Solution:
Let's make,
mechanic #1's rate = x
mechanic #2's rate = y
Note that their rate is dollars per hour.
Now, mechanic #1 worked for 20 hours. Then, we get the following equation:
20x = money earned by mechanic #1
On the other hand, mechanic #2 worked for 15 hours. Then, we get the following equation:
15y = money earned by mechanic #2
together they charged a total of $2250. So the amount of money earned by both mechanics is:
20x + 15y = 2250 EQUATION 1
On the other hand, the sum of the two rates was:
x + y = 125 EQUATION 2
From the equation, if we solve for x, we get:
x = 125-y EQUATION 3
plug (125-y) in for "x" in equation 1 to get everything in terms of one variable:
20(125-y)+15y = 2250
this is equivalent to
2500-20y +15y = 2250
this is equivalent to
2500 -5y = 2250
this is equivalent to
-5y = 2250 -2500
this is equivalent to:
-5y = -250
or
5y = 250
solving for y, we get:
[tex]y\text{ =}\frac{250}{5}=50[/tex]now, replacing this into equation 3, we get:
x = 125-y = 125 - (50) = 75
so that, we can conclude that the correct answer is:
mechanic #1 charged 75 $/hr
mechanic #2 charged 50 $/hr
Which of the expressions equal −5
Answer:
-5+0=-5
(-6)+1=-5
-7+2=-5
Step-by-step explanation:
how do i solve this for standard equation and foci?
For this problem, we are given the graph of an ellipse, and we need to determine its expression in the standard form.
The standard equation of an ellipse is given below:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]Where (h,k) is the center of the ellipse, a is the horizontal radius and b is the vertical radius.
The center of the ellipse on our problem is (-2,2), the vertical radius is 2 and the horizontal radius is 3. We have:
[tex]\begin{gathered} \frac{(x+2)^2}{3^2}+\frac{(y-2)^2}{2^2}=1 \\ \frac{(x+2)^2}{9}+\frac{(y-2)^2}{4}=1 \end{gathered}[/tex]In order to calculate the Foci, we need to first find the eccentricity of the ellipse, which is given by the following formula:
[tex]\begin{gathered} e=\sqrt{a^2-b^2} \\ e=\sqrt{3^2-2^2} \\ e=\sqrt{9-4}=\sqrt{5} \end{gathered}[/tex]The coordinates of the foci are given by:
[tex]\begin{gathered} F(h+e,k)=(-2-\sqrt{5},2) \\ F^{\prime}(h-e,k)=(-2+\sqrt{5},2) \end{gathered}[/tex]The coordinates for the foci are: (-2-sqrt(5), 2) and (-2+sqrt(5), 2).
How many subsets does the set T = {salsa, sour cream, queso, guacamole, pico de gallo} have?Question 49 options:a) 5b) 0c) 25d) 32
SOLUTION:
Step 1:
In this question, we are given the following:
How many subsets does the set T = {salsa, sour cream, queso, guacamole, pico de gallo} have?
Step 2:
The details of the solution are as follows:
Recall that:
The empty set and the set itelf are also part of the subsets that must be included as part of the number of subsets.
If a set has “n” elements,
then the number of subset of the given set is
[tex]2^n[/tex]Hence, the total number of subsets will be:
[tex]2^5=\text{ 32 \lparen OPTION D \rparen}[/tex]CONCLUSION:
The final answer is:
[tex]32\text{ \lparen OPTION D \rparen}[/tex]WILL GIVE BRAINIEST!!!
Answer:
x=1
Step-by-step explanation:
Both graphs intersect at 1
Answer:
x=1
Step-by-step explanation:
They sectioned at 1
Find the mean, median, and mode of the data set. Round to the hundredths, if necessary. 3, 4, 5, 7, 6, 8, 8, 5, 3, 6, 4, 5, 3, 3, 7, 7.
Mean is 5.25, Median is 5 and mode is 3.
Given,
In the question:
There are numbers:
3, 4, 5, 7, 6, 8, 8, 5, 3, 6, 4, 5, 3, 3, 7, 7.
To find the mean, median and mode.
Let's Know :
How do you find the mean median and mode?
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.
Now, According to the above statement :
To find Mean:
[tex]\frac{3+4+ 5+ 7+ 6+ 8+ 8+ 5+ 3+ 6+ 4+ 5+ 3+ 3+ 7+ 7}{16}[/tex]
= 84/16 = 5.25
For Median
Arrange in ascending order
3, 3, 3, 3, 4,4, 5,5,5, 6,6, 7, 7, 7, 8,8.
