A family taking a road trip vacation travels 126 miles in 3 hours.
We can calculate the constant of proportionality as:
[tex]\frac{126\text{ miles}}{3\text{ hours}}=42\text{ miles/hour}[/tex]Then, in 5 hours they would travel:
[tex]d=5\text{ hours}\cdot\frac{42\text{ miles}}{1\text{ hour}}=210\text{ miles}[/tex]In 5 hours they would travel 210 miles.
Translate the sentence into an inequality. A number b increased by 6 is less than or equal to -23. please help asap its due tomr
Answer: b+6 (less or equal to sign) -23
Step-by-step explanation: b increased by 6 is b+6
Answer: b+6[tex]\leq[/tex]-23 b[tex]\leq[/tex]-29
Step-by-step explanation:
Identify a set of parallel and a set of perpendicular lines in this image.
m
B
LL
OBFCG, BF 1 CG
OBECG, AD 1 EH
O AD
EH, EHL BE
O AD EH, BF 1 CG
A set of parallel lines and a set of perpendicular lines are: BF║CG, AD⊥BF.
What are Parallel Lines?Parallel lines are straight lines that are of equal distance at every point away from each other, and therefore, do not intersect each other at any point. The sign "║" is used to indicate that two lines are parallel lines.
What are Perpendicular Lines?Lines that are said to be perpendicular lines are lines that intersect each other at right angle or 90 degrees. That is, at the point of their intersection, a right angle is formed which is 90 degrees. The sign "⊥" is used to indicate that two lines are perpendicular lines.
In the image given, lines BF and CG do not intersect at any point and they are of equal distance away from each other at every point, therefore, CG and BF are perpendicular lines.
Also, we can see that a right angle is formed at the point of intersection of lines AD and BF, therefore AD and BF are perpendicular lines.
Thus, we can state that: BF║CG, AD⊥BF.
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if a number decreases by 8, the result is -21.What is the number?
Answer: it would be -13
Step-by-step explanation: -13-8=-21
HELP MEE((((((((
solve an equation and draw a graph on it
I give 20 points!! please help as soon as possible(
Which of the following is an example of a set of like terms ??
2. >>>>>>>b {18x,-x,21x} is an example of like terms because they both hold the same variables.
4.>>>>>>
[tex] = - 7(2x - 3) \\ = - 7(2x) - 7( - 3) \\ = - 14x + 21[/tex]
ATTACHED IS THE SOLUTION
consider the following basket of goods: 15 lollipops, 10 bars of chocolate, four jars of peanut butter, and two ice-cream cakes. suppose that in 1999, each lollipop was 10 cents, each bar of chocolate was $1.50, each jar of peanut butter was $2.50, and each ice-cream cake was $7.99. in 2018, each lollipop was 80 cents, each bar of chocolate was $3.75, each jar of peanut butter was $4.25, and each ice-cream cake was 12.99. what was the value of the basket in 2018?
The value of the basket in 2018 was $92.48 if the basket contains 15 lollipops, 10 bars of chocolate, four jars of peanut butter, and two ice-cream cakes.
The value of the basket in 2018 can be calculated by using multiplication and addition.
First, we multiply the cost of each good in 2018 by the number of that good in the basket to calculate their total cost.
Lollipop: $0.80 × 15 = $12
Chocolate: $3.75 × 10 = $37.5
Peanut butter: $4.25 × 4 = $17
Ice-cream cake: $12.99 × 2 = $25.98
Now the value of the basket in 2018 can be calculated by adding these amounts of each good. Therefore;
Value of basket = $12 + $37.5 + $17 + $25.98
Value of basket = $92.48
Hence the value of the basket in 2018 is $92.48
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I'm stuck with this word problem pls helped me
One of the many branches of mathematics is algebra, which is derived from the Arabic word al-jabr, which means "reunion of fractured pieces, bonesetting."Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for manipulating these symbols in formulas.
Solve the problem?
The world's best mathematicians have been baffled by a mathematical problem for decades.The Diophantine equation x3+y3+z3=k, where k is the sum of all the numbers from 1 to 100, is also referred to as the "sum of three cubes. The following will teach you how to identify the problem before moving on to any of the other four steps in the five-step process for solving algebraic problems.Determine the issue.Describe your knowledge.Plan beforehand.Execute the plan.Check to see if the response makes sense.
