Answer:
27
Step-by-step explanation:
When solving complicated equations like this, we need to remember the order of operations (PEMDAS), which is the order that we solve an equation
P arentheses
E xponents
M ultiplication
D ivision
A ddition
S ubtraction
now, here's the thing: we actually to multiplication/division at the same time, and the same thing with addition/subtraction
(as in, adding -4 is the same thing as subtracting 4, so we can't truly make a distinction between the two)
so, when we have multiple instances of multiplication/division , we solve left to right
(and then the same thing for addition/subtraction)
8 × 3 + 70 ÷ 7 - 7
so, we first need to multiply 8 by 3
8 × 3 = 24
next, we move to the right:
and we divide 70 by 7
70 ÷ 7 = 10
let's rewrite our equation:
(24) + (10) - 7
24 + 10 - 7 = 27
so, the answer to this expression is 27
hope this helps!! have a lovely day :)
Question 2(Multiple Choice Worth 1 points)
(02.02 LC)
If g(x)= x² + 3, find g(4).
11
19
16
8
Answer: 19
Step-by-step explanation:
g(4) = 4² + 3
g(4) = 16 + 3
g(4) = 19
one gym membership charges $10 a month with a sign-up fee of $45. Another gym does not charge patrons a sign-up fee but costs $25 a month. at what month is the total cost of both memberships the same?
Answer:
3 MonthsStep-by-step explanation:
Answer:
3 months
Step-by-step explanation:
G1= 10 m +45
G2=25
10 m + 45= 25 m
10 m - 25 m = -45
-15 m/-15=-45/-15
m=3
∴ it's 3 months
Chords AC and BD intersect in circle O as shown in the diagram. Two of the angle measurements are marked. What is mL CED?
Answer:
By using the formulas of circle and geometry, we find that ∠CED = 65°.
Step-by-step explanation:
We know that the measure of the interior angle is the half sum of the arcs comprising it and its opposite, so
∠CED = 0.5 × (arc AB + arc CD)
See the attached figure with letters to better understand the problem
arc AB = 82° (by central angle)
arc CD = 48° (by central angle)
Substitute the values in the formula above
∠CED = 0.5 × (82° + 48°)
∠CED = 0.5 × 130°
∠CED = 65°
Therefore the answer is ∠CED = 65°
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Andy fed his dog about 16kilogram of food in one week. he fed his cat about 2 kilogram of food in one week what is the best estimate for the total amount of food he feeds his dog and cat in2 weeks. each animal represent 4 kilogram of food
Answer:
36kg
Step-by-step explanation:
The dog eats 16kg per week, which is 32kg in 2 weeks
The cat eats 2kg per week, which is 4kg in 2 weeks
32+4=36
2. If D is the midpoint of segment AB, explain using transformations why AC = BC. Use complete sentences. (10 points)
AC is equal to BC by the corresponding side of a congruent triangle.
What is a line segment?
A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).
The midpoint of a line segment means a point that lies in the mid of the given line segment.
If D is the midpoint of segment AB, then AD = BD.
So in a triangle ACD and BCD
AD = BD (by midpoint D)
angle ADC = angle BDC = 90
CD = CD (common)
Therefore, triangle ACD and BCD are congruent.
Hence, AC = BC by the corresponding side of a congruent triangle.
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find the least nu,ber which is exactly divisible by 12 16 and 24
Answer:
The smallest number all three numbers can be divided by is 4.
Step-by-step explanation:
12/4=3
16/4=4
24/4=6
Hope this helps!
If not, I am sorry.
Which length is equivalent to 12 yards?
Answer:
36 feet
Step-by-step explanation:
1 yard 3 feet
What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (2, 5)? y 5 = x 2 y − 2 = x − 5 y − 5 = −(x − 2) y 2 = −(x 5)
The equation of the line in point-slope form is: C. y − 5 = −(x − 2).
What is the Point-Slope Equation of a Line?A line with a slope (m) and a point (a, b) is represented in point-slope form as, y - b = m(x - a).
Slopes of perpendicular lines are negative reciprocals of each other. Find the slope of the line in the graph given as follows:
Slope (m) = rise/run = 3 units/3 units = 1
Negative reciprocal of 1 is -1.
The slope of the line would be m = -1.
Substitute m = -1 and (a, b) = (2, 5) into y - b = m(x - a) to wrote the equation:
y - 5 = -1(x - 2)
y − 5 = −(x − 2)
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A chocolate chip recipe that produces 30 cookies calls for 2 1/4 cups of flour. If the math club decides to make fifteen dozen cookies for a bake sale, how many cups of flour will they need?
Answer:
2 1/4
Step-by-step explanation:
Find the measure of each missing angle.
