}{25}}=3.178$[/tex]
In case the 95 % confidence interval would be given by
[tex]$0.582 \leq \mu_1-\mu_2 \leq 3.178$[/tex]
Because all the values for the confidence interval are higher than 0, we may infer that there are significant differences between the means of the two groups in this case, with the mean for group 1 (Medicine) being considerably higher than the mean for group 2 (Placebo) at 5% of significance.
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P.L.Z HELP. 50pts
Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold.
Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work.
Slope-intercept form: y=-2/3=x+490 The slop is -2/3 and the y-intercept is unknown.
Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences.
Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.
Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology.
Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different.
Answer:
[tex]y=-\dfrac{2}{3}x+490[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Given equation:
[tex]2x + 3y = 1470[/tex]
To change the equation to slope-intercept form, isolate y:
[tex]\implies 2x + 3y -2x=1470 -2x[/tex]
[tex]\implies 3y=-2x+1470[/tex]
[tex]\implies \dfrac{3y}{3}=\dfrac{-2x+1470}{3}[/tex]
[tex]\implies y=-\dfrac{2}{3}x+\dfrac{1470}{3}[/tex]
[tex]\implies y=-\dfrac{2}{3}x+490[/tex]
Therefore:
[tex]\textsf{Slope} =-\dfrac{2}{3}[/tex][tex]\textsf{$y$-intercept}=490[/tex]To graph this line with the slope-intercept method:
Plot the y-intercept at (0, 490).The slope gives us the change in y-values over the change in x-values (rise over run). Therefore, use the slope to plot the next few points by mapping 3 units to the right and 2 units down each time:To write the equation in function notation, replace the y-variable for f(x).
[tex]\implies f(x)=-\dfrac{2}{3}x+490[/tex]
The graph of the function represents:
The number of wrap lunch specials sold given the number of sandwich lunch specials sold.The y-intercept of the graph is (0, 490).
To find the x-intercept, set the function to zero and solve for x:
[tex]\implies -\dfrac{2}{3}x+490=0[/tex]
[tex]\implies -\dfrac{2}{3}x=-490[/tex]
[tex]\implies -2x=-1470[/tex]
[tex]\implies x=735[/tex]
Therefore, the x-intercept is (735, 0).
The graph of the function is attached.
If Sal's total profit on lunch specials for the next month is $1,593 (where the profit amounts are the same) the equation would be 2x + 3y = 1593 and the function would be:
[tex]g(x)= -\dfrac{2}{3}x+531[/tex]
As the coefficient of the x-variable has not changed, the slopes of the two functions are the same.
As the total profit has changed, the intercepts are different.
The y-intercept of the first function is (0, 490) and its x-intercept is (735, 0). Whereas the y-intercept of the second function is (0, 531) and its x-intercept is (796.5, 0).
A pottery studio has 11 pounds of clay. It takes 7/8 of clay to make a coffee mug find 11 divided by 7/8.Then interpret the question.
The number of coffee mugs that can be made is 12.
How to calculate the fraction?From the information, the pottery studio has 11 pounds of clay and it It takes 7/8 of clay to make a coffee mug.
The number of coffee mugs that can be made will be:
= Number of pounds of clay / Fraction used for each mug
= 11 / 7/8
= 11 × 8/7
= 88 / 7
= 12
There'll be 12 coffee mugs.
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In solving any inequality if the variable is eliminated and a false statement such as
ANSWER:
No solution
STEP-BY-STEP EXPLANATION:
We have the following inequality:
[tex]x+7If we solve we have the following:[tex]7<-2[/tex]The value of 7 is not less than -2, so this is false.
Which means that the set has no solution
Suppose that two lines, AB and CD, are intersected by a transversal.
Which of the following reasons alone could be used to show that the lines are parallel?
The CORRECT ANSWER is
Alternate exterior angles converse
The answer is NOT
Linear pair theorem
Consecutive interior angles theorem
Congruent supplements
The reason that can be used to show that the lines are parallel is: alternate exterior angles converse.