16x+12y=744
= 16x+12y=744
16x= 744-12y
divide both sides by 16
16x/16=744-12y/16
x= 744-12y/16
744-12y by 16
x =-3y/4+93/2
solving y
16x+12y=744
12y =744-16x
divide by 12
12y/12 =744-16x/12
y= 744-16x/12
y=-4x/3+62
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Low flow showerheads use 2 1/2 gallons of water per minute. If family members shower a total of 2 1/3 hours per week, how much water does the family use for showers each week? Write an expression that represents the problem. Then solve the problem.
The expression that represents the situation is 5/2(x) and the family uses 350 gallons of water for each week.
Showerheads:
The showerhead is a bathroom fixture that directs the flow of water in a bathroom shower.
Given,
Low flow showerheads use 2 1/2 gallons of water per minute.
And the family uses 2 1/3 hours per week.
Here we need to find the expression for this situation and we also need to find the amount of water used by the family.
First, we have to convert the mixed fraction into improper fraction, then we get,
2 1/2 =5/2
So, for one minute the showerhead use 5/2 gallon of water.
So, the expression for this situation is,
=> 5/2(x).
Where x represents the amount of time in minutes.
Now, we know that the family uses the showerhead for 2 1/3 hours per week.
So, we have to convert this mixed fraction into improper fraction,
2 1/3 = 7/3
We know that, 1 hour = 60 minutes.
So, 7/3 hours is equal to,
=> 7/3 x 60 = 7 x 20 = 140
Then, the amount of water used by the family is,
=> 5/2 (140)
=> 5 x 70
=> 350
Therefore, the amount of water used by the family is 350 gallons per week.
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Angle P in Triangle PQR has the same measure as Angle S in Triangle STU. Which other condition is necessary to prove that these triangles are similar?
△PQR is congruent to △STU (△PQR ≅ △STU) under ASA condition using options (B) and (D).
What is the congruency of triangles?Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, rotate, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. Therefore, if all three sides of two triangles are the same, then the triangles are said to be congruent. If we have a side, an angle between the sides, and then another side that is congruent, we know they are congruent. In other words, side, angle, side.So, to prove that △PQR ≅ △STU:
∠P = ∠S (Given)PQ = ST (Option B)∠Q = ∠T (Option D)So, with these three conditions, △PQR ≅ △STU is under ASA condition.
Therefore, △PQR is congruent to △STU (△PQR ≅ △STU) under ASA condition using options (B) and (D).
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Steve stopped for a drink of water when he had completed 60% of his jog. He had traveled 3 miles. What is the total distance Steve jogged?
2 miles
3 miles
4 miles
5 miles
6 miles
The total distance Steve jogged is 5 miles.
what is percent?The Latin word "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions with a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.
A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.
Given:
Steve completed 60% of the Jog.
Also, he travelled 3 miles.
Let the total distance he travelled be x miles.
Then,
60% of x =3
60/100 x= 3
x= 3 x 100 / 60
x= 300/60
x= 5 miles.
Hence, total he had to jog 5 miles.
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11. FINANCIAL LITERACY The surf shop has a weekly overhead of $2300. b. How many skimboards and longboards must the shop sell each week to make a profit a. Write an inequality to represent the number of skimboards and longboards the shop sells each week to make a profit.
Skimboard costs 115 longboard costs 685
Mind doing this too?
The expression that represents the perimeter and area of the rectangle are 10x + 4 and 6x²- 24.
How to find the area and perimeter of a rectangle?The rectangle is a quadrilateral with opposite sides equal to each other.
Opposite sides of a rectangle is also parallel to each other.
Therefore,
perimeter of a rectangle = 2(l + w)
where
l = side lengthw = widthTherefore,
l = 3x + 6
w = 2x - 4
Hence,
perimeter of a rectangle = 2(3x + 6 + 2x - 4)
perimeter of a rectangle = 2(5x + 2)
perimeter of a rectangle = 10x + 4
Let's find the expression that represent the area of the rectangle.
Hence,
area of a rectangle = lw
area of a rectangle = (3x + 6)(2x - 4)
area of a rectangle = 6x² - 12x + 12x - 24
Therefore,
area of a rectangle = 6x²- 24
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Can u please help me with this answer
Answer:
option a as x=8 hope you understand my writing , if got some problem comment down
Please fully explain how to answer number 5 Thank you
Given: A right triangle with dimensions as shown in the figure
To Determine: The ratio for sin A and cos A
Solution
Given a right triangle ABC with a reference angle A, the trigonometry ratio is
[tex]\begin{gathered} sinA=\frac{opposite}{hypothenuse} \\ cosA=\frac{adjacent}{hypothenuse} \\ tanA=\frac{opposite}{adjacent} \end{gathered}[/tex]From the given right triangle with reference angle A, the hypothenuse is the side facing the right angle. The side facing angle A is the opposite, and the other side is adjacent. This is as shown below
Hence
[tex]\begin{gathered} sinA=\frac{24}{26} \\ cosA=\frac{10}{26} \end{gathered}[/tex]OPTION A is the correct option
Please help me with 24For the following exercises, write the equation for the hyperbola in standard form if it is not already, and identify the vertices and foci, and write equations of asymptotes.
