Remember that the sum of the three interior angles of a triangle is 180°.
Now, let's call the remaining angle x. We would have:
[tex]x+50+80=180[/tex]Solving for x,
[tex]\begin{gathered} x=180-50-80 \\ \Rightarrow x=50 \end{gathered}[/tex]From this, we get that the remaining anlge has to measure 50°. Now, as we already have a side that measures 4 feet, the other two sides are constrained; neither of them can have any measurement that's different to the one that constructs the remaining 50° angle.
Therefore, only one triangle can be constructed.
Y=x+5 so what is the value of the function when x=4
Answer:Y=9
Step-by-step explanation:
If y=x+5 and x=4 then it would be y=4+5
Which ordered pair is the best estimate for the solution to the system?
The ordered pair that is the best estimate for the solution to the system is (0.5, -3.5)
Ordered Pair:
An ordered pair refers to a set of two numbers used to locate a point in a coordinate plane. Here the first point refers the x - coordinate and the second value represents the y - coordinate.
Given,
Her we have the equations,
3x - 8y = 29
3x + y = -2
Now, we need to find the solution of the system.
Here we have to use the substitution method in order to solve this one.
For that, we have to rewrite the second equation as,
y = -2 - 3x.
Now, we have to apply the value of y on the equation (1), then we get,
3x - 8(-2 - 3x) = 29
3x + 16 + 24x = 29
27x = 29 - 16
27x = 13
x = 13/27
x = 0.5
When we apply the value of x into the equation, then we get the value of y as,
y = -2 - 3(0.5)
y = -2 - 1.5
y = -3.5
Therefore, the solution of the system is (0.5, - 3.5).
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The weight of an object on a scale is 165.3 lbs. The measured weight may
vary from the actual weight by at most 0.6 lbs. What is the range of actual
weights of the object?
A. 164.7 ≤ x≤ 165.9
OB. 164.72x2 165.9
C. 164.72 x≤ 165.9
D. x≤ 164.7 or x2 165.9
Russell has been training for the Emerald Valley Race. The first week he trained, he ran 5 days and took the same two routes each day. He ran 2 miles around the football field before school and ran a longer route through his neighborhood after school. By the end of the week, Russell had run a total of 30 miles.
Which equation can Russell use to find how many miles, x, he ran each day after school?
How many miles did Russell run each day after school?
The equation to find the number of miles Russel ran after school is
5 (2 + M) = 30
The number of miles Russel ran after school is 4 miles.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Number of days ran = 5
Number of miles ran before school = 2 miles
Number of miles ran after school = M miles
Total miles ran at the end of the week = 30 miles
Now,
The equation to find the number of miles Russel ran after school.
5 (2 + M) = 30
The number of miles Russel ran after school.
5 (2 + M) = 30
2 + M = 30/5
2 + M = 6
M = 6 - 2
M = 4
Thus,
The equation to find the number of miles Russel ran after school is
5 (2 + M) = 30
The number of miles Russel ran after school is 4 miles.
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esitmate the value of y when x=2.5
How many ounces of a 4% acid solution and how many ounces of a 10% acid solution must be mixed to make 24oz of a 6% acid solution
a = acid solution 4%
b = acid solution 10%
a + b = 24
0.04*a+0.1*b=0.06*24
a=24-b
0.04*(24-b) + 0.1*b = 1.44
0.96 - 0.04b + 0.1*b = 1.44
0.06*b = 0.48
b = 8 oz
a=24-b
a = 24 - 8
How many gallons of the 65% pesticide is needed to make a final solution that is 60% pesticide
we have that
the algebraic expression that represents this situation is
p(0.65)+25(0.25)=(25+p)(0.60)
solve for p
0.65p+6.25=15+0.60p
0.65p-0.60p=15-6.25
0.05p=8.75
p=175 gal262, 257, 252, ...
Find the 37th term.
Answer:
a₃₇ = 82
Step-by-step explanation:
there is a common difference between consecutive terms , that is
257 - 262 = 252 - 257 = - 5
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference ,
here a₁ = 262 and d = - 5 , then
a₃₇ = 262 + (36 × - 5) = 262 - 180 = 82
Identify ALL solutions to the inequality. There could be more than one selection.
The solutions to the given inequality x ≤ 6 are; -6, -3 and -10
What are the Solutions to the Inequality?In inequalities, there are different symbols such as;
≥ which means greater than or equal to
≤ which means less than or equal to
< which means less than
> which means greater than
Now, we are given the inequality as; x ≤ 6
This means that all valid values of x must either be equal to 6 or less than 6. Thus, any value greater than 6 for x is not valid.