There is an even no. of observations. i.e., 16 numbers.
then, there is no single middle value; the median is then usually defined to be the mean of the two middle values: so the median of
Middle two values is : (5 + 5)/2 = 10/2 = 5
Middle value is 5
For Mode:
The mode is the number that occurs most often in a data set.
Mode is 3 .
Hence, Mean is 5.25, Median is 5 and mode is 3.
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what are the solutions of the equation 6x^2+x-2= 0
Answer: The answer would be
B. 1/2
C. 1/3
Step-by-step explanation:
The solution of the equation 6x² - x - 1 = 0 are x = 1/2 and x = -1/3 after using the quadratic formula.
What is the quotient of two and two fifths ÷ five sixths?
sixty over thirty
seventy two over twenty five
fifteen over twenty-five
twenty two fifths
B ] seventy two over twenty five is the quotient of two and two fifths ÷ five sixths.
Quotient refers to the number produced by division of two numbers.
According to question,
two and two fifths = 22/5 = 5*2+2/5 = 12/5five sixths = 5/6Division of two numbers,
⇒ 12/5 / 5/6
⇒ 12/5 * 6/5
⇒ 72/25
Hence, 72/25 i.e., seventy two over twenty five is the quotient of two and two fifths ÷ five sixths.
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Given the regular nonagon (9-sided polygon) pictured below, which statements are true? Chose 2 answers. PLEASE EXPLAIN HOW YOU GOT THE ANSWER
A:The polygon has point symmetry.
B:The polygon has 40° rotational symmetry.
C:The polygon has 120° rotational symmetry.
D:The polygon has 90° rotational symmetry.
Answer:
B and C
Step-by-step explanation:
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 10.8 seconds
Step-by-step explanation:
[tex]-16t^2 + 170t+40=10\\\\16t^2 -170t-30=0\\\\t=\frac{-(-170) \pm \sqrt{(-170)^2 -4(16)(-30)}}{2(16)}\\\\t \approx 10.8 \text{ } (t > 0)[/tex]
can you pls help wit
DEF is an acute angke because the measure we can notice is less than a right angle
then the value is less than 90°
then right option should be D and E
C isnt because we can notice the angle is
Look at the graph of f(x). Which of the following are true? Select all that apply.
Answer:
Explanation:
Use the law of sines to solve the triangle if possible
The Sine rule formula is,
[tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]Given:
[tex]\begin{gathered} a=13.9in \\ A=83^0 \\ b=18.3in \\ B=? \end{gathered}[/tex]Let us solve for solve for the measure of angle B
[tex]\frac{13.9}{sin83^0}=\frac{18.3}{sinB}[/tex]Therefore,
[tex]\begin{gathered} sinB=\frac{18.3\times sin83^0}{13.9}=1.30673342266 \\ \therefore B=sin^{-1}(1.30673342266)=No\text{ solution} \end{gathered}[/tex]Hence, there are no possible solutions for this triangle (OPTION C).
A longitudinal wave has 20 compressions and 20 rarefactions in 0.1s. Find its frequency.
The frequency of the longitudinal wave is 5/2 cm.
Given:
A longitudinal wave has 20 compressions and 20 rarefactions in 0.1s.
we are asked to determine the frequency of the wave = ?
1 wave ⇒ 1 compression + 1 rarefactions
therefore,
20 waves:
0.2 s ⇒ 20 waves.
1 & ⇒ 20/0.02 × 10/1
1 & ⇒ 200/2
1 & ⇒ 100 hz
20 > = 50 cm
⇒ 50/20
= 5/2 cm
Hence we get the frequency as 5/2 cm
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is the morning temperature was 1 degrees Celsius then there was a rise of 3 degrees Celsius what is the afternoon temperature
the temperature in the morning was 1 degree celsius
then rise of 3 degree
so now the total temperature is 1 + 3 = 4 degree
so the temperature of the afternoon is 4 degrees.
x=9 and y=4 what does xy/2
Answer:
18
Step-by-step explanation:
Equation 9 x 4 / 2 = 18
First do 9 x 4 which is 36
Next do 36 / 2 which is 18
Also the "/" is another way to say to divide
Stevens new cell phone plan charges a flat monthly fee of $22.5. The plan allows an unlimited number of text messages, but each minute (m) used for the phone calls cost $0.12.