Given the equation,
[tex]-9x^2+72x+16y^2+16y+4=0[/tex]Complete squares as shown below,
[tex]\begin{gathered} -9x^2+72x-a^2=-(9x^2-72x+a^2)=-9(x^2-8x+b^2) \\ \end{gathered}[/tex]Thus,
[tex]\begin{gathered} \Rightarrow-9x^2+72x-a^2=-9(x^{}-4)^2 \\ \Rightarrow a^2=16\cdot9=144\Rightarrow a=12 \\ \Rightarrow-9x^2+72x-144=-9(x^{}-4)^2 \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} 16y^2+16y=16(y^2+y) \\ \Rightarrow16(y+\frac{1}{2})^2=16(y^2+y+\frac{1}{4}) \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} -9x^2+72x+16y^2+16y+4=0 \\ \Rightarrow-9(x-4)^2+16(y+\frac{1}{2})^2+4=-144+4 \\ \Rightarrow-9(x-4)^2+16(y+\frac{1}{2})^2=-144 \end{gathered}[/tex]Finally, the standard form is.
[tex]\begin{gathered} \Rightarrow-\frac{(x-4)^2}{16}+\frac{(y+\frac{1}{2})^2}{9}=-1 \\ \Rightarrow\frac{(x-4)^2}{16}-\frac{(y+\frac{1}{2})^2}{9}=1 \end{gathered}[/tex]As for the vertices, foci, and asymptotes,
[tex]\begin{gathered} c=\pm\sqrt[]{16+9}=\pm5 \\ \text{center:}(4,-\frac{1}{2}) \\ \Rightarrow\text{foci:}(4-5,-\frac{1}{2})_{},(4+5,-\frac{1}{2})_{} \\ \Rightarrow\text{foci:}(-1,-\frac{1}{2}),(9,-\frac{1}{2}) \end{gathered}[/tex]Foci: (-1,-1/2), (9,-1/2)
Vertices
[tex]\begin{gathered} \text{center:}(4,-\frac{1}{2}),\text{vertices:}(4\pm a,-\frac{1}{2}) \\ \text{vertices:}(4+4,-\frac{1}{2}),(4-4,-\frac{1}{2}) \\ \text{vertices:}(8,-\frac{1}{2}),(0,-\frac{1}{2}) \end{gathered}[/tex]Vertices: (8,-1/2), (0,-1/2)
Asymptotes:
[tex]\begin{gathered} y=\pm\frac{3}{4}(x-4)-\frac{1}{2} \\ \Rightarrow y=\frac{3}{4}x-\frac{7}{2} \\ \text{and} \\ y=-\frac{3}{4}x+\frac{5}{2} \end{gathered}[/tex]Asymptotes: y=3x/4-7/2 and y=-3x/4+5/2
according to the national retail federation, 34% of taxpayers used computer software to do their taxes. a sample of 125 taxpayers was selected. 4. what is the distribution of the sample proportion of the 125 taxpayers that used the computer software to do their taxes? a. n(0.34, 0.0424) b. n(0.34, 82.5) 5. what is the probability that between 28% and 40% of the taxpayers from the sample of 125 used computer software to do their taxes? a. pnorm(0.4,0.34,0.0424)-pnorm(0.28,0.34,0.0424) b. pnorm(0.4,0.34,125)- pnorm(0.28,0.34,125)
4) the distribution of the sample proportion of the 125 taxpayers that used the computer software to do their taxes is n(0.34, 0.0424) - option A
5) the probability that between 28% and 40% of the taxpayers from the sample of 125 used computer software to do their taxes is pnorm(0.4,0.34,0.0424) - pnorm(0.28,0.34,0.0424) - Option A
4) Given data:
P = 0.34 and n = 125
Since, np = 0.34 * 125 = 42.5 > 10
& n(1 - p) = 125 * 0.66 = 82.5 > 10
Therefore, the normal distribution can be used here:
Mean is μp = p = 0.34
The standard Deviation is σp = [tex]\sqrt \frac{P(1-p)}{n} = \sqrt\frac{(0.34)(0.66)}{125} = 0.0424[/tex]
The distribution of sample proportion will be;
N (0.34, 0.0424)
Therefore, option (a) is correct that is n(0.34, 0.0424)
5) The likelihood that between 28% and 40% of the 125 taxpayers in the sample used tax preparation software is calculated as follows:
pnorm (0.4, 0.34. 0.0424) - pnorm (0.28, 0.34, 0.0424)
Therefore, option A is correct that is pnorm(0.4,0.34,0.0424)-pnorm(0.28,0.34,0.0424)
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Please can someone help solve the attached:
The translation moves 5 units to the left and 2 units down, so we have:
c = -5
d = -2
How to find the values of C and D?To identify the translation, let's follow a single vertex of the triangle.
