ANSWER
The base is 7 and the height is 9.
EXPLANATION
If we consider any two pairs of points and the y-coordinates of these two points are constant (are the same), then that side forms one of the bases of the rectangle.
Consider, Q(-1, 1) and R(6, 1)
The y-values are the same.
The base of the rectangle is the absolute value of difference in the x-values.
[tex]Base = |6 - - 1| = |7| = 7[/tex]
We could have also used S(6,-8), and T(-1,-8) to obtain the same result.
For R(6, 1) and S(6,-8), the x-coordinates are the same. The height is the absolute values of difference in the y-values.
[tex]Height= |1 - - 8| = |9| = 9[/tex]
Therefore, the base is 7 and the height is 9.
Answer:
Base is 7, and Height is 9.
Step-by-step - If we consider any two pairs of points and the y-coordinates of these two points are constant (are the same), then that side forms one of the bases of the rectangle.
Consider, Q(-1, 1) and R(6, 1)
The y-values are the same.
The base of the rectangle is the absolute value of difference in the x-values.
We could have also used S(6,-8), and T(-1,-8) to obtain the same result.
For R(6, 1) and S(6,-8), the x-coordinates are the same. The height is the absolute values of difference in the y-values.
Therefore, the base is 7 and the height is 9.
Which table of values represents the equation
y = 7x - 3?
The table of values that represents the equation y = 7x - 3 is:
x y
-2 -17
-1 -10
0 -3
1 4
2 11
Option D is the correct answer.
We have,
Equation:
y = 7x - 3
Now,
Substitute x = -2, -1, 0, 1, 2 on the equation.
So,
y = 7 x (-2) - 3 = -14 - 3 = -17
y = 7 x (-1) - 3 = -7 - 3 = - 10
y = 7 x 0 - 3 = -3
y = 7 x 1 - 3 = 7 - 3 = 4
y = 7 x 2 - 3 = 14 - 3 = 11
Thus,
The table of values that represents the equation y = 7x - 3 is:
x y
-2 -17
-1 -10
0 -3
1 4
2 11
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what is the factored form of 2x^2-7x+6?
a) 2
b) y-8
c) x-4
d) x+6
[tex]
2x^2-7x+6=(2x-6)(x-1)=\boxed{2(x-3)(x-1)}
[/tex]
Hope this helps.
r3t40
A motorist travels at 35 mi/h for 4 h and then at 55 mi/h for t h. Express the distance d traveled as a function of t.
Answer:
d = 35(4) + 55(t)
Step-by-step explanation:
35 * 4 then added to 55 * the hours that "t" equals will then equal the total distance traveled, d
The distance traveled by a motorist travelling at 35 miles/hour for 4 hours and then at 55 miles/hour for t hours can be expressed as a function of time t, d(t) = 140 + 55t.
Explanation:The subject of this question is functions, which is a topic in Mathematics. To express the total distance traveled as a function of t, we need to use the formula distance = speed x time. The motorist travels at 35 miles per hour for 4 hours, and then at 55 miles per hour for t hours. Therefore, the total distance d can be calculated as follows:
d = (35 mi/h x 4 h) + (55 mi/h x t h).
So, d = 140 mi + 55t mi.
Thus, the total distance traversed by the motorist, expressed as a function of time t in hours, is d(t) = 140 + 55t.
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Which ratios are equivalent to 10:16? Check all that apply.
30 to 48
25:35
8:32
5 to 15
Answer:
30:48
Step-by-step explanation:
because 30 divides into 10 and 48 divides into 16
Answer:
Option A is correct
30 to 48
Step-by-step explanation:
Given the ratio:
10 : 16
We have to find the ratios are equivalent to 10:16.
Option A.
30 to 48
⇒[tex]\frac{30}{48}[/tex]
Divide numerator and denominator by 3 we have;
⇒[tex]\frac{10}{16}[/tex]
Option B.