Looking at the options, we cans see that -6, -3 and -10 all fall within the required interval and as such they are the solutions.
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A semicircular shape is cut out of the side of a rectangle as shown.
Calculate the shaded area, giving your answer in exact form.
Answer:
9 43/50cm²
Step-by-step explanation:
Required area
= 6 x 4 - ½ π 3²
= 24 - 4.5 π
= 24 - 4.5 x 3.14
= 24 - 14.13
= 9.87
= 9 43/50
The length of a rectangle
is two times the width of the rectangle.
The perimeter of the rectangle is 24 cm.
Draw the rectangle on the centimetre grid.
The diagram of the rectangle is attached where the length and the width are is 8cm and 4 cm
How to draw the rectangle?From the question, we have the following parameters that can be used in our computation:
The length of a rectangle is two times the width of the rectangle.The perimeter of the rectangle is 24 cm.The above parameters imply that
L = 2W
P = 2(L + W)
Where L represents the Length and W represents the width
The perimeter is given as 24
So, we have
2(L + W) = 24
So, we have
L + W = 12
Substitute L = 2W in L + W = 12
2W + W = 12
Evaluate
3W = 12
Divide by 3
W = 4
Substitute W = 4 in L = 2W
L = 2 * 4
Evaluate
L = 8
This means that the length of the rectangle is 8 cm and the width of the rectangle is 4 cm
See attachment for the rectangle
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Find the total surface area of this cuboid.
5 cm
4 cm
6 cm
Answer:
148cm^2
Hope this helps :))
Which is an equation in point-slope form of the line that passes through the points (4, 5) and (−3, −1) ?
Responses
y−1=67(x−3)
y minus 1 equals fraction 6 over 7 end fraction left parenthesis x minus 3 right parenthesis
y+1=65(x+3)
y plus 1 equals fraction 6 over 5 end fraction left parenthesis x plus 3 right parenthesis
y+3=76(x+1)
y plus 3 equals fraction 7 over 6 end fraction left parenthesis x plus 1 right parenthesis
y+1=67(x+3)
Answer:
B, second response
Step-by-step explanation:
Answer:
The slope of a function is the process of finding the rate of change of the value y (dependent variable) of the function changes with respect to that of the variable x (independent variable). The slope itself describes the direction and steepness of the line.
the slope (m) is (5 - -1) / 4 --3 = 6/7
Putting in the equation:
y - y1 = (6/7)(x - x1)
putting, y1= -1, x1= -3
y - -1 = (6/7)( x - -3)
y + 1 = 6/7(x + 3)
Answer is the letter B
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Answer: B
K12 fr fr fr
complete the statement for the graph of the domain of the function is
The domain of a function is all the values of x that is satisfied by the function.
• The domain of the function is, {x|x is all real numbers}
The range of a function is the set of all values of y that satisfies the function.
• The range of the function is ,{y | y is greater than zero}
• The graph is ,increasing, over the interval (0, ∞)
,• The graph is ,decreasing, over the interval (-∞, 0)
Identify the additive and multiplicative inverse of −17.
Answer:
Additive inverse of -17 is 17.
Multiplicative inverse of -17 is -1/17.
The temperature Monday morning was -12 degrees.by afternoon,the temperature had risen a few degrees.which of the following could be the temperature?
The temperature Monday morning was -12 degrees and by afternoon, the temperature had risen a few degrees, which means the some temperature has been added, so c. -10 degree Celsius is the right option.
What is temperature?Temperature is a measure of hotness or coldness expressed in terms of any number of arbitrary scales. It shows the direction in which heat energy will spontaneously flow, i.e., from a hotter body (one with a higher temperature) to a colder body (one at a lower temperature).
A burning match is much hotter than an iceberg, but an iceberg has much more total heat energy than a match does. Temperature is not the same as the energy of a thermodynamic system.
Similar to pressure or density, temperature is referred to as an intensive property—one that is independent of the quantity of matter being considered—as opposed to extensive properties, like mass or volume.
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Full question
The temperature Monday morning was -12 degrees.by afternoon,the temperature had risen a few degrees.which of the following could be the temperature?
a. -15 degrees
b. -12 degree
c. -10 degree
d. -14 degree
He knows the right triangle JAM contains points J (-3,8) and M (5,4) but the Psl spilled right on his coordinates for A so he only knows that x - coordinate of A is 1. If the triangle is a right triangle, what are the possibilities for the y - coordinate of point A
Four Answers:
10.4721 approximately
1.5279 approximately
-4
16
===================================================
Explanation:
Use the midpoint formula to find that N = (1,6) is the midpoint of J(-3,8) and M(5,4). I'm skipping steps so let me know if you need to see them.