Write an equation that represents the monthly cost(c) of Steven's phone bill based on how many minutes talked?
The required system of equations to express Stevens monthly fee is
22.5 + 0.12 m = c
Given : A flat monthly fee which is charged for Stevens = $22.5
The cost of each phone call = $ 0.12
Let the cost of each monthly call be represented by the letter m
And the total monthly fee be represented by the letter c
thus according to the question the equation can be expressed as :
22.5 + 0.12 m = c
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3 (2) ^2 divide [3 x 2] - 5__________________ 8 divide 4 x 2
Solution
Using BODMAS to solve the fraction
[tex]\begin{gathered} \frac{3(2)^2\div[3\times2]-5}{8\div4\times2} \\ \frac{3(4)\div6-5}{2\times2} \end{gathered}[/tex][tex]\begin{gathered} \frac{12\div6-5}{4} \\ \frac{2-5}{4} \\ =-\frac{3}{4} \end{gathered}[/tex]Therefore the answer = -3/4
if 1+3 =345+2=275+1=163+5=58then2+4=?what isnthe ?
Answer:
46
Explanation:
In each number to the right of the equality sign, the tenths place is always the rightmost number in addition and the one place is the result of the addition.
For example, in 1 +3 = 34
Therefore, for 2 + 4 we have
Hence,
[tex]2+4=46[/tex]which is our answer!
At cliffs of insanity point, the great sasquatch canyon is 7117 feet deep. from that point, a fire is seen at a location known to be 10 miles away from the base of the sheer canyon wall. what angle of depression is made by the line of sight from the canyon edge to the fire? express your answer using degree measure rounded to one decimal place.
Angle of depression is 7.7 ° made by the line of sight from the canyon edge to the fire .
What is angle of depression ?The angle of depression is the angle created by the object and the horizontal line as seen from the horizontal line. The distance between two objects is often calculated when the angles and spacing of an object from the ground are known.
Calculationlet f be the the fire
b is the base of the sheer canyon wall
o be the cliffs of insanity point that is canyon edge
so OB = 7117 Feet
bf = 10 miles = 10 * 5280 = 52800 feet
angle of depression is < xof which is equal to < ofb
let the angle of depression is [tex]\theta[/tex]
now from triangle obf ; it is a right angle triangle , where of = hypotenuse
bf = base , ob = height < ofb = [tex]\theta[/tex]
so , tan [tex]\theta[/tex] = ob/bf = 7117/52800
[tex]\theta[/tex] = [tex]tan^{-1}[/tex] ( 7117/52800) = 7.68 ° = 7.7 °
so angle of depression is 7.7 °
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The ratio of adults to children is 400 to 150
SOLUTION
In mathematics, a ratio indicates how many times one number contains another.
And when we write quantities in ratio form, we represent ratio with the symbol :
For example: The ratio of A to B is written mathematically as A:B
Another important thing we must note when writing ratios is to always express both quantities in their simplest form.
With the above explanation, we can proceed in answering the question.
The ratio of adults to children which is 400 to 150, can be written mathematically in ratio form as:
[tex]\begin{gathered} =\frac{400}{150} \\ \text{Divide both the numerator and denominator by 10} \\ =\frac{40}{15} \\ \text{Divide both the numerator and denominator by 5} \\ =\frac{8}{3} \end{gathered}[/tex]Final answer: The ratio of adults to children is:
[tex]8\colon3[/tex]16x - 4y = 3 y = 4x + 7
y in equation 1
[tex]\begin{gathered} 16x-4\mleft(4x+7\mright)=3 \\ 16x-16x-28=3 \\ -28=3 \end{gathered}[/tex]-28=3 is false, therefore the system of equations has no solution
find the greatest common factor of 615 and 570.
Given the numbers:
[tex]615\text{ and 570}[/tex]Let's find their greatest common factor:
Step 1: Let's determine the factors of the numbers.
a.) 570
The factors of 570 are: 1, 2, 3, 5, 6, 10, 15, 19, 30, 38, 57, 95, 114, 190, 285, 570
b.) 615
The factors of 615 are: 1, 3, 5, 15, 41, 123, 205, 615
Their common factors are: 1, 3, 5, 15
But the greatest among all factors is 15.
Therefore, their greatest common factor (GCF) is 15.
I need help question
Answer: with what???
Find the slope and the y-intercept of the line.
3x+y=2
Write your answers in simplest form.