25:35
⇒[tex]\frac{25}{35}[/tex]
Divide numerator and denominator by 5 we have;
⇒[tex]\frac{5}{7}[/tex]
or
5 : 7
Option C:
8 : 32
⇒1 : 4
Option D:
5 to 15
⇒[tex]\frac{5}{15}[/tex]
Divide numerator and denominator by 5 we have;
⇒[tex]\frac{1}{3}[/tex]
or
1 : 3
Therefore, the ratio equivalent to 10:16 is, 30 to 48.
Please help me .....
Answer:
150 feet of flowers would be planted along side C
[tex]a=5400[/tex]
Step-by-step explanation:
Use the pythagorean theorem to find the length of side C
[tex]a^2+b^2=c^2[/tex]
Input the corresponding numbers into the formula
[tex]90^2+120^2=c^2[/tex]
[tex]c^2=22500[/tex]
[tex]c = \sqrt{22500} \\ c=150[/tex]
150 feet of flowers would be planted along side C
To find the area multiply the base and height together, and divide the total by two
[tex]a = \frac{bh}{2}[/tex]
[tex]a = \frac{90 * 120}{2} \\ a=5400[/tex]
Answer:
a) c = 150 ftb) A = 5400 ft²Step-by-step explanation:
[tex]a)\ \text{Use the Pythagorean theorem:}\\\\leg^2+leg^2=hypotenuse^2\\\\\text{We have:}\ leg=90\ ft,\ leg=120\ ft,\ hypotenuse=c.\\\\\text{Substitute:}\\\\c^2=90^2+120^2\\\\c^2=8100+14400\\\\c^2=22500\to c=\sqrt{22500}\\\\c=150\ ft[/tex]
[tex]b)\ \text{The formula of an area of a right triangle:}\\\\A=\dfrac{ab}{2}\\\\a,\ b-legs\\\\\text{We have}\ a=90\ ft\ \text{and}\ b=120\ ft.\ \text{Substitute:}\\\\A=\dfrac{(90)(120)}{2}=(90)(60)=5400\ ft^2[/tex]
The clock face in a famous clock tower has a radius of about 3 meters. What is the area of the clock face to the nearest square meter?
Answer: 28.27
Step-by-step explanation:
A=3.14r^2
A=3.14•3^2
A=3.14•9
A=28.27
Answer: a = 28.3 m²
Step-by-step explanation:
a = πr²
a = π3²
a = 28.3 m²
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Fill in the blank.In the triangle below,z degrees =
Not enough information, please attach a photo next time.
What number is 264% of 25?
Answer:
9.47
Step-by-step explanation:
What is the measure of XZ?
Check the picture below.
The measure of XZ is 72
What is an arc?A circle's arc is referred to as a portion or section of its circumference. A chord of a circle is a straight line that might be created by joining the arc's two ends. A semicircular arc is one whose length is exactly half that of a circle.
Given
θ = arc / 2
36 = arc/2
XZ= [tex]36*2[/tex]= 72
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Sally can complete a sales route by herself in 7 hours. James can do the same job in 9 hours. How long will it take them to do it working together?
Answer:
(4 days) is the homogeneous mixture
The inside walls of a closed cooler form a right rectangular prism with dimensions 1.5 feet by 3 feet by 1 feet which Of These is the volume of the cooler
A) 6 cubic feet
B)4.5 cubic feet
C) 5.5 cubic feet
D) 18 cubic feet
Answer:
B)4.5 cubic feet
Step-by-step explanation:
To find the volume of a rectangular prism, we use the formula
V = l*w*h
V = 1.5*3*1
V = 4.5 ft^3
Subtract. (4x2+8x−2)−(2x2−4x+3) Enter your answer, in standard form, in the box.
the answer is 2x2+12z-5 (its also in the picture)
ANSWER ALL TO GET ALL POINTS
Q1: How do you identify which side is the hypotenuse of right triangles?
Q2: What does it mean to be a Pythagorean Triple? Given an example of a Pythagorean Triple.
Q3: Explain why Volume must always have cubic units.