Then draw a circle centered at N with radius NM. The equation of this circle is (x-1)^2+(y-6)^2 = 20
Plug in x = 1 and solve for y to get y = 10.4721 and y = 1.5279
These values are approximate.
------------------
The equation of line MJ is y = -0.5x + 6.5 where both decimal values are exact.
The slope here is m = -0.5 which has the negative reciprocal of 2, and this is the perpendicular slope.
The line perpendicular to MJ, that goes through M, is y = 2x-6
Plug in x = 1 to find that y = 2(1)-6 = -4
The line perpendicular to MJ, that goes through J, is y = 2x+14
Plug in x = 1 to find that y = 2(1)+14 = 16
------------------
The diagram below shows points in red of all the possible locations point A could be.
a club has 25 members. how many ways are there to choose four members of the club to serve on an executive committee?
There are 303600 ways to choose 4 members of the club to serve on an executive committee.
What is permutation and combination ?A permutation is the act of putting things or numbers in a certain order. Combinations are a method of picking things or numbers from a set of objects or collections without regard for their order.
CalculationNo. of members = 25
We are supposed to find the no. of ways to choose a president, vice-president, secretary, and treasurer of the club
No. of posts = 4
The order matters here since each member will get different posts .
So, we will use permutation over here
formula - n P r = n! / (n-r)!
n = 25
r = 4
using calculator
25 P 4 = 303600
Hence there are 303600 ways to choose 4 members of the club to serve on an executive committee.
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It takes Neil and Spencer the same amount of time to ride their bikes to school each day, though Neil lives farther away. This Saturday, they plan to study together at the library, which is the same distance from both of their houses. If their average speeds are consistent, who will get to the library in less time?
Calcule A = 1 x 2° +1 x 2¹ +0×2²+1× 2¹
Answer:
1+2+0+2=5
Step-by-step explanation:
1x2° = 1
hope it helps you
branliest??
Lanie has 33 total games downloaded on her phone and her laptop. Her laptop has 7 less than 3 times the number of games that are on her phone. How many games does Lanie have on her phone?
Enter your answer in the box.
games
The number of games in her phone is 10
What is an algebraic expression?An algebraic expression can simply be defined as an expression that is composed of terms, factors, some variables, coefficients and then constants.
They are also known to consist of some mathematical operations, which may include;
AdditionMultiplicationDivisionParenthesesBracketSubtraction, etcBased on the information given, we have;
Let the number of games in her phone be s
s + 3s - 7 = 33
collect like terms
4s = 40
Make 's' the subject
s = 40/4
s = 10 games
Hence. the number is 10
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Ben Armstrong earns $13.57 an hour plus time and a half for weekend work. Last week he worked his
regular 40 hours plus 8 hours on Saturday. What was his total pay for the week?
Ben Armstrong's total pay for working regular 40 hours plus 8 hours on Saturday is $705.64.
How is the total pay determined?The total pay is the sum of the total pay at the normal pay rate in addition to the total overtime pay at the overtime rate.
The overtime pay rate is usually a time and a half of the normal pay rate.
The normal hourly pay rate = $13.57
The overtime pay rate = 1¹/₂ of $13.57 = $20.355
The total earnings from normal working hours = $542.80 (40 x $13.57).
The total earnings from overtime hours = $162.84 (8 x $20.355).
Ben's total pay for the week = $705.64 ($542.80 + $162.84).
Thus, for the week, Ben's total pay is $705.64.
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Mini Me is similar to Dr. Evil in every way, including his size. If Mini Me is 3.5 feet tall and casts a shadow that is 4 feet long, how long will Dr. Evil's shadow be if he stands 6 feet tall?
The ratio of hieght of shadow to the height of individual is same for both individual. So height of shadow for Dr Evil's is,
[tex]\begin{gathered} \frac{h}{6}=\frac{4}{3.5} \\ h=\frac{6\cdot4}{3.5} \\ =6.857 \end{gathered}[/tex]
The shadow of Dr Evil's is 6.857 ft.
Question in picture below
57 yd² is area of triangle .
What is a triangle answer?
A triangle is a three-sided polygon in geometry with three edges and three vertices. The fact that the internal angles of a triangle add up to 180 degrees is the most crucial aspect of triangles.A triangle is a polygon with three sides. The three vertices that make up its three sides also create its three angles. Any triangle with three vertices is represented below by the symbols A B C: several triangular types: The sides of a scalene triangle are not all the same length.Area of triangle = 1/2 * b * h
= 1/2 * 19 * 6
= 19 * 3 ⇒ 57 yd²
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Mrs. Nguyen had 25 students in her English class. On her
birthday 1 student gave her chocolates, 12 gave her cards
and 2 gave her flowers.