A stockbroker has money in three accounts. The interest rates on the three accounts are 10 % ,11 %, and 12 %. If
she has twice as much money invested at 11% as she does in 10 %, three times as much at 12% as she has at be
10%, and the total interest for the year is $340, how much is invested at each rate?
Given that AUVW=AXYZ, what is the measure of ZY?
AV
70°
70°
OA. 180°
OB. 40°
O C. 90°
OD. 70°
The value ∠y is 40⁰. So the correct option is option B
What is Congruency of triangle?Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.
Here, given that; ΔUVW ≅ ΔXYZ
∠u = ∠x = 70⁰
∠v = ∠y = a⁰
∠w = ∠z = 70⁰
We know that,
Sum of angles of a triangle is 180⁰.
∠x + ∠y + ∠z = 180⁰
70⁰ + a⁰ + 70⁰ = 180⁰
a⁰ + 140⁰ = 180⁰
a⁰ = 180⁰ - 140⁰
a⁰ = 40⁰
Thus, the value ∠y is 40⁰.
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Given: AD BC and ZBCD=
ZADC
Prove: DE CE
A
D
B
Correct! Assemble the next
statement.
Intro
Angles Segments Triangles Statements Reasons
ZADC
ZDEA
ZECD
Statements
✓ 1. ZDEA and ZCEB are
vertical angles
ZBCD
ZEDC
ZCBE
ZCEB
Reasons
1. def. of vertical angles
ZDAE
In the given triangle, it should be noted that ADC is the same as BCD due to SAS congruence.
How to illustrate the information?From the information given,
AD = BC
BCD = ADC.
This depicts the concept of SAS. In this case, the two-sided will be equivalent.
Also, it should be noted that DAC and CBD are equal according to the vertical angle theorem.
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Answer:
see picture ....
Step-by-step explanation:
Use the information given in the diagrams to show that
Answer:
d = k·sin(2θ)·sin(α)/(sin(θ)·sin(β))
Step-by-step explanation:
The Law of Sines tells us that sides of a triangle are proportional to the sine of the opposite angle. This can be used along with a trig identity to demonstrate the required relation.
__
top triangleThe law of sines applied to the top triangle is ...
BC/sin(A) = AC/sin(θ)
Triangle ABC is isosceles, so the base angles at B and C are congruent. Then the angle at vertex A is ...
∠A = 180° -θ -θ = 180° -2θ
A trig identity tells us the sine of an angle is equal to the sine of its supplement. That means the sine of angle A is ...
sin(A) = sin(180° -2θ) = sin(2θ)
and our above Law of Sines equation tells us ...
BC = sin(A)/sin(θ)·AC = k·sin(2θ)/sin(θ)
__
bottom triangleThe law of sines applied to the bottom triangle is ...
DC/sin(B) = BC/sin(D)
d/sin(α) = BC/sin(β)
Multiplying by sin(α) we have ...
d = BC·sin(α)/sin(β)
__
Using our expression for BC gives the desired relation:
d = k·sin(2θ)·sin(α)/(sin(θ)·sin(β))
Line I is a perpendicular bisector
Line I is a perpendicular bisector because it bisects another line at right angles via the point of intersection or midpoint. See the Perpendicular Bisector Theorem below.
What is the perpendicular bisector theorem?According to the theorem of perpendicular bisector, any locus on the perpendicular bisector is equidistant from the terminal points of the line segment on which it is created.
Thus, Line I is a perpendicular bisector because it bisects another line at right angles via the point of intersection or midpoint. See the attached image.
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This probability distribution shows the
typical grade distribution for a Geometry
course with 35 students.
Grade
A B
C
D F
Frequency 5 10 15 3 2
Find the probability that a student earns a
Answer:
14.3%
Step-by-step explanation:
5 students got an A out of 35 total students. This means that the probability of students getting an A is 5/35 = 0.1428
what is the area of the trapezium?
Answer:
156 cm²
Explanation:
This figure is a trapezium.
Formula of Area of Trapezium = 1/2 × (a + b) × height
Here given:
a = 9 cmb = 30 cmh = 8 cm==============
Area of trapezium: 1/2 × (9 + 30) × 8 = 156 cm²
Answer:
area of the trapezium is 156
Step-by-step explanation:
Solve the given proportion.
X/3 = 6/2
x = [?]
Answer:
x = 9
Step-by-step explanation:
x/3 = 6/2
~Simplify
x/3 = 3
~Rewrite
1/3x = 3
~Multiply 3 to both sides
x = 9
Best of Luck!
Answer: x=9 ✅
Step-by-step explanation:
Hii student, I'd love to help you out! (:
In this problem, we need to solve a proportion. This is fun, right?
3,2,1 - start!
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Solving proportions is easy as winking, if you are familiar with a skill that is known as "cross multiplying".