Answer:
slope is -3
y intercept is 2
Step-by-step explanation:
3x+y=2 [subtract 3x from both sides]
y=-3x+2
slope is -3
y intercept is 2
You are playing miniature golf on the hole shown.
a. Write a polynomial that represents the area of the golf hole. Show your steps and explain how you found the polynomial.
b. Write a polynomial that represents the perimeter of the golf hole. Show your steps and explain how you found the polynomial.
Bonus:
c. Find the perimeter of the golf hole when the area is 216 square feet.
The dimensions of the golf hole found using the indicated variable expressions are as follows;
a. The area of the golf hole is 4·x² + 12·x
b. The perimeter of the golf hole is 8·x + 8
c. The perimeter of the golf hole if the area of the hole is 216 square feet is 56 feet
What is the perimeter of a geometric figure?The perimeter of a geometric figure is found by the length of the boundary of the figure.
a. The area of the gulf hole is found as follows;
The area is a composite figure, which consists of a rectangle of length 3·x and width (x + 4) and a square of length x
Which indicates that the area is A = 3·x × (x + 4) + x×x = 3·x² + 12·x + x²
The area of the hole, A = 3·x² + 12·x + x² = 4·x² + 12·x
The area of the hole is A = 4·x² + 12·x
b. The perimeter of the hole is found as follows;
P = (x + 4) + 3·x + (x + 4) + x + x + x = 8·x + 8
The perimeter of the hole = 8·x + 8
c. The area of the golf hole = 216 square feet, which indicates;
4·x² + 12·x = 216
4·x² + 12·x - 216 = 0
x² + 3·x - 54 = 0
(x + 9)·(x - 6) = 0
x = 6 or x = -9
The perimeter of the golf hole is therefore;
P = 8 × 6 + 8 = 56
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find the hcf of 91 , 112 , 49
Answer: The highest common factor of 91, 112 and 49 is 7
hope this helps :)
-2x² + 3y² + 4x - 5y-11=O
x+3y-1=0
2x+4y=6
3x-12-бу
Solve X and Y
Answer:x=12
y=−186
Step-by-step explanation:x=63x+4y=12
Consider the first equation. Subtract 63x from both sides.
x−63x=4y
Combine x and −63x to get −62x.
−62x=4y
Divide both sides by −62.
x=−
62
1
×4y
Multiply −
62
1
times 4y.
x=−
31
2
y
Substitute −
31
2y
for x in the other equation, 63x+4y=12.
63(−
31
2
)y+4y=12
Multiply 63 times −
31
2y
.
−
31
126
y+4y=12
Add −
31
126y
to 4y.
−
31
2
y=12
Divide both sides of the equation by −
31
2
, which is the same as multiplying both sides by the reciprocal of the fraction.
y=−186
Substitute −186 for y in x=−
31
2
y. Because the resulting equation contains only one variable, you can solve for x directly.
x=−
31
2
(−186)
Multiply −
31
2
times −186.
x=12
The system is now solved.
x=12,y=−186
Describe a transformation that maps triangle abc onto triangle ade.Explain why this transformation makes triangle ade similar to triangle abc
Given:
Triangle ABC is mapped onto triangle ADE.
Required:
The transformation that maps triangle ADE similar to triangle ABC.
Explanation:
A dilation process from A by a factor 3 maps triangle ABC onto triangle ADE.
In the dilation process, the transformed angle value remains constant.
[tex]\angle A\text{ is reflecxive}[/tex]Also,
[tex]\angle ABC\text{ }\cong\text{ ADE}[/tex]Therefore above transformation makes triangle ABC similar to triangle ADE.
Answer:
Thus from the explanation given above, the above transformation makes triangle ABC similar to triangle ADE.
4. Write the following quadratics as products of two binomials. f(x) = 6x2 + 66x + 60
Answer:
f(x)=(6x+6)(x+10)
Explanation:
Given the quadratic expression:
[tex]f\mleft(x\mright)=6x^2+66x+60[/tex]First, we can rewrite it in the form below:
[tex]f\mleft(x\mright)=6x^2+60x+6x+60[/tex]Next, factor the terms:
[tex]\begin{gathered} f(x)=6x(x+10)+6(x+10) \\ \implies f(x)=(6x+6)(x+10) \end{gathered}[/tex]Thus, the quadratics as a product of two binomials is:
[tex]f(x)=(6x+6)(x+10)[/tex]