The top vertex of triangle A is at (2, -3)
After a reflection about the x-axis only the y-value changes, so after the reflection the coordinates of that vertex will be:
(2, 3).
In now we apply the given translation, the new coordinates will be:
(2 + c, 3+ d)
And the coordinates of this vertex on triangle B is (-3, 1), so we have:
(2 + c, 3+ d) = (-3, 1)
2 + c = -3
c = -3 - 2 = -5
3 + d = 1
d = 1 - 3
d = -2
So the translation is defined by the values:
c = -5
d = -2
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What four consecutive integers have a sum of 86. Name them
The four consecutive integers are 20, 21, 22, and 23 whose sum is 86.
What do you mean by integer no?using sequential means.
Integers are a collection of whole integers and their antipodes, such as -3, -2, 1, 0, 1, 2, 3, etc.
86 is obtained by adding together the four consecutive integers x, (x+1), (x+2), and (x+3)
x + (x+1), (x+2), and (x+3) = 86
the smallest one, x, is now solved for: 4x + 6 = 86
The numbers are 20, 21, 22, and 23, because 4x = 80 x = 20.
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Answer:
20, 21, 22 & 23
Step-by-step explanation:
Forming the equation,
→ x + (x + 1) + (x + 2) + (x + 3) = 86
→ 4x + 6 = 86
Now the the value of x will be,
→ 4x + 6 = 86
→ 4x = 86 - 6
→ x = 80/4
→ [ x = 20 ]
Then the required numbers will be,
→ x = 20
→ x + 1 = 20 + 1 = 21
→ x + 2 = 20 + 2 = 22
→ x + 3 = 20 + 3 = 23
Hence, numbers are 20, 21, 22, 23.
Four friends want to share a package of cookies with m number of cookies in it which expression represents the numbers of cookies each friends will get
Based on the case, we know that four friends want to share their cookies package. The number of the cookies is represent by 'm'. So, how many part for each friends will get?
We can solve the case by 'fraction'. Fractions represent the parts of a whole objects. A fraction is arranged by two parts. First, numerator is the number on the top of the line. Basically, numerator is how many equal parts of the whole objects are taken. Second, denominator is the number below the line. In the other word, denominator is the total number.
If four friends want to share the whole package of cookies, is means that the package will be divided to 4 parts. The whole part is represented by 'm'. So, the fraction form that can describe this case is each friends will get [tex]\frac{1}{4}[/tex] m.
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Jessy is looking to subscribe to seventeen magazine for fashion inspiration. Before registering Jessy wants to make sure this is within her budget. Jessy knows there is an initial sign-up fee and a monthly payment required for the subscription. If the monthly subscription fee is $10 and Jessy remembers having a ball on the 2nd month for $26 write an equation that represents the total cost of subscribing to seventeen magazine.
jerry purchased a single family lot that measured 90' x 120'. the city requires a 20' setback on the front, a 15' setback along the sides and a 10' setback at the back of the lot. how big can jerry build his house?
The best measure of how big Jerry can build his house as required in the task content is; 60' by 90'.
Dimensions.It follows from the task content that the dimension of the family lot purchased by Jerry in a bid to build his house has dimensions; 90' × 120'.
Since the city requires 20' setback on the front and 10' setback at the back, it follows that the vertical length remaining and available to build his house is; 120' - 20' - 10' = 90'.
Also, the horizontal width available for him to build his house after the 15' setback along the sides is; 90' - 15' - 15' = 60'.
Therefore, the space available for Jerry to.build his house is; 60' × 90'.
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How many ways are there to split 12 people into 4 groups with 3 people in each group?