We have these two proportions:
(oh and by the way, proportions are just equivalent (equal) fractions. That's all proportions are. Nothing more)
Our proportions are:
[tex]\large\boldsymbol{\cfrac{x}{3}=\cfrac{6}{2}}[/tex]
We multiply x times 2 and 3 times 6; upon doing that we obtain.
[tex]\multimap\quad \tt 2x=18[/tex]
Did you see that? 2 fractions turned into a little equation that we can solve within 5 seconds (or faster)!
To do that we simply divide both sides by 2, since x is multiplied by 2 and we need to get it all by itself on one side of the equal sign)
[tex]\multimap\quad \tt x=9[/tex]
Woohoo! We found the answer! ✨
Cheers! (: ____________________________________Hope I helped! Best wishes.
Reach far. Aim high. Dream big.
[tex]\underbrace[/tex]
N
O O
What is the slope of the line represented by the equation y = --- 5x?
0-5
4 ~/m ~/m
+
O 5
O
The unit rate of change of yyy with respect to xxx is the amount yyy changes for a change of one unit in xxx.
Is the unit rate of change of yyy with respect to xxx less in the equation y=6.5xy=6.5xy, equals, 6, point, 5, x or in the graph below?
The unit rate of change of y with respect to x is less in the graph
How to compare the rate of change?The attached graph represents the missing information in the question
The graph passes through the following points
(0,0) and (5,1)
The rate of change of the graph is then calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
This gives
[tex]m = \frac{1-0}{5-0}[/tex]
Evaluate
m = 0.2
The equation is given as:
y = 6.5x
The slope of the above equation is 6.5
By comparison, 6.5 is greater than 0.2
Hence, the unit rate of change of y with respect to x is less in the graph
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Answer:
The equation
Step-by-step explanation:
i did it on khan academy
Do the fractions and convert to repeating or terminating decimal numbers?
It should be noted that 16/25 can be converted to a terminating decimal number is 0.64.
How to explain the fraction?
Do the fractions 6/7 and 16/25 convert to repeating or terminating decimal numbers.
In this case, 6/7 converts to repeating decimal numbers. You could represent it, so you don't have to repeat the decimals infinitely, by putting a bar over the repeating decimals like 0.857142 with a bar going over from the 8 to the 2.
Also, 16/25 can be converted to a terminating decimal number which is 0.64.
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The value of x must be greater than
0
1
3
7
Answer:
The value of x should be greater than 3.
Step-by-step explanation:
Given that,
The AB is 12 units.
The AC is 15 units.
We need to find the value of BC.
Based on the above information, the calculation is as follows:
As we know that
The sum of two sides length is always more than the 3rd one.
Based on this,
12 + 15 > x
x < 27
15 + x >12
x >-3
12 + x > 15
x >3
Which data set could be represented by the boxplot shown? (1 point)
{0, 2, 3, 5, 8, 9, 10, 10, 12}
{2, 3, 3, 4, 5, 5, 8, 10, 10}
{2, 3, 4, 5, 5, 7, 7, 9, 10}
{2, 3, 4, 5, 5, 5, 8, 9, 10
The second data set represents the boxplot because in the box plot the measure of statistics is the same as the data set option second is correct.
What is the box and whisker plot?A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.
We have given a data set and a box plot shown in the picture.
From the boxplot we can see:
Minimum value = 2
Q1 = (2+4)/2 = 3
Median = (4+6)/2 = 5
Q3 = (8+10)/2 = 9
Maximum value = 10
The second data set:
{2, 3, 3, 4, 5, 5, 8, 10, 10}
Minimum value = 2
Q1 = (2+4)/2 = 3
Median = (4+6)/2 = 5
Q3 = (8+10)/2 = 9
Maximum value = 10
Thus, the second data set represents the boxplot because in the box plot the measure of statistics is the same as the data set option second is correct.
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A researcher has a table of data with four-column variables and three-row variables. the value for the degrees of freedom in order to calculate the chi-squared statistic is __________.
The degree of freedom is 6.
What is degree of freedom?The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1)(c-1) where r is the number of rows and c is the number of columns.
Given:
rows= 3
column= 4
So, degree of freedom
= (row-1)(column-1)
=(3-1)(4-1)
=2*3
=6
Hence, the degree of freedom is 6.
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Answer:
The degree of freedom is 6.
Step-by-step explanation:
Got it right on the test.
Question 13 (4 points) (05.03) Which of the following statements best describes the graph of -5x + 2y = 1? (4 points)
A) It is a curve joining the points (-5, 2), (2, 3), and (4, 1).
B)It is a curve joining the points (-1, -3), (-1, -3), and (1, 5).
C)It is a straight line joining the points (1, 3), (3, 8), and (-3, -7).
D)It is a straight line joining the points (4, -3), (-1, 2), and (-4, 5).
Answer:
C) straight line through (1, 3) ... (-3, -7)
Step-by-step explanation:
The linear equation will describe a straight line. The slope and general location of the line on a graph can be estimated from its x- and y-intercepts.