Answer:
hypotenuse is always opposite the right angle and it is always the longest side of the triangle
Pythagorean Triple consists of three positive integers a, b, and c, such that a² + b² = c² example 3, 4, 5).
volume occupies a three dimensional space. Distance is measured in one unit of length
Step-by-step explanation:
Please help!
Use kite DEFG and the given information to solve #25 - 26.
25) If mZ1 = 42° , find m22.
26) If DE = 4x – 2 and DG = 22.5, find the value of x.
Use kite ABCD and the given information to solve #27.
27) Find the value of x.
Answer:
see explanation
Step-by-step explanation:
25
The diagonals of a kite are perpendicular to each other, hence
∠EHF = 90°
The sum of the 3 angles in a triangle = 180°
In ΔEHF
∠1 + ∠2 + 90 = 180, that is
42 + ∠2 + 90 = 180
132 + ∠2 = 180 ( subtract 132 from both sides )
∠2 = 48°
26
DE and DG are congruent sides, hence
4x - 2 = 22.5 ( add 2 to both sides )
4x = 24.5 ( divide both sides by 4 )
x = 6.125
27
∠A and ∠C are congruent, hence
∠A = ∠C = 82°
The sum of the interior angles of a kite = 360°, hence
x = 360 - (82 + 82 + 140) = 360 - 304 = 56
25). Measure of angle 2 will be 48°.
26). Value of x = 6.125
27). Value of x = 56°
Properties of a kite,Two pairs of the adjacent sides of kite are equal.Diagonals of a kite intersect each other at 90°.One pair of opposite angles are equal.25). Given in the picture,
DEFG is a kite having diagonals EG and DF perpendicular. m∠1 = 42°Apply triangle sum theorem in ΔEHF,
m∠EHF + m∠2 + m∠1 = 180°
90° + m∠2 + 42° = 180° [Since, m∠EHF = 90°]
m∠2 = 180° - 132°
m∠2 = 48°
Therefore, measure of angle 2 will be 48°.
26). Given in the question,
DE = 4x - 2 and DG = 22.5By the property of a kite,
DE = DG
(4x - 2) = 22.5
4x = 24.5
x = 6.125
Therefore, value of x will be 6.125
27). Given in the question,
Kite ABCD with m∠B = 140°, m∠C = 82°, m∠D = x°Sum of the interior angles of a kite = 360°
Therefore, m∠A + m∠B + m∠C + m∠D = 360°
By the property of a kite,
m∠A = m∠C = 82°
m∠A + m∠B + m∠A + m∠D = 360°
2(m∠A) + m∠B + m∠D = 360°
2(82°) + 140° + x° = 360°
x = 360° - 304°
x = 56°
Therefore, value of 'x' will be 56°.
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Find the measure of z
Answer:
z = 70
Step-by-step explanation:
The angles 110 and z form a straight angle and are supplementary, thus
110 + z = 180 ( subtract 110 from both sides )
z = 70
According to the general equation for conditional probability, if P(A n B) = 3/10 and P(B)= 2/5 what is p(alb)
Answer:
P(A given B) = 3/4
Step-by-step explanation:
As we know that it is conditional probability, where the probability of an event depends on the event that has certain probability of occurrence.
The formula for conditional probability is:
P(A given B) = P(A ∩B) / P(B)
Where a and B are events. The probability of event B is known and we also know probability of A∩B
So, putting the values in the formula:
[tex]P(A\ given\ B) = \frac{P(A and B)}{P(B)}\\= \frac{\frac{3}{10} }{\frac{2}{5} } \\=\frac{3}{10} *\frac{5}{2}\\=\frac{3}{4}[/tex]
So, the probability of A given B is 3/4 ..
One method of indirect measurement involves setting up a right triangle and measuring one of the
obligue angles
depression angles
elevation angles
acute angles
Answer:
Acute angles.Step-by-step explanation:
This is called the shadow method to make an indirect measurement of an specific highness. For example, indirect measurement to calculate a building highness.