What is the Alternate Exterior Angles Converse?The alternate exterior angles converse can be defined as rule that states that if two exterior angles that lie on each of the lines that is crossed by a transversal are congruent, then the lines can be said to be parallel lines.
The diagram below shows two lines that are intersected by a transversal. It also shows two pairs of alternate exterior angles, a and d, and b and c.
If angles a and d are congruent or angles b and c are congruent, then both lines can be proven to be parallel to each other by the alternate exterior angles converse.
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Here are the scores that Jenna has received on her seven quizzes: 16, 11, 20, 16, 12, 17, 18 What is the lower quartile?
Based on the scores that Jenna received on her quizzes, the lower quartile can be found to be 12
How to find the lower quartile?To find the lower quartile, use the formula:
= (Number of scores + 1) x 1/4
But before that, you need to arrange the scores that Jenna received, from ascending order:
11, 12, 16, 16, 17, 18, 20
Then use the formula to find the position of the lower quartile:
= (7 + 1) x 1/4
= 8 x 1/4
= 2
It is in the second position. The lower quartile score is therefore 12.
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Based on the scores that Jenna received on her quizzes, the lower quartile would be; 12
What is quartile?Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.
To determine the lower quartile, use the formula as;
= (Number of scores + 1) x 1/4
But before that, we need to arrange the scores that Jenna received, from ascending order which is;
11, 12, 16, 16, 17, 18, 20
Thus, use the formula for the position of the lower quartile:
= (7 + 1) x 1/4
= 8 x 1/4
= 2
Hence, It's in the second position. The lower quartile score is; 12.
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The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
The answer is 43
Step-by-step explanation:
Remember that the sum of the angles of all triangles is 180 degrees.
80+57+x=180
137+x=180
x=43
help me if you love Markiplyer and want to see his OF
It is to be noted that, given the dilation factor stated above, the coordinates of S' is (4, 3).
What is a dilation in math?The mathematical Definition of Dilation is given as a transformation that allows you to resize an object. Dilation is a technique for making items bigger or smaller. This transformation yields a picture that is identical to the original shape. However, there is a size discrepancy in the form.
The computation for the above result is given as follows:
Given that RST has vertices R(0,0), S(6, 3), and T(3, -3); and
The image R'S'T' is the image of RST after a dilation with center (0,0) with scale factor 2/3,
We must determine the coordinates of point S'.
The coordinates of S' can be determined by multiplying both the x and y - coordinates of the point S with the scale factor 2/3.
Let us look at x- coordinate with point S and multiply it with the scale factor of 2/3.
we have: 6 x 2/3 = 4
Hence, x- coordinate for S' = 4
Redo for Y
3 x 2/3 = 3
Hence, y- coordinate for S' = 3
Hence the coordinates of S' is (4, 3).
Hence having applied the principle of dilation, the coordinates of S' are (4,3)
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Which of the following properly describe
"slope"? Select all that apply.
0
A)
ratio of the change in y-values
(rise) for a segment of the graph to
the corresponding change in x-
values (run)
OB) x₂-x₂
y₂-M1
C) ₂-₁
x₂-x₂
D) run/rise
☐ E) rise/run
how do you solve for -2x + 6y = 18
Answer: x=-3(-y+3)
Step-by-step explanation:
Factor Completely.. Please help with this I am really behind..
The factors of the quadratic equation 5x^2 + 44x - 9 are (5x - 1) and (x + 9)
What is factorization?In Mathematics, factorization or factoring is defined as the breaking or decomposition of an entity (for example a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together give the original number or a matrix, etc.
In the given question, we can factorize 5x^2 + 44x - 9 by finding two factors that when they multiply will give us the original polynomial.
The factor for this polynomial or quadratic equation are (5x - 1)(x + 9).
This can be summarized as the factorization of 5x^2 + 44x - 9 is (5x -1)((x+ 9)
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