3x-1 times 3=5 times x+1
Find x
Answer:
x = -2
Step-by-step explanation:
3x - 1 × 3 = 5 × x + 1
3x - 3 = 5x + 1
3x - 5x = 1 + 3
-2x = 4
-2x/-2 = 4/-2
x = -2
2 What is the slope of the line in the picture below?
Explanation
if you know 2 points of a line you can easily find the slope using
[tex]\begin{gathered} \text{slope}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}[/tex]Let
P1(-1,5)
P2(7,1)
replace,
[tex]\begin{gathered} \text{slope}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{1-5}{7-(-1)} \\ \text{slope}=\frac{-4}{7+1}=-\frac{4}{8}=-\frac{1}{2} \\ \text{slope}=-\frac{1}{2} \end{gathered}[/tex]I hope this helps you
Harry invests £6000 in a savings account.
The account pays 3.4% compound interest per year.
Work out the value of his investment after 3
Give your answer to the nearest penny.
years.
Answer:
$6633.04
Step-by-step explanation:
6000x1.034^3=6633.04
The value of his investment after 3 years will be $6633.04.
What is compound interest?In finance and economics, interest is the payment of an amount above the repayment of the principal sum by a borrower or deposit-taking financial institution to a lender or depositor at a specific rate by a borrower or depositor. It differs from a fee that the borrower may pay to the lender or a third party.
Compound interest is the interest added to the principal amount of a loan or deposit, also known as interest on interest plus interest.
Given that Harry invests £6000 in a savings account. The account pays 3.4% compound interest per year.
The compound interest will be calculated as,
[tex]A = P( 1 + \dfrac{r}{100})^{nt[/tex]
Substitute the values in the equation above and solve,
A = 6000 x 1.034³
A = $6633.04
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Harley rides her bicycle the same distance every day for 4 days. The total distance she rides is 814 miles. How many miles does she ride each day?
Answer:
203.5
Step-by-step explanation:
just divide 814 by 4
Answer:
203.5 miles per day
Step-by-step explanation:
divide 814 by 4= 203.5
Find the slope between these two points:
(12, -18), (-15, -18)
Answer:
The slope is 0.
Step-by-step explanation:
Using the slope formula which is m= y2 - y1 / x2 - x1, plug in the x values and y values of the two points. (12,-18) is x1 and y1. (-15,-18) is x2 and y2.
When plugging it in we get -18 - (-18)/ -15 - 12. You cannot subtract a negative so it turns from subtraction to addition. So, -18 + 18 / -15 - 12 which equals 0/-27. 0 divided by any number is 0. So the slope is 0, m=0.
Hope this helps :)
find the zeros of the function and state the multiplicities
Answer:
x = -3/4, x = 0, x = 5
Explanation:
The equation can be rewritten as
[tex]m(x)=x(12x^2-51x-45)[/tex]The roots are found by equating the above to zero:
[tex]x(12x^2-51x-45)=0[/tex]One root we immediately notice is x = 0. The other roots are found using the fact that
[tex]12x^2-51x-45=0[/tex]To solve for x we use the quadratic formula which says for
[tex]ax^2+bx+c=0[/tex]the x is given by
[tex]undefined[/tex](6) If the store likes to keep 30 tiles in stock at all times how many bundles do they need to order now, after selling the 150 tiles to the customer? Think about how many you had left over from the customer when ordered 150 tiles.
function:
number of tiles: 12b+38
Where;
b=number of bundles
150+30 = 12b+38
Solve for b:
150+30 = 12b+38
180 = 12b+38
180-38 =12b
142 =12b
142/12 =b
11.8 =b
12 bundles
Which angle is supplementary to ∠NPI?
five angles all with common vertex of P, with angle NPI measuring 55.6 degrees, angle IPK measuring 44.2 degrees, angle KPL measuring 80.2 degrees, angle LPM measuring 55.6 degrees, and angle MPN measuring 124.4 degrees
∠IPK
∠NPL
∠MPN
∠LPM
Answer:
c. ∠MPN
Step-by-step explanation:
Supplementary angles sum to 180°.
(Note that supplementary angles don't have to be next to each other).
Given ∠NPI = 55.6°.
Therefore, to find the measure of the angle that is supplementary to ∠NPI, subtract the measure of ∠NPI from 180°:
⇒ 180° - ∠NPI = 180° - 55.6° = 124.4°.
The angle that measures 124.4° is ∠MPN.
Therefore, ∠MPN is supplementary to ∠NPI.