What number, when substituted for x in the following problem, will make the problem true? 6x + 8x = 10x
Answer:
There is no number when substituted for x that will make the statement true.
Step-by-step explanation:
First you would simplify the left side:
6x + 8x= 14x
14x=10x
This statement isnt true no matter what you plug in the sides will never be equal
Answer: If you substitute the number 2 for x in the problem, you’ll make it true.
6x + 8x = 10x
62 + 82 = 102
36 + 64 = 100
100 = 100
Step-by-step explanation
pennfoster
Simplify -26a^7+(-25a^7)
Answer:
-51a^7
Step-by-step explanation:
-26a^7+(-25a^7) may be re-written as a^7(-26 - 25), or -51a^7
What is the value of the rational expression x^2-2x-3/4x^2-12 when x = 3?
a) -1/4
b) 0
c) 1/4
d) Undefined
Answer:
b
Step-by-step explanation:
Given
[tex]\frac{x^2-2x-3}{4x^2-12}[/tex]
Substitute x = 3 into the expression
= [tex]\frac{3^2-2(3)-3}{4(3)^2-12}[/tex]
= [tex]\frac{9-6-3}{36-12}[/tex]
= [tex]\frac{0}{24}[/tex] = 0 → b
Answer:
b
Step-by-step explanation:
the answer is b:0
Linda had $15 in her coin bank. On her birthday, 5 relatives sent her
money as a birthday gift. Each relative sent the same amount. She
then had $115. How much money did Linda receive from each relative?
Final answer:
Linda received $20 from each of her 5 relatives, as found by subtracting her original amount from the final amount and then dividing by the number of relatives.
Explanation:
The student has asked how much money Linda received from each relative. Linda started with $15 in her coin bank and ended up with $115 after receiving equal amounts from 5 relatives. To find out how much money Linda received from each relative, you need to perform a simple subtraction to find the total amount of birthday money received, and then divide that number by 5.
Subtract the starting amount of $15 from the ending amount of $115 to find the total amount received.
Total received = $115 - $15 = $100
Divide the total received by the number of relatives to find out how much each relative gave.
Amount per relative = $100 / 5 = $20
Therefore, Linda received $20 from each of her 5 relatives.
Two triangular prisms are similar. The perimeter of each face of one prism is double the perimeter of the corresponding face of the other prism.
How are the surface areas of the figures related?
Answer:
The surface area of the larger triangular prism is 4 times the surface area of the smaller triangular prism
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its perimeters is equal to the scale factor and the ratio of its surface areas is equal to the scale factor squared
Let
z ----> the scale factor
In this problem
z=2
therefore
z²=2²=4
The surface area of the larger triangular prism is 4 times the surface area of the smaller triangular prism
Answer:
The surface area of the larger prism is 4 times the surface area of the smaller prism.
Step-by-step explanation:
Was right on edge
5/9 of students at a school are girls. If there are 3708 students at the school, how many are boys?
Answer:
1648 are boys.
Step-by-step explanation:
You divide the 3708 by 9 and get 412. Then you multiply that by 4 and get 1648
To find how many boys are in the school, first calculate the number of girls by multiplying the total students, 3708, by 5/9, resulting in 2060 girls. Subtracting this from the total gives 1648 boys.
The question asks how many students are boys in a school if 5/9 of the students are girls, and the total number of students is 3708. To solve this, first, we need to calculate the number of girls by multiplying the total number of students (3708) by 5/9. Then, to find the number of boys, we subtract the number of girls from the total number of students.
Calculate the number of girls:Therefore, there are 1648 boys in the school.
20points!
kyndal wants to buy a lamp that originally cost $82, but the lamp when on sale for 20% off. the store is having an additional sale that is 40% off the sale price. what is the price of the lamp!?