__
interceptsThe x-intercept is the value of x that satisfies the equation when y=0.
-5x +2·0 = 1
x = -1/5 . . . . . . divide by the coefficient of x
The y-intercept is the value of y that satisfies the equation when x=0.
-5·0 +2y = 1
y = 1/2 . . . . . . divide by the coefficient of y
nature of the graphThe intercept values mean the line crosses the positive y-axis and the negative x-axis. It will have a positive slope. Points on the line that have integer x- and y-coordinates will have coordinates that have the same sign.
Of the offered answer choices, A and B are eliminated because the graph is not a curve. D is eliminated because the suggested points have coordinates with opposite signs. The correct choice is C:
It is a straight line joining the points (1, 3), (3, 8), and (-3, -7)
Find the vertex and focus of the
parabola:
x² + 14x-8y + 65 = 0
I can’t figure this out!!!
Answer:
[tex]\boxed {Vertex = (-7, 2)}\\\boxed {Focus = (0, \frac{49}{8})}[/tex]
Step-by-step explanation:
Completing the square :
x² + 14x - 8y + 65 = 0
x² + 14x + 49 - 49 - 8y + 65 = 0
(x + 7)² - 8y + 16
(x + 7)² = 8y - 16
⇒ x = -7, y = 2 (Vertex)
Finding a :
⇒ x² = 4ay
⇒ (-7)² = 4(2)a
⇒ a = 49/8
Finding the focus :
⇒ (0, a)
⇒ (0, 49/8) (Focus)
The __________ and the _________ are two of the most popular and useful methods of standardizing for size and comparing distributions.
The proportion and the median are two of the most popular and useful methods of standardizing for size and comparing distributions.
Methods of standardizationProportion is the fraction of favorable cases from the total number of cases. It is defined for both population and sample.
Median is defined as the numeric value separating the higher half of a sample, a population, or a probability distribution, from the lower half of it.
Therefore, the proportion and the median are two of the most popular and useful methods of standardizing for size and comparing distributions.
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IMPORTANT, PLEASE HELP QUICKLY! 15 POINTS
Explain how to factor the expression q(x)=9x2−24x+16 to the expression q(x)=(3x−4)2 . You may show your work. Be sure to include a detailed explanation of your steps.
Answer:
Given function:
[tex]q(x)=9x^2-24x+16[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:
[tex]ac=9 \cdot 16=144[/tex]
Two numbers that multiply to 144 and sum to -24 are: -12 and -12
Rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies q(x)=9x^2-12x-12x+16[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies q(x)=3x(3x-4)-4(3x-4)[/tex]
Factor out the common term [tex](3x-4)[/tex]:
[tex]\implies q(x)=(3x-4)(3x-4)[/tex]
Therefore:
[tex]\implies q(x)=(3x-4)^2[/tex]
A fuel tank is 1/6 full. When 2 gallons of gasoline are added, the tank becomes 1/4 full. What is the total fuel capacity of the tank in gallons?
Answer:
24 gallons
Step-by-step explanation:
Since the 2 gallons of gas increased the fill ratio from 1/6 to 1/4, we can find how much of the tank the 2 gallons filled by solving the equation 1/4 - 1/6 = 1/12. This means that each gallon of gas is 1/24th of the tank.
Thus, the tank has a fuel capacity of 24 gallons.
Answer:
24
Step-by-step explanation:
Let x be the total fuel capacity of the tank, in gallons.
Then from the given information
x/6 + 2 = x/4,
Multiplying both sides by 12 to remove the fractions, we get
2x + 24 = 3x so x = 24.
Therefore, the total fuel capacity of the tank is 24 gallons.
A survey participant is randomly selected. Let F be the
event that the participant's first motor vehicle had four
cylinders and let C be the event that the participant's
first motor vehicle was a car. What is the value of PIF
The probability for event F or C is 0.80, or the value of the P(F or C) is 0.80 option (D) is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
The question is incomplete.
The complete question is:
Insurance company executives surveyed 200 young adults about their first motor vehicle. The results of the survey are given in the following two-way table(please refer to the attached picture)
A survey participant is randomly selected. Let F be the event that the participant’s first motor vehicle had four cylinders and let C be the event that the participant’s first motor vehicle was a car. What is the value of P(F or C)?
A) 0.59B) 0.68C) 0.71D) 0.80We have to find the value of P(F or C):
[tex]\rm P( F \ or \ C) = \dfrac{118+6+18+16+2}{118+6+18+16+12+20+2+6+2}[/tex]
[tex]\rm P( F \ or \ C) = \dfrac{160}{200}[/tex]
P(F or C) = 0.80
Thus, the probability for event F or C is 0.80, or the value of the P(F or C) is 0.80 option (D) is correct.
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