QUESTION: What percentage of her students brought
something for Mrs. Nguyen on her birthday?
Answer:
60% of her students brought something for Mrs. Nguyen on her birthday.
Step-by-step explanation:
She has 25 students in her class.
12 gave her cards.
2 gave her flowers.
1 gave her chocolates.
Add them together to get 12+2+1=15.
15 students out of 25 can also be written as a fraction:
[tex]\frac{15}{25}[/tex]
This equals 0.6 as a decimal. To find the percentage multiply by 100, to get 60. Therefore 60% of her students got something for her.
7. Which point is closest to -12 on the number line?
A. -47/4
B. -39/3
C. 23/-2
D.-39/-3
Answer:A
Step-by-step explanation:
Answer:
The answer to this is
Step-by-step explanation:
A, I just got done with the test if not then D.
Write the statement "the sum of a number and 12.6 is more than −3.5" as an inequality.
−3.5 + b ≥ 12.6
−3.5 + b < 12.6
b + 12.6 > −3.5
b + 12.6 ≤ −3.5
The inequality for the expression about the sum will be C. b + 12.6 > -3.5.
What is an inequality?It should be noted that an inequality shows the relation between two expressions which we got equal.
In this case, let the number be given as b. Note that sum means addition. In this case, you will add b and 12.6.
Now, it was also stated that the addition is more than -3.5. This means it's greater than and the sign is >.
Therefore, the inequality will be:
= b + 12.6 > -3.5
Note that > means greater than.
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A,B and C are the vertices or a triangle.
A has the coordinates (4,6).
B has coordinates (2,-2)
C has coordinates (-2,-4)
D is the midpoint of AB.
E is the midpoint of AC.
Prove that DE is parallel to BC.
You must show each stage of your working.
Answer:
The slopes of DE and BC are the same: 0.5. The two lines are therefore parallel.
Step-by-step explanation:
See the attached graph, made in DESMOS.
The midpoints D and E may be determined by taking the average values of x and y that form the endpoints of lines AB (midpoint D) and AC (midpoint E):
Midpoint Endpoint1 Endpoint 2 Midpoint
D A(4,6) B(2,-2) D(3,2) [(4+2)/2 =3 and (6-2)/2 = 2]
E A(4,6) C(-2,-4) E(1,1) [(4-2)/2 =1 and (6-4)/2 = 1]
If DE is parallel to BC, both lines must have the same slope. Find the slopes for DE and BC by calculating the Rise/Run (the change in y over the cahnge in x):
Slope of DE: Rise = (2-1) = 1, Run = (3-1) = 2. Slope = (1/2) or 0.5
Slope of BC: Rise = (-2-(-4)) = 2, Run = (2-(-2)) = 4. Slope = (1/2) or 0.5
The slopes of DE and BC are the same: 0.5. The two lines are therefore parallel.
Find the Simple Interest Rate
on a 3-month loan of $5000 if the maturity value of the
loan is $5125.
keeping in mind that a year has 12 months, thus 3 months will just be 3/12 of a year, so
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5125\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to \frac{3}{12}\dotfill &\frac{1}{4} \end{cases} \\\\\\ 5125=5000[1+(\frac{r}{100})(\frac{1}{4})] \implies \cfrac{5125}{5000}=1+\cfrac{r}{400}\implies \cfrac{41}{40}=\cfrac{400+r}{400} \\\\\\ 410=400+r\implies \boxed{10=r}[/tex]
What is the magnitude (size) of -9.1
A.-9.1 because |-9.1| =9.1
B. 9.1 because |-9.1| = 9.1
C.9.1 because |-9.1|= -9.1
D.0.91 because |-9.1|=0.91
B. 9.1 because |-9.1| = 9.1
Magnitude of -9.1 is 9.1
Magnitude of a number
A magnitude is the measurement or absolute value of a quantity. A magnitude is represented by a positive real number. Put simply, a magnitude is the size of some quantity. For example, the magnitude of an earthquake, measured on the Richter scale, usually varies between 1 and 10 and represents the size of the earthquake. An earthquake with a magnitude of 8 is much more trouble than an earthquake with a magnitude of 3.
The magnitude of a negative number, say -6? It is (positive) 6. Magnitudes cannot be negative. Consider the idea of a magnitude as a measure of size: there doesn't seem to be a coherent idea of negative size. To make sense of this is to understand that -6 is greater in magnitude than -5 even though -6 is a lower number. For negative numbers the order of magnitude is reversed, just as one counts in the opposite direction on the number line for negative numbers.
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