Answer:
$39.36
Step-by-step explanation:
The first sale we saw, which was 20% off, needs to be applied first as the second discount is additional. With that being said, we need to multiply 82 times 80%. This is because we removed 20% of the standard 100% amount and we are left with 80%. To convert this, keep in mind 100% is equal to 1. So 80% is equal to .80 with this logic. So 82x0.8=65.6. Now we need to take 40% off of the modified price 65.6. By converting 40% off is equal to 0.60(keyword off). Now 65.6x0.60=39.36. The final price is 39.36
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Kyndal can buy the lamp for $39.36 after a 20% and an additional 40% discount on the original price of $82.
Explanation:To solve this problem, we need to calculate 20% of $82, then subtract that from $82 to find the sale price. Then, we need to calculate 40% of that sale price and subtract it to find the final price. Let's break it down:
Calculate 20% of $82: 0.20 * 82 = $16.40.Subtract that from the original price to find the sale price: 82 - 16.40 = $65.60.Calculate 40% of the sale price: 0.40 * 65.60 = $26.24.Subtract that from the sale price to find the final price: 65.60 - 26.24 = $39.36. So the price of the lamp after all discounts is $39.36.Learn more about Percentage here:https://brainly.com/question/30697911
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The point-slope form of the equation of the line that passes through (-5, -1) and (10,-7) is
y+7=-(x-10). What is the
standard form of the equation for this line?
2x-5y = -15
2-5y=-17
2x+6y=-15
2x+5v=-17
Answer:
That should be 2x + 5y = 20.
Step-by-step explanation:
First, you have to correct this: y + 7 = -⅖(x - 10). Now, first convert to Slope-Intercept Form by moving -7 to the other side of the equivalence symbol to get y = -⅖x + 4, then finally convert to Standard Form by moving ⅖x to the other side of the equivalence symbol to end up with ⅖x + y = 4.. Now, there is an extended step when it comes to fractional coefficients, and that is multiplying the whole equation by the denominator to get rid of the denominator being there in the first place, REALLY ending with 2x + 5y = 20.
BUT, if your assignment says otherwise, then the first looks correct. I hope this helps.
What is the order of steps to calculate the volume of a prism
Image result for What is the order of steps to calculate the volume of a prism
Method 3 Calculating the Volume of a Rectangular Prism
Write down the formula for finding the volume of a rectangular prism. The formula is simply V = length * width * height. ...
Find the length. ...
Find the width. ...
Find the height. ...
Multiply the length, the width, and the height. ...
State your answer in cubic units.
The order of steps to calculate the volume of a prism is given below:
What is the Volume of Prism?The volume of a prism is defined as the amount of space a prism occupies.
Step 1: Write the given dimensions of the prism.
Step 2: Determine the volume of the prism using the formula V = B × H where V, B, and H are the volume, base area, and height of the prism.
Step 3: The value of the volume of the prism is once obtained then add the unit of volume of prism in the end (in terms of cubic units).
Example: Find the volume of a prism whose base area is 3 square inches and height is 7 inches.
Given that: B = 3 square inches, H = 7 inches
Thus, the Volume of the prism, V = B × H ⇒ V = 3 × 7 = 21 in³
Therefore, the volume of the prism is 21 cubic inches.
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Abbey is stacking boxes of candles for a store display. The volume of each cube-shaped box is 125 cubic inches. If the display has six layers of boxes, how high is the display?
Answer: 30 inches
Step-by-step explanation:
We know that the formula for calculate the volume of a cube is:
[tex]V=s^3[/tex]
Where "s" is the length of each side.
Since the volume of each cube-shaped box is 125 cubic inches, we can find "s":
[tex]125\ in^3=s^3\\\\\sqrt[3]{125\ in^3}=s\\\\s=5\ in[/tex]
We know that the display has six layers of boxes, then , to calculate the height of the display, we can multiply the value of "s" obtained before by 6. Then:
[tex]height=(5\ in)(6)=30\ in[/tex]
Answer:
Step-by-step explanation:
V=8^3
30 inches answer
PLEASE HELP, OFFERING 30 POINTS!!
If a plus b plus c equals 68 and ab plus bc plus ca equals 1121, where a, b, and c are all prime numbers, find the value of abc.
The answer is 1978 but I need an explanation on how to get that.
Answer:
This looks a lot harder than it is, because with some clever observations we can quickly eliminate most solutions.
The first thing that springs to mind is a,b,c cannot all be odd, because then the LHS is even and the RHS is odd. Thus at least one of them must be even and therefore equal to 2. So let’s break this into two cases:
Case 1: c=2.
Hence we get
a(a+b)=122=2×61
Now a must be a positive prime factor of this number, and a+b is clearly more than a, so the only solution in this case is (a,b,c)=(2,59,2). Note here that we must check 59 is prime; fortunately it is.
Case 2: c≠2.
Now the RHS is odd, so a certainly can’t be even. But then b must be even, so b=2. Then we have
a(a+2)=120+c
Adding one to each side and factorising shows
(a+1)2=121+c
from which
c=(a+12)(a−10)
(if you are confused about this step think about difference of two squares factorisations).
But we know c is a prime number, so it can’t have any non-trivial factors. Thus one of the brackets must be 1, so a=11, which yields the solution (a,b,c)=(11,2,23). Once more we must check this solution is valid — again, it is, since 11 and 23 are prime. And those are the only two solutions since our cases cover every possibility.
Step-by-step explanation:
Answer:
1978
Step-by-step explanation:
This looks a lot harder than it is, because with some clever observations we can quickly eliminate most solutions.
The first thing that springs to mind is a,b,c cannot all be odd, because then the LHS is even and the RHS is odd. Thus at least one of them must be even and therefore equal to 2. So let’s break this into two cases:
Case 1: c=2.
Hence we get
a(a+b)=122=2×61
Now a must be a positive prime factor of this number, and a+b is clearly more than a, so the only solution in this case is (a,b,c)=(2,59,2). Note here that we must check 59 is prime; fortunately it is.
Case 2: c≠2.
Now the RHS is odd, so a certainly can’t be even. But then b must be even, so b=2. Then we have
a(a+2)=120+c
Adding one to each side and factorising shows
(a+1)2=121+c
from which
c=(a+12)(a−10)
(if you are confused about this step think about difference of two squares factorisations).
But we know c is a prime number, so it can’t have any non-trivial factors. Thus one of the brackets must be 1, so a=11, which yields the solution (a,b,c)=(11,2,23). Once more we must check this solution is valid — again, it is, since 11 and 23 are prime. And those are the only two solutions since our cases cover every possibility.
Fill in each square with a digit 1-9, and fill in
each circle with an operator +, -, *, -. Use each
digit and each operator exactly once. The
resulting equation should be true. Use the
standard order of operations (PEMDAS).
What is the largest possible three-digit result
that can be obtained on the right side of the
equation?
Answer:
532
Step-by-step explanation:
To make the right hand side as large as possible, the numerator must be as large as possible and the denominator must be as small as possible. But we can only use each digit once.
Through trial and error:
(9 × 8 + 4) / (1 − 6 ÷ 7) = 532
532 is the largest possible three digit that can be obtained on the right side of equation.
What is PEMDAS?
PEMDAS is short form of parentheses, exponents, multiplication , division, addition and subtraction.
To get the the largest possible three digit from given condition, we have to make the denominator as small as possible by using subtraction and division. And we can increase the numerator.
Now, through trial and error method
we have (9 * 8 + 4) / ( 1 - 6 / 7 ) = 76 * 7 = 532
Hence 532 is the largest possible three digit that can be obtained on the right side of equation.
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The measure of b is ___ ?
Answer:
21
Step-by-step explanation:
Use Pythagorean Theorem
If you are looking for leg given the other sides of the right triangle: just do bigger square minus small square
and take square root
so 29^2 - 20^2
And then sqrt it!
sqrt(29^2-20^2)
21
Answer:
b=21
Step-by-step explanation:
a^2 + b^2 = c^2
20^2 +b^2 = 29^2
b^2+400=841
b^2=441
b=21 or b= - 21
Since we are using the values for a triangle we take the positive value.